Finite Group Databasebeta

← #28336897

Subgroups — #28336897

Order 13696.

412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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×#13133802C211yesmaximal, characteristic, complemented
2C2×#16812083C211yesmaximal, characteristic
3C2×#16812029C212yesmaximal, complemented
4#20292389C212yesmaximal, complemented
5#380×C107C211yesmaximal, characteristic, complemented
6C22×D428C2211yescharacteristic
7C22×C22⋊D107—21no—
8C2×#13133802—24no—
9C2×#13133802—22no—
10C22×C107⋊C8C2212yes—
11#16812083—22no—
12#16812083C414yescomplemented
13C2×C4⋊Dic107C2211yescharacteristic
14C2×(C2×D107)⋊C4—21no—
15#16812029—24no—
16C23×C4×C107C2211yescharacteristic
17C2×C4⋊C4×C107C2212yes—
18C2×C22⋊C4×C107—21no—
19#95×C107—21no—
20C23×D107—21no—
21C2×D428—22no—
22C2×D428—22no—
23C2×D428—21no—
24C2×D428C2×C412yes—
25C2×C22⋊D107—24no—
26C2×C22⋊D107—44no—
27C22×Dic107—21no—
28#13133802—28no—
29C2×C107⋊C8—22no—
30C2×C107⋊C8—22no—
31C2×C107⋊C8D414yescomplemented
32C4⋊Dic107—21no—
33C4⋊Dic107C2×C412yes—
34(C2×D107)⋊C4—24no—
35C24×C107D411yescharacteristic
36C22×C4×C107—22no—
37C22×C4×C107—22no—
38C22×C4×C107—22no—
39C22×C4×C107C2×C412yes—
40C22×C4×C107D412yes—
41C22×C4×C107D411yescharacteristic
42C22×C4×C107C2311yescharacteristic
43C4⋊C4×C107—22no—
44C4⋊C4×C107—22no—
45C22⋊C4×C107—42no—
46C23×C107—22no—
47C23×C107—21no—
48C23×C107—22no—
49C23×C107—21no—
50C23×C107C22⋊C412yes—
51C23×C107C2×D411yescharacteristic
52C22×D107—22no—
53C22×D107—42no—
54C22×D107—42no—
55C22×D107—41no—
56C22×D107—41no—
57C2×C4×C107—22no—
58C2×C4×C107—24no—
59C2×C4×C107—22no—
60C2×C4×C107—22no—
61C2×C4×C107—42no—
62C2×C4×C107—42no—
63C2×C4×C107—42no—
64C2×C4×C107C22⋊C412yes—
65C2×C4×C107C22×C411yescharacteristic
66C2×C4×C107C2×D412yes—
67C2×C4×C107C2×D411yescharacteristic
68C2×C4×C107#4112yes—
69C22⋊D107—48no—
70C2×Dic107—22no—
71C2×Dic107—42no—
72D428—24no—
73D428—41no—
74D428—41no—
75C107⋊C8—24no—
76C22×C107—22no—
77C22×C107—22no—
78C22×C107—22no—
79C22×C107—42no—
80C22×C107—42no—
81C22×C107C2×C22⋊C411yescharacteristic
82C22×C107#12112yes—
83C22×C107AGL(1,ℤ/8)12yes—
84C22×C107AGL(1,ℤ/8)11yescharacteristic
85C22×C107#13711yescharacteristic
86C2×D107—42no—
87C2×D107—42no—
88C2×D107—42no—
89C2×D107—82no—
90C2×D107—82no—
91C4×C107—22no—
92C4×C107—82no—
93C4×C107C4×D412yes—
94C4×C107#12011yescharacteristic
95C4×C107#12311yescharacteristic
96Dic107—42no—
97C2×C107—42no—
98C2×C107#38611yescharacteristic
99C2×C107#41711yescharacteristic
100C2×C107#41811yescharacteristic
101C2×C107#46812yes—
102C2×C107#46912yes—
103D107—82no—
104#1895—1071nomaximal, Sylow
105C107#189511yescharacteristic, complemented, Sylow
106C22×M16—1071no—
107C2×#121—1071no—
108C2×#102—1072no—
109#380D10711yescharacteristic, complemented
110#340—1072no—
111C22×D4—1071no—
112C22×D4—2141no—
113C23×C4C2×D10711yescharacteristic
114C2×M16—2144no—
115C2×M16—2142no—
116C22×C8—1072no—
117#121—1074no—
118#121—2142no—
119C2×C4⋊C4—1071no—
120C2×C4⋊C4C2×D10712yes—
121C2×C22⋊C4—21no—
122C2×C22⋊C4—2141no—
123#102—2144no—
124#95—21no—
125C24—2141no—
126C24C22⋊D10711yescharacteristic
127C2×D4—1072no—
128C2×D4—4284no—
129C2×D4—2144no—
130C2×D4—2142no—
131C2×D4—2141no—
132C2×D4—2142no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—2141no—
137C22×C4C4×D10712yes—
138C22×C4D42812yes—
139C22×C4C22⋊D10711yescharacteristic
140C22×C4C22×D10711yescharacteristic
141M16—2148no—
142C2×C8—1074no—
143C2×C8—2142no—
144C2×C8—2142no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C4⋊C4—1072no—
148C4⋊C4—2141no—
149C22⋊C4—42no—
150C22⋊C4—2144no—
151C23—22no—
152C23—22no—
153C23—21no—
154C23—21no—
155C23—4282no—
156C23—4282no—
157C23—4281no—
158C23—4281no—
159C23—2142no—
160C23(C2×D107)⋊C412yes—
161C23C2×C22⋊D10711yescharacteristic
162D4—4288no—
163D4—4281no—
164D4—4281no—
165D4—2144no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—4282no—
174C2×C4—2142no—
175C2×C4(C2×D107)⋊C412yes—
176C2×C4C2×C4×D10711yescharacteristic
177C2×C4D4×D10712yes—
178C2×C4C2×D42811yescharacteristic
179C2×C4#1313381712yes—
180C8—2144no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—8562no—
187C22—8562no—
188C22—4282no—
189C22—4282no—
190C22—4282no—
191C22C2×(C2×D107)⋊C411yescharacteristic
192C22#1681208112yes—
193C22#1681213412yes—
194C22#1681213511yescharacteristic
195C22#1681214011yescharacteristic
196C4—22no—
197C4—82no—
198C4—4282no—
199C4(C22⋊D107)⋊C412yes—
200C4#1681207911yescharacteristic
201C4#1681209311yescharacteristic
202C2—42no—
203C2—8562no—
204C2#2029250411yescharacteristic
205C2#2029262611yescharacteristic
206C2#2029263111yescharacteristic
207C2#2029287512yes—
208C2#2029287812yes—
subgroupG/H
centerC23C2×C22⋊D107
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#380×C107C2
socleC23×C107C2×D4
prime radicalC2×#16812083C2
cosocleC22×C4×C107C23
hypercenter#380D107
hypocenterC107#1895
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C22×#13133802C2semidirect
3. C2×#16812029C2semidirect
4. #20292389C2semidirect
5. #380×C107C2semidirect
12. #16812083C4semidirect
31. C2×C107⋊C8D4semidirect
105. C107#1895semidirect
109. #380D107semidirect

Maximal subgroups

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

subgroupindex
C22×#131338022
C2×#168120832
C2×#168120292
#202923892
#380×C1072
#1895107