Finite Group Databasebeta

← #7685762

Subgroups — #7685762

Order 512.

8855 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic, complemented
2C22×#550C211yesmaximal, characteristic, complemented
3#59411C213yesmaximal, complemented
4#59143C213yesmaximal, complemented
5#59039C213yesmaximal, complemented
6#59015C216yesmaximal, complemented
7#44930C216yesmaximal, complemented
8#44891C216yesmaximal, complemented
9#38952C213yesmaximal, complemented
10#38909C213yesmaximal, complemented
11#37664C216yesmaximal, complemented
12#36576C211yesmaximal, characteristic, complemented
13Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
14#36457C211yesmaximal, characteristic, complemented
15#36428C212yesmaximal, complemented
16#36154C213yesmaximal, complemented
17#36121C213yesmaximal, complemented
18#36005C212yesmaximal, complemented
19#35831C212yesmaximal, complemented
20#34700C213yesmaximal, complemented
21#34313C211yesmaximal, characteristic, complemented
22#34175C212yesmaximal, complemented
23C4×D4×Q8C211yesmaximal, characteristic, complemented
24C23×#41C2212yes—
25#3522—216no—
26C2×#559C2213yescomplemented
27C2×Q82C2211yescharacteristic, complemented
28C2×#554C2213yescomplemented
29C2×#550—216no—
30C2×#550C2213yes—
31C2×#550C2213yes—
32C2×#550C2216yes—
33C2×#550C2211yescharacteristic
34C2×#550C2212yes—
35C2×#550C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×#548C2212yescomplemented
38C2×#548C2212yescomplemented
39C2×#547C2216yescomplemented
40C2×#546C2216yes—
41C2×#542C2216yescomplemented
42C2×#532C2213yescomplemented
43C22×#127C2213yes—
44C2×#529C2213yescomplemented
45C22×#121C2216yes—
46C2×#520C2212yescomplemented
47C2×#520C2212yescomplemented
48C22×C4×Q8C2211yescharacteristic
49C22×C4×Q8C2211yescharacteristic, complemented
50C22×C4×D4C2213yes—
51#2858C2213yescomplemented
52#2857C2213yes—
53#2856C2213yescomplemented
54#2848C2216yes—
55#2709C22112yescomplemented
56#2701C22112yescomplemented
57#2691C22112yescomplemented
58#2686C22112yescomplemented
59#2672C22112yescomplemented
60#2672C22112yescomplemented
61#2671C22112yescomplemented
62#2624C2216yescomplemented
63#2620C2216yescomplemented
64#2582C2213yescomplemented
65#2567C2213yescomplemented
66#2563C2213yescomplemented
67#2548C2213yescomplemented
68#2548C2213yescomplemented
69#2544C2216yescomplemented
70#2544C2216yescomplemented
71#2544C2216yescomplemented
72#2538C2213yescomplemented
73#2537C2216yescomplemented
74#2501C2216yescomplemented
75#2491C2216yescomplemented
76#2491C2216yescomplemented
77#2487C2216yescomplemented
78#2480C2216yes—
79#2468C2216yescomplemented
80#2457C2216yescomplemented
81#2454C2213yescomplemented
82#2454C2216yescomplemented
83#2451C2216yescomplemented
84#2450C22112yescomplemented
85#2447C2213yescomplemented
86#2445C2216yescomplemented
87#2445C2216yescomplemented
88#2445C2216yescomplemented
89#2445C2216yescomplemented
90#2442C2213yes—
91#2440C2216yes—
92#2437C22112yes—
93#2435C2213yes—
94#2435C2216yes—
95#2435C2216yes—
96#2432C2216yescomplemented
97#2432C2216yescomplemented
98#2431C2216yescomplemented
99#2430C22112yescomplemented
100#2428C2216yescomplemented
101#2428C2216yescomplemented
102#2427C2216yescomplemented
103#2427C2213yescomplemented
104#2426C2216yescomplemented
105#2425C22112yescomplemented
106#2422C2216yescomplemented
107#2422C2216yescomplemented
108#2420C2213yescomplemented
109#2418C2216yes—
110#2417C2211yescharacteristic
111#2417C2216yescomplemented
112#2416C2216yescomplemented
113#2416C2216yescomplemented
114#2408C2213yes—
115#2408C2216yes—
116#2407C2216yescomplemented
117#2407C2216yescomplemented
118#2405C22112yes—
119#2395C2216yescomplemented
120#2392C2216yescomplemented
121#2366C2213yescomplemented
122#2365C2213yescomplemented
123#2361C2216yescomplemented
124#2360C2213yes—
125#2360C2213yescomplemented
126Q8×C4⋊C4C2211yescharacteristic, complemented
127Q8×C4⋊C4C2211yescharacteristic, complemented
128Q8×C4⋊C4C2212yescomplemented
129#2349C2216yescomplemented
130D4×C4⋊C4C2213yes—
131D4×C4⋊C4C2213yescomplemented
132#2341C2212yescomplemented
133#2341C2212yescomplemented
134#2341C2212yescomplemented
135#2341C2212yescomplemented
136Q8×C22⋊C4C2212yes—
137Q8×C22⋊C4C2211yescharacteristic
138Q8×C22⋊C4C2211yescharacteristic, complemented
139#2339C2216yescomplemented
140#2339C2216yescomplemented
141D4×C22⋊C4C2216yes—
142D4×C22⋊C4C2216yes—
143D4×C22⋊C4C2216yes—
144#2324C2216yescomplemented
145#2311C2216yescomplemented
146#2311C2216yescomplemented
147C4×C4⋊Q8C2213yescomplemented
148C4×#127C2213yescomplemented
149C4×#124C2213yescomplemented
150C4×C22⋊Q8C2213yes—
151C4×C22⋊Q8C2213yes—
152C4×C22⋊Q8C2213yescomplemented
153C4×#121C2213yescomplemented
154C4×#120C2216yes—
155#2293C2213yescomplemented
156#2280C2216yes—
157C2×#380C2216yes—
158C42×Q8C2211yescharacteristic, complemented
159C42×D4C2213yes—
160C22×#41—216no—
161C22×#41—216no—
162C22×#41—48no—
163C22×#41C2312yes—
164C22×#41C2316yes—
165C22×#41C2316yes—
166C22×#41C2312yes—
167C22×#41C2316yes—
168C23×Q8C2311yescharacteristic
169C23×Q8C2311yescharacteristic
170C23×D4C2316yes—
171C23×D4C2313yes—
172C23×D4C2316yes—
173C24×C4C2316yes—
174#559—224no—
175Q82—28no—
176#554—224no—
177#550—216no—
178#550—224no—
179#550—248no—
180#550—28no—
181#550—224no—
182#550D4116yescomplemented
183D4×Q8—28no—
184#548—216no—
185#548—48no—
186#547—248no—
187#546—424no—
188#542—248no—
189#532—224no—
190C2×C4⋊Q8C2313yes—
191C2×C4⋊Q8C2313yes—
192C2×C4⋊Q8C2316yes—
193C2×#127—224no—
194C2×#127C2313yes—
195C2×#127C2316yes—
196C2×#127C2316yes—
197C2×#127C2316yes—
198C2×#127C2313yes—
199#529—224no—
200C2×#126C2316yes—
201C2×#125C2313yes—
202C2×#124C2313yes—
203C2×#124C2316yes—
204C2×#124C2316yes—
205C2×#124C2316yes—
206C2×#124C2316yes—
207C2×#124C2313yes—
208C2×#124C2316yes—
209C2×#123C23112yes—
210C2×#123C2316yes—
211C2×#123C23112yes—
212C2×#123C23112yes—
213C2×C22⋊Q8C2313yes—
214C2×C22⋊Q8C2316yes—
215C2×C22⋊Q8C2313yes—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C23112yes—
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2316yes—
220C2×C22⋊Q8C2316yes—
221C2×#121—248no—
222C2×#121C2316yes—
223C2×#121C2316yes—
224C2×#121C2313yes—
225C2×#121C23112yes—
226C2×#121C2316yes—
227C2×#121C2316yes—
228C2×#121C23112yes—
229C2×#121C2313yes—
230C2×#121C2316yes—
231C2×#121C2316yes—
232C2×#121C23112yes—
233C2×#121C2316yes—
234C2×#120C2316yes—
235#520—216no—
236#520—48no—
237C2×C4×Q8—28no—
238C2×C4×Q8—28no—
239C2×C4×Q8C2313yes—
240C2×C4×Q8C2313yes—
241C2×C4×Q8C2313yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2313yes—
249C2×C4×Q8C2313yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4—224no—
252C2×C4×D4C2313yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2313yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2316yes—
265C2×C4×D4C2316yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2316yes—
269C2×C4×D4C2313yes—
270C2×#117C2316yes—
271C2×#117C2316yes—
272C22×C4⋊C4C2316yes—
273C22×C4⋊C4C2313yes—
274C22×C4⋊C4C2313yes—
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2316yes—
277C22×C22⋊C4C2316yes—
278C22×C22⋊C4C23112yes—
279C22×C42C2313yes—
280C22×C42C2313yes—
281#400C2316yes—
282#399C23112yes—
283#399C2316yes—
284#398C23112yes—
285#398C2316yes—
286#398C2312yes—
287#397C2316yes—
288#397C2316yes—
289#397C2316yes—
290#397C2316yes—
291#396C2316yes—
292#396C23112yes—
293#396C2312yes—
294#396C23112yes—
295#395C23112yes—
296#394C23112yes—
297#394C23112yes—
298#394C23112yes—
299#394C23112yes—
300#394C2316yes—
301#394C2316yes—
302#394C2316yes—
303#394C2316yes—
304#394C2316yes—
305#394C23112yes—
306#394C23112yes—
307#394C23112yes—
308#394C23112yes—
309#394C23112yes—
310#393C23112yes—
311#392C2316yes—
312#392C23112yes—
313#391C2313yes—
314#391C2313yes—
315#391C2313yes—
316#391C2316yes—
317#391C2316yes—
318#391C2313yes—
319#391C2313yes—
320#391C2316yes—
321#391C2311yescharacteristic
322#390C2313yes—
323#390C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C2316yes—
327#390C2316yes—
328#390C2316yes—
329#390C2316yes—
330#390C2316yes—
331#390C2316yes—
332#390C2316yes—
333#390C2316yes—
334#390C2316yes—
335#390C2313yes—
336#390C2313yes—
337#390C2313yes—
338#389C2316yes—
339#389C2316yes—
340#389C2313yes—
341#389C2316yes—
342#389C2316yes—
343#389C2316yes—
344#389C2316yes—
345#389C2313yes—
346#389C2313yes—
347#389C2313yes—
348#389C2313yes—
349#389C2311yescharacteristic
350#388C2316yes—
351#388C2316yes—
352#388C2316yes—
353#388C2316yes—
354#388C2316yes—
355#387C2316yes—
356#387C2316yes—
357#387C2316yes—
358#386C23112yes—
359#386C23112yes—
360#386C23112yes—
361#386C23112yes—
362#386C23112yes—
363#386C23112yes—
364#386C23112yes—
365#386C23112yes—
366#386C2316yes—
367#386C2316yes—
368#386C2316yes—
369#386C2312yes—
370#385C23112yes—
371#385C2316yes—
372#385C23112yes—
373#385C23112yes—
374#385C2316yes—
375#385C2316yes—
376#385C23112yes—
377#385C2316yes—
378#385C2316yes—
379#385C2316yes—
380#384C2313yes—
381#384C2313yes—
382#384C2316yes—
383#382C2313yes—
384#381C2316yes—
385#381C2316yes—
386#380C2316yes—
387#380C2316yes—
388#380C23112yes—
389#380C2316yes—
390#380C2316yes—
391#380C2316yes—
392#380C2316yes—
393#380C2313yes—
394#380C2313yes—
395#380C2316yes—
396#380C2313yes—
397#380C23112yes—
398#380C2311yescharacteristic
399#380C2312yes—
400#380C2316yes—
401#379C23112yes—
402#379C2316yes—
403#379C2316yes—
404#379C2316yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C4⋊C4C2313yes—
412C4×C4⋊C4C2316yes—
413C4×C4⋊C4C2313yes—
414C4×C22⋊C4C2313yes—
415C4×C22⋊C4C2313yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2313yes—
424C4×C22⋊C4C2313yes—
425C2×#95C23112yes—
426C43C2313yes—
427C25C2416yes—
428C2×#41—28no—
429C2×#41—28no—
430C2×#41—224no—
431C2×#41—224no—
432C2×#41—28no—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—224no—
436C2×#41—224no—
437C2×#41—224no—
438C2×#41—412no—
439C2×#41—412no—
440C2×#41—412no—
441C2×#41—4128no—
442C2×#41—86no—
443C2×#41C2×D4116yes—
444C22×Q8—24no—
445C22×Q8—24no—
446C22×Q8—24no—
447C22×Q8—24no—
448C22×Q8—24no—
449C22×Q8#4118yescomplemented
450C22×Q8C2411yescharacteristic
451C22×Q8C2413yes—
452C22×Q8C2413yes—
453C22×Q8C2416yes—
454C22×Q8C2411yescharacteristic
455C22×D4—212no—
456C22×D4—224no—
457C22×D4—224no—
458C22×D4—224no—
459C22×D4—212no—
460C22×D4—46no—
461C22×D4—412no—
462C22×D4—412no—
463C22×D4—86no—
464C22×D4C2413yes—
465C22×D4C2416yes—
466C22×D4C2416yes—
467C22×D4C2416yes—
468C22×D4C24112yes—
469C22×D4C2413yes—
470C22×D4C2416yes—
471C22×D4C2411yescharacteristic
472C22×D4C2416yes—
473C22×D4C24112yes—
474C22×D4C2416yes—
475C22×D4C2416yes—
476C23×C4—224no—
477C23×C4—224no—
478C23×C4—412no—
479C23×C4C2413yes—
480C23×C4C2416yes—
481C23×C4C2411yescharacteristic
482C23×C4C2412yes—
483C23×C4C2413yes—
484C23×C4C2413yes—
485C23×C4C2416yes—
486C23×C4C2416yes—
487C23×C4C2416yes—
488C23×C4C2413yes—
489C23×C4C2411yescharacteristic
490C23×C4C24112yes—
491C23×C4C24112yes—
492C4⋊Q8—212no—
493C4⋊Q8—224no—
494C4⋊Q8—212no—
495#127—224no—
496#127—224no—
497#127—224no—
498#127—212no—
499#127C2×D4124yes—
500#126—224no—
501#125—212no—
502#124—212no—
503#124—224no—
504#124—224no—
505#124—412no—
506#124—46no—
507#124—412no—
508#124—86no—
509#123—248no—
510#123—224no—
511#123—424no—
512#123—812no—
513C22⋊Q8—212no—
514C22⋊Q8—224no—
515C22⋊Q8—212no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8—248no—
519C22⋊Q8—412no—
520C22⋊Q8—412no—
521#121—224no—
522#121—248no—
523#121—212no—
524#121—224no—
525#121—224no—
526#121—224no—
527#121—248no—
528#121—424no—
529#121—46no—
530#121—412no—
531#121—412no—
532#121C2×D4148yes—
533#120—224no—
534C4×Q8—24no—
535C4×Q8—24no—
536C4×Q8—28no—
537C4×Q8—24no—
538C4×Q8—24no—
539C4×Q8—28no—
540C4×Q8—212no—
541C4×Q8—212no—
542C4×Q8—212no—
543C4×Q8—212no—
544C4×Q8—212no—
545C4×Q8C2×D418yes—
546C4×D4—212no—
547C4×D4—224no—
548C4×D4—224no—
549C4×D4—224no—
550C4×D4—212no—
551C4×D4—224no—
552C4×D4—224no—
553C4×D4—212no—
554C4×D4—24no—
555C4×D4—212no—
556C4×D4—224no—
557C4×D4—212no—
558C4×D4—412no—
559C4×D4—412no—
560C4×D4—412no—
561C4×D4—412no—
562C4×D4—412no—
563C4×D4C2×D4124yes—
564#117—224no—
565#117—412no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—212no—
569C2×C4⋊C4—212no—
570C2×C4⋊C4—412no—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2413yes—
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2413yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2416yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2416yes—
596C2×C4⋊C4C2416yes—
597C2×C4⋊C4C24112yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C2413yes—
601C2×C4⋊C4C2411yescharacteristic
602C2×C22⋊C4—224no—
603C2×C22⋊C4—424no—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2412yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2413yes—
614C2×C22⋊C4C24112yes—
615C2×C22⋊C4C2413yes—
616C2×C22⋊C4C2413yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2411yescharacteristic
619C2×C22⋊C4C2411yescharacteristic
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C24112yes—
623C2×C22⋊C4C24112yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C24112yes—
629C2×C22⋊C4C24112yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C24112yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2416yes—
638C2×C42—212no—
639C2×C42—212no—
640C2×C42C2413yes—
641C2×C42C2413yes—
642C2×C42C2416yes—
643C2×C42C2416yes—
644C2×C42C2413yes—
645C2×C42C2413yes—
646C2×C42C2413yes—
647C2×C42C2413yes—
648C2×C42C2413yes—
649C2×C42C2413yes—
650C2×C42C2413yes—
651C2×C42C2411yescharacteristic
652C2×C42C2413yes—
653C2×C42C2413yes—
654C2×C42C2413yes—
655#95C2416yes—
656#95C2416yes—
657#95C2416yes—
658#95C24112yes—
659#95C2412yes—
660#95C2412yes—
661#95C2412yes—
662#95C2412yes—
663#95C2413yes—
664#95C2413yes—
665#95C2413yes—
666#95C2413yes—
667#95C2413yes—
668#95C2413yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C2416yes—
674#95C2416yes—
675#95C2416yes—
676#95C2416yes—
677#95C2416yes—
678C24—212no—
679C24—212no—
680C24—212no—
681C24—212no—
682C24—46no—
683C24—46no—
684C24—46no—
685C24C2516yes—
686C24C2516yes—
687C24C2511yescharacteristic
688C24C2511yescharacteristic
689#41—264no—
690#41—496no—
691#41—496no—
692#41—432no—
693#41—848no—
694C2×Q8—232no—
695C2×Q8—26no—
696C2×Q8—22no—
697C2×Q8—26no—
698C2×Q8—212no—
699C2×Q8—26no—
700C2×Q8—26no—
701C2×Q8—26no—
702C2×Q8—22no—
703C2×Q8—22no—
704C2×Q8—46no—
705C2×Q8—46no—
706C2×Q8—416no—
707C2×Q8C22×D414yes—
708C2×Q8C2×#41112yes—
709C2×Q8C2×#4114yes—
710C2×Q8H(5,𝔽2)14yes—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—212no—
714C2×D4—212no—
715C2×D4—224no—
716C2×D4—212no—
717C2×D4—224no—
718C2×D4—212no—
719C2×D4—26no—
720C2×D4—212no—
721C2×D4—212no—
722C2×D4—212no—
723C2×D4—224no—
724C2×D4—212no—
725C2×D4—212no—
726C2×D4—212no—
727C2×D4—26no—
728C2×D4—212no—
729C2×D4—26no—
730C2×D4—26no—
731C2×D4—26no—
732C2×D4—448no—
733C2×D4—496no—
734C2×D4—46no—
735C2×D4—46no—
736C2×D4—412no—
737C2×D4—46no—
738C2×D4—46no—
739C2×D4—46no—
740C2×D4—412no—
741C2×D4—46no—
742C2×D4—46no—
743C2×D4—412no—
744C2×D4—46no—
745C2×D4—848no—
746C2×D4C22×D4112yes—
747C2×D4C22×D4124yes—
748C2×D4C22×D4124yes—
749C2×D4H(5,𝔽2)14yes—
750C22×C4—22no—
751C22×C4—26no—
752C22×C4—212no—
753C22×C4—212no—
754C22×C4—26no—
755C22×C4—22no—
756C22×C4—212no—
757C22×C4—24no—
758C22×C4—26no—
759C22×C4—26no—
760C22×C4—224no—
761C22×C4—22no—
762C22×C4—26no—
763C22×C4—26no—
764C22×C4—26no—
765C22×C4—24no—
766C22×C4—212no—
767C22×C4—212no—
768C22×C4—26no—
769C22×C4—212no—
770C22×C4—212no—
771C22×C4—212no—
772C22×C4—26no—
773C22×C4—212no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—42no—
777C22×C4—46no—
778C22×C4—46no—
779C22×C4—43no—
780C22×C4—43no—
781C22×C4—496no—
782C22×C4—412no—
783C22×C4—412no—
784C22×C4—412no—
785C22×C4—412no—
786C22×C4—412no—
787C22×C4C22×D4124yes—
788C22×C4C2×#41112yes—
789C22×C42−1+414yes—
790C22×C4C2512yes—
791C22×C4C2513yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2513yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2516yes—
798C22×C4C2513yes—
799C22×C4C2513yes—
800C22×C4C2516yes—
801C22×C4C2513yes—
802C22×C4C2513yes—
803C22×C4C2512yes—
804C22×C4C2513yes—
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2513yes—
808C22×C4C2511yescharacteristic
809C4⋊C4—26no—
810C4⋊C4—212no—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—212no—
814C4⋊C4—212no—
815C4⋊C4—26no—
816C4⋊C4—212no—
817C4⋊C4—24no—
818C4⋊C4—26no—
819C4⋊C4—212no—
820C4⋊C4—212no—
821C4⋊C4—26no—
822C4⋊C4—26no—
823C4⋊C4—212no—
824C4⋊C4—26no—
825C4⋊C4—212no—
826C4⋊C4—26no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—24no—
830C4⋊C4—26no—
831C4⋊C4—46no—
832C4⋊C4—42no—
833C4⋊C4—46no—
834C4⋊C4—46no—
835C4⋊C4—412no—
836C4⋊C4—46no—
837C4⋊C4—46no—
838C4⋊C4C22×D4112yes—
839C4⋊C4C22×D414yes—
840C22⋊C4—212no—
841C22⋊C4—212no—
842C22⋊C4—212no—
843C22⋊C4—224no—
844C22⋊C4—212no—
845C22⋊C4—26no—
846C22⋊C4—26no—
847C22⋊C4—212no—
848C22⋊C4—26no—
849C22⋊C4—22no—
850C22⋊C4—24no—
851C22⋊C4—212no—
852C22⋊C4—212no—
853C22⋊C4—24no—
854C22⋊C4—26no—
855C22⋊C4—212no—
856C22⋊C4—212no—
857C22⋊C4—22no—
858C22⋊C4—412no—
859C22⋊C4—412no—
860C22⋊C4—46no—
861C22⋊C4—46no—
862C22⋊C4—412no—
863C22⋊C4—42no—
864C22⋊C4—46no—
865C22⋊C4—46no—
866C22⋊C4—412no—
867C22⋊C4—46no—
868C22⋊C4—46no—
869C22⋊C4—412no—
870C22⋊C4—46no—
871C22⋊C4—46no—
872C22⋊C4—46no—
873C22⋊C4C22×D4124yes—
874C42—26no—
875C42—26no—
876C42—26no—
877C42—26no—
878C42—26no—
879C42—26no—
880C42—212no—
881C42—26no—
882C42—26no—
883C42—212no—
884C42—26no—
885C42—22no—
886C42—26no—
887C42—43no—
888C42C22×D4112yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—26no—
896C23—26no—
897C23—21no—
898C23—26no—
899C23—21no—
900C23—26no—
901C23—26no—
902C23—21no—
903C23—26no—
904C23—21no—
905C23—26no—
906C23—26no—
907C23—26no—
908C23—26no—
909C23—26no—
910C23—26no—
911C23—26no—
912C23—424no—
913C23—424no—
914C23—424no—
915C23—424no—
916C23—812no—
917C23—812no—
918C23—812no—
919C23C23×D4112yes—
920C23C22×#4112yes—
921C23C2×H(5,𝔽2)12yes—
922C23C2×H(5,𝔽2)12yes—
923C23C2×2−1+412yes—
924C23C2611yescharacteristic
925Q8—224no—
926Q8—412no—
927Q8—44no—
928Q8—812no—
929Q8#546116yescomplemented
930D4—28no—
931D4—248no—
932D4—224no—
933D4—424no—
934D4—424no—
935D4—448no—
936D4—424no—
937D4—424no—
938D4—412no—
939D4—812no—
940D4—812no—
941D4—824no—
942C2×C4—21no—
943C2×C4—23no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—23no—
947C2×C4—22no—
948C2×C4—23no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—23no—
952C2×C4—224no—
953C2×C4—248no—
954C2×C4—28no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—23no—
958C2×C4—23no—
959C2×C4—23no—
960C2×C4—26no—
961C2×C4—22no—
962C2×C4—23no—
963C2×C4—23no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—23no—
968C2×C4—26no—
969C2×C4—23no—
970C2×C4—26no—
971C2×C4—26no—
972C2×C4—23no—
973C2×C4—23no—
974C2×C4—23no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—23no—
981C2×C4—23no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—26no—
985C2×C4—21no—
986C2×C4—23no—
987C2×C4—22no—
988C2×C4—26no—
989C2×C4—23no—
990C2×C4—23no—
991C2×C4—424no—
992C2×C4—48no—
993C2×C4—424no—
994C2×C4—412no—
995C2×C4—412no—
996C2×C4—424no—
997C2×C4—412no—
998C2×C4—44no—
999C2×C4—824no—
1000C2×C4—1612no—
1001C2×C4C23×D416yes—
1002C2×C4C23×D414yes—
1003C2×C4C23×D416yes—
1004C2×C4C23×D412yes—
1005C2×C4C22×#4116yes—
1006C2×C4C22×#4116yes—
1007C2×C4C2×H(5,𝔽2)12yes—
1008C2×C4C2×H(5,𝔽2)16yes—
1009C2×C4C2×2−1+412yes—
1010C2×C4C2×2−1+412yes—
1011C2×C4#58512yes—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—22no—
1019C22—212no—
1020C22—22no—
1021C22—22no—
1022C22—212no—
1023C22—212no—
1024C22—41no—
1025C22—46no—
1026C22—46no—
1027C22—46no—
1028C22—41no—
1029C22—41no—
1030C22—46no—
1031C22—41no—
1032C22—46no—
1033C22—46no—
1034C22—46no—
1035C22—46no—
1036C22—46no—
1037C22—46no—
1038C22—46no—
1039C22—848no—
1040C22#352214yescomplemented
1041C22C24×D411yescharacteristic
1042C22C23×#4111yescharacteristic
1043C22C22×H(5,𝔽2)11yescharacteristic
1044C22C22×H(5,𝔽2)11yescharacteristic
1045C22C22×2−1+411yescharacteristic
1046C22C2×#58511yescharacteristic
1047C22H(7,𝔽2)11yescharacteristic
1048C4—26no—
1049C4—22no—
1050C4—22no—
1051C4—24no—
1052C4—26no—
1053C4—43no—
1054C4—43no—
1055C4—46no—
1056C4—43no—
1057C4—43no—
1058C4—46no—
1059C4—41no—
1060C4—42no—
1061C4—42no—
1062C4—41no—
1063C4—42no—
1064C4—43no—
1065C4C2×#546112yes—
1066C4#348914yes—
1067C2—24no—
1068C2—42no—
1069C2—412no—
1070C2—86no—
1071C2C22×#54611yescharacteristic
1072C2C2×#352211yescharacteristic
1073C2C2×#348911yescharacteristic
1074C2#6291711yescharacteristic
1075C2D4×H(5,𝔽2)11yescharacteristic
1076C2#6300611yescharacteristic
1077C2#6301411yescharacteristic
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. C2×#3522C2semidirect
2. C22×#550C2semidirect
3. #59411C2semidirect
4. #59143C2semidirect
5. #59039C2semidirect
6. #59015C2semidirect
7. #44930C2semidirect
8. #44891C2semidirect
9. #38952C2semidirect
10. #38909C2semidirect
11. #37664C2semidirect
12. #36576C2semidirect
13. Q8×C22⋊Q8C2semidirect
14. #36457C2semidirect
15. #36428C2semidirect
16. #36154C2semidirect
17. #36121C2semidirect
18. #36005C2semidirect
19. #35831C2semidirect
20. #34700C2semidirect
21. #34313C2semidirect
22. #34175C2semidirect
23. C4×D4×Q8C2semidirect
26. C2×#559C22semidirect
27. C2×Q82C22semidirect
28. C2×#554C22semidirect
37. C2×#548C22semidirect
38. C2×#548C22semidirect
39. C2×#547C22semidirect
41. C2×#542C22semidirect
42. C2×#532C22semidirect
44. C2×#529C22semidirect
46. C2×#520C22semidirect
47. C2×#520C22semidirect
49. C22×C4×Q8C22semidirect
51. #2858C22semidirect
53. #2856C22semidirect
55. #2709C22semidirect
56. #2701C22semidirect
57. #2691C22semidirect
58. #2686C22semidirect
59. #2672C22semidirect
60. #2672C22semidirect
61. #2671C22semidirect
62. #2624C22semidirect
63. #2620C22semidirect
64. #2582C22semidirect
65. #2567C22semidirect
66. #2563C22semidirect
67. #2548C22semidirect
68. #2548C22semidirect
69. #2544C22semidirect
70. #2544C22semidirect
71. #2544C22semidirect
72. #2538C22semidirect
73. #2537C22semidirect
74. #2501C22semidirect
75. #2491C22semidirect
76. #2491C22semidirect
77. #2487C22semidirect
79. #2468C22semidirect
80. #2457C22semidirect
81. #2454C22semidirect
82. #2454C22semidirect
83. #2451C22semidirect
84. #2450C22semidirect
85. #2447C22semidirect
86. #2445C22semidirect
87. #2445C22semidirect
88. #2445C22semidirect
89. #2445C22semidirect
96. #2432C22semidirect
97. #2432C22semidirect
98. #2431C22semidirect
99. #2430C22semidirect
100. #2428C22semidirect
101. #2428C22semidirect
102. #2427C22semidirect
103. #2427C22semidirect
104. #2426C22semidirect
105. #2425C22semidirect
106. #2422C22semidirect
107. #2422C22semidirect
108. #2420C22semidirect
111. #2417C22semidirect
112. #2416C22semidirect
113. #2416C22semidirect
116. #2407C22semidirect
117. #2407C22semidirect
119. #2395C22semidirect
120. #2392C22semidirect
121. #2366C22semidirect
122. #2365C22semidirect
123. #2361C22semidirect
125. #2360C22semidirect
126. Q8×C4⋊C4C22semidirect
127. Q8×C4⋊C4C22semidirect
128. Q8×C4⋊C4C22semidirect
129. #2349C22semidirect
131. D4×C4⋊C4C22semidirect
132. #2341C22semidirect
133. #2341C22semidirect
134. #2341C22semidirect
135. #2341C22semidirect
138. Q8×C22⋊C4C22semidirect
139. #2339C22semidirect
140. #2339C22semidirect
144. #2324C22semidirect
145. #2311C22semidirect
146. #2311C22semidirect
147. C4×C4⋊Q8C22semidirect
148. C4×#127C22semidirect
149. C4×#124C22semidirect
152. C4×C22⋊Q8C22semidirect
153. C4×#121C22semidirect
155. #2293C22semidirect
158. C42×Q8C22semidirect
182. #550D4semidirect
449. C22×Q8#41semidirect
929. Q8#546semidirect
1040. C22#3522semidirect

Maximal subgroups

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

subgroupindex
C2×#35222
C22×#5502
#594112
#591432
#590392
#590152
#449302
#448912
#389522
#389092
#376642
#365762
Q8×C22⋊Q82
#364572
#364282
#361542
#361212
#360052
#358312
#347002
#343132
#341752
C4×D4×Q82