Finite Group Databasebeta

← #28346860

Subgroups — #28346860

Order 13696.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#125×D107C211yesmaximal, characteristic, complemented
3#20292997C211yesmaximal, characteristic, complemented
4#20292996C211yesmaximal, characteristic, complemented
5#20292991C211yesmaximal, characteristic, complemented
6#20292980C214yesmaximal, complemented
7#20292625C214yesmaximal, complemented
8#20292579C211yesmaximal, characteristic, complemented
9#490×C107C211yesmaximal, characteristic, complemented
10C2×#13133817C2212yes—
11C2×#13133801C2212yes—
12#16812109C2211yescharacteristic
13#16812101C2211yescharacteristic
14#16812100C2212yes—
15#16812099—22no—
16#16812096C2212yes—
17#16812080—22no—
18D4×Dic107—22no—
19C4⋊C4×D107—22no—
20C4⋊C4×D107C2212yes—
21C42×D107C2211yescharacteristic
22#16812034C2214yes—
23#16812032C2214yes—
24#16812030C2214yes—
25#16812020C2211yescharacteristic
26C8×Dic107C2212yes—
27#127×C107C2211yescharacteristic
28#125×C107C2211yescharacteristic
29#102×C107C2214yes—
30#97×C107C2211yescharacteristic
31#13133817—28no—
32C2×Dic214C2312yes—
33C2×C22⋊D107—22no—
34C22×Dic107—22no—
35C2×C4×D107—22no—
36C2×C4×D107D412yes—
37C2×C4×D107C2311yescharacteristic
38#13133801—24no—
39C2×C107⋊C8C2312yes—
40C4⋊Dic107—22no—
41C4⋊Dic107—22no—
42C4⋊Dic107C2312yes—
43Dic107⋊C4—22no—
44Dic107⋊C4—22no—
45Dic107⋊C4—22no—
46C22⋊Dic107—24no—
47C4×Dic107D412yes—
48C4×Dic107C2311yescharacteristic
49C2×D4×C107—22no—
50C2×D4×C107C2312yes—
51C2×C8×C107C2312yes—
52C4⋊C4×C107—22no—
53C4⋊C4×C107C2312yes—
54C42×C107C2311yescharacteristic
55C23×C107—22no—
56C22×D107C2×D411yescharacteristic
57D4×C107—24no—
58D4×C107—44no—
59C2×C4×C107—22no—
60C2×C4×C107C2×D412yes—
61C2×C4×C107C2411yescharacteristic
62C22⋊D107—44no—
63C2×Dic107—22no—
64C2×Dic107—22no—
65C2×Dic107—44no—
66C2×Dic107C2×D412yes—
67C2×Dic107C2×D411yescharacteristic
68C4×D107—42no—
69C4×D107—44no—
70C4×D107#4114yes—
71Dic214—24no—
72C8×C107—22no—
73C107⋊C8—22no—
74C22×C107—42no—
75C22×C107—44no—
76C22×C107C22×D411yescharacteristic
77C2×D107—22no—
78C2×D107#12412yes—
79C4×C107—22no—
80C4×C107—42no—
81C4×C107C2×#4112yes—
82Dic107—22no—
83Dic107—42no—
84Dic107—42no—
85Dic107#12412yes—
86C2×C107—82no—
87C2×C107C2×#12411yescharacteristic
88C2×C107#57512yes—
89D107—22no—
90#3142—1071nomaximal, Sylow
91C107#314211yescharacteristic, complemented, Sylow
92#532—1071no—
93C2×#125—1071no—
94#491—1071no—
95#491—1071no—
96#490—1071no—
97#490D10711yescharacteristic, complemented
98#488—1074no—
99#417—1074no—
100C4×M16—1071no—
101C2×#41—1072no—
102C2×M16—1072no—
103C4⋊Q8—1071no—
104#127C2×D10711yescharacteristic
105#125—1072no—
106#125—1071no—
107#125—2142no—
108#125C2×D10711yescharacteristic
109#124—1072no—
110#121—2142no—
111C4×D4—2142no—
112C2×C4⋊C4—1072no—
113C2×C4⋊C4—2142no—
114C2×C42—1071no—
115#103—1074no—
116#103—1074no—
117#102—1074no—
118#102C2×D10714yes—
119#97—1071no—
120#97C2×D10711yescharacteristic
121C4×C8—1072no—
122#41—2148no—
123C2×Q8—1072no—
124C2×D4—22no—
125C2×D4—2142no—
126C2×D4C22×D10712yes—
127C22×C4—1071no—
128C22×C4—1072no—
129C22×C4—2142no—
130C22×C4—2142no—
131M16—2144no—
132C2×C8—1072no—
133C2×C8C22×D10712yes—
134C4⋊C4—22no—
135C4⋊C4—1072no—
136C4⋊C4—2142no—
137C4⋊C4—2142no—
138C4⋊C4—2142no—
139C4⋊C4—2142no—
140C4⋊C4—2142no—
141C4⋊C4C22×D10712yes—
142C22⋊C4—2144no—
143C42—1072no—
144C42—1071no—
145C42C22×D10711yescharacteristic
146C23—22no—
147C23—1071no—
148Q8—2144no—
149D4—24no—
150D4—44no—
151D4—4284no—
152C2×C4—22no—
153C2×C4—1071no—
154C2×C4—1074no—
155C2×C4—1072no—
156C2×C4—4282no—
157C2×C4—4284no—
158C2×C4—4284no—
159C2×C4—2142no—
160C2×C4—2142no—
161C2×C4D4×D10712yes—
162C2×C4C23×D10711yescharacteristic
163C8—22no—
164C8—2142no—
165C22—42no—
166C22—44no—
167C22—1072no—
168C22—2142no—
169C22C2×D4×D10711yescharacteristic
170C4—22no—
171C4—42no—
172C4—1072no—
173C4—4282no—
174C4—4282no—
175C4—2142no—
176C4#41×D10712yes—
177C2—82no—
178C2—2142no—
179C2#124×D10711yescharacteristic
180C2#2029342312yes—
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#490×C107C2
socleC22×C107C22×D4
prime radical#20293175C2
hypercenter#490D107
hypocenterC107#3142
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D107C2semidirect
3. #20292997C2semidirect
4. #20292996C2semidirect
5. #20292991C2semidirect
6. #20292980C2semidirect
7. #20292625C2semidirect
8. #20292579C2semidirect
9. #490×C107C2semidirect
91. C107#3142semidirect
97. #490D107semidirect

Maximal subgroups

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

subgroupindex
#202931752
#125×D1072
#202929972
#202929962
#202929912
#202929802
#202926252
#202925792
#490×C1072
#3142107