Finite Group Databasebeta

← #27193800

Subgroups — #27193800

Order 13184.

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

normal subgroups only

This group has 212 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
1#20268346C211yesmaximal, characteristic
2#20267843C211yesmaximal, characteristic
3C4⋊C8×D103C211yesmaximal, characteristic
4#20267539C211yesmaximal, characteristic, complemented
5#20267539C211yesmaximal, characteristic, complemented
6#20267537C211yesmaximal, characteristic, complemented
7#332×C103C211yesmaximal, characteristic, complemented
8C2×C8×D103—21no—
9#15693021C2211yescharacteristic
10#15693012—21no—
11#15693001C412yes—
12#15692997—21no—
13Q8×Dic103—21no—
14#15692986C412yes—
15#15692979—21no—
16C42×D103C2211yescharacteristic
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19Dic103⋊C8—21no—
20(C2×D103)⋊C8—21no—
21C8×Dic103—21no—
22C4⋊Q8×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24C4⋊C8×C103C2211yescharacteristic
25C2×Dic206C2×C412yes—
26C2×C4×D103C2×C411yescharacteristic
27C2×C4×D103D411yescharacteristic
28C2×C4×D103D411yescharacteristic
29C2×C103⋊C8—21no—
30C2×C103⋊C8—21no—
31C8×D103—42no—
32C4⋊Dic103—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103—22no—
35Dic103⋊C4—22no—
36(C2×D103)⋊C4—22no—
37C4×Dic103—22no—
38C4×Dic103C2×C411yescharacteristic
39C4×Dic103D411yescharacteristic
40C4×Dic103D411yescharacteristic
41C2×Q8×C103—21no—
42C2×C8×C103—21no—
43C2×C8×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103C2×C412yes—
46C42×C103C2311yescharacteristic
47C22×D103C22⋊C411yescharacteristic
48Q8×C103—41no—
49Q8×C103—41no—
50C2×C4×C103—22no—
51C2×C4×C103C22×C411yescharacteristic
52C2×C4×C103C2×D411yescharacteristic
53C2×C4×C103C2×D411yescharacteristic
54C2×Dic103—22no—
55C2×Dic103C22⋊C411yescharacteristic
56C2×Dic103C22⋊C411yescharacteristic
57C2×Dic103C22⋊C411yescharacteristic
58C4×D103—21no—
59C4×D103—21no—
60C4×D103—41no—
61C4×D103SD1612yes—
62C4×D103Q1612yes—
63Dic206—42no—
64C8×C103—41no—
65C8×C103—41no—
66C103⋊C8—41no—
67C103⋊C8—41no—
68C22×C103C2×C22⋊C411yescharacteristic
69C2×D103—21no—
70C2×D103—21no—
71C2×D103#10312yes—
72C4×C103—21no—
73C4×C103—42no—
74C4×C103C2×SD1611yescharacteristic
75C4×C103C2×Q1611yescharacteristic
76C4×C103#13511yescharacteristic
77C4×C103#13511yescharacteristic
78Dic103—21no—
79Dic103—21no—
80Dic103—42no—
81Dic103#10312yes—
82C2×C103#41311yescharacteristic
83C2×C103C2×#10311yescharacteristic
84C2×C103#41611yescharacteristic
85D103—22no—
86#1542—1031nomaximal, Sylow
87C103#154211yescharacteristic, complemented, Sylow
88#533—1031no—
89#431—1031no—
90C2×C4⋊C8—1031no—
91#333—1031no—
92#333—1031no—
93#332—1031no—
94#332D10311yescharacteristic, complemented
95C22×C8—2061no—
96C4⋊Q8—1031no—
97C4⋊Q8C2×D10311yescharacteristic
98#125—2061no—
99C22⋊Q8—1032no—
100C22⋊Q8—2061no—
101C4×Q8—1032no—
102C4×Q8—2061no—
103#117—2061no—
104C2×C42—1031no—
105C4⋊C8—1031no—
106C4⋊C8—1031no—
107C4⋊C8—2061no—
108C4⋊C8C2×D10311yescharacteristic
109C4⋊C8C2×D10311yescharacteristic
110C22⋊C8—2061no—
111C4×C8—2061no—
112C2×Q8—21no—
113C2×Q8—1032no—
114C22×C4—1031no—
115C22×C4—1031no—
116C22×C4—1031no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—4122no—
120C2×C8—2061no—
121C2×C8—2061no—
122C4⋊C4—21no—
123C4⋊C4—2062no—
124C4⋊C4—2062no—
125C4⋊C4—2061no—
126C4⋊C4—2061no—
127C4⋊C4C4×D10312yes—
128C22⋊C4—2062no—
129C42—1031no—
130C42—1031no—
131C42—1031no—
132C42—2062no—
133C42C22×D10311yescharacteristic
134C23—1031no—
135Q8—41no—
136Q8—41no—
137Q8—4122no—
138C2×C4—22no—
139C2×C4—1031no—
140C2×C4—1032no—
141C2×C4—1032no—
142C2×C4—1031no—
143C2×C4—1031no—
144C2×C4—4121no—
145C2×C4—2062no—
146C2×C4—2061no—
147C2×C4—2061no—
148C2×C4C2×C4×D10311yescharacteristic
149C2×C4D4×D10311yescharacteristic
150C2×C4D4×D10311yescharacteristic
151C8—41no—
152C8—41no—
153C8—4121no—
154C8—4121no—
155C22—1032no—
156C22—2061no—
157C22—2061no—
158C22C22⋊C4×D10311yescharacteristic
159C4—21no—
160C4—42no—
161C4—1032no—
162C4—4122no—
163C4—2061no—
164C4—2061no—
165C4SD16×D10311yescharacteristic
166C4Q16×D10311yescharacteristic
167C4#1569304011yescharacteristic
168C4#1569304211yescharacteristic
169C2—2062no—
170C2#2026777411yescharacteristic
171C2#103×D10311yescharacteristic
172C2#2026778411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#332×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC22×D103C22⋊C4
cosocleC42×C103C23
hypercenter#332D103
hypocenterC103#1542
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #20267539C2semidirect
5. #20267539C2semidirect
6. #20267537C2semidirect
7. #332×C103C2semidirect
87. C103#1542semidirect
94. #332D103semidirect

Maximal subgroups

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

subgroupindex
#202683462
#202678432
C4⋊C8×D1032
#202675392
#202675372
#332×C1032
#1542103