Finite Group Databasebeta

← #6940741

Subgroups — #6940741

Order 512.

1415 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36390C211yesmaximal, characteristic, complemented
2#36294C211yesmaximal, characteristic, complemented
3#32861C211yesmaximal, characteristic, complemented
4#32824C211yesmaximal, characteristic, complemented
5#32538C211yesmaximal, characteristic, complemented
6#32493C211yesmaximal, characteristic, complemented
7#31987C211yesmaximal, characteristic, complemented
8#31985C211yesmaximal, characteristic, complemented
9#31917C211yesmaximal, characteristic, complemented
10#31891C211yesmaximal, characteristic, complemented
11#31250C211yesmaximal, characteristic, complemented
12#31167C211yesmaximal, characteristic, complemented
13#30156C211yesmaximal, characteristic, complemented
14#30134C211yesmaximal, characteristic, complemented
15#30000C211yesmaximal, characteristic, complemented
16#29829C211yesmaximal, characteristic, complemented
17#29784C211yesmaximal, characteristic, complemented
18#29536C211yesmaximal, characteristic, complemented
19#28285C211yesmaximal, characteristic, complemented
20#26367C211yesmaximal, characteristic, complemented
21#26352C211yesmaximal, characteristic, complemented
22#26008C211yesmaximal, characteristic, complemented
23#25980C211yesmaximal, characteristic, complemented
24#25231C211yesmaximal, characteristic, complemented
25#25094C211yesmaximal, characteristic
26#24609C211yesmaximal, characteristic, complemented
27#24549C211yesmaximal, characteristic
28#24510C211yesmaximal, characteristic
29#24491C211yesmaximal, characteristic, complemented
30#23617C211yesmaximal, characteristic, complemented
31#21978C211yesmaximal, characteristic, complemented
32C2×#483C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#474C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#461C2211yescharacteristic
38C2×#449C2211yescharacteristic
39C2×#432C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#423C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44#2864C2211yescharacteristic
45#2863C2211yescharacteristic
46#2862C2211yescharacteristic
47#2860C2211yescharacteristic
48#2855C2211yescharacteristic
49#2854C2211yescharacteristic
50#2609—21no—
51#2596—21no—
52#2576—21no—
53#2572—21no—
54#2530—21no—
55#2529—21no—
56#2527—21no—
57#2515—21no—
58#2514C2211yescharacteristic
59#2513C2211yescharacteristic
60#2509C2211yescharacteristic
61#2508C2211yescharacteristic
62#2504C2211yescharacteristic
63#2498—21no—
64#2481—21no—
65#2478—21no—
66#2477—21no—
67#2454C2211yescharacteristic
68#2452C2211yescharacteristic
69#2447C2211yescharacteristic
70#2446C2211yescharacteristic
71#2442C2211yescharacteristic
72#2439C2211yescharacteristic
73#2432C2211yescharacteristic
74#2368—21no—
75#2362C2211yescharacteristic
76#2361C2211yescharacteristic
77#2359—21no—
78#2352—21no—
79#2345C2211yescharacteristic
80#2343—21no—
81#2339C2211yescharacteristic
82C4×#125C2211yescharacteristic
83C4×#124C2211yescharacteristic
84#2297C2211yescharacteristic
85#2293C2211yescharacteristic
86#2293C2211yescharacteristic
87C2×#389C2211yescharacteristic
88C4×#117C2211yescharacteristic
89#2101C2211yescharacteristic
90#2097C2211yescharacteristic
91#2097C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2087C2211yescharacteristic
97#2087C2211yescharacteristic
98#2087C2211yescharacteristic
99#2086C2211yescharacteristic
100#2086C2211yescharacteristic
101#2085C2211yescharacteristic
102#2074C2211yescharacteristic
103#2074C2211yescharacteristic
104#2074C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2068C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2067C2211yescharacteristic
118#2067C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2066C2211yescharacteristic
123#2066C2211yescharacteristic
124#2065C2211yescharacteristic
125#2065C2211yescharacteristic
126#2065C2211yescharacteristic
127#2065C2211yescharacteristic
128#2065C2211yescharacteristic
129#2059C2211yescharacteristic
130#2058C2211yescharacteristic
131#2057C2211yescharacteristic
132#2055C2211yescharacteristic
133#2055C2211yescharacteristic
134#2055C2211yescharacteristic
135#2055C2211yescharacteristic
136#2055C2211yescharacteristic
137#2055C2211yescharacteristic
138#2055C2211yescharacteristic
139#2054C2211yescharacteristic
140#2043C2211yescharacteristic
141#2043C2211yescharacteristic
142#2042C2211yescharacteristic
143#2026C2211yescharacteristic
144#2012C2211yescharacteristic
145#1988C2211yescharacteristic
146#1983C2211yescharacteristic
147#1983C2211yescharacteristic
148#1981C2211yescharacteristic
149#1973C2211yescharacteristic
150#1972C2211yescharacteristic
151#1949C2211yescharacteristic
152#1949C2211yescharacteristic
153#1949C2211yescharacteristic
154#1949C2211yescharacteristic
155#1943C2211yescharacteristic
156#1943C2211yescharacteristic
157#1940C2211yescharacteristic
158#1940C2211yescharacteristic
159#1940C2211yescharacteristic
160#1940C2211yescharacteristic
161#1936C2211yescharacteristic
162#1935C2211yescharacteristic
163#1935C2211yescharacteristic
164#1935C2211yescharacteristic
165#1928C2211yescharacteristic
166#1927C2211yescharacteristic
167#1926C2211yescharacteristic
168#1926C2211yescharacteristic
169#1921C2211yescharacteristic
170#1921C2211yescharacteristic
171#1920C2211yescharacteristic
172#1919C2211yescharacteristic
173#1895C2211yescharacteristic
174#1894C2211yescharacteristic
175#1880C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1875C2211yescharacteristic
180#1872C2211yescharacteristic
181#1865C2211yescharacteristic
182#1864C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1854C2211yescharacteristic
186#1852C2211yescharacteristic
187#1851C2211yescharacteristic
188#1851C2211yescharacteristic
189#1851C2211yescharacteristic
190#1851C2211yescharacteristic
191#1842C2211yescharacteristic
192#1842C2211yescharacteristic
193#1831C2211yescharacteristic
194#1831C2211yescharacteristic
195#1823C2211yescharacteristic
196#1809C2211yescharacteristic
197#1805C2211yescharacteristic
198#1804C2211yescharacteristic
199#1804C2211yescharacteristic
200#1804C2211yescharacteristic
201#1788C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#123—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×#117—21no—
224C2×#117—21no—
225C2×#117D411yescharacteristic
226C2×#117D411yescharacteristic
227C2×#117C2311yescharacteristic
228C22×C4⋊C4—21no—
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C42C2311yescharacteristic
232#483—42no—
233#479—42no—
234#478—42no—
235#474—42no—
236#468—42no—
237#461—42no—
238#449—42no—
239#432—42no—
240#428—42no—
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254#423—42no—
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269#417—42no—
270#417—42no—
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301#401—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#399—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#394—21no—
322#394—21no—
323#393—21no—
324#393—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
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#388—21no—
376#388—21no—
377#388—21no—
378#388—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#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#383—21no—
416#383—21no—
417#382—21no—
418#382—21no—
419#382—21no—
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#381—21no—
425#381—21no—
426#381—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4D411yescharacteristic
436C4×C4⋊C4D411yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4D411yescharacteristic
451C4×C22⋊C4D411yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454#376D411yescharacteristic
455#376D411yescharacteristic
456C2×#95—21no—
457C2×#95—21no—
458C43C2311yescharacteristic
459C43C2311yescharacteristic
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#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2411yescharacteristic
512C2×SD16—41no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×D8—22no—
519C2×D8—41no—
520C2×D8—41no—
521C2×M16—22no—
522C2×M16—22no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539#126—82no—
540#125—22no—
541#125—41no—
542#124—22no—
543#124—41no—
544#123—44no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—44no—
548#121—22no—
549#121—22no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—41no—
558C4×D4—44no—
559#117—42no—
560#117—42no—
561#117—44no—
562#117—41no—
563#117—41no—
564#117—82no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
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⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—82no—
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C42—22no—
642C2×C42—22no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
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×C42C2×D411yescharacteristic
658C2×C42C2×D411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665#107—22no—
666#107—22no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#106—22no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678C4⋊C8—41no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692#103—22no—
693#103—22no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#102—22no—
707#102—22no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718C22⋊C8—22no—
719C22⋊C8—22no—
720#97—41no—
721#97—41no—
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#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776C24—21no—
777C24—21no—
778C24C22×D411yescharacteristic
779#41—44no—
780#41—44no—
781#41—82no—
782#41—82no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—42no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—81no—
815C2×D42−1+412yes—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4H(5,𝔽2)12yes—
872C22×C42−1+412yes—
873C22×C4C2511yescharacteristic
874SD16—82no—
875SD16—82no—
876D8—82no—
877M16—44no—
878M16—82no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C4⋊C4—22no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4H(5,𝔽2)12yes—
956C22⋊C4—22no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C42—22no—
987C42—22no—
988C42—22no—
989C42—22no—
990C42—22no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—41no—
1004C42—41no—
1005C42—41no—
1006C42—41no—
1007C42—41no—
1008C42—42no—
1009C42—42no—
1010C42—81no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—22no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23#53712yes—
1035C23C23×D411yescharacteristic
1036Q8—41no—
1037Q8—41no—
1038Q8—41no—
1039Q8—41no—
1040Q8—41no—
1041Q8—41no—
1042Q8—41no—
1043Q8—41no—
1044Q8—162no—
1045D4—22no—
1046D4—22no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—84no—
1054D4—84no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
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—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—44no—
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—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—84no—
1139C2×C4—84no—
1140C2×C4—82no—
1141C2×C4—84no—
1142C2×C4—84no—
1143C2×C4—162no—
1144C2×C4—162no—
1145C2×C4#53712yes—
1146C2×C4#57512yes—
1147C2×C4#57512yes—
1148C2×C4C2×H(5,𝔽2)11yescharacteristic
1149C2×C4C2×H(5,𝔽2)11yescharacteristic
1150C2×C4C2×2−1+411yescharacteristic
1151C2×C4C2×2−1+411yescharacteristic
1152C2×C4#58511yescharacteristic
1153C2×C4#58511yescharacteristic
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—41no—
1166C22—41no—
1167C22—41no—
1168C22—41no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22C2×#53711yescharacteristic
1184C22#348811yescharacteristic
1185C22#348911yescharacteristic
1186C22C2×#57511yescharacteristic
1187C22C2×#57511yescharacteristic
1188C22#358511yescharacteristic
1189C22#358611yescharacteristic
1190C4—22no—
1191C4—22no—
1192C4—22no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—42no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4#353511yescharacteristic
1218C4#353811yescharacteristic
1219C4#354211yescharacteristic
1220C4#356411yescharacteristic
1221C2—42no—
1222C2—82no—
1223C2—161no—
1224C2#4198411yescharacteristic
1225C2#6091711yescharacteristic
1226C2#6093811yescharacteristic
1227C2#6196911yescharacteristic
1228C2#6197111yescharacteristic
1229C2#6211511yescharacteristic
1230C2#6212111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#449C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36390C2semidirect
2. #36294C2semidirect
3. #32861C2semidirect
4. #32824C2semidirect
5. #32538C2semidirect
6. #32493C2semidirect
7. #31987C2semidirect
8. #31985C2semidirect
9. #31917C2semidirect
10. #31891C2semidirect
11. #31250C2semidirect
12. #31167C2semidirect
13. #30156C2semidirect
14. #30134C2semidirect
15. #30000C2semidirect
16. #29829C2semidirect
17. #29784C2semidirect
18. #29536C2semidirect
19. #28285C2semidirect
20. #26367C2semidirect
21. #26352C2semidirect
22. #26008C2semidirect
23. #25980C2semidirect
24. #25231C2semidirect
26. #24609C2semidirect
29. #24491C2semidirect
30. #23617C2semidirect
31. #21978C2semidirect

Maximal subgroups

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

subgroupindex
#363902
#362942
#328612
#328242
#325382
#324932
#319872
#319852
#319172
#318912
#312502
#311672
#301562
#301342
#300002
#298292
#297842
#295362
#282852
#263672
#263522
#260082
#259802
#252312
#250942
#246092
#245492
#245102
#244912
#236172
#219782