Finite Group Databasebeta

← #28339640

Subgroups — #28339640

Order 13696.

424 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 173 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×#16812107C211yesmaximal, characteristic
2#20292534C211yesmaximal, characteristic
3#20292531C212yesmaximal
4#20292514C212yesmaximal
5#20292511C212yesmaximal
6#20292509C212yesmaximal
7#20292508C212yesmaximal
8#20292494C212yesmaximal
9#391×C107C211yesmaximal, characteristic
10C22×Dic214C2211yescharacteristic
11#16812107C418yescomplemented
12C2×C4⋊Dic107C2211yescharacteristic
13C2×Dic107⋊C4C2212yes—
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×C4×Dic107C2212yes—
17C2×C4×Dic107C2211yescharacteristic
18C2×C4×Dic107C2211yescharacteristic
19C107⋊#95C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2212yes—
25C107⋊#95C2212yes—
26C107⋊#95C2212yes—
27C22×Q8×C107C2211yescharacteristic
28C2×C4⋊C4×C107C2211yescharacteristic
29C2×C42×C107C2211yescharacteristic
30#95×C107C2212yes—
31#95×C107C2212yes—
32C2×Dic214—41no—
33C2×Dic214—41no—
34C2×Dic214C2×C414yes—
35C22×Dic107C2312yes—
36C22×Dic107C2312yes—
37C22×Dic107C2312yes—
38C22×Dic107C2312yes—
39C4⋊Dic107—41no—
40Dic107⋊C4—42no—
41Dic107⋊C4C2×C418yes—
42Dic107⋊C4C2×C418yes—
43C4×Dic107—42no—
44C4×Dic107—41no—
45C4×Dic107C2×C414yes—
46C2×Q8×C107—41no—
47C2×Q8×C107—41no—
48C2×Q8×C107C2×C414yes—
49C22×C4×C107C2312yes—
50C22×C4×C107C2312yes—
51C22×C4×C107C2311yescharacteristic
52C22×C4×C107C2311yescharacteristic
53C22×C4×C107C2311yescharacteristic
54C4⋊C4×C107—41no—
55C42×C107—41no—
56C23×C107C2411yescharacteristic
57Q8×C107—44no—
58C2×C4×C107—21no—
59C2×C4×C107—21no—
60C2×C4×C107—21no—
61C2×C4×C107—21no—
62C2×C4×C107—21no—
63C2×C4×C107—21no—
64C2×C4×C107—22no—
65C2×C4×C107—22no—
66C2×C4×C107—24no—
67C2×C4×C107—22no—
68C2×C4×C107—22no—
69C2×C4×C107C22×C412yes—
70C2×C4×C107C22×C412yes—
71C2×C4×C107C22×C412yes—
72C2×Dic107—22no—
73C2×Dic107—22no—
74C2×Dic107—22no—
75C2×Dic107—22no—
76C2×Dic107—22no—
77C2×Dic107—22no—
78C2×Dic107—22no—
79C2×Dic107—22no—
80C2×Dic107—24no—
81C2×Dic107C22×C414yes—
82C2×Dic107C22×C414yes—
83Dic214—44no—
84C22×C107C23×C411yescharacteristic
85C22×C107H(5,𝔽2)11yescharacteristic
86C22×C107H(5,𝔽2)11yescharacteristic
87C22×C1072−1+412yes—
88C22×C1072−1+412yes—
89C4×C107—22no—
90C4×C107—22no—
91C4×C107—22no—
92C4×C107—42no—
93C4×C107—42no—
94Dic107—24no—
95Dic107—24no—
96Dic107—42no—
97Dic107—42no—
98C2×C107#51811yescharacteristic
99C2×C107#51912yes—
100C2×C107#56311yescharacteristic
101C2×C107#56311yescharacteristic
102C2×C107#56312yes—
103#2381—1071nomaximal, Sylow
104C107#238111yescharacteristic, complemented, Sylow
105C2×C4⋊Q8—1071no—
106#391—1071no—
107#391—1072no—
108#391D10711yescharacteristic
109#387—1072no—
110#387—1072no—
111#387—1072no—
112#387—1072no—
113#383—1072no—
114C22×Q8—1071no—
115C22×Q8C2×D10711yescharacteristic
116C4⋊Q8—1078no—
117C2×C4⋊C4—1072no—
118C2×C4⋊C4—1072no—
119C2×C4⋊C4—1072no—
120C2×C4⋊C4—1071no—
121C2×C4⋊C4C2×D10711yescharacteristic
122C2×C42—1071no—
123C2×C42—1072no—
124C2×C42—1071no—
125C2×C42C2×D10711yescharacteristic
126#95—1072no—
127#95—1072no—
128#95—1072no—
129#95—1072no—
130#95—1072no—
131#95—1072no—
132#95—1072no—
133#95—1072no—
134#95C2×D10712yes—
135#95C2×D10712yes—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—1074no—
139C2×Q8—4281no—
140C2×Q8—4281no—
141C2×Q8C4×D10714yes—
142C22×C4—1072no—
143C22×C4—1072no—
144C22×C4—1072no—
145C22×C4—1072no—
146C22×C4C22×D10712yes—
147C22×C4C22×D10712yes—
148C22×C4C22×D10711yescharacteristic
149C22×C4C22×D10711yescharacteristic
150C22×C4C22×D10711yescharacteristic
151C4⋊C4—41no—
152C4⋊C4—1078no—
153C4⋊C4—1078no—
154C4⋊C4—4282no—
155C4⋊C4—4281no—
156C42—41no—
157C42—1074no—
158C42—4281no—
159C42—4282no—
160C23C23×D10711yescharacteristic
161Q8—44no—
162Q8—4284no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—1074no—
175C2×C4—1074no—
176C2×C4—2142no—
177C2×C4—2142no—
178C2×C4—2142no—
179C2×C4—2144no—
180C2×C4—2142no—
181C2×C4—2142no—
182C2×C4—2142no—
183C2×C4—2142no—
184C2×C4—2142no—
185C2×C4C2×C4×D10712yes—
186C2×C4C2×C4×D10712yes—
187C2×C4C2×C4×D10712yes—
188C22C22×C4×D10711yescharacteristic
189C22#1681215411yescharacteristic
190C22#1681215411yescharacteristic
191C22#1681215612yes—
192C22#1681215712yes—
193C4—22no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—42no—
198C4—4282no—
199C4—4282no—
200C4—2144no—
201C4—2144no—
202C2#2029310011yescharacteristic
203C2#2029310312yes—
204C2#2029337611yescharacteristic
205C2#2029337711yescharacteristic
206C2#2029337812yes—
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#391×C107C2
socle, prime radical, cosocleC23×C107C24
hypercenter#391D107
hypocenterC107#2381
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #16812107C4semidirect
104. C107#2381semidirect

Maximal subgroups

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

subgroupindex
C2×#168121072
#202925342
#202925312
#202925142
#202925112
#202925092
#202925082
#202924942
#391×C1072
#2381107