Finite Group Databasebeta

← #7590217

Subgroups — #7590217

Order 512.

1515 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59200C211yesmaximal, characteristic
2#59197C211yesmaximal, characteristic
3#32415C211yesmaximal, characteristic, complemented
4#32412C211yesmaximal, characteristic, complemented
5#32263C211yesmaximal, characteristic, complemented
6#32262C211yesmaximal, characteristic, complemented
7#28708C211yesmaximal, characteristic, complemented
8#27848C211yesmaximal, characteristic, complemented
9#27847C211yesmaximal, characteristic, complemented
10#27669C211yesmaximal, characteristic, complemented
11#27668C211yesmaximal, characteristic, complemented
12#27659C211yesmaximal, characteristic, complemented
13#27604C211yesmaximal, characteristic, complemented
14#27602C211yesmaximal, characteristic, complemented
15#26075C211yesmaximal, characteristic, complemented
16#26075C211yesmaximal, characteristic, complemented
17#26018C211yesmaximal, characteristic, complemented
18#26017C211yesmaximal, characteristic, complemented
19#26015C211yesmaximal, characteristic, complemented
20#26012C211yesmaximal, characteristic, complemented
21#24964C211yesmaximal, characteristic, complemented
22#24961C211yesmaximal, characteristic, complemented
23#24959C211yesmaximal, characteristic, complemented
24#24958C211yesmaximal, characteristic, complemented
25#22660C211yesmaximal, characteristic, complemented
26#22660C211yesmaximal, characteristic, complemented
27#22624C211yesmaximal, characteristic, complemented
28#22623C211yesmaximal, characteristic, complemented
29#21439C211yesmaximal, characteristic
30#20661C211yesmaximal, characteristic, complemented
31#20661C211yesmaximal, characteristic, complemented
32C23×M16C2211yescharacteristic
33C2×#499C2211yescharacteristic, complemented
34C2×#435C2211yescharacteristic
35C2×#435C2211yescharacteristic
36C2×C8×D4C2211yescharacteristic
37C2×#428C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#427C2211yescharacteristic, complemented
42#2747—21no—
43#2741—21no—
44#2735—21no—
45#2685—21no—
46#2575—21no—
47#2573—21no—
48#2569—21no—
49#2562C2211yescharacteristic
50#2562C2211yescharacteristic
51#2526—21no—
52#2518—21no—
53#2516—21no—
54#2510—21no—
55#2498—21no—
56#2497C2211yescharacteristic
57#2496C2211yescharacteristic
58#2495C2211yescharacteristic
59#2494C2211yescharacteristic
60#2493—21no—
61#2487C2211yescharacteristic
62#2486C2211yescharacteristic
63#2485C2211yescharacteristic
64#2485C2211yescharacteristic
65#2485C2211yescharacteristic
66#2485C2211yescharacteristic
67#2442C2211yescharacteristic
68#2442C2211yescharacteristic
69#2441C2211yescharacteristic
70#2441C2211yescharacteristic
71#2412—21no—
72#2373—21no—
73#2354C2211yescharacteristic
74#2354C2211yescharacteristic
75#2352C2211yescharacteristic
76#2352C2211yescharacteristic
77#2347C2211yescharacteristic
78#2346C2211yescharacteristic
79#2345C2211yescharacteristic
80#2344C2211yescharacteristic
81#2342—21no—
82C4×#120C2211yescharacteristic
83#2280C2211yescharacteristic
84#2280C2211yescharacteristic
85C2×#380C2211yescharacteristic
86C2×#380C2211yescharacteristic
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2087C2211yescharacteristic, complemented
95#2086C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic, complemented
106#2077C2211yescharacteristic, complemented
107#2077C2211yescharacteristic, complemented
108#2077C2211yescharacteristic, complemented
109#2076C2211yescharacteristic
110#2076C2211yescharacteristic
111#2076C2211yescharacteristic, complemented
112#2075C2211yescharacteristic
113#2075C2211yescharacteristic
114#2075C2211yescharacteristic, complemented
115#2059C2211yescharacteristic, complemented
116#2059C2211yescharacteristic, complemented
117#2059C2211yescharacteristic, complemented
118#2059C2211yescharacteristic, complemented
119#1989C2211yescharacteristic, complemented
120#1989C2211yescharacteristic, complemented
121#1949C2211yescharacteristic, complemented
122#1949C2211yescharacteristic, complemented
123#1947C2211yescharacteristic, complemented
124#1947C2211yescharacteristic, complemented
125#1944C2211yescharacteristic, complemented
126#1944C2211yescharacteristic, complemented
127#1943C2211yescharacteristic, complemented
128#1943C2211yescharacteristic, complemented
129#1941C2211yescharacteristic, complemented
130#1941C2211yescharacteristic, complemented
131#1921C2211yescharacteristic, complemented
132#1921C2211yescharacteristic, complemented
133#1921C2211yescharacteristic, complemented
134#1920C2211yescharacteristic, complemented
135#1920C2211yescharacteristic, complemented
136#1920C2211yescharacteristic, complemented
137#1919C2211yescharacteristic, complemented
138#1919C2211yescharacteristic, complemented
139#1919C2211yescharacteristic, complemented
140#1918C2211yescharacteristic, complemented
141#1918C2211yescharacteristic, complemented
142#1918C2211yescharacteristic, complemented
143#1870C2211yescharacteristic
144#1870C2211yescharacteristic
145#1869C2211yescharacteristic
146#1854C2211yescharacteristic
147#1854C2211yescharacteristic
148#1854C2211yescharacteristic
149#1854C2211yescharacteristic
150#1854C2211yescharacteristic, complemented
151#1854C2211yescharacteristic, complemented
152#1854C2211yescharacteristic, complemented
153#1854C2211yescharacteristic, complemented
154#1853C2211yescharacteristic
155#1853C2211yescharacteristic
156#1852C2211yescharacteristic
157#1852C2211yescharacteristic
158#1851C2211yescharacteristic
159#1851C2211yescharacteristic
160#1850C2211yescharacteristic
161#1847C2211yescharacteristic, complemented
162#1847C2211yescharacteristic, complemented
163#1825C2211yescharacteristic
164#1825C2211yescharacteristic
165#1825C2211yescharacteristic
166#1825C2211yescharacteristic
167#1825C2211yescharacteristic, complemented
168#1825C2211yescharacteristic, complemented
169#1824C2211yescharacteristic
170#1824C2211yescharacteristic
171#1823C2211yescharacteristic
172#1823C2211yescharacteristic
173#1809C2211yescharacteristic
174#1809C2211yescharacteristic
175#1809C2211yescharacteristic
176#1809C2211yescharacteristic
177#1809C2211yescharacteristic
178#1809C2211yescharacteristic
179#1809C2211yescharacteristic
180#1809C2211yescharacteristic
181#1808C2211yescharacteristic
182#1808C2211yescharacteristic
183#1808C2211yescharacteristic
184#1808C2211yescharacteristic
185#1808C2211yescharacteristic, complemented
186#1808C2211yescharacteristic, complemented
187#1807C2211yescharacteristic
188#1807C2211yescharacteristic
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic
191#1807C2211yescharacteristic, complemented
192#1779C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195C4×#107C2211yescharacteristic, complemented
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203C24×C4C2311yescharacteristic
204C22×M16—24no—
205C22×M16—24no—
206C22×M16—42no—
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#123—21no—
218C2×#120D411yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×#117—21no—
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C22⋊C4—21no—
234C22×C22⋊C4—21no—
235#499—42no—
236#435—24no—
237#435—24no—
238C8×D4—42no—
239#428—24no—
240#428—24no—
241#428—42no—
242#428—42no—
243#427—42no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283#401—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#399—21no—
293#399—21no—
294#399—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#390—21no—
316#390—21no—
317#389—21no—
318#389—21no—
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#388—21no—
332#388—21no—
333#388—21no—
334#388—21no—
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#387—21no—
353#387—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#386D411yescharacteristic
371#386D411yescharacteristic
372#386D411yescharacteristic
373#385—21no—
374#385—21no—
375#385—21no—
376#385D411yescharacteristic
377#385D411yescharacteristic
378#385D411yescharacteristic
379#384C2311yescharacteristic
380#384C2311yescharacteristic
381#383—21no—
382#383—21no—
383#382—21no—
384#382C2311yescharacteristic
385#382C2311yescharacteristic
386#381—21no—
387#381—21no—
388#381—21no—
389#381—21no—
390#380—21no—
391#380—21no—
392#380—21no—
393#380—21no—
394#380—21no—
395#380—21no—
396#380—21no—
397#380C2311yescharacteristic
398#380C2311yescharacteristic
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#379—21no—
420#379—21no—
421#379D411yescharacteristic
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
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—
442C2×#95—21no—
443C2×#95—21no—
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#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25C2×D411yescharacteristic
491C22×D4C2×D411yescharacteristic
492C22×D4C2×D411yescharacteristic
493C22×D4C2×D411yescharacteristic
494C23×C4—22no—
495C23×C4—22no—
496C23×C4—22no—
497C23×C4—22no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—41no—
503C23×C4—41no—
504C23×C4C2×D411yescharacteristic
505C23×C4C2×D411yescharacteristic
506C23×C4C2×D411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—22no—
519C2×M16—41no—
520C2×M16—41no—
521C2×M16—416no—
522C2×M16#4114yes—
523C2×M16#4114yes—
524C22×C8—22no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—41no—
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541#126—44no—
542#125—41no—
543#125—41no—
544#125—41no—
545#125—41no—
546#123—82no—
547#120—42no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—22no—
551C4×D4—22no—
552C4×D4—41no—
553C4×D4—41no—
554#117—22no—
555#117—22no—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—41no—
560#117—41no—
561#117—41no—
562#117—41no—
563#117—41no—
564#117—41no—
565#117—41no—
566#117—82no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
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—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—44no—
647C2×C22⋊C4—82no—
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675#107—22no—
676#107—22no—
677#107—22no—
678#107—22no—
679#107—22no—
680#107—22no—
681#107—41no—
682#107—41no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#106—22no—
688#106—22no—
689#106—22no—
690#106—22no—
691#106—22no—
692#106—22no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699C4⋊C8—22no—
700C4⋊C8—22no—
701C4⋊C8—41no—
702C22⋊C8—22no—
703C22⋊C8—22no—
704C22⋊C8—22no—
705C22⋊C8—22no—
706C22⋊C8—22no—
707C22⋊C8—22no—
708C22⋊C8—41no—
709C22⋊C8—41no—
710C22⋊C8—41no—
711#97—22no—
712#97—22no—
713C4×C8—22no—
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#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#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764C24—22no—
765C24—22no—
766C24—22no—
767C24—41no—
768C24—41no—
769C24—41no—
770C24—41no—
771C24C22×D411yescharacteristic
772C24C22×D411yescharacteristic
773C24C22×D411yescharacteristic
774C24C22×D411yescharacteristic
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—41no—
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—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
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—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
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×C4C22×D411yescharacteristic
855C22×C4C2×#4112yes—
856C22×C4C2×#4112yes—
857C22×C42−1+412yes—
858C22×C42−1+412yes—
859C22×C4C2511yescharacteristic
860M16—28no—
861M16—28no—
862M16—44no—
863M16—44no—
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—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—44no—
884C2×C8—44no—
885C2×C8—44no—
886C2×C8C2×#4112yes—
887C2×C8C2×#4112yes—
888C2×C8C2×#4112yes—
889C2×C8C2×#4112yes—
890C2×C8H(5,𝔽2)12yes—
891C4⋊C4—22no—
892C4⋊C4—22no—
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—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—41no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
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—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
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—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—42no—
997C42—42no—
998C42—42no—
999C42—81no—
1000C42—81no—
1001C42—81no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C42—81no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—44no—
1034C23—44no—
1035C23—44no—
1036C23—82no—
1037C23—82no—
1038C23—82no—
1039C23—82no—
1040C23#54712yes—
1041C23#54712yes—
1042C23#57512yes—
1043C23C23×D411yescharacteristic
1044D4—44no—
1045D4—82no—
1046D4—82no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
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—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—44no—
1084C2×C4—44no—
1085C2×C4—44no—
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—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—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—84no—
1143C2×C4—162no—
1144C2×C4—162no—
1145C2×C4—162no—
1146C2×C4#54712yes—
1147C2×C4#54712yes—
1148C2×C4C22×#4111yescharacteristic
1149C2×C4C22×#4111yescharacteristic
1150C2×C4C2×H(5,𝔽2)11yescharacteristic
1151C2×C4C2×2−1+411yescharacteristic
1152C2×C4C2×2−1+411yescharacteristic
1153C2×C4#58511yescharacteristic
1154C8—22no—
1155C8—22no—
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C8#55114yes—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—22no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—88no—
1191C22C2×#54711yescharacteristic
1192C22C2×#54711yescharacteristic
1193C22#349611yescharacteristic
1194C22C2×#57511yescharacteristic
1195C22#358411yescharacteristic
1196C22#358511yescharacteristic
1197C22#358611yescharacteristic
1198C4—22no—
1199C4—22no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4—81no—
1223C4—81no—
1224C4C2×#55111yescharacteristic
1225C4#349511yescharacteristic
1226C4#349511yescharacteristic
1227C4#353811yescharacteristic
1228C2—42no—
1229C2—42no—
1230C2—42no—
1231C2—81no—
1232C2#5919811yescharacteristic
1233C2#6125311yescharacteristic
1234C2#6125511yescharacteristic
1235C2#6127511yescharacteristic
1236C2#6127611yescharacteristic
1237C2#6225511yescharacteristic
1238C2#6228811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#120D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32415C2semidirect
4. #32412C2semidirect
5. #32263C2semidirect
6. #32262C2semidirect
7. #28708C2semidirect
8. #27848C2semidirect
9. #27847C2semidirect
10. #27669C2semidirect
11. #27668C2semidirect
12. #27659C2semidirect
13. #27604C2semidirect
14. #27602C2semidirect
15. #26075C2semidirect
16. #26075C2semidirect
17. #26018C2semidirect
18. #26017C2semidirect
19. #26015C2semidirect
20. #26012C2semidirect
21. #24964C2semidirect
22. #24961C2semidirect
23. #24959C2semidirect
24. #24958C2semidirect
25. #22660C2semidirect
26. #22660C2semidirect
27. #22624C2semidirect
28. #22623C2semidirect
30. #20661C2semidirect
31. #20661C2semidirect
33. C2×#499C22semidirect
41. C2×#427C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2088C22semidirect
92. #2088C22semidirect
93. #2087C22semidirect
94. #2087C22semidirect
95. #2086C22semidirect
96. #2086C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2084C22semidirect
100. #2084C22semidirect
105. #2077C22semidirect
106. #2077C22semidirect
107. #2077C22semidirect
108. #2077C22semidirect
111. #2076C22semidirect
114. #2075C22semidirect
115. #2059C22semidirect
116. #2059C22semidirect
117. #2059C22semidirect
118. #2059C22semidirect
119. #1989C22semidirect
120. #1989C22semidirect
121. #1949C22semidirect
122. #1949C22semidirect
123. #1947C22semidirect
124. #1947C22semidirect
125. #1944C22semidirect
126. #1944C22semidirect
127. #1943C22semidirect
128. #1943C22semidirect
129. #1941C22semidirect
130. #1941C22semidirect
131. #1921C22semidirect
132. #1921C22semidirect
133. #1921C22semidirect
134. #1920C22semidirect
135. #1920C22semidirect
136. #1920C22semidirect
137. #1919C22semidirect
138. #1919C22semidirect
139. #1919C22semidirect
140. #1918C22semidirect
141. #1918C22semidirect
142. #1918C22semidirect
150. #1854C22semidirect
151. #1854C22semidirect
152. #1854C22semidirect
153. #1854C22semidirect
161. #1847C22semidirect
162. #1847C22semidirect
167. #1825C22semidirect
168. #1825C22semidirect
185. #1808C22semidirect
186. #1808C22semidirect
191. #1807C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. C4×#107C22semidirect

Maximal subgroups

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

subgroupindex
#592002
#591972
#324152
#324122
#322632
#322622
#287082
#278482
#278472
#276692
#276682
#276592
#276042
#276022
#260752
#260182
#260172
#260152
#260122
#249642
#249612
#249592
#249582
#226602
#226242
#226232
#214392
#206612