Finite Group Databasebeta

← #28400371

Subgroups — #28400371

Order 14464.

440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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
1#20299155C211yesmaximal, characteristic, complemented
2#20298898C214yesmaximal, complemented
3#20298888C212yesmaximal, complemented
4#20298878C212yesmaximal, complemented
5#20298638C212yesmaximal, complemented
6#20298622C211yesmaximal, characteristic, complemented
7#20298603C212yesmaximal
8C2×C4×D4×C113C211yesmaximal, characteristic
9C2×#14268631C2212yes—
10#16813622C2211yescharacteristic, complemented
11#16813622C2211yescharacteristic, complemented
12#16813614C2212yescomplemented
13#16813601—21no—
14#16813601—21no—
15C4×Dic226—21no—
16C4×Dic226—21no—
17#16813581C2212yes—
18#16813555C2214yescomplemented
19#16813553C2214yescomplemented
20C4⋊#11744751C2212yescomplemented
21C4⋊#11744751C2212yescomplemented
22#16813543C2214yes—
23#16813543C2214yes—
24C22×D4×C113C2211yescharacteristic
25C23×C4×C113—21no—
26C4×D4×C113—21no—
27C4×D4×C113—21no—
28C4×D4×C113C2212yes—
29C4×D4×C113C2212yes—
30C2×C4⋊C4×C113C2211yescharacteristic
31C2×C22⋊C4×C113—21no—
32C2×C42×C113C2211yescharacteristic
33C2×Dic226—21no—
34C2×Dic226—21no—
35#14268631—24no—
36C2×#11744751C2314yes—
37C4⋊Dic113—21no—
38C4⋊Dic113—21no—
39C4⋊Dic113C2312yes—
40C4⋊Dic113C2312yes—
41#14268626—22no—
42#14268626—22no—
43C22⋊Dic113—22no—
44C4×Dic113—22no—
45C24×C113—21no—
46C2×D4×C113—21no—
47C2×D4×C113—22no—
48C2×D4×C113Q814yescomplemented
49C2×D4×C113C2312yes—
50C22×C4×C113—21no—
51C22×C4×C113—22no—
52C22×C4×C113—22no—
53C22×C4×C113—44no—
54C22×C4×C113D411yescharacteristic
55C22×C4×C113D411yescharacteristic
56C22×C4×C113C2311yescharacteristic
57C4⋊C4×C113—21no—
58C4⋊C4×C113C2312yes—
59C22⋊C4×C113—22no—
60C22⋊C4×C113—22no—
61C42×C113D411yescharacteristic
62C42×C113D411yescharacteristic
63C42×C113C2311yescharacteristic
64C42×C113C2311yescharacteristic
65C23×C113—24no—
66C23×C113—22no—
67C23×C113—42no—
68C23×C113—42no—
69C23×C113C2×D411yescharacteristic
70D4×C113—24no—
71D4×C113—22no—
72D4×C113C2×Q814yes—
73C2×C4×C113—22no—
74C2×C4×C113—22no—
75C2×C4×C113—41no—
76C2×C4×C113—44no—
77C2×C4×C113—42no—
78C2×C4×C113—44no—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113C2×Q812yes—
85C2×C4×C113#4112yes—
86C2×C4×C113C2411yescharacteristic
87C2×Dic113—22no—
88C2×Dic113—22no—
89Dic226—42no—
90Dic226—42no—
91#11744751—24no—
92C22×C113—21no—
93C22×C113—21no—
94C22×C113—24no—
95C22×C113—48no—
96C22×C113—42no—
97C22×C113—42no—
98C22×C113C22⋊Q812yes—
99C22×C113C22×D411yescharacteristic
100C4×C113—21no—
101C4×C113—21no—
102C4×C113—21no—
103C4×C113—42no—
104C4×C113C22⋊Q812yes—
105C4×C113AGL(1,ℤ/8)12yes—
106C4×C113C22×Q811yescharacteristic
107C4×C113C2×#4111yescharacteristic
108Dic113—42no—
109Dic113—42no—
110C2×C113—22no—
111C2×C113—44no—
112C2×C113C2×C22⋊Q811yescharacteristic
113C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
114C2×C113#57511yescharacteristic
115#3077—1131nomaximal, Sylow
116C113#307711yescharacteristic, complemented, Sylow
117#533—1131no—
118C2×C4×D4D11311yescharacteristic
119#478—1134no—
120#476—1132no—
121#474—1132no—
122#428—1132no—
123#423—1131no—
124#418—1132no—
125C22×D4C2×D11311yescharacteristic
126C23×C4—21no—
127C2×M16—1132no—
128C4⋊Q8—1131no—
129C4⋊Q8—1131no—
130#125—1132no—
131C22⋊Q8—2261no—
132C22⋊Q8—2261no—
133C4×Q8—2261no—
134C4×Q8—2261no—
135C4×D4—21no—
136C4×D4—21no—
137C4×D4C2×D11312yes—
138C4×D4C2×D11312yes—
139#117—1132no—
140C2×C4⋊C4C2×D11311yescharacteristic
141C2×C22⋊C4—21no—
142C2×C42C2×D11311yescharacteristic
143#107—1134no—
144#106—1134no—
145C4⋊C8—1132no—
146C4⋊C8—1132no—
147#102—1134no—
148#102—1134no—
149C24—21no—
150C2×Q8—2261no—
151C2×Q8—2261no—
152C2×D4—21no—
153C2×D4—22no—
154C2×D4Dic22614yescomplemented
155C2×D4C22×D11312yes—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—44no—
160C22×C4C22⋊D11311yescharacteristic
161C22×C4C22⋊D11311yescharacteristic
162C22×C4C22×D11311yescharacteristic
163M16—2264no—
164C2×C8—1134no—
165C4⋊C4—21no—
166C4⋊C4—1132no—
167C4⋊C4—1132no—
168C4⋊C4—2262no—
169C4⋊C4—2262no—
170C4⋊C4—2261no—
171C4⋊C4—2261no—
172C4⋊C4C22×D11312yes—
173C22⋊C4—22no—
174C22⋊C4—22no—
175C22⋊C4—2262no—
176C42—2262no—
177C42C22⋊D11311yescharacteristic
178C42C22⋊D11311yescharacteristic
179C42C22×D11311yescharacteristic
180C42C22×D11311yescharacteristic
181C23—24no—
182C23—22no—
183C23—42no—
184C23—42no—
185C23C2×C22⋊D11311yescharacteristic
186Q8—4522no—
187Q8—4522no—
188D4—24no—
189D4—22no—
190D4C2×Dic22614yes—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—44no—
197C2×C4—2262no—
198C2×C4—2262no—
199C2×C4C2×C22⋊D11311yescharacteristic
200C2×C4C2×C22⋊D11311yescharacteristic
201C2×C4C2×C22⋊D11311yescharacteristic
202C2×C4C2×C22⋊D11311yescharacteristic
203C2×C4C2×C22⋊D11311yescharacteristic
204C2×C4C2×Dic22612yes—
205C2×C4#1426864712yes—
206C2×C4C23×D11311yescharacteristic
207C8—2264no—
208C22—21no—
209C22—21no—
210C22—24no—
211C22—48no—
212C22—42no—
213C22—42no—
214C22#1681360112yes—
215C22C22×C22⋊D11311yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—4522no—
221C4—4522no—
222C4#1681360112yes—
223C4#1681364812yes—
224C4C22×Dic22611yescharacteristic
225C4C2×#1426864711yescharacteristic
226C2—22no—
227C2—44no—
228C2C2×#1681360111yescharacteristic
229C2C2×#1681364811yescharacteristic
230C2#2029939611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C4×D4×C113C2
socleC22×C113C22×D4
prime radicalC22×D4×C113C22
hypercenterC2×C4×D4D113
hypocenterC113#3077
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #20299155C2semidirect
2. #20298898C2semidirect
3. #20298888C2semidirect
4. #20298878C2semidirect
5. #20298638C2semidirect
6. #20298622C2semidirect
10. #16813622C22semidirect
11. #16813622C22semidirect
12. #16813614C22semidirect
18. #16813555C22semidirect
19. #16813553C22semidirect
20. C4⋊#11744751C22semidirect
21. C4⋊#11744751C22semidirect
48. C2×D4×C113Q8semidirect
116. C113#3077semidirect
154. C2×D4Dic226semidirect

Maximal subgroups

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

subgroupindex
#202991552
#202988982
#202988882
#202988782
#202986382
#202986222
#202986032
C2×C4×D4×C1132
#3077113