Finite Group Databasebeta

← #7566359

Subgroups — #7566359

Order 512.

1522 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59549C211yesmaximal, characteristic
2#36133C211yesmaximal, characteristic, complemented
3#32637C211yesmaximal, characteristic, complemented
4#32589C211yesmaximal, characteristic, complemented
5#32244C211yesmaximal, characteristic, complemented
6#30813C211yesmaximal, characteristic, complemented
7#29162C211yesmaximal, characteristic, complemented
8#29107C211yesmaximal, characteristic, complemented
9#29027C211yesmaximal, characteristic, complemented
10#28030C211yesmaximal, characteristic, complemented
11#27704C211yesmaximal, characteristic, complemented
12#27367C211yesmaximal, characteristic, complemented
13#27270C211yesmaximal, characteristic
14#27128C211yesmaximal, characteristic, complemented
15#27127C211yesmaximal, characteristic, complemented
16#26752C211yesmaximal, characteristic, complemented
17#26705C211yesmaximal, characteristic, complemented
18#26689C211yesmaximal, characteristic, complemented
19#26328C211yesmaximal, characteristic, complemented
20#26009C211yesmaximal, characteristic, complemented
21#25978C211yesmaximal, characteristic, complemented
22#24992C211yesmaximal, characteristic, complemented
23#24589C211yesmaximal, characteristic, complemented
24#24488C211yesmaximal, characteristic
25#23239C211yesmaximal, characteristic, complemented
26#23216C211yesmaximal, characteristic, complemented
27#23075C211yesmaximal, characteristic, complemented
28#22624C211yesmaximal, characteristic, complemented
29#22582C211yesmaximal, characteristic, complemented
30C4×#481C211yesmaximal, characteristic, complemented
31#21059C211yesmaximal, characteristic, complemented
32C2×#533—21no—
33C2×#486C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#476C2211yescharacteristic
36C2×#428C2211yescharacteristic
37C2×#417C2211yescharacteristic
38C2×#417C2211yescharacteristic
39#2857C2211yescharacteristic
40#2855—21no—
41#2778—21no—
42#2749—21no—
43#2592C2211yescharacteristic
44#2576—21no—
45#2551C2211yescharacteristic
46#2546C2211yescharacteristic
47#2538C2211yescharacteristic
48#2526—21no—
49#2514C2211yescharacteristic
50#2511C2211yescharacteristic
51#2506C2211yescharacteristic
52#2506C2211yescharacteristic
53#2500C2211yescharacteristic
54#2488—21no—
55#2463—21no—
56#2462—21no—
57#2462—21no—
58#2457—21no—
59#2451—21no—
60#2447C2211yescharacteristic
61#2446—21no—
62#2445C2211yescharacteristic
63#2440C2211yescharacteristic
64#2440C2211yescharacteristic
65#2438—21no—
66#2438—21no—
67#2431C2211yescharacteristic
68#2366C2211yescharacteristic
69#2365C2211yescharacteristic
70#2365C2211yescharacteristic
71#2365C2211yescharacteristic
72#2357C2211yescharacteristic
73#2353—21no—
74Q8×C4⋊C4C2211yescharacteristic
75#2346C2211yescharacteristic
76#2344C2211yescharacteristic
77#2344C2211yescharacteristic
78#2339C2211yescharacteristic
79C4×C22⋊Q8C2211yescharacteristic
80C4×#121C2211yescharacteristic
81#2297C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2096C2211yescharacteristic
88#2094C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2085C2211yescharacteristic
92#2084C2211yescharacteristic
93#2072C2211yescharacteristic
94#2071C2211yescharacteristic
95#2071C2211yescharacteristic
96#2071C2211yescharacteristic
97#2068C2211yescharacteristic
98#2067C2211yescharacteristic
99#2066C2211yescharacteristic
100#2066C2211yescharacteristic
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2058C2211yescharacteristic
104#2057C2211yescharacteristic
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2024C2211yescharacteristic
110#2024C2211yescharacteristic
111#2024C2211yescharacteristic
112#2023C2211yescharacteristic
113#2023C2211yescharacteristic
114#2023C2211yescharacteristic
115#1993C2211yescharacteristic
116#1988C2211yescharacteristic
117#1985C2211yescharacteristic
118#1984C2211yescharacteristic
119#1983C2211yescharacteristic
120#1982C2211yescharacteristic
121#1959C2211yescharacteristic
122#1949C2211yescharacteristic
123#1948C2211yescharacteristic
124#1948C2211yescharacteristic
125#1944C2211yescharacteristic
126#1941C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1935C2211yescharacteristic
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic
132#1934C2211yescharacteristic
133#1933C2211yescharacteristic
134#1933C2211yescharacteristic
135#1933C2211yescharacteristic
136#1933C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1927C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1927C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1921C2211yescharacteristic
154#1920C2211yescharacteristic
155#1920C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1917C2211yescharacteristic
164#1916C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1895C2211yescharacteristic
168#1895C2211yescharacteristic
169#1874C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1853C2211yescharacteristic
177#1851C2211yescharacteristic
178#1851C2211yescharacteristic
179#1834C2211yescharacteristic
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1824C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1802C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1776C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#106C2211yescharacteristic
191C4×#106C2211yescharacteristic
192#1771C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194#1762C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206#533—48no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#125—21no—
214C2×#125—21no—
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8D411yescharacteristic
222C2×#121C2311yescharacteristic
223C2×C4×Q8—21no—
224C2×C4×Q8—21no—
225C2×C4×Q8—21no—
226C2×C4×Q8—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4—21no—
229C2×C4×D4—21no—
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117—21no—
234C2×#117—21no—
235C2×#117C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C42—21no—
239C22×C42C2311yescharacteristic
240#486—24no—
241#481—24no—
242#476—24no—
243#428—24no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260#417—24no—
261#417—24no—
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294#401—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#396—21no—
310#396—21no—
311#395—21no—
312#395—21no—
313#395—21no—
314#395—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#393—21no—
320#392—21no—
321#392—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391D411yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#390—21no—
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389D411yescharacteristic
346#389C2311yescharacteristic
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#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#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#387D411yescharacteristic
384#387D411yescharacteristic
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385D411yescharacteristic
399#385D411yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#383—21no—
405#382—21no—
406#382C2311yescharacteristic
407#381—21no—
408#381—21no—
409#381—21no—
410#381—21no—
411#381—21no—
412#380—21no—
413#380—21no—
414#380D411yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440#376—21no—
441C2×#95—21no—
442C2×#95—21no—
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8C2×D411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2411yescharacteristic
501C22×D4C2411yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C2×D411yescharacteristic
509C23×C4C2×D411yescharacteristic
510C23×C4C2411yescharacteristic
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—41no—
515C2×M16—41no—
516C2×M16—41no—
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—44no—
532C4⋊Q8—44no—
533#127—22no—
534#127—41no—
535#125—44no—
536#125—44no—
537#124—41no—
538#124—41no—
539#123—82no—
540C22⋊Q8—24no—
541C22⋊Q8—44no—
542C22⋊Q8—44no—
543C22⋊Q8—44no—
544C22⋊Q8—82no—
545#121—22no—
546#121—22no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—44no—
550C4×Q8—44no—
551C4×Q8—44no—
552C4×Q8—44no—
553C4×D4—22no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—44no—
560C4×D4—82no—
561#117—22no—
562#117—22no—
563#117—44no—
564#117—44no—
565C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4#4114yes—
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×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⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—41no—
656C2×C42—41no—
657C2×C42—44no—
658C2×C42C2×D411yescharacteristic
659C2×C42C2×D411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666#107—22no—
667#107—22no—
668#107—41no—
669#107—41no—
670#106—22no—
671#106—22no—
672#106—22no—
673#106—22no—
674#106—22no—
675#106—22no—
676#106—41no—
677#106—41no—
678C4⋊C8—22no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682#103—22no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102#4114yes—
706C22⋊C8—22no—
707C22⋊C8—22no—
708#97—41no—
709#97—41no—
710C4×C8—22no—
711C4×C8—41no—
712C4×C8—41no—
713C4×C8—41no—
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#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763C24—21no—
764C24—21no—
765C24C22×D411yescharacteristic
766#41—44no—
767#41—44no—
768#41—82no—
769#41—82no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—41no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4C2×#4112yes—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—24no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
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—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
868C22×C42−1+412yes—
869C22×C4C2511yescharacteristic
870M16—44no—
871M16—82no—
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—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×C8C2×#4112yes—
896C4⋊C4—24no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—22no—
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—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—42no—
929C4⋊C4—42no—
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—42no—
945C4⋊C4—42no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4AGL(1,ℤ/8)14yes—
954C4⋊C4C2×#4112yes—
955C4⋊C4C2×#4112yes—
956C4⋊C4C2×#4112yes—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—41no—
960C22⋊C4—41no—
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—81no—
971C22⋊C4—81no—
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—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—41no—
996C42—41no—
997C42—42no—
998C42—42no—
999C42—42no—
1000C42—42no—
1001C42—42no—
1002C42—42no—
1003C42—42no—
1004C42—42no—
1005C42—42no—
1006C42—42no—
1007C42—81no—
1008C42—81no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—22no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23#54812yes—
1030C23C23×D411yescharacteristic
1031Q8—44no—
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—41no—
1036Q8—84no—
1037Q8—84no—
1038Q8—84no—
1039D4—22no—
1040D4—22no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—84no—
1048D4—84no—
1049D4—84no—
1050D4—162no—
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—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—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—21no—
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—44no—
1093C2×C4—48no—
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—84no—
1134C2×C4—82no—
1135C2×C4—84no—
1136C2×C4—162no—
1137C2×C4—162no—
1138C2×C4—162no—
1139C2×C4#54812yes—
1140C2×C4C2×AGL(1,ℤ/8)12yes—
1141C2×C4C2×AGL(1,ℤ/8)12yes—
1142C2×C4C2×AGL(1,ℤ/8)12yes—
1143C2×C4#57712yes—
1144C2×C4C22×#4111yescharacteristic
1145C2×C4C22×#4111yescharacteristic
1146C2×C4C2×2−1+411yescharacteristic
1147C2×C4#58511yescharacteristic
1148C2×C4#58511yescharacteristic
1149C2×C4#58511yescharacteristic
1150C8—22no—
1151C8—41no—
1152C8—41no—
1153C8—41no—
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C22—22no—
1159C22—22no—
1160C22—22no—
1161C22—41no—
1162C22—41no—
1163C22—41no—
1164C22—41no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22C2×#54811yescharacteristic
1180C22D4×#4111yescharacteristic
1181C22#348511yescharacteristic
1182C22C22×AGL(1,ℤ/8)11yescharacteristic
1183C22C2×#57711yescharacteristic
1184C22#358411yescharacteristic
1185C22#358611yescharacteristic
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—22no—
1190C4—22no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—42no—
1199C4—42no—
1200C4—41no—
1201C4—42no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4#347511yescharacteristic
1214C4#349511yescharacteristic
1215C4#351011yescharacteristic
1216C4#356411yescharacteristic
1217C2—42no—
1218C2—82no—
1219C2—161no—
1220C2#5913211yescharacteristic
1221C2#6131711yescharacteristic
1222C2#6132711yescharacteristic
1223C2#6143711yescharacteristic
1224C2#6154011yescharacteristic
1225C2#6172811yescharacteristic
1226C2#6176311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2431C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36133C2semidirect
3. #32637C2semidirect
4. #32589C2semidirect
5. #32244C2semidirect
6. #30813C2semidirect
7. #29162C2semidirect
8. #29107C2semidirect
9. #29027C2semidirect
10. #28030C2semidirect
11. #27704C2semidirect
12. #27367C2semidirect
14. #27128C2semidirect
15. #27127C2semidirect
16. #26752C2semidirect
17. #26705C2semidirect
18. #26689C2semidirect
19. #26328C2semidirect
20. #26009C2semidirect
21. #25978C2semidirect
22. #24992C2semidirect
23. #24589C2semidirect
25. #23239C2semidirect
26. #23216C2semidirect
27. #23075C2semidirect
28. #22624C2semidirect
29. #22582C2semidirect
30. C4×#481C2semidirect
31. #21059C2semidirect

Maximal subgroups

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

subgroupindex
#595492
#361332
#326372
#325892
#322442
#308132
#291622
#291072
#290272
#280302
#277042
#273672
#272702
#271282
#271272
#267522
#267052
#266892
#263282
#260092
#259782
#249922
#245892
#244882
#232392
#232162
#230752
#226242
#225822
C4×#4812
#210592