Finite Group Databasebeta

← #7032386

Subgroups — #7032386

Order 512.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45415C211yesmaximal, characteristic, complemented
2#45227C211yesmaximal, characteristic
3#32689C211yesmaximal, characteristic, complemented
4#32575C211yesmaximal, characteristic, complemented
5#32355C211yesmaximal, characteristic, complemented
6#31545C211yesmaximal, characteristic, complemented
7#31381C211yesmaximal, characteristic
8#31141C211yesmaximal, characteristic, complemented
9#31087C211yesmaximal, characteristic, complemented
10#30639C211yesmaximal, characteristic
11#29425C211yesmaximal, characteristic, complemented
12#29017C211yesmaximal, characteristic, complemented
13#27302C211yesmaximal, characteristic, complemented
14#26949C211yesmaximal, characteristic, complemented
15#26898C211yesmaximal, characteristic, complemented
16#26833C211yesmaximal, characteristic, complemented
17#26783C211yesmaximal, characteristic, complemented
18#26693C211yesmaximal, characteristic, complemented
19#26666C211yesmaximal, characteristic, complemented
20#26631C211yesmaximal, characteristic
21#26567C211yesmaximal, characteristic
22#26383C211yesmaximal, characteristic, complemented
23#26167C211yesmaximal, characteristic, complemented
24#25654C211yesmaximal, characteristic, complemented
25#24201C211yesmaximal, characteristic, complemented
26#24074C211yesmaximal, characteristic
27#23585C211yesmaximal, characteristic
28#22981C211yesmaximal, characteristic, complemented
29#22673C211yesmaximal, characteristic, complemented
30#22324C211yesmaximal, characteristic, complemented
31#22094C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#479C2211yescharacteristic
39C2×#475C2211yescharacteristic
40C2×#462C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C2×C4×Q16C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic
45#2792—21no—
46#2788—21no—
47#2763—21no—
48#2755—21no—
49#2718—21no—
50#2715—21no—
51#2698—21no—
52#2689—21no—
53#2587—21no—
54#2584C2211yescharacteristic
55#2581C2211yescharacteristic
56#2568C2211yescharacteristic
57#2567C2211yescharacteristic
58#2522—21no—
59#2511—21no—
60#2509C2211yescharacteristic
61#2508—21no—
62#2508C2211yescharacteristic
63#2496—21no—
64#2488—21no—
65#2474—21no—
66#2453C2211yescharacteristic
67#2451C2211yescharacteristic
68#2447C2211yescharacteristic
69#2446C2211yescharacteristic
70#2442C2211yescharacteristic
71#2439C2211yescharacteristic
72#2438—21no—
73#2429C2211yescharacteristic
74#2427C2211yescharacteristic
75#2421C2211yescharacteristic
76#2420C2211yescharacteristic
77#2396C2211yescharacteristic
78#2369C2211yescharacteristic
79#2367C2211yescharacteristic
80#2362C2211yescharacteristic
81#2360C2211yescharacteristic
82#2351C2211yescharacteristic
83#2351C2211yescharacteristic
84#2349C2211yescharacteristic
85#2323C2211yescharacteristic
86#2323C2211yescharacteristic
87#2317C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2097C2211yescharacteristic
91#2097C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2086C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2077C2211yescharacteristic
99#2074C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2066C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2058C2211yescharacteristic
107#2058C2211yescharacteristic
108#2057C2211yescharacteristic
109#2055C2211yescharacteristic
110#2043C2211yescharacteristic
111#2043C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2035C2211yescharacteristic
119#2033C2211yescharacteristic
120#2024C2211yescharacteristic
121#2024C2211yescharacteristic
122#2023C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2001C2211yescharacteristic
126#2001C2211yescharacteristic
127#2000C2211yescharacteristic
128#1993C2211yescharacteristic
129#1985C2211yescharacteristic
130#1984C2211yescharacteristic
131#1983C2211yescharacteristic
132#1971C2211yescharacteristic
133#1960C2211yescharacteristic
134#1949C2211yescharacteristic
135#1944C2211yescharacteristic
136#1944C2211yescharacteristic
137#1943C2211yescharacteristic
138#1942C2211yescharacteristic
139#1941C2211yescharacteristic
140#1936C2211yescharacteristic
141#1935C2211yescharacteristic
142#1933C2211yescharacteristic
143#1933C2211yescharacteristic
144#1933C2211yescharacteristic
145#1933C2211yescharacteristic
146#1928C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1925C2211yescharacteristic
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic
152#1923C2211yescharacteristic
153#1923C2211yescharacteristic
154#1921C2211yescharacteristic
155#1920C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1917C2211yescharacteristic
161#1916C2211yescharacteristic
162#1916C2211yescharacteristic
163#1916C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1875C2211yescharacteristic
171#1873C2211yescharacteristic
172#1872C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1852C2211yescharacteristic
190#1846C2211yescharacteristic
191#1825C2211yescharacteristic
192#1818C2211yescharacteristic
193#1805C2211yescharacteristic
194#1804C2211yescharacteristic
195#1804C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1750C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206#556—42no—
207#556—42no—
208#542—42no—
209#542—42no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#126—21no—
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242#488—42no—
243#485—24no—
244#483—42no—
245#481—42no—
246#479—42no—
247#475—24no—
248#462—42no—
249#440—42no—
250#440—42no—
251C4×Q16—42no—
252C4×SD16—24no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400D411yescharacteristic
317#399D411yescharacteristic
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398D411yescharacteristic
326#398D411yescharacteristic
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396D411yescharacteristic
335#396D411yescharacteristic
336#395—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#395D411yescharacteristic
342#394—21no—
343#394—21no—
344#393—21no—
345#393D411yescharacteristic
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390C2311yescharacteristic
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#386—21no—
415#386—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#384—21no—
425#384—21no—
426#382—21no—
427#382—21no—
428#382—21no—
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#381—21no—
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C2×#95—21no—
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#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8C2×D411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—21no—
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2411yescharacteristic
506C2×Q16—22no—
507C2×Q16—22no—
508C2×Q16—22no—
509C2×Q16—41no—
510C2×Q16—41no—
511C2×Q16—41no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—22no—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529#126—44no—
530#126—44no—
531#126—44no—
532#125—41no—
533#125—41no—
534#124—22no—
535#124—22no—
536#124—22no—
537#124—41no—
538#124—44no—
539#123—44no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—44no—
545C22⋊Q8—44no—
546C22⋊Q8—41no—
547C22⋊Q8—41no—
548#121—22no—
549#121—41no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572#117—22no—
573#117—41no—
574#117—41no—
575#117—44no—
576#117—41no—
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—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675#107—22no—
676#107—22no—
677#107—41no—
678#107—41no—
679#107—41no—
680#107—41no—
681#106—22no—
682#106—41no—
683#106—41no—
684#106—41no—
685#106—41no—
686#106—41no—
687#106#4114yes—
688C4⋊C8—22no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—22no—
700#103—22no—
701#103—22no—
702#103—22no—
703#103—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—41no—
717#102—41no—
718C22⋊C8—22no—
719C22⋊C8—41no—
720C22⋊C8—41no—
721C22⋊C8—41no—
722#97—41no—
723#97—41no—
724#97—41no—
725C4×C8—22no—
726C4×C8—41no—
727C4×C8—41no—
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#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782C24—21no—
783C24C22×D411yescharacteristic
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—41no—
801C2×Q8—41no—
802C2×Q8—41no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×Q8H(5,𝔽2)12yes—
810C2×Q82−1+412yes—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—42no—
817C2×D4—81no—
818C2×D4—81no—
819C2×D4H(5,𝔽2)12yes—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C2511yescharacteristic
867Q16—44no—
868Q16—82no—
869SD16—28no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8C2×#4112yes—
894C4⋊C4—24no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4C2×#4112yes—
960C4⋊C4C2×#4112yes—
961C4⋊C42−1+412yes—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—41no—
970C22⋊C4—41no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—42no—
997C42—42no—
998C42—42no—
999C42—42no—
1000C42—42no—
1001C42—42no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C42—81no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—22no—
1014C23—21no—
1015C23—21no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23C23×D411yescharacteristic
1023Q8—22no—
1024Q8—22no—
1025Q8—22no—
1026Q8—22no—
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—82no—
1036Q8—162no—
1037Q8—162no—
1038D4—22no—
1039D4—22no—
1040D4—41no—
1041D4—41no—
1042D4—162no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—84no—
1132C2×C4—162no—
1133C2×C4—162no—
1134C2×C4—162no—
1135C2×C4C22×#4111yescharacteristic
1136C2×C4C2×H(5,𝔽2)11yescharacteristic
1137C2×C4C2×H(5,𝔽2)11yescharacteristic
1138C2×C4C2×2−1+411yescharacteristic
1139C2×C4C2×2−1+411yescharacteristic
1140C2×C4#58511yescharacteristic
1141C8—22no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C8—41no—
1148C8—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—42no—
1153C22—41no—
1154C22—41no—
1155C22—42no—
1156C22—41no—
1157C22—42no—
1158C22—41no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22D4×#4111yescharacteristic
1164C22#348411yescharacteristic
1165C22#348611yescharacteristic
1166C22#358411yescharacteristic
1167C22#358411yescharacteristic
1168C22#358611yescharacteristic
1169C22#358611yescharacteristic
1170C4—41no—
1171C4—41no—
1172C4—42no—
1173C4—41no—
1174C4—41no—
1175C4—42no—
1176C4—41no—
1177C4—42no—
1178C4—42no—
1179C4—42no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4#349211yescharacteristic
1199C4#352211yescharacteristic
1200C4#353511yescharacteristic
1201C4#355911yescharacteristic
1202C2—81no—
1203C2—82no—
1204C2#4311911yescharacteristic
1205C2#6152811yescharacteristic
1206C2#6153811yescharacteristic
1207C2#6162711yescharacteristic
1208C2#6169111yescharacteristic
1209C2#6186711yescharacteristic
1210C2#6187511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45415C2semidirect
3. #32689C2semidirect
4. #32575C2semidirect
5. #32355C2semidirect
6. #31545C2semidirect
8. #31141C2semidirect
9. #31087C2semidirect
11. #29425C2semidirect
12. #29017C2semidirect
13. #27302C2semidirect
14. #26949C2semidirect
15. #26898C2semidirect
16. #26833C2semidirect
17. #26783C2semidirect
18. #26693C2semidirect
19. #26666C2semidirect
22. #26383C2semidirect
23. #26167C2semidirect
24. #25654C2semidirect
25. #24201C2semidirect
28. #22981C2semidirect
29. #22673C2semidirect
30. #22324C2semidirect
31. #22094C2semidirect

Maximal subgroups

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

subgroupindex
#454152
#452272
#326892
#325752
#323552
#315452
#313812
#311412
#310872
#306392
#294252
#290172
#273022
#269492
#268982
#268332
#267832
#266932
#266662
#266312
#265672
#263832
#261672
#256542
#242012
#240742
#235852
#229812
#226732
#223242
#220942