Finite Group Databasebeta

← C2×#20298846 #28400164

Subgroups — C2×#20298846 #28400164

Order 14464.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×#14268634C211yesmaximal, characteristic, complemented
2C22×#14268631C211yesmaximal, characteristic, complemented
3C2×#16813596C211yesmaximal, characteristic
4#20298846C218yesmaximal, direct product factor
5C2×#16813555C211yesmaximal, characteristic, complemented
6C2×#16813546C211yesmaximal, characteristic, complemented
7C2×#16813542C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C113C211yesmaximal, characteristic, complemented
9C22×D452C2211yescharacteristic
10C22×C22⋊D113—21no—
11C2×#14268634—24no—
12C2×#14268634C2214yescomplemented
13C2×#14268631—24no—
14C2×#14268631C2214yescomplemented
15C22×#11744751C2211yescharacteristic
16C22×#11744751C2211yescharacteristic
17#16813596—22no—
18#16813596C2214yes—
19C2×C4⋊Dic113C2211yescharacteristic
20C2×#14268624—21no—
21#16813555C2214yescomplemented
22#16813546C2214yescomplemented
23#16813542C2214yescomplemented
24C22×Q8×C113C2211yescharacteristic
25C23×C4×C113C2211yescharacteristic
26C22⋊Q8×C113—22no—
27C22⋊Q8×C113C2214yescomplemented
28C2×C4⋊C4×C113—21no—
29C2×C4⋊C4×C113C2211yescharacteristic
30C2×C22⋊C4×C113—21no—
31C23×D113—21no—
32C2×D452—22no—
33C2×D452—22no—
34C2×D452—21no—
35C2×D452C2312yes—
36C2×C22⋊D113—24no—
37C2×C22⋊D113—44no—
38C22×Dic113—21no—
39#14268634—28no—
40#14268631—28no—
41C2×#11744751—22no—
42C2×#11744751D414yescomplemented
43C2×#11744751C2312yes—
44C2×#11744751C2312yes—
45C4⋊Dic113—21no—
46C4⋊Dic113C2312yes—
47#14268624—24no—
48C24×C113D411yescharacteristic
49C2×Q8×C113—21no—
50C2×Q8×C113—22no—
51C2×Q8×C113—22no—
52C2×Q8×C113C2312yes—
53C22×C4×C113—22no—
54C22×C4×C113—22no—
55C22×C4×C113—21no—
56C22×C4×C113—21no—
57C22×C4×C113D411yescharacteristic
58C22×C4×C113D412yes—
59C22×C4×C113C2312yes—
60C22×C4×C113C2311yescharacteristic
61C4⋊C4×C113—24no—
62C4⋊C4×C113—21no—
63C4⋊C4×C113C2312yes—
64C22⋊C4×C113—24no—
65C23×C113—22no—
66C23×C113—22no—
67C23×C113—22no—
68C23×C113C2×D412yes—
69C23×C113C2×D411yescharacteristic
70C22×D113—22no—
71C22×D113—42no—
72C22×D113—42no—
73C22×D113—42no—
74Q8×C113—22no—
75Q8×C113—22no—
76Q8×C113—42no—
77C2×C4×C113—22no—
78C2×C4×C113—24no—
79C2×C4×C113—22no—
80C2×C4×C113—22no—
81C2×C4×C113—22no—
82C2×C4×C113—22no—
83C2×C4×C113—42no—
84C2×C4×C113—42no—
85C2×C4×C113C2×D412yes—
86C2×C4×C113C2×D412yes—
87C2×C4×C113C2×D411yescharacteristic
88C2×C4×C113#4112yes—
89C2×C4×C113C2411yescharacteristic
90C22⋊D113—48no—
91C2×Dic113—22no—
92C2×Dic113—42no—
93D452—22no—
94D452—22no—
95D452—42no—
96#11744751—22no—
97#11744751C2×D414yescomplemented
98C22×C113—22no—
99C22×C113—22no—
100C22×C113—22no—
101C22×C113—44no—
102C22×C113#12112yes—
103C22×C113AGL(1,ℤ/8)12yes—
104C22×C113#13712yes—
105C22×C113C22×D411yescharacteristic
106C2×D113—42no—
107C2×D113—42no—
108C2×D113—42no—
109C2×D113—84no—
110C4×C113—22no—
111C4×C113—42no—
112C4×C113—42no—
113C4×C113#12112yes—
114C4×C113C22×D411yescharacteristic
115C4×C113C2×#4111yescharacteristic
116Dic113—42no—
117C2×C113—42no—
118C2×C113#46814yescomplemented
119C2×C113C2×#12111yescharacteristic
120C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C113C2×#13711yescharacteristic
122D113—82no—
123C2×#468—1131nomaximal, Sylow
124C113C2×#46811yescharacteristic, complemented, Sylow
125C22×SD16—1131no—
126C22×M16—1131no—
127C2×C22⋊Q8D11311yescharacteristic, complemented
128C2×#121—1131no—
129#468—1138no—
130C2×#107—1131no—
131C2×#103—1131no—
132C2×#102—1131no—
133C22×Q8C2×D11311yescharacteristic
134C22×D4—1131no—
135C22×D4—2261no—
136C23×C4C2×D11311yescharacteristic
137C2×SD16—1134no—
138C2×SD16—2264no—
139C2×M16—1134no—
140C2×M16—2264no—
141C22×C8—1131no—
142C22×C8—1131no—
143C22⋊Q8—22no—
144C22⋊Q8C2×D11314yescomplemented
145#121—1134no—
146#121—2262no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—1131no—
149C2×C4⋊C4C2×D11311yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—2261no—
152#107—1134no—
153#103—1134no—
154#102—1134no—
155C24—2261no—
156C24C22⋊D11311yescharacteristic
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D11312yes—
161C2×D4—1132no—
162C2×D4—4524no—
163C2×D4—2264no—
164C2×D4—2262no—
165C2×D4—2261no—
166C2×D4—2262no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—2261no—
172C22×C4C22⋊D11312yes—
173C22×C4C22⋊D11311yescharacteristic
174C22×C4C22×D11312yes—
175C22×C4C22×D11311yescharacteristic
176SD16—2268no—
177M16—2268no—
178C2×C8—1134no—
179C2×C8—1132no—
180C2×C8—1132no—
181C2×C8—2262no—
182C4⋊C4—24no—
183C4⋊C4—21no—
184C4⋊C4—1132no—
185C4⋊C4—2261no—
186C4⋊C4C22×D11312yes—
187C22⋊C4—24no—
188C22⋊C4—2264no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—4522no—
193C23—4522no—
194C23—4522no—
195C23—2262no—
196C23C2×C22⋊D11312yes—
197C23C2×C22⋊D11311yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—4528no—
202D4—4522no—
203D4—2262no—
204D4—2262no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—4522no—
214C2×C4—2262no—
215C2×C4D4×D11312yes—
216C2×C4C2×C22⋊D11312yes—
217C2×C4C2×C22⋊D11311yescharacteristic
218C2×C4#1426864612yes—
219C2×C4C23×D11311yescharacteristic
220C8—1134no—
221C8—2262no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22—44no—
226C22—9044no—
227C22—4522no—
228C22—4522no—
229C22—4522no—
230C22#1681359412yes—
231C22#1681364712yes—
232C22#1681365312yes—
233C22C22×C22⋊D11311yescharacteristic
234C4—22no—
235C4—42no—
236C4—42no—
237C4—4522no—
238C4#1681359412yes—
239C4C2×D4×D11311yescharacteristic
240C4C2×#1426864611yescharacteristic
241C2—42no—
242C2—9042no—
243C2#2029884614yesdirect product factor
244C2C2×#1681359411yescharacteristic
245C2C2×#1681364711yescharacteristic
246C2C2×#1681365311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C22⋊Q8×C113C2
socleC23×C113C2×D4
prime radicalC2×#16813596C2
hypercenterC2×C22⋊Q8D113
hypocenterC113C2×#468
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14268634C2semidirect
2. C22×#14268631C2semidirect
4. #20298846C2direct (N × H)
5. C2×#16813555C2semidirect
6. C2×#16813546C2semidirect
7. C2×#16813542C2semidirect
8. C2×C22⋊Q8×C113C2semidirect
12. C2×#14268634C22semidirect
14. C2×#14268631C22semidirect
21. #16813555C22semidirect
22. #16813546C22semidirect
23. #16813542C22semidirect
27. C22⋊Q8×C113C22semidirect
42. C2×#11744751D4semidirect
97. #11744751C2×D4semidirect
118. C2×C113#468semidirect
124. C113C2×#468semidirect
127. C2×C22⋊Q8D113semidirect
144. C22⋊Q8C2×D113semidirect
243. C2#20298846direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142686342
C22×#142686312
C2×#168135962
#202988462
C2×#168135552
C2×#168135462
C2×#168135422
C2×C22⋊Q8×C1132
C2×#468113