Finite Group Databasebeta

← #28388963

Subgroups — #28388963

Order 14464.

312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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#20298650C211yesmaximal, characteristic, complemented
3#20298649C211yesmaximal, 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—
10C4×D452C2211yescharacteristic
11D4×Dic113C411yescharacteristic
12#16813584C411yescharacteristic
13C4×C22⋊D113—21no—
14#16813582—21no—
15C4⋊C4×D113C411yescharacteristic
16C22⋊C4×D113—21no—
17C42×D113C2211yescharacteristic
18C4⋊#11744751C2211yescharacteristic, complemented
19#16813551—21no—
20#16813534—21no—
21#16813534—21no—
22C4×#11744751C2211yescharacteristic, complemented
23C8×Dic113—21no—
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×D113C814yescomplemented
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
41C2×#11744751—21no—
42C2×#11744751—21no—
43C4⋊Dic113C2×C411yescharacteristic
44#14268626—21no—
45C22⋊Dic113—21no—
46#14268624—21no—
47#14268624—21no—
48C4×Dic113C2×C411yescharacteristic
49C4×Dic113D411yescharacteristic
50C4×Dic113D411yescharacteristic
51C2×D4×C113C2×C411yescharacteristic
52C22×C4×C113—21no—
53C2×C8×C113—21no—
54C2×C8×C113—21no—
55C4⋊C4×C113C2×C411yescharacteristic
56C22⋊C4×C113—21no—
57C42×C113C2311yescharacteristic
58C23×C113—21no—
59C22×D113—21no—
60C22×D113—24no—
61C22×D113—42no—
62C22×D113—42no—
63C22×D113C22⋊C411yescharacteristic
64D4×C113—21no—
65D4×C113C2×C812yes—
66C2×C4×C113—21no—
67C2×C4×C113—41no—
68C2×C4×C113—41no—
69C2×C4×C113C22×C411yescharacteristic
70C2×C4×C113C2×D411yescharacteristic
71C2×C4×C113C2×D411yescharacteristic
72C22⋊D113—24no—
73C2×Dic113—21no—
74C2×Dic113—42no—
75C2×Dic113C22⋊C411yescharacteristic
76C2×Dic113C22⋊C411yescharacteristic
77C2×Dic113C22⋊C411yescharacteristic
78D452—21no—
79D452C2×C812yes—
80C4×D113—21no—
81C4×D113—21no—
82C4×D113—41no—
83C4×D113—42no—
84C4×D113—42no—
85C4×D113—41no—
86C4×D113—41no—
87C4×D113C2×C812yes—
88C4×D113M1612yes—
89C8×C113—41no—
90C8×C113—41no—
91#11744751—41no—
92#11744751—41no—
93C22×C113—22no—
94C22×C113—41no—
95C22×C113—41no—
96C22×C113C2×C22⋊C411yescharacteristic
97C2×D113—21no—
98C2×D113—21no—
99C2×D113—22no—
100C2×D113—48no—
101C2×D113—41no—
102C2×D113—41no—
103C2×D113C22⋊C812yes—
104C4×C113—21no—
105C4×C113—41no—
106C4×C113C22×C811yescharacteristic
107C4×C113C2×M1611yescharacteristic
108C4×C113AGL(1,ℤ/8)11yescharacteristic
109C4×C113AGL(1,ℤ/8)11yescharacteristic
110Dic113—21no—
111Dic113—21no—
112Dic113—41no—
113Dic113C22⋊C812yes—
114C2×C113—42no—
115C2×C113C2×C22⋊C811yescharacteristic
116C2×C113#41811yescharacteristic
117C2×C113#42111yescharacteristic
118D113—22no—
119D113—42no—
120#1478—1131nomaximal, Sylow
121C113#147811yescharacteristic, complemented, Sylow
122C2×C4×D4—1131no—
123#431—1131no—
124#431—1131no—
125D4⋊C8—1131no—
126D4⋊C8—1131no—
127D4⋊C8—1131no—
128D4⋊C8D11311yescharacteristic, complemented
129C22×D4—1131no—
130C23×C4—2261no—
131C4×D4—1131no—
132C4×D4—1131no—
133C4×D4—1131no—
134C4×D4—2261no—
135C4×D4—2261no—
136C4×D4C2×D11311yescharacteristic
137C2×C4⋊C4—1131no—
138C2×C22⋊C4—2261no—
139C2×C42—1131no—
140C4⋊C8—1131no—
141C4⋊C8—2261no—
142C4⋊C8C2×D11311yescharacteristic, complemented
143C22⋊C8—2261no—
144C22⋊C8—2261no—
145C4×C8—1131no—
146C4×C8—2261no—
147C4×C8C2×D11311yescharacteristic, complemented
148C24—2261no—
149C2×D4—1134no—
150C2×D4—1131no—
151C2×D4—2262no—
152C2×D4—2261no—
153C2×D4C4×D11311yescharacteristic
154C22×C4—21no—
155C22×C4—1131no—
156C22×C4—1131no—
157C22×C4—1131no—
158C22×C4—4522no—
159C22×C4—4522no—
160C22×C4—2261no—
161C22×C4—2261no—
162C22×C4—2261no—
163C22×C4—2261no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—2261no—
167C2×C8—2261no—
168C4⋊C4—1131no—
169C4⋊C4—2261no—
170C4⋊C4C4×D11311yescharacteristic
171C22⋊C4—21no—
172C22⋊C4—2261no—
173C22⋊C4—2261no—
174C22⋊C4—2261no—
175C42—1131no—
176C42—1131no—
177C42—1131no—
178C42C22×D11311yescharacteristic
179C23—21no—
180C23—1131no—
181C23—4522no—
182C23—4522no—
183C23—2264no—
184C23—2261no—
185D4—21no—
186D4—1132no—
187D4—2264no—
188D4—2261no—
189D4C8×D11312yes—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—1131no—
194C2×C4—1132no—
195C2×C4—1132no—
196C2×C4—1131no—
197C2×C4—1131no—
198C2×C4—4521no—
199C2×C4—4522no—
200C2×C4—4522no—
201C2×C4—4522no—
202C2×C4—4521no—
203C2×C4—4521no—
204C2×C4—2261no—
205C2×C4—2261no—
206C2×C4—2261no—
207C2×C4C2×C4×D11311yescharacteristic
208C2×C4D4×D11311yescharacteristic
209C2×C4D4×D11311yescharacteristic
210C8—41no—
211C8—41no—
212C8—4521no—
213C8—4521no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22—1132no—
218C22—4528no—
219C22—4521no—
220C22—4521no—
221C22—2262no—
222C22—2261no—
223C22—2261no—
224C22C22⋊C4×D11311yescharacteristic
225C4—21no—
226C4—41no—
227C4—1132no—
228C4—4521no—
229C4—2261no—
230C4—2261no—
231C4C2×C8×D11311yescharacteristic
232C4M16×D11311yescharacteristic
233C4#1681364611yescharacteristic
234C4#1681364911yescharacteristic
235C2—42no—
236C2—4522no—
237C2—2262no—
238C2C22⋊C8×D11311yescharacteristic
239C2#2029860111yescharacteristic
240C2#2029861311yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutatorC4×C113C22×C8
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC2×D4×D113C4
cosocleC42×C113C23
hypercenterD4⋊C8D113
hypocenterC113#1478
LCSG ▷ 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. #20298650C2semidirect
3. #20298649C2semidirect
4. #20298327C2semidirect
5. D4⋊#11744751C2semidirect
6. #20298325C2semidirect
7. D4⋊C8×C113C2semidirect
18. C4⋊#11744751C22semidirect
22. C4×#11744751C22semidirect
25. C4⋊C8×C113C22semidirect
26. C4×C8×C113C22semidirect
31. D4×D113C8semidirect
121. C113#1478semidirect
128. D4⋊C8D113semidirect
142. C4⋊C8C2×D113semidirect
147. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D1132
#202986502
#202986492
#202983272
D4⋊#117447512
#202983252
D4⋊C8×C1132
#1478113