Finite Group Databasebeta

← #7001326

Subgroups — #7001326

Order 512.

1698 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45079C211yesmaximal, characteristic, complemented
2#42906C211yesmaximal, characteristic, complemented
3#32446C211yesmaximal, characteristic, complemented
4#32277C211yesmaximal, characteristic, complemented
5#31540C211yesmaximal, characteristic, complemented
6#31276C211yesmaximal, characteristic, complemented
7#31268C211yesmaximal, characteristic, complemented
8#30566C211yesmaximal, characteristic, complemented
9#30426C211yesmaximal, characteristic, complemented
10#30406C211yesmaximal, characteristic, complemented
11#29468C211yesmaximal, characteristic, complemented
12#28983C211yesmaximal, characteristic, complemented
13#28859C211yesmaximal, characteristic, complemented
14#28154C211yesmaximal, characteristic, complemented
15#27534C211yesmaximal, characteristic, complemented
16#27236C211yesmaximal, characteristic, complemented
17#27093C211yesmaximal, characteristic, complemented
18#26914C211yesmaximal, characteristic, complemented
19#26552C211yesmaximal, characteristic, complemented
20#25510C211yesmaximal, characteristic, complemented
21#25357C211yesmaximal, characteristic, complemented
22#25131C211yesmaximal, characteristic, complemented
23#24924C211yesmaximal, characteristic, complemented
24#24275C211yesmaximal, characteristic, complemented
25#24037C211yesmaximal, characteristic, complemented
26#23863C211yesmaximal, characteristic, complemented
27#23581C211yesmaximal, characteristic, complemented
28#23124C211yesmaximal, characteristic, complemented
29#22861C211yesmaximal, characteristic, complemented
30#22443C211yesmaximal, characteristic, complemented
31#22195C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#468C2211yescharacteristic, complemented
38C2×#466C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#449C2211yescharacteristic
43C2×#441C2211yescharacteristic, complemented
44C2×#440C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C2×#435C2211yescharacteristic
47C2×#435C2211yescharacteristic, complemented
48C2×#416C2211yescharacteristic
49#2828—21no—
50#2803—21no—
51#2803—21no—
52#2770—21no—
53#2756—21no—
54#2706—21no—
55#2685—21no—
56#2681—21no—
57#2676—21no—
58#2651—21no—
59#2649—21no—
60#2624C2211yescharacteristic, complemented
61#2595—21no—
62#2563C2211yescharacteristic
63#2562C2211yescharacteristic
64#2553—21no—
65#2542C2211yescharacteristic
66#2539—21no—
67#2538C2211yescharacteristic
68#2537C2211yescharacteristic
69#2536C2211yescharacteristic, complemented
70#2513C2211yescharacteristic, complemented
71#2495C2211yescharacteristic
72#2490C2211yescharacteristic, complemented
73#2485C2211yescharacteristic
74#2472—21no—
75#2453C2211yescharacteristic, complemented
76#2437—21no—
77#2423C2211yescharacteristic
78#2422C2211yescharacteristic
79#2414C2211yescharacteristic, complemented
80#2408C2211yescharacteristic
81#2407C2211yescharacteristic
82#2407C2211yescharacteristic
83#2407C2211yescharacteristic
84#2392C2211yescharacteristic
85#2367C2211yescharacteristic
86#2362C2211yescharacteristic, complemented
87#2341C2211yescharacteristic
88#2341C2211yescharacteristic
89D4×C22⋊C4C2211yescharacteristic
90#2324C2211yescharacteristic
91#2323C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2095C2211yescharacteristic, complemented
94#2094C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic, complemented
99#2076C2211yescharacteristic, complemented
100#2075C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic, complemented
103#2073C2211yescharacteristic
104#2071C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2058C2211yescharacteristic, complemented
107#2057C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic, complemented
110#2054C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic, complemented
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic, complemented
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic, complemented
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic, complemented
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic, complemented
125#2015C2211yescharacteristic
126#2012C2211yescharacteristic
127#2001C2211yescharacteristic, complemented
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#1999C2211yescharacteristic
131#1999C2211yescharacteristic
132#1992C2211yescharacteristic, complemented
133#1973C2211yescharacteristic
134#1972C2211yescharacteristic
135#1972C2211yescharacteristic
136#1970C2211yescharacteristic
137#1948C2211yescharacteristic, complemented
138#1942C2211yescharacteristic, complemented
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic, complemented
141#1935C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic, complemented
147#1924C2211yescharacteristic
148#1923C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1917C2211yescharacteristic, complemented
153#1917C2211yescharacteristic, complemented
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1894C2211yescharacteristic
157#1894C2211yescharacteristic, complemented
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic, complemented
160#1892C2211yescharacteristic, complemented
161#1892C2211yescharacteristic, complemented
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic, complemented
165#1880C2211yescharacteristic, complemented
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1877C2211yescharacteristic
172#1870C2211yescharacteristic
173#1870C2211yescharacteristic
174#1869C2211yescharacteristic
175#1869C2211yescharacteristic, complemented
176#1865C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1854C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1836C2211yescharacteristic, complemented
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1807C2211yescharacteristic, complemented
188#1804C2211yescharacteristic
189#1803C2211yescharacteristic, complemented
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1763C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic, complemented
201#1750C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C2×AGL(1,ℤ/8)—42no—
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#546—42no—
220#546—42no—
221#542—42no—
222#542—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×#126—21no—
225C2×#125C2311yescharacteristic
226C2×#124—21no—
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#120—21no—
246C2×#120—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261#482—42no—
262#479—42no—
263#468—42no—
264#466—42no—
265#465—24no—
266#452—24no—
267#452—42no—
268#449—42no—
269#441—42no—
270#440—42no—
271C4×SD16—42no—
272#435—42no—
273#435—42no—
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286#416—42no—
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
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×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#400—21no—
328#400—21no—
329#400—21no—
330#399—21no—
331#399—21no—
332#399—21no—
333#399—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398D411yescharacteristic
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397D411yescharacteristic
346#396—21no—
347#396—21no—
348#396D411yescharacteristic
349#396D411yescharacteristic
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394D411yescharacteristic
365#394D411yescharacteristic
366#394D411yescharacteristic
367#393—21no—
368#393—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#392D411yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390—21no—
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#389—21no—
396#389—21no—
397#389—21no—
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#383—21no—
441#382—21no—
442#382C2311yescharacteristic
443#380—21no—
444#380—21no—
445#380—21no—
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#379—21no—
458#379—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
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#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C22×Q8—21no—
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C2×D411yescharacteristic
530C22×D4C2×D411yescharacteristic
531C22×D4C2×D411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543AGL(1,ℤ/8)—416no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—41no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16#4114yes—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—41no—
561C2×D8—41no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—41no—
565C2×M16—41no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8—22no—
569C22×C8—41no—
570C22×C8—41no—
571C22×C8—41no—
572C22×C8—41no—
573C22×C8—41no—
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C4⋊Q8—41no—
583C4⋊Q8—41no—
584#126—44no—
585#125—41no—
586#125—41no—
587#124—22no—
588#124—22no—
589#124—44no—
590#123—44no—
591#123—44no—
592#123—82no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—44no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—82no—
603C22⋊Q8—82no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—44no—
608#121—41no—
609#121—41no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#121—82no—
616#120—44no—
617#120—82no—
618C4×Q8—22no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—41no—
626C4×D4—22no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638#117—41no—
639#117—41no—
640#117—41no—
641#117—41no—
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⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
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—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—44no—
723C2×C22⋊C4—82no—
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748#107—22no—
749#107—41no—
750#107—41no—
751#107—41no—
752#107—41no—
753#106—22no—
754#106—41no—
755#106—41no—
756#106—41no—
757#106—41no—
758C4⋊C8—22no—
759C4⋊C8—41no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788C22⋊C8—22no—
789C22⋊C8—22no—
790C22⋊C8—22no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796#97—22no—
797#97—41no—
798#97—41no—
799C4×C8—41no—
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#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833C24—21no—
834C24—21no—
835C24—21no—
836C24—42no—
837C24—42no—
838C24—42no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845C24C22×D411yescharacteristic
846#41—44no—
847#41—44no—
848#41—82no—
849#41—82no—
850#41—82no—
851#41—82no—
852#41—82no—
853#41—82no—
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—21no—
863C2×Q8—21no—
864C2×Q8—42no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8C2×#4112yes—
868C2×Q8H(5,𝔽2)12yes—
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—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—41no—
889C2×D4—41no—
890C2×D4—41no—
891C2×D4—41no—
892C2×D4—41no—
893C2×D4—41no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—44no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—81no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—82no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4C2×#4112yes—
923C2×D4H(5,𝔽2)12yes—
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—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C2511yescharacteristic
982Q16—44no—
983SD16—28no—
984SD16—44no—
985SD16—82no—
986D8—44no—
987D8—44no—
988M16—44no—
989M16—82no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—82no—
1013C2×C8—82no—
1014C2×C8C2×#4112yes—
1015C2×C8H(5,𝔽2)12yes—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—41no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—42no—
1128C42—81no—
1129C42—81no—
1130C42—81no—
1131C42—81no—
1132C42—81no—
1133C42—81no—
1134C42—81no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—22no—
1150C23—21no—
1151C23—22no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
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—84no—
1178C23—84no—
1179C23—84no—
1180C23—162no—
1181C23—162no—
1182C23—162no—
1183C23—162no—
1184C23C23×D411yescharacteristic
1185Q8—22no—
1186Q8—22no—
1187Q8—22no—
1188Q8—22no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—162no—
1194D4—22no—
1195D4—22no—
1196D4—22no—
1197D4—22no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—82no—
1207D4—82no—
1208D4—82no—
1209D4—84no—
1210D4—84no—
1211D4—84no—
1212D4—162no—
1213D4—162no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—22no—
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—21no—
1251C2×C4—21no—
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—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—84no—
1302C2×C4—84no—
1303C2×C4—162no—
1304C2×C4—162no—
1305C2×C4—162no—
1306C2×C4C22×#4111yescharacteristic
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4C2×H(5,𝔽2)11yescharacteristic
1310C2×C4#58511yescharacteristic
1311C2×C4#58511yescharacteristic
1312C8—22no—
1313C8—22no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—42no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—42no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—42no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—42no—
1343C22—42no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—168no—
1363C22D4×#4111yescharacteristic
1364C22#348411yescharacteristic
1365C22#349611yescharacteristic
1366C22#358411yescharacteristic
1367C22#358511yescharacteristic
1368C22#358511yescharacteristic
1369C22#358611yescharacteristic
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—42no—
1374C4—42no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4#349011yescharacteristic
1395C4#351311yescharacteristic
1396C4#355811yescharacteristic
1397C4#356011yescharacteristic
1398C2—81no—
1399C2—81no—
1400C2—81no—
1401C2—82no—
1402C2—82no—
1403C2—161no—
1404C2#4301311yescharacteristic
1405C2#6150811yescharacteristic
1406C2#6152711yescharacteristic
1407C2#6162611yescharacteristic
1408C2#6167511yescharacteristic
1409C2#6229411yescharacteristic
1410C2#6232011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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
1. #45079C2semidirect
2. #42906C2semidirect
3. #32446C2semidirect
4. #32277C2semidirect
5. #31540C2semidirect
6. #31276C2semidirect
7. #31268C2semidirect
8. #30566C2semidirect
9. #30426C2semidirect
10. #30406C2semidirect
11. #29468C2semidirect
12. #28983C2semidirect
13. #28859C2semidirect
14. #28154C2semidirect
15. #27534C2semidirect
16. #27236C2semidirect
17. #27093C2semidirect
18. #26914C2semidirect
19. #26552C2semidirect
20. #25510C2semidirect
21. #25357C2semidirect
22. #25131C2semidirect
23. #24924C2semidirect
24. #24275C2semidirect
25. #24037C2semidirect
26. #23863C2semidirect
27. #23581C2semidirect
28. #23124C2semidirect
29. #22861C2semidirect
30. #22443C2semidirect
31. #22195C2semidirect
36. C2×#479C22semidirect
37. C2×#468C22semidirect
43. C2×#441C22semidirect
47. C2×#435C22semidirect
60. #2624C22semidirect
69. #2536C22semidirect
70. #2513C22semidirect
72. #2490C22semidirect
75. #2453C22semidirect
79. #2414C22semidirect
86. #2362C22semidirect
91. #2323C22semidirect
92. #2097C22semidirect
93. #2095C22semidirect
94. #2094C22semidirect
95. #2083C22semidirect
98. #2077C22semidirect
99. #2076C22semidirect
102. #2075C22semidirect
104. #2071C22semidirect
106. #2058C22semidirect
107. #2057C22semidirect
109. #2055C22semidirect
114. #2036C22semidirect
116. #2035C22semidirect
118. #2034C22semidirect
120. #2033C22semidirect
123. #2024C22semidirect
124. #2023C22semidirect
127. #2001C22semidirect
132. #1992C22semidirect
137. #1948C22semidirect
138. #1942C22semidirect
140. #1936C22semidirect
141. #1935C22semidirect
142. #1927C22semidirect
146. #1925C22semidirect
148. #1923C22semidirect
149. #1921C22semidirect
150. #1920C22semidirect
151. #1919C22semidirect
152. #1917C22semidirect
153. #1917C22semidirect
157. #1894C22semidirect
159. #1893C22semidirect
160. #1892C22semidirect
161. #1892C22semidirect
164. #1880C22semidirect
165. #1880C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
175. #1869C22semidirect
176. #1865C22semidirect
179. #1863C22semidirect
182. #1854C22semidirect
183. #1854C22semidirect
184. #1836C22semidirect
187. #1807C22semidirect
189. #1803C22semidirect
196. #1763C22semidirect
198. C4×#103C22semidirect
200. #1752C22semidirect
201. #1750C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#450792
#429062
#324462
#322772
#315402
#312762
#312682
#305662
#304262
#304062
#294682
#289832
#288592
#281542
#275342
#272362
#270932
#269142
#265522
#255102
#253572
#251312
#249242
#242752
#240372
#238632
#235812
#231242
#228612
#224432
#221952