Finite Group Databasebeta

← #7643326

Subgroups — #7643326

Order 512.

6258 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39735C214yesmaximal, complemented
2#39352C214yesmaximal, complemented
3#39148C214yesmaximal, complemented
4#38942C214yesmaximal, complemented
5#38056C218yesmaximal, complemented
6#37662C218yesmaximal, complemented
7#37290C218yesmaximal, complemented
8#36624C211yesmaximal, characteristic, complemented
9C2×#2856C211yesmaximal, characteristic, complemented
10#35563C212yesmaximal, complemented
11#35541C212yesmaximal, complemented
12#35531C212yesmaximal, complemented
13#35514C212yesmaximal, complemented
14#35288C214yesmaximal, complemented
15#35286C211yesmaximal, characteristic, complemented
16#35278C214yesmaximal, complemented
17#35274C211yesmaximal, characteristic, complemented
18#34210C211yesmaximal, characteristic, complemented
19#34207C211yesmaximal, characteristic, complemented
20#34012C211yesmaximal, characteristic, complemented
21C2×#540C2218yescomplemented
22C2×#535C2212yes—
23C2×#535C2212yes—
24C2×#532C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C2×#525C2212yes—
27C22×#121C2214yes—
28C22×#121C2212yes—
29C2×#520C2212yes—
30C2×#518C2212yes—
31C23×C42C2211yescharacteristic
32#2867C2212yescomplemented
33#2859C2214yescomplemented
34#2858C2212yescomplemented
35#2857C2212yescomplemented
36#2856C2214yes—
37#2856C2214yes—
38#2856C2214yes—
39#2856C2214yes—
40#2856C2212yescomplemented
41#2854C2214yes—
42#2850C2214yescomplemented
43#2847C2214yes—
44#2756C22116yescomplemented
45#2753C22116yescomplemented
46#2749C22116yescomplemented
47#2706C22116yescomplemented
48#2703C22116yescomplemented
49#2699C22116yescomplemented
50#2688C22116yescomplemented
51#2671C22116yescomplemented
52#2657C2214yescomplemented
53#2647C2214yescomplemented
54#2644C2218yescomplemented
55#2641C2218yescomplemented
56#2624C2218yescomplemented
57#2619C2218yescomplemented
58#2571C2214yescomplemented
59#2552C2214yescomplemented
60#2541C2214yescomplemented
61#2541C2214yescomplemented
62#2537C2218yescomplemented
63#2535C2218yescomplemented
64#2534C2218yes—
65#2513C2218yescomplemented
66#2504C2214yescomplemented
67#2501C2214yescomplemented
68#2500C2214yescomplemented
69#2500C2214yescomplemented
70#2490C2218yescomplemented
71#2454C2218yescomplemented
72#2448C2218yescomplemented
73#2447C2218yescomplemented
74#2445C2218yescomplemented
75#2445C2218yescomplemented
76#2445C2218yescomplemented
77#2445C2218yescomplemented
78#2442C2218yes—
79#2433C2218yes—
80#2428C2218yescomplemented
81#2428C2218yescomplemented
82#2428C2218yescomplemented
83#2428C2218yescomplemented
84#2427C2218yescomplemented
85#2426C2218yescomplemented
86#2422C2218yescomplemented
87#2420C2218yescomplemented
88#2420C2218yescomplemented
89#2418C22116yes—
90#2416C2218yescomplemented
91#2414C2218yescomplemented
92#2412C22116yes—
93#2412C2218yes—
94#2410C2218yes—
95#2408C2218yes—
96#2366C2214yescomplemented
97#2366C2214yescomplemented
98#2361C2218yes—
99#2354C2214yescomplemented
100D4×C4⋊C4C2214yescomplemented
101D4×C22⋊C4C2218yes—
102#2328C2214yescomplemented
103#2328C2218yescomplemented
104#2326C2214yescomplemented
105#2324C2218yescomplemented
106#2319C2218yescomplemented
107#2317C2212yes—
108#2316C2212yes—
109#2311C2212yes—
110#2309C2212yes—
111C4×C4⋊Q8C2212yescomplemented
112C4×#127C2212yescomplemented
113C4×#127C2214yescomplemented
114C4×#121C2214yescomplemented
115C4×#121C2214yescomplemented
116#2297C2212yes—
117C2×#390C2214yes—
118C2×#390C2212yes—
119#2285C2211yescharacteristic
120#2285C2211yescharacteristic
121#2285C2211yescharacteristic
122#2285C2212yescomplemented
123#2285C2212yescomplemented
124C2×#384C2211yescharacteristic
125#2283C2214yes—
126#2283C2212yescomplemented
127#2283C2214yescomplemented
128#2283C2212yescomplemented
129#2280C2214yes—
130#2280C2211yescharacteristic
131#2280C2211yescharacteristic
132C4×#117C2211yescharacteristic
133C4×#117C2211yescharacteristic
134C4×#117C2214yescomplemented
135C22×#41C2312yes—
136C23×D4C2312yes—
137C23×D4C2314yes—
138C23×D4C2314yes—
139C24×C4C2311yescharacteristic
140C24×C4C2312yes—
141#540—432no—
142#535—48no—
143#535—48no—
144#532—28no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×#127—28no—
147C2×#127C2312yes—
148C2×#127C2311yescharacteristic
149C2×#127C2312yes—
150C2×#127C2314yes—
151C2×#127C2318yes—
152C2×#127C2318yes—
153C2×#127C2314yes—
154C2×#127C2314yes—
155C2×#125C2318yes—
156C2×#124C2312yes—
157C2×#124C2314yes—
158C2×#124C2314yes—
159#525—48no—
160C2×#123C2314yes—
161C2×#123C23116yes—
162C2×#123C23116yes—
163C2×C22⋊Q8C2314yes—
164C2×#121—48no—
165C2×#121—416no—
166C2×#121C2318yes—
167C2×#121C2314yes—
168C2×#121C2314yes—
169C2×#121C2314yes—
170C2×#121C2314yes—
171C2×#121C2318yes—
172C2×#121C2318yes—
173C2×#121C2318yes—
174C2×#121C2318yes—
175C2×#121C2318yes—
176C2×#121C23116yes—
177C2×#121C23116yes—
178C2×#121C2318yes—
179C2×#121C2314yes—
180C2×#121C2314yes—
181C2×#120C2314yes—
182C2×#120C2318yes—
183C2×#120C2318yes—
184#520—48no—
185#518—48no—
186C2×C4×Q8C2314yes—
187C2×C4×D4C2314yes—
188C2×C4×D4C2318yes—
189C2×C4×D4C2314yes—
190C2×C4×D4C2318yes—
191C2×C4×D4C2318yes—
192C2×C4×D4C2318yes—
193C2×C4×D4C2318yes—
194C2×C4×D4C2318yes—
195C2×C4×D4C2318yes—
196C2×#117C2311yescharacteristic
197C2×#117C2312yes—
198C2×#117C2311yescharacteristic
199C2×#117C2311yescharacteristic
200C2×#117C2311yescharacteristic
201C2×#117C2314yes—
202C2×#117C2314yes—
203C2×#117C2314yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2314yes—
206C22×C4⋊C4C2314yes—
207C22×C22⋊C4C2318yes—
208C22×C22⋊C4C2318yes—
209C22×C22⋊C4C2314yes—
210C22×C42—28no—
211C22×C42C2312yes—
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218#400C23116yes—
219#399C23116yes—
220#398C23116yes—
221#397C23116yes—
222#397C23116yes—
223#397C23116yes—
224#397C23116yes—
225#396C23116yes—
226#394C23116yes—
227#394C23116yes—
228#394C23116yes—
229#394C23116yes—
230#394C23116yes—
231#394C23116yes—
232#394C23116yes—
233#394C23116yes—
234#392C23116yes—
235#392C23116yes—
236#392C23116yes—
237#392C23116yes—
238#391C2314yes—
239#391C2314yes—
240#390C2318yes—
241#390C2314yes—
242#390C2318yes—
243#390C2318yes—
244#390C2318yes—
245#390C2314yes—
246#390C2314yes—
247#390C2318yes—
248#390C2318yes—
249#390C2318yes—
250#390C23116yes—
251#390C2314yes—
252#390C2314yes—
253#390C2314yes—
254#390C2314yes—
255#390C2314yes—
256#390C2318yes—
257#390C2318yes—
258#390C2318yes—
259#390C2318yes—
260#389C2318yes—
261#389C2318yes—
262#389C2318yes—
263#389C2318yes—
264#389C2318yes—
265#389C2314yes—
266#389C2318yes—
267#389C2314yes—
268#388C23116yes—
269#388C23116yes—
270#388C23116yes—
271#388C23116yes—
272#388C2318yes—
273#388C2318yes—
274#386C2318yes—
275#386C23116yes—
276#386C23116yes—
277#386C23116yes—
278#386C23116yes—
279#386C23116yes—
280#386C23116yes—
281#386C23116yes—
282#386C2318yes—
283#386C2318yes—
284#386C2318yes—
285#385C2318yes—
286#385C23116yes—
287#385C23116yes—
288#384C2312yes—
289#384C2312yes—
290#384C2314yes—
291#384C2314yes—
292#384C2312yes—
293#384C2312yes—
294#384C2311yescharacteristic
295#384C2311yescharacteristic
296#383C2314yes—
297#383C2314yes—
298#382C2314yes—
299#382C2318yes—
300#382C2312yes—
301#382C2312yes—
302#382C2314yes—
303#382C2314yes—
304#382C2311yescharacteristic
305#382C2311yescharacteristic
306#381C23116yes—
307#381C2312yes—
308#381C2314yes—
309#381C2314yes—
310#381C2312yes—
311#380C2318yes—
312#380C2318yes—
313#380C23116yes—
314#380C2314yes—
315#380C2314yes—
316#380C2314yes—
317#380C2314yes—
318#380C2312yes—
319#380C2314yes—
320#380C2312yes—
321#380C2314yes—
322#380C2314yes—
323#380C2312yes—
324#380C2312yes—
325#379C2318yes—
326#379C2312yes—
327#379C2312yes—
328C4×C4⋊C4C2318yes—
329C4×C4⋊C4C2312yes—
330C4×C4⋊C4C2314yes—
331C4×C4⋊C4C2312yes—
332C4×C4⋊C4C2312yes—
333C4×C4⋊C4C2314yes—
334C4×C4⋊C4C2314yes—
335C4×C4⋊C4C2314yes—
336C4×C4⋊C4C2314yes—
337C4×C4⋊C4C2312yes—
338C4×C22⋊C4C2314yes—
339C4×C22⋊C4C2314yes—
340C4×C22⋊C4C2314yes—
341C4×C22⋊C4C2314yes—
342C4×C22⋊C4C2314yes—
343C4×C22⋊C4C2314yes—
344C4×C22⋊C4C2314yes—
345C4×C22⋊C4C2314yes—
346#376C2314yes—
347#376C2312yes—
348#376C2314yes—
349#376C2312yes—
350C43C2312yes—
351C43C2312yes—
352C25C2411yescharacteristic
353C25C2414yes—
354C2×#41—28no—
355C2×#41—28no—
356C2×#41—28no—
357C22×Q8C2412yes—
358C22×D4—28no—
359C22×D4—216no—
360C22×D4—28no—
361C22×D4—28no—
362C22×D4—48no—
363C22×D4—48no—
364C22×D4—48no—
365C22×D4—416no—
366C22×D4C2414yes—
367C22×D4C2414yes—
368C22×D4C2414yes—
369C22×D4C2414yes—
370C22×D4C2412yes—
371C22×D4C2418yes—
372C22×D4C2418yes—
373C22×D4C24116yes—
374C22×D4C2418yes—
375C22×D4C2418yes—
376C22×D4C24116yes—
377C22×D4C2418yes—
378C23×C4—28no—
379C23×C4—24no—
380C23×C4—28no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—44no—
384C23×C4C2411yescharacteristic
385C23×C4C2414yes—
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2414yes—
395C23×C4C24116yes—
396C23×C4C2418yes—
397C23×C4C2411yescharacteristic
398C4⋊Q8—24no—
399#127—216no—
400#127—28no—
401#127—28no—
402#127—24no—
403#127—416no—
404#127—48no—
405#127—48no—
406#127—416no—
407#125—416no—
408#124—28no—
409#124—48no—
410#124—48no—
411#123—432no—
412#123—432no—
413#123—48no—
414C22⋊Q8—48no—
415#121—216no—
416#121—232no—
417#121—216no—
418#121—416no—
419#121—432no—
420#121—432no—
421#121—416no—
422#121—416no—
423#121—416no—
424#121—48no—
425#121—48no—
426#121—48no—
427#121—48no—
428#121—416no—
429#121—416no—
430#120—48no—
431#120—416no—
432#120—416no—
433C4×Q8—48no—
434C4×D4—216no—
435C4×D4—416no—
436C4×D4—416no—
437C4×D4—416no—
438C4×D4—48no—
439C4×D4—416no—
440C4×D4—416no—
441C4×D4—416no—
442C4×D4—416no—
443#117—24no—
444#117—28no—
445#117—24no—
446#117—24no—
447#117—24no—
448#117—216no—
449#117—48no—
450#117—48no—
451C2×C4⋊C4—28no—
452C2×C4⋊C4—48no—
453C2×C4⋊C4—48no—
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2411yescharacteristic
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2411yescharacteristic
462C2×C4⋊C4C2411yescharacteristic
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C24116yes—
475C2×C4⋊C4C24116yes—
476C2×C22⋊C4—416no—
477C2×C22⋊C4—416no—
478C2×C22⋊C4—48no—
479C2×C22⋊C4C2412yes—
480C2×C22⋊C4C2414yes—
481C2×C22⋊C4C24116yes—
482C2×C22⋊C4C2412yes—
483C2×C22⋊C4C2412yes—
484C2×C22⋊C4C2412yes—
485C2×C22⋊C4C2414yes—
486C2×C22⋊C4C2414yes—
487C2×C22⋊C4C2418yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C24116yes—
490C2×C22⋊C4C24116yes—
491C2×C22⋊C4C24116yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2414yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C24116yes—
497C2×C22⋊C4C24116yes—
498C2×C22⋊C4C2418yes—
499C2×C22⋊C4C24116yes—
500C2×C22⋊C4C2418yes—
501C2×C22⋊C4C24116yes—
502C2×C22⋊C4C2418yes—
503C2×C22⋊C4C2418yes—
504C2×C42—28no—
505C2×C42—24no—
506C2×C42—28no—
507C2×C42—28no—
508C2×C42—28no—
509C2×C42—28no—
510C2×C42#4118yes—
511C2×C42C2414yes—
512C2×C42C2412yes—
513C2×C42C2414yes—
514C2×C42C2412yes—
515C2×C42C2414yes—
516C2×C42C2412yes—
517C2×C42C2412yes—
518C2×C42C2414yes—
519C2×C42C2414yes—
520C2×C42C2412yes—
521C2×C42C2411yescharacteristic
522C2×C42C2411yescharacteristic
523C2×C42C2412yes—
524C2×C42C2412yes—
525C2×C42C2412yes—
526C2×C42C2412yes—
527C2×C42C2418yes—
528C2×C42C2412yes—
529C2×C42C2411yescharacteristic
530C2×C42C2411yescharacteristic
531#95C2414yes—
532#95C2414yes—
533#95C2414yes—
534#95C2414yes—
535#95C2414yes—
536#95C2414yes—
537#95C2414yes—
538#95C2414yes—
539#95C2414yes—
540#95C2414yes—
541#95C2414yes—
542#95C2414yes—
543#95C2418yes—
544#95C2418yes—
545#95C24116yes—
546#95C2418yes—
547#95C24116yes—
548#95C24116yes—
549C24—24no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—28no—
554C24—28no—
555C24—28no—
556C24—42no—
557C24—48no—
558C24—48no—
559C24C2518yes—
560C24C2514yes—
561C24C2512yes—
562C24C2511yescharacteristic
563#41—432no—
564C2×Q8—24no—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—28no—
570C2×D4—216no—
571C2×D4—232no—
572C2×D4—28no—
573C2×D4—24no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—216no—
577C2×D4—216no—
578C2×D4—28no—
579C2×D4—28no—
580C2×D4—28no—
581C2×D4—24no—
582C2×D4—216no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—24no—
586C2×D4—216no—
587C2×D4—28no—
588C2×D4—48no—
589C2×D4—48no—
590C2×D4—416no—
591C2×D4—416no—
592C2×D4—48no—
593C2×D4—48no—
594C2×D4—416no—
595C2×D4—48no—
596C2×D4—48no—
597C2×D4—416no—
598C2×D4—416no—
599C2×D4—416no—
600C2×D4—416no—
601C2×D4—432no—
602C2×D4—832no—
603C2×D4—832no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—22no—
613C22×C4—28no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—28no—
620C22×C4—24no—
621C22×C4—28no—
622C22×C4—24no—
623C22×C4—28no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—432no—
634C22×C4—48no—
635C22×C4—416no—
636C22×C4—48no—
637C22×C4—416no—
638C22×C4—416no—
639C22×C4—416no—
640C22×C4—416no—
641C22×C4C2×#4118yes—
642C22×C4C2×#4114yes—
643C22×C4H(5,𝔽2)18yes—
644C22×C4H(5,𝔽2)14yes—
645C22×C4H(5,𝔽2)14yes—
646C22×C4C2512yes—
647C22×C4C2512yes—
648C22×C4C2514yes—
649C22×C4C2514yes—
650C22×C4C2512yes—
651C22×C4C2514yes—
652C22×C4C2518yes—
653C22×C4C2512yes—
654C22×C4C2512yes—
655C22×C4C2512yes—
656C22×C4C2518yes—
657C22×C4C2512yes—
658C22×C4C2512yes—
659C22×C4C2511yescharacteristic
660C22×C4C2511yescharacteristic
661C22×C4C2512yes—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—22no—
666C4⋊C4—216no—
667C4⋊C4—22no—
668C4⋊C4—24no—
669C4⋊C4—28no—
670C4⋊C4—24no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—28no—
674C4⋊C4—28no—
675C4⋊C4—28no—
676C4⋊C4—28no—
677C4⋊C4—48no—
678C4⋊C4—48no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—48no—
682C4⋊C4—416no—
683C4⋊C4—416no—
684C22⋊C4—24no—
685C22⋊C4—28no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—216no—
692C22⋊C4—232no—
693C22⋊C4—216no—
694C22⋊C4—416no—
695C22⋊C4—416no—
696C22⋊C4—416no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—48no—
700C22⋊C4—416no—
701C22⋊C4—48no—
702C22⋊C4—48no—
703C22⋊C4—416no—
704C22⋊C4—416no—
705C22⋊C4—48no—
706C22⋊C4—48no—
707C22⋊C4—416no—
708C22⋊C4—48no—
709C42—22no—
710C42—24no—
711C42—24no—
712C42—24no—
713C42—24no—
714C42—22no—
715C42—24no—
716C42—28no—
717C42—24no—
718C42—28no—
719C42—24no—
720C42—24no—
721C42—24no—
722C42—28no—
723C42—28no—
724C42—28no—
725C42—48no—
726C42C2×#4118yes—
727C42C2×#4114yes—
728C42C2×#4114yes—
729C23—22no—
730C23—22no—
731C23—28no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—24no—
739C23—28no—
740C23—28no—
741C23—216no—
742C23—28no—
743C23—28no—
744C23—24no—
745C23—24no—
746C23—216no—
747C23—28no—
748C23—48no—
749C23—48no—
750C23—44no—
751C23—44no—
752C23—416no—
753C23—816no—
754C23—88no—
755C23—816no—
756C23—88no—
757C23C22×#4112yes—
758C23C2×H(5,𝔽2)14yes—
759C23C2×H(5,𝔽2)12yes—
760C23C2×H(5,𝔽2)12yes—
761C23C2611yescharacteristic
762Q8—48no—
763D4—416no—
764D4—416no—
765D4—416no—
766D4—48no—
767D4—416no—
768D4—432no—
769D4—816no—
770D4—816no—
771D4—832no—
772D4—168no—
773D4—1616no—
774D4—168no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—216no—
780C2×C4—216no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—216no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—28no—
809C2×C4—48no—
810C2×C4—48no—
811C2×C4—48no—
812C2×C4—44no—
813C2×C4—48no—
814C2×C4—48no—
815C2×C4—416no—
816C2×C4—48no—
817C2×C4—88no—
818C2×C4—168no—
819C2×C4—1616no—
820C2×C4#540116yescomplemented
821C2×C4C22×#4114yes—
822C2×C4C22×#4112yes—
823C2×C4C22×#4112yes—
824C2×C4C22×#4114yes—
825C2×C4C2×H(5,𝔽2)14yes—
826C2×C4C2×H(5,𝔽2)12yes—
827C2×C4C2×H(5,𝔽2)12yes—
828C2×C4C2×H(5,𝔽2)12yes—
829C2×C4C2×H(5,𝔽2)12yes—
830C2×C4C2×H(5,𝔽2)14yes—
831C2×C4#58514yes—
832C22—24no—
833C22—22no—
834C22—24no—
835C22—22no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—416no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—416no—
845C22—48no—
846C22—44no—
847C22—48no—
848C22—416no—
849C22—48no—
850C22—44no—
851C22—48no—
852C22—44no—
853C22—48no—
854C22—1616no—
855C22C2×#54014yes—
856C22C23×#4111yescharacteristic
857C22C22×H(5,𝔽2)12yes—
858C22C22×H(5,𝔽2)11yescharacteristic
859C22C22×H(5,𝔽2)11yescharacteristic
860C22C2×#58512yes—
861C4—24no—
862C4—24no—
863C4—42no—
864C4—48no—
865C4—42no—
866C4—42no—
867C4—44no—
868C4—48no—
869C4—44no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—44no—
874C4C2×#54014yes—
875C4C2×#54014yes—
876C4#349418yes—
877C2—24no—
878C2—44no—
879C2—84no—
880C2—88no—
881C2C22×#54011yescharacteristic
882C2C2×#349412yes—
883C2#6283211yescharacteristic
884C2#6283412yes—
885C2#6283611yescharacteristic
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. #39735C2semidirect
2. #39352C2semidirect
3. #39148C2semidirect
4. #38942C2semidirect
5. #38056C2semidirect
6. #37662C2semidirect
7. #37290C2semidirect
8. #36624C2semidirect
9. C2×#2856C2semidirect
10. #35563C2semidirect
11. #35541C2semidirect
12. #35531C2semidirect
13. #35514C2semidirect
14. #35288C2semidirect
15. #35286C2semidirect
16. #35278C2semidirect
17. #35274C2semidirect
18. #34210C2semidirect
19. #34207C2semidirect
20. #34012C2semidirect
21. C2×#540C22semidirect
32. #2867C22semidirect
33. #2859C22semidirect
34. #2858C22semidirect
35. #2857C22semidirect
40. #2856C22semidirect
42. #2850C22semidirect
44. #2756C22semidirect
45. #2753C22semidirect
46. #2749C22semidirect
47. #2706C22semidirect
48. #2703C22semidirect
49. #2699C22semidirect
50. #2688C22semidirect
51. #2671C22semidirect
52. #2657C22semidirect
53. #2647C22semidirect
54. #2644C22semidirect
55. #2641C22semidirect
56. #2624C22semidirect
57. #2619C22semidirect
58. #2571C22semidirect
59. #2552C22semidirect
60. #2541C22semidirect
61. #2541C22semidirect
62. #2537C22semidirect
63. #2535C22semidirect
65. #2513C22semidirect
66. #2504C22semidirect
67. #2501C22semidirect
68. #2500C22semidirect
69. #2500C22semidirect
70. #2490C22semidirect
71. #2454C22semidirect
72. #2448C22semidirect
73. #2447C22semidirect
74. #2445C22semidirect
75. #2445C22semidirect
76. #2445C22semidirect
77. #2445C22semidirect
80. #2428C22semidirect
81. #2428C22semidirect
82. #2428C22semidirect
83. #2428C22semidirect
84. #2427C22semidirect
85. #2426C22semidirect
86. #2422C22semidirect
87. #2420C22semidirect
88. #2420C22semidirect
90. #2416C22semidirect
91. #2414C22semidirect
96. #2366C22semidirect
97. #2366C22semidirect
99. #2354C22semidirect
100. D4×C4⋊C4C22semidirect
102. #2328C22semidirect
103. #2328C22semidirect
104. #2326C22semidirect
105. #2324C22semidirect
106. #2319C22semidirect
111. C4×C4⋊Q8C22semidirect
112. C4×#127C22semidirect
113. C4×#127C22semidirect
114. C4×#121C22semidirect
115. C4×#121C22semidirect
122. #2285C22semidirect
123. #2285C22semidirect
126. #2283C22semidirect
127. #2283C22semidirect
128. #2283C22semidirect
134. C4×#117C22semidirect
820. C2×C4#540semidirect

Maximal subgroups

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

subgroupindex
#397352
#393522
#391482
#389422
#380562
#376622
#372902
#366242
C2×#28562
#355632
#355412
#355312
#355142
#352882
#352862
#352782
#352742
#342102
#342072
#340122