Finite Group Databasebeta

← #9712338

Subgroups — #9712338

Order 512.

5458 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#58260C211yesmaximal, characteristic, complemented
2#57180C216yesmaximal, complemented
3#55351C216yesmaximal, complemented
4#54011C216yesmaximal, complemented
5#53380C212yesmaximal, complemented
6#50893C213yesmaximal, complemented
7#49750C213yesmaximal, complemented
8#49572C216yesmaximal, complemented
9#47689C216yesmaximal, complemented
10#44657C213yesmaximal, complemented
11#43894C213yesmaximal, complemented
12#42966C213yesmaximal, complemented
13#41627C213yesmaximal, complemented
14#40129C216yesmaximal, complemented
15#39444C216yesmaximal, complemented
16C2×#562C2213yescomplemented
17C2×#546C2213yescomplemented
18C2×#538C2213yescomplemented
19C2×#538C2216yescomplemented
20C2×#535C2213yescomplemented
21#2860C2216yescomplemented
22#2835C2211yescharacteristic, complemented
23#2828C2216yescomplemented
24#2818C2216yescomplemented
25#2813C2216yescomplemented
26#2812C2213yescomplemented
27#2812C2213yescomplemented
28#2803C2216yescomplemented
29#2803C2216yescomplemented
30#2795C2213yescomplemented
31#2783C2216yescomplemented
32#2782C2216yescomplemented
33#2781C2216yescomplemented
34#2781C2216yescomplemented
35#2769C2213yescomplemented
36#2756C2216yescomplemented
37#2756C2216yescomplemented
38#2753C2216yescomplemented
39#2753C2216yescomplemented
40#2736C2211yescharacteristic, complemented
41#2733C2216yescomplemented
42#2733C2216yescomplemented
43#2732C2216yescomplemented
44#2730C2216yescomplemented
45#2723C2216yescomplemented
46#2718C2216yescomplemented
47#2718C2216yescomplemented
48#2714C2216yescomplemented
49#2714C2216yescomplemented
50#2711C2216yescomplemented
51#2706C2216yescomplemented
52#2703C2216yescomplemented
53#2685C2216yescomplemented
54#2682C2216yescomplemented
55#2681C2216yescomplemented
56#2679C2213yes—
57#2679C2216yescomplemented
58#2679C2213yescomplemented
59#2678C2216yescomplemented
60#2678C2216yescomplemented
61#2678C2216yescomplemented
62#2675C2216yescomplemented
63#2673C2216yescomplemented
64#2673C2216yescomplemented
65#2673C2216yescomplemented
66#2671C2216yescomplemented
67#2670C2213yescomplemented
68#2669C2216yes—
69#2669C2216yescomplemented
70#2669C2216yescomplemented
71#2669C2216yescomplemented
72#2669C2216yescomplemented
73#2669C2216yescomplemented
74#2661C2216yescomplemented
75#2661C2216yescomplemented
76#2636C2216yescomplemented
77#2636C2216yescomplemented
78#2633C2213yescomplemented
79#2631C2213yes—
80#2624C2213yescomplemented
81#2619C2216yescomplemented
82#2617C2216yescomplemented
83#2609C2213yescomplemented
84#2601C2216yescomplemented
85#2598C2216yescomplemented
86#2582C2213yescomplemented
87#2566C2213yescomplemented
88#2559C2216yescomplemented
89#2559C2216yescomplemented
90#2559C2216yescomplemented
91#2554C2216yescomplemented
92#2554C2216yescomplemented
93#2548C2216yescomplemented
94#2543C2213yes—
95#2541C2216yes—
96#2540C2213yescomplemented
97#2539C2216yescomplemented
98#2539C2216yescomplemented
99#2519C2216yescomplemented
100#2518C2216yescomplemented
101#2500C2216yescomplemented
102#2495C2216yescomplemented
103#2476C2216yescomplemented
104#2464C2216yescomplemented
105#2464C2216yescomplemented
106#2461C2216yescomplemented
107#2456C2216yescomplemented
108#2455C2213yescomplemented
109#2455C2216yescomplemented
110#2445C2216yescomplemented
111#2437C2213yescomplemented
112#2433C2213yescomplemented
113#2433C2213yescomplemented
114#2433C2216yescomplemented
115#2431C2216yescomplemented
116#2428C2216yescomplemented
117#2426C2216yescomplemented
118#2426C2216yescomplemented
119#2424C2216yescomplemented
120#2424C2216yescomplemented
121#2424C2216yescomplemented
122#2424C2216yescomplemented
123#2422C2216yescomplemented
124#2414C2216yescomplemented
125#2411C2216yescomplemented
126#2410C2216yescomplemented
127#2410C2216yescomplemented
128#2408C2213yes—
129#2407C2216yescomplemented
130#2403C2213yescomplemented
131#2395C2213yescomplemented
132C2×#392C2211yescharacteristic, complemented
133#2375C2211yescharacteristic
134#2368C2213yescomplemented
135#2362C2216yescomplemented
136#2358C2213yescomplemented
137#2358C2216yescomplemented
138#2341C2213yescomplemented
139#2337C2216yescomplemented
140#2337C2213yescomplemented
141#2321C2213yescomplemented
142C4×#127C2212yescomplemented
143C4×#124C2216yescomplemented
144C22×#41C2313yes—
145C23×D4C2313yes—
146C23×D4C2313yes—
147#562—412no—
148#546—412no—
149#538—412no—
150#538—424no—
151#535—412no—
152C2×#127C2312yes—
153C2×#127C2316yes—
154C2×#127C2316yes—
155C2×#127C2316yes—
156C2×#126C2316yes—
157C2×#126C2316yes—
158C2×#126C2316yes—
159C2×#125C2313yes—
160C2×#124C2316yes—
161C2×#124C2313yes—
162C2×#124C2316yes—
163C2×#124C2313yes—
164C2×#123C2316yes—
165C2×#123C2316yes—
166C2×#123C2316yes—
167C2×#123C2316yes—
168C2×#123C2316yes—
169C2×#123C2316yes—
170C2×C22⋊Q8C2316yes—
171C2×C22⋊Q8C2313yes—
172C2×C22⋊Q8C2316yes—
173C2×#121C2316yes—
174C2×#121C2316yes—
175C2×#121C2316yes—
176C2×#121C2313yes—
177C2×#121C2316yes—
178C2×#121C2316yes—
179C2×#121C2313yes—
180C2×#121C2316yes—
181C2×#121C2316yes—
182C2×#121C2316yes—
183C2×#121C2316yes—
184C2×#121C2316yes—
185C2×#121C2316yes—
186C2×#121C2316yes—
187C2×#121C2316yes—
188C2×#120C2313yes—
189C2×#120C2316yes—
190C2×#120C2313yes—
191C2×#120C2311yescharacteristic
192C2×#120C2316yes—
193C2×#120C2316yes—
194C2×#120C2316yes—
195C2×#120C2316yes—
196C2×#120C2316yes—
197C2×#120C2316yes—
198C2×#120C2316yes—
199C2×#120C2316yes—
200C2×#120C2316yes—
201C2×C4×Q8C2316yes—
202C2×C4×D4C2316yes—
203C2×C4×D4C2316yes—
204C2×C4×D4C2313yes—
205C2×C4×D4C2316yes—
206C2×C4×D4C2313yes—
207C2×C4×D4C2316yes—
208C2×#117C2313yes—
209C2×#117C2316yes—
210C22×C22⋊C4C2313yes—
211C22×C22⋊C4C2316yes—
212C22×C22⋊C4C2316yes—
213#400C2316yes—
214#400C2316yes—
215#400C2316yes—
216#400C2313yes—
217#399C2316yes—
218#399C2316yes—
219#399C2313yes—
220#399C2316yes—
221#398C2313yes—
222#398C2316yes—
223#398C2313yes—
224#398C2316yes—
225#398C2316yes—
226#397C2316yes—
227#397C2316yes—
228#397C2313yes—
229#397C2316yes—
230#397C2316yes—
231#397C2316yes—
232#397C2313yes—
233#396C2316yes—
234#396C2316yes—
235#396C2316yes—
236#396C2316yes—
237#396C2316yes—
238#396C2316yes—
239#396C2316yes—
240#395C2312yes—
241#394C2316yes—
242#394C2316yes—
243#394C2316yes—
244#394C2316yes—
245#394C2316yes—
246#394C2316yes—
247#394C2316yes—
248#394C2316yes—
249#394C2316yes—
250#394C2316yes—
251#394C2313yes—
252#394C2316yes—
253#394C2316yes—
254#394C2316yes—
255#394C2316yes—
256#394C2316yes—
257#394C2316yes—
258#394C2316yes—
259#394C2316yes—
260#394C2316yes—
261#394C2316yes—
262#394C2316yes—
263#394C2316yes—
264#394C2316yes—
265#394C2316yes—
266#394C2316yes—
267#394C2316yes—
268#394C2316yes—
269#394C2316yes—
270#394C2316yes—
271#393C2311yescharacteristic
272#393C2313yes—
273#392C2316yes—
274#392C2316yes—
275#392C2316yes—
276#392C2316yes—
277#392C2316yes—
278#392C2316yes—
279#392C2316yes—
280#392C2316yes—
281#392C2316yes—
282#392C2316yes—
283#392C2316yes—
284#392C2316yes—
285#392C2313yes—
286#392C2313yes—
287#392C2312yes—
288#392C2316yes—
289#392C2313yes—
290#392C2316yes—
291#392C2316yes—
292#392C2316yes—
293#392C2316yes—
294#392C2316yes—
295#392C2316yes—
296#392C2316yes—
297#392C2316yes—
298#391C2316yes—
299#391C2316yes—
300#390C2316yes—
301#390C2316yes—
302#390C2313yes—
303#390C2313yes—
304#390C2316yes—
305#390C2316yes—
306#390C2316yes—
307#390C2316yes—
308#390C2316yes—
309#390C2316yes—
310#390C2316yes—
311#390C2316yes—
312#390C2316yes—
313#390C2316yes—
314#390C2316yes—
315#390C2316yes—
316#390C2316yes—
317#390C2316yes—
318#390C2316yes—
319#389C2316yes—
320#389C2316yes—
321#389C2316yes—
322#389C2316yes—
323#389C2316yes—
324#388C2316yes—
325#388C2316yes—
326#388C2316yes—
327#388C2316yes—
328#388C2316yes—
329#388C2316yes—
330#388C2316yes—
331#388C2316yes—
332#388C2316yes—
333#388C2316yes—
334#388C2316yes—
335#388C2316yes—
336#388C2316yes—
337#388C2316yes—
338#388C2316yes—
339#388C2316yes—
340#388C2316yes—
341#388C2316yes—
342#388C2316yes—
343#388C2316yes—
344#388C2316yes—
345#388C2316yes—
346#388C2316yes—
347#388C2316yes—
348#388C2316yes—
349#388C2316yes—
350#387C2316yes—
351#387C2316yes—
352#387C2316yes—
353#387C2316yes—
354#386C2316yes—
355#386C2313yes—
356#386C2316yes—
357#386C2316yes—
358#386C2316yes—
359#386C2316yes—
360#386C2316yes—
361#386C2316yes—
362#386C2316yes—
363#386C2316yes—
364#386C2316yes—
365#386C2316yes—
366#386C2316yes—
367#386C2316yes—
368#386C2316yes—
369#386C2316yes—
370#386C2316yes—
371#385C2316yes—
372#385C2316yes—
373#385C2313yes—
374#385C2316yes—
375#385C2316yes—
376#385C2316yes—
377#385C2316yes—
378#385C2316yes—
379#385C2316yes—
380#385C2316yes—
381#385C2316yes—
382#384C2312yes—
383#384C2313yes—
384#383C2316yes—
385#383C2313yes—
386#382C2313yes—
387#382C2316yes—
388#382C2316yes—
389#380C2316yes—
390#380C2313yes—
391#380C2316yes—
392#379C2313yes—
393#379C2312yes—
394#379C2313yes—
395#379C2313yes—
396C4×C4⋊C4C2313yes—
397C4×C4⋊C4C2316yes—
398C4×C4⋊C4C2316yes—
399C4×C22⋊C4C2313yes—
400C4×C22⋊C4C2313yes—
401C4×C22⋊C4C2316yes—
402C4×C22⋊C4C2316yes—
403C4×C22⋊C4C2316yes—
404C4×C22⋊C4C2316yes—
405C4×C22⋊C4C2316yes—
406C2×#95C2311yescharacteristic
407C43C2312yes—
408C25C2413yes—
409C25C2413yes—
410C25C2411yescharacteristic
411C2×#41—212no—
412C2×#41—86no—
413C22×Q8C2411yescharacteristic
414C22×Q8C2413yes—
415C22×D4—46no—
416C22×D4—46no—
417C22×D4—86no—
418C22×D4—86no—
419C22×D4C2413yes—
420C22×D4C2416yes—
421C22×D4C2416yes—
422C22×D4C2413yes—
423C22×D4C2416yes—
424C22×D4C2416yes—
425C22×D4C2413yes—
426C22×D4C2416yes—
427C22×D4C2416yes—
428C22×D4C2416yes—
429C22×D4C2416yes—
430C22×D4C2413yes—
431C22×D4C2416yes—
432C22×D4C2416yes—
433C22×D4C2416yes—
434C22×D4C2413yes—
435C22×D4C2416yes—
436C22×D4C2416yes—
437C22×D4C2416yes—
438C23×C4C2416yes—
439C23×C4C2413yes—
440C23×C4C2416yes—
441C23×C4C2413yes—
442C23×C4C2411yescharacteristic
443C23×C4C2416yes—
444C23×C4C2416yes—
445#127—412no—
446#127—44no—
447#127—86no—
448#127—86no—
449#126—412no—
450#126—412no—
451#126—412no—
452#125—46no—
453#124—224no—
454#124—224no—
455#124—212no—
456#124—46no—
457#123—412no—
458#123—412no—
459#123—412no—
460#123—412no—
461#123—412no—
462#123—412no—
463C22⋊Q8—212no—
464C22⋊Q8—224no—
465C22⋊Q8—412no—
466#121—412no—
467#121—412no—
468#121—412no—
469#121—46no—
470#121—412no—
471#121—412no—
472#121—412no—
473#121—412no—
474#121—412no—
475#121—412no—
476#121—46no—
477#121—86no—
478#121—86no—
479#121—86no—
480#121—86no—
481#120—412no—
482#120—412no—
483#120—412no—
484#120—412no—
485#120—412no—
486#120—412no—
487#120—46no—
488#120—412no—
489#120—42no—
490#120—46no—
491#120—86no—
492#120—86no—
493#120—86no—
494C4×Q8—86no—
495C4×D4—412no—
496C4×D4—412no—
497C4×D4—412no—
498C4×D4—46no—
499C4×D4—46no—
500C4×D4—86no—
501#117—46no—
502#117—86no—
503C2×C4⋊C4C2413yes—
504C2×C4⋊C4C2416yes—
505C2×C4⋊C4C2416yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C2416yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2413yes—
510C2×C4⋊C4C2413yes—
511C2×C4⋊C4C2416yes—
512C2×C4⋊C4C2416yes—
513C2×C4⋊C4C2413yes—
514C2×C4⋊C4C2416yes—
515C2×C4⋊C4C2416yes—
516C2×C4⋊C4C2416yes—
517C2×C4⋊C4C2416yes—
518C2×C4⋊C4C2416yes—
519C2×C4⋊C4C2416yes—
520C2×C4⋊C4C2416yes—
521C2×C4⋊C4C2413yes—
522C2×C4⋊C4C2413yes—
523C2×C4⋊C4C2413yes—
524C2×C22⋊C4—46no—
525C2×C22⋊C4—412no—
526C2×C22⋊C4—412no—
527C2×C22⋊C4C2416yes—
528C2×C22⋊C4C2416yes—
529C2×C22⋊C4C2416yes—
530C2×C22⋊C4C2416yes—
531C2×C22⋊C4C2416yes—
532C2×C22⋊C4C2416yes—
533C2×C22⋊C4C2416yes—
534C2×C22⋊C4C2416yes—
535C2×C22⋊C4C2413yes—
536C2×C22⋊C4C2416yes—
537C2×C22⋊C4C2416yes—
538C2×C22⋊C4C2416yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2416yes—
541C2×C22⋊C4C2413yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C2416yes—
545C2×C22⋊C4C2416yes—
546C2×C22⋊C4C2416yes—
547C2×C22⋊C4C2416yes—
548C2×C22⋊C4C2416yes—
549C2×C22⋊C4C2416yes—
550C2×C22⋊C4C2416yes—
551C2×C22⋊C4C2416yes—
552C2×C22⋊C4C2413yes—
553C2×C22⋊C4C2413yes—
554C2×C22⋊C4C2416yes—
555C2×C22⋊C4C2416yes—
556C2×C22⋊C4C2416yes—
557C2×C22⋊C4C2416yes—
558C2×C22⋊C4C2416yes—
559C2×C22⋊C4C2416yes—
560C2×C22⋊C4C2416yes—
561C2×C22⋊C4C2416yes—
562C2×C22⋊C4C2416yes—
563C2×C22⋊C4C2416yes—
564C2×C22⋊C4C2413yes—
565C2×C22⋊C4C2413yes—
566C2×C22⋊C4C2416yes—
567C2×C22⋊C4C2416yes—
568C2×C22⋊C4C2416yes—
569C2×C22⋊C4C2416yes—
570C2×C22⋊C4C2416yes—
571C2×C42C2416yes—
572C2×C42C2413yes—
573C2×C42C2416yes—
574C2×C42C2413yes—
575C2×C42C2416yes—
576C2×C42C2416yes—
577C2×C42C2413yes—
578C2×C42C2416yes—
579C2×C42C2412yes—
580#95C2413yes—
581#95C2411yescharacteristic
582#95C2413yes—
583#95C2416yes—
584#95C2416yes—
585#95C2413yes—
586#95C2416yes—
587#95C2416yes—
588#95C2416yes—
589#95C2416yes—
590#95C2416yes—
591#95C2416yes—
592#95C2416yes—
593#95C2416yes—
594#95C2416yes—
595#95C2416yes—
596#95C2413yes—
597#95C2416yes—
598#95C2416yes—
599#95C2416yes—
600#95C2416yes—
601#95C2413yes—
602#95C2416yes—
603C24—26no—
604C24—43no—
605C24—46no—
606C24—43no—
607C24—46no—
608C24—46no—
609C24—43no—
610C24—43no—
611C24—46no—
612C24—43no—
613C24—43no—
614C24—41no—
615C24—43no—
616C24C2513yes—
617C24C2516yes—
618C24C2516yes—
619C24C2511yescharacteristic
620#41—824no—
621C2×Q8—46no—
622C2×Q8—43no—
623C2×Q8H(5,𝔽2)112yes—
624C2×D4—26no—
625C2×D4—212no—
626C2×D4—26no—
627C2×D4—212no—
628C2×D4—212no—
629C2×D4—212no—
630C2×D4—26no—
631C2×D4—46no—
632C2×D4—43no—
633C2×D4—46no—
634C2×D4—46no—
635C2×D4—46no—
636C2×D4—46no—
637C2×D4—46no—
638C2×D4—46no—
639C2×D4—46no—
640C2×D4—46no—
641C2×D4—46no—
642C2×D4—46no—
643C2×D4—43no—
644C2×D4—46no—
645C2×D4—46no—
646C2×D4—46no—
647C2×D4—46no—
648C2×D4—46no—
649C2×D4—46no—
650C2×D4—46no—
651C2×D4—46no—
652C2×D4—46no—
653C2×D4—46no—
654C2×D4—46no—
655C2×D4—46no—
656C2×D4—46no—
657C2×D4—46no—
658C2×D4—46no—
659C2×D4—46no—
660C2×D4—46no—
661C2×D4—46no—
662C2×D4—46no—
663C2×D4—46no—
664C2×D4—46no—
665C2×D4—46no—
666C2×D4—46no—
667C2×D4—46no—
668C2×D4—46no—
669C2×D4—46no—
670C2×D4—46no—
671C2×D4—43no—
672C2×D4—46no—
673C2×D4—46no—
674C2×D4—43no—
675C2×D4—46no—
676C2×D4—46no—
677C2×D4—824no—
678C2×D4—824no—
679C22×C4—26no—
680C22×C4—26no—
681C22×C4—212no—
682C22×C4—212no—
683C22×C4—46no—
684C22×C4—46no—
685C22×C4—46no—
686C22×C4—46no—
687C22×C4—46no—
688C22×C4—46no—
689C22×C4—43no—
690C22×C4—46no—
691C22×C4—46no—
692C22×C4—46no—
693C22×C4—46no—
694C22×C4—46no—
695C22×C4—46no—
696C22×C4C2513yes—
697C22×C4C2516yes—
698C22×C4C2513yes—
699C22×C4C2516yes—
700C22×C4C2516yes—
701C22×C4C2513yes—
702C22×C4C2512yes—
703C22×C4C2513yes—
704C22×C4C2516yes—
705C22×C4C2513yes—
706C22×C4C2516yes—
707C4⋊C4—26no—
708C4⋊C4—212no—
709C4⋊C4—212no—
710C4⋊C4—212no—
711C4⋊C4—212no—
712C4⋊C4—43no—
713C4⋊C4—43no—
714C4⋊C4—46no—
715C4⋊C4—46no—
716C4⋊C4—43no—
717C4⋊C4—46no—
718C4⋊C4—46no—
719C4⋊C4—46no—
720C4⋊C4—46no—
721C4⋊C4—46no—
722C4⋊C4—46no—
723C4⋊C4—46no—
724C4⋊C4—43no—
725C4⋊C4—46no—
726C4⋊C4—43no—
727C4⋊C4—43no—
728C22⋊C4—26no—
729C22⋊C4—212no—
730C22⋊C4—212no—
731C22⋊C4—212no—
732C22⋊C4—212no—
733C22⋊C4—212no—
734C22⋊C4—212no—
735C22⋊C4—212no—
736C22⋊C4—212no—
737C22⋊C4—212no—
738C22⋊C4—212no—
739C22⋊C4—212no—
740C22⋊C4—212no—
741C22⋊C4—212no—
742C22⋊C4—43no—
743C22⋊C4—46no—
744C22⋊C4—46no—
745C22⋊C4—46no—
746C22⋊C4—46no—
747C22⋊C4—46no—
748C22⋊C4—46no—
749C22⋊C4—46no—
750C22⋊C4—46no—
751C22⋊C4—43no—
752C22⋊C4—46no—
753C22⋊C4—46no—
754C22⋊C4—43no—
755C22⋊C4—46no—
756C22⋊C4—46no—
757C22⋊C4—46no—
758C22⋊C4—46no—
759C22⋊C4—43no—
760C22⋊C4—46no—
761C22⋊C4—46no—
762C22⋊C4—46no—
763C22⋊C4—43no—
764C22⋊C4—46no—
765C22⋊C4—46no—
766C22⋊C4—46no—
767C22⋊C4—46no—
768C22⋊C4—46no—
769C22⋊C4—46no—
770C22⋊C4—46no—
771C22⋊C4—46no—
772C42—212no—
773C42—26no—
774C42—212no—
775C42—43no—
776C42—46no—
777C42—46no—
778C42—43no—
779C42—46no—
780C42—42no—
781C23—23no—
782C23—23no—
783C23—26no—
784C23—26no—
785C23—26no—
786C23—26no—
787C23—26no—
788C23—26no—
789C23—23no—
790C23—26no—
791C23—26no—
792C23—23no—
793C23—26no—
794C23—26no—
795C23—26no—
796C23—26no—
797C23—23no—
798C23—26no—
799C23—26no—
800C23—26no—
801C23—26no—
802C23—86no—
803C23—812no—
804C23—812no—
805C23—86no—
806C23—86no—
807C23—812no—
808C23—163no—
809C23—163no—
810C23—163no—
811C23—161no—
812C23—166no—
813C23—163no—
814C23—163no—
815C23#58512yes—
816C23C2611yescharacteristic
817Q8—412no—
818Q8—161no—
819D4—412no—
820D4—812no—
821D4—86no—
822D4—812no—
823D4—812no—
824D4—86no—
825D4—812no—
826D4—812no—
827D4—812no—
828D4—812no—
829D4—812no—
830D4—166no—
831D4—166no—
832D4—163no—
833D4—163no—
834D4—166no—
835D4—166no—
836D4—166no—
837D4—166no—
838C2×C4—26no—
839C2×C4—26no—
840C2×C4—26no—
841C2×C4—23no—
842C2×C4—26no—
843C2×C4—26no—
844C2×C4—26no—
845C2×C4—26no—
846C2×C4—23no—
847C2×C4—26no—
848C2×C4—26no—
849C2×C4—26no—
850C2×C4—26no—
851C2×C4—23no—
852C2×C4—23no—
853C2×C4—26no—
854C2×C4—26no—
855C2×C4—23no—
856C2×C4—26no—
857C2×C4—23no—
858C2×C4—26no—
859C2×C4—26no—
860C2×C4—26no—
861C2×C4—26no—
862C2×C4—26no—
863C2×C4—412no—
864C2×C4—812no—
865C2×C4—86no—
866C2×C4—812no—
867C2×C4—161no—
868C2×C4—166no—
869C2×C4—166no—
870C2×C4C2×H(5,𝔽2)16yes—
871C2×C4C2×H(5,𝔽2)112yes—
872C22—26no—
873C22—41no—
874C22—43no—
875C22—46no—
876C22—46no—
877C22—43no—
878C22—43no—
879C22—46no—
880C22—46no—
881C22—46no—
882C22—46no—
883C22—46no—
884C22—46no—
885C22—46no—
886C22—46no—
887C22—46no—
888C22—46no—
889C22—46no—
890C22—43no—
891C22—46no—
892C22—46no—
893C22—46no—
894C22—1612no—
895C22—1612no—
896C22—164no—
897C22C22×H(5,𝔽2)13yes—
898C22C2×#58511yescharacteristic
899C22H(7,𝔽2)13yes—
900C4—26no—
901C4—212no—
902C4—42no—
903C4—46no—
904C4—43no—
905C4—43no—
906C4—43no—
907C4—46no—
908C4—43no—
909C4—46no—
910C4—46no—
911C2—42no—
912C2—86no—
913C2—86no—
914C2—83no—
915C2#6286313yes—
916C2#6289913yes—
917C2#6304011yescharacteristic
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. #58260C2semidirect
2. #57180C2semidirect
3. #55351C2semidirect
4. #54011C2semidirect
5. #53380C2semidirect
6. #50893C2semidirect
7. #49750C2semidirect
8. #49572C2semidirect
9. #47689C2semidirect
10. #44657C2semidirect
11. #43894C2semidirect
12. #42966C2semidirect
13. #41627C2semidirect
14. #40129C2semidirect
15. #39444C2semidirect
16. C2×#562C22semidirect
17. C2×#546C22semidirect
18. C2×#538C22semidirect
19. C2×#538C22semidirect
20. C2×#535C22semidirect
21. #2860C22semidirect
22. #2835C22semidirect
23. #2828C22semidirect
24. #2818C22semidirect
25. #2813C22semidirect
26. #2812C22semidirect
27. #2812C22semidirect
28. #2803C22semidirect
29. #2803C22semidirect
30. #2795C22semidirect
31. #2783C22semidirect
32. #2782C22semidirect
33. #2781C22semidirect
34. #2781C22semidirect
35. #2769C22semidirect
36. #2756C22semidirect
37. #2756C22semidirect
38. #2753C22semidirect
39. #2753C22semidirect
40. #2736C22semidirect
41. #2733C22semidirect
42. #2733C22semidirect
43. #2732C22semidirect
44. #2730C22semidirect
45. #2723C22semidirect
46. #2718C22semidirect
47. #2718C22semidirect
48. #2714C22semidirect
49. #2714C22semidirect
50. #2711C22semidirect
51. #2706C22semidirect
52. #2703C22semidirect
53. #2685C22semidirect
54. #2682C22semidirect
55. #2681C22semidirect
57. #2679C22semidirect
58. #2679C22semidirect
59. #2678C22semidirect
60. #2678C22semidirect
61. #2678C22semidirect
62. #2675C22semidirect
63. #2673C22semidirect
64. #2673C22semidirect
65. #2673C22semidirect
66. #2671C22semidirect
67. #2670C22semidirect
69. #2669C22semidirect
70. #2669C22semidirect
71. #2669C22semidirect
72. #2669C22semidirect
73. #2669C22semidirect
74. #2661C22semidirect
75. #2661C22semidirect
76. #2636C22semidirect
77. #2636C22semidirect
78. #2633C22semidirect
80. #2624C22semidirect
81. #2619C22semidirect
82. #2617C22semidirect
83. #2609C22semidirect
84. #2601C22semidirect
85. #2598C22semidirect
86. #2582C22semidirect
87. #2566C22semidirect
88. #2559C22semidirect
89. #2559C22semidirect
90. #2559C22semidirect
91. #2554C22semidirect
92. #2554C22semidirect
93. #2548C22semidirect
96. #2540C22semidirect
97. #2539C22semidirect
98. #2539C22semidirect
99. #2519C22semidirect
100. #2518C22semidirect
101. #2500C22semidirect
102. #2495C22semidirect
103. #2476C22semidirect
104. #2464C22semidirect
105. #2464C22semidirect
106. #2461C22semidirect
107. #2456C22semidirect
108. #2455C22semidirect
109. #2455C22semidirect
110. #2445C22semidirect
111. #2437C22semidirect
112. #2433C22semidirect
113. #2433C22semidirect
114. #2433C22semidirect
115. #2431C22semidirect
116. #2428C22semidirect
117. #2426C22semidirect
118. #2426C22semidirect
119. #2424C22semidirect
120. #2424C22semidirect
121. #2424C22semidirect
122. #2424C22semidirect
123. #2422C22semidirect
124. #2414C22semidirect
125. #2411C22semidirect
126. #2410C22semidirect
127. #2410C22semidirect
129. #2407C22semidirect
130. #2403C22semidirect
131. #2395C22semidirect
132. C2×#392C22semidirect
134. #2368C22semidirect
135. #2362C22semidirect
136. #2358C22semidirect
137. #2358C22semidirect
138. #2341C22semidirect
139. #2337C22semidirect
140. #2337C22semidirect
141. #2321C22semidirect
142. C4×#127C22semidirect
143. C4×#124C22semidirect

Maximal subgroups

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

subgroupindex
#582602
#571802
#553512
#540112
#533802
#508932
#497502
#495722
#476892
#446572
#438942
#429662
#416272
#401292
#394442