Finite Group Databasebeta

← #7658869

Subgroups — #7658869

Order 512.

5544 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42983C213yesmaximal, complemented
2#42975C213yesmaximal, complemented
3#42920C216yesmaximal, complemented
4#42642C216yesmaximal, complemented
5#42634C216yesmaximal, complemented
6#42627C216yesmaximal, complemented
7#42619C216yesmaximal, complemented
8#37514C213yesmaximal, complemented
9#37492C216yesmaximal, complemented
10#36670C213yesmaximal, complemented
11#36082C212yesmaximal, complemented
12#35948C212yesmaximal, complemented
13#35898C212yesmaximal, complemented
14#35801C212yesmaximal, complemented
15#35771C212yesmaximal, complemented
16#35748C211yesmaximal, characteristic, complemented
17#35737C211yesmaximal, characteristic, complemented
18#34293C212yesmaximal, complemented
19#34258C211yesmaximal, characteristic, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×Q82C2211yescharacteristic, complemented
22C2×D4×Q8C2211yescharacteristic, complemented
23C2×#548C2212yes—
24C2×#548C2212yes—
25C2×#548C2212yes—
26C2×#520C2211yescharacteristic
27C2×#519C2212yescomplemented
28C2×C4×#41C2211yescharacteristic
29#2833C2213yescomplemented
30#2832C2211yescharacteristic, complemented
31#2831C2216yescomplemented
32#2830C2213yescomplemented
33#2830C2216yescomplemented
34#2829C2216yescomplemented
35#2828C2213yescomplemented
36#2827C2216yescomplemented
37#2826C2216yescomplemented
38#2825C2216yescomplemented
39#2824C2216yescomplemented
40#2797C22112yescomplemented
41#2779C22112yescomplemented
42#2736C2216yescomplemented
43#2736C2216yescomplemented
44#2735C22112yescomplemented
45#2735C2216yescomplemented
46#2730C22112yescomplemented
47#2702C22112yescomplemented
48#2685C22112yescomplemented
49#2670C2216yescomplemented
50#2662C22112yescomplemented
51#2653C22112yescomplemented
52#2651C22112yescomplemented
53#2649C22112yescomplemented
54#2644C2216yescomplemented
55#2640C2216yescomplemented
56#2628C2213yescomplemented
57#2626C22112yescomplemented
58#2624C2216yescomplemented
59#2622C22112yescomplemented
60#2621C2213yescomplemented
61#2620C2216yescomplemented
62#2616C2216yes—
63#2593C2216yescomplemented
64#2592C2216yescomplemented
65#2586C2216yescomplemented
66#2580C2213yescomplemented
67#2547C2216yescomplemented
68#2547C2213yescomplemented
69#2545C2216yescomplemented
70#2542C2213yescomplemented
71#2538C2216yescomplemented
72#2535C2213yescomplemented
73#2513C2216yescomplemented
74#2512C2216yescomplemented
75#2512C2216yescomplemented
76#2500C2216yescomplemented
77#2497C2216yescomplemented
78#2496C2216yescomplemented
79#2494C2216yescomplemented
80#2492C2216yescomplemented
81#2492C2216yescomplemented
82#2491C2216yescomplemented
83#2491C2216yescomplemented
84#2485C2216yescomplemented
85#2480C22112yescomplemented
86#2472C22112yescomplemented
87#2452C2216yescomplemented
88#2448C2216yescomplemented
89#2448C2216yescomplemented
90#2440C2216yescomplemented
91#2435C2216yes—
92#2435C2216yes—
93#2435C2216yes—
94#2429C2216yescomplemented
95#2427C2216yescomplemented
96#2426C2216yescomplemented
97#2423C2216yescomplemented
98#2421C2216yescomplemented
99#2417C2216yescomplemented
100#2415C2216yescomplemented
101#2414C2216yescomplemented
102#2408C2216yes—
103#2408C2216yes—
104#2408C2216yes—
105#2401C2216yescomplemented
106#2398C2216yescomplemented
107#2396C2213yescomplemented
108#2395C2216yescomplemented
109#2392C2216yescomplemented
110#2392C2213yescomplemented
111#2388C2216yes—
112#2367C2216yescomplemented
113#2363C2216yescomplemented
114#2362C2216yescomplemented
115#2354C2216yescomplemented
116#2351C2211yescharacteristic, complemented
117#2351C2211yescharacteristic, complemented
118Q8×C4⋊C4C2212yescomplemented
119Q8×C4⋊C4C2212yescomplemented
120#2341C2212yes—
121#2341C2212yes—
122#2341C2212yes—
123#2341C2212yes—
124#2341C2212yes—
125Q8×C22⋊C4C2212yescomplemented
126Q8×C22⋊C4C2212yescomplemented
127D4×C22⋊C4C2216yes—
128D4×C22⋊C4C2216yes—
129#2326C2216yescomplemented
130#2324C2216yescomplemented
131#2311C2213yes—
132#2309C2213yes—
133C4×C22⋊Q8C2216yescomplemented
134#2297C2213yes—
135C2×#390C2213yes—
136#2290C2216yescomplemented
137#2276C2212yescomplemented
138C2×H(5,𝔽2)—28no—
139C2×H(5,𝔽2)—44no—
140C2×H(5,𝔽2)—44no—
141C22×#41C2312yes—
142C22×#41C2311yescharacteristic
143C22×#41C2313yes—
144C23×Q8C2312yes—
145C23×D4C2313yes—
146C23×D4C2316yes—
147Q82—44no—
148D4×Q8—44no—
149#548—216no—
150#548—48no—
151#548—48no—
152C2×C4⋊Q8C2313yes—
153C2×C4⋊Q8C2313yes—
154C2×C4⋊Q8C2316yes—
155C2×#126C23112yes—
156C2×#124C2316yes—
157C2×#124C2316yes—
158C2×#124C2316yes—
159C2×#124C23112yes—
160C2×C22⋊Q8C2316yes—
161C2×C22⋊Q8C2316yes—
162C2×C22⋊Q8C2316yes—
163C2×C22⋊Q8C2316yes—
164C2×C22⋊Q8C23112yes—
165C2×#121C2316yes—
166C2×#121C2316yes—
167C2×#121C2316yes—
168C2×#120C23112yes—
169#520—44no—
170#519—48no—
171C4×#41—44no—
172C2×C4×Q8C2311yescharacteristic
173C2×C4×Q8C2312yes—
174C2×C4×Q8C2312yes—
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2311yescharacteristic
178C2×C4×Q8C2313yes—
179C2×C4×Q8C2316yes—
180C2×C4×Q8C2316yes—
181C2×C4×D4C2316yes—
182C2×C4×D4C2316yes—
183C2×C4×D4C2313yes—
184C2×C4×D4C2313yes—
185C2×C4×D4C2316yes—
186C2×C4×D4C2316yes—
187C2×C4×D4C2313yes—
188C2×#117C2313yes—
189C2×#117C2313yes—
190C2×#117C2316yes—
191C2×#117C2316yes—
192C22×C4⋊C4C2313yes—
193C22×C22⋊C4C23112yes—
194C22×C42C2313yes—
195#401C2316yes—
196#400C2316yes—
197#400C2316yes—
198#400C2316yes—
199#400C2316yes—
200#400C2312yes—
201#400C2316yes—
202#400C2313yes—
203#399C2313yes—
204#399C2316yes—
205#399C2316yes—
206#399C23112yes—
207#398C2316yes—
208#398C2316yes—
209#398C2316yes—
210#398C2313yes—
211#398C2316yes—
212#397C2316yes—
213#397C2316yes—
214#397C2316yes—
215#397C2316yes—
216#397C2316yes—
217#397C2312yes—
218#397C2316yes—
219#397C2313yes—
220#397C2316yes—
221#397C2316yes—
222#397C23112yes—
223#397C23112yes—
224#397C23112yes—
225#397C2316yes—
226#397C2316yes—
227#397C23112yes—
228#396C2316yes—
229#396C2316yes—
230#396C2316yes—
231#396C2316yes—
232#396C2316yes—
233#396C23112yes—
234#396C23112yes—
235#396C23112yes—
236#395C2311yescharacteristic
237#395C2316yes—
238#395C2316yes—
239#394C2316yes—
240#394C2316yes—
241#394C2316yes—
242#394C2316yes—
243#394C2312yes—
244#394C2316yes—
245#394C2316yes—
246#394C2316yes—
247#394C2316yes—
248#394C2316yes—
249#394C2311yescharacteristic
250#394C2316yes—
251#394C23112yes—
252#394C23112yes—
253#394C23112yes—
254#394C23112yes—
255#394C23112yes—
256#393C2312yes—
257#393C2313yes—
258#393C2316yes—
259#393C23112yes—
260#393C2312yes—
261#393C23112yes—
262#393C2316yes—
263#392C2316yes—
264#392C2313yes—
265#392C2316yes—
266#392C2316yes—
267#392C2316yes—
268#391C2313yes—
269#391C2311yescharacteristic
270#391C2316yes—
271#391C23112yes—
272#391C2316yes—
273#391C2316yes—
274#391C2316yes—
275#390C2313yes—
276#390C2316yes—
277#390C2316yes—
278#390C2316yes—
279#390C2313yes—
280#390C2316yes—
281#390C23112yes—
282#390C2316yes—
283#390C2316yes—
284#390C2316yes—
285#390C2316yes—
286#390C2316yes—
287#390C2316yes—
288#390C2316yes—
289#390C23112yes—
290#389C2316yes—
291#389C2316yes—
292#389C23112yes—
293#389C2316yes—
294#389C2316yes—
295#389C2316yes—
296#389C2316yes—
297#388C2316yes—
298#388C2312yes—
299#388C23112yes—
300#388C23112yes—
301#388C23112yes—
302#388C23112yes—
303#388C23112yes—
304#388C23112yes—
305#388C23112yes—
306#388C23112yes—
307#388C23112yes—
308#388C23112yes—
309#388C23112yes—
310#388C23112yes—
311#387C2316yes—
312#387C2316yes—
313#387C23112yes—
314#387C23112yes—
315#386C23112yes—
316#386C2316yes—
317#386C2316yes—
318#386C2316yes—
319#386C2316yes—
320#386C23112yes—
321#385C2316yes—
322#385C2316yes—
323#385C23112yes—
324#385C23112yes—
325#384C2316yes—
326#384C2316yes—
327#382C2313yes—
328#382C2313yes—
329#380C2316yes—
330#380C2316yes—
331#380C2316yes—
332#380C2316yes—
333#380C2316yes—
334#380C2316yes—
335#380C2316yes—
336#380C23112yes—
337#379C2316yes—
338#379C2316yes—
339#379C23112yes—
340#379C23112yes—
341#379C23112yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C23112yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C2316yes—
346C4×C4⋊C4C2316yes—
347C4×C4⋊C4C2313yes—
348C4×C4⋊C4C2313yes—
349C4×C4⋊C4C2316yes—
350C4×C22⋊C4C2316yes—
351C4×C22⋊C4C2316yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C2316yes—
357C4×C22⋊C4C23112yes—
358#376C2316yes—
359C25C2416yes—
360H(5,𝔽2)—464no—
361C2×#41—28no—
362C2×#41—24no—
363C2×#41—24no—
364C2×#41—28no—
365C2×#41—28no—
366C2×#41—212no—
367C2×#41—46no—
368C2×#41—46no—
369C2×#41#4118yes—
370C22×Q8—28no—
371C22×Q8—28no—
372C22×Q8—28no—
373C22×Q8C2416yes—
374C22×Q8C2411yescharacteristic
375C22×Q8C2411yescharacteristic
376C22×Q8C2416yes—
377C22×Q8C2411yescharacteristic
378C22×D4—224no—
379C22×D4—212no—
380C22×D4—46no—
381C22×D4—46no—
382C22×D4—412no—
383C22×D4—412no—
384C22×D4C2416yes—
385C22×D4C2413yes—
386C22×D4C2416yes—
387C22×D4C2416yes—
388C22×D4C2413yes—
389C22×D4C2411yescharacteristic
390C22×D4C2416yes—
391C22×D4C2416yes—
392C23×C4C2416yes—
393C23×C4C2416yes—
394C23×C4C2413yes—
395C23×C4C2416yes—
396C23×C4C2416yes—
397C4⋊Q8—46no—
398C4⋊Q8—412no—
399C4⋊Q8—46no—
400#126—812no—
401#124—224no—
402#124—412no—
403#124—412no—
404#124—812no—
405C22⋊Q8—224no—
406C22⋊Q8—412no—
407C22⋊Q8—412no—
408C22⋊Q8—412no—
409C22⋊Q8—812no—
410#121—224no—
411#121—412no—
412#121—412no—
413#120—812no—
414C4×Q8—28no—
415C4×Q8—28no—
416C4×Q8—28no—
417C4×Q8—24no—
418C4×Q8—24no—
419C4×Q8—28no—
420C4×Q8—46no—
421C4×Q8—412no—
422C4×Q8—412no—
423C4×D4—224no—
424C4×D4—412no—
425C4×D4—46no—
426C4×D4—46no—
427C4×D4—412no—
428C4×D4—412no—
429C4×D4—46no—
430#117—412no—
431#117—46no—
432#117—46no—
433#117—412no—
434C2×C4⋊C4—46no—
435C2×C4⋊C4C2413yes—
436C2×C4⋊C4C2413yes—
437C2×C4⋊C4C2416yes—
438C2×C4⋊C4C2416yes—
439C2×C4⋊C4C2416yes—
440C2×C4⋊C4C2416yes—
441C2×C4⋊C4C2416yes—
442C2×C4⋊C4C2413yes—
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2416yes—
445C2×C4⋊C4C2416yes—
446C2×C4⋊C4C2416yes—
447C2×C4⋊C4C2416yes—
448C2×C4⋊C4C2413yes—
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2413yes—
451C2×C4⋊C4C2416yes—
452C2×C4⋊C4C2416yes—
453C2×C4⋊C4C2416yes—
454C2×C4⋊C4C24112yes—
455C2×C4⋊C4C2416yes—
456C2×C4⋊C4C2416yes—
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C24112yes—
460C2×C22⋊C4—812no—
461C2×C22⋊C4C2412yes—
462C2×C22⋊C4C2416yes—
463C2×C22⋊C4C24112yes—
464C2×C22⋊C4C2416yes—
465C2×C22⋊C4C2416yes—
466C2×C22⋊C4C24112yes—
467C2×C22⋊C4C24112yes—
468C2×C22⋊C4C2412yes—
469C2×C22⋊C4C2416yes—
470C2×C22⋊C4C2416yes—
471C2×C22⋊C4C2413yes—
472C2×C22⋊C4C2413yes—
473C2×C22⋊C4C2412yes—
474C2×C22⋊C4C2412yes—
475C2×C22⋊C4C2416yes—
476C2×C22⋊C4C2416yes—
477C2×C22⋊C4C2416yes—
478C2×C22⋊C4C24112yes—
479C2×C22⋊C4C24112yes—
480C2×C22⋊C4C24112yes—
481C2×C22⋊C4C24112yes—
482C2×C22⋊C4C24112yes—
483C2×C22⋊C4C2416yes—
484C2×C22⋊C4C2416yes—
485C2×C22⋊C4C2416yes—
486C2×C22⋊C4C2416yes—
487C2×C22⋊C4C2412yes—
488C2×C22⋊C4C2412yes—
489C2×C22⋊C4C2416yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C2416yes—
492C2×C22⋊C4C2416yes—
493C2×C22⋊C4C2416yes—
494C2×C22⋊C4C2416yes—
495C2×C42—46no—
496C2×C42C2413yes—
497C2×C42C2416yes—
498C2×C42C2413yes—
499C2×C42C2416yes—
500C2×C42C2416yes—
501C2×C42C2416yes—
502C2×C42C2413yes—
503C2×C42C24112yes—
504C2×C42C24112yes—
505C2×C42C2411yescharacteristic
506#95C2412yes—
507#95C2416yes—
508#95C2416yes—
509#95C2416yes—
510#95C2416yes—
511#95C2412yes—
512#95C2412yes—
513#95C2412yes—
514#95C2412yes—
515#95C2412yes—
516#95C2416yes—
517#95C2416yes—
518#95C2416yes—
519#95C2416yes—
520#95C2416yes—
521#95C2416yes—
522#95C2416yes—
523#95C2416yes—
524#95C2416yes—
525#95C2411yescharacteristic
526#95C2411yescharacteristic
527#95C24112yes—
528#95C2413yes—
529#95C2413yes—
530#95C2416yes—
531#95C2416yes—
532#95C2416yes—
533#95C24112yes—
534#95C2416yes—
535#95C2416yes—
536C24—212no—
537C24—46no—
538C24—46no—
539C24—412no—
540C24—412no—
541C24C2516yes—
542C24C2512yes—
543C24C2513yes—
544#41—232no—
545#41—448no—
546#41—432no—
547C2×Q8—212no—
548C2×Q8—22no—
549C2×Q8—212no—
550C2×Q8—212no—
551C2×Q8—41no—
552C2×Q8—42no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—412no—
556C2×Q8—46no—
557C2×Q8—432no—
558C2×Q8C2×#4114yes—
559C2×Q8H(5,𝔽2)14yes—
560C2×Q8H(5,𝔽2)14yes—
561C2×D4—212no—
562C2×D4—212no—
563C2×D4—26no—
564C2×D4—212no—
565C2×D4—26no—
566C2×D4—26no—
567C2×D4—212no—
568C2×D4—212no—
569C2×D4—41no—
570C2×D4—43no—
571C2×D4—43no—
572C2×D4—46no—
573C2×D4—46no—
574C2×D4—42no—
575C2×D4—448no—
576C2×D4—46no—
577C2×D4—46no—
578C2×D4—46no—
579C2×D4—46no—
580C2×D4—46no—
581C2×D4—46no—
582C2×D4—46no—
583C2×D4—46no—
584C2×D4—496no—
585C2×D4C2×#41112yes—
586C22×C4—26no—
587C22×C4—26no—
588C22×C4—212no—
589C22×C4—212no—
590C22×C4—212no—
591C22×C4—212no—
592C22×C4—212no—
593C22×C4—212no—
594C22×C4—46no—
595C22×C4—46no—
596C22×C4—46no—
597C22×C4—412no—
598C22×C4—46no—
599C22×C4C2×#41112yes—
600C22×C4C2512yes—
601C22×C4C2512yes—
602C22×C4C2512yes—
603C22×C4C2511yescharacteristic
604C22×C4C2516yes—
605C22×C4C2511yescharacteristic
606C22×C4C2512yes—
607C22×C4C2513yes—
608C22×C4C2516yes—
609C22×C4C2516yes—
610C22×C4C2516yes—
611C22×C4C2516yes—
612C22×C4C2512yes—
613C22×C4C2513yes—
614C22×C4C2511yescharacteristic
615C22×C4C2513yes—
616C4⋊C4—212no—
617C4⋊C4—212no—
618C4⋊C4—26no—
619C4⋊C4—26no—
620C4⋊C4—212no—
621C4⋊C4—212no—
622C4⋊C4—212no—
623C4⋊C4—43no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—412no—
627C4⋊C4—41no—
628C4⋊C4—46no—
629C4⋊C4—46no—
630C4⋊C4—46no—
631C4⋊C4—46no—
632C4⋊C4—43no—
633C4⋊C4—46no—
634C4⋊C4—43no—
635C4⋊C4—46no—
636C4⋊C4—46no—
637C4⋊C4—46no—
638C4⋊C4—412no—
639C4⋊C4—46no—
640C4⋊C4—46no—
641C22⋊C4—212no—
642C22⋊C4—224no—
643C22⋊C4—24no—
644C22⋊C4—46no—
645C22⋊C4—46no—
646C22⋊C4—412no—
647C22⋊C4—412no—
648C22⋊C4—42no—
649C22⋊C4—46no—
650C22⋊C4—46no—
651C22⋊C4—46no—
652C22⋊C4—42no—
653C22⋊C4—46no—
654C22⋊C4—46no—
655C22⋊C4—46no—
656C22⋊C4—42no—
657C22⋊C4—46no—
658C22⋊C4—43no—
659C22⋊C4—43no—
660C22⋊C4—46no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—46no—
664C22⋊C4—46no—
665C22⋊C4—46no—
666C22⋊C4—412no—
667C22⋊C4—412no—
668C22⋊C4—412no—
669C22⋊C4—412no—
670C22⋊C4—412no—
671C22⋊C4—46no—
672C22⋊C4—46no—
673C22⋊C4—46no—
674C22⋊C4—46no—
675C42—212no—
676C42—212no—
677C42—26no—
678C42—212no—
679C42—26no—
680C42—212no—
681C42—41no—
682C42—43no—
683C42—412no—
684C42—412no—
685C23—23no—
686C23—23no—
687C23—26no—
688C23—26no—
689C23—22no—
690C23—26no—
691C23—22no—
692C23—22no—
693C23—26no—
694C23—26no—
695C23—22no—
696C23—26no—
697C23—26no—
698C23—22no—
699C23—26no—
700C23—26no—
701C23—22no—
702C23—22no—
703C23—424no—
704C23—824no—
705C23—166no—
706C23—1612no—
707C23—166no—
708C23C22×#4116yes—
709C23C2611yescharacteristic
710Q8—44no—
711Q8—44no—
712Q8—424no—
713Q8—166no—
714Q8#538116yes—
715D4—224no—
716D4—412no—
717D4—424no—
718D4—44no—
719D4—424no—
720D4—812no—
721D4—812no—
722D4—812no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—224no—
726C2×C4—22no—
727C2×C4—26no—
728C2×C4—26no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—26no—
736C2×C4—26no—
737C2×C4—23no—
738C2×C4—26no—
739C2×C4—23no—
740C2×C4—26no—
741C2×C4—26no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—26no—
745C2×C4—26no—
746C2×C4—26no—
747C2×C4—22no—
748C2×C4—26no—
749C2×C4—26no—
750C2×C4—26no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—26no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—26no—
761C2×C4—26no—
762C2×C4—26no—
763C2×C4—22no—
764C2×C4—424no—
765C2×C4—424no—
766C2×C4—812no—
767C2×C4—166no—
768C2×C4C22×#4112yes—
769C2×C4C22×#4116yes—
770C2×C4C2×H(5,𝔽2)16yes—
771C2×C4C2×H(5,𝔽2)16yes—
772C22—212no—
773C22—26no—
774C22—43no—
775C22—46no—
776C22—43no—
777C22—42no—
778C22—46no—
779C22—42no—
780C22—46no—
781C22—42no—
782C22—46no—
783C22—42no—
784C22—46no—
785C22—42no—
786C22—42no—
787C22—46no—
788C22—46no—
789C22—42no—
790C22—46no—
791C22—1624no—
792C22C23×#4111yescharacteristic
793C22C22×H(5,𝔽2)11yescharacteristic
794C22C22×H(5,𝔽2)11yescharacteristic
795C22H(7,𝔽2)12yes—
796C222−1+612yes—
797C4—22no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—46no—
803C4—42no—
804C4—46no—
805C4—43no—
806C4—43no—
807C4—46no—
808C4—42no—
809C4—46no—
810C4—42no—
811C4—46no—
812C4C2×#538112yes—
813C2—46no—
814C2—82no—
815C2—86no—
816C2C22×#53811yescharacteristic
817C2#6285712yes—
818C2#6304811yescharacteristic
819C2#6305212yes—
820C2#6306611yescharacteristic
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. #42983C2semidirect
2. #42975C2semidirect
3. #42920C2semidirect
4. #42642C2semidirect
5. #42634C2semidirect
6. #42627C2semidirect
7. #42619C2semidirect
8. #37514C2semidirect
9. #37492C2semidirect
10. #36670C2semidirect
11. #36082C2semidirect
12. #35948C2semidirect
13. #35898C2semidirect
14. #35801C2semidirect
15. #35771C2semidirect
16. #35748C2semidirect
17. #35737C2semidirect
18. #34293C2semidirect
19. #34258C2semidirect
21. C2×Q82C22semidirect
22. C2×D4×Q8C22semidirect
27. C2×#519C22semidirect
29. #2833C22semidirect
30. #2832C22semidirect
31. #2831C22semidirect
32. #2830C22semidirect
33. #2830C22semidirect
34. #2829C22semidirect
35. #2828C22semidirect
36. #2827C22semidirect
37. #2826C22semidirect
38. #2825C22semidirect
39. #2824C22semidirect
40. #2797C22semidirect
41. #2779C22semidirect
42. #2736C22semidirect
43. #2736C22semidirect
44. #2735C22semidirect
45. #2735C22semidirect
46. #2730C22semidirect
47. #2702C22semidirect
48. #2685C22semidirect
49. #2670C22semidirect
50. #2662C22semidirect
51. #2653C22semidirect
52. #2651C22semidirect
53. #2649C22semidirect
54. #2644C22semidirect
55. #2640C22semidirect
56. #2628C22semidirect
57. #2626C22semidirect
58. #2624C22semidirect
59. #2622C22semidirect
60. #2621C22semidirect
61. #2620C22semidirect
63. #2593C22semidirect
64. #2592C22semidirect
65. #2586C22semidirect
66. #2580C22semidirect
67. #2547C22semidirect
68. #2547C22semidirect
69. #2545C22semidirect
70. #2542C22semidirect
71. #2538C22semidirect
72. #2535C22semidirect
73. #2513C22semidirect
74. #2512C22semidirect
75. #2512C22semidirect
76. #2500C22semidirect
77. #2497C22semidirect
78. #2496C22semidirect
79. #2494C22semidirect
80. #2492C22semidirect
81. #2492C22semidirect
82. #2491C22semidirect
83. #2491C22semidirect
84. #2485C22semidirect
85. #2480C22semidirect
86. #2472C22semidirect
87. #2452C22semidirect
88. #2448C22semidirect
89. #2448C22semidirect
90. #2440C22semidirect
94. #2429C22semidirect
95. #2427C22semidirect
96. #2426C22semidirect
97. #2423C22semidirect
98. #2421C22semidirect
99. #2417C22semidirect
100. #2415C22semidirect
101. #2414C22semidirect
105. #2401C22semidirect
106. #2398C22semidirect
107. #2396C22semidirect
108. #2395C22semidirect
109. #2392C22semidirect
110. #2392C22semidirect
112. #2367C22semidirect
113. #2363C22semidirect
114. #2362C22semidirect
115. #2354C22semidirect
116. #2351C22semidirect
117. #2351C22semidirect
118. Q8×C4⋊C4C22semidirect
119. Q8×C4⋊C4C22semidirect
125. Q8×C22⋊C4C22semidirect
126. Q8×C22⋊C4C22semidirect
129. #2326C22semidirect
130. #2324C22semidirect
133. C4×C22⋊Q8C22semidirect
136. #2290C22semidirect
137. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#429832
#429752
#429202
#426422
#426342
#426272
#426192
#375142
#374922
#366702
#360822
#359482
#358982
#358012
#357712
#357482
#357372
#342932
#342582