Finite Group Databasebeta

← #28344731

Subgroups — #28344731

Order 13696.

348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#20292568C212yesmaximal
2#20292561C212yesmaximal
3#20292559C212yesmaximal
4#20292557C212yesmaximal
5#20292548C212yesmaximal
6#20292547C211yesmaximal, characteristic
7#20292496C211yesmaximal, characteristic
8#20292494C212yesmaximal
9#400×C107C211yesmaximal, characteristic
10C22×Dic214C2211yescharacteristic
11C2×C4⋊Dic107C2211yescharacteristic
12C2×C4⋊Dic107C2212yes—
13C2×C4⋊Dic107C2212yes—
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×Dic107⋊C4C2212yes—
17C2×Dic107⋊C4C2212yes—
18C2×C4×Dic107C2211yescharacteristic
19C107⋊#95C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2211yescharacteristic
25C107⋊#95C2212yes—
26C2×C4⋊C4×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28#95×C107C2212yes—
29#95×C107C2212yes—
30#95×C107C2211yescharacteristic
31C2×Dic214—42no—
32C2×Dic214—41no—
33C22×Dic107C2312yes—
34C22×Dic107C2312yes—
35C22×Dic107C2312yes—
36C22×Dic107C2312yes—
37C4⋊Dic107—42no—
38C4⋊Dic107—41no—
39C4⋊Dic107—42no—
40Dic107⋊C4—42no—
41Dic107⋊C4—42no—
42Dic107⋊C4—42no—
43Dic107⋊C4—42no—
44C4×Dic107Q814yescomplemented
45C22×C4×C107C2311yescharacteristic
46C22×C4×C107C2311yescharacteristic
47C22×C4×C107C2312yes—
48C22×C4×C107C2312yes—
49C22×C4×C107C2311yescharacteristic
50C4⋊C4×C107—41no—
51C4⋊C4×C107—41no—
52C23×C107C2411yescharacteristic
53C2×C4×C107—21no—
54C2×C4×C107—21no—
55C2×C4×C107—21no—
56C2×C4×C107—22no—
57C2×C4×C107—21no—
58C2×C4×C107—22no—
59C2×C4×C107—22no—
60C2×C4×C107—22no—
61C2×C4×C107—22no—
62C2×C4×C107—22no—
63C2×C4×C107—24no—
64C2×C4×C107C2×Q812yes—
65C2×Dic107—22no—
66C2×Dic107—22no—
67C2×Dic107—22no—
68C2×Dic107—22no—
69C2×Dic107—22no—
70C2×Dic107—22no—
71C2×Dic107—22no—
72C2×Dic107—22no—
73C2×Dic107—22no—
74C2×Dic107—22no—
75C2×Dic107—22no—
76C2×Dic107C2×Q814yes—
77Dic214—44no—
78C22×C107C22×Q811yescharacteristic
79C22×C107H(5,𝔽2)11yescharacteristic
80C22×C107H(5,𝔽2)12yes—
81C22×C1072−1+412yes—
82C22×C1072−1+411yescharacteristic
83C4×C107—22no—
84C4×C107—41no—
85C4×C107—41no—
86C4×C107—42no—
87C4×C107—42no—
88Dic107—24no—
89Dic107—42no—
90Dic107—42no—
91Dic107—42no—
92C2×C107#54411yescharacteristic
93C2×C107#54412yes—
94C2×C107#56011yescharacteristic
95C2×C107#56311yescharacteristic
96C2×C107#56312yes—
97#2843—1071nomaximal, Sylow
98C107#284311yescharacteristic, complemented, Sylow
99#400—1072no—
100#400D10711yescharacteristic
101#398—1072no—
102#398—1072no—
103#398—1072no—
104#395—1071no—
105#395—1072no—
106#384—1071no—
107#383—1072no—
108C22×Q8—1071no—
109C2×C4⋊C4—1072no—
110C2×C4⋊C4—1072no—
111C2×C4⋊C4—1072no—
112C2×C4⋊C4—1072no—
113C2×C4⋊C4—1071no—
114C2×C4⋊C4—1072no—
115C2×C4⋊C4—1072no—
116C2×C4⋊C4C2×D10711yescharacteristic
117C2×C4⋊C4C2×D10711yescharacteristic
118C2×C42—1071no—
119#95—1072no—
120#95—1072no—
121#95—1072no—
122#95—1072no—
123#95—1072no—
124#95—1071no—
125#95—1072no—
126#95C2×D10712yes—
127#95C2×D10712yes—
128#95C2×D10711yescharacteristic
129C2×Q8—4281no—
130C2×Q8—4282no—
131C22×C4—1072no—
132C22×C4—1072no—
133C22×C4—1072no—
134C22×C4—1072no—
135C22×C4C22×D10712yes—
136C22×C4C22×D10712yes—
137C22×C4C22×D10711yescharacteristic
138C22×C4C22×D10711yescharacteristic
139C22×C4C22×D10711yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—4282no—
143C4⋊C4—4282no—
144C4⋊C4—4282no—
145C4⋊C4—4282no—
146C4⋊C4—4281no—
147C4⋊C4—4282no—
148C4⋊C4—4282no—
149C42—1074no—
150C23C23×D10711yescharacteristic
151Q8—4284no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—1074no—
164C2×C4—2142no—
165C2×C4—2142no—
166C2×C4—2142no—
167C2×C4—2142no—
168C2×C4—2142no—
169C2×C4—2142no—
170C2×C4—2142no—
171C2×C4—2142no—
172C2×C4—2142no—
173C2×C4—2142no—
174C2×C4—2142no—
175C2×C4Q8×D10712yes—
176C22C2×Q8×D10711yescharacteristic
177C22#1681215411yescharacteristic
178C22#1681215512yes—
179C22#1681215612yes—
180C22#1681215611yescharacteristic
181C4—22no—
182C4—42no—
183C4—42no—
184C4—41no—
185C4—41no—
186C4—4282no—
187C4—4282no—
188C4—4282no—
189C4—2144no—
190C2#2029325611yescharacteristic
191C2#2029325712yes—
192C2#2029336711yescharacteristic
193C2#2029337711yescharacteristic
194C2#2029337912yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#400×C107C2
hypercenter#400D107
hypocenterC107#2843
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
44. C4×Dic107Q8semidirect
98. C107#2843semidirect

Maximal subgroups

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

subgroupindex
#202925682
#202925612
#202925592
#202925572
#202925482
#202925472
#202924962
#202924942
#400×C1072
#2843107