Finite Group Databasebeta

← #6851151

Subgroups — #6851151

Order 512.

1280 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36564C211yesmaximal, characteristic
2#34815C211yesmaximal, characteristic
3#33153C211yesmaximal, characteristic
4#32506C211yesmaximal, characteristic, complemented
5#32505C211yesmaximal, characteristic, complemented
6#32360C211yesmaximal, characteristic, complemented
7#32358C211yesmaximal, characteristic, complemented
8#32152C211yesmaximal, characteristic, complemented
9#32150C211yesmaximal, characteristic, complemented
10#31872C211yesmaximal, characteristic, complemented
11#31868C211yesmaximal, characteristic, complemented
12#29971C211yesmaximal, characteristic
13#29971C211yesmaximal, characteristic
14#29304C211yesmaximal, characteristic
15#29299C211yesmaximal, characteristic
16#29245C211yesmaximal, characteristic
17#29245C211yesmaximal, characteristic
18#28956C211yesmaximal, characteristic, complemented
19#28954C211yesmaximal, characteristic, complemented
20#28009C211yesmaximal, characteristic, complemented
21#28006C211yesmaximal, characteristic, complemented
22#27955C211yesmaximal, characteristic
23#27682C211yesmaximal, characteristic
24#27313C211yesmaximal, characteristic, complemented
25#27311C211yesmaximal, characteristic, complemented
26#26879C211yesmaximal, characteristic, complemented
27#26877C211yesmaximal, characteristic, complemented
28#22629C211yesmaximal, characteristic
29#22083C211yesmaximal, characteristic
30#22077C211yesmaximal, characteristic
31#21583C211yesmaximal, characteristic
32C2×#485C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2586—21no—
37#2586—21no—
38#2567C2211yescharacteristic
39#2551C2211yescharacteristic
40#2549—21no—
41#2549—21no—
42#2509C2211yescharacteristic
43#2509C2211yescharacteristic
44#2508C2211yescharacteristic
45#2508C2211yescharacteristic
46#2507—21no—
47#2507C2211yescharacteristic
48#2507C2211yescharacteristic
49#2507C2211yescharacteristic
50#2507C2211yescharacteristic
51#2506C2211yescharacteristic
52#2506C2211yescharacteristic
53#2505—21no—
54#2505—21no—
55#2473—21no—
56#2473—21no—
57#2451C2211yescharacteristic
58#2451C2211yescharacteristic
59#2440—21no—
60#2402—21no—
61#2402—21no—
62#2369—21no—
63#2369C2211yescharacteristic
64Q8×C4⋊C4C2211yescharacteristic
65#2345—21no—
66C4×#125—21no—
67C4×#125—21no—
68C4×C22⋊Q8C2211yescharacteristic
69C4×C22⋊Q8C2211yescharacteristic
70C4×C22⋊Q8C2211yescharacteristic
71#2296C2211yescharacteristic
72#2296C2211yescharacteristic
73#2296C2211yescharacteristic
74#2296C2211yescharacteristic
75#2285C2211yescharacteristic
76C4×#117C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78#2101C2211yescharacteristic
79#2101C2211yescharacteristic
80#2099C2211yescharacteristic
81#2099C2211yescharacteristic
82#2099C2211yescharacteristic
83#2099C2211yescharacteristic
84#2097C2211yescharacteristic
85#2097C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2087C2211yescharacteristic
93#2087C2211yescharacteristic
94#2087C2211yescharacteristic
95#2087C2211yescharacteristic
96#2087C2211yescharacteristic
97#2087C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2084C2211yescharacteristic
102#2083C2211yescharacteristic
103#2083C2211yescharacteristic
104#2083C2211yescharacteristic
105#2083C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2066C2211yescharacteristic
109#2066C2211yescharacteristic
110#2058C2211yescharacteristic
111#2058C2211yescharacteristic
112#2058C2211yescharacteristic
113#2058C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2057C2211yescharacteristic
117#2057C2211yescharacteristic
118#1993C2211yescharacteristic
119#1993C2211yescharacteristic
120#1987C2211yescharacteristic
121#1987C2211yescharacteristic
122#1948C2211yescharacteristic
123#1948C2211yescharacteristic
124#1947C2211yescharacteristic
125#1947C2211yescharacteristic
126#1944C2211yescharacteristic
127#1944C2211yescharacteristic
128#1944C2211yescharacteristic
129#1943C2211yescharacteristic
130#1943C2211yescharacteristic
131#1943C2211yescharacteristic
132#1942C2211yescharacteristic
133#1942C2211yescharacteristic
134#1942C2211yescharacteristic
135#1941C2211yescharacteristic
136#1941C2211yescharacteristic
137#1941C2211yescharacteristic
138#1939C2211yescharacteristic
139#1939C2211yescharacteristic
140#1935C2211yescharacteristic
141#1935C2211yescharacteristic
142#1933C2211yescharacteristic
143#1933C2211yescharacteristic
144#1928C2211yescharacteristic
145#1927C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1920C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1918C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1917C2211yescharacteristic
161#1917C2211yescharacteristic
162#1917C2211yescharacteristic
163#1917C2211yescharacteristic
164#1873C2211yescharacteristic
165#1873C2211yescharacteristic
166#1873C2211yescharacteristic
167#1865C2211yescharacteristic
168#1865C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1863C2211yescharacteristic
172#1863C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1847C2211yescharacteristic
185#1847C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1803C2211yescharacteristic
190#1803C2211yescharacteristic
191#1797C2211yescharacteristic
192#1797C2211yescharacteristic
193#1797C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196#1770C2211yescharacteristic
197#1770C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200#1749C2211yescharacteristic
201#1749C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#125—21no—
208C2×#125—21no—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8—21no—
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C22×C4⋊C4D411yescharacteristic
221C22×C4⋊C4D411yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225#485Q818yescomplemented
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C2×C22⋊C8C2311yescharacteristic
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270#400—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#398—21no—
279#398—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#395—21no—
293#395—21no—
294#395—21no—
295#395—21no—
296#395—21no—
297#395—21no—
298#391—21no—
299#391—21no—
300#391—21no—
301#391—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391C2311yescharacteristic
306#391C2311yescharacteristic
307#391C2311yescharacteristic
308#389—21no—
309#389—21no—
310#389—21no—
311#389—21no—
312#389—21no—
313#389—21no—
314#389—21no—
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#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
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#389C2311yescharacteristic
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#385—21no—
364#385—21no—
365#385—21no—
366#385—21no—
367#385—21no—
368#385—21no—
369#385—21no—
370#385—21no—
371#385—21no—
372#385—21no—
373#385—21no—
374#384—21no—
375#384C2311yescharacteristic
376#384C2311yescharacteristic
377#384C2311yescharacteristic
378#384C2311yescharacteristic
379#384C2311yescharacteristic
380#382—21no—
381#382—21no—
382#382C2311yescharacteristic
383#382C2311yescharacteristic
384#380—21no—
385#380—21no—
386#380—21no—
387#380—21no—
388#380—21no—
389#380C2311yescharacteristic
390#380C2311yescharacteristic
391#380C2311yescharacteristic
392C4×C4⋊C4—21no—
393C4×C4⋊C4—21no—
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4D411yescharacteristic
408C4×C4⋊C4D411yescharacteristic
409C4×C4⋊C4D411yescharacteristic
410C4×C4⋊C4D411yescharacteristic
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×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427#376—21no—
428C2×#95D411yescharacteristic
429C2×#95D411yescharacteristic
430C43—21no—
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
479C22×Q8—21no—
480C22×Q8—21no—
481C22×Q8—21no—
482C22×Q8C2411yescharacteristic
483C23×C4C2×D411yescharacteristic
484C23×C4C2×D411yescharacteristic
485C23×C4C2×D411yescharacteristic
486C23×C4C2×D411yescharacteristic
487C23×C4C2×D411yescharacteristic
488C23×C4C2×D411yescharacteristic
489C23×C4C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C4⋊Q8—41no—
499C4⋊Q8—41no—
500C4⋊Q8—41no—
501C4⋊Q8—41no—
502C4⋊Q8—41no—
503C4⋊Q8—41no—
504C4⋊Q8—44no—
505#125—44no—
506#125—44no—
507C22⋊Q8—22no—
508C22⋊Q8—82no—
509C22⋊Q8—82no—
510C22⋊Q8—82no—
511C22⋊Q8C2×Q814yes—
512C4×Q8—41no—
513C4×Q8—41no—
514C4×Q8—41no—
515C4×Q8—41no—
516C4×Q8—41no—
517C4×Q8—41no—
518#117—22no—
519#117—41no—
520#117—41no—
521#117—41no—
522#117—41no—
523#117—41no—
524#117—41no—
525#117C2×Q814yes—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
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—42no—
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42—41no—
621C2×C42C2×D411yescharacteristic
622C2×C42C2×D411yescharacteristic
623C2×C42C2×D411yescharacteristic
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633#107—41no—
634#107—41no—
635#107—41no—
636#107—41no—
637#107—41no—
638#107—41no—
639#107—41no—
640#107—41no—
641#107—41no—
642#107C2×Q814yes—
643#106—41no—
644#106—41no—
645#106—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649#106—41no—
650#106—41no—
651#106—41no—
652#106C2×Q814yes—
653C4⋊C8—41no—
654C4⋊C8—41no—
655C4⋊C8—41no—
656C4⋊C8—41no—
657C4⋊C8—41no—
658C4⋊C8—41no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663#103—41no—
664#103—41no—
665#103C2×Q814yes—
666#103C2×Q814yes—
667C22⋊C8—22no—
668C22⋊C8—22no—
669C22⋊C8—22no—
670C22⋊C8C2×Q814yes—
671#97—41no—
672#97—41no—
673#97—41no—
674#97—41no—
675C4×C8—41no—
676C4×C8—41no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
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#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730C24C22×D411yescharacteristic
731C2×Q8—21no—
732C2×Q8—21no—
733C2×Q8—21no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—42no—
737C2×Q8—42no—
738C2×Q8—42no—
739C2×Q8—81no—
740C2×Q8—81no—
741C2×Q8—81no—
742C2×Q8—81no—
743C2×Q8—81no—
744C2×Q8—81no—
745C2×Q8C22×Q812yes—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—41no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—41no—
774C22×C4—41no—
775C22×C4—41no—
776C22×C4—41no—
777C22×C4—41no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×Q812yes—
798C22×C42−1+412yes—
799C22×C4C2511yescharacteristic
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
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×C8C22×Q812yes—
823C2×C8C22×Q812yes—
824C4⋊C4—24no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
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—41no—
858C4⋊C4—41no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
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#13714yes—
901C4⋊C4C22×Q812yes—
902C4⋊C4C22×Q812yes—
903C4⋊C4C22×Q812yes—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—42no—
910C22⋊C4—42no—
911C22⋊C4—42no—
912C42—24no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—41no—
926C42—41no—
927C42—41no—
928C42—41no—
929C42—41no—
930C42—41no—
931C42—42no—
932C42—42no—
933C42—42no—
934C42—42no—
935C42—42no—
936C42—42no—
937C42—42no—
938C42—81no—
939C42—81no—
940C42—81no—
941C42—81no—
942C42—81no—
943C42—81no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23D4×Q812yes—
951C23C23×D411yescharacteristic
952Q8—22no—
953Q8—22no—
954Q8—41no—
955Q8—41no—
956Q8—162no—
957Q8—162no—
958Q8—162no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
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—21no—
984C2×C4—21no—
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—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—44no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
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—82no—
1047C2×C4—82no—
1048C2×C4—82no—
1049C2×C4—82no—
1050C2×C4—82no—
1051C2×C4D4×Q812yes—
1052C2×C4C2×#13712yes—
1053C2×C4C2×#13712yes—
1054C2×C4C2×#13712yes—
1055C2×C4#57512yes—
1056C2×C4C23×Q811yescharacteristic
1057C2×C4C2×2−1+411yescharacteristic
1058C2×C4#58511yescharacteristic
1059C2×C4#58511yescharacteristic
1060C2×C4#58511yescharacteristic
1061C2×C4#58511yescharacteristic
1062C8—22no—
1063C8—22no—
1064C8—41no—
1065C8—41no—
1066C8—41no—
1067C8—41no—
1068C8—41no—
1069C8—41no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—41no—
1074C22—41no—
1075C22—41no—
1076C22—41no—
1077C22#344911yescharacteristic
1078C22C2×D4×Q811yescharacteristic
1079C22#348511yescharacteristic
1080C22C22×#13711yescharacteristic
1081C22C2×#57511yescharacteristic
1082C22#358411yescharacteristic
1083C22#358511yescharacteristic
1084C4—22no—
1085C4—22no—
1086C4—22no—
1087C4—22no—
1088C4—22no—
1089C4—41no—
1090C4—41no—
1091C4—41no—
1092C4—41no—
1093C4—41no—
1094C4—41no—
1095C4—41no—
1096C4—41no—
1097C4—42no—
1098C4—42no—
1099C4—42no—
1100C4—42no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4#350411yescharacteristic
1114C4#350411yescharacteristic
1115C4#355311yescharacteristic
1116C4#355311yescharacteristic
1117C2—42no—
1118C2#3958911yescharacteristic
1119C2#6096311yescharacteristic
1120C2#6098511yescharacteristic
1121C2#6136511yescharacteristic
1122C2Q8×#13711yescharacteristic
1123C2#6172511yescharacteristic
1124C2#6174211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #32506C2semidirect
5. #32505C2semidirect
6. #32360C2semidirect
7. #32358C2semidirect
8. #32152C2semidirect
9. #32150C2semidirect
10. #31872C2semidirect
11. #31868C2semidirect
18. #28956C2semidirect
19. #28954C2semidirect
20. #28009C2semidirect
21. #28006C2semidirect
24. #27313C2semidirect
25. #27311C2semidirect
26. #26879C2semidirect
27. #26877C2semidirect
225. #485Q8semidirect

Maximal subgroups

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

subgroupindex
#365642
#348152
#331532
#325062
#325052
#323602
#323582
#321522
#321502
#318722
#318682
#299712
#293042
#292992
#292452
#289562
#289542
#280092
#280062
#279552
#276822
#273132
#273112
#268792
#268772
#226292
#220832
#220772
#215832