Finite Group Databasebeta

← #6454994

Subgroups — #6454994

Order 512.

1504 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35213C211yesmaximal, characteristic, complemented
2#34197C211yesmaximal, characteristic
3#26116C211yesmaximal, characteristic, complemented
4#26114C211yesmaximal, characteristic, complemented
5#26096C211yesmaximal, characteristic, complemented
6#26094C211yesmaximal, characteristic, complemented
7#26050C211yesmaximal, characteristic, complemented
8#26048C211yesmaximal, characteristic, complemented
9#26030C211yesmaximal, characteristic, complemented
10#26028C211yesmaximal, characteristic, complemented
11#26003C211yesmaximal, characteristic, complemented
12#26001C211yesmaximal, characteristic, complemented
13#25995C211yesmaximal, characteristic, complemented
14#25993C211yesmaximal, characteristic, complemented
15#25961C211yesmaximal, characteristic
16#25959C211yesmaximal, characteristic
17#25953C211yesmaximal, characteristic
18#25951C211yesmaximal, characteristic
19#23791C211yesmaximal, characteristic, complemented
20#23790C211yesmaximal, characteristic, complemented
21#23787C211yesmaximal, characteristic, complemented
22#23786C211yesmaximal, characteristic, complemented
23#21626C211yesmaximal, characteristic, complemented
24#21625C211yesmaximal, characteristic, complemented
25#21622C211yesmaximal, characteristic, complemented
26#21621C211yesmaximal, characteristic, complemented
27#21366C211yesmaximal, characteristic, complemented
28#21351C211yesmaximal, characteristic, complemented
29#20818C211yesmaximal, characteristic, complemented
30#20742C211yesmaximal, characteristic
31C4×#416C211yesmaximal, characteristic
32C2×C4×#41C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#477C2211yescharacteristic
36C2×#475C2211yescharacteristic
37C2×#432C2211yescharacteristic
38C2×#416C2211yescharacteristic
39C2×#416C2211yescharacteristic
40C22×C4×C8C2211yescharacteristic
41#2863—21no—
42#2863—21no—
43#2667—21no—
44#2665—21no—
45#2612—21no—
46#2612—21no—
47#2608—21no—
48#2607—21no—
49#2570C2211yescharacteristic
50#2570C2211yescharacteristic
51#2550C2211yescharacteristic
52#2550C2211yescharacteristic
53#2441C2211yescharacteristic
54#2441C2211yescharacteristic
55#2439C2211yescharacteristic
56#2439C2211yescharacteristic
57#2357—21no—
58#2357—21no—
59#2357C2211yescharacteristic
60#2357C2211yescharacteristic
61#2351C2211yescharacteristic
62#2351C2211yescharacteristic
63#2346—21no—
64#2346—21no—
65#2346C2211yescharacteristic
66#2346C2211yescharacteristic
67#2341C2211yescharacteristic
68#2341C2211yescharacteristic
69#2331C2211yescharacteristic
70#2331C2211yescharacteristic
71#2330C2211yescharacteristic
72#2330C2211yescharacteristic
73#2319—21no—
74#2319—21no—
75#2319C2211yescharacteristic
76#2319C2211yescharacteristic
77#2283—21no—
78#2283—21no—
79#2283C2211yescharacteristic
80#2283C2211yescharacteristic
81#2283C2211yescharacteristic
82#2276C2211yescharacteristic
83#2276C2211yescharacteristic
84C4×#117C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2094C2211yescharacteristic
90#2093C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2087C2211yescharacteristic
98#2087C2211yescharacteristic
99#2086C2211yescharacteristic
100#2086C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2058C2211yescharacteristic
112#2057C2211yescharacteristic
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1988C2211yescharacteristic
120#1987C2211yescharacteristic
121#1949C2211yescharacteristic
122#1949C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1948C2211yescharacteristic
128#1947C2211yescharacteristic
129#1939C2211yescharacteristic
130#1939C2211yescharacteristic
131#1939C2211yescharacteristic
132#1939C2211yescharacteristic
133#1921C2211yescharacteristic
134#1921C2211yescharacteristic
135#1920C2211yescharacteristic
136#1920C2211yescharacteristic
137#1919C2211yescharacteristic
138#1919C2211yescharacteristic
139#1918C2211yescharacteristic
140#1918C2211yescharacteristic
141#1865C2211yescharacteristic
142#1865C2211yescharacteristic
143#1865C2211yescharacteristic
144#1865C2211yescharacteristic
145#1863C2211yescharacteristic
146#1863C2211yescharacteristic
147#1863C2211yescharacteristic
148#1863C2211yescharacteristic
149#1854C2211yescharacteristic
150#1854C2211yescharacteristic
151#1854C2211yescharacteristic
152#1854C2211yescharacteristic
153#1850C2211yescharacteristic
154#1850C2211yescharacteristic
155#1850C2211yescharacteristic
156#1850C2211yescharacteristic
157#1846C2211yescharacteristic
158#1846C2211yescharacteristic
159#1835C2211yescharacteristic
160#1835C2211yescharacteristic
161#1825C2211yescharacteristic
162#1825C2211yescharacteristic
163#1808C2211yescharacteristic
164#1808C2211yescharacteristic
165#1807C2211yescharacteristic
166#1807C2211yescharacteristic
167#1805C2211yescharacteristic
168#1805C2211yescharacteristic
169#1805C2211yescharacteristic
170#1805C2211yescharacteristic
171#1804C2211yescharacteristic
172#1804C2211yescharacteristic
173#1803C2211yescharacteristic
174#1803C2211yescharacteristic
175#1788C2211yescharacteristic
176#1788C2211yescharacteristic
177#1776C2211yescharacteristic
178#1776C2211yescharacteristic
179#1776C2211yescharacteristic
180#1776C2211yescharacteristic
181C4×#107C2211yescharacteristic
182C4×#107C2211yescharacteristic
183C4×#106C2211yescharacteristic
184C4×#106C2211yescharacteristic
185#1768C2211yescharacteristic
186#1768C2211yescharacteristic
187#1768C2211yescharacteristic
188#1768C2211yescharacteristic
189#1763C2211yescharacteristic
190#1763C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193C4×#103C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C4×#41—24no—
211C4×#41Q818yescomplemented
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×D4—21no—
219C2×C4×D4—21no—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×#117—21no—
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C42—21no—
227C22×C42C2311yescharacteristic
228#479—24no—
229#479—24no—
230#477—24no—
231#475—24no—
232#432—24no—
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259#416—24no—
260#416—24no—
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×C4×C8—24no—
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286#400—21no—
287#400—21no—
288#399—21no—
289#399—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#396—21no—
295#396—21no—
296#396—21no—
297#396—21no—
298#395—21no—
299#395—21no—
300#393—21no—
301#393—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391—21no—
309#391—21no—
310#390—21no—
311#390—21no—
312#390—21no—
313#390—21no—
314#390C2311yescharacteristic
315#390C2311yescharacteristic
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#384C2311yescharacteristic
371#384C2311yescharacteristic
372#383—21no—
373#383—21no—
374#383D411yescharacteristic
375#383D411yescharacteristic
376#382—21no—
377#382—21no—
378#382—21no—
379#382—21no—
380#382D411yescharacteristic
381#382D411yescharacteristic
382#382C2311yescharacteristic
383#382C2311yescharacteristic
384#382C2311yescharacteristic
385#382C2311yescharacteristic
386#382C2311yescharacteristic
387#382C2311yescharacteristic
388#381—21no—
389#381—21no—
390#381—21no—
391#381—21no—
392#381—21no—
393#381—21no—
394#381D411yescharacteristic
395#381D411yescharacteristic
396#380—21no—
397#380—21no—
398#380—21no—
399#380—21no—
400#380D411yescharacteristic
401#380D411yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438#376—21no—
439#376—21no—
440#376—21no—
441#376—21no—
442#376—21no—
443#376—21no—
444#376—21no—
445#376C2311yescharacteristic
446#376C2311yescharacteristic
447C43—21no—
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C2×#41C2×Q814yes—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2411yescharacteristic
505C22×C8—22no—
506C22×C8—22no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523#125—22no—
524#125—22no—
525#125—41no—
526#125—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8C2×Q814yes—
538C4×Q8C2×Q814yes—
539C4×D4—28no—
540C4×D4—28no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4C2×Q814yes—
544C4×D4C2×Q814yes—
545#117—22no—
546#117—28no—
547#117—22no—
548#117—22no—
549#117—41no—
550#117—41no—
551#117C2×Q814yes—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C22⋊C4C2×D411yescharacteristic
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—28no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D411yescharacteristic
643C2×C42C2×Q814yes—
644C2×C42#4114yes—
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651#107—22no—
652#107—22no—
653#107—22no—
654#107—22no—
655#107—41no—
656#107—41no—
657#107—41no—
658#107—41no—
659#106—22no—
660#106—22no—
661#106—22no—
662#106—22no—
663#106—41no—
664#106—41no—
665#106—41no—
666#106—41no—
667C4⋊C8—22no—
668C4⋊C8—22no—
669C4⋊C8—22no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—41no—
674C4⋊C8—41no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—22no—
683#103#4114yes—
684#103#4114yes—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693C22⋊C8—22no—
694C22⋊C8—22no—
695#97—22no—
696#97—22no—
697C4×C8—22no—
698C4×C8—22no—
699C4×C8—22no—
700C4×C8—22no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
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#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757C24—21no—
758C24C22×D411yescharacteristic
759#41—28no—
760#41—44no—
761#41—44no—
762#41—44no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8—81no—
769C2×Q8—81no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8C22×Q812yes—
773C2×Q8C2×#4112yes—
774C2×Q8C2×#4112yes—
775C2×D4—24no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4C22×Q812yes—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4C22⋊Q814yes—
817C22×C4C22⋊Q814yes—
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×Q812yes—
832C22×C4C2×#4112yes—
833C22×C4C2511yescharacteristic
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—44no—
857C2×C8—44no—
858C2×C8C2×#4112yes—
859C2×C8C2×#4112yes—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—41no—
887C4⋊C4—41no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4C22×Q812yes—
917C4⋊C4C22×Q812yes—
918C4⋊C4C2×#4112yes—
919C4⋊C4C2×#4112yes—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—41no—
924C22⋊C4—41no—
925C22⋊C4—41no—
926C22⋊C4—41no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—42no—
953C42—42no—
954C42—42no—
955C42—42no—
956C42—42no—
957C42—42no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42—81no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42—81no—
970C42C22⋊Q814yes—
971C42C22⋊Q814yes—
972C42C22×Q812yes—
973C42C22×Q812yes—
974C42C2×#4112yes—
975C42C2×#4112yes—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23C2×C22⋊Q812yes—
990C23C23×D411yescharacteristic
991Q8—22no—
992Q8—22no—
993Q8—22no—
994Q8—162no—
995Q8—162no—
996Q8#53314yes—
997D4—22no—
998D4—22no—
999D4—48no—
1000D4—41no—
1001D4—41no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—44no—
1048C2×C4—44no—
1049C2×C4—48no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—84no—
1089C2×C4—84no—
1090C2×C4C2×C22⋊Q812yes—
1091C2×C4C2×C22⋊Q812yes—
1092C2×C4C2×C22⋊Q812yes—
1093C2×C4C2×C22⋊Q812yes—
1094C2×C4C2×C22⋊Q812yes—
1095C2×C4C23×Q811yescharacteristic
1096C2×C4C22×#4111yescharacteristic
1097C2×C4C22×#4111yescharacteristic
1098C2×C4C22×#4111yescharacteristic
1099C2×C4#58511yescharacteristic
1100C2×C4#58511yescharacteristic
1101C8—22no—
1102C8—22no—
1103C8—41no—
1104C8—41no—
1105C8—41no—
1106C8—41no—
1107C8—41no—
1108C8—41no—
1109C22—22no—
1110C22—22no—
1111C22—22no—
1112C22—41no—
1113C22—41no—
1114C22—41no—
1115C22—41no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22C22×C22⋊Q811yescharacteristic
1124C22D4×#4111yescharacteristic
1125C22D4×#4111yescharacteristic
1126C22#358411yescharacteristic
1127C22#358411yescharacteristic
1128C22#358411yescharacteristic
1129C22#358411yescharacteristic
1130C4—22no—
1131C4—22no—
1132C4—22no—
1133C4—22no—
1134C4—22no—
1135C4—24no—
1136C4—41no—
1137C4—41no—
1138C4—42no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—42no—
1144C4—41no—
1145C4—41no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4C2×#53311yescharacteristic
1159C4#345811yescharacteristic
1160C4#347511yescharacteristic
1161C4#347511yescharacteristic
1162C2—42no—
1163C2—82no—
1164C2#3473911yescharacteristic
1165C2#6048911yescharacteristic
1166C2#6048911yescharacteristic
1167C2#6148611yescharacteristic
1168C2#6148811yescharacteristic
1169C2#6150011yescharacteristic
1170C2#6150211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35213C2semidirect
3. #26116C2semidirect
4. #26114C2semidirect
5. #26096C2semidirect
6. #26094C2semidirect
7. #26050C2semidirect
8. #26048C2semidirect
9. #26030C2semidirect
10. #26028C2semidirect
11. #26003C2semidirect
12. #26001C2semidirect
13. #25995C2semidirect
14. #25993C2semidirect
19. #23791C2semidirect
20. #23790C2semidirect
21. #23787C2semidirect
22. #23786C2semidirect
23. #21626C2semidirect
24. #21625C2semidirect
25. #21622C2semidirect
26. #21621C2semidirect
27. #21366C2semidirect
28. #21351C2semidirect
29. #20818C2semidirect
211. C4×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#352132
#341972
#261162
#261142
#260962
#260942
#260502
#260482
#260302
#260282
#260032
#260012
#259952
#259932
#259612
#259592
#259532
#259512
#237912
#237902
#237872
#237862
#216262
#216252
#216222
#216212
#213662
#213512
#208182
#207422
C4×#4162