Finite Group Databasebeta

← C2×#20292862 #28346028

Subgroups — C2×#20292862 #28346028

Order 13696.

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

normal subgroups only

This group has 616 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×#13133803C211yesmaximal, characteristic, complemented
2C22×C8×D107C211yesmaximal, characteristic, complemented
3C2×#16812084C211yesmaximal, characteristic, complemented
4C2×#16812080C211yesmaximal, characteristic, complemented
5#20292862C218yesmaximal, direct product factor
6C2×#16812042C211yesmaximal, characteristic, complemented
7C2×#16812031C211yesmaximal, characteristic, complemented
8C2×#102×C107C211yesmaximal, characteristic, complemented
9C22×D428—21no—
10C22×D428C2211yescharacteristic
11C22×C22⋊D107—21no—
12C22×C4×D107C2211yescharacteristic
13C2×#13133803—24no—
14C2×#13133803C2214yescomplemented
15C22×C107⋊C8C2211yescharacteristic
16C2×C8×D107—24no—
17C2×C8×D107C2214yescomplemented
18#16812084—22no—
19#16812084C2214yescomplemented
20#16812080—22no—
21#16812080C2214yescomplemented
22C2×C4⋊Dic107C2211yescharacteristic
23C2×C22⋊Dic107—21no—
24C2×(C2×D107)⋊C4—21no—
25#16812042C2214yescomplemented
26#16812031C2214yescomplemented
27C22×D4×C107C2211yescharacteristic
28C22×C8×C107C2211yescharacteristic
29C2×C4⋊C4×C107C2211yescharacteristic
30#102×C107C2214yescomplemented
31C23×D107—21no—
32C23×D107D411yescharacteristic
33C2×D428—22no—
34C2×D428—22no—
35C2×D428—24no—
36C2×D428—21no—
37C2×D428—44no—
38C2×D428C2312yes—
39C2×C22⋊D107—24no—
40C2×C22⋊D107—44no—
41C22×Dic107—21no—
42C22×Dic107D411yescharacteristic
43C2×C4×D107—22no—
44C2×C4×D107—22no—
45C2×C4×D107D412yes—
46C2×C4×D107C2312yes—
47#13133803—28no—
48C2×C107⋊C8D414yescomplemented
49C2×C107⋊C8C2312yes—
50C8×D107—28no—
51C4⋊Dic107—21no—
52C4⋊Dic107C2312yes—
53C22⋊Dic107—24no—
54(C2×D107)⋊C4—24no—
55C24×C107—21no—
56C2×D4×C107—22no—
57C2×D4×C107—21no—
58C2×D4×C107—22no—
59C2×D4×C107C2312yes—
60C22×C4×C107—21no—
61C22×C4×C107C2311yescharacteristic
62C2×C8×C107—22no—
63C2×C8×C107C2312yes—
64C4⋊C4×C107—21no—
65C4⋊C4×C107C2312yes—
66C23×C107—22no—
67C23×C107—42no—
68C23×C107—42no—
69C23×C107—42no—
70C23×C107C2×D411yescharacteristic
71C22×D107—22no—
72C22×D107—22no—
73C22×D107—22no—
74C22×D107—42no—
75C22×D107—42no—
76C22×D107—42no—
77C22×D107D814yescomplemented
78C22×D107C2×D412yes—
79D4×C107—22no—
80D4×C107—22no—
81D4×C107—42no—
82C2×C4×C107—22no—
83C2×C4×C107—42no—
84C2×C4×C107C2×D411yescharacteristic
85C2×C4×C107C2×D412yes—
86C2×C4×C107#4112yes—
87C2×C4×C107C2411yescharacteristic
88C22⋊D107—48no—
89C2×Dic107—22no—
90C2×Dic107—22no—
91C2×Dic107—42no—
92C2×Dic107C2×D412yes—
93D428—22no—
94D428—22no—
95D428—48no—
96D428—42no—
97C4×D107—24no—
98C4×D107—22no—
99C4×D107—22no—
100C8×C107—22no—
101C107⋊C8C2×D414yescomplemented
102C22×C107—42no—
103C22×C107—42no—
104C22×C107—42no—
105C22×C107—84no—
106C22×C107#12112yes—
107C22×C107C2×D812yes—
108C22×C107#13512yes—
109C22×C107C22×D411yescharacteristic
110C2×D107—22no—
111C2×D107—22no—
112C2×D107—28no—
113C2×D107—42no—
114C2×D107—42no—
115C2×D107—42no—
116C2×D107—84no—
117C2×D107C2×D814yescomplemented
118C4×C107—42no—
119C4×C107#12112yes—
120C4×C107C22×D411yescharacteristic
121C4×C107C2×#4111yescharacteristic
122Dic107—22no—
123Dic107—42no—
124C2×C107—82no—
125C2×C107#46614yescomplemented
126C2×C107C2×#12111yescharacteristic
127C2×C107C22×D811yescharacteristic
128C2×C107C2×#13511yescharacteristic
129D107—24no—
130D107—82no—
131C2×#466—1071nomaximal, Sylow
132C107C2×#46611yescharacteristic, complemented, Sylow
133C22×D8—1071no—
134C23×C8—1071no—
135C2×#121—1071no—
136C2×#121—1071no—
137#466—1078no—
138C2×#107—1071no—
139C2×#102—1071no—
140C2×#102D10711yescharacteristic, complemented
141C22×D4—1071no—
142C22×D4—2141no—
143C22×D4—2141no—
144C22×D4C2×D10711yescharacteristic
145C23×C4—1071no—
146C2×D8—1074no—
147C2×D8—2144no—
148C22×C8—1071no—
149C22×C8—1074no—
150C22×C8—2144no—
151C22×C8C2×D10711yescharacteristic
152#121—1074no—
153#121—1074no—
154#121—2142no—
155#121—2142no—
156C2×C4⋊C4—1071no—
157C2×C4⋊C4C2×D10711yescharacteristic
158C2×C22⋊C4—2141no—
159C2×C22⋊C4—2141no—
160#107—1074no—
161#102—1074no—
162#102C2×D10714yescomplemented
163C24—21no—
164C24—1071no—
165C24—2141no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—22no—
169C2×D4—1072no—
170C2×D4—4284no—
171C2×D4—4284no—
172C2×D4—2144no—
173C2×D4—2144no—
174C2×D4—2141no—
175C2×D4—2142no—
176C2×D4—2142no—
177C2×D4C22×D10712yes—
178C22×C4—21no—
179C22×C4—1071no—
180C22×C4—1072no—
181C22×C4—1072no—
182C22×C4—2141no—
183C22×C4—2142no—
184C22×C4—2142no—
185C22×C4C22×D10711yescharacteristic
186D8—2148no—
187C2×C8—22no—
188C2×C8—1074no—
189C2×C8—1072no—
190C2×C8—2148no—
191C2×C8C22×D10712yes—
192C4⋊C4—21no—
193C4⋊C4—1072no—
194C4⋊C4—2141no—
195C4⋊C4C22×D10712yes—
196C22⋊C4—2144no—
197C22⋊C4—2144no—
198C23—22no—
199C23—42no—
200C23—42no—
201C23—42no—
202C23—1074no—
203C23—1072no—
204C23—4282no—
205C23—4282no—
206C23—4282no—
207C23—2142no—
208C23—2142no—
209C23—2142no—
210C23D4×D10711yescharacteristic
211D4—22no—
212D4—22no—
213D4—42no—
214D4—4288no—
215D4—4288no—
216D4—4282no—
217D4—2142no—
218D4—2142no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—1072no—
222C2×C4—4282no—
223C2×C4—2142no—
224C2×C4—2142no—
225C2×C4—2144no—
226C2×C4—2142no—
227C2×C4—2142no—
228C2×C4D4×D10711yescharacteristic
229C2×C4D4×D10712yes—
230C2×C4#1313381812yes—
231C2×C4C23×D10711yescharacteristic
232C8—22no—
233C8—1074no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—84no—
238C22—8564no—
239C22—1074no—
240C22—4282no—
241C22—4282no—
242C22—4282no—
243C22—2142no—
244C22—2148no—
245C22—2142no—
246C22#1681208212yes—
247C22D8×D10712yes—
248C22#1681213012yes—
249C22C2×D4×D10711yescharacteristic
250C4—42no—
251C4—4282no—
252C4—2142no—
253C4#1681208212yes—
254C4C2×D4×D10711yescharacteristic
255C4C2×#1313381811yescharacteristic
256C2—82no—
257C2—8562no—
258C2—2144no—
259C2#2029286214yesdirect product factor
260C2C2×#1681208211yescharacteristic
261C2C2×D8×D10711yescharacteristic
262C2C2×#1681213011yescharacteristic
subgroupG/H
centerC23D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#102×C107C2
socleC23×C107C2×D4
hypercenterC2×#102D107
hypocenterC107C2×#466
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#13133803C2semidirect
2. C22×C8×D107C2semidirect
3. C2×#16812084C2semidirect
4. C2×#16812080C2semidirect
5. #20292862C2direct (N × H)
6. C2×#16812042C2semidirect
7. C2×#16812031C2semidirect
8. C2×#102×C107C2semidirect
14. C2×#13133803C22semidirect
17. C2×C8×D107C22semidirect
19. #16812084C22semidirect
21. #16812080C22semidirect
25. #16812042C22semidirect
26. #16812031C22semidirect
30. #102×C107C22semidirect
48. C2×C107⋊C8D4semidirect
77. C22×D107D8semidirect
101. C107⋊C8C2×D4semidirect
117. C2×D107C2×D8semidirect
125. C2×C107#466semidirect
132. C107C2×#466semidirect
140. C2×#102D107semidirect
162. #102C2×D107semidirect
259. C2#20292862direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131338032
C22×C8×D1072
C2×#168120842
C2×#168120802
#202928622
C2×#168120422
C2×#168120312
C2×#102×C1072
C2×#466107