Finite Group Databasebeta

← #7308130

Subgroups — #7308130

Order 512.

1704 conjugacy classes of subgroups.

The subgroup lattice has 1421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45002C211yesmaximal, characteristic
2#42828C211yesmaximal, characteristic, complemented
3#32170C211yesmaximal, characteristic, complemented
4#32116C211yesmaximal, characteristic, complemented
5#31823C211yesmaximal, characteristic, complemented
6#31649C211yesmaximal, characteristic, complemented
7#31491C211yesmaximal, characteristic, complemented
8#31392C211yesmaximal, characteristic, complemented
9#31215C211yesmaximal, characteristic, complemented
10#31027C211yesmaximal, characteristic, complemented
11#30527C211yesmaximal, characteristic, complemented
12#30521C211yesmaximal, characteristic, complemented
13#30474C211yesmaximal, characteristic, complemented
14#30469C211yesmaximal, characteristic, complemented
15#29726C211yesmaximal, characteristic, complemented
16#29673C211yesmaximal, characteristic, complemented
17#28133C211yesmaximal, characteristic, complemented
18#27536C211yesmaximal, characteristic, complemented
19#27223C211yesmaximal, characteristic, complemented
20#26928C211yesmaximal, characteristic, complemented
21#26903C211yesmaximal, characteristic, complemented
22#26739C211yesmaximal, characteristic, complemented
23#26586C211yesmaximal, characteristic, complemented
24#25377C211yesmaximal, characteristic, complemented
25#25325C211yesmaximal, characteristic, complemented
26#24358C211yesmaximal, characteristic, complemented
27#24356C211yesmaximal, characteristic, complemented
28#24247C211yesmaximal, characteristic, complemented
29#24164C211yesmaximal, characteristic, complemented
30#23852C211yesmaximal, characteristic, complemented
31#23319C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#540C2211yescharacteristic
35C2×#497C2211yescharacteristic, complemented
36C2×#486C2211yescharacteristic
37C2×#483C2211yescharacteristic, complemented
38C2×#479C2211yescharacteristic, complemented
39C2×#464C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#460C2211yescharacteristic
42C2×#461C2211yescharacteristic
43C2×#461C2211yescharacteristic
44C2×#461C2211yescharacteristic, complemented
45C2×#452C2211yescharacteristic
46C2×#452C2211yescharacteristic
47C2×#452C2211yescharacteristic
48C2×#451C2211yescharacteristic
49C2×#448C2211yescharacteristic
50C2×#450C2211yescharacteristic
51C2×C4×SD16C2211yescharacteristic
52#2833—21no—
53#2806—21no—
54#2779—21no—
55#2770—21no—
56#2759—21no—
57#2706—21no—
58#2693—21no—
59#2688—21no—
60#2668—21no—
61#2653—21no—
62#2650—21no—
63#2621C2211yescharacteristic, complemented
64#2589—21no—
65#2568C2211yescharacteristic, complemented
66#2544C2211yescharacteristic
67#2536C2211yescharacteristic
68#2535—21no—
69#2514C2211yescharacteristic, complemented
70#2494C2211yescharacteristic
71#2492C2211yescharacteristic
72#2492C2211yescharacteristic, complemented
73#2489C2211yescharacteristic
74#2454C2211yescharacteristic
75#2447C2211yescharacteristic
76#2446C2211yescharacteristic, complemented
77#2434C2211yescharacteristic
78#2433C2211yescharacteristic
79#2431C2211yescharacteristic
80#2429C2211yescharacteristic, complemented
81#2427C2211yescharacteristic
82#2424—21no—
83#2418—21no—
84#2416C2211yescharacteristic
85#2412—21no—
86#2409C2211yescharacteristic
87#2395C2211yescharacteristic
88#2366C2211yescharacteristic
89#2365C2211yescharacteristic, complemented
90#2361C2211yescharacteristic
91Q8×C22⋊C4C2211yescharacteristic
92D4×C22⋊C4C2211yescharacteristic
93#2323C2211yescharacteristic, complemented
94#2311C2211yescharacteristic
95#2101C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2075C2211yescharacteristic
99#2074C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2056C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2056C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic, complemented
115#2043C2211yescharacteristic, complemented
116#2042C2211yescharacteristic, complemented
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic, complemented
121#2026C2211yescharacteristic, complemented
122#2026C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2016C2211yescharacteristic, complemented
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic, complemented
129#2014C2211yescharacteristic
130#2014C2211yescharacteristic
131#2014C2211yescharacteristic
132#2014C2211yescharacteristic
133#2013C2211yescharacteristic
134#2013C2211yescharacteristic
135#2001C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic, complemented
141#2000C2211yescharacteristic, complemented
142#2000C2211yescharacteristic, complemented
143#1989C2211yescharacteristic, complemented
144#1988C2211yescharacteristic, complemented
145#1983C2211yescharacteristic, complemented
146#1982C2211yescharacteristic
147#1969C2211yescharacteristic, complemented
148#1968C2211yescharacteristic
149#1968C2211yescharacteristic, complemented
150#1958C2211yescharacteristic
151#1954C2211yescharacteristic
152#1940C2211yescharacteristic, complemented
153#1939C2211yescharacteristic, complemented
154#1936C2211yescharacteristic
155#1935C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1927C2211yescharacteristic, complemented
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic, complemented
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic, complemented
166#1920C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1893C2211yescharacteristic
170#1892C2211yescharacteristic
171#1892C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic, complemented
182#1872C2211yescharacteristic, complemented
183#1872C2211yescharacteristic, complemented
184#1869C2211yescharacteristic
185#1864C2211yescharacteristic
186#1864C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1862C2211yescharacteristic
189#1850C2211yescharacteristic
190#1850C2211yescharacteristic
191#1824C2211yescharacteristic, complemented
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1804C2211yescharacteristic, complemented
195#1798C2211yescharacteristic, complemented
196#1798C2211yescharacteristic, complemented
197#1788C2211yescharacteristic
198#1787C2211yescharacteristic
199#1786C2211yescharacteristic
200#1786C2211yescharacteristic
201#1762C2211yescharacteristic
202C4×#103C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16—42no—
210C22×SD16—42no—
211C22×SD16—42no—
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C23×C8C2311yescharacteristic
222#546—42no—
223#546—42no—
224#540—42no—
225#540—42no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×#127C2311yescharacteristic
230C2×#127C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#123—21no—
235C2×#123—21no—
236C2×#123—21no—
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×#121—21no—
243C2×#121—21no—
244C2×#121—21no—
245C2×#121—21no—
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×#120—21no—
251C2×#120—21no—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C22⋊C4—21no—
265C22×C22⋊C4—21no—
266#497—42no—
267#486—42no—
268#483—42no—
269#479—42no—
270#464—42no—
271#461—42no—
272#461—42no—
273#461—42no—
274#460—42no—
275#460—42no—
276#452—42no—
277#452—42no—
278#452—42no—
279#451—42no—
280#450—42no—
281#448—42no—
282C4×SD16—42no—
283C2×#107C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336#401—21no—
337#401—21no—
338#400—21no—
339#400—21no—
340#400—21no—
341#400—21no—
342#400—21no—
343#400—21no—
344#400—21no—
345#400D411yescharacteristic
346#399—21no—
347#399D411yescharacteristic
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398D411yescharacteristic
354#397—21no—
355#397—21no—
356#397—21no—
357#397—21no—
358#397—21no—
359#397—21no—
360#397—21no—
361#397D411yescharacteristic
362#397D411yescharacteristic
363#397D411yescharacteristic
364#396—21no—
365#396—21no—
366#396—21no—
367#395—21no—
368#395—21no—
369#395—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394D411yescharacteristic
376#394D411yescharacteristic
377#393—21no—
378#393—21no—
379#393—21no—
380#392—21no—
381#392—21no—
382#392—21no—
383#392—21no—
384#391—21no—
385#391—21no—
386#391—21no—
387#391—21no—
388#391—21no—
389#391—21no—
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#390—21no—
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#389—21no—
408#389—21no—
409#389—21no—
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#388—21no—
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#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#383—21no—
452#382—21no—
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#381—21no—
456#380—21no—
457#380—21no—
458#380—21no—
459#380—21no—
460#380—21no—
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#379—21no—
466C4×C4⋊C4—21no—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C22⋊C4—21no—
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8—22no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4—41no—
536C22×D4C2×D411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C2×Q16—22no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16—41no—
582C2×SD16—41no—
583C2×SD16—41no—
584C2×SD16—41no—
585C2×SD16—416no—
586C22×C8—41no—
587C22×C8—41no—
588C22×C8—41no—
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C22×C8C2411yescharacteristic
597C4⋊Q8—22no—
598C4⋊Q8—41no—
599C4⋊Q8—41no—
600C4⋊Q8—41no—
601C4⋊Q8—41no—
602C4⋊Q8—41no—
603#127—22no—
604#127—22no—
605#127—41no—
606#127—41no—
607#125—22no—
608#125—41no—
609#124—22no—
610#124—41no—
611#124—41no—
612#124—41no—
613#123—44no—
614#123—44no—
615#123—44no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626#121—22no—
627#121—22no—
628#121—41no—
629#121—41no—
630#121—44no—
631#121—44no—
632#121—44no—
633#121—41no—
634#121—41no—
635#121—82no—
636#120—44no—
637#120—82no—
638#120—82no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×D4—22no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4—82no—
656C4×D4—82no—
657#117—41no—
658#117—41no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—41no—
680C2×C4⋊C4—41no—
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
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—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—44no—
728C2×C22⋊C4—82no—
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750#107—41no—
751#106—22no—
752#106—41no—
753#106—41no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756C4⋊C8—41no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797C22⋊C8—41no—
798C22⋊C8—41no—
799C22⋊C8—41no—
800#97—41no—
801C4×C8—41no—
802C4×C8—41no—
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#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850C24—21no—
851C24—21no—
852C24—21no—
853C24—42no—
854C24—42no—
855C24—42no—
856C24—81no—
857C24—81no—
858C24—81no—
859C24—81no—
860C24C22×D411yescharacteristic
861C24C22×D411yescharacteristic
862#41—82no—
863#41—82no—
864#41—82no—
865#41—82no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—44no—
892C2×Q8—81no—
893C2×Q8—81no—
894C2×Q8—81no—
895C2×Q8—81no—
896C2×Q8—82no—
897C2×Q8—82no—
898C2×Q8—82no—
899C2×Q8H(5,𝔽2)12yes—
900C2×D4—24no—
901C2×D4—22no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—41no—
919C2×D4—41no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—44no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—82no—
941C2×D4—82no—
942C2×D4—82no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4—81no—
947C2×D4—81no—
948C2×D4—81no—
949C2×D4—81no—
950C2×D4H(5,𝔽2)12yes—
951C2×D4H(5,𝔽2)12yes—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4—81no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C2511yescharacteristic
1011Q16—82no—
1012Q16—82no—
1013Q16—82no—
1014SD16—44no—
1015SD16—44no—
1016SD16—44no—
1017SD16—44no—
1018SD16—44no—
1019SD16—82no—
1020SD16—82no—
1021SD16—82no—
1022SD16—82no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—44no—
1048C4⋊C4—22no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4—81no—
1092C4⋊C4H(5,𝔽2)12yes—
1093C22⋊C4—24no—
1094C22⋊C4—22no—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—22no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—42no—
1144C42—81no—
1145C42—81no—
1146C42—81no—
1147C42—81no—
1148C42—81no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—22no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—22no—
1162C23—21no—
1163C23—21no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—84no—
1184C23—84no—
1185C23—84no—
1186C23—162no—
1187C23—162no—
1188C23—162no—
1189C23—162no—
1190C23#57712yes—
1191C23C23×D411yescharacteristic
1192Q8—22no—
1193Q8—22no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—84no—
1209Q8—162no—
1210D4—22no—
1211D4—22no—
1212D4—22no—
1213D4—22no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—84no—
1223D4—82no—
1224D4—84no—
1225D4—84no—
1226D4—84no—
1227D4—162no—
1228D4—162no—
1229D4—162no—
1230D4—162no—
1231D4—162no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—84no—
1315C2×C4—84no—
1316C2×C4—162no—
1317C2×C4—162no—
1318C2×C4—162no—
1319C2×C4—162no—
1320C2×C4—162no—
1321C2×C4#57712yes—
1322C2×C4C2×H(5,𝔽2)11yescharacteristic
1323C2×C4C2×H(5,𝔽2)11yescharacteristic
1324C2×C4C2×H(5,𝔽2)11yescharacteristic
1325C2×C4C2×H(5,𝔽2)11yescharacteristic
1326C2×C4#58511yescharacteristic
1327C2×C4#58511yescharacteristic
1328C8—41no—
1329C8—41no—
1330C8—41no—
1331C8—41no—
1332C8—41no—
1333C8—41no—
1334C8—41no—
1335C8—41no—
1336C22—22no—
1337C22—22no—
1338C22—22no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—42no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—42no—
1348C22—41no—
1349C22—42no—
1350C22—41no—
1351C22—41no—
1352C22—42no—
1353C22—42no—
1354C22—41no—
1355C22—42no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—168no—
1372C22#348411yescharacteristic
1373C22#348811yescharacteristic
1374C22#348811yescharacteristic
1375C22C2×#57711yescharacteristic
1376C22C2×#57711yescharacteristic
1377C22#358411yescharacteristic
1378C22#358611yescharacteristic
1379C4—22no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—42no—
1389C4—41no—
1390C4—41no—
1391C4—41no—
1392C4—42no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4#353211yescharacteristic
1405C4#354211yescharacteristic
1406C4#355811yescharacteristic
1407C4#356011yescharacteristic
1408C2—42no—
1409C2—81no—
1410C2—82no—
1411C2—82no—
1412C2—161no—
1413C2#4784411yescharacteristic
1414C2#6164011yescharacteristic
1415C2#6168011yescharacteristic
1416C2#6200811yescharacteristic
1417C2#6203011yescharacteristic
1418C2#6205511yescharacteristic
1419C2#6206311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45002C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42828C2semidirect
3. #32170C2semidirect
4. #32116C2semidirect
5. #31823C2semidirect
6. #31649C2semidirect
7. #31491C2semidirect
8. #31392C2semidirect
9. #31215C2semidirect
10. #31027C2semidirect
11. #30527C2semidirect
12. #30521C2semidirect
13. #30474C2semidirect
14. #30469C2semidirect
15. #29726C2semidirect
16. #29673C2semidirect
17. #28133C2semidirect
18. #27536C2semidirect
19. #27223C2semidirect
20. #26928C2semidirect
21. #26903C2semidirect
22. #26739C2semidirect
23. #26586C2semidirect
24. #25377C2semidirect
25. #25325C2semidirect
26. #24358C2semidirect
27. #24356C2semidirect
28. #24247C2semidirect
29. #24164C2semidirect
30. #23852C2semidirect
31. #23319C2semidirect
35. C2×#497C22semidirect
37. C2×#483C22semidirect
38. C2×#479C22semidirect
44. C2×#461C22semidirect
63. #2621C22semidirect
65. #2568C22semidirect
69. #2514C22semidirect
72. #2492C22semidirect
76. #2446C22semidirect
80. #2429C22semidirect
89. #2365C22semidirect
93. #2323C22semidirect
95. #2101C22semidirect
96. #2088C22semidirect
99. #2074C22semidirect
101. #2073C22semidirect
102. #2066C22semidirect
103. #2066C22semidirect
105. #2056C22semidirect
106. #2056C22semidirect
107. #2056C22semidirect
108. #2056C22semidirect
114. #2055C22semidirect
115. #2043C22semidirect
116. #2042C22semidirect
120. #2033C22semidirect
121. #2026C22semidirect
122. #2026C22semidirect
123. #2024C22semidirect
125. #2016C22semidirect
128. #2015C22semidirect
140. #2000C22semidirect
141. #2000C22semidirect
142. #2000C22semidirect
143. #1989C22semidirect
144. #1988C22semidirect
145. #1983C22semidirect
147. #1969C22semidirect
149. #1968C22semidirect
152. #1940C22semidirect
153. #1939C22semidirect
155. #1935C22semidirect
156. #1933C22semidirect
157. #1927C22semidirect
158. #1927C22semidirect
159. #1927C22semidirect
163. #1924C22semidirect
165. #1923C22semidirect
166. #1920C22semidirect
167. #1916C22semidirect
168. #1916C22semidirect
174. #1880C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
181. #1877C22semidirect
182. #1872C22semidirect
183. #1872C22semidirect
186. #1864C22semidirect
187. #1863C22semidirect
191. #1824C22semidirect
194. #1804C22semidirect
195. #1798C22semidirect
196. #1798C22semidirect
202. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#450022
#428282
#321702
#321162
#318232
#316492
#314912
#313922
#312152
#310272
#305272
#305212
#304742
#304692
#297262
#296732
#281332
#275362
#272232
#269282
#269032
#267392
#265862
#253772
#253252
#243582
#243562
#242472
#241642
#238522
#233192