Finite Group Databasebeta

← C2×#20292831 #28345878

Subgroups — C2×#20292831 #28345878

Order 13696.

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×#13133807C211yesmaximal, characteristic
2C22×#13133805C211yesmaximal, characteristic
3C2×#16812107C211yesmaximal, characteristic, complemented
4C2×#16812071C211yesmaximal, characteristic
5#20292831C218yesmaximal, direct product factor
6C2×Dic107⋊C8C211yesmaximal, characteristic, complemented
7C2×#16812032C211yesmaximal, characteristic, complemented
8C2×#103×C107C211yesmaximal, characteristic, complemented
9C22×Dic214C2211yescharacteristic
10C22×D428C2211yescharacteristic
11C22×C4×D107—21no—
12C2×#13133807—24no—
13C2×#13133807C2214yes—
14C2×#13133805—24no—
15C2×#13133805C2214yes—
16C22×C107⋊C8C2211yescharacteristic
17#16812107—22no—
18#16812107C2214yescomplemented
19#16812071—22no—
20#16812071C2214yes—
21C2×Dic107⋊C4—21no—
22C2×Dic107⋊C4—21no—
23C2×(C2×D107)⋊C4—21no—
24C2×C4×Dic107C2211yescharacteristic
25Dic107⋊C8C2214yescomplemented
26#16812032C2214yescomplemented
27C22×Q8×C107C2211yescharacteristic
28C22×C8×C107C2211yescharacteristic
29C2×C4⋊C4×C107C2211yescharacteristic
30#103×C107C2214yescomplemented
31C23×D107—21no—
32C2×Dic214—22no—
33C2×Dic214—22no—
34C2×Dic214—21no—
35C2×Dic214C2312yes—
36C2×D428—21no—
37C2×D428—22no—
38C2×D428D414yes—
39C2×D428C2312yes—
40C22×Dic107—21no—
41C22×Dic107D411yescharacteristic
42C22×Dic107D411yescharacteristic
43C2×C4×D107—24no—
44C2×C4×D107—44no—
45#13133807—28no—
46#13133805—28no—
47C2×C107⋊C8—22no—
48C2×C107⋊C8C2312yes—
49Dic107⋊C4—24no—
50Dic107⋊C4—24no—
51(C2×D107)⋊C4—24no—
52C4×Dic107D412yes—
53C4×Dic107C2312yes—
54C2×Q8×C107—21no—
55C2×Q8×C107—22no—
56C2×Q8×C107—22no—
57C2×Q8×C107C2312yes—
58C22×C4×C107—21no—
59C22×C4×C107—21no—
60C22×C4×C107C2311yescharacteristic
61C2×C8×C107—22no—
62C2×C8×C107C2312yes—
63C4⋊C4×C107—21no—
64C4⋊C4×C107C2312yes—
65C23×C107C2×D411yescharacteristic
66C22×D107—24no—
67C22×D107—22no—
68C22×D107—42no—
69C22×D107—42no—
70Q8×C107—22no—
71Q8×C107—22no—
72Q8×C107—42no—
73C2×C4×C107—22no—
74C2×C4×C107—22no—
75C2×C4×C107—42no—
76C2×C4×C107—42no—
77C2×C4×C107C2×D411yescharacteristic
78C2×C4×C107C2×D412yes—
79C2×C4×C107#4112yes—
80C2×C4×C107C2411yescharacteristic
81C2×Dic107—22no—
82C2×Dic107—22no—
83C2×Dic107—42no—
84C2×Dic107SD1614yescomplemented
85C2×Dic107C2×D412yes—
86C2×Dic107C2×D412yes—
87D428—24no—
88D428—22no—
89D428C2×D414yes—
90C4×D107—48no—
91Dic214—22no—
92Dic214—22no—
93Dic214—42no—
94C8×C107—22no—
95C107⋊C8—22no—
96C22×C107#12112yes—
97C22×C107C2×SD1612yes—
98C22×C107#13712yes—
99C22×C107C22×D411yescharacteristic
100C2×D107—24no—
101C2×D107—42no—
102C2×D107—42no—
103C2×D107—48no—
104C4×C107—42no—
105C4×C107—42no—
106C4×C107#12112yes—
107C4×C107C22×D411yescharacteristic
108C4×C107C2×#4111yescharacteristic
109Dic107—22no—
110Dic107—42no—
111Dic107C2×SD1614yescomplemented
112C2×C107#46114yescomplemented
113C2×C107C2×#12111yescharacteristic
114C2×C107C22×SD1611yescharacteristic
115C2×C107C2×#13711yescharacteristic
116D107—44no—
117C2×#461—1071nomaximal, Sylow
118C107C2×#46111yescharacteristic, complemented, Sylow
119C22×SD16—1071no—
120C22×SD16—1071no—
121C2×C4⋊Q8—1071no—
122C2×C4×D4—1071no—
123#461—1078no—
124C2×C4⋊C8—1071no—
125C2×#103—1071no—
126C2×#103D10711yescharacteristic, complemented
127C22×Q8—1071no—
128C22×Q8C2×D10711yescharacteristic
129C22×D4—1071no—
130C23×C4—2141no—
131C2×SD16—1074no—
132C2×SD16—1074no—
133C2×SD16—2144no—
134C2×SD16—2144no—
135C22×C8—1071no—
136C22×C8C2×D10711yescharacteristic
137C4⋊Q8—1074no—
138C4⋊Q8—2142no—
139C4×D4—1074no—
140C4×D4—2142no—
141C2×C4⋊C4—2141no—
142C2×C4⋊C4—2141no—
143C2×C4⋊C4C2×D10711yescharacteristic
144C2×C22⋊C4—2141no—
145C2×C42—1071no—
146C4⋊C8—1074no—
147#103—1074no—
148#103C2×D10714yescomplemented
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—1074no—
159C2×D4—1072no—
160C2×D4—2141no—
161C2×D4—2142no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—1071no—
165C22×C4—1071no—
166C22×C4—4284no—
167C22×C4—2144no—
168C22×C4—2141no—
169C22×C4C22×D10711yescharacteristic
170SD16—2148no—
171SD16—2148no—
172C2×C8—22no—
173C2×C8—1072no—
174C2×C8—2142no—
175C2×C8C22×D10712yes—
176C4⋊C4—21no—
177C4⋊C4—2144no—
178C4⋊C4—2144no—
179C4⋊C4C22×D10712yes—
180C22⋊C4—2144no—
181C42—1072no—
182C42—1072no—
183C23—4282no—
184C23—4282no—
185C23—2144no—
186C23—2142no—
187C23D4×D10711yescharacteristic
188Q8—22no—
189Q8—22no—
190Q8—42no—
191Q8—4282no—
192Q8—2142no—
193Q8—2142no—
194D4—1074no—
195D4—2144no—
196D4—2142no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—1074no—
202C2×C4—1072no—
203C2×C4—1072no—
204C2×C4—4288no—
205C2×C4—4282no—
206C2×C4—2142no—
207C2×C4—2142no—
208C2×C4D4×D10711yescharacteristic
209C2×C4D4×D10712yes—
210C2×C4#1313381812yes—
211C2×C4C23×D10711yescharacteristic
212C8—22no—
213C8—2142no—
214C22—4282no—
215C22—4282no—
216C22—4288no—
217C22—2144no—
218C22#1681208212yes—
219C22SD16×D10712yes—
220C22#1681214112yes—
221C22C2×D4×D10711yescharacteristic
222C4—42no—
223C4—42no—
224C4—1074no—
225C4—4282no—
226C4—2142no—
227C4#1681208212yes—
228C4C2×D4×D10711yescharacteristic
229C4C2×#1313381811yescharacteristic
230C2—4284no—
231C2#2029283114yesdirect product factor
232C2C2×#1681208211yescharacteristic
233C2C2×SD16×D10711yescharacteristic
234C2C2×#1681214111yescharacteristic
subgroupG/H
centerC23D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#103×C107C2
socleC23×C107C2×D4
prime radicalC22×D428C22
hypercenterC2×#103D107
hypocenterC107C2×#461
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#16812107C2semidirect
5. #20292831C2direct (N × H)
6. C2×Dic107⋊C8C2semidirect
7. C2×#16812032C2semidirect
8. C2×#103×C107C2semidirect
18. #16812107C22semidirect
25. Dic107⋊C8C22semidirect
26. #16812032C22semidirect
30. #103×C107C22semidirect
84. C2×Dic107SD16semidirect
111. Dic107C2×SD16semidirect
112. C2×C107#461semidirect
118. C107C2×#461semidirect
126. C2×#103D107semidirect
148. #103C2×D107semidirect
231. C2#20292831direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131338072
C22×#131338052
C2×#168121072
C2×#168120712
#202928312
C2×Dic107⋊C82
C2×#168120322
C2×#103×C1072
C2×#461107