Finite Group Databasebeta

← #7679882

Subgroups — #7679882

Order 512.

7447 conjugacy classes of subgroups.

The subgroup lattice has 2030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#59824C212yesmaximal, complemented
4#59656C212yesmaximal, complemented
5#59654C212yesmaximal, complemented
6#59417C212yesmaximal, complemented
7#59025C212yesmaximal, complemented
8#59020C212yesmaximal, complemented
9#59005C212yesmaximal, complemented
10#58999C212yesmaximal, complemented
11#44364C214yesmaximal, complemented
12#44160C214yesmaximal, complemented
13#43539C214yesmaximal, complemented
14#43537C214yesmaximal, complemented
15#39471C211yesmaximal, characteristic, complemented
16#39470C212yesmaximal, complemented
17#39340C211yesmaximal, characteristic, complemented
18#39334C212yesmaximal, complemented
19#39136C211yesmaximal, characteristic, complemented
20#39124C211yesmaximal, characteristic, complemented
21#38040C212yesmaximal, complemented
22#38034C212yesmaximal, complemented
23#36579C211yesmaximal, characteristic, complemented
24Q8×#121C211yesmaximal, characteristic, complemented
25#36404C211yesmaximal, characteristic, complemented
26#36259C211yesmaximal, characteristic, complemented
27#35568C212yesmaximal, complemented
28#35521C212yesmaximal, complemented
29#35297C211yesmaximal, characteristic, complemented
30#35258C212yesmaximal, complemented
31#34979C211yesmaximal, characteristic, complemented
32#34935C211yesmaximal, characteristic, complemented
33#34267C212yesmaximal, complemented
34#34242C211yesmaximal, characteristic, complemented
35C4×#535C211yesmaximal, characteristic, complemented
36#3520—216no—
37#3480—216no—
38C2×#559C2212yes—
39C2×#559C2211yescharacteristic, complemented
40C2×#557C2211yescharacteristic, complemented
41C2×#556C2211yescharacteristic
42C2×#556C2211yescharacteristic
43C2×#556C2212yescomplemented
44C2×#554C2212yes—
45C2×#553C2212yes—
46C2×#553C2211yescharacteristic
47C2×#553C2212yescomplemented
48C2×#553C2211yescharacteristic, complemented
49C2×#552C2212yes—
50C2×#551C2214yes—
51C2×#550C2211yescharacteristic
52C2×D4×Q8C2211yescharacteristic
53C2×D4×Q8C2212yescomplemented
54C2×#548C2212yes—
55C2×#548C2211yescharacteristic
56C2×#548C2211yescharacteristic, complemented
57C2×#547C2211yescharacteristic
58C2×#547C2211yescharacteristic
59C2×#547C2212yescomplemented
60C2×#546C2212yes—
61C2×#542C2212yes—
62C2×#539C2214yes—
63C2×#537C2212yes—
64C2×#535C2211yescharacteristic
65C2×#533C2211yescharacteristic
66C2×#532C2212yes—
67C2×#532C2211yescharacteristic, complemented
68C2×#529C2212yes—
69C2×#529C2211yescharacteristic
70C2×#529C2212yescomplemented
71C2×#529C2211yescharacteristic, complemented
72C2×#525C2212yes—
73C2×#525C2212yes—
74C22×C22⋊Q8C2212yes—
75C2×#520C2212yes—
76C2×C4×#41C2211yescharacteristic
77C2×C4×#41C2211yescharacteristic
78C2×C4×#41C2211yescharacteristic, complemented
79C2×C4×#41C2212yescomplemented
80C22×C4×Q8C2211yescharacteristic, complemented
81C22×C4×D4C2211yescharacteristic
82#2857C2212yescomplemented
83#2857C2211yescharacteristic, complemented
84#2857C2211yescharacteristic, complemented
85#2857C2211yescharacteristic, complemented
86#2857C2211yescharacteristic, complemented
87#2855C2212yescomplemented
88#2854C2212yes—
89#2850C2212yes—
90#2727C2214yescomplemented
91#2723C2214yescomplemented
92#2721C2214yescomplemented
93#2719C2214yescomplemented
94#2710C2214yescomplemented
95#2705C2214yescomplemented
96#2703C2214yes—
97#2703C2214yescomplemented
98#2700C2214yes—
99#2700C2214yescomplemented
100#2697C2214yes—
101#2696C2214yescomplemented
102#2689C2214yes—
103#2681C2214yes—
104#2681C2214yes—
105#2681C2214yescomplemented
106#2678C2214yes—
107#2674C2214yes—
108#2674C2214yes—
109#2673C2214yes—
110#2672C2214yescomplemented
111#2671C2214yescomplemented
112#2669C2214yes—
113#2668C2214yes—
114#2628C2212yescomplemented
115#2625C2212yes—
116#2620C2212yes—
117#2616C2212yes—
118#2616C2212yescomplemented
119#2615C2212yes—
120#2611C2214yescomplemented
121#2592C2212yes—
122#2584C2212yescomplemented
123#2581C2212yescomplemented
124#2581C2212yescomplemented
125#2568C2211yescharacteristic, complemented
126#2563C2212yescomplemented
127#2562C2212yescomplemented
128#2560C2214yescomplemented
129#2558C2214yes—
130#2557C2214yescomplemented
131#2555C2214yes—
132#2554C2214yes—
133#2554C2214yescomplemented
134#2553C2214yescomplemented
135#2550C2214yescomplemented
136#2547C2211yescharacteristic, complemented
137#2546C2212yescomplemented
138#2546C2211yescharacteristic, complemented
139#2542C2211yescharacteristic, complemented
140#2540C2212yes—
141#2540C2212yescomplemented
142#2540C2212yescomplemented
143#2538C2211yescharacteristic
144#2538C2211yescharacteristic
145#2538C2212yes—
146#2538C2212yescomplemented
147#2538C2212yescomplemented
148#2537C2211yescharacteristic
149#2537C2211yescharacteristic
150#2537C2212yescomplemented
151#2536C2212yes—
152#2536C2212yescomplemented
153#2535C2212yes—
154#2535C2212yes—
155#2534C2214yes—
156#2519C2214yescomplemented
157#2499C2212yes—
158#2492C2212yescomplemented
159#2491C2214yescomplemented
160#2490C2214yescomplemented
161#2489C2212yescomplemented
162#2488C2214yescomplemented
163#2487C2212yescomplemented
164#2486C2212yes—
165#2486C2212yescomplemented
166#2485C2212yes—
167#2485C2212yes—
168#2481C2214yescomplemented
169#2481C2214yescomplemented
170#2480C2214yes—
171#2475C2214yescomplemented
172#2472C2214yes—
173#2472C2214yes—
174#2471C2214yescomplemented
175#2470C2214yescomplemented
176#2469C2214yescomplemented
177#2469C2214yescomplemented
178#2467C2214yescomplemented
179#2466C2214yescomplemented
180#2465C2214yescomplemented
181#2464C2214yescomplemented
182#2463C2214yescomplemented
183#2461C2214yescomplemented
184#2461C2214yescomplemented
185#2459C2214yescomplemented
186#2457C2214yescomplemented
187#2457C2214yescomplemented
188#2457C2214yescomplemented
189#2456C2214yescomplemented
190#2455C2214yescomplemented
191#2452C2214yescomplemented
192#2449C2214yescomplemented
193#2445C2214yes—
194#2443C2214yes—
195#2441C2212yescomplemented
196#2440C2214yescomplemented
197#2440C2212yescomplemented
198#2436C2212yescomplemented
199#2432C2212yes—
200#2431C2212yescomplemented
201#2429C2212yescomplemented
202#2429C2212yescomplemented
203#2429C2214yescomplemented
204#2428C2214yes—
205#2428C2212yescomplemented
206#2426C2212yescomplemented
207#2425C2214yescomplemented
208#2424C2214yes—
209#2421C2212yescomplemented
210#2420C2214yes—
211#2420C2212yescomplemented
212#2419C2214yes—
213#2417C2214yescomplemented
214#2417C2212yescomplemented
215#2417C2212yescomplemented
216#2416C2212yes—
217#2416C2212yescomplemented
218#2415C2212yes—
219#2415C2212yes—
220#2415C2212yes—
221#2415C2212yes—
222#2415C2212yescomplemented
223#2415C2212yescomplemented
224#2414C2212yes—
225#2414C2212yescomplemented
226#2413C2214yescomplemented
227#2409C2212yescomplemented
228#2409C2212yescomplemented
229#2408C2212yes—
230#2407C2212yes—
231#2407C2212yes—
232#2407C2212yescomplemented
233#2407C2212yescomplemented
234#2395C2214yes—
235#2392C2214yes—
236#2373C2214yescomplemented
237#2364C2214yescomplemented
238#2364C2214yescomplemented
239#2363C2212yes—
240#2363C2214yescomplemented
241#2362C2212yes—
242#2362C2214yescomplemented
243#2362C2212yescomplemented
244#2361C2214yescomplemented
245#2361C2214yescomplemented
246#2361C2214yescomplemented
247#2360C2212yescomplemented
248#2360C2214yescomplemented
249#2355C2211yescharacteristic, complemented
250#2354C2212yes—
251#2354C2211yescharacteristic, complemented
252#2352C2212yes—
253#2352C2212yescomplemented
254#2352C2212yescomplemented
255Q8×C4⋊C4C2211yescharacteristic, complemented
256D4×C4⋊C4C2211yescharacteristic, complemented
257Q8×C22⋊C4C2212yescomplemented
258#2339C2212yescomplemented
259#2335C2214yes—
260#2328C2212yes—
261#2326C2212yes—
262#2324C2211yescharacteristic
263#2324C2211yescharacteristic
264#2324C2211yescharacteristic
265#2324C2211yescharacteristic
266#2324C2212yes—
267#2323C2212yescomplemented
268#2323C2212yescomplemented
269#2323C2212yescomplemented
270#2321C2212yes—
271#2321C2212yes—
272#2317C2211yescharacteristic
273#2314C2212yescomplemented
274#2311C2211yescharacteristic
275#2311C2212yescomplemented
276#2309C2211yescharacteristic
277C4×C4⋊Q8C2212yescomplemented
278C4×#127C2212yes—
279C4×#125C2212yescomplemented
280C4×#124C2212yes—
281C4×#124C2212yescomplemented
282C4×#124C2212yescomplemented
283C4×C22⋊Q8C2212yescomplemented
284C4×C22⋊Q8C2212yescomplemented
285C4×C22⋊Q8C2212yescomplemented
286C4×#121C2211yescharacteristic
287C4×#121C2211yescharacteristic
288C4×#121C2211yescharacteristic
289C4×#121C2211yescharacteristic
290C4×#121C2212yes—
291C4×#121C2212yes—
292C4×#121C2212yes—
293C4×#120C2212yes—
294C4×#120C2212yes—
295#2297C2212yes—
296C2×#389C2212yescomplemented
297#2285C2211yescharacteristic
298#2280C2212yes—
299#2274C2212yescomplemented
300C4×#117C2211yescharacteristic
301C22×#41C2311yescharacteristic
302C22×#41C2312yes—
303C22×#41C2311yescharacteristic
304C22×#41C2311yescharacteristic
305C22×#41C2312yes—
306C22×#41C2312yes—
307C23×Q8C2311yescharacteristic
308C23×Q8C2312yes—
309C23×D4C2311yescharacteristic
310C24×C4C2312yes—
311#559—28no—
312#559—216no—
313#557—28no—
314#556—216no—
315#556—28no—
316#556—28no—
317#554—216no—
318#553—216no—
319#553—28no—
320#553—216no—
321#553—28no—
322#552—216no—
323#551—232no—
324#550—28no—
325D4×Q8—28no—
326D4×Q8—48no—
327#548—216no—
328#548—28no—
329#548—28no—
330#547—28no—
331#547—28no—
332#547—48no—
333#546—216no—
334#542—216no—
335#539—232no—
336#537—216no—
337#535—28no—
338#533—28no—
339#532—216no—
340#532—28no—
341C2×C4⋊Q8C2312yes—
342C2×C4⋊Q8C2312yes—
343C2×C4⋊Q8C2311yescharacteristic
344C2×C4⋊Q8C2311yescharacteristic
345C2×C4⋊Q8C2312yes—
346C2×C4⋊Q8C2311yescharacteristic
347C2×C4⋊Q8C2314yes—
348C2×#127C2312yes—
349C2×#127C2312yes—
350C2×#127C2311yescharacteristic
351#529—28no—
352#529—216no—
353#529—216no—
354#529D4116yescomplemented
355C2×#126C2312yes—
356C2×#126C2312yes—
357C2×#126C2312yes—
358C2×#126C2312yes—
359C2×#126C2312yes—
360C2×#126C2314yes—
361C2×#126C2314yes—
362C2×#126C2312yes—
363C2×#125C2312yes—
364C2×#125C2312yes—
365C2×#125C2311yescharacteristic
366C2×#125C2312yes—
367C2×#125C2314yes—
368C2×#125C2311yescharacteristic
369C2×#124C2312yes—
370C2×#124C2312yes—
371C2×#124C2312yes—
372C2×#124C2311yescharacteristic
373C2×#124C2312yes—
374C2×#124C2312yes—
375C2×#124C2312yes—
376C2×#124C2312yes—
377C2×#124C2314yes—
378C2×#124C2312yes—
379C2×#124C2311yescharacteristic
380#525—216no—
381#525—48no—
382C2×#123C2314yes—
383C2×#123C2314yes—
384C2×#123C2314yes—
385C2×#123C2312yes—
386C2×#123C2312yes—
387C2×#123C2312yes—
388C2×#123C2312yes—
389C2×#123C2312yes—
390C2×#123C2314yes—
391C2×#123C2314yes—
392C2×#123C2314yes—
393C2×#123C2314yes—
394C2×#123C2312yes—
395C2×C22⋊Q8—216no—
396C2×C22⋊Q8C2314yes—
397C2×C22⋊Q8C2312yes—
398C2×C22⋊Q8C2312yes—
399C2×C22⋊Q8C2312yes—
400C2×C22⋊Q8C2314yes—
401C2×C22⋊Q8C2312yes—
402C2×C22⋊Q8C2312yes—
403C2×C22⋊Q8C2312yes—
404C2×C22⋊Q8C2311yescharacteristic
405C2×C22⋊Q8C2312yes—
406C2×C22⋊Q8C2312yes—
407C2×C22⋊Q8C2312yes—
408C2×C22⋊Q8C2314yes—
409C2×C22⋊Q8C2312yes—
410C2×C22⋊Q8C2312yes—
411C2×C22⋊Q8C2312yes—
412C2×C22⋊Q8C2314yes—
413C2×C22⋊Q8C2314yes—
414C2×C22⋊Q8C2312yes—
415C2×C22⋊Q8C2312yes—
416C2×C22⋊Q8C2312yes—
417C2×C22⋊Q8C2314yes—
418C2×C22⋊Q8C2312yes—
419C2×C22⋊Q8C2314yes—
420C2×C22⋊Q8C2311yescharacteristic
421C2×#121C2311yescharacteristic
422C2×#121C2311yescharacteristic
423C2×#121C2312yes—
424C2×#121C2311yescharacteristic
425C2×#121C2312yes—
426C2×#121C2314yes—
427C2×#121C2314yes—
428C2×#121C2314yes—
429C2×#121C2311yescharacteristic
430C2×#121C2312yes—
431C2×#121C2312yes—
432C2×#121C2311yescharacteristic
433C2×#121C2312yes—
434C2×#121C2312yes—
435C2×#121C2312yes—
436C2×#121C2311yescharacteristic
437C2×#121C2312yes—
438C2×#121C2312yes—
439C2×#121C2312yes—
440C2×#121C2314yes—
441C2×#121C2312yes—
442C2×#121C2312yes—
443C2×#121C2312yes—
444C2×#121C2314yes—
445C2×#121C2311yescharacteristic
446C2×#121C2311yescharacteristic
447C2×#120C2312yes—
448C2×#120C2312yes—
449C2×#120C2314yes—
450C2×#120C2314yes—
451#520—216no—
452C4×#41—28no—
453C4×#41—216no—
454C4×#41—28no—
455C4×#41—28no—
456C2×C4×Q8—28no—
457C2×C4×Q8C2311yescharacteristic
458C2×C4×Q8C2312yes—
459C2×C4×Q8C2311yescharacteristic
460C2×C4×Q8C2312yes—
461C2×C4×Q8C2312yes—
462C2×C4×Q8C2311yescharacteristic
463C2×C4×Q8C2312yes—
464C2×C4×Q8C2311yescharacteristic
465C2×C4×Q8C2311yescharacteristic
466C2×C4×Q8C2311yescharacteristic
467C2×C4×Q8C2312yes—
468C2×C4×Q8C2311yescharacteristic
469C2×C4×Q8C2312yes—
470C2×C4×Q8C2312yes—
471C2×C4×Q8C2312yes—
472C2×C4×Q8C2311yescharacteristic
473C2×C4×D4—28no—
474C2×C4×D4C2311yescharacteristic
475C2×C4×D4C2312yes—
476C2×C4×D4C2311yescharacteristic
477C2×C4×D4C2312yes—
478C2×C4×D4C2311yescharacteristic
479C2×C4×D4C2311yescharacteristic
480C2×C4×D4C2311yescharacteristic
481C2×C4×D4C2311yescharacteristic
482C2×C4×D4C2312yes—
483C2×C4×D4C2312yes—
484C2×C4×D4C2311yescharacteristic
485C2×C4×D4C2312yes—
486C2×C4×D4C2312yes—
487C2×C4×D4C2312yes—
488C2×C4×D4C2314yes—
489C2×C4×D4C2314yes—
490C2×C4×D4C2312yes—
491C2×C4×D4C2312yes—
492C2×C4×D4C2312yes—
493C2×C4×D4C2312yes—
494C2×C4×D4C2311yescharacteristic
495C2×C4×D4C2311yescharacteristic
496C2×C4×D4C2312yes—
497C2×C4×D4C2311yescharacteristic
498C2×C4×D4C2311yescharacteristic
499C2×C4×D4C2311yescharacteristic
500C2×C4×D4C2311yescharacteristic
501C2×C4×D4C2312yes—
502C2×C4×D4C2312yes—
503C2×C4×D4C2312yes—
504C2×C4×D4C2314yes—
505C2×C4×D4C2312yes—
506C2×C4×D4C2312yes—
507C2×C4×D4C2312yes—
508C2×C4×D4C2312yes—
509C2×C4×D4C2312yes—
510C2×C4×D4C2314yes—
511C2×C4×D4C2314yes—
512C2×C4×D4C2314yes—
513C2×C4×D4C2311yescharacteristic
514C2×C4×D4C2312yes—
515C2×#117C2311yescharacteristic
516C2×#117C2311yescharacteristic
517C2×#117C2311yescharacteristic
518C2×#117C2311yescharacteristic
519C2×#117C2312yes—
520C2×#117C2311yescharacteristic
521C2×#117C2312yes—
522C2×#117C2312yes—
523C2×#117C2314yes—
524C2×#117C2312yes—
525C2×#117C2311yescharacteristic
526C2×#117C2312yes—
527C2×#117C2311yescharacteristic
528C2×#117C2312yes—
529C2×#117C2312yes—
530C2×#117C2312yes—
531C22×C4⋊C4C2311yescharacteristic
532C22×C4⋊C4C2312yes—
533C22×C4⋊C4C2312yes—
534C22×C4⋊C4C2311yescharacteristic
535C22×C4⋊C4C2312yes—
536C22×C4⋊C4C2314yes—
537C22×C4⋊C4C2312yes—
538C22×C4⋊C4C2314yes—
539C22×C22⋊C4C2312yes—
540C22×C22⋊C4C2314yes—
541C22×C42C2312yes—
542C22×C42C2312yes—
543C22×C42C2311yescharacteristic
544C22×C42C2311yescharacteristic
545C22×C42C2312yes—
546C22×C42C2311yescharacteristic
547#400C2314yes—
548#400C2314yes—
549#400C2314yes—
550#400C2314yes—
551#400C2314yes—
552#399C2314yes—
553#399C2314yes—
554#399C2314yes—
555#399C2314yes—
556#398C2314yes—
557#398C2314yes—
558#398C2314yes—
559#398C2314yes—
560#398C2314yes—
561#398C2314yes—
562#398C2314yes—
563#397C2314yes—
564#397C2314yes—
565#397C2314yes—
566#397C2314yes—
567#397C2314yes—
568#397C2314yes—
569#397C2314yes—
570#397C2314yes—
571#397C2314yes—
572#397C2314yes—
573#396C2314yes—
574#396C2314yes—
575#396C2314yes—
576#396C2314yes—
577#396C2314yes—
578#396C2314yes—
579#396C2314yes—
580#396C2314yes—
581#396C2314yes—
582#396C2314yes—
583#395C2314yes—
584#395C2314yes—
585#395C2314yes—
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#393C2314yes—
606#393C2314yes—
607#393C2314yes—
608#393C2314yes—
609#393C2314yes—
610#392C2314yes—
611#392C2314yes—
612#392C2314yes—
613#392C2314yes—
614#392C2314yes—
615#392C2314yes—
616#392C2314yes—
617#392C2314yes—
618#392C2314yes—
619#391C2314yes—
620#391C2312yes—
621#391C2312yes—
622#391C2312yes—
623#391C2314yes—
624#391C2312yes—
625#391C2312yes—
626#391C2312yes—
627#391C2312yes—
628#391C2312yes—
629#391C2312yes—
630#391C2312yes—
631#391C2314yes—
632#391C2312yes—
633#390C2314yes—
634#390C2312yes—
635#390C2312yes—
636#390C2312yes—
637#390C2312yes—
638#390C2312yes—
639#390C2312yes—
640#390C2314yes—
641#390C2311yescharacteristic
642#390C2311yescharacteristic
643#390C2311yescharacteristic
644#390C2311yescharacteristic
645#390C2312yes—
646#390C2314yes—
647#390C2314yes—
648#390C2314yes—
649#390C2312yes—
650#390C2312yes—
651#390C2312yes—
652#390C2314yes—
653#390C2312yes—
654#390C2314yes—
655#390C2314yes—
656#389C2312yes—
657#389C2312yes—
658#389C2314yes—
659#389C2314yes—
660#389C2311yescharacteristic
661#389C2311yescharacteristic
662#389C2311yescharacteristic
663#389C2311yescharacteristic
664#389C2312yes—
665#389C2314yes—
666#389C2314yes—
667#389C2312yes—
668#389C2314yes—
669#389C2312yes—
670#389C2312yes—
671#389C2312yes—
672#389C2312yes—
673#389C2312yes—
674#389C2312yes—
675#389C2312yes—
676#389C2314yes—
677#389C2312yes—
678#389C2312yes—
679#389C2314yes—
680#389C2314yes—
681#389C2314yes—
682#389C2314yes—
683#389C2312yes—
684#389C2314yes—
685#388C2314yes—
686#388C2314yes—
687#388C2314yes—
688#388C2314yes—
689#388C2314yes—
690#388C2314yes—
691#388C2312yes—
692#388C2312yes—
693#388C2312yes—
694#388C2312yes—
695#388C2312yes—
696#388C2312yes—
697#388C2312yes—
698#388C2312yes—
699#388C2314yes—
700#388C2314yes—
701#388C2314yes—
702#388C2314yes—
703#388C2314yes—
704#388C2314yes—
705#388C2314yes—
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#387C2314yes—
720#387C2314yes—
721#387C2314yes—
722#387C2314yes—
723#387C2314yes—
724#387C2314yes—
725#387C2314yes—
726#387C2314yes—
727#387C2314yes—
728#387C2314yes—
729#387C2314yes—
730#387C2314yes—
731#387C2314yes—
732#387C2314yes—
733#386C2312yes—
734#386C2312yes—
735#386C2312yes—
736#386C2314yes—
737#386C2314yes—
738#386C2312yes—
739#386C2312yes—
740#386C2312yes—
741#386C2312yes—
742#386C2312yes—
743#386C2312yes—
744#386C2312yes—
745#386C2314yes—
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#385C2312yes—
763#385C2312yes—
764#385C2312yes—
765#385C2312yes—
766#385C2312yes—
767#385C2312yes—
768#385C2314yes—
769#385C2314yes—
770#385C2314yes—
771#385C2314yes—
772#385C2314yes—
773#385C2314yes—
774#385C2314yes—
775#385C2314yes—
776#385C2314yes—
777#384C2312yes—
778#384C2312yes—
779#384C2312yes—
780#384C2311yescharacteristic
781#384C2311yescharacteristic
782#382C2312yes—
783#382C2314yes—
784#382C2312yes—
785#382C2312yes—
786#382C2312yes—
787#381C2314yes—
788#381C2314yes—
789#381C2314yes—
790#380C2312yes—
791#380C2312yes—
792#380C2312yes—
793#380C2312yes—
794#380C2311yescharacteristic
795#380C2312yes—
796#380C2312yes—
797#380C2312yes—
798#380C2311yescharacteristic
799#380C2311yescharacteristic
800#380C2311yescharacteristic
801#380C2312yes—
802#380C2312yes—
803#380C2312yes—
804#380C2312yes—
805#380C2312yes—
806#380C2312yes—
807#380C2312yes—
808#380C2314yes—
809#380C2312yes—
810#380C2312yes—
811#380C2314yes—
812#380C2312yes—
813#380C2312yes—
814#380C2312yes—
815#380C2312yes—
816#380C2314yes—
817#379C2312yes—
818#379C2312yes—
819#379C2314yes—
820C4×C4⋊C4C2314yes—
821C4×C4⋊C4C2314yes—
822C4×C4⋊C4C2312yes—
823C4×C4⋊C4C2312yes—
824C4×C4⋊C4C2314yes—
825C4×C4⋊C4C2312yes—
826C4×C4⋊C4C2314yes—
827C4×C4⋊C4C2314yes—
828C4×C4⋊C4C2312yes—
829C4×C4⋊C4C2311yescharacteristic
830C4×C4⋊C4C2311yescharacteristic
831C4×C4⋊C4C2312yes—
832C4×C4⋊C4C2312yes—
833C4×C4⋊C4C2311yescharacteristic
834C4×C4⋊C4C2311yescharacteristic
835C4×C4⋊C4C2314yes—
836C4×C22⋊C4C2314yes—
837C4×C22⋊C4C2312yes—
838C4×C22⋊C4C2314yes—
839C4×C22⋊C4C2312yes—
840C4×C22⋊C4C2314yes—
841C4×C22⋊C4C2312yes—
842C4×C22⋊C4C2314yes—
843C4×C22⋊C4C2314yes—
844C4×C22⋊C4C2314yes—
845C4×C22⋊C4C2314yes—
846C4×C22⋊C4C2314yes—
847C4×C22⋊C4C2312yes—
848C4×C22⋊C4C2314yes—
849C4×C22⋊C4C2312yes—
850C4×C22⋊C4C2312yes—
851C4×C22⋊C4C2314yes—
852C4×C22⋊C4C2314yes—
853#376C2312yes—
854C2×#95C2314yes—
855C43C2312yes—
856C25C2412yes—
857C2×#41—24no—
858C2×#41—24no—
859C2×#41—24no—
860C2×#41—28no—
861C2×#41—28no—
862C2×#41—28no—
863C2×#41—24no—
864C2×#41—24no—
865C2×#41—28no—
866C2×#41—24no—
867C2×#41—28no—
868C2×#41—42no—
869C2×#41—44no—
870C2×#41—44no—
871C2×#41—42no—
872C2×#41—42no—
873C2×#41—44no—
874C2×#41—44no—
875C22×Q8—24no—
876C22×Q8—24no—
877C22×Q8—28no—
878C22×Q8—42no—
879C22×Q8—44no—
880C22×Q8—44no—
881C22×Q8C2412yes—
882C22×Q8C2412yes—
883C22×Q8C2412yes—
884C22×Q8C2412yes—
885C22×Q8C2411yescharacteristic
886C22×Q8C2411yescharacteristic
887C22×Q8C2411yescharacteristic
888C22×Q8C2414yes—
889C22×D4—24no—
890C22×D4—24no—
891C22×D4—42no—
892C22×D4C2411yescharacteristic
893C22×D4C2411yescharacteristic
894C22×D4C2411yescharacteristic
895C22×D4C2412yes—
896C22×D4C2411yescharacteristic
897C22×D4C2414yes—
898C22×D4C2412yes—
899C22×D4C2412yes—
900C22×D4C2412yes—
901C22×D4C2411yescharacteristic
902C22×D4C2412yes—
903C22×D4C2412yes—
904C22×D4C2411yescharacteristic
905C22×D4C2411yescharacteristic
906C22×D4C2414yes—
907C22×D4C2412yes—
908C22×D4C2412yes—
909C22×D4C2412yes—
910C22×D4C2412yes—
911C22×D4C2412yes—
912C22×D4C2414yes—
913C22×D4C2414yes—
914C22×D4C2412yes—
915C22×D4C2412yes—
916C23×C4—28no—
917C23×C4—44no—
918C23×C4—44no—
919C23×C4C2411yescharacteristic
920C23×C4C2412yes—
921C23×C4C2411yescharacteristic
922C23×C4C2411yescharacteristic
923C23×C4C2412yes—
924C23×C4C2412yes—
925C23×C4C2414yes—
926C23×C4C2412yes—
927C23×C4C2412yes—
928C23×C4C2412yes—
929C23×C4C2412yes—
930C23×C4C2411yescharacteristic
931C23×C4C2411yescharacteristic
932C23×C4C2411yescharacteristic
933C23×C4C2414yes—
934C23×C4C2412yes—
935C23×C4C2412yes—
936C23×C4C2414yes—
937C23×C4C2412yes—
938C23×C4C2411yescharacteristic
939C23×C4C2414yes—
940C23×C4C2412yes—
941C23×C4C2412yes—
942C23×C4C2412yes—
943C23×C4C2411yescharacteristic
944C23×C4C2411yescharacteristic
945C4⋊Q8—28no—
946C4⋊Q8—28no—
947C4⋊Q8—24no—
948C4⋊Q8—24no—
949C4⋊Q8—24no—
950C4⋊Q8—28no—
951C4⋊Q8—48no—
952#127—28no—
953#127—24no—
954#127—28no—
955#126—28no—
956#126—28no—
957#126—28no—
958#126—216no—
959#126—216no—
960#126—28no—
961#126—28no—
962#126C2×D4116yes—
963#125—28no—
964#125—28no—
965#125—24no—
966#125—216no—
967#125—28no—
968#125C2×D418yes—
969#124—24no—
970#124—28no—
971#124—28no—
972#124—28no—
973#124—28no—
974#124—28no—
975#124—216no—
976#124—28no—
977#124—28no—
978#124—44no—
979#124C2×D418yes—
980#123—28no—
981#123—28no—
982#123—28no—
983#123—216no—
984#123—216no—
985#123—28no—
986#123—28no—
987#123—216no—
988#123—216no—
989#123—48no—
990#123—48no—
991#123—48no—
992#123C2×D4116yes—
993C22⋊Q8—28no—
994C22⋊Q8—24no—
995C22⋊Q8—28no—
996C22⋊Q8—28no—
997C22⋊Q8—28no—
998C22⋊Q8—28no—
999C22⋊Q8—28no—
1000C22⋊Q8—28no—
1001C22⋊Q8—216no—
1002C22⋊Q8—28no—
1003C22⋊Q8—28no—
1004C22⋊Q8—28no—
1005C22⋊Q8—216no—
1006C22⋊Q8—28no—
1007C22⋊Q8—216no—
1008C22⋊Q8—28no—
1009C22⋊Q8—216no—
1010C22⋊Q8—216no—
1011C22⋊Q8—48no—
1012C22⋊Q8—48no—
1013C22⋊Q8—44no—
1014C22⋊Q8—44no—
1015C22⋊Q8—44no—
1016C22⋊Q8—44no—
1017C22⋊Q8C2×D418yes—
1018#121—28no—
1019#121—28no—
1020#121—24no—
1021#121—28no—
1022#121—24no—
1023#121—28no—
1024#121—216no—
1025#121—216no—
1026#121—28no—
1027#121—24no—
1028#121—24no—
1029#121—24no—
1030#121—28no—
1031#121—24no—
1032#121—28no—
1033#121—28no—
1034#121—28no—
1035#121—28no—
1036#121—216no—
1037#121—216no—
1038#121—48no—
1039#121—44no—
1040#121—44no—
1041#121—44no—
1042#121C2×D418yes—
1043#121#4118yescomplemented
1044#120—216no—
1045#120—28no—
1046#120—28no—
1047#120—48no—
1048C4×Q8—24no—
1049C4×Q8—24no—
1050C4×Q8—28no—
1051C4×Q8—24no—
1052C4×Q8—28no—
1053C4×Q8—28no—
1054C4×Q8—24no—
1055C4×Q8—28no—
1056C4×Q8—24no—
1057C4×Q8—24no—
1058C4×Q8—24no—
1059C4×Q8—28no—
1060C4×Q8—28no—
1061C4×Q8—28no—
1062C4×Q8—44no—
1063C4×Q8C2×D418yes—
1064C4×D4—24no—
1065C4×D4—216no—
1066C4×D4—28no—
1067C4×D4—28no—
1068C4×D4—24no—
1069C4×D4—24no—
1070C4×D4—24no—
1071C4×D4—28no—
1072C4×D4—24no—
1073C4×D4—28no—
1074C4×D4—28no—
1075C4×D4—28no—
1076C4×D4—28no—
1077C4×D4—28no—
1078C4×D4—28no—
1079C4×D4—28no—
1080C4×D4—28no—
1081C4×D4—216no—
1082C4×D4—216no—
1083C4×D4—24no—
1084C4×D4—28no—
1085C4×D4—24no—
1086C4×D4—24no—
1087C4×D4—24no—
1088C4×D4—28no—
1089C4×D4—24no—
1090C4×D4—24no—
1091C4×D4—24no—
1092C4×D4—24no—
1093C4×D4—28no—
1094C4×D4—28no—
1095C4×D4—44no—
1096C4×D4—44no—
1097C4×D4—44no—
1098C4×D4—44no—
1099C4×D4—44no—
1100C4×D4—48no—
1101C4×D4—48no—
1102C4×D4—48no—
1103C4×D4C2×D418yes—
1104C4×D4C2×D4116yes—
1105#117—24no—
1106#117—24no—
1107#117—28no—
1108#117—24no—
1109#117—216no—
1110#117—28no—
1111#117—24no—
1112#117—28no—
1113#117—24no—
1114#117—28no—
1115#117—24no—
1116#117—28no—
1117#117—44no—
1118#117—42no—
1119#117—44no—
1120#117C2×D4116yes—
1121C2×C4⋊C4—24no—
1122C2×C4⋊C4—28no—
1123C2×C4⋊C4—28no—
1124C2×C4⋊C4—24no—
1125C2×C4⋊C4—216no—
1126C2×C4⋊C4—28no—
1127C2×C4⋊C4—28no—
1128C2×C4⋊C4—48no—
1129C2×C4⋊C4C2411yescharacteristic
1130C2×C4⋊C4C2414yes—
1131C2×C4⋊C4C2411yescharacteristic
1132C2×C4⋊C4C2412yes—
1133C2×C4⋊C4C2412yes—
1134C2×C4⋊C4C2412yes—
1135C2×C4⋊C4C2411yescharacteristic
1136C2×C4⋊C4C2412yes—
1137C2×C4⋊C4C2414yes—
1138C2×C4⋊C4C2414yes—
1139C2×C4⋊C4C2414yes—
1140C2×C4⋊C4C2414yes—
1141C2×C4⋊C4C2412yes—
1142C2×C4⋊C4C2412yes—
1143C2×C4⋊C4C2412yes—
1144C2×C4⋊C4C2412yes—
1145C2×C4⋊C4C2414yes—
1146C2×C4⋊C4C2414yes—
1147C2×C4⋊C4C2411yescharacteristic
1148C2×C4⋊C4C2411yescharacteristic
1149C2×C4⋊C4C2411yescharacteristic
1150C2×C4⋊C4C2411yescharacteristic
1151C2×C4⋊C4C2412yes—
1152C2×C4⋊C4C2412yes—
1153C2×C4⋊C4C2411yescharacteristic
1154C2×C4⋊C4C2411yescharacteristic
1155C2×C4⋊C4C2412yes—
1156C2×C4⋊C4C2411yescharacteristic
1157C2×C4⋊C4C2411yescharacteristic
1158C2×C4⋊C4C2412yes—
1159C2×C4⋊C4C2412yes—
1160C2×C4⋊C4C2412yes—
1161C2×C4⋊C4C2411yescharacteristic
1162C2×C4⋊C4C2412yes—
1163C2×C4⋊C4C2412yes—
1164C2×C4⋊C4C2411yescharacteristic
1165C2×C4⋊C4C2412yes—
1166C2×C4⋊C4C2412yes—
1167C2×C4⋊C4C2412yes—
1168C2×C4⋊C4C2414yes—
1169C2×C4⋊C4C2414yes—
1170C2×C4⋊C4C2414yes—
1171C2×C4⋊C4C2414yes—
1172C2×C4⋊C4C2414yes—
1173C2×C4⋊C4C2414yes—
1174C2×C4⋊C4C2412yes—
1175C2×C4⋊C4C2414yes—
1176C2×C4⋊C4C2412yes—
1177C2×C4⋊C4C2412yes—
1178C2×C4⋊C4C2412yes—
1179C2×C4⋊C4C2414yes—
1180C2×C4⋊C4C2414yes—
1181C2×C4⋊C4C2414yes—
1182C2×C4⋊C4C2414yes—
1183C2×C4⋊C4C2412yes—
1184C2×C4⋊C4C2412yes—
1185C2×C4⋊C4C2414yes—
1186C2×C4⋊C4C2411yescharacteristic
1187C2×C4⋊C4C2412yes—
1188C2×C4⋊C4C2411yescharacteristic
1189C2×C4⋊C4C2412yes—
1190C2×C4⋊C4C2412yes—
1191C2×C4⋊C4C2412yes—
1192C2×C4⋊C4C2411yescharacteristic
1193C2×C22⋊C4—28no—
1194C2×C22⋊C4—216no—
1195C2×C22⋊C4C2412yes—
1196C2×C22⋊C4C2414yes—
1197C2×C22⋊C4C2412yes—
1198C2×C22⋊C4C2412yes—
1199C2×C22⋊C4C2412yes—
1200C2×C22⋊C4C2414yes—
1201C2×C22⋊C4C2414yes—
1202C2×C22⋊C4C2411yescharacteristic
1203C2×C22⋊C4C2411yescharacteristic
1204C2×C22⋊C4C2414yes—
1205C2×C22⋊C4C2411yescharacteristic
1206C2×C22⋊C4C2411yescharacteristic
1207C2×C22⋊C4C2412yes—
1208C2×C22⋊C4C2412yes—
1209C2×C22⋊C4C2412yes—
1210C2×C22⋊C4C2412yes—
1211C2×C22⋊C4C2412yes—
1212C2×C22⋊C4C2412yes—
1213C2×C22⋊C4C2411yescharacteristic
1214C2×C22⋊C4C2412yes—
1215C2×C22⋊C4C2411yescharacteristic
1216C2×C22⋊C4C2412yes—
1217C2×C22⋊C4C2414yes—
1218C2×C22⋊C4C2414yes—
1219C2×C22⋊C4C2414yes—
1220C2×C22⋊C4C2414yes—
1221C2×C22⋊C4C2412yes—
1222C2×C22⋊C4C2412yes—
1223C2×C22⋊C4C2412yes—
1224C2×C22⋊C4C2412yes—
1225C2×C22⋊C4C2412yes—
1226C2×C22⋊C4C2412yes—
1227C2×C22⋊C4C2412yes—
1228C2×C22⋊C4C2414yes—
1229C2×C22⋊C4C2414yes—
1230C2×C22⋊C4C2414yes—
1231C2×C22⋊C4C2414yes—
1232C2×C22⋊C4C2412yes—
1233C2×C22⋊C4C2414yes—
1234C2×C22⋊C4C2414yes—
1235C2×C22⋊C4C2414yes—
1236C2×C22⋊C4C2412yes—
1237C2×C22⋊C4C2412yes—
1238C2×C22⋊C4C2414yes—
1239C2×C22⋊C4C2412yes—
1240C2×C22⋊C4C2414yes—
1241C2×C22⋊C4C2412yes—
1242C2×C22⋊C4C2412yes—
1243C2×C22⋊C4C2412yes—
1244C2×C22⋊C4C2412yes—
1245C2×C22⋊C4C2412yes—
1246C2×C22⋊C4C2414yes—
1247C2×C22⋊C4C2414yes—
1248C2×C22⋊C4C2414yes—
1249C2×C22⋊C4C2414yes—
1250C2×C22⋊C4C2414yes—
1251C2×C22⋊C4C2414yes—
1252C2×C22⋊C4C2414yes—
1253C2×C22⋊C4C2412yes—
1254C2×C22⋊C4C2412yes—
1255C2×C22⋊C4C2414yes—
1256C2×C22⋊C4C2412yes—
1257C2×C22⋊C4C2412yes—
1258C2×C22⋊C4C2414yes—
1259C2×C22⋊C4C2412yes—
1260C2×C22⋊C4C2412yes—
1261C2×C22⋊C4C2412yes—
1262C2×C22⋊C4C2412yes—
1263C2×C22⋊C4C2412yes—
1264C2×C22⋊C4C2412yes—
1265C2×C42—28no—
1266C2×C42—28no—
1267C2×C42—24no—
1268C2×C42—24no—
1269C2×C42—28no—
1270C2×C42C2×D418yes—
1271C2×C42C2411yescharacteristic
1272C2×C42C2411yescharacteristic
1273C2×C42C2414yes—
1274C2×C42C2414yes—
1275C2×C42C2412yes—
1276C2×C42C2412yes—
1277C2×C42C2411yescharacteristic
1278C2×C42C2412yes—
1279C2×C42C2412yes—
1280C2×C42C2411yescharacteristic
1281C2×C42C2412yes—
1282C2×C42C2412yes—
1283C2×C42C2412yes—
1284C2×C42C2412yes—
1285C2×C42C2412yes—
1286C2×C42C2411yescharacteristic
1287C2×C42C2411yescharacteristic
1288C2×C42C2412yes—
1289C2×C42C2414yes—
1290C2×C42C2412yes—
1291C2×C42C2414yes—
1292C2×C42C2414yes—
1293C2×C42C2412yes—
1294C2×C42C2412yes—
1295C2×C42C2414yes—
1296C2×C42C2411yescharacteristic
1297C2×C42C2412yes—
1298C2×C42C2411yescharacteristic
1299C2×C42C2411yescharacteristic
1300C2×C42C2411yescharacteristic
1301#95C2412yes—
1302#95C2414yes—
1303#95C2414yes—
1304#95C2414yes—
1305#95C2412yes—
1306#95C2412yes—
1307#95C2412yes—
1308#95C2412yes—
1309#95C2414yes—
1310#95C2414yes—
1311#95C2414yes—
1312#95C2412yes—
1313#95C2414yes—
1314#95C2414yes—
1315#95C2414yes—
1316#95C2414yes—
1317#95C2414yes—
1318#95C2414yes—
1319#95C2414yes—
1320#95C2412yes—
1321#95C2414yes—
1322#95C2412yes—
1323#95C2414yes—
1324#95C2412yes—
1325#95C2414yes—
1326#95C2412yes—
1327#95C2414yes—
1328#95C2412yes—
1329#95C2412yes—
1330#95C2414yes—
1331#95C2414yes—
1332#95C2414yes—
1333#95C2414yes—
1334#95C2414yes—
1335#95C2414yes—
1336#95C2414yes—
1337#95C2414yes—
1338#95C2414yes—
1339#95C2414yes—
1340#95C2414yes—
1341C24—24no—
1342C24—24no—
1343C24—42no—
1344C24—42no—
1345C24—42no—
1346C24—42no—
1347C24—42no—
1348C24C2512yes—
1349C24C2512yes—
1350C24C2511yescharacteristic
1351C24C2511yescharacteristic
1352C24C2512yes—
1353C24C2512yes—
1354C24C2511yescharacteristic
1355#41—416no—
1356#41—432no—
1357#41—432no—
1358#41—416no—
1359#41—416no—
1360#41—816no—
1361C2×Q8—22no—
1362C2×Q8—24no—
1363C2×Q8—24no—
1364C2×Q8—24no—
1365C2×Q8—22no—
1366C2×Q8—24no—
1367C2×Q8—28no—
1368C2×Q8—24no—
1369C2×Q8—24no—
1370C2×Q8—22no—
1371C2×Q8—22no—
1372C2×Q8—24no—
1373C2×Q8—24no—
1374C2×Q8—22no—
1375C2×Q8—22no—
1376C2×Q8—24no—
1377C2×Q8—24no—
1378C2×Q8—42no—
1379C2×Q8—42no—
1380C2×Q8—41no—
1381C2×Q8—44no—
1382C2×Q8—44no—
1383C2×Q8—416no—
1384C2×Q8—816no—
1385C2×Q8C22×D414yes—
1386C2×Q8H(5,𝔽2)14yes—
1387C2×D4—28no—
1388C2×D4—22no—
1389C2×D4—24no—
1390C2×D4—24no—
1391C2×D4—24no—
1392C2×D4—22no—
1393C2×D4—24no—
1394C2×D4—22no—
1395C2×D4—24no—
1396C2×D4—24no—
1397C2×D4—28no—
1398C2×D4—24no—
1399C2×D4—22no—
1400C2×D4—24no—
1401C2×D4—28no—
1402C2×D4—24no—
1403C2×D4—24no—
1404C2×D4—28no—
1405C2×D4—22no—
1406C2×D4—24no—
1407C2×D4—22no—
1408C2×D4—24no—
1409C2×D4—22no—
1410C2×D4—22no—
1411C2×D4—24no—
1412C2×D4—22no—
1413C2×D4—22no—
1414C2×D4—24no—
1415C2×D4—24no—
1416C2×D4—22no—
1417C2×D4—24no—
1418C2×D4—22no—
1419C2×D4—24no—
1420C2×D4—22no—
1421C2×D4—22no—
1422C2×D4—22no—
1423C2×D4—22no—
1424C2×D4—416no—
1425C2×D4—42no—
1426C2×D4—42no—
1427C2×D4—42no—
1428C2×D4—42no—
1429C2×D4—42no—
1430C2×D4—42no—
1431C2×D4—41no—
1432C2×D4—42no—
1433C2×D4—41no—
1434C2×D4—42no—
1435C2×D4—42no—
1436C2×D4—42no—
1437C2×D4—44no—
1438C2×D4—41no—
1439C2×D4—44no—
1440C2×D4—44no—
1441C2×D4—42no—
1442C2×D4—42no—
1443C2×D4—42no—
1444C2×D4—44no—
1445C2×D4—44no—
1446C2×D4—42no—
1447C2×D4—42no—
1448C2×D4—42no—
1449C2×D4—42no—
1450C2×D4—42no—
1451C2×D4—44no—
1452C2×D4—44no—
1453C2×D4—42no—
1454C2×D4—42no—
1455C2×D4—44no—
1456C2×D4C22×D414yes—
1457C2×D4C22×D418yes—
1458C2×D4C2×#4114yes—
1459C2×D4C2×#4118yes—
1460C22×C4—22no—
1461C22×C4—24no—
1462C22×C4—22no—
1463C22×C4—22no—
1464C22×C4—22no—
1465C22×C4—24no—
1466C22×C4—22no—
1467C22×C4—22no—
1468C22×C4—24no—
1469C22×C4—28no—
1470C22×C4—24no—
1471C22×C4—24no—
1472C22×C4—28no—
1473C22×C4—24no—
1474C22×C4—22no—
1475C22×C4—22no—
1476C22×C4—24no—
1477C22×C4—24no—
1478C22×C4—22no—
1479C22×C4—28no—
1480C22×C4—24no—
1481C22×C4—24no—
1482C22×C4—22no—
1483C22×C4—24no—
1484C22×C4—24no—
1485C22×C4—24no—
1486C22×C4—24no—
1487C22×C4—22no—
1488C22×C4—22no—
1489C22×C4—24no—
1490C22×C4—24no—
1491C22×C4—22no—
1492C22×C4—22no—
1493C22×C4—24no—
1494C22×C4—24no—
1495C22×C4—24no—
1496C22×C4—22no—
1497C22×C4—24no—
1498C22×C4—22no—
1499C22×C4—24no—
1500C22×C4—22no—
1501C22×C4—28no—
1502C22×C4—24no—
1503C22×C4—24no—
1504C22×C4—28no—
1505C22×C4—41no—
1506C22×C4—41no—
1507C22×C4—42no—
1508C22×C4—44no—
1509C22×C4—42no—
1510C22×C4—42no—
1511C22×C4—44no—
1512C22×C4—44no—
1513C22×C4—42no—
1514C22×C4—42no—
1515C22×C4—44no—
1516C22×C4—42no—
1517C22×C4—42no—
1518C22×C4—42no—
1519C22×C4—42no—
1520C22×C4—42no—
1521C22×C4—42no—
1522C22×C4—42no—
1523C22×C4—44no—
1524C22×C4—41no—
1525C22×C4—41no—
1526C22×C4—41no—
1527C22×C4—41no—
1528C22×C4—42no—
1529C22×C4—42no—
1530C22×C4—42no—
1531C22×C4—44no—
1532C22×C4—44no—
1533C22×C4—816no—
1534C22×C4C22×D418yes—
1535C22×C4C22×D414yes—
1536C22×C4C22×D414yes—
1537C22×C4C22×D414yes—
1538C22×C4C2×#4114yes—
1539C22×C4C2512yes—
1540C22×C4C2512yes—
1541C22×C4C2511yescharacteristic
1542C22×C4C2512yes—
1543C22×C4C2514yes—
1544C22×C4C2511yescharacteristic
1545C22×C4C2514yes—
1546C22×C4C2512yes—
1547C22×C4C2511yescharacteristic
1548C22×C4C2512yes—
1549C22×C4C2514yes—
1550C22×C4C2512yes—
1551C22×C4C2514yes—
1552C22×C4C2512yes—
1553C22×C4C2511yescharacteristic
1554C22×C4C2511yescharacteristic
1555C22×C4C2511yescharacteristic
1556C22×C4C2511yescharacteristic
1557C22×C4C2512yes—
1558C22×C4C2511yescharacteristic
1559C22×C4C2511yescharacteristic
1560C22×C4C2512yes—
1561C22×C4C2512yes—
1562C22×C4C2511yescharacteristic
1563C22×C4C2512yes—
1564C22×C4C2512yes—
1565C22×C4C2511yescharacteristic
1566C22×C4C2511yescharacteristic
1567C4⋊C4—22no—
1568C4⋊C4—28no—
1569C4⋊C4—24no—
1570C4⋊C4—22no—
1571C4⋊C4—24no—
1572C4⋊C4—24no—
1573C4⋊C4—22no—
1574C4⋊C4—24no—
1575C4⋊C4—28no—
1576C4⋊C4—28no—
1577C4⋊C4—24no—
1578C4⋊C4—24no—
1579C4⋊C4—24no—
1580C4⋊C4—28no—
1581C4⋊C4—22no—
1582C4⋊C4—22no—
1583C4⋊C4—24no—
1584C4⋊C4—24no—
1585C4⋊C4—22no—
1586C4⋊C4—22no—
1587C4⋊C4—24no—
1588C4⋊C4—22no—
1589C4⋊C4—24no—
1590C4⋊C4—22no—
1591C4⋊C4—22no—
1592C4⋊C4—24no—
1593C4⋊C4—24no—
1594C4⋊C4—24no—
1595C4⋊C4—24no—
1596C4⋊C4—28no—
1597C4⋊C4—28no—
1598C4⋊C4—28no—
1599C4⋊C4—24no—
1600C4⋊C4—22no—
1601C4⋊C4—28no—
1602C4⋊C4—28no—
1603C4⋊C4—28no—
1604C4⋊C4—28no—
1605C4⋊C4—24no—
1606C4⋊C4—24no—
1607C4⋊C4—28no—
1608C4⋊C4—28no—
1609C4⋊C4—22no—
1610C4⋊C4—24no—
1611C4⋊C4—22no—
1612C4⋊C4—42no—
1613C4⋊C4—44no—
1614C4⋊C4—42no—
1615C4⋊C4—42no—
1616C4⋊C4—44no—
1617C4⋊C4—42no—
1618C4⋊C4—42no—
1619C4⋊C4—42no—
1620C4⋊C4—44no—
1621C4⋊C4—44no—
1622C4⋊C4—44no—
1623C4⋊C4—44no—
1624C4⋊C4C22×D414yes—
1625C4⋊C4C22×D418yes—
1626C4⋊C4C22×D414yes—
1627C4⋊C4C22×D418yes—
1628C4⋊C4C22×D418yes—
1629C4⋊C4C22×D418yes—
1630C4⋊C4C2×#4114yes—
1631C22⋊C4—28no—
1632C22⋊C4—22no—
1633C22⋊C4—24no—
1634C22⋊C4—24no—
1635C22⋊C4—22no—
1636C22⋊C4—28no—
1637C22⋊C4—24no—
1638C22⋊C4—24no—
1639C22⋊C4—28no—
1640C22⋊C4—28no—
1641C22⋊C4—24no—
1642C22⋊C4—24no—
1643C22⋊C4—24no—
1644C22⋊C4—24no—
1645C22⋊C4—28no—
1646C22⋊C4—28no—
1647C22⋊C4—22no—
1648C22⋊C4—22no—
1649C22⋊C4—28no—
1650C22⋊C4—24no—
1651C22⋊C4—22no—
1652C22⋊C4—24no—
1653C22⋊C4—24no—
1654C22⋊C4—24no—
1655C22⋊C4—24no—
1656C22⋊C4—22no—
1657C22⋊C4—28no—
1658C22⋊C4—24no—
1659C22⋊C4—24no—
1660C22⋊C4—24no—
1661C22⋊C4—24no—
1662C22⋊C4—24no—
1663C22⋊C4—24no—
1664C22⋊C4—28no—
1665C22⋊C4—28no—
1666C22⋊C4—28no—
1667C22⋊C4—42no—
1668C22⋊C4—42no—
1669C22⋊C4—42no—
1670C22⋊C4—42no—
1671C22⋊C4—44no—
1672C22⋊C4—44no—
1673C22⋊C4—44no—
1674C22⋊C4—42no—
1675C22⋊C4—44no—
1676C22⋊C4—44no—
1677C22⋊C4—42no—
1678C22⋊C4—42no—
1679C22⋊C4—42no—
1680C22⋊C4—42no—
1681C22⋊C4—44no—
1682C22⋊C4—44no—
1683C22⋊C4—42no—
1684C22⋊C4—42no—
1685C22⋊C4—44no—
1686C22⋊C4—44no—
1687C22⋊C4—42no—
1688C22⋊C4—42no—
1689C22⋊C4—44no—
1690C22⋊C4—44no—
1691C22⋊C4—44no—
1692C22⋊C4—44no—
1693C22⋊C4—44no—
1694C22⋊C4—44no—
1695C22⋊C4C22×D418yes—
1696C22⋊C4C22×D418yes—
1697C22⋊C4C22×D418yes—
1698C22⋊C4C22×D418yes—
1699C22⋊C4C22×D418yes—
1700C22⋊C4C2×#4118yes—
1701C42—22no—
1702C42—24no—
1703C42—22no—
1704C42—24no—
1705C42—22no—
1706C42—24no—
1707C42—24no—
1708C42—24no—
1709C42—22no—
1710C42—24no—
1711C42—22no—
1712C42—24no—
1713C42—22no—
1714C42—28no—
1715C42—28no—
1716C42—24no—
1717C42—24no—
1718C42—24no—
1719C42—42no—
1720C42—42no—
1721C42—44no—
1722C42—44no—
1723C42—42no—
1724C42—44no—
1725C42—44no—
1726C42C22×D414yes—
1727C42C22×D414yes—
1728C42C22×D418yes—
1729C42C22×D414yes—
1730C42C22×D414yes—
1731C23—22no—
1732C23—21no—
1733C23—21no—
1734C23—22no—
1735C23—22no—
1736C23—21no—
1737C23—21no—
1738C23—22no—
1739C23—21no—
1740C23—22no—
1741C23—21no—
1742C23—22no—
1743C23—21no—
1744C23—21no—
1745C23—22no—
1746C23—22no—
1747C23—22no—
1748C23—22no—
1749C23—22no—
1750C23—21no—
1751C23—21no—
1752C23—22no—
1753C23—21no—
1754C23—21no—
1755C23—22no—
1756C23—21no—
1757C23—22no—
1758C23—22no—
1759C23—22no—
1760C23—21no—
1761C23—22no—
1762C23—21no—
1763C23—22no—
1764C23—21no—
1765C23—22no—
1766C23—21no—
1767C23—22no—
1768C23—22no—
1769C23—22no—
1770C23—22no—
1771C23—22no—
1772C23—21no—
1773C23—22no—
1774C23—21no—
1775C23—22no—
1776C23—48no—
1777C23—48no—
1778C23—84no—
1779C23—84no—
1780C23—84no—
1781C23—84no—
1782C23—84no—
1783C23C23×D412yes—
1784C23C23×D414yes—
1785C23C22×#4112yes—
1786C23C22×#4114yes—
1787C23C2611yescharacteristic
1788Q8—28no—
1789Q8—28no—
1790Q8—48no—
1791Q8—48no—
1792Q8—44no—
1793Q8—48no—
1794Q8—48no—
1795Q8—88no—
1796D4—28no—
1797D4—28no—
1798D4—48no—
1799D4—48no—
1800D4—48no—
1801D4—48no—
1802D4—48no—
1803D4—48no—
1804D4—44no—
1805D4—48no—
1806D4—44no—
1807D4—48no—
1808D4—44no—
1809D4—416no—
1810D4—44no—
1811D4—44no—
1812D4—84no—
1813D4—84no—
1814D4—88no—
1815D4—84no—
1816D4—84no—
1817D4—84no—
1818D4—88no—
1819D4—88no—
1820C2×C4—21no—
1821C2×C4—22no—
1822C2×C4—21no—
1823C2×C4—22no—
1824C2×C4—22no—
1825C2×C4—21no—
1826C2×C4—22no—
1827C2×C4—22no—
1828C2×C4—21no—
1829C2×C4—21no—
1830C2×C4—21no—
1831C2×C4—22no—
1832C2×C4—22no—
1833C2×C4—21no—
1834C2×C4—21no—
1835C2×C4—22no—
1836C2×C4—22no—
1837C2×C4—21no—
1838C2×C4—21no—
1839C2×C4—22no—
1840C2×C4—28no—
1841C2×C4—216no—
1842C2×C4—28no—
1843C2×C4—28no—
1844C2×C4—21no—
1845C2×C4—21no—
1846C2×C4—22no—
1847C2×C4—21no—
1848C2×C4—21no—
1849C2×C4—22no—
1850C2×C4—24no—
1851C2×C4—21no—
1852C2×C4—22no—
1853C2×C4—24no—
1854C2×C4—22no—
1855C2×C4—22no—
1856C2×C4—21no—
1857C2×C4—24no—
1858C2×C4—22no—
1859C2×C4—24no—
1860C2×C4—22no—
1861C2×C4—24no—
1862C2×C4—24no—
1863C2×C4—22no—
1864C2×C4—22no—
1865C2×C4—24no—
1866C2×C4—21no—
1867C2×C4—21no—
1868C2×C4—22no—
1869C2×C4—22no—
1870C2×C4—22no—
1871C2×C4—22no—
1872C2×C4—24no—
1873C2×C4—21no—
1874C2×C4—22no—
1875C2×C4—21no—
1876C2×C4—24no—
1877C2×C4—24no—
1878C2×C4—22no—
1879C2×C4—22no—
1880C2×C4—21no—
1881C2×C4—22no—
1882C2×C4—22no—
1883C2×C4—22no—
1884C2×C4—24no—
1885C2×C4—24no—
1886C2×C4—22no—
1887C2×C4—21no—
1888C2×C4—22no—
1889C2×C4—21no—
1890C2×C4—21no—
1891C2×C4—21no—
1892C2×C4—44no—
1893C2×C4—48no—
1894C2×C4—48no—
1895C2×C4—48no—
1896C2×C4—416no—
1897C2×C4—44no—
1898C2×C4—48no—
1899C2×C4—48no—
1900C2×C4—48no—
1901C2×C4—44no—
1902C2×C4—44no—
1903C2×C4—88no—
1904C2×C4—84no—
1905C2×C4—82no—
1906C2×C4—82no—
1907C2×C4—84no—
1908C2×C4—84no—
1909C2×C4—84no—
1910C2×C4—88no—
1911C2×C4—84no—
1912C2×C4—84no—
1913C2×C4—88no—
1914C2×C4C23×D412yes—
1915C2×C4C23×D414yes—
1916C2×C4C23×D412yes—
1917C2×C4C23×D412yes—
1918C2×C4C23×D414yes—
1919C2×C4C23×D414yes—
1920C2×C4C23×D412yes—
1921C2×C4C23×D412yes—
1922C2×C4C23×D412yes—
1923C2×C4C22×#4114yes—
1924C2×C4C22×#4112yes—
1925C2×C4C22×#4112yes—
1926C2×C4C2×H(5,𝔽2)14yes—
1927C2×C4C2×H(5,𝔽2)12yes—
1928C2×C4#58512yes—
1929C2×C4#58512yes—
1930C22—22no—
1931C22—24no—
1932C22—22no—
1933C22—24no—
1934C22—22no—
1935C22—24no—
1936C22—22no—
1937C22—24no—
1938C22—22no—
1939C22—24no—
1940C22—22no—
1941C22—24no—
1942C22—42no—
1943C22—41no—
1944C22—42no—
1945C22—41no—
1946C22—41no—
1947C22—42no—
1948C22—41no—
1949C22—42no—
1950C22—41no—
1951C22—42no—
1952C22—42no—
1953C22—41no—
1954C22—41no—
1955C22—42no—
1956C22—42no—
1957C22—41no—
1958C22—41no—
1959C22—42no—
1960C22—42no—
1961C22—41no—
1962C22—42no—
1963C22—42no—
1964C22—42no—
1965C22—42no—
1966C22—41no—
1967C22—41no—
1968C22—42no—
1969C22—42no—
1970C22—42no—
1971C22—42no—
1972C22—41no—
1973C22—41no—
1974C22—42no—
1975C22—42no—
1976C22—42no—
1977C22—41no—
1978C22—42no—
1979C22—816no—
1980C22C24×D411yescharacteristic
1981C22C23×#4111yescharacteristic
1982C22C22×H(5,𝔽2)11yescharacteristic
1983C22C2×#58511yescharacteristic
1984C22C2×#58511yescharacteristic
1985C222−1+611yescharacteristic
1986C222−1+611yescharacteristic
1987C4—24no—
1988C4—22no—
1989C4—24no—
1990C4—24no—
1991C4—22no—
1992C4—22no—
1993C4—24no—
1994C4—24no—
1995C4—22no—
1996C4—22no—
1997C4—44no—
1998C4—42no—
1999C4—41no—
2000C4—42no—
2001C4—42no—
2002C4—41no—
2003C4—44no—
2004C4—42no—
2005C4—41no—
2006C4—41no—
2007C4—42no—
2008C4—44no—
2009C4—42no—
2010C4—41no—
2011C4—42no—
2012C4—44no—
2013C4D4×#4114yes—
2014C4#348814yes—
2015C2—42no—
2016C2—44no—
2017C2—44no—
2018C2—42no—
2019C2—81no—
2020C2—82no—
2021C2—82no—
2022C2C2×D4×#4111yescharacteristic
2023C2C2×#348811yescharacteristic
2024C2#6285911yescharacteristic
2025C2#6292211yescharacteristic
2026C2#6293911yescharacteristic
2027C2#6298411yescharacteristic
2028C2#6299511yescharacteristic
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×#3520C2semidirect
2. C2×#3480C2semidirect
3. #59824C2semidirect
4. #59656C2semidirect
5. #59654C2semidirect
6. #59417C2semidirect
7. #59025C2semidirect
8. #59020C2semidirect
9. #59005C2semidirect
10. #58999C2semidirect
11. #44364C2semidirect
12. #44160C2semidirect
13. #43539C2semidirect
14. #43537C2semidirect
15. #39471C2semidirect
16. #39470C2semidirect
17. #39340C2semidirect
18. #39334C2semidirect
19. #39136C2semidirect
20. #39124C2semidirect
21. #38040C2semidirect
22. #38034C2semidirect
23. #36579C2semidirect
24. Q8×#121C2semidirect
25. #36404C2semidirect
26. #36259C2semidirect
27. #35568C2semidirect
28. #35521C2semidirect
29. #35297C2semidirect
30. #35258C2semidirect
31. #34979C2semidirect
32. #34935C2semidirect
33. #34267C2semidirect
34. #34242C2semidirect
35. C4×#535C2semidirect
39. C2×#559C22semidirect
40. C2×#557C22semidirect
43. C2×#556C22semidirect
47. C2×#553C22semidirect
48. C2×#553C22semidirect
53. C2×D4×Q8C22semidirect
56. C2×#548C22semidirect
59. C2×#547C22semidirect
67. C2×#532C22semidirect
70. C2×#529C22semidirect
71. C2×#529C22semidirect
78. C2×C4×#41C22semidirect
79. C2×C4×#41C22semidirect
80. C22×C4×Q8C22semidirect
82. #2857C22semidirect
83. #2857C22semidirect
84. #2857C22semidirect
85. #2857C22semidirect
86. #2857C22semidirect
87. #2855C22semidirect
90. #2727C22semidirect
91. #2723C22semidirect
92. #2721C22semidirect
93. #2719C22semidirect
94. #2710C22semidirect
95. #2705C22semidirect
97. #2703C22semidirect
99. #2700C22semidirect
101. #2696C22semidirect
105. #2681C22semidirect
110. #2672C22semidirect
111. #2671C22semidirect
114. #2628C22semidirect
118. #2616C22semidirect
120. #2611C22semidirect
122. #2584C22semidirect
123. #2581C22semidirect
124. #2581C22semidirect
125. #2568C22semidirect
126. #2563C22semidirect
127. #2562C22semidirect
128. #2560C22semidirect
130. #2557C22semidirect
133. #2554C22semidirect
134. #2553C22semidirect
135. #2550C22semidirect
136. #2547C22semidirect
137. #2546C22semidirect
138. #2546C22semidirect
139. #2542C22semidirect
141. #2540C22semidirect
142. #2540C22semidirect
146. #2538C22semidirect
147. #2538C22semidirect
150. #2537C22semidirect
152. #2536C22semidirect
156. #2519C22semidirect
158. #2492C22semidirect
159. #2491C22semidirect
160. #2490C22semidirect
161. #2489C22semidirect
162. #2488C22semidirect
163. #2487C22semidirect
165. #2486C22semidirect
168. #2481C22semidirect
169. #2481C22semidirect
171. #2475C22semidirect
174. #2471C22semidirect
175. #2470C22semidirect
176. #2469C22semidirect
177. #2469C22semidirect
178. #2467C22semidirect
179. #2466C22semidirect
180. #2465C22semidirect
181. #2464C22semidirect
182. #2463C22semidirect
183. #2461C22semidirect
184. #2461C22semidirect
185. #2459C22semidirect
186. #2457C22semidirect
187. #2457C22semidirect
188. #2457C22semidirect
189. #2456C22semidirect
190. #2455C22semidirect
191. #2452C22semidirect
192. #2449C22semidirect
195. #2441C22semidirect
196. #2440C22semidirect
197. #2440C22semidirect
198. #2436C22semidirect
200. #2431C22semidirect
201. #2429C22semidirect
202. #2429C22semidirect
203. #2429C22semidirect
205. #2428C22semidirect
206. #2426C22semidirect
207. #2425C22semidirect
209. #2421C22semidirect
211. #2420C22semidirect
213. #2417C22semidirect
214. #2417C22semidirect
215. #2417C22semidirect
217. #2416C22semidirect
222. #2415C22semidirect
223. #2415C22semidirect
225. #2414C22semidirect
226. #2413C22semidirect
227. #2409C22semidirect
228. #2409C22semidirect
232. #2407C22semidirect
233. #2407C22semidirect
236. #2373C22semidirect
237. #2364C22semidirect
238. #2364C22semidirect
240. #2363C22semidirect
242. #2362C22semidirect
243. #2362C22semidirect
244. #2361C22semidirect
245. #2361C22semidirect
246. #2361C22semidirect
247. #2360C22semidirect
248. #2360C22semidirect
249. #2355C22semidirect
251. #2354C22semidirect
253. #2352C22semidirect
254. #2352C22semidirect
255. Q8×C4⋊C4C22semidirect
256. D4×C4⋊C4C22semidirect
257. Q8×C22⋊C4C22semidirect
258. #2339C22semidirect
267. #2323C22semidirect
268. #2323C22semidirect
269. #2323C22semidirect
273. #2314C22semidirect
275. #2311C22semidirect
277. C4×C4⋊Q8C22semidirect
279. C4×#125C22semidirect
281. C4×#124C22semidirect
282. C4×#124C22semidirect
283. C4×C22⋊Q8C22semidirect
284. C4×C22⋊Q8C22semidirect
285. C4×C22⋊Q8C22semidirect
296. C2×#389C22semidirect
299. #2274C22semidirect
354. #529D4semidirect
1043. #121#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
C2×#34802
#598242
#596562
#596542
#594172
#590252
#590202
#590052
#589992
#443642
#441602
#435392
#435372
#394712
#394702
#393402
#393342
#391362
#391242
#380402
#380342
#365792
Q8×#1212
#364042
#362592
#355682
#355212
#352972
#352582
#349792
#349352
#342672
#342422
C4×#5352