Finite Group Databasebeta

← #7273668

Subgroups — #7273668

Order 512.

1340 conjugacy classes of subgroups.

The subgroup lattice has 1147 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40071C211yesmaximal, characteristic
2#39368C211yesmaximal, characteristic
3#32741C211yesmaximal, characteristic
4#32682C211yesmaximal, characteristic, complemented
5#32630C211yesmaximal, characteristic, complemented
6#32483C211yesmaximal, characteristic, complemented
7#31984C211yesmaximal, characteristic, complemented
8#31888C211yesmaximal, characteristic, complemented
9#31876C211yesmaximal, characteristic, complemented
10#31760C211yesmaximal, characteristic
11#31708C211yesmaximal, characteristic
12#30957C211yesmaximal, characteristic, complemented
13#30816C211yesmaximal, characteristic, complemented
14#30779C211yesmaximal, characteristic
15#30635C211yesmaximal, characteristic
16#29244C211yesmaximal, characteristic
17#28955C211yesmaximal, characteristic, complemented
18#28675C211yesmaximal, characteristic, complemented
19#28639C211yesmaximal, characteristic, complemented
20#28057C211yesmaximal, characteristic, complemented
21#27461C211yesmaximal, characteristic
22#27413C211yesmaximal, characteristic
23#27371C211yesmaximal, characteristic, complemented
24#27349C211yesmaximal, characteristic
25#27331C211yesmaximal, characteristic
26#26869C211yesmaximal, characteristic, complemented
27#26456C211yesmaximal, characteristic, complemented
28#26038C211yesmaximal, characteristic, complemented
29#24702C211yesmaximal, characteristic
30#24602C211yesmaximal, characteristic
31#22100C211yesmaximal, characteristic
32C2×#544—21no—
33C2×#500C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#484C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×C8×Q8C2211yescharacteristic
38C2×#431C2211yescharacteristic
39#2857C2211yescharacteristic
40#2855C2211yescharacteristic
41#2770—21no—
42#2766—21no—
43#2762—21no—
44#2734—21no—
45#2729—21no—
46#2726—21no—
47#2713—21no—
48#2713—21no—
49#2655—21no—
50#2627—21no—
51#2568C2211yescharacteristic
52#2551C2211yescharacteristic
53#2551C2211yescharacteristic
54#2546C2211yescharacteristic
55#2546C2211yescharacteristic
56#2546C2211yescharacteristic
57#2527—21no—
58#2515—21no—
59#2514C2211yescharacteristic
60#2506C2211yescharacteristic
61#2506C2211yescharacteristic
62#2506C2211yescharacteristic
63#2506C2211yescharacteristic
64#2494C2211yescharacteristic
65#2492C2211yescharacteristic
66#2489C2211yescharacteristic
67#2453C2211yescharacteristic
68#2451C2211yescharacteristic
69#2446C2211yescharacteristic
70#2440C2211yescharacteristic
71#2440C2211yescharacteristic
72#2438—21no—
73#2438—21no—
74#2429C2211yescharacteristic
75#2370C2211yescharacteristic
76#2356C2211yescharacteristic
77#2344C2211yescharacteristic
78#2344C2211yescharacteristic
79#2331—21no—
80C4×C22⋊Q8C2211yescharacteristic
81C4×C22⋊Q8C2211yescharacteristic
82C2×#389C2211yescharacteristic
83#2101C2211yescharacteristic
84#2095C2211yescharacteristic
85#2095C2211yescharacteristic
86#2088C2211yescharacteristic
87#2087C2211yescharacteristic
88#2087C2211yescharacteristic
89#2086C2211yescharacteristic
90#2086C2211yescharacteristic
91#2086C2211yescharacteristic
92#2086C2211yescharacteristic
93#2086C2211yescharacteristic
94#2086C2211yescharacteristic
95#2085C2211yescharacteristic
96#2084C2211yescharacteristic
97#2083C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic
102#2072C2211yescharacteristic
103#2072C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2066C2211yescharacteristic
114#2066C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2057C2211yescharacteristic
118#2057C2211yescharacteristic
119#2057C2211yescharacteristic
120#2057C2211yescharacteristic
121#2057C2211yescharacteristic
122#2043C2211yescharacteristic
123#2043C2211yescharacteristic
124#2036C2211yescharacteristic
125#2036C2211yescharacteristic
126#2036C2211yescharacteristic
127#2036C2211yescharacteristic
128#2024C2211yescharacteristic
129#2024C2211yescharacteristic
130#2024C2211yescharacteristic
131#1992C2211yescharacteristic
132#1989C2211yescharacteristic
133#1988C2211yescharacteristic
134#1988C2211yescharacteristic
135#1988C2211yescharacteristic
136#1987C2211yescharacteristic
137#1984C2211yescharacteristic
138#1981C2211yescharacteristic
139#1949C2211yescharacteristic
140#1947C2211yescharacteristic
141#1947C2211yescharacteristic
142#1943C2211yescharacteristic
143#1942C2211yescharacteristic
144#1942C2211yescharacteristic
145#1942C2211yescharacteristic
146#1942C2211yescharacteristic
147#1942C2211yescharacteristic
148#1942C2211yescharacteristic
149#1940C2211yescharacteristic
150#1940C2211yescharacteristic
151#1939C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1935C2211yescharacteristic
155#1933C2211yescharacteristic
156#1933C2211yescharacteristic
157#1933C2211yescharacteristic
158#1933C2211yescharacteristic
159#1933C2211yescharacteristic
160#1933C2211yescharacteristic
161#1928C2211yescharacteristic
162#1928C2211yescharacteristic
163#1928C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1924C2211yescharacteristic
167#1924C2211yescharacteristic
168#1923C2211yescharacteristic
169#1923C2211yescharacteristic
170#1921C2211yescharacteristic
171#1921C2211yescharacteristic
172#1920C2211yescharacteristic
173#1920C2211yescharacteristic
174#1920C2211yescharacteristic
175#1919C2211yescharacteristic
176#1919C2211yescharacteristic
177#1918C2211yescharacteristic
178#1918C2211yescharacteristic
179#1918C2211yescharacteristic
180#1918C2211yescharacteristic
181#1916C2211yescharacteristic
182#1916C2211yescharacteristic
183#1872C2211yescharacteristic
184#1872C2211yescharacteristic
185#1872C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1863C2211yescharacteristic
190#1853C2211yescharacteristic
191#1852C2211yescharacteristic
192#1852C2211yescharacteristic
193#1836C2211yescharacteristic
194#1824C2211yescharacteristic
195#1803C2211yescharacteristic
196#1803C2211yescharacteristic
197#1797C2211yescharacteristic
198#1776C2211yescharacteristic
199C4×#107C2211yescharacteristic
200C4×#106C2211yescharacteristic
201#1770C2211yescharacteristic
202#1763C2211yescharacteristic
203#544—48no—
204C2×C4⋊Q8—21no—
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8D411yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×#117—21no—
229C2×#117—21no—
230C22×C4⋊C4—21no—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C42C2311yescharacteristic
234#500—42no—
235#487—42no—
236#484—42no—
237#477—42no—
238C8×Q8—42no—
239#431—42no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290#401—21no—
291#401—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#400—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#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#397—21no—
320#397—21no—
321#396—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#395—21no—
329#393—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391D411yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389D411yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
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#389C2311yescharacteristic
374#389C2311yescharacteristic
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387D411yescharacteristic
401#387D411yescharacteristic
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385D411yescharacteristic
407#385D411yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#383—21no—
412#383—21no—
413#382—21no—
414#382—21no—
415#382C2311yescharacteristic
416#381—21no—
417#381—21no—
418#381—21no—
419#380—21no—
420#380D411yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376—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#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8C2×D411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C2×D411yescharacteristic
495C23×C4C2×D411yescharacteristic
496C23×C4C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C4⋊Q8—41no—
506C4⋊Q8—41no—
507C4⋊Q8—41no—
508C4⋊Q8—41no—
509C4⋊Q8—41no—
510C4⋊Q8—41no—
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514C4⋊Q8—41no—
515C4⋊Q8—44no—
516C4⋊Q8—44no—
517C4⋊Q8—44no—
518C4⋊Q8—44no—
519C4⋊Q8—44no—
520#125—22no—
521#125—41no—
522#125—44no—
523#125—44no—
524#125—44no—
525#125—44no—
526C22⋊Q8—24no—
527C22⋊Q8—22no—
528C22⋊Q8—44no—
529C22⋊Q8—44no—
530C22⋊Q8—41no—
531C22⋊Q8—44no—
532C22⋊Q8—41no—
533C22⋊Q8—41no—
534C4×Q8—22no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540#117—44no—
541#117—44no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
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—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—44no—
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C22⋊C4C2×D411yescharacteristic
619C2×C22⋊C4C2×D411yescharacteristic
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—41no—
631C2×C42—41no—
632C2×C42C2×D411yescharacteristic
633C2×C42C2×D411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640#107—22no—
641#107—22no—
642#107—22no—
643#107—22no—
644#107—22no—
645#107—22no—
646#107—41no—
647#107—41no—
648#107—41no—
649#107—41no—
650#107—41no—
651#107—41no—
652#106—22no—
653#106—22no—
654#106—41no—
655#106—41no—
656C4⋊C8—22no—
657C4⋊C8—41no—
658C4⋊C8—41no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663C4⋊C8—41no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—41no—
671#103—41no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680C22⋊C8—22no—
681C22⋊C8—41no—
682C22⋊C8—41no—
683C22⋊C8—41no—
684#97—41no—
685#97—41no—
686C4×C8—22no—
687C4×C8—22no—
688C4×C8—22no—
689C4×C8—41no—
690#95—21no—
691#95—21no—
692#95—21no—
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#95—21no—
739#95—21no—
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
750C24C22×D411yescharacteristic
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×Q8—21no—
763C2×Q8—41no—
764C2×Q8—41no—
765C2×Q8—42no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8—42no—
769C2×Q8—81no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8—81no—
773C2×Q8—81no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×Q8—81no—
777C2×Q8AGL(1,ℤ/8)14yes—
778C22×C4—24no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—81no—
811C22×C4—81no—
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C2511yescharacteristic
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×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8H(5,𝔽2)12yes—
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—22no—
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—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—41no—
882C4⋊C4—41no—
883C4⋊C4—41no—
884C4⋊C4—41no—
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—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
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⋊C4—81no—
924C4⋊C42−1+412yes—
925C4⋊C42−1+412yes—
926C4⋊C42−1+412yes—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—22no—
930C22⋊C4—22no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—41no—
950C42—41no—
951C42—42no—
952C42—42no—
953C42—42no—
954C42—42no—
955C42—42no—
956C42—42no—
957C42—42no—
958C42—81no—
959C42—81no—
960C42—81no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23#57812yes—
968C23C23×D411yescharacteristic
969Q8—44no—
970Q8—41no—
971Q8—41no—
972Q8—41no—
973Q8—41no—
974Q8—41no—
975Q8—41no—
976Q8—41no—
977Q8—41no—
978Q8—162no—
979Q8—162no—
980Q8—162no—
981Q8—162no—
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—22no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—22no—
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—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—44no—
1021C2×C4—48no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
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—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—82no—
1072C2×C4—162no—
1073C2×C4C2×AGL(1,ℤ/8)12yes—
1074C2×C4C2×AGL(1,ℤ/8)12yes—
1075C2×C4C2×AGL(1,ℤ/8)12yes—
1076C2×C4#57812yes—
1077C2×C4C2×H(5,𝔽2)11yescharacteristic
1078C2×C4C2×2−1+411yescharacteristic
1079C2×C4C2×2−1+411yescharacteristic
1080C2×C4C2×2−1+411yescharacteristic
1081C2×C4#58511yescharacteristic
1082C2×C4#58511yescharacteristic
1083C8—22no—
1084C8—41no—
1085C8—41no—
1086C8—41no—
1087C8—41no—
1088C8—41no—
1089C8—41no—
1090C8—41no—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—41no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22#348611yescharacteristic
1099C22#348911yescharacteristic
1100C22#349611yescharacteristic
1101C22C22×AGL(1,ℤ/8)11yescharacteristic
1102C22C2×#57811yescharacteristic
1103C22C2×#57811yescharacteristic
1104C22#358411yescharacteristic
1105C4—22no—
1106C4—22no—
1107C4—22no—
1108C4—22no—
1109C4—41no—
1110C4—41no—
1111C4—41no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—41no—
1116C4—42no—
1117C4—42no—
1118C4—41no—
1119C4—41no—
1120C4—42no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4#354411yescharacteristic
1135C4#354711yescharacteristic
1136C4#355511yescharacteristic
1137C4#356511yescharacteristic
1138C2—42no—
1139C2#4745411yescharacteristic
1140C2#6183711yescharacteristic
1141C2#6186611yescharacteristic
1142C2#6214811yescharacteristic
1143C2#6221411yescharacteristic
1144C2#6225311yescharacteristic
1145C2#6227111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
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
4. #32682C2semidirect
5. #32630C2semidirect
6. #32483C2semidirect
7. #31984C2semidirect
8. #31888C2semidirect
9. #31876C2semidirect
12. #30957C2semidirect
13. #30816C2semidirect
17. #28955C2semidirect
18. #28675C2semidirect
19. #28639C2semidirect
20. #28057C2semidirect
23. #27371C2semidirect
26. #26869C2semidirect
27. #26456C2semidirect
28. #26038C2semidirect

Maximal subgroups

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

subgroupindex
#400712
#393682
#327412
#326822
#326302
#324832
#319842
#318882
#318762
#317602
#317082
#309572
#308162
#307792
#306352
#292442
#289552
#286752
#286392
#280572
#274612
#274132
#273712
#273492
#273312
#268692
#264562
#260382
#247022
#246022
#221002