Finite Group Databasebeta

← #6911933

Subgroups — #6911933

Order 512.

1512 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36207C211yesmaximal, characteristic
2#36130C211yesmaximal, characteristic
3#32725C211yesmaximal, characteristic, complemented
4#32711C211yesmaximal, characteristic
5#32065C211yesmaximal, characteristic, complemented
6#31856C211yesmaximal, characteristic, complemented
7#31452C211yesmaximal, characteristic, complemented
8#31316C211yesmaximal, characteristic, complemented
9#30803C211yesmaximal, characteristic, complemented
10#30790C211yesmaximal, characteristic, complemented
11#30650C211yesmaximal, characteristic, complemented
12#30550C211yesmaximal, characteristic, complemented
13#30361C211yesmaximal, characteristic, complemented
14#30013C211yesmaximal, characteristic, complemented
15#29923C211yesmaximal, characteristic, complemented
16#29897C211yesmaximal, characteristic
17#29597C211yesmaximal, characteristic
18#29478C211yesmaximal, characteristic, complemented
19#27630C211yesmaximal, characteristic, complemented
20#27522C211yesmaximal, characteristic, complemented
21#27405C211yesmaximal, characteristic, complemented
22#27173C211yesmaximal, characteristic, complemented
23#27034C211yesmaximal, characteristic, complemented
24#26622C211yesmaximal, characteristic, complemented
25#26560C211yesmaximal, characteristic, complemented
26#26559C211yesmaximal, characteristic, complemented
27#25677C211yesmaximal, characteristic, complemented
28#24906C211yesmaximal, characteristic, complemented
29#24010C211yesmaximal, characteristic
30#23571C211yesmaximal, characteristic, complemented
31#21904C211yesmaximal, characteristic
32C2×#533C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#491C2211yescharacteristic, complemented
36C2×#484C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#451C2211yescharacteristic
40C2×C4×Q16C2211yescharacteristic, complemented
41C2×C4×Q16C2211yescharacteristic, complemented
42#2857C2211yescharacteristic
43#2855C2211yescharacteristic
44#2855C2211yescharacteristic
45#2851C2211yescharacteristic
46#2848C2211yescharacteristic
47#2848C2211yescharacteristic
48#2575—21no—
49#2556—21no—
50#2549—21no—
51#2517—21no—
52#2515—21no—
53#2505—21no—
54#2499C2211yescharacteristic
55#2496C2211yescharacteristic
56#2495C2211yescharacteristic
57#2492C2211yescharacteristic
58#2489C2211yescharacteristic
59#2482—21no—
60#2480—21no—
61#2473—21no—
62#2465—21no—
63#2441C2211yescharacteristic
64#2440C2211yescharacteristic
65#2438—21no—
66#2437—21no—
67#2434C2211yescharacteristic
68#2429C2211yescharacteristic
69#2429C2211yescharacteristic
70#2423C2211yescharacteristic
71#2423C2211yescharacteristic
72#2373—21no—
73#2362C2211yescharacteristic
74#2360—21no—
75#2360C2211yescharacteristic
76#2346C2211yescharacteristic
77#2343—21no—
78#2342—21no—
79Q8×C22⋊C4C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic
81C4×C22⋊Q8C2211yescharacteristic
82#2285C2211yescharacteristic
83#2280C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2099C2211yescharacteristic, complemented
87#2097C2211yescharacteristic, complemented
88#2096C2211yescharacteristic, complemented
89#2095C2211yescharacteristic, complemented
90#2095C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2076C2211yescharacteristic
97#2075C2211yescharacteristic
98#2075C2211yescharacteristic
99#2072C2211yescharacteristic, complemented
100#2072C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2066C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2057C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2056C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2043C2211yescharacteristic, complemented
111#2043C2211yescharacteristic, complemented
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic
126#2035C2211yescharacteristic
127#2035C2211yescharacteristic
128#2035C2211yescharacteristic
129#2035C2211yescharacteristic
130#2026C2211yescharacteristic, complemented
131#2024C2211yescharacteristic, complemented
132#2016C2211yescharacteristic, complemented
133#2016C2211yescharacteristic, complemented
134#2001C2211yescharacteristic
135#2001C2211yescharacteristic
136#2001C2211yescharacteristic
137#2001C2211yescharacteristic
138#2001C2211yescharacteristic
139#2001C2211yescharacteristic
140#2001C2211yescharacteristic
141#1993C2211yescharacteristic, complemented
142#1981C2211yescharacteristic, complemented
143#1981C2211yescharacteristic, complemented
144#1971C2211yescharacteristic, complemented
145#1960C2211yescharacteristic, complemented
146#1948C2211yescharacteristic, complemented
147#1947C2211yescharacteristic, complemented
148#1947C2211yescharacteristic, complemented
149#1947C2211yescharacteristic, complemented
150#1944C2211yescharacteristic, complemented
151#1942C2211yescharacteristic, complemented
152#1941C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1935C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1928C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1927C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1924C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1924C2211yescharacteristic
165#1923C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1923C2211yescharacteristic
169#1920C2211yescharacteristic, complemented
170#1919C2211yescharacteristic, complemented
171#1918C2211yescharacteristic, complemented
172#1918C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1873C2211yescharacteristic
176#1873C2211yescharacteristic
177#1873C2211yescharacteristic
178#1873C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1865C2211yescharacteristic, complemented
181#1865C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1863C2211yescharacteristic, complemented
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic
187#1853C2211yescharacteristic
188#1852C2211yescharacteristic
189#1824C2211yescharacteristic
190#1803C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1797C2211yescharacteristic
193#1797C2211yescharacteristic
194#1787C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197#1779C2211yescharacteristic
198#1779C2211yescharacteristic
199C4×#103C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201#1749C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208#533—42no—
209#533—42no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126—21no—
214C2×#125—21no—
215C2×#125C2311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—42no—
221C2×C22⋊Q8—42no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C4×Q8—21no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×#117—21no—
238C2×#117—21no—
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C22×C4⋊C4—21no—
242C22×C4⋊C4C2311yescharacteristic
243C22×C22⋊C4—21no—
244C22×C22⋊C4D411yescharacteristic
245C22×C22⋊C4D411yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248#501—42no—
249#491—42no—
250#485—42no—
251#485—42no—
252#484—42no—
253#451—42no—
254C4×Q16—42no—
255C4×Q16—42no—
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#399—21no—
320#399—21no—
321#399—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#395—21no—
336#395—21no—
337#395—21no—
338#393—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#383—21no—
411#382—21no—
412#382—21no—
413#382—21no—
414#382C2311yescharacteristic
415#381—21no—
416#381—21no—
417#381—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#379—21no—
433#379—21no—
434#379—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4D411yescharacteristic
450C4×C22⋊C4D411yescharacteristic
451C4×C22⋊C4D411yescharacteristic
452C4×C22⋊C4D411yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457#376—21no—
458C2×#95D411yescharacteristic
459C2×#95D411yescharacteristic
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25C2×D411yescharacteristic
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—22no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8—41no—
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—41no—
506C23×C4—41no—
507C23×C4—41no—
508C23×C4—41no—
509C23×C4—41no—
510C23×C4—41no—
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C2×Q16—22no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×Q16—41no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16—41no—
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544#126—44no—
545#125—41no—
546#125—41no—
547#125—44no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—44no—
553C22⋊Q8—44no—
554C22⋊Q8—44no—
555C22⋊Q8—41no—
556C22⋊Q8—41no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—44no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×Q8—44no—
581#117—44no—
582#117—41no—
583#117—41no—
584#117—44no—
585#117—41no—
586#117—41no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—22no—
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—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—41no—
625C2×C4⋊C4—44no—
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×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—24no—
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—42no—
662C2×C22⋊C4—44no—
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—41no—
682C2×C42—41no—
683C2×C42—41no—
684C2×C42—41no—
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693#107—22no—
694#107—22no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#106—22no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710#103—22no—
711#103—22no—
712#103—22no—
713#103—22no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748#97—41no—
749#97—41no—
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#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800C24—22no—
801C24—22no—
802C24—41no—
803C24—41no—
804C24—41no—
805C24—41no—
806C24—41no—
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809C24C22×D411yescharacteristic
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—42no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—82no—
840C2×Q8—82no—
841C2×Q8—82no—
842C2×Q8—82no—
843C2×Q8H(5,𝔽2)12yes—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—22no—
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—21no—
867C22×C4—21no—
868C22×C4—22no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—82no—
904C22×C4—82no—
905C22×C4—82no—
906C22×C4—82no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C2511yescharacteristic
921Q16—44no—
922Q16—44no—
923Q16—82no—
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—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C4⋊C4—24no—
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—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
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—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4H(5,𝔽2)12yes—
1008C22⋊C4—24no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4#13714yes—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—41no—
1047C42—41no—
1048C42—41no—
1049C42—41no—
1050C42—42no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—42no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—44no—
1080C23—44no—
1081C23—82no—
1082C23—82no—
1083C23—82no—
1084C23—82no—
1085C23—82no—
1086C23C2×#13712yes—
1087C23#57812yes—
1088C23C23×D411yescharacteristic
1089Q8—22no—
1090Q8—22no—
1091Q8—41no—
1092Q8—41no—
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—84no—
1106Q8—84no—
1107C2×C4—21no—
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—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—44no—
1140C2×C4—44no—
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—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—82no—
1200C2×C4—82no—
1201C2×C4—82no—
1202C2×C4—82no—
1203C2×C4—82no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4C2×#13712yes—
1207C2×C4C2×#13712yes—
1208C2×C4#57512yes—
1209C2×C4C2×H(5,𝔽2)11yescharacteristic
1210C2×C4C2×H(5,𝔽2)11yescharacteristic
1211C2×C4#58511yescharacteristic
1212C2×C4#58511yescharacteristic
1213C2×C4#58511yescharacteristic
1214C2×C4#58511yescharacteristic
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—88no—
1245C22#344911yescharacteristic
1246C22#348411yescharacteristic
1247C22#348511yescharacteristic
1248C22C22×#13711yescharacteristic
1249C22C2×#57511yescharacteristic
1250C22C2×#57811yescharacteristic
1251C22#358411yescharacteristic
1252C4—22no—
1253C4—22no—
1254C4—22no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—42no—
1261C4—41no—
1262C4—41no—
1263C4—42no—
1264C4—41no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4#353311yescharacteristic
1280C4#354011yescharacteristic
1281C4#356011yescharacteristic
1282C4#356211yescharacteristic
1283C2—42no—
1284C2—42no—
1285C2—81no—
1286C2#4059611yescharacteristic
1287C2#6095211yescharacteristic
1288C2#6100211yescharacteristic
1289C2#6159911yescharacteristic
1290C2#6160211yescharacteristic
1291C2#6173811yescharacteristic
1292C2#6174211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32725C2semidirect
5. #32065C2semidirect
6. #31856C2semidirect
7. #31452C2semidirect
8. #31316C2semidirect
9. #30803C2semidirect
10. #30790C2semidirect
11. #30650C2semidirect
12. #30550C2semidirect
13. #30361C2semidirect
14. #30013C2semidirect
15. #29923C2semidirect
18. #29478C2semidirect
19. #27630C2semidirect
20. #27522C2semidirect
21. #27405C2semidirect
22. #27173C2semidirect
23. #27034C2semidirect
24. #26622C2semidirect
25. #26560C2semidirect
26. #26559C2semidirect
27. #25677C2semidirect
28. #24906C2semidirect
30. #23571C2semidirect
34. C2×#501C22semidirect
35. C2×#491C22semidirect
40. C2×C4×Q16C22semidirect
41. C2×C4×Q16C22semidirect
85. #2101C22semidirect
86. #2099C22semidirect
87. #2097C22semidirect
88. #2096C22semidirect
89. #2095C22semidirect
90. #2095C22semidirect
91. #2088C22semidirect
99. #2072C22semidirect
100. #2072C22semidirect
101. #2068C22semidirect
102. #2066C22semidirect
103. #2066C22semidirect
104. #2066C22semidirect
105. #2059C22semidirect
106. #2057C22semidirect
107. #2056C22semidirect
108. #2056C22semidirect
109. #2056C22semidirect
110. #2043C22semidirect
111. #2043C22semidirect
130. #2026C22semidirect
131. #2024C22semidirect
132. #2016C22semidirect
133. #2016C22semidirect
141. #1993C22semidirect
142. #1981C22semidirect
143. #1981C22semidirect
144. #1971C22semidirect
145. #1960C22semidirect
146. #1948C22semidirect
147. #1947C22semidirect
148. #1947C22semidirect
149. #1947C22semidirect
150. #1944C22semidirect
151. #1942C22semidirect
152. #1941C22semidirect
153. #1935C22semidirect
154. #1935C22semidirect
155. #1933C22semidirect
156. #1933C22semidirect
157. #1928C22semidirect
158. #1927C22semidirect
159. #1927C22semidirect
160. #1927C22semidirect
169. #1920C22semidirect
170. #1919C22semidirect
171. #1918C22semidirect
172. #1918C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
179. #1865C22semidirect
180. #1865C22semidirect
181. #1865C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
184. #1863C22semidirect
190. #1803C22semidirect
191. #1803C22semidirect
199. C4×#103C22semidirect
200. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#362072
#361302
#327252
#327112
#320652
#318562
#314522
#313162
#308032
#307902
#306502
#305502
#303612
#300132
#299232
#298972
#295972
#294782
#276302
#275222
#274052
#271732
#270342
#266222
#265602
#265592
#256772
#249062
#240102
#235712
#219042