Finite Group Databasebeta

← #7641976

Subgroups — #7641976

Order 512.

6244 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37626C214yesmaximal, complemented
2#37625C214yesmaximal, complemented
3#37587C218yesmaximal, complemented
4#37493C218yesmaximal, complemented
5#35288C214yesmaximal, complemented
6#35286C211yesmaximal, characteristic, complemented
7#35278C214yesmaximal, complemented
8#35274C211yesmaximal, characteristic, complemented
9#35273C211yesmaximal, characteristic, complemented
10#35272C211yesmaximal, characteristic, complemented
11#35256C212yesmaximal, complemented
12#35254C212yesmaximal, complemented
13#35226C218yesmaximal, complemented
14#35197C214yesmaximal, complemented
15#35171C214yesmaximal, complemented
16#35168C212yesmaximal, complemented
17#35152C212yesmaximal, complemented
18C4×#532C211yesmaximal, characteristic, complemented
19C2×C4×#127C211yesmaximal, characteristic, complemented
20#34026C211yesmaximal, characteristic, complemented
21C2×#540C2218yescomplemented
22C2×#537C2212yes—
23C2×#535C2212yes—
24C2×#535C2212yes—
25C2×#535C2212yes—
26C2×#532C2211yescharacteristic
27C22×#127C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C2×C4×#41C2212yes—
30C22×C4×D4C2212yes—
31C22×C4×D4C2214yes—
32#2867C2212yes—
33#2859C2214yescomplemented
34#2858C2212yes—
35#2857C2212yescomplemented
36#2856C2214yes—
37#2856C2214yescomplemented
38#2856C2212yescomplemented
39#2854C2218yescomplemented
40#2850C2214yescomplemented
41#2849C2218yes—
42#2847C2218yes—
43#2829C22116yescomplemented
44#2828C22116yescomplemented
45#2661C22116yescomplemented
46#2657C2214yes—
47#2648C22116yescomplemented
48#2647C2214yescomplemented
49#2644C2218yescomplemented
50#2641C2218yescomplemented
51#2635C22116yescomplemented
52#2630C22116yescomplemented
53#2624C2218yescomplemented
54#2624C2218yescomplemented
55#2622C2218yes—
56#2620C2214yescomplemented
57#2620C2214yescomplemented
58#2619C2214yes—
59#2619C2218yescomplemented
60#2619C2214yescomplemented
61#2617C2218yes—
62#2571C2214yescomplemented
63#2552C2214yescomplemented
64#2548C2214yes—
65#2541C2214yes—
66#2541C2214yes—
67#2541C2214yes—
68#2538C2214yescomplemented
69#2537C2214yescomplemented
70#2513C2218yescomplemented
71#2490C2218yescomplemented
72#2464C22116yescomplemented
73#2457C22116yescomplemented
74#2454C2218yescomplemented
75#2448C2218yescomplemented
76#2447C2218yescomplemented
77#2445C2218yescomplemented
78#2445C2218yescomplemented
79#2445C2218yescomplemented
80#2445C2218yescomplemented
81#2442C2218yes—
82#2433C2218yes—
83#2428C2218yescomplemented
84#2428C2218yescomplemented
85#2428C2218yescomplemented
86#2428C2218yescomplemented
87#2428C2218yescomplemented
88#2427C2218yescomplemented
89#2427C2218yescomplemented
90#2426C2218yescomplemented
91#2424C22116yes—
92#2422C2218yescomplemented
93#2420C2218yescomplemented
94#2420C2218yescomplemented
95#2418C22116yes—
96#2416C2218yes—
97#2408C2218yes—
98#2328C2218yescomplemented
99#2324C2218yescomplemented
100#2319C2218yescomplemented
101#2317C2212yes—
102#2316C2212yes—
103#2311C2212yes—
104#2309C2212yes—
105C4×C4⋊Q8C2212yescomplemented
106C4×#127C2214yes—
107C4×#127C2214yes—
108C4×#127C2214yes—
109C4×#127C2214yes—
110C4×#127C2212yescomplemented
111C4×#124C2214yescomplemented
112C4×#121C2214yes—
113C4×#121C2214yes—
114#2298C2214yescomplemented
115#2297C2212yes—
116#2297C2211yescharacteristic
117#2297C2211yescharacteristic
118#2296C2211yescharacteristic
119#2296C2211yescharacteristic
120#2295C2212yescomplemented
121#2295C2212yescomplemented
122#2293C2212yescomplemented
123#2293C2212yescomplemented
124#2293C2214yescomplemented
125C2×#390C2214yes—
126C2×#390C2212yes—
127#2290C2214yes—
128#2290C2214yes—
129#2285C2211yescharacteristic
130C2×#384C2211yescharacteristic
131C42×D4C2214yescomplemented
132C4×#117C2211yescharacteristic
133C4×#117C2214yescomplemented
134C2×C43C2211yescharacteristic
135C22×#41C2312yes—
136C22×#41C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2314yes—
139C24×C4C2314yes—
140#540—432no—
141#537—48no—
142#535—48no—
143#535—48no—
144#535—48no—
145#532—28no—
146C2×C4⋊Q8C2311yescharacteristic
147C2×#127—28no—
148C2×#127C2312yes—
149C2×#127C2312yes—
150C2×#127C2314yes—
151C2×#127C2311yescharacteristic
152C2×#127C2318yes—
153C2×#127C2314yes—
154C2×#127C2318yes—
155C2×#127C2314yes—
156C2×#127C2314yes—
157C2×#125C2318yes—
158C2×#124C2312yes—
159C2×#124C2314yes—
160C2×#124C2314yes—
161C2×#124C2314yes—
162C2×#123C23116yes—
163C2×#123C23116yes—
164C2×C22⋊Q8C2314yes—
165C2×C22⋊Q8C2314yes—
166C2×#121C2314yes—
167C2×#121C2318yes—
168C2×#121C2318yes—
169C2×#121C23116yes—
170C2×#121C2314yes—
171C2×#121C2318yes—
172C2×#121C2318yes—
173C2×#121C2318yes—
174C2×#121C2318yes—
175C2×#121C2314yes—
176C2×#121C2314yes—
177C2×#121C2314yes—
178C2×#121C23116yes—
179C2×#120C2318yes—
180C2×#120C2318yes—
181C2×#120C2318yes—
182C4×#41—28no—
183C4×#41—48no—
184C2×C4×Q8C2312yes—
185C2×C4×Q8C2314yes—
186C2×C4×D4—48no—
187C2×C4×D4—416no—
188C2×C4×D4C2318yes—
189C2×C4×D4C2314yes—
190C2×C4×D4C2314yes—
191C2×C4×D4C2312yes—
192C2×C4×D4C2314yes—
193C2×C4×D4C2318yes—
194C2×C4×D4C2318yes—
195C2×C4×D4C2318yes—
196C2×C4×D4C2318yes—
197C2×C4×D4C2318yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2318yes—
201C2×#117C2311yescharacteristic
202C2×#117C2312yes—
203C2×#117C2311yescharacteristic
204C2×#117C2311yescharacteristic
205C2×#117C2314yes—
206C2×#117C2312yes—
207C2×#117C2314yes—
208C2×#117C2314yes—
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2314yes—
211C22×C22⋊C4C2314yes—
212C22×C22⋊C4C2318yes—
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2314yes—
218C22×C42C2312yes—
219C22×C42C2311yescharacteristic
220#400C23116yes—
221#399C23116yes—
222#398C23116yes—
223#397C23116yes—
224#397C23116yes—
225#397C23116yes—
226#397C23116yes—
227#396C23116yes—
228#396C23116yes—
229#394C23116yes—
230#394C23116yes—
231#394C23116yes—
232#394C23116yes—
233#394C23116yes—
234#394C23116yes—
235#394C23116yes—
236#394C23116yes—
237#394C23116yes—
238#394C23116yes—
239#392C23116yes—
240#392C23116yes—
241#392C23116yes—
242#392C23116yes—
243#392C23116yes—
244#391C2314yes—
245#391C2314yes—
246#391C2311yescharacteristic
247#391C2311yescharacteristic
248#391C2312yes—
249#390C2318yes—
250#390C2314yes—
251#390C2314yes—
252#390C2318yes—
253#390C2318yes—
254#390C2318yes—
255#390C2318yes—
256#390C2314yes—
257#390C2314yes—
258#390C2314yes—
259#390C2318yes—
260#390C2318yes—
261#390C2314yes—
262#390C2318yes—
263#390C2318yes—
264#390C23116yes—
265#390C2318yes—
266#390C2318yes—
267#390C2318yes—
268#390C2311yescharacteristic
269#390C2311yescharacteristic
270#390C2312yes—
271#389C2314yes—
272#389C2314yes—
273#389C2318yes—
274#389C2318yes—
275#389C2318yes—
276#389C2318yes—
277#389C2318yes—
278#389C2318yes—
279#389C2312yes—
280#389C2312yes—
281#389C2312yes—
282#389C2312yes—
283#388C2314yes—
284#388C2318yes—
285#388C23116yes—
286#388C23116yes—
287#388C23116yes—
288#388C2318yes—
289#388C2314yes—
290#388C2314yes—
291#388C2314yes—
292#387C2314yes—
293#387C2314yes—
294#387C2314yes—
295#387C2314yes—
296#386C2318yes—
297#386C23116yes—
298#386C23116yes—
299#386C23116yes—
300#386C23116yes—
301#386C23116yes—
302#386C2312yes—
303#386C2314yes—
304#386C2312yes—
305#386C2314yes—
306#386C2314yes—
307#385C2318yes—
308#385C23116yes—
309#385C2312yes—
310#385C2312yes—
311#385C2314yes—
312#384C2314yes—
313#384C2312yes—
314#384C2312yes—
315#384C2312yes—
316#384C2314yes—
317#382C2314yes—
318#382C2318yes—
319#382C2312yes—
320#381C23116yes—
321#380C2318yes—
322#380C2318yes—
323#380C23116yes—
324#380C2318yes—
325#380C2314yes—
326#379C2318yes—
327C4×C4⋊C4C2314yes—
328C4×C4⋊C4C2314yes—
329C4×C4⋊C4C2312yes—
330C4×C4⋊C4C2314yes—
331C4×C4⋊C4C2314yes—
332C4×C4⋊C4C2314yes—
333C4×C4⋊C4C2314yes—
334C4×C4⋊C4C2314yes—
335C4×C4⋊C4C2312yes—
336C4×C22⋊C4C2318yes—
337C4×C22⋊C4C2314yes—
338C4×C22⋊C4C2318yes—
339C4×C22⋊C4C2314yes—
340C4×C22⋊C4C2314yes—
341C4×C22⋊C4C2314yes—
342C4×C22⋊C4C2314yes—
343C4×C22⋊C4C2318yes—
344#376C2314yes—
345#376C2314yes—
346#376C2312yes—
347C43C2312yes—
348C43C2312yes—
349C43C2312yes—
350C43C2312yes—
351C43C2312yes—
352C25C2414yes—
353C2×#41—24no—
354C2×#41—28no—
355C2×#41—28no—
356C2×#41—24no—
357C2×#41—28no—
358C2×#41—24no—
359C22×Q8C2411yescharacteristic
360C22×Q8C2412yes—
361C22×D4—216no—
362C22×D4—28no—
363C22×D4—28no—
364C22×D4—28no—
365C22×D4—48no—
366C22×D4—48no—
367C22×D4C2414yes—
368C22×D4C2412yes—
369C22×D4C2414yes—
370C22×D4C2414yes—
371C22×D4C2411yescharacteristic
372C22×D4C2414yes—
373C22×D4C2412yes—
374C22×D4C2418yes—
375C22×D4C2418yes—
376C22×D4C24116yes—
377C22×D4C2418yes—
378C22×D4C24116yes—
379C22×D4C2418yes—
380C22×D4C2418yes—
381C23×C4—416no—
382C23×C4—48no—
383C23×C4C2414yes—
384C23×C4C2414yes—
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2411yescharacteristic
390C23×C4C2414yes—
391C23×C4C24116yes—
392C23×C4C2418yes—
393C23×C4C2411yescharacteristic
394C4⋊Q8—24no—
395#127—28no—
396#127—28no—
397#127—216no—
398#127—24no—
399#127—416no—
400#127—48no—
401#127—48no—
402#127—48no—
403#127—416no—
404#125—416no—
405#124—28no—
406#124—48no—
407#124—48no—
408#124—48no—
409#123—432no—
410#123—432no—
411C22⋊Q8—48no—
412C22⋊Q8—48no—
413#121—216no—
414#121—432no—
415#121—432no—
416#121—416no—
417#121—416no—
418#121—416no—
419#121—48no—
420#121—48no—
421#121—48no—
422#121—48no—
423#121—416no—
424#121—416no—
425#121—416no—
426#120—416no—
427#120—416no—
428#120—416no—
429C4×Q8—28no—
430C4×Q8—48no—
431C4×D4—216no—
432C4×D4—28no—
433C4×D4—216no—
434C4×D4—232no—
435C4×D4—216no—
436C4×D4—416no—
437C4×D4—416no—
438C4×D4—416no—
439C4×D4—416no—
440C4×D4—48no—
441C4×D4—48no—
442C4×D4—416no—
443C4×D4—416no—
444#117—24no—
445#117—28no—
446#117—24no—
447#117—24no—
448#117—28no—
449#117—216no—
450#117—48no—
451#117—48no—
452C2×C4⋊C4—28no—
453C2×C4⋊C4—48no—
454C2×C4⋊C4C2414yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2418yes—
457C2×C4⋊C4C2414yes—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2411yescharacteristic
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2418yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C24116yes—
474C2×C4⋊C4C24116yes—
475C2×C22⋊C4—416no—
476C2×C22⋊C4—48no—
477C2×C22⋊C4C24116yes—
478C2×C22⋊C4C2414yes—
479C2×C22⋊C4C2412yes—
480C2×C22⋊C4C2414yes—
481C2×C22⋊C4C2412yes—
482C2×C22⋊C4C2412yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C2414yes—
485C2×C22⋊C4C2418yes—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C24116yes—
488C2×C22⋊C4C24116yes—
489C2×C22⋊C4C2418yes—
490C2×C22⋊C4C2414yes—
491C2×C22⋊C4C2414yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C24116yes—
494C2×C22⋊C4C24116yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C2418yes—
498C2×C22⋊C4C2418yes—
499C2×C22⋊C4C24116yes—
500C2×C22⋊C4C24116yes—
501C2×C22⋊C4C24116yes—
502C2×C42—24no—
503C2×C42—24no—
504C2×C42—28no—
505C2×C42—28no—
506C2×C42—48no—
507C2×C42—44no—
508C2×C42#4118yes—
509C2×C42C2411yescharacteristic
510C2×C42C2414yes—
511C2×C42C2412yes—
512C2×C42C2412yes—
513C2×C42C2412yes—
514C2×C42C2412yes—
515C2×C42C2414yes—
516C2×C42C2414yes—
517C2×C42C2412yes—
518C2×C42C2412yes—
519C2×C42C2412yes—
520C2×C42C2412yes—
521C2×C42C2412yes—
522C2×C42C2412yes—
523C2×C42C2412yes—
524C2×C42C2414yes—
525C2×C42C2411yescharacteristic
526C2×C42C2418yes—
527C2×C42C2412yes—
528C2×C42C2412yes—
529C2×C42C2411yescharacteristic
530C2×C42C2412yes—
531C2×C42C2411yescharacteristic
532C2×C42C2412yes—
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#95C2418yes—
546#95C24116yes—
547#95C24116yes—
548#95C24116yes—
549C24—28no—
550C24—28no—
551C24—28no—
552C24—48no—
553C24—48no—
554C24C2518yes—
555C24C2512yes—
556C24C2514yes—
557C24C2511yescharacteristic
558#41—416no—
559#41—432no—
560C2×Q8—22no—
561C2×Q8—24no—
562C2×Q8—24no—
563C2×Q8—22no—
564C2×Q8—24no—
565C2×Q8—22no—
566C2×D4—24no—
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—24no—
570C2×D4—28no—
571C2×D4—24no—
572C2×D4—22no—
573C2×D4—28no—
574C2×D4—24no—
575C2×D4—216no—
576C2×D4—28no—
577C2×D4—28no—
578C2×D4—216no—
579C2×D4—216no—
580C2×D4—28no—
581C2×D4—28no—
582C2×D4—28no—
583C2×D4—24no—
584C2×D4—22no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—28no—
590C2×D4—216no—
591C2×D4—48no—
592C2×D4—48no—
593C2×D4—464no—
594C2×D4—416no—
595C2×D4—48no—
596C2×D4—48no—
597C2×D4—416no—
598C2×D4—416no—
599C2×D4—416no—
600C2×D4—48no—
601C2×D4—416no—
602C2×D4—416no—
603C2×D4—416no—
604C2×D4—416no—
605C2×D4—416no—
606C2×D4—432no—
607C22×C4—22no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—22no—
612C22×C4—24no—
613C22×C4—28no—
614C22×C4—24no—
615C22×C4—28no—
616C22×C4—28no—
617C22×C4—24no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—24no—
621C22×C4—28no—
622C22×C4—24no—
623C22×C4—28no—
624C22×C4—232no—
625C22×C4—216no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—416no—
631C22×C4—416no—
632C22×C4—48no—
633C22×C4—832no—
634C22×C4C2×#4118yes—
635C22×C4C2×#4114yes—
636C22×C4H(5,𝔽2)14yes—
637C22×C4H(5,𝔽2)14yes—
638C22×C4C2512yes—
639C22×C4C2514yes—
640C22×C4C2512yes—
641C22×C4C2514yes—
642C22×C4C2512yes—
643C22×C4C2514yes—
644C22×C4C2518yes—
645C22×C4C2512yes—
646C22×C4C2518yes—
647C22×C4C2512yes—
648C22×C4C2512yes—
649C22×C4C2512yes—
650C22×C4C2512yes—
651C22×C4C2511yescharacteristic
652C22×C4C2511yescharacteristic
653C22×C4C2512yes—
654C4⋊C4—24no—
655C4⋊C4—28no—
656C4⋊C4—28no—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—216no—
660C4⋊C4—28no—
661C4⋊C4—24no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—28no—
665C4⋊C4—28no—
666C4⋊C4—28no—
667C4⋊C4—28no—
668C4⋊C4—48no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—416no—
674C4⋊C4—416no—
675C22⋊C4—24no—
676C22⋊C4—28no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—28no—
680C22⋊C4—216no—
681C22⋊C4—232no—
682C22⋊C4—28no—
683C22⋊C4—28no—
684C22⋊C4—216no—
685C22⋊C4—416no—
686C22⋊C4—416no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C22⋊C4—416no—
692C22⋊C4—416no—
693C22⋊C4—48no—
694C22⋊C4—48no—
695C22⋊C4—416no—
696C22⋊C4—48no—
697C22⋊C4—48no—
698C22⋊C4—416no—
699C22⋊C4—416no—
700C42—24no—
701C42—28no—
702C42—22no—
703C42—22no—
704C42—24no—
705C42—24no—
706C42—24no—
707C42—24no—
708C42—24no—
709C42—24no—
710C42—28no—
711C42—24no—
712C42—24no—
713C42—28no—
714C42—24no—
715C42—24no—
716C42—28no—
717C42—42no—
718C42—42no—
719C42—48no—
720C42C2×#4114yes—
721C42C2×#4114yes—
722C42C2×#4118yes—
723C42H(5,𝔽2)18yes—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—28no—
729C23—24no—
730C23—216no—
731C23—28no—
732C23—22no—
733C23—28no—
734C23—28no—
735C23—24no—
736C23—24no—
737C23—22no—
738C23—24no—
739C23—28no—
740C23—216no—
741C23—432no—
742C23—416no—
743C23—88no—
744C23—816no—
745C23—88no—
746C23C22×#4112yes—
747C23C2×H(5,𝔽2)12yes—
748C23C2×H(5,𝔽2)12yes—
749C23C2611yescharacteristic
750Q8—44no—
751Q8—48no—
752D4—432no—
753D4—48no—
754D4—416no—
755D4—416no—
756D4—416no—
757D4—44no—
758D4—48no—
759D4—416no—
760D4—432no—
761D4—168no—
762D4—168no—
763D4—1616no—
764D4—1616no—
765D4—168no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—216no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—28no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—28no—
788C2×C4—216no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—48no—
802C2×C4—44no—
803C2×C4—416no—
804C2×C4—48no—
805C2×C4—416no—
806C2×C4—816no—
807C2×C4—832no—
808C2×C4—88no—
809C2×C4#540116yescomplemented
810C2×C4C22×#4114yes—
811C2×C4C22×#4112yes—
812C2×C4C22×#4112yes—
813C2×C4C22×#4114yes—
814C2×C4C2×H(5,𝔽2)14yes—
815C2×C4C2×H(5,𝔽2)14yes—
816C2×C4C2×H(5,𝔽2)12yes—
817C2×C4C2×H(5,𝔽2)12yes—
818C2×C4C2×H(5,𝔽2)12yes—
819C2×C4C2×H(5,𝔽2)12yes—
820C2×C4C2×H(5,𝔽2)14yes—
821C2×C4#58514yes—
822C22—22no—
823C22—24no—
824C22—22no—
825C22—24no—
826C22—48no—
827C22—42no—
828C22—44no—
829C22—48no—
830C22—44no—
831C22—416no—
832C22—44no—
833C22—48no—
834C22—42no—
835C22—42no—
836C22—44no—
837C22—48no—
838C22—44no—
839C22—416no—
840C22—48no—
841C22—832no—
842C22C2×#54014yes—
843C22C23×#4111yescharacteristic
844C22C22×H(5,𝔽2)12yes—
845C22C22×H(5,𝔽2)11yescharacteristic
846C22C22×H(5,𝔽2)11yescharacteristic
847C22C2×#58512yes—
848C4—24no—
849C4—24no—
850C4—24no—
851C4—48no—
852C4—42no—
853C4—42no—
854C4—48no—
855C4—44no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—44no—
860C4—44no—
861C4C2×#54014yes—
862C4C2×#54014yes—
863C4#346018yes—
864C2—24no—
865C2—84no—
866C2—82no—
867C2—88no—
868C2C22×#54011yescharacteristic
869C2C2×#346012yes—
870C2#6283211yescharacteristic
871C2#6283412yes—
872C2#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. #37626C2semidirect
2. #37625C2semidirect
3. #37587C2semidirect
4. #37493C2semidirect
5. #35288C2semidirect
6. #35286C2semidirect
7. #35278C2semidirect
8. #35274C2semidirect
9. #35273C2semidirect
10. #35272C2semidirect
11. #35256C2semidirect
12. #35254C2semidirect
13. #35226C2semidirect
14. #35197C2semidirect
15. #35171C2semidirect
16. #35168C2semidirect
17. #35152C2semidirect
18. C4×#532C2semidirect
19. C2×C4×#127C2semidirect
20. #34026C2semidirect
21. C2×#540C22semidirect
33. #2859C22semidirect
35. #2857C22semidirect
37. #2856C22semidirect
38. #2856C22semidirect
39. #2854C22semidirect
40. #2850C22semidirect
43. #2829C22semidirect
44. #2828C22semidirect
45. #2661C22semidirect
47. #2648C22semidirect
48. #2647C22semidirect
49. #2644C22semidirect
50. #2641C22semidirect
51. #2635C22semidirect
52. #2630C22semidirect
53. #2624C22semidirect
54. #2624C22semidirect
56. #2620C22semidirect
57. #2620C22semidirect
59. #2619C22semidirect
60. #2619C22semidirect
62. #2571C22semidirect
63. #2552C22semidirect
68. #2538C22semidirect
69. #2537C22semidirect
70. #2513C22semidirect
71. #2490C22semidirect
72. #2464C22semidirect
73. #2457C22semidirect
74. #2454C22semidirect
75. #2448C22semidirect
76. #2447C22semidirect
77. #2445C22semidirect
78. #2445C22semidirect
79. #2445C22semidirect
80. #2445C22semidirect
83. #2428C22semidirect
84. #2428C22semidirect
85. #2428C22semidirect
86. #2428C22semidirect
87. #2428C22semidirect
88. #2427C22semidirect
89. #2427C22semidirect
90. #2426C22semidirect
92. #2422C22semidirect
93. #2420C22semidirect
94. #2420C22semidirect
98. #2328C22semidirect
99. #2324C22semidirect
100. #2319C22semidirect
105. C4×C4⋊Q8C22semidirect
110. C4×#127C22semidirect
111. C4×#124C22semidirect
114. #2298C22semidirect
120. #2295C22semidirect
121. #2295C22semidirect
122. #2293C22semidirect
123. #2293C22semidirect
124. #2293C22semidirect
131. C42×D4C22semidirect
133. C4×#117C22semidirect
809. C2×C4#540semidirect

Maximal subgroups

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

subgroupindex
#376262
#376252
#375872
#374932
#352882
#352862
#352782
#352742
#352732
#352722
#352562
#352542
#352262
#351972
#351712
#351682
#351522
C4×#5322
C2×C4×#1272
#340262