Finite Group Databasebeta

← C2×#20292921 #28346231

Subgroups — C2×#20292921 #28346231

Order 13696.

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

normal subgroups only

This group has 416 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
1C2×#16812108C211yesmaximal, characteristic
2C2×#16812074C211yesmaximal, characteristic
3#20292921C218yesmaximal, direct product factor
4C2×#16812042C211yesmaximal, characteristic
5C2×Dic107⋊C8C211yesmaximal, characteristic
6C2×#16812034C211yesmaximal, characteristic
7C2×#16812032C211yesmaximal, characteristic
8C2×#107×C107C211yesmaximal, characteristic
9C22×Dic214—21no—
10C22×Dic214C2211yescharacteristic
11C22×C107⋊C8C2211yescharacteristic
12#16812108—22no—
13#16812108C2214yes—
14#16812074—22no—
15#16812074C2214yes—
16C2×C4⋊Dic107C2211yescharacteristic
17C2×Dic107⋊C4—21no—
18C2×Dic107⋊C4—21no—
19C2×C4×Dic107—21no—
20C2×C4×Dic107C2211yescharacteristic
21#16812042C2214yes—
22Dic107⋊C8C2214yes—
23#16812034C2214yes—
24#16812032C2214yes—
25C22×C8×C107C2211yescharacteristic
26C2×C4⋊C4×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28#107×C107C2214yes—
29C2×Dic214—21no—
30C2×Dic214—22no—
31C2×Dic214—24no—
32C2×Dic214—44no—
33C2×Dic214Q814yescomplemented
34C2×Dic214C2312yes—
35C22×Dic107—21no—
36C22×Dic107—21no—
37C22×Dic107D411yescharacteristic
38C22×Dic107D411yescharacteristic
39C2×C107⋊C8—22no—
40C2×C107⋊C8C2312yes—
41C4⋊Dic107—21no—
42C4⋊Dic107C2312yes—
43Dic107⋊C4—24no—
44Dic107⋊C4—24no—
45C4×Dic107—24no—
46C4×Dic107D412yes—
47C4×Dic107C2312yes—
48C22×C4×C107—21no—
49C22×C4×C107—21no—
50C22×C4×C107C2311yescharacteristic
51C2×C8×C107—22no—
52C2×C8×C107C2312yes—
53C4⋊C4×C107—21no—
54C4⋊C4×C107—21no—
55C4⋊C4×C107C2312yes—
56C4⋊C4×C107C2312yes—
57C23×C107C2×D411yescharacteristic
58C2×C4×C107—22no—
59C2×C4×C107—22no—
60C2×C4×C107—42no—
61C2×C4×C107—42no—
62C2×C4×C107C2×D411yescharacteristic
63C2×C4×C107C2×Q812yes—
64C2×C4×C107#4112yes—
65C2×C4×C107C2411yescharacteristic
66C2×Dic107—24no—
67C2×Dic107—22no—
68C2×Dic107—22no—
69C2×Dic107—22no—
70C2×Dic107—42no—
71C2×Dic107Q1614yes—
72C2×Dic107C2×D412yes—
73C2×Dic107C2×D412yes—
74Dic214—24no—
75Dic214—22no—
76Dic214—48no—
77Dic214C2×Q814yescomplemented
78C8×C107—22no—
79C107⋊C8—22no—
80C22×C107C22⋊Q812yes—
81C22×C107C2×Q1612yes—
82C22×C107AGL(1,ℤ/8)12yes—
83C22×C107C22×D411yescharacteristic
84C4×C107—42no—
85C4×C107—42no—
86C4×C107C22⋊Q812yes—
87C4×C107C22×Q811yescharacteristic
88C4×C107C2×#4111yescharacteristic
89Dic107—24no—
90Dic107—22no—
91Dic107—42no—
92Dic107C2×Q1614yes—
93C2×C107#47714yescomplemented
94C2×C107C2×C22⋊Q811yescharacteristic
95C2×C107C22×Q1611yescharacteristic
96C2×C107C2×AGL(1,ℤ/8)11yescharacteristic
97C2×#477—1071nomaximal, Sylow
98C107C2×#47711yescharacteristic, complemented, Sylow
99C2×C4⋊Q8—1071no—
100C2×C4×Q8—1071no—
101#477—1078no—
102C2×#107—1071no—
103C2×#107D10711yescharacteristic
104C2×C4⋊C8—1071no—
105C2×#103—1071no—
106C2×#103—1071no—
107C22×Q8—1071no—
108C22×Q8—2141no—
109C22×C8—1071no—
110C22×C8C2×D10711yescharacteristic
111C4⋊Q8—1074no—
112C4⋊Q8—2142no—
113C4×Q8—1074no—
114C4×Q8—2142no—
115C2×C4⋊C4—1071no—
116C2×C4⋊C4—2141no—
117C2×C4⋊C4—2141no—
118C2×C4⋊C4C2×D10711yescharacteristic
119C2×C4⋊C4C2×D10711yescharacteristic
120C2×C42—1071no—
121C2×C42—2141no—
122#107—1074no—
123#107C2×D10714yes—
124C4⋊C8—1074no—
125#103—1074no—
126#103—1074no—
127C2×Q8—1074no—
128C2×Q8—1072no—
129C2×Q8—4284no—
130C2×Q8—2144no—
131C2×Q8—2141no—
132C2×Q8—2142no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—1071no—
136C22×C4—1071no—
137C22×C4—2141no—
138C22×C4—2141no—
139C22×C4C22×D10711yescharacteristic
140C2×C8—22no—
141C2×C8—1072no—
142C2×C8—2142no—
143C2×C8C22×D10712yes—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—1072no—
147C4⋊C4—2144no—
148C4⋊C4—2144no—
149C4⋊C4—2141no—
150C4⋊C4C22×D10712yes—
151C4⋊C4C22×D10712yes—
152C42—1072no—
153C42—1072no—
154C42—2144no—
155C23D4×D10711yescharacteristic
156Q8—1074no—
157Q8—4288no—
158Q8—2144no—
159Q8—2142no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—1074no—
165C2×C4—1072no—
166C2×C4—1072no—
167C2×C4—4282no—
168C2×C4—2142no—
169C2×C4—2144no—
170C2×C4—2142no—
171C2×C4—2142no—
172C2×C4D4×D10711yescharacteristic
173C2×C4Q8×D10712yes—
174C2×C4#1313381812yes—
175C2×C4C23×D10711yescharacteristic
176C8—22no—
177C8—2142no—
178C22#1681208712yes—
179C22Q16×D10712yes—
180C22#1681213312yes—
181C22C2×D4×D10711yescharacteristic
182C4—42no—
183C4—42no—
184C4—1074no—
185C4—4282no—
186C4—2144no—
187C4—2142no—
188C4#1681208712yes—
189C4C2×Q8×D10711yescharacteristic
190C4C2×#1313381811yescharacteristic
191C2#2029292114yesdirect product factor
192C2C2×#1681208711yescharacteristic
193C2C2×Q16×D10711yescharacteristic
194C2C2×#1681213311yescharacteristic
subgroupG/H
centerC23D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#107×C107C2
socle, prime radicalC23×C107C2×D4
hypercenterC2×#107D107
hypocenterC107C2×#477
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #20292921C2direct (N × H)
33. C2×Dic214Q8semidirect
77. Dic214C2×Q8semidirect
93. C2×C107#477semidirect
98. C107C2×#477semidirect
191. C2#20292921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168121082
C2×#168120742
#202929212
C2×#168120422
C2×Dic107⋊C82
C2×#168120342
C2×#168120322
C2×#107×C1072
C2×#477107