Finite Group Databasebeta

← #6940665

Subgroups — #6940665

Order 512.

1624 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36280C211yesmaximal, characteristic, complemented
2#36264C211yesmaximal, characteristic
3#32860C211yesmaximal, characteristic, complemented
4#32819C211yesmaximal, characteristic, complemented
5#32525C211yesmaximal, characteristic, complemented
6#32474C211yesmaximal, characteristic, complemented
7#31966C211yesmaximal, characteristic, complemented
8#31966C211yesmaximal, characteristic, complemented
9#31902C211yesmaximal, characteristic, complemented
10#31870C211yesmaximal, characteristic, complemented
11#31240C211yesmaximal, characteristic, complemented
12#31156C211yesmaximal, characteristic, complemented
13#30149C211yesmaximal, characteristic, complemented
14#30127C211yesmaximal, characteristic, complemented
15#29998C211yesmaximal, characteristic, complemented
16#29826C211yesmaximal, characteristic, complemented
17#29774C211yesmaximal, characteristic, complemented
18#29534C211yesmaximal, characteristic, complemented
19#28280C211yesmaximal, characteristic, complemented
20#26340C211yesmaximal, characteristic, complemented
21#26338C211yesmaximal, characteristic, complemented
22#25992C211yesmaximal, characteristic, complemented
23#25958C211yesmaximal, characteristic, complemented
24#25202C211yesmaximal, characteristic, complemented
25#25080C211yesmaximal, characteristic
26#24603C211yesmaximal, characteristic, complemented
27#24530C211yesmaximal, characteristic, complemented
28#24501C211yesmaximal, characteristic, complemented
29#24478C211yesmaximal, characteristic
30C2×#2065C211yesmaximal, characteristic, complemented
31#21972C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#481C2211yescharacteristic
34C2×#475C2211yescharacteristic, complemented
35C2×#476C2211yescharacteristic
36C2×#476C2211yescharacteristic, complemented
37C2×#465C2211yescharacteristic
38C2×#460C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#431C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×C4⋊C8C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2863C2211yescharacteristic, complemented
46#2860C2211yescharacteristic
47#2859C2211yescharacteristic, complemented
48#2858C2211yescharacteristic
49#2855C2211yescharacteristic
50#2854C2211yescharacteristic
51#2612—21no—
52#2610—21no—
53#2606—21no—
54#2603—21no—
55#2585—21no—
56#2554—21no—
57#2512C2211yescharacteristic
58#2511C2211yescharacteristic, complemented
59#2507C2211yescharacteristic, complemented
60#2507C2211yescharacteristic, complemented
61#2502C2211yescharacteristic
62#2473—21no—
63#2472—21no—
64#2462—21no—
65#2461—21no—
66#2452C2211yescharacteristic
67#2451C2211yescharacteristic, complemented
68#2445C2211yescharacteristic
69#2445C2211yescharacteristic
70#2440C2211yescharacteristic
71#2440C2211yescharacteristic
72#2438—21no—
73#2433C2211yescharacteristic
74#2411—21no—
75#2361C2211yescharacteristic
76#2360—21no—
77#2360C2211yescharacteristic
78#2358—21no—
79#2345C2211yescharacteristic
80#2343—21no—
81D4×C22⋊C4C2211yescharacteristic
82C4×C4⋊Q8C2211yescharacteristic, complemented
83C4×#127C2211yescharacteristic
84#2295C2211yescharacteristic, complemented
85#2293C2211yescharacteristic
86C2×#390C2211yescharacteristic
87C2×#389C2211yescharacteristic
88C4×#117C2211yescharacteristic
89#2099C2211yescharacteristic, complemented
90#2096C2211yescharacteristic, complemented
91#2094C2211yescharacteristic
92#2094C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2088C2211yescharacteristic, complemented
99#2088C2211yescharacteristic, complemented
100#2088C2211yescharacteristic, complemented
101#2084C2211yescharacteristic, complemented
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2065C2211yescharacteristic
122#2065C2211yescharacteristic
123#2065C2211yescharacteristic
124#2065C2211yescharacteristic, complemented
125#2065C2211yescharacteristic, complemented
126#2065C2211yescharacteristic, complemented
127#2065C2211yescharacteristic, complemented
128#2065C2211yescharacteristic, complemented
129#2058C2211yescharacteristic, complemented
130#2058C2211yescharacteristic, complemented
131#2058C2211yescharacteristic, complemented
132#2055C2211yescharacteristic
133#2055C2211yescharacteristic
134#2055C2211yescharacteristic
135#2055C2211yescharacteristic
136#2055C2211yescharacteristic
137#2055C2211yescharacteristic, complemented
138#2055C2211yescharacteristic, complemented
139#2055C2211yescharacteristic, complemented
140#2041C2211yescharacteristic
141#2041C2211yescharacteristic
142#2041C2211yescharacteristic
143#2023C2211yescharacteristic
144#2014C2211yescharacteristic
145#1988C2211yescharacteristic, complemented
146#1982C2211yescharacteristic
147#1982C2211yescharacteristic
148#1982C2211yescharacteristic
149#1968C2211yescharacteristic
150#1968C2211yescharacteristic
151#1948C2211yescharacteristic, complemented
152#1948C2211yescharacteristic, complemented
153#1948C2211yescharacteristic, complemented
154#1948C2211yescharacteristic, complemented
155#1941C2211yescharacteristic, complemented
156#1941C2211yescharacteristic, complemented
157#1939C2211yescharacteristic, complemented
158#1939C2211yescharacteristic, complemented
159#1939C2211yescharacteristic, complemented
160#1939C2211yescharacteristic, complemented
161#1934C2211yescharacteristic
162#1934C2211yescharacteristic
163#1934C2211yescharacteristic, complemented
164#1934C2211yescharacteristic, complemented
165#1927C2211yescharacteristic, complemented
166#1926C2211yescharacteristic
167#1926C2211yescharacteristic
168#1926C2211yescharacteristic
169#1920C2211yescharacteristic, complemented
170#1919C2211yescharacteristic, complemented
171#1919C2211yescharacteristic, complemented
172#1919C2211yescharacteristic, complemented
173#1893C2211yescharacteristic
174#1892C2211yescharacteristic
175#1880C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic, complemented
179#1874C2211yescharacteristic
180#1872C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1864C2211yescharacteristic, complemented
185#1853C2211yescharacteristic
186#1853C2211yescharacteristic
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic
189#1850C2211yescharacteristic
190#1850C2211yescharacteristic
191#1842C2211yescharacteristic, complemented
192#1842C2211yescharacteristic, complemented
193#1831C2211yescharacteristic, complemented
194#1831C2211yescharacteristic, complemented
195#1824C2211yescharacteristic
196#1807C2211yescharacteristic
197#1802C2211yescharacteristic
198#1802C2211yescharacteristic
199#1802C2211yescharacteristic
200#1802C2211yescharacteristic, complemented
201#1786C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#551—48no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#125—21no—
217C2×#124—21no—
218C2×#124—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C2×#120—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117—21no—
238C2×#117D411yescharacteristic
239C2×#117D411yescharacteristic
240C22×C4⋊C4—21no—
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247C22×C42C2311yescharacteristic
248#481—42no—
249#476—42no—
250#476—42no—
251#475—42no—
252#465—42no—
253#460—42no—
254#450—42no—
255#431—42no—
256C2×#106—42no—
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8—42no—
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#102—42no—
291C2×#102—42no—
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×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#400—21no—
318#400—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#396—21no—
330#396—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#393—21no—
339#392—21no—
340#392—21no—
341#391—21no—
342#391—21no—
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#390—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—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#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#383—21no—
432#382—21no—
433#381—21no—
434#380—21no—
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#379—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4D411yescharacteristic
441C4×C4⋊C4D411yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4D411yescharacteristic
452C4×C22⋊C4D411yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455#376—21no—
456#376D411yescharacteristic
457#376D411yescharacteristic
458C2×#95—21no—
459C43C2311yescharacteristic
460C43C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C25—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8C2411yescharacteristic
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2411yescharacteristic
519C2×SD16—22no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C22×C8—22no—
529C22×C8—22no—
530C22×C8—41no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C4⋊Q8—22no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546#127—22no—
547#127—41no—
548#127—41no—
549#127—41no—
550#126—44no—
551#126—44no—
552#125—82no—
553#124—44no—
554#124—82no—
555#123—44no—
556#123—44no—
557#123—44no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—44no—
561C22⋊Q8—44no—
562C22⋊Q8—44no—
563#121—22no—
564#121—22no—
565#120—44no—
566#120—44no—
567C4×Q8—22no—
568C4×Q8—41no—
569C4×Q8—82no—
570C4×D4—22no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—44no—
577C4×D4—44no—
578C4×D4—82no—
579#117—42no—
580#117—44no—
581#117SD1618yescomplemented
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
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—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—82no—
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—44no—
666C2×C22⋊C4—44no—
667C2×C22⋊C4—82no—
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C42—22no—
673C2×C42—22no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#106—22no—
696#106—22no—
697#106—22no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
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—
748C22⋊C8—22no—
749C22⋊C8—22no—
750C4×C8—41no—
751C4×C8—41no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
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#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792C24—21no—
793C24—21no—
794C24—21no—
795C24—42no—
796C24—42no—
797C24—42no—
798C24—42no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24C22×D411yescharacteristic
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—42no—
810C2×Q8—42no—
811C2×Q8—42no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—81no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—82no—
846C2×D4—82no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D42−1+412yes—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—22no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4C2×SD1614yes—
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4H(5,𝔽2)12yes—
910C22×C42−1+412yes—
911C22×C4C2511yescharacteristic
912SD16—82no—
913SD16—82no—
914SD16—82no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
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—44no—
940C2×C8—82no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
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—41no—
965C4⋊C4—41no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4C2×SD1614yes—
998C4⋊C4C2×SD1614yes—
999C4⋊C4H(5,𝔽2)12yes—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
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⋊C4C2×SD1614yes—
1032C22⋊C4C2×SD1614yes—
1033C42—22no—
1034C42—22no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—41no—
1048C42—41no—
1049C42—41no—
1050C42—41no—
1051C42—41no—
1052C42—41no—
1053C42—42no—
1054C42—42no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42C2×SD1614yes—
1059C42C2×SD1614yes—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—22no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
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—41no—
1085C23—84no—
1086C23—84no—
1087C23—84no—
1088C23—84no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23#53712yes—
1093C23C22×SD1612yes—
1094C23#57512yes—
1095C23C23×D411yescharacteristic
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—84no—
1101Q8—162no—
1102D4—22no—
1103D4—22no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—84no—
1115D4—84no—
1116D4—84no—
1117D4—84no—
1118D4—162no—
1119D4—162no—
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—28no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
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—84no—
1197C2×C4—82no—
1198C2×C4—84no—
1199C2×C4—162no—
1200C2×C4—162no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4#53712yes—
1204C2×C4C22×SD1612yes—
1205C2×C4C22×SD1612yes—
1206C2×C4C22×SD1612yes—
1207C2×C4C22×SD1612yes—
1208C2×C4C22×SD1612yes—
1209C2×C4C22×SD1612yes—
1210C2×C4C2×H(5,𝔽2)11yescharacteristic
1211C2×C4C2×H(5,𝔽2)11yescharacteristic
1212C2×C4C2×2−1+411yescharacteristic
1213C2×C4C2×2−1+411yescharacteristic
1214C2×C4#58511yescharacteristic
1215C2×C4#58511yescharacteristic
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—22no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—168no—
1252C22#324614yes—
1253C22C2×#53711yescharacteristic
1254C22#348811yescharacteristic
1255C22#348911yescharacteristic
1256C22C23×SD1611yescharacteristic
1257C22C2×#57511yescharacteristic
1258C22#358511yescharacteristic
1259C22#358511yescharacteristic
1260C4—22no—
1261C4—22no—
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—42no—
1272C4—41no—
1273C4—41no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4#353511yescharacteristic
1287C4#353811yescharacteristic
1288C4#354211yescharacteristic
1289C4#356411yescharacteristic
1290C2—24no—
1291C2—82no—
1292C2—161no—
1293C2—161no—
1294C2#4198411yescharacteristic
1295C2C2×#324611yescharacteristic
1296C2#6093711yescharacteristic
1297C2#6195111yescharacteristic
1298C2#6197111yescharacteristic
1299C2#6209611yescharacteristic
1300C2#6211911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36280C2semidirect
3. #32860C2semidirect
4. #32819C2semidirect
5. #32525C2semidirect
6. #32474C2semidirect
7. #31966C2semidirect
8. #31966C2semidirect
9. #31902C2semidirect
10. #31870C2semidirect
11. #31240C2semidirect
12. #31156C2semidirect
13. #30149C2semidirect
14. #30127C2semidirect
15. #29998C2semidirect
16. #29826C2semidirect
17. #29774C2semidirect
18. #29534C2semidirect
19. #28280C2semidirect
20. #26340C2semidirect
21. #26338C2semidirect
22. #25992C2semidirect
23. #25958C2semidirect
24. #25202C2semidirect
26. #24603C2semidirect
27. #24530C2semidirect
28. #24501C2semidirect
30. C2×#2065C2semidirect
31. #21972C2semidirect
34. C2×#475C22semidirect
36. C2×#476C22semidirect
45. #2863C22semidirect
47. #2859C22semidirect
58. #2511C22semidirect
59. #2507C22semidirect
60. #2507C22semidirect
67. #2451C22semidirect
82. C4×C4⋊Q8C22semidirect
84. #2295C22semidirect
89. #2099C22semidirect
90. #2096C22semidirect
92. #2094C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2088C22semidirect
98. #2088C22semidirect
99. #2088C22semidirect
100. #2088C22semidirect
101. #2084C22semidirect
104. #2071C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
124. #2065C22semidirect
125. #2065C22semidirect
126. #2065C22semidirect
127. #2065C22semidirect
128. #2065C22semidirect
129. #2058C22semidirect
130. #2058C22semidirect
131. #2058C22semidirect
137. #2055C22semidirect
138. #2055C22semidirect
139. #2055C22semidirect
145. #1988C22semidirect
151. #1948C22semidirect
152. #1948C22semidirect
153. #1948C22semidirect
154. #1948C22semidirect
155. #1941C22semidirect
156. #1941C22semidirect
157. #1939C22semidirect
158. #1939C22semidirect
159. #1939C22semidirect
160. #1939C22semidirect
163. #1934C22semidirect
164. #1934C22semidirect
165. #1927C22semidirect
169. #1920C22semidirect
170. #1919C22semidirect
171. #1919C22semidirect
172. #1919C22semidirect
178. #1877C22semidirect
181. #1865C22semidirect
184. #1864C22semidirect
191. #1842C22semidirect
192. #1842C22semidirect
193. #1831C22semidirect
194. #1831C22semidirect
200. #1802C22semidirect
581. #117SD16semidirect

Maximal subgroups

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

subgroupindex
#362802
#362642
#328602
#328192
#325252
#324742
#319662
#319022
#318702
#312402
#311562
#301492
#301272
#299982
#298262
#297742
#295342
#282802
#263402
#263382
#259922
#259582
#252022
#250802
#246032
#245302
#245012
#244782
C2×#20652
#219722