Finite Group Databasebeta

← #28335115

Subgroups — #28335115

Order 13696.

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

normal subgroups only

This group has 212 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#20292679C211yesmaximal, characteristic
3C4⋊C8×D107C211yesmaximal, characteristic
4#20292376C211yesmaximal, characteristic, complemented
5#20292374C211yesmaximal, characteristic, complemented
6#20292372C211yesmaximal, characteristic, complemented
7#333×C107C211yesmaximal, characteristic, complemented
8C2×C8×D107—21no—
9#16812109C2211yescharacteristic
10#16812100—21no—
11#16812089—21no—
12#16812085C412yes—
13Q8×Dic107C412yes—
14#16812074—21no—
15#16812067—21no—
16C42×D107C2211yescharacteristic
17C4⋊(C107⋊C8)C2211yescharacteristic
18C4⋊(C107⋊C8)C2211yescharacteristic
19Dic107⋊C8—21no—
20(C2×D107)⋊C8—21no—
21C8×Dic107—21no—
22C4⋊Q8×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24C4⋊C8×C107C2211yescharacteristic
25C2×Dic214—21no—
26C2×C4×D107C2×C411yescharacteristic
27C2×C4×D107D411yescharacteristic
28C2×C4×D107D411yescharacteristic
29C2×C107⋊C8—21no—
30C2×C107⋊C8—21no—
31C8×D107—42no—
32C4⋊Dic107—21no—
33C4⋊Dic107—22no—
34C4⋊Dic107C2×C412yes—
35Dic107⋊C4—22no—
36(C2×D107)⋊C4—22no—
37C4×Dic107—22no—
38C4×Dic107C2×C411yescharacteristic
39C4×Dic107D411yescharacteristic
40C4×Dic107D411yescharacteristic
41C2×Q8×C107C2×C412yes—
42C2×C8×C107—21no—
43C2×C8×C107—21no—
44C4⋊C4×C107—21no—
45C4⋊C4×C107—21no—
46C42×C107C2311yescharacteristic
47C22×D107C22⋊C411yescharacteristic
48Q8×C107—42no—
49C2×C4×C107—22no—
50C2×C4×C107C22×C411yescharacteristic
51C2×C4×C107C2×D411yescharacteristic
52C2×C4×C107C2×D411yescharacteristic
53C2×Dic107—22no—
54C2×Dic107C22⋊C411yescharacteristic
55C2×Dic107C22⋊C411yescharacteristic
56C2×Dic107C22⋊C411yescharacteristic
57C4×D107—21no—
58C4×D107—21no—
59C4×D107—41no—
60C4×D107SD1612yes—
61C4×D107Q1612yes—
62Dic214—41no—
63Dic214—41no—
64C8×C107—41no—
65C8×C107—41no—
66C107⋊C8—41no—
67C107⋊C8—41no—
68C22×C107C2×C22⋊C411yescharacteristic
69C2×D107—21no—
70C2×D107—21no—
71C2×D107#10312yes—
72C4×C107—21no—
73C4×C107—42no—
74C4×C107C2×SD1611yescharacteristic
75C4×C107C2×Q1611yescharacteristic
76C4×C107#13511yescharacteristic
77C4×C107#13511yescharacteristic
78Dic107—21no—
79Dic107—21no—
80Dic107—42no—
81Dic107#10312yes—
82C2×C107#41311yescharacteristic
83C2×C107C2×#10311yescharacteristic
84C2×C107#41611yescharacteristic
85D107—22no—
86#1542—1071nomaximal, Sylow
87C107#154211yescharacteristic, complemented, Sylow
88#533—1071no—
89#431—1071no—
90C2×C4⋊C8—1071no—
91#333—1071no—
92#333D10711yescharacteristic, complemented
93#332—1071no—
94#332—1071no—
95C22×C8—2141no—
96C4⋊Q8—1071no—
97C4⋊Q8C2×D10711yescharacteristic
98#125—2141no—
99C22⋊Q8—1072no—
100C22⋊Q8—2141no—
101C4×Q8—1072no—
102C4×Q8—2141no—
103#117—2141no—
104C2×C42—1071no—
105C4⋊C8—1071no—
106C4⋊C8—1071no—
107C4⋊C8—2141no—
108C4⋊C8C2×D10711yescharacteristic
109C4⋊C8C2×D10711yescharacteristic
110C22⋊C8—2141no—
111C4×C8—2141no—
112C2×Q8—2141no—
113C2×Q8C4×D10712yes—
114C22×C4—1071no—
115C22×C4—1071no—
116C22×C4—1071no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—4282no—
120C2×C8—2141no—
121C2×C8—2141no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—1072no—
125C4⋊C4—2142no—
126C4⋊C4—2142no—
127C4⋊C4—2141no—
128C22⋊C4—2142no—
129C42—1071no—
130C42—1071no—
131C42—1071no—
132C42—2142no—
133C42C22×D10711yescharacteristic
134C23—1071no—
135Q8—42no—
136Q8—4281no—
137Q8—4281no—
138C2×C4—22no—
139C2×C4—1071no—
140C2×C4—1072no—
141C2×C4—1072no—
142C2×C4—1071no—
143C2×C4—1071no—
144C2×C4—4281no—
145C2×C4—2142no—
146C2×C4—2141no—
147C2×C4—2141no—
148C2×C4C2×C4×D10711yescharacteristic
149C2×C4D4×D10711yescharacteristic
150C2×C4D4×D10711yescharacteristic
151C8—41no—
152C8—41no—
153C8—4281no—
154C8—4281no—
155C22—1072no—
156C22—2141no—
157C22—2141no—
158C22C22⋊C4×D10711yescharacteristic
159C4—21no—
160C4—42no—
161C4—1072no—
162C4—4282no—
163C4—2141no—
164C4—2141no—
165C4SD16×D10711yescharacteristic
166C4Q16×D10711yescharacteristic
167C4#1681213011yescharacteristic
168C4#1681213211yescharacteristic
169C2—2142no—
170C2#2029260811yescharacteristic
171C2#103×D10711yescharacteristic
172C2#2029262211yescharacteristic
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#1542
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
87. C107#1542semidirect
92. #333D107semidirect

Maximal subgroups

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

subgroupindex
#202931822
#202926792
C4⋊C8×D1072
#202923762
#202923742
#202923722
#333×C1072
#1542107