Finite Group Databasebeta

← #7652672

Subgroups — #7652672

Order 512.

5432 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42892C214yesmaximal, complemented
2#42866C214yesmaximal, complemented
3#42860C214yesmaximal, complemented
4#42843C214yesmaximal, complemented
5#42024C218yesmaximal, complemented
6#40194C214yesmaximal, complemented
7#40100C214yesmaximal, complemented
8#39786C214yesmaximal, complemented
9#39215C214yesmaximal, complemented
10#38488C218yesmaximal, complemented
11#35660C211yesmaximal, characteristic, complemented
12#35660C211yesmaximal, characteristic, complemented
13#35649C211yesmaximal, characteristic, complemented
14#35649C211yesmaximal, characteristic, complemented
15#35629C211yesmaximal, characteristic, complemented
16#35557C211yesmaximal, characteristic, complemented
17#35328C211yesmaximal, characteristic, complemented
18#35273C211yesmaximal, characteristic, complemented
19#35153C211yesmaximal, characteristic, complemented
20C2×#2565C211yesmaximal, characteristic, complemented
21#34744C211yesmaximal, characteristic, complemented
22#34744C211yesmaximal, characteristic, complemented
23#34268C211yesmaximal, characteristic, complemented
24#34268C211yesmaximal, characteristic, complemented
25#34257C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#537C2211yescharacteristic
29C2×#537C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#536C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C22×#125C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2857C2212yes—
40#2856C2212yes—
41#2854C2214yes—
42#2850C2212yes—
43#2850C2212yes—
44#2831C2218yes—
45#2829C2218yes—
46#2803C2218yes—
47#2800C2218yes—
48#2797C2218yes—
49#2787C2218yes—
50#2786C2218yes—
51#2781C2218yes—
52#2780C2218yes—
53#2775C2218yes—
54#2774C2218yes—
55#2768C2218yes—
56#2756C2218yes—
57#2751C2218yes—
58#2745C2218yes—
59#2714C2218yes—
60#2708C2218yes—
61#2695C2218yes—
62#2666C2218yes—
63#2661C2218yes—
64#2653C2218yes—
65#2652C2218yes—
66#2651C2218yes—
67#2648C2218yes—
68#2621C2212yes—
69#2620C2212yes—
70#2620C2212yes—
71#2619C2212yes—
72#2618C2214yes—
73#2597C2218yes—
74#2595C2218yes—
75#2591C2214yes—
76#2591C2214yes—
77#2578C2218yes—
78#2576C2218yes—
79#2574C2218yes—
80#2565C2214yes—
81#2565C2214yes—
82#2565C2214yes—
83#2565C2214yes—
84#2554C2218yes—
85#2543C2218yes—
86#2538C2214yes—
87#2537C2214yes—
88#2536C2214yes—
89#2535C2214yes—
90#2514C2214yes—
91#2513C2214yes—
92#2512C2214yes—
93#2511C2214yes—
94#2510C2218yes—
95#2504C2214yes—
96#2504C2214yes—
97#2497C2214yes—
98#2496C2214yes—
99#2495C2214yes—
100#2494C2214yes—
101#2490C2214yes—
102#2490C2214yes—
103#2490C2214yes—
104#2490C2214yes—
105#2489C2214yes—
106#2489C2214yes—
107#2489C2214yes—
108#2489C2214yes—
109#2481C2218yes—
110#2448C2212yes—
111#2448C2212yes—
112#2447C2212yes—
113#2447C2212yes—
114#2446C2212yes—
115#2446C2212yes—
116#2445C2212yes—
117#2445C2212yes—
118#2444C2214yes—
119#2444C2214yes—
120#2443C2214yes—
121#2443C2214yes—
122#2436C2212yes—
123#2436C2212yes—
124#2434C2212yes—
125#2434C2212yes—
126#2432C2212yes—
127#2432C2212yes—
128#2431C2212yes—
129#2431C2212yes—
130#2430C2218yes—
131#2430C2218yes—
132#2429C2214yes—
133#2429C2214yes—
134#2426C2214yes—
135#2426C2214yes—
136#2416C2218yes—
137#2409C2214yes—
138#2409C2214yes—
139#2407C2214yes—
140#2407C2214yes—
141#2395C2214yes—
142#2395C2214yes—
143C2×#398C2214yes—
144#2367C2214yes—
145#2367C2214yes—
146#2365C2214yes—
147#2365C2214yes—
148#2359C2218yes—
149#2359C2218yes—
150#2341C2214yes—
151#2341C2214yes—
152Q8×C22⋊C4C2214yes—
153Q8×C22⋊C4C2214yes—
154#2334C2218yes—
155#2333C2218yes—
156#2323C2214yes—
157#2323C2214yes—
158#2316C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2214yes—
162#2311C2211yescharacteristic
163#2311C2211yescharacteristic
164#2311C2211yescharacteristic
165#2311C2211yescharacteristic
166C4×C22⋊Q8C2214yes—
167C4×C22⋊Q8C2214yes—
168C4×#123C2214yes—
169C4×#123C2214yes—
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2214yes—
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179C2×#391C2211yescharacteristic
180C2×#391C2211yescharacteristic
181C2×#387C2214yes—
182C2×#384C2211yescharacteristic
183C2×#382C2211yescharacteristic
184#2274C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2311yescharacteristic
194C22×#41C2314yes—
195C22×#41C2312yes—
196C22×#41C2312yes—
197C23×Q8C2311yescharacteristic
198C23×Q8C2312yes—
199C23×Q8C2312yes—
200#537—44no—
201#537—44no—
202#537—44no—
203#536—28no—
204#536—28no—
205#532—44no—
206#532—44no—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#126C2318yes—
214C2×#125—44no—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#124C2312yes—
218C2×#124C2312yes—
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123C2314yes—
224C2×#123C2314yes—
225C2×#123C2314yes—
226C2×#123C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×#121C2318yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2314yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247#519—44no—
248C4×#41—44no—
249C4×#41—44no—
250C2×C4×Q8—44no—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2314yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2314yes—
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281C22×C42C2312yes—
282C22×C42C2312yes—
283C22×C42C2312yes—
284#401C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2314yes—
289#400C2318yes—
290#400C2318yes—
291#400C2314yes—
292#399C2314yes—
293#399C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2318yes—
300#398C2318yes—
301#398C2314yes—
302#397C2318yes—
303#397C2318yes—
304#397C2314yes—
305#397C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2314yes—
312#397C2318yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#395C2318yes—
322#395C2318yes—
323#394C2314yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2314yes—
330#394C2318yes—
331#394C2318yes—
332#394C2314yes—
333#394C2314yes—
334#394C2318yes—
335#393C2318yes—
336#393C2318yes—
337#392C2318yes—
338#392C2318yes—
339#392C2318yes—
340#391C2312yes—
341#391C2312yes—
342#391C2314yes—
343#391C2314yes—
344#391C2312yes—
345#391C2312yes—
346#391C2318yes—
347#391C2312yes—
348#391C2312yes—
349#391C2312yes—
350#391C2312yes—
351#391C2312yes—
352#391C2312yes—
353#391C2312yes—
354#391C2312yes—
355#391C2318yes—
356#391C2312yes—
357#391C2312yes—
358#391C2312yes—
359#391C2312yes—
360#390C2318yes—
361#390C2312yes—
362#390C2312yes—
363#390C2312yes—
364#390C2312yes—
365#390C2312yes—
366#390C2312yes—
367#390C2318yes—
368#390C2318yes—
369#390C2318yes—
370#390C2312yes—
371#390C2312yes—
372#390C2318yes—
373#390C2318yes—
374#390C2312yes—
375#390C2312yes—
376#390C2312yes—
377#390C2312yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2312yes—
382#389C2318yes—
383#389C2318yes—
384#389C2318yes—
385#389C2318yes—
386#389C2312yes—
387#389C2312yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2314yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2314yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2314yes—
422#386C2312yes—
423#386C2314yes—
424#386C2312yes—
425#386C2314yes—
426#386C2314yes—
427#386C2314yes—
428#386C2314yes—
429#386C2314yes—
430#386C2318yes—
431#386C2318yes—
432#386C2314yes—
433#386C2318yes—
434#386C2314yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2312yes—
439#386C2312yes—
440#386C2312yes—
441#386C2312yes—
442#386C2312yes—
443#386C2314yes—
444#386C2314yes—
445#386C2312yes—
446#385C2314yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2314yes—
452#385C2314yes—
453#385C2318yes—
454#385C2318yes—
455#385C2314yes—
456#384C2312yes—
457#384C2312yes—
458#384C2314yes—
459#383C2318yes—
460#382C2312yes—
461#382C2312yes—
462#382C2314yes—
463#382C2318yes—
464#382C2318yes—
465#381C2314yes—
466#381C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2318yes—
470#380C2318yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2318yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2314yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C2×#95C2314yes—
504C2×#95C2314yes—
505C2×#95C2314yes—
506C2×#95C2312yes—
5072−1+4—464no—
508C2×#41—28no—
509C2×#41—28no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—216no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—24no—
522C2×#41—24no—
523C2×#41—48no—
524C2×#41—48no—
525C2×#41—44no—
526C2×#41—44no—
527C2×#41—44no—
528C2×#41—44no—
529C22×Q8—28no—
530C22×Q8—28no—
531C22×Q8—24no—
532C22×Q8—24no—
533C22×Q8—44no—
534C22×Q8—44no—
535C22×Q8—44no—
536C22×Q8—44no—
537C22×Q8#4118yes—
538C22×Q8C2411yescharacteristic
539C22×Q8C2411yescharacteristic
540C22×Q8C2411yescharacteristic
541C22×Q8C2411yescharacteristic
542C22×Q8C2412yes—
543C22×Q8C2412yes—
544C22×Q8C2414yes—
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2411yescharacteristic
548C22×D4C2411yescharacteristic
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2411yescharacteristic
553C22×D4C2414yes—
554C22×D4C2414yes—
555C22×D4C2414yes—
556C22×D4C2414yes—
557C22×D4C2414yes—
558C22×D4C2414yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2411yescharacteristic
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2411yescharacteristic
570C23×C4C2412yes—
571C23×C4C2414yes—
572C23×C4C2414yes—
573C23×C4C2414yes—
574C23×C4C2414yes—
575C23×C4C2411yescharacteristic
576C4⋊Q8—28no—
577C4⋊Q8—28no—
578C4⋊Q8—42no—
579C4⋊Q8—42no—
580#127—42no—
581#127—42no—
582#126—416no—
583#125—48no—
584#125—48no—
585#124—28no—
586#124—28no—
587#124—42no—
588#124—42no—
589#124—42no—
590#124—42no—
591#123—216no—
592#123—216no—
593#123—48no—
594#123—48no—
595C22⋊Q8—216no—
596C22⋊Q8—216no—
597C22⋊Q8—44no—
598C22⋊Q8—44no—
599C22⋊Q8—44no—
600C22⋊Q8—44no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
603#121—416no—
604#121—44no—
605#121—44no—
606#121—44no—
607#121—44no—
608#121—44no—
609#121—44no—
610#121—48no—
611#121—48no—
612#121—48no—
613#121—48no—
614#121—48no—
615C4×Q8—48no—
616C4×Q8—48no—
617C4×Q8—44no—
618C4×Q8—44no—
619C4×Q8—48no—
620C4×Q8—48no—
621C4×D4—44no—
622C4×D4—44no—
623C4×D4—48no—
624C4×D4—48no—
625C4×D4—48no—
626C4×D4—48no—
627#117—24no—
628#117—24no—
629#117—24no—
630#117—24no—
631#117—44no—
632#117—44no—
633#117—48no—
634C2×C4⋊C4—24no—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—48no—
638C2×C4⋊C4—44no—
639C2×C4⋊C4—44no—
640C2×C4⋊C4—44no—
641C2×C4⋊C4—44no—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2418yes—
712C2×C42—24no—
713C2×C42—24no—
714C2×C42—24no—
715C2×C42—44no—
716C2×C42—44no—
717C2×C42—44no—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2418yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2418yes—
734C2×C42C2418yes—
735C2×C42C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771C24C2512yes—
772C24C2512yes—
773C24C2512yes—
774C24C2512yes—
775C24C2511yescharacteristic
776#41—464no—
777#41—432no—
778#41—432no—
779#41—416no—
780#41—416no—
781#41—416no—
782#41—416no—
783C2×Q8—232no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—28no—
787C2×Q8—22no—
788C2×Q8—22no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—22no—
794C2×Q8—22no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—22no—
799C2×Q8—22no—
800C2×Q8—22no—
801C2×Q8—44no—
802C2×Q8—44no—
803C2×Q8—432no—
804C2×Q8—432no—
805C2×Q8C2×#4118yes—
806C2×Q8C2×#4118yes—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—28no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—22no—
832C2×D4—28no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—48no—
844C2×D4—48no—
845C2×D4—48no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—28no—
858C22×C4—28no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—28no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—42no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—42no—
888C22×C4C2×#4118yes—
889C22×C4C2×#4114yes—
890C22×C4H(5,𝔽2)14yes—
891C22×C4H(5,𝔽2)14yes—
892C22×C4C2512yes—
893C22×C4C2512yes—
894C22×C4C2512yes—
895C22×C4C2514yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2514yes—
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2512yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2512yes—
906C22×C4C2512yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2512yes—
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—216no—
915C4⋊C4—216no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—216no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—28no—
928C4⋊C4—48no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—48no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—48no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—48no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—24no—
950C22⋊C4—216no—
951C22⋊C4—216no—
952C22⋊C4—28no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—48no—
968C22⋊C4—48no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—48no—
981C22⋊C4—48no—
982C42—24no—
983C42—24no—
984C42—22no—
985C42—22no—
986C42—22no—
987C42—22no—
988C42—24no—
989C42—24no—
990C42—24no—
991C42—24no—
992C42—24no—
993C42—24no—
994C42—44no—
995C42—44no—
996C42—48no—
997C42—48no—
998C42—48no—
999C42—48no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23C22×#4112yes—
1023C23C2×H(5,𝔽2)12yes—
1024C23C2×H(5,𝔽2)12yes—
1025C23C2611yescharacteristic
1026Q8—216no—
1027Q8—216no—
1028Q8—416no—
1029Q8—44no—
1030Q8—44no—
1031Q8—44no—
1032Q8—44no—
1033D4—416no—
1034D4—48no—
1035D4—48no—
1036D4—48no—
1037D4—48no—
1038D4—44no—
1039D4—44no—
1040D4—44no—
1041D4—44no—
1042D4—88no—
1043D4—88no—
1044D4—164no—
1045D4—164no—
1046D4—164no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—216no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—28no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—28no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—28no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—48no—
1098C2×C4—416no—
1099C2×C4—416no—
1100C2×C4—44no—
1101C2×C4—44no—
1102C2×C4—48no—
1103C2×C4—48no—
1104C2×C4—48no—
1105C2×C4—48no—
1106C2×C4—88no—
1107C2×C4—84no—
1108C2×C4—84no—
1109C2×C4—84no—
1110C2×C4—84no—
1111C2×C4—88no—
1112C2×C4#538116yes—
1113C2×C4C22×#4118yes—
1114C2×C4C22×#4112yes—
1115C2×C4C22×#4112yes—
1116C2×C4C2×H(5,𝔽2)12yes—
1117C2×C4C2×H(5,𝔽2)12yes—
1118C2×C4C2×H(5,𝔽2)12yes—
1119C2×C4C2×H(5,𝔽2)12yes—
1120C2×C4#58514yes—
1121C22—24no—
1122C22—22no—
1123C22—22no—
1124C22—24no—
1125C22—44no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—44no—
1142C22—44no—
1143C22—44no—
1144C22—44no—
1145C22C2×#53814yes—
1146C22C23×#4111yescharacteristic
1147C22C22×H(5,𝔽2)11yescharacteristic
1148C22C22×H(5,𝔽2)11yescharacteristic
1149C22C2×#58512yes—
1150C222−1+612yes—
1151C4—28no—
1152C4—24no—
1153C4—44no—
1154C4—44no—
1155C4—42no—
1156C4—44no—
1157C4—44no—
1158C4—42no—
1159C4—44no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—44no—
1166C4—44no—
1167C4—42no—
1168C4—42no—
1169C4C2×#53814yes—
1170C4C2×#53814yes—
1171C2—24no—
1172C2—82no—
1173C2—82no—
1174C2—82no—
1175C2—82no—
1176C2C22×#53811yescharacteristic
1177C2#6283611yescharacteristic
1178C2#6288711yescharacteristic
1179C2#6292712yes—
1180C2#6300712yes—
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. #42892C2semidirect
2. #42866C2semidirect
3. #42860C2semidirect
4. #42843C2semidirect
5. #42024C2semidirect
6. #40194C2semidirect
7. #40100C2semidirect
8. #39786C2semidirect
9. #39215C2semidirect
10. #38488C2semidirect
11. #35660C2semidirect
12. #35660C2semidirect
13. #35649C2semidirect
14. #35649C2semidirect
15. #35629C2semidirect
16. #35557C2semidirect
17. #35328C2semidirect
18. #35273C2semidirect
19. #35153C2semidirect
20. C2×#2565C2semidirect
21. #34744C2semidirect
22. #34744C2semidirect
23. #34268C2semidirect
24. #34268C2semidirect
25. #34257C2semidirect

Maximal subgroups

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

subgroupindex
#428922
#428662
#428602
#428432
#420242
#401942
#401002
#397862
#392152
#384882
#356602
#356492
#356292
#355572
#353282
#352732
#351532
C2×#25652
#347442
#342682
#342572