Finite Group Databasebeta

← #28402381

Subgroups — #28402381

Order 14464.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D452C211yesmaximal, characteristic, complemented
2#20298946C211yesmaximal, characteristic, complemented
3#20298911C212yesmaximal, complemented
4#20298875C211yesmaximal, characteristic, complemented
5#20298832C212yesmaximal, complemented
6#20298793C211yesmaximal, characteristic, complemented
7#20298731C212yesmaximal, complemented
8C4×#14268632C211yesmaximal, characteristic, complemented
9D4×#11744751C211yesmaximal, characteristic, complemented
10C2×#16813542C212yesmaximal, complemented
11#547×C113C211yesmaximal, characteristic, complemented
12C22×D452C2212yes—
13C2×D4×D113—21no—
14C2×#14268632C2211yescharacteristic
15C2×#14268632C2212yescomplemented
16C22×#11744751C2212yescomplemented
17#16813619C2211yescharacteristic
18#16813597—21no—
19#16813596C2212yes—
20#16813592—22no—
21C4×D452C2211yescharacteristic
22#16813555C2212yescomplemented
23#16813555C2211yescharacteristic, complemented
24C4⋊#11744751C2211yescharacteristic, complemented
25#16813543C2211yescharacteristic, complemented
26#16813542C2211yescharacteristic
27#16813542C2212yes—
28#16813542C2212yescomplemented
29#16813542C2212yescomplemented
30#16813542C2212yescomplemented
31C22⋊#11744751C2212yescomplemented
32C4×#11744751C2211yescharacteristic, complemented
33C2×#41×C113—21no—
34C4⋊Q8×C113C2211yescharacteristic, complemented
35#123×C113—22no—
36C22⋊Q8×C113—21no—
37#121×C113C2212yescomplemented
38C4×D4×C113C2211yescharacteristic
39C4×D4×C113C2211yescharacteristic, complemented
40C2×C4⋊C4×C113C2212yescomplemented
41C23×D113—22no—
42C2×D452—24no—
43C2×D452—22no—
44C2×D452—21no—
45C2×D452—21no—
46C2×D452—42no—
47C2×D452C2312yes—
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—22no—
50D4×D113—44no—
51C2×C4×D113—21no—
52#14268632—22no—
53#14268632—42no—
54C2×#11744751—42no—
55C2×#11744751C2311yescharacteristic
56C2×#11744751C2312yes—
57C2×#11744751C2311yescharacteristic
58C4⋊Dic113C2311yescharacteristic
59#14268624—21no—
60#14268624—22no—
61#41×C113—44no—
62C2×Q8×C113—21no—
63C2×D4×C113—22no—
64C2×D4×C113D411yescharacteristic
65C2×D4×C113C2311yescharacteristic
66C22×C4×C113—22no—
67C22×C4×C113—21no—
68C22×C4×C113C2312yes—
69C4⋊C4×C113—22no—
70C4⋊C4×C113—21no—
71C4⋊C4×C113D411yescharacteristic
72C4⋊C4×C113C2311yescharacteristic
73C4⋊C4×C113C2312yes—
74C22⋊C4×C113—21no—
75C22⋊C4×C113—22no—
76C22⋊C4×C113D412yes—
77C42×C113C2311yescharacteristic
78C23×C113—21no—
79C23×C113C2×D412yes—
80C22×D113—21no—
81C22×D113—22no—
82C22×D113—44no—
83C22×D113—44no—
84C22×D113—82no—
85Q8×C113—42no—
86D4×C113—21no—
87D4×C113—21no—
88D4×C113—44no—
89D4×C113D814yescomplemented
90C2×C4×C113—22no—
91C2×C4×C113—22no—
92C2×C4×C113—21no—
93C2×C4×C113—22no—
94C2×C4×C113—44no—
95C2×C4×C113—42no—
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2×D412yes—
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2411yescharacteristic
100C22⋊D113—44no—
101C2×Dic113—21no—
102D452—22no—
103D452—21no—
104D452—22no—
105D452—44no—
106D452—42no—
107D452—81no—
108D452#4112yescomplemented
109C4×D113—42no—
110#11744751—21no—
111#11744751—21no—
112#11744751—22no—
113C22×C113—22no—
114C22×C113—22no—
115C22×C113—41no—
116C22×C113—41no—
117C22×C113—41no—
118C22×C113C2×D814yes—
119C22×C113C22×D411yescharacteristic
120C2×D113—22no—
121C2×D113—41no—
122C2×D113—41no—
123C2×D113—42no—
124C2×D113—42no—
125C2×D113—42no—
126C2×D113—88no—
127C4×C113—22no—
128C4×C113—21no—
129C4×C113—41no—
130C4×C113—42no—
131C4×C113C2×D812yes—
132C4×C113C2×#4111yescharacteristic
133C4×C113H(5,𝔽2)11yescharacteristic
134Dic113—41no—
135C2×C113—24no—
136C2×C113—81no—
137C2×C113#54611yescharacteristic
138C2×C113C22×D811yescharacteristic
139C2×C113#57711yescharacteristic
140D113—42no—
141D113—82no—
142#3294—1131nomaximal, Sylow
143C113#329411yescharacteristic, complemented, Sylow
144#547D11311yescharacteristic, complemented
145D42—1131no—
146#486—1131no—
147#480—1132no—
148#474—1131no—
149#466—1132no—
150#459—1131no—
151#447—1132no—
152C4×D8—1131no—
153C8×D4—1131no—
154C2×#102—1132no—
155C2×#41—21no—
156C22×D4—1132no—
157C22×D4—2261no—
158C2×D8—1132no—
159C2×D8—1131no—
160C22×C8—1132no—
161C4⋊Q8C2×D11311yescharacteristic, complemented
162#127—1131no—
163#123—22no—
164C22⋊Q8—21no—
165#121—1132no—
166#121—2261no—
167#121C2×D11312yescomplemented
168#120—2262no—
169C4×D4—1131no—
170C4×D4C2×D11311yescharacteristic
171C4×D4C2×D11311yescharacteristic, complemented
172C2×C4⋊C4C2×D11312yescomplemented
173#107—1131no—
174#107—1132no—
175C4⋊C8—1131no—
176#102—1131no—
177#102—1131no—
178#102—1132no—
179#102—1132no—
180#102—1132no—
181#102—1132no—
182C22⋊C8—1132no—
183C4×C8—1131no—
184C24—2262no—
185#41—44no—
186C2×Q8—21no—
187C2×D4—22no—
188C2×D4—1131no—
189C2×D4—1132no—
190C2×D4—4522no—
191C2×D4—4524no—
192C2×D4—2264no—
193C2×D4—2262no—
194C2×D4—2261no—
195C2×D4—2262no—
196C2×D4—2261no—
197C2×D4C22⋊D11311yescharacteristic
198C2×D4C22×D11311yescharacteristic
199C22×C4—22no—
200C22×C4—21no—
201C22×C4—2261no—
202C22×C4C22×D11312yes—
203D8—4522no—
204D8—2262no—
205C2×C8—1131no—
206C2×C8—1131no—
207C2×C8—1132no—
208C2×C8—4522no—
209C4⋊C4—22no—
210C4⋊C4—21no—
211C4⋊C4—1131no—
212C4⋊C4C22⋊D11311yescharacteristic
213C4⋊C4C22×D11311yescharacteristic
214C4⋊C4C22×D11312yes—
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—2261no—
218C22⋊C4—2262no—
219C22⋊C4C22⋊D11312yes—
220C42C22×D11311yescharacteristic
221C23—21no—
222C23—9042no—
223C23—4524no—
224C23—4524no—
225C23—2262no—
226C23—2261no—
227C23C2×C22⋊D11312yes—
228Q8—42no—
229D4—21no—
230D4—21no—
231D4—44no—
232D4—1132no—
233D4—9041no—
234D4—4524no—
235D4—4524no—
236D4—4522no—
237D4—2262no—
238D4—2262no—
239D4—2261no—
240D4#1426863214yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—4522no—
248C2×C4—2261no—
249C2×C4C2×C22⋊D11311yescharacteristic
250C2×C4C2×C22⋊D11312yes—
251C2×C4C2×C22⋊D11311yescharacteristic
252C2×C4C23×D11311yescharacteristic
253C8—2261no—
254C8—2261no—
255C8—2262no—
256C22—22no—
257C22—22no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—9048no—
262C22—4522no—
263C22—4522no—
264C22—4522no—
265C22—4521no—
266C22—4521no—
267C22—2262no—
268C22C2×#1426863214yes—
269C22C22×C22⋊D11311yescharacteristic
270C4—21no—
271C4—22no—
272C4—41no—
273C4—42no—
274C4—4521no—
275C4C2×#1426863212yes—
276C4#41×D11311yescharacteristic
277C4#1681366811yescharacteristic
278C2—24no—
279C2—81no—
280C2—9042no—
281C2—4522no—
282C2#2029923611yescharacteristic
283C2C22×#1426863211yescharacteristic
284C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#547×C113C2
socleC22×C113C22×D4
hypercenter#547D113
hypocenterC113#3294
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. D4×D452C2semidirect
2. #20298946C2semidirect
3. #20298911C2semidirect
4. #20298875C2semidirect
5. #20298832C2semidirect
6. #20298793C2semidirect
7. #20298731C2semidirect
8. C4×#14268632C2semidirect
9. D4×#11744751C2semidirect
10. C2×#16813542C2semidirect
11. #547×C113C2semidirect
15. C2×#14268632C22semidirect
16. C22×#11744751C22semidirect
22. #16813555C22semidirect
23. #16813555C22semidirect
24. C4⋊#11744751C22semidirect
25. #16813543C22semidirect
28. #16813542C22semidirect
29. #16813542C22semidirect
30. #16813542C22semidirect
31. C22⋊#11744751C22semidirect
32. C4×#11744751C22semidirect
34. C4⋊Q8×C113C22semidirect
37. #121×C113C22semidirect
39. C4×D4×C113C22semidirect
40. C2×C4⋊C4×C113C22semidirect
89. D4×C113D8semidirect
108. D452#41semidirect
143. C113#3294semidirect
144. #547D113semidirect
161. C4⋊Q8C2×D113semidirect
167. #121C2×D113semidirect
171. C4×D4C2×D113semidirect
172. C2×C4⋊C4C2×D113semidirect
240. D4#14268632semidirect

Maximal subgroups

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

subgroupindex
D4×D4522
#202989462
#202989112
#202988752
#202988322
#202987932
#202987312
C4×#142686322
D4×#117447512
C2×#168135422
#547×C1132
#3294113