Finite Group Databasebeta

← #7576161

Subgroups — #7576161

Order 512.

1427 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59963C211yesmaximal, characteristic, complemented
2D4×#125C211yesmaximal, characteristic
3#32392C211yesmaximal, characteristic, complemented
4#32310C211yesmaximal, characteristic, complemented
5#31572C211yesmaximal, characteristic, complemented
6#31472C211yesmaximal, characteristic, complemented
7#29581C211yesmaximal, characteristic, complemented
8#29581C211yesmaximal, characteristic, complemented
9#29034C211yesmaximal, characteristic, complemented
10#28955C211yesmaximal, characteristic, complemented
11#28050C211yesmaximal, characteristic, complemented
12#28007C211yesmaximal, characteristic, complemented
13#27573C211yesmaximal, characteristic
14#27566C211yesmaximal, characteristic
15#27375C211yesmaximal, characteristic, complemented
16#27322C211yesmaximal, characteristic, complemented
17#27312C211yesmaximal, characteristic
18#27294C211yesmaximal, characteristic
19#26884C211yesmaximal, characteristic, complemented
20#26773C211yesmaximal, characteristic, complemented
21#26398C211yesmaximal, characteristic
22#26398C211yesmaximal, characteristic
23#26182C211yesmaximal, characteristic
24#26166C211yesmaximal, characteristic
25#23265C211yesmaximal, characteristic, complemented
26#23002C211yesmaximal, characteristic
27#22978C211yesmaximal, characteristic
28#22762C211yesmaximal, characteristic
29#22677C211yesmaximal, characteristic
30#21121C211yesmaximal, characteristic
31#21121C211yesmaximal, characteristic
32C22×#125—21no—
33C2×#478C2211yescharacteristic
34C2×#461C2211yescharacteristic
35C2×#440C2211yescharacteristic
36C2×#440C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×C4×SD16C2211yescharacteristic
39#2859C2211yescharacteristic
40#2851—21no—
41#2767—21no—
42#2719—21no—
43#2585—21no—
44#2552C2211yescharacteristic
45#2552C2211yescharacteristic
46#2533—21no—
47#2533—21no—
48#2528—21no—
49#2528—21no—
50#2514C2211yescharacteristic
51#2511C2211yescharacteristic
52#2509C2211yescharacteristic
53#2506C2211yescharacteristic
54#2506C2211yescharacteristic
55#2506C2211yescharacteristic
56#2506C2211yescharacteristic
57#2506C2211yescharacteristic
58#2473—21no—
59#2473—21no—
60#2473—21no—
61#2473—21no—
62#2453C2211yescharacteristic
63#2453C2211yescharacteristic
64#2446C2211yescharacteristic
65#2446C2211yescharacteristic
66#2442—21no—
67#2442—21no—
68#2370—21no—
69#2370C2211yescharacteristic
70#2365C2211yescharacteristic
71#2355C2211yescharacteristic
72#2351C2211yescharacteristic
73D4×C4⋊C4C2211yescharacteristic
74D4×C4⋊C4C2211yescharacteristic
75D4×C4⋊C4C2211yescharacteristic
76D4×C4⋊C4C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78D4×C4⋊C4C2211yescharacteristic
79C4×#125C2211yescharacteristic
80#2295C2211yescharacteristic
81#2295C2211yescharacteristic
82C42×D4C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2096C2211yescharacteristic
90#2096C2211yescharacteristic
91#2096C2211yescharacteristic
92#2095C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2086C2211yescharacteristic
96#2086C2211yescharacteristic
97#2085C2211yescharacteristic
98#2084C2211yescharacteristic
99#2083C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2083C2211yescharacteristic
103#2072C2211yescharacteristic
104#2072C2211yescharacteristic
105#2072C2211yescharacteristic
106#2072C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2066C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2043C2211yescharacteristic
114#2043C2211yescharacteristic
115#1992C2211yescharacteristic
116#1956C2211yescharacteristic
117#1948C2211yescharacteristic
118#1947C2211yescharacteristic
119#1943C2211yescharacteristic
120#1943C2211yescharacteristic
121#1943C2211yescharacteristic
122#1943C2211yescharacteristic
123#1943C2211yescharacteristic
124#1942C2211yescharacteristic
125#1942C2211yescharacteristic
126#1941C2211yescharacteristic
127#1935C2211yescharacteristic
128#1935C2211yescharacteristic
129#1935C2211yescharacteristic
130#1935C2211yescharacteristic
131#1935C2211yescharacteristic
132#1935C2211yescharacteristic
133#1935C2211yescharacteristic
134#1933C2211yescharacteristic
135#1928C2211yescharacteristic
136#1928C2211yescharacteristic
137#1927C2211yescharacteristic
138#1927C2211yescharacteristic
139#1921C2211yescharacteristic
140#1921C2211yescharacteristic
141#1921C2211yescharacteristic
142#1920C2211yescharacteristic
143#1920C2211yescharacteristic
144#1920C2211yescharacteristic
145#1920C2211yescharacteristic
146#1920C2211yescharacteristic
147#1918C2211yescharacteristic
148#1918C2211yescharacteristic
149#1918C2211yescharacteristic
150#1918C2211yescharacteristic
151#1917C2211yescharacteristic
152#1917C2211yescharacteristic
153#1917C2211yescharacteristic
154#1917C2211yescharacteristic
155#1917C2211yescharacteristic
156#1917C2211yescharacteristic
157#1916C2211yescharacteristic
158#1916C2211yescharacteristic
159#1877C2211yescharacteristic
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1865C2211yescharacteristic
168#1865C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1847C2211yescharacteristic
184#1834C2211yescharacteristic
185#1804C2211yescharacteristic
186#1803C2211yescharacteristic
187#1803C2211yescharacteristic
188#1802C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1770C2211yescharacteristic
194#1770C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1745C2211yescharacteristic
202#1745C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#125—21no—
207C2×#125—21no—
208C2×#125—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125—21no—
213C2×#125—21no—
214C2×#125—48no—
215C2×#125D411yescharacteristic
216C2×#125C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C22×C4⋊C4—21no—
229C22×C4⋊C4—21no—
230C22×C4⋊C4—21no—
231C22×C4⋊C4—21no—
232C22×C4⋊C4—21no—
233C22×C4⋊C4—21no—
234C22×C42—21no—
235#478—24no—
236#461—24no—
237#440—24no—
238#440—24no—
239#440—24no—
240C4×SD16—24no—
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287#401—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389D411yescharacteristic
335#389D411yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
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#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387D411yescharacteristic
382#387D411yescharacteristic
383#387D411yescharacteristic
384#387D411yescharacteristic
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#383—21no—
405#382—21no—
406#382—21no—
407#382—21no—
408#382D411yescharacteristic
409#382C2311yescharacteristic
410#380—21no—
411#380—21no—
412#380—21no—
413#380—21no—
414#380—21no—
415#380—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438#376—21no—
439#376—21no—
440C43C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
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#336C2311yescharacteristic
470#336C2311yescharacteristic
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
485C22×Q8C2411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×D4C2411yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16#4114yes—
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C4⋊Q8—22no—
510C4⋊Q8—41no—
511#125—24no—
512#125—22no—
513#125—41no—
514#125—44no—
515#125—44no—
516#125—44no—
517#125—44no—
518#125—44no—
519#125—44no—
520#125—44no—
521#125—44no—
522C4×Q8—22no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—41no—
527C4×Q8—41no—
528C4×Q8—41no—
529C4×Q8—41no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—41no—
539C4×D4—41no—
540C4×D4—41no—
541C4×D4—41no—
542C4×D4—41no—
543C4×D4—41no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—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—44no—
587C2×C4⋊C4—44no—
588C2×C4⋊C4—44no—
589C2×C4⋊C4—44no—
590C2×C4⋊C4—44no—
591C2×C4⋊C4—44no—
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2×D411yescharacteristic
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×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—44no—
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2×D411yescharacteristic
639C2×C42C2×D411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647#107—22no—
648#107—22no—
649#107—22no—
650#107—22no—
651#107—22no—
652#107—22no—
653#107—41no—
654#107—41no—
655#106—22no—
656#106—22no—
657#106—41no—
658#106—41no—
659#106—41no—
660#106—41no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—41no—
664C4⋊C8—41no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—22no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102#4114yes—
685#97—22no—
686#97—22no—
687#97—22no—
688#97—41no—
689#97—41no—
690#97—41no—
691C4×C8—22no—
692C4×C8—41no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750C24—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8C2×#4112yes—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4C2×#4112yes—
767C2×D4C2×#4112yes—
768C2×D42−1+412yes—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—81no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4—81no—
803C22×C4—81no—
804C22×C4—81no—
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C2511yescharacteristic
820SD16—28no—
821SD16—44no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8C2×#4112yes—
845C2×C8C2×#4112yes—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—41no—
876C4⋊C4—41no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4AGL(1,ℤ/8)14yes—
924C4⋊C4C2×#4112yes—
925C4⋊C42−1+412yes—
926C22⋊C4—24no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C42—22no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—41no—
949C42—41no—
950C42—41no—
951C42—42no—
952C42—42no—
953C42—42no—
954C42—42no—
955C42—42no—
956C42—42no—
957C42—42no—
958C42—42no—
959C42—81no—
960C42—81no—
961C42—81no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23C23×D411yescharacteristic
970Q8—22no—
971Q8—22no—
972Q8—41no—
973Q8—41no—
974Q8—41no—
975Q8—41no—
976Q8—41no—
977Q8—41no—
978D4—22no—
979D4—22no—
980D4—22no—
981D4#55214yes—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—48no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—84no—
1068C2×C4—84no—
1069C2×C4—84no—
1070C2×C4—84no—
1071C2×C4—84no—
1072C2×C4—84no—
1073C2×C4C2×AGL(1,ℤ/8)12yes—
1074C2×C4C2×AGL(1,ℤ/8)12yes—
1075C2×C4C2×AGL(1,ℤ/8)12yes—
1076C2×C4C22×#4111yescharacteristic
1077C2×C4C22×#4111yescharacteristic
1078C2×C4C2×2−1+411yescharacteristic
1079C2×C4C2×2−1+411yescharacteristic
1080C2×C4#58511yescharacteristic
1081C2×C4#58511yescharacteristic
1082C8—22no—
1083C8—22no—
1084C8—41no—
1085C8—41no—
1086C8—41no—
1087C8—41no—
1088C8—41no—
1089C8—41no—
1090C22—24no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22D4×#4111yescharacteristic
1098C22D4×#4111yescharacteristic
1099C22#348611yescharacteristic
1100C22C22×AGL(1,ℤ/8)11yescharacteristic
1101C22#358611yescharacteristic
1102C22#358611yescharacteristic
1103C22#358611yescharacteristic
1104C4—22no—
1105C4—22no—
1106C4—22no—
1107C4—41no—
1108C4—42no—
1109C4—41no—
1110C4—41no—
1111C4—41no—
1112C4—42no—
1113C4—41no—
1114C4—41no—
1115C4—41no—
1116C4—41no—
1117C4—41no—
1118C4—41no—
1119C4—42no—
1120C4—41no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4C2×#55211yescharacteristic
1134C4#351511yescharacteristic
1135C4#351511yescharacteristic
1136C4#355311yescharacteristic
1137C2—44no—
1138C2#5916111yescharacteristic
1139C2#6145211yescharacteristic
1140C2#6146611yescharacteristic
1141C2#6151711yescharacteristic
1142C2#6151711yescharacteristic
1143C2#6182711yescharacteristic
1144C2#6187711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59963C2semidirect
3. #32392C2semidirect
4. #32310C2semidirect
5. #31572C2semidirect
6. #31472C2semidirect
7. #29581C2semidirect
8. #29581C2semidirect
9. #29034C2semidirect
10. #28955C2semidirect
11. #28050C2semidirect
12. #28007C2semidirect
15. #27375C2semidirect
16. #27322C2semidirect
19. #26884C2semidirect
20. #26773C2semidirect
25. #23265C2semidirect

Maximal subgroups

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

subgroupindex
#599632
D4×#1252
#323922
#323102
#315722
#314722
#295812
#290342
#289552
#280502
#280072
#275732
#275662
#273752
#273222
#273122
#272942
#268842
#267732
#263982
#261822
#261662
#232652
#230022
#229782
#227622
#226772
#211212