Finite Group Databasebeta

← #6564306

Subgroups — #6564306

Order 512.

1342 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39158C211yesmaximal, characteristic
2#34403C211yesmaximal, characteristic, complemented
3#30158C211yesmaximal, characteristic, complemented
4#30157C211yesmaximal, characteristic, complemented
5#29941C211yesmaximal, characteristic, complemented
6#29527C211yesmaximal, characteristic, complemented
7#29524C211yesmaximal, characteristic, complemented
8#29281C211yesmaximal, characteristic, complemented
9#29281C211yesmaximal, characteristic, complemented
10#27485C211yesmaximal, characteristic, complemented
11#27481C211yesmaximal, characteristic, complemented
12#27468C211yesmaximal, characteristic, complemented
13#27464C211yesmaximal, characteristic, complemented
14#27354C211yesmaximal, characteristic
15#27350C211yesmaximal, characteristic
16#27339C211yesmaximal, characteristic
17#27335C211yesmaximal, characteristic
18#26458C211yesmaximal, characteristic, complemented
19#26456C211yesmaximal, characteristic, complemented
20#25818C211yesmaximal, characteristic, complemented
21#25466C211yesmaximal, characteristic, complemented
22#25466C211yesmaximal, characteristic, complemented
23#24304C211yesmaximal, characteristic
24#23842C211yesmaximal, characteristic, complemented
25#23842C211yesmaximal, characteristic, complemented
26#23764C211yesmaximal, characteristic
27#23169C211yesmaximal, characteristic, complemented
28#23167C211yesmaximal, characteristic, complemented
29#23076C211yesmaximal, characteristic, complemented
30#23072C211yesmaximal, characteristic, complemented
31#22635C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic
37#2857C2211yescharacteristic
38#2759—21no—
39#2759—21no—
40#2700—21no—
41#2700—21no—
42#2644C2211yescharacteristic
43#2644C2211yescharacteristic
44#2563C2211yescharacteristic
45#2551C2211yescharacteristic
46#2547—21no—
47#2494—21no—
48#2494C2211yescharacteristic
49#2494C2211yescharacteristic
50#2491C2211yescharacteristic
51#2491C2211yescharacteristic
52#2485—21no—
53#2439—21no—
54#2378—21no—
55#2378—21no—
56#2370C2211yescharacteristic
57#2370C2211yescharacteristic
58#2370C2211yescharacteristic
59#2370C2211yescharacteristic
60#2369C2211yescharacteristic
61#2356—21no—
62#2356—21no—
63#2354C2211yescharacteristic
64#2347C2211yescharacteristic
65#2347C2211yescharacteristic
66#2346C2211yescharacteristic
67#2346C2211yescharacteristic
68#2332—21no—
69#2332—21no—
70#2331C2211yescharacteristic
71#2331C2211yescharacteristic
72#2331C2211yescharacteristic
73#2331C2211yescharacteristic
74#2331C2211yescharacteristic
75#2331C2211yescharacteristic
76#2320—21no—
77#2320—21no—
78C4×#121C2211yescharacteristic
79#2283C2211yescharacteristic
80#2283C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2092C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2087C2211yescharacteristic
88#2086C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2075C2211yescharacteristic
102#2073C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2058C2211yescharacteristic
108#2058C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2058C2211yescharacteristic
112#2057C2211yescharacteristic
113#2057C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2057C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic
121#1992C2211yescharacteristic
122#1992C2211yescharacteristic
123#1989C2211yescharacteristic
124#1989C2211yescharacteristic
125#1988C2211yescharacteristic
126#1988C2211yescharacteristic
127#1988C2211yescharacteristic
128#1988C2211yescharacteristic
129#1987C2211yescharacteristic
130#1987C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1948C2211yescharacteristic
136#1947C2211yescharacteristic
137#1944C2211yescharacteristic
138#1943C2211yescharacteristic
139#1942C2211yescharacteristic
140#1941C2211yescharacteristic
141#1940C2211yescharacteristic
142#1940C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1923C2211yescharacteristic
158#1923C2211yescharacteristic
159#1921C2211yescharacteristic
160#1921C2211yescharacteristic
161#1921C2211yescharacteristic
162#1921C2211yescharacteristic
163#1920C2211yescharacteristic
164#1920C2211yescharacteristic
165#1920C2211yescharacteristic
166#1920C2211yescharacteristic
167#1919C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1919C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1875C2211yescharacteristic
176#1875C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1832C2211yescharacteristic
184#1832C2211yescharacteristic
185#1797C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C4×#107C2211yescharacteristic
194C4×#106C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1749C2211yescharacteristic
201#1746C2211yescharacteristic
202#1746C2211yescharacteristic
203#533—24no—
204#533—24no—
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×#124—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×#121C2311yescharacteristic
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×C4×D4—21no—
222C2×C4×D4C2311yescharacteristic
223C2×#117—21no—
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C42C2311yescharacteristic
227#501—24no—
228#501—24no—
229#478—24no—
230#478—24no—
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×C22⋊C8C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C22⋊C8C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275#401—21no—
276#401—21no—
277#397—21no—
278#397—21no—
279#397—21no—
280#397—21no—
281#397—21no—
282#397—21no—
283#397—21no—
284#397—21no—
285#396—21no—
286#396—21no—
287#395—21no—
288#395—21no—
289#394—21no—
290#394—21no—
291#393—21no—
292#393—21no—
293#393—21no—
294#393—21no—
295#391—21no—
296#391—21no—
297#391—21no—
298#391—21no—
299#391—21no—
300#391—21no—
301#391—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391—21no—
309#391—21no—
310#390C2311yescharacteristic
311#390C2311yescharacteristic
312#390C2311yescharacteristic
313#390C2311yescharacteristic
314#390C2311yescharacteristic
315#389—21no—
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
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#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#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#386—21no—
375#384C2311yescharacteristic
376#383—21no—
377#383—21no—
378#383—21no—
379#383D411yescharacteristic
380#383D411yescharacteristic
381#382—21no—
382#382—21no—
383#382D411yescharacteristic
384#382D411yescharacteristic
385#382C2311yescharacteristic
386#382C2311yescharacteristic
387#382C2311yescharacteristic
388#382C2311yescharacteristic
389#381—21no—
390#381D411yescharacteristic
391#381D411yescharacteristic
392#380—21no—
393#380—21no—
394#380—21no—
395#380—21no—
396#380D411yescharacteristic
397#380D411yescharacteristic
398#380C2311yescharacteristic
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4C2311yescharacteristic
430C4×C22⋊C4C2311yescharacteristic
431#376—21no—
432#376—21no—
433#376—21no—
434#376C2311yescharacteristic
435#376C2311yescharacteristic
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#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8—21no—
489C22×D4—21no—
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C23×C4C2×D411yescharacteristic
493C23×C4C2×D411yescharacteristic
494C23×C4C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C4⋊Q8—22no—
504C4⋊Q8—22no—
505C4⋊Q8—22no—
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508C4⋊Q8—22no—
509C4⋊Q8—22no—
510C4⋊Q8—22no—
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513C4⋊Q8—82no—
514#125—22no—
515#125—22no—
516#125#4114yes—
517#125#4114yes—
518#124—82no—
519#124—82no—
520C22⋊Q8—28no—
521C22⋊Q8—28no—
522C22⋊Q8—82no—
523#121—22no—
524#121—41no—
525C4×Q8—28no—
526C4×Q8—28no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—82no—
530#117—22no—
531#117—22no—
532#117—22no—
533#117—22no—
534#117—82no—
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⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊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—22no—
606C2×C42—22no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42C2×D411yescharacteristic
623C2×C42C2×D411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630#107—22no—
631#107—22no—
632#107—22no—
633#107—22no—
634#107—22no—
635#107—22no—
636#107—22no—
637#107—22no—
638#107—41no—
639#107—41no—
640#106—22no—
641#106—22no—
642#106—22no—
643#106—22no—
644#106—22no—
645#106—22no—
646#106—22no—
647#106—22no—
648#106—41no—
649#106—41no—
650C4⋊C8—22no—
651C4⋊C8—22no—
652C4⋊C8—41no—
653C4⋊C8—41no—
654C4⋊C8—41no—
655C4⋊C8—41no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—22no—
660#102—22no—
661#102—22no—
662#102—41no—
663#102—41no—
664C22⋊C8—22no—
665C22⋊C8—22no—
666C22⋊C8—41no—
667C22⋊C8—41no—
668#97—22no—
669#97—22no—
670#97—22no—
671#97—22no—
672C4×C8—22no—
673C4×C8—22no—
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#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
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
732#95C2×D411yescharacteristic
733C24—21no—
734C24C22×D411yescharacteristic
735C2×Q8—24no—
736C2×Q8—24no—
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—
748C2×Q8—81no—
749C2×Q8—81no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—81no—
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—21no—
770C22×C4—22no—
771C22×C4—22no—
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—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C2511yescharacteristic
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C82−1+412yes—
826C2×C82−1+412yes—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—24no—
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—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—41no—
859C4⋊C4—41no—
860C4⋊C4—41no—
861C4⋊C4—41no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—81no—
867C4⋊C4—81no—
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⋊C4C2×#4112yes—
883C4⋊C4C2×#4112yes—
884C4⋊C4C2×#4112yes—
885C4⋊C4C2×#4112yes—
886C4⋊C42−1+412yes—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—41no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C22⋊C4—41no—
893C22⋊C4—42no—
894C22⋊C4—42no—
895C22⋊C4—42no—
896C22⋊C4—42no—
897C22⋊C4—81no—
898C22⋊C4—81no—
899C22⋊C4—81no—
900C22⋊C4—81no—
901C22⋊C4—81no—
902C22⋊C4—81no—
903C22⋊C4—81no—
904C22⋊C4—81no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C42—24no—
911C42—24no—
912C42—22no—
913C42—22no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—42no—
925C42—81no—
926C42—81no—
927C42—81no—
928C42—81no—
929C42—81no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42—81no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42C2×#4112yes—
940C42C2×#4112yes—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23C23×D411yescharacteristic
956Q8—84no—
957Q8—84no—
958Q8—162no—
959Q8—162no—
960Q8—162no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—84no—
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—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
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—82no—
1053C2×C4—82no—
1054C2×C4—84no—
1055C2×C4#52512yes—
1056C2×C4#52512yes—
1057C2×C4C22×#4111yescharacteristic
1058C2×C4C22×#4111yescharacteristic
1059C2×C4C2×2−1+411yescharacteristic
1060C2×C4C2×2−1+411yescharacteristic
1061C2×C4C2×2−1+411yescharacteristic
1062C2×C4#58511yescharacteristic
1063C8—22no—
1064C8—22no—
1065C8—41no—
1066C8—41no—
1067C8—41no—
1068C8—41no—
1069C8—41no—
1070C8—41no—
1071C22—41no—
1072C22—41no—
1073C22—41no—
1074C22—41no—
1075C22—41no—
1076C22—41no—
1077C22—41no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22C2×#52511yescharacteristic
1086C22#348911yescharacteristic
1087C22#349911yescharacteristic
1088C22#358411yescharacteristic
1089C22#358511yescharacteristic
1090C22#358511yescharacteristic
1091C22#358611yescharacteristic
1092C4—22no—
1093C4—22no—
1094C4—41no—
1095C4—41no—
1096C4—42no—
1097C4—41no—
1098C4—41no—
1099C4—41no—
1100C4—41no—
1101C4—41no—
1102C4—42no—
1103C4—42no—
1104C4—41no—
1105C4—41no—
1106C4—42no—
1107C4—42no—
1108C4—41no—
1109C4—41no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4#351811yescharacteristic
1121C4#351811yescharacteristic
1122C4#352311yescharacteristic
1123C4#352311yescharacteristic
1124C2—81no—
1125C2—161no—
1126C2#3600711yescharacteristic
1127C2#6056711yescharacteristic
1128C2#6058711yescharacteristic
1129C2#6216111yescharacteristic
1130C2#6222311yescharacteristic
1131C2#6249711yescharacteristic
1132C2#6251811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34403C2semidirect
3. #30158C2semidirect
4. #30157C2semidirect
5. #29941C2semidirect
6. #29527C2semidirect
7. #29524C2semidirect
8. #29281C2semidirect
9. #29281C2semidirect
10. #27485C2semidirect
11. #27481C2semidirect
12. #27468C2semidirect
13. #27464C2semidirect
18. #26458C2semidirect
19. #26456C2semidirect
20. #25818C2semidirect
21. #25466C2semidirect
22. #25466C2semidirect
24. #23842C2semidirect
25. #23842C2semidirect
27. #23169C2semidirect
28. #23167C2semidirect
29. #23076C2semidirect
30. #23072C2semidirect
31. #22635C2semidirect

Maximal subgroups

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

subgroupindex
#391582
#344032
#301582
#301572
#299412
#295272
#295242
#292812
#274852
#274812
#274682
#274642
#273542
#273502
#273392
#273352
#264582
#264562
#258182
#254662
#243042
#238422
#237642
#231692
#231672
#230762
#230722
#226352