Finite Group Databasebeta

← #7509399

Subgroups — #7509399

Order 512.

1381 conjugacy classes of subgroups.

The subgroup lattice has 1193 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35613C211yesmaximal, characteristic, complemented
2#35553C211yesmaximal, characteristic
3#32428C211yesmaximal, characteristic, complemented
4#32408C211yesmaximal, characteristic, complemented
5#32381C211yesmaximal, characteristic, complemented
6#32344C211yesmaximal, characteristic, complemented
7#32311C211yesmaximal, characteristic, complemented
8#32280C211yesmaximal, characteristic, complemented
9#32259C211yesmaximal, characteristic, complemented
10#32205C211yesmaximal, characteristic, complemented
11#32002C211yesmaximal, characteristic
12#31934C211yesmaximal, characteristic, complemented
13#31693C211yesmaximal, characteristic, complemented
14#31610C211yesmaximal, characteristic, complemented
15#31329C211yesmaximal, characteristic, complemented
16#31092C211yesmaximal, characteristic, complemented
17#30671C211yesmaximal, characteristic, complemented
18#30558C211yesmaximal, characteristic
19#23845C211yesmaximal, characteristic, complemented
20#23789C211yesmaximal, characteristic, complemented
21#23769C211yesmaximal, characteristic, complemented
22#23763C211yesmaximal, characteristic, complemented
23#23760C211yesmaximal, characteristic, complemented
24#23707C211yesmaximal, characteristic, complemented
25#21619C211yesmaximal, characteristic, complemented
26#21588C211yesmaximal, characteristic, complemented
27C4×#465C211yesmaximal, characteristic, complemented
28#21369C211yesmaximal, characteristic, complemented
29#21133C211yesmaximal, characteristic, complemented
30#21103C211yesmaximal, characteristic, complemented
31#20816C211yesmaximal, characteristic, complemented
32C2×#482C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×C4×SD16C2211yescharacteristic
36C2×#433C2211yescharacteristic
37C22×C4×C8C2211yescharacteristic
38#2590—21no—
39#2577—21no—
40#2575—21no—
41#2575—21no—
42#2570C2211yescharacteristic
43#2563C2211yescharacteristic
44#2560—21no—
45#2553—21no—
46#2542C2211yescharacteristic
47#2535C2211yescharacteristic
48#2517—21no—
49#2515—21no—
50#2511C2211yescharacteristic
51#2508—21no—
52#2507C2211yescharacteristic
53#2502C2211yescharacteristic
54#2497C2211yescharacteristic
55#2496C2211yescharacteristic
56#2496C2211yescharacteristic
57#2489C2211yescharacteristic
58#2488—21no—
59#2486C2211yescharacteristic
60#2478—21no—
61#2477—21no—
62#2471—21no—
63#2470—21no—
64#2467—21no—
65#2450—21no—
66#2441C2211yescharacteristic
67#2422C2211yescharacteristic
68#2420C2211yescharacteristic
69#2415C2211yescharacteristic
70#2331C2211yescharacteristic
71#2330C2211yescharacteristic
72#2324C2211yescharacteristic
73#2323C2211yescharacteristic
74#2320C2211yescharacteristic
75#2314C2211yescharacteristic
76C4×C22⋊Q8C2211yescharacteristic
77C4×#121C2211yescharacteristic
78#2290C2211yescharacteristic
79#2285C2211yescharacteristic
80#2285C2211yescharacteristic
81#2275C2211yescharacteristic
82#2274C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2097C2211yescharacteristic
88#2097C2211yescharacteristic
89#2096C2211yescharacteristic
90#2094C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2084C2211yescharacteristic
97#2084C2211yescharacteristic
98#2084C2211yescharacteristic
99#2083C2211yescharacteristic
100#2083C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2077C2211yescharacteristic
107#2076C2211yescharacteristic
108#2072C2211yescharacteristic
109#2072C2211yescharacteristic
110#2071C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2066C2211yescharacteristic
114#2065C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2058C2211yescharacteristic
118#2058C2211yescharacteristic
119#2058C2211yescharacteristic
120#2055C2211yescharacteristic
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic
126#2034C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2024C2211yescharacteristic
130#2000C2211yescharacteristic
131#1989C2211yescharacteristic
132#1968C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1948C2211yescharacteristic
136#1948C2211yescharacteristic
137#1948C2211yescharacteristic
138#1941C2211yescharacteristic
139#1934C2211yescharacteristic
140#1933C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1923C2211yescharacteristic
146#1923C2211yescharacteristic
147#1920C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1916C2211yescharacteristic
154#1916C2211yescharacteristic
155#1893C2211yescharacteristic
156#1892C2211yescharacteristic
157#1877C2211yescharacteristic
158#1877C2211yescharacteristic
159#1874C2211yescharacteristic
160#1869C2211yescharacteristic
161#1869C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1854C2211yescharacteristic
167#1854C2211yescharacteristic
168#1853C2211yescharacteristic
169#1853C2211yescharacteristic
170#1853C2211yescharacteristic
171#1850C2211yescharacteristic
172#1850C2211yescharacteristic
173#1844C2211yescharacteristic
174#1844C2211yescharacteristic
175#1834C2211yescharacteristic
176#1834C2211yescharacteristic
177#1825C2211yescharacteristic
178#1807C2211yescharacteristic
179#1807C2211yescharacteristic
180#1807C2211yescharacteristic
181#1807C2211yescharacteristic
182#1807C2211yescharacteristic
183#1802C2211yescharacteristic
184#1776C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188C4×#106C2211yescharacteristic
189C4×#106C2211yescharacteristic
190C4×#106C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C4×#106C2211yescharacteristic
193#1768C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1750C2211yescharacteristic
201#1749C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#126—21no—
208C2×#126—21no—
209C2×#125C2311yescharacteristic
210C2×#123—21no—
211C2×#123—21no—
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×#117—21no—
225C2×#117—21no—
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C42C2311yescharacteristic
230#482—24no—
231#478—24no—
232#465—24no—
233C4×SD16—24no—
234#433—24no—
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×C4×C8—24no—
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#399—21no—
293#399—21no—
294#399—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#396—21no—
310#396—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#393—21no—
315#393—21no—
316#392—21no—
317#391—21no—
318#391—21no—
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#390—21no—
324#390—21no—
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388D411yescharacteristic
353#388D411yescharacteristic
354#387—21no—
355#387—21no—
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#387D411yescharacteristic
374#387D411yescharacteristic
375#386—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386D411yescharacteristic
381#386D411yescharacteristic
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385D411yescharacteristic
388#385D411yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#383—21no—
396#382—21no—
397#382—21no—
398#382—21no—
399#382—21no—
400#382—21no—
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#381—21no—
404#381—21no—
405#380—21no—
406#380—21no—
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376C2311yescharacteristic
443C2×#95—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×Q8C2411yescharacteristic
486C22×D4—21no—
487C22×D4—21no—
488C22×D4C2×D411yescharacteristic
489C22×D4C2411yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C2×D411yescharacteristic
495C23×C4C2×D411yescharacteristic
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—41no—
501C22×C8—22no—
502C22×C8—22no—
503C22×C8—22no—
504C22×C8—41no—
505C22×C8—41no—
506C22×C8—41no—
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517#126—82no—
518#126—82no—
519#125—22no—
520#125—41no—
521#123—82no—
522#123—82no—
523C22⋊Q8—22no—
524C22⋊Q8—41no—
525C22⋊Q8—41no—
526C22⋊Q8—41no—
527C22⋊Q8—82no—
528C22⋊Q8—82no—
529#121—22no—
530#121—22no—
531#121—41no—
532#121—41no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—41no—
539C4×D4—41no—
540C4×D4—41no—
541C4×D4—41no—
542C4×D4—41no—
543C4×D4—82no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—41no—
548#117—82no—
549#117—82no—
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—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651#107—22no—
652#107—22no—
653#107—41no—
654#107—41no—
655#106—22no—
656#106—22no—
657#106—22no—
658#106—22no—
659#106—41no—
660#106—41no—
661#106—41no—
662#106—41no—
663#106—41no—
664#106—41no—
665#106—41no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—41no—
674#103—22no—
675#103—22no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—41no—
685#102—41no—
686#102—41no—
687#102#4114yes—
688C22⋊C8—22no—
689C22⋊C8—22no—
690C22⋊C8—22no—
691C22⋊C8—41no—
692C22⋊C8—41no—
693C22⋊C8—41no—
694#97—22no—
695#97—22no—
696C4×C8—22no—
697C4×C8—22no—
698C4×C8—22no—
699C4×C8#4114yes—
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#95—21no—
741#95—21no—
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24—21no—
753C24C22×D411yescharacteristic
754C24C22×D411yescharacteristic
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8—81no—
763C2×Q8—81no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—42no—
775C2×D4—81no—
776C2×D4—81no—
777C2×D4—81no—
778C2×D4C2×#4112yes—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—41no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C2511yescharacteristic
837SD16—44no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—44no—
860C2×C8—44no—
861C2×C8C2×#4112yes—
862C2×C8C2×#4112yes—
863C2×C8C2×#4112yes—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—41no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4C2×#4112yes—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—22no—
930C22⋊C4—22no—
931C22⋊C4—41no—
932C22⋊C4—41no—
933C22⋊C4—41no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C42—22no—
957C42—22no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—42no—
967C42—42no—
968C42—81no—
969C42—81no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42C2×#4112yes—
979C422−1+412yes—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—22no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23#57712yes—
1001C23C23×D411yescharacteristic
1002Q8—41no—
1003Q8—41no—
1004Q8—41no—
1005Q8—41no—
1006Q8—162no—
1007D4—22no—
1008D4—22no—
1009D4—41no—
1010D4—41no—
1011D4—82no—
1012D4—84no—
1013D4—162no—
1014C2×C4—28no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—44no—
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—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—162no—
1102C2×C4—162no—
1103C2×C4—162no—
1104C2×C4—162no—
1105C2×C4#54712yes—
1106C2×C4#54712yes—
1107C2×C4#57712yes—
1108C2×C4#57712yes—
1109C2×C4C22×#4111yescharacteristic
1110C2×C4C22×#4111yescharacteristic
1111C2×C4C2×2−1+411yescharacteristic
1112C2×C4#58511yescharacteristic
1113C2×C4#58511yescharacteristic
1114C2×C4#58511yescharacteristic
1115C8—22no—
1116C8—22no—
1117C8—22no—
1118C8—41no—
1119C8—41no—
1120C8—41no—
1121C8—41no—
1122C8—41no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—42no—
1131C22—41no—
1132C22—42no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—42no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22#344911yescharacteristic
1145C22C2×#54711yescharacteristic
1146C22D4×#4111yescharacteristic
1147C22C2×#57711yescharacteristic
1148C22C2×#57711yescharacteristic
1149C22C2×#57711yescharacteristic
1150C22#358411yescharacteristic
1151C4—22no—
1152C4—22no—
1153C4—22no—
1154C4—22no—
1155C4—41no—
1156C4—41no—
1157C4—42no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4#345511yescharacteristic
1179C4#346111yescharacteristic
1180C4#347511yescharacteristic
1181C4#353111yescharacteristic
1182C2—42no—
1183C2—81no—
1184C2—82no—
1185C2#5214711yescharacteristic
1186C2#6100111yescharacteristic
1187C2#6101211yescharacteristic
1188C2#6125911yescharacteristic
1189C2#6126311yescharacteristic
1190C2#6148311yescharacteristic
1191C2#6149311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35613C2semidirect
3. #32428C2semidirect
4. #32408C2semidirect
5. #32381C2semidirect
6. #32344C2semidirect
7. #32311C2semidirect
8. #32280C2semidirect
9. #32259C2semidirect
10. #32205C2semidirect
12. #31934C2semidirect
13. #31693C2semidirect
14. #31610C2semidirect
15. #31329C2semidirect
16. #31092C2semidirect
17. #30671C2semidirect
19. #23845C2semidirect
20. #23789C2semidirect
21. #23769C2semidirect
22. #23763C2semidirect
23. #23760C2semidirect
24. #23707C2semidirect
25. #21619C2semidirect
26. #21588C2semidirect
27. C4×#465C2semidirect
28. #21369C2semidirect
29. #21133C2semidirect
30. #21103C2semidirect
31. #20816C2semidirect

Maximal subgroups

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

subgroupindex
#356132
#355532
#324282
#324082
#323812
#323442
#323112
#322802
#322592
#322052
#320022
#319342
#316932
#316102
#313292
#310922
#306712
#305582
#238452
#237892
#237692
#237632
#237602
#237072
#216192
#215882
C4×#4652
#213692
#211332
#211032
#208162