Finite Group Databasebeta

← #8096699

Subgroups — #8096699

Order 512.

5478 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52662C213yesmaximal, complemented
2#52494C216yesmaximal, complemented
3#52422C213yesmaximal, complemented
4#52325C216yesmaximal, complemented
5#52096C213yesmaximal, complemented
6#46225C216yesmaximal, complemented
7#46214C216yesmaximal, complemented
8#45823C216yesmaximal, complemented
9#45477C213yesmaximal, complemented
10#45452C216yesmaximal, complemented
11#36339C213yesmaximal, complemented
12#36147C216yesmaximal, complemented
13#35924C211yesmaximal, characteristic, complemented
14#35918C212yesmaximal, complemented
15#35684C213yesmaximal, complemented
16C2×H(3,𝔽4)C2213yescomplemented
17C2×#560C2213yes—
18C2×#532C2216yes—
19C2×#525C2216yescomplemented
20#2855C2216yescomplemented
21#2850C2216yescomplemented
22#2850C2216yescomplemented
23#2847C2216yescomplemented
24#2847C2213yescomplemented
25#2837C2216yescomplemented
26#2832C2213yescomplemented
27#2832C2216yescomplemented
28#2830C2213yescomplemented
29#2826C2216yescomplemented
30#2824C2216yescomplemented
31#2819C2216yescomplemented
32#2819C2216yescomplemented
33#2818C2212yescomplemented
34#2815C2213yescomplemented
35#2813C2216yescomplemented
36#2813C2216yescomplemented
37#2812C2216yescomplemented
38#2812C2211yescharacteristic, complemented
39#2775C2216yescomplemented
40#2771C2213yescomplemented
41#2767C2216yescomplemented
42#2731C2216yescomplemented
43#2731C2216yescomplemented
44#2728C2213yescomplemented
45#2723C2216yescomplemented
46#2717C2213yescomplemented
47#2715C2216yescomplemented
48#2702C2216yescomplemented
49#2702C2216yescomplemented
50#2686C2216yescomplemented
51#2679C2213yescomplemented
52#2677C2213yescomplemented
53#2676C2216yes—
54#2676C2216yes—
55#2676C2216yes—
56#2676C2216yescomplemented
57#2676C2216yescomplemented
58#2675C2211yescharacteristic, complemented
59#2674C2216yescomplemented
60#2673C2216yescomplemented
61#2672C2216yescomplemented
62#2671C2216yescomplemented
63#2671C2216yescomplemented
64#2670C2213yescomplemented
65#2669C2216yes—
66#2669C2213yes—
67#2669C2216yescomplemented
68#2669C2216yescomplemented
69#2669C2216yescomplemented
70#2669C2216yescomplemented
71#2668C2213yescomplemented
72#2668C2213yescomplemented
73#2665C2213yescomplemented
74#2648C2216yescomplemented
75#2635C2216yescomplemented
76#2631C2213yescomplemented
77#2607C2216yescomplemented
78#2605C2213yescomplemented
79#2587C2216yescomplemented
80#2574C2216yescomplemented
81#2572C2216yescomplemented
82#2559C2216yescomplemented
83#2557C2216yescomplemented
84#2557C2216yescomplemented
85#2555C2216yes—
86#2549C2213yescomplemented
87#2544C2213yes—
88#2543C2213yes—
89#2534C2213yescomplemented
90#2531C2216yescomplemented
91#2521C2216yescomplemented
92#2518C2216yescomplemented
93#2516C2216yescomplemented
94#2492C2216yescomplemented
95#2476C2216yescomplemented
96#2476C2216yescomplemented
97#2472C2216yescomplemented
98#2467C2216yescomplemented
99#2467C2216yescomplemented
100#2459C2216yescomplemented
101#2459C2216yescomplemented
102#2459C2216yescomplemented
103#2459C2216yescomplemented
104#2459C2216yescomplemented
105#2457C2216yescomplemented
106#2457C2216yescomplemented
107#2457C2216yescomplemented
108#2444C2216yescomplemented
109#2444C2216yescomplemented
110#2439C2216yescomplemented
111#2431C2216yes—
112#2431C2216yes—
113#2428C2216yes—
114#2428C2216yes—
115#2427C2216yescomplemented
116#2424C2216yescomplemented
117#2424C2216yescomplemented
118#2424C2216yescomplemented
119#2424C2216yescomplemented
120#2424C2216yescomplemented
121#2420C2216yescomplemented
122#2404C2216yescomplemented
123#2404C2216yescomplemented
124#2404C2213yescomplemented
125#2397C2213yescomplemented
126#2392C2216yescomplemented
127#2388C2213yes—
128#2388C2216yescomplemented
129#2379C2216yescomplemented
130#2376C2216yescomplemented
131#2372C2213yescomplemented
132#2364C2213yescomplemented
133#2364C2216yescomplemented
134#2363C2216yescomplemented
135#2353C2213yescomplemented
136#2339C2213yescomplemented
137#2339C2216yescomplemented
138C4×#121C2216yescomplemented
139C4×#120C2213yescomplemented
140#2290C2216yescomplemented
141#2275C2211yescharacteristic, complemented
142#2273C2211yescharacteristic, complemented
143C2×C4×C22⋊C4C2213yescomplemented
144C22×#41C2313yes—
145C22×#41C2316yes—
146C24×C4C2313yes—
147H(3,𝔽4)—412no—
148#560—412no—
149#532—424no—
150C2×C4⋊Q8C2316yes—
151C2×#127C2313yes—
152C2×#127C2316yes—
153C2×#127C2312yes—
154C2×#126C2316yes—
155C2×#126C2312yes—
156C2×#124C2316yes—
157C2×#124C2316yes—
158C2×#124C2316yes—
159C2×#124C2316yes—
160C2×#124C2313yes—
161C2×#124C2316yes—
162C2×#124C2313yes—
163#525—424no—
164C2×#123C2316yes—
165C2×#123C2316yes—
166C2×#123C2313yes—
167C2×C22⋊Q8C2316yes—
168C2×C22⋊Q8C2316yes—
169C2×C22⋊Q8C2316yes—
170C2×#121C2316yes—
171C2×#121C2316yes—
172C2×#121C2316yes—
173C2×#121C2313yes—
174C2×#121C2316yes—
175C2×#121C2316yes—
176C2×#121C2316yes—
177C2×#121C2316yes—
178C2×#121C2316yes—
179C2×#121C2316yes—
180C2×#121C2316yes—
181C2×#121C2316yes—
182C2×#121C2316yes—
183C2×#120C2313yes—
184C2×#120C2316yes—
185C2×#120C2316yes—
186C2×#120C2313yes—
187C2×#120C2316yes—
188C2×#120C2316yes—
189C2×#120C2316yes—
190C2×#120C2316yes—
191C2×#120C2312yes—
192C2×C4×D4C2316yes—
193C2×C4×D4C2316yes—
194C2×C4×D4C2316yes—
195C2×C4×D4C2316yes—
196C2×C4×D4C2313yes—
197C2×C4×D4C2316yes—
198C2×C4×D4C2316yes—
199C2×C4×D4C2316yes—
200C2×C4×D4C2313yes—
201C2×#117C2316yes—
202C22×C22⋊C4C2316yes—
203C22×C22⋊C4C2313yes—
204C22×C42C2316yes—
205#400C2316yes—
206#400C2316yes—
207#400C2316yes—
208#400C2316yes—
209#400C2316yes—
210#399C2313yes—
211#399C2316yes—
212#399C2316yes—
213#399C2313yes—
214#398C2313yes—
215#398C2316yes—
216#398C2316yes—
217#397C2316yes—
218#397C2316yes—
219#397C2313yes—
220#397C2316yes—
221#397C2316yes—
222#397C2316yes—
223#397C2316yes—
224#397C2316yes—
225#396C2316yes—
226#396C2316yes—
227#396C2316yes—
228#396C2316yes—
229#396C2316yes—
230#396C2312yes—
231#396C2316yes—
232#395C2316yes—
233#395C2313yes—
234#395C2316yes—
235#394C2316yes—
236#394C2316yes—
237#394C2316yes—
238#394C2316yes—
239#394C2316yes—
240#394C2316yes—
241#394C2316yes—
242#394C2316yes—
243#394C2316yes—
244#394C2316yes—
245#394C2316yes—
246#394C2316yes—
247#394C2316yes—
248#394C2316yes—
249#394C2316yes—
250#394C2316yes—
251#394C2316yes—
252#394C2316yes—
253#394C2316yes—
254#394C2313yes—
255#394C2316yes—
256#394C2313yes—
257#394C2316yes—
258#394C2316yes—
259#394C2316yes—
260#393C2316yes—
261#393C2316yes—
262#393C2316yes—
263#393C2316yes—
264#393C2316yes—
265#393C2316yes—
266#393C2316yes—
267#393C2313yes—
268#393C2316yes—
269#392C2316yes—
270#392C2316yes—
271#392C2316yes—
272#392C2316yes—
273#392C2316yes—
274#392C2316yes—
275#392C2316yes—
276#392C2316yes—
277#392C2316yes—
278#392C2316yes—
279#392C2313yes—
280#392C2311yescharacteristic
281#392C2316yes—
282#392C2313yes—
283#392C2316yes—
284#392C2316yes—
285#392C2316yes—
286#392C2316yes—
287#392C2313yes—
288#391C2316yes—
289#391C2316yes—
290#391C2316yes—
291#391C2313yes—
292#391C2316yes—
293#391C2316yes—
294#391C2316yes—
295#390C2313yes—
296#390C2316yes—
297#390C2316yes—
298#390C2316yes—
299#390C2316yes—
300#390C2316yes—
301#389C2316yes—
302#389C2316yes—
303#389C2316yes—
304#389C2316yes—
305#388C2316yes—
306#388C2316yes—
307#388C2316yes—
308#388C2316yes—
309#388C2316yes—
310#388C2316yes—
311#388C2316yes—
312#388C2316yes—
313#388C2316yes—
314#388C2316yes—
315#388C2316yes—
316#388C2316yes—
317#388C2316yes—
318#388C2316yes—
319#388C2316yes—
320#388C2316yes—
321#388C2316yes—
322#388C2316yes—
323#388C2316yes—
324#388C2316yes—
325#388C2316yes—
326#387C2316yes—
327#387C2316yes—
328#387C2316yes—
329#387C2316yes—
330#387C2316yes—
331#387C2316yes—
332#387C2316yes—
333#387C2316yes—
334#387C2316yes—
335#387C2316yes—
336#387C2316yes—
337#386C2316yes—
338#386C2316yes—
339#386C2316yes—
340#386C2316yes—
341#386C2316yes—
342#386C2316yes—
343#386C2316yes—
344#386C2316yes—
345#386C2316yes—
346#386C2316yes—
347#386C2316yes—
348#386C2316yes—
349#386C2316yes—
350#386C2316yes—
351#386C2313yes—
352#386C2316yes—
353#386C2316yes—
354#386C2316yes—
355#386C2316yes—
356#386C2316yes—
357#386C2316yes—
358#386C2316yes—
359#386C2316yes—
360#386C2316yes—
361#386C2316yes—
362#386C2316yes—
363#386C2316yes—
364#385C2316yes—
365#385C2316yes—
366#385C2316yes—
367#385C2316yes—
368#385C2316yes—
369#385C2316yes—
370#385C2313yes—
371#383C2312yes—
372#383C2313yes—
373#382C2316yes—
374#382C2316yes—
375#381C2313yes—
376#381C2316yes—
377#381C2316yes—
378#381C2316yes—
379#381C2313yes—
380#380C2316yes—
381#380C2316yes—
382#380C2316yes—
383#380C2313yes—
384#380C2316yes—
385#380C2313yes—
386#379C2311yescharacteristic
387#379C2313yes—
388C4×C4⋊C4C2316yes—
389C4×C4⋊C4C2313yes—
390C4×C22⋊C4C2316yes—
391C4×C22⋊C4C2316yes—
392C4×C22⋊C4C2316yes—
393C4×C22⋊C4C2313yes—
394C4×C22⋊C4C2316yes—
395C4×C22⋊C4C2316yes—
396C4×C22⋊C4C2316yes—
397C4×C22⋊C4C2313yes—
398C4×C22⋊C4C2316yes—
399C4×C22⋊C4C2313yes—
400C4×C22⋊C4C2316yes—
401C4×C22⋊C4C2316yes—
402#376C2313yes—
403#376C2311yescharacteristic
404C2×#95C2313yes—
405C2×#95C2312yes—
406C2×#95C2313yes—
407C25C2413yes—
408C25C2411yescharacteristic
409C2×#41—46no—
410C2×#41—412no—
411C2×#41—412no—
412C2×#41—412no—
413C2×#41—412no—
414C22×Q8C2416yes—
415C22×Q8C2413yes—
416C22×Q8C2413yes—
417C22×D4C2413yes—
418C22×D4C2416yes—
419C22×D4C2416yes—
420C22×D4C2416yes—
421C22×D4C2413yes—
422C22×D4C2416yes—
423C22×D4C2416yes—
424C22×D4C2411yescharacteristic
425C22×D4C2416yes—
426C22×D4C2416yes—
427C22×D4C2413yes—
428C22×D4C2416yes—
429C22×D4C2416yes—
430C22×D4C2416yes—
431C22×D4C2413yes—
432C22×D4C2416yes—
433C23×C4—412no—
434C23×C4—46no—
435C23×C4C2416yes—
436C23×C4C2416yes—
437C23×C4C2413yes—
438C23×C4C2413yes—
439C23×C4C2413yes—
440C23×C4C2416yes—
441C23×C4C2416yes—
442C23×C4C2413yes—
443C23×C4C2416yes—
444C4⋊Q8—412no—
445#127—412no—
446#127—46no—
447#127—82no—
448#126—412no—
449#126—82no—
450#124—224no—
451#124—46no—
452#124—412no—
453#124—412no—
454#124—412no—
455#124—46no—
456#124—412no—
457#123—224no—
458#123—46no—
459#123—412no—
460C22⋊Q8—412no—
461C22⋊Q8—412no—
462C22⋊Q8—86no—
463#121—224no—
464#121—46no—
465#121—412no—
466#121—412no—
467#121—412no—
468#121—412no—
469#121—412no—
470#121—412no—
471#121—412no—
472#121—412no—
473#121—412no—
474#121—86no—
475#121—86no—
476#120—212no—
477#120—412no—
478#120—412no—
479#120—412no—
480#120—412no—
481#120—412no—
482#120—46no—
483#120—82no—
484#120—86no—
485C4×D4—224no—
486C4×D4—412no—
487C4×D4—412no—
488C4×D4—46no—
489C4×D4—46no—
490C4×D4—412no—
491C4×D4—412no—
492C4×D4—412no—
493C4×D4—412no—
494#117—412no—
495C2×C4⋊C4C2416yes—
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C2416yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C2416yes—
501C2×C4⋊C4C2416yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C2413yes—
504C2×C4⋊C4C2413yes—
505C2×C4⋊C4C2416yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C2416yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2413yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C2416yes—
512C2×C22⋊C4—46no—
513C2×C22⋊C4—412no—
514C2×C22⋊C4C2416yes—
515C2×C22⋊C4C2416yes—
516C2×C22⋊C4C2416yes—
517C2×C22⋊C4C2416yes—
518C2×C22⋊C4C2416yes—
519C2×C22⋊C4C2416yes—
520C2×C22⋊C4C2416yes—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2416yes—
523C2×C22⋊C4C2416yes—
524C2×C22⋊C4C2416yes—
525C2×C22⋊C4C2416yes—
526C2×C22⋊C4C2416yes—
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⋊C4C2413yes—
538C2×C22⋊C4C2416yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2416yes—
541C2×C22⋊C4C2416yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C2413yes—
545C2×C22⋊C4C2416yes—
546C2×C22⋊C4C2416yes—
547C2×C22⋊C4C2416yes—
548C2×C22⋊C4C2416yes—
549C2×C22⋊C4C2413yes—
550C2×C22⋊C4C2416yes—
551C2×C22⋊C4C2413yes—
552C2×C22⋊C4C2416yes—
553C2×C22⋊C4C2413yes—
554C2×C42—412no—
555C2×C42C2416yes—
556C2×C42C2413yes—
557C2×C42C2416yes—
558C2×C42C2416yes—
559C2×C42C2416yes—
560C2×C42C2413yes—
561C2×C42C2413yes—
562C2×C42C2412yes—
563C2×C42C2416yes—
564#95C2411yescharacteristic
565#95C2416yes—
566#95C2416yes—
567#95C2413yes—
568#95C2413yes—
569#95C2413yes—
570#95C2416yes—
571#95C2413yes—
572#95C2413yes—
573#95C2416yes—
574#95C2413yes—
575#95C2413yes—
576#95C2411yescharacteristic
577#95C2413yes—
578#95C2416yes—
579#95C2416yes—
580#95C2416yes—
581#95C2416yes—
582#95C2416yes—
583#95C2416yes—
584#95C2416yes—
585#95C2416yes—
586#95C2416yes—
587#95C2416yes—
588#95C2416yes—
589#95C2416yes—
590#95C2416yes—
591#95C2416yes—
592#95C2416yes—
593#95C2416yes—
594#95C2416yes—
595#95C2416yes—
596C24—26no—
597C24—46no—
598C24—43no—
599C24—43no—
600C24—46no—
601C24—43no—
602C24—43no—
603C24—41no—
604C24C2513yes—
605C24C2516yes—
606C24C2512yes—
607C24C2513yes—
608#41—848no—
609#41—824no—
610C2×Q8—212no—
611C2×Q8—46no—
612C2×Q8—46no—
613C2×Q8—46no—
614C2×Q8—43no—
615C2×Q8—43no—
616C2×Q8—43no—
617C2×Q8—43no—
618C2×D4—212no—
619C2×D4—212no—
620C2×D4—212no—
621C2×D4—26no—
622C2×D4—212no—
623C2×D4—212no—
624C2×D4—212no—
625C2×D4—212no—
626C2×D4—43no—
627C2×D4—46no—
628C2×D4—43no—
629C2×D4—46no—
630C2×D4—46no—
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—43no—
643C2×D4—46no—
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—43no—
653C2×D4—46no—
654C2×D4—43no—
655C2×D4—46no—
656C2×D4—46no—
657C2×D4—46no—
658C2×D4—43no—
659C2×D4—46no—
660C2×D4—46no—
661C2×D4—43no—
662C22×C4—212no—
663C22×C4—212no—
664C22×C4—212no—
665C22×C4—212no—
666C22×C4—212no—
667C22×C4—212no—
668C22×C4—26no—
669C22×C4—26no—
670C22×C4—212no—
671C22×C4—46no—
672C22×C4—46no—
673C22×C4—43no—
674C22×C4—46no—
675C22×C4—46no—
676C22×C4—46no—
677C22×C4—46no—
678C22×C4—46no—
679C22×C4—46no—
680C22×C4—46no—
681C22×C4—46no—
682C22×C4—46no—
683C22×C4—43no—
684C22×C4—43no—
685C22×C4—43no—
686C22×C4—824no—
687C22×C4C2511yescharacteristic
688C22×C4C2516yes—
689C22×C4C2513yes—
690C22×C4C2516yes—
691C22×C4C2516yes—
692C22×C4C2516yes—
693C22×C4C2516yes—
694C22×C4C2513yes—
695C22×C4C2513yes—
696C22×C4C2516yes—
697C22×C4C2513yes—
698C4⋊C4—212no—
699C4⋊C4—212no—
700C4⋊C4—212no—
701C4⋊C4—212no—
702C4⋊C4—46no—
703C4⋊C4—43no—
704C4⋊C4—43no—
705C4⋊C4—46no—
706C4⋊C4—46no—
707C4⋊C4—46no—
708C4⋊C4—46no—
709C4⋊C4—43no—
710C4⋊C4—46no—
711C4⋊C4—46no—
712C4⋊C4—46no—
713C4⋊C4—46no—
714C4⋊C4—46no—
715C22⋊C4—212no—
716C22⋊C4—212no—
717C22⋊C4—212no—
718C22⋊C4—212no—
719C22⋊C4—212no—
720C22⋊C4—212no—
721C22⋊C4—212no—
722C22⋊C4—212no—
723C22⋊C4—212no—
724C22⋊C4—212no—
725C22⋊C4—212no—
726C22⋊C4—46no—
727C22⋊C4—46no—
728C22⋊C4—46no—
729C22⋊C4—46no—
730C22⋊C4—43no—
731C22⋊C4—43no—
732C22⋊C4—46no—
733C22⋊C4—46no—
734C22⋊C4—46no—
735C22⋊C4—46no—
736C22⋊C4—46no—
737C22⋊C4—46no—
738C22⋊C4—46no—
739C22⋊C4—46no—
740C22⋊C4—46no—
741C22⋊C4—46no—
742C22⋊C4—46no—
743C22⋊C4—43no—
744C22⋊C4—46no—
745C22⋊C4—46no—
746C22⋊C4—46no—
747C22⋊C4—46no—
748C22⋊C4—46no—
749C22⋊C4—46no—
750C22⋊C4—43no—
751C22⋊C4—46no—
752C22⋊C4—43no—
753C22⋊C4—46no—
754C22⋊C4H(5,𝔽2)112yes—
755C42—212no—
756C42—212no—
757C42—26no—
758C42—46no—
759C42—46no—
760C42—46no—
761C42—43no—
762C42—43no—
763C42—42no—
764C23—26no—
765C23—23no—
766C23—26no—
767C23—23no—
768C23—26no—
769C23—26no—
770C23—26no—
771C23—26no—
772C23—26no—
773C23—23no—
774C23—26no—
775C23—26no—
776C23—26no—
777C23—23no—
778C23—26no—
779C23—26no—
780C23—22no—
781C23—23no—
782C23—26no—
783C23—412no—
784C23—44no—
785C23—812no—
786C23—86no—
787C23—86no—
788C23—812no—
789C23—163no—
790C23—163no—
791C23C2×H(5,𝔽2)16yes—
792C23C2611yescharacteristic
793Q8—812no—
794Q8—86no—
795Q8—163no—
796D4—424no—
797D4—412no—
798D4—44no—
799D4—812no—
800D4—812no—
801D4—86no—
802D4—812no—
803D4—812no—
804D4—812no—
805D4—812no—
806D4—812no—
807D4—163no—
808D4—166no—
809D4—166no—
810D4—166no—
811D4—163no—
812C2×C4—26no—
813C2×C4—26no—
814C2×C4—26no—
815C2×C4—26no—
816C2×C4—26no—
817C2×C4—26no—
818C2×C4—23no—
819C2×C4—26no—
820C2×C4—26no—
821C2×C4—26no—
822C2×C4—26no—
823C2×C4—26no—
824C2×C4—26no—
825C2×C4—23no—
826C2×C4—23no—
827C2×C4—26no—
828C2×C4—26no—
829C2×C4—26no—
830C2×C4—23no—
831C2×C4—26no—
832C2×C4—23no—
833C2×C4—26no—
834C2×C4—26no—
835C2×C4—26no—
836C2×C4—23no—
837C2×C4—26no—
838C2×C4—412no—
839C2×C4—424no—
840C2×C4—424no—
841C2×C4—86no—
842C2×C4—812no—
843C2×C4—86no—
844C2×C4—812no—
845C2×C4—812no—
846C2×C4—163no—
847C2×C4C2×H(5,𝔽2)112yes—
848C2×C4#58516yes—
849C22—212no—
850C22—26no—
851C22—43no—
852C22—46no—
853C22—43no—
854C22—46no—
855C22—46no—
856C22—43no—
857C22—46no—
858C22—46no—
859C22—46no—
860C22—43no—
861C22—46no—
862C22—46no—
863C22—46no—
864C22—46no—
865C22—46no—
866C22—42no—
867C22—46no—
868C22—43no—
869C22—824no—
870C22—164no—
871C22C22×H(5,𝔽2)13yes—
872C22C2×#58513yes—
873C22H(7,𝔽2)11yescharacteristic
874C4—26no—
875C4—212no—
876C4—46no—
877C4—43no—
878C4—43no—
879C4—46no—
880C4—46no—
881C4—46no—
882C4—46no—
883C4—43no—
884C4—41no—
885C2—46no—
886C2—82no—
887C2—86no—
888C2—83no—
889C2#6269411yescharacteristic
890C2#6293013yes—
891C2#6301213yes—
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. #52662C2semidirect
2. #52494C2semidirect
3. #52422C2semidirect
4. #52325C2semidirect
5. #52096C2semidirect
6. #46225C2semidirect
7. #46214C2semidirect
8. #45823C2semidirect
9. #45477C2semidirect
10. #45452C2semidirect
11. #36339C2semidirect
12. #36147C2semidirect
13. #35924C2semidirect
14. #35918C2semidirect
15. #35684C2semidirect
16. C2×H(3,𝔽4)C22semidirect
19. C2×#525C22semidirect
20. #2855C22semidirect
21. #2850C22semidirect
22. #2850C22semidirect
23. #2847C22semidirect
24. #2847C22semidirect
25. #2837C22semidirect
26. #2832C22semidirect
27. #2832C22semidirect
28. #2830C22semidirect
29. #2826C22semidirect
30. #2824C22semidirect
31. #2819C22semidirect
32. #2819C22semidirect
33. #2818C22semidirect
34. #2815C22semidirect
35. #2813C22semidirect
36. #2813C22semidirect
37. #2812C22semidirect
38. #2812C22semidirect
39. #2775C22semidirect
40. #2771C22semidirect
41. #2767C22semidirect
42. #2731C22semidirect
43. #2731C22semidirect
44. #2728C22semidirect
45. #2723C22semidirect
46. #2717C22semidirect
47. #2715C22semidirect
48. #2702C22semidirect
49. #2702C22semidirect
50. #2686C22semidirect
51. #2679C22semidirect
52. #2677C22semidirect
56. #2676C22semidirect
57. #2676C22semidirect
58. #2675C22semidirect
59. #2674C22semidirect
60. #2673C22semidirect
61. #2672C22semidirect
62. #2671C22semidirect
63. #2671C22semidirect
64. #2670C22semidirect
67. #2669C22semidirect
68. #2669C22semidirect
69. #2669C22semidirect
70. #2669C22semidirect
71. #2668C22semidirect
72. #2668C22semidirect
73. #2665C22semidirect
74. #2648C22semidirect
75. #2635C22semidirect
76. #2631C22semidirect
77. #2607C22semidirect
78. #2605C22semidirect
79. #2587C22semidirect
80. #2574C22semidirect
81. #2572C22semidirect
82. #2559C22semidirect
83. #2557C22semidirect
84. #2557C22semidirect
86. #2549C22semidirect
89. #2534C22semidirect
90. #2531C22semidirect
91. #2521C22semidirect
92. #2518C22semidirect
93. #2516C22semidirect
94. #2492C22semidirect
95. #2476C22semidirect
96. #2476C22semidirect
97. #2472C22semidirect
98. #2467C22semidirect
99. #2467C22semidirect
100. #2459C22semidirect
101. #2459C22semidirect
102. #2459C22semidirect
103. #2459C22semidirect
104. #2459C22semidirect
105. #2457C22semidirect
106. #2457C22semidirect
107. #2457C22semidirect
108. #2444C22semidirect
109. #2444C22semidirect
110. #2439C22semidirect
115. #2427C22semidirect
116. #2424C22semidirect
117. #2424C22semidirect
118. #2424C22semidirect
119. #2424C22semidirect
120. #2424C22semidirect
121. #2420C22semidirect
122. #2404C22semidirect
123. #2404C22semidirect
124. #2404C22semidirect
125. #2397C22semidirect
126. #2392C22semidirect
128. #2388C22semidirect
129. #2379C22semidirect
130. #2376C22semidirect
131. #2372C22semidirect
132. #2364C22semidirect
133. #2364C22semidirect
134. #2363C22semidirect
135. #2353C22semidirect
136. #2339C22semidirect
137. #2339C22semidirect
138. C4×#121C22semidirect
139. C4×#120C22semidirect
140. #2290C22semidirect
141. #2275C22semidirect
142. #2273C22semidirect
143. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#526622
#524942
#524222
#523252
#520962
#462252
#462142
#458232
#454772
#454522
#363392
#361472
#359242
#359182
#356842