Finite Group Databasebeta

← #28344218

Subgroups — #28344218

Order 13696.

352 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C107⋊#401C212yesmaximal
2#20292568C212yesmaximal
3#20292557C211yesmaximal, characteristic
4#20292547C211yesmaximal, characteristic
5#20292531C212yesmaximal
6#20292514C212yesmaximal
7#20292511C212yesmaximal
8#20292508C212yesmaximal
9#382×C107C211yesmaximal, characteristic
10C22×Dic214C2211yescharacteristic
11C2×C4⋊Dic107C2211yescharacteristic
12C2×Dic107⋊C4C2212yes—
13C2×Dic107⋊C4C2212yes—
14C2×Dic107⋊C4C2212yes—
15C2×C4×Dic107C2212yes—
16C107⋊#95C2212yes—
17C107⋊#95C2212yes—
18C107⋊#95C2212yes—
19C107⋊#95C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2211yescharacteristic
25C107⋊#95C2211yescharacteristic
26C2×C4⋊C4×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—
38Dic107⋊C4—24no—
39Dic107⋊C4—24no—
40Dic107⋊C4—24no—
41C4×Dic107—42no—
42C22×C4×C107C2312yes—
43C22×C4×C107C2311yescharacteristic
44C22×C4×C107C2312yes—
45C22×C4×C107C2311yescharacteristic
46C22×C4×C107C2311yescharacteristic
47C4⋊C4×C107—41no—
48C4⋊C4×C107—41no—
49C42×C107—22no—
50C23×C107C2411yescharacteristic
51C2×C4×C107—21no—
52C2×C4×C107—21no—
53C2×C4×C107—22no—
54C2×C4×C107—22no—
55C2×C4×C107—22no—
56C2×C4×C107—22no—
57C2×C4×C107—22no—
58C2×C4×C107—21no—
59C2×C4×C107—21no—
60C2×C4×C107—22no—
61C2×C4×C107—24no—
62C2×C4×C107#4112yes—
63C2×Dic107—22no—
64C2×Dic107—22no—
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#4114yes—
75Dic214—44no—
76C22×C107C2×#4112yes—
77C22×C107C2×#4111yescharacteristic
78C22×C107H(5,𝔽2)11yescharacteristic
79C22×C1072−1+412yes—
80C22×C1072−1+411yescharacteristic
81C4×C107—22no—
82C4×C107—41no—
83C4×C107—41no—
84C4×C107—42no—
85C4×C107—42no—
86Dic107—24no—
87Dic107—42no—
88Dic107—42no—
89Dic107—42no—
90C2×C107#53911yescharacteristic
91C2×C107#54112yes—
92C2×C107#55111yescharacteristic
93C2×C107#55612yes—
94C2×C107#56311yescharacteristic
95#2789—1071nomaximal, Sylow
96C107#278911yescharacteristic, complemented, Sylow
97#401—1072no—
98#400—1072no—
99#398—1071no—
100#395—1071no—
101#391—1072no—
102#387—1072no—
103#387—1072no—
104#387—1072no—
105#382D10711yescharacteristic
106C22×Q8—1071no—
107C2×C4⋊C4—1071no—
108C2×C4⋊C4—1072no—
109C2×C4⋊C4—1072no—
110C2×C4⋊C4—1072no—
111C2×C4⋊C4C2×D10711yescharacteristic
112C2×C4⋊C4C2×D10711yescharacteristic
113C2×C42—1072no—
114C2×C42C2×D10711yescharacteristic
115#95—1072no—
116#95—1072no—
117#95—1072no—
118#95—1072no—
119#95—1072no—
120#95—1072no—
121#95—1072no—
122#95—1072no—
123#95—1071no—
124#95—1071no—
125#95C2×D10712yes—
126#95C2×D10712yes—
127C2×Q8—4281no—
128C2×Q8—2144no—
129C22×C4—1072no—
130C22×C4—1072no—
131C22×C4—1072no—
132C22×C4—1072no—
133C22×C4C22×D10712yes—
134C22×C4C22×D10712yes—
135C22×C4C22×D10711yescharacteristic
136C22×C4C22×D10711yescharacteristic
137C22×C4C22×D10711yescharacteristic
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—4281no—
141C4⋊C4—2144no—
142C4⋊C4—2144no—
143C4⋊C4—2144no—
144C42—22no—
145C42—4282no—
146C23C23×D10711yescharacteristic
147Q8—4284no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—24no—
158C2×C4—22no—
159C2×C4—1074no—
160C2×C4—2142no—
161C2×C4—2142no—
162C2×C4—2142no—
163C2×C4—2142no—
164C2×C4—2142no—
165C2×C4—2142no—
166C2×C4—2142no—
167C2×C4—2142no—
168C2×C4—2142no—
169C2×C4—2142no—
170C2×C4—2142no—
171C2×C4#1313381812yes—
172C22#41×D10712yes—
173C22C2×#1313381811yescharacteristic
174C22#1681215411yescharacteristic
175C22#1681215612yes—
176C22#1681215711yescharacteristic
177C4—22no—
178C4—42no—
179C4—41no—
180C4—41no—
181C4—42no—
182C4—4282no—
183C4—4282no—
184C4—4282no—
185C4—2144no—
186C2#2029322411yescharacteristic
187C2#2029323612yes—
188C2#2029330711yescharacteristic
189C2#2029334512yes—
190C2#2029337711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#382×C107C2
hypercenter#382D107
hypocenterC107#2789
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
96. C107#2789semidirect

Maximal subgroups

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

subgroupindex
C107⋊#4012
#202925682
#202925572
#202925472
#202925312
#202925142
#202925112
#202925082
#382×C1072
#2789107