Finite Group Databasebeta

← #28389015

Subgroups — #28389015

Order 14464.

316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×D4×D113C211yesmaximal, characteristic
2#20298654C211yesmaximal, characteristic, complemented
3C4×#14268630C211yesmaximal, characteristic, complemented
4#20298327C211yesmaximal, characteristic, complemented
5D4⋊#11744751C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic, complemented
8C2×D4×D113C411yescharacteristic
9C22×C4×D113—21no—
10C2×#14268630—21no—
11C4×D452C2211yescharacteristic
12D4×Dic113C411yescharacteristic
13#16813584C411yescharacteristic
14C4×C22⋊D113—21no—
15#16813582—21no—
16C4⋊C4×D113C411yescharacteristic
17C22⋊C4×D113—21no—
18C42×D113C2211yescharacteristic
19C4⋊#11744751C2211yescharacteristic, complemented
20#16813534—21no—
21#16813532—21no—
22#16813532—21no—
23C4×#11744751C2211yescharacteristic, complemented
24C4×D4×C113C2211yescharacteristic
25C4⋊C8×C113C2211yescharacteristic, complemented
26C4×C8×C113C2211yescharacteristic, complemented
27C23×D113—21no—
28C2×D452C2×C411yescharacteristic
29C2×C22⋊D113—21no—
30D4×D113—22no—
31D4×D113—22no—
32C22×Dic113—21no—
33C2×C4×D113—21no—
34C2×C4×D113—21no—
35C2×C4×D113—21no—
36C2×C4×D113—42no—
37C2×C4×D113—42no—
38C2×C4×D113C2×C411yescharacteristic
39C2×C4×D113D411yescharacteristic
40C2×C4×D113D411yescharacteristic
41#14268630—24no—
42C2×#11744751—21no—
43C2×#11744751—21no—
44C4⋊Dic113C2×C411yescharacteristic
45#14268626—21no—
46C22⋊Dic113—21no—
47#14268624—21no—
48#14268624—21no—
49C4×Dic113C2×C411yescharacteristic
50C4×Dic113D411yescharacteristic
51C4×Dic113D411yescharacteristic
52C2×D4×C113C2×C411yescharacteristic
53C22×C4×C113—21no—
54C2×C8×C113—21no—
55C2×C8×C113—21no—
56C4⋊C4×C113C2×C411yescharacteristic
57C22⋊C4×C113—21no—
58C42×C113C2311yescharacteristic
59C23×C113—21no—
60C22×D113—24no—
61C22×D113—21no—
62C22×D113—42no—
63C22×D113—42no—
64C22×D113C22⋊C411yescharacteristic
65D4×C113—21no—
66D4×C113M1612yescomplemented
67C2×C4×C113—21no—
68C2×C4×C113—41no—
69C2×C4×C113—41no—
70C2×C4×C113C22×C411yescharacteristic
71C2×C4×C113C2×D411yescharacteristic
72C2×C4×C113C2×D411yescharacteristic
73C22⋊D113—24no—
74C2×Dic113—21no—
75C2×Dic113—42no—
76C2×Dic113C22⋊C411yescharacteristic
77C2×Dic113C22⋊C411yescharacteristic
78C2×Dic113C22⋊C411yescharacteristic
79D452—21no—
80D452M1612yescomplemented
81C4×D113—22no—
82C4×D113—21no—
83C4×D113—21no—
84C4×D113—21no—
85C4×D113—21no—
86C4×D113—42no—
87C4×D113—42no—
88C4×D113—41no—
89C4×D113—41no—
90C8×C113—22no—
91C8×C113—41no—
92#11744751—22no—
93#11744751—41no—
94C22×C113—22no—
95C22×C113—41no—
96C22×C113—41no—
97C22×C113C2×C22⋊C411yescharacteristic
98C2×D113—21no—
99C2×D113—21no—
100C2×D113—22no—
101C2×D113—48no—
102C2×D113—41no—
103C2×D113—41no—
104C2×D113#10412yes—
105C4×C113—21no—
106C4×C113—41no—
107C4×C113C2×M1611yescharacteristic
108C4×C113C2×M1611yescharacteristic
109C4×C113AGL(1,ℤ/8)11yescharacteristic
110C4×C113AGL(1,ℤ/8)11yescharacteristic
111Dic113—21no—
112Dic113—21no—
113Dic113—21no—
114Dic113—41no—
115C2×C113—42no—
116C2×C113#40711yescharacteristic
117C2×C113#41811yescharacteristic
118C2×C113C2×#10411yescharacteristic
119D113—22no—
120D113—42no—
121#1490—1131nomaximal, Sylow
122C113#149011yescharacteristic, complemented, Sylow
123C2×C4×D4—1131no—
124#432—1131no—
125C4×M16—1131no—
126D4⋊C8—1131no—
127D4⋊C8—1131no—
128D4⋊C8—1131no—
129D4⋊C8D11311yescharacteristic, complemented
130C22×D4—1131no—
131C23×C4—2261no—
132C2×M16—2261no—
133C4×D4—1131no—
134C4×D4—1131no—
135C4×D4—1131no—
136C4×D4—2261no—
137C4×D4—2261no—
138C4×D4C2×D11311yescharacteristic
139C2×C4⋊C4—1131no—
140C2×C22⋊C4—2261no—
141C2×C42—1131no—
142C4⋊C8—1131no—
143C4⋊C8C2×D11311yescharacteristic, complemented
144C22⋊C8—2261no—
145#97—2261no—
146#97—2261no—
147C4×C8—1131no—
148C4×C8C2×D11311yescharacteristic, complemented
149C24—2261no—
150C2×D4—1131no—
151C2×D4—2261no—
152C2×D4—2262no—
153C2×D4—2262no—
154C2×D4C4×D11311yescharacteristic
155C22×C4—21no—
156C22×C4—1131no—
157C22×C4—1131no—
158C22×C4—1131no—
159C22×C4—4522no—
160C22×C4—4522no—
161C22×C4—2261no—
162C22×C4—2261no—
163C22×C4—2261no—
164C22×C4—2261no—
165M16—2264no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—2261no—
169C2×C8—2261no—
170C4⋊C4—1131no—
171C4⋊C4—2261no—
172C4⋊C4C4×D11311yescharacteristic
173C22⋊C4—21no—
174C22⋊C4—2261no—
175C22⋊C4—2261no—
176C22⋊C4—2261no—
177C42—1131no—
178C42—1131no—
179C42—1131no—
180C42C22×D11311yescharacteristic
181C23—21no—
182C23—1131no—
183C23—4522no—
184C23—4522no—
185C23—2264no—
186C23—2261no—
187D4—21no—
188D4—1132no—
189D4—2264no—
190D4—2261no—
191D4#1426863012yescomplemented
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—1131no—
196C2×C4—1131no—
197C2×C4—1131no—
198C2×C4—4522no—
199C2×C4—4522no—
200C2×C4—4522no—
201C2×C4—4521no—
202C2×C4—4521no—
203C2×C4—2262no—
204C2×C4—2261no—
205C2×C4—2261no—
206C2×C4—2261no—
207C2×C4—2261no—
208C2×C4—2261no—
209C2×C4C2×C4×D11311yescharacteristic
210C2×C4D4×D11311yescharacteristic
211C2×C4D4×D11311yescharacteristic
212C8—22no—
213C8—41no—
214C8—4521no—
215C8—2262no—
216C22—22no—
217C22—41no—
218C22—41no—
219C22—1132no—
220C22—4528no—
221C22—4521no—
222C22—4521no—
223C22—2262no—
224C22—2261no—
225C22—2261no—
226C22C22⋊C4×D11311yescharacteristic
227C4—21no—
228C4—41no—
229C4—4521no—
230C4—2261no—
231C4—2261no—
232C4—2261no—
233C4M16×D11311yescharacteristic
234C4C2×#1426863011yescharacteristic
235C4#1681364611yescharacteristic
236C4#1681364911yescharacteristic
237C2—42no—
238C2—4522no—
239C2—2262no—
240C2#2029856011yescharacteristic
241C2#2029860111yescharacteristic
242C2#104×D11311yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC2×D4×D113C4
cosocleC42×C113C23
hypercenterD4⋊C8D113
hypocenterC113#1490
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20298654C2semidirect
3. C4×#14268630C2semidirect
4. #20298327C2semidirect
5. D4⋊#11744751C2semidirect
6. #20298325C2semidirect
7. D4⋊C8×C113C2semidirect
19. C4⋊#11744751C22semidirect
23. C4×#11744751C22semidirect
25. C4⋊C8×C113C22semidirect
26. C4×C8×C113C22semidirect
66. D4×C113M16semidirect
80. D452M16semidirect
122. C113#1490semidirect
129. D4⋊C8D113semidirect
143. C4⋊C8C2×D113semidirect
148. C4×C8C2×D113semidirect
191. D4#14268630semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D1132
#202986542
C4×#142686302
#202983272
D4⋊#117447512
#202983252
D4⋊C8×C1132
#1490113