Finite Group Databasebeta

← #6407225

Subgroups — #6407225

Order 512.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1209 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34893C211yesmaximal, characteristic
2#23256C211yesmaximal, characteristic, complemented
3#23255C211yesmaximal, characteristic, complemented
4#23246C211yesmaximal, characteristic, complemented
5#23246C211yesmaximal, characteristic, complemented
6#23245C211yesmaximal, characteristic, complemented
7#23244C211yesmaximal, characteristic, complemented
8#23152C211yesmaximal, characteristic, complemented
9#22957C211yesmaximal, characteristic, complemented
10#22954C211yesmaximal, characteristic, complemented
11#22823C211yesmaximal, characteristic, complemented
12#22702C211yesmaximal, characteristic
13#22702C211yesmaximal, characteristic
14#22648C211yesmaximal, characteristic
15#22631C211yesmaximal, characteristic, complemented
16#22630C211yesmaximal, characteristic, complemented
17#22315C211yesmaximal, characteristic, complemented
18#22305C211yesmaximal, characteristic, complemented
19#22297C211yesmaximal, characteristic, complemented
20#22294C211yesmaximal, characteristic, complemented
21#22292C211yesmaximal, characteristic, complemented
22#22291C211yesmaximal, characteristic, complemented
23#21674C211yesmaximal, characteristic, complemented
24#21606C211yesmaximal, characteristic, complemented
25#21603C211yesmaximal, characteristic, complemented
26#21345C211yesmaximal, characteristic, complemented
27#21027C211yesmaximal, characteristic, complemented
28#21024C211yesmaximal, characteristic, complemented
29#20563C211yesmaximal, characteristic
30#20556C211yesmaximal, characteristic
31#20492C211yesmaximal, characteristic
32C2×#446C2211yescharacteristic
33C2×#446C2211yescharacteristic
34C2×#435C2211yescharacteristic
35C2×#435C2211yescharacteristic
36C2×#435C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C2×#423C2211yescharacteristic
39C22×C4⋊C8C2211yescharacteristic
40C2×#405C2211yescharacteristic
41C2×#405C2211yescharacteristic
42#2589C411yescharacteristic
43#2589C411yescharacteristic
44#2587C411yescharacteristic
45#2587C411yescharacteristic
46#2584C411yescharacteristic
47#2580C411yescharacteristic
48#2566C411yescharacteristic
49#2550C411yescharacteristic
50#2522C411yescharacteristic
51#2522C411yescharacteristic
52#2509C411yescharacteristic
53#2507C411yescharacteristic
54#2465C411yescharacteristic
55#2465C411yescharacteristic
56#2454C411yescharacteristic
57#2452C411yescharacteristic
58#2396C2211yescharacteristic
59#2396C2211yescharacteristic
60#2396C2211yescharacteristic
61#2396C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63C4×#125C2211yescharacteristic
64C4×#125C2211yescharacteristic
65C4×C22⋊Q8C2211yescharacteristic
66C4×C22⋊Q8C2211yescharacteristic
67#2296C2211yescharacteristic
68#2296C2211yescharacteristic
69#2293C2211yescharacteristic
70#2293C2211yescharacteristic
71C42×Q8C2211yescharacteristic
72C42×D4C2211yescharacteristic
73#1985C2211yescharacteristic
74#1985C2211yescharacteristic
75#1985C2211yescharacteristic
76#1985C2211yescharacteristic
77#1985C2211yescharacteristic
78#1985C2211yescharacteristic
79#1984C2211yescharacteristic
80#1984C2211yescharacteristic
81#1984C2211yescharacteristic
82#1984C2211yescharacteristic
83#1940C2211yescharacteristic
84#1940C2211yescharacteristic
85#1940C2211yescharacteristic
86#1940C2211yescharacteristic
87#1940C2211yescharacteristic
88#1940C2211yescharacteristic
89#1940C2211yescharacteristic
90#1940C2211yescharacteristic
91#1940C2211yescharacteristic
92#1940C2211yescharacteristic
93#1939C2211yescharacteristic
94#1939C2211yescharacteristic
95#1939C2211yescharacteristic
96#1939C2211yescharacteristic
97#1939C2211yescharacteristic
98#1939C2211yescharacteristic
99#1917C2211yescharacteristic
100#1917C2211yescharacteristic
101#1917C2211yescharacteristic
102#1917C2211yescharacteristic
103#1917C2211yescharacteristic
104#1917C2211yescharacteristic
105#1917C2211yescharacteristic
106#1917C2211yescharacteristic
107#1917C2211yescharacteristic
108#1917C2211yescharacteristic
109#1917C2211yescharacteristic
110#1917C2211yescharacteristic
111#1917C2211yescharacteristic
112#1917C2211yescharacteristic
113#1917C2211yescharacteristic
114#1917C2211yescharacteristic
115#1917C2211yescharacteristic
116#1917C2211yescharacteristic
117#1916C2211yescharacteristic
118#1916C2211yescharacteristic
119#1916C2211yescharacteristic
120#1916C2211yescharacteristic
121#1916C2211yescharacteristic
122#1916C2211yescharacteristic
123#1916C2211yescharacteristic
124#1916C2211yescharacteristic
125#1916C2211yescharacteristic
126#1916C2211yescharacteristic
127#1916C2211yescharacteristic
128#1916C2211yescharacteristic
129#1916C2211yescharacteristic
130#1916C2211yescharacteristic
131#1851C2211yescharacteristic
132#1851C2211yescharacteristic
133#1851C2211yescharacteristic
134#1851C2211yescharacteristic
135#1851C2211yescharacteristic
136#1851C2211yescharacteristic
137#1850C2211yescharacteristic
138#1850C2211yescharacteristic
139#1850C2211yescharacteristic
140#1850C2211yescharacteristic
141#1850C2211yescharacteristic
142#1850C2211yescharacteristic
143#1842C2211yescharacteristic
144#1831C2211yescharacteristic
145#1831C2211yescharacteristic
146#1798C2211yescharacteristic
147#1798C2211yescharacteristic
148#1798C2211yescharacteristic
149#1798C2211yescharacteristic
150#1797C2211yescharacteristic
151#1797C2211yescharacteristic
152#1771C2211yescharacteristic
153#1771C2211yescharacteristic
154#1771C2211yescharacteristic
155#1771C2211yescharacteristic
156#1771C2211yescharacteristic
157#1771C2211yescharacteristic
158#1771C2211yescharacteristic
159#1771C2211yescharacteristic
160#1771C2211yescharacteristic
161#1771C2211yescharacteristic
162#1771C2211yescharacteristic
163#1771C2211yescharacteristic
164#1770C2211yescharacteristic
165#1770C2211yescharacteristic
166C8×C4⋊C4C2211yescharacteristic
167C8×C4⋊C4C2211yescharacteristic
168#1767C2211yescharacteristic
169#1767C2211yescharacteristic
170#1767C2211yescharacteristic
171#1767C2211yescharacteristic
172#1767C2211yescharacteristic
173C4×C4⋊C8C2211yescharacteristic
174#1753C2211yescharacteristic
175#1753C2211yescharacteristic
176#1753C2211yescharacteristic
177#1753C2211yescharacteristic
178#1753C2211yescharacteristic
179#1753C2211yescharacteristic
180#1752C2211yescharacteristic
181#1752C2211yescharacteristic
182#1752C2211yescharacteristic
183#1752C2211yescharacteristic
184C8×C22⋊C4C2211yescharacteristic
185C8×C22⋊C4C2211yescharacteristic
186#1750C2211yescharacteristic
187#1750C2211yescharacteristic
188#1750C2211yescharacteristic
189#1750C2211yescharacteristic
190#1749C2211yescharacteristic
191C4×C22⋊C8C2211yescharacteristic
192#1745C2211yescharacteristic
193#1745C2211yescharacteristic
194#1729C2211yescharacteristic
195#1729C2211yescharacteristic
196#1729C2211yescharacteristic
197#1729C2211yescharacteristic
198#1729C2211yescharacteristic
199#1729C2211yescharacteristic
200#1728C2211yescharacteristic
201C2×#336C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C2×C4⋊Q8C2×C411yescharacteristic
212C2×#125C2×C411yescharacteristic
213C2×#125C2×C411yescharacteristic
214C2×C22⋊Q8C2×C411yescharacteristic
215C2×C22⋊Q8C2×C411yescharacteristic
216C2×C4×Q8C2×C411yescharacteristic
217C2×C4×Q8C2×C411yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×D4C2×C411yescharacteristic
222C2×C4×D4C2×C411yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C22×C42C2311yescharacteristic
229C22×C42C2311yescharacteristic
230#446—42no—
231#446—42no—
232#435—24no—
233#435—24no—
234#435—24no—
235#435Q818yescomplemented
236#423—42no—
237C2×C4⋊C8—42no—
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
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
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C22⋊C8C2311yescharacteristic
265C2×C22⋊C8C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C22⋊C8C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272#405—42no—
273#405—42no—
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300#400C2×C411yescharacteristic
301#400C2×C411yescharacteristic
302#400C2×C411yescharacteristic
303#400C2×C411yescharacteristic
304#399C2×C411yescharacteristic
305#399C2×C411yescharacteristic
306#399C2×C411yescharacteristic
307#399C2×C411yescharacteristic
308#398C2×C411yescharacteristic
309#398C2×C411yescharacteristic
310#398C2×C411yescharacteristic
311#398C2×C411yescharacteristic
312#398C2×C411yescharacteristic
313#398C2×C411yescharacteristic
314#398C2×C411yescharacteristic
315#398C2×C411yescharacteristic
316#396C2×C411yescharacteristic
317#396C2×C411yescharacteristic
318#396C2×C411yescharacteristic
319#396C2×C411yescharacteristic
320#396C2×C411yescharacteristic
321#396C2×C411yescharacteristic
322#396C2×C411yescharacteristic
323#396C2×C411yescharacteristic
324#395C2×C411yescharacteristic
325#395C2×C411yescharacteristic
326#395C2×C411yescharacteristic
327#395C2×C411yescharacteristic
328#393C2×C411yescharacteristic
329#393C2×C411yescharacteristic
330#393C2×C411yescharacteristic
331#393C2×C411yescharacteristic
332#391C2×C411yescharacteristic
333#391C2×C411yescharacteristic
334#391C2×C411yescharacteristic
335#391C2×C411yescharacteristic
336#390C2×C411yescharacteristic
337#390C2×C411yescharacteristic
338#390C2×C411yescharacteristic
339#390C2×C411yescharacteristic
340#389C2×C411yescharacteristic
341#389C2×C411yescharacteristic
342#389C2×C411yescharacteristic
343#389C2×C411yescharacteristic
344#389C2×C411yescharacteristic
345#389C2×C411yescharacteristic
346#389C2×C411yescharacteristic
347#389C2×C411yescharacteristic
348#389C2×C411yescharacteristic
349#389C2×C411yescharacteristic
350#389C2×C411yescharacteristic
351#389C2×C411yescharacteristic
352#389C2×C411yescharacteristic
353#389C2×C411yescharacteristic
354#389C2×C411yescharacteristic
355#389C2×C411yescharacteristic
356#389C2×C411yescharacteristic
357#389C2×C411yescharacteristic
358#389C2×C411yescharacteristic
359#389C2×C411yescharacteristic
360#389C2×C411yescharacteristic
361#389C2×C411yescharacteristic
362#388C2×C411yescharacteristic
363#388C2×C411yescharacteristic
364#388C2×C411yescharacteristic
365#388C2×C411yescharacteristic
366#388C2×C411yescharacteristic
367#388C2×C411yescharacteristic
368#388C2×C411yescharacteristic
369#388C2×C411yescharacteristic
370#387C2×C411yescharacteristic
371#387C2×C411yescharacteristic
372#387C2×C411yescharacteristic
373#387C2×C411yescharacteristic
374#387C2×C411yescharacteristic
375#387C2×C411yescharacteristic
376#387C2×C411yescharacteristic
377#387C2×C411yescharacteristic
378#387C2×C411yescharacteristic
379#387C2×C411yescharacteristic
380#387C2×C411yescharacteristic
381#387C2×C411yescharacteristic
382#385C2×C411yescharacteristic
383#385C2×C411yescharacteristic
384#385C2×C411yescharacteristic
385#385C2×C411yescharacteristic
386#385C2×C411yescharacteristic
387#385C2×C411yescharacteristic
388#385C2×C411yescharacteristic
389#385C2×C411yescharacteristic
390#385C2×C411yescharacteristic
391#385C2×C411yescharacteristic
392#385C2×C411yescharacteristic
393#385C2×C411yescharacteristic
394#384C2×C411yescharacteristic
395#382C2×C411yescharacteristic
396#382C2×C411yescharacteristic
397#380C2×C411yescharacteristic
398#380C2×C411yescharacteristic
399C4×C4⋊C4C2×C411yescharacteristic
400C4×C4⋊C4C2×C411yescharacteristic
401C4×C4⋊C4C2×C411yescharacteristic
402C4×C4⋊C4C2×C411yescharacteristic
403C4×C4⋊C4C2×C411yescharacteristic
404C4×C4⋊C4C2×C411yescharacteristic
405C4×C4⋊C4C2×C411yescharacteristic
406C4×C4⋊C4C2×C411yescharacteristic
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4C2×C411yescharacteristic
424C4×C22⋊C4C2×C411yescharacteristic
425C4×C22⋊C4C2×C411yescharacteristic
426C4×C22⋊C4C2×C411yescharacteristic
427C4×C22⋊C4C2311yescharacteristic
428C4×C22⋊C4C2311yescharacteristic
429C4×C22⋊C4C2311yescharacteristic
430C4×C22⋊C4C2311yescharacteristic
431C4×C22⋊C4C2311yescharacteristic
432C4×C22⋊C4C2311yescharacteristic
433C43C2311yescharacteristic
434C43C2311yescharacteristic
435C43C2311yescharacteristic
436#336C2311yescharacteristic
437#336C2311yescharacteristic
438#336C2311yescharacteristic
439#336C2311yescharacteristic
440#336C2311yescharacteristic
441#336C2311yescharacteristic
442#336C2311yescharacteristic
443#336C2311yescharacteristic
444#336C2311yescharacteristic
445#336C2311yescharacteristic
446#336C2311yescharacteristic
447#336C2311yescharacteristic
448#336C2311yescharacteristic
449#336C2311yescharacteristic
450#336C2311yescharacteristic
451#336C2311yescharacteristic
452#336C2311yescharacteristic
453#336C2311yescharacteristic
454#336C2311yescharacteristic
455#336C2311yescharacteristic
456#336C2311yescharacteristic
457#336C2311yescharacteristic
458#336C2311yescharacteristic
459#336C2311yescharacteristic
460#336C2311yescharacteristic
461#336C2311yescharacteristic
462#336C2311yescharacteristic
463#336C2311yescharacteristic
464#336C2311yescharacteristic
465#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C22×Q8C22×C411yescharacteristic
489C22×Q8C22×C411yescharacteristic
490C22×Q8C22×C411yescharacteristic
491C22×D4C22×C411yescharacteristic
492C23×C4C22×C411yescharacteristic
493C23×C4C22×C411yescharacteristic
494C23×C4C22×C411yescharacteristic
495C23×C4C22×C411yescharacteristic
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—22no—
502C2×M16—41no—
503C2×M16—41no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16—41no—
509C2×M16C2×Q814yes—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—22no—
513C22×C8—22no—
514C22×C8—41no—
515C22×C8—41no—
516C22×C8—41no—
517C22×C8—41no—
518C22×C8—41no—
519C22×C8—41no—
520C22×C8—41no—
521C22×C8C2×Q814yes—
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C4⋊Q8—42no—
539#125—42no—
540#125—42no—
541C22⋊Q8—42no—
542C22⋊Q8—42no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—42no—
550C4×Q8—42no—
551C4×D4—42no—
552C4×D4—42no—
553C4×D4C2×Q814yes—
554C4×D4#4114yes—
555#117—41no—
556#117—41no—
557#117—41no—
558#117—41no—
559#117—41no—
560#117—41no—
561#117—41no—
562#117—41no—
563C2×C4⋊C4C22×C411yescharacteristic
564C2×C4⋊C4C22×C411yescharacteristic
565C2×C4⋊C4C22×C411yescharacteristic
566C2×C4⋊C4C22×C411yescharacteristic
567C2×C4⋊C4C22×C411yescharacteristic
568C2×C4⋊C4C22×C411yescharacteristic
569C2×C4⋊C4C22×C411yescharacteristic
570C2×C4⋊C4C22×C411yescharacteristic
571C2×C4⋊C4C22×C411yescharacteristic
572C2×C4⋊C4C22×C411yescharacteristic
573C2×C4⋊C4C22×C411yescharacteristic
574C2×C4⋊C4C22×C411yescharacteristic
575C2×C4⋊C4C22×C411yescharacteristic
576C2×C4⋊C4C22×C411yescharacteristic
577C2×C4⋊C4C22×C411yescharacteristic
578C2×C4⋊C4C22×C411yescharacteristic
579C2×C4⋊C4C22×C411yescharacteristic
580C2×C4⋊C4C22×C411yescharacteristic
581C2×C4⋊C4C22×C411yescharacteristic
582C2×C4⋊C4C22×C411yescharacteristic
583C2×C4⋊C4C22×C411yescharacteristic
584C2×C4⋊C4C22×C411yescharacteristic
585C2×C4⋊C4C22×C411yescharacteristic
586C2×C4⋊C4C22×C411yescharacteristic
587C2×C4⋊C4C22×C411yescharacteristic
588C2×C4⋊C4C22×C411yescharacteristic
589C2×C4⋊C4C22×C411yescharacteristic
590C2×C4⋊C4C22×C411yescharacteristic
591C2×C4⋊C4C22×C411yescharacteristic
592C2×C4⋊C4C22×C411yescharacteristic
593C2×C4⋊C4C22×C411yescharacteristic
594C2×C4⋊C4C22×C411yescharacteristic
595C2×C4⋊C4C22×C411yescharacteristic
596C2×C4⋊C4C22×C411yescharacteristic
597C2×C4⋊C4C22×C411yescharacteristic
598C2×C4⋊C4C22×C411yescharacteristic
599C2×C4⋊C4C22×C411yescharacteristic
600C2×C4⋊C4C22×C411yescharacteristic
601C2×C4⋊C4C22×C411yescharacteristic
602C2×C4⋊C4C22×C411yescharacteristic
603C2×C4⋊C4C22×C411yescharacteristic
604C2×C4⋊C4C22×C411yescharacteristic
605C2×C4⋊C4C22×C411yescharacteristic
606C2×C4⋊C4C22×C411yescharacteristic
607C2×C4⋊C4C22×C411yescharacteristic
608C2×C4⋊C4C22×C411yescharacteristic
609C2×C4⋊C4C22×C411yescharacteristic
610C2×C4⋊C4C22×C411yescharacteristic
611C2×C4⋊C4C22×C411yescharacteristic
612C2×C4⋊C4C22×C411yescharacteristic
613C2×C22⋊C4C22×C411yescharacteristic
614C2×C22⋊C4C22×C411yescharacteristic
615C2×C22⋊C4C22×C411yescharacteristic
616C2×C22⋊C4C22×C411yescharacteristic
617C2×C22⋊C4C22×C411yescharacteristic
618C2×C22⋊C4C22×C411yescharacteristic
619C2×C22⋊C4C22×C411yescharacteristic
620C2×C22⋊C4C22×C411yescharacteristic
621C2×C22⋊C4C22×C411yescharacteristic
622C2×C22⋊C4C22×C411yescharacteristic
623C2×C22⋊C4C22×C411yescharacteristic
624C2×C22⋊C4C22×C411yescharacteristic
625C2×C22⋊C4C22×C411yescharacteristic
626C2×C22⋊C4C22×C411yescharacteristic
627C2×C22⋊C4C22×C411yescharacteristic
628C2×C22⋊C4C22×C411yescharacteristic
629C2×C22⋊C4C22×C411yescharacteristic
630C2×C22⋊C4C22×C411yescharacteristic
631C2×C22⋊C4C22×C411yescharacteristic
632C2×C22⋊C4C22×C411yescharacteristic
633C2×C22⋊C4C22×C411yescharacteristic
634C2×C22⋊C4C22×C411yescharacteristic
635C2×C42—41no—
636C2×C42—41no—
637C2×C42—41no—
638C2×C42—41no—
639C2×C42C22×C411yescharacteristic
640C2×C42C22×C411yescharacteristic
641C2×C42C22×C411yescharacteristic
642C2×C42C22×C411yescharacteristic
643C2×C42C22×C411yescharacteristic
644C2×C42C22×C411yescharacteristic
645C2×C42C22×C411yescharacteristic
646C2×C42C22×C411yescharacteristic
647C2×C42C22×C411yescharacteristic
648C2×C42C22×C411yescharacteristic
649C2×C42C22×C411yescharacteristic
650C2×C42C22×C411yescharacteristic
651C2×C42C22×C411yescharacteristic
652C2×C42C22×C411yescharacteristic
653C2×C42C22×C411yescharacteristic
654C2×C42C22×C411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C4⋊C8—22no—
669C4⋊C8—22no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—22no—
674C4⋊C8—22no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678C4⋊C8—41no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692C4⋊C8—41no—
693C4⋊C8C2×Q814yes—
694C22⋊C8—22no—
695C22⋊C8—22no—
696C22⋊C8—22no—
697C22⋊C8—22no—
698C22⋊C8—22no—
699C22⋊C8—22no—
700C22⋊C8C2×Q814yes—
701C22⋊C8C2×Q814yes—
702#97—22no—
703#97—22no—
704#97—22no—
705#97—22no—
706#97—22no—
707#97—41no—
708#97—41no—
709#97—41no—
710#97—41no—
711#97—41no—
712#97—41no—
713#97—41no—
714#97—41no—
715#97—41no—
716#97—41no—
717#97C2×Q814yes—
718C4×C8—22no—
719C4×C8—41no—
720C4×C8—41no—
721C4×C8—41no—
722C4×C8—41no—
723C4×C8—41no—
724C4×C8—41no—
725C4×C8—41no—
726C4×C8—41no—
727C4×C8—41no—
728#95C22×C411yescharacteristic
729#95C22×C411yescharacteristic
730#95C22×C411yescharacteristic
731#95C22×C411yescharacteristic
732#95C22×C411yescharacteristic
733#95C22×C411yescharacteristic
734#95C22×C411yescharacteristic
735#95C22×C411yescharacteristic
736#95C22×C411yescharacteristic
737#95C22×C411yescharacteristic
738#95C22×C411yescharacteristic
739#95C22×C411yescharacteristic
740#95C22×C411yescharacteristic
741#95C22×C411yescharacteristic
742#95C22×C411yescharacteristic
743#95C22×C411yescharacteristic
744#95C22×C411yescharacteristic
745#95C22×C411yescharacteristic
746#95C22×C411yescharacteristic
747#95C22×C411yescharacteristic
748#95C22×C411yescharacteristic
749#95C22×C411yescharacteristic
750#95C22×C411yescharacteristic
751#95C22×C411yescharacteristic
752#95C22×C411yescharacteristic
753#95C22×C411yescharacteristic
754#95C22×C411yescharacteristic
755#95C22×C411yescharacteristic
756#95C22×C411yescharacteristic
757#95C22×C411yescharacteristic
758#95C22×C411yescharacteristic
759#95C22×C411yescharacteristic
760#95C22×C411yescharacteristic
761#95C22×C411yescharacteristic
762#95C22×C411yescharacteristic
763#95C22×C411yescharacteristic
764#95C22×C411yescharacteristic
765#95C22×C411yescharacteristic
766#95C22×C411yescharacteristic
767#95C22×C411yescharacteristic
768#95C22×C411yescharacteristic
769#95C22×C411yescharacteristic
770#95C22×C411yescharacteristic
771#95C22×C411yescharacteristic
772C24C23×C411yescharacteristic
773C24C23×C411yescharacteristic
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—41no—
777C2×Q8—41no—
778C2×Q8—41no—
779C2×Q8—41no—
780C2×Q8—41no—
781C2×Q8—41no—
782C2×Q8—41no—
783C2×D4—41no—
784C2×D4—41no—
785C2×D4C4×Q814yes—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—41no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4C23×C411yescharacteristic
807C22×C4C23×C411yescharacteristic
808C22×C4C23×C411yescharacteristic
809C22×C4C23×C411yescharacteristic
810C22×C4C23×C411yescharacteristic
811C22×C4C23×C411yescharacteristic
812C22×C4C23×C411yescharacteristic
813C22×C4C23×C411yescharacteristic
814C22×C4C23×C411yescharacteristic
815C22×C4C23×C411yescharacteristic
816C22×C4C23×C411yescharacteristic
817C22×C4C23×C411yescharacteristic
818C22×C4C23×C411yescharacteristic
819C22×C4C23×C411yescharacteristic
820C22×C4C23×C411yescharacteristic
821C22×C4C23×C411yescharacteristic
822C22×C4C23×C411yescharacteristic
823C22×C4C23×C411yescharacteristic
824C22×C4C23×C411yescharacteristic
825C22×C4C23×C411yescharacteristic
826C22×C4C23×C411yescharacteristic
827C22×C4C23×C411yescharacteristic
828C22×C4C23×C411yescharacteristic
829C22×C4C23×C411yescharacteristic
830C22×C4C23×C411yescharacteristic
831C22×C4C23×C411yescharacteristic
832C22×C4C23×C411yescharacteristic
833C22×C4C23×C411yescharacteristic
834C22×C4C22×Q812yes—
835C22×C4C22×Q812yes—
836C22×C4C2×#4112yes—
837C22×C4C2×#4112yes—
838C22×C4C2511yescharacteristic
839M16—44no—
840M16—44no—
841M16—82no—
842M16—82no—
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—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—44no—
887C2×C8—44no—
888C2×C8—82no—
889C2×C8—82no—
890C2×C8C22×Q812yes—
891C2×C8C22×Q812yes—
892C2×C8C22×Q812yes—
893C2×C8C22×Q812yes—
894C2×C8H(5,𝔽2)12yes—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—22no—
905C4⋊C4—22no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4C4×Q814yes—
945C22⋊C4—22no—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—41no—
953C22⋊C4—41no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4C4×Q814yes—
966C22⋊C4C4×Q814yes—
967C42—22no—
968C42—22no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—41no—
994C42—41no—
995C42—41no—
996C42—41no—
997C42—41no—
998C42—41no—
999C42—41no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42—41no—
1004C42—41no—
1005C42—41no—
1006C42—41no—
1007C42C22×Q812yes—
1008C42C2×#4112yes—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23C2×C4×Q812yes—
1022C23C2×C4×Q812yes—
1023C23C24×C411yescharacteristic
1024Q8—44no—
1025Q8—82no—
1026Q8—82no—
1027D4—44no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
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—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—44no—
1114C2×C4—82no—
1115C2×C4—82no—
1116C2×C4—82no—
1117C2×C4C2×C4×Q812yes—
1118C2×C4C2×C4×Q812yes—
1119C2×C4C2×C4×Q812yes—
1120C2×C4C2×C4×Q812yes—
1121C2×C4#56812yes—
1122C2×C4#56812yes—
1123C2×C4#56812yes—
1124C2×C4C23×Q811yescharacteristic
1125C2×C4C22×#4111yescharacteristic
1126C2×C4C2×H(5,𝔽2)11yescharacteristic
1127C2×C4#58511yescharacteristic
1128C2×C4#58511yescharacteristic
1129C2×C4#58511yescharacteristic
1130C8—22no—
1131C8—22no—
1132C8—22no—
1133C8—22no—
1134C8—22no—
1135C8—41no—
1136C8—41no—
1137C8—41no—
1138C8—41no—
1139C8—41no—
1140C8—41no—
1141C8—41no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C22—22no—
1147C22—22no—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22C22×C4×Q811yescharacteristic
1161C22#342811yescharacteristic
1162C22C4×H(5,𝔽2)11yescharacteristic
1163C22C2×#56811yescharacteristic
1164C22C2×#56811yescharacteristic
1165C22C2×#56811yescharacteristic
1166C22#357311yescharacteristic
1167C4—22no—
1168C4—22no—
1169C4—22no—
1170C4—22no—
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—41no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4#350111yescharacteristic
1196C4#350411yescharacteristic
1197C4#351311yescharacteristic
1198C4#352111yescharacteristic
1199C2—42no—
1200C2—42no—
1201C2#3433311yescharacteristic
1202C2#6019211yescharacteristic
1203C2#6019511yescharacteristic
1204C2#6029311yescharacteristic
1205C2#6030211yescharacteristic
1206C2#6031611yescharacteristic
1207C2#6032411yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC22×D4C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #23256C2semidirect
3. #23255C2semidirect
4. #23246C2semidirect
5. #23246C2semidirect
6. #23245C2semidirect
7. #23244C2semidirect
8. #23152C2semidirect
9. #22957C2semidirect
10. #22954C2semidirect
11. #22823C2semidirect
15. #22631C2semidirect
16. #22630C2semidirect
17. #22315C2semidirect
18. #22305C2semidirect
19. #22297C2semidirect
20. #22294C2semidirect
21. #22292C2semidirect
22. #22291C2semidirect
23. #21674C2semidirect
24. #21606C2semidirect
25. #21603C2semidirect
26. #21345C2semidirect
27. #21027C2semidirect
28. #21024C2semidirect
235. #435Q8semidirect

Maximal subgroups

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

subgroupindex
#348932
#232562
#232552
#232462
#232452
#232442
#231522
#229572
#229542
#228232
#227022
#226482
#226312
#226302
#223152
#223052
#222972
#222942
#222922
#222912
#216742
#216062
#216032
#213452
#210272
#210242
#205632
#205562
#204922