Finite Group Databasebeta

← #28400491

Subgroups — #28400491

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299110C211yesmaximal, characteristic
2#117×D113C211yesmaximal, characteristic, complemented
3#20298942C211yesmaximal, characteristic, complemented
4#20298941C211yesmaximal, characteristic, complemented
5#20298935C211yesmaximal, characteristic, complemented
6#20298930C211yesmaximal, characteristic, complemented
7#20298925C211yesmaximal, characteristic, complemented
8#20298924C211yesmaximal, characteristic, complemented
9#20298918C211yesmaximal, characteristic, complemented
10#20298913C211yesmaximal, characteristic, complemented
11#20298634C211yesmaximal, characteristic, complemented
12#20298595C211yesmaximal, characteristic, complemented
13#20298592C211yesmaximal, characteristic, complemented
14C2×#16813534C211yesmaximal, characteristic, complemented
15#427×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×C4×D113C2211yescharacteristic
18C22×#11744751C2211yescharacteristic
19#16813606—21no—
20#16813602C2211yescharacteristic
21#16813602C2211yescharacteristic
22#16813597C2211yescharacteristic
23#16813597C2211yescharacteristic
24#16813592—21no—
25C4×D452—21no—
26C4×D452—21no—
27#16813581C2211yescharacteristic
28#16813580C2211yescharacteristic
29#16813580C2211yescharacteristic
30#16813579—21no—
31#16813578—21no—
32C4⋊C4×D113C2211yescharacteristic
33C4⋊C4×D113C2211yescharacteristic
34C22⋊C4×D113—21no—
35C42×D113—21no—
36#16813555C2211yescharacteristic, complemented
37#16813555C2211yescharacteristic, complemented
38#16813553C2211yescharacteristic, complemented
39#16813553C2211yescharacteristic, complemented
40#16813547C2211yescharacteristic, complemented
41#16813547C2211yescharacteristic, complemented
42#16813545C2211yescharacteristic, complemented
43#16813545C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic, complemented
46#16813542C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic, complemented
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C22×C8×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic, complemented
56#107×C113C2211yescharacteristic, complemented
57#106×C113C2211yescharacteristic, complemented
58#106×C113C2211yescharacteristic, complemented
59C23×D113D411yescharacteristic
60#14268647—22no—
61#14268647—22no—
62C2×Dic226C2311yescharacteristic
63C2×D452—21no—
64C2×D452—21no—
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67C22×Dic113D411yescharacteristic
68C2×C4×D113—22no—
69C2×C4×D113—22no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113D411yescharacteristic
74C2×C4×D113D411yescharacteristic
75C2×C4×D113C2311yescharacteristic
76C2×C4×D113C2311yescharacteristic
77C2×#11744751—22no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C4⋊Dic113—21no—
81C4⋊Dic113—21no—
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C22×C4×C113C2311yescharacteristic
97C2×C8×C113—22no—
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C42×C113—21no—
107C42×C113—21no—
108C23×C113C2×D411yescharacteristic
109C22×D113—22no—
110C22×D113—22no—
111C22×D113—21no—
112C22×D113—41no—
113C22×D113C2×D411yescharacteristic
114C22×D113C2×D411yescharacteristic
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113#4112yes—
121C2×C4×C113#4112yes—
122C2×C4×C113C2411yescharacteristic
123C22⋊D113—42no—
124C2×Dic113—22no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130D452—21no—
131D452—21no—
132D452—42no—
133D452—42no—
134C4×D113—22no—
135C4×D113—22no—
136C4×D113—21no—
137C4×D113—21no—
138C4×D113—21no—
139C4×D113—21no—
140C4×D113—42no—
141C4×D113—42no—
142C4×D113—42no—
143Dic226—21no—
144Dic226—21no—
145C8×C113—21no—
146C8×C113—21no—
147#11744751—21no—
148#11744751—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113#12312yes—
152C22×C113C22×D411yescharacteristic
153C2×D113—21no—
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—44no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—41no—
162C2×D113#13512yes—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113—41no—
167C4×C113#12312yes—
168C4×C113C2×#4111yescharacteristic
169C4×C113C2×#4111yescharacteristic
170Dic113—21no—
171Dic113—21no—
172Dic113—41no—
173Dic113—41no—
174Dic113—41no—
175C2×C113—22no—
176C2×C113C2×#12311yescharacteristic
177C2×C113C2×#13511yescharacteristic
178C2×C113#57511yescharacteristic
179D113—22no—
180D113—41no—
181D113—81no—
182#3091—1131nomaximal, Sylow
183C113#309111yescharacteristic, complemented, Sylow
184#525—1131no—
185C2×#117—1131no—
186#485—1131no—
187#485—1131no—
188#484—1131no—
189#483—1131no—
190#482—1131no—
191#482—1131no—
192#481—1131no—
193#480—1131no—
194#427—1131no—
195#427D11311yescharacteristic, complemented
196#416—1131no—
197#416—1131no—
198C2×C22⋊C8—1131no—
199C2×#41—1131no—
200C23×C4—1131no—
201C22×C8—1131no—
202C22×C8C2×D11311yescharacteristic
203#123—2261no—
204C22⋊Q8—1131no—
205C22⋊Q8—1131no—
206#121—1131no—
207#121—1131no—
208#120—2261no—
209C4×D4—2261no—
210C4×D4—2261no—
211#117—1131no—
212#117—1131no—
213#117—1131no—
214#117—2261no—
215#117—2261no—
216#117C2×D11311yescharacteristic
217#117C2×D11311yescharacteristic
218C2×C4⋊C4—1131no—
219C2×C4⋊C4—1131no—
220C2×C22⋊C4—2261no—
221C2×C42—2261no—
222#107—1131no—
223#107—1131no—
224#107C2×D11311yescharacteristic, complemented
225#107C2×D11311yescharacteristic, complemented
226#106—1131no—
227#106—1131no—
228#106C2×D11311yescharacteristic, complemented
229#106C2×D11311yescharacteristic, complemented
230#103—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#102—1131no—
235#102—1131no—
236#102—1131no—
237#102—1131no—
238C22⋊C8—1131no—
239C22⋊C8—1131no—
240C22⋊C8—1131no—
241C22⋊C8—1131no—
242C24—1131no—
243#41—2262no—
244#41—2262no—
245C2×Q8—1131no—
246C2×D4—1131no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4—2261no—
250C22×C4—1131no—
251C22×C4—1131no—
252C22×C4—1131no—
253C22×C4—1131no—
254C22×C4—1131no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4—2262no—
259C22×C4—2262no—
260C22×C4C22×D11311yescharacteristic
261C2×C8—22no—
262C2×C8—1131no—
263C2×C8—1131no—
264C2×C8—2262no—
265C2×C8C22×D11311yescharacteristic
266C2×C8C22×D11311yescharacteristic
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4C22×D11311yescharacteristic
274C4⋊C4C22×D11311yescharacteristic
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—21no—
287C42—21no—
288C42—2261no—
289C42—2261no—
290C42—2261no—
291C23—1131no—
292C23—1131no—
293C23—4521no—
294C23—2262no—
295C23—2261no—
296C23—2262no—
297C23D4×D11311yescharacteristic
298Q8—2261no—
299Q8—2261no—
300D4—4522no—
301D4—4522no—
302D4—4522no—
303D4—2261no—
304D4—2261no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—4522no—
312C2×C4—4522no—
313C2×C4—4522no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2262no—
318C2×C4—2262no—
319C2×C4—2262no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4D4×D11311yescharacteristic
325C2×C4#1426864712yes—
326C2×C4#1426864812yes—
327C2×C4C23×D11311yescharacteristic
328C8—21no—
329C8—21no—
330C8—2261no—
331C8—2261no—
332C22—21no—
333C22—21no—
334C22—1132no—
335C22—4524no—
336C22—4521no—
337C22—4521no—
338C22—4521no—
339C22—2261no—
340C22—2261no—
341C22—2261no—
342C22—2261no—
343C22—2261no—
344C22#1681360712yes—
345C22C2×D4×D11311yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—4521no—
351C4—4521no—
352C4—4521no—
353C4—2261no—
354C4—2261no—
355C4#1681360712yes—
356C4C2×#1426864711yescharacteristic
357C4C2×#1426864811yescharacteristic
358C2—22no—
359C2—9041no—
360C2—4521no—
361C2—2262no—
362C2C2×#1681360711yescharacteristic
363C2#135×D11311yescharacteristic
364C2#2029939511yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#427×C113C2
socleC22×C113C22×D4
prime radical#20299110C2
hypercenter#427D113
hypocenterC113#3091
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #117×D113C2semidirect
3. #20298942C2semidirect
4. #20298941C2semidirect
5. #20298935C2semidirect
6. #20298930C2semidirect
7. #20298925C2semidirect
8. #20298924C2semidirect
9. #20298918C2semidirect
10. #20298913C2semidirect
11. #20298634C2semidirect
12. #20298595C2semidirect
13. #20298592C2semidirect
14. C2×#16813534C2semidirect
15. #427×C113C2semidirect
36. #16813555C22semidirect
37. #16813555C22semidirect
38. #16813553C22semidirect
39. #16813553C22semidirect
40. #16813547C22semidirect
41. #16813547C22semidirect
42. #16813545C22semidirect
43. #16813545C22semidirect
44. #16813544C22semidirect
45. #16813544C22semidirect
46. #16813542C22semidirect
47. #16813542C22semidirect
55. #107×C113C22semidirect
56. #107×C113C22semidirect
57. #106×C113C22semidirect
58. #106×C113C22semidirect
183. C113#3091semidirect
195. #427D113semidirect
224. #107C2×D113semidirect
225. #107C2×D113semidirect
228. #106C2×D113semidirect
229. #106C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991102
#117×D1132
#202989422
#202989412
#202989352
#202989302
#202989252
#202989242
#202989182
#202989132
#202986342
#202985952
#202985922
C2×#168135342
#427×C1132
#3091113