Finite Group Databasebeta

← #6380017

Subgroups — #6380017

Order 512.

1586 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34109C211yesmaximal, characteristic
2#22642C211yesmaximal, characteristic, complemented
3#22640C211yesmaximal, characteristic, complemented
4#22636C211yesmaximal, characteristic, complemented
5#22634C211yesmaximal, characteristic, complemented
6#22631C211yesmaximal, characteristic, complemented
7#22630C211yesmaximal, characteristic, complemented
8#22605C211yesmaximal, characteristic, complemented
9#22605C211yesmaximal, characteristic, complemented
10#22594C211yesmaximal, characteristic, complemented
11#22594C211yesmaximal, characteristic, complemented
12#22594C211yesmaximal, characteristic, complemented
13#22593C211yesmaximal, characteristic, complemented
14#22559C211yesmaximal, characteristic
15#22558C211yesmaximal, characteristic
16#22555C211yesmaximal, characteristic
17#22554C211yesmaximal, characteristic
18#21437C211yesmaximal, characteristic, complemented
19#21437C211yesmaximal, characteristic, complemented
20#21435C211yesmaximal, characteristic, complemented
21#21431C211yesmaximal, characteristic, complemented
22#21357C211yesmaximal, characteristic, complemented
23#21357C211yesmaximal, characteristic, complemented
24#20786C211yesmaximal, characteristic, complemented
25#20780C211yesmaximal, characteristic, complemented
26#20716C211yesmaximal, characteristic
27#20478C211yesmaximal, characteristic, complemented
28#20475C211yesmaximal, characteristic, complemented
29#20468C211yesmaximal, characteristic, complemented
30#20467C211yesmaximal, characteristic, complemented
31#20379C211yesmaximal, characteristic
32C22×#117C2211yescharacteristic
33C2×#433C2211yescharacteristic
34C2×#433C2211yescharacteristic
35C2×#433C2211yescharacteristic
36C2×#433C2211yescharacteristic
37C2×#432C2211yescharacteristic
38C2×#432C2211yescharacteristic
39C2×#407C2211yescharacteristic
40C22×C22⋊C8C2211yescharacteristic
41C2×#405C2211yescharacteristic
42C2×#405C2211yescharacteristic
43#2347C411yescharacteristic
44#2347C411yescharacteristic
45#2346C411yescharacteristic
46#2346C411yescharacteristic
47#2345C411yescharacteristic
48#2345C411yescharacteristic
49#2344C411yescharacteristic
50#2344C411yescharacteristic
51#2343C411yescharacteristic
52#2343C411yescharacteristic
53#2343C411yescharacteristic
54#2343C411yescharacteristic
55#2342C411yescharacteristic
56#2342C411yescharacteristic
57#2342C411yescharacteristic
58#2342C411yescharacteristic
59#2298C2211yescharacteristic
60#2298C2211yescharacteristic
61#2298C2211yescharacteristic
62#2298C2211yescharacteristic
63#2296C2211yescharacteristic
64#2296C2211yescharacteristic
65#2283C2211yescharacteristic
66#2283C2211yescharacteristic
67#2280C2211yescharacteristic
68C4×#117C2211yescharacteristic
69C4×#117C2211yescharacteristic
70C4×#117C2211yescharacteristic
71C4×#117C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73#1940C2211yescharacteristic, complemented
74#1940C2211yescharacteristic, complemented
75#1940C2211yescharacteristic, complemented
76#1940C2211yescharacteristic, complemented
77#1939C2211yescharacteristic, complemented
78#1939C2211yescharacteristic, complemented
79#1939C2211yescharacteristic, complemented
80#1939C2211yescharacteristic, complemented
81#1924C2211yescharacteristic
82#1924C2211yescharacteristic
83#1924C2211yescharacteristic
84#1924C2211yescharacteristic
85#1924C2211yescharacteristic
86#1924C2211yescharacteristic
87#1924C2211yescharacteristic
88#1924C2211yescharacteristic
89#1924C2211yescharacteristic
90#1924C2211yescharacteristic
91#1923C2211yescharacteristic
92#1923C2211yescharacteristic
93#1923C2211yescharacteristic
94#1923C2211yescharacteristic
95#1923C2211yescharacteristic
96#1923C2211yescharacteristic
97#1917C2211yescharacteristic, complemented
98#1917C2211yescharacteristic, complemented
99#1917C2211yescharacteristic, complemented
100#1917C2211yescharacteristic, complemented
101#1917C2211yescharacteristic, complemented
102#1917C2211yescharacteristic, complemented
103#1917C2211yescharacteristic, complemented
104#1917C2211yescharacteristic, complemented
105#1917C2211yescharacteristic, complemented
106#1917C2211yescharacteristic, complemented
107#1916C2211yescharacteristic, complemented
108#1916C2211yescharacteristic, complemented
109#1916C2211yescharacteristic, complemented
110#1916C2211yescharacteristic, complemented
111#1916C2211yescharacteristic, complemented
112#1916C2211yescharacteristic, complemented
113#1851C2211yescharacteristic
114#1851C2211yescharacteristic
115#1851C2211yescharacteristic
116#1851C2211yescharacteristic
117#1850C2211yescharacteristic
118#1850C2211yescharacteristic
119#1850C2211yescharacteristic
120#1850C2211yescharacteristic
121#1840C2211yescharacteristic, complemented
122#1840C2211yescharacteristic, complemented
123#1840C2211yescharacteristic, complemented
124#1840C2211yescharacteristic, complemented
125#1831C2211yescharacteristic, complemented
126#1831C2211yescharacteristic, complemented
127#1831C2211yescharacteristic, complemented
128#1831C2211yescharacteristic, complemented
129#1818C2211yescharacteristic
130#1818C2211yescharacteristic
131#1818C2211yescharacteristic
132#1818C2211yescharacteristic
133#1817C2211yescharacteristic
134#1817C2211yescharacteristic
135#1798C2211yescharacteristic
136#1798C2211yescharacteristic
137#1798C2211yescharacteristic
138#1798C2211yescharacteristic
139#1797C2211yescharacteristic
140#1797C2211yescharacteristic
141#1797C2211yescharacteristic
142#1797C2211yescharacteristic
143#1779C2211yescharacteristic
144#1779C2211yescharacteristic
145#1771C2211yescharacteristic, complemented
146#1771C2211yescharacteristic, complemented
147#1771C2211yescharacteristic, complemented
148#1771C2211yescharacteristic, complemented
149#1770C2211yescharacteristic, complemented
150#1770C2211yescharacteristic, complemented
151#1770C2211yescharacteristic, complemented
152C8×C4⋊C4C2211yescharacteristic, complemented
153#1768C2211yescharacteristic, complemented
154#1768C2211yescharacteristic, complemented
155#1768C2211yescharacteristic, complemented
156#1768C2211yescharacteristic, complemented
157#1768C2211yescharacteristic, complemented
158#1768C2211yescharacteristic, complemented
159#1768C2211yescharacteristic, complemented
160#1768C2211yescharacteristic, complemented
161#1767C2211yescharacteristic, complemented
162#1767C2211yescharacteristic, complemented
163C4×C4⋊C8C2211yescharacteristic, complemented
164C4×C4⋊C8C2211yescharacteristic, complemented
165#1753C2211yescharacteristic
166#1753C2211yescharacteristic
167#1753C2211yescharacteristic
168#1753C2211yescharacteristic
169#1752C2211yescharacteristic
170#1752C2211yescharacteristic
171#1752C2211yescharacteristic
172C8×C22⋊C4C2211yescharacteristic
173#1750C2211yescharacteristic
174#1750C2211yescharacteristic
175#1750C2211yescharacteristic
176#1750C2211yescharacteristic
177#1750C2211yescharacteristic
178#1750C2211yescharacteristic
179#1750C2211yescharacteristic
180#1750C2211yescharacteristic
181#1749C2211yescharacteristic
182#1749C2211yescharacteristic
183#1749C2211yescharacteristic
184#1749C2211yescharacteristic
185C4×C22⋊C8C2211yescharacteristic
186C4×C22⋊C8C2211yescharacteristic
187C4×C22⋊C8C2211yescharacteristic
188C4×C22⋊C8C2211yescharacteristic
189#1746C2211yescharacteristic, complemented
190#1746C2211yescharacteristic, complemented
191#1745C2211yescharacteristic, complemented
192#1745C2211yescharacteristic, complemented
193#1745C2211yescharacteristic, complemented
194#1745C2211yescharacteristic, complemented
195#1744C2211yescharacteristic, complemented
196#1744C2211yescharacteristic, complemented
197#1729C2211yescharacteristic
198#1729C2211yescharacteristic
199#1726C2211yescharacteristic, complemented
200#1726C2211yescharacteristic, complemented
201C4×#97C2211yescharacteristic, complemented
202C4×#97C2211yescharacteristic, complemented
203C24×C4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×#117—24no—
209C2×#117—24no—
210C2×#117C2×C411yescharacteristic
211C2×#117C2×C411yescharacteristic
212C2×#117C2×C411yescharacteristic
213C2×#117C2×C411yescharacteristic
214C2×#117C2×C411yescharacteristic
215C2×#117C2×C411yescharacteristic
216C2×#117C2×C411yescharacteristic
217C2×#117C2×C411yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C22×C4⋊C4C2×C411yescharacteristic
225C22×C4⋊C4C2×C411yescharacteristic
226C22×C22⋊C4C2×C411yescharacteristic
227C22×C22⋊C4C2×C411yescharacteristic
228C22×C22⋊C4C2×C411yescharacteristic
229C22×C22⋊C4C2×C411yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234#433—24no—
235#433—24no—
236#433—24no—
237#433—24no—
238#432—24no—
239#432—24no—
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
260#407—24no—
261C2×C22⋊C8—24no—
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊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
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282#405—24no—
283#405—24no—
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312#389C2×C411yescharacteristic
313#389C2×C411yescharacteristic
314#389C2×C411yescharacteristic
315#389C2×C411yescharacteristic
316#389C2×C411yescharacteristic
317#389C2×C411yescharacteristic
318#389C2×C411yescharacteristic
319#389C2×C411yescharacteristic
320#388C2×C411yescharacteristic
321#388C2×C411yescharacteristic
322#388C2×C411yescharacteristic
323#388C2×C411yescharacteristic
324#388C2×C411yescharacteristic
325#388C2×C411yescharacteristic
326#388C2×C411yescharacteristic
327#388C2×C411yescharacteristic
328#388C2×C411yescharacteristic
329#388C2×C411yescharacteristic
330#388C2×C411yescharacteristic
331#388C2×C411yescharacteristic
332#388C2×C411yescharacteristic
333#388C2×C411yescharacteristic
334#388C2×C411yescharacteristic
335#388C2×C411yescharacteristic
336#387C2×C411yescharacteristic
337#387C2×C411yescharacteristic
338#387C2×C411yescharacteristic
339#387C2×C411yescharacteristic
340#387C2×C411yescharacteristic
341#387C2×C411yescharacteristic
342#387C2×C411yescharacteristic
343#387C2×C411yescharacteristic
344#387C2×C411yescharacteristic
345#387C2×C411yescharacteristic
346#387C2×C411yescharacteristic
347#387C2×C411yescharacteristic
348#387C2×C411yescharacteristic
349#387C2×C411yescharacteristic
350#387C2×C411yescharacteristic
351#387C2×C411yescharacteristic
352#385C2×C411yescharacteristic
353#385C2×C411yescharacteristic
354#385C2×C411yescharacteristic
355#385C2×C411yescharacteristic
356#385C2×C411yescharacteristic
357#385C2×C411yescharacteristic
358#385C2×C411yescharacteristic
359#385C2×C411yescharacteristic
360#383C2×C411yescharacteristic
361#383C2×C411yescharacteristic
362#383C2×C411yescharacteristic
363#383C2×C411yescharacteristic
364#382C2×C411yescharacteristic
365#382C2×C411yescharacteristic
366#382C2×C411yescharacteristic
367#382C2×C411yescharacteristic
368#381C2×C411yescharacteristic
369#381C2×C411yescharacteristic
370#381C2×C411yescharacteristic
371#381C2×C411yescharacteristic
372#381C2×C411yescharacteristic
373#381C2×C411yescharacteristic
374#380C2×C411yescharacteristic
375#380C2×C411yescharacteristic
376#380C2×C411yescharacteristic
377#380C2×C411yescharacteristic
378#380C2×C411yescharacteristic
379#380C2×C411yescharacteristic
380#380C2×C411yescharacteristic
381#380C2×C411yescharacteristic
382#379C2×C411yescharacteristic
383#379C2×C411yescharacteristic
384C4×C4⋊C4C2×C411yescharacteristic
385C4×C4⋊C4C2×C411yescharacteristic
386C4×C4⋊C4C2×C411yescharacteristic
387C4×C4⋊C4C2×C411yescharacteristic
388C4×C4⋊C4C2×C411yescharacteristic
389C4×C4⋊C4C2×C411yescharacteristic
390C4×C4⋊C4C2×C411yescharacteristic
391C4×C4⋊C4C2×C411yescharacteristic
392C4×C4⋊C4C2×C411yescharacteristic
393C4×C4⋊C4C2×C411yescharacteristic
394C4×C4⋊C4C2×C411yescharacteristic
395C4×C4⋊C4C2×C411yescharacteristic
396C4×C4⋊C4C2311yescharacteristic
397C4×C4⋊C4C2311yescharacteristic
398C4×C4⋊C4C2311yescharacteristic
399C4×C4⋊C4C2311yescharacteristic
400C4×C4⋊C4C2311yescharacteristic
401C4×C4⋊C4C2311yescharacteristic
402C4×C4⋊C4C2311yescharacteristic
403C4×C4⋊C4C2311yescharacteristic
404C4×C22⋊C4C2×C411yescharacteristic
405C4×C22⋊C4C2×C411yescharacteristic
406C4×C22⋊C4C2×C411yescharacteristic
407C4×C22⋊C4C2×C411yescharacteristic
408C4×C22⋊C4C2×C411yescharacteristic
409C4×C22⋊C4C2×C411yescharacteristic
410C4×C22⋊C4C2×C411yescharacteristic
411C4×C22⋊C4C2×C411yescharacteristic
412C4×C22⋊C4C2×C411yescharacteristic
413C4×C22⋊C4C2×C411yescharacteristic
414C4×C22⋊C4C2×C411yescharacteristic
415C4×C22⋊C4C2×C411yescharacteristic
416C4×C22⋊C4C2×C411yescharacteristic
417C4×C22⋊C4C2×C411yescharacteristic
418C4×C22⋊C4C2×C411yescharacteristic
419C4×C22⋊C4C2×C411yescharacteristic
420C4×C22⋊C4C2311yescharacteristic
421C4×C22⋊C4C2311yescharacteristic
422C4×C22⋊C4C2311yescharacteristic
423C4×C22⋊C4C2311yescharacteristic
424C4×C22⋊C4C2311yescharacteristic
425C4×C22⋊C4C2311yescharacteristic
426C4×C22⋊C4C2311yescharacteristic
427C4×C22⋊C4C2311yescharacteristic
428#376C2×C411yescharacteristic
429#376C2×C411yescharacteristic
430#376C2×C411yescharacteristic
431#376C2×C411yescharacteristic
432#376C2311yescharacteristic
433#376C2311yescharacteristic
434#376C2311yescharacteristic
435#376C2311yescharacteristic
436C2×#95C2×C411yescharacteristic
437C2×#95C2×C411yescharacteristic
438C43C2311yescharacteristic
439C43C2311yescharacteristic
440C43C2311yescharacteristic
441C43C2311yescharacteristic
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
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25C22×C411yescharacteristic
491C23×C4—22no—
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—22no—
495C23×C4—41no—
496C23×C4—41no—
497C23×C4C22×C411yescharacteristic
498C23×C4C22×C411yescharacteristic
499C23×C4C22×C411yescharacteristic
500C23×C4C22×C411yescharacteristic
501C23×C4C22×C411yescharacteristic
502C23×C4C22×C411yescharacteristic
503C23×C4C22×C411yescharacteristic
504C23×C4C22×C411yescharacteristic
505C23×C4C22×C411yescharacteristic
506C23×C4C22×C411yescharacteristic
507C23×C4C22×C411yescharacteristic
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—41no—
516C2×M16—41no—
517C22×C8—22no—
518C22×C8—22no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8—41no—
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
538C22×C8C2411yescharacteristic
539#117—22no—
540#117—22no—
541#117—22no—
542#117—22no—
543#117—24no—
544#117—24no—
545#117—24no—
546#117—24no—
547#117—22no—
548#117—22no—
549#117—22no—
550#117—22no—
551#117—41no—
552#117—41no—
553#117—42no—
554#117—42no—
555#117—42no—
556#117—42no—
557#117#4114yes—
558#117#4114yes—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4C22×C411yescharacteristic
562C2×C4⋊C4C22×C411yescharacteristic
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×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4C22×C411yescharacteristic
594C2×C22⋊C4C22×C411yescharacteristic
595C2×C22⋊C4C22×C411yescharacteristic
596C2×C22⋊C4C22×C411yescharacteristic
597C2×C22⋊C4C22×C411yescharacteristic
598C2×C22⋊C4C22×C411yescharacteristic
599C2×C22⋊C4C22×C411yescharacteristic
600C2×C22⋊C4C22×C411yescharacteristic
601C2×C22⋊C4C22×C411yescharacteristic
602C2×C22⋊C4C22×C411yescharacteristic
603C2×C22⋊C4C22×C411yescharacteristic
604C2×C22⋊C4C22×C411yescharacteristic
605C2×C22⋊C4C22×C411yescharacteristic
606C2×C22⋊C4C22×C411yescharacteristic
607C2×C22⋊C4C22×C411yescharacteristic
608C2×C22⋊C4C22×C411yescharacteristic
609C2×C22⋊C4C22×C411yescharacteristic
610C2×C22⋊C4C22×C411yescharacteristic
611C2×C22⋊C4C22×C411yescharacteristic
612C2×C22⋊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×C42—22no—
622C2×C42—22no—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—41no—
628C2×C42—41no—
629C2×C42C22×C411yescharacteristic
630C2×C42C22×C411yescharacteristic
631C2×C42C22×C411yescharacteristic
632C2×C42C22×C411yescharacteristic
633C2×C42C22×C411yescharacteristic
634C2×C42C22×C411yescharacteristic
635C2×C42C22×C411yescharacteristic
636C2×C42C22×C411yescharacteristic
637C2×C42C22×C411yescharacteristic
638C2×C42C22×C411yescharacteristic
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×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C4⋊C8—22no—
666C4⋊C8—22no—
667C4⋊C8—22no—
668C4⋊C8—22no—
669C4⋊C8—22no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—22no—
674C4⋊C8—22no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677C4⋊C8—41no—
678C4⋊C8—41no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C22⋊C8—22no—
686C22⋊C8—22no—
687C22⋊C8—22no—
688C22⋊C8—22no—
689C22⋊C8—22no—
690C22⋊C8—22no—
691C22⋊C8—22no—
692C22⋊C8—22no—
693C22⋊C8—22no—
694C22⋊C8—22no—
695C22⋊C8—22no—
696C22⋊C8—22no—
697C22⋊C8—22no—
698C22⋊C8—22no—
699C22⋊C8—41no—
700C22⋊C8—41no—
701C22⋊C8—41no—
702C22⋊C8—41no—
703C22⋊C8#4114yes—
704C22⋊C8#4114yes—
705#97—22no—
706#97—22no—
707#97—22no—
708#97—22no—
709#97—22no—
710#97—22no—
711#97—22no—
712#97—22no—
713#97—22no—
714#97—22no—
715#97—22no—
716#97—22no—
717#97—41no—
718#97—41no—
719#97—41no—
720#97—41no—
721C4×C8—22no—
722C4×C8—22no—
723C4×C8—22no—
724C4×C8—22no—
725C4×C8—22no—
726C4×C8—22no—
727C4×C8—22no—
728C4×C8—22no—
729C4×C8—41no—
730C4×C8—41no—
731C4×C8—41no—
732C4×C8—41no—
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
772#95C22×C411yescharacteristic
773#95C22×C411yescharacteristic
774#95C22×C411yescharacteristic
775#95C22×C411yescharacteristic
776#95C22×C411yescharacteristic
777#95C22×C411yescharacteristic
778#95C22×C411yescharacteristic
779#95C22×C411yescharacteristic
780#95C22×C411yescharacteristic
781C24—22no—
782C24—22no—
783C24—22no—
784C24—41no—
785C24—41no—
786C24—41no—
787C24—41no—
788C24C23×C411yescharacteristic
789C24C23×C411yescharacteristic
790C24C23×C411yescharacteristic
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4C23×C411yescharacteristic
843C22×C4C23×C411yescharacteristic
844C22×C4C23×C411yescharacteristic
845C22×C4C23×C411yescharacteristic
846C22×C4C23×C411yescharacteristic
847C22×C4C23×C411yescharacteristic
848C22×C4C23×C411yescharacteristic
849C22×C4C23×C411yescharacteristic
850C22×C4C23×C411yescharacteristic
851C22×C4C23×C411yescharacteristic
852C22×C4C23×C411yescharacteristic
853C22×C4C23×C411yescharacteristic
854C22×C4C23×C411yescharacteristic
855C22×C4C23×C411yescharacteristic
856C22×C4C23×C411yescharacteristic
857C22×C4C23×C411yescharacteristic
858C22×C4C23×C411yescharacteristic
859C22×C4C23×C411yescharacteristic
860C22×C4C23×C411yescharacteristic
861C22×C4C23×C411yescharacteristic
862C22×C4C23×C411yescharacteristic
863C22×C4C23×C411yescharacteristic
864C22×C4C23×C411yescharacteristic
865C22×C4C23×C411yescharacteristic
866C22×C4C23×C411yescharacteristic
867C22×C4C23×C411yescharacteristic
868C22×C4C23×C411yescharacteristic
869C22×C4C2×#4112yes—
870C22×C4C2×#4112yes—
871C22×C4C2×#4112yes—
872C22×C4C2×#4112yes—
873C22×C4C2511yescharacteristic
874M16—44no—
875M16—44no—
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—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
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×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—44no—
921C2×C8—44no—
922C2×C8C2×#4112yes—
923C2×C8C2×#4112yes—
924C2×C8C2×#4112yes—
925C2×C8C2×#4112yes—
926C4⋊C4—22no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
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⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4#11714yes—
953C4⋊C4#11714yes—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
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—41no—
977C22⋊C4—41no—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4#11714yes—
981C22⋊C4#11714yes—
982C42—22no—
983C42—22no—
984C42—22no—
985C42—22no—
986C42—22no—
987C42—22no—
988C42—22no—
989C42—22no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—41no—
1011C42—41no—
1012C42—41no—
1013C42—41no—
1014C42—41no—
1015C42—41no—
1016C42—41no—
1017C42—41no—
1018C42—41no—
1019C42—41no—
1020C42—41no—
1021C42—41no—
1022C42—41no—
1023C42—41no—
1024C42—41no—
1025C42—41no—
1026C42C2×#4112yes—
1027C42C2×#4112yes—
1028C42C2×#4112yes—
1029C42C2×#4112yes—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—44no—
1049C23—44no—
1050C23—44no—
1051C23—82no—
1052C23—82no—
1053C23—82no—
1054C23—82no—
1055C23C2×#11712yes—
1056C23C4×#4112yes—
1057C23#56812yes—
1058C23C24×C411yescharacteristic
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—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
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—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—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—44no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—44no—
1145C2×C4—44no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—82no—
1151C2×C4—82no—
1152C2×C4—82no—
1153C2×C4—82no—
1154C2×C4—82no—
1155C2×C4—82no—
1156C2×C4C2×#11712yes—
1157C2×C4C2×#11712yes—
1158C2×C4C2×#11712yes—
1159C2×C4C2×#11712yes—
1160C2×C4C2×#11712yes—
1161C2×C4C4×#4112yes—
1162C2×C4#56812yes—
1163C2×C4C22×#4111yescharacteristic
1164C2×C4C22×#4111yescharacteristic
1165C2×C4C22×#4111yescharacteristic
1166C2×C4C22×#4111yescharacteristic
1167C2×C4#58511yescharacteristic
1168C2×C4#58511yescharacteristic
1169C8—22no—
1170C8—22no—
1171C8—22no—
1172C8—22no—
1173C8—41no—
1174C8—41no—
1175C8—41no—
1176C8—41no—
1177C8—41no—
1178C8—41no—
1179C8—41no—
1180C8—41no—
1181C8—41no—
1182C8—41no—
1183C8—41no—
1184C8—41no—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—22no—
1192C22—22no—
1193C22—22no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—88no—
1207C22C22×#11711yescharacteristic
1208C22C2×C4×#4111yescharacteristic
1209C22#342811yescharacteristic
1210C22C2×#56811yescharacteristic
1211C22C2×#56811yescharacteristic
1212C22#357311yescharacteristic
1213C22#357311yescharacteristic
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—22no—
1218C4—22no—
1219C4—22no—
1220C4—22no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—41no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4#347511yescharacteristic
1242C4#347511yescharacteristic
1243C4#347511yescharacteristic
1244C4#347511yescharacteristic
1245C2—42no—
1246C2—42no—
1247C2—42no—
1248C2#3410911yescharacteristic
1249C2#6012811yescharacteristic
1250C2#6012911yescharacteristic
1251C2#6021611yescharacteristic
1252C2#6021711yescharacteristic
1253C2#6029911yescharacteristic
1254C2#6029911yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC25C22×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. #22642C2semidirect
3. #22640C2semidirect
4. #22636C2semidirect
5. #22634C2semidirect
6. #22631C2semidirect
7. #22630C2semidirect
8. #22605C2semidirect
9. #22605C2semidirect
10. #22594C2semidirect
11. #22594C2semidirect
12. #22594C2semidirect
13. #22593C2semidirect
18. #21437C2semidirect
19. #21437C2semidirect
20. #21435C2semidirect
21. #21431C2semidirect
22. #21357C2semidirect
23. #21357C2semidirect
24. #20786C2semidirect
25. #20780C2semidirect
27. #20478C2semidirect
28. #20475C2semidirect
29. #20468C2semidirect
30. #20467C2semidirect
73. #1940C22semidirect
74. #1940C22semidirect
75. #1940C22semidirect
76. #1940C22semidirect
77. #1939C22semidirect
78. #1939C22semidirect
79. #1939C22semidirect
80. #1939C22semidirect
97. #1917C22semidirect
98. #1917C22semidirect
99. #1917C22semidirect
100. #1917C22semidirect
101. #1917C22semidirect
102. #1917C22semidirect
103. #1917C22semidirect
104. #1917C22semidirect
105. #1917C22semidirect
106. #1917C22semidirect
107. #1916C22semidirect
108. #1916C22semidirect
109. #1916C22semidirect
110. #1916C22semidirect
111. #1916C22semidirect
112. #1916C22semidirect
121. #1840C22semidirect
122. #1840C22semidirect
123. #1840C22semidirect
124. #1840C22semidirect
125. #1831C22semidirect
126. #1831C22semidirect
127. #1831C22semidirect
128. #1831C22semidirect
145. #1771C22semidirect
146. #1771C22semidirect
147. #1771C22semidirect
148. #1771C22semidirect
149. #1770C22semidirect
150. #1770C22semidirect
151. #1770C22semidirect
152. C8×C4⋊C4C22semidirect
153. #1768C22semidirect
154. #1768C22semidirect
155. #1768C22semidirect
156. #1768C22semidirect
157. #1768C22semidirect
158. #1768C22semidirect
159. #1768C22semidirect
160. #1768C22semidirect
161. #1767C22semidirect
162. #1767C22semidirect
163. C4×C4⋊C8C22semidirect
164. C4×C4⋊C8C22semidirect
189. #1746C22semidirect
190. #1746C22semidirect
191. #1745C22semidirect
192. #1745C22semidirect
193. #1745C22semidirect
194. #1745C22semidirect
195. #1744C22semidirect
196. #1744C22semidirect
199. #1726C22semidirect
200. #1726C22semidirect
201. C4×#97C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#341092
#226422
#226402
#226362
#226342
#226312
#226302
#226052
#225942
#225932
#225592
#225582
#225552
#225542
#214372
#214352
#214312
#213572
#207862
#207802
#207162
#204782
#204752
#204682
#204672
#203792