Finite Group Databasebeta

← #7699560

Subgroups — #7699560

Order 512.

9024 conjugacy classes of subgroups.

The subgroup lattice has 1087 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3482C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#59807C216yesmaximal, complemented
4#59410C213yesmaximal, complemented
5#59049C213yesmaximal, complemented
6#59046C216yesmaximal, complemented
7#59040C213yesmaximal, complemented
8#59022C216yesmaximal, complemented
9#36583C211yesmaximal, characteristic, complemented
10#36576C212yesmaximal, complemented
11#36483C212yesmaximal, complemented
12#36455C211yesmaximal, characteristic, complemented
13#36445C211yesmaximal, characteristic, complemented
14#36429C212yesmaximal, complemented
15#36260C213yesmaximal, complemented
16#36258C213yesmaximal, complemented
17#36153C213yesmaximal, complemented
18#36150C213yesmaximal, complemented
19#36144C216yesmaximal, complemented
20C4×D4×Q8C211yesmaximal, characteristic, complemented
21C4×#550C211yesmaximal, characteristic, complemented
22C4×#546C213yesmaximal, complemented
23C2×#2341C212yesmaximal, complemented
24C23×#41C2212yes—
25#3482—216no—
26C2×#557C2211yescharacteristic, complemented
27C2×#556C2213yescomplemented
28C2×#552C2216yescomplemented
29D4×#41—216no—
30C2×#550C2211yescharacteristic
31C2×#550C2211yescharacteristic
32C2×#550C2212yescomplemented
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2212yes—
35C2×#548C2212yescomplemented
36C2×#547C2213yes—
37C2×#547C2213yes—
38C2×#546C2213yes—
39C2×#546C2216yes—
40C2×#546C2216yes—
41C2×D42C2213yes—
42C2×#533C2213yescomplemented
43C2×#532C2213yes—
44C2×#529C2216yescomplemented
45C2×#525C2216yes—
46C2×C4×#41C2211yescharacteristic
47C2×C4×#41C2213yes—
48C2×C4×#41C2211yescharacteristic, complemented
49C22×C4×Q8C2212yescomplemented
50C22×C4×Q8C2212yescomplemented
51C22×C4×D4C2213yes—
52#2858C2213yescomplemented
53#2857C2213yescomplemented
54#2856C2216yescomplemented
55#2856C2213yescomplemented
56#2854C2216yescomplemented
57#2847C2216yescomplemented
58#2714C22112yescomplemented
59#2705C22112yescomplemented
60#2694C22112yescomplemented
61#2554C22112yescomplemented
62#2548C2213yescomplemented
63#2548C2216yescomplemented
64#2547C2213yescomplemented
65#2542C2213yescomplemented
66#2541C2213yescomplemented
67#2540C2216yescomplemented
68#2540C2216yescomplemented
69#2539C22112yescomplemented
70#2539C22112yescomplemented
71#2538C2213yescomplemented
72#2538C2216yescomplemented
73#2537C2213yescomplemented
74#2501C2216yescomplemented
75#2490C2216yescomplemented
76#2490C2216yescomplemented
77#2490C2216yescomplemented
78#2486C2216yescomplemented
79#2471C22112yescomplemented
80#2467C22112yescomplemented
81#2454C2216yescomplemented
82#2454C2216yescomplemented
83#2448C2216yescomplemented
84#2448C2216yescomplemented
85#2441C2216yescomplemented
86#2433C2216yescomplemented
87#2431C2216yescomplemented
88#2431C2216yescomplemented
89#2428C2216yescomplemented
90#2427C2216yescomplemented
91#2426C2216yescomplemented
92#2426C2216yescomplemented
93#2426C2216yescomplemented
94#2425C22112yescomplemented
95#2424C22112yescomplemented
96#2423C2216yescomplemented
97#2423C2216yescomplemented
98#2417C2216yescomplemented
99#2416C2216yescomplemented
100#2416C2216yescomplemented
101#2414C2216yescomplemented
102#2414C2216yescomplemented
103#2414C2216yescomplemented
104#2412C22112yescomplemented
105#2411C22112yescomplemented
106#2408C2216yescomplemented
107#2407C2216yescomplemented
108#2407C2216yescomplemented
109#2367C2213yescomplemented
110#2366C2213yescomplemented
111#2365C2213yescomplemented
112#2364C2216yescomplemented
113#2363C2216yescomplemented
114#2363C2213yescomplemented
115#2363C2213yescomplemented
116#2363C2213yescomplemented
117#2360C2213yescomplemented
118#2360C2216yescomplemented
119#2359C2216yescomplemented
120#2358C2216yescomplemented
121#2354C2213yescomplemented
122#2352C2213yescomplemented
123Q8×C4⋊C4C2211yescharacteristic, complemented
124Q8×C4⋊C4C2212yescomplemented
125Q8×C4⋊C4C2211yescharacteristic, complemented
126#2349C2211yescharacteristic
127D4×C4⋊C4C2213yes—
128#2342C2216yescomplemented
129#2341C2211yescharacteristic
130#2341C2212yes—
131#2341C2216yescomplemented
132#2341C2216yescomplemented
133#2341C2212yescomplemented
134#2341C2216yescomplemented
135#2341C2216yescomplemented
136#2341C2212yescomplemented
137#2341C2212yescomplemented
138#2341C2211yescharacteristic, complemented
139Q8×C22⋊C4C2212yescomplemented
140#2339C2213yes—
141D4×C22⋊C4C2213yes—
142C4×C4⋊Q8C2213yescomplemented
143C4×#127C2213yescomplemented
144C4×#124C2213yescomplemented
145C4×C22⋊Q8C2216yescomplemented
146C4×C22⋊Q8C2213yescomplemented
147C4×#123C2216yescomplemented
148C4×#121C2213yescomplemented
149C4×#121C2213yescomplemented
150C4×#121C2216yescomplemented
151C4×#121C2213yescomplemented
152C4×#120C2216yescomplemented
153C2×#390C2216yescomplemented
154C2×#390C2216yescomplemented
155C2×#380C2216yescomplemented
156C42×Q8C2211yescharacteristic, complemented
157C42×D4C2213yes—
158C42×D4C2213yescomplemented
159C2×C4×C22⋊C4C2216yescomplemented
160C22×#41—216no—
161C22×#41—216no—
162C22×#41—48no—
163C22×#41C2312yes—
164C22×#41C2313yes—
165C22×#41C2311yescharacteristic
166C22×#41C2316yes—
167C22×#41C2316yes—
168C22×#41C2311yescharacteristic
169C23×Q8C2312yes—
170C23×D4C2313yes—
171C23×D4C2316yes—
172C24×C4C2316yes—
173#557—28no—
174#556—224no—
175#552—248no—
176#550—28no—
177#550—28no—
178#550—48no—
179D4×Q8D4116yescomplemented
180#548—216no—
181#548—216no—
182#547—224no—
183#547—224no—
184#546—248no—
185#546—224no—
186#546—424no—
187D42—224no—
188#533—224no—
189#532—224no—
190C2×C4⋊Q8C2313yes—
191C2×C4⋊Q8C2313yes—
192C2×#127C2313yes—
193C2×#127C2313yes—
194C2×#127C2316yes—
195#529—248no—
196C2×#126C23112yes—
197C2×#125C2316yes—
198C2×#125C2316yes—
199C2×#124C2313yes—
200C2×#124C2316yes—
201C2×#124C2316yes—
202C2×#124C2316yes—
203#525—248no—
204C2×#123C2316yes—
205C2×#123C23112yes—
206C2×#123C23112yes—
207C2×#123C23112yes—
208C2×C22⋊Q8C2313yes—
209C2×C22⋊Q8C2316yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C2316yes—
212C2×C22⋊Q8C2316yes—
213C2×C22⋊Q8C2316yes—
214C2×#121C2313yes—
215C2×#121C2316yes—
216C2×#121C2316yes—
217C2×#121C2316yes—
218C2×#121C2313yes—
219C2×#121C2313yes—
220C2×#121C2316yes—
221C2×#121C2316yes—
222C2×#121C2316yes—
223C2×#121C2316yes—
224C2×#121C2316yes—
225C2×#121C2316yes—
226C2×#121C2316yes—
227C2×#121C23112yes—
228C2×#120C2316yes—
229C2×#120C23112yes—
230C2×#120C23112yes—
231C4×#41—28no—
232C4×#41—28no—
233C4×#41—224no—
234C2×C4×Q8—216no—
235C2×C4×Q8—48no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2316yes—
242C2×C4×Q8C2316yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2313yes—
245C2×C4×Q8C2313yes—
246C2×C4×Q8C2316yes—
247C2×C4×Q8C2316yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4—224no—
250C2×C4×D4C2313yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C2313yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2313yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2313yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2316yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2316yes—
264C2×C4×D4C2313yes—
265C2×C4×D4C2316yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2313yes—
268C2×C4×D4C2316yes—
269C2×C4×D4C2313yes—
270C2×C4×D4C2311yescharacteristic
271C2×#117C2316yes—
272C2×#117C2313yes—
273C2×#117C2313yes—
274C2×#117C2313yes—
275C2×#117C2316yes—
276C22×C4⋊C4C2313yes—
277C22×C4⋊C4C2316yes—
278C22×C4⋊C4C2316yes—
279C22×C22⋊C4C2316yes—
280C22×C22⋊C4C2316yes—
281C22×C22⋊C4C2316yes—
282C22×C22⋊C4C23112yes—
283C22×C42C2316yes—
284C22×C42C2313yes—
285C22×C42C2313yes—
286C22×C42C2316yes—
287#399C23112yes—
288#399C23112yes—
289#399C23112yes—
290#398C23112yes—
291#397C23112yes—
292#397C23112yes—
293#396C23112yes—
294#396C23112yes—
295#396C23112yes—
296#394C23112yes—
297#394C23112yes—
298#394C23112yes—
299#394C23112yes—
300#394C23112yes—
301#392C23112yes—
302#392C23112yes—
303#392C23112yes—
304#392C23112yes—
305#391C2316yes—
306#391C2313yes—
307#391C2313yes—
308#391C2316yes—
309#390C2313yes—
310#390C2313yes—
311#390C2316yes—
312#390C2316yes—
313#390C2313yes—
314#390C2313yes—
315#390C2313yes—
316#390C2316yes—
317#390C2316yes—
318#390C2316yes—
319#390C2316yes—
320#390C23112yes—
321#390C23112yes—
322#390C2316yes—
323#390C2316yes—
324#390C23112yes—
325#390C23112yes—
326#390C2316yes—
327#390C2316yes—
328#390C2313yes—
329#390C23112yes—
330#390C2316yes—
331#390C23112yes—
332#390C2316yes—
333#390C2316yes—
334#390C2316yes—
335#389C2316yes—
336#389C2316yes—
337#389C2313yes—
338#389C2316yes—
339#389C2316yes—
340#389C2316yes—
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2316yes—
344#389C2313yes—
345#389C2316yes—
346#388C2316yes—
347#388C2316yes—
348#388C2316yes—
349#388C2316yes—
350#388C23112yes—
351#388C23112yes—
352#388C2316yes—
353#388C2316yes—
354#388C2316yes—
355#388C2316yes—
356#388C2316yes—
357#387C2316yes—
358#387C2316yes—
359#387C2316yes—
360#387C23112yes—
361#386C2316yes—
362#386C23112yes—
363#386C23112yes—
364#386C2316yes—
365#386C2316yes—
366#386C2316yes—
367#386C2316yes—
368#386C2316yes—
369#386C2316yes—
370#386C2316yes—
371#386C2316yes—
372#385C2316yes—
373#385C2316yes—
374#385C23112yes—
375#385C2312yes—
376#385C2312yes—
377#385C2316yes—
378#384C2313yes—
379#384C2313yes—
380#384C2316yes—
381#382C2311yescharacteristic
382#381C2316yes—
383#380C2316yes—
384#380C2316yes—
385#380C2316yes—
386#380C2313yes—
387#380C2313yes—
388#380C2313yes—
389#380C23112yes—
390#380C2316yes—
391#380C2316yes—
392#380C23112yes—
393#380C2313yes—
394#380C2312yes—
395#380C2316yes—
396#379C2316yes—
397C4×C4⋊C4C2313yes—
398C4×C4⋊C4C2316yes—
399C4×C4⋊C4C2313yes—
400C4×C4⋊C4C2311yescharacteristic
401C4×C4⋊C4C2313yes—
402C4×C4⋊C4C2313yes—
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2313yes—
408C4×C22⋊C4C2313yes—
409C4×C22⋊C4C2313yes—
410C4×C22⋊C4C2316yes—
411C4×C22⋊C4C2313yes—
412C4×C22⋊C4C2316yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2313yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2313yes—
425C2×#95C2316yes—
426C2×#95C2312yes—
427C43C2313yes—
428C25C2416yes—
429C2×#41—24no—
430C2×#41—24no—
431C2×#41—224no—
432C2×#41—224no—
433C2×#41—28no—
434C2×#41—24no—
435C2×#41—28no—
436C2×#41—24no—
437C2×#41—24no—
438C2×#41—28no—
439C2×#41—212no—
440C2×#41—212no—
441C2×#41—224no—
442C2×#41—212no—
443C2×#41—224no—
444C2×#41—412no—
445C2×#41—412no—
446C2×#41—4128no—
447C2×#41#4118yescomplemented
448C22×Q8—28no—
449C22×Q8—28no—
450C22×Q8C2×D4116yes—
451C22×Q8C2413yes—
452C22×Q8C2416yes—
453C22×Q8C2411yescharacteristic
454C22×D4—212no—
455C22×D4—212no—
456C22×D4—224no—
457C22×D4—212no—
458C22×D4—224no—
459C22×D4—412no—
460C22×D4C2416yes—
461C22×D4C2416yes—
462C22×D4C2413yes—
463C22×D4C2413yes—
464C22×D4C2416yes—
465C22×D4C2413yes—
466C22×D4C24112yes—
467C22×D4C2413yes—
468C22×D4C2416yes—
469C22×D4C2416yes—
470C22×D4C2416yes—
471C22×D4C24112yes—
472C22×D4C2411yescharacteristic
473C23×C4—224no—
474C23×C4—224no—
475C23×C4—412no—
476C23×C4C2416yes—
477C23×C4C2413yes—
478C23×C4C2413yes—
479C23×C4C2413yes—
480C23×C4C2416yes—
481C23×C4C2412yes—
482C23×C4C2416yes—
483C23×C4C2413yes—
484C23×C4C2412yes—
485C23×C4C2416yes—
486C23×C4C2416yes—
487C23×C4C2413yes—
488C23×C4C2416yes—
489C23×C4C2413yes—
490C23×C4C2412yes—
491C4⋊Q8—212no—
492C4⋊Q8C2×D4124yes—
493#127—212no—
494#127—212no—
495#127—412no—
496#126—248no—
497#125—224no—
498#125—224no—
499#124—224no—
500#124—224no—
501#124—212no—
502#124—412no—
503#123—248no—
504#123—248no—
505#123—224no—
506#123—424no—
507C22⋊Q8—224no—
508C22⋊Q8—224no—
509C22⋊Q8—224no—
510C22⋊Q8—212no—
511C22⋊Q8—412no—
512C22⋊Q8C2×D4148yes—
513#121—212no—
514#121—224no—
515#121—224no—
516#121—212no—
517#121—224no—
518#121—224no—
519#121—224no—
520#121—224no—
521#121—212no—
522#121—412no—
523#121—412no—
524#121—412no—
525#121—412no—
526#121—424no—
527#120—248no—
528#120—224no—
529#120—424no—
530C4×Q8—24no—
531C4×Q8—224no—
532C4×Q8—28no—
533C4×Q8—224no—
534C4×Q8—24no—
535C4×Q8—24no—
536C4×Q8—24no—
537C4×Q8—28no—
538C4×Q8—212no—
539C4×Q8—212no—
540C4×Q8—412no—
541C4×Q8—412no—
542C4×Q8C2×D418yes—
543C4×D4—24no—
544C4×D4—24no—
545C4×D4—212no—
546C4×D4—224no—
547C4×D4—224no—
548C4×D4—212no—
549C4×D4—212no—
550C4×D4—212no—
551C4×D4—212no—
552C4×D4—224no—
553C4×D4—224no—
554C4×D4—224no—
555C4×D4—212no—
556C4×D4—212no—
557C4×D4—212no—
558C4×D4—212no—
559C4×D4—412no—
560C4×D4—412no—
561C4×D4—46no—
562C4×D4C2×D4124yes—
563C4×D4#4118yescomplemented
564#117—212no—
565#117—212no—
566#117—212no—
567#117—224no—
568#117—224no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—212no—
571C2×C4⋊C4—412no—
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2413yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C24112yes—
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2413yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2413yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C24112yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C24112yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2413yes—
597C2×C4⋊C4C2413yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C22⋊C4—224no—
601C2×C22⋊C4—224no—
602C2×C22⋊C4—412no—
603C2×C22⋊C4—424no—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2413yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C24112yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C24112yes—
620C2×C22⋊C4C2413yes—
621C2×C22⋊C4C2413yes—
622C2×C22⋊C4C2413yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C24112yes—
626C2×C22⋊C4C24112yes—
627C2×C22⋊C4C24112yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2413yes—
634C2×C22⋊C4C24112yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2412yes—
638C2×C42—224no—
639C2×C42—212no—
640C2×C42—212no—
641C2×C42—412no—
642C2×C42C2413yes—
643C2×C42C2413yes—
644C2×C42C2416yes—
645C2×C42C2416yes—
646C2×C42C2411yescharacteristic
647C2×C42C2413yes—
648C2×C42C2413yes—
649C2×C42C2416yes—
650C2×C42C2411yescharacteristic
651C2×C42C2413yes—
652C2×C42C2416yes—
653C2×C42C2413yes—
654C2×C42C2413yes—
655C2×C42C2413yes—
656C2×C42C2416yes—
657C2×C42C2416yes—
658C2×C42C2413yes—
659C2×C42C2413yes—
660C2×C42C2411yescharacteristic
661#95C2411yescharacteristic
662#95C2413yes—
663#95C2412yes—
664#95C2412yes—
665#95C2412yes—
666#95C2416yes—
667#95C2416yes—
668#95C2416yes—
669#95C2411yescharacteristic
670#95C2412yes—
671#95C2413yes—
672#95C2413yes—
673#95C2416yes—
674#95C2416yes—
675#95C2416yes—
676#95C2413yes—
677#95C2416yes—
678#95C2416yes—
679#95C2416yes—
680#95C24112yes—
681#95C2416yes—
682C24—212no—
683C24—212no—
684C24—212no—
685C24—212no—
686C24—46no—
687C24—46no—
688C24—46no—
689C24C2516yes—
690C24C2513yes—
691C24C2513yes—
692C24C2512yes—
693#41—232no—
694#41—496no—
695#41—496no—
696#41—416no—
697#41—432no—
698#41—448no—
699C2×Q8—264no—
700C2×Q8—26no—
701C2×Q8—212no—
702C2×Q8—26no—
703C2×Q8—212no—
704C2×Q8—26no—
705C2×Q8C22×D4124yes—
706C2×Q8C22×D414yes—
707C2×Q8C2×#4114yes—
708C2×Q8H(5,𝔽2)14yes—
709C2×D4—212no—
710C2×D4—212no—
711C2×D4—26no—
712C2×D4—212no—
713C2×D4—212no—
714C2×D4—224no—
715C2×D4—212no—
716C2×D4—212no—
717C2×D4—212no—
718C2×D4—26no—
719C2×D4—26no—
720C2×D4—26no—
721C2×D4—224no—
722C2×D4—212no—
723C2×D4—212no—
724C2×D4—26no—
725C2×D4—26no—
726C2×D4—26no—
727C2×D4—212no—
728C2×D4—212no—
729C2×D4—26no—
730C2×D4—26no—
731C2×D4—26no—
732C2×D4—212no—
733C2×D4—496no—
734C2×D4—43no—
735C2×D4—412no—
736C2×D4—46no—
737C2×D4—46no—
738C2×D4—46no—
739C2×D4—46no—
740C2×D4—46no—
741C2×D4—46no—
742C2×D4—412no—
743C2×D4—412no—
744C2×D4—412no—
745C2×D4—448no—
746C2×D4C22×D414yes—
747C2×D4C2×#41112yes—
748C2×D4C2×#4114yes—
749C2×D4H(5,𝔽2)14yes—
750C22×C4—26no—
751C22×C4—212no—
752C22×C4—212no—
753C22×C4—26no—
754C22×C4—24no—
755C22×C4—212no—
756C22×C4—24no—
757C22×C4—212no—
758C22×C4—212no—
759C22×C4—212no—
760C22×C4—212no—
761C22×C4—26no—
762C22×C4—26no—
763C22×C4—26no—
764C22×C4—26no—
765C22×C4—212no—
766C22×C4—212no—
767C22×C4—212no—
768C22×C4—26no—
769C22×C4—26no—
770C22×C4—26no—
771C22×C4—24no—
772C22×C4—212no—
773C22×C4—212no—
774C22×C4—26no—
775C22×C4—26no—
776C22×C4—26no—
777C22×C4—212no—
778C22×C4—24no—
779C22×C4—26no—
780C22×C4—26no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—46no—
784C22×C4—46no—
785C22×C4—42no—
786C22×C4—43no—
787C22×C4—42no—
788C22×C4—496no—
789C22×C4—46no—
790C22×C4—46no—
791C22×C4—43no—
792C22×C4—43no—
793C22×C4C22×D4124yes—
794C22×C4C2×#41112yes—
795C22×C4C2×#4118yescomplemented
796C22×C4C2513yes—
797C22×C4C2512yes—
798C22×C4C2511yescharacteristic
799C22×C4C2516yes—
800C22×C4C2512yes—
801C22×C4C2513yes—
802C22×C4C2513yes—
803C22×C4C2511yescharacteristic
804C22×C4C2516yes—
805C22×C4C2513yes—
806C22×C4C2513yes—
807C22×C4C2516yes—
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2512yes—
811C22×C4C2511yescharacteristic
812C22×C4C2511yescharacteristic
813C22×C4C2513yes—
814C22×C4C2511yescharacteristic
815C4⋊C4—22no—
816C4⋊C4—26no—
817C4⋊C4—212no—
818C4⋊C4—212no—
819C4⋊C4—224no—
820C4⋊C4—22no—
821C4⋊C4—26no—
822C4⋊C4—212no—
823C4⋊C4—212no—
824C4⋊C4—212no—
825C4⋊C4—22no—
826C4⋊C4—26no—
827C4⋊C4—26no—
828C4⋊C4—212no—
829C4⋊C4—26no—
830C4⋊C4—212no—
831C4⋊C4—26no—
832C4⋊C4—22no—
833C4⋊C4—412no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—46no—
837C4⋊C4—46no—
838C4⋊C4—412no—
839C4⋊C4C22×D4112yes—
840C4⋊C4C22×D4112yes—
841C4⋊C4C22×D4124yes—
842C4⋊C4C2×#4114yescomplemented
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—26no—
846C22⋊C4—212no—
847C22⋊C4—212no—
848C22⋊C4—212no—
849C22⋊C4—212no—
850C22⋊C4—212no—
851C22⋊C4—212no—
852C22⋊C4—224no—
853C22⋊C4—224no—
854C22⋊C4—26no—
855C22⋊C4—212no—
856C22⋊C4—212no—
857C22⋊C4—212no—
858C22⋊C4—26no—
859C22⋊C4—26no—
860C22⋊C4—212no—
861C22⋊C4—26no—
862C22⋊C4—212no—
863C22⋊C4—46no—
864C22⋊C4—46no—
865C22⋊C4—46no—
866C22⋊C4—412no—
867C22⋊C4—412no—
868C22⋊C4—412no—
869C22⋊C4—46no—
870C22⋊C4—43no—
871C22⋊C4—46no—
872C22⋊C4—46no—
873C22⋊C4—46no—
874C22⋊C4—412no—
875C22⋊C4C22×D4124yes—
876C22⋊C4C2×#4118yescomplemented
877C42—22no—
878C42—26no—
879C42—22no—
880C42—26no—
881C42—26no—
882C42—212no—
883C42—212no—
884C42—26no—
885C42—212no—
886C42—26no—
887C42—26no—
888C42—212no—
889C42—26no—
890C42—46no—
891C42—46no—
892C42—43no—
893C42—43no—
894C42C22×D4112yes—
895C42C2×#4114yescomplemented
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—23no—
901C23—23no—
902C23—23no—
903C23—23no—
904C23—23no—
905C23—23no—
906C23—23no—
907C23—26no—
908C23—26no—
909C23—23no—
910C23—23no—
911C23—26no—
912C23—26no—
913C23—23no—
914C23—23no—
915C23—26no—
916C23—26no—
917C23—23no—
918C23—26no—
919C23—23no—
920C23—424no—
921C23—424no—
922C23—424no—
923C23—424no—
924C23—812no—
925C23—812no—
926C23—812no—
927C23C23×D414yes—
928C23C22×#4116yes—
929C23C22×#4114yes—
930C23C2×H(5,𝔽2)14yes—
931C23C2611yescharacteristic
932Q8—248no—
933Q8—412no—
934Q8#546116yescomplemented
935D4—224no—
936D4—412no—
937D4—448no—
938D4—424no—
939D4—424no—
940D4—424no—
941D4—412no—
942D4—412no—
943D4—812no—
944D4—812no—
945D4—812no—
946D4—1612no—
947D4#550116yescomplemented
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—26no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—26no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—23no—
958C2×C4—21no—
959C2×C4—23no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—224no—
963C2×C4—248no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—23no—
968C2×C4—23no—
969C2×C4—26no—
970C2×C4—22no—
971C2×C4—23no—
972C2×C4—21no—
973C2×C4—23no—
974C2×C4—26no—
975C2×C4—23no—
976C2×C4—22no—
977C2×C4—23no—
978C2×C4—26no—
979C2×C4—23no—
980C2×C4—23no—
981C2×C4—26no—
982C2×C4—21no—
983C2×C4—23no—
984C2×C4—26no—
985C2×C4—22no—
986C2×C4—23no—
987C2×C4—23no—
988C2×C4—26no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—23no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—48no—
995C2×C4—412no—
996C2×C4—424no—
997C2×C4—48no—
998C2×C4—48no—
999C2×C4—424no—
1000C2×C4—424no—
1001C2×C4—424no—
1002C2×C4—412no—
1003C2×C4—412no—
1004C2×C4—412no—
1005C2×C4—86no—
1006C2×C4—812no—
1007C2×C4C23×D416yes—
1008C2×C4C23×D4112yes—
1009C2×C4C23×D416yes—
1010C2×C4C23×D412yes—
1011C2×C4C22×#4112yes—
1012C2×C4C22×#4112yes—
1013C2×C4C22×#4114yes—
1014C2×C4C22×#4112yes—
1015C2×C4C22×#4116yes—
1016C2×C4C22×#4112yes—
1017C2×C4C2×H(5,𝔽2)16yes—
1018C2×C4C2×H(5,𝔽2)12yes—
1019C2×C4#58512yes—
1020C22—24no—
1021C22—24no—
1022C22—24no—
1023C22—24no—
1024C22—24no—
1025C22—24no—
1026C22—26no—
1027C22—26no—
1028C22—26no—
1029C22—43no—
1030C22—43no—
1031C22—43no—
1032C22—43no—
1033C22—43no—
1034C22—46no—
1035C22—43no—
1036C22—46no—
1037C22—43no—
1038C22—46no—
1039C22—43no—
1040C22—46no—
1041C22—46no—
1042C22—43no—
1043C22—43no—
1044C22—46no—
1045C22—43no—
1046C22—46no—
1047C22—848no—
1048C22C2×#55018yes—
1049C22C24×D411yescharacteristic
1050C22C23×#4111yescharacteristic
1051C22C23×#4111yescharacteristic
1052C22C22×H(5,𝔽2)11yescharacteristic
1053C22C22×H(5,𝔽2)11yescharacteristic
1054C22C2×#58511yescharacteristic
1055C222−1+611yescharacteristic
1056C4—22no—
1057C4—24no—
1058C4—22no—
1059C4—26no—
1060C4—22no—
1061C4—212no—
1062C4—22no—
1063C4—43no—
1064C4—42no—
1065C4—41no—
1066C4—43no—
1067C4—46no—
1068C4—41no—
1069C4—42no—
1070C4—43no—
1071C4—43no—
1072C4—46no—
1073C4C2×#546112yes—
1074C4C2×#55014yes—
1075C2—28no—
1076C2—46no—
1077C2—83no—
1078C2—86no—
1079C2C22×#54611yescharacteristic
1080C2C22×#55011yescharacteristic
1081C2#41211yescharacteristic
1082C2#6298411yescharacteristic
1083C2#6298511yescharacteristic
1084C2#6300211yescharacteristic
1085C2#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×#3482C2semidirect
2. C2×D4×#41C2semidirect
3. #59807C2semidirect
4. #59410C2semidirect
5. #59049C2semidirect
6. #59046C2semidirect
7. #59040C2semidirect
8. #59022C2semidirect
9. #36583C2semidirect
10. #36576C2semidirect
11. #36483C2semidirect
12. #36455C2semidirect
13. #36445C2semidirect
14. #36429C2semidirect
15. #36260C2semidirect
16. #36258C2semidirect
17. #36153C2semidirect
18. #36150C2semidirect
19. #36144C2semidirect
20. C4×D4×Q8C2semidirect
21. C4×#550C2semidirect
22. C4×#546C2semidirect
23. C2×#2341C2semidirect
26. C2×#557C22semidirect
27. C2×#556C22semidirect
28. C2×#552C22semidirect
32. C2×#550C22semidirect
35. C2×#548C22semidirect
42. C2×#533C22semidirect
44. C2×#529C22semidirect
48. C2×C4×#41C22semidirect
49. C22×C4×Q8C22semidirect
50. C22×C4×Q8C22semidirect
52. #2858C22semidirect
53. #2857C22semidirect
54. #2856C22semidirect
55. #2856C22semidirect
56. #2854C22semidirect
57. #2847C22semidirect
58. #2714C22semidirect
59. #2705C22semidirect
60. #2694C22semidirect
61. #2554C22semidirect
62. #2548C22semidirect
63. #2548C22semidirect
64. #2547C22semidirect
65. #2542C22semidirect
66. #2541C22semidirect
67. #2540C22semidirect
68. #2540C22semidirect
69. #2539C22semidirect
70. #2539C22semidirect
71. #2538C22semidirect
72. #2538C22semidirect
73. #2537C22semidirect
74. #2501C22semidirect
75. #2490C22semidirect
76. #2490C22semidirect
77. #2490C22semidirect
78. #2486C22semidirect
79. #2471C22semidirect
80. #2467C22semidirect
81. #2454C22semidirect
82. #2454C22semidirect
83. #2448C22semidirect
84. #2448C22semidirect
85. #2441C22semidirect
86. #2433C22semidirect
87. #2431C22semidirect
88. #2431C22semidirect
89. #2428C22semidirect
90. #2427C22semidirect
91. #2426C22semidirect
92. #2426C22semidirect
93. #2426C22semidirect
94. #2425C22semidirect
95. #2424C22semidirect
96. #2423C22semidirect
97. #2423C22semidirect
98. #2417C22semidirect
99. #2416C22semidirect
100. #2416C22semidirect
101. #2414C22semidirect
102. #2414C22semidirect
103. #2414C22semidirect
104. #2412C22semidirect
105. #2411C22semidirect
106. #2408C22semidirect
107. #2407C22semidirect
108. #2407C22semidirect
109. #2367C22semidirect
110. #2366C22semidirect
111. #2365C22semidirect
112. #2364C22semidirect
113. #2363C22semidirect
114. #2363C22semidirect
115. #2363C22semidirect
116. #2363C22semidirect
117. #2360C22semidirect
118. #2360C22semidirect
119. #2359C22semidirect
120. #2358C22semidirect
121. #2354C22semidirect
122. #2352C22semidirect
123. Q8×C4⋊C4C22semidirect
124. Q8×C4⋊C4C22semidirect
125. Q8×C4⋊C4C22semidirect
128. #2342C22semidirect
131. #2341C22semidirect
132. #2341C22semidirect
133. #2341C22semidirect
134. #2341C22semidirect
135. #2341C22semidirect
136. #2341C22semidirect
137. #2341C22semidirect
138. #2341C22semidirect
139. Q8×C22⋊C4C22semidirect
142. C4×C4⋊Q8C22semidirect
143. C4×#127C22semidirect
144. C4×#124C22semidirect
145. C4×C22⋊Q8C22semidirect
146. C4×C22⋊Q8C22semidirect
147. C4×#123C22semidirect
148. C4×#121C22semidirect
149. C4×#121C22semidirect
150. C4×#121C22semidirect
151. C4×#121C22semidirect
152. C4×#120C22semidirect
153. C2×#390C22semidirect
154. C2×#390C22semidirect
155. C2×#380C22semidirect
156. C42×Q8C22semidirect
158. C42×D4C22semidirect
159. C2×C4×C22⋊C4C22semidirect
179. D4×Q8D4semidirect
447. C2×#41#41semidirect
563. C4×D4#41semidirect
795. C22×C4C2×#41semidirect
842. C4⋊C4C2×#41semidirect
876. C22⋊C4C2×#41semidirect
895. C42C2×#41semidirect
934. Q8#546semidirect
947. D4#550semidirect

Maximal subgroups

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

subgroupindex
C2×#34822
C2×D4×#412
#598072
#594102
#590492
#590462
#590402
#590222
#365832
#365762
#364832
#364552
#364452
#364292
#362602
#362582
#361532
#361502
#361442
C4×D4×Q82
C4×#5502
C4×#5462
C2×#23412