Finite Group Databasebeta

← #7627564

Subgroups — #7627564

Order 512.

8450 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3488C211yesmaximal, characteristic
2#34495C216yesmaximal, complemented
3#34493C216yesmaximal, complemented
4#34476C216yesmaximal, complemented
5#34471C216yesmaximal, complemented
6#34438C216yesmaximal, complemented
7#34414C216yesmaximal, complemented
8#34379C213yesmaximal, complemented
9#34363C213yesmaximal, complemented
10#34362C213yesmaximal, complemented
11#34342C213yesmaximal, complemented
12#34313C212yesmaximal, complemented
13#34312C212yesmaximal, complemented
14#34295C212yesmaximal, complemented
15#34293C212yesmaximal, complemented
16#34263C212yesmaximal, complemented
17#34258C212yesmaximal, complemented
18#34175C211yesmaximal, characteristic, complemented
19#34174C211yesmaximal, characteristic, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C23×#41C2211yescharacteristic
22#3488C4132yescomplemented
23C2×#550C2212yes—
24C2×#548C2212yes—
25C2×#546C2216yes—
26C2×D42C2216yes—
27C2×#537C2213yes—
28C2×#535C2213yes—
29C2×#525C2213yes—
30C22×#121C2213yes—
31C2×#520C2211yescharacteristic
32C2×#520C2212yescomplemented
33C2×#520C2212yescomplemented
34C2×#519C2212yescomplemented
35C2×C4×#41C2212yescomplemented
36#2378C2211yescharacteristic, complemented
37#2378C2213yescomplemented
38#2378C2216yescomplemented
39#2377C2213yescomplemented
40#2377C2213yescomplemented
41#2377C2216yescomplemented
42#2377C2216yescomplemented
43#2377C22112yescomplemented
44#2376C2216yescomplemented
45#2376C2216yescomplemented
46#2375C2216yescomplemented
47#2375C2216yescomplemented
48#2375C22112yescomplemented
49#2368C2216yescomplemented
50#2367C2216yescomplemented
51#2367C2216yescomplemented
52#2366C2216yescomplemented
53#2366C2216yescomplemented
54#2364C2216yescomplemented
55#2363C2216yescomplemented
56#2363C2216yescomplemented
57#2363C22112yescomplemented
58#2363C2216yescomplemented
59#2362C2216yescomplemented
60#2361C2216yescomplemented
61#2361C2216yescomplemented
62#2361C2216yescomplemented
63#2360C2216yescomplemented
64#2358C22112yescomplemented
65#2357C2216yescomplemented
66#2354C2216yescomplemented
67#2354C2216yescomplemented
68#2352C2216yescomplemented
69#2352C2216yescomplemented
70#2351C2212yescomplemented
71Q8×C4⋊C4C2212yescomplemented
72D4×C4⋊C4C2216yescomplemented
73#2345C2216yescomplemented
74#2344C2216yescomplemented
75#2342C22112yescomplemented
76#2341C2212yes—
77#2341C2212yes—
78#2341C2212yescomplemented
79#2341C2211yescharacteristic, complemented
80#2341C2212yescomplemented
81#2341C2216yescomplemented
82#2341C2213yescomplemented
83#2341C2213yescomplemented
84#2341C2211yescharacteristic, complemented
85Q8×C22⋊C4C2211yescharacteristic, complemented
86Q8×C22⋊C4C2211yescharacteristic, complemented
87#2339C2216yescomplemented
88D4×C22⋊C4C2216yescomplemented
89D4×C22⋊C4C2216yescomplemented
90D4×C22⋊C4C22112yescomplemented
91D4×C22⋊C4C2213yescomplemented
92D4×C22⋊C4C2213yescomplemented
93D4×C22⋊C4C2216yescomplemented
94D4×C22⋊C4C2216yescomplemented
95#2335C22112yescomplemented
96#2333C22112yescomplemented
97#2333C22112yescomplemented
98#2328C2216yescomplemented
99#2326C2216yescomplemented
100#2325C22112yescomplemented
101#2324C2216yescomplemented
102#2324C2216yescomplemented
103#2324C2216yescomplemented
104#2324C2216yescomplemented
105#2324C2216yescomplemented
106#2324C22112yescomplemented
107#2323C2216yescomplemented
108#2321C22112yescomplemented
109#2321C22112yescomplemented
110#2321C22112yescomplemented
111#2319C2216yescomplemented
112#2315C2216yescomplemented
113#2314C2216yescomplemented
114#2312C2216yescomplemented
115#2311C2216yescomplemented
116#2311C2216yescomplemented
117#2309C2216yescomplemented
118#2309C2216yescomplemented
119#2309C2216yescomplemented
120#2308C2216yescomplemented
121C4×#127C2216yescomplemented
122C4×#124C2216yescomplemented
123C4×C22⋊Q8C2216yescomplemented
124C4×#121C2216yescomplemented
125#2298C2216yescomplemented
126#2297C2216yescomplemented
127#2293C2216yescomplemented
128#2293C2216yescomplemented
129#2293C2216yescomplemented
130C2×#390C2216yescomplemented
131#2290C2216yescomplemented
132#2290C2216yescomplemented
133#2280C2213yescomplemented
134#2280C2213yescomplemented
135#2280C2213yescomplemented
136C2×#380C2213yescomplemented
137#2276C2212yescomplemented
138C42×Q8C2212yescomplemented
139C2×H(5,𝔽2)—48no—
140C2×H(5,𝔽2)C2×C4116yescomplemented
141C22×#41—48no—
142C22×#41C2×C4116yescomplemented
143C22×#41C2311yescharacteristic
144C22×#41C2311yescharacteristic
145C22×#41C2312yes—
146C22×#41C2313yes—
147C22×#41C2313yes—
148C22×#41C2313yes—
149C23×Q8C2311yescharacteristic
150C23×D4C2313yes—
151C23×D4C2316yes—
152C23×D4C2313yes—
153C23×D4C2316yes—
154C24×C4C2313yes—
155#550C2×C4132yescomplemented
156#548C2×C4132yescomplemented
157#546C2×C4196yescomplemented
158D42C2×C4196yescomplemented
159#537C2×C4148yescomplemented
160#535C2×C4148yescomplemented
161C2×#127C2316yes—
162C2×#124C2316yes—
163#525C2×C4148yescomplemented
164C2×#123C2316yes—
165C2×C22⋊Q8C2316yes—
166C2×C22⋊Q8C2313yes—
167C2×C22⋊Q8C2311yescharacteristic
168C2×#121C2×C4148yescomplemented
169C2×#121C2316yes—
170C2×#121C2316yes—
171C2×#121C23112yes—
172C2×#121C2316yes—
173C2×#121C2316yes—
174C2×#121C2313yes—
175C2×#121C2313yes—
176C2×#120C23112yes—
177C2×#120C2316yes—
178#520—48no—
179#520—48no—
180#520C2×C4116yescomplemented
181#519—48no—
182C4×#41—48no—
183C2×C4×Q8C2312yes—
184C2×C4×Q8C2312yes—
185C2×C4×Q8C2312yes—
186C2×C4×Q8C2312yes—
187C2×C4×Q8C2316yes—
188C2×C4×Q8C2316yes—
189C2×C4×Q8C2312yes—
190C2×C4×D4C2316yes—
191C2×C4×D4C2316yes—
192C2×C4×D4C2316yes—
193C2×C4×D4C2316yes—
194C2×C4×D4C2316yes—
195C2×C4×D4C2316yes—
196C2×C4×D4C23112yes—
197C2×C4×D4C23112yes—
198C2×C4×D4C23112yes—
199C2×C4×D4C2316yes—
200C2×C4×D4C2316yes—
201C2×C4×D4C2316yes—
202C2×#117C2316yes—
203C2×#117C2316yes—
204C2×#117C2316yes—
205C2×#117C2316yes—
206C2×#117C2316yes—
207C2×#117C23112yes—
208C2×#117C2313yes—
209C22×C4⋊C4C2316yes—
210C22×C4⋊C4C2316yes—
211C22×C4⋊C4C2313yes—
212C22×C22⋊C4C23112yes—
213C22×C22⋊C4C23112yes—
214C22×C22⋊C4C2316yes—
215C22×C22⋊C4C2316yes—
216C22×C42C2316yes—
217#391C2316yes—
218#391C2316yes—
219#391C2316yes—
220#391C2312yes—
221#390C2316yes—
222#390C23112yes—
223#390C2316yes—
224#390C2316yes—
225#390C2316yes—
226#390C2316yes—
227#390C2316yes—
228#390C23112yes—
229#390C2316yes—
230#390C2316yes—
231#390C23112yes—
232#390C23112yes—
233#390C23112yes—
234#390C23112yes—
235#390C2316yes—
236#390C2316yes—
237#390C2316yes—
238#390C2316yes—
239#390C2316yes—
240#390C2316yes—
241#390C2316yes—
242#390C2316yes—
243#389C2316yes—
244#389C2316yes—
245#389C2316yes—
246#389C2316yes—
247#389C2316yes—
248#389C2316yes—
249#389C2316yes—
250#389C2312yes—
251#388C2316yes—
252#388C23112yes—
253#388C23112yes—
254#388C23112yes—
255#388C23112yes—
256#388C23112yes—
257#388C2316yes—
258#388C2316yes—
259#388C2316yes—
260#388C2316yes—
261#388C2316yes—
262#388C2316yes—
263#388C23112yes—
264#388C23112yes—
265#388C23112yes—
266#388C2316yes—
267#388C2316yes—
268#388C2316yes—
269#388C2316yes—
270#388C2316yes—
271#388C2312yes—
272#388C2312yes—
273#388C2316yes—
274#388C2316yes—
275#387C2316yes—
276#387C23112yes—
277#387C23112yes—
278#387C2316yes—
279#387C2316yes—
280#387C2316yes—
281#387C2316yes—
282#387C2312yes—
283#387C2316yes—
284#387C2312yes—
285#386C2316yes—
286#386C23112yes—
287#386C23112yes—
288#386C23112yes—
289#386C23112yes—
290#386C23112yes—
291#386C23112yes—
292#386C23112yes—
293#386C23112yes—
294#386C2316yes—
295#386C23112yes—
296#386C2316yes—
297#386C2316yes—
298#386C23112yes—
299#386C2316yes—
300#386C2316yes—
301#386C2316yes—
302#386C2316yes—
303#385C2316yes—
304#385C23112yes—
305#385C23112yes—
306#385C23112yes—
307#385C2316yes—
308#385C23112yes—
309#385C2316yes—
310#385C2316yes—
311#384C2316yes—
312#382C2316yes—
313#381C23112yes—
314#381C2316yes—
315#381C2311yescharacteristic
316#381C2313yes—
317#380C2316yes—
318#380C2316yes—
319#380C2316yes—
320#380C2316yes—
321#380C2316yes—
322#380C2316yes—
323#380C2313yes—
324#380C2313yes—
325#380C23112yes—
326#380C2313yes—
327#380C2313yes—
328#380C2313yes—
329#380C2313yes—
330#380C2316yes—
331#380C2313yes—
332#380C2311yescharacteristic
333#379C2313yes—
334#379C2316yes—
335#379C23112yes—
336#379C2313yes—
337#379C2316yes—
338#379C23112yes—
339C4×C4⋊C4C2316yes—
340C4×C4⋊C4C2316yes—
341C4×C4⋊C4C2316yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C23112yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C2316yes—
346C4×C4⋊C4C2316yes—
347C4×C4⋊C4C2316yes—
348C4×C22⋊C4C23112yes—
349C4×C22⋊C4C23112yes—
350C4×C22⋊C4C23112yes—
351C4×C22⋊C4C23112yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C23112yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C2313yes—
357C4×C22⋊C4C2313yes—
358C4×C22⋊C4C2316yes—
359C4×C22⋊C4C2316yes—
360C4×C22⋊C4C2316yes—
361C4×C22⋊C4C2313yes—
362C4×C22⋊C4C2313yes—
363#376C2316yes—
364C2×#95C2316yes—
365C43C2316yes—
366C25C2416yes—
367C25C2413yes—
368H(5,𝔽2)—464no—
369C2×#41—28no—
370C2×#41—28no—
371C2×#41—28no—
372C2×#41—28no—
373C2×#41—412no—
374C2×#41—412no—
375C2×#41—412no—
376C2×#41—464no—
377C2×#41C22×C418yes—
378C2×#41C22×C4116yes—
379C2×#41C22×C418yes—
380C2×#41C22×C4124yes—
381C2×#41C22×C4124yes—
382C2×#41C22×C4124yes—
383C22×Q8—28no—
384C22×Q8C22×C418yes—
385C22×Q8C2413yes—
386C22×Q8C2411yescharacteristic
387C22×Q8C2411yescharacteristic
388C22×D4—412no—
389C22×D4—412no—
390C22×D4—412no—
391C22×D4—412no—
392C22×D4—812no—
393C22×D4C22×C4124yes—
394C22×D4C22×C4124yes—
395C22×D4C22×C4148yes—
396C22×D4C22×C4148yes—
397C22×D4C2416yes—
398C22×D4C2413yes—
399C22×D4C2413yes—
400C22×D4C2416yes—
401C22×D4C24112yes—
402C22×D4C2416yes—
403C22×D4C2416yes—
404C22×D4C2416yes—
405C22×D4C2413yes—
406C23×C4—412no—
407C23×C4C22×C4124yes—
408C23×C4C2413yes—
409C23×C4C2416yes—
410C23×C4C2413yes—
411C23×C4C2413yes—
412C23×C4C24112yes—
413C23×C4C2416yes—
414C23×C4C2416yes—
415C23×C4C24112yes—
416C23×C4C2413yes—
417C23×C4C2416yes—
418C23×C4C2411yescharacteristic
419C23×C4C2413yes—
420#127C22×C4148yes—
421#124C22×C4148yes—
422#123C22×C4148yes—
423C22⋊Q8C22×C418yes—
424C22⋊Q8C22×C4124yes—
425C22⋊Q8C22×C4148yes—
426#121C22×C4124yes—
427#121C22×C4148yes—
428#121C22×C4148yes—
429#121C22×C4148yes—
430#121C22×C4124yes—
431#121C22×C4196yes—
432#121C22×C4148yes—
433#120C22×C4148yes—
434#120C22×C4196yes—
435C4×Q8—28no—
436C4×Q8—28no—
437C4×Q8—28no—
438C4×Q8—28no—
439C4×Q8—412no—
440C4×Q8—412no—
441C4×Q8C22×C4116yes—
442C4×D4—412no—
443C4×D4—412no—
444C4×D4—412no—
445C4×D4—412no—
446C4×D4—412no—
447C4×D4—412no—
448C4×D4—812no—
449C4×D4—812no—
450C4×D4—812no—
451C4×D4C22×C4148yes—
452C4×D4C22×C4148yes—
453C4×D4C22×C4148yes—
454#117—412no—
455#117—412no—
456#117—412no—
457#117—412no—
458#117—412no—
459#117—812no—
460#117C22×C4124yes—
461C2×C4⋊C4—412no—
462C2×C4⋊C4—412no—
463C2×C4⋊C4C22×C4124yes—
464C2×C4⋊C4C2416yes—
465C2×C4⋊C4C2416yes—
466C2×C4⋊C4C2416yes—
467C2×C4⋊C4C2416yes—
468C2×C4⋊C4C2416yes—
469C2×C4⋊C4C2416yes—
470C2×C4⋊C4C2412yes—
471C2×C4⋊C4C2412yes—
472C2×C4⋊C4C2416yes—
473C2×C4⋊C4C24112yes—
474C2×C4⋊C4C2416yes—
475C2×C4⋊C4C2416yes—
476C2×C4⋊C4C2416yes—
477C2×C4⋊C4C2416yes—
478C2×C4⋊C4C2412yes—
479C2×C4⋊C4C2413yes—
480C2×C4⋊C4C2416yes—
481C2×C4⋊C4C2411yescharacteristic
482C2×C4⋊C4C2412yes—
483C2×C4⋊C4C2416yes—
484C2×C22⋊C4—86no—
485C2×C22⋊C4—812no—
486C2×C22⋊C4—812no—
487C2×C22⋊C4C22×C4148yes—
488C2×C22⋊C4C2413yes—
489C2×C22⋊C4C24112yes—
490C2×C22⋊C4C2413yes—
491C2×C22⋊C4C2416yes—
492C2×C22⋊C4C2416yes—
493C2×C22⋊C4C2416yes—
494C2×C22⋊C4C2416yes—
495C2×C22⋊C4C24112yes—
496C2×C22⋊C4C24112yes—
497C2×C22⋊C4C24112yes—
498C2×C22⋊C4C2416yes—
499C2×C22⋊C4C2412yes—
500C2×C22⋊C4C2416yes—
501C2×C22⋊C4C2416yes—
502C2×C22⋊C4C24112yes—
503C2×C22⋊C4C2416yes—
504C2×C22⋊C4C2416yes—
505C2×C22⋊C4C2416yes—
506C2×C22⋊C4C2416yes—
507C2×C22⋊C4C2416yes—
508C2×C22⋊C4C2416yes—
509C2×C22⋊C4C2416yes—
510C2×C22⋊C4C2411yescharacteristic
511C2×C22⋊C4C2416yes—
512C2×C22⋊C4C2411yescharacteristic
513C2×C22⋊C4C2416yes—
514C2×C22⋊C4C2416yes—
515C2×C22⋊C4C2416yes—
516C2×C22⋊C4C24112yes—
517C2×C22⋊C4C2416yes—
518C2×C22⋊C4C2412yes—
519C2×C22⋊C4C2416yes—
520C2×C22⋊C4C2416yes—
521C2×C42—412no—
522C2×C42C2416yes—
523C2×C42C2416yes—
524C2×C42C2416yes—
525C2×C42C2416yes—
526C2×C42C2416yes—
527C2×C42C2416yes—
528C2×C42C24112yes—
529C2×C42C24112yes—
530C2×C42C2416yes—
531C2×C42C2416yes—
532C2×C42C2412yes—
533C2×C42C2412yes—
534C2×C42C2416yes—
535#95C2416yes—
536#95C2416yes—
537#95C2416yes—
538#95C2412yes—
539#95C2416yes—
540#95C2416yes—
541#95C2416yes—
542#95C2411yescharacteristic
543#95C2413yes—
544#95C2413yes—
545#95C2416yes—
546#95C2412yes—
547#95C2411yescharacteristic
548#95C2416yes—
549#95C2412yes—
550#95C2416yes—
551#95C2416yes—
552#95C24112yes—
553#95C2412yes—
554#95C2412yes—
555#95C2416yes—
556#95C2416yes—
557#95C2416yes—
558#95C2416yes—
559#95C24112yes—
560#95C2412yes—
561C24—43no—
562C24—46no—
563C24—46no—
564C24—43no—
565C24—46no—
566C24—412no—
567C24—412no—
568C24—46no—
569C24C23×C4124yes—
570C24C23×C4112yes—
571C24C2511yescharacteristic
572C24C2513yes—
573C24C2516yes—
574C24C2513yes—
575#41—232no—
576#41—232no—
577#41—264no—
578#41—448no—
579#41—448no—
580#41—448no—
581C2×Q8—232no—
582C2×Q8—212no—
583C2×Q8—42no—
584C2×Q8C23×C4112yes—
585C2×Q8C23×C414yes—
586C2×Q8C23×C414yes—
587C2×Q8H(5,𝔽2)18yes—
588C2×D4—212no—
589C2×D4—212no—
590C2×D4—212no—
591C2×D4—212no—
592C2×D4—448no—
593C2×D4—448no—
594C2×D4—496no—
595C2×D4—46no—
596C2×D4—412no—
597C2×D4—412no—
598C2×D4—46no—
599C2×D4—46no—
600C2×D4—46no—
601C2×D4—412no—
602C2×D4—46no—
603C2×D4—46no—
604C2×D4—46no—
605C2×D4—848no—
606C2×D4C23×C4112yes—
607C2×D4C23×C4124yes—
608C2×D4C23×C4112yes—
609C2×D4C23×C4124yes—
610C2×D4C23×C4124yes—
611C2×D4C23×C4124yes—
612C2×D4C23×C4148yes—
613C2×D4C23×C4124yes—
614C2×D4C23×C4112yes—
615C22×C4—212no—
616C22×C4—212no—
617C22×C4—212no—
618C22×C4—212no—
619C22×C4—212no—
620C22×C4—448no—
621C22×C4—412no—
622C22×C4—42no—
623C22×C4—46no—
624C22×C4—46no—
625C22×C4—46no—
626C22×C4—46no—
627C22×C4—46no—
628C22×C4—46no—
629C22×C4—46no—
630C22×C4—46no—
631C22×C4—412no—
632C22×C4—412no—
633C22×C4—412no—
634C22×C4—412no—
635C22×C4—412no—
636C22×C4—412no—
637C22×C4C23×C4112yes—
638C22×C4C23×C4112yes—
639C22×C4C23×C4112yes—
640C22×C4C23×C4124yes—
641C22×C4C23×C4112yes—
642C22×C4C23×C4124yes—
643C22×C4C23×C414yes—
644C22×C4C23×C4112yes—
645C22×C4C2512yes—
646C22×C4C2516yes—
647C22×C4C2516yes—
648C22×C4C2512yes—
649C22×C4C2516yes—
650C22×C4C2512yes—
651C22×C4C2512yes—
652C22×C4C2516yes—
653C22×C4C2511yescharacteristic
654C22×C4C2512yes—
655C22×C4C2516yes—
656C22×C4C2513yes—
657C22×C4C2512yes—
658C22×C4C2511yescharacteristic
659C22×C4C2513yes—
660C4⋊C4—212no—
661C4⋊C4—212no—
662C4⋊C4—212no—
663C4⋊C4—212no—
664C4⋊C4—46no—
665C4⋊C4—46no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—46no—
670C4⋊C4—46no—
671C4⋊C4—46no—
672C4⋊C4—412no—
673C4⋊C4—46no—
674C4⋊C4—46no—
675C4⋊C4C23×C4112yes—
676C4⋊C4C23×C4124yes—
677C4⋊C4C23×C414yes—
678C4⋊C4C23×C418yes—
679C4⋊C4C23×C4124yes—
680C22⋊C4—46no—
681C22⋊C4—46no—
682C22⋊C4—43no—
683C22⋊C4—46no—
684C22⋊C4—412no—
685C22⋊C4—46no—
686C22⋊C4—43no—
687C22⋊C4—412no—
688C22⋊C4—412no—
689C22⋊C4—412no—
690C22⋊C4—41no—
691C22⋊C4—46no—
692C22⋊C4—46no—
693C22⋊C4—46no—
694C22⋊C4—41no—
695C22⋊C4—42no—
696C22⋊C4—46no—
697C22⋊C4—46no—
698C22⋊C4—46no—
699C22⋊C4—46no—
700C22⋊C4—46no—
701C22⋊C4—412no—
702C22⋊C4—46no—
703C22⋊C4—46no—
704C22⋊C4—46no—
705C22⋊C4—46no—
706C22⋊C4—46no—
707C22⋊C4C23×C4124yes—
708C22⋊C4C23×C4148yes—
709C22⋊C4C23×C4124yes—
710C22⋊C4C23×C418yes—
711C22⋊C4C23×C4124yes—
712C22⋊C4C23×C4124yes—
713C42—212no—
714C42—212no—
715C42—212no—
716C42—212no—
717C42—42no—
718C42—46no—
719C42—42no—
720C42—412no—
721C42—46no—
722C42—412no—
723C42—46no—
724C42—46no—
725C42C23×C4124yes—
726C23—22no—
727C23—26no—
728C23—26no—
729C23—26no—
730C23—26no—
731C23—21no—
732C23—23no—
733C23—26no—
734C23—26no—
735C23—26no—
736C23—23no—
737C23—26no—
738C23—26no—
739C23—22no—
740C23—23no—
741C23—21no—
742C23—23no—
743C23—26no—
744C23—412no—
745C23—412no—
746C23—412no—
747C23—424no—
748C23—424no—
749C23—424no—
750C23—812no—
751C23—812no—
752C23—1612no—
753C23—1612no—
754C23C24×C4112yes—
755C23C24×C412yes—
756C23C24×C416yes—
757C23C24×C416yes—
758C23C2611yescharacteristic
759Q8—224no—
760Q8—44no—
761Q8#518116yes—
762D4—224no—
763D4—248no—
764D4—224no—
765D4—412no—
766D4—424no—
767D4—424no—
768D4—424no—
769D4—448no—
770D4—424no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—26no—
778C2×C4—26no—
779C2×C4—22no—
780C2×C4—224no—
781C2×C4—224no—
782C2×C4—224no—
783C2×C4—248no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—26no—
789C2×C4—26no—
790C2×C4—26no—
791C2×C4—26no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—26no—
795C2×C4—26no—
796C2×C4—26no—
797C2×C4—26no—
798C2×C4—26no—
799C2×C4—26no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—26no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—26no—
807C2×C4—22no—
808C2×C4—44no—
809C2×C4—412no—
810C2×C4—412no—
811C2×C4—424no—
812C2×C4—812no—
813C2×C4—812no—
814C2×C4—1612no—
815C2×C4—1612no—
816C2×C4C24×C414yes—
817C2×C4C24×C4112yes—
818C2×C4C24×C412yes—
819C2×C4C24×C416yes—
820C2×C4C24×C414yes—
821C2×C4C24×C412yes—
822C2×C4C24×C416yes—
823C2×C4C2×H(5,𝔽2)112yes—
824C22—22no—
825C22—26no—
826C22—26no—
827C22—212no—
828C22—26no—
829C22—22no—
830C22—26no—
831C22—212no—
832C22—26no—
833C22—212no—
834C22—22no—
835C22—26no—
836C22—46no—
837C22—46no—
838C22—42no—
839C22—46no—
840C22—46no—
841C22—46no—
842C22—46no—
843C22—46no—
844C22—42no—
845C22—46no—
846C22—824no—
847C22—1624no—
848C22C25×C411yescharacteristic
849C22C22×H(5,𝔽2)12yes—
850C22H(7,𝔽2)12yes—
851C22H(7,𝔽2)11yescharacteristic
852C222−1+611yescharacteristic
853C4—22no—
854C4—22no—
855C4—24no—
856C4—26no—
857C4—212no—
858C4—24no—
859C4—42no—
860C4—42no—
861C4—46no—
862C4—42no—
863C4—42no—
864C4—46no—
865C4—46no—
866C4—46no—
867C4C2×#518112yes—
868C2—46no—
869C2—42no—
870C2—46no—
871C2—412no—
872C2C22×#51811yescharacteristic
873C2#6265211yescharacteristic
874C2#6265411yescharacteristic
875C2#6305212yes—
876C2#6306612yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3488C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #34495C2semidirect
3. #34493C2semidirect
4. #34476C2semidirect
5. #34471C2semidirect
6. #34438C2semidirect
7. #34414C2semidirect
8. #34379C2semidirect
9. #34363C2semidirect
10. #34362C2semidirect
11. #34342C2semidirect
12. #34313C2semidirect
13. #34312C2semidirect
14. #34295C2semidirect
15. #34293C2semidirect
16. #34263C2semidirect
17. #34258C2semidirect
18. #34175C2semidirect
19. #34174C2semidirect
22. #3488C4semidirect
32. C2×#520C22semidirect
33. C2×#520C22semidirect
34. C2×#519C22semidirect
35. C2×C4×#41C22semidirect
36. #2378C22semidirect
37. #2378C22semidirect
38. #2378C22semidirect
39. #2377C22semidirect
40. #2377C22semidirect
41. #2377C22semidirect
42. #2377C22semidirect
43. #2377C22semidirect
44. #2376C22semidirect
45. #2376C22semidirect
46. #2375C22semidirect
47. #2375C22semidirect
48. #2375C22semidirect
49. #2368C22semidirect
50. #2367C22semidirect
51. #2367C22semidirect
52. #2366C22semidirect
53. #2366C22semidirect
54. #2364C22semidirect
55. #2363C22semidirect
56. #2363C22semidirect
57. #2363C22semidirect
58. #2363C22semidirect
59. #2362C22semidirect
60. #2361C22semidirect
61. #2361C22semidirect
62. #2361C22semidirect
63. #2360C22semidirect
64. #2358C22semidirect
65. #2357C22semidirect
66. #2354C22semidirect
67. #2354C22semidirect
68. #2352C22semidirect
69. #2352C22semidirect
70. #2351C22semidirect
71. Q8×C4⋊C4C22semidirect
72. D4×C4⋊C4C22semidirect
73. #2345C22semidirect
74. #2344C22semidirect
75. #2342C22semidirect
78. #2341C22semidirect
79. #2341C22semidirect
80. #2341C22semidirect
81. #2341C22semidirect
82. #2341C22semidirect
83. #2341C22semidirect
84. #2341C22semidirect
85. Q8×C22⋊C4C22semidirect
86. Q8×C22⋊C4C22semidirect
87. #2339C22semidirect
88. D4×C22⋊C4C22semidirect
89. D4×C22⋊C4C22semidirect
90. D4×C22⋊C4C22semidirect
91. D4×C22⋊C4C22semidirect
92. D4×C22⋊C4C22semidirect
93. D4×C22⋊C4C22semidirect
94. D4×C22⋊C4C22semidirect
95. #2335C22semidirect
96. #2333C22semidirect
97. #2333C22semidirect
98. #2328C22semidirect
99. #2326C22semidirect
100. #2325C22semidirect
101. #2324C22semidirect
102. #2324C22semidirect
103. #2324C22semidirect
104. #2324C22semidirect
105. #2324C22semidirect
106. #2324C22semidirect
107. #2323C22semidirect
108. #2321C22semidirect
109. #2321C22semidirect
110. #2321C22semidirect
111. #2319C22semidirect
112. #2315C22semidirect
113. #2314C22semidirect
114. #2312C22semidirect
115. #2311C22semidirect
116. #2311C22semidirect
117. #2309C22semidirect
118. #2309C22semidirect
119. #2309C22semidirect
120. #2308C22semidirect
121. C4×#127C22semidirect
122. C4×#124C22semidirect
123. C4×C22⋊Q8C22semidirect
124. C4×#121C22semidirect
125. #2298C22semidirect
126. #2297C22semidirect
127. #2293C22semidirect
128. #2293C22semidirect
129. #2293C22semidirect
130. C2×#390C22semidirect
131. #2290C22semidirect
132. #2290C22semidirect
133. #2280C22semidirect
134. #2280C22semidirect
135. #2280C22semidirect
136. C2×#380C22semidirect
137. #2276C22semidirect
138. C42×Q8C22semidirect
140. C2×H(5,𝔽2)C2×C4semidirect
142. C22×#41C2×C4semidirect
155. #550C2×C4semidirect
156. #548C2×C4semidirect
157. #546C2×C4semidirect
158. D42C2×C4semidirect
159. #537C2×C4semidirect
160. #535C2×C4semidirect
163. #525C2×C4semidirect
168. C2×#121C2×C4semidirect
180. #520C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#34882
#344952
#344932
#344762
#344712
#344382
#344142
#343792
#343632
#343622
#343422
#343132
#343122
#342952
#342932
#342632
#342582
#341752
#341742