Finite Group Databasebeta

← #28335180

Subgroups — #28335180

Order 13696.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#20293175C211yesmaximal, characteristic
2#20292683C211yesmaximal, characteristic, complemented
3#20292649C211yesmaximal, characteristic, complemented
4#20292374C211yesmaximal, characteristic, complemented
5#20292372C211yesmaximal, characteristic, complemented
6#20292371C211yesmaximal, characteristic, complemented
7#331×C107C211yesmaximal, characteristic, complemented
8C2×#13133817—21no—
9C2×#13133801—21no—
10#16812109C2211yescharacteristic
11#16812096—21no—
12#16812080—21no—
13#16812080C412yes—
14D4×Dic107—21no—
15D4×Dic107C412yes—
16C42×D107C2211yescharacteristic
17C4⋊(C107⋊C8)C2211yescharacteristic
18C4⋊(C107⋊C8)C2211yescharacteristic
19Dic107⋊C8—21no—
20(C2×D107)⋊C8—21no—
21#16812019—21no—
22#127×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24C4⋊C8×C107C2211yescharacteristic
25#13133817—42no—
26#13133817—42no—
27C2×Dic214—21no—
28C2×C22⋊D107—22no—
29C22×Dic107—22no—
30C2×C4×D107C2×C411yescharacteristic
31C2×C4×D107D411yescharacteristic
32C2×C4×D107D411yescharacteristic
33#13133801—42no—
34C2×C107⋊C8—21no—
35C2×C107⋊C8—21no—
36C4⋊Dic107—21no—
37C4⋊Dic107C2×C412yes—
38C22⋊Dic107—22no—
39C22⋊Dic107—22no—
40C4×Dic107C2×C411yescharacteristic
41C4×Dic107D411yescharacteristic
42C4×Dic107D411yescharacteristic
43C2×D4×C107—21no—
44C2×D4×C107—21no—
45C2×D4×C107C2×C412yes—
46C2×C8×C107—21no—
47C2×C8×C107—21no—
48C42×C107C2311yescharacteristic
49C23×C107—22no—
50C22×D107C22⋊C411yescharacteristic
51D4×C107—42no—
52D4×C107—41no—
53D4×C107—41no—
54D4×C107—41no—
55D4×C107—41no—
56C2×C4×C107C22×C411yescharacteristic
57C2×C4×C107C2×D411yescharacteristic
58C2×C4×C107C2×D411yescharacteristic
59C22⋊D107—44no—
60C2×Dic107—22no—
61C2×Dic107—44no—
62C2×Dic107C22⋊C411yescharacteristic
63C2×Dic107C22⋊C411yescharacteristic
64C2×Dic107C22⋊C411yescharacteristic
65C4×D107—21no—
66C4×D107—21no—
67C4×D107—21no—
68C4×D107—21no—
69C4×D107—41no—
70Dic214—41no—
71Dic214—41no—
72C8×C107—41no—
73C8×C107—41no—
74C107⋊C8—41no—
75C107⋊C8—41no—
76C22×C107—42no—
77C22×C107—42no—
78C22×C107—42no—
79C22×C107C2×C22⋊C411yescharacteristic
80C2×D107—21no—
81C2×D107—21no—
82C2×D107—21no—
83C4×C107—21no—
84C4×C107AGL(1,ℤ/8)11yescharacteristic
85C4×C107AGL(1,ℤ/8)11yescharacteristic
86C4×C107AGL(1,ℤ/8)11yescharacteristic
87C4×C107#13711yescharacteristic
88Dic107—21no—
89Dic107—21no—
90Dic107—21no—
91Dic107—42no—
92C2×C107—82no—
93C2×C107#41311yescharacteristic
94C2×C107#41711yescharacteristic
95C2×C107#41811yescharacteristic
96D107—41no—
97#1557—1071nomaximal, Sylow
98C107#155711yescharacteristic, complemented, Sylow
99#532—1071no—
100#432—1071no—
101#423—1071no—
102#332—1071no—
103#332—1071no—
104#331—1071no—
105#331D10711yescharacteristic, complemented
106C2×#41—2141no—
107C2×M16—2141no—
108C4⋊Q8—1071no—
109#127C2×D10711yescharacteristic
110#124—2141no—
111#121—1072no—
112#121—2141no—
113C4×D4—1072no—
114C4×D4—2141no—
115C2×C42—1071no—
116C4⋊C8—1071no—
117C4⋊C8—1071no—
118C4⋊C8—2141no—
119C4⋊C8C2×D10711yescharacteristic
120C4⋊C8C2×D10711yescharacteristic
121C22⋊C8—2141no—
122#97—2141no—
123#41—4282no—
124#41—4282no—
125C2×Q8—2141no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—2142no—
129C2×D4C4×D10712yes—
130C22×C4—1071no—
131C22×C4—1071no—
132C22×C4—1071no—
133C22×C4—2142no—
134M16—4282no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—2141no—
138C2×C8—2141no—
139C4⋊C4—1072no—
140C4⋊C4—2141no—
141C22⋊C4—2142no—
142C22⋊C4—2142no—
143C42—1071no—
144C42—1071no—
145C42—1071no—
146C42C22×D10711yescharacteristic
147C23—22no—
148C23—1071no—
149Q8—4281no—
150Q8—4281no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—4284no—
157C2×C4—1071no—
158C2×C4—1071no—
159C2×C4—1071no—
160C2×C4—4281no—
161C2×C4—4284no—
162C2×C4—2142no—
163C2×C4—2141no—
164C2×C4—2141no—
165C2×C4—2141no—
166C2×C4—2141no—
167C2×C4C2×C4×D10711yescharacteristic
168C2×C4D4×D10711yescharacteristic
169C2×C4D4×D10711yescharacteristic
170C8—41no—
171C8—41no—
172C8—4281no—
173C8—4281no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—2141no—
178C22—2141no—
179C22—2141no—
180C22C22⋊C4×D10711yescharacteristic
181C4—21no—
182C4—4282no—
183C4—2141no—
184C4—2141no—
185C4—2141no—
186C4#1681213311yescharacteristic
187C4#1681213311yescharacteristic
188C4#1681213611yescharacteristic
189C4#1681213811yescharacteristic
190C2—82no—
191C2—4281no—
192C2#2029260811yescharacteristic
193C2#2029262511yescharacteristic
194C2#2029263011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
Fitting#331×C107C2
socleC22×C107C2×C22⋊C4
prime radical#20293175C2
cosocleC42×C107C23
hypercenter#331D107
hypocenterC107#1557
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20292683C2semidirect
3. #20292649C2semidirect
4. #20292374C2semidirect
5. #20292372C2semidirect
6. #20292371C2semidirect
7. #331×C107C2semidirect
98. C107#1557semidirect
105. #331D107semidirect

Maximal subgroups

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

subgroupindex
#202931752
#202926832
#202926492
#202923742
#202923722
#202923712
#331×C1072
#1557107