Finite Group Databasebeta

← #7030559

Subgroups — #7030559

Order 512.

1548 conjugacy classes of subgroups.

The subgroup lattice has 1295 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59862C211yesmaximal, characteristic
2#59071C211yesmaximal, characteristic, complemented
3#32639C211yesmaximal, characteristic, complemented
4#32584C211yesmaximal, characteristic, complemented
5#32441C211yesmaximal, characteristic, complemented
6#31939C211yesmaximal, characteristic, complemented
7#31857C211yesmaximal, characteristic, complemented
8#31649C211yesmaximal, characteristic, complemented
9#30996C211yesmaximal, characteristic
10#30464C211yesmaximal, characteristic
11#29416C211yesmaximal, characteristic, complemented
12#28883C211yesmaximal, characteristic, complemented
13#27577C211yesmaximal, characteristic, complemented
14#27392C211yesmaximal, characteristic, complemented
15#27220C211yesmaximal, characteristic, complemented
16#27176C211yesmaximal, characteristic, complemented
17#27069C211yesmaximal, characteristic, complemented
18#26614C211yesmaximal, characteristic, complemented
19#26589C211yesmaximal, characteristic, complemented
20#26269C211yesmaximal, characteristic, complemented
21#26189C211yesmaximal, characteristic, complemented
22#25640C211yesmaximal, characteristic, complemented
23#25156C211yesmaximal, characteristic
24#24917C211yesmaximal, characteristic
25#24199C211yesmaximal, characteristic, complemented
26#23933C211yesmaximal, characteristic
27#23577C211yesmaximal, characteristic, complemented
28#23006C211yesmaximal, characteristic, complemented
29#22765C211yesmaximal, characteristic, complemented
30#22327C211yesmaximal, characteristic, complemented
31#22049C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic, complemented
33C2×#533C2211yescharacteristic
34C2×#497C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×#464C2211yescharacteristic
37C2×#461C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#441C2211yescharacteristic, complemented
42C2×#441C2211yescharacteristic, complemented
43C2×#440C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic
45#2796—21no—
46#2751—21no—
47#2719—21no—
48#2719—21no—
49#2595—21no—
50#2592C2211yescharacteristic
51#2580C2211yescharacteristic
52#2568C2211yescharacteristic, complemented
53#2561—21no—
54#2546C2211yescharacteristic, complemented
55#2516—21no—
56#2513C2211yescharacteristic
57#2513C2211yescharacteristic
58#2503C2211yescharacteristic
59#2489—21no—
60#2483—21no—
61#2482—21no—
62#2475—21no—
63#2475—21no—
64#2453—21no—
65#2448C2211yescharacteristic
66#2447C2211yescharacteristic
67#2446C2211yescharacteristic, complemented
68#2446C2211yescharacteristic, complemented
69#2435C2211yescharacteristic
70#2429—21no—
71#2429C2211yescharacteristic
72#2429C2211yescharacteristic
73#2421C2211yescharacteristic
74#2421C2211yescharacteristic
75#2367C2211yescharacteristic
76#2365—21no—
77#2365C2211yescharacteristic, complemented
78#2357C2211yescharacteristic
79#2351C2211yescharacteristic, complemented
80#2351C2211yescharacteristic, complemented
81#2344C2211yescharacteristic
82#2342—21no—
83D4×C22⋊C4C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×C22⋊Q8C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87C2×#390C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2075C2211yescharacteristic
95#2074C2211yescharacteristic, complemented
96#2074C2211yescharacteristic, complemented
97#2073C2211yescharacteristic
98#2068C2211yescharacteristic, complemented
99#2068C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2058C2211yescharacteristic, complemented
103#2056C2211yescharacteristic, complemented
104#2055C2211yescharacteristic
105#2055C2211yescharacteristic
106#2043C2211yescharacteristic, complemented
107#2043C2211yescharacteristic, complemented
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2035C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2024C2211yescharacteristic, complemented
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#2016C2211yescharacteristic, complemented
118#2016C2211yescharacteristic, complemented
119#2015C2211yescharacteristic
120#2015C2211yescharacteristic
121#2013C2211yescharacteristic
122#2013C2211yescharacteristic
123#2013C2211yescharacteristic
124#2013C2211yescharacteristic
125#2001C2211yescharacteristic
126#2001C2211yescharacteristic
127#2001C2211yescharacteristic
128#1985C2211yescharacteristic, complemented
129#1985C2211yescharacteristic, complemented
130#1981C2211yescharacteristic, complemented
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1969C2211yescharacteristic, complemented
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1960C2211yescharacteristic, complemented
137#1958C2211yescharacteristic
138#1949C2211yescharacteristic, complemented
139#1943C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic, complemented
145#1933C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1927C2211yescharacteristic, complemented
149#1927C2211yescharacteristic, complemented
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1921C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1916C2211yescharacteristic, 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#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1872C2211yescharacteristic
181#1872C2211yescharacteristic
182#1872C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic
186#1863C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1863C2211yescharacteristic, complemented
189#1852C2211yescharacteristic
190#1835C2211yescharacteristic, complemented
191#1817C2211yescharacteristic
192#1805C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1804C2211yescharacteristic
195#1786C2211yescharacteristic
196#1770C2211yescharacteristic, complemented
197#1770C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1763C2211yescharacteristic, complemented
201C4×#103C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
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⋊Q8—21no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#125—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8D411yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C4×Q8—21no—
235C2×C4×Q8—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117—21no—
248C2×#117—21no—
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C42C2311yescharacteristic
254#497—42no—
255#464—24no—
256#464—42no—
257#461—42no—
258#450—24no—
259#450—42no—
260#450—42no—
261#441—42no—
262#441—42no—
263#440—42no—
264C4×SD16—24no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
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×#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×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—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#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#396—21no—
343#396—21no—
344#394—21no—
345#394—21no—
346#393—21no—
347#393—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391D411yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390—21no—
361#390—21no—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389D411yescharacteristic
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#387—21no—
403#387—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#387D411yescharacteristic
415#387D411yescharacteristic
416#386—21no—
417#386—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385D411yescharacteristic
425#385D411yescharacteristic
426#382—21no—
427#382—21no—
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#381—21no—
433#381—21no—
434#381—21no—
435#381—21no—
436#381—21no—
437#380D411yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379—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#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×Q8C2411yescharacteristic
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×Q16—22no—
516C2×Q16—22no—
517C2×Q16—22no—
518C2×Q16—41no—
519C2×Q16—41no—
520C2×Q16—41no—
521C2×Q16—41no—
522C2×Q16—41no—
523C2×Q16—41no—
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—
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C4⋊Q8—22no—
551C4⋊Q8—22no—
552C4⋊Q8—22no—
553C4⋊Q8—22no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—44no—
559#125—44no—
560#125—44no—
561#125—44no—
562#125—44no—
563#124—22no—
564#124—41no—
565#124—41no—
566#124—41no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—42no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—44no—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—44no—
596C4×Q8—44no—
597C4×D4—22no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601#117—44no—
602#117—82no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
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—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—44no—
681C2×C22⋊C4—82no—
682C2×C22⋊C4—82no—
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—41no—
700C2×C42—41no—
701C2×C42C2×D411yescharacteristic
702C2×C42C2×D411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#107—41no—
710#107—41no—
711#107—41no—
712#106—22no—
713#106—41no—
714#106—41no—
715#106—41no—
716C4⋊C8—22no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—22no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
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#103—41no—
740#102—22no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102#4114yes—
750C22⋊C8—22no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754#97—41no—
755#97—41no—
756#97—41no—
757#97—41no—
758C4×C8—22no—
759C4×C8—41no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
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#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—21no—
809C24—21no—
810C24—42no—
811C24—42no—
812C24—42no—
813C24—42no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24C22×D411yescharacteristic
818C2×Q8—22no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
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—41no—
842C2×Q8—41no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
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—42no—
860C2×D4—42no—
861C2×D4—81no—
862C2×D4—82no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—82no—
866C2×D4C2×#4112yes—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—22no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C2511yescharacteristic
916Q16—44no—
917Q16—44no—
918Q16—82no—
919SD16—44no—
920SD16—44no—
921SD16—82no—
922SD16—82no—
923SD16—82no—
924SD16—82no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8C2×#4112yes—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—22no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4C2×#4112yes—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—41no—
1051C42—41no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—42no—
1056C42—42no—
1057C42—42no—
1058C42—42no—
1059C42—42no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C42—81no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—22no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—84no—
1085C23—84no—
1086C23—84no—
1087C23—84no—
1088C23—162no—
1089C23—162no—
1090C23—162no—
1091C23#57712yes—
1092C23C23×D411yescharacteristic
1093Q8—22no—
1094Q8—22no—
1095Q8—22no—
1096Q8—22no—
1097Q8—44no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—84no—
1111D4—22no—
1112D4—22no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—84no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
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—44no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
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—82no—
1206C2×C4—84no—
1207C2×C4—162no—
1208C2×C4—162no—
1209C2×C4#57512yes—
1210C2×C4C22×#4111yescharacteristic
1211C2×C4C2×H(5,𝔽2)11yescharacteristic
1212C2×C4C2×H(5,𝔽2)11yescharacteristic
1213C2×C4#58511yescharacteristic
1214C2×C4#58511yescharacteristic
1215C2×C4#58511yescharacteristic
1216C8—22no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—168no—
1246C22D4×#4111yescharacteristic
1247C22#348411yescharacteristic
1248C22#348711yescharacteristic
1249C22C2×#57511yescharacteristic
1250C22C2×#57711yescharacteristic
1251C22#358611yescharacteristic
1252C22#358611yescharacteristic
1253C4—22no—
1254C4—41no—
1255C4—41no—
1256C4—42no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—42no—
1261C4—42no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4#349411yescharacteristic
1281C4#351311yescharacteristic
1282C4#353311yescharacteristic
1283C4#356011yescharacteristic
1284C2—42no—
1285C2—82no—
1286C2—161no—
1287C2#4311511yescharacteristic
1288C2#6146111yescharacteristic
1289C2#6152011yescharacteristic
1290C2#6158311yescharacteristic
1291C2#6161111yescharacteristic
1292C2#6190411yescharacteristic
1293C2#6194311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
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. #59071C2semidirect
3. #32639C2semidirect
4. #32584C2semidirect
5. #32441C2semidirect
6. #31939C2semidirect
7. #31857C2semidirect
8. #31649C2semidirect
11. #29416C2semidirect
12. #28883C2semidirect
13. #27577C2semidirect
14. #27392C2semidirect
15. #27220C2semidirect
16. #27176C2semidirect
17. #27069C2semidirect
18. #26614C2semidirect
19. #26589C2semidirect
20. #26269C2semidirect
21. #26189C2semidirect
22. #25640C2semidirect
25. #24199C2semidirect
27. #23577C2semidirect
28. #23006C2semidirect
29. #22765C2semidirect
30. #22327C2semidirect
32. C2×#557C22semidirect
41. C2×#441C22semidirect
42. C2×#441C22semidirect
52. #2568C22semidirect
54. #2546C22semidirect
67. #2446C22semidirect
68. #2446C22semidirect
77. #2365C22semidirect
79. #2351C22semidirect
80. #2351C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2097C22semidirect
92. #2088C22semidirect
93. #2085C22semidirect
95. #2074C22semidirect
96. #2074C22semidirect
98. #2068C22semidirect
99. #2068C22semidirect
102. #2058C22semidirect
103. #2056C22semidirect
106. #2043C22semidirect
107. #2043C22semidirect
114. #2024C22semidirect
117. #2016C22semidirect
118. #2016C22semidirect
128. #1985C22semidirect
129. #1985C22semidirect
130. #1981C22semidirect
133. #1969C22semidirect
136. #1960C22semidirect
138. #1949C22semidirect
139. #1943C22semidirect
144. #1935C22semidirect
145. #1933C22semidirect
146. #1928C22semidirect
147. #1927C22semidirect
148. #1927C22semidirect
149. #1927C22semidirect
156. #1921C22semidirect
157. #1920C22semidirect
158. #1920C22semidirect
159. #1920C22semidirect
160. #1917C22semidirect
161. #1917C22semidirect
162. #1916C22semidirect
163. #1916C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
177. #1878C22semidirect
183. #1865C22semidirect
186. #1863C22semidirect
187. #1863C22semidirect
188. #1863C22semidirect
190. #1835C22semidirect
192. #1805C22semidirect
193. #1805C22semidirect
196. #1770C22semidirect
197. #1770C22semidirect
198. #1763C22semidirect
199. #1763C22semidirect
200. #1763C22semidirect
201. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#598622
#590712
#326392
#325842
#324412
#319392
#318572
#316492
#309962
#304642
#294162
#288832
#275772
#273922
#272202
#271762
#270692
#266142
#265892
#262692
#261892
#256402
#251562
#249172
#241992
#239332
#235772
#230062
#227652
#223272
#220492