Finite Group Databasebeta

← #27196452

Subgroups — #27196452

Order 13184.

360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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×Dic103⋊C8C211yesmaximal, characteristic, complemented
2C2×#15692942C212yesmaximal, complemented
3#20267694C212yesmaximal, complemented
4#20267554C211yesmaximal, characteristic, complemented
5C22×D8×C103C211yesmaximal, characteristic
6C22×C103⋊C8C2211yescharacteristic
7C2×C4⋊Dic103C2212yes—
8C2×C22⋊Dic103—22no—
9C2×C22⋊Dic103—22no—
10C2×C4×Dic103C2211yescharacteristic
11Dic103⋊C8—22no—
12#15692942—24no—
13C22×D4×C103C2212yes—
14C2×D8×C103—24no—
15C2×D8×C103—22no—
16C22×C8×C103C2211yescharacteristic
17C22×Dic103—22no—
18C22×Dic103D411yescharacteristic
19C22×Dic103D411yescharacteristic
20C2×C103⋊C8—22no—
21C2×C103⋊C8—21no—
22C4⋊Dic103—22no—
23C4⋊Dic103—22no—
24C22⋊Dic103—44no—
25C22⋊Dic103—44no—
26C4×Dic103—21no—
27C4×Dic103—21no—
28C24×C103—22no—
29C2×D4×C103—22no—
30C2×D4×C103—22no—
31C2×D4×C103—22no—
32C2×D4×C103—22no—
33C2×D4×C103—22no—
34C2×D4×C103D414yes—
35C22×C4×C103C2311yescharacteristic
36D8×C103—28no—
37C2×C8×C103—22no—
38C2×C8×C103D412yes—
39C23×C103—24no—
40C23×C103—42no—
41C23×C103—42no—
42C23×C103—42no—
43C23×C103—42no—
44C23×C103—42no—
45C23×C103—42no—
46C23×C103C2×D411yescharacteristic
47D4×C103—24no—
48D4×C103—24no—
49D4×C103—42no—
50D4×C103—42no—
51C2×C4×C103C2×D412yes—
52C2×C4×C103C2×D411yescharacteristic
53C2×C4×C103#4111yescharacteristic
54C2×C4×C103#4112yes—
55C2×Dic103—21no—
56C2×Dic103—21no—
57C2×Dic103—21no—
58C2×Dic103—22no—
59C2×Dic103—42no—
60C2×Dic103—42no—
61C2×Dic103—42no—
62C2×Dic103D812yescomplemented
63C8×C103—22no—
64C103⋊C8—41no—
65C22×C103—44no—
66C22×C103—44no—
67C22×C103—44no—
68C22×C103—82no—
69C22×C103—82no—
70C22×C103—82no—
71C22×C103—82no—
72C22×C103#12111yescharacteristic
73C22×C103#12112yes—
74C22×C103C2×D811yescharacteristic
75C22×C103#13511yescharacteristic
76C22×C103AGL(1,ℤ/8)12yes—
77C4×C103#12011yescharacteristic
78C4×C103#12312yes—
79C4×C103#12411yescharacteristic
80Dic103—22no—
81Dic103—41no—
82Dic103—82no—
83C2×C103—84no—
84C2×C103#39411yescharacteristic
85C2×C103#45912yes—
86C2×C103#46312yes—
87C2×C103#46611yescharacteristic
88C2×C103#46911yescharacteristic
89#2054—1031nomaximal, Sylow
90C103#205411yescharacteristic, complemented, Sylow
91C22×D8D10311yescharacteristic
92C2×C4⋊C8—1031no—
93C2×#102—1032no—
94#390—1032no—
95#340—1031no—
96C22×D4C2×D10312yes—
97C2×D8—24no—
98C2×D8—22no—
99C22×C8—1031no—
100C22×C8C2×D10311yescharacteristic
101C2×C4⋊C4—1032no—
102C2×C22⋊C4—2062no—
103C2×C22⋊C4—2062no—
104C2×C42—1031no—
105C4⋊C8—2062no—
106#102—2064no—
107C24—22no—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4—22no—
112C2×D4—22no—
113C2×D4C22⋊D10314yes—
114C22×C4—1031no—
115C22×C4—1031no—
116C22×C4—2062no—
117C22×C4C22×D10311yescharacteristic
118D8—28no—
119C2×C8—22no—
120C2×C8—2062no—
121C2×C8—2061no—
122C2×C8C22⋊D10312yes—
123C4⋊C4—2062no—
124C4⋊C4—2062no—
125C22⋊C4—4124no—
126C22⋊C4—4124no—
127C42—2061no—
128C42—2061no—
129C23—24no—
130C23—42no—
131C23—42no—
132C23—42no—
133C23—42no—
134C23—42no—
135C23—42no—
136C23D4×D10311yescharacteristic
137D4—24no—
138D4—24no—
139D4—42no—
140D4—42no—
141C2×C4—1032no—
142C2×C4—4122no—
143C2×C4—4122no—
144C2×C4—4122no—
145C2×C4—2061no—
146C2×C4—2062no—
147C2×C4—2061no—
148C2×C4—2061no—
149C2×C4C2×C22⋊D10312yes—
150C2×C4C2×C22⋊D10311yescharacteristic
151C2×C4#1311010411yescharacteristic
152C2×C4#1311010412yes—
153C8—22no—
154C8—4121no—
155C22—44no—
156C22—44no—
157C22—44no—
158C22—82no—
159C22—82no—
160C22—82no—
161C22—82no—
162C22#1569299211yescharacteristic
163C22#1569299312yes—
164C22D8×D10311yescharacteristic
165C22#1569304011yescharacteristic
166C22#1569304512yes—
167C4—8242no—
168C4—4121no—
169C4—2062no—
170C4#1569299011yescharacteristic
171C4#1569300212yes—
172C4#1569300811yescharacteristic
173C2—84no—
174C2#2026770511yescharacteristic
175C2#2026798412yes—
176C2#2026800412yes—
177C2#2026802411yescharacteristic
178C2#2026804111yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting, prime radicalC22×D8×C103C2
socleC23×C103C2×D4
hypercenterC22×D8D103
hypocenterC103#2054
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×Dic103⋊C8C2semidirect
2. C2×#15692942C2semidirect
3. #20267694C2semidirect
4. #20267554C2semidirect
62. C2×Dic103D8semidirect
90. C103#2054semidirect

Maximal subgroups

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

subgroupindex
C2×Dic103⋊C82
C2×#156929422
#202676942
#202675542
C22×D8×C1032
#2054103