Finite Group Databasebeta

← #7584519

Subgroups — #7584519

Order 512.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1167 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59502C211yesmaximal, characteristic, complemented
2#36490C211yesmaximal, characteristic
3#31484C211yesmaximal, characteristic, complemented
4#31239C211yesmaximal, characteristic, complemented
5#31132C211yesmaximal, characteristic
6#30602C211yesmaximal, characteristic
7#29514C211yesmaximal, characteristic, complemented
8#29450C211yesmaximal, characteristic, complemented
9#29025C211yesmaximal, characteristic, complemented
10#28079C211yesmaximal, characteristic
11#28001C211yesmaximal, characteristic, complemented
12#27452C211yesmaximal, characteristic, complemented
13#27378C211yesmaximal, characteristic, complemented
14#27177C211yesmaximal, characteristic, complemented
15#27165C211yesmaximal, characteristic, complemented
16#27052C211yesmaximal, characteristic, complemented
17#26856C211yesmaximal, characteristic, complemented
18#26805C211yesmaximal, characteristic
19#26783C211yesmaximal, characteristic, complemented
20#26659C211yesmaximal, characteristic
21#26173C211yesmaximal, characteristic, complemented
22#26094C211yesmaximal, characteristic, complemented
23#25994C211yesmaximal, characteristic, complemented
24#25033C211yesmaximal, characteristic, complemented
25#23282C211yesmaximal, characteristic, complemented
26#23133C211yesmaximal, characteristic, complemented
27#23111C211yesmaximal, characteristic, complemented
28#22977C211yesmaximal, characteristic, complemented
29#22916C211yesmaximal, characteristic
30#21616C211yesmaximal, characteristic, complemented
31#21119C211yesmaximal, characteristic, complemented
32C2×#480C2211yescharacteristic
33C2×#477C2211yescharacteristic
34C2×#477C2211yescharacteristic
35C2×#467C2211yescharacteristic
36C2×#464C2211yescharacteristic
37C2×C4×Q16C2211yescharacteristic
38#2866—21no—
39#2860C2211yescharacteristic
40#2762—21no—
41#2698—21no—
42#2611—21no—
43#2597—21no—
44#2590—21no—
45#2589—21no—
46#2575—21no—
47#2570C2211yescharacteristic
48#2528—21no—
49#2521—21no—
50#2515—21no—
51#2509C2211yescharacteristic
52#2508C2211yescharacteristic
53#2506C2211yescharacteristic
54#2494C2211yescharacteristic
55#2491C2211yescharacteristic
56#2469—21no—
57#2468—21no—
58#2462—21no—
59#2451C2211yescharacteristic
60#2451C2211yescharacteristic
61#2448C2211yescharacteristic
62#2440C2211yescharacteristic
63#2426C2211yescharacteristic
64#2423C2211yescharacteristic
65#2421C2211yescharacteristic
66#2421C2211yescharacteristic
67#2367C2211yescharacteristic
68#2365C2211yescharacteristic
69#2362—21no—
70#2361C2211yescharacteristic
71#2360C2211yescharacteristic
72#2360C2211yescharacteristic
73#2357C2211yescharacteristic
74#2355C2211yescharacteristic
75#2351C2211yescharacteristic
76#2345C2211yescharacteristic
77#2344C2211yescharacteristic
78C4×C4⋊Q8C2211yescharacteristic
79C4×#126C2211yescharacteristic
80C4×#124—21no—
81#2295C2211yescharacteristic
82C42×Q8C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2093C2211yescharacteristic
88#2092C2211yescharacteristic
89#2087C2211yescharacteristic
90#2087C2211yescharacteristic
91#2086C2211yescharacteristic
92#2083C2211yescharacteristic
93#2077C2211yescharacteristic
94#2074C2211yescharacteristic
95#2074C2211yescharacteristic
96#2074C2211yescharacteristic
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#1987C2211yescharacteristic
117#1973C2211yescharacteristic
118#1969C2211yescharacteristic
119#1959C2211yescharacteristic
120#1949C2211yescharacteristic
121#1949C2211yescharacteristic
122#1948C2211yescharacteristic
123#1947C2211yescharacteristic
124#1944C2211yescharacteristic
125#1943C2211yescharacteristic
126#1943C2211yescharacteristic
127#1942C2211yescharacteristic
128#1942C2211yescharacteristic
129#1942C2211yescharacteristic
130#1939C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1924C2211yescharacteristic
144#1924C2211yescharacteristic
145#1923C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1918C2211yescharacteristic
150#1918C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1918C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1916C2211yescharacteristic
161#1893C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1877C2211yescharacteristic
168#1872C2211yescharacteristic
169#1872C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1865C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1862C2211yescharacteristic
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic
180#1850C2211yescharacteristic
181#1846C2211yescharacteristic
182#1824C2211yescharacteristic
183#1808C2211yescharacteristic
184#1804C2211yescharacteristic
185#1803C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188C4×#107C2211yescharacteristic
189#1771C2211yescharacteristic
190#1771C2211yescharacteristic
191#1767C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1752C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201#1744C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#126D411yescharacteristic
210C2×#125—21no—
211C2×#124—21no—
212C2×#124C2311yescharacteristic
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230#480—24no—
231#477—24no—
232#477—24no—
233#467—24no—
234#464—24no—
235C4×Q16—24no—
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285#401—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—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#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#396—21no—
307#395—21no—
308#395—21no—
309#395—21no—
310#394—21no—
311#394—21no—
312#393—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#390—21no—
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
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#388D411yescharacteristic
365#388D411yescharacteristic
366#388D411yescharacteristic
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#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#387D411yescharacteristic
391#387D411yescharacteristic
392#387D411yescharacteristic
393#386—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#383D411yescharacteristic
402#382—21no—
403#382—21no—
404#382—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#381—21no—
409#381—21no—
410#380—21no—
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
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×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376—21no—
442C43—21no—
443C43C2311yescharacteristic
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×C4—21no—
493C23×C4C2411yescharacteristic
494C2×Q16—41no—
495C2×Q16—41no—
496C2×Q16#4114yes—
497C2×SD16—22no—
498C2×SD16—41no—
499C2×SD16—41no—
500C22×C8—22no—
501C22×C8—41no—
502C22×C8—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—41no—
514C4⋊Q8—41no—
515#126—42no—
516#126—82no—
517#125—82no—
518#124—22no—
519#124—41no—
520#124—44no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C22⋊Q8—44no—
524C22⋊Q8—41no—
525C22⋊Q8—41no—
526#121—22no—
527#121—41no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—82no—
541C4×Q8—82no—
542C4×D4—22no—
543C4×D4—41no—
544C4×D4—82no—
545#117—82no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
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—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
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×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42C2×D411yescharacteristic
639C2×C42C2×D411yescharacteristic
640C2×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648#107—22no—
649#107—22no—
650#107—22no—
651#107—22no—
652#107—22no—
653#107—22no—
654#107—41no—
655#107—41no—
656#107—41no—
657#107—41no—
658#107#4114yes—
659#106—41no—
660#106—41no—
661#106—41no—
662C4⋊C8—22no—
663C4⋊C8—22no—
664C4⋊C8—22no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—41no—
678#103—41no—
679#103—41no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—41no—
684#102—41no—
685#102—41no—
686#102—41no—
687C22⋊C8—22no—
688C22⋊C8—41no—
689C22⋊C8—41no—
690#97—41no—
691#97—41no—
692#97—41no—
693#97—41no—
694C4×C8—22no—
695C4×C8—41no—
696C4×C8—41no—
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#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
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
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24—21no—
753C24C22×D411yescharacteristic
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8—81no—
769C2×Q8—81no—
770C2×Q8C2×#4112yes—
771C2×Q8C2×#4112yes—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—81no—
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—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—81no—
807C22×C4—81no—
808C22×C4—81no—
809C22×C4—81no—
810C22×C4—81no—
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×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C2511yescharacteristic
825Q16—44no—
826SD16—82no—
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×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—82no—
850C2×C8C2×#4112yes—
851C2×C8C2×#4112yes—
852C4⋊C4—22no—
853C4⋊C4—22no—
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—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
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—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4C2×#4112yes—
913C4⋊C4C2×#4112yes—
914C4⋊C42−1+412yes—
915C22⋊C4—22no—
916C22⋊C4—22no—
917C22⋊C4—22no—
918C22⋊C4—22no—
919C22⋊C4—22no—
920C22⋊C4—41no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C42—22no—
939C42—22no—
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—41no—
953C42—41no—
954C42—42no—
955C42—42no—
956C42—42no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—42no—
962C42—42no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23#57512yes—
983C23C23×D411yescharacteristic
984Q8—22no—
985Q8—22no—
986Q8—22no—
987Q8—22no—
988Q8—41no—
989Q8—41no—
990Q8—41no—
991Q8—41no—
992Q8—84no—
993Q8—84no—
994D4—41no—
995D4—41no—
996D4—41no—
997D4—41no—
998D4—84no—
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—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
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—21no—
1040C2×C4—21no—
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—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—84no—
1086C2×C4—162no—
1087C2×C4—162no—
1088C2×C4#57612yes—
1089C2×C4#57812yes—
1090C2×C4C22×#4111yescharacteristic
1091C2×C4C22×#4111yescharacteristic
1092C2×C4C2×2−1+411yescharacteristic
1093C2×C4#58511yescharacteristic
1094C2×C4#58511yescharacteristic
1095C2×C4#58511yescharacteristic
1096C8—22no—
1097C8—22no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C8—41no—
1102C8—41no—
1103C8—41no—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22D4×#4111yescharacteristic
1119C22D4×#4111yescharacteristic
1120C22#348911yescharacteristic
1121C22C2×#57511yescharacteristic
1122C22C2×#57611yescharacteristic
1123C22C2×#57811yescharacteristic
1124C22#358611yescharacteristic
1125C4—22no—
1126C4—22no—
1127C4—41no—
1128C4—41no—
1129C4—42no—
1130C4—42no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—42no—
1135C4—42no—
1136C4—41no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—42no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4#348211yescharacteristic
1154C4#349111yescharacteristic
1155C4#351211yescharacteristic
1156C4#356511yescharacteristic
1157C2—42no—
1158C2—161no—
1159C2#5917811yescharacteristic
1160C2#6144411yescharacteristic
1161C2#6145811yescharacteristic
1162C2#6148511yescharacteristic
1163C2#6152511yescharacteristic
1164C2#6213011yescharacteristic
1165C2#6218011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59502C2semidirect
3. #31484C2semidirect
4. #31239C2semidirect
7. #29514C2semidirect
8. #29450C2semidirect
9. #29025C2semidirect
11. #28001C2semidirect
12. #27452C2semidirect
13. #27378C2semidirect
14. #27177C2semidirect
15. #27165C2semidirect
16. #27052C2semidirect
17. #26856C2semidirect
19. #26783C2semidirect
21. #26173C2semidirect
22. #26094C2semidirect
23. #25994C2semidirect
24. #25033C2semidirect
25. #23282C2semidirect
26. #23133C2semidirect
27. #23111C2semidirect
28. #22977C2semidirect
30. #21616C2semidirect
31. #21119C2semidirect

Maximal subgroups

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

subgroupindex
#595022
#364902
#314842
#312392
#311322
#306022
#295142
#294502
#290252
#280792
#280012
#274522
#273782
#271772
#271652
#270522
#268562
#268052
#267832
#266592
#261732
#260942
#259942
#250332
#232822
#231332
#231112
#229772
#229162
#216162
#211192