Finite Group Databasebeta

← #28334787

Subgroups — #28334787

Order 13696.

440 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C22×(C2×D107)⋊C4C211yesmaximal, characteristic
2#20292591C211yesmaximal, characteristic, complemented
3#20292350C214yesmaximal, complemented
4#407×C107C211yesmaximal, characteristic, complemented
5C24×D107C411yescharacteristic
6C23×Dic107C411yescharacteristic
7C2×#13133802—21no—
8C2×(C2×D107)⋊C4—21no—
9C2×(C2×D107)⋊C4—21no—
10C2×(C2×D107)⋊C4—21no—
11C2×(C2×D107)⋊C4—21no—
12C2×(C2×D107)⋊C4C412yes—
13C2×(C2×D107)⋊C4C2212yes—
14C22⋊(C107⋊C8)—21no—
15C22⋊(C107⋊C8)C2212yescomplemented
16C23×C4×C107C2211yescharacteristic
17C2×M16×C107—21no—
18C22⋊C8×C107—21no—
19C22⋊C8×C107C2212yescomplemented
20C23×D107—21no—
21C23×D107—21no—
22C23×D107—24no—
23C23×D107—42no—
24C23×D107—42no—
25C23×D107C2×C412yes—
26C22×Dic107—21no—
27C22×Dic107—21no—
28C22×Dic107—42no—
29C22×Dic107C2×C412yes—
30#13133802—42no—
31C2×C107⋊C8—22no—
32(C2×D107)⋊C4—22no—
33(C2×D107)⋊C4—22no—
34(C2×D107)⋊C4—22no—
35(C2×D107)⋊C4—22no—
36C24×C107C2×C411yescharacteristic
37C22×C4×C107—42no—
38C22×C4×C107C2×C411yescharacteristic
39C22×C4×C107D411yescharacteristic
40C22×C4×C107D411yescharacteristic
41C22×C4×C107D411yescharacteristic
42C22×C4×C107D411yescharacteristic
43C22×C4×C107C2311yescharacteristic
44M16×C107—42no—
45C2×C8×C107—22no—
46C23×C107—22no—
47C23×C107—22no—
48C23×C107—22no—
49C23×C107C22⋊C411yescharacteristic
50C23×C107C22⋊C411yescharacteristic
51C23×C107C22×C411yescharacteristic
52C22×D107—24no—
53C22×D107—24no—
54C22×D107—22no—
55C22×D107—22no—
56C22×D107—416no—
57C22×D107—42no—
58C22×D107—42no—
59C22×D107—42no—
60C22×D107—42no—
61C22×D107—42no—
62C22×D107—42no—
63C22×D107M1614yescomplemented
64C2×C4×C107—22no—
65C2×C4×C107—22no—
66C2×C4×C107—41no—
67C2×C4×C107—41no—
68C2×C4×C107—41no—
69C2×C4×C107—41no—
70C2×C4×C107C22⋊C411yescharacteristic
71C2×C4×C107C22⋊C411yescharacteristic
72C2×C4×C107C2×D411yescharacteristic
73C2×C4×C107C2×D411yescharacteristic
74C2×Dic107—22no—
75C2×Dic107—42no—
76C2×Dic107—42no—
77C2×Dic107—42no—
78C8×C107—42no—
79C107⋊C8—42no—
80C22×C107—28no—
81C22×C107—21no—
82C22×C107—21no—
83C22×C107—21no—
84C22×C107—21no—
85C22×C107—21no—
86C22×C107—21no—
87C22×C107#9912yes—
88C22×C107#10012yes—
89C22×C107C2×C22⋊C411yescharacteristic
90C22×C107C2×M1612yes—
91C2×D107—24no—
92C2×D107—48no—
93C2×D107—48no—
94C2×D107—44no—
95C2×D107—42no—
96C2×D107—42no—
97C2×D107—44no—
98C4×C107—21no—
99C4×C107—21no—
100C4×C107—21no—
101C4×C107—21no—
102Dic107—42no—
103C2×C107—22no—
104C2×C107—22no—
105C2×C107—22no—
106C2×C107#40711yescharacteristic
107C2×C107C2×#9911yescharacteristic
108C2×C107C2×#10011yescharacteristic
109D107—44no—
110#1462—1071nomaximal, Sylow
111C107#146211yescharacteristic, complemented, Sylow
112C22×C22⋊C4—1071no—
113#407—1071no—
114#407D10711yescharacteristic, complemented
115#323—1074no—
116C25—1071no—
117C23×C4—1071no—
118C23×C4C2×D10711yescharacteristic
119C2×M16—21no—
120C2×M16—2141no—
121C2×C22⋊C4—1072no—
122C2×C22⋊C4—1072no—
123C2×C22⋊C4—2141no—
124C2×C22⋊C4—2141no—
125C2×C22⋊C4—2141no—
126C2×C22⋊C4—2141no—
127C22⋊C8—21no—
128C22⋊C8—1072no—
129C22⋊C8—2141no—
130C22⋊C8C2×D10712yescomplemented
131C24—1072no—
132C24—4282no—
133C24—4282no—
134C24—2144no—
135C24—2141no—
136C24—2141no—
137C24C4×D10711yescharacteristic
138C22×C4—42no—
139C22×C4—1072no—
140C22×C4—4282no—
141C22×C4—2141no—
142C22×C4—2141no—
143C22×C4C4×D10711yescharacteristic
144C22×C4D42811yescharacteristic
145C22×C4D42811yescharacteristic
146C22×C4C22⋊D10711yescharacteristic
147C22×C4C22⋊D10711yescharacteristic
148C22×C4C22×D10711yescharacteristic
149M16—42no—
150M16—4282no—
151C2×C8—22no—
152C2×C8—2142no—
153C22⋊C4—2142no—
154C22⋊C4—2142no—
155C22⋊C4—2142no—
156C22⋊C4—2142no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—1074no—
161C23—4282no—
162C23—4282no—
163C23—42816no—
164C23—4282no—
165C23—4282no—
166C23—4282no—
167C23—4282no—
168C23—2144no—
169C23—2144no—
170C23—2142no—
171C23—2142no—
172C23(C2×D107)⋊C411yescharacteristic
173C23(C2×D107)⋊C411yescharacteristic
174C23C2×C4×D10711yescharacteristic
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—4282no—
182C2×C4—4282no—
183C2×C4—4282no—
184C2×C4—2142no—
185C2×C4(C2×D107)⋊C411yescharacteristic
186C2×C4(C2×D107)⋊C411yescharacteristic
187C2×C4C2×C22⋊D10711yescharacteristic
188C2×C4C2×D42811yescharacteristic
189C8—42no—
190C8—4282no—
191C22—28no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—4284no—
199C22—4284no—
200C22—4288no—
201C22—4288no—
202C22—4282no—
203C22—4282no—
204C22—2144no—
205C22#1681202312yes—
206C22#1681202512yes—
207C22C2×(C2×D107)⋊C411yescharacteristic
208C22M16×D10712yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—4282no—
214C2—22no—
215C2—22no—
216C2—22no—
217C2—4284no—
218C2#2029259011yescharacteristic
219C2C2×#1681202311yescharacteristic
220C2C2×#1681202511yescharacteristic
subgroupG/H
centerC22C2×(C2×D107)⋊C4
commutatorC23×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#407×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC24×D107C4
cosocleC22×C4×C107C23
hypercenter#407D107
hypocenterC107#1462
LCSG ▷ C23×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #20292591C2semidirect
3. #20292350C2semidirect
4. #407×C107C2semidirect
15. C22⋊(C107⋊C8)C22semidirect
19. C22⋊C8×C107C22semidirect
63. C22×D107M16semidirect
111. C107#1462semidirect
114. #407D107semidirect
130. C22⋊C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D107)⋊C42
#202925912
#202923502
#407×C1072
#1462107