Finite Group Databasebeta

← #6741144

Subgroups — #6741144

Order 512.

1271 conjugacy classes of subgroups.

The subgroup lattice has 1131 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40071C211yesmaximal, characteristic
2#36564C211yesmaximal, characteristic
3#33100C211yesmaximal, characteristic
4#32683C211yesmaximal, characteristic, complemented
5#32631C211yesmaximal, characteristic, complemented
6#32244C211yesmaximal, characteristic, complemented
7#31742C211yesmaximal, characteristic
8#31446C211yesmaximal, characteristic
9#31120C211yesmaximal, characteristic
10#30965C211yesmaximal, characteristic, complemented
11#30801C211yesmaximal, characteristic
12#30367C211yesmaximal, characteristic
13#30168C211yesmaximal, characteristic
14#29038C211yesmaximal, characteristic, complemented
15#28972C211yesmaximal, characteristic, complemented
16#27457C211yesmaximal, characteristic
17#27409C211yesmaximal, characteristic
18#27384C211yesmaximal, characteristic, complemented
19#27345C211yesmaximal, characteristic
20#27327C211yesmaximal, characteristic
21#27146C211yesmaximal, characteristic, complemented
22#27021C211yesmaximal, characteristic, complemented
23#27020C211yesmaximal, characteristic, complemented
24#26882C211yesmaximal, characteristic, complemented
25#26711C211yesmaximal, characteristic, complemented
26#26322C211yesmaximal, characteristic, complemented
27#26278C211yesmaximal, characteristic, complemented
28#23167C211yesmaximal, characteristic, complemented
29#23077C211yesmaximal, characteristic, complemented
30#22319C211yesmaximal, characteristic
31#21579C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#483C2211yescharacteristic
34C2×#475C2211yescharacteristic
35#2857—21no—
36#2857C2211yescharacteristic
37#2855C2211yescharacteristic
38#2770—21no—
39#2766—21no—
40#2762—21no—
41#2729—21no—
42#2655—21no—
43#2586—21no—
44#2586—21no—
45#2568C2211yescharacteristic
46#2567C2211yescharacteristic
47#2551C2211yescharacteristic
48#2549—21no—
49#2549—21no—
50#2546C2211yescharacteristic
51#2527—21no—
52#2515—21no—
53#2514C2211yescharacteristic
54#2507—21no—
55#2507C2211yescharacteristic
56#2507C2211yescharacteristic
57#2494C2211yescharacteristic
58#2492C2211yescharacteristic
59#2489C2211yescharacteristic
60#2453C2211yescharacteristic
61#2451—21no—
62#2451C2211yescharacteristic
63#2446C2211yescharacteristic
64#2440C2211yescharacteristic
65#2440C2211yescharacteristic
66#2429C2211yescharacteristic
67#2370C2211yescharacteristic
68#2369C2211yescharacteristic
69#2369C2211yescharacteristic
70#2369C2211yescharacteristic
71#2356C2211yescharacteristic
72Q8×C4⋊C4C2211yescharacteristic
73#2345C2211yescharacteristic
74#2345C2211yescharacteristic
75#2331—21no—
76C4×C22⋊Q8—21no—
77C4×C22⋊Q8C2211yescharacteristic
78C4×C22⋊Q8C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80#2101C2211yescharacteristic
81#2100C2211yescharacteristic
82#2100C2211yescharacteristic
83#2095C2211yescharacteristic
84#2095C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2086C2211yescharacteristic
88#2085C2211yescharacteristic
89#2084C2211yescharacteristic
90#2084C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2075C2211yescharacteristic
94#2075C2211yescharacteristic
95#2072C2211yescharacteristic
96#2072C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2066C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2058C2211yescharacteristic
105#2058C2211yescharacteristic
106#2058C2211yescharacteristic
107#2058C2211yescharacteristic
108#2057C2211yescharacteristic
109#2043C2211yescharacteristic
110#2043C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2024C2211yescharacteristic
116#2024C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#1993C2211yescharacteristic
121#1990C2211yescharacteristic
122#1989C2211yescharacteristic
123#1988C2211yescharacteristic
124#1988C2211yescharacteristic
125#1984C2211yescharacteristic
126#1984C2211yescharacteristic
127#1981C2211yescharacteristic
128#1956C2211yescharacteristic
129#1949C2211yescharacteristic
130#1948C2211yescharacteristic
131#1947C2211yescharacteristic
132#1944C2211yescharacteristic
133#1943C2211yescharacteristic
134#1943C2211yescharacteristic
135#1941C2211yescharacteristic
136#1941C2211yescharacteristic
137#1935C2211yescharacteristic
138#1935C2211yescharacteristic
139#1935C2211yescharacteristic
140#1935C2211yescharacteristic
141#1935C2211yescharacteristic
142#1933C2211yescharacteristic
143#1933C2211yescharacteristic
144#1928C2211yescharacteristic
145#1928C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1928C2211yescharacteristic
149#1928C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1923C2211yescharacteristic
158#1923C2211yescharacteristic
159#1921C2211yescharacteristic
160#1921C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1920C2211yescharacteristic
164#1919C2211yescharacteristic
165#1919C2211yescharacteristic
166#1919C2211yescharacteristic
167#1919C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1919C2211yescharacteristic
171#1919C2211yescharacteristic
172#1919C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1918C2211yescharacteristic
176#1917C2211yescharacteristic
177#1917C2211yescharacteristic
178#1917C2211yescharacteristic
179#1917C2211yescharacteristic
180#1872C2211yescharacteristic
181#1872C2211yescharacteristic
182#1872C2211yescharacteristic
183#1865C2211yescharacteristic
184#1865C2211yescharacteristic
185#1865C2211yescharacteristic
186#1865C2211yescharacteristic
187#1853C2211yescharacteristic
188#1852C2211yescharacteristic
189#1852C2211yescharacteristic
190#1823C2211yescharacteristic
191#1817C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#107C2211yescharacteristic
196C4×#106C2211yescharacteristic
197#1771C2211yescharacteristic
198#1771C2211yescharacteristic
199#1763C2211yescharacteristic
200#1763C2211yescharacteristic
201#1763C2211yescharacteristic
202#1749C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8—21no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8D411yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C4×Q8—21no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C42—21no—
224C22×C42C2311yescharacteristic
225#501—24no—
226#483—24no—
227#475—24no—
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×C22⋊C8C2311yescharacteristic
265C2×C22⋊C8C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C22⋊C8C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274#401—21no—
275#401—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#397—21no—
296#397—21no—
297#396—21no—
298#395—21no—
299#395—21no—
300#395—21no—
301#395—21no—
302#395—21no—
303#395—21no—
304#395—21no—
305#393—21no—
306#391—21no—
307#391—21no—
308#391—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391D411yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389D411yescharacteristic
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#389C2311yescharacteristic
357#388—21no—
358#388—21no—
359#388—21no—
360#388—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#387D411yescharacteristic
381#387D411yescharacteristic
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385D411yescharacteristic
387#385D411yescharacteristic
388#384—21no—
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#383—21no—
393#383—21no—
394#382—21no—
395#382—21no—
396#382C2311yescharacteristic
397#381—21no—
398#380—21no—
399#380—21no—
400#380—21no—
401#380D411yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4C2311yescharacteristic
432C4×C22⋊C4C2311yescharacteristic
433#376—21no—
434C2×#95—21no—
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#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8—21no—
483C22×Q8—21no—
484C22×Q8—21no—
485C22×Q8C2×D411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4C2×D411yescharacteristic
491C23×C4C2×D411yescharacteristic
492C23×C4C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C4⋊Q8—22no—
502C4⋊Q8—22no—
503C4⋊Q8—41no—
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506C4⋊Q8—41no—
507C4⋊Q8—41no—
508C4⋊Q8—41no—
509C4⋊Q8—41no—
510C4⋊Q8—41no—
511C4⋊Q8—44no—
512C4⋊Q8—82no—
513#125—22no—
514#125—41no—
515C22⋊Q8—24no—
516C22⋊Q8—22no—
517C22⋊Q8—41no—
518C22⋊Q8—41no—
519C22⋊Q8—41no—
520C22⋊Q8—82no—
521C22⋊Q8—82no—
522C22⋊Q8—82no—
523C4×Q8—22no—
524C4×Q8—41no—
525C4×Q8—41no—
526C4×Q8—41no—
527C4×Q8—41no—
528C4×Q8—41no—
529C4×Q8—82no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—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⋊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—41no—
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4C2×D411yescharacteristic
600C2×C22⋊C4C2×D411yescharacteristic
601C2×C22⋊C4C2×D411yescharacteristic
602C2×C22⋊C4C2×D411yescharacteristic
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—41no—
618C2×C42—41no—
619C2×C42—82no—
620C2×C42C2×D411yescharacteristic
621C2×C42C2×D411yescharacteristic
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628#107—22no—
629#107—22no—
630#107—22no—
631#107—22no—
632#107—41no—
633#107—41no—
634#106—22no—
635#106—22no—
636#106—22no—
637#106—22no—
638#106—22no—
639#106—41no—
640#106—41no—
641#106—41no—
642#106—41no—
643#106#4114yes—
644C4⋊C8—22no—
645C4⋊C8—41no—
646C4⋊C8—41no—
647C4⋊C8—41no—
648#103—22no—
649#103—22no—
650#103—22no—
651#103—22no—
652#103—22no—
653#103—22no—
654#103—22no—
655#103—22no—
656#103—41no—
657#103—41no—
658#103—41no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663#103—41no—
664C22⋊C8—22no—
665C22⋊C8—41no—
666C22⋊C8—41no—
667C22⋊C8—41no—
668#97—22no—
669#97—41no—
670#97—41no—
671#97—41no—
672C4×C8—41no—
673C4×C8—41no—
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#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734C24C22×D411yescharacteristic
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—41no—
748C2×Q8—41no—
749C2×Q8—42no—
750C2×Q8—42no—
751C2×Q8—42no—
752C2×Q8—42no—
753C2×Q8—81no—
754C2×Q8—81no—
755C2×Q8—81no—
756C2×Q8—81no—
757C2×Q8—81no—
758C2×Q8—81no—
759C2×Q8—81no—
760C2×Q8—81no—
761C2×Q8#13714yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—22no—
768C22×C4—22no—
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×C4—21no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4—41no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C2511yescharacteristic
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—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8C2×#4112yes—
834C4⋊C4—24no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
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—21no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—41no—
866C4⋊C4—41no—
867C4⋊C4—41no—
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—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
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⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4C2×#4112yes—
904C4⋊C4C2×#4112yes—
905C4⋊C42−1+412yes—
906C4⋊C42−1+412yes—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—22no—
910C22⋊C4—22no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—81no—
916C22⋊C4—81no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—41no—
930C42—41no—
931C42—42no—
932C42—42no—
933C42—42no—
934C42—42no—
935C42—42no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42—81no—
940C42—81no—
941C42—81no—
942C42—81no—
943C42—81no—
944C42—81no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23—21no—
951C23#57712yes—
952C23C23×D411yescharacteristic
953Q8—44no—
954Q8—41no—
955Q8—41no—
956Q8—41no—
957Q8—41no—
958Q8—41no—
959Q8—41no—
960Q8—41no—
961Q8—41no—
962Q8—162no—
963Q8—162no—
964Q8—162no—
965Q8—162no—
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—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—22no—
986C2×C4—22no—
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—22no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—44no—
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—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—82no—
1056C2×C4—84no—
1057C2×C4—84no—
1058C2×C4C2×#13712yes—
1059C2×C4C2×#13712yes—
1060C2×C4C2×#13712yes—
1061C2×C4C22×#4111yescharacteristic
1062C2×C4C2×2−1+411yescharacteristic
1063C2×C4C2×2−1+411yescharacteristic
1064C2×C4#58511yescharacteristic
1065C2×C4#58511yescharacteristic
1066C2×C4#58511yescharacteristic
1067C8—22no—
1068C8—41no—
1069C8—41no—
1070C8—41no—
1071C8—41no—
1072C8—41no—
1073C8—41no—
1074C8—41no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—41no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22D4×#4111yescharacteristic
1083C22#348511yescharacteristic
1084C22#348611yescharacteristic
1085C22C22×#13711yescharacteristic
1086C22C2×#57711yescharacteristic
1087C22#358511yescharacteristic
1088C22#358611yescharacteristic
1089C4—22no—
1090C4—22no—
1091C4—22no—
1092C4—41no—
1093C4—41no—
1094C4—41no—
1095C4—42no—
1096C4—41no—
1097C4—41no—
1098C4—41no—
1099C4—41no—
1100C4—41no—
1101C4—41no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—41no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4#346111yescharacteristic
1119C4#351811yescharacteristic
1120C4#355711yescharacteristic
1121C4#356511yescharacteristic
1122C2—42no—
1123C2#3782311yescharacteristic
1124C2#6147011yescharacteristic
1125C2#6152111yescharacteristic
1126C2#6170911yescharacteristic
1127C2#6175311yescharacteristic
1128C2#6183811yescharacteristic
1129C2#6187311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #32683C2semidirect
5. #32631C2semidirect
6. #32244C2semidirect
10. #30965C2semidirect
14. #29038C2semidirect
15. #28972C2semidirect
18. #27384C2semidirect
21. #27146C2semidirect
22. #27021C2semidirect
23. #27020C2semidirect
24. #26882C2semidirect
25. #26711C2semidirect
26. #26322C2semidirect
27. #26278C2semidirect
28. #23167C2semidirect
29. #23077C2semidirect

Maximal subgroups

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

subgroupindex
#400712
#365642
#331002
#326832
#326312
#322442
#317422
#314462
#311202
#309652
#308012
#303672
#301682
#290382
#289722
#274572
#274092
#273842
#273452
#273272
#271462
#270212
#270202
#268822
#267112
#263222
#262782
#231672
#230772
#223192
#215792