Finite Group Databasebeta

← #6791881

Subgroups — #6791881

Order 512.

1638 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#37748C211yesmaximal, characteristic
2#35604C211yesmaximal, characteristic, complemented
3#33037C211yesmaximal, characteristic, complemented
4#31650C211yesmaximal, characteristic, complemented
5#31638C211yesmaximal, characteristic, complemented
6#31598C211yesmaximal, characteristic, complemented
7#31578C211yesmaximal, characteristic, complemented
8#31278C211yesmaximal, characteristic, complemented
9#31271C211yesmaximal, characteristic, complemented
10#30424C211yesmaximal, characteristic, complemented
11#30421C211yesmaximal, characteristic, complemented
12#29947C211yesmaximal, characteristic, complemented
13#29927C211yesmaximal, characteristic, complemented
14#29362C211yesmaximal, characteristic, complemented
15#29263C211yesmaximal, characteristic, complemented
16#29068C211yesmaximal, characteristic, complemented
17#29059C211yesmaximal, characteristic, complemented
18#27544C211yesmaximal, characteristic, complemented
19#27520C211yesmaximal, characteristic, complemented
20#26986C211yesmaximal, characteristic, complemented
21#26971C211yesmaximal, characteristic, complemented
22#24921C211yesmaximal, characteristic, complemented
23#24907C211yesmaximal, characteristic, complemented
24#24757C211yesmaximal, characteristic, complemented
25#24718C211yesmaximal, characteristic, complemented
26#24220C211yesmaximal, characteristic, complemented
27#24154C211yesmaximal, characteristic, complemented
28#22755C211yesmaximal, characteristic, complemented
29#21893C211yesmaximal, characteristic, complemented
30#21813C211yesmaximal, characteristic, complemented
31#21515C211yesmaximal, characteristic, complemented
32C2×#535C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#475C2211yescharacteristic, complemented
35C2×#470C2211yescharacteristic, complemented
36C2×#468C2211yescharacteristic
37C2×#464C2211yescharacteristic
38C2×#460C2211yescharacteristic
39C2×#452C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic, complemented
43C2×#433C2211yescharacteristic
44C2×#423C2211yescharacteristic, complemented
45#2850C2211yescharacteristic
46#2688—21no—
47#2686—21no—
48#2684—21no—
49#2668—21no—
50#2640C2211yescharacteristic
51#2628C2211yescharacteristic
52#2596—21no—
53#2588—21no—
54#2570C2211yescharacteristic, complemented
55#2567C2211yescharacteristic, complemented
56#2547C2211yescharacteristic
57#2536C2211yescharacteristic
58#2530—21no—
59#2529—21no—
60#2521—21no—
61#2520—21no—
62#2497C2211yescharacteristic
63#2496C2211yescharacteristic, complemented
64#2478—21no—
65#2474—21no—
66#2447C2211yescharacteristic
67#2445C2211yescharacteristic
68#2444—21no—
69#2430—21no—
70#2428C2211yescharacteristic
71#2427C2211yescharacteristic
72#2423C2211yescharacteristic
73#2421C2211yescharacteristic, complemented
74#2418—21no—
75#2408C2211yescharacteristic
76#2407C2211yescharacteristic
77#2404—21no—
78#2339C2211yescharacteristic
79D4×C22⋊C4C2211yescharacteristic
80#2331C2211yescharacteristic, complemented
81#2328C2211yescharacteristic
82#2323C2211yescharacteristic
83#2314C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic, complemented
85#2290C2211yescharacteristic
86#2285C2211yescharacteristic, complemented
87#2276C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2096C2211yescharacteristic, complemented
91#2093C2211yescharacteristic
92#2092C2211yescharacteristic
93#2092C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2076C2211yescharacteristic
101#2075C2211yescharacteristic
102#2074C2211yescharacteristic, complemented
103#2073C2211yescharacteristic
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2068C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2056C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2042C2211yescharacteristic
111#2041C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic, complemented
114#2036C2211yescharacteristic, complemented
115#2035C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic, complemented
120#2024C2211yescharacteristic, complemented
121#2023C2211yescharacteristic
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2014C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic, complemented
128#1988C2211yescharacteristic, complemented
129#1987C2211yescharacteristic, complemented
130#1987C2211yescharacteristic, complemented
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1982C2211yescharacteristic
135#1982C2211yescharacteristic
136#1982C2211yescharacteristic
137#1961C2211yescharacteristic
138#1959C2211yescharacteristic
139#1958C2211yescharacteristic
140#1957C2211yescharacteristic
141#1949C2211yescharacteristic, complemented
142#1949C2211yescharacteristic, complemented
143#1949C2211yescharacteristic, complemented
144#1943C2211yescharacteristic, complemented
145#1941C2211yescharacteristic, complemented
146#1936C2211yescharacteristic
147#1935C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic, complemented
158#1924C2211yescharacteristic
159#1923C2211yescharacteristic
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1895C2211yescharacteristic
165#1895C2211yescharacteristic, complemented
166#1895C2211yescharacteristic, complemented
167#1894C2211yescharacteristic, complemented
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic, complemented
176#1870C2211yescharacteristic
177#1870C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic, complemented
181#1864C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic, complemented
184#1832C2211yescharacteristic, complemented
185#1805C2211yescharacteristic, complemented
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic
188#1802C2211yescharacteristic, complemented
189#1802C2211yescharacteristic, complemented
190#1798C2211yescharacteristic
191#1797C2211yescharacteristic, complemented
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1768C2211yescharacteristic, complemented
199#1762C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202#1753C2211yescharacteristic, complemented
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212#535—24no—
213#535—42no—
214#532—24no—
215#532—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#126—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#123—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117—21no—
249C2×#117C2311yescharacteristic
250C22×C22⋊C4—21no—
251C22×C42C2311yescharacteristic
252#475—42no—
253#470—42no—
254#468—42no—
255#464—42no—
256#460—24no—
257#452—42no—
258#450—42no—
259#440—42no—
260C4×SD16—42no—
261#433—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270#423—42no—
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
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#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#396—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#392—21no—
353#392—21no—
354#392—21no—
355#391—21no—
356#391—21no—
357#391—21no—
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#389—21no—
369#389—21no—
370#389—21no—
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388D411yescharacteristic
389#388D411yescharacteristic
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387D411yescharacteristic
403#387D411yescharacteristic
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386D411yescharacteristic
419#386D411yescharacteristic
420#385—21no—
421#385—21no—
422#385—21no—
423#385D411yescharacteristic
424#385D411yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#382—21no—
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#381—21no—
433#381—21no—
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460#376—21no—
461#376C2311yescharacteristic
462C2×#95—21no—
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—44no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—82no—
502C2×#41—82no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2×D411yescharacteristic
532C23×C4C2×D411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×Q16—22no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C4⋊Q8—22no—
562C4⋊Q8—22no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565#127—22no—
566#127—22no—
567#127—41no—
568#127#4114yes—
569#126—82no—
570#124—22no—
571#124—22no—
572#124—22no—
573#124—41no—
574#124—44no—
575#124—82no—
576#123—82no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583#121—22no—
584#121—22no—
585#121—41no—
586#121—41no—
587#121—44no—
588#121—44no—
589#121—44no—
590#121—41no—
591#121—41no—
592#121—82no—
593#120—44no—
594#120—44no—
595#120—82no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—44no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613#117—22no—
614#117—22no—
615#117—82no—
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⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×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—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—82no—
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C42—22no—
694C2×C42—22no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710#107—41no—
711#107—41no—
712#107—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718C4⋊C8—22no—
719C4⋊C8—22no—
720C4⋊C8—22no—
721C4⋊C8—22no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724#103—22no—
725#103—22no—
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#102—22no—
736#102—22no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
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—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762#97—41no—
763#97—41no—
764C4×C8—41no—
765C4×C8—41no—
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#95—21no—
799#95—21no—
800#95—21no—
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—21no—
814C24—42no—
815C24—42no—
816C24—81no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823#41—82no—
824#41—82no—
825#41—82no—
826#41—82no—
827#41—816no—
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—42no—
840C2×Q8—42no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8H(5,𝔽2)12yes—
846C2×D4—24no—
847C2×D4—24no—
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—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—82no—
888C2×D4—82no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4C2×#4112yes—
897C2×D4C2×#4112yes—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
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—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
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×C4C2511yescharacteristic
957Q16—82no—
958SD16—44no—
959SD16—44no—
960SD16—82no—
961M16—82no—
962M16—82no—
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×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—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—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—41no—
1013C4⋊C4—41no—
1014C4⋊C4—42no—
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—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C42—22no—
1075C42—22no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42C2×#4112yes—
1093C42H(5,𝔽2)12yes—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—22no—
1104C23—22no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—84no—
1130C23—84no—
1131C23—162no—
1132C23—162no—
1133C23—162no—
1134C23—162no—
1135C23—162no—
1136C23C23×D411yescharacteristic
1137Q8—22no—
1138Q8—22no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—84no—
1146Q8—162no—
1147D4—22no—
1148D4—22no—
1149D4—22no—
1150D4—22no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—84no—
1160D4—84no—
1161D4—82no—
1162D4—84no—
1163D4—84no—
1164D4—84no—
1165D4—84no—
1166D4—162no—
1167D4—162no—
1168D4—162no—
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—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—44no—
1204C2×C4—44no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—84no—
1252C2×C4—84no—
1253C2×C4—84no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4#54612yes—
1257C2×C4#54612yes—
1258C2×C4#57712yes—
1259C2×C4C22×#4111yescharacteristic
1260C2×C4C2×H(5,𝔽2)11yescharacteristic
1261C2×C4C2×H(5,𝔽2)11yescharacteristic
1262C2×C4#58511yescharacteristic
1263C2×C4#58511yescharacteristic
1264C2×C4#58511yescharacteristic
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C22—41no—
1274C22—42no—
1275C22—42no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—42no—
1288C22—42no—
1289C22—41no—
1290C22—42no—
1291C22—42no—
1292C22—41no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—168no—
1309C22#344911yescharacteristic
1310C22C2×#54611yescharacteristic
1311C22#348811yescharacteristic
1312C22C2×#57711yescharacteristic
1313C22#358511yescharacteristic
1314C22#358511yescharacteristic
1315C22#358611yescharacteristic
1316C4—22no—
1317C4—22no—
1318C4—22no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—42no—
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#351311yescharacteristic
1342C4#352111yescharacteristic
1343C4#355811yescharacteristic
1344C4#356211yescharacteristic
1345C2—81no—
1346C2—81no—
1347C2—82no—
1348C2—82no—
1349C2—161no—
1350C2#3890211yescharacteristic
1351C2#6099111yescharacteristic
1352C2#6100311yescharacteristic
1353C2#6117711yescharacteristic
1354C2#6118411yescharacteristic
1355C2#6204511yescharacteristic
1356C2#6209211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37748C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35604C2semidirect
3. #33037C2semidirect
4. #31650C2semidirect
5. #31638C2semidirect
6. #31598C2semidirect
7. #31578C2semidirect
8. #31278C2semidirect
9. #31271C2semidirect
10. #30424C2semidirect
11. #30421C2semidirect
12. #29947C2semidirect
13. #29927C2semidirect
14. #29362C2semidirect
15. #29263C2semidirect
16. #29068C2semidirect
17. #29059C2semidirect
18. #27544C2semidirect
19. #27520C2semidirect
20. #26986C2semidirect
21. #26971C2semidirect
22. #24921C2semidirect
23. #24907C2semidirect
24. #24757C2semidirect
25. #24718C2semidirect
26. #24220C2semidirect
27. #24154C2semidirect
28. #22755C2semidirect
29. #21893C2semidirect
30. #21813C2semidirect
31. #21515C2semidirect
34. C2×#475C22semidirect
35. C2×#470C22semidirect
42. C2×C4×SD16C22semidirect
44. C2×#423C22semidirect
54. #2570C22semidirect
55. #2567C22semidirect
63. #2496C22semidirect
73. #2421C22semidirect
80. #2331C22semidirect
84. C4×C22⋊Q8C22semidirect
86. #2285C22semidirect
87. #2276C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2096C22semidirect
93. #2092C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
102. #2074C22semidirect
104. #2072C22semidirect
106. #2068C22semidirect
108. #2056C22semidirect
113. #2036C22semidirect
114. #2036C22semidirect
119. #2034C22semidirect
120. #2024C22semidirect
123. #2023C22semidirect
127. #2000C22semidirect
128. #1988C22semidirect
129. #1987C22semidirect
130. #1987C22semidirect
141. #1949C22semidirect
142. #1949C22semidirect
143. #1949C22semidirect
144. #1943C22semidirect
145. #1941C22semidirect
147. #1935C22semidirect
148. #1935C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1927C22semidirect
153. #1927C22semidirect
157. #1925C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
165. #1895C22semidirect
166. #1895C22semidirect
167. #1894C22semidirect
171. #1880C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
175. #1877C22semidirect
180. #1864C22semidirect
181. #1864C22semidirect
183. #1862C22semidirect
184. #1832C22semidirect
185. #1805C22semidirect
188. #1802C22semidirect
189. #1802C22semidirect
191. #1797C22semidirect
198. #1768C22semidirect
199. #1762C22semidirect
201. #1753C22semidirect
202. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#377482
#356042
#330372
#316502
#316382
#315982
#315782
#312782
#312712
#304242
#304212
#299472
#299272
#293622
#292632
#290682
#290592
#275442
#275202
#269862
#269712
#249212
#249072
#247572
#247182
#242202
#241542
#227552
#218932
#218132
#215152