Finite Group Databasebeta

← #6530053

Subgroups — #6530053

Order 512.

1364 conjugacy classes of subgroups.

The subgroup lattice has 1115 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35578C211yesmaximal, characteristic
2#34434C211yesmaximal, characteristic
3#29294C211yesmaximal, characteristic, complemented
4#29293C211yesmaximal, characteristic, complemented
5#29288C211yesmaximal, characteristic, complemented
6#29286C211yesmaximal, characteristic, complemented
7#29283C211yesmaximal, characteristic, complemented
8#29282C211yesmaximal, characteristic, complemented
9#29278C211yesmaximal, characteristic, complemented
10#29277C211yesmaximal, characteristic, complemented
11#26524C211yesmaximal, characteristic, complemented
12#26521C211yesmaximal, characteristic, complemented
13#26516C211yesmaximal, characteristic, complemented
14#26512C211yesmaximal, characteristic, complemented
15#26456C211yesmaximal, characteristic, complemented
16#26454C211yesmaximal, characteristic, complemented
17#26448C211yesmaximal, characteristic, complemented
18#26440C211yesmaximal, characteristic, complemented
19#26014C211yesmaximal, characteristic
20#26008C211yesmaximal, characteristic
21#26005C211yesmaximal, characteristic
22#26005C211yesmaximal, characteristic
23#25997C211yesmaximal, characteristic
24#25994C211yesmaximal, characteristic
25#25989C211yesmaximal, characteristic
26#25988C211yesmaximal, characteristic
27#21980C211yesmaximal, characteristic
28#21968C211yesmaximal, characteristic
29#21843C211yesmaximal, characteristic
30#21368C211yesmaximal, characteristic
31#21315C211yesmaximal, characteristic
32C2×#544C2211yescharacteristic
33C2×#433C2211yescharacteristic
34C2×#424C2211yescharacteristic
35#2590—21no—
36#2589—21no—
37#2586—21no—
38#2570C2211yescharacteristic
39#2556—21no—
40#2552C2211yescharacteristic
41#2551C2211yescharacteristic
42#2550C2211yescharacteristic
43#2465—21no—
44#2462—21no—
45#2451—21no—
46#2441C2211yescharacteristic
47#2440C2211yescharacteristic
48#2440C2211yescharacteristic
49#2439C2211yescharacteristic
50#2429—21no—
51#2381—21no—
52#2378—21no—
53#2370C2211yescharacteristic
54#2370C2211yescharacteristic
55#2369C2211yescharacteristic
56#2365—21no—
57#2365C2211yescharacteristic
58#2362—21no—
59#2347C2211yescharacteristic
60#2347C2211yescharacteristic
61#2345C2211yescharacteristic
62#2344C2211yescharacteristic
63#2336—21no—
64#2336—21no—
65#2332—21no—
66#2331C2211yescharacteristic
67#2331C2211yescharacteristic
68#2330C2211yescharacteristic
69#2330C2211yescharacteristic
70#2323—21no—
71#2314C2211yescharacteristic
72#2314C2211yescharacteristic
73C4×C4⋊Q8C2211yescharacteristic
74C4×C4⋊Q8C2211yescharacteristic
75C4×C4⋊Q8C2211yescharacteristic
76C4×#125C2211yescharacteristic
77#2298C2211yescharacteristic
78#2274C2211yescharacteristic
79#2101C2211yescharacteristic
80#2101C2211yescharacteristic
81#2100C2211yescharacteristic
82#2100C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2087C2211yescharacteristic
92#2087C2211yescharacteristic
93#2087C2211yescharacteristic
94#2087C2211yescharacteristic
95#2087C2211yescharacteristic
96#2086C2211yescharacteristic
97#2086C2211yescharacteristic
98#2086C2211yescharacteristic
99#2086C2211yescharacteristic
100#2086C2211yescharacteristic
101#2086C2211yescharacteristic
102#2086C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2058C2211yescharacteristic
106#2057C2211yescharacteristic
107#2057C2211yescharacteristic
108#2057C2211yescharacteristic
109#2057C2211yescharacteristic
110#2057C2211yescharacteristic
111#1993C2211yescharacteristic
112#1992C2211yescharacteristic
113#1991C2211yescharacteristic
114#1990C2211yescharacteristic
115#1989C2211yescharacteristic
116#1989C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1989C2211yescharacteristic
120#1989C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1988C2211yescharacteristic
124#1988C2211yescharacteristic
125#1988C2211yescharacteristic
126#1988C2211yescharacteristic
127#1988C2211yescharacteristic
128#1988C2211yescharacteristic
129#1988C2211yescharacteristic
130#1988C2211yescharacteristic
131#1987C2211yescharacteristic
132#1987C2211yescharacteristic
133#1987C2211yescharacteristic
134#1987C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1948C2211yescharacteristic
144#1947C2211yescharacteristic
145#1947C2211yescharacteristic
146#1947C2211yescharacteristic
147#1947C2211yescharacteristic
148#1947C2211yescharacteristic
149#1947C2211yescharacteristic
150#1947C2211yescharacteristic
151#1947C2211yescharacteristic
152#1947C2211yescharacteristic
153#1947C2211yescharacteristic
154#1947C2211yescharacteristic
155#1940C2211yescharacteristic
156#1940C2211yescharacteristic
157#1939C2211yescharacteristic
158#1939C2211yescharacteristic
159#1921C2211yescharacteristic
160#1921C2211yescharacteristic
161#1921C2211yescharacteristic
162#1921C2211yescharacteristic
163#1921C2211yescharacteristic
164#1921C2211yescharacteristic
165#1921C2211yescharacteristic
166#1920C2211yescharacteristic
167#1919C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1918C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic
179#1851C2211yescharacteristic
180#1851C2211yescharacteristic
181#1850C2211yescharacteristic
182#1850C2211yescharacteristic
183#1843C2211yescharacteristic
184#1842C2211yescharacteristic
185#1832C2211yescharacteristic
186#1831C2211yescharacteristic
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1824C2211yescharacteristic
190#1823C2211yescharacteristic
191#1809C2211yescharacteristic
192#1809C2211yescharacteristic
193#1808C2211yescharacteristic
194#1808C2211yescharacteristic
195#1776C2211yescharacteristic
196#1776C2211yescharacteristic
197C4×#107C2211yescharacteristic
198C4×#107C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205#544—24no—
206#544Q818yescomplemented
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125—21no—
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C4×Q8—21no—
224C2×C4×Q8—21no—
225C2×C4×Q8—21no—
226C2×C4×Q8—21no—
227C2×#117—21no—
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233#433—24no—
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250#424—24no—
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C22⋊C8C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269#400—21no—
270#399—21no—
271#398—21no—
272#398—21no—
273#398—21no—
274#398—21no—
275#398—21no—
276#398—21no—
277#396—21no—
278#396—21no—
279#395—21no—
280#395—21no—
281#395—21no—
282#395—21no—
283#395—21no—
284#393—21no—
285#391—21no—
286#391—21no—
287#391—21no—
288#391—21no—
289#391—21no—
290#391—21no—
291#391—21no—
292#391—21no—
293#391—21no—
294#391—21no—
295#391—21no—
296#391—21no—
297#389—21no—
298#389—21no—
299#389—21no—
300#389—21no—
301#389—21no—
302#389—21no—
303#389—21no—
304#389—21no—
305#389—21no—
306#389—21no—
307#389—21no—
308#389—21no—
309#389—21no—
310#389—21no—
311#389C2311yescharacteristic
312#389C2311yescharacteristic
313#389C2311yescharacteristic
314#389C2311yescharacteristic
315#389C2311yescharacteristic
316#389C2311yescharacteristic
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#388—21no—
328#388—21no—
329#388—21no—
330#388—21no—
331#388—21no—
332#388—21no—
333#388—21no—
334#388—21no—
335#388D411yescharacteristic
336#388D411yescharacteristic
337#388D411yescharacteristic
338#388D411yescharacteristic
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#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
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#387D411yescharacteristic
368#387D411yescharacteristic
369#387D411yescharacteristic
370#387D411yescharacteristic
371#385—21no—
372#385—21no—
373#384C2311yescharacteristic
374#384C2311yescharacteristic
375#384C2311yescharacteristic
376#384C2311yescharacteristic
377#384C2311yescharacteristic
378#383—21no—
379#383—21no—
380#382C2311yescharacteristic
381#382C2311yescharacteristic
382#382C2311yescharacteristic
383#381—21no—
384#380—21no—
385#380C2311yescharacteristic
386#380C2311yescharacteristic
387#380C2311yescharacteristic
388#380C2311yescharacteristic
389C4×C4⋊C4—21no—
390C4×C4⋊C4—21no—
391C4×C4⋊C4—21no—
392C4×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
402C4×C4⋊C4C2311yescharacteristic
403C4×C4⋊C4C2311yescharacteristic
404C4×C4⋊C4C2311yescharacteristic
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2311yescharacteristic
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4C2311yescharacteristic
423C4×C22⋊C4C2311yescharacteristic
424#376C2311yescharacteristic
425C43C2311yescharacteristic
426#340C2311yescharacteristic
427#340C2311yescharacteristic
428#340C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
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#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
482C22×Q8—21no—
483C22×Q8—21no—
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C2411yescharacteristic
490C2×M16—22no—
491C2×M16—41no—
492C2×M16—41no—
493C22×C8—22no—
494C22×C8—41no—
495C22×C8—41no—
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C4⋊Q8—28no—
505C4⋊Q8—22no—
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508C4⋊Q8—22no—
509C4⋊Q8—22no—
510C4⋊Q8—41no—
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513C4⋊Q8—82no—
514C4⋊Q8C2×Q814yes—
515C4⋊Q8C2×Q814yes—
516#125—28no—
517#125—22no—
518#125—22no—
519#125—22no—
520#125—41no—
521#125—82no—
522#125C2×Q814yes—
523#125C2×Q814yes—
524C22⋊Q8—28no—
525C22⋊Q8—28no—
526C22⋊Q8—82no—
527C22⋊Q8—82no—
528C4×Q8—82no—
529C4×Q8—82no—
530C4×Q8—82no—
531C4×Q8—82no—
532#117—22no—
533#117—22no—
534#117—41no—
535#117—82no—
536#117C2×Q814yes—
537#117C2×Q814yes—
538#117#4114yes—
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—22no—
547C2×C4⋊C4—22no—
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—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×Q814yes—
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×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
611C2×C22⋊C4C2×D411yescharacteristic
612C2×C22⋊C4C2×D411yescharacteristic
613C2×C22⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42C2×D411yescharacteristic
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644#107—22no—
645#107—22no—
646#107—22no—
647#107—41no—
648#107—41no—
649#107—41no—
650#107—41no—
651#107—41no—
652#107—41no—
653#107—41no—
654#107—41no—
655#107—41no—
656#106—22no—
657#106—41no—
658#106—41no—
659#106—41no—
660C4⋊C8—22no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—22no—
664C4⋊C8—22no—
665C4⋊C8—22no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672C4⋊C8—41no—
673C4⋊C8—41no—
674C22⋊C8—22no—
675C22⋊C8—22no—
676#97—22no—
677C4×C8—22no—
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#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732C24C22×D411yescharacteristic
733C2×Q8—24no—
734C2×Q8—24no—
735C2×Q8—42no—
736C2×Q8—42no—
737C2×Q8—42no—
738C2×Q8—42no—
739C2×Q8—42no—
740C2×Q8—81no—
741C2×Q8—81no—
742C2×Q8—81no—
743C2×Q8—81no—
744C2×Q8—81no—
745C2×Q8—81no—
746C2×Q8—81no—
747C2×Q8—81no—
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—21no—
758C22×C4—24no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—42no—
770C22×C4—81no—
771C22×C4—81no—
772C22×C4—81no—
773C22×C4—81no—
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×Q812yes—
788C22×C4C2×#4112yes—
789C22×C4C2511yescharacteristic
790M16—82no—
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×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—82no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—22no—
824C4⋊C4—22no—
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—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—41no—
852C4⋊C4—41no—
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—42no—
867C4⋊C4—42no—
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—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4C22⋊Q814yes—
886C4⋊C4C22⋊Q814yes—
887C4⋊C4C22×Q812yes—
888C4⋊C4C22×Q812yes—
889C4⋊C4C22×Q812yes—
890C4⋊C4C22×Q812yes—
891C4⋊C42−1+412yes—
892C4⋊C42−1+412yes—
893C22⋊C4—24no—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—41no—
897C22⋊C4—41no—
898C22⋊C4—42no—
899C22⋊C4—81no—
900C22⋊C4—81no—
901C22⋊C4—81no—
902C22⋊C4—81no—
903C22⋊C4C22⋊Q814yes—
904C22⋊C4C22⋊Q814yes—
905C42—24no—
906C42—22no—
907C42—22no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—41no—
917C42—41no—
918C42—42no—
919C42—42no—
920C42—81no—
921C42—81no—
922C42—81no—
923C42—81no—
924C42—81no—
925C42—81no—
926C42—81no—
927C42—81no—
928C42—81no—
929C42—81no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42C22×Q812yes—
936C42C22×Q812yes—
937C42C2×#4112yes—
938C42C2×#4112yes—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23C2×C22⋊Q812yes—
946C23C23×D411yescharacteristic
947Q8—84no—
948Q8—84no—
949Q8—84no—
950Q8—84no—
951Q8—162no—
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—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—21no—
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—22no—
988C2×C4—22no—
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—84no—
1037C2×C4—162no—
1038C2×C4C2×C22⋊Q812yes—
1039C2×C4C2×C22⋊Q812yes—
1040C2×C4C2×C22⋊Q812yes—
1041C2×C4C2×C22⋊Q812yes—
1042C2×C4C2×C22⋊Q812yes—
1043C2×C4#57612yes—
1044C2×C4#57812yes—
1045C2×C4C23×Q811yescharacteristic
1046C2×C4C22×#4111yescharacteristic
1047C2×C4C2×2−1+411yescharacteristic
1048C2×C4C2×2−1+411yescharacteristic
1049C2×C4#58511yescharacteristic
1050C2×C4#58511yescharacteristic
1051C8—41no—
1052C8—41no—
1053C8—41no—
1054C8—41no—
1055C8—41no—
1056C8—41no—
1057C8—41no—
1058C8—41no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—41no—
1063C22—41no—
1064C22—41no—
1065C22—41no—
1066C22C22×C22⋊Q811yescharacteristic
1067C22#348911yescharacteristic
1068C22#348911yescharacteristic
1069C22C2×#57611yescharacteristic
1070C22C2×#57811yescharacteristic
1071C22#358511yescharacteristic
1072C22#358611yescharacteristic
1073C4—22no—
1074C4—22no—
1075C4—22no—
1076C4—22no—
1077C4—22no—
1078C4—22no—
1079C4—22no—
1080C4—41no—
1081C4—41no—
1082C4—42no—
1083C4—42no—
1084C4—42no—
1085C4—42no—
1086C4—41no—
1087C4—42no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—42no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4#350211yescharacteristic
1103C4#350211yescharacteristic
1104C4#350911yescharacteristic
1105C4#351011yescharacteristic
1106C2—42no—
1107C2#3566211yescharacteristic
1108C2#6049411yescharacteristic
1109C2#6049811yescharacteristic
1110C2#6216311yescharacteristic
1111C2#6219211yescharacteristic
1112C2#6220111yescharacteristic
1113C2#6222611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #29294C2semidirect
4. #29293C2semidirect
5. #29288C2semidirect
6. #29286C2semidirect
7. #29283C2semidirect
8. #29282C2semidirect
9. #29278C2semidirect
10. #29277C2semidirect
11. #26524C2semidirect
12. #26521C2semidirect
13. #26516C2semidirect
14. #26512C2semidirect
15. #26456C2semidirect
16. #26454C2semidirect
17. #26448C2semidirect
18. #26440C2semidirect
206. #544Q8semidirect

Maximal subgroups

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

subgroupindex
#355782
#344342
#292942
#292932
#292882
#292862
#292832
#292822
#292782
#292772
#265242
#265212
#265162
#265122
#264562
#264542
#264482
#264402
#260142
#260082
#260052
#259972
#259942
#259892
#259882
#219802
#219682
#218432
#213682
#213152