Finite Group Databasebeta

← #7584626

Subgroups — #7584626

Order 512.

1311 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45210C211yesmaximal, characteristic, complemented
2#35895C211yesmaximal, characteristic
3#31485C211yesmaximal, characteristic, complemented
4#31239C211yesmaximal, characteristic, complemented
5#31132C211yesmaximal, characteristic
6#30618C211yesmaximal, characteristic
7#29527C211yesmaximal, characteristic, complemented
8#29458C211yesmaximal, characteristic, complemented
9#29025C211yesmaximal, characteristic, complemented
10#28077C211yesmaximal, characteristic
11#28000C211yesmaximal, characteristic, complemented
12#27445C211yesmaximal, characteristic, complemented
13#27364C211yesmaximal, characteristic, complemented
14#27185C211yesmaximal, characteristic, complemented
15#27164C211yesmaximal, characteristic, complemented
16#27059C211yesmaximal, characteristic, complemented
17#26873C211yesmaximal, characteristic, complemented
18#26805C211yesmaximal, characteristic
19#26765C211yesmaximal, characteristic, complemented
20#26671C211yesmaximal, characteristic
21#26189C211yesmaximal, characteristic, complemented
22#26091C211yesmaximal, characteristic, complemented
23#26005C211yesmaximal, characteristic, complemented
24#25047C211yesmaximal, characteristic, complemented
25#23291C211yesmaximal, characteristic, complemented
26#23139C211yesmaximal, characteristic, complemented
27#23111C211yesmaximal, characteristic, complemented
28#22977C211yesmaximal, characteristic, complemented
29#22931C211yesmaximal, characteristic
30#21625C211yesmaximal, characteristic, complemented
31#21127C211yesmaximal, characteristic, complemented
32C2×#480C2211yescharacteristic
33C2×#477C2211yescharacteristic
34C2×#477C2211yescharacteristic
35C2×#470C2211yescharacteristic
36C2×#464C2211yescharacteristic
37C2×#441C2211yescharacteristic
38#2774—21no—
39#2770—21no—
40#2762—21no—
41#2719—21no—
42#2651—21no—
43#2644C2211yescharacteristic
44#2594—21no—
45#2577—21no—
46#2571C2211yescharacteristic
47#2556—21no—
48#2532—21no—
49#2531—21no—
50#2524—21no—
51#2517—21no—
52#2507C2211yescharacteristic
53#2506C2211yescharacteristic
54#2506C2211yescharacteristic
55#2495C2211yescharacteristic
56#2491C2211yescharacteristic
57#2489—21no—
58#2474—21no—
59#2451C2211yescharacteristic
60#2451C2211yescharacteristic
61#2448—21no—
62#2448C2211yescharacteristic
63#2440C2211yescharacteristic
64#2426C2211yescharacteristic
65#2423C2211yescharacteristic
66#2423C2211yescharacteristic
67#2421C2211yescharacteristic
68#2401C2211yescharacteristic
69#2396—21no—
70#2367C2211yescharacteristic
71#2365C2211yescharacteristic
72#2363C2211yescharacteristic
73#2362C2211yescharacteristic
74#2360C2211yescharacteristic
75#2355C2211yescharacteristic
76#2354C2211yescharacteristic
77#2351C2211yescharacteristic
78#2347C2211yescharacteristic
79#2345C2211yescharacteristic
80#2331C2211yescharacteristic
81#2320C2211yescharacteristic
82#2276C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2092C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2086C2211yescharacteristic
92#2083C2211yescharacteristic
93#2076C2211yescharacteristic
94#2074C2211yescharacteristic
95#2072C2211yescharacteristic
96#2072C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2068C2211yescharacteristic
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2057C2211yescharacteristic
104#2057C2211yescharacteristic
105#2057C2211yescharacteristic
106#2055C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2036C2211yescharacteristic
110#2035C2211yescharacteristic
111#2035C2211yescharacteristic
112#2033C2211yescharacteristic
113#2023C2211yescharacteristic
114#2000C2211yescharacteristic
115#1993C2211yescharacteristic
116#1988C2211yescharacteristic
117#1973C2211yescharacteristic
118#1969C2211yescharacteristic
119#1959C2211yescharacteristic
120#1949C2211yescharacteristic
121#1949C2211yescharacteristic
122#1947C2211yescharacteristic
123#1947C2211yescharacteristic
124#1944C2211yescharacteristic
125#1943C2211yescharacteristic
126#1943C2211yescharacteristic
127#1943C2211yescharacteristic
128#1942C2211yescharacteristic
129#1942C2211yescharacteristic
130#1939C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1935C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1933C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1927C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1924C2211yescharacteristic
144#1924C2211yescharacteristic
145#1923C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1916C2211yescharacteristic
161#1895C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1877C2211yescharacteristic
168#1873C2211yescharacteristic
169#1872C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1854C2211yescharacteristic
179#1852C2211yescharacteristic
180#1851C2211yescharacteristic
181#1844C2211yescharacteristic
182#1825C2211yescharacteristic
183#1809C2211yescharacteristic
184#1805C2211yescharacteristic
185#1802C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188C4×#107C2211yescharacteristic
189#1771C2211yescharacteristic
190#1771C2211yescharacteristic
191#1768C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1746C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125—21no—
209C2×#125—21no—
210C2×#124—21no—
211C2×#124C2311yescharacteristic
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×C4×Q8—21no—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×#117—21no—
225C2×#117C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227#480—24no—
228#477—24no—
229#477—24no—
230#470—24no—
231#464—24no—
232#441—24no—
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
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×#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×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282#401D411yescharacteristic
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400D411yescharacteristic
290#400D411yescharacteristic
291#400D411yescharacteristic
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#398—21no—
302#398—21no—
303#398—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397D411yescharacteristic
311#397D411yescharacteristic
312#397D411yescharacteristic
313#396—21no—
314#396—21no—
315#396D411yescharacteristic
316#395—21no—
317#395—21no—
318#395—21no—
319#394—21no—
320#394—21no—
321#393—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#390—21no—
333#390—21no—
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
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#389C2311yescharacteristic
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#386—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#383—21no—
403#383—21no—
404#383—21no—
405#382—21no—
406#382—21no—
407#382—21no—
408#382—21no—
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#380—21no—
412#380—21no—
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376—21no—
443#376C2311yescharacteristic
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×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×D4—21no—
489C22×D4C2411yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4C2411yescharacteristic
493C2×Q16—41no—
494C2×Q16—41no—
495C2×Q16#4114yes—
496C2×SD16—22no—
497C2×SD16—41no—
498C2×SD16—41no—
499C2×M16—22no—
500C2×M16—41no—
501C2×M16—41no—
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C4⋊Q8—22no—
511C4⋊Q8—22no—
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514#125—82no—
515#125—82no—
516#124—22no—
517#124—41no—
518#124—82no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—41no—
522C22⋊Q8—41no—
523C22⋊Q8—82no—
524#121—22no—
525#121—41no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—82no—
539C4×D4—22no—
540C4×D4—41no—
541#117—22no—
542#117—41no—
543#117—82no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C22⋊C4C2×D411yescharacteristic
619C2×C22⋊C4C2×D411yescharacteristic
620C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643#107—22no—
644#107—22no—
645#107—22no—
646#107—41no—
647#107—41no—
648#107—41no—
649#107—41no—
650#107—41no—
651#107#4114yes—
652#106—22no—
653#106—22no—
654#106—22no—
655#106—41no—
656#106—41no—
657C4⋊C8—22no—
658C4⋊C8—22no—
659C4⋊C8—22no—
660C4⋊C8—41no—
661C4⋊C8—41no—
662#103—22no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—41no—
673#103—41no—
674#103—41no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—41no—
679#102—41no—
680#102—41no—
681#102—41no—
682C22⋊C8—22no—
683C22⋊C8—41no—
684C22⋊C8—41no—
685#97—22no—
686#97—41no—
687#97—41no—
688#97—41no—
689C4×C8—41no—
690C4×C8—41no—
691C4×C8—41no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749C24—21no—
750C24C22×D411yescharacteristic
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8—42no—
763C2×Q8—42no—
764C2×Q8—81no—
765C2×Q8—81no—
766C2×Q8—81no—
767C2×Q8C2×#4112yes—
768C2×Q8C2×#4112yes—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—81no—
777C2×D4—81no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—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—42no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—81no—
803C22×C4—81no—
804C22×C4—81no—
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C2511yescharacteristic
819Q16—44no—
820SD16—82no—
821M16—82no—
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×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8C2×#4112yes—
845C2×C8C2×#4112yes—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4—41no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—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⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4C2×#4112yes—
908C4⋊C4C2×#4112yes—
909C4⋊C42−1+412yes—
910C22⋊C4—22no—
911C22⋊C4—41no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C22⋊C4—41no—
915C22⋊C4—41no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—42no—
947C42—42no—
948C42—42no—
949C42—42no—
950C42—42no—
951C42—42no—
952C42—42no—
953C42—42no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42—81no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23C23×D411yescharacteristic
977Q8—22no—
978Q8—22no—
979Q8—22no—
980Q8—22no—
981Q8—41no—
982Q8—41no—
983Q8—41no—
984Q8—41no—
985Q8—84no—
986Q8—162no—
987D4—41no—
988D4—41no—
989D4—41no—
990D4—41no—
991D4—162no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
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—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—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—84no—
1080C2×C4—162no—
1081C2×C4#57812yes—
1082C2×C4C22×#4111yescharacteristic
1083C2×C4C22×#4111yescharacteristic
1084C2×C4C2×2−1+411yescharacteristic
1085C2×C4#58511yescharacteristic
1086C2×C4#58511yescharacteristic
1087C2×C4#58511yescharacteristic
1088C8—22no—
1089C8—22no—
1090C8—41no—
1091C8—41no—
1092C8—41no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—41no—
1102C22—41no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22D4×#4111yescharacteristic
1111C22D4×#4111yescharacteristic
1112C22#348911yescharacteristic
1113C22C2×#57811yescharacteristic
1114C22#358511yescharacteristic
1115C22#358511yescharacteristic
1116C22#358611yescharacteristic
1117C4—22no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—42no—
1122C4—42no—
1123C4—41no—
1124C4—41no—
1125C4—42no—
1126C4—42no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—42no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4#348211yescharacteristic
1146C4#349111yescharacteristic
1147C4#351211yescharacteristic
1148C4#356511yescharacteristic
1149C2—81no—
1150C2—161no—
1151C2#5917811yescharacteristic
1152C2#6150511yescharacteristic
1153C2#6151511yescharacteristic
1154C2#6154411yescharacteristic
1155C2#6155811yescharacteristic
1156C2#6216511yescharacteristic
1157C2#6222911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45210C2semidirect
3. #31485C2semidirect
4. #31239C2semidirect
7. #29527C2semidirect
8. #29458C2semidirect
9. #29025C2semidirect
11. #28000C2semidirect
12. #27445C2semidirect
13. #27364C2semidirect
14. #27185C2semidirect
15. #27164C2semidirect
16. #27059C2semidirect
17. #26873C2semidirect
19. #26765C2semidirect
21. #26189C2semidirect
22. #26091C2semidirect
23. #26005C2semidirect
24. #25047C2semidirect
25. #23291C2semidirect
26. #23139C2semidirect
27. #23111C2semidirect
28. #22977C2semidirect
30. #21625C2semidirect
31. #21127C2semidirect

Maximal subgroups

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

subgroupindex
#452102
#358952
#314852
#312392
#311322
#306182
#295272
#294582
#290252
#280772
#280002
#274452
#273642
#271852
#271642
#270592
#268732
#268052
#267652
#266712
#261892
#260912
#260052
#250472
#232912
#231392
#231112
#229772
#229312
#216252
#211272