Finite Group Databasebeta

← #6606532

Subgroups — #6606532

Order 512.

1771 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3349C211yesmaximal, characteristic, complemented
2C2×#2966C211yesmaximal, characteristic
3#38051C211yesmaximal, characteristic
4#38048C211yesmaximal, characteristic
5#33219C211yesmaximal, characteristic, complemented
6#33141C211yesmaximal, characteristic, complemented
7#33130C211yesmaximal, characteristic, complemented
8#28686C211yesmaximal, characteristic, complemented
9#28278C211yesmaximal, characteristic, complemented
10#27671C211yesmaximal, characteristic, complemented
11#27664C211yesmaximal, characteristic, complemented
12#25474C211yesmaximal, characteristic, complemented
13#25471C211yesmaximal, characteristic, complemented
14#25239C211yesmaximal, characteristic, complemented
15#25239C211yesmaximal, characteristic, complemented
16#25234C211yesmaximal, characteristic, complemented
17#25233C211yesmaximal, characteristic, complemented
18#24793C211yesmaximal, characteristic, complemented
19#24785C211yesmaximal, characteristic, complemented
20#24715C211yesmaximal, characteristic, complemented
21#24714C211yesmaximal, characteristic, complemented
22#24614C211yesmaximal, characteristic, complemented
23#24613C211yesmaximal, characteristic, complemented
24#24611C211yesmaximal, characteristic, complemented
25#24611C211yesmaximal, characteristic, complemented
26#22660C211yesmaximal, characteristic, complemented
27#22490C211yesmaximal, characteristic, complemented
28#22486C211yesmaximal, characteristic, complemented
29#21542C211yesmaximal, characteristic, complemented
30#21160C211yesmaximal, characteristic, complemented
31#21151C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#3349—28no—
36C2×#501C2211yescharacteristic
37C2×#484C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#485C2211yescharacteristic
40C2×#485C2211yescharacteristic
41C2×#479C2211yescharacteristic
42C2×#477C2211yescharacteristic
43C2×#470C2211yescharacteristic
44C2×#470C2211yescharacteristic
45C2×#467C2211yescharacteristic
46#2966—28no—
47C2×#446C2211yescharacteristic
48C2×C8×Q8C2211yescharacteristic
49C2×#441C2211yescharacteristic
50C2×#436C2211yescharacteristic
51C2×#435C2211yescharacteristic
52C2×#435C2211yescharacteristic
53C2×C8×D4C2211yescharacteristic
54C2×C8×D4C2211yescharacteristic
55C2×C8×D4C2211yescharacteristic
56C2×#433C2211yescharacteristic
57C2×#433C2211yescharacteristic
58C2×#432C2211yescharacteristic
59C2×#428C2211yescharacteristic
60C2×#428C2211yescharacteristic
61C2×#427C2211yescharacteristic
62C2×#427C2211yescharacteristic
63C2×#405C2211yescharacteristic
64C2×#405C2211yescharacteristic
65C22×C4×C8C2211yescharacteristic
66#2855C2211yescharacteristic
67#2855C2211yescharacteristic
68#2724—21no—
69#2718—21no—
70#2718—21no—
71#2717—21no—
72#2701—21no—
73#2698—21no—
74#2689—21no—
75#2686—21no—
76#2629C2211yescharacteristic
77#2628C2211yescharacteristic
78#2625C2211yescharacteristic
79#2625C2211yescharacteristic
80#2584C2211yescharacteristic
81#2582C2211yescharacteristic
82#2581C2211yescharacteristic
83#2567C2211yescharacteristic
84#2521—21no—
85#2519—21no—
86#2506—21no—
87#2496—21no—
88#2487C2211yescharacteristic
89#2485C2211yescharacteristic
90#2485C2211yescharacteristic
91#2485C2211yescharacteristic
92#2478—21no—
93#2474—21no—
94#2469—21no—
95#2462—21no—
96#2417C2211yescharacteristic
97#2415C2211yescharacteristic
98#2415C2211yescharacteristic
99#2415C2211yescharacteristic
100#2354C2211yescharacteristic
101#2352C2211yescharacteristic
102#2323C2211yescharacteristic
103#2323C2211yescharacteristic
104#2317C2211yescharacteristic
105#2316C2211yescharacteristic
106#2296C2211yescharacteristic
107#2296C2211yescharacteristic
108#2088C2211yescharacteristic
109#2088C2211yescharacteristic
110#2088C2211yescharacteristic
111#2087C2211yescharacteristic
112#2087C2211yescharacteristic
113#2087C2211yescharacteristic
114#2086C2211yescharacteristic
115#2086C2211yescharacteristic
116#2077C2211yescharacteristic
117#2076C2211yescharacteristic
118#2075C2211yescharacteristic
119#2075C2211yescharacteristic
120#2068C2211yescharacteristic
121#2068C2211yescharacteristic
122#2068C2211yescharacteristic
123#2068C2211yescharacteristic
124#2068C2211yescharacteristic
125#2066C2211yescharacteristic
126#2066C2211yescharacteristic
127#2066C2211yescharacteristic
128#2036C2211yescharacteristic
129#2036C2211yescharacteristic
130#2036C2211yescharacteristic
131#2035C2211yescharacteristic
132#1991C2211yescharacteristic
133#1990C2211yescharacteristic
134#1989C2211yescharacteristic
135#1988C2211yescharacteristic
136#1971C2211yescharacteristic
137#1969C2211yescharacteristic
138#1969C2211yescharacteristic
139#1949C2211yescharacteristic
140#1947C2211yescharacteristic
141#1944C2211yescharacteristic
142#1944C2211yescharacteristic
143#1944C2211yescharacteristic
144#1943C2211yescharacteristic
145#1943C2211yescharacteristic
146#1943C2211yescharacteristic
147#1943C2211yescharacteristic
148#1942C2211yescharacteristic
149#1942C2211yescharacteristic
150#1942C2211yescharacteristic
151#1942C2211yescharacteristic
152#1942C2211yescharacteristic
153#1942C2211yescharacteristic
154#1942C2211yescharacteristic
155#1941C2211yescharacteristic
156#1941C2211yescharacteristic
157#1941C2211yescharacteristic
158#1941C2211yescharacteristic
159#1941C2211yescharacteristic
160#1935C2211yescharacteristic
161#1935C2211yescharacteristic
162#1935C2211yescharacteristic
163#1935C2211yescharacteristic
164#1933C2211yescharacteristic
165#1933C2211yescharacteristic
166#1933C2211yescharacteristic
167#1933C2211yescharacteristic
168#1933C2211yescharacteristic
169#1933C2211yescharacteristic
170#1892C2211yescharacteristic
171#1892C2211yescharacteristic
172#1892C2211yescharacteristic
173#1892C2211yescharacteristic
174#1892C2211yescharacteristic
175#1892C2211yescharacteristic
176#1873C2211yescharacteristic
177#1873C2211yescharacteristic
178#1873C2211yescharacteristic
179#1872C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1852C2211yescharacteristic
184#1847C2211yescharacteristic
185#1825C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1823C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic
192#1809C2211yescharacteristic
193#1808C2211yescharacteristic
194#1808C2211yescharacteristic
195#1807C2211yescharacteristic
196#1805C2211yescharacteristic
197#1803C2211yescharacteristic
198#1776C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203#1735C2211yescharacteristic
204C2×#340C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#556—24no—
213#556—24no—
214#552—24no—
215#552—24no—
216C2×C4⋊Q8C2311yescharacteristic
217#529—24no—
218#529—24no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#126—21no—
222C2×#126D411yescharacteristic
223C2×#126D411yescharacteristic
224C2×#125—21no—
225C2×#125D411yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124—21no—
228C2×#124D411yescharacteristic
229C2×#123—21no—
230C2×#123D411yescharacteristic
231C2×#123D411yescharacteristic
232C2×C22⋊Q8D411yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×#121D411yescharacteristic
240C2×C4×Q8—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117—21no—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C42C2311yescharacteristic
259#501—24no—
260#485—24no—
261#485—24no—
262#485—24no—
263#484—24no—
264#479—24no—
265#477—24no—
266#470—24no—
267#470—24no—
268#467—24no—
269#446—24no—
270C8×Q8—24no—
271#441—24no—
272#436—24no—
273#435—24no—
274#435D418yes—
275C8×D4—24no—
276C8×D4—24no—
277C8×D4—24no—
278#433—24no—
279#433—24no—
280#432—24no—
281#428—24no—
282#428—24no—
283#427—24no—
284#427—24no—
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330#405—24no—
331#405—24no—
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×C4×C8—24no—
337C2×C4×C8C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339C2×C4×C8C2311yescharacteristic
340C2×C4×C8C2311yescharacteristic
341C2×C4×C8C2311yescharacteristic
342C2×C4×C8C2311yescharacteristic
343#400—21no—
344#400—21no—
345#400—21no—
346#400—21no—
347#400—21no—
348#399—21no—
349#399—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398—21no—
356#398—21no—
357#398—21no—
358#397—21no—
359#397—21no—
360#397—21no—
361#397—21no—
362#397—21no—
363#397—21no—
364#397—21no—
365#397—21no—
366#397—21no—
367#397—21no—
368#396—21no—
369#396—21no—
370#396—21no—
371#395—21no—
372#395—21no—
373#395—21no—
374#395—21no—
375#395—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394—21no—
382#393—21no—
383#391—21no—
384#391—21no—
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#390—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#384—21no—
458#384—21no—
459#384C2311yescharacteristic
460#382—21no—
461#382C2311yescharacteristic
462#381—21no—
463#381—21no—
464#380—21no—
465#380—21no—
466#380—21no—
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477C4×C4⋊C4—21no—
478C4×C4⋊C4—21no—
479C4×C4⋊C4—21no—
480C4×C4⋊C4—21no—
481C4×C4⋊C4—21no—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C22⋊C4—21no—
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#340C2311yescharacteristic
514#340C2311yescharacteristic
515C22×Q8—21no—
516C22×Q8C2×D411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16C2×D414yes—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—22no—
545C22×C8—22no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8C2×D414yes—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560#126—24no—
561#126—24no—
562#126—44no—
563#126—44no—
564#126—44no—
565#125—24no—
566#125—22no—
567#125—22no—
568#125—44no—
569#124—24no—
570#124—44no—
571#123—24no—
572#123—24no—
573#123—44no—
574C22⋊Q8—24no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587#121—24no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—44no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4C2×D414yes—
600C4×D4#4114yes—
601#117—22no—
602#117—22no—
603#117—22no—
604#117—22no—
605#117—22no—
606#117—22no—
607#117—22no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—22no—
612#117—22no—
613#117—22no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—44no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—22no—
730#107—22no—
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—22no—
736#107—22no—
737#107—22no—
738#107—22no—
739#107—41no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—22no—
746#106—41no—
747#106#4114yes—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753C4⋊C8C2×D414yes—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8C2×D414yes—
773C22⋊C8C2×D414yes—
774#97—22no—
775#97—22no—
776#97—22no—
777#97C2×D414yes—
778C4×C8—22no—
779C4×C8—22no—
780C4×C8—22no—
781C4×C8—22no—
782C4×C8—22no—
783C4×C8—22no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828C24C22×D411yescharacteristic
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—41no—
846C2×Q8—42no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4#12114yes—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D412yes—
911C22×C4C22×D412yes—
912C22×C4C22×D411yescharacteristic
913C22×C4C2×#4112yes—
914C22×C4C2×#4112yes—
915C22×C4C2511yescharacteristic
916Q16—44no—
917M16—28no—
918M16—44no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—28no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—44no—
938C2×C8—44no—
939C2×C8—44no—
940C2×C8C22×D412yes—
941C2×C8C22×D412yes—
942C2×C8C22×D412yes—
943C2×C8C22×D412yes—
944C2×C8C2×#4112yes—
945C2×C82−1+412yes—
946C2×C82−1+412yes—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4#12114yes—
1016C4⋊C4C2×#4112yes—
1017C4⋊C4C2×#4112yes—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4#12114yes—
1049C22⋊C4#12114yes—
1050C42—22no—
1051C42—22no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—42no—
1059C42—42no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—42no—
1064C42—42no—
1065C42—42no—
1066C42—81no—
1067C42—81no—
1068C42C22×D412yes—
1069C42C2×#4112yes—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23C2×#12112yes—
1090C23C2×#12112yes—
1091C23C23×D411yescharacteristic
1092Q8—44no—
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—84no—
1102D4—44no—
1103D4—44no—
1104D4—44no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—44no—
1144C2×C4—44no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—84no—
1196C2×C4—162no—
1197C2×C4C2×#12112yes—
1198C2×C4C2×#12112yes—
1199C2×C4C2×#12112yes—
1200C2×C4C2×#12112yes—
1201C2×C4#57812yes—
1202C2×C4C23×D411yescharacteristic
1203C2×C4C22×#4111yescharacteristic
1204C2×C4C22×#4111yescharacteristic
1205C2×C4C2×2−1+411yescharacteristic
1206C2×C4C2×2−1+411yescharacteristic
1207C2×C4#58511yescharacteristic
1208C8—22no—
1209C8—22no—
1210C8—22no—
1211C8—22no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C8#54714yes—
1216C22—22no—
1217C22—22no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22C22×#12111yescharacteristic
1238C22D4×#4111yescharacteristic
1239C22#349911yescharacteristic
1240C22C2×#57811yescharacteristic
1241C22#358411yescharacteristic
1242C22#358411yescharacteristic
1243C22#358411yescharacteristic
1244C4—22no—
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—42no—
1255C4—42no—
1256C4—41no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4C2×#54711yescharacteristic
1272C4#348211yescharacteristic
1273C4#348911yescharacteristic
1274C4#351511yescharacteristic
1275C2—42no—
1276C2—42no—
1277C2—81no—
1278C2#3625911yescharacteristic
1279C2#6045311yescharacteristic
1280C2#6045911yescharacteristic
1281C2#6149211yescharacteristic
1282C2#6150011yescharacteristic
1283C2#6248911yescharacteristic
1284C2#6249611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3349C2semidirect
5. #33219C2semidirect
6. #33141C2semidirect
7. #33130C2semidirect
8. #28686C2semidirect
9. #28278C2semidirect
10. #27671C2semidirect
11. #27664C2semidirect
12. #25474C2semidirect
13. #25471C2semidirect
14. #25239C2semidirect
15. #25239C2semidirect
16. #25234C2semidirect
17. #25233C2semidirect
18. #24793C2semidirect
19. #24785C2semidirect
20. #24715C2semidirect
21. #24714C2semidirect
22. #24614C2semidirect
23. #24613C2semidirect
24. #24611C2semidirect
25. #24611C2semidirect
26. #22660C2semidirect
27. #22490C2semidirect
28. #22486C2semidirect
29. #21542C2semidirect
30. #21160C2semidirect
31. #21151C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33492
C2×#29662
#380512
#380482
#332192
#331412
#331302
#286862
#282782
#276712
#276642
#254742
#254712
#252392
#252342
#252332
#247932
#247852
#247152
#247142
#246142
#246132
#246112
#226602
#224902
#224862
#215422
#211602
#211512