Finite Group Databasebeta

← #28335135

Subgroups — #28335135

Order 13696.

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

normal subgroups only

This group has 260 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#20293175C211yesmaximal, characteristic
2#20292649C211yesmaximal, characteristic, complemented
3C4⋊C8×D107C211yesmaximal, 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—
10C2×C8×D107—21no—
11#16812109C2211yescharacteristic
12#16812096—21no—
13#16812080—21no—
14#16812080C412yes—
15D4×Dic107—21no—
16D4×Dic107C412yes—
17C42×D107C2211yescharacteristic
18C4⋊(C107⋊C8)C2211yescharacteristic
19C4⋊(C107⋊C8)C2211yescharacteristic
20Dic107⋊C8—21no—
21Dic107⋊C8—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—
36C8×D107—42no—
37C4⋊Dic107—21no—
38C4⋊Dic107C2×C412yes—
39C22⋊Dic107—22no—
40C22⋊Dic107—22no—
41C4×Dic107C2×C411yescharacteristic
42C4×Dic107D411yescharacteristic
43C4×Dic107D411yescharacteristic
44C2×D4×C107—21no—
45C2×D4×C107—21no—
46C2×D4×C107C2×C412yes—
47C2×C8×C107—21no—
48C2×C8×C107—21no—
49C42×C107C2311yescharacteristic
50C23×C107—22no—
51C22×D107C22⋊C411yescharacteristic
52D4×C107—42no—
53D4×C107—41no—
54D4×C107—41no—
55D4×C107—41no—
56D4×C107—41no—
57C2×C4×C107C22×C411yescharacteristic
58C2×C4×C107C2×D411yescharacteristic
59C2×C4×C107C2×D411yescharacteristic
60C22⋊D107—44no—
61C2×Dic107—22no—
62C2×Dic107—44no—
63C2×Dic107C22⋊C411yescharacteristic
64C2×Dic107C22⋊C411yescharacteristic
65C2×Dic107C22⋊C411yescharacteristic
66C4×D107—21no—
67C4×D107—21no—
68C4×D107—41no—
69C4×D107D812yes—
70C4×D107SD1612yes—
71Dic214—41no—
72Dic214—41no—
73C8×C107—41no—
74C8×C107—41no—
75C107⋊C8—41no—
76C107⋊C8—41no—
77C22×C107—42no—
78C22×C107—42no—
79C22×C107—42no—
80C22×C107C2×C22⋊C411yescharacteristic
81C2×D107—21no—
82C2×D107—21no—
83C2×D107#10212yes—
84C4×C107—21no—
85C4×C107C2×D811yescharacteristic
86C4×C107C2×SD1611yescharacteristic
87C4×C107AGL(1,ℤ/8)11yescharacteristic
88C4×C107#13711yescharacteristic
89Dic107—21no—
90Dic107—21no—
91Dic107—42no—
92Dic107#10212yes—
93C2×C107—82no—
94C2×C107#41311yescharacteristic
95C2×C107C2×#10211yescharacteristic
96C2×C107#41711yescharacteristic
97D107—22no—
98#1547—1071nomaximal, Sylow
99C107#154711yescharacteristic, complemented, Sylow
100#532—1071no—
101#423—1071no—
102C2×C4⋊C8—1071no—
103#332—1071no—
104#332—1071no—
105#331—1071no—
106#331D10711yescharacteristic, complemented
107C2×#41—2141no—
108C2×M16—2141no—
109C22×C8—2141no—
110C4⋊Q8—1071no—
111#127C2×D10711yescharacteristic
112#124—2141no—
113#121—1072no—
114#121—2141no—
115C4×D4—1072no—
116C4×D4—2141no—
117C2×C42—1071no—
118C4⋊C8—1071no—
119C4⋊C8—1071no—
120C4⋊C8—2141no—
121C4⋊C8—2141no—
122C4⋊C8C2×D10711yescharacteristic
123C4⋊C8C2×D10711yescharacteristic
124#41—4282no—
125#41—4282no—
126C2×Q8—2141no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—2142no—
130C2×D4C4×D10712yes—
131C22×C4—1071no—
132C22×C4—1071no—
133C22×C4—1071no—
134C22×C4—2142no—
135M16—4282no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—4282no—
139C2×C8—2141no—
140C2×C8—2141no—
141C4⋊C4—1072no—
142C4⋊C4—2141no—
143C22⋊C4—2142no—
144C22⋊C4—2142no—
145C42—1071no—
146C42—1071no—
147C42—1071no—
148C42C22×D10711yescharacteristic
149C23—22no—
150C23—1071no—
151Q8—4281no—
152Q8—4281no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—4284no—
159C2×C4—1071no—
160C2×C4—1072no—
161C2×C4—1072no—
162C2×C4—1071no—
163C2×C4—1071no—
164C2×C4—4281no—
165C2×C4—4284no—
166C2×C4—2142no—
167C2×C4—2141no—
168C2×C4—2141no—
169C2×C4C2×C4×D10711yescharacteristic
170C2×C4D4×D10711yescharacteristic
171C2×C4D4×D10711yescharacteristic
172C8—41no—
173C8—41no—
174C8—4281no—
175C8—4281no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—1072no—
180C22—2141no—
181C22—2141no—
182C22C22⋊C4×D10711yescharacteristic
183C4—21no—
184C4—1072no—
185C4—4282no—
186C4—2141no—
187C4—2141no—
188C4D8×D10711yescharacteristic
189C4SD16×D10711yescharacteristic
190C4#1681213311yescharacteristic
191C4#1681213811yescharacteristic
192C2—82no—
193C2—2142no—
194C2#2029260811yescharacteristic
195C2#102×D10711yescharacteristic
196C2#2029262511yescharacteristic
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#1547
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. #20292649C2semidirect
3. C4⋊C8×D107C2semidirect
4. #20292374C2semidirect
5. #20292372C2semidirect
6. #20292371C2semidirect
7. #331×C107C2semidirect
99. C107#1547semidirect
106. #331D107semidirect

Maximal subgroups

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

subgroupindex
#202931752
#202926492
C4⋊C8×D1072
#202923742
#202923722
#202923712
#331×C1072
#1547107