Finite Group Databasebeta

← #6608792

Subgroups — #6608792

Order 512.

1610 conjugacy classes of subgroups.

The subgroup lattice has 1303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36291C211yesmaximal, characteristic
2#36278C211yesmaximal, characteristic, complemented
3#33268C211yesmaximal, characteristic, complemented
4#33145C211yesmaximal, characteristic, complemented
5#33053C211yesmaximal, characteristic, complemented
6#29483C211yesmaximal, characteristic, complemented
7#29480C211yesmaximal, characteristic, complemented
8#29451C211yesmaximal, characteristic, complemented
9#29448C211yesmaximal, characteristic, complemented
10#29303C211yesmaximal, characteristic, complemented
11#28960C211yesmaximal, characteristic, complemented
12#28918C211yesmaximal, characteristic, complemented
13#28896C211yesmaximal, characteristic, complemented
14#28858C211yesmaximal, characteristic, complemented
15#28311C211yesmaximal, characteristic, complemented
16#28072C211yesmaximal, characteristic, complemented
17#28041C211yesmaximal, characteristic, complemented
18#26967C211yesmaximal, characteristic, complemented
19#26829C211yesmaximal, characteristic, complemented
20#25248C211yesmaximal, characteristic, complemented
21#25248C211yesmaximal, characteristic, complemented
22#25128C211yesmaximal, characteristic
23#25128C211yesmaximal, characteristic
24#22922C211yesmaximal, characteristic, complemented
25#22922C211yesmaximal, characteristic, complemented
26#22874C211yesmaximal, characteristic, complemented
27#22874C211yesmaximal, characteristic, complemented
28C4×#468C211yesmaximal, characteristic, complemented
29#21279C211yesmaximal, characteristic, complemented
30C2×#1936C211yesmaximal, characteristic, complemented
31#20491C211yesmaximal, characteristic, complemented
32C2×#491C2211yescharacteristic, complemented
33C2×#484C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45C2×C4×M16C2211yescharacteristic, complemented
46C22×#97C2211yescharacteristic
47#2863C2211yescharacteristic, complemented
48#2860C2211yescharacteristic
49#2857C2211yescharacteristic
50#2855C2211yescharacteristic, complemented
51#2854C2211yescharacteristic
52#2851C2211yescharacteristic
53#2608—21no—
54#2606—21no—
55#2595—21no—
56#2590—21no—
57#2587—21no—
58#2579—21no—
59#2569—21no—
60#2516—21no—
61#2513C2211yescharacteristic
62#2507C2211yescharacteristic, complemented
63#2497C2211yescharacteristic, complemented
64#2490C2211yescharacteristic
65#2487C2211yescharacteristic
66#2480—21no—
67#2471—21no—
68#2467—21no—
69#2454C2211yescharacteristic
70#2446C2211yescharacteristic, complemented
71#2429C2211yescharacteristic, complemented
72#2420C2211yescharacteristic
73#2418—21no—
74#2417C2211yescharacteristic
75#2417C2211yescharacteristic
76#2408C2211yescharacteristic
77#2360C2211yescharacteristic
78#2360C2211yescharacteristic
79#2358—21no—
80#2353—21no—
81#2345—21no—
82#2345C2211yescharacteristic
83#2342—21no—
84D4×C22⋊C4C2211yescharacteristic
85C4×C22⋊Q8C2211yescharacteristic, complemented
86C4×#121C2211yescharacteristic
87#2295C2211yescharacteristic, complemented
88#2293C2211yescharacteristic
89C2×#390C2211yescharacteristic
90C2×#389C2211yescharacteristic
91C42×D4C2211yescharacteristic
92#2093C2211yescharacteristic
93#2093C2211yescharacteristic
94#2086C2211yescharacteristic, complemented
95#2086C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2075C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2035C2211yescharacteristic, complemented
109#2035C2211yescharacteristic, complemented
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2013C2211yescharacteristic
113#2013C2211yescharacteristic
114#2000C2211yescharacteristic
115#2000C2211yescharacteristic
116#1992C2211yescharacteristic, complemented
117#1973C2211yescharacteristic
118#1973C2211yescharacteristic
119#1973C2211yescharacteristic
120#1973C2211yescharacteristic
121#1973C2211yescharacteristic
122#1973C2211yescharacteristic
123#1968C2211yescharacteristic
124#1968C2211yescharacteristic
125#1960C2211yescharacteristic, complemented
126#1944C2211yescharacteristic, complemented
127#1944C2211yescharacteristic, complemented
128#1944C2211yescharacteristic, complemented
129#1944C2211yescharacteristic, complemented
130#1943C2211yescharacteristic, complemented
131#1943C2211yescharacteristic, complemented
132#1942C2211yescharacteristic, complemented
133#1942C2211yescharacteristic, complemented
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1933C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1921C2211yescharacteristic, complemented
159#1921C2211yescharacteristic, complemented
160#1921C2211yescharacteristic, complemented
161#1921C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1894C2211yescharacteristic, complemented
165#1894C2211yescharacteristic, complemented
166#1892C2211yescharacteristic
167#1892C2211yescharacteristic
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1863C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1836C2211yescharacteristic, complemented
183#1809C2211yescharacteristic, complemented
184#1809C2211yescharacteristic, complemented
185C4×#107C2211yescharacteristic, complemented
186C4×#107C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189#1767C2211yescharacteristic, complemented
190C4×#103C2211yescharacteristic, complemented
191C4×#103C2211yescharacteristic, complemented
192C4×#102C2211yescharacteristic
193C4×#102C2211yescharacteristic
194#1753C2211yescharacteristic, complemented
195#1753C2211yescharacteristic, complemented
196C8×C22⋊C4C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198#1749C2211yescharacteristic
199#1749C2211yescharacteristic, complemented
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C4×#97C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126—21no—
214C2×#125C2311yescharacteristic
215C2×#123—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4D411yescharacteristic
227C2×C4×D4D411yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C22×C4⋊C4—21no—
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C22⋊C4—21no—
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241#491—42no—
242#484—24no—
243#484—24no—
244#468—24no—
245#468—42no—
246#450—24no—
247#450—24no—
248C4×SD16—24no—
249C4×SD16—42no—
250#435—24no—
251#435—24no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102—24no—
279C2×#102—42no—
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C4×M16—42no—
297C2×#97—42no—
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310#400—21no—
311#400—21no—
312#400—21no—
313#399—21no—
314#399—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#392—21no—
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#390—21no—
341#390—21no—
342#390—21no—
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—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#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#384C2311yescharacteristic
421#383—21no—
422#382C2311yescharacteristic
423#381—21no—
424#381—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#379—21no—
438#379—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4D411yescharacteristic
442C4×C4⋊C4D411yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4D411yescharacteristic
455C4×C22⋊C4D411yescharacteristic
456C4×C22⋊C4D411yescharacteristic
457C4×C22⋊C4D411yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460#376—21no—
461C2×#95—21no—
462C43C2311yescharacteristic
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#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4C2×D411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2×D411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C2×M16—41no—
537C22×C8—22no—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553#126—82no—
554#125—41no—
555#125—41no—
556#123—82no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—41no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565#121—22no—
566#121—41no—
567#121—41no—
568#121—41no—
569#120—44no—
570C4×Q8—22no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—24no—
577C4×D4—22no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—42no—
582C4×D4—82no—
583#117—82no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
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—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
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—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—44no—
666C2×C22⋊C4—82no—
667C2×C22⋊C4—82no—
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—41no—
681C2×C42—41no—
682C2×C42—41no—
683C2×C42—41no—
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2×D411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697#107—22no—
698#107—22no—
699#107—22no—
700#107—22no—
701#107—22no—
702#107—41no—
703#107—41no—
704#107—41no—
705#106—22no—
706#106—41no—
707#106—41no—
708#106—41no—
709C4⋊C8—22no—
710C4⋊C8—22no—
711#103—22no—
712#103—22no—
713#103—22no—
714#103—22no—
715#103—22no—
716#103—22no—
717#103—22no—
718#103—22no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—41no—
733#102—41no—
734#102#4114yes—
735C22⋊C8—22no—
736C22⋊C8—22no—
737C22⋊C8#4114yes—
738C22⋊C8#4114yes—
739#97—22no—
740#97—22no—
741#97—22no—
742#97—22no—
743#97—41no—
744#97—41no—
745#97—41no—
746#97—41no—
747C4×C8—22no—
748C4×C8—22no—
749C4×C8—41no—
750C4×C8—41no—
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#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795C24—21no—
796C24—21no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—42no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—82no—
840C2×D4—82no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4C2×#4112yes—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C2×#4112yes—
910C22×C4C2×#4112yes—
911C22×C4C2511yescharacteristic
912SD16—44no—
913SD16—44no—
914SD16—82no—
915SD16—82no—
916M16—44no—
917M16—44no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—44no—
937C2×C8—44no—
938C2×C8C2×#4112yes—
939C2×C8C2×#4112yes—
940C2×C8C2×#4112yes—
941C2×C8C2×#4112yes—
942C2×C8C2×#4112yes—
943C2×C8H(5,𝔽2)12yes—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—41no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4C2×#4112yes—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—41no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4#13714yes—
1036C42—22no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—41no—
1048C42—41no—
1049C42—41no—
1050C42—41no—
1051C42—41no—
1052C42—41no—
1053C42—41no—
1054C42—42no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—22no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—84no—
1086C23—84no—
1087C23—84no—
1088C23—84no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23#53212yes—
1093C23C2×#13712yes—
1094C23#57512yes—
1095C23C23×D411yescharacteristic
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104D4—22no—
1105D4—22no—
1106D4—44no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—84no—
1114D4—84no—
1115D4—162no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—82no—
1200C2×C4—84no—
1201C2×C4—82no—
1202C2×C4—82no—
1203C2×C4—82no—
1204C2×C4—84no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4—162no—
1208C2×C4#53212yes—
1209C2×C4C2×#13712yes—
1210C2×C4C2×#13712yes—
1211C2×C4C22×#4111yescharacteristic
1212C2×C4C22×#4111yescharacteristic
1213C2×C4C22×#4111yescharacteristic
1214C2×C4C2×H(5,𝔽2)11yescharacteristic
1215C2×C4#58511yescharacteristic
1216C2×C4#58511yescharacteristic
1217C8—22no—
1218C8—22no—
1219C8—22no—
1220C8—22no—
1221C8—22no—
1222C8—22no—
1223C8—41no—
1224C8—41no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22—41no—
1232C22—42no—
1233C22—41no—
1234C22—41no—
1235C22—42no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—42no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—168no—
1253C22#317214yes—
1254C22C2×#53211yescharacteristic
1255C22D4×#4111yescharacteristic
1256C22#349611yescharacteristic
1257C22C22×#13711yescharacteristic
1258C22C2×#57511yescharacteristic
1259C22#358511yescharacteristic
1260C22#358511yescharacteristic
1261C4—22no—
1262C4—22no—
1263C4—22no—
1264C4—41no—
1265C4—41no—
1266C4—42no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4#347511yescharacteristic
1288C4#348111yescharacteristic
1289C4#351311yescharacteristic
1290C4#352111yescharacteristic
1291C2—24no—
1292C2—81no—
1293C2—82no—
1294C2—161no—
1295C2#3626611yescharacteristic
1296C2C2×#317211yescharacteristic
1297C2#6072511yescharacteristic
1298C2#6145311yescharacteristic
1299C2#6145411yescharacteristic
1300C2#6229611yescharacteristic
1301C2#6230111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36278C2semidirect
3. #33268C2semidirect
4. #33145C2semidirect
5. #33053C2semidirect
6. #29483C2semidirect
7. #29480C2semidirect
8. #29451C2semidirect
9. #29448C2semidirect
10. #29303C2semidirect
11. #28960C2semidirect
12. #28918C2semidirect
13. #28896C2semidirect
14. #28858C2semidirect
15. #28311C2semidirect
16. #28072C2semidirect
17. #28041C2semidirect
18. #26967C2semidirect
19. #26829C2semidirect
20. #25248C2semidirect
21. #25248C2semidirect
24. #22922C2semidirect
25. #22922C2semidirect
26. #22874C2semidirect
27. #22874C2semidirect
28. C4×#468C2semidirect
29. #21279C2semidirect
30. C2×#1936C2semidirect
31. #20491C2semidirect
32. C2×#491C22semidirect
45. C2×C4×M16C22semidirect
47. #2863C22semidirect
50. #2855C22semidirect
62. #2507C22semidirect
63. #2497C22semidirect
70. #2446C22semidirect
71. #2429C22semidirect
85. C4×C22⋊Q8C22semidirect
87. #2295C22semidirect
94. #2086C22semidirect
95. #2086C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2075C22semidirect
99. #2075C22semidirect
102. #2066C22semidirect
103. #2066C22semidirect
104. #2059C22semidirect
105. #2059C22semidirect
108. #2035C22semidirect
109. #2035C22semidirect
116. #1992C22semidirect
125. #1960C22semidirect
126. #1944C22semidirect
127. #1944C22semidirect
128. #1944C22semidirect
129. #1944C22semidirect
130. #1943C22semidirect
131. #1943C22semidirect
132. #1942C22semidirect
133. #1942C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
148. #1935C22semidirect
149. #1935C22semidirect
152. #1933C22semidirect
153. #1933C22semidirect
154. #1928C22semidirect
155. #1928C22semidirect
158. #1921C22semidirect
159. #1921C22semidirect
160. #1921C22semidirect
161. #1921C22semidirect
164. #1894C22semidirect
165. #1894C22semidirect
176. #1863C22semidirect
177. #1863C22semidirect
182. #1836C22semidirect
183. #1809C22semidirect
184. #1809C22semidirect
185. C4×#107C22semidirect
186. C4×#107C22semidirect
187. #1771C22semidirect
188. #1771C22semidirect
189. #1767C22semidirect
190. C4×#103C22semidirect
191. C4×#103C22semidirect
194. #1753C22semidirect
195. #1753C22semidirect
199. #1749C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#362912
#362782
#332682
#331452
#330532
#294832
#294802
#294512
#294482
#293032
#289602
#289182
#288962
#288582
#283112
#280722
#280412
#269672
#268292
#252482
#251282
#229222
#228742
C4×#4682
#212792
C2×#19362
#204912