Finite Group Databasebeta

← C2×#20292876 #28346052

Subgroups — C2×#20292876 #28346052

Order 13696.

544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133805C211yesmaximal, characteristic, complemented
2C22×#13133801C211yesmaximal, characteristic, complemented
3C2×#16812085C211yesmaximal, characteristic, complemented
4C2×#16812084C211yesmaximal, characteristic
5#20292876C218yesmaximal, direct product factor
6C2×#16812042C211yesmaximal, characteristic, complemented
7C2×#16812031C211yesmaximal, characteristic, complemented
8C2×#103×C107C211yesmaximal, characteristic, complemented
9C22×D428—21no—
10C22×D428C2211yescharacteristic
11C22×C4×D107C2211yescharacteristic
12C2×#13133805—24no—
13C2×#13133805C2214yescomplemented
14C2×#13133801—24no—
15C2×#13133801C2214yescomplemented
16C22×C107⋊C8C2211yescharacteristic
17#16812085—22no—
18#16812085C2214yescomplemented
19#16812084—22no—
20#16812084C2214yes—
21C2×C4⋊Dic107C2211yescharacteristic
22C2×Dic107⋊C4—21no—
23C2×(C2×D107)⋊C4—21no—
24C2×(C2×D107)⋊C4—21no—
25#16812042C2214yescomplemented
26#16812031C2214yescomplemented
27C22×Q8×C107C2211yescharacteristic
28C22×C8×C107C2211yescharacteristic
29C2×C4⋊C4×C107C2211yescharacteristic
30#103×C107C2214yescomplemented
31C23×D107—21no—
32C23×D107D411yescharacteristic
33C2×D428—22no—
34C2×D428—22no—
35C2×D428—24no—
36C2×D428—21no—
37C2×D428—44no—
38C2×D428C2312yes—
39C22×Dic107—21no—
40C22×Dic107D411yescharacteristic
41C2×C4×D107—22no—
42C2×C4×D107—22no—
43C2×C4×D107D412yes—
44C2×C4×D107C2312yes—
45#13133805—28no—
46#13133801—28no—
47C2×C107⋊C8D414yescomplemented
48C2×C107⋊C8C2312yes—
49C4⋊Dic107—21no—
50C4⋊Dic107C2312yes—
51Dic107⋊C4—24no—
52(C2×D107)⋊C4—24no—
53(C2×D107)⋊C4—24no—
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—22no—
67C22×D107—22no—
68C22×D107—22no—
69C22×D107—22no—
70C22×D107—42no—
71C22×D107—42no—
72C22×D107—42no—
73C22×D107C2×D412yes—
74Q8×C107—22no—
75Q8×C107—22no—
76Q8×C107—42no—
77C2×C4×C107—22no—
78C2×C4×C107—22no—
79C2×C4×C107—42no—
80C2×C4×C107—42no—
81C2×C4×C107C2×D411yescharacteristic
82C2×C4×C107C2×D412yes—
83C2×C4×C107#4112yes—
84C2×C4×C107C2411yescharacteristic
85C2×Dic107—22no—
86C2×Dic107—22no—
87C2×Dic107—42no—
88C2×Dic107C2×D412yes—
89D428—22no—
90D428—22no—
91D428—48no—
92D428—42no—
93C4×D107—24no—
94C4×D107—22no—
95C4×D107—22no—
96C8×C107—22no—
97C107⋊C8C2×D414yescomplemented
98C22×C107#12112yes—
99C22×C107AGL(1,ℤ/8)12yes—
100C22×C107#13712yes—
101C22×C107C22×D411yescharacteristic
102C2×D107—22no—
103C2×D107—22no—
104C2×D107—22no—
105C2×D107—44no—
106C2×D107—42no—
107C2×D107—42no—
108C2×D107—42no—
109C2×D107—84no—
110C4×C107—42no—
111C4×C107—42no—
112C4×C107#12112yes—
113C4×C107C22×D411yescharacteristic
114C4×C107C2×#4111yescharacteristic
115Dic107—22no—
116Dic107—42no—
117C2×C107#46814yescomplemented
118C2×C107C2×#12111yescharacteristic
119C2×C107C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C107C2×#13711yescharacteristic
121D107—42no—
122D107—82no—
123C2×#468—1071nomaximal, Sylow
124C107C2×#46811yescharacteristic, complemented, Sylow
125C22×SD16—1071no—
126C22×M16—1071no—
127C2×C22⋊Q8—1071no—
128C2×#121—1071no—
129#468—1078no—
130C2×#107—1071no—
131C2×#103D10711yescharacteristic, complemented
132C2×#102—1071no—
133C22×Q8C2×D10711yescharacteristic
134C22×D4—1071no—
135C22×D4—2141no—
136C23×C4—1071no—
137C2×SD16—1074no—
138C2×SD16—2144no—
139C2×M16—1074no—
140C2×M16—2144no—
141C22×C8—1071no—
142C22×C8C2×D10711yescharacteristic
143C22⋊Q8—1074no—
144C22⋊Q8—2142no—
145#121—1074no—
146#121—2142no—
147C2×C4⋊C4—1071no—
148C2×C4⋊C4—2141no—
149C2×C4⋊C4C2×D10711yescharacteristic
150C2×C22⋊C4—2141no—
151C2×C22⋊C4—2141no—
152#107—1074no—
153#103C2×D10714yescomplemented
154#102—1074no—
155C24—1071no—
156C24—2141no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D10712yes—
161C2×D4—1072no—
162C2×D4—4284no—
163C2×D4—2144no—
164C2×D4—2141no—
165C2×D4—2142no—
166C2×D4—2142no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—1071no—
170C22×C4—1072no—
171C22×C4—1072no—
172C22×C4—2141no—
173C22×C4—2142no—
174C22×C4—2142no—
175C22×C4C22×D10711yescharacteristic
176SD16—2148no—
177M16—2148no—
178C2×C8—22no—
179C2×C8—1074no—
180C2×C8—1072no—
181C2×C8C22×D10712yes—
182C4⋊C4—21no—
183C4⋊C4—1072no—
184C4⋊C4—2144no—
185C4⋊C4—2141no—
186C4⋊C4C22×D10712yes—
187C22⋊C4—2144no—
188C22⋊C4—2144no—
189C23—1072no—
190C23—4282no—
191C23—4282no—
192C23—4282no—
193C23—2142no—
194C23—2142no—
195C23—2142no—
196C23—2142no—
197C23D4×D10711yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—4288no—
202D4—4282no—
203D4—2142no—
204D4—2142no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—1072no—
210C2×C4—4282no—
211C2×C4—2142no—
212C2×C4—2142no—
213C2×C4—2144no—
214C2×C4—2142no—
215C2×C4—2142no—
216C2×C4D4×D10711yescharacteristic
217C2×C4D4×D10712yes—
218C2×C4#1313381812yes—
219C2×C4C23×D10711yescharacteristic
220C8—22no—
221C8—1074no—
222C22—8564no—
223C22—4282no—
224C22—4282no—
225C22—4282no—
226C22—4284no—
227C22—2142no—
228C22—2142no—
229C22—2142no—
230C22#1681208212yes—
231C22#1681213612yes—
232C22#1681214112yes—
233C22C2×D4×D10711yescharacteristic
234C4—42no—
235C4—42no—
236C4—4282no—
237C4—2142no—
238C4#1681208212yes—
239C4C2×D4×D10711yescharacteristic
240C4C2×#1313381811yescharacteristic
241C2—8562no—
242C2—4282no—
243C2#2029287614yesdirect product factor
244C2C2×#1681208211yescharacteristic
245C2C2×#1681213611yescharacteristic
246C2C2×#1681214111yescharacteristic
subgroupG/H
centerC23D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#103×C107C2
socleC23×C107C2×D4
prime radicalC2×#16812084C2
hypercenterC2×#103D107
hypocenterC107C2×#468
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
1. C22×#13133805C2semidirect
2. C22×#13133801C2semidirect
3. C2×#16812085C2semidirect
5. #20292876C2direct (N × H)
6. C2×#16812042C2semidirect
7. C2×#16812031C2semidirect
8. C2×#103×C107C2semidirect
13. C2×#13133805C22semidirect
15. C2×#13133801C22semidirect
18. #16812085C22semidirect
25. #16812042C22semidirect
26. #16812031C22semidirect
30. #103×C107C22semidirect
47. C2×C107⋊C8D4semidirect
97. C107⋊C8C2×D4semidirect
117. C2×C107#468semidirect
124. C107C2×#468semidirect
131. C2×#103D107semidirect
153. #103C2×D107semidirect
243. C2#20292876direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131338052
C22×#131338012
C2×#168120852
C2×#168120842
#202928762
C2×#168120422
C2×#168120312
C2×#103×C1072
C2×#468107