Finite Group Databasebeta

← #28400369

Subgroups — #28400369

Order 14464.

440 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299154C211yesmaximal, characteristic, complemented
2C4×D4×D113C211yesmaximal, characteristic
3#20298899C211yesmaximal, characteristic, complemented
4#20298898C211yesmaximal, characteristic, complemented
5#20298895C211yesmaximal, characteristic, complemented
6#20298887C211yesmaximal, characteristic, complemented
7#20298886C211yesmaximal, characteristic, complemented
8#20298877C211yesmaximal, characteristic, complemented
9#20298876C211yesmaximal, characteristic, complemented
10#20298639C211yesmaximal, characteristic, complemented
11#20298637C211yesmaximal, characteristic, complemented
12#20298620C211yesmaximal, characteristic, complemented
13#20298601C211yesmaximal, characteristic
14#20298601C211yesmaximal, characteristic
15#478×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C22×C4×D113—21no—
18C2×#14268630C2211yescharacteristic
19C2×#14268630C2211yescharacteristic
20#16813621C2211yescharacteristic, complemented
21#16813621C2211yescharacteristic, complemented
22#16813614C2211yescharacteristic, complemented
23#16813600—21no—
24#16813600—21no—
25#16813587—21no—
26#16813587—21no—
27C4×D452C2211yescharacteristic
28D4×Dic113C2211yescharacteristic
29#16813584C2211yescharacteristic
30C4×C22⋊D113—21no—
31#16813582—21no—
32#16813580C2211yescharacteristic
33#16813580C2211yescharacteristic
34C4⋊C4×D113C2211yescharacteristic
35C22⋊C4×D113—21no—
36C42×D113C2211yescharacteristic
37#16813556C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813553C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43C4⋊#11744751C2211yescharacteristic, complemented
44#16813551C2211yescharacteristic, complemented
45#16813551C2211yescharacteristic, complemented
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813542C2211yescharacteristic
51#16813542C2211yescharacteristic
52#125×C113C2211yescharacteristic, complemented
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C23×D113—21no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64D4×D113—22no—
65D4×D113Q814yescomplemented
66C22×Dic113—21no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—44no—
71C2×C4×D113D411yescharacteristic
72C2×C4×D113D411yescharacteristic
73C2×C4×D113C2311yescharacteristic
74#14268630—22no—
75#14268630—22no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113D411yescharacteristic
94C4×Dic113D411yescharacteristic
95C4×Dic113C2311yescharacteristic
96C2×D4×C113C2311yescharacteristic
97C22×C4×C113—21no—
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C4⋊C4×C113—21no—
101C4⋊C4×C113—21no—
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C42×C113C2311yescharacteristic
107C23×C113—21no—
108C22×D113—21no—
109C22×D113—24no—
110C22×D113—42no—
111C22×D113—42no—
112C22×D113C2×D411yescharacteristic
113D4×C113—21no—
114D4×C113C2×Q812yes—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—42no—
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C22⋊D113—24no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—42no—
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130D452—21no—
131D452C2×Q812yes—
132C4×D113—22no—
133C4×D113—41no—
134C4×D113—42no—
135C4×D113—42no—
136C4×D113—42no—
137C4×D113C2×Q812yes—
138C4×D113#4112yes—
139Dic226—42no—
140Dic226—42no—
141C8×C113—21no—
142C8×C113—21no—
143#11744751—21no—
144#11744751—21no—
145C22×C113—22no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113C22×D411yescharacteristic
149C2×D113—21no—
150C2×D113—21no—
151C2×D113—22no—
152C2×D113—48no—
153C2×D113—41no—
154C2×D113—41no—
155C2×D113C22⋊Q812yes—
156C4×C113—21no—
157C4×C113—21no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113C22×Q811yescharacteristic
162C4×C113C2×#4111yescharacteristic
163Dic113—21no—
164Dic113—41no—
165Dic113—41no—
166Dic113—41no—
167Dic113C22⋊Q812yes—
168Dic113AGL(1,ℤ/8)12yes—
169C2×C113—42no—
170C2×C113C2×C22⋊Q811yescharacteristic
171C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C113#57511yescharacteristic
173D113—22no—
174D113—42no—
175#3077—1131nomaximal, Sylow
176C113#307711yescharacteristic, complemented, Sylow
177#533—1131no—
178C2×C4×D4—1131no—
179#478—1131no—
180#478—1131no—
181#478—1131no—
182#478D11311yescharacteristic, complemented
183#476—1131no—
184#476—1131no—
185#474—1131no—
186#474—1131no—
187#428—1131no—
188#428—1131no—
189#423—1131no—
190#418—1131no—
191#418—1131no—
192C22×D4—1131no—
193C23×C4—2261no—
194C2×M16—1131no—
195C2×M16—1131no—
196C4⋊Q8—1131no—
197C4⋊Q8—1131no—
198#125—1131no—
199#125C2×D11311yescharacteristic, complemented
200C22⋊Q8—2261no—
201C22⋊Q8—2261no—
202C4×Q8—2261no—
203C4×Q8—2261no—
204C4×D4—1131no—
205C4×D4—1131no—
206C4×D4—1131no—
207C4×D4—2261no—
208C4×D4—2261no—
209C4×D4C2×D11311yescharacteristic
210#117—1131no—
211#117—1131no—
212C2×C4⋊C4—1131no—
213C2×C22⋊C4—2261no—
214C2×C42—1131no—
215#107—1131no—
216#107—1131no—
217#107—1131no—
218#107C2×D11311yescharacteristic, complemented
219#106—1131no—
220#106—1131no—
221#106—1131no—
222#106C2×D11311yescharacteristic, complemented
223C4⋊C8—1131no—
224C4⋊C8—1131no—
225C4⋊C8—1131no—
226C4⋊C8C2×D11311yescharacteristic, complemented
227#102—1131no—
228#102—1131no—
229#102—1131no—
230#102—1131no—
231#102—1131no—
232#102—1131no—
233#102C2×D11311yescharacteristic
234#102C2×D11311yescharacteristic
235C24—2261no—
236C2×Q8—2261no—
237C2×Q8—2261no—
238C2×D4—1134no—
239C2×D4—1131no—
240C2×D4—2262no—
241C2×D4—2261no—
242C2×D4C22×D11311yescharacteristic
243C22×C4—21no—
244C22×C4—1131no—
245C22×C4—1131no—
246C22×C4—1131no—
247C22×C4—4524no—
248C22×C4—2261no—
249C22×C4—2261no—
250C22×C4—2261no—
251C22×C4—2261no—
252M16—2262no—
253M16—2262no—
254C2×C8—1131no—
255C2×C8—1131no—
256C2×C8C22×D11311yescharacteristic
257C2×C8C22×D11311yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—1131no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4C22×D11311yescharacteristic
269C4⋊C4C22×D11311yescharacteristic
270C4⋊C4C22×D11311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C42—1131no—
278C42—1131no—
279C42—1131no—
280C42—2261no—
281C42—2261no—
282C42C22×D11311yescharacteristic
283C23—21no—
284C23—1131no—
285C23—4522no—
286C23—4522no—
287C23—2264no—
288C23—2261no—
289Q8—4522no—
290Q8—4522no—
291D4—21no—
292D4—1132no—
293D4—2264no—
294D4—2261no—
295D4Q8×D11312yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—1131no—
301C2×C4—1131no—
302C2×C4—1132no—
303C2×C4—1132no—
304C2×C4—1131no—
305C2×C4—4522no—
306C2×C4—4521no—
307C2×C4—4522no—
308C2×C4—4522no—
309C2×C4—4522no—
310C2×C4—2262no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4D4×D11311yescharacteristic
315C2×C4D4×D11311yescharacteristic
316C2×C4C23×D11311yescharacteristic
317C8—21no—
318C8—21no—
319C8—2261no—
320C8—2261no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—1132no—
325C22—4528no—
326C22—4521no—
327C22—4521no—
328C22—2262no—
329C22—2261no—
330C22—2261no—
331C22C2×D4×D11311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—1132no—
338C4—1132no—
339C4—4521no—
340C4—4521no—
341C4—4521no—
342C4—2261no—
343C4C2×Q8×D11311yescharacteristic
344C4#41×D11311yescharacteristic
345C2—42no—
346C2—4522no—
347C2—2262no—
348C2C22⋊Q8×D11311yescharacteristic
349C2AGL(1,ℤ/8)×D11311yescharacteristic
350C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#478×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#478D113
hypocenterC113#3077
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #20299154C2semidirect
3. #20298899C2semidirect
4. #20298898C2semidirect
5. #20298895C2semidirect
6. #20298887C2semidirect
7. #20298886C2semidirect
8. #20298877C2semidirect
9. #20298876C2semidirect
10. #20298639C2semidirect
11. #20298637C2semidirect
12. #20298620C2semidirect
15. #478×C113C2semidirect
20. #16813621C22semidirect
21. #16813621C22semidirect
22. #16813614C22semidirect
37. #16813556C22semidirect
38. #16813555C22semidirect
39. #16813555C22semidirect
40. #16813554C22semidirect
41. #16813553C22semidirect
42. #16813553C22semidirect
43. C4⋊#11744751C22semidirect
44. #16813551C22semidirect
45. #16813551C22semidirect
52. #125×C113C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
56. C4⋊C8×C113C22semidirect
65. D4×D113Q8semidirect
176. C113#3077semidirect
182. #478D113semidirect
199. #125C2×D113semidirect
218. #107C2×D113semidirect
222. #106C2×D113semidirect
226. C4⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991542
C4×D4×D1132
#202988992
#202988982
#202988952
#202988872
#202988862
#202988772
#202988762
#202986392
#202986372
#202986202
#202986012
#478×C1132
#3077113