Finite Group Databasebeta

← #28335148

Subgroups — #28335148

Order 13696.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#20293182C211yesmaximal, characteristic
2#20292649C211yesmaximal, characteristic
3C4⋊C8×D107C211yesmaximal, characteristic
4#20292376C211yesmaximal, characteristic, complemented
5#20292374C211yesmaximal, characteristic, complemented
6#20292372C211yesmaximal, characteristic, complemented
7#333×C107C211yesmaximal, characteristic, complemented
8C2×#13133801—21no—
9C2×C8×D107—21no—
10#16812109C2211yescharacteristic
11#16812100—21no—
12#16812089—21no—
13#16812085C412yes—
14Q8×Dic107C412yes—
15#16812074—21no—
16#16812067—21no—
17C42×D107C2211yescharacteristic
18C4⋊(C107⋊C8)C2211yescharacteristic
19C4⋊(C107⋊C8)C2211yescharacteristic
20Dic107⋊C8—21no—
21Dic107⋊C8—21no—
22C4⋊Q8×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24C4⋊C8×C107C2211yescharacteristic
25C2×Dic214—21no—
26C2×C4×D107C2×C411yescharacteristic
27C2×C4×D107D411yescharacteristic
28C2×C4×D107D411yescharacteristic
29#13133801—42no—
30C2×C107⋊C8—21no—
31C2×C107⋊C8—21no—
32C8×D107—42no—
33C4⋊Dic107—21no—
34C4⋊Dic107—22no—
35C4⋊Dic107C2×C412yes—
36Dic107⋊C4—22no—
37(C2×D107)⋊C4—22no—
38C4×Dic107—22no—
39C4×Dic107C2×C411yescharacteristic
40C4×Dic107D411yescharacteristic
41C4×Dic107D411yescharacteristic
42C2×Q8×C107C2×C412yes—
43C2×C8×C107—21no—
44C2×C8×C107—21no—
45C4⋊C4×C107—21no—
46C4⋊C4×C107—21no—
47C42×C107C2311yescharacteristic
48C22×D107C22⋊C411yescharacteristic
49Q8×C107—42no—
50C2×C4×C107—22no—
51C2×C4×C107C22×C411yescharacteristic
52C2×C4×C107C2×D411yescharacteristic
53C2×C4×C107C2×D411yescharacteristic
54C2×Dic107—22no—
55C2×Dic107C22⋊C411yescharacteristic
56C2×Dic107C22⋊C411yescharacteristic
57C2×Dic107C22⋊C411yescharacteristic
58C4×D107—21no—
59C4×D107—21no—
60C4×D107—41no—
61C4×D107SD1612yes—
62C4×D107Q1612yes—
63Dic214—41no—
64Dic214—41no—
65C8×C107—41no—
66C8×C107—41no—
67C107⋊C8—41no—
68C107⋊C8—41no—
69C22×C107C2×C22⋊C411yescharacteristic
70C2×D107—21no—
71C2×D107—21no—
72C2×D107#10312yes—
73C4×C107—21no—
74C4×C107—42no—
75C4×C107C2×SD1611yescharacteristic
76C4×C107C2×Q1611yescharacteristic
77C4×C107AGL(1,ℤ/8)11yescharacteristic
78C4×C107#13711yescharacteristic
79Dic107—21no—
80Dic107—21no—
81Dic107—42no—
82Dic107#10312yes—
83C2×C107#41311yescharacteristic
84C2×C107C2×#10311yescharacteristic
85C2×C107#41711yescharacteristic
86D107—22no—
87#1550—1071nomaximal, Sylow
88C107#155011yescharacteristic, complemented, Sylow
89#533—1071no—
90#423—1071no—
91C2×C4⋊C8—1071no—
92#333—1071no—
93#333D10711yescharacteristic, complemented
94#332—1071no—
95#332—1071no—
96C2×M16—2141no—
97C22×C8—2141no—
98C4⋊Q8—1071no—
99C4⋊Q8C2×D10711yescharacteristic
100#125—2141no—
101C22⋊Q8—1072no—
102C22⋊Q8—2141no—
103C4×Q8—1072no—
104C4×Q8—2141no—
105#117—2141no—
106C2×C42—1071no—
107C4⋊C8—1071no—
108C4⋊C8—1071no—
109C4⋊C8—2141no—
110C4⋊C8—2141no—
111C4⋊C8C2×D10711yescharacteristic
112C4⋊C8C2×D10711yescharacteristic
113C2×Q8—2141no—
114C2×Q8C4×D10712yes—
115C22×C4—1071no—
116C22×C4—1071no—
117C22×C4—1071no—
118M16—4282no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—4282no—
122C2×C8—2141no—
123C2×C8—2141no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—1072no—
127C4⋊C4—2142no—
128C4⋊C4—2142no—
129C4⋊C4—2141no—
130C22⋊C4—2142no—
131C42—1071no—
132C42—1071no—
133C42—1071no—
134C42—2142no—
135C42C22×D10711yescharacteristic
136C23—1071no—
137Q8—42no—
138Q8—4281no—
139Q8—4281no—
140C2×C4—22no—
141C2×C4—1071no—
142C2×C4—1072no—
143C2×C4—1072no—
144C2×C4—1071no—
145C2×C4—1071no—
146C2×C4—4281no—
147C2×C4—2142no—
148C2×C4—2141no—
149C2×C4—2141no—
150C2×C4C2×C4×D10711yescharacteristic
151C2×C4D4×D10711yescharacteristic
152C2×C4D4×D10711yescharacteristic
153C8—41no—
154C8—41no—
155C8—4281no—
156C8—4281no—
157C22—1072no—
158C22—2141no—
159C22—2141no—
160C22C22⋊C4×D10711yescharacteristic
161C4—21no—
162C4—42no—
163C4—1072no—
164C4—4282no—
165C4—2141no—
166C4—2141no—
167C4SD16×D10711yescharacteristic
168C4Q16×D10711yescharacteristic
169C4#1681213611yescharacteristic
170C4#1681214111yescharacteristic
171C2—2142no—
172C2#2029260811yescharacteristic
173C2#103×D10711yescharacteristic
174C2#2029262711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
Fitting#333×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC22×D107C22⋊C4
cosocleC42×C107C23
hypercenter#333D107
hypocenterC107#1550
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #20292376C2semidirect
5. #20292374C2semidirect
6. #20292372C2semidirect
7. #333×C107C2semidirect
88. C107#1550semidirect
93. #333D107semidirect

Maximal subgroups

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

subgroupindex
#202931822
#202926492
C4⋊C8×D1072
#202923762
#202923742
#202923722
#333×C1072
#1550107