Finite Group Databasebeta

← #7074539

Subgroups — #7074539

Order 512.

1605 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45404C211yesmaximal, characteristic
2#42714C211yesmaximal, characteristic, complemented
3#32471C211yesmaximal, characteristic, complemented
4#32034C211yesmaximal, characteristic, complemented
5#31976C211yesmaximal, characteristic, complemented
6#31206C211yesmaximal, characteristic, complemented
7#31159C211yesmaximal, characteristic, complemented
8#31038C211yesmaximal, characteristic, complemented
9#31028C211yesmaximal, characteristic, complemented
10#30404C211yesmaximal, characteristic, complemented
11#29487C211yesmaximal, characteristic, complemented
12#28981C211yesmaximal, characteristic, complemented
13#28968C211yesmaximal, characteristic, complemented
14#28556C211yesmaximal, characteristic, complemented
15#27404C211yesmaximal, characteristic, complemented
16#26941C211yesmaximal, characteristic, complemented
17#26808C211yesmaximal, characteristic, complemented
18#26259C211yesmaximal, characteristic, complemented
19#25769C211yesmaximal, characteristic, complemented
20#25542C211yesmaximal, characteristic, complemented
21#25420C211yesmaximal, characteristic, complemented
22#25111C211yesmaximal, characteristic, complemented
23#24924C211yesmaximal, characteristic, complemented
24#24516C211yesmaximal, characteristic, complemented
25#24123C211yesmaximal, characteristic, complemented
26#24037C211yesmaximal, characteristic, complemented
27#23713C211yesmaximal, characteristic, complemented
28#23089C211yesmaximal, characteristic, complemented
29#22933C211yesmaximal, characteristic, complemented
30#22873C211yesmaximal, characteristic, complemented
31#22052C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#497C2211yescharacteristic
35C2×#485C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#475C2211yescharacteristic, complemented
39C2×#467C2211yescharacteristic, complemented
40C2×#465C2211yescharacteristic
41C2×#461C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#441C2211yescharacteristic, complemented
47C2×C4×Q16C2211yescharacteristic, complemented
48C2×C8×D4C2211yescharacteristic, complemented
49C2×#433C2211yescharacteristic
50C2×#416C2211yescharacteristic
51#2837—21no—
52#2803—21no—
53#2793—21no—
54#2777—21no—
55#2777—21no—
56#2714—21no—
57#2705—21no—
58#2685—21no—
59#2670—21no—
60#2651—21no—
61#2651—21no—
62#2625C2211yescharacteristic
63#2542C2211yescharacteristic
64#2538C2211yescharacteristic
65#2507—21no—
66#2507C2211yescharacteristic, complemented
67#2491C2211yescharacteristic
68#2485C2211yescharacteristic
69#2485C2211yescharacteristic
70#2480—21no—
71#2472—21no—
72#2458—21no—
73#2452C2211yescharacteristic
74#2448C2211yescharacteristic
75#2446C2211yescharacteristic, complemented
76#2429C2211yescharacteristic, complemented
77#2426—21no—
78#2426C2211yescharacteristic
79#2423C2211yescharacteristic, complemented
80#2415C2211yescharacteristic
81#2415C2211yescharacteristic, complemented
82#2415C2211yescharacteristic, complemented
83#2414C2211yescharacteristic
84#2408C2211yescharacteristic
85#2407C2211yescharacteristic
86#2392C2211yescharacteristic
87#2363C2211yescharacteristic
88#2362C2211yescharacteristic, complemented
89#2347C2211yescharacteristic, complemented
90#2341C2211yescharacteristic
91#2323C2211yescharacteristic
92#2323C2211yescharacteristic
93#2309C2211yescharacteristic
94#2094C2211yescharacteristic
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2071C2211yescharacteristic
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2057C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2043C2211yescharacteristic, complemented
114#2043C2211yescharacteristic, complemented
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic, complemented
123#2035C2211yescharacteristic, complemented
124#2034C2211yescharacteristic
125#2024C2211yescharacteristic, complemented
126#2001C2211yescharacteristic
127#2001C2211yescharacteristic
128#2001C2211yescharacteristic, complemented
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1990C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1971C2211yescharacteristic, complemented
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic
141#1968C2211yescharacteristic
142#1955C2211yescharacteristic
143#1955C2211yescharacteristic, complemented
144#1954C2211yescharacteristic
145#1944C2211yescharacteristic, complemented
146#1944C2211yescharacteristic, complemented
147#1943C2211yescharacteristic, complemented
148#1939C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1933C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1925C2211yescharacteristic
159#1924C2211yescharacteristic, complemented
160#1923C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1892C2211yescharacteristic, complemented
167#1892C2211yescharacteristic, complemented
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1875C2211yescharacteristic
175#1873C2211yescharacteristic
176#1873C2211yescharacteristic
177#1873C2211yescharacteristic, complemented
178#1873C2211yescharacteristic, complemented
179#1869C2211yescharacteristic
180#1869C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1865C2211yescharacteristic, complemented
183#1864C2211yescharacteristic
184#1862C2211yescharacteristic
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic
187#1854C2211yescharacteristic, complemented
188#1854C2211yescharacteristic, complemented
189#1854C2211yescharacteristic, complemented
190#1803C2211yescharacteristic, complemented
191#1788C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199#1752C2211yescharacteristic, complemented
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1750C2211yescharacteristic
202#1735C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#556—42no—
214#556—42no—
215#546—42no—
216#546—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#126—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×C4×Q8—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C22⋊C4—21no—
255#497—42no—
256#485—42no—
257#482—24no—
258#482—42no—
259#475—42no—
260#467—42no—
261#465—42no—
262#461—42no—
263#452—24no—
264#452—42no—
265#450—24no—
266#450—42no—
267#441—42no—
268C4×Q16—42no—
269C8×D4—42no—
270#433—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#416—42no—
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#400—21no—
331#400—21no—
332#399—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398D411yescharacteristic
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397D411yescharacteristic
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396D411yescharacteristic
358#396D411yescharacteristic
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394D411yescharacteristic
370#394D411yescharacteristic
371#394D411yescharacteristic
372#393—21no—
373#393—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392D411yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#390—21no—
384#390—21no—
385#390—21no—
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390—21no—
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#386—21no—
446#386—21no—
447#385—21no—
448#385—21no—
449#384—21no—
450#384C2311yescharacteristic
451#383—21no—
452#380—21no—
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#379—21no—
461#379—21no—
462#379—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C22×D4C2×D411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C22×C8—22no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8—41no—
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C4⋊Q8—22no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567#126—44no—
568#126—44no—
569#124—22no—
570#124—41no—
571#124—44no—
572#124—82no—
573#123—44no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—82no—
591#121—22no—
592#121—22no—
593#121—41no—
594#121—41no—
595#121—44no—
596#121—41no—
597#121—41no—
598#120—44no—
599#120—82no—
600C4×Q8—22no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—44no—
609C4×D4—22no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617#117—22no—
618#117—22no—
619#117—41no—
620#117—41no—
621#117—41no—
622#117—41no—
623#117—41no—
624#117—41no—
625#117—41no—
626#117—41no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—44no—
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—22no—
737#107—22no—
738#107—41no—
739#107—41no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—41no—
744#106—41no—
745#106—41no—
746C4⋊C8—22no—
747C4⋊C8—41no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102#4114yes—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8—22no—
781C22⋊C8—22no—
782C22⋊C8—22no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788#97—22no—
789#97—41no—
790#97—41no—
791C4×C8—41no—
792C4×C8—41no—
793C4×C8—41no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829C24—21no—
830C24—21no—
831C24—42no—
832C24—42no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24C22×D411yescharacteristic
839C24C22×D411yescharacteristic
840C24C22×D411yescharacteristic
841#41—44no—
842#41—82no—
843#41—82no—
844#41—82no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—42no—
863C2×Q8—42no—
864C2×Q8—81no—
865C2×Q8H(5,𝔽2)12yes—
866C2×D4—22no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—81no—
893C2×D4—82no—
894C2×D4—82no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4C2×#4112yes—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C2511yescharacteristic
956Q16—44no—
957Q16—44no—
958SD16—82no—
959SD16—82no—
960SD16—82no—
961SD16—82no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—82no—
985C2×C8—82no—
986C2×C8C2×#4112yes—
987C2×C8H(5,𝔽2)12yes—
988C4⋊C4—24no—
989C4⋊C4—22no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4C2×#4112yes—
1042C4⋊C4H(5,𝔽2)12yes—
1043C22⋊C4—24no—
1044C22⋊C4—22no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—22no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—84no—
1147C23—84no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23C23×D411yescharacteristic
1154Q8—22no—
1155Q8—22no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—84no—
1167D4—22no—
1168D4—22no—
1169D4—44no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—82no—
1177D4—82no—
1178D4—84no—
1179D4—84no—
1180D4—162no—
1181D4—162no—
1182D4—162no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—84no—
1270C2×C4—162no—
1271C2×C4#57712yes—
1272C2×C4C22×#4111yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4C2×H(5,𝔽2)11yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4#58511yescharacteristic
1277C2×C4#58511yescharacteristic
1278C8—22no—
1279C8—22no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C22—41no—
1287C22—42no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—42no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—42no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—168no—
1322C22D4×#4111yescharacteristic
1323C22#348411yescharacteristic
1324C22#349611yescharacteristic
1325C22C2×#57711yescharacteristic
1326C22#358411yescharacteristic
1327C22#358411yescharacteristic
1328C22#358611yescharacteristic
1329C4—22no—
1330C4—42no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—42no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—42no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4#350811yescharacteristic
1355C4#351311yescharacteristic
1356C4#353411yescharacteristic
1357C4#355111yescharacteristic
1358C2—81no—
1359C2—81no—
1360C2—81no—
1361C2—82no—
1362C2—161no—
1363C2#4392611yescharacteristic
1364C2#6149311yescharacteristic
1365C2#6152811yescharacteristic
1366C2#6161511yescharacteristic
1367C2#6164011yescharacteristic
1368C2#6228211yescharacteristic
1369C2#6234511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45404C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42714C2semidirect
3. #32471C2semidirect
4. #32034C2semidirect
5. #31976C2semidirect
6. #31206C2semidirect
7. #31159C2semidirect
8. #31038C2semidirect
9. #31028C2semidirect
10. #30404C2semidirect
11. #29487C2semidirect
12. #28981C2semidirect
13. #28968C2semidirect
14. #28556C2semidirect
15. #27404C2semidirect
16. #26941C2semidirect
17. #26808C2semidirect
18. #26259C2semidirect
19. #25769C2semidirect
20. #25542C2semidirect
21. #25420C2semidirect
22. #25111C2semidirect
23. #24924C2semidirect
24. #24516C2semidirect
25. #24123C2semidirect
26. #24037C2semidirect
27. #23713C2semidirect
28. #23089C2semidirect
29. #22933C2semidirect
30. #22873C2semidirect
31. #22052C2semidirect
35. C2×#485C22semidirect
38. C2×#475C22semidirect
39. C2×#467C22semidirect
46. C2×#441C22semidirect
47. C2×C4×Q16C22semidirect
48. C2×C8×D4C22semidirect
66. #2507C22semidirect
75. #2446C22semidirect
76. #2429C22semidirect
79. #2423C22semidirect
81. #2415C22semidirect
82. #2415C22semidirect
88. #2362C22semidirect
89. #2347C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2088C22semidirect
100. #2077C22semidirect
101. #2077C22semidirect
103. #2068C22semidirect
106. #2066C22semidirect
108. #2057C22semidirect
109. #2056C22semidirect
113. #2043C22semidirect
114. #2043C22semidirect
119. #2036C22semidirect
122. #2035C22semidirect
123. #2035C22semidirect
125. #2024C22semidirect
128. #2001C22semidirect
134. #1990C22semidirect
138. #1971C22semidirect
143. #1955C22semidirect
145. #1944C22semidirect
146. #1944C22semidirect
147. #1943C22semidirect
148. #1939C22semidirect
154. #1933C22semidirect
155. #1933C22semidirect
156. #1928C22semidirect
159. #1924C22semidirect
160. #1923C22semidirect
161. #1920C22semidirect
162. #1920C22semidirect
163. #1918C22semidirect
166. #1892C22semidirect
167. #1892C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
177. #1873C22semidirect
178. #1873C22semidirect
181. #1865C22semidirect
182. #1865C22semidirect
187. #1854C22semidirect
188. #1854C22semidirect
189. #1854C22semidirect
190. #1803C22semidirect
194. #1776C22semidirect
195. #1771C22semidirect
197. C4×#103C22semidirect
198. C4×#103C22semidirect
199. #1752C22semidirect
200. C8×C22⋊C4C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#454042
#427142
#324712
#320342
#319762
#312062
#311592
#310382
#310282
#304042
#294872
#289812
#289682
#285562
#274042
#269412
#268082
#262592
#257692
#255422
#254202
#251112
#249242
#245162
#241232
#240372
#237132
#230892
#229332
#228732
#220522