Finite Group Databasebeta

← #7050376

Subgroups — #7050376

Order 512.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59807C211yesmaximal, characteristic
2#59234C211yesmaximal, characteristic, complemented
3#32258C211yesmaximal, characteristic, complemented
4#31793C211yesmaximal, characteristic, complemented
5#31260C211yesmaximal, characteristic, complemented
6#31044C211yesmaximal, characteristic, complemented
7#30970C211yesmaximal, characteristic, complemented
8#30832C211yesmaximal, characteristic, complemented
9#30570C211yesmaximal, characteristic, complemented
10#30409C211yesmaximal, characteristic, complemented
11#29416C211yesmaximal, characteristic, complemented
12#28935C211yesmaximal, characteristic, complemented
13#27800C211yesmaximal, characteristic, complemented
14#27582C211yesmaximal, characteristic, complemented
15#27442C211yesmaximal, characteristic, complemented
16#27417C211yesmaximal, characteristic, complemented
17#27353C211yesmaximal, characteristic, complemented
18#27252C211yesmaximal, characteristic, complemented
19#27212C211yesmaximal, characteristic, complemented
20#26814C211yesmaximal, characteristic, complemented
21#26213C211yesmaximal, characteristic, complemented
22#25898C211yesmaximal, characteristic, complemented
23#25716C211yesmaximal, characteristic, complemented
24#25546C211yesmaximal, characteristic, complemented
25#24874C211yesmaximal, characteristic, complemented
26#24436C211yesmaximal, characteristic, complemented
27#23762C211yesmaximal, characteristic, complemented
28#22933C211yesmaximal, characteristic, complemented
29#22569C211yesmaximal, characteristic, complemented
30#22339C211yesmaximal, characteristic, complemented
31#22049C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#489C2211yescharacteristic
36C2×#485C2211yescharacteristic, complemented
37C2×#482C2211yescharacteristic
38C2×#477C2211yescharacteristic, complemented
39C2×#476C2211yescharacteristic
40C2×#467C2211yescharacteristic, complemented
41C2×#465C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#416C2211yescharacteristic
45#2775—21no—
46#2775—21no—
47#2714—21no—
48#2694—21no—
49#2554—21no—
50#2551C2211yescharacteristic, complemented
51#2547C2211yescharacteristic
52#2547C2211yescharacteristic
53#2539—21no—
54#2538C2211yescharacteristic, complemented
55#2513—21no—
56#2495—21no—
57#2492C2211yescharacteristic, complemented
58#2492C2211yescharacteristic, complemented
59#2491—21no—
60#2490—21no—
61#2490C2211yescharacteristic
62#2486C2211yescharacteristic
63#2474—21no—
64#2474—21no—
65#2454C2211yescharacteristic
66#2448C2211yescharacteristic
67#2426C2211yescharacteristic
68#2415C2211yescharacteristic
69#2415C2211yescharacteristic
70#2414C2211yescharacteristic
71#2412—21no—
72#2411—21no—
73#2408C2211yescharacteristic
74#2407C2211yescharacteristic
75#2369—21no—
76#2363C2211yescharacteristic
77#2355C2211yescharacteristic, complemented
78#2354C2211yescharacteristic, complemented
79#2347C2211yescharacteristic, complemented
80#2347C2211yescharacteristic, complemented
81#2342—21no—
82#2341C2211yescharacteristic
83C4×C22⋊Q8C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×#121C2211yescharacteristic
86C2×#390C2211yescharacteristic
87#2285C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2095C2211yescharacteristic, complemented
90#2093C2211yescharacteristic
91#2093C2211yescharacteristic
92#2087C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2075C2211yescharacteristic
95#2075C2211yescharacteristic
96#2075C2211yescharacteristic
97#2075C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2072C2211yescharacteristic, complemented
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2057C2211yescharacteristic, complemented
106#2057C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2042C2211yescharacteristic
109#2036C2211yescharacteristic, complemented
110#2036C2211yescharacteristic, complemented
111#2036C2211yescharacteristic, complemented
112#2036C2211yescharacteristic, complemented
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2015C2211yescharacteristic
125#2001C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1989C2211yescharacteristic, complemented
129#1983C2211yescharacteristic
130#1973C2211yescharacteristic
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1955C2211yescharacteristic
134#1955C2211yescharacteristic
135#1944C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1935C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1927C2211yescharacteristic, complemented
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1924C2211yescharacteristic, complemented
151#1924C2211yescharacteristic, complemented
152#1920C2211yescharacteristic, complemented
153#1920C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1878C2211yescharacteristic, complemented
163#1878C2211yescharacteristic, complemented
164#1878C2211yescharacteristic, complemented
165#1877C2211yescharacteristic
166#1875C2211yescharacteristic
167#1875C2211yescharacteristic
168#1873C2211yescharacteristic, complemented
169#1872C2211yescharacteristic
170#1869C2211yescharacteristic
171#1869C2211yescharacteristic
172#1869C2211yescharacteristic, complemented
173#1869C2211yescharacteristic, complemented
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1854C2211yescharacteristic, complemented
179#1854C2211yescharacteristic, complemented
180#1854C2211yescharacteristic, complemented
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1825C2211yescharacteristic, complemented
185#1817C2211yescharacteristic
186#1808C2211yescharacteristic, complemented
187#1808C2211yescharacteristic, complemented
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1752C2211yescharacteristic, complemented
200#1752C2211yescharacteristic, complemented
201#1749C2211yescharacteristic
202#1735C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#552—42no—
211#552—42no—
212#546—42no—
213#546—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124—21no—
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121D411yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117—21no—
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C42C2311yescharacteristic
255#501—42no—
256#489—42no—
257#485—42no—
258#482—24no—
259#477—42no—
260#476—42no—
261#467—42no—
262#465—42no—
263#452—42no—
264#450—24no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280#416—24no—
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321#400—21no—
322#400—21no—
323#399—21no—
324#399—21no—
325#398—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#395—21no—
340#395—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#393—21no—
349#393—21no—
350#392—21no—
351#392—21no—
352#392—21no—
353#391—21no—
354#391—21no—
355#391—21no—
356#391—21no—
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390D411yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389D411yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
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#388D411yescharacteristic
406#388D411yescharacteristic
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#386—21no—
412#386—21no—
413#386D411yescharacteristic
414#386D411yescharacteristic
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#383—21no—
422#383—21no—
423#382—21no—
424#382—21no—
425#381—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380D411yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2×D411yescharacteristic
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C2×Q16—22no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555C4⋊Q8—44no—
556#126—44no—
557#125—22no—
558#125—41no—
559#125—44no—
560#124—22no—
561#124—41no—
562#124—82no—
563#124—82no—
564#123—44no—
565#123—44no—
566#123—82no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577#121—22no—
578#121—22no—
579#121—42no—
580#121—41no—
581#121—41no—
582#121—44no—
583#121—41no—
584#121—41no—
585#120—44no—
586#120—82no—
587C4×Q8—22no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×D4—22no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601#117—22no—
602#117—22no—
603#117—22no—
604#117—44no—
605#117—41no—
606#117—41no—
607#117—41no—
608#117—82no—
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—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
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—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—44no—
688C2×C22⋊C4—44no—
689C2×C22⋊C4—82no—
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—41no—
713C2×C42—41no—
714C2×C42C2×D411yescharacteristic
715C2×C42C2×D411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720#107—22no—
721#107—41no—
722#107—41no—
723#107—41no—
724#107—41no—
725#107—41no—
726#107—41no—
727#107—41no—
728#107—41no—
729#106—22no—
730#106—22no—
731#106—22no—
732#106—22no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735#103—22no—
736#103—22no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—22no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102#4114yes—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771#97—41no—
772#97—41no—
773#97—41no—
774#97—41no—
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#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—42no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24C22×D411yescharacteristic
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823#41—44no—
824#41—82no—
825#41—82no—
826#41—82no—
827C2×Q8—21no—
828C2×Q8—21no—
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—42no—
839C2×Q8—42no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8H(5,𝔽2)12yes—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—22no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—81no—
872C2×D4—82no—
873C2×D4—82no—
874C2×D4—82no—
875C2×D4—82no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4C2×#4112yes—
885C22×C4—22no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
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—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C2511yescharacteristic
944Q16—82no—
945SD16—82no—
946SD16—82no—
947C2×C8—21no—
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—21no—
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—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—82no—
971C2×C8—82no—
972C2×C8C2×#4112yes—
973C4⋊C4—24no—
974C4⋊C4—22no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
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—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4C2×#4112yes—
1024C4⋊C4H(5,𝔽2)12yes—
1025C22⋊C4—24no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
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—42no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—22no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—84no—
1128C23—84no—
1129C23—84no—
1130C23—84no—
1131C23—162no—
1132C23—162no—
1133C23—162no—
1134C23#57612yes—
1135C23C23×D411yescharacteristic
1136Q8—22no—
1137Q8—22no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—162no—
1145Q8—162no—
1146D4—22no—
1147D4—22no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—82no—
1155D4—82no—
1156D4—82no—
1157D4—84no—
1158D4—84no—
1159D4—162no—
1160D4—162no—
1161D4—162no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—44no—
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—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—82no—
1250C2×C4—84no—
1251C2×C4—84no—
1252C2×C4—162no—
1253C2×C4#57512yes—
1254C2×C4C22×#4111yescharacteristic
1255C2×C4C2×H(5,𝔽2)11yescharacteristic
1256C2×C4C2×H(5,𝔽2)11yescharacteristic
1257C2×C4#58511yescharacteristic
1258C2×C4#58511yescharacteristic
1259C2×C4#58511yescharacteristic
1260C8—22no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—42no—
1280C22—41no—
1281C22—41no—
1282C22—42no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—42no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—168no—
1304C22D4×#4111yescharacteristic
1305C22#348411yescharacteristic
1306C22#348511yescharacteristic
1307C22C2×#57511yescharacteristic
1308C22C2×#57611yescharacteristic
1309C22#358611yescharacteristic
1310C22#358611yescharacteristic
1311C4—22no—
1312C4—41no—
1313C4—42no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—42no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—42no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4#349411yescharacteristic
1337C4#351411yescharacteristic
1338C4#354511yescharacteristic
1339C4#355111yescharacteristic
1340C2—42no—
1341C2—81no—
1342C2—81no—
1343C2—82no—
1344C2—161no—
1345C2#4354311yescharacteristic
1346C2#6146111yescharacteristic
1347C2#6152311yescharacteristic
1348C2#6160511yescharacteristic
1349C2#6167411yescharacteristic
1350C2#6171211yescharacteristic
1351C2#6174411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59807C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59234C2semidirect
3. #32258C2semidirect
4. #31793C2semidirect
5. #31260C2semidirect
6. #31044C2semidirect
7. #30970C2semidirect
8. #30832C2semidirect
9. #30570C2semidirect
10. #30409C2semidirect
11. #29416C2semidirect
12. #28935C2semidirect
13. #27800C2semidirect
14. #27582C2semidirect
15. #27442C2semidirect
16. #27417C2semidirect
17. #27353C2semidirect
18. #27252C2semidirect
19. #27212C2semidirect
20. #26814C2semidirect
21. #26213C2semidirect
22. #25898C2semidirect
23. #25716C2semidirect
24. #25546C2semidirect
25. #24874C2semidirect
26. #24436C2semidirect
27. #23762C2semidirect
28. #22933C2semidirect
29. #22569C2semidirect
30. #22339C2semidirect
31. #22049C2semidirect
34. C2×#501C22semidirect
36. C2×#485C22semidirect
38. C2×#477C22semidirect
40. C2×#467C22semidirect
50. #2551C22semidirect
54. #2538C22semidirect
57. #2492C22semidirect
58. #2492C22semidirect
77. #2355C22semidirect
78. #2354C22semidirect
79. #2347C22semidirect
80. #2347C22semidirect
88. #2100C22semidirect
89. #2095C22semidirect
92. #2087C22semidirect
93. #2084C22semidirect
97. #2075C22semidirect
98. #2075C22semidirect
99. #2072C22semidirect
102. #2068C22semidirect
104. #2059C22semidirect
105. #2057C22semidirect
106. #2057C22semidirect
109. #2036C22semidirect
110. #2036C22semidirect
111. #2036C22semidirect
112. #2036C22semidirect
121. #2026C22semidirect
128. #1989C22semidirect
135. #1944C22semidirect
139. #1935C22semidirect
140. #1927C22semidirect
141. #1927C22semidirect
150. #1924C22semidirect
151. #1924C22semidirect
152. #1920C22semidirect
153. #1920C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
156. #1917C22semidirect
157. #1917C22semidirect
162. #1878C22semidirect
163. #1878C22semidirect
164. #1878C22semidirect
168. #1873C22semidirect
172. #1869C22semidirect
173. #1869C22semidirect
175. #1863C22semidirect
176. #1863C22semidirect
177. #1863C22semidirect
178. #1854C22semidirect
179. #1854C22semidirect
180. #1854C22semidirect
184. #1825C22semidirect
186. #1808C22semidirect
187. #1808C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. #1763C22semidirect
196. #1763C22semidirect
197. #1763C22semidirect
199. #1752C22semidirect
200. #1752C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#598072
#592342
#322582
#317932
#312602
#310442
#309702
#308322
#305702
#304092
#294162
#289352
#278002
#275822
#274422
#274172
#273532
#272522
#272122
#268142
#262132
#258982
#257162
#255462
#248742
#244362
#237622
#229332
#225692
#223392
#220492