Finite Group Databasebeta

← #28344345

Subgroups — #28344345

Order 13696.

376 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 137 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#20292569C212yesmaximal
2#20292566C211yesmaximal, characteristic
3#20292561C212yesmaximal
4#20292547C211yesmaximal, characteristic
5#20292534C212yesmaximal
6#20292531C212yesmaximal
7#20292514C212yesmaximal
8#20292511C212yesmaximal
9#391×C107C211yesmaximal, characteristic
10C22×Dic214C2211yescharacteristic
11C2×C4⋊Dic107C2211yescharacteristic
12C2×C4⋊Dic107C2212yes—
13C2×Dic107⋊C4C2212yes—
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×C4×Dic107C2212yes—
17C107⋊#95C2212yes—
18C107⋊#95C2212yes—
19C107⋊#95C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2211yescharacteristic
25C107⋊#95C2211yescharacteristic
26C22×Q8×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28C2×C42×C107C2211yescharacteristic
29#95×C107C2212yes—
30#95×C107C2212yes—
31C2×Dic214—24no—
32C2×Dic214—41no—
33C22×Dic107C2312yes—
34C22×Dic107C2312yes—
35C22×Dic107C2312yes—
36C22×Dic107C2312yes—
37C4⋊Dic107—41no—
38C4⋊Dic107—42no—
39Dic107⋊C4—24no—
40Dic107⋊C4—24no—
41Dic107⋊C4—42no—
42C4×Dic107—42no—
43C2×Q8×C107—41no—
44C2×Q8×C107—41no—
45C2×Q8×C107Q814yescomplemented
46C22×C4×C107C2311yescharacteristic
47C22×C4×C107C2312yes—
48C22×C4×C107C2311yescharacteristic
49C22×C4×C107C2312yes—
50C22×C4×C107C2311yescharacteristic
51C4⋊C4×C107—41no—
52C42×C107—41no—
53C23×C107C2411yescharacteristic
54Q8×C107—44no—
55C2×C4×C107—21no—
56C2×C4×C107—21no—
57C2×C4×C107—22no—
58C2×C4×C107—22no—
59C2×C4×C107—22no—
60C2×C4×C107—22no—
61C2×C4×C107—22no—
62C2×C4×C107—22no—
63C2×C4×C107—21no—
64C2×C4×C107—21no—
65C2×C4×C107—22no—
66C2×C4×C107C2×Q814yes—
67C2×C4×C107C2×Q812yes—
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—24no—
78C2×Dic107#4114yes—
79Dic214—44no—
80C22×C107C22×Q811yescharacteristic
81C22×C107C2×#4112yes—
82C22×C107H(5,𝔽2)11yescharacteristic
83C22×C107H(5,𝔽2)11yescharacteristic
84C22×C1072−1+412yes—
85C4×C107—22no—
86C4×C107—24no—
87C4×C107—42no—
88C4×C107—41no—
89C4×C107—41no—
90Dic107—24no—
91Dic107—42no—
92Dic107—42no—
93Dic107—42no—
94C2×C107#54212yes—
95C2×C107#54311yescharacteristic
96C2×C107#55111yescharacteristic
97C2×C107#55712yes—
98C2×C107#56311yescharacteristic
99#2799—1071nomaximal, Sylow
100C107#279911yescharacteristic, complemented, Sylow
101#400—1071no—
102#400—1072no—
103#398—1072no—
104#395—1071no—
105#391—1072no—
106#391—1072no—
107#391D10711yescharacteristic
108#387—1072no—
109#387—1072no—
110C22×Q8—1071no—
111C22×Q8C2×D10711yescharacteristic
112C2×C4⋊C4—1072no—
113C2×C4⋊C4—1071no—
114C2×C4⋊C4—1072no—
115C2×C4⋊C4—1072no—
116C2×C4⋊C4—1072no—
117C2×C4⋊C4C2×D10711yescharacteristic
118C2×C42—1072no—
119C2×C42C2×D10711yescharacteristic
120#95—1072no—
121#95—1072no—
122#95—1072no—
123#95—1072no—
124#95—1072no—
125#95—1072no—
126#95—1072no—
127#95—1071no—
128#95—1071no—
129#95C2×D10712yes—
130#95C2×D10712yes—
131C2×Q8—41no—
132C2×Q8—41no—
133C2×Q8—4281no—
134C2×Q8—2144no—
135C2×Q8Dic21414yescomplemented
136C22×C4—1072no—
137C22×C4—1072no—
138C22×C4—1072no—
139C22×C4—1072no—
140C22×C4C22×D10711yescharacteristic
141C22×C4C22×D10712yes—
142C22×C4C22×D10711yescharacteristic
143C22×C4C22×D10711yescharacteristic
144C22×C4C22×D10712yes—
145C4⋊C4—41no—
146C4⋊C4—4282no—
147C4⋊C4—4282no—
148C4⋊C4—4281no—
149C4⋊C4—2144no—
150C4⋊C4—2144no—
151C42—41no—
152C42—4282no—
153C23C23×D10711yescharacteristic
154Q8—44no—
155Q8—4284no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—1074no—
168C2×C4—2142no—
169C2×C4—2142no—
170C2×C4—2142no—
171C2×C4—2142no—
172C2×C4—2142no—
173C2×C4—2144no—
174C2×C4—2142no—
175C2×C4—2142no—
176C2×C4—2142no—
177C2×C4—2142no—
178C2×C4C2×Dic21412yes—
179C2×C4C2×Dic21414yes—
180C22C22×Dic21411yescharacteristic
181C22#41×D10712yes—
182C22#1681215411yescharacteristic
183C22#1681215411yescharacteristic
184C22#1681215712yes—
185C4—22no—
186C4—24no—
187C4—42no—
188C4—41no—
189C4—41no—
190C4—4282no—
191C4—4282no—
192C4—4282no—
193C4—2144no—
194C2#2029324712yes—
195C2#2029325311yescharacteristic
196C2#2029330711yescharacteristic
197C2#2029335312yes—
198C2#2029337611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#391×C107C2
hypercenter#391D107
hypocenterC107#2799
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
45. C2×Q8×C107Q8semidirect
100. C107#2799semidirect
135. C2×Q8Dic214semidirect

Maximal subgroups

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

subgroupindex
#202925692
#202925662
#202925612
#202925472
#202925342
#202925312
#202925142
#202925112
#391×C1072
#2799107