Finite Group Databasebeta

← C2×#20298697 #28399352

Subgroups — C2×#20298697 #28399352

Order 14464.

544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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×#14268636C211yesmaximal, characteristic
2C2×#16813587C211yesmaximal, characteristic, complemented
3C2×#16813584C211yesmaximal, characteristic
4#20298697C218yesmaximal, direct product factor
5C2×#16813545C211yesmaximal, characteristic, complemented
6C2×#16813542C211yesmaximal, characteristic
7C2×#16813532C211yesmaximal, characteristic, complemented
8C2×#107×C113C211yesmaximal, characteristic, complemented
9C22×Dic226C2211yescharacteristic
10C22×D452C2211yescharacteristic
11C22×C4×D113—21no—
12C2×#14268636C418yescomplemented
13C2×#14268636C2214yes—
14C22×#11744751C2211yescharacteristic
15#16813587—22no—
16#16813587C2214yescomplemented
17#16813584—22no—
18#16813584C2214yes—
19C2×#14268626—21no—
20C2×#14268624—21no—
21C2×C4×Dic113—21no—
22C2×C4×Dic113C2211yescharacteristic
23#16813545C2214yescomplemented
24#16813542C2214yes—
25#16813532C2214yescomplemented
26C22×C8×C113C2211yescharacteristic
27C2×C4⋊C4×C113C2211yescharacteristic
28C2×C4⋊C4×C113C2211yescharacteristic
29#107×C113C2214yescomplemented
30C23×D113—21no—
31C2×Dic226—21no—
32C2×Dic226—22no—
33C2×Dic226C2×C414yescomplemented
34C2×Dic226C2312yes—
35C2×D452—21no—
36C2×D452—22no—
37C2×D452C2×C414yes—
38C2×D452C2312yes—
39C22×Dic113—21no—
40C22×Dic113D411yescharacteristic
41C22×Dic113D411yescharacteristic
42C2×C4×D113—24no—
43C2×C4×D113—44no—
44#14268636C2×C4116yescomplemented
45C2×#11744751—22no—
46C2×#11744751C2312yes—
47#14268626—24no—
48#14268624—24no—
49C4×Dic113—24no—
50C4×Dic113D412yes—
51C4×Dic113C2312yes—
52C22×C4×C113—21no—
53C22×C4×C113—21no—
54C22×C4×C113C2311yescharacteristic
55C2×C8×C113C2×C414yescomplemented
56C2×C8×C113C2312yes—
57C4⋊C4×C113—21no—
58C4⋊C4×C113—21no—
59C4⋊C4×C113C2312yes—
60C4⋊C4×C113C2312yes—
61C23×C113C2×D411yescharacteristic
62C22×D113—24no—
63C22×D113—22no—
64C22×D113—42no—
65C22×D113—42no—
66C2×C4×C113—22no—
67C2×C4×C113—22no—
68C2×C4×C113—42no—
69C2×C4×C113—42no—
70C2×C4×C113C22×C412yes—
71C2×C4×C113C2×D411yescharacteristic
72C2×C4×C113#4112yes—
73C2×C4×C113C2411yescharacteristic
74C2×Dic113—24no—
75C2×Dic113—22no—
76C2×Dic113—22no—
77C2×Dic113—22no—
78C2×Dic113C2×D412yes—
79C2×Dic113C2×D412yes—
80D452—24no—
81D452—22no—
82D452C22×C414yes—
83C4×D113—48no—
84Dic226—24no—
85Dic226—22no—
86Dic226C22×C414yescomplemented
87C8×C113C22×C414yescomplemented
88#11744751—22no—
89C22×C113C4×D412yes—
90C22×C113AGL(1,ℤ/8)12yes—
91C22×C113#13712yes—
92C22×C113C22×D411yescharacteristic
93C2×D113—24no—
94C2×D113—42no—
95C2×D113—42no—
96C2×D113—48no—
97C4×C113—42no—
98C4×C113—42no—
99C4×C113C4×D412yes—
100C4×C113C23×C411yescharacteristic
101C4×C113C2×#4111yescharacteristic
102Dic113—24no—
103Dic113—22no—
104Dic113—22no—
105C2×C113#44014yescomplemented
106C2×C113C2×C4×D411yescharacteristic
107C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
108C2×C113C2×#13711yescharacteristic
109D113—44no—
110C2×#440—1131nomaximal, Sylow
111C113C2×#44011yescharacteristic, complemented, Sylow
112C22×SD16—1131no—
113C2×C4×Q8—1131no—
114C2×C4×D4—1131no—
115#440—1138no—
116C2×#107D11311yescharacteristic, complemented
117C2×#103—1131no—
118C2×#102—1131no—
119C2×#97—1131no—
120C22×Q8—1131no—
121C22×D4—1131no—
122C23×C4—2261no—
123C2×SD16—1138no—
124C2×SD16—1134no—
125C22×C8—1131no—
126C22×C8C2×D11311yescharacteristic
127C4×Q8—1134no—
128C4×Q8—2262no—
129C4×D4—1134no—
130C4×D4—2262no—
131C2×C4⋊C4—2261no—
132C2×C4⋊C4C2×D11311yescharacteristic
133C2×C4⋊C4C2×D11311yescharacteristic
134C2×C22⋊C4—2261no—
135C2×C42—1131no—
136C2×C42—2261no—
137#107C2×D11314yescomplemented
138#103—1134no—
139#102—1134no—
140#97—1134no—
141C24—2261no—
142C2×Q8—1134no—
143C2×Q8—1132no—
144C2×Q8—2261no—
145C2×Q8—2262no—
146C2×D4—1134no—
147C2×D4—1132no—
148C2×D4—2261no—
149C2×D4—2262no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—1131no—
153C22×C4—1131no—
154C22×C4—4524no—
155C22×C4—2264no—
156C22×C4—2261no—
157C22×C4C22×D11311yescharacteristic
158SD16—11316no—
159C2×C8—1132no—
160C2×C8—2262no—
161C2×C8C4×D11314yescomplemented
162C2×C8C22×D11312yes—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—2264no—
166C4⋊C4C22×D11312yes—
167C4⋊C4C22×D11312yes—
168C22⋊C4—2264no—
169C42—1132no—
170C42—1132no—
171C42—2264no—
172C23—4522no—
173C23—4522no—
174C23—2264no—
175C23—2262no—
176C23D4×D11311yescharacteristic
177Q8—1134no—
178Q8—2264no—
179Q8—2262no—
180D4—1134no—
181D4—2264no—
182D4—2262no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—1132no—
188C2×C4—1132no—
189C2×C4—4528no—
190C2×C4—2264no—
191C2×C4—2262no—
192C2×C4—2262no—
193C2×C4—2262no—
194C2×C4C2×C4×D11312yes—
195C2×C4D4×D11311yescharacteristic
196C2×C4#1426864812yes—
197C2×C4C23×D11311yescharacteristic
198C8—2262no—
199C8C2×C4×D11314yescomplemented
200C22—4522no—
201C22—4522no—
202C22—4528no—
203C22—2264no—
204C22#1681358412yes—
205C22#1681364612yes—
206C22#1681365412yes—
207C22C2×D4×D11311yescharacteristic
208C4—42no—
209C4—42no—
210C4—2264no—
211C4—2262no—
212C4—2262no—
213C4#1681358412yes—
214C4C22×C4×D11311yescharacteristic
215C4C2×#1426864811yescharacteristic
216C2—4524no—
217C2#2029869714yesdirect product factor
218C2C2×#1681358411yescharacteristic
219C2C2×#1681364611yescharacteristic
220C2C2×#1681365411yescharacteristic
subgroupG/H
centerC23D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
FittingC2×#107×C113C2
socleC23×C113C2×D4
prime radicalC22×D452C22
cosocleC2×C4×C113C24
hypercenterC2×#107D113
hypocenterC113C2×#440
LCSG ▷ 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×#16813587C2semidirect
4. #20298697C2direct (N × H)
5. C2×#16813545C2semidirect
7. C2×#16813532C2semidirect
8. C2×#107×C113C2semidirect
12. C2×#14268636C4semidirect
16. #16813587C22semidirect
23. #16813545C22semidirect
25. #16813532C22semidirect
29. #107×C113C22semidirect
33. C2×Dic226C2×C4semidirect
44. #14268636C2×C4semidirect
55. C2×C8×C113C2×C4semidirect
86. Dic226C22×C4semidirect
87. C8×C113C22×C4semidirect
105. C2×C113#440semidirect
111. C113C2×#440semidirect
116. C2×#107D113semidirect
137. #107C2×D113semidirect
161. C2×C8C4×D113semidirect
199. C8C2×C4×D113semidirect
217. C2#20298697direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142686362
C2×#168135872
C2×#168135842
#202986972
C2×#168135452
C2×#168135422
C2×#168135322
C2×#107×C1132
C2×#440113