Finite Group Databasebeta

← #7620248

Subgroups — #7620248

Order 512.

1331 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45172C211yesmaximal, characteristic, complemented
2#45039C211yesmaximal, characteristic, complemented
3#32389C211yesmaximal, characteristic, complemented
4#31080C211yesmaximal, characteristic, complemented
5#30946C211yesmaximal, characteristic, complemented
6#30778C211yesmaximal, characteristic, complemented
7#29401C211yesmaximal, characteristic, complemented
8#29400C211yesmaximal, characteristic, complemented
9#29079C211yesmaximal, characteristic, complemented
10#28992C211yesmaximal, characteristic
11#28973C211yesmaximal, characteristic, complemented
12#28869C211yesmaximal, characteristic, complemented
13#28799C211yesmaximal, characteristic, complemented
14#28787C211yesmaximal, characteristic, complemented
15#28077C211yesmaximal, characteristic, complemented
16#28032C211yesmaximal, characteristic, complemented
17#27514C211yesmaximal, characteristic, complemented
18#27474C211yesmaximal, characteristic, complemented
19#27463C211yesmaximal, characteristic, complemented
20#26884C211yesmaximal, characteristic, complemented
21#26861C211yesmaximal, characteristic, complemented
22#26812C211yesmaximal, characteristic
23#26546C211yesmaximal, characteristic
24#26370C211yesmaximal, characteristic, complemented
25#23065C211yesmaximal, characteristic, complemented
26#22979C211yesmaximal, characteristic, complemented
27#22944C211yesmaximal, characteristic, complemented
28#22941C211yesmaximal, characteristic, complemented
29#21725C211yesmaximal, characteristic, complemented
30#21671C211yesmaximal, characteristic, complemented
31#21284C211yesmaximal, characteristic, complemented
32C2×#500C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×C4×D8C2211yescharacteristic
38#2788—21no—
39#2781—21no—
40#2764—21no—
41#2751—21no—
42#2745—21no—
43#2716—21no—
44#2715—21no—
45#2707—21no—
46#2596—21no—
47#2573—21no—
48#2571C2211yescharacteristic
49#2551C2211yescharacteristic
50#2547—21no—
51#2521—21no—
52#2513C2211yescharacteristic
53#2512C2211yescharacteristic
54#2508C2211yescharacteristic
55#2506C2211yescharacteristic
56#2496C2211yescharacteristic
57#2495C2211yescharacteristic
58#2493—21no—
59#2491C2211yescharacteristic
60#2491C2211yescharacteristic
61#2489—21no—
62#2488—21no—
63#2466—21no—
64#2454C2211yescharacteristic
65#2452C2211yescharacteristic
66#2442C2211yescharacteristic
67#2439C2211yescharacteristic
68#2422C2211yescharacteristic
69#2420C2211yescharacteristic
70#2401C2211yescharacteristic
71#2370C2211yescharacteristic
72#2369C2211yescharacteristic
73#2363C2211yescharacteristic
74#2361C2211yescharacteristic
75#2357C2211yescharacteristic
76#2349C2211yescharacteristic
77#2347C2211yescharacteristic
78#2345C2211yescharacteristic
79#2331C2211yescharacteristic
80#2331C2211yescharacteristic
81#2319C2211yescharacteristic
82#2319C2211yescharacteristic
83#2093C2211yescharacteristic
84#2093C2211yescharacteristic
85#2092C2211yescharacteristic
86#2092C2211yescharacteristic
87#2088C2211yescharacteristic
88#2086C2211yescharacteristic
89#2086C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2084C2211yescharacteristic
95#2083C2211yescharacteristic
96#2077C2211yescharacteristic
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2067C2211yescharacteristic
102#2065C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2058C2211yescharacteristic
106#2058C2211yescharacteristic
107#2057C2211yescharacteristic
108#2057C2211yescharacteristic
109#2054C2211yescharacteristic
110#2034C2211yescharacteristic
111#2033C2211yescharacteristic
112#2023C2211yescharacteristic
113#2023C2211yescharacteristic
114#1999C2211yescharacteristic
115#1993C2211yescharacteristic
116#1993C2211yescharacteristic
117#1993C2211yescharacteristic
118#1991C2211yescharacteristic
119#1972C2211yescharacteristic
120#1972C2211yescharacteristic
121#1949C2211yescharacteristic
122#1949C2211yescharacteristic
123#1948C2211yescharacteristic
124#1947C2211yescharacteristic
125#1943C2211yescharacteristic
126#1943C2211yescharacteristic
127#1943C2211yescharacteristic
128#1943C2211yescharacteristic
129#1943C2211yescharacteristic
130#1942C2211yescharacteristic
131#1942C2211yescharacteristic
132#1942C2211yescharacteristic
133#1936C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1924C2211yescharacteristic
148#1923C2211yescharacteristic
149#1923C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1920C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1917C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1895C2211yescharacteristic
168#1895C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1846C2211yescharacteristic
182#1840C2211yescharacteristic
183#1834C2211yescharacteristic
184#1809C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187C4×#107C2211yescharacteristic
188C4×#107C2211yescharacteristic
189C4×#106C2211yescharacteristic
190C4×#106C2211yescharacteristic
191#1771C2211yescharacteristic
192#1770C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1736C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126—21no—
210C2×#126—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×#124—21no—
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226#500—24no—
227#482—24no—
228#480—24no—
229#478—24no—
230#474—24no—
231C4×D8—24no—
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
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×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280#401D411yescharacteristic
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400D411yescharacteristic
289#400D411yescharacteristic
290#400D411yescharacteristic
291#399—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397D411yescharacteristic
303#397D411yescharacteristic
304#397D411yescharacteristic
305#396—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#396D411yescharacteristic
310#395—21no—
311#395—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#393—21no—
317#393—21no—
318#393—21no—
319#393—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#390—21no—
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389C2311yescharacteristic
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#388—21no—
357#388—21no—
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#387—21no—
373#387—21no—
374#387—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#386—21no—
385#386—21no—
386#386—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#383—21no—
397#383—21no—
398#382—21no—
399#382—21no—
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#381—21no—
405#381—21no—
406#381—21no—
407#381—21no—
408#380—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412#380—21no—
413#380—21no—
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440#376C2311yescharacteristic
441C2×#95—21no—
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×D4—21no—
488C22×D4—21no—
489C22×D4C2411yescharacteristic
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C2411yescharacteristic
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—41no—
500C2×M16—22no—
501C2×M16—41no—
502C2×M16—41no—
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8—41no—
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517C4⋊Q8—82no—
518#126—82no—
519#126—82no—
520#125—22no—
521#125—41no—
522#125—82no—
523#124—82no—
524#124—82no—
525#123—82no—
526C22⋊Q8—82no—
527#121—22no—
528#121—22no—
529#121—41no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—41no—
536C4×D4—41no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—82no—
540#117—22no—
541#117—41no—
542C2×C4⋊C4—22no—
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⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
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×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⋊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⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C22⋊C4C2×D411yescharacteristic
619C2×C22⋊C4C2×D411yescharacteristic
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
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×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640#107—22no—
641#107—22no—
642#107—22no—
643#107—22no—
644#107—22no—
645#107—22no—
646#107—22no—
647#107—22no—
648#107—41no—
649#107—41no—
650#107#4114yes—
651#106—22no—
652#106—22no—
653#106—22no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658#106—41no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8—22no—
662#102—22no—
663#102—22no—
664#102—22no—
665#102—22no—
666#102—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—41no—
672#102—41no—
673#102—41no—
674#102—41no—
675#102#4114yes—
676C22⋊C8—22no—
677C22⋊C8—22no—
678C22⋊C8—22no—
679#97—22no—
680#97—41no—
681#97—41no—
682#97—41no—
683C4×C8—22no—
684C4×C8—22no—
685C4×C8—22no—
686C4×C8—22no—
687C4×C8—41no—
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#95—21no—
725#95—21no—
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
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
742C24—21no—
743C24—21no—
744C24C22×D411yescharacteristic
745C2×Q8—42no—
746C2×Q8—42no—
747C2×Q8—42no—
748C2×Q8—81no—
749C2×Q8—81no—
750C2×Q8—81no—
751C2×Q8—81no—
752C2×Q8—81no—
753C2×Q8—81no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—42no—
766C2×D4—42no—
767C2×D4—42no—
768C2×D4—81no—
769C2×D4—81no—
770C2×D4—81no—
771C2×D4C2×#4112yes—
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—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4—81no—
803C22×C4—81no—
804C22×C4—81no—
805C22×C4—81no—
806C22×C4—81no—
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×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C2511yescharacteristic
821D8—44no—
822M16—82no—
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×C8C2×#4112yes—
844C2×C8C2×#4112yes—
845C2×C82−1+412yes—
846C2×C82−1+412yes—
847C4⋊C4—22no—
848C4⋊C4—22no—
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—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—41no—
875C4⋊C4—41no—
876C4⋊C4—41no—
877C4⋊C4—41no—
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—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⋊C4—81no—
904C4⋊C4C2×#4112yes—
905C4⋊C4C2×#4112yes—
906C4⋊C4C2×#4112yes—
907C22⋊C4—22no—
908C22⋊C4—41no—
909C22⋊C4—41no—
910C22⋊C4—41no—
911C22⋊C4—41no—
912C22⋊C4—41no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—42no—
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—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—42no—
953C42—42no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42—81no—
962C42—81no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—22no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23C23×D411yescharacteristic
985Q8—162no—
986Q8—162no—
987Q8—162no—
988D4—22no—
989D4—22no—
990D4—41no—
991D4—41no—
992D4—41no—
993D4—41no—
994D4—41no—
995D4—41no—
996D4—84no—
997D4—162no—
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—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
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—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—162no—
1083C2×C4—162no—
1084C2×C4—162no—
1085C2×C4—162no—
1086C2×C4—162no—
1087C2×C4#57612yes—
1088C2×C4C22×#4111yescharacteristic
1089C2×C4C22×#4111yescharacteristic
1090C2×C4C2×2−1+411yescharacteristic
1091C2×C4C2×2−1+411yescharacteristic
1092C2×C4#58511yescharacteristic
1093C2×C4#58511yescharacteristic
1094C8—22no—
1095C8—22no—
1096C8—22no—
1097C8—22no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C8—41no—
1102C22—41no—
1103C22—42no—
1104C22—41no—
1105C22—41no—
1106C22—42no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—42no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22D4×#4111yescharacteristic
1124C22D4×#4111yescharacteristic
1125C22#349911yescharacteristic
1126C22C2×#57611yescharacteristic
1127C22#358411yescharacteristic
1128C22#358511yescharacteristic
1129C22#358611yescharacteristic
1130C4—22no—
1131C4—41no—
1132C4—41no—
1133C4—42no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—42no—
1144C4—42no—
1145C4—41no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4#348211yescharacteristic
1158C4#349511yescharacteristic
1159C4#350711yescharacteristic
1160C4#356411yescharacteristic
1161C2—81no—
1162C2—82no—
1163C2—161no—
1164C2#5984011yescharacteristic
1165C2#6147511yescharacteristic
1166C2#6151811yescharacteristic
1167C2#6153711yescharacteristic
1168C2#6153911yescharacteristic
1169C2#6251511yescharacteristic
1170C2#6252411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#1999C22
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. #45172C2semidirect
2. #45039C2semidirect
3. #32389C2semidirect
4. #31080C2semidirect
5. #30946C2semidirect
6. #30778C2semidirect
7. #29401C2semidirect
8. #29400C2semidirect
9. #29079C2semidirect
11. #28973C2semidirect
12. #28869C2semidirect
13. #28799C2semidirect
14. #28787C2semidirect
15. #28077C2semidirect
16. #28032C2semidirect
17. #27514C2semidirect
18. #27474C2semidirect
19. #27463C2semidirect
20. #26884C2semidirect
21. #26861C2semidirect
24. #26370C2semidirect
25. #23065C2semidirect
26. #22979C2semidirect
27. #22944C2semidirect
28. #22941C2semidirect
29. #21725C2semidirect
30. #21671C2semidirect
31. #21284C2semidirect

Maximal subgroups

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

subgroupindex
#451722
#450392
#323892
#310802
#309462
#307782
#294012
#294002
#290792
#289922
#289732
#288692
#287992
#287872
#280772
#280322
#275142
#274742
#274632
#268842
#268612
#268122
#265462
#263702
#230652
#229792
#229442
#229412
#217252
#216712
#212842