Finite Group Databasebeta

← #7049565

Subgroups — #7049565

Order 512.

1427 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45308C211yesmaximal, characteristic, complemented
2#44903C211yesmaximal, characteristic
3#32293C211yesmaximal, characteristic, complemented
4#31833C211yesmaximal, characteristic, complemented
5#31629C211yesmaximal, characteristic, complemented
6#31520C211yesmaximal, characteristic, complemented
7#31377C211yesmaximal, characteristic, complemented
8#31270C211yesmaximal, characteristic
9#31085C211yesmaximal, characteristic, complemented
10#31058C211yesmaximal, characteristic
11#29077C211yesmaximal, characteristic, complemented
12#28130C211yesmaximal, characteristic, complemented
13#28074C211yesmaximal, characteristic, complemented
14#27643C211yesmaximal, characteristic, complemented
15#27510C211yesmaximal, characteristic, complemented
16#27496C211yesmaximal, characteristic, complemented
17#27452C211yesmaximal, characteristic, complemented
18#27239C211yesmaximal, characteristic, complemented
19#27125C211yesmaximal, characteristic, complemented
20#26299C211yesmaximal, characteristic, complemented
21#24917C211yesmaximal, characteristic, complemented
22#24905C211yesmaximal, characteristic, complemented
23#24894C211yesmaximal, characteristic, complemented
24#24892C211yesmaximal, characteristic, complemented
25#24694C211yesmaximal, characteristic, complemented
26#24541C211yesmaximal, characteristic, complemented
27#23769C211yesmaximal, characteristic, complemented
28#22865C211yesmaximal, characteristic, complemented
29#22806C211yesmaximal, characteristic, complemented
30#22366C211yesmaximal, characteristic, complemented
31#22052C211yesmaximal, characteristic, complemented
32C2×#485C2211yescharacteristic
33C2×#477C2211yescharacteristic, complemented
34C2×#448C2211yescharacteristic
35C2×#448C2211yescharacteristic
36C2×#450C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C2×#419C2211yescharacteristic, complemented
41#2789—21no—
42#2759—21no—
43#2759—21no—
44#2752—21no—
45#2742—21no—
46#2735—21no—
47#2730—21no—
48#2685—21no—
49#2612—21no—
50#2563C2211yescharacteristic
51#2561—21no—
52#2560—21no—
53#2542C2211yescharacteristic
54#2531—21no—
55#2531—21no—
56#2523—21no—
57#2516—21no—
58#2513C2211yescharacteristic
59#2512C2211yescharacteristic
60#2500C2211yescharacteristic
61#2494C2211yescharacteristic, complemented
62#2494C2211yescharacteristic, complemented
63#2491C2211yescharacteristic
64#2472—21no—
65#2451C2211yescharacteristic, complemented
66#2451C2211yescharacteristic, complemented
67#2439C2211yescharacteristic
68#2421C2211yescharacteristic
69#2421C2211yescharacteristic
70#2420C2211yescharacteristic
71#2409C2211yescharacteristic
72#2408C2211yescharacteristic
73#2395C2211yescharacteristic
74#2363C2211yescharacteristic
75#2357C2211yescharacteristic
76#2356C2211yescharacteristic, complemented
77#2356C2211yescharacteristic, complemented
78#2354C2211yescharacteristic
79Q8×C22⋊C4C2211yescharacteristic, complemented
80Q8×C22⋊C4C2211yescharacteristic, complemented
81D4×C22⋊C4C2211yescharacteristic
82#2323C2211yescharacteristic
83#2323C2211yescharacteristic
84#2314C2211yescharacteristic
85#2309C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2097C2211yescharacteristic, complemented
89#2096C2211yescharacteristic, complemented
90#2092C2211yescharacteristic
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic, complemented
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic, complemented
103#2074C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2072C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2065C2211yescharacteristic
108#2058C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2036C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic
126#1993C2211yescharacteristic, complemented
127#1990C2211yescharacteristic, complemented
128#1987C2211yescharacteristic, complemented
129#1973C2211yescharacteristic
130#1968C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic
133#1954C2211yescharacteristic
134#1949C2211yescharacteristic, complemented
135#1947C2211yescharacteristic, complemented
136#1947C2211yescharacteristic, complemented
137#1940C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1935C2211yescharacteristic, complemented
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1933C2211yescharacteristic, complemented
144#1928C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1928C2211yescharacteristic, complemented
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic, complemented
156#1923C2211yescharacteristic
157#1923C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1873C2211yescharacteristic
173#1870C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1863C2211yescharacteristic, complemented
177#1862C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic, complemented
180#1854C2211yescharacteristic, complemented
181#1851C2211yescharacteristic, complemented
182#1846C2211yescharacteristic, complemented
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic, complemented
185#1809C2211yescharacteristic, complemented
186#1805C2211yescharacteristic, complemented
187#1805C2211yescharacteristic, complemented
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1803C2211yescharacteristic, complemented
191#1798C2211yescharacteristic
192#1787C2211yescharacteristic, complemented
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196C4×#106C2211yescharacteristic, complemented
197C4×#106C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201#1753C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#124—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#120—21no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C22×C22⋊C4—21no—
232#485—42no—
233#477—42no—
234#450—24no—
235#450—42no—
236#448—24no—
237#448—42no—
238#440—42no—
239C4×SD16—24no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257#419—42no—
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294#401—21no—
295#401—21no—
296#400—21no—
297#400—21no—
298#400D411yescharacteristic
299#399—21no—
300#399—21no—
301#399D411yescharacteristic
302#398—21no—
303#398—21no—
304#398D411yescharacteristic
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397D411yescharacteristic
314#397D411yescharacteristic
315#397D411yescharacteristic
316#396—21no—
317#396—21no—
318#395—21no—
319#395—21no—
320#395—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394D411yescharacteristic
327#394D411yescharacteristic
328#393—21no—
329#393—21no—
330#393—21no—
331#393—21no—
332#393—21no—
333#392—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#390—21no—
348#390—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389—21no—
361#389—21no—
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
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#388—21no—
389#387—21no—
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#387—21no—
403#387—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#385—21no—
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#383—21no—
413#383—21no—
414#382—21no—
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#381—21no—
420#381—21no—
421#380—21no—
422#380—21no—
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#379—21no—
432#379—21no—
433#379—21no—
434#379—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451#376—21no—
452#376—21no—
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—22no—
492C22×Q8—22no—
493C22×Q8—41no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
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#4114yes—
528C2×M16—41no—
529C2×M16—41no—
530C2×M16—41no—
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543#126—82no—
544#124—82no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—41no—
548C22⋊Q8—41no—
549C22⋊Q8—82no—
550C22⋊Q8—82no—
551#121—22no—
552#121—41no—
553#121—41no—
554#121—41no—
555#120—82no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×D4—22no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570#117—41no—
571#117—41no—
572#117—41no—
573#117—41no—
574#117—41no—
575#117—41no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
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—82no—
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673#107—41no—
674#107—41no—
675#107—41no—
676#107—41no—
677#107—41no—
678#107—41no—
679#106—22no—
680#106—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684#106—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689C4⋊C8—41no—
690#103—22no—
691#103—22no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714C22⋊C8—22no—
715C22⋊C8—22no—
716C22⋊C8—41no—
717C22⋊C8—41no—
718C22⋊C8—41no—
719C22⋊C8—41no—
720C22⋊C8—41no—
721#97—41no—
722#97—41no—
723C4×C8—22no—
724C4×C8—41no—
725C4×C8—41no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
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#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776C24—21no—
777C24—21no—
778C24—42no—
779C24—42no—
780C24—81no—
781C24—81no—
782C24—81no—
783C24—81no—
784C24—81no—
785C24C22×D411yescharacteristic
786C24C22×D411yescharacteristic
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—42no—
798C2×Q8—42no—
799C2×Q8—42no—
800C2×Q8—44no—
801C2×Q8—81no—
802C2×Q8—81no—
803C2×Q8—81no—
804C2×Q8—81no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×Q8—82no—
808C2×Q8—82no—
809C2×Q8—82no—
810C2×Q8C2×#4112yes—
811C2×Q8H(5,𝔽2)12yes—
812C2×D4—22no—
813C2×D4—21no—
814C2×D4—21no—
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—41no—
825C2×D4—41no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—81no—
830C2×D4—82no—
831C2×D4—82no—
832C2×D4—82no—
833C2×D4—82no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4C2×#4112yes—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C2511yescharacteristic
888SD16—44no—
889SD16—44no—
890SD16—82no—
891SD16—82no—
892M16—82no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8C2×#4112yes—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—41no—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—41no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—42no—
1019C42—42no—
1020C42—42no—
1021C42—81no—
1022C42—81no—
1023C42—81no—
1024C42—81no—
1025C42—81no—
1026C42—81no—
1027C42—81no—
1028C42—81no—
1029C42—81no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—22no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—84no—
1059C23—84no—
1060C23—162no—
1061C23—162no—
1062C23—162no—
1063C23—162no—
1064C23—162no—
1065C23C23×D411yescharacteristic
1066Q8—22no—
1067Q8—22no—
1068Q8—22no—
1069Q8—22no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—41no—
1074Q8—84no—
1075Q8—162no—
1076Q8—162no—
1077D4—22no—
1078D4—22no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—82no—
1086D4—84no—
1087D4—162no—
1088D4—162no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
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—84no—
1175C2×C4—162no—
1176C2×C4—162no—
1177C2×C4#57712yes—
1178C2×C4C22×#4111yescharacteristic
1179C2×C4C2×H(5,𝔽2)11yescharacteristic
1180C2×C4#58511yescharacteristic
1181C2×C4#58511yescharacteristic
1182C2×C4#58511yescharacteristic
1183C2×C4#58511yescharacteristic
1184C8—22no—
1185C8—41no—
1186C8—41no—
1187C8—41no—
1188C8—41no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C22—41no—
1193C22—41no—
1194C22—42no—
1195C22—41no—
1196C22—42no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—42no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—168no—
1221C22D4×#4111yescharacteristic
1222C22#348511yescharacteristic
1223C22#348811yescharacteristic
1224C22C2×#57711yescharacteristic
1225C22#358411yescharacteristic
1226C22#358511yescharacteristic
1227C22#358611yescharacteristic
1228C4—22no—
1229C4—41no—
1230C4—41no—
1231C4—42no—
1232C4—42no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4#349111yescharacteristic
1255C4#351311yescharacteristic
1256C4#354511yescharacteristic
1257C4#356811yescharacteristic
1258C2—81no—
1259C2—81no—
1260C2—82no—
1261C2—161no—
1262C2#4354111yescharacteristic
1263C2#6147411yescharacteristic
1264C2#6151311yescharacteristic
1265C2#6175311yescharacteristic
1266C2#6180411yescharacteristic
1267C2#6202911yescharacteristic
1268C2#6203511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45308C2semidirect
3. #32293C2semidirect
4. #31833C2semidirect
5. #31629C2semidirect
6. #31520C2semidirect
7. #31377C2semidirect
9. #31085C2semidirect
11. #29077C2semidirect
12. #28130C2semidirect
13. #28074C2semidirect
14. #27643C2semidirect
15. #27510C2semidirect
16. #27496C2semidirect
17. #27452C2semidirect
18. #27239C2semidirect
19. #27125C2semidirect
20. #26299C2semidirect
21. #24917C2semidirect
22. #24905C2semidirect
23. #24894C2semidirect
24. #24892C2semidirect
25. #24694C2semidirect
26. #24541C2semidirect
27. #23769C2semidirect
28. #22865C2semidirect
29. #22806C2semidirect
30. #22366C2semidirect
31. #22052C2semidirect
33. C2×#477C22semidirect
40. C2×#419C22semidirect
61. #2494C22semidirect
62. #2494C22semidirect
65. #2451C22semidirect
66. #2451C22semidirect
76. #2356C22semidirect
77. #2356C22semidirect
79. Q8×C22⋊C4C22semidirect
80. Q8×C22⋊C4C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2097C22semidirect
89. #2096C22semidirect
92. #2088C22semidirect
93. #2086C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
96. #2084C22semidirect
98. #2077C22semidirect
102. #2075C22semidirect
103. #2074C22semidirect
104. #2072C22semidirect
105. #2072C22semidirect
108. #2058C22semidirect
123. #2024C22semidirect
126. #1993C22semidirect
127. #1990C22semidirect
128. #1987C22semidirect
134. #1949C22semidirect
135. #1947C22semidirect
136. #1947C22semidirect
137. #1940C22semidirect
140. #1935C22semidirect
143. #1933C22semidirect
144. #1928C22semidirect
145. #1928C22semidirect
146. #1928C22semidirect
147. #1928C22semidirect
155. #1924C22semidirect
157. #1923C22semidirect
158. #1920C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
174. #1865C22semidirect
176. #1863C22semidirect
179. #1854C22semidirect
180. #1854C22semidirect
181. #1851C22semidirect
182. #1846C22semidirect
184. #1825C22semidirect
185. #1809C22semidirect
186. #1805C22semidirect
187. #1805C22semidirect
190. #1803C22semidirect
192. #1787C22semidirect
195. #1776C22semidirect
196. C4×#106C22semidirect
197. C4×#106C22semidirect
198. C8×C4⋊C4C22semidirect
199. #1763C22semidirect
200. C4×#103C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#453082
#449032
#322932
#318332
#316292
#315202
#313772
#312702
#310852
#310582
#290772
#281302
#280742
#276432
#275102
#274962
#274522
#272392
#271252
#262992
#249172
#249052
#248942
#248922
#246942
#245412
#237692
#228652
#228062
#223662
#220522