Finite Group Databasebeta

← C2×#20292949 #28346343

Subgroups — C2×#20292949 #28346343

Order 13696.

468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812080C211yesmaximal, characteristic
2C2×#16812067C211yesmaximal, characteristic, complemented
3#20292949C218yesmaximal, direct product factor
4C2×#16812043C211yesmaximal, characteristic, complemented
5C2×#16812040C211yesmaximal, characteristic, complemented
6C2×#16812030C211yesmaximal, characteristic, complemented
7C2×(C2×D107)⋊C8C211yesmaximal, characteristic, complemented
8C2×#102×C107C211yesmaximal, characteristic, complemented
9C22×C22⋊D107—21no—
10C22×C4×D107C2211yescharacteristic
11C22×C107⋊C8C2211yescharacteristic
12#16812080—22no—
13#16812080C2214yes—
14#16812067—22no—
15#16812067C2214yescomplemented
16C2×C4⋊Dic107C2211yescharacteristic
17C2×C4⋊Dic107C2211yescharacteristic
18C2×C22⋊Dic107—21no—
19C2×(C2×D107)⋊C4—21no—
20C2×C4×Dic107—21no—
21#16812043C2214yescomplemented
22#16812040C2214yescomplemented
23#16812030C2214yescomplemented
24(C2×D107)⋊C8C2214yescomplemented
25C22×D4×C107C2211yescharacteristic
26C22×C8×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28#102×C107C2214yescomplemented
29C23×D107D411yescharacteristic
30C2×C22⋊D107—24no—
31C2×C22⋊D107—44no—
32C22×Dic107—21no—
33C22×Dic107—21no—
34C22×Dic107D411yescharacteristic
35C2×C4×D107—22no—
36C2×C4×D107—22no—
37C2×C4×D107D412yes—
38C2×C4×D107C2312yes—
39C2×C107⋊C8—22no—
40C2×C107⋊C8C2312yes—
41C4⋊Dic107—21no—
42C4⋊Dic107—21no—
43C4⋊Dic107C2312yes—
44C4⋊Dic107C2312yes—
45C22⋊Dic107—24no—
46(C2×D107)⋊C4—24no—
47C4×Dic107—24no—
48C24×C107—21no—
49C2×D4×C107—21no—
50C2×D4×C107—22no—
51C2×D4×C107—22no—
52C2×D4×C107C2312yes—
53C22×C4×C107—21no—
54C22×C4×C107C2311yescharacteristic
55C2×C8×C107—22no—
56C2×C8×C107C2312yes—
57C4⋊C4×C107—21no—
58C4⋊C4×C107C2312yes—
59C23×C107—22no—
60C23×C107—42no—
61C23×C107—42no—
62C23×C107—42no—
63C23×C107C2×D411yescharacteristic
64C22×D107—22no—
65C22×D107—22no—
66C22×D107—22no—
67C22×D107C2×D412yes—
68D4×C107—22no—
69D4×C107—22no—
70D4×C107—42no—
71C2×C4×C107—22no—
72C2×C4×C107—42no—
73C2×C4×C107C2×D411yescharacteristic
74C2×C4×C107#4112yes—
75C2×C4×C107#4112yes—
76C2×C4×C107C2411yescharacteristic
77C22⋊D107—48no—
78C2×Dic107—22no—
79C2×Dic107—22no—
80C2×Dic107—22no—
81C2×Dic107—42no—
82C2×Dic107—42no—
83C2×Dic107C2×D412yes—
84C4×D107—24no—
85C4×D107—22no—
86C4×D107—22no—
87C8×C107—22no—
88C107⋊C8—22no—
89C22×C107—42no—
90C22×C107—42no—
91C22×C107—42no—
92C22×C107—84no—
93C22×C107#12312yes—
94C22×C107#13512yes—
95C22×C107AGL(1,ℤ/8)12yes—
96C22×C107C22×D411yescharacteristic
97C2×D107—22no—
98C2×D107—22no—
99C2×D107—22no—
100C2×D107—44no—
101C4×C107—42no—
102C4×C107#12312yes—
103C4×C107C2×#4111yescharacteristic
104C4×C107C2×#4111yescharacteristic
105Dic107—22no—
106Dic107—42no—
107Dic107—42no—
108C2×C107—82no—
109C2×C107#48214yescomplemented
110C2×C107C2×#12311yescharacteristic
111C2×C107C2×#13511yescharacteristic
112C2×C107C2×AGL(1,ℤ/8)11yescharacteristic
113D107—42no—
114C2×#482—1071nomaximal, Sylow
115C107C2×#48211yescharacteristic, complemented, Sylow
116C2×#121—1071no—
117C2×#117—1071no—
118#482—1078no—
119C2×#107—1071no—
120C2×#106—1071no—
121C2×#102—1071no—
122C2×#102D10711yescharacteristic, complemented
123C2×C22⋊C8—1071no—
124C22×D4—2141no—
125C22×D4C2×D10711yescharacteristic
126C23×C4—1071no—
127C22×C8—1071no—
128C22×C8C2×D10711yescharacteristic
129#121—1074no—
130#121—2142no—
131#117—1074no—
132#117—2142no—
133C2×C4⋊C4—1071no—
134C2×C4⋊C4—1071no—
135C2×C4⋊C4C2×D10711yescharacteristic
136C2×C22⋊C4—2141no—
137C2×C22⋊C4—2141no—
138C2×C42—2141no—
139#107—1074no—
140#106—1074no—
141#102—1074no—
142#102C2×D10714yescomplemented
143C22⋊C8—1074no—
144C24—21no—
145C24—1071no—
146C2×D4—21no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—4284no—
150C2×D4—2144no—
151C2×D4C22×D10712yes—
152C22×C4—21no—
153C22×C4—1071no—
154C22×C4—1072no—
155C22×C4—1072no—
156C22×C4—2141no—
157C22×C4—2141no—
158C22×C4—2142no—
159C22×C4—2142no—
160C22×C4C22×D10711yescharacteristic
161C2×C8—22no—
162C2×C8—1072no—
163C2×C8—2142no—
164C2×C8C22×D10712yes—
165C4⋊C4—21no—
166C4⋊C4—1072no—
167C4⋊C4—1072no—
168C4⋊C4—2141no—
169C4⋊C4—2141no—
170C4⋊C4C22×D10712yes—
171C22⋊C4—2144no—
172C22⋊C4—2144no—
173C42—2144no—
174C23—22no—
175C23—42no—
176C23—42no—
177C23—42no—
178C23—1072no—
179C23—2142no—
180C23—2142no—
181C23—2142no—
182C23D4×D10711yescharacteristic
183D4—22no—
184D4—22no—
185D4—42no—
186D4—4288no—
187C2×C4—22no—
188C2×C4—42no—
189C2×C4—1072no—
190C2×C4—4282no—
191C2×C4—4282no—
192C2×C4—2142no—
193C2×C4—2142no—
194C2×C4—2142no—
195C2×C4—2144no—
196C2×C4—2142no—
197C2×C4—2142no—
198C2×C4D4×D10711yescharacteristic
199C2×C4#1313381712yes—
200C2×C4#1313381812yes—
201C2×C4C23×D10711yescharacteristic
202C8—22no—
203C8—2142no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—84no—
208C22—4284no—
209C22—2142no—
210C22—2142no—
211C22—2142no—
212C22#1681209112yes—
213C22#1681212812yes—
214C22#1681213612yes—
215C22C2×D4×D10711yescharacteristic
216C4—42no—
217C4—4282no—
218C4—4282no—
219C4—2142no—
220C4#1681209112yes—
221C4C2×#1313381711yescharacteristic
222C4C2×#1313381811yescharacteristic
223C2—82no—
224C2—4282no—
225C2#2029294914yesdirect product factor
226C2C2×#1681209111yescharacteristic
227C2C2×#1681212811yescharacteristic
228C2C2×#1681213611yescharacteristic
subgroupG/H
centerC23D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#102×C107C2
socleC23×C107C2×D4
prime radicalC2×#16812080C2
hypercenterC2×#102D107
hypocenterC107C2×#482
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
2. C2×#16812067C2semidirect
3. #20292949C2direct (N × H)
4. C2×#16812043C2semidirect
5. C2×#16812040C2semidirect
6. C2×#16812030C2semidirect
7. C2×(C2×D107)⋊C8C2semidirect
8. C2×#102×C107C2semidirect
15. #16812067C22semidirect
21. #16812043C22semidirect
22. #16812040C22semidirect
23. #16812030C22semidirect
24. (C2×D107)⋊C8C22semidirect
28. #102×C107C22semidirect
109. C2×C107#482semidirect
115. C107C2×#482semidirect
122. C2×#102D107semidirect
142. #102C2×D107semidirect
225. C2#20292949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168120802
C2×#168120672
#202929492
C2×#168120432
C2×#168120402
C2×#168120302
C2×(C2×D107)⋊C82
C2×#102×C1072
C2×#482107