Finite Group Databasebeta

← #27194417

Subgroups — #27194417

Order 13184.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#20268511C211yesmaximal, characteristic
2#20268189C211yesmaximal, characteristic, complemented
3#20268071C211yesmaximal, characteristic
4#20268002C211yesmaximal, characteristic, complemented
5#20267536C211yesmaximal, characteristic, complemented
6#20267523C211yesmaximal, characteristic, complemented
7D4⋊C8×C103C211yesmaximal, characteristic
8C2×Dic412—21no—
9#15693021C2211yescharacteristic
10#15693021C2211yescharacteristic
11#15693014—22no—
12#15693008—21no—
13#15693000—21no—
14C4×Dic206C2211yescharacteristic
15#15692986—21no—
16#15692980—21no—
17#15692954—21no—
18#15692953—22no—
19C4⋊(C103⋊C8)C2211yescharacteristic
20#15692946—21no—
21#15692942—21no—
22C4×D4×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24C4×C8×C103C2211yescharacteristic
25C2×Dic206—21no—
26C2×Dic206—21no—
27C2×Dic206D411yescharacteristic
28Dic412—42no—
29C2×C103⋊C8—21no—
30C4⋊Dic103—21no—
31C4⋊Dic103—21no—
32C4⋊Dic103—21no—
33C4⋊Dic103D411yescharacteristic
34C4⋊Dic103D412yes—
35Dic103⋊C4—22no—
36Dic103⋊C4—21no—
37C22⋊Dic103—22no—
38C22⋊Dic103—22no—
39C4×Dic103—22no—
40C4×Dic103—21no—
41C2×D4×C103D411yescharacteristic
42C22×C4×C103—21no—
43C2×C8×C103—21no—
44C2×C8×C103—21no—
45C4⋊C4×C103D411yescharacteristic
46C22⋊C4×C103—21no—
47C42×C103C2311yescharacteristic
48C23×C103—21no—
49D4×C103—21no—
50D4×C103—21no—
51C2×C4×C103—21no—
52C2×C4×C103—41no—
53C2×C4×C103—41no—
54C2×C4×C103C2×D411yescharacteristic
55C2×C4×C103C2×D411yescharacteristic
56C2×C4×C103C2×D411yescharacteristic
57C2×Dic103—21no—
58C2×Dic103—21no—
59C2×Dic103—22no—
60C2×Dic103—41no—
61Dic206—21no—
62Dic206—21no—
63Dic206—41no—
64Dic206—41no—
65Dic206—41no—
66Dic206—41no—
67C8×C103—22no—
68C8×C103—41no—
69C103⋊C8—41no—
70C22×C103—41no—
71C22×C103—41no—
72C22×C103—41no—
73C22×C103#12011yescharacteristic
74C4×C103—21no—
75C4×C103—41no—
76C4×C103#13511yescharacteristic
77C4×C103#13511yescharacteristic
78C4×C103AGL(1,ℤ/8)11yescharacteristic
79C4×C103#13711yescharacteristic
80Dic103—41no—
81Dic103—42no—
82Dic103—41no—
83Dic103—81no—
84C2×C103—81no—
85C2×C103#44911yescharacteristic
86C2×C103#45211yescharacteristic
87C2×C103#45611yescharacteristic
88#1652—1031nomaximal, Sylow
89C103#165211yescharacteristic, complemented, Sylow
90#556—1031no—
91#498—1031no—
92#474—1031no—
93#462—1031no—
94#332—1031no—
95Q8⋊C8—1031no—
96D4⋊C8D10311yescharacteristic
97C2×Q16—2061no—
98C4⋊Q8—1031no—
99C4⋊Q8—1031no—
100#126—2062no—
101#124—2061no—
102C22⋊Q8—2061no—
103C4×Q8—1031no—
104C4×Q8—2061no—
105C4×D4C2×D10311yescharacteristic
106#117—2061no—
107#107—2061no—
108#106—2062no—
109C4⋊C8—1031no—
110C4⋊C8C2×D10311yescharacteristic
111#103—2061no—
112#102—2061no—
113C4×C8C2×D10311yescharacteristic
114C2×Q8—1031no—
115C2×Q8—2061no—
116C2×Q8—2061no—
117C2×D4D41211yescharacteristic
118C22×C4—21no—
119Q16—4122no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—2061no—
123C4⋊C4—1031no—
124C4⋊C4—1032no—
125C4⋊C4—2062no—
126C4⋊C4—2061no—
127C4⋊C4—2061no—
128C4⋊C4—2061no—
129C4⋊C4—2061no—
130C4⋊C4D41211yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—2062no—
133C22⋊C4—2062no—
134C42—2062no—
135C42—2061no—
136C42C22×D10311yescharacteristic
137C23—21no—
138Q8—4121no—
139Q8—4121no—
140Q8—4121no—
141Q8—4121no—
142Q8—2061no—
143Q8—2061no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—4121no—
150C2×C4—2061no—
151C2×C4—2062no—
152C2×C4—2061no—
153C2×C4D4×D10311yescharacteristic
154C2×C4D4×D10311yescharacteristic
155C2×C4C2×D41211yescharacteristic
156C8—22no—
157C8—41no—
158C8—4121no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1569299111yescharacteristic
163C4—21no—
164C4—41no—
165C4—8241no—
166C4—4121no—
167C4—4122no—
168C4—4121no—
169C4#1569304211yescharacteristic
170C4#1569304311yescharacteristic
171C4#1569304511yescharacteristic
172C4#1569305411yescharacteristic
173C2—81no—
174C2#2026793711yescharacteristic
175C2#2026795511yescharacteristic
176C2#2026797511yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
FittingD4⋊C8×C103C2
socleC22×C103#120
prime radicalC2×D4×C103D4
hypercenterD4⋊C8D103
hypocenterC103#1652
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20268189C2semidirect
4. #20268002C2semidirect
5. #20267536C2semidirect
6. #20267523C2semidirect
89. C103#1652semidirect

Maximal subgroups

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

subgroupindex
#202685112
#202681892
#202680712
#202680022
#202675362
#202675232
D4⋊C8×C1032
#1652103