Finite Group Databasebeta

← C2×#20293008 #28346879

Subgroups — C2×#20293008 #28346879

Order 13696.

592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13133808C211yesmaximal, characteristic, complemented
2C22×#13133807C211yesmaximal, characteristic, complemented
3C22×#13133803C211yesmaximal, characteristic
4C2×#16812098C211yesmaximal, characteristic, complemented
5C2×#16812096C211yesmaximal, characteristic, complemented
6#20293008C218yesmaximal, direct product factor
7C2×C8×Dic107C211yesmaximal, characteristic, complemented
8C22×SD16×C107C211yesmaximal, characteristic, complemented
9C22×Dic214C2211yescharacteristic
10C22×D428C2211yescharacteristic
11C2×#13133808—24no—
12C2×#13133808C2214yescomplemented
13C2×#13133807—24no—
14C2×#13133807C2214yescomplemented
15C2×#13133803—24no—
16C2×#13133803C2214yes—
17C22×C107⋊C8C2211yescharacteristic
18#16812098—22no—
19#16812098C2214yescomplemented
20#16812096—22no—
21#16812096C2214yescomplemented
22C2×C22⋊Dic107—22no—
23C2×(C2×D107)⋊C4—22no—
24C2×C4×Dic107C2211yescharacteristic
25C8×Dic107C2214yescomplemented
26C22×Q8×C107C2211yescharacteristic
27C22×D4×C107C2211yescharacteristic
28C2×SD16×C107—24no—
29C2×SD16×C107C2214yescomplemented
30C22×C8×C107C2211yescharacteristic
31C23×D107—21no—
32C2×Dic214—22no—
33C2×Dic214—22no—
34C2×Dic214—21no—
35C2×Dic214C2312yes—
36C2×D428—22no—
37C2×D428—22no—
38C2×D428—21no—
39C2×D428C2312yes—
40C22×Dic107—21no—
41C22×Dic107D412yes—
42#13133808—28no—
43#13133807—28no—
44#13133803—28no—
45C2×C107⋊C8D414yes—
46C2×C107⋊C8C2312yes—
47C22⋊Dic107—28no—
48(C2×D107)⋊C4—28no—
49C4×Dic107D412yes—
50C4×Dic107C2312yes—
51C24×C107—21no—
52C2×Q8×C107—21no—
53C2×Q8×C107—22no—
54C2×Q8×C107—22no—
55C2×Q8×C107C2312yes—
56C2×D4×C107—22no—
57C2×D4×C107—22no—
58C2×D4×C107—21no—
59C2×D4×C107C2312yes—
60C22×C4×C107—21no—
61C22×C4×C107C2311yescharacteristic
62SD16×C107—28no—
63C2×C8×C107D414yes—
64C2×C8×C107C2312yes—
65C23×C107—22no—
66C23×C107—42no—
67C23×C107—44no—
68C23×C107C2×D411yescharacteristic
69C22×D107—22no—
70C22×D107—42no—
71C22×D107—44no—
72Q8×C107—22no—
73Q8×C107—22no—
74Q8×C107—42no—
75D4×C107—22no—
76D4×C107—22no—
77D4×C107—42no—
78C2×C4×C107—22no—
79C2×C4×C107—42no—
80C2×C4×C107C2×D411yescharacteristic
81C2×C4×C107C2×D412yes—
82C2×C4×C107C2×D412yes—
83C2×C4×C107C2411yescharacteristic
84C2×Dic107—24no—
85C2×Dic107—22no—
86C2×Dic107—42no—
87C2×Dic107C2×D414yes—
88D428—22no—
89D428—22no—
90D428—42no—
91Dic214—22no—
92Dic214—22no—
93Dic214—42no—
94C8×C107C2×D414yes—
95C107⋊C8C2×D414yes—
96C22×C107—42no—
97C22×C107—44no—
98C22×C107—84no—
99C22×C107#12712yes—
100C22×C107#13514yes—
101C22×C107C22×D411yescharacteristic
102C2×D107—42no—
103C2×D107—44no—
104C2×D107—84no—
105C4×C107—42no—
106C4×C107#12712yes—
107C4×C107C22×D411yescharacteristic
108C4×C107C22×D411yescharacteristic
109Dic107—24no—
110Dic107—42no—
111C2×C107—82no—
112C2×C107#49514yescomplemented
113C2×C107C2×#12711yescharacteristic
114C2×C107C2×#13512yes—
115D107—82no—
116C2×#495—1071nomaximal, Sylow
117C107C2×#49511yescharacteristic, complemented, Sylow
118C22×Q16—1071no—
119C22×SD16—1071no—
120C22×SD16D10711yescharacteristic, complemented
121C22×D8—1071no—
122C2×#124—1071no—
123C2×#124—1071no—
124#495—1078no—
125C2×C4×C8—1071no—
126C22×Q8—1071no—
127C22×Q8C2×D10711yescharacteristic
128C22×D4—1071no—
129C22×D4C2×D10711yescharacteristic
130C2×Q16—1074no—
131C2×Q16—2144no—
132C2×SD16—24no—
133C2×SD16—1074no—
134C2×SD16—2144no—
135C2×SD16C2×D10714yescomplemented
136C2×D8—1074no—
137C2×D8—2144no—
138C22×C8—1071no—
139C22×C8C2×D10711yescharacteristic
140#124—1074no—
141#124—1074no—
142#124—2142no—
143#124—2142no—
144C2×C22⋊C4—2142no—
145C2×C22⋊C4—2142no—
146C2×C42—1071no—
147C4×C8—1074no—
148C24—21no—
149C24—2141no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—1072no—
154C2×Q8—2142no—
155C2×Q8—2142no—
156C2×Q8—2141no—
157C2×Q8C22×D10712yes—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—22no—
161C2×D4—1072no—
162C2×D4—2141no—
163C2×D4—2142no—
164C2×D4—2142no—
165C2×D4C22×D10712yes—
166C22×C4—21no—
167C22×C4—1072no—
168C22×C4—2141no—
169C22×C4C22×D10711yescharacteristic
170Q16—2148no—
171SD16—28no—
172SD16—2148no—
173D8—2148no—
174C2×C8—1074no—
175C2×C8—1072no—
176C2×C8C22⋊D10714yes—
177C2×C8C22×D10712yes—
178C22⋊C4—2148no—
179C22⋊C4—2148no—
180C42—1072no—
181C42—1072no—
182C23—22no—
183C23—42no—
184C23—44no—
185C23—4282no—
186C23—4284no—
187C23—2142no—
188C23D4×D10711yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—4282no—
193Q8—2142no—
194Q8—2142no—
195D4—22no—
196D4—22no—
197D4—42no—
198D4—4282no—
199D4—2142no—
200D4—2142no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—1074no—
204C2×C4—4282no—
205C2×C4—2142no—
206C2×C4—2144no—
207C2×C4D4×D10711yescharacteristic
208C2×C4D4×D10712yes—
209C2×C4C2×C22⋊D10712yes—
210C2×C4C23×D10711yescharacteristic
211C8—1074no—
212C8C2×C22⋊D10714yes—
213C22—44no—
214C22—42no—
215C22—84no—
216C22—8564no—
217C22—4284no—
218C22—4282no—
219C22#1681210512yes—
220C22#1681213014yes—
221C22C2×D4×D10711yescharacteristic
222C4—42no—
223C4—4282no—
224C4—2144no—
225C4#1681210512yes—
226C4C2×D4×D10711yescharacteristic
227C4C22×C22⋊D10711yescharacteristic
228C2—82no—
229C2—8562no—
230C2#2029300814yesdirect product factor
231C2C2×#1681210511yescharacteristic
232C2C2×#1681213012yes—
subgroupG/H
centerC23D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC22×SD16×C107C2
socleC23×C107C2×D4
prime radicalC22×#13133803C2
hypercenterC22×SD16D107
hypocenterC107C2×#495
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#13133808C2semidirect
2. C22×#13133807C2semidirect
4. C2×#16812098C2semidirect
5. C2×#16812096C2semidirect
6. #20293008C2direct (N × H)
7. C2×C8×Dic107C2semidirect
8. C22×SD16×C107C2semidirect
12. C2×#13133808C22semidirect
14. C2×#13133807C22semidirect
19. #16812098C22semidirect
21. #16812096C22semidirect
25. C8×Dic107C22semidirect
29. C2×SD16×C107C22semidirect
112. C2×C107#495semidirect
117. C107C2×#495semidirect
120. C22×SD16D107semidirect
135. C2×SD16C2×D107semidirect
230. C2#20293008direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131338082
C22×#131338072
C22×#131338032
C2×#168120982
C2×#168120962
#202930082
C2×C8×Dic1072
C22×SD16×C1072
C2×#495107