Finite Group Databasebeta

← #8928642

Subgroups — #8928642

Order 512.

5654 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57962C214yesmaximal, complemented
2#57960C218yesmaximal, complemented
3#57959C218yesmaximal, complemented
4#56584C214yesmaximal, complemented
5#51531C214yesmaximal, complemented
6#48777C218yesmaximal, complemented
7#46999C212yesmaximal, complemented
8#46997C212yesmaximal, complemented
9#46386C212yesmaximal, complemented
10#46288C214yesmaximal, complemented
11#45562C218yesmaximal, complemented
12#37117C212yesmaximal, complemented
13#36967C211yesmaximal, characteristic, complemented
14#36966C211yesmaximal, characteristic, complemented
15#36718C212yesmaximal, complemented
16#35616C211yesmaximal, characteristic, complemented
17#35347C212yesmaximal, complemented
18C22×H(5,𝔽2)C2211yescharacteristic
19C2×#555C2214yescomplemented
20C2×#543C2211yescharacteristic, complemented
21C2×#536C2212yescomplemented
22C2×#534C2214yescomplemented
23C2×#534C2211yescharacteristic, complemented
24C22×#124C2211yescharacteristic
25C22×#121C2212yes—
26#2855C2212yescomplemented
27#2854C2212yescomplemented
28#2849C2214yescomplemented
29#2848C2214yescomplemented
30#2842C2212yescomplemented
31#2835C2214yescomplemented
32#2831C2218yescomplemented
33#2827C2218yescomplemented
34#2826C2218yescomplemented
35#2824C2214yescomplemented
36#2807C2214yescomplemented
37#2805C2214yescomplemented
38#2804C2214yescomplemented
39#2796C2218yescomplemented
40#2780C2218yescomplemented
41#2779C2218yescomplemented
42#2771C2218yescomplemented
43#2761C2218yescomplemented
44#2750C2218yescomplemented
45#2743C2218yescomplemented
46#2743C2218yescomplemented
47#2743C2218yescomplemented
48#2734C2214yescomplemented
49#2732C2214yescomplemented
50#2731C2214yescomplemented
51#2710C2218yescomplemented
52#2708C2218yescomplemented
53#2706C2218yescomplemented
54#2700C2218yescomplemented
55#2697C2218yescomplemented
56#2696C2218yescomplemented
57#2693C2214yescomplemented
58#2693C2218yescomplemented
59#2688C2218yescomplemented
60#2686C2218yescomplemented
61#2686C2218yescomplemented
62#2682C2218yescomplemented
63#2682C2214yescomplemented
64#2681C2218yescomplemented
65#2681C2218yescomplemented
66#2674C2218yescomplemented
67#2674C2218yescomplemented
68#2672C2218yescomplemented
69#2672C2218yescomplemented
70#2672C2218yescomplemented
71#2671C2218yescomplemented
72#2670C2214yescomplemented
73#2670C2218yescomplemented
74#2668C2218yescomplemented
75#2668C2214yescomplemented
76#2635C2218yescomplemented
77#2628C2218yescomplemented
78#2626C2212yescomplemented
79#2626C2214yescomplemented
80#2624C2218yescomplemented
81#2623C2214yescomplemented
82#2617C2212yescomplemented
83#2609C2218yescomplemented
84#2583C2214yescomplemented
85#2561C2212yescomplemented
86#2539C2212yescomplemented
87#2534C2218yescomplemented
88#2505C2218yescomplemented
89#2488C2218yescomplemented
90#2483C2214yescomplemented
91#2483C2212yescomplemented
92#2482C2218yescomplemented
93#2471C2218yescomplemented
94#2471C2218yescomplemented
95#2470C2218yescomplemented
96#2470C2218yescomplemented
97#2470C2218yescomplemented
98#2457C2218yescomplemented
99#2450C2218yescomplemented
100#2438C2218yescomplemented
101#2437C2214yescomplemented
102#2436C2212yescomplemented
103#2435C2218yescomplemented
104#2435C2214yescomplemented
105#2434C2212yescomplemented
106#2432C2218yescomplemented
107#2430C2218yes—
108#2430C2218yescomplemented
109#2418C2218yescomplemented
110#2418C2218yescomplemented
111#2412C2214yescomplemented
112#2411C2218yescomplemented
113#2411C2218yescomplemented
114#2410C2218yes—
115#2410C2218yescomplemented
116#2410C2214yescomplemented
117#2406C2214yescomplemented
118#2405C2212yes—
119#2405C2212yes—
120#2405C2212yes—
121#2405C2212yes—
122#2405C2212yescomplemented
123#2405C2212yescomplemented
124#2405C2212yescomplemented
125#2405C2212yescomplemented
126#2404C2214yescomplemented
127#2403C2212yes—
128#2403C2212yes—
129#2379C2214yescomplemented
130#2377C2218yescomplemented
131#2312C2211yescharacteristic, complemented
132#2312C2211yescharacteristic, complemented
133#2312C2212yescomplemented
134#2309C2211yescharacteristic
135#2308C2212yes—
136#2308C2212yescomplemented
137#2297C2212yescomplemented
138C2×#386C2214yescomplemented
139C2×H(5,𝔽2)—44no—
140C2×H(5,𝔽2)—48no—
141C22×#41C2312yes—
142C22×#41C2314yes—
143C23×Q8C2311yescharacteristic
144C23×D4C2312yes—
145C23×D4C2311yescharacteristic
146C23×D4C2314yes—
147C23×D4C2312yes—
148C23×D4C2312yes—
149C23×D4C2312yes—
150C24×C4C2312yes—
151#555—416no—
152#543—44no—
153#536—48no—
154#534—44no—
155#534—416no—
156C2×C4⋊Q8C2314yes—
157C2×C4⋊Q8C2314yes—
158C2×#124—44no—
159C2×#124C2314yes—
160C2×#124C2318yes—
161C2×#124C2314yes—
162C2×#124C2318yes—
163C2×#123C2314yes—
164C2×#123C2314yes—
165C2×#123C2314yes—
166C2×#123C2314yes—
167C2×#123C2314yes—
168C2×#123C2318yes—
169C2×#123C2314yes—
170C2×#123C2314yes—
171C2×#123C2318yes—
172C2×#123C2318yes—
173C2×C22⋊Q8C2312yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2312yes—
177C2×C22⋊Q8C2318yes—
178C2×C22⋊Q8C2318yes—
179C2×#121—48no—
180C2×#121C2318yes—
181C2×#121C2312yes—
182C2×#121C2318yes—
183C2×#121C2318yes—
184C2×#121C2318yes—
185C2×#121C2318yes—
186C2×#121C2312yes—
187C2×#120C2314yes—
188C2×#120C2314yes—
189C2×#120C2318yes—
190C2×#120C2314yes—
191C2×#120C2314yes—
192C2×#120C2314yes—
193C2×C4×D4C2318yes—
194C2×#117C2312yes—
195C2×#117C2318yes—
196C2×#117C2318yes—
197C22×C4⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2314yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2314yes—
206C22×C22⋊C4C2318yes—
207C22×C42C2311yescharacteristic
208#400C2318yes—
209#400C2318yes—
210#400C2318yes—
211#400C2318yes—
212#400C2318yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#399C2318yes—
217#399C2314yes—
218#399C2318yes—
219#399C2318yes—
220#399C2314yes—
221#399C2318yes—
222#398C2318yes—
223#398C2318yes—
224#398C2318yes—
225#397C2314yes—
226#397C2318yes—
227#397C2318yes—
228#397C2318yes—
229#397C2318yes—
230#397C2318yes—
231#397C2318yes—
232#397C2314yes—
233#397C2318yes—
234#396C2318yes—
235#396C2318yes—
236#396C2318yes—
237#396C2318yes—
238#396C2318yes—
239#396C2318yes—
240#396C2318yes—
241#396C2318yes—
242#395C2318yes—
243#395C2318yes—
244#395C2318yes—
245#394C2318yes—
246#394C2318yes—
247#394C2318yes—
248#394C2318yes—
249#394C2318yes—
250#394C2318yes—
251#394C2318yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#393C2314yes—
262#393C2318yes—
263#393C2314yes—
264#393C2318yes—
265#393C2318yes—
266#392C2314yes—
267#392C2318yes—
268#392C2314yes—
269#392C2318yes—
270#392C2318yes—
271#392C2318yes—
272#391C2314yes—
273#391C2314yes—
274#391C2314yes—
275#391C2314yes—
276#390C2318yes—
277#390C2314yes—
278#390C2318yes—
279#390C2318yes—
280#390C2314yes—
281#390C2318yes—
282#389C2318yes—
283#389C2318yes—
284#389C2314yes—
285#389C2314yes—
286#389C2318yes—
287#389C2318yes—
288#388C2318yes—
289#388C2318yes—
290#388C2318yes—
291#388C2318yes—
292#388C2318yes—
293#388C2318yes—
294#388C2318yes—
295#388C2318yes—
296#388C2318yes—
297#388C2318yes—
298#388C2318yes—
299#388C2318yes—
300#387C2318yes—
301#387C2318yes—
302#387C2318yes—
303#387C2318yes—
304#387C2318yes—
305#387C2318yes—
306#386C2318yes—
307#386C2318yes—
308#386C2318yes—
309#386C2318yes—
310#386C2318yes—
311#386C2318yes—
312#386C2318yes—
313#386C2318yes—
314#386C2314yes—
315#386C2314yes—
316#386C2314yes—
317#386C2314yes—
318#386C2318yes—
319#386C2318yes—
320#386C2318yes—
321#386C2318yes—
322#386C2318yes—
323#386C2314yes—
324#386C2314yes—
325#386C2314yes—
326#386C2314yes—
327#386C2318yes—
328#386C2314yes—
329#386C2314yes—
330#385C2314yes—
331#385C2318yes—
332#385C2318yes—
333#385C2318yes—
334#385C2314yes—
335#385C2318yes—
336#385C2314yes—
337#385C2314yes—
338#385C2314yes—
339#385C2314yes—
340#385C2318yes—
341#385C2314yes—
342#385C2318yes—
343#385C2314yes—
344#385C2314yes—
345#385C2314yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#382C2318yes—
351#381C2314yes—
352#381C2314yes—
353#381C2314yes—
354#381C2314yes—
355#381C2318yes—
356#381C2318yes—
357#380C2314yes—
358#380C2312yes—
359#380C2312yes—
360#380C2318yes—
361#380C2318yes—
362#380C2318yes—
363#380C2318yes—
364#379C2314yes—
365#379C2312yes—
366#379C2312yes—
367#379C2312yes—
368#379C2312yes—
369#379C2314yes—
370#379C2314yes—
371#379C2314yes—
372#379C2314yes—
373#379C2314yes—
374#379C2314yes—
375#379C2314yes—
376C4×C22⋊C4C2312yes—
377C4×C22⋊C4C2314yes—
378C4×C22⋊C4C2312yes—
379C4×C22⋊C4C2318yes—
380C2×#95C2318yes—
381C25C2412yes—
382C25C2412yes—
383C25C2412yes—
384C25C2411yescharacteristic
385C25C2411yescharacteristic
386H(5,𝔽2)—464no—
387C2×#41—28no—
388C2×#41—44no—
389C2×#41—44no—
390C2×#41—48no—
391C2×#41—48no—
392C2×#41—48no—
393C22×Q8—42no—
394C22×Q8—44no—
395C22×Q8C2414yes—
396C22×Q8C2412yes—
397C22×Q8C2412yes—
398C22×Q8C2412yes—
399C22×D4—28no—
400C22×D4—24no—
401C22×D4—28no—
402C22×D4—216no—
403C22×D4—44no—
404C22×D4—48no—
405C22×D4—44no—
406C22×D4—48no—
407C22×D4—44no—
408C22×D4—48no—
409C22×D4—48no—
410C22×D4—48no—
411C22×D4—84no—
412C22×D4C2414yes—
413C22×D4C2414yes—
414C22×D4C2414yes—
415C22×D4C2418yes—
416C22×D4C2414yes—
417C22×D4C2418yes—
418C22×D4C2414yes—
419C22×D4C2414yes—
420C22×D4C2418yes—
421C22×D4C2412yes—
422C22×D4C2412yes—
423C22×D4C2412yes—
424C23×C4—44no—
425C23×C4—84no—
426C23×C4C2411yescharacteristic
427C23×C4C2414yes—
428C23×C4C2418yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2412yes—
436C23×C4C2412yes—
437C23×C4C2418yes—
438C23×C4C2418yes—
439C23×C4C2412yes—
440C4⋊Q8—48no—
441C4⋊Q8—48no—
442#124—216no—
443#124—416no—
444#124—416no—
445#124—48no—
446#123—48no—
447#123—48no—
448#123—48no—
449#123—416no—
450#123—48no—
451#123—48no—
452#123—88no—
453#123—84no—
454#123—88no—
455#123—84no—
456C22⋊Q8—416no—
457C22⋊Q8—44no—
458C22⋊Q8—44no—
459C22⋊Q8—48no—
460C22⋊Q8—48no—
461C22⋊Q8—88no—
462#121—232no—
463#121—416no—
464#121—416no—
465#121—416no—
466#121—44no—
467#121—44no—
468#121—416no—
469#120—48no—
470#120—48no—
471#120—416no—
472#120—48no—
473#120—84no—
474#120—84no—
475C4×D4—416no—
476#117—44no—
477#117—416no—
478#117—416no—
479C2×C4⋊C4—44no—
480C2×C4⋊C4C2418yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2418yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2412yes—
486C2×C4⋊C4C2412yes—
487C2×C4⋊C4C2418yes—
488C2×C4⋊C4C2414yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2418yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2414yes—
501C2×C22⋊C4—28no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—44no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—48no—
508C2×C22⋊C4—88no—
509C2×C22⋊C4—84no—
510C2×C22⋊C4C2414yes—
511C2×C22⋊C4C2414yes—
512C2×C22⋊C4C2414yes—
513C2×C22⋊C4C2414yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2418yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2414yes—
519C2×C22⋊C4C2414yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2414yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C2418yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C2414yes—
530C2×C22⋊C4C2414yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2414yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2418yes—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2414yes—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2414yes—
548C2×C42—42no—
549C2×C42C2414yes—
550C2×C42C2418yes—
551C2×C42C2414yes—
552C2×C42C2414yes—
553C2×C42C2414yes—
554#95C2418yes—
555#95C2418yes—
556#95C2418yes—
557#95C2418yes—
558#95C2414yes—
559#95C2418yes—
560#95C2418yes—
561#95C2414yes—
562#95C2418yes—
563#95C2414yes—
564#95C2414yes—
565#95C2418yes—
566#95C2418yes—
567#95C2418yes—
568#95C2418yes—
569#95C2418yes—
570#95C2418yes—
571#95C2418yes—
572#95C2418yes—
573#95C2418yes—
574#95C2418yes—
575#95C2418yes—
576C24—28no—
577C24—24no—
578C24—22no—
579C24—24no—
580C24—28no—
581C24—44no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—44no—
588C24—44no—
589C24—44no—
590C24—44no—
591C24—44no—
592C24—42no—
593C24—42no—
594C24—44no—
595C24H(5,𝔽2)14yes—
596C24C2512yes—
597C24C2514yes—
598C24C2512yes—
599C24C2511yescharacteristic
600C24C2514yes—
601#41—432no—
602#41—464no—
603C2×Q8—24no—
604C2×Q8—28no—
605C2×Q8—42no—
606C2×Q8—42no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8—44no—
612C2×Q8—44no—
613C2×Q8—88no—
614C2×D4—28no—
615C2×D4—28no—
616C2×D4—28no—
617C2×D4—28no—
618C2×D4—28no—
619C2×D4—28no—
620C2×D4—216no—
621C2×D4—28no—
622C2×D4—216no—
623C2×D4—28no—
624C2×D4—28no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—416no—
633C2×D4—48no—
634C2×D4—48no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—48no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—48no—
641C2×D4—42no—
642C2×D4—48no—
643C2×D4—42no—
644C2×D4—48no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—48no—
648C2×D4—464no—
649C2×D4—432no—
650C2×D4—432no—
651C2×D4—816no—
652C2×D4—816no—
653C2×D4H(5,𝔽2)18yes—
654C22×C4—22no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—28no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—24no—
663C22×C4—22no—
664C22×C4—24no—
665C22×C4—216no—
666C22×C4—28no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—42no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—48no—
673C22×C4—48no—
674C22×C4—48no—
675C22×C4—48no—
676C22×C4—48no—
677C22×C4—48no—
678C22×C4—44no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—44no—
683C22×C4—48no—
684C22×C4—42no—
685C22×C4—48no—
686C22×C4—816no—
687C22×C4C2512yes—
688C22×C4C2518yes—
689C22×C4C2514yes—
690C22×C4C2514yes—
691C22×C4C2518yes—
692C22×C4C2514yes—
693C22×C4C2518yes—
694C22×C4C2512yes—
695C22×C4C2512yes—
696C22×C4C2512yes—
697C22×C4C2514yes—
698C22×C4C2512yes—
699C4⋊C4—216no—
700C4⋊C4—48no—
701C4⋊C4—48no—
702C4⋊C4—44no—
703C4⋊C4—48no—
704C4⋊C4—48no—
705C4⋊C4—44no—
706C4⋊C4—42no—
707C4⋊C4—48no—
708C4⋊C4—42no—
709C4⋊C4—44no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—44no—
713C4⋊C4—48no—
714C4⋊C4—48no—
715C4⋊C4—48no—
716C4⋊C4—48no—
717C4⋊C4—48no—
718C4⋊C4—48no—
719C4⋊C4—44no—
720C22⋊C4—28no—
721C22⋊C4—28no—
722C22⋊C4—28no—
723C22⋊C4—28no—
724C22⋊C4—216no—
725C22⋊C4—216no—
726C22⋊C4—216no—
727C22⋊C4—216no—
728C22⋊C4—44no—
729C22⋊C4—48no—
730C22⋊C4—44no—
731C22⋊C4—48no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—48no—
735C22⋊C4—44no—
736C22⋊C4—48no—
737C22⋊C4—48no—
738C22⋊C4—44no—
739C22⋊C4—48no—
740C22⋊C4—48no—
741C22⋊C4—44no—
742C22⋊C4—44no—
743C22⋊C4—48no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—48no—
747C22⋊C4—44no—
748C22⋊C4—48no—
749C22⋊C4—44no—
750C22⋊C4—48no—
751C22⋊C4—48no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—48no—
755C22⋊C4—44no—
756C22⋊C4—48no—
757C22⋊C4—48no—
758C42—28no—
759C42—44no—
760C42—48no—
761C42—44no—
762C42—44no—
763C23—216no—
764C23—22no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—28no—
769C23—24no—
770C23—22no—
771C23—22no—
772C23—24no—
773C23—28no—
774C23—28no—
775C23—22no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—28no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—48no—
787C23—44no—
788C23—48no—
789C23—84no—
790C23—816no—
791C23—84no—
792C23—84no—
793C23—816no—
794C23—82no—
795C23—82no—
796C23—84no—
797C23—164no—
798C23—168no—
799C23—164no—
800C23—162no—
801C23—162no—
802C23C2×H(5,𝔽2)14yes—
803C23C2×H(5,𝔽2)18yes—
804C23C2×H(5,𝔽2)12yes—
805C23C2611yescharacteristic
806Q8—48no—
807Q8—88no—
808Q8—162no—
809Q8—162no—
810D4—48no—
811D4—416no—
812D4—416no—
813D4—416no—
814D4—416no—
815D4—816no—
816D4—816no—
817D4—88no—
818D4—88no—
819D4—168no—
820D4—162no—
821D4—162no—
822C2×C4—28no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—28no—
826C2×C4—22no—
827C2×C4—28no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—28no—
842C2×C4—28no—
843C2×C4—24no—
844C2×C4—28no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—24no—
848C2×C4—28no—
849C2×C4—24no—
850C2×C4—28no—
851C2×C4—28no—
852C2×C4—416no—
853C2×C4—48no—
854C2×C4—48no—
855C2×C4—48no—
856C2×C4—816no—
857C2×C4—82no—
858C2×C4—82no—
859C2×C4—84no—
860C2×C4—84no—
861C2×C4—82no—
862C2×C4—82no—
863C2×C4—816no—
864C2×C4—816no—
865C2×C4C2×H(5,𝔽2)14yes—
866C22—216no—
867C22—22no—
868C22—24no—
869C22—28no—
870C22—24no—
871C22—22no—
872C22—22no—
873C22—24no—
874C22—48no—
875C22—48no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—48no—
880C22—48no—
881C22—48no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—42no—
886C22—44no—
887C22—42no—
888C22—816no—
889C22—164no—
890C22—168no—
891C22—168no—
892C22—164no—
893C22C22×H(5,𝔽2)12yes—
894C22C22×H(5,𝔽2)11yescharacteristic
895C22H(7,𝔽2)12yes—
896C222−1+612yes—
897C4—24no—
898C4—48no—
899C4—48no—
900C4—48no—
901C4—44no—
902C4—44no—
903C4—42no—
904C4—42no—
905C4—44no—
906C4—44no—
907C4—42no—
908C4—42no—
909C2—48no—
910C2—44no—
911C2—42no—
912C2—84no—
913C2—82no—
914C2#6281711yescharacteristic
915C2#6286211yescharacteristic
916C2#6287111yescharacteristic
917C2#6304914yes—
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. #57962C2semidirect
2. #57960C2semidirect
3. #57959C2semidirect
4. #56584C2semidirect
5. #51531C2semidirect
6. #48777C2semidirect
7. #46999C2semidirect
8. #46997C2semidirect
9. #46386C2semidirect
10. #46288C2semidirect
11. #45562C2semidirect
12. #37117C2semidirect
13. #36967C2semidirect
14. #36966C2semidirect
15. #36718C2semidirect
16. #35616C2semidirect
17. #35347C2semidirect
19. C2×#555C22semidirect
20. C2×#543C22semidirect
21. C2×#536C22semidirect
22. C2×#534C22semidirect
23. C2×#534C22semidirect
26. #2855C22semidirect
27. #2854C22semidirect
28. #2849C22semidirect
29. #2848C22semidirect
30. #2842C22semidirect
31. #2835C22semidirect
32. #2831C22semidirect
33. #2827C22semidirect
34. #2826C22semidirect
35. #2824C22semidirect
36. #2807C22semidirect
37. #2805C22semidirect
38. #2804C22semidirect
39. #2796C22semidirect
40. #2780C22semidirect
41. #2779C22semidirect
42. #2771C22semidirect
43. #2761C22semidirect
44. #2750C22semidirect
45. #2743C22semidirect
46. #2743C22semidirect
47. #2743C22semidirect
48. #2734C22semidirect
49. #2732C22semidirect
50. #2731C22semidirect
51. #2710C22semidirect
52. #2708C22semidirect
53. #2706C22semidirect
54. #2700C22semidirect
55. #2697C22semidirect
56. #2696C22semidirect
57. #2693C22semidirect
58. #2693C22semidirect
59. #2688C22semidirect
60. #2686C22semidirect
61. #2686C22semidirect
62. #2682C22semidirect
63. #2682C22semidirect
64. #2681C22semidirect
65. #2681C22semidirect
66. #2674C22semidirect
67. #2674C22semidirect
68. #2672C22semidirect
69. #2672C22semidirect
70. #2672C22semidirect
71. #2671C22semidirect
72. #2670C22semidirect
73. #2670C22semidirect
74. #2668C22semidirect
75. #2668C22semidirect
76. #2635C22semidirect
77. #2628C22semidirect
78. #2626C22semidirect
79. #2626C22semidirect
80. #2624C22semidirect
81. #2623C22semidirect
82. #2617C22semidirect
83. #2609C22semidirect
84. #2583C22semidirect
85. #2561C22semidirect
86. #2539C22semidirect
87. #2534C22semidirect
88. #2505C22semidirect
89. #2488C22semidirect
90. #2483C22semidirect
91. #2483C22semidirect
92. #2482C22semidirect
93. #2471C22semidirect
94. #2471C22semidirect
95. #2470C22semidirect
96. #2470C22semidirect
97. #2470C22semidirect
98. #2457C22semidirect
99. #2450C22semidirect
100. #2438C22semidirect
101. #2437C22semidirect
102. #2436C22semidirect
103. #2435C22semidirect
104. #2435C22semidirect
105. #2434C22semidirect
106. #2432C22semidirect
108. #2430C22semidirect
109. #2418C22semidirect
110. #2418C22semidirect
111. #2412C22semidirect
112. #2411C22semidirect
113. #2411C22semidirect
115. #2410C22semidirect
116. #2410C22semidirect
117. #2406C22semidirect
122. #2405C22semidirect
123. #2405C22semidirect
124. #2405C22semidirect
125. #2405C22semidirect
126. #2404C22semidirect
129. #2379C22semidirect
130. #2377C22semidirect
131. #2312C22semidirect
132. #2312C22semidirect
133. #2312C22semidirect
136. #2308C22semidirect
137. #2297C22semidirect
138. C2×#386C22semidirect

Maximal subgroups

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

subgroupindex
#579622
#579602
#579592
#565842
#515312
#487772
#469992
#469972
#463862
#462882
#455622
#371172
#369672
#369662
#367182
#356162
#353472