Finite Group Databasebeta

← #6608009

Subgroups — #6608009

Order 512.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36306C211yesmaximal, characteristic, complemented
2#36293C211yesmaximal, characteristic, complemented
3#33265C211yesmaximal, characteristic, complemented
4#33240C211yesmaximal, characteristic, complemented
5#33128C211yesmaximal, characteristic, complemented
6#29557C211yesmaximal, characteristic, complemented
7#29556C211yesmaximal, characteristic, complemented
8#29497C211yesmaximal, characteristic, complemented
9#29496C211yesmaximal, characteristic, complemented
10#28876C211yesmaximal, characteristic, complemented
11#28874C211yesmaximal, characteristic, complemented
12#28011C211yesmaximal, characteristic, complemented
13#27260C211yesmaximal, characteristic, complemented
14#27256C211yesmaximal, characteristic, complemented
15#26823C211yesmaximal, characteristic, complemented
16#26819C211yesmaximal, characteristic, complemented
17#26481C211yesmaximal, characteristic, complemented
18#26251C211yesmaximal, characteristic, complemented
19#26251C211yesmaximal, characteristic, complemented
20#26062C211yesmaximal, characteristic, complemented
21#25776C211yesmaximal, characteristic
22#24502C211yesmaximal, characteristic, complemented
23#24500C211yesmaximal, characteristic
24#23022C211yesmaximal, characteristic, complemented
25#22871C211yesmaximal, characteristic, complemented
26#22870C211yesmaximal, characteristic
27C22⋊C4×SD16C211yesmaximal, characteristic, complemented
28C4×#495C211yesmaximal, characteristic, complemented
29#21274C211yesmaximal, characteristic, complemented
30C2×#1968C211yesmaximal, characteristic, complemented
31C8×#117C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#499C2211yescharacteristic, complemented
34C2×#495C2211yescharacteristic
35C2×#495C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#488C2211yescharacteristic, complemented
38C2×#465C2211yescharacteristic
39C2×#451C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×C4×Q16C2211yescharacteristic, complemented
42C2×C4×SD16C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic, complemented
45C2×C4×D8C2211yescharacteristic
46C2×#431C2211yescharacteristic
47C22×#106C2211yescharacteristic
48C22×#103C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×C4×C8C2211yescharacteristic
51#2863C2211yescharacteristic, complemented
52#2861C2211yescharacteristic
53#2861C2211yescharacteristic, complemented
54#2860C2211yescharacteristic
55#2855C2211yescharacteristic
56#2854C2211yescharacteristic
57#2597—21no—
58#2589—21no—
59#2532—21no—
60#2532—21no—
61#2531—21no—
62#2527—21no—
63#2526—21no—
64#2514C2211yescharacteristic, complemented
65#2513C2211yescharacteristic
66#2510—21no—
67#2498—21no—
68#2482—21no—
69#2480—21no—
70#2479—21no—
71#2454C2211yescharacteristic
72#2453C2211yescharacteristic, complemented
73#2448C2211yescharacteristic
74#2448C2211yescharacteristic, complemented
75#2447C2211yescharacteristic
76#2447C2211yescharacteristic, complemented
77#2442C2211yescharacteristic
78#2442C2211yescharacteristic
79#2436C2211yescharacteristic
80#2435C2211yescharacteristic
81#2361C2211yescharacteristic
82#2360C2211yescharacteristic
83#2359—21no—
84#2353—21no—
85#2342—21no—
86#2342—21no—
87Q8×C22⋊C4C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89C4×#124C2211yescharacteristic
90C4×#124C2211yescharacteristic, complemented
91#2295C2211yescharacteristic, complemented
92C2×#391C2211yescharacteristic
93#2293C2211yescharacteristic
94C2×#390C2211yescharacteristic
95C4×#117C2211yescharacteristic
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2074C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic, complemented
113#2042C2211yescharacteristic, complemented
114#2026C2211yescharacteristic, complemented
115#2025C2211yescharacteristic
116#2015C2211yescharacteristic
117#2015C2211yescharacteristic
118#2012C2211yescharacteristic
119#2012C2211yescharacteristic
120#1970C2211yescharacteristic
121#1970C2211yescharacteristic
122#1970C2211yescharacteristic
123#1969C2211yescharacteristic, complemented
124#1969C2211yescharacteristic, complemented
125#1969C2211yescharacteristic, complemented
126#1968C2211yescharacteristic
127#1968C2211yescharacteristic
128#1968C2211yescharacteristic
129#1968C2211yescharacteristic
130#1968C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic
133#1968C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic, complemented
139#1968C2211yescharacteristic, complemented
140#1968C2211yescharacteristic, complemented
141#1958C2211yescharacteristic
142#1958C2211yescharacteristic, complemented
143#1941C2211yescharacteristic, complemented
144#1941C2211yescharacteristic, complemented
145#1941C2211yescharacteristic, complemented
146#1941C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic, complemented
154#1934C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1933C2211yescharacteristic, complemented
158#1933C2211yescharacteristic, complemented
159#1933C2211yescharacteristic, complemented
160#1933C2211yescharacteristic, complemented
161#1933C2211yescharacteristic, complemented
162#1928C2211yescharacteristic, complemented
163#1927C2211yescharacteristic, complemented
164#1926C2211yescharacteristic, complemented
165#1925C2211yescharacteristic
166#1893C2211yescharacteristic
167#1892C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1874C2211yescharacteristic
177#1872C2211yescharacteristic
178#1865C2211yescharacteristic, complemented
179#1864C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1862C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1846C2211yescharacteristic, complemented
185#1807C2211yescharacteristic
186#1787C2211yescharacteristic
187#1786C2211yescharacteristic
188C4×#106C2211yescharacteristic, complemented
189C8×C4⋊C4C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191C8×C4⋊C4C2211yescharacteristic, complemented
192C8×C4⋊C4C2211yescharacteristic, complemented
193C4×#103C2211yescharacteristic, complemented
194C4×#102C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1744C2211yescharacteristic, complemented
200#1744C2211yescharacteristic, complemented
201C42×C8C2211yescharacteristic, complemented
202C42×C8C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16—24no—
208C22×SD16—24no—
209C22×SD16—42no—
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117—21no—
237C2×#117D411yescharacteristic
238C2×#117D411yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C42C2311yescharacteristic
245#499—42no—
246#495—24no—
247#495—42no—
248#488—42no—
249#488—42no—
250#465—24no—
251#451—24no—
252#447—24no—
253C4×Q16—42no—
254C4×SD16—24no—
255C4×SD16—42no—
256C4×SD16—42no—
257C4×D8—42no—
258#431—24no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106—42no—
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×#103—42no—
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102—42no—
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C4×C8—24no—
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#401—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#399—21no—
328#399—21no—
329#399—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#396—21no—
342#394—21no—
343#394—21no—
344#393—21no—
345#393—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#389—21no—
375#389—21no—
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
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#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#383—21no—
437#383—21no—
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#381—21no—
441#381—21no—
442#381—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#379—21no—
450#379—21no—
451#379—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4D411yescharacteristic
454C4×C4⋊C4D411yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4D411yescharacteristic
467C4×C22⋊C4D411yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470#376—21no—
471#376D411yescharacteristic
472#376D411yescharacteristic
473C2×#95—21no—
474C2×#95—21no—
475C43C2311yescharacteristic
476C43C2311yescharacteristic
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#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8—21no—
501C22×Q8—22no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—22no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—416no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16#4114yes—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8—22no—
562C22×C8—41no—
563C22×C8#4114yes—
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572#126—82no—
573#125—41no—
574#125—41no—
575#125—41no—
576#125—41no—
577#124—22no—
578#124—22no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#123—44no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588#121—22no—
589#121—22no—
590C4×Q8—22no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×D4—22no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—44no—
603#117—24no—
604#117—24no—
605#117—82no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
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—44no—
682C2×C22⋊C4—44no—
683C2×C22⋊C4—82no—
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C42—22no—
689C2×C42—22no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711#107—41no—
712#107—41no—
713#107—41no—
714#107—41no—
715#106—22no—
716#106—22no—
717#106—22no—
718#106—22no—
719#106—22no—
720#106—41no—
721#106—41no—
722C4⋊C8—22no—
723C4⋊C8—22no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754C22⋊C8—22no—
755C22⋊C8#4114yes—
756C4×C8—22no—
757C4×C8—22no—
758C4×C8—22no—
759C4×C8—22no—
760C4×C8—22no—
761C4×C8—22no—
762C4×C8—22no—
763C4×C8—22no—
764C4×C8—22no—
765C4×C8—22no—
766C4×C8—22no—
767C4×C8—22no—
768C4×C8—41no—
769C4×C8—41no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
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#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818C24—21no—
819C24—21no—
820C24—21no—
821C24—42no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24C22×D411yescharacteristic
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—42no—
847C2×Q8—44no—
848C2×Q8—44no—
849C2×Q8—42no—
850C2×Q8—81no—
851C2×Q8—82no—
852C2×Q8—82no—
853C2×Q8C2×#4112yes—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—82no—
879C2×D4—82no—
880C2×D4—81no—
881C2×D4C2×#4112yes—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—22no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—41no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4#13514yes—
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C2×#4112yes—
937C22×C4C2×#4112yes—
938C22×C4C2511yescharacteristic
939Q16—44no—
940Q16—82no—
941SD16—28no—
942SD16—44no—
943SD16—44no—
944SD16—44no—
945SD16—44no—
946D8—44no—
947D8—82no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—28no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—44no—
967C2×C8C2×#4112yes—
968C2×C8C2×#4112yes—
969C2×C8C2×#4112yes—
970C2×C8C2×#4112yes—
971C2×C8C2×#4112yes—
972C2×C8H(5,𝔽2)12yes—
973C2×C8H(5,𝔽2)12yes—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
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—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4#13514yes—
1059C42—22no—
1060C42—22no—
1061C42—22no—
1062C42—22no—
1063C42—22no—
1064C42—22no—
1065C42—22no—
1066C42—22no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—41no—
1080C42—41no—
1081C42—42no—
1082C42—42no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—22no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—84no—
1112C23—84no—
1113C23—84no—
1114C23—84no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23#53212yes—
1119C23C2×#13512yes—
1120C23C2×#13512yes—
1121C23C23×D411yescharacteristic
1122Q8—22no—
1123Q8—22no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—84no—
1135D4—22no—
1136D4—22no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—84no—
1148D4—84no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—28no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—44no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
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—84no—
1228C2×C4—84no—
1229C2×C4—162no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4#53212yes—
1234C2×C4C2×#13512yes—
1235C2×C4C2×#13512yes—
1236C2×C4C2×#13512yes—
1237C2×C4C2×#13512yes—
1238C2×C4#57712yes—
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C22×#4111yescharacteristic
1241C2×C4C22×#4111yescharacteristic
1242C2×C4C2×H(5,𝔽2)11yescharacteristic
1243C2×C4C2×H(5,𝔽2)11yescharacteristic
1244C2×C4#58511yescharacteristic
1245C8—22no—
1246C8—22no—
1247C8—22no—
1248C8—22no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8#55114yes—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—168no—
1281C22#316814yes—
1282C22C2×#53211yescharacteristic
1283C22D4×#4111yescharacteristic
1284C22#349811yescharacteristic
1285C22C22×#13511yescharacteristic
1286C22C22×#13511yescharacteristic
1287C22C2×#57711yescharacteristic
1288C22#358411yescharacteristic
1289C4—22no—
1290C4—22no—
1291C4—22no—
1292C4—22no—
1293C4—22no—
1294C4—22no—
1295C4—41no—
1296C4—42no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4C2×#55111yescharacteristic
1316C4#348111yescharacteristic
1317C4#349411yescharacteristic
1318C4#351411yescharacteristic
1319C2—24no—
1320C2—82no—
1321C2—161no—
1322C2—161no—
1323C2#3626411yescharacteristic
1324C2C2×#316811yescharacteristic
1325C2#6070611yescharacteristic
1326C2#6142811yescharacteristic
1327C2#6143211yescharacteristic
1328C2#6241411yescharacteristic
1329C2#6241911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36306C2semidirect
2. #36293C2semidirect
3. #33265C2semidirect
4. #33240C2semidirect
5. #33128C2semidirect
6. #29557C2semidirect
7. #29556C2semidirect
8. #29497C2semidirect
9. #29496C2semidirect
10. #28876C2semidirect
11. #28874C2semidirect
12. #28011C2semidirect
13. #27260C2semidirect
14. #27256C2semidirect
15. #26823C2semidirect
16. #26819C2semidirect
17. #26481C2semidirect
18. #26251C2semidirect
19. #26251C2semidirect
20. #26062C2semidirect
22. #24502C2semidirect
24. #23022C2semidirect
25. #22871C2semidirect
27. C22⋊C4×SD16C2semidirect
28. C4×#495C2semidirect
29. #21274C2semidirect
30. C2×#1968C2semidirect
31. C8×#117C2semidirect
33. C2×#499C22semidirect
37. C2×#488C22semidirect
41. C2×C4×Q16C22semidirect
44. C2×C4×SD16C22semidirect
51. #2863C22semidirect
53. #2861C22semidirect
64. #2514C22semidirect
72. #2453C22semidirect
74. #2448C22semidirect
76. #2447C22semidirect
90. C4×#124C22semidirect
91. #2295C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2074C22semidirect
100. #2068C22semidirect
101. #2068C22semidirect
104. #2059C22semidirect
105. #2059C22semidirect
106. #2056C22semidirect
107. #2056C22semidirect
112. #2042C22semidirect
113. #2042C22semidirect
114. #2026C22semidirect
123. #1969C22semidirect
124. #1969C22semidirect
125. #1969C22semidirect
138. #1968C22semidirect
139. #1968C22semidirect
140. #1968C22semidirect
142. #1958C22semidirect
143. #1941C22semidirect
144. #1941C22semidirect
145. #1941C22semidirect
146. #1941C22semidirect
147. #1941C22semidirect
153. #1934C22semidirect
154. #1934C22semidirect
155. #1933C22semidirect
156. #1933C22semidirect
157. #1933C22semidirect
158. #1933C22semidirect
159. #1933C22semidirect
160. #1933C22semidirect
161. #1933C22semidirect
162. #1928C22semidirect
163. #1927C22semidirect
164. #1926C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
178. #1865C22semidirect
179. #1864C22semidirect
180. #1863C22semidirect
184. #1846C22semidirect
188. C4×#106C22semidirect
189. C8×C4⋊C4C22semidirect
190. C8×C4⋊C4C22semidirect
191. C8×C4⋊C4C22semidirect
192. C8×C4⋊C4C22semidirect
193. C4×#103C22semidirect
199. #1744C22semidirect
200. #1744C22semidirect
201. C42×C8C22semidirect
202. C42×C8C22semidirect

Maximal subgroups

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

subgroupindex
#363062
#362932
#332652
#332402
#331282
#295572
#295562
#294972
#294962
#288762
#288742
#280112
#272602
#272562
#268232
#268192
#264812
#262512
#260622
#257762
#245022
#245002
#230222
#228712
#228702
C22⋊C4×SD162
C4×#4952
#212742
C2×#19682
C8×#1172