Finite Group Databasebeta

← #6795444

Subgroups — #6795444

Order 512.

1254 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36199C211yesmaximal, characteristic
2#34948C211yesmaximal, characteristic
3#33152C211yesmaximal, characteristic
4#32397C211yesmaximal, characteristic, complemented
5#32393C211yesmaximal, characteristic, complemented
6#32381C211yesmaximal, characteristic, complemented
7#32377C211yesmaximal, characteristic, complemented
8#32331C211yesmaximal, characteristic, complemented
9#32327C211yesmaximal, characteristic, complemented
10#32317C211yesmaximal, characteristic, complemented
11#32313C211yesmaximal, characteristic, complemented
12#29911C211yesmaximal, characteristic
13#29911C211yesmaximal, characteristic
14#28838C211yesmaximal, characteristic, complemented
15#28837C211yesmaximal, characteristic, complemented
16#27954C211yesmaximal, characteristic
17#27741C211yesmaximal, characteristic, complemented
18#27741C211yesmaximal, characteristic, complemented
19#27682C211yesmaximal, characteristic
20#27618C211yesmaximal, characteristic
21#27615C211yesmaximal, characteristic
22#26525C211yesmaximal, characteristic, complemented
23#26523C211yesmaximal, characteristic, complemented
24#26105C211yesmaximal, characteristic, complemented
25#26105C211yesmaximal, characteristic, complemented
26#24611C211yesmaximal, characteristic
27#24604C211yesmaximal, characteristic
28#22601C211yesmaximal, characteristic
29#21989C211yesmaximal, characteristic
30#21984C211yesmaximal, characteristic
31#21583C211yesmaximal, characteristic
32C2×#485C2211yescharacteristic
33C2×#432C2211yescharacteristic
34C2×#431C2211yescharacteristic
35#2855C2211yescharacteristic
36#2855C2211yescharacteristic
37#2851C2211yescharacteristic
38#2571C2211yescharacteristic
39#2571C2211yescharacteristic
40#2570C2211yescharacteristic
41#2570C2211yescharacteristic
42#2570C2211yescharacteristic
43#2570C2211yescharacteristic
44#2570C2211yescharacteristic
45#2569—21no—
46#2569—21no—
47#2565C2211yescharacteristic
48#2552C2211yescharacteristic
49#2552C2211yescharacteristic
50#2528—21no—
51#2524—21no—
52#2524—21no—
53#2514C2211yescharacteristic
54#2511C2211yescharacteristic
55#2508C2211yescharacteristic
56#2506C2211yescharacteristic
57#2493—21no—
58#2484—21no—
59#2473—21no—
60#2442—21no—
61#2442—21no—
62#2402—21no—
63#2402—21no—
64#2371—21no—
65#2370C2211yescharacteristic
66#2356C2211yescharacteristic
67#2343—21no—
68C4×#125—21no—
69C4×#125—21no—
70C4×C22⋊Q8C2211yescharacteristic
71#2296C2211yescharacteristic
72#2296C2211yescharacteristic
73#2285C2211yescharacteristic
74#2285C2211yescharacteristic
75#2285C2211yescharacteristic
76#2285C2211yescharacteristic
77#2283C2211yescharacteristic
78C4×#117C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2097C2211yescharacteristic
91#2097C2211yescharacteristic
92#2097C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2087C2211yescharacteristic
99#2086C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2085C2211yescharacteristic
105#2085C2211yescharacteristic
106#2084C2211yescharacteristic
107#2084C2211yescharacteristic
108#2084C2211yescharacteristic
109#2083C2211yescharacteristic
110#2083C2211yescharacteristic
111#2083C2211yescharacteristic
112#2072C2211yescharacteristic
113#2072C2211yescharacteristic
114#2072C2211yescharacteristic
115#2072C2211yescharacteristic
116#2068C2211yescharacteristic
117#2068C2211yescharacteristic
118#2066C2211yescharacteristic
119#2066C2211yescharacteristic
120#1992C2211yescharacteristic
121#1992C2211yescharacteristic
122#1989C2211yescharacteristic
123#1989C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1948C2211yescharacteristic
135#1947C2211yescharacteristic
136#1944C2211yescharacteristic
137#1943C2211yescharacteristic
138#1942C2211yescharacteristic
139#1941C2211yescharacteristic
140#1940C2211yescharacteristic
141#1940C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1933C2211yescharacteristic
145#1933C2211yescharacteristic
146#1928C2211yescharacteristic
147#1927C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1921C2211yescharacteristic
153#1920C2211yescharacteristic
154#1920C2211yescharacteristic
155#1920C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1917C2211yescharacteristic
163#1917C2211yescharacteristic
164#1916C2211yescharacteristic
165#1916C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic
168#1873C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1847C2211yescharacteristic
179#1847C2211yescharacteristic
180#1847C2211yescharacteristic
181#1847C2211yescharacteristic
182#1845C2211yescharacteristic
183#1844C2211yescharacteristic
184#1836C2211yescharacteristic
185#1836C2211yescharacteristic
186#1834C2211yescharacteristic
187#1834C2211yescharacteristic
188#1825C2211yescharacteristic
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic
191#1817C2211yescharacteristic
192#1817C2211yescharacteristic
193#1803C2211yescharacteristic
194#1803C2211yescharacteristic
195#1797C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198#1771C2211yescharacteristic
199#1771C2211yescharacteristic
200#1763C2211yescharacteristic
201#1763C2211yescharacteristic
202#1749C2211yescharacteristic
203C2×#125—21no—
204C2×#125—21no—
205C2×#125—21no—
206C2×#125C2311yescharacteristic
207C2×C22⋊Q8C2311yescharacteristic
208C2×C4×Q8C2311yescharacteristic
209C2×#117—21no—
210C2×#117C2311yescharacteristic
211C2×#117C2311yescharacteristic
212C2×#117C2311yescharacteristic
213C2×#117C2311yescharacteristic
214C22×C4⋊C4D411yescharacteristic
215C22×C4⋊C4D411yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219#485—24no—
220#432—24no—
221#431—24no—
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×C22⋊C8C2311yescharacteristic
257C2×C22⋊C8C2311yescharacteristic
258C2×C22⋊C8C2311yescharacteristic
259C2×C22⋊C8C2311yescharacteristic
260C2×#97C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×#97C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266#401—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#398—21no—
282#398—21no—
283#398—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#391C2311yescharacteristic
295#391C2311yescharacteristic
296#391C2311yescharacteristic
297#391C2311yescharacteristic
298#391C2311yescharacteristic
299#389—21no—
300#389—21no—
301#389—21no—
302#389—21no—
303#389—21no—
304#389C2311yescharacteristic
305#389C2311yescharacteristic
306#389C2311yescharacteristic
307#389C2311yescharacteristic
308#389C2311yescharacteristic
309#389C2311yescharacteristic
310#389C2311yescharacteristic
311#389C2311yescharacteristic
312#389C2311yescharacteristic
313#389C2311yescharacteristic
314#389C2311yescharacteristic
315#389C2311yescharacteristic
316#389C2311yescharacteristic
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#387—21no—
320#387—21no—
321#387—21no—
322#387—21no—
323#387—21no—
324#387—21no—
325#387—21no—
326#387—21no—
327#387—21no—
328#387—21no—
329#387—21no—
330#387—21no—
331#387—21no—
332#387—21no—
333#387—21no—
334#387—21no—
335#387—21no—
336#387—21no—
337#387—21no—
338#387—21no—
339#387—21no—
340#387—21no—
341#387—21no—
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#385—21no—
348#385—21no—
349#385—21no—
350#385—21no—
351#385—21no—
352#385—21no—
353#385—21no—
354#385—21no—
355#385—21no—
356#384C2311yescharacteristic
357#384C2311yescharacteristic
358#384C2311yescharacteristic
359#384C2311yescharacteristic
360#384C2311yescharacteristic
361#384C2311yescharacteristic
362#384C2311yescharacteristic
363#384C2311yescharacteristic
364#383—21no—
365#383—21no—
366#383—21no—
367#382—21no—
368#382—21no—
369#382—21no—
370#382—21no—
371#382C2311yescharacteristic
372#382C2311yescharacteristic
373#382C2311yescharacteristic
374#382C2311yescharacteristic
375#382C2311yescharacteristic
376#382C2311yescharacteristic
377#382C2311yescharacteristic
378#382C2311yescharacteristic
379#382C2311yescharacteristic
380#381—21no—
381#381—21no—
382#381—21no—
383#380—21no—
384#380—21no—
385#380—21no—
386#380—21no—
387#380—21no—
388#380—21no—
389#380—21no—
390#380C2311yescharacteristic
391#380C2311yescharacteristic
392#380C2311yescharacteristic
393C4×C4⋊C4—21no—
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4D411yescharacteristic
407C4×C4⋊C4D411yescharacteristic
408C4×C4⋊C4D411yescharacteristic
409C4×C4⋊C4D411yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427#376—21no—
428#376—21no—
429#376—21no—
430C2×#95D411yescharacteristic
431C2×#95D411yescharacteristic
432C43—21no—
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
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#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8C2411yescharacteristic
482C23×C4C2×D411yescharacteristic
483C23×C4C2×D411yescharacteristic
484C23×C4C2×D411yescharacteristic
485C23×C4C2×D411yescharacteristic
486C23×C4C2×D411yescharacteristic
487C23×C4C2×D411yescharacteristic
488C23×C4C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497#125—22no—
498#125—22no—
499#125—44no—
500#125—44no—
501#125—44no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C4×Q8—22no—
505C4×Q8—22no—
506#117—22no—
507#117—22no—
508#117—41no—
509#117—41no—
510#117—41no—
511#117—41no—
512#117—41no—
513#117—41no—
514#117—44no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
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—42no—
551C2×C4⋊C4—42no—
552C2×C4⋊C4C2×D411yescharacteristic
553C2×C4⋊C4C2×D411yescharacteristic
554C2×C4⋊C4C2×D411yescharacteristic
555C2×C4⋊C4C2×D411yescharacteristic
556C2×C4⋊C4C2×D411yescharacteristic
557C2×C4⋊C4C2×D411yescharacteristic
558C2×C4⋊C4C2×D411yescharacteristic
559C2×C4⋊C4C2×D411yescharacteristic
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—21no—
590C2×C42—21no—
591C2×C42—21no—
592C2×C42—21no—
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×C42—21no—
602C2×C42—21no—
603C2×C42C2×D411yescharacteristic
604C2×C42C2×D411yescharacteristic
605C2×C42C2×D411yescharacteristic
606C2×C42C2×D411yescharacteristic
607C2×C42C2×D411yescharacteristic
608C2×C42C2×D411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615#107—22no—
616#107—41no—
617#107—41no—
618#107—41no—
619#107—41no—
620#107—41no—
621#107—41no—
622#107—41no—
623#107—41no—
624#107—41no—
625#106—22no—
626#106—41no—
627#106—41no—
628#106—41no—
629#106—41no—
630#106—41no—
631#106—41no—
632#106—41no—
633#106—41no—
634#106—41no—
635C4⋊C8—22no—
636C4⋊C8—22no—
637C4⋊C8—22no—
638C4⋊C8—22no—
639C4⋊C8—22no—
640C4⋊C8—22no—
641#103—22no—
642#103—22no—
643#103—41no—
644#103—41no—
645#103—41no—
646#103—41no—
647#103—41no—
648#103—41no—
649C22⋊C8—22no—
650C22⋊C8—22no—
651C22⋊C8—22no—
652C22⋊C8#4114yes—
653#97—22no—
654#97—22no—
655#97—22no—
656#97—22no—
657C4×C8—22no—
658C4×C8—22no—
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#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722C24C22×D411yescharacteristic
723C2×Q8—21no—
724C2×Q8—21no—
725C2×Q8—21no—
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
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—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D411yescharacteristic
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C2×#4112yes—
781C22×C42−1+412yes—
782C22×C4C2511yescharacteristic
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8C2×#4112yes—
806C2×C8C2×#4112yes—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—22no—
810C4⋊C4—22no—
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—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—41no—
842C4⋊C4—41no—
843C4⋊C4—41no—
844C4⋊C4—41no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C22⋊C4—42no—
881C22⋊C4—42no—
882C22⋊C4—42no—
883C22⋊C4—42no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—42no—
888C42—22no—
889C42—22no—
890C42—22no—
891C42—22no—
892C42—22no—
893C42—22no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—21no—
904C42—42no—
905C42—42no—
906C42—42no—
907C42—42no—
908C42—42no—
909C42—42no—
910C42—42no—
911C42—42no—
912C42—42no—
913C42—42no—
914C42—81no—
915C42—81no—
916C42—81no—
917C42—81no—
918C422−1+412yes—
919C422−1+412yes—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—21no—
926C23#54712yes—
927C23C23×D411yescharacteristic
928Q8—41no—
929Q8—41no—
930Q8—41no—
931Q8—41no—
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—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—44no—
971C2×C4—44no—
972C2×C4—44no—
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—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—82no—
1022C2×C4—82no—
1023C2×C4—82no—
1024C2×C4#53612yes—
1025C2×C4#53612yes—
1026C2×C4#54712yes—
1027C2×C4#57512yes—
1028C2×C4#57512yes—
1029C2×C4C22×#4111yescharacteristic
1030C2×C4C2×2−1+411yescharacteristic
1031C2×C4C2×2−1+411yescharacteristic
1032C2×C4C2×2−1+411yescharacteristic
1033C2×C4#58511yescharacteristic
1034C2×C4#58511yescharacteristic
1035C8—22no—
1036C8—22no—
1037C8—41no—
1038C8—41no—
1039C8—41no—
1040C8—41no—
1041C8—41no—
1042C8—41no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22C2×#53611yescharacteristic
1051C22C2×#54711yescharacteristic
1052C22#348711yescharacteristic
1053C22C2×#57511yescharacteristic
1054C22C2×#57511yescharacteristic
1055C22#358411yescharacteristic
1056C22#358611yescharacteristic
1057C4—22no—
1058C4—22no—
1059C4—22no—
1060C4—22no—
1061C4—22no—
1062C4—41no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—81no—
1071C4—81no—
1072C4—81no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4#351511yescharacteristic
1087C4#351511yescharacteristic
1088C4#356311yescharacteristic
1089C4#356311yescharacteristic
1090C2—42no—
1091C2#3891911yescharacteristic
1092C2#6086211yescharacteristic
1093C2#6087611yescharacteristic
1094C2#6124311yescharacteristic
1095C2#6125311yescharacteristic
1096C2#6189711yescharacteristic
1097C2#6190811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #32397C2semidirect
5. #32393C2semidirect
6. #32381C2semidirect
7. #32377C2semidirect
8. #32331C2semidirect
9. #32327C2semidirect
10. #32317C2semidirect
11. #32313C2semidirect
14. #28838C2semidirect
15. #28837C2semidirect
17. #27741C2semidirect
18. #27741C2semidirect
22. #26525C2semidirect
23. #26523C2semidirect
24. #26105C2semidirect
25. #26105C2semidirect

Maximal subgroups

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

subgroupindex
#361992
#349482
#331522
#323972
#323932
#323812
#323772
#323312
#323272
#323172
#323132
#299112
#288382
#288372
#279542
#277412
#276822
#276182
#276152
#265252
#265232
#261052
#246112
#246042
#226012
#219892
#219842
#215832