Finite Group Databasebeta

← #27193678

Subgroups — #27193678

Order 13184.

274 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 73 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×#15693000C211yesmaximal, characteristic
2#20267654C211yesmaximal, characteristic
3#20267529C214yesmaximal, complemented
4#407×C103C211yesmaximal, characteristic
5C22×Dic206C411yescharacteristic, complemented
6#15693000—21no—
7#15693000—21no—
8#15693000C412yescomplemented
9#15693000C2212yes—
10C2×C4⋊Dic103C411yescharacteristic, complemented
11C2×Dic103⋊C4—21no—
12C2×C22⋊Dic103—21no—
13C2×C22⋊Dic103—21no—
14C103⋊#95—21no—
15C103⋊#95C2212yes—
16C23×C4×C103C2211yescharacteristic
17C2×M16×C103—21no—
18C22⋊C8×C103—21no—
19C22⋊C8×C103C2212yes—
20C2×Dic206—21no—
21C2×Dic206—42no—
22C2×Dic206C2×C412yes—
23C22×Dic103—21no—
24C22×Dic103—21no—
25C22×Dic103—22no—
26C4⋊Dic103—21no—
27C4⋊Dic103C2×C412yes—
28Dic103⋊C4—22no—
29Dic103⋊C4—22no—
30C22⋊Dic103—22no—
31C22⋊Dic103—22no—
32C22⋊Dic103—42no—
33C24×C103D411yescharacteristic
34C22×C4×C103—42no—
35C22×C4×C103C2×C411yescharacteristic
36C22×C4×C103C2×C411yescharacteristic
37C22×C4×C103D411yescharacteristic
38C22×C4×C103D411yescharacteristic
39C22×C4×C103D411yescharacteristic
40C22×C4×C103C2311yescharacteristic
41M16×C103—42no—
42C2×C8×C103—22no—
43C23×C103—22no—
44C23×C103—22no—
45C23×C103—41no—
46C23×C103C22⋊C411yescharacteristic
47C23×C103C22⋊C411yescharacteristic
48C23×C103C2×D411yescharacteristic
49C2×C4×C103—22no—
50C2×C4×C103—22no—
51C2×C4×C103—41no—
52C2×C4×C103—41no—
53C2×C4×C103—41no—
54C2×C4×C103—41no—
55C2×C4×C103C22⋊C411yescharacteristic
56C2×C4×C103C22⋊C411yescharacteristic
57C2×C4×C103C22×C411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×Dic103—22no—
60C2×Dic103—22no—
61C2×Dic103—42no—
62C2×Dic103—42no—
63C2×Dic103—42no—
64C2×Dic103—42no—
65C2×Dic103—42no—
66Dic206—42no—
67Dic206—42no—
68C8×C103—42no—
69C22×C103—21no—
70C22×C103—21no—
71C22×C103—21no—
72C22×C103—21no—
73C22×C103—21no—
74C22×C103—21no—
75C22×C103—21no—
76C22×C103—44no—
77C22×C103#9912yes—
78C22×C103C2×C22⋊C411yescharacteristic
79C22×C103#13712yes—
80C4×C103—21no—
81C4×C103—21no—
82C4×C103—21no—
83C4×C103—21no—
84Dic103—42no—
85Dic103—42no—
86Dic103—82no—
87C2×C103—22no—
88C2×C103—22no—
89C2×C103—41no—
90C2×C103C2×#9911yescharacteristic
91C2×C103#41911yescharacteristic
92C2×C103#42111yescharacteristic
93#1511—1031nomaximal, Sylow
94C103#151111yescharacteristic, complemented, Sylow
95C2×C22⋊Q8—1031no—
96#407D10311yescharacteristic
97#381—1031no—
98#328—1034no—
99C22×Q8—1031no—
100C23×C4C2×D10311yescharacteristic
101C2×M16—21no—
102C22⋊Q8—1032no—
103C22⋊Q8—1032no—
104C22⋊Q8—2061no—
105C22⋊Q8—2061no—
106C2×C4⋊C4—1031no—
107C2×C4⋊C4—2061no—
108C2×C22⋊C4—2061no—
109C2×C22⋊C4—2061no—
110C22⋊C8—21no—
111C22⋊C8C2×D10312yes—
112#95—1032no—
113#95—2061no—
114C24D41211yescharacteristic
115C2×Q8—1032no—
116C2×Q8—4122no—
117C2×Q8—2061no—
118C22×C4—42no—
119C22×C4—2062no—
120C22×C4—2061no—
121C22×C4—2061no—
122C22×C4C4×D10311yescharacteristic
123C22×C4C4×D10311yescharacteristic
124C22×C4D41211yescharacteristic
125C22×C4C22⋊D10311yescharacteristic
126C22×C4C22⋊D10311yescharacteristic
127C22×C4C22×D10311yescharacteristic
128M16—42no—
129C2×C8—22no—
130C4⋊C4—1032no—
131C4⋊C4—2062no—
132C4⋊C4—2061no—
133C4⋊C4—2062no—
134C22⋊C4—4122no—
135C22⋊C4—2062no—
136C22⋊C4—2062no—
137C23—22no—
138C23—22no—
139C23—41no—
140C23(C2×D103)⋊C411yescharacteristic
141C23(C2×D103)⋊C411yescharacteristic
142C23C2×D41211yescharacteristic
143Q8—4122no—
144Q8—4122no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—4122no—
152C2×C4—4122no—
153C2×C4—4122no—
154C2×C4—4122no—
155C2×C4—4122no—
156C2×C4—2062no—
157C2×C4—2062no—
158C2×C4(C2×D103)⋊C411yescharacteristic
159C2×C4(C2×D103)⋊C411yescharacteristic
160C2×C4C2×C4×D10311yescharacteristic
161C2×C4C2×C22⋊D10311yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#1569293512yes—
172C22C2×(C2×D103)⋊C411yescharacteristic
173C22#1569305412yes—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—8242no—
179C4—4122no—
180C4—4122no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#1569293511yescharacteristic
185C2#2026780111yescharacteristic
186C2#2026780711yescharacteristic
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#407×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC24×C103D4
cosocleC22×C4×C103C23
hypercenter#407D103
hypocenterC103#1511
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #20267529C2semidirect
5. C22×Dic206C4semidirect
8. #15693000C4semidirect
10. C2×C4⋊Dic103C4semidirect
94. C103#1511semidirect

Maximal subgroups

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

subgroupindex
C2×#156930002
#202676542
#202675292
#407×C1032
#1511103