Finite Group Databasebeta

← #7044939

Subgroups — #7044939

Order 512.

1312 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59664C211yesmaximal, characteristic
2#59321C211yesmaximal, characteristic
3#32591C211yesmaximal, characteristic, complemented
4#32553C211yesmaximal, characteristic, complemented
5#32480C211yesmaximal, characteristic, complemented
6#32332C211yesmaximal, characteristic, complemented
7#32310C211yesmaximal, characteristic, complemented
8#31824C211yesmaximal, characteristic, complemented
9#31472C211yesmaximal, characteristic, complemented
10#31456C211yesmaximal, characteristic, complemented
11#29243C211yesmaximal, characteristic
12#27715C211yesmaximal, characteristic
13#27697C211yesmaximal, characteristic
14#27648C211yesmaximal, characteristic
15#27569C211yesmaximal, characteristic, complemented
16#27425C211yesmaximal, characteristic, complemented
17#27375C211yesmaximal, characteristic, complemented
18#27141C211yesmaximal, characteristic, complemented
19#26524C211yesmaximal, characteristic, complemented
20#26276C211yesmaximal, characteristic, complemented
21#26108C211yesmaximal, characteristic, complemented
22#26000C211yesmaximal, characteristic
23#25992C211yesmaximal, characteristic
24#25206C211yesmaximal, characteristic
25#25206C211yesmaximal, characteristic
26#25004C211yesmaximal, characteristic, complemented
27C2×#2099C211yesmaximal, characteristic
28#22932C211yesmaximal, characteristic
29#22922C211yesmaximal, characteristic
30#22291C211yesmaximal, characteristic
31#22183C211yesmaximal, characteristic
32C2×#484C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#467C2211yescharacteristic
35#2805—21no—
36#2791—21no—
37#2791—21no—
38#2791—21no—
39#2590—21no—
40#2582C2211yescharacteristic
41#2581C2211yescharacteristic
42#2565—21no—
43#2552C2211yescharacteristic
44#2552C2211yescharacteristic
45#2552C2211yescharacteristic
46#2550—21no—
47#2546C2211yescharacteristic
48#2511C2211yescharacteristic
49#2511C2211yescharacteristic
50#2508C2211yescharacteristic
51#2506—21no—
52#2506C2211yescharacteristic
53#2505—21no—
54#2502C2211yescharacteristic
55#2502C2211yescharacteristic
56#2473—21no—
57#2473—21no—
58#2473—21no—
59#2453C2211yescharacteristic
60#2451C2211yescharacteristic
61#2442—21no—
62#2442C2211yescharacteristic
63#2440—21no—
64#2440C2211yescharacteristic
65#2370C2211yescharacteristic
66#2368—21no—
67#2360—21no—
68#2360C2211yescharacteristic
69#2360C2211yescharacteristic
70#2355C2211yescharacteristic
71Q8×C4⋊C4C2211yescharacteristic
72Q8×C4⋊C4C2211yescharacteristic
73#2345C2211yescharacteristic
74#2345C2211yescharacteristic
75C4×C22⋊Q8C2211yescharacteristic
76C4×C22⋊Q8C2211yescharacteristic
77C4×C22⋊Q8C2211yescharacteristic
78C2×#389C2211yescharacteristic
79C2×#384C2211yescharacteristic
80#2101C2211yescharacteristic
81#2100C2211yescharacteristic
82#2100C2211yescharacteristic
83#2099C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2099C2211yescharacteristic
92#2099C2211yescharacteristic
93#2099C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2086C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2083C2211yescharacteristic
103#2083C2211yescharacteristic
104#2074C2211yescharacteristic
105#2072C2211yescharacteristic
106#2072C2211yescharacteristic
107#2072C2211yescharacteristic
108#2072C2211yescharacteristic
109#2072C2211yescharacteristic
110#2068C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2059C2211yescharacteristic
115#2058C2211yescharacteristic
116#2056C2211yescharacteristic
117#2056C2211yescharacteristic
118#2026C2211yescharacteristic
119#2024C2211yescharacteristic
120#1992C2211yescharacteristic
121#1990C2211yescharacteristic
122#1989C2211yescharacteristic
123#1988C2211yescharacteristic
124#1985C2211yescharacteristic
125#1984C2211yescharacteristic
126#1949C2211yescharacteristic
127#1948C2211yescharacteristic
128#1947C2211yescharacteristic
129#1947C2211yescharacteristic
130#1947C2211yescharacteristic
131#1947C2211yescharacteristic
132#1943C2211yescharacteristic
133#1942C2211yescharacteristic
134#1940C2211yescharacteristic
135#1939C2211yescharacteristic
136#1935C2211yescharacteristic
137#1935C2211yescharacteristic
138#1935C2211yescharacteristic
139#1933C2211yescharacteristic
140#1933C2211yescharacteristic
141#1933C2211yescharacteristic
142#1928C2211yescharacteristic
143#1928C2211yescharacteristic
144#1928C2211yescharacteristic
145#1927C2211yescharacteristic
146#1927C2211yescharacteristic
147#1927C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1920C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1918C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1917C2211yescharacteristic
161#1917C2211yescharacteristic
162#1916C2211yescharacteristic
163#1916C2211yescharacteristic
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1872C2211yescharacteristic
171#1872C2211yescharacteristic
172#1865C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1863C2211yescharacteristic
178#1853C2211yescharacteristic
179#1852C2211yescharacteristic
180#1850C2211yescharacteristic
181#1850C2211yescharacteristic
182#1836C2211yescharacteristic
183#1834C2211yescharacteristic
184#1824C2211yescharacteristic
185#1824C2211yescharacteristic
186#1807C2211yescharacteristic
187#1803C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190#1803C2211yescharacteristic
191#1797C2211yescharacteristic
192#1776C2211yescharacteristic
193C4×#107C2211yescharacteristic
194#1763C2211yescharacteristic
195C4×#103C2211yescharacteristic
196#1752C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198C2×#340C2211yescharacteristic
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8D411yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C4×Q8—21no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C22×C4⋊C4—21no—
224C22×C4⋊C4—21no—
225C22×C4⋊C4—21no—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C42C2311yescharacteristic
231#484—24no—
232#484—24no—
233#467—24no—
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×C22⋊C8C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#395—21no—
301#395—21no—
302#395—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391D411yescharacteristic
307#391C2311yescharacteristic
308#391C2311yescharacteristic
309#391C2311yescharacteristic
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#389—21no—
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389D411yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387D411yescharacteristic
370#387D411yescharacteristic
371#385—21no—
372#385—21no—
373#385—21no—
374#385—21no—
375#385—21no—
376#385—21no—
377#385—21no—
378#385—21no—
379#385—21no—
380#385—21no—
381#385D411yescharacteristic
382#385D411yescharacteristic
383#384—21no—
384#384—21no—
385#384—21no—
386#384C2311yescharacteristic
387#384C2311yescharacteristic
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#382—21no—
396#382—21no—
397#382C2311yescharacteristic
398#380—21no—
399#380—21no—
400#380—21no—
401#380D411yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4C2311yescharacteristic
427C4×C22⋊C4C2311yescharacteristic
428C2×#95—21no—
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
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#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8C2×D411yescharacteristic
483C22×Q8C2411yescharacteristic
484C22×Q8C2411yescharacteristic
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C2×D411yescharacteristic
490C23×C4C2×D411yescharacteristic
491C23×C4C2411yescharacteristic
492C2×Q16—22no—
493C2×Q16—41no—
494C2×Q16—41no—
495C22×C8—22no—
496C22×C8—22no—
497C22×C8—41no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C4⋊Q8—41no—
510C4⋊Q8—41no—
511C4⋊Q8—82no—
512#125—22no—
513#125—41no—
514#125—82no—
515#125—82no—
516#125—82no—
517#125—82no—
518C22⋊Q8—22no—
519C22⋊Q8—24no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—44no—
523C22⋊Q8#4114yes—
524C4×Q8—22no—
525C4×Q8—41no—
526C4×Q8—41no—
527C4×Q8—41no—
528C4×Q8—41no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—82no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
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—21no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—82no—
591C2×C4⋊C4—82no—
592C2×C4⋊C4—82no—
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⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
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—21no—
636C2×C42—41no—
637C2×C42—41no—
638C2×C42C2×D411yescharacteristic
639C2×C42C2×D411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646#107—22no—
647#107—22no—
648#107—22no—
649#107—22no—
650#107—22no—
651#107—22no—
652#107—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657C4⋊C8—41no—
658C4⋊C8—41no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663#103—22no—
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—
677C22⋊C8—22no—
678C22⋊C8—22no—
679#97—41no—
680#97—41no—
681C4×C8—41no—
682C4×C8—41no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
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#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737C24C22×D411yescharacteristic
738C2×Q8—22no—
739C2×Q8—22no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—41no—
752C2×Q8—42no—
753C2×Q8—81no—
754C2×Q8—81no—
755C2×Q8C2×#4112yes—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
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—41no—
781C22×C4—41no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—81no—
788C22×C4—81no—
789C22×C4—81no—
790C22×C4—81no—
791C22×C4—81no—
792C22×C4—81no—
793C22×C4—81no—
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C2×#4112yes—
808C22×C42−1+412yes—
809C22×C4C2511yescharacteristic
810Q16—82no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
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—82no—
836C2×C8—82no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
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—41no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
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—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
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⋊C4C2×#4112yes—
920C4⋊C42−1+412yes—
921C22⋊C4—24no—
922C22⋊C4—22no—
923C22⋊C4—22no—
924C22⋊C4—22no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4#13714yes—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—41no—
942C42—41no—
943C42—42no—
944C42—42no—
945C42—42no—
946C42—42no—
947C42—81no—
948C42—81no—
949C42—81no—
950C42—81no—
951C42—81no—
952C42—81no—
953C42—81no—
954C42—81no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23#54812yes—
960C23C2×#13712yes—
961C23#57812yes—
962C23C23×D411yescharacteristic
963Q8—22no—
964Q8—22no—
965Q8—44no—
966Q8—41no—
967Q8—41no—
968Q8—41no—
969Q8—41no—
970Q8—41no—
971Q8—41no—
972Q8—162no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
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—22no—
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—44no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
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—84no—
1062C2×C4—162no—
1063C2×C4—162no—
1064C2×C4—162no—
1065C2×C4#54812yes—
1066C2×C4C2×#13712yes—
1067C2×C4C2×#13712yes—
1068C2×C4#57612yes—
1069C2×C4#57712yes—
1070C2×C4C22×#4111yescharacteristic
1071C2×C4C2×2−1+411yescharacteristic
1072C2×C4C2×2−1+411yescharacteristic
1073C2×C4#58511yescharacteristic
1074C2×C4#58511yescharacteristic
1075C2×C4#58511yescharacteristic
1076C8—41no—
1077C8—41no—
1078C8—41no—
1079C8—41no—
1080C8—41no—
1081C8—41no—
1082C8—41no—
1083C8—41no—
1084C22—22no—
1085C22—22no—
1086C22—22no—
1087C22—22no—
1088C22—22no—
1089C22—22no—
1090C22#337414yes—
1091C22C2×#54811yescharacteristic
1092C22#348511yescharacteristic
1093C22#348911yescharacteristic
1094C22C22×#13711yescharacteristic
1095C22C2×#57611yescharacteristic
1096C22C2×#57711yescharacteristic
1097C22C2×#57811yescharacteristic
1098C4—22no—
1099C4—22no—
1100C4—22no—
1101C4—22no—
1102C4—22no—
1103C4—42no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4—41no—
1108C4—41no—
1109C4—42no—
1110C4—41no—
1111C4—41no—
1112C4—41no—
1113C4—42no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4#351511yescharacteristic
1128C4#352111yescharacteristic
1129C4#356311yescharacteristic
1130C4#356411yescharacteristic
1131C2—24no—
1132C2#4353211yescharacteristic
1133C2C2×#337411yescharacteristic
1134C2#6132911yescharacteristic
1135C2#6172611yescharacteristic
1136C2#6176711yescharacteristic
1137C2#6213111yescharacteristic
1138C2#6220111yescharacteristic
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
3. #32591C2semidirect
4. #32553C2semidirect
5. #32480C2semidirect
6. #32332C2semidirect
7. #32310C2semidirect
8. #31824C2semidirect
9. #31472C2semidirect
10. #31456C2semidirect
15. #27569C2semidirect
16. #27425C2semidirect
17. #27375C2semidirect
18. #27141C2semidirect
19. #26524C2semidirect
20. #26276C2semidirect
21. #26108C2semidirect
26. #25004C2semidirect

Maximal subgroups

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

subgroupindex
#596642
#593212
#325912
#325532
#324802
#323322
#323102
#318242
#314722
#314562
#292432
#277152
#276972
#276482
#275692
#274252
#273752
#271412
#265242
#262762
#261082
#260002
#259922
#252062
#250042
C2×#20992
#229322
#229222
#222912
#221832