Finite Group Databasebeta

← #28335155

Subgroups — #28335155

Order 13696.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#20293178C211yesmaximal, characteristic
2#20292683C211yesmaximal, characteristic, complemented
3C4⋊C8×D107C211yesmaximal, characteristic, complemented
4#20292376C211yesmaximal, characteristic, complemented
5#20292370C211yesmaximal, characteristic, complemented
6#20292370C211yesmaximal, characteristic, complemented
7#333×C107C211yesmaximal, characteristic, complemented
8C2×#13133819C412yes—
9C2×C8×D107—21no—
10#16812106C2211yescharacteristic
11#16812098C412yes—
12#16812084—21no—
13#16812084—21no—
14#16812071—21no—
15#16812071—21no—
16C42×D107C2211yescharacteristic
17C4⋊(C107⋊C8)C2211yescharacteristic
18C4⋊(C107⋊C8)C2211yescharacteristic
19Dic107⋊C8—21no—
20(C2×D107)⋊C8—21no—
21#16812019—21no—
22C4⋊Q8×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24C4⋊C8×C107C2211yescharacteristic
25#13133819—44no—
26C2×D428—22no—
27C2×D428—21no—
28C2×D428—21no—
29C2×D428C2×C412yes—
30C2×C4×D107—22no—
31C2×C4×D107C2×C411yescharacteristic
32C2×C4×D107D411yescharacteristic
33C2×C4×D107D411yescharacteristic
34C2×C107⋊C8—21no—
35C2×C107⋊C8—21no—
36C8×D107—42no—
37(C2×D107)⋊C4—22no—
38(C2×D107)⋊C4—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×D107—22no—
49C22×D107C22⋊C411yescharacteristic
50Q8×C107—42no—
51C2×C4×C107—22no—
52C2×C4×C107C22×C411yescharacteristic
53C2×C4×C107C2×D411yescharacteristic
54C2×C4×C107C2×D411yescharacteristic
55C2×Dic107C22⋊C411yescharacteristic
56C2×Dic107C22⋊C411yescharacteristic
57C2×Dic107C22⋊C411yescharacteristic
58D428—42no—
59D428—44no—
60D428—41no—
61D428—41no—
62D428—41no—
63D428—41no—
64C4×D107—22no—
65C4×D107—21no—
66C4×D107—21no—
67C4×D107—21no—
68C4×D107—21no—
69C4×D107—44no—
70C8×C107—41no—
71C8×C107—41no—
72C107⋊C8—41no—
73C107⋊C8—41no—
74C22×C107C2×C22⋊C411yescharacteristic
75C2×D107—21no—
76C2×D107—21no—
77C2×D107—42no—
78C2×D107—42no—
79C2×D107—42no—
80C2×D107#10012yes—
81C4×C107—21no—
82C4×C107—42no—
83C4×C107#13511yescharacteristic
84C4×C107#13511yescharacteristic
85C4×C107AGL(1,ℤ/8)11yescharacteristic
86C4×C107#13711yescharacteristic
87Dic107—21no—
88Dic107—21no—
89Dic107—21no—
90C2×C107C2×#10011yescharacteristic
91C2×C107#41611yescharacteristic
92C2×C107#41711yescharacteristic
93D107—22no—
94D107—82no—
95#1551—1071nomaximal, Sylow
96C107#155111yescharacteristic, complemented, Sylow
97#532—1071no—
98#432—1071no—
99C2×C4⋊C8—1071no—
100#333—1071no—
101#333D10711yescharacteristic, complemented
102#331—1071no—
103#331—1071no—
104C2×#41—1072no—
105C22×C8—2141no—
106C4⋊Q8C2×D10711yescharacteristic
107#127—1071no—
108#124—1072no—
109#121—2141no—
110#121—2141no—
111C4×D4—2141no—
112C4×D4—2141no—
113C2×C42—1071no—
114C4⋊C8—1071no—
115C4⋊C8—1071no—
116C4⋊C8—2141no—
117C4⋊C8C2×D10711yescharacteristic
118C4⋊C8C2×D10711yescharacteristic
119C22⋊C8—2141no—
120#97—2141no—
121#41—4284no—
122C2×Q8C4×D10712yes—
123C2×D4—1072no—
124C2×D4—2142no—
125C2×D4—2141no—
126C2×D4—2141no—
127C22×C4—1071no—
128C22×C4—1071no—
129C22×C4—1071no—
130C22×C4—2142no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—4282no—
134C2×C8—2141no—
135C2×C8—2141no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C22⋊C4—2142no—
139C22⋊C4—2142no—
140C42—1071no—
141C42—1071no—
142C42—1071no—
143C42C22×D10711yescharacteristic
144C23—1071no—
145C23—2142no—
146Q8—42no—
147D4—4282no—
148D4—4284no—
149D4—4281no—
150D4—4281no—
151D4—4281no—
152D4—4281no—
153C2×C4—22no—
154C2×C4—1071no—
155C2×C4—1071no—
156C2×C4—1071no—
157C2×C4—4284no—
158C2×C4—2142no—
159C2×C4—2141no—
160C2×C4—2141no—
161C2×C4—2141no—
162C2×C4—2141no—
163C2×C4C2×C4×D10711yescharacteristic
164C2×C4D4×D10711yescharacteristic
165C2×C4D4×D10711yescharacteristic
166C8—41no—
167C8—41no—
168C8—4281no—
169C8—4281no—
170C22—1072no—
171C22—4282no—
172C22—4282no—
173C22—4282no—
174C22—2141no—
175C22—2141no—
176C22C22⋊C4×D10711yescharacteristic
177C4—21no—
178C4—42no—
179C4—2141no—
180C4—2141no—
181C4—2141no—
182C4#1681213011yescharacteristic
183C4#1681213211yescharacteristic
184C4#1681213611yescharacteristic
185C4#1681214111yescharacteristic
186C2—8562no—
187C2—2142no—
188C2#100×D10711yescharacteristic
189C2#2029262211yescharacteristic
190C2#2029262711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
Fitting#333×C107C2
socleC22×C107C2×C22⋊C4
prime radical#20293178C2
cosocleC42×C107C23
hypercenter#333D107
hypocenterC107#1551
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
2. #20292683C2semidirect
3. C4⋊C8×D107C2semidirect
4. #20292376C2semidirect
5. #20292370C2semidirect
6. #20292370C2semidirect
7. #333×C107C2semidirect
96. C107#1551semidirect
101. #333D107semidirect

Maximal subgroups

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

subgroupindex
#202931782
#202926832
C4⋊C8×D1072
#202923762
#202923702
#333×C1072
#1551107