Finite Group Databasebeta

← #28344261

Subgroups — #28344261

Order 13696.

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

normal subgroups only

This group has 384 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
1#20292557C212yesmaximal
2#20292548C212yesmaximal
3#20292547C211yesmaximal, characteristic
4#20292526C212yesmaximal
5#20292524C212yesmaximal
6#20292509C212yesmaximal
7#20292508C212yesmaximal
8#20292496C211yesmaximal, characteristic
9#398×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
19C2×C4×Dic107C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2211yescharacteristic
25C107⋊#95C2212yes—
26C2×C4⋊C4×C107C2212yes—
27C2×C4⋊C4×C107C2211yescharacteristic
28C2×C4⋊C4×C107C2211yescharacteristic
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⋊C4Q818yescomplemented
44C4×Dic107—22no—
45C4×Dic107—42no—
46C22×C4×C107C2311yescharacteristic
47C22×C4×C107C2311yescharacteristic
48C22×C4×C107C2312yes—
49C22×C4×C107C2312yes—
50C22×C4×C107C2311yescharacteristic
51C4⋊C4×C107—24no—
52C4⋊C4×C107—41no—
53C4⋊C4×C107—41no—
54C23×C107C2411yescharacteristic
55C2×C4×C107—22no—
56C2×C4×C107—21no—
57C2×C4×C107—22no—
58C2×C4×C107—21no—
59C2×C4×C107—22no—
60C2×C4×C107—21no—
61C2×C4×C107—22no—
62C2×C4×C107—21no—
63C2×C4×C107—22no—
64C2×C4×C107—22no—
65C2×C4×C107—22no—
66C2×C4×C107C2×Q814yes—
67C2×C4×C107#4112yes—
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×Dic107—22no—
77C2×Dic107—22no—
78C2×Dic107C2×Q814yes—
79C2×Dic107C2×Q814yes—
80Dic214—44no—
81C22×C107C22×Q812yes—
82C22×C107C2×#4111yescharacteristic
83C22×C107H(5,𝔽2)11yescharacteristic
84C22×C107H(5,𝔽2)12yes—
85C22×C1072−1+411yescharacteristic
86C4×C107—22no—
87C4×C107—24no—
88C4×C107—42no—
89C4×C107—41no—
90C4×C107—41no—
91Dic107—24no—
92Dic107—24no—
93Dic107—42no—
94Dic107—42no—
95C2×C107#53911yescharacteristic
96C2×C107#54412yes—
97C2×C107#55412yes—
98C2×C107Q8211yescharacteristic
99C2×C107#56011yescharacteristic
100#2792—1071nomaximal, Sylow
101C107#279211yescharacteristic, complemented, Sylow
102#398—1072no—
103#398D10711yescharacteristic
104#395—1071no—
105#395—1072no—
106#389—1072no—
107#389—1072no—
108#387—1072no—
109#387—1072no—
110#384—1071no—
111C22×Q8—1071no—
112C2×C4⋊C4—1072no—
113C2×C4⋊C4—1072no—
114C2×C4⋊C4—1072no—
115C2×C4⋊C4—1072no—
116C2×C4⋊C4—1071no—
117C2×C4⋊C4—1072no—
118C2×C4⋊C4—1072no—
119C2×C4⋊C4C2×D10712yes—
120C2×C4⋊C4C2×D10711yescharacteristic
121C2×C4⋊C4C2×D10711yescharacteristic
122C2×C42—1072no—
123C2×C42—1071no—
124#95—1071no—
125#95—1072no—
126#95—1072no—
127#95—1072no—
128#95—1072no—
129#95—1072no—
130#95C2×D10712yes—
131#95C2×D10711yescharacteristic
132C2×Q8—4281no—
133C2×Q8—4282no—
134C22×C4—1072no—
135C22×C4—1072no—
136C22×C4—1072no—
137C22×C4—1072no—
138C22×C4C22×D10712yes—
139C22×C4C22×D10711yescharacteristic
140C22×C4C22×D10711yescharacteristic
141C22×C4C22×D10712yes—
142C22×C4C22×D10711yescharacteristic
143C4⋊C4—24no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—1078no—
147C4⋊C4—4282no—
148C4⋊C4—4282no—
149C4⋊C4—4282no—
150C4⋊C4—4281no—
151C4⋊C4—4282no—
152C4⋊C4—4282no—
153C42—4282no—
154C42—2142no—
155C23C23×D10711yescharacteristic
156Q8—4284no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—1074no—
169C2×C4—1074no—
170C2×C4—2142no—
171C2×C4—2142no—
172C2×C4—2142no—
173C2×C4—2142no—
174C2×C4—2142no—
175C2×C4—2142no—
176C2×C4—2142no—
177C2×C4—2142no—
178C2×C4—2142no—
179C2×C4—2142no—
180C2×C4Q8×D10714yes—
181C2×C4#1313381712yes—
182C22C2×Q8×D10712yes—
183C22C2×#1313381711yescharacteristic
184C22#1681215411yescharacteristic
185C22#1681215512yes—
186C22#1681215611yescharacteristic
187C4—22no—
188C4—24no—
189C4—42no—
190C4—41no—
191C4—41no—
192C4—4282no—
193C4—4282no—
194C4—2144no—
195C4—2144no—
196C2#2029322211yescharacteristic
197C2#2029325712yes—
198C2#2029333512yes—
199C2#2029335711yescharacteristic
200C2#2029336711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#398×C107C2
hypercenter#398D107
hypocenterC107#2792
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
43. Dic107⋊C4Q8semidirect
101. C107#2792semidirect

Maximal subgroups

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

subgroupindex
#202925572
#202925482
#202925472
#202925262
#202925242
#202925092
#202925082
#202924962
#398×C1072
#2792107