Finite Group Databasebeta

← #7680455

Subgroups — #7680455

Order 512.

7599 conjugacy classes of subgroups.

The subgroup lattice has 2053 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×#3475C211yesmaximal, characteristic, complemented
3#59810C212yesmaximal, complemented
4#59550C212yesmaximal, complemented
5#59146C212yesmaximal, complemented
6#59129C212yesmaximal, complemented
7#59129C212yesmaximal, complemented
8#59086C212yesmaximal, complemented
9#59066C212yesmaximal, complemented
10#59059C212yesmaximal, complemented
11#44333C214yesmaximal, complemented
12#44209C214yesmaximal, complemented
13#43921C214yesmaximal, complemented
14#43915C214yesmaximal, complemented
15#39725C211yesmaximal, characteristic, complemented
16#39599C211yesmaximal, characteristic, complemented
17#38920C211yesmaximal, characteristic, complemented
18#38914C212yesmaximal, complemented
19#38909C211yesmaximal, characteristic, complemented
20#38909C212yesmaximal, complemented
21#37836C212yesmaximal, complemented
22#37657C212yesmaximal, complemented
23#36505C211yesmaximal, characteristic, complemented
24#36455C211yesmaximal, characteristic, complemented
25#36153C211yesmaximal, characteristic, complemented
26#36101C211yesmaximal, characteristic, complemented
27#35567C212yesmaximal, complemented
28#35520C212yesmaximal, complemented
29#35292C211yesmaximal, characteristic, complemented
30#35261C212yesmaximal, complemented
31#34976C211yesmaximal, characteristic, complemented
32#34937C211yesmaximal, characteristic, complemented
33#34243C211yesmaximal, characteristic, complemented
34#34202C212yesmaximal, complemented
35C4×#537C211yesmaximal, characteristic, complemented
36#3517—216no—
37C2×#557C2211yescharacteristic, complemented
38#3475—216no—
39C2×#556C2211yescharacteristic
40C2×#555C2211yescharacteristic
41C2×#554C2211yescharacteristic
42C2×#553C2212yes—
43C2×#553C2212yescomplemented
44C2×#553C2214yescomplemented
45C2×#552C2211yescharacteristic
46C2×#552C2212yes—
47C2×#552C2211yescharacteristic
48C2×#551C2212yes—
49C2×#551C2212yes—
50C2×#550C2211yescharacteristic
51C2×#550C2212yes—
52C2×#550C2212yes—
53C2×#550C2212yescomplemented
54C2×#550C2211yescharacteristic, complemented
55C2×#547C2211yescharacteristic
56C2×#547C2211yescharacteristic
57C2×#547C2212yescomplemented
58C2×#546C2211yescharacteristic
59C2×#546C2211yescharacteristic
60C2×#546C2212yes—
61C2×#540C2214yescomplemented
62C2×#540C2212yescomplemented
63C2×#537C2211yescharacteristic
64C2×#533C2211yescharacteristic
65C2×#532C2212yes—
66C2×#532C2212yes—
67C2×#532C2211yescharacteristic, complemented
68C2×#529C2212yes—
69C2×#529C2211yescharacteristic
70C2×#529C2212yes—
71C2×#529C2211yescharacteristic
72C2×#529C2212yescomplemented
73C2×#525C2212yes—
74C2×#525C2212yes—
75C2×#520C2212yescomplemented
76C2×C4×#41C2211yescharacteristic
77C2×C4×#41C2211yescharacteristic
78C2×C4×#41C2211yescharacteristic
79C2×C4×#41C2211yescharacteristic, complemented
80C22×C4×D4C2211yescharacteristic
81C22×#117C2212yes—
82#2857C2211yescharacteristic
83#2857C2211yescharacteristic, complemented
84#2856C2211yescharacteristic
85#2856C2212yescomplemented
86#2856C2211yescharacteristic, complemented
87#2851C2212yescomplemented
88#2847C2212yes—
89#2847C2212yes—
90#2726C2214yescomplemented
91#2723C2214yescomplemented
92#2721C2214yescomplemented
93#2718C2214yescomplemented
94#2711C2214yescomplemented
95#2706C2214yescomplemented
96#2705C2214yes—
97#2704C2214yes—
98#2702C2214yescomplemented
99#2693C2214yes—
100#2691C2214yescomplemented
101#2691C2214yescomplemented
102#2691C2214yescomplemented
103#2686C2214yescomplemented
104#2681C2214yescomplemented
105#2676C2214yes—
106#2673C2214yescomplemented
107#2671C2214yes—
108#2671C2214yes—
109#2671C2214yescomplemented
110#2671C2214yescomplemented
111#2671C2214yescomplemented
112#2669C2214yes—
113#2669C2214yes—
114#2629C2212yes—
115#2624C2212yescomplemented
116#2624C2212yescomplemented
117#2624C2212yescomplemented
118#2619C2212yes—
119#2615C2212yes—
120#2609C2214yescomplemented
121#2592C2212yescomplemented
122#2584C2212yescomplemented
123#2582C2211yescharacteristic, complemented
124#2582C2212yescomplemented
125#2580C2212yescomplemented
126#2580C2212yescomplemented
127#2562C2212yescomplemented
128#2559C2214yescomplemented
129#2558C2214yescomplemented
130#2555C2214yescomplemented
131#2554C2214yescomplemented
132#2553C2214yescomplemented
133#2548C2211yescharacteristic, complemented
134#2548C2212yescomplemented
135#2547C2211yescharacteristic
136#2546C2211yescharacteristic, complemented
137#2546C2212yescomplemented
138#2545C2212yescomplemented
139#2544C2212yes—
140#2544C2212yes—
141#2544C2214yescomplemented
142#2543C2214yescomplemented
143#2543C2214yescomplemented
144#2542C2212yescomplemented
145#2541C2211yescharacteristic
146#2541C2212yescomplemented
147#2540C2212yes—
148#2540C2212yes—
149#2538C2211yescharacteristic
150#2538C2211yescharacteristic, complemented
151#2537C2211yescharacteristic
152#2537C2212yescomplemented
153#2536C2212yescomplemented
154#2535C2212yes—
155#2491C2212yescomplemented
156#2489C2212yescomplemented
157#2487C2212yescomplemented
158#2486C2212yes—
159#2485C2212yescomplemented
160#2485C2212yescomplemented
161#2479C2214yescomplemented
162#2477C2214yescomplemented
163#2476C2214yescomplemented
164#2476C2214yescomplemented
165#2475C2214yescomplemented
166#2473C2214yescomplemented
167#2471C2214yes—
168#2471C2214yes—
169#2468C2214yescomplemented
170#2466C2214yescomplemented
171#2464C2214yes—
172#2464C2214yes—
173#2464C2214yes—
174#2463C2214yescomplemented
175#2461C2214yescomplemented
176#2460C2214yescomplemented
177#2459C2214yescomplemented
178#2456C2214yes—
179#2456C2214yes—
180#2455C2214yes—
181#2455C2214yes—
182#2454C2212yescomplemented
183#2454C2214yescomplemented
184#2451C2212yescomplemented
185#2450C2214yescomplemented
186#2446C2212yescomplemented
187#2445C2212yes—
188#2445C2214yescomplemented
189#2443C2214yescomplemented
190#2443C2214yescomplemented
191#2443C2214yescomplemented
192#2433C2212yes—
193#2432C2212yes—
194#2432C2212yes—
195#2432C2212yescomplemented
196#2429C2212yes—
197#2429C2212yes—
198#2428C2212yes—
199#2428C2214yes—
200#2428C2214yes—
201#2428C2212yes—
202#2428C2214yescomplemented
203#2428C2214yescomplemented
204#2427C2212yes—
205#2427C2214yescomplemented
206#2427C2212yescomplemented
207#2425C2214yes—
208#2424C2214yes—
209#2424C2214yes—
210#2424C2214yes—
211#2424C2214yes—
212#2424C2214yes—
213#2422C2214yescomplemented
214#2417C2212yes—
215#2416C2212yes—
216#2416C2212yescomplemented
217#2416C2212yescomplemented
218#2416C2212yescomplemented
219#2414C2212yes—
220#2414C2212yes—
221#2414C2212yescomplemented
222#2414C2214yescomplemented
223#2414C2212yescomplemented
224#2414C2212yescomplemented
225#2412C2214yes—
226#2407C2212yes—
227#2407C2212yes—
228#2407C2212yes—
229#2407C2212yes—
230#2407C2212yes—
231#2407C2212yescomplemented
232#2407C2212yescomplemented
233#2407C2212yescomplemented
234#2392C2214yescomplemented
235#2392C2214yescomplemented
236#2370C2212yescomplemented
237#2367C2212yes—
238#2367C2212yes—
239#2366C2212yes—
240#2362C2212yescomplemented
241#2361C2212yes—
242#2359C2214yescomplemented
243#2359C2214yescomplemented
244#2359C2214yescomplemented
245#2358C2214yes—
246#2358C2214yes—
247#2355C2211yescharacteristic, complemented
248#2354C2211yescharacteristic
249#2354C2214yes—
250#2352C2214yes—
251#2352C2212yescomplemented
252#2352C2214yescomplemented
253Q8×C4⋊C4C2211yescharacteristic, complemented
254D4×C4⋊C4C2211yescharacteristic
255D4×C4⋊C4C2214yescomplemented
256D4×C4⋊C4C2212yescomplemented
257#2341C2212yescomplemented
258#2339C2212yes—
259#2334C2214yescomplemented
260#2325C2212yes—
261#2325C2212yescomplemented
262#2324C2212yes—
263#2324C2211yescharacteristic
264#2324C2212yes—
265#2324C2212yes—
266#2324C2211yescharacteristic, complemented
267#2324C2212yescomplemented
268#2323C2212yes—
269#2323C2211yescharacteristic
270#2323C2212yescomplemented
271#2323C2211yescharacteristic, complemented
272#2317C2212yescomplemented
273#2316C2211yescharacteristic, complemented
274#2314C2212yescomplemented
275#2311C2211yescharacteristic
276#2311C2211yescharacteristic, complemented
277#2311C2212yescomplemented
278C4×C22⋊Q8C2211yescharacteristic
279C4×C22⋊Q8C2212yescomplemented
280C4×C22⋊Q8C2212yescomplemented
281C4×C22⋊Q8C2211yescharacteristic, complemented
282C4×C22⋊Q8C2212yescomplemented
283C4×C22⋊Q8C2212yescomplemented
284C4×C22⋊Q8C2212yescomplemented
285C4×#121C2211yescharacteristic
286C4×#121C2212yes—
287C4×#121C2212yes—
288C4×#121C2212yes—
289C4×#121C2212yes—
290C4×#121C2212yescomplemented
291C4×#121C2211yescharacteristic, complemented
292C4×#121C2212yescomplemented
293C4×#121C2212yescomplemented
294C4×#121C2212yescomplemented
295C4×#121C2212yescomplemented
296#2297C2212yescomplemented
297#2285C2211yescharacteristic, complemented
298C2×#380C2212yes—
299#2274C2212yescomplemented
300C2×C4×C4⋊C4C2211yescharacteristic, complemented
301C22×#41C2311yescharacteristic
302C22×#41C2311yescharacteristic
303C22×#41C2312yes—
304C22×#41C2311yescharacteristic
305C22×#41C2311yescharacteristic
306C22×#41C2312yes—
307C22×#41C2312yes—
308C22×#41C2312yes—
309C23×D4C2311yescharacteristic
310C24×C4C2312yes—
311#557—28no—
312#556—28no—
313#555—28no—
314#554—28no—
315#553—232no—
316#553—216no—
317#553—216no—
318#552—216no—
319#552—28no—
320#552—28no—
321#551—216no—
322#551—216no—
323#550—216no—
324#550—28no—
325#550—28no—
326#550—216no—
327#550—48no—
328#547—28no—
329#547—216no—
330#547—28no—
331#546—28no—
332#546—28no—
333#546—48no—
334#540—232no—
335#540—216no—
336#537—28no—
337#533—28no—
338#532—216no—
339#532—28no—
340#532—48no—
341C2×C4⋊Q8C2311yescharacteristic
342C2×C4⋊Q8C2312yes—
343C2×C4⋊Q8C2311yescharacteristic
344C2×C4⋊Q8C2311yescharacteristic
345C2×C4⋊Q8C2312yes—
346C2×#127C2311yescharacteristic
347C2×#127C2312yes—
348C2×#127C2312yes—
349C2×#127C2314yes—
350C2×#127C2312yes—
351C2×#127C2314yes—
352#529—216no—
353#529—216no—
354#529—28no—
355#529—216no—
356#529D4116yescomplemented
357C2×#126C2312yes—
358C2×#126C2312yes—
359C2×#126C2312yes—
360C2×#126C2312yes—
361C2×#126C2312yes—
362C2×#126C2314yes—
363C2×#126C2312yes—
364C2×#125C2312yes—
365C2×#125C2312yes—
366C2×#125C2312yes—
367C2×#125C2311yescharacteristic
368C2×#125C2312yes—
369C2×#125C2314yes—
370C2×#125C2311yescharacteristic
371C2×#124C2312yes—
372C2×#124C2312yes—
373C2×#124C2312yes—
374C2×#124C2311yescharacteristic
375C2×#124C2312yes—
376C2×#124C2312yes—
377C2×#124C2314yes—
378C2×#124C2311yescharacteristic
379#525—216no—
380#525—216no—
381C2×#123C2314yes—
382C2×#123C2312yes—
383C2×#123C2312yes—
384C2×#123C2314yes—
385C2×#123C2312yes—
386C2×#123C2312yes—
387C2×#123C2312yes—
388C2×#123C2314yes—
389C2×#123C2312yes—
390C2×#123C2312yes—
391C2×#123C2314yes—
392C2×#123C2314yes—
393C2×#123C2314yes—
394C2×#123C2312yes—
395C2×C22⋊Q8C2311yescharacteristic
396C2×C22⋊Q8C2312yes—
397C2×C22⋊Q8C2311yescharacteristic
398C2×C22⋊Q8C2312yes—
399C2×C22⋊Q8C2312yes—
400C2×C22⋊Q8C2312yes—
401C2×C22⋊Q8C2311yescharacteristic
402C2×C22⋊Q8C2312yes—
403C2×C22⋊Q8C2312yes—
404C2×C22⋊Q8C2312yes—
405C2×C22⋊Q8C2312yes—
406C2×C22⋊Q8C2311yescharacteristic
407C2×C22⋊Q8C2312yes—
408C2×C22⋊Q8C2312yes—
409C2×C22⋊Q8C2312yes—
410C2×C22⋊Q8C2311yescharacteristic
411C2×C22⋊Q8C2311yescharacteristic
412C2×#121C2312yes—
413C2×#121C2311yescharacteristic
414C2×#121C2312yes—
415C2×#121C2311yescharacteristic
416C2×#121C2312yes—
417C2×#121C2312yes—
418C2×#121C2312yes—
419C2×#121C2312yes—
420C2×#121C2312yes—
421C2×#121C2311yescharacteristic
422C2×#121C2312yes—
423C2×#121C2312yes—
424C2×#121C2312yes—
425C2×#121C2312yes—
426C2×#121C2314yes—
427C2×#121C2312yes—
428C2×#121C2312yes—
429C2×#121C2314yes—
430C2×#121C2312yes—
431C2×#121C2314yes—
432C2×#121C2314yes—
433C2×#121C2314yes—
434C2×#121C2312yes—
435C2×#121C2314yes—
436C2×#121C2314yes—
437C2×#121C2312yes—
438C2×#121C2312yes—
439C2×#121C2312yes—
440C2×#121C2312yes—
441C2×#121C2312yes—
442C2×#121C2314yes—
443C2×#121C2314yes—
444C2×#121C2314yes—
445C2×#121C2314yes—
446C2×#121C2314yes—
447C2×#121C2312yes—
448C2×#121C2312yes—
449C2×#121C2314yes—
450C2×#121C2314yes—
451C2×#121C2311yescharacteristic
452C2×#120C2314yes—
453C2×#120C2312yes—
454C2×#120C2312yes—
455C2×#120C2314yes—
456C2×#120C2314yes—
457#520—216no—
458C4×#41—28no—
459C4×#41—28no—
460C4×#41—28no—
461C4×#41—28no—
462C2×C4×Q8C2311yescharacteristic
463C2×C4×Q8C2312yes—
464C2×C4×Q8C2311yescharacteristic
465C2×C4×Q8C2312yes—
466C2×C4×Q8C2311yescharacteristic
467C2×C4×Q8C2311yescharacteristic
468C2×C4×Q8C2311yescharacteristic
469C2×C4×Q8C2311yescharacteristic
470C2×C4×Q8C2312yes—
471C2×C4×Q8C2311yescharacteristic
472C2×C4×Q8C2312yes—
473C2×C4×Q8C2311yescharacteristic
474C2×C4×D4—28no—
475C2×C4×D4C2312yes—
476C2×C4×D4C2311yescharacteristic
477C2×C4×D4C2311yescharacteristic
478C2×C4×D4C2312yes—
479C2×C4×D4C2312yes—
480C2×C4×D4C2312yes—
481C2×C4×D4C2311yescharacteristic
482C2×C4×D4C2312yes—
483C2×C4×D4C2311yescharacteristic
484C2×C4×D4C2311yescharacteristic
485C2×C4×D4C2314yes—
486C2×C4×D4C2314yes—
487C2×C4×D4C2314yes—
488C2×C4×D4C2314yes—
489C2×C4×D4C2312yes—
490C2×C4×D4C2311yescharacteristic
491C2×C4×D4C2311yescharacteristic
492C2×C4×D4C2312yes—
493C2×C4×D4C2311yescharacteristic
494C2×C4×D4C2312yes—
495C2×C4×D4C2312yes—
496C2×C4×D4C2311yescharacteristic
497C2×C4×D4C2311yescharacteristic
498C2×C4×D4C2312yes—
499C2×C4×D4C2312yes—
500C2×C4×D4C2311yescharacteristic
501C2×C4×D4C2311yescharacteristic
502C2×C4×D4C2312yes—
503C2×C4×D4C2311yescharacteristic
504C2×C4×D4C2312yes—
505C2×C4×D4C2314yes—
506C2×C4×D4C2314yes—
507C2×C4×D4C2312yes—
508C2×C4×D4C2314yes—
509C2×C4×D4C2314yes—
510C2×C4×D4C2314yes—
511C2×C4×D4C2312yes—
512C2×C4×D4C2312yes—
513C2×C4×D4C2314yes—
514C2×C4×D4C2314yes—
515C2×C4×D4C2311yescharacteristic
516C2×C4×D4C2312yes—
517C2×#117—216no—
518C2×#117C2311yescharacteristic
519C2×#117C2311yescharacteristic
520C2×#117C2312yes—
521C2×#117C2312yes—
522C2×#117C2311yescharacteristic
523C2×#117C2312yes—
524C2×#117C2312yes—
525C2×#117C2311yescharacteristic
526C2×#117C2312yes—
527C2×#117C2314yes—
528C2×#117C2312yes—
529C2×#117C2312yes—
530C2×#117C2312yes—
531C2×#117C2312yes—
532C2×#117C2311yescharacteristic
533C2×#117C2312yes—
534C2×#117C2311yescharacteristic
535C2×#117C2312yes—
536C2×#117C2312yes—
537C22×C4⋊C4C2311yescharacteristic
538C22×C4⋊C4C2312yes—
539C22×C4⋊C4C2312yes—
540C22×C4⋊C4C2314yes—
541C22×C4⋊C4C2312yes—
542C22×C4⋊C4C2311yescharacteristic
543C22×C4⋊C4C2311yescharacteristic
544C22×C4⋊C4C2312yes—
545C22×C22⋊C4C2312yes—
546C22×C22⋊C4C2312yes—
547C22×C22⋊C4C2312yes—
548C22×C22⋊C4C2314yes—
549C22×C42C2312yes—
550C22×C42C2311yescharacteristic
551C22×C42C2311yescharacteristic
552C22×C42C2312yes—
553C22×C42C2312yes—
554C22×C42C2312yes—
555C22×C42C2311yescharacteristic
556#400C2314yes—
557#400C2314yes—
558#399C2314yes—
559#399C2314yes—
560#399C2314yes—
561#399C2314yes—
562#399C2314yes—
563#398C2314yes—
564#398C2314yes—
565#398C2314yes—
566#398C2314yes—
567#398C2314yes—
568#398C2314yes—
569#398C2314yes—
570#398C2314yes—
571#398C2314yes—
572#397C2314yes—
573#397C2314yes—
574#397C2314yes—
575#397C2314yes—
576#397C2314yes—
577#397C2314yes—
578#396C2314yes—
579#396C2314yes—
580#396C2314yes—
581#396C2314yes—
582#396C2314yes—
583#396C2314yes—
584#396C2314yes—
585#396C2314yes—
586#395C2314yes—
587#394C2314yes—
588#394C2314yes—
589#394C2314yes—
590#394C2314yes—
591#394C2314yes—
592#394C2314yes—
593#394C2314yes—
594#394C2314yes—
595#394C2314yes—
596#394C2314yes—
597#394C2314yes—
598#394C2314yes—
599#394C2314yes—
600#394C2314yes—
601#394C2314yes—
602#394C2314yes—
603#394C2314yes—
604#394C2314yes—
605#394C2314yes—
606#394C2314yes—
607#394C2314yes—
608#394C2314yes—
609#394C2314yes—
610#394C2314yes—
611#394C2314yes—
612#394C2314yes—
613#393C2314yes—
614#393C2314yes—
615#392C2314yes—
616#392C2314yes—
617#392C2314yes—
618#392C2314yes—
619#392C2314yes—
620#392C2314yes—
621#392C2314yes—
622#392C2314yes—
623#392C2314yes—
624#392C2314yes—
625#392C2314yes—
626#392C2314yes—
627#392C2314yes—
628#391C2312yes—
629#391C2311yescharacteristic
630#391C2312yes—
631#391C2311yescharacteristic
632#391C2312yes—
633#391C2314yes—
634#391C2312yes—
635#391C2312yes—
636#391C2312yes—
637#391C2312yes—
638#391C2312yes—
639#390C2312yes—
640#390C2312yes—
641#390C2311yescharacteristic
642#390C2312yes—
643#390C2311yescharacteristic
644#390C2312yes—
645#390C2312yes—
646#390C2314yes—
647#390C2314yes—
648#390C2312yes—
649#390C2314yes—
650#390C2312yes—
651#390C2312yes—
652#390C2312yes—
653#390C2312yes—
654#390C2312yes—
655#390C2314yes—
656#390C2312yes—
657#390C2314yes—
658#390C2314yes—
659#390C2312yes—
660#390C2312yes—
661#390C2312yes—
662#390C2314yes—
663#390C2312yes—
664#390C2314yes—
665#390C2314yes—
666#389C2311yescharacteristic
667#389C2311yescharacteristic
668#389C2312yes—
669#389C2311yescharacteristic
670#389C2312yes—
671#389C2311yescharacteristic
672#389C2312yes—
673#389C2312yes—
674#389C2312yes—
675#389C2312yes—
676#389C2314yes—
677#389C2312yes—
678#389C2312yes—
679#389C2312yes—
680#389C2312yes—
681#389C2312yes—
682#389C2312yes—
683#389C2312yes—
684#389C2314yes—
685#389C2314yes—
686#389C2314yes—
687#389C2314yes—
688#389C2314yes—
689#389C2312yes—
690#389C2312yes—
691#389C2312yes—
692#388C2314yes—
693#388C2314yes—
694#388C2314yes—
695#388C2314yes—
696#388C2312yes—
697#388C2312yes—
698#388C2314yes—
699#388C2314yes—
700#388C2312yes—
701#388C2312yes—
702#388C2312yes—
703#388C2312yes—
704#388C2312yes—
705#388C2312yes—
706#388C2314yes—
707#388C2314yes—
708#388C2314yes—
709#388C2314yes—
710#388C2314yes—
711#388C2314yes—
712#388C2314yes—
713#388C2314yes—
714#388C2314yes—
715#388C2314yes—
716#388C2314yes—
717#388C2314yes—
718#388C2314yes—
719#388C2314yes—
720#387C2314yes—
721#387C2314yes—
722#387C2312yes—
723#387C2314yes—
724#387C2312yes—
725#387C2312yes—
726#387C2312yes—
727#387C2314yes—
728#387C2314yes—
729#387C2314yes—
730#387C2314yes—
731#387C2314yes—
732#387C2314yes—
733#387C2314yes—
734#386C2312yes—
735#386C2312yes—
736#386C2312yes—
737#386C2312yes—
738#386C2314yes—
739#386C2314yes—
740#386C2312yes—
741#386C2312yes—
742#386C2312yes—
743#386C2314yes—
744#386C2314yes—
745#386C2312yes—
746#386C2314yes—
747#386C2314yes—
748#386C2314yes—
749#386C2314yes—
750#386C2314yes—
751#386C2314yes—
752#386C2314yes—
753#386C2314yes—
754#386C2314yes—
755#386C2314yes—
756#386C2314yes—
757#386C2314yes—
758#386C2314yes—
759#386C2314yes—
760#386C2314yes—
761#386C2314yes—
762#386C2314yes—
763#386C2314yes—
764#386C2314yes—
765#386C2314yes—
766#385C2314yes—
767#385C2314yes—
768#385C2314yes—
769#385C2312yes—
770#385C2312yes—
771#385C2312yes—
772#385C2314yes—
773#385C2314yes—
774#385C2312yes—
775#385C2314yes—
776#385C2314yes—
777#385C2314yes—
778#385C2314yes—
779#385C2314yes—
780#385C2314yes—
781#385C2314yes—
782#385C2314yes—
783#385C2314yes—
784#385C2314yes—
785#385C2314yes—
786#385C2314yes—
787#385C2314yes—
788#384C2312yes—
789#384C2314yes—
790#384C2311yescharacteristic
791#384C2311yescharacteristic
792#382C2312yes—
793#382C2314yes—
794#382C2312yes—
795#381C2314yes—
796#380C2311yescharacteristic
797#380C2312yes—
798#380C2312yes—
799#380C2312yes—
800#380C2311yescharacteristic
801#380C2311yescharacteristic
802#380C2311yescharacteristic
803#380C2312yes—
804#380C2312yes—
805#380C2314yes—
806#380C2314yes—
807#380C2312yes—
808#380C2312yes—
809#380C2312yes—
810#380C2312yes—
811#380C2312yes—
812#380C2312yes—
813#380C2312yes—
814#380C2314yes—
815#380C2312yes—
816#380C2312yes—
817#380C2312yes—
818#380C2314yes—
819#380C2314yes—
820#380C2312yes—
821#380C2312yes—
822#380C2312yes—
823C4×C4⋊C4C2312yes—
824C4×C4⋊C4C2311yescharacteristic
825C4×C4⋊C4C2312yes—
826C4×C4⋊C4C2311yescharacteristic
827C4×C4⋊C4C2312yes—
828C4×C4⋊C4C2312yes—
829C4×C4⋊C4C2314yes—
830C4×C4⋊C4C2312yes—
831C4×C4⋊C4C2311yescharacteristic
832C4×C4⋊C4C2311yescharacteristic
833C4×C4⋊C4C2314yes—
834C4×C4⋊C4C2314yes—
835C4×C4⋊C4C2314yes—
836C4×C4⋊C4C2312yes—
837C4×C4⋊C4C2312yes—
838C4×C4⋊C4C2312yes—
839C4×C4⋊C4C2312yes—
840C4×C4⋊C4C2312yes—
841C4×C22⋊C4C2314yes—
842C4×C22⋊C4C2312yes—
843C4×C22⋊C4C2314yes—
844C4×C22⋊C4C2312yes—
845C4×C22⋊C4C2314yes—
846C4×C22⋊C4C2314yes—
847C4×C22⋊C4C2314yes—
848C4×C22⋊C4C2314yes—
849C4×C22⋊C4C2314yes—
850C4×C22⋊C4C2312yes—
851C4×C22⋊C4C2312yes—
852C4×C22⋊C4C2314yes—
853C4×C22⋊C4C2314yes—
854C2×#95C2312yes—
855C2×#95C2314yes—
856C25C2412yes—
857C2×#41—24no—
858C2×#41—28no—
859C2×#41—28no—
860C2×#41—24no—
861C2×#41—28no—
862C2×#41—24no—
863C2×#41—24no—
864C2×#41—24no—
865C2×#41—24no—
866C2×#41—24no—
867C2×#41—28no—
868C2×#41—28no—
869C2×#41—24no—
870C2×#41—42no—
871C2×#41—44no—
872C2×#41—42no—
873C2×#41—42no—
874C2×#41—42no—
875C2×#41—44no—
876C2×#41—44no—
877C2×#41—44no—
878C2×#41—44no—
879C2×#41—44no—
880C2×#41—44no—
881C22×Q8C2411yescharacteristic
882C22×Q8C2412yes—
883C22×Q8C2411yescharacteristic
884C22×Q8C2411yescharacteristic
885C22×Q8C2411yescharacteristic
886C22×Q8C2412yes—
887C22×D4—24no—
888C22×D4—24no—
889C22×D4—42no—
890C22×D4C2411yescharacteristic
891C22×D4C2412yes—
892C22×D4C2412yes—
893C22×D4C2414yes—
894C22×D4C2411yescharacteristic
895C22×D4C2411yescharacteristic
896C22×D4C2412yes—
897C22×D4C2412yes—
898C22×D4C2414yes—
899C22×D4C2411yescharacteristic
900C22×D4C2412yes—
901C22×D4C2412yes—
902C22×D4C2411yescharacteristic
903C22×D4C2411yescharacteristic
904C22×D4C2412yes—
905C22×D4C2414yes—
906C22×D4C2414yes—
907C22×D4C2412yes—
908C22×D4C2414yes—
909C22×D4C2414yes—
910C22×D4C2412yes—
911C22×D4C2414yes—
912C22×D4C2412yes—
913C22×D4C2414yes—
914C22×D4C2414yes—
915C22×D4C2414yes—
916C22×D4C2414yes—
917C22×D4C2412yes—
918C23×C4—28no—
919C23×C4—28no—
920C23×C4—44no—
921C23×C4C2411yescharacteristic
922C23×C4C2411yescharacteristic
923C23×C4C2411yescharacteristic
924C23×C4C2412yes—
925C23×C4C2412yes—
926C23×C4C2412yes—
927C23×C4C2412yes—
928C23×C4C2412yes—
929C23×C4C2412yes—
930C23×C4C2414yes—
931C23×C4C2412yes—
932C23×C4C2412yes—
933C23×C4C2412yes—
934C23×C4C2411yescharacteristic
935C23×C4C2411yescharacteristic
936C23×C4C2411yescharacteristic
937C23×C4C2411yescharacteristic
938C23×C4C2412yes—
939C23×C4C2414yes—
940C23×C4C2412yes—
941C23×C4C2414yes—
942C23×C4C2414yes—
943C23×C4C2412yes—
944C23×C4C2412yes—
945C23×C4C2411yescharacteristic
946C23×C4C2414yes—
947C23×C4C2412yes—
948C23×C4C2411yescharacteristic
949C4⋊Q8—28no—
950C4⋊Q8—24no—
951C4⋊Q8—24no—
952C4⋊Q8—24no—
953C4⋊Q8—44no—
954#127—28no—
955#127—216no—
956#127—28no—
957#127—24no—
958#127—28no—
959#127—48no—
960#126—28no—
961#126—216no—
962#126—28no—
963#126—28no—
964#126—28no—
965#126—28no—
966#126C2×D4116yes—
967#125—28no—
968#125—28no—
969#125—24no—
970#125—28no—
971#125—216no—
972#125—28no—
973#125C2×D418yes—
974#124—24no—
975#124—28no—
976#124—28no—
977#124—28no—
978#124—28no—
979#124—44no—
980#124—84no—
981#124C2×D418yes—
982#123—28no—
983#123—216no—
984#123—28no—
985#123—216no—
986#123—216no—
987#123—28no—
988#123—28no—
989#123—28no—
990#123—28no—
991#123—28no—
992#123—216no—
993#123—216no—
994#123—48no—
995#123C2×D4116yes—
996C22⋊Q8—24no—
997C22⋊Q8—28no—
998C22⋊Q8—24no—
999C22⋊Q8—28no—
1000C22⋊Q8—28no—
1001C22⋊Q8—24no—
1002C22⋊Q8—28no—
1003C22⋊Q8—28no—
1004C22⋊Q8—24no—
1005C22⋊Q8—28no—
1006C22⋊Q8—28no—
1007C22⋊Q8—28no—
1008C22⋊Q8—44no—
1009C22⋊Q8—44no—
1010C22⋊Q8—44no—
1011C22⋊Q8C2×D418yes—
1012C22⋊Q8#4118yescomplemented
1013#121—28no—
1014#121—28no—
1015#121—24no—
1016#121—216no—
1017#121—28no—
1018#121—28no—
1019#121—28no—
1020#121—28no—
1021#121—28no—
1022#121—28no—
1023#121—24no—
1024#121—28no—
1025#121—216no—
1026#121—28no—
1027#121—24no—
1028#121—28no—
1029#121—28no—
1030#121—28no—
1031#121—216no—
1032#121—216no—
1033#121—216no—
1034#121—216no—
1035#121—216no—
1036#121—28no—
1037#121—28no—
1038#121—48no—
1039#121—48no—
1040#121—48no—
1041#121—48no—
1042#121—44no—
1043#121—44no—
1044#121—44no—
1045#121—44no—
1046#121—44no—
1047#121—48no—
1048#121—82no—
1049#121—84no—
1050#121—84no—
1051#121—82no—
1052#121C2×D418yes—
1053#120—28no—
1054#120—28no—
1055#120—216no—
1056#120—48no—
1057#120—84no—
1058C4×Q8—24no—
1059C4×Q8—28no—
1060C4×Q8—24no—
1061C4×Q8—24no—
1062C4×Q8—24no—
1063C4×Q8—24no—
1064C4×Q8—24no—
1065C4×Q8—24no—
1066C4×Q8—28no—
1067C4×Q8—28no—
1068C4×Q8—44no—
1069C4×Q8C2×D418yes—
1070C4×D4—24no—
1071C4×D4—28no—
1072C4×D4—28no—
1073C4×D4—28no—
1074C4×D4—24no—
1075C4×D4—28no—
1076C4×D4—24no—
1077C4×D4—24no—
1078C4×D4—28no—
1079C4×D4—24no—
1080C4×D4—28no—
1081C4×D4—24no—
1082C4×D4—24no—
1083C4×D4—28no—
1084C4×D4—28no—
1085C4×D4—216no—
1086C4×D4—216no—
1087C4×D4—28no—
1088C4×D4—216no—
1089C4×D4—216no—
1090C4×D4—216no—
1091C4×D4—216no—
1092C4×D4—24no—
1093C4×D4—28no—
1094C4×D4—24no—
1095C4×D4—24no—
1096C4×D4—24no—
1097C4×D4—24no—
1098C4×D4—24no—
1099C4×D4—28no—
1100C4×D4—28no—
1101C4×D4—28no—
1102C4×D4—44no—
1103C4×D4—44no—
1104C4×D4—44no—
1105C4×D4—48no—
1106C4×D4—48no—
1107C4×D4—48no—
1108C4×D4—84no—
1109C4×D4—84no—
1110C4×D4C2×D418yes—
1111C4×D4C2×D4116yes—
1112#117—28no—
1113#117—24no—
1114#117—24no—
1115#117—24no—
1116#117—28no—
1117#117—28no—
1118#117—28no—
1119#117—24no—
1120#117—216no—
1121#117—28no—
1122#117—28no—
1123#117—28no—
1124#117—24no—
1125#117—28no—
1126#117—24no—
1127#117—28no—
1128#117—28no—
1129#117—82no—
1130#117C2×D4116yes—
1131C2×C4⋊C4—28no—
1132C2×C4⋊C4—28no—
1133C2×C4⋊C4—28no—
1134C2×C4⋊C4—24no—
1135C2×C4⋊C4—216no—
1136C2×C4⋊C4—24no—
1137C2×C4⋊C4—44no—
1138C2×C4⋊C4—42no—
1139C2×C4⋊C4C2411yescharacteristic
1140C2×C4⋊C4C2411yescharacteristic
1141C2×C4⋊C4C2411yescharacteristic
1142C2×C4⋊C4C2411yescharacteristic
1143C2×C4⋊C4C2412yes—
1144C2×C4⋊C4C2414yes—
1145C2×C4⋊C4C2411yescharacteristic
1146C2×C4⋊C4C2412yes—
1147C2×C4⋊C4C2412yes—
1148C2×C4⋊C4C2412yes—
1149C2×C4⋊C4C2412yes—
1150C2×C4⋊C4C2412yes—
1151C2×C4⋊C4C2412yes—
1152C2×C4⋊C4C2414yes—
1153C2×C4⋊C4C2411yescharacteristic
1154C2×C4⋊C4C2412yes—
1155C2×C4⋊C4C2411yescharacteristic
1156C2×C4⋊C4C2412yes—
1157C2×C4⋊C4C2411yescharacteristic
1158C2×C4⋊C4C2412yes—
1159C2×C4⋊C4C2411yescharacteristic
1160C2×C4⋊C4C2411yescharacteristic
1161C2×C4⋊C4C2411yescharacteristic
1162C2×C4⋊C4C2412yes—
1163C2×C4⋊C4C2412yes—
1164C2×C4⋊C4C2412yes—
1165C2×C4⋊C4C2411yescharacteristic
1166C2×C4⋊C4C2411yescharacteristic
1167C2×C4⋊C4C2412yes—
1168C2×C4⋊C4C2412yes—
1169C2×C4⋊C4C2412yes—
1170C2×C4⋊C4C2414yes—
1171C2×C4⋊C4C2412yes—
1172C2×C4⋊C4C2414yes—
1173C2×C4⋊C4C2414yes—
1174C2×C4⋊C4C2412yes—
1175C2×C4⋊C4C2412yes—
1176C2×C4⋊C4C2412yes—
1177C2×C4⋊C4C2412yes—
1178C2×C4⋊C4C2412yes—
1179C2×C4⋊C4C2414yes—
1180C2×C4⋊C4C2412yes—
1181C2×C4⋊C4C2412yes—
1182C2×C4⋊C4C2412yes—
1183C2×C4⋊C4C2412yes—
1184C2×C4⋊C4C2414yes—
1185C2×C4⋊C4C2414yes—
1186C2×C4⋊C4C2414yes—
1187C2×C4⋊C4C2414yes—
1188C2×C4⋊C4C2412yes—
1189C2×C4⋊C4C2414yes—
1190C2×C4⋊C4C2414yes—
1191C2×C4⋊C4C2414yes—
1192C2×C4⋊C4C2414yes—
1193C2×C4⋊C4C2412yes—
1194C2×C4⋊C4C2412yes—
1195C2×C4⋊C4C2412yes—
1196C2×C4⋊C4C2412yes—
1197C2×C4⋊C4C2411yescharacteristic
1198C2×C4⋊C4C2411yescharacteristic
1199C2×C4⋊C4C2412yes—
1200C2×C4⋊C4C2412yes—
1201C2×C4⋊C4C2411yescharacteristic
1202C2×C4⋊C4C2412yes—
1203C2×C22⋊C4—28no—
1204C2×C22⋊C4—28no—
1205C2×C22⋊C4—28no—
1206C2×C22⋊C4—48no—
1207C2×C22⋊C4C2411yescharacteristic
1208C2×C22⋊C4C2411yescharacteristic
1209C2×C22⋊C4C2412yes—
1210C2×C22⋊C4C2412yes—
1211C2×C22⋊C4C2412yes—
1212C2×C22⋊C4C2412yes—
1213C2×C22⋊C4C2412yes—
1214C2×C22⋊C4C2412yes—
1215C2×C22⋊C4C2412yes—
1216C2×C22⋊C4C2414yes—
1217C2×C22⋊C4C2414yes—
1218C2×C22⋊C4C2412yes—
1219C2×C22⋊C4C2412yes—
1220C2×C22⋊C4C2414yes—
1221C2×C22⋊C4C2412yes—
1222C2×C22⋊C4C2412yes—
1223C2×C22⋊C4C2412yes—
1224C2×C22⋊C4C2414yes—
1225C2×C22⋊C4C2411yescharacteristic
1226C2×C22⋊C4C2411yescharacteristic
1227C2×C22⋊C4C2412yes—
1228C2×C22⋊C4C2412yes—
1229C2×C22⋊C4C2411yescharacteristic
1230C2×C22⋊C4C2411yescharacteristic
1231C2×C22⋊C4C2414yes—
1232C2×C22⋊C4C2414yes—
1233C2×C22⋊C4C2414yes—
1234C2×C22⋊C4C2412yes—
1235C2×C22⋊C4C2414yes—
1236C2×C22⋊C4C2414yes—
1237C2×C22⋊C4C2414yes—
1238C2×C22⋊C4C2412yes—
1239C2×C22⋊C4C2414yes—
1240C2×C22⋊C4C2414yes—
1241C2×C22⋊C4C2412yes—
1242C2×C22⋊C4C2412yes—
1243C2×C22⋊C4C2412yes—
1244C2×C22⋊C4C2412yes—
1245C2×C22⋊C4C2414yes—
1246C2×C22⋊C4C2414yes—
1247C2×C22⋊C4C2414yes—
1248C2×C22⋊C4C2414yes—
1249C2×C22⋊C4C2414yes—
1250C2×C22⋊C4C2414yes—
1251C2×C22⋊C4C2412yes—
1252C2×C22⋊C4C2412yes—
1253C2×C22⋊C4C2412yes—
1254C2×C22⋊C4C2414yes—
1255C2×C22⋊C4C2414yes—
1256C2×C22⋊C4C2414yes—
1257C2×C22⋊C4C2412yes—
1258C2×C22⋊C4C2412yes—
1259C2×C22⋊C4C2412yes—
1260C2×C22⋊C4C2414yes—
1261C2×C22⋊C4C2414yes—
1262C2×C22⋊C4C2414yes—
1263C2×C22⋊C4C2414yes—
1264C2×C22⋊C4C2414yes—
1265C2×C22⋊C4C2414yes—
1266C2×C22⋊C4C2414yes—
1267C2×C22⋊C4C2414yes—
1268C2×C22⋊C4C2414yes—
1269C2×C22⋊C4C2412yes—
1270C2×C22⋊C4C2414yes—
1271C2×C22⋊C4C2412yes—
1272C2×C22⋊C4C2412yes—
1273C2×C22⋊C4C2412yes—
1274C2×C22⋊C4C2412yes—
1275C2×C22⋊C4C2412yes—
1276C2×C22⋊C4C2412yes—
1277C2×C42—28no—
1278C2×C42—28no—
1279C2×C42—24no—
1280C2×C42—24no—
1281C2×C42—28no—
1282C2×C42—44no—
1283C2×C42C2×D418yes—
1284C2×C42C2412yes—
1285C2×C42C2412yes—
1286C2×C42C2411yescharacteristic
1287C2×C42C2412yes—
1288C2×C42C2411yescharacteristic
1289C2×C42C2412yes—
1290C2×C42C2412yes—
1291C2×C42C2412yes—
1292C2×C42C2412yes—
1293C2×C42C2411yescharacteristic
1294C2×C42C2414yes—
1295C2×C42C2414yes—
1296C2×C42C2411yescharacteristic
1297C2×C42C2411yescharacteristic
1298C2×C42C2411yescharacteristic
1299C2×C42C2412yes—
1300C2×C42C2412yes—
1301C2×C42C2412yes—
1302C2×C42C2414yes—
1303C2×C42C2412yes—
1304C2×C42C2412yes—
1305C2×C42C2414yes—
1306C2×C42C2414yes—
1307C2×C42C2411yescharacteristic
1308C2×C42C2411yescharacteristic
1309C2×C42C2412yes—
1310C2×C42C2411yescharacteristic
1311C2×C42C2411yescharacteristic
1312#95C2412yes—
1313#95C2412yes—
1314#95C2414yes—
1315#95C2414yes—
1316#95C2412yes—
1317#95C2412yes—
1318#95C2412yes—
1319#95C2414yes—
1320#95C2412yes—
1321#95C2412yes—
1322#95C2412yes—
1323#95C2414yes—
1324#95C2414yes—
1325#95C2414yes—
1326#95C2412yes—
1327#95C2412yes—
1328#95C2414yes—
1329#95C2414yes—
1330#95C2414yes—
1331#95C2414yes—
1332#95C2412yes—
1333#95C2412yes—
1334#95C2414yes—
1335#95C2414yes—
1336#95C2412yes—
1337#95C2414yes—
1338#95C2414yes—
1339#95C2414yes—
1340#95C2414yes—
1341#95C2414yes—
1342#95C2414yes—
1343#95C2414yes—
1344#95C2412yes—
1345#95C2412yes—
1346#95C2412yes—
1347#95C2414yes—
1348#95C2414yes—
1349#95C2414yes—
1350C24—24no—
1351C24—24no—
1352C24—24no—
1353C24—42no—
1354C24—42no—
1355C24—42no—
1356C24—42no—
1357C24C2511yescharacteristic
1358C24C2514yes—
1359C24C2512yes—
1360C24C2512yes—
1361C24C2511yescharacteristic
1362C24C2511yescharacteristic
1363C24C2512yes—
1364#41—416no—
1365#41—416no—
1366#41—432no—
1367#41—416no—
1368#41—416no—
1369#41—816no—
1370#41—816no—
1371#41—816no—
1372C2×Q8—22no—
1373C2×Q8—22no—
1374C2×Q8—22no—
1375C2×Q8—24no—
1376C2×Q8—24no—
1377C2×Q8—22no—
1378C2×Q8—22no—
1379C2×Q8—24no—
1380C2×Q8—22no—
1381C2×Q8—22no—
1382C2×Q8—22no—
1383C2×Q8—22no—
1384C2×Q8—24no—
1385C2×Q8—41no—
1386C2×Q8—42no—
1387C2×Q8—42no—
1388C2×Q8C22×D414yes—
1389C2×Q8C2×#4114yes—
1390C2×D4—22no—
1391C2×D4—24no—
1392C2×D4—22no—
1393C2×D4—24no—
1394C2×D4—24no—
1395C2×D4—28no—
1396C2×D4—22no—
1397C2×D4—22no—
1398C2×D4—28no—
1399C2×D4—24no—
1400C2×D4—24no—
1401C2×D4—24no—
1402C2×D4—24no—
1403C2×D4—28no—
1404C2×D4—28no—
1405C2×D4—28no—
1406C2×D4—28no—
1407C2×D4—24no—
1408C2×D4—28no—
1409C2×D4—28no—
1410C2×D4—22no—
1411C2×D4—22no—
1412C2×D4—24no—
1413C2×D4—22no—
1414C2×D4—24no—
1415C2×D4—24no—
1416C2×D4—24no—
1417C2×D4—28no—
1418C2×D4—28no—
1419C2×D4—28no—
1420C2×D4—28no—
1421C2×D4—22no—
1422C2×D4—24no—
1423C2×D4—24no—
1424C2×D4—22no—
1425C2×D4—24no—
1426C2×D4—22no—
1427C2×D4—24no—
1428C2×D4—22no—
1429C2×D4—22no—
1430C2×D4—22no—
1431C2×D4—24no—
1432C2×D4—24no—
1433C2×D4—42no—
1434C2×D4—42no—
1435C2×D4—44no—
1436C2×D4—42no—
1437C2×D4—41no—
1438C2×D4—41no—
1439C2×D4—44no—
1440C2×D4—42no—
1441C2×D4—42no—
1442C2×D4—41no—
1443C2×D4—42no—
1444C2×D4—42no—
1445C2×D4—42no—
1446C2×D4—44no—
1447C2×D4—44no—
1448C2×D4—44no—
1449C2×D4—44no—
1450C2×D4—44no—
1451C2×D4—44no—
1452C2×D4—44no—
1453C2×D4—44no—
1454C2×D4—44no—
1455C2×D4—44no—
1456C2×D4—42no—
1457C2×D4—42no—
1458C2×D4—44no—
1459C2×D4—42no—
1460C2×D4—42no—
1461C2×D4—44no—
1462C2×D4—42no—
1463C2×D4—42no—
1464C2×D4—44no—
1465C2×D4—44no—
1466C2×D4—44no—
1467C2×D4—44no—
1468C2×D4—44no—
1469C2×D4—44no—
1470C2×D4—44no—
1471C2×D4—416no—
1472C2×D4C22×D414yes—
1473C2×D4C22×D418yes—
1474C2×D4H(5,𝔽2)14yes—
1475C22×C4—22no—
1476C22×C4—22no—
1477C22×C4—24no—
1478C22×C4—22no—
1479C22×C4—24no—
1480C22×C4—22no—
1481C22×C4—22no—
1482C22×C4—22no—
1483C22×C4—24no—
1484C22×C4—24no—
1485C22×C4—24no—
1486C22×C4—24no—
1487C22×C4—28no—
1488C22×C4—24no—
1489C22×C4—24no—
1490C22×C4—24no—
1491C22×C4—22no—
1492C22×C4—22no—
1493C22×C4—24no—
1494C22×C4—22no—
1495C22×C4—24no—
1496C22×C4—24no—
1497C22×C4—24no—
1498C22×C4—28no—
1499C22×C4—24no—
1500C22×C4—28no—
1501C22×C4—24no—
1502C22×C4—24no—
1503C22×C4—22no—
1504C22×C4—24no—
1505C22×C4—24no—
1506C22×C4—22no—
1507C22×C4—22no—
1508C22×C4—24no—
1509C22×C4—22no—
1510C22×C4—22no—
1511C22×C4—22no—
1512C22×C4—24no—
1513C22×C4—22no—
1514C22×C4—24no—
1515C22×C4—24no—
1516C22×C4—22no—
1517C22×C4—24no—
1518C22×C4—28no—
1519C22×C4—28no—
1520C22×C4—24no—
1521C22×C4—41no—
1522C22×C4—42no—
1523C22×C4—42no—
1524C22×C4—42no—
1525C22×C4—41no—
1526C22×C4—44no—
1527C22×C4—42no—
1528C22×C4—42no—
1529C22×C4—42no—
1530C22×C4—432no—
1531C22×C4—42no—
1532C22×C4—42no—
1533C22×C4—44no—
1534C22×C4—42no—
1535C22×C4—44no—
1536C22×C4—44no—
1537C22×C4—42no—
1538C22×C4—42no—
1539C22×C4—42no—
1540C22×C4—42no—
1541C22×C4—41no—
1542C22×C4—41no—
1543C22×C4—42no—
1544C22×C4—42no—
1545C22×C4—42no—
1546C22×C4—41no—
1547C22×C4—41no—
1548C22×C4—42no—
1549C22×C4—44no—
1550C22×C4—44no—
1551C22×C4—44no—
1552C22×C4—44no—
1553C22×C4—44no—
1554C22×C4—44no—
1555C22×C4C22×D414yes—
1556C22×C4C22×D414yes—
1557C22×C4C22×D418yes—
1558C22×C4C22×D414yes—
1559C22×C4C2×#4114yes—
1560C22×C4C2512yes—
1561C22×C4C2512yes—
1562C22×C4C2514yes—
1563C22×C4C2512yes—
1564C22×C4C2514yes—
1565C22×C4C2512yes—
1566C22×C4C2511yescharacteristic
1567C22×C4C2511yescharacteristic
1568C22×C4C2511yescharacteristic
1569C22×C4C2512yes—
1570C22×C4C2512yes—
1571C22×C4C2512yes—
1572C22×C4C2514yes—
1573C22×C4C2511yescharacteristic
1574C22×C4C2512yes—
1575C22×C4C2511yescharacteristic
1576C22×C4C2511yescharacteristic
1577C22×C4C2511yescharacteristic
1578C22×C4C2512yes—
1579C22×C4C2511yescharacteristic
1580C22×C4C2511yescharacteristic
1581C22×C4C2512yes—
1582C22×C4C2512yes—
1583C22×C4C2512yes—
1584C22×C4C2512yes—
1585C22×C4C2511yescharacteristic
1586C22×C4C2511yescharacteristic
1587C22×C4C2511yescharacteristic
1588C4⋊C4—22no—
1589C4⋊C4—22no—
1590C4⋊C4—24no—
1591C4⋊C4—22no—
1592C4⋊C4—28no—
1593C4⋊C4—22no—
1594C4⋊C4—24no—
1595C4⋊C4—24no—
1596C4⋊C4—24no—
1597C4⋊C4—24no—
1598C4⋊C4—24no—
1599C4⋊C4—28no—
1600C4⋊C4—24no—
1601C4⋊C4—24no—
1602C4⋊C4—22no—
1603C4⋊C4—22no—
1604C4⋊C4—22no—
1605C4⋊C4—22no—
1606C4⋊C4—24no—
1607C4⋊C4—24no—
1608C4⋊C4—24no—
1609C4⋊C4—22no—
1610C4⋊C4—22no—
1611C4⋊C4—28no—
1612C4⋊C4—24no—
1613C4⋊C4—24no—
1614C4⋊C4—28no—
1615C4⋊C4—24no—
1616C4⋊C4—24no—
1617C4⋊C4—24no—
1618C4⋊C4—24no—
1619C4⋊C4—22no—
1620C4⋊C4—24no—
1621C4⋊C4—28no—
1622C4⋊C4—24no—
1623C4⋊C4—24no—
1624C4⋊C4—22no—
1625C4⋊C4—22no—
1626C4⋊C4—24no—
1627C4⋊C4—24no—
1628C4⋊C4—44no—
1629C4⋊C4—42no—
1630C4⋊C4—42no—
1631C4⋊C4—42no—
1632C4⋊C4—42no—
1633C4⋊C4—42no—
1634C4⋊C4—42no—
1635C4⋊C4—44no—
1636C4⋊C4—44no—
1637C4⋊C4—42no—
1638C4⋊C4—44no—
1639C4⋊C4—44no—
1640C4⋊C4—44no—
1641C4⋊C4—44no—
1642C4⋊C4—44no—
1643C4⋊C4—44no—
1644C4⋊C4C22×D418yes—
1645C4⋊C4C22×D418yes—
1646C4⋊C4C22×D414yes—
1647C4⋊C4C22×D414yes—
1648C4⋊C4C22×D418yes—
1649C4⋊C4C22×D418yes—
1650C4⋊C4C2×#4114yes—
1651C4⋊C4C2×#4118yes—
1652C22⋊C4—24no—
1653C22⋊C4—24no—
1654C22⋊C4—24no—
1655C22⋊C4—24no—
1656C22⋊C4—22no—
1657C22⋊C4—24no—
1658C22⋊C4—22no—
1659C22⋊C4—24no—
1660C22⋊C4—28no—
1661C22⋊C4—28no—
1662C22⋊C4—28no—
1663C22⋊C4—22no—
1664C22⋊C4—22no—
1665C22⋊C4—24no—
1666C22⋊C4—24no—
1667C22⋊C4—24no—
1668C22⋊C4—24no—
1669C22⋊C4—24no—
1670C22⋊C4—24no—
1671C22⋊C4—28no—
1672C22⋊C4—24no—
1673C22⋊C4—24no—
1674C22⋊C4—28no—
1675C22⋊C4—22no—
1676C22⋊C4—24no—
1677C22⋊C4—22no—
1678C22⋊C4—28no—
1679C22⋊C4—28no—
1680C22⋊C4—28no—
1681C22⋊C4—24no—
1682C22⋊C4—28no—
1683C22⋊C4—28no—
1684C22⋊C4—28no—
1685C22⋊C4—28no—
1686C22⋊C4—24no—
1687C22⋊C4—24no—
1688C22⋊C4—24no—
1689C22⋊C4—42no—
1690C22⋊C4—44no—
1691C22⋊C4—44no—
1692C22⋊C4—44no—
1693C22⋊C4—44no—
1694C22⋊C4—42no—
1695C22⋊C4—42no—
1696C22⋊C4—42no—
1697C22⋊C4—44no—
1698C22⋊C4—44no—
1699C22⋊C4—44no—
1700C22⋊C4—44no—
1701C22⋊C4—44no—
1702C22⋊C4—44no—
1703C22⋊C4—42no—
1704C22⋊C4—44no—
1705C22⋊C4—44no—
1706C22⋊C4—44no—
1707C22⋊C4—44no—
1708C22⋊C4—42no—
1709C22⋊C4—44no—
1710C22⋊C4—42no—
1711C22⋊C4—44no—
1712C22⋊C4—44no—
1713C22⋊C4—44no—
1714C22⋊C4—44no—
1715C22⋊C4—42no—
1716C22⋊C4C22×D418yes—
1717C22⋊C4C22×D418yes—
1718C22⋊C4C22×D418yes—
1719C22⋊C4C22×D418yes—
1720C22⋊C4C22×D418yes—
1721C22⋊C4C2×#4118yes—
1722C42—22no—
1723C42—24no—
1724C42—24no—
1725C42—24no—
1726C42—22no—
1727C42—24no—
1728C42—24no—
1729C42—24no—
1730C42—24no—
1731C42—22no—
1732C42—22no—
1733C42—22no—
1734C42—22no—
1735C42—24no—
1736C42—28no—
1737C42—28no—
1738C42—24no—
1739C42—24no—
1740C42—42no—
1741C42—42no—
1742C42—44no—
1743C42—44no—
1744C42—44no—
1745C42C22×D414yes—
1746C42C22×D414yes—
1747C42C22×D414yes—
1748C42C22×D418yes—
1749C42C22×D414yes—
1750C23—21no—
1751C23—22no—
1752C23—22no—
1753C23—22no—
1754C23—21no—
1755C23—21no—
1756C23—22no—
1757C23—21no—
1758C23—22no—
1759C23—21no—
1760C23—21no—
1761C23—22no—
1762C23—21no—
1763C23—21no—
1764C23—22no—
1765C23—22no—
1766C23—21no—
1767C23—22no—
1768C23—22no—
1769C23—21no—
1770C23—21no—
1771C23—22no—
1772C23—21no—
1773C23—22no—
1774C23—21no—
1775C23—22no—
1776C23—24no—
1777C23—24no—
1778C23—21no—
1779C23—22no—
1780C23—24no—
1781C23—21no—
1782C23—22no—
1783C23—21no—
1784C23—22no—
1785C23—22no—
1786C23—24no—
1787C23—24no—
1788C23—21no—
1789C23—22no—
1790C23—24no—
1791C23—21no—
1792C23—24no—
1793C23—21no—
1794C23—22no—
1795C23—48no—
1796C23—48no—
1797C23—48no—
1798C23—84no—
1799C23—84no—
1800C23—84no—
1801C23—84no—
1802C23C23×D412yes—
1803C23C23×D414yes—
1804C23C22×#4112yes—
1805C23C2×H(5,𝔽2)14yes—
1806C23C2611yescharacteristic
1807Q8—28no—
1808Q8—28no—
1809Q8—44no—
1810Q8—44no—
1811Q8—48no—
1812Q8—84no—
1813D4—28no—
1814D4—28no—
1815D4—48no—
1816D4—416no—
1817D4—48no—
1818D4—44no—
1819D4—44no—
1820D4—416no—
1821D4—48no—
1822D4—48no—
1823D4—48no—
1824D4—44no—
1825D4—44no—
1826D4—48no—
1827D4—48no—
1828D4—84no—
1829D4—84no—
1830D4—88no—
1831D4—88no—
1832D4—84no—
1833D4—88no—
1834D4—88no—
1835D4—84no—
1836D4—88no—
1837D4—88no—
1838D4—88no—
1839D4—88no—
1840D4—164no—
1841C2×C4—22no—
1842C2×C4—21no—
1843C2×C4—22no—
1844C2×C4—21no—
1845C2×C4—22no—
1846C2×C4—21no—
1847C2×C4—22no—
1848C2×C4—22no—
1849C2×C4—21no—
1850C2×C4—21no—
1851C2×C4—21no—
1852C2×C4—22no—
1853C2×C4—22no—
1854C2×C4—21no—
1855C2×C4—22no—
1856C2×C4—21no—
1857C2×C4—22no—
1858C2×C4—21no—
1859C2×C4—21no—
1860C2×C4—22no—
1861C2×C4—28no—
1862C2×C4—216no—
1863C2×C4—28no—
1864C2×C4—28no—
1865C2×C4—21no—
1866C2×C4—21no—
1867C2×C4—22no—
1868C2×C4—21no—
1869C2×C4—22no—
1870C2×C4—22no—
1871C2×C4—22no—
1872C2×C4—21no—
1873C2×C4—22no—
1874C2×C4—21no—
1875C2×C4—24no—
1876C2×C4—24no—
1877C2×C4—22no—
1878C2×C4—22no—
1879C2×C4—21no—
1880C2×C4—22no—
1881C2×C4—22no—
1882C2×C4—22no—
1883C2×C4—24no—
1884C2×C4—22no—
1885C2×C4—24no—
1886C2×C4—21no—
1887C2×C4—22no—
1888C2×C4—21no—
1889C2×C4—22no—
1890C2×C4—21no—
1891C2×C4—21no—
1892C2×C4—24no—
1893C2×C4—22no—
1894C2×C4—24no—
1895C2×C4—22no—
1896C2×C4—24no—
1897C2×C4—22no—
1898C2×C4—21no—
1899C2×C4—22no—
1900C2×C4—24no—
1901C2×C4—22no—
1902C2×C4—24no—
1903C2×C4—21no—
1904C2×C4—21no—
1905C2×C4—22no—
1906C2×C4—22no—
1907C2×C4—22no—
1908C2×C4—22no—
1909C2×C4—22no—
1910C2×C4—21no—
1911C2×C4—22no—
1912C2×C4—21no—
1913C2×C4—44no—
1914C2×C4—48no—
1915C2×C4—416no—
1916C2×C4—48no—
1917C2×C4—48no—
1918C2×C4—48no—
1919C2×C4—48no—
1920C2×C4—48no—
1921C2×C4—48no—
1922C2×C4—44no—
1923C2×C4—44no—
1924C2×C4—44no—
1925C2×C4—48no—
1926C2×C4—84no—
1927C2×C4—84no—
1928C2×C4—84no—
1929C2×C4—82no—
1930C2×C4—82no—
1931C2×C4—84no—
1932C2×C4—88no—
1933C2×C4—88no—
1934C2×C4—88no—
1935C2×C4—84no—
1936C2×C4—164no—
1937C2×C4C23×D412yes—
1938C2×C4C23×D414yes—
1939C2×C4C23×D412yes—
1940C2×C4C23×D412yes—
1941C2×C4C23×D412yes—
1942C2×C4C23×D414yes—
1943C2×C4C23×D414yes—
1944C2×C4C23×D412yes—
1945C2×C4C23×D412yes—
1946C2×C4C22×#4114yes—
1947C2×C4C22×#4112yes—
1948C2×C4C22×#4114yes—
1949C2×C4C22×#4112yes—
1950C2×C4C2×H(5,𝔽2)12yes—
1951C2×C4#58512yes—
1952C2×C4#58512yes—
1953C22—24no—
1954C22—22no—
1955C22—22no—
1956C22—22no—
1957C22—24no—
1958C22—24no—
1959C22—22no—
1960C22—24no—
1961C22—24no—
1962C22—22no—
1963C22—24no—
1964C22—22no—
1965C22—41no—
1966C22—42no—
1967C22—41no—
1968C22—42no—
1969C22—42no—
1970C22—41no—
1971C22—42no—
1972C22—41no—
1973C22—41no—
1974C22—42no—
1975C22—41no—
1976C22—42no—
1977C22—41no—
1978C22—42no—
1979C22—42no—
1980C22—41no—
1981C22—44no—
1982C22—41no—
1983C22—42no—
1984C22—44no—
1985C22—41no—
1986C22—42no—
1987C22—41no—
1988C22—42no—
1989C22—44no—
1990C22—42no—
1991C22—41no—
1992C22—44no—
1993C22—42no—
1994C22—44no—
1995C22—41no—
1996C22—44no—
1997C22—42no—
1998C22—41no—
1999C22—41no—
2000C22—42no—
2001C22—44no—
2002C22—816no—
2003C22C24×D411yescharacteristic
2004C22C23×#4111yescharacteristic
2005C22C22×H(5,𝔽2)11yescharacteristic
2006C22C2×#58511yescharacteristic
2007C22C2×#58511yescharacteristic
2008C22H(7,𝔽2)11yescharacteristic
2009C222−1+611yescharacteristic
2010C4—24no—
2011C4—22no—
2012C4—24no—
2013C4—22no—
2014C4—22no—
2015C4—24no—
2016C4—24no—
2017C4—22no—
2018C4—22no—
2019C4—24no—
2020C4—42no—
2021C4—44no—
2022C4—41no—
2023C4—42no—
2024C4—41no—
2025C4—42no—
2026C4—44no—
2027C4—41no—
2028C4—42no—
2029C4—42no—
2030C4—41no—
2031C4—42no—
2032C4—42no—
2033C4—44no—
2034C4—42no—
2035C4—41no—
2036C4D4×#4114yes—
2037C4#348814yes—
2038C2—42no—
2039C2—44no—
2040C2—44no—
2041C2—42no—
2042C2—84no—
2043C2—81no—
2044C2—82no—
2045C2C2×D4×#4111yescharacteristic
2046C2C2×#348811yescharacteristic
2047C2#6285311yescharacteristic
2048C2#6292011yescharacteristic
2049C2#6296711yescharacteristic
2050C2#6298511yescharacteristic
2051C2#6300611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3517C2semidirect
2. C2×#3475C2semidirect
3. #59810C2semidirect
4. #59550C2semidirect
5. #59146C2semidirect
6. #59129C2semidirect
7. #59129C2semidirect
8. #59086C2semidirect
9. #59066C2semidirect
10. #59059C2semidirect
11. #44333C2semidirect
12. #44209C2semidirect
13. #43921C2semidirect
14. #43915C2semidirect
15. #39725C2semidirect
16. #39599C2semidirect
17. #38920C2semidirect
18. #38914C2semidirect
19. #38909C2semidirect
20. #38909C2semidirect
21. #37836C2semidirect
22. #37657C2semidirect
23. #36505C2semidirect
24. #36455C2semidirect
25. #36153C2semidirect
26. #36101C2semidirect
27. #35567C2semidirect
28. #35520C2semidirect
29. #35292C2semidirect
30. #35261C2semidirect
31. #34976C2semidirect
32. #34937C2semidirect
33. #34243C2semidirect
34. #34202C2semidirect
35. C4×#537C2semidirect
37. C2×#557C22semidirect
43. C2×#553C22semidirect
44. C2×#553C22semidirect
53. C2×#550C22semidirect
54. C2×#550C22semidirect
57. C2×#547C22semidirect
61. C2×#540C22semidirect
62. C2×#540C22semidirect
67. C2×#532C22semidirect
72. C2×#529C22semidirect
75. C2×#520C22semidirect
79. C2×C4×#41C22semidirect
83. #2857C22semidirect
85. #2856C22semidirect
86. #2856C22semidirect
87. #2851C22semidirect
90. #2726C22semidirect
91. #2723C22semidirect
92. #2721C22semidirect
93. #2718C22semidirect
94. #2711C22semidirect
95. #2706C22semidirect
98. #2702C22semidirect
100. #2691C22semidirect
101. #2691C22semidirect
102. #2691C22semidirect
103. #2686C22semidirect
104. #2681C22semidirect
106. #2673C22semidirect
109. #2671C22semidirect
110. #2671C22semidirect
111. #2671C22semidirect
115. #2624C22semidirect
116. #2624C22semidirect
117. #2624C22semidirect
120. #2609C22semidirect
121. #2592C22semidirect
122. #2584C22semidirect
123. #2582C22semidirect
124. #2582C22semidirect
125. #2580C22semidirect
126. #2580C22semidirect
127. #2562C22semidirect
128. #2559C22semidirect
129. #2558C22semidirect
130. #2555C22semidirect
131. #2554C22semidirect
132. #2553C22semidirect
133. #2548C22semidirect
134. #2548C22semidirect
136. #2546C22semidirect
137. #2546C22semidirect
138. #2545C22semidirect
141. #2544C22semidirect
142. #2543C22semidirect
143. #2543C22semidirect
144. #2542C22semidirect
146. #2541C22semidirect
150. #2538C22semidirect
152. #2537C22semidirect
153. #2536C22semidirect
155. #2491C22semidirect
156. #2489C22semidirect
157. #2487C22semidirect
159. #2485C22semidirect
160. #2485C22semidirect
161. #2479C22semidirect
162. #2477C22semidirect
163. #2476C22semidirect
164. #2476C22semidirect
165. #2475C22semidirect
166. #2473C22semidirect
169. #2468C22semidirect
170. #2466C22semidirect
174. #2463C22semidirect
175. #2461C22semidirect
176. #2460C22semidirect
177. #2459C22semidirect
182. #2454C22semidirect
183. #2454C22semidirect
184. #2451C22semidirect
185. #2450C22semidirect
186. #2446C22semidirect
188. #2445C22semidirect
189. #2443C22semidirect
190. #2443C22semidirect
191. #2443C22semidirect
195. #2432C22semidirect
202. #2428C22semidirect
203. #2428C22semidirect
205. #2427C22semidirect
206. #2427C22semidirect
213. #2422C22semidirect
216. #2416C22semidirect
217. #2416C22semidirect
218. #2416C22semidirect
221. #2414C22semidirect
222. #2414C22semidirect
223. #2414C22semidirect
224. #2414C22semidirect
231. #2407C22semidirect
232. #2407C22semidirect
233. #2407C22semidirect
234. #2392C22semidirect
235. #2392C22semidirect
236. #2370C22semidirect
240. #2362C22semidirect
242. #2359C22semidirect
243. #2359C22semidirect
244. #2359C22semidirect
247. #2355C22semidirect
251. #2352C22semidirect
252. #2352C22semidirect
253. Q8×C4⋊C4C22semidirect
255. D4×C4⋊C4C22semidirect
256. D4×C4⋊C4C22semidirect
257. #2341C22semidirect
259. #2334C22semidirect
261. #2325C22semidirect
266. #2324C22semidirect
267. #2324C22semidirect
270. #2323C22semidirect
271. #2323C22semidirect
272. #2317C22semidirect
273. #2316C22semidirect
274. #2314C22semidirect
276. #2311C22semidirect
277. #2311C22semidirect
279. C4×C22⋊Q8C22semidirect
280. C4×C22⋊Q8C22semidirect
281. C4×C22⋊Q8C22semidirect
282. C4×C22⋊Q8C22semidirect
283. C4×C22⋊Q8C22semidirect
284. C4×C22⋊Q8C22semidirect
290. C4×#121C22semidirect
291. C4×#121C22semidirect
292. C4×#121C22semidirect
293. C4×#121C22semidirect
294. C4×#121C22semidirect
295. C4×#121C22semidirect
296. #2297C22semidirect
297. #2285C22semidirect
299. #2274C22semidirect
300. C2×C4×C4⋊C4C22semidirect
356. #529D4semidirect
1012. C22⋊Q8#41semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#35172
C2×#34752
#598102
#595502
#591462
#591292
#590862
#590662
#590592
#443332
#442092
#439212
#439152
#397252
#395992
#389202
#389142
#389092
#378362
#376572
#365052
#364552
#361532
#361012
#355672
#355202
#352922
#352612
#349762
#349372
#342432
#342022
C4×#5372