Finite Group Databasebeta

← #6497957

Subgroups — #6497957

Order 512.

1227 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37295C211yesmaximal, characteristic
2#37291C211yesmaximal, characteristic
3#33318C211yesmaximal, characteristic, complemented
4#33262C211yesmaximal, characteristic, complemented
5#33217C211yesmaximal, characteristic
6#33217C211yesmaximal, characteristic
7#30232C211yesmaximal, characteristic, complemented
8#30232C211yesmaximal, characteristic, complemented
9#29879C211yesmaximal, characteristic
10#29877C211yesmaximal, characteristic
11#28003C211yesmaximal, characteristic, complemented
12#28002C211yesmaximal, characteristic, complemented
13#28000C211yesmaximal, characteristic, complemented
14#28000C211yesmaximal, characteristic, complemented
15#27999C211yesmaximal, characteristic, complemented
16#27998C211yesmaximal, characteristic, complemented
17#27997C211yesmaximal, characteristic, complemented
18#27996C211yesmaximal, characteristic, complemented
19#27848C211yesmaximal, characteristic
20#27847C211yesmaximal, characteristic
21#27846C211yesmaximal, characteristic
22#27845C211yesmaximal, characteristic
23#27838C211yesmaximal, characteristic
24#27837C211yesmaximal, characteristic
25#27835C211yesmaximal, characteristic
26#27835C211yesmaximal, characteristic
27#22253C211yesmaximal, characteristic, complemented
28#22252C211yesmaximal, characteristic, complemented
29#21730C211yesmaximal, characteristic, complemented
30#21730C211yesmaximal, characteristic, complemented
31#20481C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#498C2211yescharacteristic
36C2×#431C2211yescharacteristic
37C22×#97C2211yescharacteristic
38#2857C2211yescharacteristic
39#2857C2211yescharacteristic
40#2851C2211yescharacteristic
41#2851C2211yescharacteristic
42#2776—21no—
43#2769—21no—
44#2766—21no—
45#2762—21no—
46#2762—21no—
47#2758—21no—
48#2755—21no—
49#2747—21no—
50#2744—21no—
51#2739—21no—
52#2722—21no—
53#2719—21no—
54#2704—21no—
55#2698—21no—
56#2690—21no—
57#2689—21no—
58#2660C2211yescharacteristic
59#2660C2211yescharacteristic
60#2647C2211yescharacteristic
61#2647C2211yescharacteristic
62#2509C2211yescharacteristic
63#2509C2211yescharacteristic
64#2508C2211yescharacteristic
65#2508C2211yescharacteristic
66#2507C2211yescharacteristic
67#2507C2211yescharacteristic
68#2506C2211yescharacteristic
69#2506C2211yescharacteristic
70#2497C2211yescharacteristic
71#2497C2211yescharacteristic
72#2496C2211yescharacteristic
73#2496C2211yescharacteristic
74#2495C2211yescharacteristic
75#2495C2211yescharacteristic
76#2494C2211yescharacteristic
77#2494C2211yescharacteristic
78#2331C2211yescharacteristic
79#2331C2211yescharacteristic
80#2330C2211yescharacteristic
81#2330C2211yescharacteristic
82#2283C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2100C2211yescharacteristic
92#2100C2211yescharacteristic
93#2100C2211yescharacteristic
94#2100C2211yescharacteristic
95#2099C2211yescharacteristic
96#2099C2211yescharacteristic
97#2099C2211yescharacteristic
98#2099C2211yescharacteristic
99#2088C2211yescharacteristic
100#2088C2211yescharacteristic
101#2088C2211yescharacteristic
102#2088C2211yescharacteristic
103#2088C2211yescharacteristic
104#2088C2211yescharacteristic
105#2087C2211yescharacteristic
106#2086C2211yescharacteristic
107#2077C2211yescharacteristic
108#2077C2211yescharacteristic
109#2077C2211yescharacteristic
110#2077C2211yescharacteristic
111#2077C2211yescharacteristic
112#2077C2211yescharacteristic
113#2076C2211yescharacteristic
114#2075C2211yescharacteristic
115#1993C2211yescharacteristic
116#1993C2211yescharacteristic
117#1992C2211yescharacteristic
118#1992C2211yescharacteristic
119#1991C2211yescharacteristic
120#1991C2211yescharacteristic
121#1990C2211yescharacteristic
122#1990C2211yescharacteristic
123#1944C2211yescharacteristic
124#1944C2211yescharacteristic
125#1944C2211yescharacteristic
126#1944C2211yescharacteristic
127#1944C2211yescharacteristic
128#1944C2211yescharacteristic
129#1944C2211yescharacteristic
130#1944C2211yescharacteristic
131#1943C2211yescharacteristic
132#1943C2211yescharacteristic
133#1943C2211yescharacteristic
134#1943C2211yescharacteristic
135#1943C2211yescharacteristic
136#1943C2211yescharacteristic
137#1943C2211yescharacteristic
138#1943C2211yescharacteristic
139#1942C2211yescharacteristic
140#1942C2211yescharacteristic
141#1942C2211yescharacteristic
142#1942C2211yescharacteristic
143#1941C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1920C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1847C2211yescharacteristic
164#1847C2211yescharacteristic
165#1847C2211yescharacteristic
166#1847C2211yescharacteristic
167#1847C2211yescharacteristic
168#1847C2211yescharacteristic
169#1846C2211yescharacteristic
170#1846C2211yescharacteristic
171#1844C2211yescharacteristic
172#1844C2211yescharacteristic
173#1835C2211yescharacteristic
174#1834C2211yescharacteristic
175#1808C2211yescharacteristic
176#1808C2211yescharacteristic
177#1808C2211yescharacteristic
178#1808C2211yescharacteristic
179#1807C2211yescharacteristic
180#1807C2211yescharacteristic
181#1807C2211yescharacteristic
182#1807C2211yescharacteristic
183#1776C2211yescharacteristic
184#1776C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187C4×#107C2211yescharacteristic
188C4×#107C2211yescharacteristic
189C4×#106C2211yescharacteristic
190C4×#106C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1771C2211yescharacteristic
195#1752C2211yescharacteristic
196#1752C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1746C2211yescharacteristic
200#1746C2211yescharacteristic
201#1726C2211yescharacteristic
202#1726C2211yescharacteristic
203C23×C8C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#126—21no—
208C2×#126—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C22×C42C2311yescharacteristic
216#501—24no—
217#501—24no—
218#499—24no—
219#498—24no—
220#431—24no—
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C22⋊C8C2311yescharacteristic
248C2×C22⋊C8C2311yescharacteristic
249C2×#97—24no—
250C2×#97C2311yescharacteristic
251C2×#97C2311yescharacteristic
252C2×#97C2311yescharacteristic
253C2×#97C2311yescharacteristic
254C2×#97C2311yescharacteristic
255C2×#97C2311yescharacteristic
256C2×#97C2311yescharacteristic
257C2×#97C2311yescharacteristic
258C2×C4×C8C2311yescharacteristic
259C2×C4×C8C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264#401—21no—
265#401—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#396—21no—
307#396—21no—
308#395—21no—
309#395—21no—
310#395—21no—
311#395—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#383—21no—
395#383—21no—
396#383D411yescharacteristic
397#383D411yescharacteristic
398#382—21no—
399#382—21no—
400#382D411yescharacteristic
401#382D411yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#381D411yescharacteristic
409#381D411yescharacteristic
410#380—21no—
411#380—21no—
412#380D411yescharacteristic
413#380D411yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C22⋊C4C2311yescharacteristic
433C4×C22⋊C4C2311yescharacteristic
434#376C2311yescharacteristic
435#376C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C23×C4C2×D411yescharacteristic
487C23×C4C2×D411yescharacteristic
488C23×C4C2411yescharacteristic
489C22×C8—22no—
490C22×C8—22no—
491C22×C8—22no—
492C22×C8—22no—
493C22×C8—22no—
494C22×C8—22no—
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C4⋊Q8—22no—
504C4⋊Q8—22no—
505C4⋊Q8—22no—
506C4⋊Q8—22no—
507#126—82no—
508#126—82no—
509#125—22no—
510#125—22no—
511#125—22no—
512#125—22no—
513#125—82no—
514#125—82no—
515C22⋊Q8—82no—
516C22⋊Q8—82no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4C2×D411yescharacteristic
560C2×C4⋊C4C2×D411yescharacteristic
561C2×C4⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4C2×D411yescharacteristic
588C2×C22⋊C4C2×D411yescharacteristic
589C2×C22⋊C4C2×D411yescharacteristic
590C2×C22⋊C4C2×D411yescharacteristic
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42C2×D411yescharacteristic
602C2×C42C2×D411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609#107—22no—
610#107—22no—
611#107—22no—
612#107—22no—
613#107—22no—
614#107—22no—
615#107—22no—
616#107—22no—
617#107—22no—
618#107—22no—
619#106—22no—
620#106—22no—
621#106—22no—
622#106—22no—
623#106—22no—
624#106—22no—
625#106—22no—
626#106—22no—
627#106—22no—
628#106—22no—
629#106—22no—
630#106—22no—
631#106—22no—
632#106—22no—
633C4⋊C8—22no—
634C4⋊C8—22no—
635C22⋊C8—22no—
636C22⋊C8—22no—
637#97—22no—
638#97—22no—
639#97—22no—
640#97—22no—
641#97—22no—
642#97—22no—
643#97—22no—
644#97#4114yes—
645C4×C8—22no—
646C4×C8—22no—
647C4×C8—22no—
648C4×C8—22no—
649C4×C8—22no—
650C4×C8#4114yes—
651#95—21no—
652#95—21no—
653#95—21no—
654#95—21no—
655#95—21no—
656#95—21no—
657#95—21no—
658#95—21no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95C2×D411yescharacteristic
704#95C2×D411yescharacteristic
705#95C2×D411yescharacteristic
706#95C2×D411yescharacteristic
707#95C2×D411yescharacteristic
708#95C2×D411yescharacteristic
709#95C2×D411yescharacteristic
710#95C2×D411yescharacteristic
711#95C2×D411yescharacteristic
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719C24C22×D411yescharacteristic
720C2×Q8—42no—
721C2×Q8—42no—
722C2×Q8—81no—
723C2×Q8—81no—
724C2×Q8—81no—
725C2×Q8—81no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—41no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4C22×D411yescharacteristic
755C22×C4C22×D411yescharacteristic
756C22×C4C22×D411yescharacteristic
757C22×C4C22×D411yescharacteristic
758C22×C4C22×D411yescharacteristic
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C22×D411yescharacteristic
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C2511yescharacteristic
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—44no—
785C2×C8—44no—
786C2×C8C2×#4112yes—
787C2×C8C2×#4112yes—
788C2×C8C2×#4112yes—
789C2×C8C2×#4112yes—
790C2×C82−1+412yes—
791C2×C82−1+412yes—
792C2×C82−1+412yes—
793C2×C82−1+412yes—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—41no—
827C4⋊C4—41no—
828C4⋊C4—41no—
829C4⋊C4—41no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—81no—
841C4⋊C4—81no—
842C4⋊C4—81no—
843C4⋊C4—81no—
844C4⋊C4—81no—
845C4⋊C4—81no—
846C4⋊C4—81no—
847C4⋊C4—81no—
848C4⋊C4—81no—
849C4⋊C4—81no—
850C4⋊C4—81no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—41no—
875C22⋊C4—41no—
876C22⋊C4—42no—
877C22⋊C4—42no—
878C22⋊C4—42no—
879C22⋊C4—42no—
880C22⋊C4—81no—
881C22⋊C4—81no—
882C22⋊C4—81no—
883C22⋊C4—81no—
884C42—22no—
885C42—22no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—21no—
890C42—21no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—81no—
897C42—81no—
898C42—81no—
899C42—81no—
900C42—81no—
901C42—81no—
902C42—81no—
903C42—81no—
904C42C2×#4112yes—
905C42C2×#4112yes—
906C23—21no—
907C23—21no—
908C23—21no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23#57712yes—
913C23C23×D411yescharacteristic
914Q8—162no—
915Q8—162no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—44no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—82no—
1007C2×C4#53212yes—
1008C2×C4#53212yes—
1009C2×C4C22×#4111yescharacteristic
1010C2×C4C22×#4111yescharacteristic
1011C2×C4C2×2−1+411yescharacteristic
1012C2×C4C2×2−1+411yescharacteristic
1013C2×C4C2×2−1+411yescharacteristic
1014C2×C4C2×2−1+411yescharacteristic
1015C8—22no—
1016C8—22no—
1017C8—41no—
1018C8—41no—
1019C8—41no—
1020C8—41no—
1021C8#54114yes—
1022C8#54114yes—
1023C22—22no—
1024C22—22no—
1025C22—22no—
1026C22—41no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22C2×#53211yescharacteristic
1031C22#349911yescharacteristic
1032C22#349911yescharacteristic
1033C22C2×#57711yescharacteristic
1034C22#358411yescharacteristic
1035C22#358511yescharacteristic
1036C22#358611yescharacteristic
1037C4—22no—
1038C4—22no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—41no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4—81no—
1053C4—81no—
1054C4—81no—
1055C4—81no—
1056C4—81no—
1057C4—81no—
1058C4—81no—
1059C4—81no—
1060C4—81no—
1061C4—81no—
1062C4—81no—
1063C4—81no—
1064C4—81no—
1065C4—81no—
1066C4C2×#54111yescharacteristic
1067C4C2×#54111yescharacteristic
1068C4#350911yescharacteristic
1069C4#350911yescharacteristic
1070C2—42no—
1071C2#3531911yescharacteristic
1072C2#6070611yescharacteristic
1073C2#6070911yescharacteristic
1074C2#6251311yescharacteristic
1075C2#6251411yescharacteristic
1076C2#6251711yescharacteristic
1077C2#6251811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33318C2semidirect
4. #33262C2semidirect
7. #30232C2semidirect
8. #30232C2semidirect
11. #28003C2semidirect
12. #28002C2semidirect
13. #28000C2semidirect
14. #28000C2semidirect
15. #27999C2semidirect
16. #27998C2semidirect
17. #27997C2semidirect
18. #27996C2semidirect
27. #22253C2semidirect
28. #22252C2semidirect
29. #21730C2semidirect
30. #21730C2semidirect

Maximal subgroups

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

subgroupindex
#372952
#372912
#333182
#332622
#332172
#302322
#298792
#298772
#280032
#280022
#280002
#279992
#279982
#279972
#279962
#278482
#278472
#278462
#278452
#278382
#278372
#278352
#222532
#222522
#217302
#204812