Finite Group Databasebeta

← #28338123

Subgroups — #28338123

Order 13696.

258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 55 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#20292599C212yesmaximal, complemented
3#20292421C212yesmaximal, complemented
4#20292420C211yesmaximal, characteristic, complemented
5#353×C107C211yesmaximal, characteristic, complemented
6C2×#13133817C411yescharacteristic, complemented
7C2×#13133817C2211yescharacteristic
8#16812109C411yescharacteristic, complemented
9#16812096C411yescharacteristic, complemented
10#16812096C2211yescharacteristic
11#16812080—22no—
12D4×Dic107—22no—
13#16812065—22no—
14C42×D107C411yescharacteristic, complemented
15#16812024C2212yes—
16#16812023—22no—
17#127×C107C2211yescharacteristic
18#99×C107C2212yes—
19#13133817—41no—
20#13133817—41no—
21#13133817—41no—
22#13133817—41no—
23C2×Dic214C2×C411yescharacteristic
24C2×Dic214C2×C411yescharacteristic
25C2×C22⋊D107—21no—
26C2×C22⋊D107D412yes—
27C22×Dic107—21no—
28C22×Dic107D412yes—
29C2×C4×D107—21no—
30C2×C4×D107C2×C411yescharacteristic
31C4⋊Dic107—22no—
32Dic107⋊C4—42no—
33C22⋊Dic107—22no—
34C22⋊Dic107—22no—
35C22⋊Dic107—22no—
36C4×Dic107—21no—
37C4×Dic107—42no—
38C4×Dic107C2×C411yescharacteristic
39C2×D4×C107—22no—
40C2×D4×C107C2×C411yescharacteristic
41C2×D4×C107C2311yescharacteristic
42C22⋊C4×C107—22no—
43C42×C107C2×C411yescharacteristic
44C23×C107—21no—
45C23×C107C2×D412yes—
46C22×D107C22⋊C411yescharacteristic
47D4×C107—41no—
48D4×C107—41no—
49D4×C107—44no—
50C2×C4×C107—21no—
51C2×C4×C107—42no—
52C2×C4×C107C22×C411yescharacteristic
53C22⋊D107—42no—
54C22⋊D107—42no—
55C2×Dic107—22no—
56C2×Dic107—22no—
57C2×Dic107—21no—
58C2×Dic107—21no—
59C2×Dic107—41no—
60C2×Dic107—41no—
61C2×Dic107—42no—
62C2×Dic107C22⋊C412yes—
63C2×Dic107C22⋊C411yescharacteristic
64C4×D107—21no—
65C4×D107—21no—
66C4×D107—42no—
67Dic214—41no—
68Dic214—41no—
69C22×C107—22no—
70C22×C107—42no—
71C22×C107—42no—
72C22×C107—41no—
73C22×C107C2×C22⋊C411yescharacteristic
74C2×D107—21no—
75C2×D107—41no—
76C4×C107—22no—
77C4×C107—21no—
78C4×C107—82no—
79Dic107—22no—
80Dic107—41no—
81Dic107—41no—
82Dic107—82no—
83Dic107#9911yescharacteristic
84Dic107#9911yescharacteristic
85C2×C107—21no—
86C2×C107—42no—
87C2×C107—81no—
88C2×C107C2×#9911yescharacteristic
89D107—41no—
90#2126—1071nomaximal, Sylow
91C107#212611yescharacteristic, complemented, Sylow
92#532—1071no—
93#410—1072no—
94#354—1072no—
95#353—1071no—
96#353D10711yescharacteristic, complemented
97C2×#41—1071no—
98C2×#41—1071no—
99C4⋊Q8—1071no—
100#127C2×D10711yescharacteristic
101#124—1071no—
102#124—1071no—
103#121—2142no—
104C4×D4—2142no—
105#117—2142no—
106C2×C42—1071no—
107#99—1072no—
108#99—2142no—
109#99C2×D10712yes—
110#41—4281no—
111#41—4281no—
112#41—4281no—
113#41—4281no—
114C2×Q8—1071no—
115C2×Q8—1071no—
116C2×D4—22no—
117C2×D4—1072no—
118C2×D4—2141no—
119C2×D4C4×D10711yescharacteristic
120C2×D4C22×D10711yescharacteristic
121C22×C4—1072no—
122C22×C4—1071no—
123C22×C4—2141no—
124C22×C4—2141no—
125C4⋊C4—4282no—
126C4⋊C4—2142no—
127C22⋊C4—22no—
128C22⋊C4—2142no—
129C22⋊C4—2142no—
130C22⋊C4—2142no—
131C42—1071no—
132C42—4282no—
133C42—2141no—
134C42C4×D10711yescharacteristic
135C23—21no—
136C23—1071no—
137C23D4×D10712yes—
138Q8—4281no—
139Q8—4281no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—4282no—
144D4—4282no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—1071no—
148C2×C4—1072no—
149C2×C4—4282no—
150C2×C4—4282no—
151C2×C4—4281no—
152C2×C4—4281no—
153C2×C4—2141no—
154C2×C4—2141no—
155C2×C4—2142no—
156C2×C4—2142no—
157C2×C4—2141no—
158C2×C4—2141no—
159C2×C4C2×C4×D10711yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—4281no—
165C22—2141no—
166C22C22⋊C4×D10711yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—8562no—
171C4—1071no—
172C4—1071no—
173C4—4281no—
174C4—4281no—
175C4—2142no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—4281no—
180C2#99×D10711yescharacteristic
subgroupG/H
centerC2#99×D107
commutatorC2×C4×C107C22×C4
FrattiniC2×D4C22×D107
Fitting#353×C107C2
socleC2×C107C2×#99
prime radical#20293175C2
cosocleC2×D4×C107C23
hypercenter#353D107
hypocenterC107#2126
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #20292599C2semidirect
3. #20292421C2semidirect
4. #20292420C2semidirect
5. #353×C107C2semidirect
6. C2×#13133817C4semidirect
8. #16812109C4semidirect
9. #16812096C4semidirect
14. C42×D107C4semidirect
91. C107#2126semidirect
96. #353D107semidirect

Maximal subgroups

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

subgroupindex
#202931752
#202925992
#202924212
#202924202
#353×C1072
#2126107