Finite Group Databasebeta

← #7712563

Subgroups — #7712563

Order 512.

7324 conjugacy classes of subgroups.

The subgroup lattice has 1876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3561C211yesmaximal, characteristic, complemented
2C2×#3444C211yesmaximal, characteristic, complemented
3#59108C214yesmaximal, complemented
4#59007C214yesmaximal, complemented
5#46227C212yesmaximal, complemented
6#46224C212yesmaximal, complemented
7#46134C212yesmaximal, complemented
8#46133C212yesmaximal, complemented
9#39719C212yesmaximal, complemented
10#39335C212yesmaximal, complemented
11#37806C214yesmaximal, complemented
12#37761C212yesmaximal, complemented
13#37752C212yesmaximal, complemented
14#37738C214yesmaximal, complemented
15#37697C212yesmaximal, complemented
16#37688C212yesmaximal, complemented
17#37651C212yesmaximal, complemented
18#37648C212yesmaximal, complemented
19#37555C211yesmaximal, characteristic, complemented
20#37546C211yesmaximal, characteristic, complemented
21#37379C212yesmaximal, complemented
22#37280C212yesmaximal, complemented
23#36625C211yesmaximal, characteristic, complemented
24C2×#2850C211yesmaximal, characteristic, complemented
25#36504C212yesmaximal, complemented
26#36374C212yesmaximal, complemented
27#36360C212yesmaximal, complemented
28#36274C212yesmaximal, complemented
29#35308C212yesmaximal, complemented
30#35258C212yesmaximal, complemented
31#34382C211yesmaximal, characteristic, complemented
32#3561—216no—
33C2×#563C2212yescomplemented
34C2×#562C2212yescomplemented
35C2×#556C2212yescomplemented
36C2×#551C2214yes—
37C2×D4×Q8C2212yes—
38C2×#548C2212yescomplemented
39C2×#546C2212yes—
40C2×#543C2212yes—
41C2×#542C2214yescomplemented
42C2×#542C2212yescomplemented
43C2×#538C2212yes—
44C2×#537C2212yes—
45C2×#536C2212yescomplemented
46C2×#536C2212yescomplemented
47#3444—216no—
48C2×#533C2211yescharacteristic
49C2×#533C2211yescharacteristic
50C2×#533C2211yescharacteristic, complemented
51C2×#533C2211yescharacteristic, complemented
52C2×#532C2211yescharacteristic
53C2×#532C2211yescharacteristic, complemented
54C2×#532C2211yescharacteristic, complemented
55C2×#529C2211yescharacteristic
56C2×#529C2212yes—
57C2×#529C2211yescharacteristic
58C2×#529C2212yescomplemented
59C2×#529C2211yescharacteristic, complemented
60C2×#529C2211yescharacteristic, complemented
61C2×#529C2212yescomplemented
62C2×#529C2212yescomplemented
63C22×#124C2211yescharacteristic
64C2×#525C2212yes—
65C2×#525C2211yescharacteristic
66C2×#525C2212yes—
67C2×#525C2211yescharacteristic
68C22×C22⋊Q8C2211yescharacteristic
69C22×#121C2211yescharacteristic
70C2×C4×#41C2212yes—
71C2×C4×#41C2211yescharacteristic, complemented
72C2×C4×#41C2211yescharacteristic, complemented
73C2×C4×#41C2212yescomplemented
74C23×C42C2211yescharacteristic
75#2857C2211yescharacteristic, complemented
76#2857C2211yescharacteristic, complemented
77#2857C2211yescharacteristic, complemented
78#2857C2211yescharacteristic, complemented
79#2857C2212yescomplemented
80#2855C2212yes—
81#2855C2212yes—
82#2855C2212yescomplemented
83#2854C2212yescomplemented
84#2851C2212yescomplemented
85#2851C2212yescomplemented
86#2850C2212yes—
87#2850C2212yes—
88#2850C2212yes—
89#2850C2212yes—
90#2850C2212yes—
91#2850C2212yes—
92#2850C2212yes—
93#2850C2212yes—
94#2850C2212yescomplemented
95#2848C2212yes—
96#2848C2212yes—
97#2822C2212yescomplemented
98#2820C2212yescomplemented
99#2820C2212yescomplemented
100#2819C2212yescomplemented
101#2729C2214yescomplemented
102#2728C2214yescomplemented
103#2727C2214yescomplemented
104#2723C2214yescomplemented
105#2723C2214yescomplemented
106#2720C2214yescomplemented
107#2718C2214yescomplemented
108#2716C2214yescomplemented
109#2712C2214yescomplemented
110#2710C2214yescomplemented
111#2706C2214yescomplemented
112#2704C2214yescomplemented
113#2703C2214yescomplemented
114#2702C2214yescomplemented
115#2696C2214yescomplemented
116#2695C2214yescomplemented
117#2692C2214yescomplemented
118#2682C2214yes—
119#2681C2214yes—
120#2681C2214yescomplemented
121#2681C2214yescomplemented
122#2680C2214yescomplemented
123#2677C2214yescomplemented
124#2677C2214yescomplemented
125#2676C2214yescomplemented
126#2675C2214yes—
127#2674C2214yescomplemented
128#2673C2214yescomplemented
129#2672C2214yescomplemented
130#2671C2214yes—
131#2671C2214yescomplemented
132#2671C2214yescomplemented
133#2662C2214yescomplemented
134#2659C2212yes—
135#2639C2212yes—
136#2637C2214yescomplemented
137#2628C2212yescomplemented
138#2626C2212yes—
139#2621C2212yescomplemented
140#2621C2212yescomplemented
141#2620C2212yes—
142#2620C2212yescomplemented
143#2620C2212yescomplemented
144#2617C2212yes—
145#2616C2212yescomplemented
146#2615C2212yes—
147#2592C2212yescomplemented
148#2592C2212yescomplemented
149#2582C2212yescomplemented
150#2581C2212yescomplemented
151#2580C2212yescomplemented
152#2568C2212yescomplemented
153#2560C2214yescomplemented
154#2555C2214yescomplemented
155#2542C2212yescomplemented
156#2540C2212yes—
157#2540C2212yescomplemented
158#2537C2212yes—
159#2536C2212yescomplemented
160#2536C2212yescomplemented
161#2519C2214yescomplemented
162#2498C2214yes—
163#2491C2214yescomplemented
164#2479C2214yescomplemented
165#2479C2214yescomplemented
166#2477C2214yescomplemented
167#2477C2214yescomplemented
168#2476C2214yescomplemented
169#2475C2214yescomplemented
170#2474C2214yescomplemented
171#2472C2214yes—
172#2471C2214yescomplemented
173#2469C2214yescomplemented
174#2467C2214yescomplemented
175#2467C2214yescomplemented
176#2467C2214yescomplemented
177#2465C2214yescomplemented
178#2465C2214yescomplemented
179#2464C2214yescomplemented
180#2463C2214yescomplemented
181#2461C2214yescomplemented
182#2461C2214yescomplemented
183#2459C2214yescomplemented
184#2459C2214yescomplemented
185#2458C2214yescomplemented
186#2457C2214yescomplemented
187#2456C2214yescomplemented
188#2455C2214yescomplemented
189#2451C2214yescomplemented
190#2450C2214yes—
191#2450C2214yescomplemented
192#2444C2214yescomplemented
193#2443C2214yes—
194#2440C2214yes—
195#2439C2214yescomplemented
196#2438C2214yes—
197#2438C2214yescomplemented
198#2437C2214yes—
199#2430C2214yescomplemented
200#2429C2214yescomplemented
201#2429C2214yescomplemented
202#2427C2214yescomplemented
203#2427C2214yescomplemented
204#2425C2214yescomplemented
205#2425C2214yescomplemented
206#2425C2214yescomplemented
207#2425C2214yescomplemented
208#2424C2214yes—
209#2423C2214yescomplemented
210#2418C2214yes—
211#2418C2214yes—
212#2417C2212yes—
213#2417C2212yes—
214#2417C2212yescomplemented
215#2416C2212yes—
216#2415C2212yescomplemented
217#2414C2212yescomplemented
218#2411C2214yes—
219#2410C2214yes—
220#2409C2212yes—
221#2409C2212yescomplemented
222#2409C2212yescomplemented
223#2408C2212yes—
224#2408C2214yes—
225#2407C2212yes—
226#2407C2212yescomplemented
227#2407C2214yescomplemented
228#2404C2214yes—
229#2382C2212yescomplemented
230#2379C2212yescomplemented
231#2364C2214yescomplemented
232#2363C2214yescomplemented
233#2359C2214yes—
234#2359C2214yescomplemented
235#2358C2214yes—
236#2355C2212yescomplemented
237#2354C2214yescomplemented
238#2352C2212yes—
239#2352C2212yescomplemented
240#2349C2214yes—
241D4×C4⋊C4C2212yes—
242#2342C2214yes—
243#2339C2214yes—
244#2334C2214yescomplemented
245#2329C2212yes—
246#2325C2212yes—
247#2324C2212yes—
248#2323C2212yescomplemented
249#2317C2212yescomplemented
250#2314C2212yescomplemented
251C4×C22⋊Q8C2212yescomplemented
252C4×C22⋊Q8C2212yescomplemented
253C4×C22⋊Q8C2212yescomplemented
254C4×C22⋊Q8C2212yescomplemented
255C4×C22⋊Q8C2212yescomplemented
256C4×#121C2212yescomplemented
257#2297C2212yescomplemented
258#2296C2212yes—
259C2×#391C2211yescharacteristic
260C2×#391C2212yescomplemented
261C2×#390C2211yescharacteristic
262C2×#388C2212yes—
263C2×#388C2212yes—
264C2×#386C2212yes—
265C2×#386C2212yes—
266#2285C2211yescharacteristic
267C2×#382C2211yescharacteristic
268#2280C2212yes—
269C22×#41C2312yes—
270C22×#41C2312yes—
271C22×#41C2311yescharacteristic
272C22×#41C2311yescharacteristic
273C22×#41C2312yes—
274C23×Q8C2311yescharacteristic
275C23×Q8C2312yes—
276C23×D4C2311yescharacteristic
277C23×D4C2312yes—
278C24×C4C2311yescharacteristic
279C24×C4C2311yescharacteristic
280C24×C4C2311yescharacteristic
281#563—216no—
282#562—216no—
283#556—216no—
284#551—232no—
285D4×Q8—216no—
286#548—216no—
287#546—216no—
288#543—216no—
289#542—232no—
290#542—216no—
291#538—216no—
292#537—48no—
293#536—216no—
294#536—48no—
295#533—28no—
296#533—28no—
297#533—28no—
298#533—28no—
299#532—28no—
300#532—28no—
301#532—28no—
302C2×C4⋊Q8C2312yes—
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2311yescharacteristic
305C2×C4⋊Q8C2314yes—
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2314yes—
310C2×#127C2311yescharacteristic
311#529—216no—
312#529—216no—
313#529—28no—
314#529—28no—
315#529—216no—
316#529—216no—
317#529—28no—
318#529D4116yescomplemented
319C2×#126C2314yes—
320C2×#126C2312yes—
321C2×#126C2312yes—
322C2×#126C2312yes—
323C2×#126C2314yes—
324C2×#126C2314yes—
325C2×#126C2312yes—
326C2×#125C2311yescharacteristic
327C2×#125C2312yes—
328C2×#125C2312yes—
329C2×#125C2312yes—
330C2×#125C2311yescharacteristic
331C2×#124—28no—
332C2×#124C2311yescharacteristic
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2312yes—
338C2×#124C2312yes—
339C2×#124C2312yes—
340C2×#124C2314yes—
341C2×#124C2314yes—
342C2×#124C2314yes—
343C2×#124C2311yescharacteristic
344#525—216no—
345#525—28no—
346#525—28no—
347#525—216no—
348C2×#123C2312yes—
349C2×#123C2312yes—
350C2×#123C2312yes—
351C2×#123C2312yes—
352C2×#123C2312yes—
353C2×#123C2314yes—
354C2×#123C2314yes—
355C2×#123C2314yes—
356C2×#123C2314yes—
357C2×#123C2314yes—
358C2×#123C2314yes—
359C2×#123C2314yes—
360C2×#123C2312yes—
361C2×C22⋊Q8—44no—
362C2×C22⋊Q8C2312yes—
363C2×C22⋊Q8C2312yes—
364C2×C22⋊Q8C2312yes—
365C2×C22⋊Q8C2312yes—
366C2×C22⋊Q8C2312yes—
367C2×C22⋊Q8C2312yes—
368C2×C22⋊Q8C2311yescharacteristic
369C2×C22⋊Q8C2314yes—
370C2×C22⋊Q8C2312yes—
371C2×C22⋊Q8C2312yes—
372C2×C22⋊Q8C2312yes—
373C2×C22⋊Q8C2311yescharacteristic
374C2×C22⋊Q8C2311yescharacteristic
375C2×C22⋊Q8C2314yes—
376C2×C22⋊Q8C2314yes—
377C2×C22⋊Q8C2314yes—
378C2×C22⋊Q8C2314yes—
379C2×C22⋊Q8C2314yes—
380C2×C22⋊Q8C2314yes—
381C2×C22⋊Q8C2312yes—
382C2×C22⋊Q8C2312yes—
383C2×C22⋊Q8C2312yes—
384C2×C22⋊Q8C2312yes—
385C2×C22⋊Q8C2312yes—
386C2×C22⋊Q8C2312yes—
387C2×C22⋊Q8C2312yes—
388C2×C22⋊Q8C2312yes—
389C2×C22⋊Q8C2312yes—
390C2×C22⋊Q8C2312yes—
391C2×C22⋊Q8C2314yes—
392C2×C22⋊Q8C2311yescharacteristic
393C2×#121—44no—
394C2×#121C2312yes—
395C2×#121C2312yes—
396C2×#121C2311yescharacteristic
397C2×#121C2311yescharacteristic
398C2×#121C2312yes—
399C2×#121C2312yes—
400C2×#121C2312yes—
401C2×#121C2311yescharacteristic
402C2×#121C2312yes—
403C2×#121C2314yes—
404C2×#121C2314yes—
405C2×#121C2312yes—
406C2×#121C2312yes—
407C2×#121C2312yes—
408C2×#121C2312yes—
409C2×#121C2312yes—
410C2×#121C2314yes—
411C2×#121C2314yes—
412C2×#121C2314yes—
413C2×#121C2314yes—
414C2×#121C2314yes—
415C2×#121C2311yescharacteristic
416C2×#120C2314yes—
417C2×#120C2312yes—
418C2×#120C2312yes—
419C2×#120C2314yes—
420C4×#41—28no—
421C4×#41—216no—
422C4×#41—28no—
423C4×#41—216no—
424C2×C4×Q8C2312yes—
425C2×C4×Q8C2312yes—
426C2×C4×Q8C2311yescharacteristic
427C2×C4×Q8C2312yes—
428C2×C4×Q8C2312yes—
429C2×C4×Q8C2312yes—
430C2×C4×Q8C2312yes—
431C2×C4×Q8C2311yescharacteristic
432C2×C4×Q8C2312yes—
433C2×C4×Q8C2311yescharacteristic
434C2×C4×Q8C2311yescharacteristic
435C2×C4×D4C2312yes—
436C2×C4×D4C2314yes—
437C2×C4×D4C2312yes—
438C2×C4×D4C2312yes—
439C2×C4×D4C2314yes—
440C2×C4×D4C2312yes—
441C2×C4×D4C2312yes—
442C2×C4×D4C2312yes—
443C2×C4×D4C2312yes—
444C2×C4×D4C2312yes—
445C2×C4×D4C2312yes—
446C2×C4×D4C2312yes—
447C2×C4×D4C2312yes—
448C2×C4×D4C2312yes—
449C2×C4×D4C2312yes—
450C2×C4×D4C2312yes—
451C2×C4×D4C2312yes—
452C2×C4×D4C2311yescharacteristic
453C2×C4×D4C2312yes—
454C2×C4×D4C2311yescharacteristic
455C2×C4×D4C2311yescharacteristic
456C2×C4×D4C2314yes—
457C2×C4×D4C2314yes—
458C2×C4×D4C2312yes—
459C2×C4×D4C2311yescharacteristic
460C2×#117C2312yes—
461C2×#117C2312yes—
462C2×#117C2312yes—
463C2×#117C2314yes—
464C2×#117C2312yes—
465C2×#117C2312yes—
466C2×#117C2312yes—
467C2×#117C2312yes—
468C2×#117C2311yescharacteristic
469C2×#117C2311yescharacteristic
470C2×#117C2312yes—
471C2×#117C2312yes—
472C2×#117C2312yes—
473C2×#117C2312yes—
474C22×C4⋊C4C2312yes—
475C22×C4⋊C4C2311yescharacteristic
476C22×C4⋊C4C2311yescharacteristic
477C22×C4⋊C4C2312yes—
478C22×C22⋊C4C2312yes—
479C22×C22⋊C4C2314yes—
480C22×C22⋊C4C2312yes—
481C22×C22⋊C4C2312yes—
482C22×C22⋊C4C2312yes—
483C22×C22⋊C4C2312yes—
484C22×C22⋊C4C2312yes—
485C22×C42—28no—
486C22×C42C2311yescharacteristic
487C22×C42C2311yescharacteristic
488C22×C42C2311yescharacteristic
489C22×C42C2311yescharacteristic
490C22×C42C2311yescharacteristic
491C22×C42C2311yescharacteristic
492C22×C42C2311yescharacteristic
493C22×C42C2311yescharacteristic
494C22×C42C2312yes—
495C22×C42C2312yes—
496C22×C42C2311yescharacteristic
497C22×C42C2311yescharacteristic
498C22×C42C2311yescharacteristic
499C22×C42C2311yescharacteristic
500#400C2314yes—
501#400C2314yes—
502#400C2314yes—
503#400C2314yes—
504#399C2314yes—
505#399C2314yes—
506#399C2314yes—
507#399C2314yes—
508#399C2314yes—
509#399C2314yes—
510#398C2314yes—
511#398C2314yes—
512#398C2314yes—
513#398C2314yes—
514#398C2314yes—
515#398C2314yes—
516#398C2314yes—
517#398C2314yes—
518#398C2314yes—
519#398C2314yes—
520#398C2314yes—
521#397C2314yes—
522#397C2314yes—
523#397C2314yes—
524#397C2314yes—
525#397C2314yes—
526#397C2314yes—
527#397C2314yes—
528#396C2314yes—
529#396C2314yes—
530#396C2314yes—
531#396C2314yes—
532#396C2314yes—
533#396C2314yes—
534#396C2314yes—
535#396C2314yes—
536#396C2314yes—
537#396C2314yes—
538#395C2314yes—
539#395C2314yes—
540#395C2314yes—
541#395C2314yes—
542#395C2314yes—
543#395C2314yes—
544#394C2314yes—
545#394C2314yes—
546#394C2314yes—
547#394C2314yes—
548#394C2314yes—
549#394C2314yes—
550#394C2314yes—
551#394C2314yes—
552#394C2314yes—
553#394C2314yes—
554#394C2314yes—
555#394C2314yes—
556#394C2314yes—
557#394C2314yes—
558#394C2314yes—
559#394C2314yes—
560#394C2314yes—
561#394C2314yes—
562#394C2314yes—
563#393C2314yes—
564#393C2314yes—
565#393C2314yes—
566#393C2314yes—
567#393C2314yes—
568#393C2314yes—
569#393C2314yes—
570#393C2314yes—
571#392C2314yes—
572#392C2314yes—
573#392C2314yes—
574#392C2314yes—
575#392C2314yes—
576#392C2314yes—
577#392C2314yes—
578#392C2314yes—
579#392C2314yes—
580#391C2314yes—
581#391C2312yes—
582#391C2312yes—
583#391C2312yes—
584#391C2312yes—
585#391C2312yes—
586#391C2312yes—
587#391C2314yes—
588#391C2314yes—
589#391C2312yes—
590#391C2312yes—
591#391C2312yes—
592#391C2312yes—
593#391C2312yes—
594#391C2312yes—
595#391C2314yes—
596#391C2314yes—
597#390C2314yes—
598#390C2312yes—
599#390C2312yes—
600#390C2312yes—
601#390C2312yes—
602#390C2312yes—
603#390C2312yes—
604#390C2314yes—
605#390C2314yes—
606#390C2314yes—
607#390C2314yes—
608#390C2314yes—
609#390C2314yes—
610#389C2314yes—
611#389C2314yes—
612#389C2312yes—
613#389C2314yes—
614#389C2312yes—
615#389C2312yes—
616#389C2314yes—
617#389C2314yes—
618#389C2312yes—
619#389C2312yes—
620#389C2312yes—
621#389C2312yes—
622#389C2312yes—
623#389C2312yes—
624#389C2312yes—
625#389C2314yes—
626#389C2314yes—
627#389C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2314yes—
655#388C2314yes—
656#388C2314yes—
657#388C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#384C2311yescharacteristic
721#384C2311yescharacteristic
722#384C2312yes—
723#384C2314yes—
724#382C2312yes—
725#382C2312yes—
726#382C2314yes—
727#382C2312yes—
728#382C2312yes—
729#382C2312yes—
730#382C2312yes—
731#381C2314yes—
732#381C2314yes—
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2314yes—
742#380C2312yes—
743#380C2312yes—
744#380C2312yes—
745#380C2312yes—
746#380C2314yes—
747#380C2314yes—
748#380C2314yes—
749#380C2314yes—
750#380C2314yes—
751#380C2312yes—
752#380C2312yes—
753#379C2314yes—
754#379C2314yes—
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2314yes—
761C4×C4⋊C4C2314yes—
762C4×C4⋊C4C2314yes—
763C4×C22⋊C4C2314yes—
764C4×C22⋊C4C2314yes—
765C4×C22⋊C4C2314yes—
766C4×C22⋊C4C2314yes—
767C4×C22⋊C4C2314yes—
768C4×C22⋊C4C2314yes—
769C4×C22⋊C4C2314yes—
770C4×C22⋊C4C2314yes—
771C2×#95C2312yes—
772C2×#95C2312yes—
773C2×#95C2314yes—
774C2×#95C2312yes—
775C2×#95C2314yes—
776C2×#95C2312yes—
777C25C2411yescharacteristic
778C25C2412yes—
779C2×#41—24no—
780C2×#41—28no—
781C2×#41—24no—
782C2×#41—28no—
783C2×#41—28no—
784C2×#41—28no—
785C2×#41—28no—
786C2×#41—44no—
787C2×#41—42no—
788C2×#41—42no—
789C2×#41—44no—
790C2×#41—42no—
791C2×#41—42no—
792C2×#41—44no—
793C2×#41—44no—
794C22×Q8—24no—
795C22×Q8—28no—
796C22×Q8—42no—
797C22×Q8—44no—
798C22×Q8—42no—
799C22×Q8—44no—
800C22×Q8C2412yes—
801C22×Q8C2412yes—
802C22×Q8C2412yes—
803C22×Q8C2412yes—
804C22×Q8C2411yescharacteristic
805C22×Q8C2412yes—
806C22×Q8C2412yes—
807C22×Q8C2414yes—
808C22×Q8C2411yescharacteristic
809C22×D4—24no—
810C22×D4—42no—
811C22×D4—42no—
812C22×D4—44no—
813C22×D4—44no—
814C22×D4—44no—
815C22×D4C2412yes—
816C22×D4C2412yes—
817C22×D4C2412yes—
818C22×D4C2412yes—
819C22×D4C2412yes—
820C22×D4C2412yes—
821C22×D4C2412yes—
822C22×D4C2412yes—
823C22×D4C2412yes—
824C22×D4C2411yescharacteristic
825C22×D4C2414yes—
826C22×D4C2414yes—
827C22×D4C2412yes—
828C22×D4C2414yes—
829C22×D4C2414yes—
830C22×D4C2414yes—
831C22×D4C2414yes—
832C22×D4C2411yescharacteristic
833C23×C4—24no—
834C23×C4—24no—
835C23×C4—24no—
836C23×C4—24no—
837C23×C4—24no—
838C23×C4—42no—
839C23×C4—42no—
840C23×C4—42no—
841C23×C4—42no—
842C23×C4C2411yescharacteristic
843C23×C4C2412yes—
844C23×C4C2411yescharacteristic
845C23×C4C2411yescharacteristic
846C23×C4C2411yescharacteristic
847C23×C4C2412yes—
848C23×C4C2412yes—
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2411yescharacteristic
860C23×C4C2411yescharacteristic
861C23×C4C2412yes—
862C23×C4C2411yescharacteristic
863C23×C4C2411yescharacteristic
864C23×C4C2412yes—
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2414yes—
868C23×C4C2414yes—
869C23×C4C2414yes—
870C23×C4C2411yescharacteristic
871C23×C4C2414yes—
872C23×C4C2411yescharacteristic
873C4⋊Q8—24no—
874C4⋊Q8—24no—
875C4⋊Q8—24no—
876C4⋊Q8—216no—
877C4⋊Q8—24no—
878C4⋊Q8—24no—
879C4⋊Q8—28no—
880C4⋊Q8—48no—
881#127—24no—
882#126—28no—
883#126—216no—
884#126—216no—
885#126—216no—
886#126—28no—
887#126—28no—
888#126C2×D4116yescomplemented
889#125—28no—
890#125—28no—
891#125—24no—
892#125—28no—
893#125C2×D418yescomplemented
894#124—28no—
895#124—28no—
896#124—216no—
897#124—216no—
898#124—28no—
899#124—28no—
900#124—28no—
901#124—28no—
902#124—24no—
903#124—28no—
904#124—48no—
905#124C2×D418yescomplemented
906#123—28no—
907#123—28no—
908#123—28no—
909#123—216no—
910#123—28no—
911#123—28no—
912#123—216no—
913#123—216no—
914#123—216no—
915#123—48no—
916#123—48no—
917#123—48no—
918#123C2×D4116yes—
919C22⋊Q8—24no—
920C22⋊Q8—216no—
921C22⋊Q8—24no—
922C22⋊Q8—28no—
923C22⋊Q8—28no—
924C22⋊Q8—28no—
925C22⋊Q8—28no—
926C22⋊Q8—28no—
927C22⋊Q8—28no—
928C22⋊Q8—28no—
929C22⋊Q8—28no—
930C22⋊Q8—24no—
931C22⋊Q8—216no—
932C22⋊Q8—216no—
933C22⋊Q8—216no—
934C22⋊Q8—216no—
935C22⋊Q8—28no—
936C22⋊Q8—216no—
937C22⋊Q8—216no—
938C22⋊Q8—44no—
939C22⋊Q8—44no—
940C22⋊Q8—48no—
941C22⋊Q8—44no—
942C22⋊Q8—44no—
943C22⋊Q8—44no—
944C22⋊Q8—44no—
945C22⋊Q8—44no—
946C22⋊Q8—44no—
947C22⋊Q8—44no—
948C22⋊Q8—44no—
949C22⋊Q8C2×D418yes—
950#121—24no—
951#121—28no—
952#121—216no—
953#121—24no—
954#121—28no—
955#121—28no—
956#121—24no—
957#121—28no—
958#121—28no—
959#121—28no—
960#121—216no—
961#121—44no—
962#121—48no—
963#121—48no—
964#121—48no—
965#121—48no—
966#121—48no—
967#121—44no—
968#121—44no—
969#121—44no—
970#121—44no—
971#121C2×D418yes—
972#120—28no—
973#120—216no—
974#120—28no—
975#120—48no—
976C4×Q8—24no—
977C4×Q8—28no—
978C4×Q8—28no—
979C4×Q8—28no—
980C4×Q8—24no—
981C4×Q8—28no—
982C4×Q8—24no—
983C4×Q8—28no—
984C4×Q8—28no—
985C4×Q8—28no—
986C4×Q8C2×D418yescomplemented
987C4×D4—28no—
988C4×D4—24no—
989C4×D4—216no—
990C4×D4—28no—
991C4×D4—28no—
992C4×D4—28no—
993C4×D4—28no—
994C4×D4—28no—
995C4×D4—28no—
996C4×D4—24no—
997C4×D4—28no—
998C4×D4—28no—
999C4×D4—28no—
1000C4×D4—28no—
1001C4×D4—28no—
1002C4×D4—28no—
1003C4×D4—28no—
1004C4×D4—216no—
1005C4×D4—28no—
1006C4×D4—24no—
1007C4×D4—28no—
1008C4×D4—48no—
1009C4×D4—48no—
1010C4×D4C2×D4116yes—
1011C4×D4C2×D418yescomplemented
1012#117—28no—
1013#117—24no—
1014#117—24no—
1015#117—28no—
1016#117—28no—
1017#117—216no—
1018#117—28no—
1019#117—28no—
1020#117—28no—
1021#117—28no—
1022#117—28no—
1023#117—44no—
1024#117—44no—
1025#117C2×D4116yescomplemented
1026C2×C4⋊C4—42no—
1027C2×C4⋊C4—42no—
1028C2×C4⋊C4—44no—
1029C2×C4⋊C4—44no—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2411yescharacteristic
1039C2×C4⋊C4C2411yescharacteristic
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2414yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2414yes—
1053C2×C4⋊C4C2414yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2414yes—
1058C2×C4⋊C4C2412yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2412yes—
1061C2×C4⋊C4C2412yes—
1062C2×C4⋊C4C2414yes—
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2414yes—
1065C2×C4⋊C4C2412yes—
1066C2×C4⋊C4C2412yes—
1067C2×C4⋊C4C2414yes—
1068C2×C4⋊C4C2414yes—
1069C2×C4⋊C4C2414yes—
1070C2×C4⋊C4C2414yes—
1071C2×C4⋊C4C2414yes—
1072C2×C4⋊C4C2414yes—
1073C2×C4⋊C4C2412yes—
1074C2×C4⋊C4C2412yes—
1075C2×C4⋊C4C2414yes—
1076C2×C4⋊C4C2414yes—
1077C2×C4⋊C4C2414yes—
1078C2×C4⋊C4C2414yes—
1079C2×C4⋊C4C2412yes—
1080C2×C4⋊C4C2411yescharacteristic
1081C2×C4⋊C4C2411yescharacteristic
1082C2×C4⋊C4C2412yes—
1083C2×C4⋊C4C2412yes—
1084C2×C4⋊C4C2412yes—
1085C2×C22⋊C4—28no—
1086C2×C22⋊C4—28no—
1087C2×C22⋊C4—28no—
1088C2×C22⋊C4—216no—
1089C2×C22⋊C4—44no—
1090C2×C22⋊C4—44no—
1091C2×C22⋊C4—44no—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2414yes—
1118C2×C22⋊C4C2414yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2414yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2414yes—
1134C2×C22⋊C4C2414yes—
1135C2×C22⋊C4C2414yes—
1136C2×C22⋊C4C2414yes—
1137C2×C22⋊C4C2414yes—
1138C2×C22⋊C4C2414yes—
1139C2×C22⋊C4C2414yes—
1140C2×C22⋊C4C2414yes—
1141C2×C22⋊C4C2414yes—
1142C2×C22⋊C4C2414yes—
1143C2×C22⋊C4C2412yes—
1144C2×C22⋊C4C2412yes—
1145C2×C22⋊C4C2412yes—
1146C2×C22⋊C4C2412yes—
1147C2×C22⋊C4C2412yes—
1148C2×C42—28no—
1149C2×C42—24no—
1150C2×C42—24no—
1151C2×C42—24no—
1152C2×C42—28no—
1153C2×C42—24no—
1154C2×C42—24no—
1155C2×C42—24no—
1156C2×C42—24no—
1157C2×C42—24no—
1158C2×C42—24no—
1159C2×C42—24no—
1160C2×C42—24no—
1161C2×C42C2×D418yes—
1162C2×C42C2411yescharacteristic
1163C2×C42C2411yescharacteristic
1164C2×C42C2412yes—
1165C2×C42C2412yes—
1166C2×C42C2412yes—
1167C2×C42C2412yes—
1168C2×C42C2412yes—
1169C2×C42C2414yes—
1170C2×C42C2414yes—
1171C2×C42C2411yescharacteristic
1172C2×C42C2411yescharacteristic
1173C2×C42C2411yescharacteristic
1174C2×C42C2411yescharacteristic
1175C2×C42C2411yescharacteristic
1176C2×C42C2411yescharacteristic
1177C2×C42C2411yescharacteristic
1178C2×C42C2411yescharacteristic
1179C2×C42C2411yescharacteristic
1180C2×C42C2411yescharacteristic
1181C2×C42C2414yes—
1182C2×C42C2414yes—
1183C2×C42C2414yes—
1184C2×C42C2414yes—
1185C2×C42C2411yescharacteristic
1186C2×C42C2412yes—
1187C2×C42C2411yescharacteristic
1188C2×C42C2411yescharacteristic
1189C2×C42C2411yescharacteristic
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216#95C2414yes—
1217#95C2414yes—
1218#95C2414yes—
1219#95C2414yes—
1220#95C2414yes—
1221#95C2414yes—
1222#95C2414yes—
1223#95C2414yes—
1224#95C2414yes—
1225#95C2414yes—
1226C24—22no—
1227C24—22no—
1228C24—22no—
1229C24—22no—
1230C24—22no—
1231C24—24no—
1232C24—24no—
1233C24—24no—
1234C24—41no—
1235C24—41no—
1236C24—42no—
1237C24—42no—
1238C24—42no—
1239C24—42no—
1240C24C2514yes—
1241C24C2512yes—
1242C24C2512yes—
1243C24C2511yescharacteristic
1244C24C2511yescharacteristic
1245C24C2511yescharacteristic
1246#41—432no—
1247#41—432no—
1248#41—416no—
1249#41—416no—
1250#41—816no—
1251C2×Q8—24no—
1252C2×Q8—24no—
1253C2×Q8—22no—
1254C2×Q8—24no—
1255C2×Q8—24no—
1256C2×Q8—24no—
1257C2×Q8—28no—
1258C2×Q8—24no—
1259C2×Q8—24no—
1260C2×Q8—24no—
1261C2×Q8—24no—
1262C2×Q8—24no—
1263C2×Q8—24no—
1264C2×Q8—24no—
1265C2×Q8—42no—
1266C2×Q8—41no—
1267C2×Q8—41no—
1268C2×Q8—42no—
1269C2×Q8—41no—
1270C2×Q8—41no—
1271C2×Q8—42no—
1272C2×Q8—42no—
1273C2×Q8—42no—
1274C2×Q8—44no—
1275C2×Q8—42no—
1276C2×Q8—44no—
1277C2×Q8—88no—
1278C2×Q8—816no—
1279C2×Q8C22×D414yes—
1280C2×D4—24no—
1281C2×D4—24no—
1282C2×D4—24no—
1283C2×D4—24no—
1284C2×D4—24no—
1285C2×D4—24no—
1286C2×D4—24no—
1287C2×D4—24no—
1288C2×D4—24no—
1289C2×D4—24no—
1290C2×D4—24no—
1291C2×D4—24no—
1292C2×D4—24no—
1293C2×D4—28no—
1294C2×D4—28no—
1295C2×D4—28no—
1296C2×D4—28no—
1297C2×D4—24no—
1298C2×D4—24no—
1299C2×D4—22no—
1300C2×D4—24no—
1301C2×D4—24no—
1302C2×D4—24no—
1303C2×D4—24no—
1304C2×D4—24no—
1305C2×D4—24no—
1306C2×D4—42no—
1307C2×D4—41no—
1308C2×D4—41no—
1309C2×D4—42no—
1310C2×D4—42no—
1311C2×D4—41no—
1312C2×D4—41no—
1313C2×D4—42no—
1314C2×D4—42no—
1315C2×D4—42no—
1316C2×D4—44no—
1317C2×D4—44no—
1318C2×D4—42no—
1319C2×D4—44no—
1320C2×D4—44no—
1321C2×D4—44no—
1322C2×D4—44no—
1323C2×D4—44no—
1324C2×D4—42no—
1325C2×D4—44no—
1326C2×D4—44no—
1327C2×D4—44no—
1328C2×D4—44no—
1329C2×D4—44no—
1330C2×D4—44no—
1331C2×D4—44no—
1332C2×D4—88no—
1333C2×D4—816no—
1334C2×D4C22×D418yes—
1335C2×D4C22×D414yes—
1336C22×C4—22no—
1337C22×C4—22no—
1338C22×C4—22no—
1339C22×C4—22no—
1340C22×C4—22no—
1341C22×C4—22no—
1342C22×C4—22no—
1343C22×C4—22no—
1344C22×C4—24no—
1345C22×C4—22no—
1346C22×C4—22no—
1347C22×C4—22no—
1348C22×C4—24no—
1349C22×C4—22no—
1350C22×C4—22no—
1351C22×C4—24no—
1352C22×C4—24no—
1353C22×C4—22no—
1354C22×C4—22no—
1355C22×C4—24no—
1356C22×C4—28no—
1357C22×C4—24no—
1358C22×C4—24no—
1359C22×C4—22no—
1360C22×C4—22no—
1361C22×C4—22no—
1362C22×C4—22no—
1363C22×C4—22no—
1364C22×C4—22no—
1365C22×C4—22no—
1366C22×C4—22no—
1367C22×C4—22no—
1368C22×C4—22no—
1369C22×C4—24no—
1370C22×C4—24no—
1371C22×C4—24no—
1372C22×C4—22no—
1373C22×C4—22no—
1374C22×C4—22no—
1375C22×C4—24no—
1376C22×C4—22no—
1377C22×C4—22no—
1378C22×C4—22no—
1379C22×C4—22no—
1380C22×C4—24no—
1381C22×C4—24no—
1382C22×C4—22no—
1383C22×C4—24no—
1384C22×C4—24no—
1385C22×C4—22no—
1386C22×C4—22no—
1387C22×C4—24no—
1388C22×C4—28no—
1389C22×C4—28no—
1390C22×C4—41no—
1391C22×C4—41no—
1392C22×C4—41no—
1393C22×C4—41no—
1394C22×C4—41no—
1395C22×C4—41no—
1396C22×C4—41no—
1397C22×C4—41no—
1398C22×C4—41no—
1399C22×C4—41no—
1400C22×C4—41no—
1401C22×C4—41no—
1402C22×C4—41no—
1403C22×C4—41no—
1404C22×C4—42no—
1405C22×C4—42no—
1406C22×C4—42no—
1407C22×C4—42no—
1408C22×C4—416no—
1409C22×C4—416no—
1410C22×C4—42no—
1411C22×C4—42no—
1412C22×C4—42no—
1413C22×C4—42no—
1414C22×C4—44no—
1415C22×C4—44no—
1416C22×C4—44no—
1417C22×C4—44no—
1418C22×C4—42no—
1419C22×C4—44no—
1420C22×C4—42no—
1421C22×C4—44no—
1422C22×C4—44no—
1423C22×C4—44no—
1424C22×C4—44no—
1425C22×C4—416no—
1426C22×C4C22×D414yes—
1427C22×C4C22×D414yes—
1428C22×C4C22×D418yes—
1429C22×C4C22×D414yes—
1430C22×C4H(5,𝔽2)14yes—
1431C22×C42−1+414yes—
1432C22×C4C2514yes—
1433C22×C4C2514yes—
1434C22×C4C2514yes—
1435C22×C4C2512yes—
1436C22×C4C2514yes—
1437C22×C4C2511yescharacteristic
1438C22×C4C2514yes—
1439C22×C4C2512yes—
1440C22×C4C2514yes—
1441C22×C4C2514yes—
1442C22×C4C2511yescharacteristic
1443C22×C4C2512yes—
1444C22×C4C2511yescharacteristic
1445C22×C4C2511yescharacteristic
1446C22×C4C2512yes—
1447C22×C4C2511yescharacteristic
1448C22×C4C2511yescharacteristic
1449C22×C4C2512yes—
1450C22×C4C2512yes—
1451C22×C4C2511yescharacteristic
1452C22×C4C2511yescharacteristic
1453C22×C4C2511yescharacteristic
1454C22×C4C2511yescharacteristic
1455C22×C4C2511yescharacteristic
1456C22×C4C2511yescharacteristic
1457C4⋊C4—24no—
1458C4⋊C4—24no—
1459C4⋊C4—24no—
1460C4⋊C4—24no—
1461C4⋊C4—22no—
1462C4⋊C4—22no—
1463C4⋊C4—24no—
1464C4⋊C4—24no—
1465C4⋊C4—24no—
1466C4⋊C4—24no—
1467C4⋊C4—24no—
1468C4⋊C4—24no—
1469C4⋊C4—24no—
1470C4⋊C4—24no—
1471C4⋊C4—28no—
1472C4⋊C4—24no—
1473C4⋊C4—24no—
1474C4⋊C4—24no—
1475C4⋊C4—28no—
1476C4⋊C4—28no—
1477C4⋊C4—28no—
1478C4⋊C4—28no—
1479C4⋊C4—28no—
1480C4⋊C4—24no—
1481C4⋊C4—24no—
1482C4⋊C4—24no—
1483C4⋊C4—24no—
1484C4⋊C4—28no—
1485C4⋊C4—28no—
1486C4⋊C4—28no—
1487C4⋊C4—24no—
1488C4⋊C4—42no—
1489C4⋊C4—44no—
1490C4⋊C4—42no—
1491C4⋊C4—44no—
1492C4⋊C4—42no—
1493C4⋊C4—42no—
1494C4⋊C4—44no—
1495C4⋊C4—44no—
1496C4⋊C4—44no—
1497C4⋊C4—44no—
1498C4⋊C4—42no—
1499C4⋊C4—42no—
1500C4⋊C4—44no—
1501C4⋊C4—44no—
1502C4⋊C4—44no—
1503C4⋊C4—44no—
1504C4⋊C4—44no—
1505C4⋊C4—44no—
1506C4⋊C4C22×D418yes—
1507C4⋊C4C22×D414yes—
1508C4⋊C4C22×D418yes—
1509C4⋊C4C22×D414yes—
1510C4⋊C4C22×D418yes—
1511C4⋊C4C22×D418yes—
1512C22⋊C4—28no—
1513C22⋊C4—24no—
1514C22⋊C4—24no—
1515C22⋊C4—24no—
1516C22⋊C4—28no—
1517C22⋊C4—28no—
1518C22⋊C4—28no—
1519C22⋊C4—28no—
1520C22⋊C4—28no—
1521C22⋊C4—28no—
1522C22⋊C4—28no—
1523C22⋊C4—28no—
1524C22⋊C4—28no—
1525C22⋊C4—28no—
1526C22⋊C4—28no—
1527C22⋊C4—24no—
1528C22⋊C4—24no—
1529C22⋊C4—24no—
1530C22⋊C4—24no—
1531C22⋊C4—24no—
1532C22⋊C4—24no—
1533C22⋊C4—24no—
1534C22⋊C4—24no—
1535C22⋊C4—24no—
1536C22⋊C4—24no—
1537C22⋊C4—28no—
1538C22⋊C4—28no—
1539C22⋊C4—28no—
1540C22⋊C4—28no—
1541C22⋊C4—28no—
1542C22⋊C4—28no—
1543C22⋊C4—44no—
1544C22⋊C4—44no—
1545C22⋊C4—44no—
1546C22⋊C4—44no—
1547C22⋊C4—44no—
1548C22⋊C4—44no—
1549C22⋊C4—44no—
1550C22⋊C4—44no—
1551C22⋊C4—44no—
1552C22⋊C4—44no—
1553C22⋊C4—44no—
1554C22⋊C4—44no—
1555C22⋊C4—44no—
1556C22⋊C4—44no—
1557C22⋊C4—44no—
1558C22⋊C4—44no—
1559C22⋊C4—44no—
1560C22⋊C4—44no—
1561C22⋊C4—44no—
1562C22⋊C4—44no—
1563C22⋊C4C22×D418yes—
1564C22⋊C4C22×D418yes—
1565C22⋊C4C22×D418yes—
1566C22⋊C4C22×D418yes—
1567C22⋊C4C22×D418yes—
1568C42—22no—
1569C42—22no—
1570C42—22no—
1571C42—22no—
1572C42—22no—
1573C42—22no—
1574C42—22no—
1575C42—22no—
1576C42—22no—
1577C42—22no—
1578C42—22no—
1579C42—22no—
1580C42—24no—
1581C42—24no—
1582C42—24no—
1583C42—24no—
1584C42—24no—
1585C42—28no—
1586C42—28no—
1587C42—44no—
1588C42—44no—
1589C42—44no—
1590C42—44no—
1591C42C22×D414yes—
1592C42C22×D414yes—
1593C42C22×D414yes—
1594C42C22×D414yes—
1595C42C22×D418yes—
1596C23—21no—
1597C23—21no—
1598C23—21no—
1599C23—21no—
1600C23—28no—
1601C23—21no—
1602C23—21no—
1603C23—21no—
1604C23—22no—
1605C23—21no—
1606C23—21no—
1607C23—22no—
1608C23—21no—
1609C23—21no—
1610C23—22no—
1611C23—22no—
1612C23—22no—
1613C23—21no—
1614C23—21no—
1615C23—22no—
1616C23—21no—
1617C23—21no—
1618C23—21no—
1619C23—24no—
1620C23—22no—
1621C23—24no—
1622C23—22no—
1623C23—24no—
1624C23—22no—
1625C23—24no—
1626C23—22no—
1627C23—22no—
1628C23—22no—
1629C23—24no—
1630C23—24no—
1631C23—24no—
1632C23—22no—
1633C23—44no—
1634C23—44no—
1635C23—44no—
1636C23—44no—
1637C23—44no—
1638C23—44no—
1639C23—48no—
1640C23—84no—
1641C23—84no—
1642C23—84no—
1643C23—84no—
1644C23—84no—
1645C23—84no—
1646C23C23×D414yes—
1647C23C23×D412yes—
1648C23C2×H(5,𝔽2)12yes—
1649C23C2×2−1+412yes—
1650C23#58512yes—
1651C23#58512yes—
1652C23C2611yescharacteristic
1653Q8—44no—
1654Q8—48no—
1655Q8—48no—
1656Q8—44no—
1657Q8—48no—
1658Q8—48no—
1659Q8—84no—
1660Q8—84no—
1661Q8—88no—
1662D4—216no—
1663D4—44no—
1664D4—48no—
1665D4—48no—
1666D4—48no—
1667D4—48no—
1668D4—44no—
1669D4—48no—
1670D4—48no—
1671D4—48no—
1672D4—48no—
1673D4—84no—
1674D4—88no—
1675D4—88no—
1676D4—88no—
1677D4—88no—
1678D4—88no—
1679D4—164no—
1680C2×C4—28no—
1681C2×C4—21no—
1682C2×C4—21no—
1683C2×C4—21no—
1684C2×C4—21no—
1685C2×C4—22no—
1686C2×C4—21no—
1687C2×C4—21no—
1688C2×C4—21no—
1689C2×C4—22no—
1690C2×C4—21no—
1691C2×C4—22no—
1692C2×C4—22no—
1693C2×C4—21no—
1694C2×C4—21no—
1695C2×C4—21no—
1696C2×C4—22no—
1697C2×C4—21no—
1698C2×C4—21no—
1699C2×C4—21no—
1700C2×C4—21no—
1701C2×C4—21no—
1702C2×C4—21no—
1703C2×C4—21no—
1704C2×C4—22no—
1705C2×C4—28no—
1706C2×C4—28no—
1707C2×C4—28no—
1708C2×C4—28no—
1709C2×C4—216no—
1710C2×C4—21no—
1711C2×C4—21no—
1712C2×C4—22no—
1713C2×C4—22no—
1714C2×C4—22no—
1715C2×C4—24no—
1716C2×C4—24no—
1717C2×C4—24no—
1718C2×C4—24no—
1719C2×C4—24no—
1720C2×C4—24no—
1721C2×C4—24no—
1722C2×C4—24no—
1723C2×C4—21no—
1724C2×C4—22no—
1725C2×C4—24no—
1726C2×C4—22no—
1727C2×C4—24no—
1728C2×C4—24no—
1729C2×C4—24no—
1730C2×C4—24no—
1731C2×C4—24no—
1732C2×C4—24no—
1733C2×C4—24no—
1734C2×C4—21no—
1735C2×C4—22no—
1736C2×C4—24no—
1737C2×C4—24no—
1738C2×C4—22no—
1739C2×C4—22no—
1740C2×C4—22no—
1741C2×C4—24no—
1742C2×C4—24no—
1743C2×C4—24no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—44no—
1747C2×C4—44no—
1748C2×C4—44no—
1749C2×C4—44no—
1750C2×C4—44no—
1751C2×C4—44no—
1752C2×C4—44no—
1753C2×C4—48no—
1754C2×C4—48no—
1755C2×C4—44no—
1756C2×C4—44no—
1757C2×C4—44no—
1758C2×C4—44no—
1759C2×C4—48no—
1760C2×C4—48no—
1761C2×C4—44no—
1762C2×C4—44no—
1763C2×C4—48no—
1764C2×C4—88no—
1765C2×C4—88no—
1766C2×C4—84no—
1767C2×C4—84no—
1768C2×C4—88no—
1769C2×C4—84no—
1770C2×C4—164no—
1771C2×C4C23×D412yes—
1772C2×C4C23×D414yes—
1773C2×C4C23×D412yes—
1774C2×C4C23×D412yes—
1775C2×C4C23×D412yes—
1776C2×C4C23×D412yes—
1777C2×C4C23×D414yes—
1778C2×C4C23×D414yes—
1779C2×C4C23×D412yes—
1780C2×C4C2×H(5,𝔽2)12yes—
1781C2×C4C2×H(5,𝔽2)12yes—
1782C2×C4C2×2−1+412yes—
1783C2×C4C2×2−1+412yes—
1784C2×C4#58512yes—
1785C2×C4#58512yes—
1786C22—22no—
1787C22—22no—
1788C22—22no—
1789C22—22no—
1790C22—22no—
1791C22—22no—
1792C22—22no—
1793C22—22no—
1794C22—24no—
1795C22—24no—
1796C22—22no—
1797C22—24no—
1798C22—22no—
1799C22—22no—
1800C22—22no—
1801C22—416no—
1802C22—42no—
1803C22—41no—
1804C22—41no—
1805C22—42no—
1806C22—41no—
1807C22—41no—
1808C22—41no—
1809C22—41no—
1810C22—41no—
1811C22—42no—
1812C22—42no—
1813C22—41no—
1814C22—42no—
1815C22—44no—
1816C22—42no—
1817C22—44no—
1818C22—42no—
1819C22—44no—
1820C22—42no—
1821C22—44no—
1822C22—42no—
1823C22—44no—
1824C22—44no—
1825C22—42no—
1826C22—42no—
1827C22—44no—
1828C22—168no—
1829C22#348914yes—
1830C22C24×D411yescharacteristic
1831C22C22×H(5,𝔽2)11yescharacteristic
1832C22C22×2−1+411yescharacteristic
1833C22C2×#58511yescharacteristic
1834C22C2×#58511yescharacteristic
1835C22C2×#58511yescharacteristic
1836C22C2×#58511yescharacteristic
1837C4—22no—
1838C4—22no—
1839C4—24no—
1840C4—22no—
1841C4—22no—
1842C4—22no—
1843C4—22no—
1844C4—24no—
1845C4—22no—
1846C4—22no—
1847C4—22no—
1848C4—24no—
1849C4—44no—
1850C4—41no—
1851C4—42no—
1852C4—44no—
1853C4—44no—
1854C4—42no—
1855C4—41no—
1856C4—42no—
1857C4—44no—
1858C4—44no—
1859C4—44no—
1860C4—44no—
1861C4#348814yes—
1862C2—24no—
1863C2—44no—
1864C2—42no—
1865C2—42no—
1866C2—82no—
1867C2—84no—
1868C2#6274311yescharacteristic
1869C2#6275211yescharacteristic
1870C2C2×#348811yescharacteristic
1871C2C2×#348911yescharacteristic
1872C2#6281111yescharacteristic
1873C2#6282411yescharacteristic
1874C2#6283511yescharacteristic
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×#3561C2semidirect
2. C2×#3444C2semidirect
3. #59108C2semidirect
4. #59007C2semidirect
5. #46227C2semidirect
6. #46224C2semidirect
7. #46134C2semidirect
8. #46133C2semidirect
9. #39719C2semidirect
10. #39335C2semidirect
11. #37806C2semidirect
12. #37761C2semidirect
13. #37752C2semidirect
14. #37738C2semidirect
15. #37697C2semidirect
16. #37688C2semidirect
17. #37651C2semidirect
18. #37648C2semidirect
19. #37555C2semidirect
20. #37546C2semidirect
21. #37379C2semidirect
22. #37280C2semidirect
23. #36625C2semidirect
24. C2×#2850C2semidirect
25. #36504C2semidirect
26. #36374C2semidirect
27. #36360C2semidirect
28. #36274C2semidirect
29. #35308C2semidirect
30. #35258C2semidirect
31. #34382C2semidirect
33. C2×#563C22semidirect
34. C2×#562C22semidirect
35. C2×#556C22semidirect
38. C2×#548C22semidirect
41. C2×#542C22semidirect
42. C2×#542C22semidirect
45. C2×#536C22semidirect
46. C2×#536C22semidirect
50. C2×#533C22semidirect
51. C2×#533C22semidirect
53. C2×#532C22semidirect
54. C2×#532C22semidirect
58. C2×#529C22semidirect
59. C2×#529C22semidirect
60. C2×#529C22semidirect
61. C2×#529C22semidirect
62. C2×#529C22semidirect
71. C2×C4×#41C22semidirect
72. C2×C4×#41C22semidirect
73. C2×C4×#41C22semidirect
75. #2857C22semidirect
76. #2857C22semidirect
77. #2857C22semidirect
78. #2857C22semidirect
79. #2857C22semidirect
82. #2855C22semidirect
83. #2854C22semidirect
84. #2851C22semidirect
85. #2851C22semidirect
94. #2850C22semidirect
97. #2822C22semidirect
98. #2820C22semidirect
99. #2820C22semidirect
100. #2819C22semidirect
101. #2729C22semidirect
102. #2728C22semidirect
103. #2727C22semidirect
104. #2723C22semidirect
105. #2723C22semidirect
106. #2720C22semidirect
107. #2718C22semidirect
108. #2716C22semidirect
109. #2712C22semidirect
110. #2710C22semidirect
111. #2706C22semidirect
112. #2704C22semidirect
113. #2703C22semidirect
114. #2702C22semidirect
115. #2696C22semidirect
116. #2695C22semidirect
117. #2692C22semidirect
120. #2681C22semidirect
121. #2681C22semidirect
122. #2680C22semidirect
123. #2677C22semidirect
124. #2677C22semidirect
125. #2676C22semidirect
127. #2674C22semidirect
128. #2673C22semidirect
129. #2672C22semidirect
131. #2671C22semidirect
132. #2671C22semidirect
133. #2662C22semidirect
136. #2637C22semidirect
137. #2628C22semidirect
139. #2621C22semidirect
140. #2621C22semidirect
142. #2620C22semidirect
143. #2620C22semidirect
145. #2616C22semidirect
147. #2592C22semidirect
148. #2592C22semidirect
149. #2582C22semidirect
150. #2581C22semidirect
151. #2580C22semidirect
152. #2568C22semidirect
153. #2560C22semidirect
154. #2555C22semidirect
155. #2542C22semidirect
157. #2540C22semidirect
159. #2536C22semidirect
160. #2536C22semidirect
161. #2519C22semidirect
163. #2491C22semidirect
164. #2479C22semidirect
165. #2479C22semidirect
166. #2477C22semidirect
167. #2477C22semidirect
168. #2476C22semidirect
169. #2475C22semidirect
170. #2474C22semidirect
172. #2471C22semidirect
173. #2469C22semidirect
174. #2467C22semidirect
175. #2467C22semidirect
176. #2467C22semidirect
177. #2465C22semidirect
178. #2465C22semidirect
179. #2464C22semidirect
180. #2463C22semidirect
181. #2461C22semidirect
182. #2461C22semidirect
183. #2459C22semidirect
184. #2459C22semidirect
185. #2458C22semidirect
186. #2457C22semidirect
187. #2456C22semidirect
188. #2455C22semidirect
189. #2451C22semidirect
191. #2450C22semidirect
192. #2444C22semidirect
195. #2439C22semidirect
197. #2438C22semidirect
199. #2430C22semidirect
200. #2429C22semidirect
201. #2429C22semidirect
202. #2427C22semidirect
203. #2427C22semidirect
204. #2425C22semidirect
205. #2425C22semidirect
206. #2425C22semidirect
207. #2425C22semidirect
209. #2423C22semidirect
214. #2417C22semidirect
216. #2415C22semidirect
217. #2414C22semidirect
221. #2409C22semidirect
222. #2409C22semidirect
226. #2407C22semidirect
227. #2407C22semidirect
229. #2382C22semidirect
230. #2379C22semidirect
231. #2364C22semidirect
232. #2363C22semidirect
234. #2359C22semidirect
236. #2355C22semidirect
237. #2354C22semidirect
239. #2352C22semidirect
244. #2334C22semidirect
248. #2323C22semidirect
249. #2317C22semidirect
250. #2314C22semidirect
251. C4×C22⋊Q8C22semidirect
252. C4×C22⋊Q8C22semidirect
253. C4×C22⋊Q8C22semidirect
254. C4×C22⋊Q8C22semidirect
255. C4×C22⋊Q8C22semidirect
256. C4×#121C22semidirect
257. #2297C22semidirect
260. C2×#391C22semidirect
318. #529D4semidirect
888. #126C2×D4semidirect
893. #125C2×D4semidirect
905. #124C2×D4semidirect
986. C4×Q8C2×D4semidirect
1011. C4×D4C2×D4semidirect
1025. #117C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35612
C2×#34442
#591082
#590072
#462272
#462242
#461342
#461332
#397192
#393352
#378062
#377612
#377522
#377382
#376972
#376882
#376512
#376482
#375552
#375462
#373792
#372802
#366252
C2×#28502
#365042
#363742
#363602
#362742
#353082
#352582
#343822