Finite Group Databasebeta

← #6608507

Subgroups — #6608507

Order 512.

1389 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36307C211yesmaximal, characteristic
2#36280C211yesmaximal, characteristic
3#33270C211yesmaximal, characteristic, complemented
4#33259C211yesmaximal, characteristic, complemented
5#33136C211yesmaximal, characteristic
6#29583C211yesmaximal, characteristic, complemented
7#29581C211yesmaximal, characteristic, complemented
8#29522C211yesmaximal, characteristic, complemented
9#29520C211yesmaximal, characteristic, complemented
10#28964C211yesmaximal, characteristic, complemented
11#28961C211yesmaximal, characteristic, complemented
12#28040C211yesmaximal, characteristic, complemented
13#28039C211yesmaximal, characteristic, complemented
14#28016C211yesmaximal, characteristic, complemented
15#27998C211yesmaximal, characteristic, complemented
16#27997C211yesmaximal, characteristic, complemented
17#27933C211yesmaximal, characteristic
18#27715C211yesmaximal, characteristic
19#27713C211yesmaximal, characteristic
20#26489C211yesmaximal, characteristic, complemented
21#26071C211yesmaximal, characteristic
22#24609C211yesmaximal, characteristic
23#24606C211yesmaximal, characteristic
24#23024C211yesmaximal, characteristic
25#22922C211yesmaximal, characteristic
26#22920C211yesmaximal, characteristic
27#22609C211yesmaximal, characteristic
28C4×#501C211yesmaximal, characteristic, complemented
29#21278C211yesmaximal, characteristic, complemented
30C2×#1943C211yesmaximal, characteristic
31#20479C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#467C2211yescharacteristic
36C2×C4×Q16C2211yescharacteristic
37C2×#432C2211yescharacteristic
38C22×#107C2211yescharacteristic
39C22×#106C2211yescharacteristic
40C22×#97C2211yescharacteristic
41#2864C2211yescharacteristic
42#2863C2211yescharacteristic
43#2863C2211yescharacteristic
44#2859C2211yescharacteristic
45#2855C2211yescharacteristic
46#2855C2211yescharacteristic
47#2612—21no—
48#2606—21no—
49#2590—21no—
50#2585—21no—
51#2533—21no—
52#2533—21no—
53#2528—21no—
54#2514C2211yescharacteristic
55#2511C2211yescharacteristic
56#2509C2211yescharacteristic
57#2508C2211yescharacteristic
58#2507C2211yescharacteristic
59#2507C2211yescharacteristic
60#2503C2211yescharacteristic
61#2502C2211yescharacteristic
62#2493—21no—
63#2484—21no—
64#2473—21no—
65#2462—21no—
66#2453C2211yescharacteristic
67#2451C2211yescharacteristic
68#2442C2211yescharacteristic
69#2440C2211yescharacteristic
70#2438—21no—
71#2360—21no—
72#2360C2211yescharacteristic
73#2360C2211yescharacteristic
74#2345C2211yescharacteristic
75#2344—21no—
76#2344C2211yescharacteristic
77#2343—21no—
78#2343—21no—
79C4×C4⋊Q8C2211yescharacteristic
80C4×#125C2211yescharacteristic
81#2295C2211yescharacteristic
82#2295C2211yescharacteristic
83C2×#389C2211yescharacteristic
84C2×#389C2211yescharacteristic
85C4×#117C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2097C2211yescharacteristic
91#2097C2211yescharacteristic
92#2096C2211yescharacteristic
93#2096C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2086C2211yescharacteristic
97#2086C2211yescharacteristic
98#2085C2211yescharacteristic
99#2083C2211yescharacteristic
100#2074C2211yescharacteristic
101#2072C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2059C2211yescharacteristic
107#2057C2211yescharacteristic
108#2026C2211yescharacteristic
109#2024C2211yescharacteristic
110#1993C2211yescharacteristic
111#1992C2211yescharacteristic
112#1971C2211yescharacteristic
113#1971C2211yescharacteristic
114#1971C2211yescharacteristic
115#1971C2211yescharacteristic
116#1969C2211yescharacteristic
117#1944C2211yescharacteristic
118#1944C2211yescharacteristic
119#1944C2211yescharacteristic
120#1944C2211yescharacteristic
121#1944C2211yescharacteristic
122#1943C2211yescharacteristic
123#1943C2211yescharacteristic
124#1943C2211yescharacteristic
125#1943C2211yescharacteristic
126#1943C2211yescharacteristic
127#1943C2211yescharacteristic
128#1943C2211yescharacteristic
129#1943C2211yescharacteristic
130#1943C2211yescharacteristic
131#1943C2211yescharacteristic
132#1943C2211yescharacteristic
133#1942C2211yescharacteristic
134#1942C2211yescharacteristic
135#1941C2211yescharacteristic
136#1941C2211yescharacteristic
137#1941C2211yescharacteristic
138#1935C2211yescharacteristic
139#1935C2211yescharacteristic
140#1935C2211yescharacteristic
141#1935C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1935C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1928C2211yescharacteristic
155#1927C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1872C2211yescharacteristic
167#1872C2211yescharacteristic
168#1865C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1863C2211yescharacteristic
172#1853C2211yescharacteristic
173#1852C2211yescharacteristic
174#1847C2211yescharacteristic
175#1847C2211yescharacteristic
176#1847C2211yescharacteristic
177#1836C2211yescharacteristic
178#1836C2211yescharacteristic
179#1824C2211yescharacteristic
180#1823C2211yescharacteristic
181#1807C2211yescharacteristic
182C4×#107C2211yescharacteristic
183C4×#107C2211yescharacteristic
184C4×#106C2211yescharacteristic
185C4×#106C2211yescharacteristic
186C4×#106C2211yescharacteristic
187#1771C2211yescharacteristic
188#1771C2211yescharacteristic
189#1771C2211yescharacteristic
190#1771C2211yescharacteristic
191C4×#103C2211yescharacteristic
192C4×#103C2211yescharacteristic
193#1752C2211yescharacteristic
194#1752C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic
197#1745C2211yescharacteristic
198#1745C2211yescharacteristic
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C4×#97C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8C2311yescharacteristic
211C2×C22⋊Q8C2311yescharacteristic
212C2×C4×Q8—21no—
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×#117—21no—
216C2×#117D411yescharacteristic
217C2×#117D411yescharacteristic
218C22×C4⋊C4—21no—
219C22×C4⋊C4—21no—
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C42C2311yescharacteristic
225#501—24no—
226#484—24no—
227#483—24no—
228#467—24no—
229C4×Q16—24no—
230#432—24no—
231C2×#107—24no—
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106—24no—
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×#97—24no—
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285#401—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#400—21no—
295#400—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#395—21no—
308#395—21no—
309#391—21no—
310#391—21no—
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
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#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#387—21no—
357#387—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#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#383—21no—
403#383—21no—
404#383—21no—
405#382—21no—
406#382—21no—
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#381—21no—
411#381—21no—
412#381—21no—
413#381—21no—
414#381—21no—
415#380—21no—
416#380—21no—
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4D411yescharacteristic
425C4×C4⋊C4D411yescharacteristic
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×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4D411yescharacteristic
438C4×C22⋊C4D411yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376—21no—
442#376—21no—
443#376D411yescharacteristic
444#376D411yescharacteristic
445C2×#95—21no—
446C2×#95—21no—
447C43C2311yescharacteristic
448C43C2311yescharacteristic
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#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C2×D411yescharacteristic
495C23×C4C2×D411yescharacteristic
496C23×C4C2411yescharacteristic
497C2×Q16—22no—
498C2×Q16—22no—
499C2×Q16—22no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—22no—
503C22×C8—22no—
504C22×C8—41no—
505C22×C8#4114yes—
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C4⋊Q8—22no—
515C4⋊Q8—41no—
516#125—22no—
517#125—41no—
518#125—82no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C22⋊Q8—44no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—41no—
527C4×Q8—41no—
528C4×Q8—82no—
529#117—24no—
530#117—42no—
531#117—44no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
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⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4—44no—
580C2×C4⋊C4—82no—
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4C2×D411yescharacteristic
604C2×C22⋊C4C2×D411yescharacteristic
605C2×C22⋊C4C2×D411yescharacteristic
606C2×C22⋊C4C2×D411yescharacteristic
607C2×C42—22no—
608C2×C42—22no—
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×C42C2×D411yescharacteristic
618C2×C42C2×D411yescharacteristic
619C2×C42C2×D411yescharacteristic
620C2×C42C2×D411yescharacteristic
621C2×C42C2×D411yescharacteristic
622C2×C42C2×D411yescharacteristic
623C2×C42C2×D411yescharacteristic
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633#107—22no—
634#107—22no—
635#107—22no—
636#107—22no—
637#107—22no—
638#107—22no—
639#107—22no—
640#107—41no—
641#107#4114yes—
642#106—22no—
643#106—22no—
644#106—22no—
645#106—22no—
646#106—22no—
647#106—22no—
648#106—22no—
649#106—22no—
650#106—22no—
651#106—41no—
652C4⋊C8—22no—
653C4⋊C8—22no—
654#103—22no—
655#103—22no—
656#103—22no—
657#103—22no—
658#103—22no—
659#103—22no—
660#103—22no—
661#103—22no—
662#103—22no—
663#103—22no—
664#103—41no—
665#103—41no—
666#103—41no—
667#103—41no—
668C22⋊C8—22no—
669C22⋊C8#4114yes—
670#97—22no—
671#97—22no—
672#97—22no—
673#97—22no—
674#97—22no—
675#97—22no—
676#97—22no—
677#97—22no—
678#97—22no—
679#97—41no—
680C4×C8—22no—
681C4×C8—22no—
682C4×C8—22no—
683C4×C8—41no—
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#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748C24C22×D411yescharacteristic
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8—42no—
763C2×Q8—81no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
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×C4—21no—
787C22×C4—21no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C2×#4112yes—
816C22×C4C2×#4112yes—
817C22×C4C2511yescharacteristic
818Q16—44no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—28no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—44no—
838C2×C8C2×#4112yes—
839C2×C8C2×#4112yes—
840C2×C8C2×#4112yes—
841C2×C8C2×#4112yes—
842C2×C8C2×#4112yes—
843C2×C82−1+412yes—
844C2×C82−1+412yes—
845C4⋊C4—22no—
846C4⋊C4—22no—
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—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—41no—
874C4⋊C4—41no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4C2×#4112yes—
915C4⋊C4C2×#4112yes—
916C22⋊C4—22no—
917C22⋊C4—22no—
918C22⋊C4—22no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4#13714yes—
924C42—22no—
925C42—22no—
926C42—22no—
927C42—22no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—41no—
941C42—41no—
942C42—41no—
943C42—41no—
944C42—41no—
945C42—41no—
946C42—42no—
947C42—42no—
948C42—42no—
949C42—42no—
950C42—81no—
951C42—81no—
952C42—81no—
953C42—81no—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23#53212yes—
959C23C2×#13712yes—
960C23#57512yes—
961C23C23×D411yescharacteristic
962Q8—41no—
963Q8—41no—
964Q8—41no—
965Q8—41no—
966Q8—41no—
967Q8—41no—
968Q8—41no—
969Q8—41no—
970Q8—84no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
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—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—44no—
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—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—82no—
1061C2×C4—84no—
1062C2×C4—84no—
1063C2×C4—84no—
1064C2×C4—162no—
1065C2×C4#53212yes—
1066C2×C4C2×#13712yes—
1067C2×C4C2×#13712yes—
1068C2×C4C22×#4111yescharacteristic
1069C2×C4C22×#4111yescharacteristic
1070C2×C4C22×#4111yescharacteristic
1071C2×C4C2×2−1+411yescharacteristic
1072C2×C4C2×2−1+411yescharacteristic
1073C2×C4#58511yescharacteristic
1074C8—22no—
1075C8—22no—
1076C8—22no—
1077C8—22no—
1078C8—41no—
1079C8—41no—
1080C8—41no—
1081C8#55214yes—
1082C22—22no—
1083C22—22no—
1084C22—22no—
1085C22—22no—
1086C22—22no—
1087C22—22no—
1088C22#317214yes—
1089C22C2×#53211yescharacteristic
1090C22D4×#4111yescharacteristic
1091C22#349911yescharacteristic
1092C22C22×#13711yescharacteristic
1093C22C2×#57511yescharacteristic
1094C22#358511yescharacteristic
1095C22#358611yescharacteristic
1096C4—22no—
1097C4—22no—
1098C4—22no—
1099C4—41no—
1100C4—41no—
1101C4—41no—
1102C4—41no—
1103C4—42no—
1104C4—42no—
1105C4—41no—
1106C4—41no—
1107C4—41no—
1108C4—41no—
1109C4—41no—
1110C4—41no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4C2×#55211yescharacteristic
1126C4#348211yescharacteristic
1127C4#349511yescharacteristic
1128C4#351511yescharacteristic
1129C2—24no—
1130C2#3626511yescharacteristic
1131C2C2×#317211yescharacteristic
1132C2#6070911yescharacteristic
1133C2#6145411yescharacteristic
1134C2#6145711yescharacteristic
1135C2#6250411yescharacteristic
1136C2#6250511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33270C2semidirect
4. #33259C2semidirect
6. #29583C2semidirect
7. #29581C2semidirect
8. #29522C2semidirect
9. #29520C2semidirect
10. #28964C2semidirect
11. #28961C2semidirect
12. #28040C2semidirect
13. #28039C2semidirect
14. #28016C2semidirect
15. #27998C2semidirect
16. #27997C2semidirect
20. #26489C2semidirect
28. C4×#501C2semidirect
29. #21278C2semidirect

Maximal subgroups

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

subgroupindex
#363072
#362802
#332702
#332592
#331362
#295832
#295812
#295222
#295202
#289642
#289612
#280402
#280392
#280162
#279982
#279972
#279332
#277152
#277132
#264892
#260712
#246092
#246062
#230242
#229222
#229202
#226092
C4×#5012
#212782
C2×#19432
#204792