Finite Group Databasebeta

← #7030304

Subgroups — #7030304

Order 512.

1613 conjugacy classes of subgroups.

The subgroup lattice has 1339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59637C211yesmaximal, characteristic
2#59067C211yesmaximal, characteristic, complemented
3#32647C211yesmaximal, characteristic, complemented
4#32573C211yesmaximal, characteristic, complemented
5#32442C211yesmaximal, characteristic, complemented
6#31947C211yesmaximal, characteristic, complemented
7#31853C211yesmaximal, characteristic, complemented
8#31638C211yesmaximal, characteristic, complemented
9#30988C211yesmaximal, characteristic
10#30456C211yesmaximal, characteristic
11#29414C211yesmaximal, characteristic, complemented
12#28883C211yesmaximal, characteristic, complemented
13#27572C211yesmaximal, characteristic, complemented
14#27396C211yesmaximal, characteristic, complemented
15#27220C211yesmaximal, characteristic, complemented
16#27164C211yesmaximal, characteristic, complemented
17#27069C211yesmaximal, characteristic, complemented
18#26605C211yesmaximal, characteristic, complemented
19#26603C211yesmaximal, characteristic, complemented
20#26260C211yesmaximal, characteristic, complemented
21#26179C211yesmaximal, characteristic, complemented
22#25630C211yesmaximal, characteristic, complemented
23#25176C211yesmaximal, characteristic, complemented
24#24921C211yesmaximal, characteristic, complemented
25#24199C211yesmaximal, characteristic, complemented
26#23933C211yesmaximal, characteristic, complemented
27#23574C211yesmaximal, characteristic, complemented
28#23003C211yesmaximal, characteristic, complemented
29#22775C211yesmaximal, characteristic, complemented
30#22323C211yesmaximal, characteristic, complemented
31#22049C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic, complemented
33C2×#533C2211yescharacteristic
34C2×#492C2211yescharacteristic
35C2×#460C2211yescharacteristic
36C2×#460C2211yescharacteristic
37C2×#461C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C2×#440C2211yescharacteristic, complemented
44C2×#440C2211yescharacteristic, complemented
45#2797—21no—
46#2752—21no—
47#2720—21no—
48#2720—21no—
49#2602—21no—
50#2580C2211yescharacteristic
51#2567C2211yescharacteristic, complemented
52#2567C2211yescharacteristic, complemented
53#2557—21no—
54#2552—21no—
55#2548C2211yescharacteristic
56#2513C2211yescharacteristic
57#2513C2211yescharacteristic
58#2504C2211yescharacteristic
59#2472—21no—
60#2462—21no—
61#2462—21no—
62#2453—21no—
63#2446C2211yescharacteristic, complemented
64#2446C2211yescharacteristic, complemented
65#2445C2211yescharacteristic
66#2445C2211yescharacteristic
67#2441—21no—
68#2433C2211yescharacteristic
69#2429C2211yescharacteristic
70#2429C2211yescharacteristic
71#2423C2211yescharacteristic
72#2423C2211yescharacteristic
73#2418—21no—
74#2412—21no—
75#2366C2211yescharacteristic
76#2365C2211yescharacteristic, complemented
77#2362—21no—
78#2358—21no—
79#2357C2211yescharacteristic
80Q8×C4⋊C4C2211yescharacteristic, complemented
81Q8×C4⋊C4C2211yescharacteristic, complemented
82#2345C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×C22⋊Q8C2211yescharacteristic
86C4×#121C2211yescharacteristic
87C2×#390C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2093C2211yescharacteristic
92#2087C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2076C2211yescharacteristic
95#2074C2211yescharacteristic, complemented
96#2071C2211yescharacteristic
97#2071C2211yescharacteristic, complemented
98#2068C2211yescharacteristic, complemented
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2057C2211yescharacteristic, complemented
103#2055C2211yescharacteristic
104#2055C2211yescharacteristic
105#2055C2211yescharacteristic, complemented
106#2043C2211yescharacteristic, complemented
107#2043C2211yescharacteristic, complemented
108#2041C2211yescharacteristic
109#2041C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2034C2211yescharacteristic
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic, complemented
117#2014C2211yescharacteristic
118#2014C2211yescharacteristic
119#2013C2211yescharacteristic
120#2013C2211yescharacteristic
121#2013C2211yescharacteristic
122#2013C2211yescharacteristic
123#2013C2211yescharacteristic, complemented
124#2013C2211yescharacteristic, complemented
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1985C2211yescharacteristic, complemented
129#1984C2211yescharacteristic, complemented
130#1981C2211yescharacteristic, complemented
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic, complemented
135#1968C2211yescharacteristic
136#1960C2211yescharacteristic, complemented
137#1957C2211yescharacteristic
138#1947C2211yescharacteristic, complemented
139#1942C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1933C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1928C2211yescharacteristic, complemented
148#1927C2211yescharacteristic, complemented
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic, complemented
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1921C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic, complemented
175#1880C2211yescharacteristic, complemented
176#1880C2211yescharacteristic, complemented
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic, complemented
180#1872C2211yescharacteristic
181#1872C2211yescharacteristic
182#1872C2211yescharacteristic
183#1863C2211yescharacteristic, complemented
184#1863C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic, complemented
189#1852C2211yescharacteristic
190#1836C2211yescharacteristic, complemented
191#1817C2211yescharacteristic
192#1805C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1770C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201C4×#103C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213#557—42no—
214#557—42no—
215#533—42no—
216#533—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#125—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#125—21no—
227C2×#124—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8D411yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×C4×Q8—21no—
239C2×C4×Q8—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117—21no—
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258C22×C42C2311yescharacteristic
259#492—42no—
260#461—42no—
261#460—24no—
262#460—42no—
263#450—24no—
264#450—42no—
265#450—42no—
266#440—24no—
267#440—42no—
268#440—42no—
269#440—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321#400—21no—
322#400—21no—
323#399—21no—
324#399—21no—
325#399—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#396—21no—
339#396—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#393—21no—
351#392—21no—
352#392—21no—
353#391—21no—
354#391D411yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389D411yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
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#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387D411yescharacteristic
416#387D411yescharacteristic
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385D411yescharacteristic
430#385D411yescharacteristic
431#384—21no—
432#384—21no—
433#384—21no—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#381—21no—
439#380—21no—
440#380D411yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8C2×D411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2×D411yescharacteristic
519C23×C4C2×D411yescharacteristic
520C23×C4C2411yescharacteristic
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C4⋊Q8—22no—
557C4⋊Q8—22no—
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564#127—22no—
565#127—41no—
566#127—41no—
567#127—41no—
568#125—44no—
569#125—44no—
570#125—44no—
571#125—44no—
572#124—82no—
573#123—82no—
574#123—82no—
575C22⋊Q8—24no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—44no—
583#121—41no—
584#121—41no—
585#120—44no—
586#120—82no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—44no—
604C4×Q8—44no—
605C4×D4—22no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—82no—
612C4×D4—82no—
613#117—44no—
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—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
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—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—82no—
697C2×C22⋊C4—82no—
698C2×C22⋊C4—82no—
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
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—21no—
713C2×C42—21no—
714C2×C42—41no—
715C2×C42—41no—
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724#107—22no—
725#107—41no—
726#107—41no—
727#107—41no—
728#107—41no—
729#107—41no—
730#106—41no—
731C4⋊C8—22no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735#103—22no—
736#103—22no—
737#103—22no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#102—22no—
751#102—22no—
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—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102#4114yes—
765C22⋊C8—22no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769#97—22no—
770#97—41no—
771#97—41no—
772#97—41no—
773C4×C8—41no—
774C4×C8—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#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813C24—21no—
814C24—21no—
815C24—21no—
816C24—42no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24C22×D411yescharacteristic
824C2×Q8—22no—
825C2×Q8—22no—
826C2×Q8—21no—
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—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—42no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8H(5,𝔽2)12yes—
847C2×Q8H(5,𝔽2)12yes—
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—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—82no—
884C2×D4—82no—
885C2×D4—82no—
886C2×D4—82no—
887C2×D4C2×#4112yes—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—22no—
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—21no—
908C22×C4—21no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
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×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C2511yescharacteristic
939SD16—44no—
940SD16—44no—
941SD16—44no—
942SD16—44no—
943SD16—82no—
944SD16—82no—
945SD16—82no—
946SD16—82no—
947SD16—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—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—21no—
971C2×C8C2×#4112yes—
972C4⋊C4—24no—
973C4⋊C4—24no—
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—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
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—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4C2×#4112yes—
1031C22⋊C4—22no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
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—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
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—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4#13714yes—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—41no—
1079C42—41no—
1080C42—42no—
1081C42—42no—
1082C42—42no—
1083C42—42no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—42no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—22no—
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—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—84no—
1119C23—84no—
1120C23—84no—
1121C23—84no—
1122C23—162no—
1123C23—162no—
1124C23—162no—
1125C23C2×#13712yes—
1126C23C23×D411yescharacteristic
1127Q8—22no—
1128Q8—22no—
1129Q8—22no—
1130Q8—22no—
1131Q8—44no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—84no—
1141D4—22no—
1142D4—22no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—84no—
1154D4—84no—
1155D4—84no—
1156D4—162no—
1157D4—162no—
1158D4—162no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
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—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—22no—
1188C2×C4—22no—
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—21no—
1198C2×C4—44no—
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—82no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4C2×#13712yes—
1245C2×C4C2×#13712yes—
1246C2×C4#57712yes—
1247C2×C4C22×#4111yescharacteristic
1248C2×C4C2×H(5,𝔽2)11yescharacteristic
1249C2×C4C2×H(5,𝔽2)11yescharacteristic
1250C2×C4#58511yescharacteristic
1251C2×C4#58511yescharacteristic
1252C2×C4#58511yescharacteristic
1253C8—22no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—168no—
1290C22D4×#4111yescharacteristic
1291C22#348411yescharacteristic
1292C22#348711yescharacteristic
1293C22C22×#13711yescharacteristic
1294C22C2×#57711yescharacteristic
1295C22#358511yescharacteristic
1296C22#358511yescharacteristic
1297C4—22no—
1298C4—22no—
1299C4—22no—
1300C4—41no—
1301C4—41no—
1302C4—42no—
1303C4—42no—
1304C4—41no—
1305C4—41no—
1306C4—42no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4#349411yescharacteristic
1324C4#351311yescharacteristic
1325C4#353311yescharacteristic
1326C4#356011yescharacteristic
1327C2—42no—
1328C2—82no—
1329C2—161no—
1330C2—161no—
1331C2#4311511yescharacteristic
1332C2#6145311yescharacteristic
1333C2#6155111yescharacteristic
1334C2#6159311yescharacteristic
1335C2#6165111yescharacteristic
1336C2#6189211yescharacteristic
1337C2#6192111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59067C2semidirect
3. #32647C2semidirect
4. #32573C2semidirect
5. #32442C2semidirect
6. #31947C2semidirect
7. #31853C2semidirect
8. #31638C2semidirect
11. #29414C2semidirect
12. #28883C2semidirect
13. #27572C2semidirect
14. #27396C2semidirect
15. #27220C2semidirect
16. #27164C2semidirect
17. #27069C2semidirect
18. #26605C2semidirect
19. #26603C2semidirect
20. #26260C2semidirect
21. #26179C2semidirect
22. #25630C2semidirect
23. #25176C2semidirect
24. #24921C2semidirect
25. #24199C2semidirect
26. #23933C2semidirect
27. #23574C2semidirect
28. #23003C2semidirect
29. #22775C2semidirect
30. #22323C2semidirect
31. #22049C2semidirect
32. C2×#557C22semidirect
43. C2×#440C22semidirect
44. C2×#440C22semidirect
51. #2567C22semidirect
52. #2567C22semidirect
63. #2446C22semidirect
64. #2446C22semidirect
76. #2365C22semidirect
80. Q8×C4⋊C4C22semidirect
81. Q8×C4⋊C4C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2097C22semidirect
92. #2087C22semidirect
93. #2085C22semidirect
95. #2074C22semidirect
97. #2071C22semidirect
98. #2068C22semidirect
100. #2067C22semidirect
102. #2057C22semidirect
105. #2055C22semidirect
106. #2043C22semidirect
107. #2043C22semidirect
116. #2023C22semidirect
123. #2013C22semidirect
124. #2013C22semidirect
128. #1985C22semidirect
129. #1984C22semidirect
130. #1981C22semidirect
134. #1973C22semidirect
136. #1960C22semidirect
138. #1947C22semidirect
139. #1942C22semidirect
143. #1936C22semidirect
145. #1933C22semidirect
146. #1928C22semidirect
147. #1928C22semidirect
148. #1927C22semidirect
151. #1925C22semidirect
156. #1921C22semidirect
157. #1921C22semidirect
158. #1920C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1917C22semidirect
162. #1917C22semidirect
163. #1916C22semidirect
174. #1880C22semidirect
175. #1880C22semidirect
176. #1880C22semidirect
179. #1877C22semidirect
183. #1863C22semidirect
184. #1863C22semidirect
185. #1863C22semidirect
188. #1862C22semidirect
190. #1836C22semidirect
192. #1805C22semidirect
193. #1805C22semidirect
196. #1771C22semidirect
197. #1770C22semidirect
198. #1763C22semidirect
199. #1763C22semidirect
200. C4×#103C22semidirect
201. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#596372
#590672
#326472
#325732
#324422
#319472
#318532
#316382
#309882
#304562
#294142
#288832
#275722
#273962
#272202
#271642
#270692
#266052
#266032
#262602
#261792
#256302
#251762
#249212
#241992
#239332
#235742
#230032
#227752
#223232
#220492