Finite Group Databasebeta

← #28401175

Subgroups — #28401175

Order 14464.

364 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299150C211yesmaximal, characteristic, complemented
2#20299134C211yesmaximal, characteristic
3#20299005C211yesmaximal, characteristic, complemented
4#20298991C211yesmaximal, characteristic, complemented
5#20298965C211yesmaximal, characteristic, complemented
6#20298959C211yesmaximal, characteristic, complemented
7#20298854C211yesmaximal, characteristic, complemented
8#20298846C211yesmaximal, characteristic
9#20298844C211yesmaximal, characteristic
10Q16×Dic113C211yesmaximal, characteristic, complemented
11#20298690C211yesmaximal, characteristic, complemented
12#20298685C211yesmaximal, characteristic, complemented
13#20298683C211yesmaximal, characteristic, complemented
14M16×Dic113C211yesmaximal, characteristic, complemented
15#470×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268631C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813620C2211yescharacteristic
22#16813617—21no—
23#16813613C2211yescharacteristic
24#16813612—21no—
25#16813611C2211yescharacteristic
26#16813606—21no—
27#16813601C2211yescharacteristic
28#16813599—21no—
29#16813596C2211yescharacteristic
30Q8×Dic113C2211yescharacteristic
31Q8×Dic113C2211yescharacteristic
32#16813587—21no—
33#16813587C2211yescharacteristic
34#16813584C2211yescharacteristic
35#16813582—21no—
36#16813580—21no—
37#16813578—21no—
38C2×C4×Dic113C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813532C2211yescharacteristic
49#16813532C2211yescharacteristic
50C8×Dic113C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C22×Dic113D411yescharacteristic
64C22×Dic113D411yescharacteristic
65C2×C4×D113—21no—
66#14268637—22no—
67#14268636—22no—
68#14268634—22no—
69#14268631—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113—21no—
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83C22⋊Dic113—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88C4×Dic113—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113D411yescharacteristic
92C4×Dic113D411yescharacteristic
93C4×Dic113C2311yescharacteristic
94C4×Dic113C2311yescharacteristic
95C2×Q8×C113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C22×C4×C113C2311yescharacteristic
98Q16×C113—22no—
99M16×C113—22no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113—21no—
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C22⋊C4×C113—21no—
108C23×C113C2×D411yescharacteristic
109C22×D113—21no—
110Q8×C113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C22⋊D113—42no—
123C2×Dic113—22no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—41no—
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132D452—21no—
133D452—21no—
134C4×D113—42no—
135Dic226—21no—
136Dic226—21no—
137Dic226—42no—
138C8×C113—21no—
139C8×C113#4112yes—
140#11744751—21no—
141#11744751#4112yes—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113C22×D411yescharacteristic
146C2×D113—41no—
147C2×D113—41no—
148C2×D113—41no—
149C4×C113—21no—
150C4×C113—41no—
151C4×C113—41no—
152C4×C113—41no—
153C4×C113—41no—
154C4×C113C2×#4111yescharacteristic
155C4×C113C2×#4111yescharacteristic
156Dic113—21no—
157Dic113—21no—
158Dic113—21no—
159Dic113—41no—
160Dic113—41no—
161Dic113—41no—
162Dic113#13712yes—
163C2×C113—41no—
164C2×C113#53211yescharacteristic
165C2×C113C2×#13711yescharacteristic
166C2×C113#57511yescharacteristic
167D113—81no—
168#3172—1131nomaximal, Sylow
169C113#317211yescharacteristic, complemented, Sylow
170#533—1131no—
171#529—1131no—
172#501—1131no—
173#497—1131no—
174#491—1131no—
175#489—1131no—
176#470—1131no—
177#470D11311yescharacteristic, complemented
178#468—1131no—
179#468—1131no—
180C4×Q16—1131no—
181C4×Q16—1131no—
182C4×SD16—1131no—
183C4×SD16—1131no—
184C4×M16—1131no—
185C2×Q16—1131no—
186C2×Q16C2×D11311yescharacteristic
187C2×SD16—1131no—
188C2×SD16—1131no—
189C2×M16—1131no—
190C2×M16C2×D11311yescharacteristic
191C4⋊Q8—1131no—
192C4⋊Q8—1131no—
193#126—2261no—
194#125—1131no—
195#125—2261no—
196#124—1131no—
197#123—2261no—
198C22⋊Q8—1131no—
199C22⋊Q8—2261no—
200C22⋊Q8C2×D11311yescharacteristic
201C22⋊Q8C2×D11311yescharacteristic
202#121—1131no—
203C4×Q8—1131no—
204C4×Q8—1131no—
205C4×Q8—1131no—
206C4×Q8—2261no—
207C4×D4—1131no—
208C4×D4—2261no—
209#117—2261no—
210#117—2261no—
211C2×C42—1131no—
212#107—1131no—
213#107—1131no—
214#106—1131no—
215#106C2×D11311yescharacteristic
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103C2×D11311yescharacteristic
221#103C2×D11311yescharacteristic
222#102—1131no—
223#102—1131no—
224#97—1131no—
225#97—1131no—
226C4×C8—1131no—
227C4×C8—1131no—
228C2×Q8—1131no—
229C2×Q8—2261no—
230C2×Q8C22×D11311yescharacteristic
231C2×Q8C22×D11311yescharacteristic
232C2×D4—1131no—
233C2×D4—2261no—
234C22×C4—1131no—
235C22×C4—1131no—
236C22×C4—2261no—
237C22×C4C22×D11311yescharacteristic
238Q16—22no—
239Q16—2262no—
240SD16—2262no—
241SD16—2262no—
242M16—22no—
243M16—2262no—
244C2×C8—1131no—
245C2×C8—1131no—
246C2×C8C22×D11311yescharacteristic
247C2×C8C22×D11311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—1131no—
251C4⋊C4—1131no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4C22×D11311yescharacteristic
262C4⋊C4C22×D11311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C42—1131no—
271C42—1131no—
272C42—1131no—
273C42—1131no—
274C42—2261no—
275C42—2261no—
276C42—2261no—
277C23—2261no—
278C23D4×D11311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—4522no—
284Q8—2261no—
285Q8—2261no—
286D4—4522no—
287D4—2261no—
288D4—2261no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—1131no—
296C2×C4—1131no—
297C2×C4—1131no—
298C2×C4—1131no—
299C2×C4—4522no—
300C2×C4—4521no—
301C2×C4—2262no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4D4×D11311yescharacteristic
306C2×C4C23×D11311yescharacteristic
307C8—21no—
308C8—1132no—
309C8—2261no—
310C8#1426864612yes—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—4521no—
315C22—4521no—
316C22—4521no—
317C22C2×D4×D11311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—1132no—
324C4—4521no—
325C4—4521no—
326C4—4521no—
327C4—2261no—
328C4—2261no—
329C4—2261no—
330C4#41×D11311yescharacteristic
331C4C2×#1426864611yescharacteristic
332C2—41no—
333C2—9041no—
334C2#2029914311yescharacteristic
335C2#137×D11311yescharacteristic
336C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#470×C113C2
socleC22×C113C22×D4
prime radical#16813596C22
hypercenter#470D113
hypocenterC113#3172
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #20299150C2semidirect
3. #20299005C2semidirect
4. #20298991C2semidirect
5. #20298965C2semidirect
6. #20298959C2semidirect
7. #20298854C2semidirect
10. Q16×Dic113C2semidirect
11. #20298690C2semidirect
12. #20298685C2semidirect
13. #20298683C2semidirect
14. M16×Dic113C2semidirect
15. #470×C113C2semidirect
169. C113#3172semidirect
177. #470D113semidirect

Maximal subgroups

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

subgroupindex
#202991502
#202991342
#202990052
#202989912
#202989652
#202989592
#202988542
#202988462
#202988442
Q16×Dic1132
#202986902
#202986852
#202986832
M16×Dic1132
#470×C1132
#3172113