Finite Group Databasebeta

← #7590723

Subgroups — #7590723

Order 512.

1277 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45329C211yesmaximal, characteristic
2#45065C211yesmaximal, characteristic
3#32221C211yesmaximal, characteristic
4#32220C211yesmaximal, characteristic
5#32220C211yesmaximal, characteristic
6#32218C211yesmaximal, characteristic
7#28821C211yesmaximal, characteristic, complemented
8#28278C211yesmaximal, characteristic, complemented
9#28028C211yesmaximal, characteristic, complemented
10#28020C211yesmaximal, characteristic, complemented
11#27846C211yesmaximal, characteristic
12#27835C211yesmaximal, characteristic
13#27797C211yesmaximal, characteristic
14#27792C211yesmaximal, characteristic
15#27642C211yesmaximal, characteristic
16#27639C211yesmaximal, characteristic
17#27137C211yesmaximal, characteristic, complemented
18#27132C211yesmaximal, characteristic, complemented
19#27128C211yesmaximal, characteristic, complemented
20#27127C211yesmaximal, characteristic, complemented
21#26029C211yesmaximal, characteristic, complemented
22#26022C211yesmaximal, characteristic, complemented
23#25000C211yesmaximal, characteristic, complemented
24#24996C211yesmaximal, characteristic, complemented
25#23167C211yesmaximal, characteristic, complemented
26#23161C211yesmaximal, characteristic, complemented
27#22818C211yesmaximal, characteristic, complemented
28#22729C211yesmaximal, characteristic, complemented
29#21605C211yesmaximal, characteristic
30#21530C211yesmaximal, characteristic
31#20822C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#500C2211yescharacteristic
34C2×#467C2211yescharacteristic
35C2×#446C2211yescharacteristic
36C2×#441C2211yescharacteristic
37C2×#405C2211yescharacteristic
38#2810—21no—
39#2798—21no—
40#2783—21no—
41#2776—21no—
42#2767—21no—
43#2759—21no—
44#2758—21no—
45#2716—21no—
46#2605—21no—
47#2604—21no—
48#2588—21no—
49#2582C2211yescharacteristic
50#2581—21no—
51#2581C2211yescharacteristic
52#2551C2211yescharacteristic
53#2550C2211yescharacteristic
54#2525—21no—
55#2514C2211yescharacteristic
56#2511C2211yescharacteristic
57#2511C2211yescharacteristic
58#2511C2211yescharacteristic
59#2497C2211yescharacteristic
60#2496C2211yescharacteristic
61#2496C2211yescharacteristic
62#2495C2211yescharacteristic
63#2492C2211yescharacteristic
64#2492C2211yescharacteristic
65#2492C2211yescharacteristic
66#2489C2211yescharacteristic
67#2469—21no—
68#2469—21no—
69#2446—21no—
70#2396C2211yescharacteristic
71#2370C2211yescharacteristic
72#2369C2211yescharacteristic
73#2365C2211yescharacteristic
74#2365C2211yescharacteristic
75#2356C2211yescharacteristic
76#2355C2211yescharacteristic
77#2355C2211yescharacteristic
78Q8×C4⋊C4C2211yescharacteristic
79#2323C2211yescharacteristic
80#2323C2211yescharacteristic
81#2314C2211yescharacteristic
82#2314C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2077C2211yescharacteristic
88#2077C2211yescharacteristic
89#2077C2211yescharacteristic
90#2075C2211yescharacteristic
91#2074C2211yescharacteristic
92#2072C2211yescharacteristic
93#2072C2211yescharacteristic
94#2072C2211yescharacteristic
95#2068C2211yescharacteristic
96#2068C2211yescharacteristic
97#2068C2211yescharacteristic
98#2066C2211yescharacteristic
99#2066C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2059C2211yescharacteristic
104#2058C2211yescharacteristic
105#2057C2211yescharacteristic
106#2057C2211yescharacteristic
107#2036C2211yescharacteristic
108#2036C2211yescharacteristic
109#2036C2211yescharacteristic
110#2035C2211yescharacteristic
111#2026C2211yescharacteristic
112#2024C2211yescharacteristic
113#2024C2211yescharacteristic
114#2024C2211yescharacteristic
115#1989C2211yescharacteristic
116#1988C2211yescharacteristic
117#1988C2211yescharacteristic
118#1988C2211yescharacteristic
119#1984C2211yescharacteristic
120#1971C2211yescharacteristic
121#1971C2211yescharacteristic
122#1971C2211yescharacteristic
123#1969C2211yescharacteristic
124#1969C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1948C2211yescharacteristic
129#1948C2211yescharacteristic
130#1948C2211yescharacteristic
131#1947C2211yescharacteristic
132#1947C2211yescharacteristic
133#1944C2211yescharacteristic
134#1943C2211yescharacteristic
135#1943C2211yescharacteristic
136#1941C2211yescharacteristic
137#1941C2211yescharacteristic
138#1939C2211yescharacteristic
139#1933C2211yescharacteristic
140#1933C2211yescharacteristic
141#1928C2211yescharacteristic
142#1928C2211yescharacteristic
143#1928C2211yescharacteristic
144#1928C2211yescharacteristic
145#1928C2211yescharacteristic
146#1928C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1920C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1918C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1894C2211yescharacteristic
168#1894C2211yescharacteristic
169#1851C2211yescharacteristic
170#1851C2211yescharacteristic
171#1847C2211yescharacteristic
172#1847C2211yescharacteristic
173#1847C2211yescharacteristic
174#1844C2211yescharacteristic
175#1835C2211yescharacteristic
176#1834C2211yescharacteristic
177#1809C2211yescharacteristic
178#1809C2211yescharacteristic
179#1808C2211yescharacteristic
180#1807C2211yescharacteristic
181#1807C2211yescharacteristic
182#1805C2211yescharacteristic
183#1805C2211yescharacteristic
184#1803C2211yescharacteristic
185#1803C2211yescharacteristic
186#1798C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C4×#107C2211yescharacteristic
194C4×#106C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1770C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201#1752C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C4×Q8—21no—
216C2×C4×Q8—21no—
217C2×C4×Q8—21no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×#117C2311yescharacteristic
222#501—24no—
223#500—24no—
224#467—24no—
225#446—24no—
226#441—24no—
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C22⋊C8C2311yescharacteristic
268#405—24no—
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277#401—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400D411yescharacteristic
295#399D411yescharacteristic
296#398—21no—
297#398—21no—
298#398—21no—
299#398D411yescharacteristic
300#398D411yescharacteristic
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#396—21no—
306#396D411yescharacteristic
307#396D411yescharacteristic
308#395—21no—
309#395—21no—
310#395—21no—
311#395—21no—
312#395D411yescharacteristic
313#393—21no—
314#393—21no—
315#393—21no—
316#393D411yescharacteristic
317#391—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—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#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#383—21no—
407#383—21no—
408#383—21no—
409#382—21no—
410#382—21no—
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443#376—21no—
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#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8C2×D411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C23×C4C2411yescharacteristic
491C2×Q16—22no—
492C2×Q16—22no—
493C2×Q16—22no—
494C2×M16—22no—
495C2×M16—41no—
496C2×M16—41no—
497C22×C8—22no—
498C22×C8—22no—
499C22×C8—22no—
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C4⋊Q8—22no—
509C4⋊Q8—22no—
510C4⋊Q8—22no—
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514C4⋊Q8—82no—
515#126—82no—
516#126—82no—
517#125—22no—
518#125—41no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—41no—
522C22⋊Q8—41no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—82no—
530C4×Q8—82no—
531C4×Q8—82no—
532#117—22no—
533#117—22no—
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⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4C2×D411yescharacteristic
597C2×C22⋊C4C2×D411yescharacteristic
598C2×C22⋊C4C2×D411yescharacteristic
599C2×C22⋊C4C2×D411yescharacteristic
600C2×C22⋊C4C2×D411yescharacteristic
601C2×C22⋊C4C2×D411yescharacteristic
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624#107—22no—
625#107—22no—
626#107—22no—
627#107—22no—
628#107—22no—
629#107—41no—
630#107—41no—
631#107—41no—
632#107#4114yes—
633#106—22no—
634#106—22no—
635#106—22no—
636#106—22no—
637#106—22no—
638#106—41no—
639#106—41no—
640#106—41no—
641#106—41no—
642#106—41no—
643C4⋊C8—22no—
644C4⋊C8—22no—
645C4⋊C8—22no—
646C4⋊C8—22no—
647C4⋊C8—41no—
648C4⋊C8—41no—
649#103—22no—
650#103—22no—
651#103—22no—
652#103—22no—
653#103—41no—
654#103—41no—
655#103—41no—
656#103—41no—
657#103—41no—
658#103—41no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663C22⋊C8—41no—
664C22⋊C8—41no—
665#97—22no—
666#97—22no—
667#97—22no—
668#97#4114yes—
669C4×C8—22no—
670C4×C8—22no—
671C4×C8—22no—
672C4×C8—22no—
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#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739C24C22×D411yescharacteristic
740C2×Q8—22no—
741C2×Q8—22no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—41no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8—81no—
761C2×Q8—81no—
762C2×Q8—81no—
763C2×Q8—81no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C2511yescharacteristic
800Q16—44no—
801M16—44no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—44no—
823C2×C8C2×#4112yes—
824C2×C8C2×#4112yes—
825C2×C8C2×#4112yes—
826C2×C82−1+412yes—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—41no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4C2×#4112yes—
894C4⋊C4C2×#4112yes—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—41no—
900C22⋊C4—41no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—81no—
904C22⋊C4—81no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42—42no—
921C42—42no—
922C42—42no—
923C42—42no—
924C42—81no—
925C42—81no—
926C42—81no—
927C42—81no—
928C42—81no—
929C42—81no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42C2×#4112yes—
936C422−1+412yes—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23C23×D411yescharacteristic
945Q8—44no—
946Q8—41no—
947Q8—41no—
948Q8—41no—
949Q8—41no—
950Q8—41no—
951Q8—41no—
952Q8—41no—
953Q8—41no—
954Q8—84no—
955Q8—84no—
956Q8—162no—
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—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
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—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4#54712yes—
1045C2×C4#54712yes—
1046C2×C4#57712yes—
1047C2×C4#57812yes—
1048C2×C4C22×#4111yescharacteristic
1049C2×C4C22×#4111yescharacteristic
1050C2×C4C2×2−1+411yescharacteristic
1051C2×C4C2×2−1+411yescharacteristic
1052C2×C4#58511yescharacteristic
1053C2×C4#58511yescharacteristic
1054C8—22no—
1055C8—41no—
1056C8—41no—
1057C8—41no—
1058C8—41no—
1059C8—41no—
1060C8—41no—
1061C8#55614yes—
1062C22—41no—
1063C22—41no—
1064C22—41no—
1065C22—41no—
1066C22—41no—
1067C22—41no—
1068C22—41no—
1069C22C2×#54711yescharacteristic
1070C22D4×#4111yescharacteristic
1071C22#349711yescharacteristic
1072C22C2×#57711yescharacteristic
1073C22C2×#57811yescharacteristic
1074C22#358511yescharacteristic
1075C22#358611yescharacteristic
1076C4—22no—
1077C4—22no—
1078C4—22no—
1079C4—22no—
1080C4—41no—
1081C4—42no—
1082C4—42no—
1083C4—41no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—81no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4C2×#55611yescharacteristic
1106C4#349311yescharacteristic
1107C4#351811yescharacteristic
1108C4#355511yescharacteristic
1109C2—81no—
1110C2#5924411yescharacteristic
1111C2#6127311yescharacteristic
1112C2#6128111yescharacteristic
1113C2#6152211yescharacteristic
1114C2#6154411yescharacteristic
1115C2#6238211yescharacteristic
1116C2#6239011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
7. #28821C2semidirect
8. #28278C2semidirect
9. #28028C2semidirect
10. #28020C2semidirect
17. #27137C2semidirect
18. #27132C2semidirect
19. #27128C2semidirect
20. #27127C2semidirect
21. #26029C2semidirect
22. #26022C2semidirect
23. #25000C2semidirect
24. #24996C2semidirect
25. #23167C2semidirect
26. #23161C2semidirect
27. #22818C2semidirect
28. #22729C2semidirect

Maximal subgroups

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

subgroupindex
#453292
#450652
#322212
#322202
#322182
#288212
#282782
#280282
#280202
#278462
#278352
#277972
#277922
#276422
#276392
#271372
#271322
#271282
#271272
#260292
#260222
#250002
#249962
#231672
#231612
#228182
#227292
#216052
#215302
#208222