Finite Group Databasebeta

← C2×#20292967 #28346352

Subgroups — C2×#20292967 #28346352

Order 13696.

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

normal subgroups only

This group has 416 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×#16812085C211yesmaximal, characteristic
2C2×#16812067C211yesmaximal, characteristic
3#20292967C218yesmaximal, direct product factor
4C2×#16812043C211yesmaximal, characteristic, complemented
5C2×#16812040C211yesmaximal, characteristic, complemented
6C2×#16812033C211yesmaximal, characteristic, complemented
7C2×(C2×D107)⋊C8C211yesmaximal, characteristic
8C2×#103×C107C211yesmaximal, characteristic, complemented
9C22×C4×D107C2211yescharacteristic
10C22×C107⋊C8C2211yescharacteristic
11#16812085—22no—
12#16812085C2214yes—
13#16812067—22no—
14#16812067C2214yes—
15C2×C4⋊Dic107C2211yescharacteristic
16C2×C4⋊Dic107C2211yescharacteristic
17C2×Dic107⋊C4—21no—
18C2×(C2×D107)⋊C4—21no—
19C2×(C2×D107)⋊C4—21no—
20C2×C4×Dic107—21no—
21#16812043C2214yescomplemented
22#16812040C2214yescomplemented
23#16812033C2214yescomplemented
24(C2×D107)⋊C8C2214yes—
25C22×Q8×C107C2211yescharacteristic
26C22×C8×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28#103×C107C2214yescomplemented
29C23×D107D411yescharacteristic
30C22×Dic107—21no—
31C22×Dic107—21no—
32C22×Dic107D411yescharacteristic
33C2×C4×D107—22no—
34C2×C4×D107—22no—
35C2×C4×D107D412yes—
36C2×C4×D107C2312yes—
37C2×C107⋊C8—22no—
38C2×C107⋊C8C2312yes—
39C4⋊Dic107—21no—
40C4⋊Dic107—21no—
41C4⋊Dic107C2312yes—
42C4⋊Dic107C2312yes—
43Dic107⋊C4—24no—
44(C2×D107)⋊C4—24no—
45(C2×D107)⋊C4—24no—
46C4×Dic107—24no—
47C2×Q8×C107—21no—
48C2×Q8×C107—22no—
49C2×Q8×C107—22no—
50C2×Q8×C107C2312yes—
51C22×C4×C107—21no—
52C22×C4×C107—21no—
53C22×C4×C107C2311yescharacteristic
54C2×C8×C107—22no—
55C2×C8×C107C2312yes—
56C4⋊C4×C107—21no—
57C4⋊C4×C107C2312yes—
58C23×C107C2×D411yescharacteristic
59C22×D107—22no—
60C22×D107—22no—
61C22×D107—22no—
62C22×D107C2×D412yes—
63Q8×C107—22no—
64Q8×C107—22no—
65Q8×C107—42no—
66C2×C4×C107—22no—
67C2×C4×C107—22no—
68C2×C4×C107—42no—
69C2×C4×C107—42no—
70C2×C4×C107C2×D411yescharacteristic
71C2×C4×C107#4112yes—
72C2×C4×C107#4112yes—
73C2×C4×C107C2411yescharacteristic
74C2×Dic107—22no—
75C2×Dic107—22no—
76C2×Dic107—22no—
77C2×Dic107—42no—
78C2×Dic107—42no—
79C2×Dic107C2×D412yes—
80C4×D107—24no—
81C4×D107—22no—
82C4×D107—22no—
83C8×C107—22no—
84C107⋊C8—22no—
85C22×C107#12312yes—
86C22×C107#13512yes—
87C22×C107#13712yes—
88C22×C107C22×D411yescharacteristic
89C2×D107—22no—
90C2×D107—22no—
91C2×D107—22no—
92C2×D107—44no—
93C4×C107—42no—
94C4×C107—42no—
95C4×C107#12312yes—
96C4×C107C2×#4111yescharacteristic
97C4×C107C2×#4111yescharacteristic
98Dic107—22no—
99Dic107—42no—
100Dic107—42no—
101C2×C107#48514yescomplemented
102C2×C107C2×#12311yescharacteristic
103C2×C107C2×#13511yescharacteristic
104C2×C107C2×#13711yescharacteristic
105D107—42no—
106C2×#485—1071nomaximal, Sylow
107C107C2×#48511yescharacteristic, complemented, Sylow
108C2×C22⋊Q8—1071no—
109C2×#117—1071no—
110#485—1078no—
111C2×#107—1071no—
112C2×#106—1071no—
113C2×#103—1071no—
114C2×#103D10711yescharacteristic, complemented
115C2×C22⋊C8—1071no—
116C22×Q8C2×D10711yescharacteristic
117C23×C4—1071no—
118C22×C8—1071no—
119C22×C8C2×D10711yescharacteristic
120C22⋊Q8—1074no—
121C22⋊Q8—2142no—
122#117—1074no—
123#117—2142no—
124C2×C4⋊C4—1071no—
125C2×C4⋊C4—1071no—
126C2×C4⋊C4—2141no—
127C2×C4⋊C4C2×D10711yescharacteristic
128C2×C22⋊C4—2141no—
129C2×C22⋊C4—2141no—
130C2×C42—2141no—
131#107—1074no—
132#106—1074no—
133#103—1074no—
134#103C2×D10714yescomplemented
135C22⋊C8—1074no—
136C24—1071no—
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8C22×D10712yes—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—1071no—
144C22×C4—1072no—
145C22×C4—1072no—
146C22×C4—2141no—
147C22×C4—2141no—
148C22×C4—2142no—
149C22×C4—2142no—
150C22×C4C22×D10711yescharacteristic
151C2×C8—22no—
152C2×C8—1072no—
153C2×C8—2142no—
154C2×C8C22×D10712yes—
155C4⋊C4—21no—
156C4⋊C4—1072no—
157C4⋊C4—1072no—
158C4⋊C4—2144no—
159C4⋊C4—2141no—
160C4⋊C4—2141no—
161C4⋊C4C22×D10712yes—
162C22⋊C4—2144no—
163C22⋊C4—2144no—
164C42—2144no—
165C23—1072no—
166C23—2142no—
167C23—2142no—
168C23—2142no—
169C23D4×D10711yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—42no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—1072no—
178C2×C4—4282no—
179C2×C4—4282no—
180C2×C4—2142no—
181C2×C4—2142no—
182C2×C4—2142no—
183C2×C4—2144no—
184C2×C4—2142no—
185C2×C4—2142no—
186C2×C4D4×D10711yescharacteristic
187C2×C4#1313381712yes—
188C2×C4#1313381812yes—
189C2×C4C23×D10711yescharacteristic
190C8—22no—
191C8—2142no—
192C22—4284no—
193C22—2142no—
194C22—2142no—
195C22—2142no—
196C22#1681209112yes—
197C22#1681213212yes—
198C22#1681213812yes—
199C22C2×D4×D10711yescharacteristic
200C4—42no—
201C4—42no—
202C4—4282no—
203C4—4282no—
204C4—2142no—
205C4#1681209112yes—
206C4C2×#1313381711yescharacteristic
207C4C2×#1313381811yescharacteristic
208C2—4282no—
209C2#2029296714yesdirect product factor
210C2C2×#1681209111yescharacteristic
211C2C2×#1681213211yescharacteristic
212C2C2×#1681213811yescharacteristic
subgroupG/H
centerC23D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#103×C107C2
socleC23×C107C2×D4
prime radicalC23×D107D4
hypercenterC2×#103D107
hypocenterC107C2×#485
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. #20292967C2direct (N × H)
4. C2×#16812043C2semidirect
5. C2×#16812040C2semidirect
6. C2×#16812033C2semidirect
8. C2×#103×C107C2semidirect
21. #16812043C22semidirect
22. #16812040C22semidirect
23. #16812033C22semidirect
28. #103×C107C22semidirect
101. C2×C107#485semidirect
107. C107C2×#485semidirect
114. C2×#103D107semidirect
134. #103C2×D107semidirect
209. C2#20292967direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168120852
C2×#168120672
#202929672
C2×#168120432
C2×#168120402
C2×#168120332
C2×(C2×D107)⋊C82
C2×#103×C1072
C2×#485107