Finite Group Databasebeta

← C2×#20292836 #28345898

Subgroups — C2×#20292836 #28345898

Order 13696.

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

normal subgroups only

This group has 480 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×Dic428C211yesmaximal, characteristic
2C22×#13133808C211yesmaximal, characteristic
3C2×#16812107C211yesmaximal, characteristic
4C2×#16812074C211yesmaximal, characteristic
5#20292836C218yesmaximal, direct product factor
6C2×Dic107⋊C8C211yesmaximal, characteristic
7C2×#16812032C211yesmaximal, characteristic
8C2×#103×C107C211yesmaximal, characteristic
9C22×Dic214C2211yescharacteristic
10C22×Dic214C2211yescharacteristic
11C2×Dic428—24no—
12C2×Dic428C2214yes—
13C2×#13133808—24no—
14C2×#13133808C2214yes—
15C22×C107⋊C8C2211yescharacteristic
16#16812107—22no—
17#16812107C2214yes—
18#16812074—22no—
19#16812074C2214yes—
20C2×Dic107⋊C4—21no—
21C2×Dic107⋊C4—21no—
22C2×Dic107⋊C4—21no—
23C2×C4×Dic107—21no—
24C2×C4×Dic107C2211yescharacteristic
25Dic107⋊C8C2214yes—
26#16812032C2214yes—
27C22×Q8×C107C2211yescharacteristic
28C22×C8×C107C2211yescharacteristic
29C2×C4⋊C4×C107C2211yescharacteristic
30#103×C107C2214yes—
31C2×Dic214—21no—
32C2×Dic214—22no—
33C2×Dic214—22no—
34C2×Dic214—22no—
35C2×Dic214—21no—
36C2×Dic214D414yes—
37C2×Dic214C2312yes—
38C2×Dic214C2312yes—
39C22×Dic107—21no—
40C22×Dic107—21no—
41C22×Dic107D411yescharacteristic
42C22×Dic107D411yescharacteristic
43Dic428—28no—
44#13133808—28no—
45C2×C107⋊C8—22no—
46C2×C107⋊C8C2312yes—
47Dic107⋊C4—24no—
48Dic107⋊C4—24no—
49Dic107⋊C4—24no—
50C4×Dic107—24no—
51C4×Dic107D412yes—
52C4×Dic107C2312yes—
53C2×Q8×C107—21no—
54C2×Q8×C107—22no—
55C2×Q8×C107—22no—
56C2×Q8×C107C2312yes—
57C22×C4×C107—21no—
58C22×C4×C107—21no—
59C22×C4×C107C2311yescharacteristic
60C2×C8×C107—22no—
61C2×C8×C107C2312yes—
62C4⋊C4×C107—21no—
63C4⋊C4×C107C2312yes—
64C23×C107C2×D411yescharacteristic
65Q8×C107—22no—
66Q8×C107—22no—
67Q8×C107—42no—
68C2×C4×C107—22no—
69C2×C4×C107—22no—
70C2×C4×C107—42no—
71C2×C4×C107—42no—
72C2×C4×C107C2×D411yescharacteristic
73C2×C4×C107C2×D412yes—
74C2×C4×C107#4112yes—
75C2×C4×C107C2411yescharacteristic
76C2×Dic107—24no—
77C2×Dic107—22no—
78C2×Dic107—22no—
79C2×Dic107—22no—
80C2×Dic107—42no—
81C2×Dic107Q1614yescomplemented
82C2×Dic107C2×D412yes—
83C2×Dic107C2×D412yes—
84Dic214—24no—
85Dic214—22no—
86Dic214—22no—
87Dic214—22no—
88Dic214—42no—
89Dic214C2×D414yes—
90C8×C107—22no—
91C107⋊C8—22no—
92C22×C107#12112yes—
93C22×C107C2×Q1612yes—
94C22×C107#13712yes—
95C22×C107C22×D411yescharacteristic
96C4×C107—42no—
97C4×C107—42no—
98C4×C107#12112yes—
99C4×C107C22×D411yescharacteristic
100C4×C107C2×#4111yescharacteristic
101Dic107—24no—
102Dic107—22no—
103Dic107—42no—
104Dic107C2×Q1614yescomplemented
105C2×C107#46214yescomplemented
106C2×C107C2×#12111yescharacteristic
107C2×C107C22×Q1611yescharacteristic
108C2×C107C2×#13711yescharacteristic
109C2×#462—1071nomaximal, Sylow
110C107C2×#46211yescharacteristic, complemented, Sylow
111C22×Q16—1071no—
112C22×Q16—1071no—
113C2×C4⋊Q8—1071no—
114C2×C4×Q8—1071no—
115#462—1078no—
116C2×C4⋊C8—1071no—
117C2×#103—1071no—
118C2×#103D10711yescharacteristic
119C22×Q8—1071no—
120C22×Q8—1071no—
121C22×Q8C2×D10711yescharacteristic
122C2×Q16—1074no—
123C2×Q16—1074no—
124C2×Q16—2144no—
125C2×Q16—2144no—
126C22×C8—1071no—
127C22×C8C2×D10711yescharacteristic
128C4⋊Q8—1074no—
129C4⋊Q8—2142no—
130C4×Q8—1074no—
131C4×Q8—2142no—
132C2×C4⋊C4—2141no—
133C2×C4⋊C4—2141no—
134C2×C4⋊C4—2141no—
135C2×C4⋊C4C2×D10711yescharacteristic
136C2×C42—1071no—
137C2×C42—2141no—
138C4⋊C8—1074no—
139#103—1074no—
140#103C2×D10714yes—
141C2×Q8—21no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—1074no—
145C2×Q8—1072no—
146C2×Q8—1072no—
147C2×Q8—2142no—
148C2×Q8—2142no—
149C2×Q8—2141no—
150C2×Q8—2141no—
151C2×Q8—2142no—
152C2×Q8C22×D10712yes—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—1071no—
156C22×C4—1071no—
157C22×C4—2141no—
158C22×C4—2141no—
159C22×C4C22×D10711yescharacteristic
160Q16—2148no—
161Q16—2148no—
162C2×C8—22no—
163C2×C8—1072no—
164C2×C8—2142no—
165C2×C8C22×D10712yes—
166C4⋊C4—21no—
167C4⋊C4—2144no—
168C4⋊C4—2144no—
169C4⋊C4—2144no—
170C4⋊C4C22×D10712yes—
171C42—1072no—
172C42—1072no—
173C42—2144no—
174C23D4×D10711yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—42no—
178Q8—1074no—
179Q8—4282no—
180Q8—2142no—
181Q8—2142no—
182Q8—2144no—
183Q8—2142no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—1074no—
189C2×C4—1072no—
190C2×C4—1072no—
191C2×C4—4282no—
192C2×C4—2142no—
193C2×C4—2144no—
194C2×C4—2142no—
195C2×C4—2142no—
196C2×C4D4×D10711yescharacteristic
197C2×C4D4×D10712yes—
198C2×C4#1313381812yes—
199C2×C4C23×D10711yescharacteristic
200C8—22no—
201C8—2142no—
202C22#1681208212yes—
203C22Q16×D10712yes—
204C22#1681213812yes—
205C22C2×D4×D10711yescharacteristic
206C4—42no—
207C4—42no—
208C4—1074no—
209C4—4282no—
210C4—2142no—
211C4—2144no—
212C4#1681208212yes—
213C4C2×D4×D10711yescharacteristic
214C4C2×#1313381811yescharacteristic
215C2#2029283614yesdirect product factor
216C2C2×#1681208211yescharacteristic
217C2C2×Q16×D10711yescharacteristic
218C2C2×#1681213811yescharacteristic
subgroupG/H
centerC23D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#103×C107C2
socle, prime radicalC23×C107C2×D4
hypercenterC2×#103D107
hypocenterC107C2×#462
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
5. #20292836C2direct (N × H)
81. C2×Dic107Q16semidirect
104. Dic107C2×Q16semidirect
105. C2×C107#462semidirect
110. C107C2×#462semidirect
215. C2#20292836direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Dic4282
C22×#131338082
C2×#168121072
C2×#168120742
#202928362
C2×Dic107⋊C82
C2×#168120322
C2×#103×C1072
C2×#462107