Finite Group Databasebeta

← #7699561

Subgroups — #7699561

Order 512.

8916 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3483C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#59568C216yesmaximal, complemented
4#59412C213yesmaximal, complemented
5#59099C216yesmaximal, complemented
6#59041C213yesmaximal, complemented
7#59033C213yesmaximal, complemented
8#59018C216yesmaximal, complemented
9Q8×#124C211yesmaximal, characteristic, complemented
10#36456C211yesmaximal, characteristic, complemented
11#36444C211yesmaximal, characteristic, complemented
12#36432C212yesmaximal, complemented
13#36430C212yesmaximal, complemented
14#36429C212yesmaximal, complemented
15#36415C213yesmaximal, complemented
16#36404C213yesmaximal, complemented
17#36160C213yesmaximal, complemented
18#36149C213yesmaximal, complemented
19#36147C216yesmaximal, complemented
20C4×#550C211yesmaximal, characteristic, complemented
21C4×#550C211yesmaximal, characteristic, complemented
22C4×#546C213yesmaximal, complemented
23C22⋊C4×#41C212yesmaximal, complemented
24C23×#41C2212yes—
25#3483—216no—
26C2×Q82C2211yescharacteristic, complemented
27C2×#555C2213yescomplemented
28C2×#555C2216yescomplemented
29D4×#41—216no—
30C2×#550C2211yescharacteristic
31C2×#550C2211yescharacteristic
32C2×#550C2213yescomplemented
33C2×#550C2212yescomplemented
34C2×D4×Q8C2211yescharacteristic
35C2×#548C2212yes—
36C2×#548C2212yescomplemented
37C2×#547C2213yes—
38C2×#546C2213yes—
39C2×#546C2216yes—
40C2×D42C2213yes—
41C2×#532C2213yes—
42C2×#532C2216yescomplemented
43C2×#532C2213yescomplemented
44C2×#525C2216yes—
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2213yescomplemented
47C2×C4×#41C2212yescomplemented
48C2×C4×#41C2211yescharacteristic, complemented
49C2×C4×#41C2212yescomplemented
50C22×C4×D4C2213yes—
51#2862C2213yescomplemented
52#2857C2213yescomplemented
53#2857C2213yescomplemented
54#2855C2216yescomplemented
55#2850C2216yescomplemented
56#2847C2216yescomplemented
57#2688C22112yescomplemented
58#2684C22112yescomplemented
59#2678C22112yescomplemented
60#2568C2213yescomplemented
61#2563C2213yes—
62#2563C2213yescomplemented
63#2557C22112yescomplemented
64#2557C22112yescomplemented
65#2547C2213yescomplemented
66#2544C2216yescomplemented
67#2538C2213yescomplemented
68#2537C2213yes—
69#2535C2216yescomplemented
70#2535C2216yescomplemented
71#2535C2216yescomplemented
72#2499C2216yescomplemented
73#2492C2216yescomplemented
74#2492C2216yescomplemented
75#2485C2216yescomplemented
76#2472C22112yescomplemented
77#2470C22112yescomplemented
78#2459C22112yescomplemented
79#2457C22112yescomplemented
80#2452C2216yescomplemented
81#2447C2216yescomplemented
82#2447C2216yescomplemented
83#2447C2216yescomplemented
84#2444C22112yescomplemented
85#2439C2216yescomplemented
86#2433C2216yescomplemented
87#2431C2216yescomplemented
88#2431C2216yescomplemented
89#2428C2216yescomplemented
90#2427C2216yescomplemented
91#2427C2216yescomplemented
92#2427C2216yescomplemented
93#2424C22112yescomplemented
94#2422C2216yescomplemented
95#2420C2216yescomplemented
96#2420C2216yescomplemented
97#2420C2216yescomplemented
98#2415C2216yescomplemented
99#2415C2216yescomplemented
100#2414C2216yescomplemented
101#2408C2216yes—
102#2408C2216yescomplemented
103#2407C2216yescomplemented
104#2407C2216yescomplemented
105#2407C2216yescomplemented
106#2407C2216yescomplemented
107#2404C22112yescomplemented
108#2367C2211yescharacteristic
109#2366C2213yescomplemented
110#2366C2213yescomplemented
111#2364C2216yescomplemented
112#2363C2213yes—
113#2363C2213yescomplemented
114#2363C2216yescomplemented
115#2363C2213yescomplemented
116#2360C2213yescomplemented
117#2359C2216yescomplemented
118#2358C2216yescomplemented
119#2354C2213yescomplemented
120#2354C2213yescomplemented
121#2352C2216yescomplemented
122#2352C2213yescomplemented
123#2351C2212yescomplemented
124Q8×C4⋊C4C2211yescharacteristic, complemented
125Q8×C4⋊C4C2211yescharacteristic, complemented
126#2349C2213yescomplemented
127#2342C2216yescomplemented
128#2341C2211yescharacteristic
129#2341C2212yes—
130#2341C2212yescomplemented
131#2341C2211yescharacteristic, complemented
132Q8×C22⋊C4C2212yescomplemented
133Q8×C22⋊C4C2212yescomplemented
134Q8×C22⋊C4C2212yescomplemented
135#2339C2216yescomplemented
136#2339C2216yescomplemented
137#2339C2216yescomplemented
138#2339C2213yescomplemented
139D4×C22⋊C4C2213yes—
140D4×C22⋊C4C2216yescomplemented
141D4×C22⋊C4C2216yescomplemented
142C4×#127C2213yescomplemented
143C4×#127C2213yescomplemented
144C4×#124C2213yes—
145C4×C22⋊Q8C2213yescomplemented
146C4×#123C2216yescomplemented
147C4×#121C2213yes—
148C4×#121C2216yescomplemented
149C4×#121C2213yescomplemented
150C4×#121C2213yescomplemented
151C4×#121C2216yescomplemented
152C4×#120C2216yescomplemented
153#2297C2216yescomplemented
154#2297C2216yescomplemented
155#2280C2216yescomplemented
156C42×Q8C2211yescharacteristic, complemented
157C42×D4C2213yescomplemented
158C42×D4C2213yescomplemented
159C2×C4×C22⋊C4C2216yescomplemented
160C22×#41—216no—
161C22×#41—216no—
162C22×#41—48no—
163C22×#41C2311yescharacteristic
164C22×#41C2316yes—
165C22×#41C2316yes—
166C22×#41C2313yes—
167C22×#41C2312yes—
168C22×#41C2311yescharacteristic
169C22×#41C2316yes—
170C23×Q8C2312yes—
171C23×D4C2316yes—
172C23×D4C2313yes—
173C24×C4C2316yes—
174Q82—28no—
175#555—248no—
176#555—224no—
177#550—216no—
178#550—28no—
179#550—224no—
180#550D4116yescomplemented
181D4×Q8—28no—
182#548—216no—
183#548—48no—
184#547—224no—
185#546—224no—
186#546—248no—
187D42—224no—
188#532—224no—
189#532—224no—
190#532—248no—
191C2×C4⋊Q8C2313yes—
192C2×C4⋊Q8C2313yes—
193C2×C4⋊Q8C2316yes—
194C2×#127C2313yes—
195C2×#127C2316yes—
196C2×#127C2313yes—
197C2×#124C2316yes—
198C2×#124C2316yes—
199C2×#124C23112yes—
200C2×#124C2316yes—
201C2×#124C2311yescharacteristic
202#525—248no—
203C2×#123C2316yes—
204C2×#123C23112yes—
205C2×C22⋊Q8C2316yes—
206C2×C22⋊Q8C2313yes—
207C2×C22⋊Q8C2316yes—
208C2×C22⋊Q8C2316yes—
209C2×C22⋊Q8C2316yes—
210C2×#121C2313yes—
211C2×#121C2316yes—
212C2×#121C2313yes—
213C2×#121C2313yes—
214C2×#121C2316yes—
215C2×#121C2316yes—
216C2×#121C2316yes—
217C2×#121C2316yes—
218C2×#121C2316yes—
219C2×#121C2316yes—
220C2×#121C23112yes—
221C2×#121C2316yes—
222C2×#121C2316yes—
223C2×#120C2316yes—
224C2×#120C23112yes—
225C2×#120C23112yes—
226C4×#41—216no—
227C4×#41—28no—
228C4×#41—28no—
229C4×#41—224no—
230C4×#41—48no—
231C2×C4×Q8C2313yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—224no—
241C2×C4×D4C2313yes—
242C2×C4×D4C2313yes—
243C2×C4×D4C2313yes—
244C2×C4×D4C2313yes—
245C2×C4×D4C2313yes—
246C2×C4×D4C2313yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2316yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C2316yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2313yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2316yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2313yes—
264C2×C4×D4C2316yes—
265C2×C4×D4C2316yes—
266C2×C4×D4C2313yes—
267C2×#117C2316yes—
268C2×#117C2313yes—
269C2×#117C2313yes—
270C2×#117C2313yes—
271C2×#117C2316yes—
272C2×#117C2316yes—
273C22×C4⋊C4C2313yes—
274C22×C22⋊C4C2316yes—
275C22×C22⋊C4C2316yes—
276C22×C22⋊C4C2316yes—
277C22×C42C2316yes—
278C22×C42C2313yes—
279C22×C42C2313yes—
280C22×C42C2316yes—
281#400C23112yes—
282#397C23112yes—
283#397C23112yes—
284#397C23112yes—
285#397C23112yes—
286#397C23112yes—
287#396C23112yes—
288#394C23112yes—
289#394C23112yes—
290#394C23112yes—
291#394C23112yes—
292#394C23112yes—
293#393C23112yes—
294#393C23112yes—
295#392C23112yes—
296#392C23112yes—
297#392C23112yes—
298#392C23112yes—
299#391C2313yes—
300#391C2316yes—
301#391C2316yes—
302#391C2316yes—
303#391C2311yescharacteristic
304#391C2316yes—
305#391C2316yes—
306#391C2316yes—
307#391C2316yes—
308#391C2316yes—
309#391C2316yes—
310#390C2313yes—
311#390C2313yes—
312#390C2316yes—
313#390C2316yes—
314#390C2316yes—
315#390C2316yes—
316#390C2316yes—
317#390C2313yes—
318#390C2316yes—
319#390C2311yescharacteristic
320#390C2313yes—
321#390C2316yes—
322#390C2316yes—
323#390C2313yes—
324#390C2316yes—
325#389C2313yes—
326#389C2316yes—
327#389C2313yes—
328#389C2313yes—
329#389C2316yes—
330#389C2316yes—
331#389C2316yes—
332#389C2313yes—
333#389C2316yes—
334#388C2316yes—
335#388C23112yes—
336#388C2312yes—
337#388C2316yes—
338#388C2316yes—
339#388C2316yes—
340#388C2316yes—
341#388C2316yes—
342#388C23112yes—
343#388C2312yes—
344#388C2316yes—
345#387C2316yes—
346#387C23112yes—
347#387C2316yes—
348#387C2316yes—
349#386C2316yes—
350#386C23112yes—
351#386C23112yes—
352#386C2316yes—
353#386C2316yes—
354#386C23112yes—
355#386C23112yes—
356#386C23112yes—
357#386C23112yes—
358#386C23112yes—
359#386C23112yes—
360#386C2316yes—
361#386C2316yes—
362#386C2316yes—
363#386C2316yes—
364#386C2316yes—
365#386C23112yes—
366#386C2316yes—
367#385C2316yes—
368#385C2316yes—
369#385C23112yes—
370#385C2316yes—
371#385C2316yes—
372#385C2312yes—
373#384C2313yes—
374#384C2313yes—
375#382C2316yes—
376#382C2316yes—
377#382C2313yes—
378#381C23112yes—
379#381C2316yes—
380#381C23112yes—
381#380C2316yes—
382#380C2316yes—
383#380C2313yes—
384#380C2316yes—
385#380C2316yes—
386#380C2316yes—
387#380C2316yes—
388#380C2313yes—
389#380C2316yes—
390#380C2313yes—
391#380C2313yes—
392#380C2316yes—
393#380C2316yes—
394#379C2316yes—
395#379C23112yes—
396C4×C4⋊C4C2313yes—
397C4×C4⋊C4C2313yes—
398C4×C4⋊C4C2311yescharacteristic
399C4×C4⋊C4C2313yes—
400C4×C4⋊C4C2316yes—
401C4×C4⋊C4C2311yescharacteristic
402C4×C4⋊C4C2313yes—
403C4×C4⋊C4C2313yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2313yes—
406C4×C22⋊C4C2313yes—
407C4×C22⋊C4C2316yes—
408C4×C22⋊C4C2316yes—
409C4×C22⋊C4C2313yes—
410C4×C22⋊C4C2313yes—
411C4×C22⋊C4C2316yes—
412C4×C22⋊C4C2313yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2313yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2313yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C23112yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2312yes—
424C2×#95C2316yes—
425C2×#95C2316yes—
426C43C2313yes—
427C25C2416yes—
428C2×#41—24no—
429C2×#41—24no—
430C2×#41—28no—
431C2×#41—24no—
432C2×#41—212no—
433C2×#41—28no—
434C2×#41—24no—
435C2×#41—24no—
436C2×#41—212no—
437C2×#41—224no—
438C2×#41—224no—
439C2×#41—224no—
440C2×#41—224no—
441C2×#41—224no—
442C2×#41—412no—
443C2×#41—412no—
444C2×#41—412no—
445C2×#41—46no—
446C2×#41—4128no—
447C2×#41—86no—
448C2×#41C2×D4116yes—
449C2×#41#4118yescomplemented
450C22×Q8—28no—
451C22×Q8—28no—
452C22×Q8—28no—
453C22×Q8C2416yes—
454C22×Q8C2411yescharacteristic
455C22×Q8C2416yes—
456C22×Q8C2411yescharacteristic
457C22×D4—212no—
458C22×D4—224no—
459C22×D4—212no—
460C22×D4—224no—
461C22×D4—46no—
462C22×D4—412no—
463C22×D4C2413yes—
464C22×D4C2413yes—
465C22×D4C2416yes—
466C22×D4C2416yes—
467C22×D4C24112yes—
468C22×D4C2413yes—
469C22×D4C2416yes—
470C22×D4C2411yescharacteristic
471C22×D4C2413yes—
472C22×D4C2416yes—
473C22×D4C2416yes—
474C22×D4C24112yes—
475C22×D4C2416yes—
476C23×C4—224no—
477C23×C4—224no—
478C23×C4—412no—
479C23×C4C2413yes—
480C23×C4C2413yes—
481C23×C4C2413yes—
482C23×C4C2416yes—
483C23×C4C2416yes—
484C23×C4C2416yes—
485C23×C4C2416yes—
486C23×C4C2413yes—
487C23×C4C2412yes—
488C23×C4C2416yes—
489C23×C4C2416yes—
490C23×C4C2413yes—
491C23×C4C2413yes—
492C23×C4C2416yes—
493C23×C4C2416yes—
494C4⋊Q8—224no—
495C4⋊Q8—212no—
496C4⋊Q8—212no—
497#127—224no—
498#127—212no—
499#127C2×D4124yes—
500#124—224no—
501#124—224no—
502#124—248no—
503#124—412no—
504#124#4118yescomplemented
505#123—248no—
506#123—224no—
507C22⋊Q8—212no—
508C22⋊Q8—224no—
509C22⋊Q8—224no—
510C22⋊Q8—412no—
511C22⋊Q8—86no—
512#121—224no—
513#121—224no—
514#121—224no—
515#121—224no—
516#121—224no—
517#121—248no—
518#121—212no—
519#121—212no—
520#121—224no—
521#121—212no—
522#121—224no—
523#121—412no—
524#121C2×D4148yes—
525#120—248no—
526#120—224no—
527#120—812no—
528C4×Q8—24no—
529C4×Q8—24no—
530C4×Q8—28no—
531C4×Q8—24no—
532C4×Q8—24no—
533C4×Q8—28no—
534C4×Q8—24no—
535C4×Q8—212no—
536C4×Q8C2×D418yes—
537C4×D4—212no—
538C4×D4—212no—
539C4×D4—224no—
540C4×D4—224no—
541C4×D4—224no—
542C4×D4—224no—
543C4×D4—224no—
544C4×D4—212no—
545C4×D4—24no—
546C4×D4—212no—
547C4×D4—212no—
548C4×D4—224no—
549C4×D4—224no—
550C4×D4—212no—
551C4×D4—212no—
552C4×D4—212no—
553C4×D4—212no—
554C4×D4—212no—
555C4×D4—46no—
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—212no—
565#117—212no—
566#117—212no—
567#117—224no—
568#117—412no—
569C2×C4⋊C4—212no—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2413yes—
576C2×C4⋊C4C2413yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2413yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2413yes—
594C2×C22⋊C4—224no—
595C2×C22⋊C4—224no—
596C2×C22⋊C4—412no—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2413yes—
600C2×C22⋊C4C2413yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C24112yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C24112yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2413yes—
613C2×C22⋊C4C2413yes—
614C2×C22⋊C4C2413yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C24112yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C24112yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2413yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C24112yes—
627C2×C22⋊C4C24112yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C42—224no—
632C2×C42—212no—
633C2×C42—212no—
634C2×C42—412no—
635C2×C42C2416yes—
636C2×C42C2413yes—
637C2×C42C2413yes—
638C2×C42C2411yescharacteristic
639C2×C42C2413yes—
640C2×C42C2412yes—
641C2×C42C2411yescharacteristic
642C2×C42C2413yes—
643C2×C42C2413yes—
644C2×C42C2416yes—
645C2×C42C2416yes—
646C2×C42C2413yes—
647C2×C42C2413yes—
648C2×C42C2416yes—
649C2×C42C2413yes—
650C2×C42C2413yes—
651C2×C42C2412yes—
652C2×C42C2413yes—
653C2×C42C2411yescharacteristic
654#95C2411yescharacteristic
655#95C2412yes—
656#95C2413yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C2411yescharacteristic
663#95C2412yes—
664#95C2416yes—
665#95C2413yes—
666#95C2413yes—
667#95C2413yes—
668#95C2416yes—
669#95C24112yes—
670#95C24112yes—
671#95C2416yes—
672#95C2416yes—
673#95C2412yes—
674#95C2416yes—
675#95C2416yes—
676#95C24112yes—
677#95C24112yes—
678C24—212no—
679C24—212no—
680C24—212no—
681C24—46no—
682C24—46no—
683C24—46no—
684C24—46no—
685C24C2513yes—
686C24C2516yes—
687C24C2512yes—
688C24C2513yes—
689#41—232no—
690#41—264no—
691#41—496no—
692#41—496no—
693#41—448no—
694#41—416no—
695#41—848no—
696C2×Q8—22no—
697C2×Q8—212no—
698C2×Q8—212no—
699C2×Q8—212no—
700C2×Q8—212no—
701C2×Q8—22no—
702C2×Q8—46no—
703C2×Q8—46no—
704C2×Q8—432no—
705C2×Q8C22×D414yes—
706C2×Q8C2×#4114yes—
707C2×Q8C2×#4114yescomplemented
708C2×Q8H(5,𝔽2)14yes—
709C2×D4—212no—
710C2×D4—212no—
711C2×D4—224no—
712C2×D4—26no—
713C2×D4—212no—
714C2×D4—224no—
715C2×D4—224no—
716C2×D4—212no—
717C2×D4—212no—
718C2×D4—22no—
719C2×D4—26no—
720C2×D4—26no—
721C2×D4—26no—
722C2×D4—212no—
723C2×D4—26no—
724C2×D4—212no—
725C2×D4—26no—
726C2×D4—212no—
727C2×D4—26no—
728C2×D4—26no—
729C2×D4—26no—
730C2×D4—22no—
731C2×D4—43no—
732C2×D4—46no—
733C2×D4—46no—
734C2×D4—412no—
735C2×D4—46no—
736C2×D4—46no—
737C2×D4—46no—
738C2×D4—46no—
739C2×D4—46no—
740C2×D4—46no—
741C2×D4—412no—
742C2×D4—412no—
743C2×D4—448no—
744C2×D4—496no—
745C2×D4C22×D4112yes—
746C2×D4C22×D4124yes—
747C2×D4C22×D4124yes—
748C2×D4C2×#4114yes—
749C2×D4C2×#41112yes—
750C22×C4—26no—
751C22×C4—212no—
752C22×C4—212no—
753C22×C4—26no—
754C22×C4—212no—
755C22×C4—212no—
756C22×C4—212no—
757C22×C4—212no—
758C22×C4—26no—
759C22×C4—26no—
760C22×C4—26no—
761C22×C4—26no—
762C22×C4—212no—
763C22×C4—24no—
764C22×C4—212no—
765C22×C4—212no—
766C22×C4—26no—
767C22×C4—26no—
768C22×C4—26no—
769C22×C4—24no—
770C22×C4—212no—
771C22×C4—212no—
772C22×C4—26no—
773C22×C4—212no—
774C22×C4—212no—
775C22×C4—26no—
776C22×C4—26no—
777C22×C4—26no—
778C22×C4—26no—
779C22×C4—212no—
780C22×C4—42no—
781C22×C4—46no—
782C22×C4—46no—
783C22×C4—46no—
784C22×C4—43no—
785C22×C4—46no—
786C22×C4—496no—
787C22×C4—46no—
788C22×C4—46no—
789C22×C4—46no—
790C22×C4—43no—
791C22×C4—46no—
792C22×C4—46no—
793C22×C4—43no—
794C22×C4C22×D4124yes—
795C22×C4C2×#41112yes—
796C22×C4C2512yes—
797C22×C4C2513yes—
798C22×C4C2516yes—
799C22×C4C2513yes—
800C22×C4C2516yes—
801C22×C4C2513yes—
802C22×C4C2516yes—
803C22×C4C2513yes—
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2512yes—
807C22×C4C2513yes—
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2512yes—
812C22×C4C2511yescharacteristic
813C22×C4C2513yes—
814C22×C4C2511yescharacteristic
815C4⋊C4—26no—
816C4⋊C4—212no—
817C4⋊C4—24no—
818C4⋊C4—26no—
819C4⋊C4—26no—
820C4⋊C4—212no—
821C4⋊C4—212no—
822C4⋊C4—26no—
823C4⋊C4—212no—
824C4⋊C4—22no—
825C4⋊C4—26no—
826C4⋊C4—26no—
827C4⋊C4—26no—
828C4⋊C4—212no—
829C4⋊C4—26no—
830C4⋊C4—212no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—46no—
834C4⋊C4—46no—
835C4⋊C4—46no—
836C4⋊C4—46no—
837C4⋊C4C22×D414yes—
838C4⋊C4C22×D4112yes—
839C22⋊C4—212no—
840C22⋊C4—212no—
841C22⋊C4—224no—
842C22⋊C4—224no—
843C22⋊C4—212no—
844C22⋊C4—26no—
845C22⋊C4—24no—
846C22⋊C4—212no—
847C22⋊C4—212no—
848C22⋊C4—212no—
849C22⋊C4—212no—
850C22⋊C4—26no—
851C22⋊C4—212no—
852C22⋊C4—212no—
853C22⋊C4—26no—
854C22⋊C4—26no—
855C22⋊C4—24no—
856C22⋊C4—26no—
857C22⋊C4—46no—
858C22⋊C4—46no—
859C22⋊C4—412no—
860C22⋊C4—46no—
861C22⋊C4—46no—
862C22⋊C4—46no—
863C22⋊C4—43no—
864C22⋊C4—42no—
865C22⋊C4—46no—
866C22⋊C4—412no—
867C22⋊C4—46no—
868C22⋊C4—412no—
869C22⋊C4—412no—
870C22⋊C4C22×D4124yes—
871C22⋊C4C2×#4118yescomplemented
872C22⋊C4C2×#4118yescomplemented
873C42—22no—
874C42—24no—
875C42—26no—
876C42—22no—
877C42—26no—
878C42—212no—
879C42—26no—
880C42—26no—
881C42—212no—
882C42—26no—
883C42—26no—
884C42—212no—
885C42—26no—
886C42—42no—
887C42—46no—
888C42—43no—
889C42—43no—
890C42C22×D4112yes—
891C42C2×#4114yescomplemented
892C23—22no—
893C23—23no—
894C23—23no—
895C23—26no—
896C23—22no—
897C23—26no—
898C23—26no—
899C23—22no—
900C23—23no—
901C23—22no—
902C23—23no—
903C23—23no—
904C23—26no—
905C23—26no—
906C23—22no—
907C23—23no—
908C23—22no—
909C23—26no—
910C23—23no—
911C23—23no—
912C23—23no—
913C23—23no—
914C23—23no—
915C23—23no—
916C23—23no—
917C23—424no—
918C23—424no—
919C23—424no—
920C23—812no—
921C23—812no—
922C23—812no—
923C23—812no—
924C23C23×D4112yes—
925C23C22×#4114yes—
926C23C22×#4116yes—
927C23C2611yescharacteristic
928Q8—28no—
929Q8—424no—
930Q8—812no—
931Q8#546116yescomplemented
932D4—224no—
933D4—248no—
934D4—28no—
935D4—224no—
936D4—424no—
937D4—412no—
938D4—424no—
939D4—424no—
940D4—448no—
941D4—412no—
942D4—812no—
943D4—812no—
944D4—824no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—23no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—23no—
958C2×C4—21no—
959C2×C4—224no—
960C2×C4—248no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—23no—
964C2×C4—23no—
965C2×C4—26no—
966C2×C4—26no—
967C2×C4—23no—
968C2×C4—26no—
969C2×C4—21no—
970C2×C4—23no—
971C2×C4—23no—
972C2×C4—26no—
973C2×C4—22no—
974C2×C4—23no—
975C2×C4—26no—
976C2×C4—26no—
977C2×C4—21no—
978C2×C4—23no—
979C2×C4—23no—
980C2×C4—23no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—23no—
985C2×C4—23no—
986C2×C4—26no—
987C2×C4—23no—
988C2×C4—26no—
989C2×C4—26no—
990C2×C4—21no—
991C2×C4—48no—
992C2×C4—412no—
993C2×C4—424no—
994C2×C4—424no—
995C2×C4—424no—
996C2×C4—424no—
997C2×C4—424no—
998C2×C4—412no—
999C2×C4—412no—
1000C2×C4—412no—
1001C2×C4—812no—
1002C2×C4—86no—
1003C2×C4—812no—
1004C2×C4C23×D414yes—
1005C2×C4C23×D416yes—
1006C2×C4C23×D416yes—
1007C2×C4C23×D412yes—
1008C2×C4C22×#4112yes—
1009C2×C4C22×#4112yes—
1010C2×C4C22×#4114yes—
1011C2×C4C22×#4112yes—
1012C2×C4C22×#4116yes—
1013C2×C4C22×#4112yes—
1014C2×C4C2×H(5,𝔽2)16yes—
1015C2×C4#58512yes—
1016C2×C4#58512yes—
1017C22—24no—
1018C22—212no—
1019C22—26no—
1020C22—26no—
1021C22—212no—
1022C22—212no—
1023C22—24no—
1024C22—26no—
1025C22—24no—
1026C22—46no—
1027C22—43no—
1028C22—43no—
1029C22—42no—
1030C22—46no—
1031C22—42no—
1032C22—46no—
1033C22—43no—
1034C22—42no—
1035C22—42no—
1036C22—43no—
1037C22—46no—
1038C22—43no—
1039C22—43no—
1040C22—43no—
1041C22—43no—
1042C22—43no—
1043C22—43no—
1044C22—43no—
1045C22—848no—
1046C22C24×D411yescharacteristic
1047C22C23×#4111yescharacteristic
1048C22C23×#4111yescharacteristic
1049C22C22×H(5,𝔽2)11yescharacteristic
1050C22C2×#58511yescharacteristic
1051C22C2×#58511yescharacteristic
1052C22H(7,𝔽2)11yescharacteristic
1053C4—22no—
1054C4—22no—
1055C4—26no—
1056C4—22no—
1057C4—24no—
1058C4—24no—
1059C4—22no—
1060C4—46no—
1061C4—46no—
1062C4—41no—
1063C4—43no—
1064C4—43no—
1065C4—42no—
1066C4—41no—
1067C4—46no—
1068C4—43no—
1069C4—43no—
1070C4C2×#546112yes—
1071C4D4×#4114yes—
1072C2—412no—
1073C2—46no—
1074C2—44no—
1075C2—83no—
1076C2C22×#54611yescharacteristic
1077C2C2×D4×#4111yescharacteristic
1078C2#41211yescharacteristic
1079C2#6298611yescharacteristic
1080C2#6298711yescharacteristic
1081C2#6299411yescharacteristic
1082C2#6302211yescharacteristic
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×#3483C2semidirect
2. C2×D4×#41C2semidirect
3. #59568C2semidirect
4. #59412C2semidirect
5. #59099C2semidirect
6. #59041C2semidirect
7. #59033C2semidirect
8. #59018C2semidirect
9. Q8×#124C2semidirect
10. #36456C2semidirect
11. #36444C2semidirect
12. #36432C2semidirect
13. #36430C2semidirect
14. #36429C2semidirect
15. #36415C2semidirect
16. #36404C2semidirect
17. #36160C2semidirect
18. #36149C2semidirect
19. #36147C2semidirect
20. C4×#550C2semidirect
21. C4×#550C2semidirect
22. C4×#546C2semidirect
23. C22⋊C4×#41C2semidirect
26. C2×Q82C22semidirect
27. C2×#555C22semidirect
28. C2×#555C22semidirect
32. C2×#550C22semidirect
33. C2×#550C22semidirect
36. C2×#548C22semidirect
42. C2×#532C22semidirect
43. C2×#532C22semidirect
46. C2×C4×#41C22semidirect
47. C2×C4×#41C22semidirect
48. C2×C4×#41C22semidirect
49. C2×C4×#41C22semidirect
51. #2862C22semidirect
52. #2857C22semidirect
53. #2857C22semidirect
54. #2855C22semidirect
55. #2850C22semidirect
56. #2847C22semidirect
57. #2688C22semidirect
58. #2684C22semidirect
59. #2678C22semidirect
60. #2568C22semidirect
62. #2563C22semidirect
63. #2557C22semidirect
64. #2557C22semidirect
65. #2547C22semidirect
66. #2544C22semidirect
67. #2538C22semidirect
69. #2535C22semidirect
70. #2535C22semidirect
71. #2535C22semidirect
72. #2499C22semidirect
73. #2492C22semidirect
74. #2492C22semidirect
75. #2485C22semidirect
76. #2472C22semidirect
77. #2470C22semidirect
78. #2459C22semidirect
79. #2457C22semidirect
80. #2452C22semidirect
81. #2447C22semidirect
82. #2447C22semidirect
83. #2447C22semidirect
84. #2444C22semidirect
85. #2439C22semidirect
86. #2433C22semidirect
87. #2431C22semidirect
88. #2431C22semidirect
89. #2428C22semidirect
90. #2427C22semidirect
91. #2427C22semidirect
92. #2427C22semidirect
93. #2424C22semidirect
94. #2422C22semidirect
95. #2420C22semidirect
96. #2420C22semidirect
97. #2420C22semidirect
98. #2415C22semidirect
99. #2415C22semidirect
100. #2414C22semidirect
102. #2408C22semidirect
103. #2407C22semidirect
104. #2407C22semidirect
105. #2407C22semidirect
106. #2407C22semidirect
107. #2404C22semidirect
109. #2366C22semidirect
110. #2366C22semidirect
111. #2364C22semidirect
113. #2363C22semidirect
114. #2363C22semidirect
115. #2363C22semidirect
116. #2360C22semidirect
117. #2359C22semidirect
118. #2358C22semidirect
119. #2354C22semidirect
120. #2354C22semidirect
121. #2352C22semidirect
122. #2352C22semidirect
123. #2351C22semidirect
124. Q8×C4⋊C4C22semidirect
125. Q8×C4⋊C4C22semidirect
126. #2349C22semidirect
127. #2342C22semidirect
130. #2341C22semidirect
131. #2341C22semidirect
132. Q8×C22⋊C4C22semidirect
133. Q8×C22⋊C4C22semidirect
134. Q8×C22⋊C4C22semidirect
135. #2339C22semidirect
136. #2339C22semidirect
137. #2339C22semidirect
138. #2339C22semidirect
140. D4×C22⋊C4C22semidirect
141. D4×C22⋊C4C22semidirect
142. C4×#127C22semidirect
143. C4×#127C22semidirect
145. C4×C22⋊Q8C22semidirect
146. C4×#123C22semidirect
148. C4×#121C22semidirect
149. C4×#121C22semidirect
150. C4×#121C22semidirect
151. C4×#121C22semidirect
152. C4×#120C22semidirect
153. #2297C22semidirect
154. #2297C22semidirect
155. #2280C22semidirect
156. C42×Q8C22semidirect
157. C42×D4C22semidirect
158. C42×D4C22semidirect
159. C2×C4×C22⋊C4C22semidirect
180. #550D4semidirect
449. C2×#41#41semidirect
504. #124#41semidirect
707. C2×Q8C2×#41semidirect
871. C22⋊C4C2×#41semidirect
872. C22⋊C4C2×#41semidirect
891. C42C2×#41semidirect
931. Q8#546semidirect

Maximal subgroups

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

subgroupindex
C2×#34832
C2×D4×#412
#595682
#594122
#590992
#590412
#590332
#590182
Q8×#1242
#364562
#364442
#364322
#364302
#364292
#364152
#364042
#361602
#361492
#361472
C4×#5502
C4×#5462
C22⋊C4×#412