Finite Group Databasebeta

← #7684696

Subgroups — #7684696

Order 512.

8935 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3498C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#59420C213yesmaximal, complemented
4#59143C213yesmaximal, complemented
5#59035C213yesmaximal, complemented
6#59030C216yesmaximal, complemented
7#45352C216yesmaximal, complemented
8#45105C216yesmaximal, complemented
9#39468C213yesmaximal, complemented
10#38957C213yesmaximal, complemented
11#37786C216yesmaximal, complemented
12#36583C211yesmaximal, characteristic, complemented
13#36576C211yesmaximal, characteristic, complemented
14#36445C211yesmaximal, characteristic, complemented
15#36433C212yesmaximal, complemented
16#36258C213yesmaximal, complemented
17#36121C213yesmaximal, complemented
18#36082C212yesmaximal, complemented
19#35831C212yesmaximal, complemented
20#34715C213yesmaximal, complemented
21#34313C211yesmaximal, characteristic, complemented
22#34258C212yesmaximal, complemented
23C4×#548C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2212yes—
25#3498—216no—
26#3480—216no—
27C2×#559C2213yescomplemented
28C2×#557C2211yescharacteristic, complemented
29C2×#556C2213yescomplemented
30C2×#553C2216yescomplemented
31C2×#550C2212yes—
32C2×#550C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2212yescomplemented
36C2×#548C2212yescomplemented
37C2×#546C2216yescomplemented
38C2×D42C2213yes—
39C2×D42C2216yes—
40C2×D42C2213yes—
41C2×#535C2216yes—
42C2×#532C2213yes—
43C2×#532C2213yescomplemented
44C22×#127C2213yes—
45C2×#529C2216yescomplemented
46C2×#520C2212yescomplemented
47C2×C4×#41C2211yescharacteristic
48C2×C4×#41C2212yescomplemented
49C2×C4×#41C2213yescomplemented
50C22×C4×Q8C2211yescharacteristic, complemented
51#2858C2213yescomplemented
52#2857C2213yescomplemented
53#2856C2213yescomplemented
54#2854C2216yescomplemented
55#2715C22112yescomplemented
56#2709C22112yescomplemented
57#2697C22112yescomplemented
58#2691C22112yescomplemented
59#2685C22112yescomplemented
60#2685C22112yescomplemented
61#2668C22112yescomplemented
62#2620C2216yescomplemented
63#2616C2216yescomplemented
64#2548C2213yescomplemented
65#2548C2213yescomplemented
66#2547C2213yescomplemented
67#2544C2216yescomplemented
68#2544C2216yescomplemented
69#2542C2213yescomplemented
70#2538C2213yescomplemented
71#2538C2213yescomplemented
72#2537C2216yescomplemented
73#2534C22112yescomplemented
74#2500C2216yescomplemented
75#2490C2216yescomplemented
76#2490C2216yescomplemented
77#2485C2216yescomplemented
78#2476C2216yescomplemented
79#2474C2216yescomplemented
80#2459C2216yescomplemented
81#2456C2216yescomplemented
82#2454C2216yescomplemented
83#2451C2213yescomplemented
84#2445C2213yescomplemented
85#2445C2216yescomplemented
86#2445C2216yescomplemented
87#2445C2216yescomplemented
88#2441C2216yescomplemented
89#2439C2211yescharacteristic, complemented
90#2435C2216yescomplemented
91#2435C2216yescomplemented
92#2435C2216yescomplemented
93#2435C2216yescomplemented
94#2435C2216yescomplemented
95#2431C2213yescomplemented
96#2428C2216yescomplemented
97#2428C2216yescomplemented
98#2427C2216yescomplemented
99#2427C2216yescomplemented
100#2426C2216yescomplemented
101#2426C2213yescomplemented
102#2426C2216yescomplemented
103#2424C22112yescomplemented
104#2422C2216yescomplemented
105#2420C2213yescomplemented
106#2420C2216yescomplemented
107#2418C22112yescomplemented
108#2417C2216yescomplemented
109#2416C2216yescomplemented
110#2416C2216yescomplemented
111#2414C2213yescomplemented
112#2411C22112yescomplemented
113#2408C2216yescomplemented
114#2408C2216yescomplemented
115#2408C2216yescomplemented
116#2408C2216yescomplemented
117#2407C2213yescomplemented
118#2405C22112yescomplemented
119#2392C2216yescomplemented
120#2388C2216yescomplemented
121#2367C2213yescomplemented
122#2366C2213yescomplemented
123#2362C2213yescomplemented
124#2361C2216yescomplemented
125#2361C2213yescomplemented
126#2352C2213yescomplemented
127#2351C2211yescharacteristic, complemented
128Q8×C4⋊C4C2211yescharacteristic, complemented
129Q8×C4⋊C4C2212yescomplemented
130D4×C4⋊C4C2213yescomplemented
131#2341C2212yes—
132#2341C2211yescharacteristic
133#2341C2212yescomplemented
134#2341C2212yescomplemented
135#2341C2212yescomplemented
136#2341C2212yescomplemented
137Q8×C22⋊C4C2211yescharacteristic, complemented
138D4×C22⋊C4C2216yescomplemented
139D4×C22⋊C4C2216yescomplemented
140D4×C22⋊C4C2216yescomplemented
141D4×C22⋊C4C2216yescomplemented
142D4×C22⋊C4C2216yescomplemented
143D4×C22⋊C4C2216yescomplemented
144#2324C2216yescomplemented
145#2311C2216yescomplemented
146#2309C2216yescomplemented
147C4×#127C2213yescomplemented
148C4×#124C2213yescomplemented
149C4×#124C2213yescomplemented
150C4×C22⋊Q8C2213yescomplemented
151C4×C22⋊Q8C2213yescomplemented
152C4×#123C2216yescomplemented
153C4×#121C2213yescomplemented
154C4×#121C2213yescomplemented
155#2297C2216yescomplemented
156#2293C2213yescomplemented
157C2×#390C2216yescomplemented
158C42×Q8C2211yescharacteristic, complemented
159C42×D4C2213yescomplemented
160C2×H(5,𝔽2)—216no—
161C2×H(5,𝔽2)—216no—
162C2×H(5,𝔽2)—48no—
163C22×#41C2312yes—
164C22×#41C2316yes—
165C22×#41C2313yes—
166C22×#41C2312yes—
167C22×#41C2311yescharacteristic
168C23×Q8C2311yescharacteristic
169C23×D4C2316yes—
170C23×D4C2316yes—
171C23×D4C2316yes—
172C23×D4C2316yes—
173C23×D4C2316yes—
174#559—224no—
175#557—28no—
176#556—224no—
177#553—248no—
178#550—216no—
179#550—28no—
180#550D4116yescomplemented
181#548—216no—
182#548—28no—
183#548—48no—
184#546—424no—
185D42—224no—
186D42—248no—
187D42—224no—
188#535—248no—
189#532—224no—
190#532—224no—
191C2×C4⋊Q8C2313yes—
192C2×C4⋊Q8C2311yescharacteristic
193C2×#127—224no—
194C2×#127C2313yes—
195C2×#127C2313yes—
196C2×#127C2316yes—
197C2×#127C2316yes—
198C2×#127C2313yes—
199#529—248no—
200C2×#126C23112yes—
201C2×#125C2316yes—
202C2×#124C2313yes—
203C2×#124C2316yes—
204C2×#124C2316yes—
205C2×#124C2316yes—
206C2×#124C2313yes—
207C2×#124C2316yes—
208C2×#124C2316yes—
209C2×#123C23112yes—
210C2×#123C23112yes—
211C2×#123C2316yes—
212C2×C22⋊Q8C2313yes—
213C2×C22⋊Q8C2316yes—
214C2×C22⋊Q8C2316yes—
215C2×C22⋊Q8C2316yes—
216C2×C22⋊Q8C2313yes—
217C2×#121C2316yes—
218C2×#121C2313yes—
219C2×#121C2313yes—
220C2×#121C2313yes—
221C2×#121C2316yes—
222C2×#121C2316yes—
223C2×#121C2313yes—
224C2×#121C2316yes—
225C2×#121C2316yes—
226C2×#121C2316yes—
227C2×#121C2316yes—
228C2×#121C23112yes—
229C2×#121C2316yes—
230C2×#121C2316yes—
231C2×#120C23112yes—
232C2×#120C23112yes—
233C2×#120C23112yes—
234#520—48no—
235C4×#41—216no—
236C4×#41—28no—
237C4×#41—224no—
238C2×C4×Q8—28no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2313yes—
246C2×C4×Q8C2313yes—
247C2×C4×Q8C2313yes—
248C2×C4×Q8C2313yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2313yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2313yes—
255C2×C4×D4C2313yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2316yes—
264C2×C4×D4C2316yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2313yes—
269C2×#117C2316yes—
270C2×#117C2313yes—
271C2×#117C2311yescharacteristic
272C2×#117C2316yes—
273C2×#117C2316yes—
274C22×C4⋊C4C2313yes—
275C22×C4⋊C4C2316yes—
276C22×C22⋊C4C23112yes—
277C22×C22⋊C4C23112yes—
278C22×C42C2316yes—
279C22×C42C2313yes—
280C22×C42C2313yes—
281#399C23112yes—
282#398C2316yes—
283#397C2316yes—
284#397C23112yes—
285#397C23112yes—
286#396C2316yes—
287#396C23112yes—
288#396C2312yes—
289#396C23112yes—
290#396C23112yes—
291#395C2316yes—
292#394C23112yes—
293#394C23112yes—
294#394C23112yes—
295#394C23112yes—
296#394C23112yes—
297#394C2316yes—
298#394C2316yes—
299#394C2316yes—
300#394C2316yes—
301#394C2316yes—
302#394C2316yes—
303#394C23112yes—
304#394C23112yes—
305#394C23112yes—
306#394C23112yes—
307#394C23112yes—
308#393C2312yes—
309#392C2316yes—
310#392C2316yes—
311#392C2316yes—
312#392C2316yes—
313#391C2316yes—
314#391C2313yes—
315#391C2313yes—
316#391C2313yes—
317#391C2313yes—
318#391C2312yes—
319#390C2313yes—
320#390C2316yes—
321#390C2316yes—
322#390C2313yes—
323#390C2316yes—
324#390C23112yes—
325#390C2316yes—
326#390C2316yes—
327#390C2316yes—
328#390C2316yes—
329#390C2313yes—
330#390C2313yes—
331#390C2316yes—
332#390C2316yes—
333#390C2316yes—
334#390C2316yes—
335#390C2316yes—
336#390C2316yes—
337#390C2316yes—
338#390C2316yes—
339#390C2316yes—
340#390C2313yes—
341#390C2316yes—
342#390C2313yes—
343#389C2316yes—
344#389C2313yes—
345#389C2316yes—
346#389C2316yes—
347#389C2316yes—
348#389C2313yes—
349#389C2313yes—
350#389C2313yes—
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#388C2316yes—
354#388C2316yes—
355#388C23112yes—
356#388C2316yes—
357#388C2316yes—
358#388C2316yes—
359#388C2316yes—
360#388C2316yes—
361#388C2316yes—
362#388C2316yes—
363#388C2316yes—
364#387C2316yes—
365#387C2316yes—
366#387C2312yes—
367#387C2316yes—
368#386C23112yes—
369#386C23112yes—
370#386C23112yes—
371#386C2316yes—
372#386C2316yes—
373#386C2316yes—
374#386C2316yes—
375#386C2316yes—
376#386C23112yes—
377#386C23112yes—
378#386C23112yes—
379#386C2316yes—
380#386C2316yes—
381#385C23112yes—
382#385C2316yes—
383#385C2316yes—
384#385C2316yes—
385#384C2313yes—
386#384C2316yes—
387#382C2313yes—
388#382C2311yescharacteristic
389#381C2316yes—
390#380C2313yes—
391#380C2316yes—
392#380C2316yes—
393#380C2316yes—
394#380C2316yes—
395#380C2313yes—
396#380C2316yes—
397#380C2313yes—
398#380C2316yes—
399#380C2311yescharacteristic
400#380C23112yes—
401#379C23112yes—
402#379C23112yes—
403#379C23112yes—
404#379C23112yes—
405#379C23112yes—
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2316yes—
410C4×C4⋊C4C2313yes—
411C4×C4⋊C4C2313yes—
412C4×C4⋊C4C2313yes—
413C4×C4⋊C4C2313yes—
414C4×C22⋊C4C2313yes—
415C4×C22⋊C4C2313yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2313yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2313yes—
424C4×C22⋊C4C2313yes—
425C4×C22⋊C4C2311yescharacteristic
426C43C2313yes—
427C25C24112yes—
428H(5,𝔽2)—4128no—
429C2×#41—24no—
430C2×#41—28no—
431C2×#41—28no—
432C2×#41—28no—
433C2×#41—28no—
434C2×#41—24no—
435C2×#41—28no—
436C2×#41—212no—
437C2×#41—224no—
438C2×#41—224no—
439C2×#41—212no—
440C2×#41—412no—
441C2×#41—46no—
442C2×#41C2×D4116yes—
443C2×#41#4118yescomplemented
444C22×Q8—24no—
445C22×Q8—24no—
446C22×Q8—24no—
447C22×Q8C2413yes—
448C22×Q8C2413yes—
449C22×Q8C2412yes—
450C22×Q8C2411yescharacteristic
451C22×D4—224no—
452C22×D4—224no—
453C22×D4—224no—
454C22×D4—224no—
455C22×D4—224no—
456C22×D4—224no—
457C22×D4—224no—
458C22×D4—224no—
459C22×D4—412no—
460C22×D4—412no—
461C22×D4—412no—
462C22×D4—412no—
463C22×D4—412no—
464C22×D4—412no—
465C22×D4—86no—
466C22×D4C2413yes—
467C22×D4C2416yes—
468C22×D4C2413yes—
469C22×D4C2416yes—
470C22×D4C2416yes—
471C22×D4C2416yes—
472C22×D4C2416yes—
473C22×D4C2416yes—
474C22×D4C2416yes—
475C22×D4C2413yes—
476C22×D4C2413yes—
477C22×D4C2416yes—
478C22×D4C24112yes—
479C22×D4C2416yes—
480C22×D4C2416yes—
481C23×C4C2413yes—
482C23×C4C2413yes—
483C23×C4C2416yes—
484C23×C4C2416yes—
485C23×C4C2413yes—
486C23×C4C2416yes—
487C23×C4C2413yes—
488C23×C4C2411yescharacteristic
489C23×C4C2416yes—
490C23×C4C2413yes—
491C23×C4C24112yes—
492C4⋊Q8—24no—
493C4⋊Q8—212no—
494#127—212no—
495#127—224no—
496#127—224no—
497#127—212no—
498#127C2×D4124yes—
499#126—248no—
500#125—224no—
501#124—224no—
502#124—224no—
503#124—212no—
504#124—224no—
505#124—46no—
506#124—412no—
507#124—412no—
508#123—248no—
509#123—424no—
510#123—412no—
511C22⋊Q8—224no—
512C22⋊Q8—212no—
513C22⋊Q8—46no—
514C22⋊Q8—412no—
515C22⋊Q8—412no—
516#121—212no—
517#121—224no—
518#121—224no—
519#121—224no—
520#121—212no—
521#121—224no—
522#121—212no—
523#121—212no—
524#121—224no—
525#121—224no—
526#121—424no—
527#121—412no—
528#121—86no—
529#121C2×D4148yes—
530#120—248no—
531#120—248no—
532#120—424no—
533C4×Q8—24no—
534C4×Q8—28no—
535C4×Q8—24no—
536C4×Q8—24no—
537C4×Q8—24no—
538C4×Q8—28no—
539C4×Q8—212no—
540C4×Q8—212no—
541C4×Q8—212no—
542C4×Q8—212no—
543C4×Q8C2×D418yes—
544C4×D4—224no—
545C4×D4—224no—
546C4×D4—212no—
547C4×D4—224no—
548C4×D4—224no—
549C4×D4—224no—
550C4×D4—212no—
551C4×D4—212no—
552C4×D4—212no—
553C4×D4—224no—
554C4×D4—212no—
555C4×D4—212no—
556C4×D4—412no—
557C4×D4—412no—
558C4×D4—412no—
559C4×D4—412no—
560C4×D4—46no—
561C4×D4—86no—
562C4×D4C2×D4124yes—
563#117—224no—
564#117—24no—
565#117—212no—
566#117—224no—
567#117—412no—
568C2×C4⋊C4—212no—
569C2×C4⋊C4—412no—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2413yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2413yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C24112yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C22⋊C4—424no—
598C2×C22⋊C4—812no—
599C2×C22⋊C4C2413yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C24112yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2411yescharacteristic
606C2×C22⋊C4C2411yescharacteristic
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C24112yes—
612C2×C22⋊C4C2413yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C24112yes—
618C2×C22⋊C4C24112yes—
619C2×C22⋊C4C24112yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C24112yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2413yes—
627C2×C22⋊C4C24112yes—
628C2×C22⋊C4C24112yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2416yes—
636C2×C42—224no—
637C2×C42—212no—
638C2×C42—212no—
639C2×C42C2412yes—
640C2×C42C2413yes—
641C2×C42C2413yes—
642C2×C42C2416yes—
643C2×C42C2413yes—
644C2×C42C2416yes—
645C2×C42C2413yes—
646C2×C42C2413yes—
647C2×C42C2416yes—
648C2×C42C2413yes—
649C2×C42C2413yes—
650C2×C42C2413yes—
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2413yes—
654C2×C42C2413yes—
655C2×C42C2413yes—
656#95C2411yescharacteristic
657#95C2411yescharacteristic
658#95C2412yes—
659#95C2412yes—
660#95C2412yes—
661#95C2412yes—
662#95C2412yes—
663#95C2413yes—
664#95C2413yes—
665#95C2413yes—
666#95C2413yes—
667#95C2416yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C2416yes—
674#95C2416yes—
675#95C2416yes—
676#95C2416yes—
677#95C2416yes—
678C24—224no—
679C24—224no—
680C24—412no—
681C24—412no—
682C24—412no—
683C24—412no—
684C24—412no—
685C24C2516yes—
686C24C2516yes—
687C24C2513yes—
688C24C2511yescharacteristic
689#41—264no—
690#41—232no—
691#41—496no—
692#41—448no—
693#41—432no—
694C2×Q8—26no—
695C2×Q8—26no—
696C2×Q8—24no—
697C2×Q8—26no—
698C2×Q8—24no—
699C2×Q8—26no—
700C2×Q8—26no—
701C2×Q8—26no—
702C2×Q8—42no—
703C2×Q8—416no—
704C2×Q8C22×D414yes—
705C2×Q8C2×#4114yes—
706C2×Q8H(5,𝔽2)14yes—
707C2×D4—212no—
708C2×D4—212no—
709C2×D4—212no—
710C2×D4—212no—
711C2×D4—26no—
712C2×D4—212no—
713C2×D4—212no—
714C2×D4—26no—
715C2×D4—212no—
716C2×D4—224no—
717C2×D4—212no—
718C2×D4—26no—
719C2×D4—26no—
720C2×D4—212no—
721C2×D4—212no—
722C2×D4—212no—
723C2×D4—212no—
724C2×D4—212no—
725C2×D4—212no—
726C2×D4—212no—
727C2×D4—26no—
728C2×D4—26no—
729C2×D4—26no—
730C2×D4—212no—
731C2×D4—26no—
732C2×D4—212no—
733C2×D4—26no—
734C2×D4—496no—
735C2×D4—496no—
736C2×D4—43no—
737C2×D4—46no—
738C2×D4—46no—
739C2×D4—46no—
740C2×D4—46no—
741C2×D4—46no—
742C2×D4—46no—
743C2×D4—46no—
744C2×D4—46no—
745C2×D4—412no—
746C2×D4—46no—
747C2×D4—46no—
748C2×D4—46no—
749C2×D4—412no—
750C2×D4—496no—
751C2×D4—848no—
752C2×D4—848no—
753C2×D4C22×D4124yes—
754C2×D4C22×D4112yes—
755C2×D4C22×D4124yes—
756C2×D4C2×#41112yes—
757C22×C4—22no—
758C22×C4—26no—
759C22×C4—212no—
760C22×C4—212no—
761C22×C4—26no—
762C22×C4—22no—
763C22×C4—212no—
764C22×C4—212no—
765C22×C4—26no—
766C22×C4—26no—
767C22×C4—26no—
768C22×C4—212no—
769C22×C4—26no—
770C22×C4—212no—
771C22×C4—212no—
772C22×C4—26no—
773C22×C4—26no—
774C22×C4—212no—
775C22×C4—26no—
776C22×C4—26no—
777C22×C4—26no—
778C22×C4—43no—
779C22×C4—46no—
780C22×C4—46no—
781C22×C4—43no—
782C22×C4—43no—
783C22×C4—46no—
784C22×C4—412no—
785C22×C4—412no—
786C22×C4—412no—
787C22×C4C22×D4124yes—
788C22×C4C2×#41112yes—
789C22×C4H(5,𝔽2)14yescomplemented
790C22×C4C2512yes—
791C22×C4C2511yescharacteristic
792C22×C4C2513yes—
793C22×C4C2513yes—
794C22×C4C2513yes—
795C22×C4C2511yescharacteristic
796C22×C4C2512yes—
797C22×C4C2513yes—
798C22×C4C2512yes—
799C22×C4C2516yes—
800C22×C4C2513yes—
801C22×C4C2516yes—
802C22×C4C2513yes—
803C22×C4C2512yes—
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2513yes—
808C22×C4C2511yescharacteristic
809C4⋊C4—26no—
810C4⋊C4—212no—
811C4⋊C4—22no—
812C4⋊C4—26no—
813C4⋊C4—212no—
814C4⋊C4—212no—
815C4⋊C4—212no—
816C4⋊C4—24no—
817C4⋊C4—22no—
818C4⋊C4—212no—
819C4⋊C4—26no—
820C4⋊C4—26no—
821C4⋊C4—26no—
822C4⋊C4—212no—
823C4⋊C4—26no—
824C4⋊C4—26no—
825C4⋊C4—26no—
826C4⋊C4—22no—
827C4⋊C4—24no—
828C4⋊C4—46no—
829C4⋊C4—42no—
830C4⋊C4—46no—
831C4⋊C4—46no—
832C4⋊C4—412no—
833C4⋊C4—46no—
834C4⋊C4C22×D4112yes—
835C4⋊C4C22×D414yes—
836C22⋊C4—224no—
837C22⋊C4—212no—
838C22⋊C4—212no—
839C22⋊C4—224no—
840C22⋊C4—26no—
841C22⋊C4—212no—
842C22⋊C4—26no—
843C22⋊C4—24no—
844C22⋊C4—212no—
845C22⋊C4—212no—
846C22⋊C4—212no—
847C22⋊C4—22no—
848C22⋊C4—26no—
849C22⋊C4—212no—
850C22⋊C4—22no—
851C22⋊C4—412no—
852C22⋊C4—412no—
853C22⋊C4—46no—
854C22⋊C4—46no—
855C22⋊C4—46no—
856C22⋊C4—412no—
857C22⋊C4—46no—
858C22⋊C4—46no—
859C22⋊C4—43no—
860C22⋊C4—42no—
861C22⋊C4—412no—
862C22⋊C4—46no—
863C22⋊C4—46no—
864C22⋊C4—412no—
865C22⋊C4—412no—
866C22⋊C4—46no—
867C22⋊C4—46no—
868C22⋊C4—46no—
869C22⋊C4—46no—
870C22⋊C4—46no—
871C22⋊C4—46no—
872C22⋊C4C22×D4124yes—
873C42—24no—
874C42—26no—
875C42—22no—
876C42—26no—
877C42—212no—
878C42—26no—
879C42—26no—
880C42—212no—
881C42—26no—
882C42—26no—
883C42—26no—
884C42—212no—
885C42—26no—
886C42—22no—
887C42—43no—
888C42—43no—
889C42C22×D4112yes—
890C23—21no—
891C23—23no—
892C23—21no—
893C23—26no—
894C23—23no—
895C23—21no—
896C23—26no—
897C23—26no—
898C23—23no—
899C23—21no—
900C23—23no—
901C23—23no—
902C23—26no—
903C23—21no—
904C23—26no—
905C23—23no—
906C23—26no—
907C23—21no—
908C23—26no—
909C23—26no—
910C23—26no—
911C23—26no—
912C23—26no—
913C23—26no—
914C23—26no—
915C23—448no—
916C23—824no—
917C23—824no—
918C23—824no—
919C23—824no—
920C23—1612no—
921C23—1612no—
922C23C23×D4112yes—
923C23C22×#4116yes—
924C23C2×H(5,𝔽2)12yes—
925C23C2611yescharacteristic
926Q8—48no—
927Q8—412no—
928Q8—412no—
929Q8#546116yescomplemented
930D4—224no—
931D4—248no—
932D4—224no—
933D4—424no—
934D4—424no—
935D4—424no—
936D4—424no—
937D4—412no—
938D4—424no—
939D4—424no—
940D4—424no—
941D4—412no—
942D4—812no—
943D4—812no—
944D4—824no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—23no—
952C2×C4—21no—
953C2×C4—23no—
954C2×C4—21no—
955C2×C4—248no—
956C2×C4—224no—
957C2×C4—28no—
958C2×C4—22no—
959C2×C4—23no—
960C2×C4—23no—
961C2×C4—23no—
962C2×C4—26no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—23no—
966C2×C4—23no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—23no—
971C2×C4—23no—
972C2×C4—26no—
973C2×C4—23no—
974C2×C4—26no—
975C2×C4—23no—
976C2×C4—26no—
977C2×C4—23no—
978C2×C4—22no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—23no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—23no—
986C2×C4—22no—
987C2×C4—26no—
988C2×C4—23no—
989C2×C4—21no—
990C2×C4—23no—
991C2×C4—22no—
992C2×C4—23no—
993C2×C4—26no—
994C2×C4—412no—
995C2×C4—424no—
996C2×C4—424no—
997C2×C4—412no—
998C2×C4—412no—
999C2×C4—86no—
1000C2×C4—812no—
1001C2×C4—1612no—
1002C2×C4C23×D414yes—
1003C2×C4C23×D416yes—
1004C2×C4C23×D416yes—
1005C2×C4C23×D412yes—
1006C2×C4C22×#4112yes—
1007C2×C4C22×#4116yes—
1008C2×C4C2×H(5,𝔽2)12yes—
1009C2×C4C2×H(5,𝔽2)16yes—
1010C2×C4C2×H(5,𝔽2)12yes—
1011C2×C4#58512yes—
1012C2×C4#58512yes—
1013C22—212no—
1014C22—26no—
1015C22—22no—
1016C22—212no—
1017C22—22no—
1018C22—26no—
1019C22—22no—
1020C22—26no—
1021C22—212no—
1022C22—43no—
1023C22—41no—
1024C22—41no—
1025C22—46no—
1026C22—41no—
1027C22—46no—
1028C22—43no—
1029C22—43no—
1030C22—46no—
1031C22—46no—
1032C22—43no—
1033C22—41no—
1034C22—46no—
1035C22—46no—
1036C22—46no—
1037C22—46no—
1038C22—46no—
1039C22—46no—
1040C22—46no—
1041C22—1648no—
1042C22C24×D411yescharacteristic
1043C22C23×#4111yescharacteristic
1044C22C22×H(5,𝔽2)11yescharacteristic
1045C22C22×H(5,𝔽2)11yescharacteristic
1046C22C2×#58511yescharacteristic
1047C22C2×#58511yescharacteristic
1048C22H(7,𝔽2)11yescharacteristic
1049C4—22no—
1050C4—26no—
1051C4—22no—
1052C4—24no—
1053C4—22no—
1054C4—43no—
1055C4—42no—
1056C4—41no—
1057C4—42no—
1058C4—41no—
1059C4—46no—
1060C4—43no—
1061C4—43no—
1062C4—43no—
1063C4—46no—
1064C4—42no—
1065C4—43no—
1066C4C2×#546112yes—
1067C4#348814yes—
1068C2—42no—
1069C2—412no—
1070C2—46no—
1071C2—86no—
1072C2C22×#54611yescharacteristic
1073C2C2×#348811yescharacteristic
1074C2#6280011yescharacteristic
1075C2#6291611yescharacteristic
1076C2#6298711yescharacteristic
1077C2#6301011yescharacteristic
1078C2#6303511yescharacteristic
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×#3498C2semidirect
2. C2×#3480C2semidirect
3. #59420C2semidirect
4. #59143C2semidirect
5. #59035C2semidirect
6. #59030C2semidirect
7. #45352C2semidirect
8. #45105C2semidirect
9. #39468C2semidirect
10. #38957C2semidirect
11. #37786C2semidirect
12. #36583C2semidirect
13. #36576C2semidirect
14. #36445C2semidirect
15. #36433C2semidirect
16. #36258C2semidirect
17. #36121C2semidirect
18. #36082C2semidirect
19. #35831C2semidirect
20. #34715C2semidirect
21. #34313C2semidirect
22. #34258C2semidirect
23. C4×#548C2semidirect
27. C2×#559C22semidirect
28. C2×#557C22semidirect
29. C2×#556C22semidirect
30. C2×#553C22semidirect
35. C2×#548C22semidirect
36. C2×#548C22semidirect
37. C2×#546C22semidirect
43. C2×#532C22semidirect
45. C2×#529C22semidirect
46. C2×#520C22semidirect
48. C2×C4×#41C22semidirect
49. C2×C4×#41C22semidirect
50. C22×C4×Q8C22semidirect
51. #2858C22semidirect
52. #2857C22semidirect
53. #2856C22semidirect
54. #2854C22semidirect
55. #2715C22semidirect
56. #2709C22semidirect
57. #2697C22semidirect
58. #2691C22semidirect
59. #2685C22semidirect
60. #2685C22semidirect
61. #2668C22semidirect
62. #2620C22semidirect
63. #2616C22semidirect
64. #2548C22semidirect
65. #2548C22semidirect
66. #2547C22semidirect
67. #2544C22semidirect
68. #2544C22semidirect
69. #2542C22semidirect
70. #2538C22semidirect
71. #2538C22semidirect
72. #2537C22semidirect
73. #2534C22semidirect
74. #2500C22semidirect
75. #2490C22semidirect
76. #2490C22semidirect
77. #2485C22semidirect
78. #2476C22semidirect
79. #2474C22semidirect
80. #2459C22semidirect
81. #2456C22semidirect
82. #2454C22semidirect
83. #2451C22semidirect
84. #2445C22semidirect
85. #2445C22semidirect
86. #2445C22semidirect
87. #2445C22semidirect
88. #2441C22semidirect
89. #2439C22semidirect
90. #2435C22semidirect
91. #2435C22semidirect
92. #2435C22semidirect
93. #2435C22semidirect
94. #2435C22semidirect
95. #2431C22semidirect
96. #2428C22semidirect
97. #2428C22semidirect
98. #2427C22semidirect
99. #2427C22semidirect
100. #2426C22semidirect
101. #2426C22semidirect
102. #2426C22semidirect
103. #2424C22semidirect
104. #2422C22semidirect
105. #2420C22semidirect
106. #2420C22semidirect
107. #2418C22semidirect
108. #2417C22semidirect
109. #2416C22semidirect
110. #2416C22semidirect
111. #2414C22semidirect
112. #2411C22semidirect
113. #2408C22semidirect
114. #2408C22semidirect
115. #2408C22semidirect
116. #2408C22semidirect
117. #2407C22semidirect
118. #2405C22semidirect
119. #2392C22semidirect
120. #2388C22semidirect
121. #2367C22semidirect
122. #2366C22semidirect
123. #2362C22semidirect
124. #2361C22semidirect
125. #2361C22semidirect
126. #2352C22semidirect
127. #2351C22semidirect
128. Q8×C4⋊C4C22semidirect
129. Q8×C4⋊C4C22semidirect
130. D4×C4⋊C4C22semidirect
133. #2341C22semidirect
134. #2341C22semidirect
135. #2341C22semidirect
136. #2341C22semidirect
137. Q8×C22⋊C4C22semidirect
138. D4×C22⋊C4C22semidirect
139. D4×C22⋊C4C22semidirect
140. D4×C22⋊C4C22semidirect
141. D4×C22⋊C4C22semidirect
142. D4×C22⋊C4C22semidirect
143. D4×C22⋊C4C22semidirect
144. #2324C22semidirect
145. #2311C22semidirect
146. #2309C22semidirect
147. C4×#127C22semidirect
148. C4×#124C22semidirect
149. C4×#124C22semidirect
150. C4×C22⋊Q8C22semidirect
151. C4×C22⋊Q8C22semidirect
152. C4×#123C22semidirect
153. C4×#121C22semidirect
154. C4×#121C22semidirect
155. #2297C22semidirect
156. #2293C22semidirect
157. C2×#390C22semidirect
158. C42×Q8C22semidirect
159. C42×D4C22semidirect
180. #550D4semidirect
443. C2×#41#41semidirect
789. C22×C4H(5,𝔽2)semidirect
929. Q8#546semidirect

Maximal subgroups

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

subgroupindex
C2×#34982
C2×#34802
#594202
#591432
#590352
#590302
#453522
#451052
#394682
#389572
#377862
#365832
#365762
#364452
#364332
#362582
#361212
#360822
#358312
#347152
#343132
#342582
C4×#5482