Finite Group Databasebeta

← #6784595

Subgroups — #6784595

Order 512.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36386C211yesmaximal, characteristic
2#36382C211yesmaximal, characteristic, complemented
3#33176C211yesmaximal, characteristic, complemented
4#32349C211yesmaximal, characteristic, complemented
5#32279C211yesmaximal, characteristic, complemented
6#32085C211yesmaximal, characteristic, complemented
7#31837C211yesmaximal, characteristic, complemented
8#31639C211yesmaximal, characteristic, complemented
9#31287C211yesmaximal, characteristic, complemented
10#30742C211yesmaximal, characteristic, complemented
11#30450C211yesmaximal, characteristic, complemented
12#30347C211yesmaximal, characteristic, complemented
13#30323C211yesmaximal, characteristic, complemented
14#29563C211yesmaximal, characteristic, complemented
15#29502C211yesmaximal, characteristic, complemented
16#29338C211yesmaximal, characteristic, complemented
17#28311C211yesmaximal, characteristic, complemented
18#25557C211yesmaximal, characteristic, complemented
19#25557C211yesmaximal, characteristic, complemented
20#25229C211yesmaximal, characteristic, complemented
21#25229C211yesmaximal, characteristic, complemented
22#25105C211yesmaximal, characteristic, complemented
23#25105C211yesmaximal, characteristic, complemented
24#24657C211yesmaximal, characteristic, complemented
25#24511C211yesmaximal, characteristic, complemented
26#24442C211yesmaximal, characteristic
27#24442C211yesmaximal, characteristic
28#22156C211yesmaximal, characteristic, complemented
29#22048C211yesmaximal, characteristic, complemented
30#21108C211yesmaximal, characteristic, complemented
31#21095C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#494C2211yescharacteristic, complemented
35C2×#484C2211yescharacteristic
36C2×#484C2211yescharacteristic
37C2×#470C2211yescharacteristic
38C2×#470C2211yescharacteristic
39C2×#470C2211yescharacteristic
40C2×#470C2211yescharacteristic
41C2×#464C2211yescharacteristic
42C2×#464C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#432C2211yescharacteristic, complemented
48C2×#418C2211yescharacteristic
49C2×#418C2211yescharacteristic
50C2×C4×M16C2211yescharacteristic
51#2863C2211yescharacteristic, complemented
52#2861C2211yescharacteristic
53#2857C2211yescharacteristic
54#2857C2211yescharacteristic
55#2855C2211yescharacteristic, complemented
56#2850C2211yescharacteristic
57#2585—21no—
58#2577—21no—
59#2573—21no—
60#2566C2211yescharacteristic
61#2559—21no—
62#2559—21no—
63#2558—21no—
64#2558—21no—
65#2545C2211yescharacteristic
66#2534—21no—
67#2534—21no—
68#2530—21no—
69#2506C2211yescharacteristic, complemented
70#2503C2211yescharacteristic
71#2500C2211yescharacteristic
72#2496C2211yescharacteristic, complemented
73#2468—21no—
74#2460—21no—
75#2446C2211yescharacteristic, complemented
76#2435C2211yescharacteristic
77#2432C2211yescharacteristic
78#2429C2211yescharacteristic, complemented
79#2415C2211yescharacteristic
80#2415C2211yescharacteristic
81#2373—21no—
82#2370—21no—
83#2362C2211yescharacteristic
84#2362C2211yescharacteristic
85#2342—21no—
86#2342—21no—
87C4×#124C2211yescharacteristic
88C4×C22⋊Q8C2211yescharacteristic, complemented
89#2297C2211yescharacteristic
90#2296C2211yescharacteristic
91#2295C2211yescharacteristic, complemented
92C2×#390C2211yescharacteristic
93C42×D4C2211yescharacteristic
94#2100C2211yescharacteristic, complemented
95#2100C2211yescharacteristic, complemented
96#2093C2211yescharacteristic
97#2093C2211yescharacteristic
98#2085C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2074C2211yescharacteristic, complemented
101#2074C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2059C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2056C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2043C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2036C2211yescharacteristic, complemented
119#2036C2211yescharacteristic, complemented
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2026C2211yescharacteristic, complemented
123#2026C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2013C2211yescharacteristic
129#2013C2211yescharacteristic
130#2001C2211yescharacteristic, complemented
131#2001C2211yescharacteristic, complemented
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1971C2211yescharacteristic, complemented
141#1971C2211yescharacteristic, complemented
142#1971C2211yescharacteristic, complemented
143#1971C2211yescharacteristic, complemented
144#1956C2211yescharacteristic, complemented
145#1956C2211yescharacteristic, complemented
146#1949C2211yescharacteristic, complemented
147#1949C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1935C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1935C2211yescharacteristic, complemented
155#1935C2211yescharacteristic, complemented
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1934C2211yescharacteristic
160#1928C2211yescharacteristic, complemented
161#1928C2211yescharacteristic, complemented
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1923C2211yescharacteristic, complemented
165#1923C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1873C2211yescharacteristic
177#1873C2211yescharacteristic
178#1873C2211yescharacteristic
179#1873C2211yescharacteristic
180#1873C2211yescharacteristic, complemented
181#1873C2211yescharacteristic, complemented
182#1870C2211yescharacteristic
183#1870C2211yescharacteristic
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic
186#1863C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1854C2211yescharacteristic, complemented
189#1854C2211yescharacteristic, complemented
190#1851C2211yescharacteristic
191#1851C2211yescharacteristic
192#1844C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1805C2211yescharacteristic, complemented
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1767C2211yescharacteristic, complemented
198#1749C2211yescharacteristic
199#1749C2211yescharacteristic, complemented
200#1745C2211yescharacteristic, complemented
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215#552—42no—
216#552—42no—
217#546—42no—
218#546—42no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4D411yescharacteristic
245C2×C4×D4D411yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117—21no—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258#494—42no—
259#484—42no—
260#484—42no—
261#470—42no—
262#470—42no—
263#470—42no—
264#470—42no—
265#464—24no—
266#464—42no—
267#452—24no—
268#452—42no—
269#450—42no—
270#450—42no—
271#432—42no—
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284#418—24no—
285#418—42no—
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C4×M16—42no—
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
366#390—21no—
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#383—21no—
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#381—21no—
439#381—21no—
440#381—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#379—21no—
448#379—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4D411yescharacteristic
456C4×C4⋊C4D411yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4D411yescharacteristic
466C4×C22⋊C4D411yescharacteristic
467C4×C22⋊C4D411yescharacteristic
468C4×C22⋊C4D411yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471#376—21no—
472C43C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—22no—
558C2×M16—22no—
559C2×M16—41no—
560C2×M16—41no—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573#126—44no—
574#126—44no—
575#125—41no—
576#125—41no—
577#125—44no—
578#125—44no—
579#124—22no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#123—44no—
586#123—44no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601#121—44no—
602#121—41no—
603#121—41no—
604#120—44no—
605C4×Q8—22no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—42no—
616C4×D4—42no—
617#117—22no—
618#117—44no—
619#117—41no—
620#117—41no—
621#117—41no—
622#117—41no—
623#117—41no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
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—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
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—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—44no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4—44no—
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—41no—
718C2×C42—41no—
719C2×C42—41no—
720C2×C42—41no—
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2×D411yescharacteristic
727C2×C42C2×D411yescharacteristic
728C2×C42C2×D411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734#107—41no—
735#107—41no—
736#107—41no—
737#107—41no—
738#106—41no—
739#106—41no—
740#106—41no—
741#106—41no—
742C4⋊C8—22no—
743C4⋊C8—22no—
744C4⋊C8—41no—
745C4⋊C8—41no—
746#103—22no—
747#103—22no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102#4114yes—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8—22no—
781C22⋊C8—22no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784#97—22no—
785#97—41no—
786#97—41no—
787#97—41no—
788C4×C8—22no—
789C4×C8—41no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832C24—21no—
833C24—21no—
834C24—42no—
835C24—42no—
836C24—42no—
837C24—42no—
838C24—81no—
839C24—81no—
840C24—81no—
841C24C22×D411yescharacteristic
842C24C22×D411yescharacteristic
843#41—82no—
844#41—82no—
845#41—82no—
846#41—82no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×D4—22no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—82no—
893C2×D4—82no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4C2×#4112yes—
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—21no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4H(5,𝔽2)12yes—
957C22×C4H(5,𝔽2)12yes—
958C22×C4C2511yescharacteristic
959Q16—82no—
960Q16—82no—
961Q16—82no—
962Q16—82no—
963SD16—82no—
964SD16—82no—
965SD16—82no—
966SD16—82no—
967M16—44no—
968M16—44no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8C2×#4112yes—
992C2×C8H(5,𝔽2)12yes—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4C2×#4112yes—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—41no—
1094C42—41no—
1095C42—41no—
1096C42—41no—
1097C42—41no—
1098C42—41no—
1099C42—41no—
1100C42—41no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—81no—
1108C42—81no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—22no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—84no—
1137C23—84no—
1138C23—84no—
1139C23—84no—
1140C23—162no—
1141C23—162no—
1142C23—162no—
1143C23#53512yes—
1144C23C23×D411yescharacteristic
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161D4—22no—
1162D4—22no—
1163D4—44no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—84no—
1171D4—84no—
1172D4—162no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
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—22no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
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—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—82no—
1257C2×C4—82no—
1258C2×C4—82no—
1259C2×C4—82no—
1260C2×C4—84no—
1261C2×C4—84no—
1262C2×C4—162no—
1263C2×C4#53512yes—
1264C2×C4#57512yes—
1265C2×C4#57512yes—
1266C2×C4C22×#4111yescharacteristic
1267C2×C4C2×H(5,𝔽2)11yescharacteristic
1268C2×C4C2×H(5,𝔽2)11yescharacteristic
1269C2×C4C2×H(5,𝔽2)11yescharacteristic
1270C2×C4#58511yescharacteristic
1271C2×C4#58511yescharacteristic
1272C8—22no—
1273C8—22no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—42no—
1289C22—41no—
1290C22—42no—
1291C22—41no—
1292C22—42no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—168no—
1309C22C2×#53511yescharacteristic
1310C22D4×#4111yescharacteristic
1311C22#349611yescharacteristic
1312C22C2×#57511yescharacteristic
1313C22C2×#57511yescharacteristic
1314C22#358611yescharacteristic
1315C22#358611yescharacteristic
1316C4—22no—
1317C4—22no—
1318C4—22no—
1319C4—41no—
1320C4—42no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4#349411yescharacteristic
1343C4#351911yescharacteristic
1344C4#353411yescharacteristic
1345C4#356011yescharacteristic
1346C2—42no—
1347C2—81no—
1348C2—82no—
1349C2—161no—
1350C2#3842311yescharacteristic
1351C2#6080111yescharacteristic
1352C2#6082611yescharacteristic
1353C2#6146111yescharacteristic
1354C2#6146311yescharacteristic
1355C2#6230211yescharacteristic
1356C2#6230211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36382C2semidirect
3. #33176C2semidirect
4. #32349C2semidirect
5. #32279C2semidirect
6. #32085C2semidirect
7. #31837C2semidirect
8. #31639C2semidirect
9. #31287C2semidirect
10. #30742C2semidirect
11. #30450C2semidirect
12. #30347C2semidirect
13. #30323C2semidirect
14. #29563C2semidirect
15. #29502C2semidirect
16. #29338C2semidirect
17. #28311C2semidirect
18. #25557C2semidirect
19. #25557C2semidirect
20. #25229C2semidirect
21. #25229C2semidirect
22. #25105C2semidirect
23. #25105C2semidirect
24. #24657C2semidirect
25. #24511C2semidirect
28. #22156C2semidirect
29. #22048C2semidirect
30. #21108C2semidirect
31. #21095C2semidirect
34. C2×#494C22semidirect
47. C2×#432C22semidirect
51. #2863C22semidirect
55. #2855C22semidirect
69. #2506C22semidirect
72. #2496C22semidirect
75. #2446C22semidirect
78. #2429C22semidirect
88. C4×C22⋊Q8C22semidirect
91. #2295C22semidirect
94. #2100C22semidirect
95. #2100C22semidirect
98. #2085C22semidirect
99. #2085C22semidirect
100. #2074C22semidirect
101. #2074C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
106. #2059C22semidirect
107. #2059C22semidirect
108. #2056C22semidirect
109. #2056C22semidirect
112. #2043C22semidirect
113. #2043C22semidirect
118. #2036C22semidirect
119. #2036C22semidirect
122. #2026C22semidirect
123. #2026C22semidirect
130. #2001C22semidirect
131. #2001C22semidirect
140. #1971C22semidirect
141. #1971C22semidirect
142. #1971C22semidirect
143. #1971C22semidirect
144. #1956C22semidirect
145. #1956C22semidirect
146. #1949C22semidirect
147. #1949C22semidirect
152. #1935C22semidirect
153. #1935C22semidirect
154. #1935C22semidirect
155. #1935C22semidirect
160. #1928C22semidirect
161. #1928C22semidirect
164. #1923C22semidirect
165. #1923C22semidirect
166. #1916C22semidirect
167. #1916C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
180. #1873C22semidirect
181. #1873C22semidirect
186. #1863C22semidirect
187. #1863C22semidirect
188. #1854C22semidirect
189. #1854C22semidirect
192. #1844C22semidirect
193. #1805C22semidirect
194. #1805C22semidirect
197. #1767C22semidirect
199. #1749C22semidirect
200. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#363862
#363822
#331762
#323492
#322792
#320852
#318372
#316392
#312872
#307422
#304502
#303472
#303232
#295632
#295022
#293382
#283112
#255572
#252292
#251052
#246572
#245112
#244422
#221562
#220482
#211082
#210952