Finite Group Databasebeta

← #28335036

Subgroups — #28335036

Order 13696.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#20293161C211yesmaximal, characteristic
2#20292680C211yesmaximal, characteristic, complemented
3#20292363C212yesmaximal, complemented
4#20292360C212yesmaximal
5#383×C107C211yesmaximal, characteristic, complemented
6#16812103—21no—
7#16812101C411yescharacteristic, complemented
8#16812097C411yescharacteristic, complemented
9#16812092—21no—
10#16812088C2211yescharacteristic
11#16812083C2211yescharacteristic
12C4×Dic214C411yescharacteristic, complemented
13C4×D428C411yescharacteristic, complemented
14C4×C22⋊D107—21no—
15#16812066—21no—
16C4⋊(C107⋊C8)—21no—
17C22⋊(C107⋊C8)C2212yes—
18C4×C107⋊C8—21no—
19C2×C42×C107C2211yescharacteristic
20#95×C107—21no—
21#95×C107—21no—
22#95×C107C2212yes—
23C2×Dic214C2×C411yescharacteristic
24C2×D428C2×C411yescharacteristic
25C2×C22⋊D107—21no—
26C2×C4×D107—21no—
27C2×C107⋊C8—22no—
28C4⋊Dic107C2×C411yescharacteristic
29C4⋊Dic107C2×C411yescharacteristic
30Dic107⋊C4—21no—
31Dic107⋊C4—21no—
32Dic107⋊C4—21no—
33Dic107⋊C4—21no—
34C22⋊Dic107—21no—
35(C2×D107)⋊C4—21no—
36(C2×D107)⋊C4—21no—
37(C2×D107)⋊C4—21no—
38(C2×D107)⋊C4—21no—
39C4×Dic107—21no—
40C22×C4×C107—22no—
41C22×C4×C107D411yescharacteristic
42C22×C4×C107D411yescharacteristic
43C22×C4×C107C2311yescharacteristic
44C42×C107C2×C411yescharacteristic
45C42×C107C2×C411yescharacteristic
46C42×C107D411yescharacteristic
47C42×C107D411yescharacteristic
48C23×C107C2×D411yescharacteristic
49C22×D107—21no—
50C2×C4×C107—22no—
51C2×C4×C107—41no—
52C2×C4×C107—41no—
53C2×C4×C107—42no—
54C2×C4×C107—42no—
55C2×C4×C107—42no—
56C2×C4×C107C22⋊C411yescharacteristic
57C2×C4×C107C22⋊C411yescharacteristic
58C2×C4×C107C22⋊C411yescharacteristic
59C2×C4×C107C22⋊C411yescharacteristic
60C2×C4×C107C22×C411yescharacteristic
61C2×C4×C107C2×D411yescharacteristic
62C22⋊D107—42no—
63C2×Dic107—21no—
64C2×Dic107—21no—
65C2×Dic107—21no—
66D428—41no—
67C4×D107—42no—
68Dic214—41no—
69C107⋊C8—42no—
70C22×C107—21no—
71C22×C107—21no—
72C22×C107C2×C22⋊C411yescharacteristic
73C22×C107#13512yes—
74C2×D107—41no—
75C2×D107—41no—
76C2×D107—41no—
77C4×C107—21no—
78C4×C107—21no—
79C4×C107—21no—
80C4×C107—21no—
81C4×C107—21no—
82C4×C107—21no—
83C4×C107—82no—
84Dic107—41no—
85Dic107—41no—
86Dic107—41no—
87C2×C107—22no—
88C2×C107#41011yescharacteristic
89C2×C107#41611yescharacteristic
90C2×C107#42111yescharacteristic
91D107—81no—
92#1521—1071nomaximal, Sylow
93C107#152111yescharacteristic, complemented, Sylow
94#529—1071no—
95#431—1071no—
96#383D10711yescharacteristic, complemented
97#328—1072no—
98#327—1072no—
99#126—2141no—
100#125—1071no—
101#124—1071no—
102#123—2141no—
103C22⋊Q8—1071no—
104#121—1071no—
105C4×Q8—1071no—
106C4×D4—1071no—
107C4×D4—2141no—
108#117—2141no—
109C2×C42C2×D10711yescharacteristic
110C4⋊C8—2141no—
111C22⋊C8—1072no—
112C4×C8—2141no—
113#95—21no—
114#95—21no—
115#95C2×D10712yes—
116C2×Q8—1071no—
117C2×D4—1071no—
118C2×D4—2141no—
119C22×C4—22no—
120C22×C4—2141no—
121C22×C4C22⋊D10711yescharacteristic
122C22×C4C22⋊D10711yescharacteristic
123C22×C4C22×D10711yescharacteristic
124C2×C8—2142no—
125C4⋊C4—1071no—
126C4⋊C4—1071no—
127C4⋊C4—2141no—
128C4⋊C4—2141no—
129C4⋊C4—2141no—
130C4⋊C4—2141no—
131C22⋊C4—2141no—
132C22⋊C4—2141no—
133C22⋊C4—2141no—
134C22⋊C4—2141no—
135C22⋊C4—2141no—
136C42—2141no—
137C42C4×D10711yescharacteristic
138C42C4×D10711yescharacteristic
139C42D42811yescharacteristic
140C42D42811yescharacteristic
141C23—2141no—
142C23C2×C22⋊D10711yescharacteristic
143Q8—4281no—
144D4—4281no—
145D4—4282no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—4282no—
153C2×C4—2141no—
154C2×C4—2141no—
155C2×C4—2141no—
156C2×C4(C2×D107)⋊C411yescharacteristic
157C2×C4(C2×D107)⋊C411yescharacteristic
158C2×C4(C2×D107)⋊C411yescharacteristic
159C2×C4(C2×D107)⋊C411yescharacteristic
160C2×C4C2×C4×D10711yescharacteristic
161C2×C4C2×D42811yescharacteristic
162C8—4282no—
163C22—21no—
164C22—21no—
165C22—4281no—
166C22—4281no—
167C22—4281no—
168C22C2×(C2×D107)⋊C411yescharacteristic
169C22#1681212912yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—4281no—
178C4—4281no—
179C4—4281no—
180C2—22no—
181C2—8561no—
182C2#2029260011yescharacteristic
183C2#2029262111yescharacteristic
184C2#2029264511yescharacteristic
subgroupG/H
centerC22C2×(C2×D107)⋊C4
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#383×C107C2
socleC22×C107C2×C22⋊C4
prime radical#16812083C22
cosocleC22×C4×C107C23
hypercenter#383D107
hypocenterC107#1521
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #20292680C2semidirect
3. #20292363C2semidirect
5. #383×C107C2semidirect
7. #16812101C4semidirect
8. #16812097C4semidirect
12. C4×Dic214C4semidirect
13. C4×D428C4semidirect
93. C107#1521semidirect
96. #383D107semidirect

Maximal subgroups

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

subgroupindex
#202931612
#202926802
#202923632
#202923602
#383×C1072
#1521107