Finite Group Databasebeta

← #6777225

Subgroups — #6777225

Order 512.

1399 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36402C211yesmaximal, characteristic, complemented
2#34917C211yesmaximal, characteristic, complemented
3#33080C211yesmaximal, characteristic, complemented
4#32354C211yesmaximal, characteristic, complemented
5#32322C211yesmaximal, characteristic, complemented
6#31646C211yesmaximal, characteristic, complemented
7#31582C211yesmaximal, characteristic, complemented
8#31387C211yesmaximal, characteristic, complemented
9#31323C211yesmaximal, characteristic, complemented
10#31321C211yesmaximal, characteristic, complemented
11#30560C211yesmaximal, characteristic
12#30111C211yesmaximal, characteristic, complemented
13#30008C211yesmaximal, characteristic, complemented
14#29516C211yesmaximal, characteristic, complemented
15#29399C211yesmaximal, characteristic, complemented
16#29046C211yesmaximal, characteristic, complemented
17#28846C211yesmaximal, characteristic, complemented
18#27893C211yesmaximal, characteristic, complemented
19#27858C211yesmaximal, characteristic, complemented
20#27837C211yesmaximal, characteristic, complemented
21#27625C211yesmaximal, characteristic, complemented
22#27618C211yesmaximal, characteristic, complemented
23#27109C211yesmaximal, characteristic, complemented
24#27045C211yesmaximal, characteristic, complemented
25#26959C211yesmaximal, characteristic, complemented
26#26669C211yesmaximal, characteristic, complemented
27#26552C211yesmaximal, characteristic, complemented
28#22785C211yesmaximal, characteristic, complemented
29#22181C211yesmaximal, characteristic, complemented
30#22080C211yesmaximal, characteristic, complemented
31#21114C211yesmaximal, characteristic, complemented
32C2×#482C2211yescharacteristic
33C2×#466C2211yescharacteristic
34C2×C4×SD16C2211yescharacteristic
35#2860C2211yescharacteristic
36#2855C2211yescharacteristic
37#2850C2211yescharacteristic
38#2603—21no—
39#2600—21no—
40#2597—21no—
41#2595—21no—
42#2594—21no—
43#2578—21no—
44#2576—21no—
45#2576—21no—
46#2570C2211yescharacteristic
47#2566C2211yescharacteristic
48#2562C2211yescharacteristic
49#2535C2211yescharacteristic
50#2515—21no—
51#2508C2211yescharacteristic
52#2497C2211yescharacteristic
53#2494C2211yescharacteristic
54#2494C2211yescharacteristic
55#2457—21no—
56#2447C2211yescharacteristic
57#2426C2211yescharacteristic
58#2422C2211yescharacteristic
59#2420C2211yescharacteristic
60#2415C2211yescharacteristic
61#2414C2211yescharacteristic
62#2401—21no—
63#2392—21no—
64#2373—21no—
65#2363C2211yescharacteristic
66#2362C2211yescharacteristic
67#2357—21no—
68C4×#125C2211yescharacteristic
69C4×#123—21no—
70C4×#121C2211yescharacteristic
71C4×#121C2211yescharacteristic
72C4×#121C2211yescharacteristic
73#2296C2211yescharacteristic
74#2295C2211yescharacteristic
75#2290—21no—
76#2285C2211yescharacteristic
77#2283C2211yescharacteristic
78C42×D4C2211yescharacteristic
79C42×D4C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2095C2211yescharacteristic
86#2092C2211yescharacteristic
87#2092C2211yescharacteristic
88#2088C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2083C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2074C2211yescharacteristic
97#2072C2211yescharacteristic
98#2066C2211yescharacteristic
99#2065C2211yescharacteristic
100#2059C2211yescharacteristic
101#2059C2211yescharacteristic
102#2055C2211yescharacteristic
103#2042C2211yescharacteristic
104#2036C2211yescharacteristic
105#2035C2211yescharacteristic
106#2035C2211yescharacteristic
107#2035C2211yescharacteristic
108#2034C2211yescharacteristic
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2026C2211yescharacteristic
115#2025C2211yescharacteristic
116#2012C2211yescharacteristic
117#2000C2211yescharacteristic
118#2000C2211yescharacteristic
119#1999C2211yescharacteristic
120#1958C2211yescharacteristic
121#1958C2211yescharacteristic
122#1948C2211yescharacteristic
123#1948C2211yescharacteristic
124#1942C2211yescharacteristic
125#1942C2211yescharacteristic
126#1941C2211yescharacteristic
127#1941C2211yescharacteristic
128#1934C2211yescharacteristic
129#1934C2211yescharacteristic
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic
132#1928C2211yescharacteristic
133#1928C2211yescharacteristic
134#1928C2211yescharacteristic
135#1927C2211yescharacteristic
136#1926C2211yescharacteristic
137#1926C2211yescharacteristic
138#1926C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1923C2211yescharacteristic
143#1923C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1920C2211yescharacteristic
148#1920C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1916C2211yescharacteristic
157#1916C2211yescharacteristic
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic
160#1892C2211yescharacteristic
161#1892C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1875C2211yescharacteristic
169#1869C2211yescharacteristic
170#1869C2211yescharacteristic
171#1865C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1846C2211yescharacteristic
183#1839C2211yescharacteristic
184#1835C2211yescharacteristic
185#1825C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1817C2211yescharacteristic
189#1808C2211yescharacteristic
190#1808C2211yescharacteristic
191#1808C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1797C2211yescharacteristic
195C4×#107C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1744C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×#126—21no—
208C2×#125C2311yescharacteristic
209C2×#124C2311yescharacteristic
210C2×#123—21no—
211C2×C22⋊Q8C2311yescharacteristic
212C2×C22⋊Q8C2311yescharacteristic
213C2×#121C2311yescharacteristic
214C2×#121C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×D4—21no—
219C2×C4×D4—21no—
220C2×C4×D4—21no—
221C2×C4×D4D411yescharacteristic
222C2×C4×D4D411yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×#117—21no—
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C22×C42—21no—
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234#482—24no—
235#466—24no—
236C4×SD16—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283#401—21no—
284#401—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#398—21no—
290#398—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#396—21no—
300#396—21no—
301#396—21no—
302#396—21no—
303#394—21no—
304#394—21no—
305#394—21no—
306#394—21no—
307#394—21no—
308#394—21no—
309#392—21no—
310#392—21no—
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#390—21no—
315#390—21no—
316#390—21no—
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#390C2311yescharacteristic
321#390C2311yescharacteristic
322#389—21no—
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#388—21no—
336#388—21no—
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#388—21no—
353#388—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#386—21no—
368#386—21no—
369#386—21no—
370#386—21no—
371#386—21no—
372#386—21no—
373#386—21no—
374#386—21no—
375#386—21no—
376#385—21no—
377#385—21no—
378#385—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#384C2311yescharacteristic
384#384C2311yescharacteristic
385#383—21no—
386#382—21no—
387#382—21no—
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#381—21no—
393#381—21no—
394#381—21no—
395#381—21no—
396#380—21no—
397#380C2311yescharacteristic
398#380C2311yescharacteristic
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405C4×C4⋊C4—21no—
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⋊C4D411yescharacteristic
413C4×C4⋊C4D411yescharacteristic
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×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4D411yescharacteristic
431C4×C22⋊C4D411yescharacteristic
432C4×C22⋊C4D411yescharacteristic
433C4×C22⋊C4D411yescharacteristic
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436#376—21no—
437#376—21no—
438C43C2311yescharacteristic
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×Q8C2411yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4C2×D411yescharacteristic
487C22×D4C2411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4C2×D411yescharacteristic
494C23×C4C2×D411yescharacteristic
495C23×C4C2×D411yescharacteristic
496C23×C4C2×D411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C2×SD16—22no—
500C2×SD16—41no—
501C2×SD16—41no—
502C2×D8—22no—
503C2×D8—41no—
504C2×D8—41no—
505C22×C8—22no—
506C22×C8—41no—
507C22×C8—41no—
508C22×C8—41no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519#126—44no—
520#125—41no—
521#125—41no—
522#124—41no—
523#124—41no—
524#123—44no—
525C22⋊Q8—41no—
526C22⋊Q8—41no—
527C22⋊Q8—41no—
528C22⋊Q8—41no—
529#121—22no—
530#121—22no—
531#121—22no—
532#121—41no—
533#121—41no—
534#121—41no—
535#121—41no—
536#121—41no—
537C4×Q8—22no—
538C4×Q8—41no—
539C4×D4—24no—
540C4×D4—22no—
541C4×D4—42no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—44no—
552C4×D4—44no—
553C4×D4—82no—
554#117—22no—
555#117—41no—
556#117—41no—
557#117—41no—
558#117—82no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—41no—
645C2×C42—41no—
646C2×C42—41no—
647C2×C42—41no—
648C2×C42—82no—
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2×D411yescharacteristic
655C2×C42C2×D411yescharacteristic
656C2×C42C2×D411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662#107—22no—
663#107—22no—
664#107—41no—
665#107—41no—
666#107—41no—
667#107—41no—
668#107—41no—
669#106—22no—
670#106—22no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678#103—22no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#102—22no—
686#102—22no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102#4114yes—
698C22⋊C8—22no—
699C22⋊C8—41no—
700C22⋊C8—41no—
701C22⋊C8—41no—
702C22⋊C8—41no—
703C22⋊C8—41no—
704C4×C8—22no—
705C4×C8—41no—
706C4×C8—41no—
707C4×C8—41no—
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#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755C24—21no—
756C24—21no—
757C24C22×D411yescharacteristic
758C24C22×D411yescharacteristic
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×D4—22no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—42no—
780C2×D4—42no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—81no—
787C2×D4—81no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4C2×#4112yes—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4#13514yes—
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C2511yescharacteristic
855SD16—44no—
856D8—82no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—82no—
881C2×C8—82no—
882C2×C8C2×#4112yes—
883C4⋊C4—22no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4C2×#4112yes—
933C22⋊C4—22no—
934C22⋊C4—22no—
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—41no—
938C22⋊C4—41no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C42—22no—
972C42—22no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—41no—
984C42—41no—
985C42—41no—
986C42—41no—
987C42—41no—
988C42—41no—
989C42—42no—
990C42—42no—
991C42—42no—
992C42—42no—
993C42—42no—
994C42—42no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42—81no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—22no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23C2×#13512yes—
1027C23C23×D411yescharacteristic
1028Q8—41no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032D4—22no—
1033D4—22no—
1034D4—44no—
1035D4—41no—
1036D4—41no—
1037D4—41no—
1038D4—41no—
1039D4—41no—
1040D4—41no—
1041D4—84no—
1042D4—84no—
1043D4—84no—
1044D4—162no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—44no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—82no—
1130C2×C4—84no—
1131C2×C4—84no—
1132C2×C4—82no—
1133C2×C4—82no—
1134C2×C4—84no—
1135C2×C4—162no—
1136C2×C4C2×#13512yes—
1137C2×C4C2×#13512yes—
1138C2×C4#57512yes—
1139C2×C4C22×#4111yescharacteristic
1140C2×C4#58511yescharacteristic
1141C2×C4#58511yescharacteristic
1142C2×C4#58511yescharacteristic
1143C2×C4#58511yescharacteristic
1144C2×C4#58511yescharacteristic
1145C8—22no—
1146C8—41no—
1147C8—41no—
1148C8—41no—
1149C8—41no—
1150C8—41no—
1151C8—41no—
1152C8—41no—
1153C22—22no—
1154C22—22no—
1155C22—22no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—42no—
1162C22—41no—
1163C22—41no—
1164C22—41no—
1165C22—41no—
1166C22—41no—
1167C22—42no—
1168C22—42no—
1169C22—41no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22#344911yescharacteristic
1182C22D4×#4111yescharacteristic
1183C22#348511yescharacteristic
1184C22C22×#13511yescharacteristic
1185C22C2×#57511yescharacteristic
1186C22#358411yescharacteristic
1187C22#358511yescharacteristic
1188C4—22no—
1189C4—22no—
1190C4—22no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—41no—
1200C4—42no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4#349311yescharacteristic
1215C4#352111yescharacteristic
1216C4#356611yescharacteristic
1217C4#356711yescharacteristic
1218C2—42no—
1219C2—81no—
1220C2—82no—
1221C2—161no—
1222C2#3837711yescharacteristic
1223C2#6094811yescharacteristic
1224C2#6099811yescharacteristic
1225C2#6142711yescharacteristic
1226C2#6145611yescharacteristic
1227C2#6169911yescharacteristic
1228C2#6174311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30560C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36402C2semidirect
2. #34917C2semidirect
3. #33080C2semidirect
4. #32354C2semidirect
5. #32322C2semidirect
6. #31646C2semidirect
7. #31582C2semidirect
8. #31387C2semidirect
9. #31323C2semidirect
10. #31321C2semidirect
12. #30111C2semidirect
13. #30008C2semidirect
14. #29516C2semidirect
15. #29399C2semidirect
16. #29046C2semidirect
17. #28846C2semidirect
18. #27893C2semidirect
19. #27858C2semidirect
20. #27837C2semidirect
21. #27625C2semidirect
22. #27618C2semidirect
23. #27109C2semidirect
24. #27045C2semidirect
25. #26959C2semidirect
26. #26669C2semidirect
27. #26552C2semidirect
28. #22785C2semidirect
29. #22181C2semidirect
30. #22080C2semidirect
31. #21114C2semidirect

Maximal subgroups

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

subgroupindex
#364022
#349172
#330802
#323542
#323222
#316462
#315822
#313872
#313232
#313212
#305602
#301112
#300082
#295162
#293992
#290462
#288462
#278932
#278582
#278372
#276252
#276182
#271092
#270452
#269592
#266692
#265522
#227852
#221812
#220802
#211142