Finite Group Databasebeta

← #28335061

Subgroups — #28335061

Order 13696.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#125×D107C211yesmaximal, characteristic
2#20292682C211yesmaximal, characteristic
3#20292579C211yesmaximal, characteristic
4#20292369C211yesmaximal, characteristic, complemented
5#20292368C211yesmaximal, characteristic, complemented
6#20292368C211yesmaximal, characteristic, complemented
7#330×C107C211yesmaximal, characteristic, complemented
8C2×#13133801—21no—
9#16812101C2211yescharacteristic
10#16812100C411yescharacteristic
11#16812100C411yescharacteristic
12#16812099—21no—
13#16812099—21no—
14C4⋊C4×D107—21no—
15C4⋊C4×D107—21no—
16C4⋊C4×D107C411yescharacteristic
17C4⋊C4×D107C411yescharacteristic
18C42×D107C2211yescharacteristic
19Dic107⋊C8—21no—
20(C2×D107)⋊C8—21no—
21#16812020C2211yescharacteristic
22#16812020C2211yescharacteristic
23C8×Dic107—21no—
24#125×C107C2211yescharacteristic
25#97×C107C2211yescharacteristic
26#97×C107C2211yescharacteristic
27C2×C4×D107—21no—
28C2×C4×D107—21no—
29C2×C4×D107C2×C411yescharacteristic
30C2×C4×D107D411yescharacteristic
31C2×C4×D107D411yescharacteristic
32#13133801—24no—
33C2×C107⋊C8—21no—
34C2×C107⋊C8—21no—
35C4⋊Dic107—21no—
36C4⋊Dic107—21no—
37C4⋊Dic107C2×C411yescharacteristic
38C4⋊Dic107C2×C411yescharacteristic
39Dic107⋊C4—21no—
40Dic107⋊C4—21no—
41Dic107⋊C4—21no—
42Dic107⋊C4—21no—
43Dic107⋊C4—21no—
44Dic107⋊C4—21no—
45C4×Dic107C2×C411yescharacteristic
46C4×Dic107D411yescharacteristic
47C4×Dic107D411yescharacteristic
48C2×C8×C107—21no—
49C2×C8×C107—21no—
50C4⋊C4×C107—21no—
51C4⋊C4×C107—21no—
52C4⋊C4×C107C2×C411yescharacteristic
53C4⋊C4×C107C2×C411yescharacteristic
54C42×C107C2311yescharacteristic
55C22×D107C22⋊C411yescharacteristic
56C2×C4×C107—21no—
57C2×C4×C107—21no—
58C2×C4×C107C22×C411yescharacteristic
59C2×C4×C107C2×D411yescharacteristic
60C2×C4×C107C2×D411yescharacteristic
61C2×Dic107—21no—
62C2×Dic107—21no—
63C2×Dic107C22⋊C411yescharacteristic
64C2×Dic107C22⋊C411yescharacteristic
65C2×Dic107C22⋊C411yescharacteristic
66C4×D107—22no—
67C4×D107—22no—
68C4×D107—41no—
69C4×D107—42no—
70C4×D107—42no—
71C8×C107—22no—
72C8×C107—41no—
73C107⋊C8—22no—
74C107⋊C8—41no—
75C22×C107C2×C22⋊C411yescharacteristic
76C2×D107—21no—
77C2×D107—21no—
78C2×D107#10412yes—
79C4×C107—21no—
80C4×C107—21no—
81C4×C107—21no—
82C4×C107—41no—
83C4×C107—41no—
84Dic107—21no—
85Dic107—21no—
86Dic107—41no—
87Dic107—41no—
88Dic107#10112yes—
89C2×C107C2×#10111yescharacteristic
90C2×C107C2×#10411yescharacteristic
91C2×C107#42111yescharacteristic
92D107—22no—
93#1528—1071nomaximal, Sylow
94C107#152811yescharacteristic, complemented, Sylow
95C2×#125—1071no—
96#432—1071no—
97C4×M16—1071no—
98#330—1071no—
99#330—1071no—
100#330—1071no—
101#330D10711yescharacteristic, complemented
102C2×M16—2141no—
103#125—1071no—
104#125—1071no—
105#125—1071no—
106#125—2141no—
107#125—2141no—
108#125C2×D10711yescharacteristic
109C2×C4⋊C4—1071no—
110C2×C4⋊C4—1071no—
111C2×C4⋊C4—2141no—
112C2×C4⋊C4—2141no—
113C2×C42—1071no—
114C4⋊C8—2141no—
115C22⋊C8—2141no—
116#97—1071no—
117#97—1071no—
118#97C2×D10711yescharacteristic
119#97C2×D10711yescharacteristic
120C4×C8—2141no—
121C22×C4—1071no—
122C22×C4—1071no—
123C22×C4—1071no—
124C22×C4—2141no—
125C22×C4—2141no—
126M16—2144no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—2141no—
130C2×C8—2141no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—1071no—
134C4⋊C4—1071no—
135C4⋊C4—2141no—
136C4⋊C4—2141no—
137C4⋊C4—2141no—
138C4⋊C4—2141no—
139C4⋊C4—2141no—
140C4⋊C4—2141no—
141C4⋊C4—2141no—
142C4⋊C4—2141no—
143C4⋊C4C4×D10711yescharacteristic
144C4⋊C4C4×D10711yescharacteristic
145C42—1071no—
146C42—1071no—
147C42—1071no—
148C42C22×D10711yescharacteristic
149C23—1071no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—1071no—
153C2×C4—1071no—
154C2×C4—1071no—
155C2×C4—4281no—
156C2×C4—4282no—
157C2×C4—4282no—
158C2×C4—2142no—
159C2×C4—2142no—
160C2×C4—2141no—
161C2×C4—2141no—
162C2×C4C2×C4×D10711yescharacteristic
163C2×C4D4×D10711yescharacteristic
164C2×C4D4×D10711yescharacteristic
165C8—22no—
166C8—41no—
167C8—4281no—
168C8—2142no—
169C22—1072no—
170C22—2141no—
171C22—2141no—
172C22C22⋊C4×D10711yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—1072no—
179C4—4281no—
180C4—4281no—
181C4—2141no—
182C4—2141no—
183C2—2142no—
184C2#101×D10711yescharacteristic
185C2#104×D10711yescharacteristic
186C2#2029264211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
Fitting#330×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC22×D107C22⋊C4
cosocleC42×C107C23
hypercenter#330D107
hypocenterC107#1528
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #20292369C2semidirect
5. #20292368C2semidirect
6. #20292368C2semidirect
7. #330×C107C2semidirect
94. C107#1528semidirect
101. #330D107semidirect

Maximal subgroups

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

subgroupindex
#125×D1072
#202926822
#202925792
#202923692
#202923682
#330×C1072
#1528107