Finite Group Databasebeta

← C2×#20298913 #28400447

Subgroups — C2×#20298913 #28400447

Order 14464.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#16813597C211yesmaximal, characteristic
2C2×C4⋊C4×D113C211yesmaximal, characteristic, complemented
3#20298913C218yesmaximal, direct product factor
4C2×#16813555C211yesmaximal, characteristic, complemented
5C2×#16813544C211yesmaximal, characteristic, complemented
6C2×#16813542C211yesmaximal, characteristic, complemented
7C2×#16813534C211yesmaximal, characteristic, complemented
8C2×#107×C113C211yesmaximal, characteristic, complemented
9C22×D452—21no—
10C22×D452C2211yescharacteristic
11C22×C4×D113—21no—
12C22×C4×D113C2211yescharacteristic
13C22×#11744751C2211yescharacteristic
14#16813597—22no—
15#16813597C2214yes—
16C2×C4⋊Dic113C2211yescharacteristic
17C2×#14268626—21no—
18C4⋊C4×D113—22no—
19C4⋊C4×D113C2214yescomplemented
20C2×#14268624—21no—
21#16813555C2214yescomplemented
22#16813544C2214yescomplemented
23#16813542C2214yescomplemented
24#16813534C2214yescomplemented
25C22×C8×C113C2211yescharacteristic
26C2×C4⋊C4×C113C2211yescharacteristic
27C2×C4⋊C4×C113C2211yescharacteristic
28#107×C113C2214yescomplemented
29C23×D113—21no—
30C23×D113D411yescharacteristic
31C2×D452—22no—
32C2×D452—22no—
33C2×D452—24no—
34C2×D452—21no—
35C2×D452—44no—
36C2×D452C2312yes—
37C22×Dic113—21no—
38C22×Dic113D411yescharacteristic
39C2×C4×D113—22no—
40C2×C4×D113—22no—
41C2×C4×D113—24no—
42C2×C4×D113—44no—
43C2×C4×D113D412yes—
44C2×C4×D113C2312yes—
45C2×#11744751—22no—
46C2×#11744751C2312yes—
47C4⋊Dic113—21no—
48C4⋊Dic113C2312yes—
49#14268626—24no—
50#14268624—24no—
51C22×C4×C113—21no—
52C22×C4×C113—21no—
53C22×C4×C113C2311yescharacteristic
54C2×C8×C113—22no—
55C2×C8×C113C2312yes—
56C4⋊C4×C113—21no—
57C4⋊C4×C113—21no—
58C4⋊C4×C113C2312yes—
59C4⋊C4×C113C2312yes—
60C23×C113C2×D411yescharacteristic
61C22×D113—22no—
62C22×D113—22no—
63C22×D113—22no—
64C22×D113—42no—
65C22×D113—42no—
66C22×D113—42no—
67C22×D113D814yes—
68C22×D113C2×D412yes—
69C2×C4×C113—22no—
70C2×C4×C113—22no—
71C2×C4×C113—42no—
72C2×C4×C113—42no—
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113#4112yes—
75C2×C4×C113#4112yes—
76C2×C4×C113C2411yescharacteristic
77C2×Dic113—22no—
78C2×Dic113—22no—
79C2×Dic113—42no—
80C2×Dic113C2×D412yes—
81D452—22no—
82D452—22no—
83D452—48no—
84D452—42no—
85C4×D113—24no—
86C4×D113—22no—
87C4×D113—22no—
88C4×D113—48no—
89C8×C113—22no—
90#11744751—22no—
91C22×C113#12312yes—
92C22×C113C2×D812yes—
93C22×C113#13712yes—
94C22×C113C22×D411yescharacteristic
95C2×D113—22no—
96C2×D113—22no—
97C2×D113—28no—
98C2×D113—42no—
99C2×D113—42no—
100C2×D113—42no—
101C2×D113—84no—
102C2×D113C2×D814yes—
103C4×C113—42no—
104C4×C113—42no—
105C4×C113#12312yes—
106C4×C113C2×#4111yescharacteristic
107C4×C113C2×#4111yescharacteristic
108Dic113—22no—
109Dic113—42no—
110C2×C113#48014yescomplemented
111C2×C113C2×#12311yescharacteristic
112C2×C113C22×D811yescharacteristic
113C2×C113C2×#13711yescharacteristic
114D113—24no—
115D113—82no—
116C2×#480—1131nomaximal, Sylow
117C113C2×#48011yescharacteristic, complemented, Sylow
118C2×#121—1131no—
119C22×C4⋊C4—1131no—
120#480—1138no—
121C2×#107—1131no—
122C2×#107D11311yescharacteristic, complemented
123C2×#102—1131no—
124C2×#102—1131no—
125C2×C22⋊C8—1131no—
126C22×D4—1131no—
127C22×D4—2261no—
128C23×C4—1131no—
129C23×C4—2261no—
130C22×C8—1131no—
131C22×C8C2×D11311yescharacteristic
132#121—1134no—
133#121—2262no—
134C2×C4⋊C4—1131no—
135C2×C4⋊C4—1134no—
136C2×C4⋊C4—2262no—
137C2×C4⋊C4—2261no—
138C2×C4⋊C4C2×D11311yescharacteristic
139C2×C4⋊C4C2×D11311yescharacteristic
140C2×C22⋊C4—2261no—
141#107—1134no—
142#107C2×D11314yescomplemented
143#102—1134no—
144#102—1134no—
145C22⋊C8—1134no—
146C24—1131no—
147C24—2261no—
148C2×D4—1132no—
149C2×D4—4524no—
150C2×D4—2264no—
151C2×D4—2261no—
152C2×D4—2262no—
153C2×D4—2262no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—1131no—
157C22×C4—1132no—
158C22×C4—1132no—
159C22×C4—4524no—
160C22×C4—2264no—
161C22×C4—2261no—
162C22×C4—2262no—
163C22×C4—2262no—
164C22×C4C22×D11311yescharacteristic
165C2×C8—22no—
166C2×C8—1132no—
167C2×C8—2262no—
168C2×C8C22×D11312yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—1132no—
172C4⋊C4—2264no—
173C4⋊C4—2261no—
174C4⋊C4C22×D11312yes—
175C4⋊C4C22×D11312yes—
176C22⋊C4—2264no—
177C23—1134no—
178C23—1132no—
179C23—4522no—
180C23—4522no—
181C23—4522no—
182C23—2262no—
183C23—2262no—
184C23—2262no—
185C23D4×D11311yescharacteristic
186D4—4528no—
187D4—4522no—
188D4—2262no—
189D4—2262no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—1132no—
195C2×C4—4528no—
196C2×C4—4522no—
197C2×C4—2262no—
198C2×C4—2262no—
199C2×C4—2264no—
200C2×C4—2262no—
201C2×C4—2262no—
202C2×C4D4×D11311yescharacteristic
203C2×C4#1426864712yes—
204C2×C4#1426864812yes—
205C2×C4C23×D11311yescharacteristic
206C8—22no—
207C8—2262no—
208C22—1134no—
209C22—9044no—
210C22—4522no—
211C22—4522no—
212C22—4522no—
213C22—2262no—
214C22—2262no—
215C22—2268no—
216C22#1681360712yes—
217C22D8×D11312yes—
218C22#1681365412yes—
219C22C2×D4×D11311yescharacteristic
220C4—42no—
221C4—42no—
222C4—4522no—
223C4—2262no—
224C4#1681360712yes—
225C4C2×#1426864711yescharacteristic
226C4C2×#1426864811yescharacteristic
227C2—9042no—
228C2—2264no—
229C2#2029891314yesdirect product factor
230C2C2×#1681360711yescharacteristic
231C2C2×D8×D11311yescharacteristic
232C2C2×#1681365411yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#107×C113C2
socleC23×C113C2×D4
prime radicalC2×#16813597C2
hypercenterC2×#107D113
hypocenterC113C2×#480
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D113C2semidirect
3. #20298913C2direct (N × H)
4. C2×#16813555C2semidirect
5. C2×#16813544C2semidirect
6. C2×#16813542C2semidirect
7. C2×#16813534C2semidirect
8. C2×#107×C113C2semidirect
19. C4⋊C4×D113C22semidirect
21. #16813555C22semidirect
22. #16813544C22semidirect
23. #16813542C22semidirect
24. #16813534C22semidirect
28. #107×C113C22semidirect
110. C2×C113#480semidirect
117. C113C2×#480semidirect
122. C2×#107D113semidirect
142. #107C2×D113semidirect
229. C2#20298913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168135972
C2×C4⋊C4×D1132
#202989132
C2×#168135552
C2×#168135442
C2×#168135422
C2×#168135342
C2×#107×C1132
C2×#480113