Finite Group Databasebeta

← #28334773

Subgroups — #28334773

Order 13696.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#16812066C211yesmaximal, characteristic
2#20292680C211yesmaximal, characteristic, complemented
3#20292352C212yesmaximal, complemented
4#20292350C212yesmaximal
5#431×C107C211yesmaximal, characteristic, complemented
6C22×C4×D107C411yescharacteristic
7#16812066—21no—
8#16812066—21no—
9#16812066—21no—
10#16812066—21no—
11C2×Dic107⋊C4C411yescharacteristic
12C2×Dic107⋊C4C2211yescharacteristic
13C2×(C2×D107)⋊C4C411yescharacteristic
14C2×(C2×D107)⋊C4C2211yescharacteristic
15C2×C4×Dic107C411yescharacteristic
16C4⋊(C107⋊C8)—21no—
17C22⋊(C107⋊C8)C2212yes—
18C4×C107⋊C8—21no—
19C2×C42×C107C2211yescharacteristic
20C4⋊C8×C107—21no—
21C22⋊C8×C107C2212yes—
22C4×C8×C107—21no—
23C23×D107C2×C411yescharacteristic
24C22×Dic107C2×C411yescharacteristic
25C22×Dic107C2×C411yescharacteristic
26C22×Dic107C2×C411yescharacteristic
27C2×C4×D107—21no—
28C2×C4×D107—21no—
29C2×C4×D107—22no—
30C2×C4×D107C814yescomplemented
31C2×C107⋊C8—22no—
32Dic107⋊C4—21no—
33Dic107⋊C4—21no—
34Dic107⋊C4—21no—
35Dic107⋊C4—21no—
36(C2×D107)⋊C4—21no—
37(C2×D107)⋊C4—21no—
38(C2×D107)⋊C4—21no—
39(C2×D107)⋊C4—21no—
40C4×Dic107—21no—
41C4×Dic107—21no—
42C22×C4×C107C2×C411yescharacteristic
43C22×C4×C107C2×C411yescharacteristic
44C22×C4×C107C2311yescharacteristic
45C2×C8×C107—22no—
46C42×C107D411yescharacteristic
47C42×C107D411yescharacteristic
48C42×C107D411yescharacteristic
49C42×C107D411yescharacteristic
50C23×C107C22×C411yescharacteristic
51C22×D107—21no—
52C22×D107—21no—
53C22×D107—41no—
54C22×D107—41no—
55C22×D107C2×C812yes—
56C2×C4×C107—41no—
57C2×C4×C107—41no—
58C2×C4×C107C22⋊C411yescharacteristic
59C2×C4×C107C22⋊C411yescharacteristic
60C2×C4×C107C22⋊C411yescharacteristic
61C2×C4×C107C22⋊C411yescharacteristic
62C2×C4×C107C2×C812yes—
63C2×C4×C107M1612yes—
64C2×C4×C107C2×D411yescharacteristic
65C2×C4×C107C2×D411yescharacteristic
66C2×Dic107—21no—
67C2×Dic107—21no—
68C2×Dic107—21no—
69C2×Dic107—21no—
70C2×Dic107—41no—
71C2×Dic107—41no—
72C2×Dic107C2×C812yes—
73C4×D107—24no—
74C4×D107—24no—
75C8×C107—42no—
76C107⋊C8—42no—
77C22×C107—21no—
78C22×C107—21no—
79C22×C107C2×C22⋊C411yescharacteristic
80C22×C107C22×C811yescharacteristic
81C22×C107C2×M1611yescharacteristic
82C2×D107—22no—
83C2×D107—42no—
84C2×D107—41no—
85C2×D107—41no—
86C2×D107—42no—
87C4×C107—21no—
88C4×C107—21no—
89C4×C107—21no—
90C4×C107—21no—
91C4×C107C22⋊C812yes—
92C4×C107C22⋊C812yes—
93Dic107—22no—
94Dic107—41no—
95Dic107—41no—
96C2×C107—21no—
97C2×C107—21no—
98C2×C107C2×C22⋊C811yescharacteristic
99C2×C107#41011yescharacteristic
100C2×C107#41311yescharacteristic
101D107—42no—
102#1458—1071nomaximal, Sylow
103C107#145811yescharacteristic, complemented, Sylow
104C2×#117—1071no—
105#431—1071no—
106#431D10711yescharacteristic, complemented
107#324—1072no—
108#323—1072no—
109C23×C4—1071no—
110#117—2141no—
111#117—2141no—
112#117—2141no—
113#117—2141no—
114C2×C4⋊C4—1071no—
115C2×C4⋊C4—1071no—
116C2×C22⋊C4—1071no—
117C2×C22⋊C4—1071no—
118C2×C42—1071no—
119C2×C42C2×D10711yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—2141no—
122C22⋊C8—1072no—
123C22⋊C8C2×D10712yes—
124C4×C8—21no—
125C4×C8—2141no—
126C24—1071no—
127C22×C4—1071no—
128C22×C4—1074no—
129C22×C4—1071no—
130C22×C4—1071no—
131C22×C4—2141no—
132C22×C4—2141no—
133C22×C4—2142no—
134C22×C4C4×D10711yescharacteristic
135C22×C4C4×D10711yescharacteristic
136C22×C4C22×D10711yescharacteristic
137C2×C8—22no—
138C2×C8—2142no—
139C4⋊C4—2141no—
140C4⋊C4—2141no—
141C4⋊C4—2141no—
142C4⋊C4—2141no—
143C22⋊C4—2141no—
144C22⋊C4—2141no—
145C22⋊C4—2141no—
146C22⋊C4—2141no—
147C42—2141no—
148C42—2141no—
149C42D42811yescharacteristic
150C42D42811yescharacteristic
151C42C22⋊D10711yescharacteristic
152C42C22⋊D10711yescharacteristic
153C23—1072no—
154C23—4281no—
155C23—4281no—
156C23—2141no—
157C23—2141no—
158C23C2×C4×D10711yescharacteristic
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—1072no—
162C2×C4—4281no—
163C2×C4—4281no—
164C2×C4—2141no—
165C2×C4—2141no—
166C2×C4—2141no—
167C2×C4—2141no—
168C2×C4—2144no—
169C2×C4—2144no—
170C2×C4(C2×D107)⋊C411yescharacteristic
171C2×C4(C2×D107)⋊C411yescharacteristic
172C2×C4(C2×D107)⋊C411yescharacteristic
173C2×C4(C2×D107)⋊C411yescharacteristic
174C2×C4C8×D10712yes—
175C2×C4#1313380112yes—
176C2×C4C2×C22⋊D10711yescharacteristic
177C2×C4C2×D42811yescharacteristic
178C8—42no—
179C8—4282no—
180C22—21no—
181C22—21no—
182C22—4282no—
183C22—4282no—
184C22—4281no—
185C22—4281no—
186C22—2142no—
187C22C2×(C2×D107)⋊C411yescharacteristic
188C22C2×C8×D10711yescharacteristic
189C22C2×#1313380111yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—4281no—
195C4—4281no—
196C4—2142no—
197C4(C2×D107)⋊C812yes—
198C4(C2×D107)⋊C812yes—
199C2—21no—
200C2—21no—
201C2—4282no—
202C2C2×(C2×D107)⋊C811yescharacteristic
203C2#2029260011yescharacteristic
204C2#2029260911yescharacteristic
subgroupG/H
centerC2×C4(C2×D107)⋊C4
commutatorC22×C107C22×C8
FrattiniC22×C4C22×D107
Fitting#431×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC23×D107C2×C4
cosocleC22×C4×C107C23
hypercenter#431D107
hypocenterC107#1458
LCSG ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #20292680C2semidirect
3. #20292352C2semidirect
5. #431×C107C2semidirect
30. C2×C4×D107C8semidirect
103. C107#1458semidirect
106. #431D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120662
#202926802
#202923522
#202923502
#431×C1072
#1458107