Finite Group Databasebeta

← #28400437

Subgroups — #28400437

Order 14464.

376 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299228C211yesmaximal, characteristic, complemented
2#20299077C211yesmaximal, characteristic
3#20298904C211yesmaximal, characteristic, complemented
4#20298902C211yesmaximal, characteristic, complemented
5#20298900C211yesmaximal, characteristic, complemented
6#20298888C211yesmaximal, characteristic, complemented
7#20298886C211yesmaximal, characteristic, complemented
8#20298884C211yesmaximal, characteristic, complemented
9#20298882C211yesmaximal, characteristic, complemented
10#20298639C211yesmaximal, characteristic, complemented
11#106×D113C211yesmaximal, characteristic, complemented
12#20298623C211yesmaximal, characteristic, complemented
13#20298596C211yesmaximal, characteristic
14#20298591C211yesmaximal, characteristic
15#478×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×#14268630C2211yescharacteristic
18C2×C8×D113C2211yescharacteristic
19#16813622C2211yescharacteristic
20#16813621—21no—
21#16813621C2211yescharacteristic
22#16813613C2211yescharacteristic
23#16813612—21no—
24#16813602—21no—
25#16813600—21no—
26C4×Dic226C2211yescharacteristic
27#16813587C2211yescharacteristic
28D4×Dic113C2211yescharacteristic
29C4×C22⋊D113—21no—
30#16813582—21no—
31#16813580C2211yescharacteristic
32#16813579C2211yescharacteristic
33#16813578—21no—
34C2×#14268626—21no—
35C4⋊C4×D113C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813555C2211yescharacteristic
38#16813554C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813553C2211yescharacteristic
43C4⋊#11744751C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813545C2211yescharacteristic
50#16813543C2211yescharacteristic
51#16813543C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—22no—
60#14268646Q814yescomplemented
61C2×Dic226—21no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64C2×C22⋊D113—21no—
65C22×Dic113—21no—
66C22×Dic113—21no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113C2311yescharacteristic
70#14268630—22no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C8×D113—22no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626D411yescharacteristic
86#14268626D411yescharacteristic
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624D411yescharacteristic
90#14268624D411yescharacteristic
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C2×D4×C113C2311yescharacteristic
96C22×C4×C113—21no—
97C2×C8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C4⋊C4×C113—21no—
100C4⋊C4×C113—21no—
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C22⋊C4×C113—21no—
105C42×C113C2311yescharacteristic
106C23×C113—21no—
107C22×D113C2×D411yescharacteristic
108D4×C113—21no—
109D4×C113C2×Q812yes—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—81no—
114C2×C4×C113C2×D411yescharacteristic
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2411yescharacteristic
117C22⋊D113—24no—
118C2×Dic113—21no—
119C2×Dic113—24no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—81no—
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127C4×D113—81no—
128C4×D113—81no—
129C4×D113C2×Q812yes—
130C4×D113#4112yes—
131Dic226—21no—
132Dic226—81no—
133Dic226—81no—
134Dic226C2×Q812yes—
135C8×C113—21no—
136C8×C113—21no—
137#11744751—21no—
138#11744751—21no—
139C22×C113—22no—
140C22×C113—41no—
141C22×C113—41no—
142C22×C113C22×D411yescharacteristic
143C2×D113—21no—
144C2×D113—21no—
145C2×D113C22⋊Q812yes—
146C4×C113—21no—
147C4×C113—21no—
148C4×C113—41no—
149C4×C113—41no—
150C4×C113—41no—
151C4×C113C22×Q811yescharacteristic
152C4×C113C2×#4111yescharacteristic
153Dic113—22no—
154Dic113—21no—
155Dic113—21no—
156Dic113—41no—
157Dic113—41no—
158Dic113—41no—
159Dic113C22⋊Q812yes—
160C2×C113—42no—
161C2×C113C2×C22⋊Q811yescharacteristic
162C2×C113#57711yescharacteristic
163C2×C113#57711yescharacteristic
164D113—22no—
165#3084—1131nomaximal, Sylow
166C113#308411yescharacteristic, complemented, Sylow
167#544—1131no—
168#520—1131no—
169#479—1131no—
170#479—1131no—
171#478—1131no—
172#478D11311yescharacteristic, complemented
173#476—1131no—
174#476—1131no—
175#475—1131no—
176#475—1131no—
177#428—1131no—
178C2×#106—1131no—
179#424—1131no—
180#417—1131no—
181#416—1131no—
182C2×#41—1131no—
183C2×M16—1131no—
184C22×C8—1131no—
185C4⋊Q8—1131no—
186C4⋊Q8—1131no—
187C4⋊Q8—2261no—
188#125—1131no—
189#125—2261no—
190#125C2×D11311yescharacteristic
191C22⋊Q8—2261no—
192C22⋊Q8—2261no—
193C4×Q8—1131no—
194C4×Q8—1131no—
195C4×D4—1131no—
196C4×D4—2261no—
197C4×D4—2261no—
198C4×D4C2×D11311yescharacteristic
199#117—1131no—
200#117—1131no—
201#117—2261no—
202C2×C4⋊C4—1131no—
203C2×C4⋊C4—1131no—
204C2×C4⋊C4—2261no—
205#107—1131no—
206#107C2×D11311yescharacteristic
207#106—1131no—
208#106—1131no—
209#106—1131no—
210#106—1131no—
211#106—1131no—
212#106C2×D11311yescharacteristic
213C4⋊C8—1131no—
214C4⋊C8—1131no—
215C4⋊C8—1131no—
216C4⋊C8C2×D11311yescharacteristic
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#102—1131no—
222#102—1131no—
223#102C2×D11311yescharacteristic
224#102C2×D11311yescharacteristic
225#41—1134no—
226#41—2262no—
227C2×Q8—1131no—
228C2×Q8—2261no—
229C2×Q8—2261no—
230C2×D4—2261no—
231C2×D4C22×D11311yescharacteristic
232C22×C4—21no—
233C22×C4—1131no—
234C22×C4—2261no—
235C22×C4—2261no—
236C22×C4—2261no—
237C22×C4—2261no—
238M16—2262no—
239C2×C8—1131no—
240C2×C8—1131no—
241C2×C8—2262no—
242C2×C8C22×D11311yescharacteristic
243C2×C8C22×D11311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—1131no—
247C4⋊C4—1131no—
248C4⋊C4—1131no—
249C4⋊C4—1131no—
250C4⋊C4—1131no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4C22×D11311yescharacteristic
260C4⋊C4C22×D11311yescharacteristic
261C4⋊C4C22×D11311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—1131no—
264C22⋊C4—1131no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C42—1131no—
268C42—2261no—
269C42—2261no—
270C42—2261no—
271C42C22×D11311yescharacteristic
272C23—21no—
273C23—1131no—
274Q8—1132no—
275Q8—9041no—
276Q8—9041no—
277Q8—2261no—
278D4—21no—
279D4—2264no—
280D4Q8×D11312yes—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—1131no—
286C2×C4—1132no—
287C2×C4—1132no—
288C2×C4—1131no—
289C2×C4—1131no—
290C2×C4—9041no—
291C2×C4—9041no—
292C2×C4—9041no—
293C2×C4—2264no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4—2261no—
297C2×C4—2261no—
298C2×C4D4×D11311yescharacteristic
299C2×C4D4×D11311yescharacteristic
300C2×C4C23×D11311yescharacteristic
301C8—21no—
302C8—21no—
303C8—2261no—
304C8—2261no—
305C22—22no—
306C22—41no—
307C22—41no—
308C22—1132no—
309C22—2261no—
310C22—2261no—
311C22C2×D4×D11311yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—1132no—
318C4—4521no—
319C4—4521no—
320C4—4521no—
321C4—2262no—
322C4—2261no—
323C4—2261no—
324C4C2×Q8×D11311yescharacteristic
325C4#41×D11311yescharacteristic
326C2—42no—
327C2—2262no—
328C2C22⋊Q8×D11311yescharacteristic
329C2#2029940511yescharacteristic
330C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#478×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268646C22
hypercenter#478D113
hypocenterC113#3084
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. #20299228C2semidirect
3. #20298904C2semidirect
4. #20298902C2semidirect
5. #20298900C2semidirect
6. #20298888C2semidirect
7. #20298886C2semidirect
8. #20298884C2semidirect
9. #20298882C2semidirect
10. #20298639C2semidirect
11. #106×D113C2semidirect
12. #20298623C2semidirect
15. #478×C113C2semidirect
60. #14268646Q8semidirect
166. C113#3084semidirect
172. #478D113semidirect

Maximal subgroups

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

subgroupindex
#202992282
#202990772
#202989042
#202989022
#202989002
#202988882
#202988862
#202988842
#202988822
#202986392
#106×D1132
#202986232
#202985962
#202985912
#478×C1132
#3084113