Finite Group Databasebeta

← #27194238

Subgroups — #27194238

Order 13184.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#20268519C211yesmaximal, characteristic, complemented
2#20268137C211yesmaximal, characteristic
3#20267988C211yesmaximal, characteristic
4#20267538C211yesmaximal, characteristic, complemented
5Q8⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6#20267521C211yesmaximal, characteristic, complemented
7#460×C103C211yesmaximal, characteristic
8C2×#13110093—21no—
9#15693021C2211yescharacteristic
10#15693019—21no—
11#15693013—21no—
12#15693011—22no—
13C4×Dic206—21no—
14C4×Dic206C2211yescharacteristic
15#15692986—21no—
16C4⋊(C103⋊C8)C2211yescharacteristic
17#15692942—22no—
18#15692942—21no—
19C4×C103⋊C8C2211yescharacteristic
20C2×SD16×C103—21no—
21#127×C103C2211yescharacteristic
22C4×Q8×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24#102×C103—21no—
25C2×Dic206—21no—
26C2×Dic206D411yescharacteristic
27#13110093—42no—
28C2×C103⋊C8—21no—
29C2×C103⋊C8—21no—
30C4⋊Dic103—21no—
31C4⋊Dic103D411yescharacteristic
32C4⋊Dic103D412yes—
33Dic103⋊C4—22no—
34Dic103⋊C4—22no—
35Dic103⋊C4—22no—
36Dic103⋊C4—21no—
37C4×Dic103—22no—
38C4×Dic103—21no—
39C2×Q8×C103D411yescharacteristic
40C2×D4×C103—21no—
41C2×D4×C103—21no—
42C2×D4×C103—21no—
43SD16×C103—42no—
44C2×C8×C103—21no—
45C4⋊C4×C103—21no—
46C4⋊C4×C103D411yescharacteristic
47C42×C103—21no—
48C42×C103C2311yescharacteristic
49C23×C103—41no—
50Q8×C103—21no—
51Q8×C103—21no—
52D4×C103—42no—
53D4×C103—41no—
54D4×C103—41no—
55D4×C103—41no—
56D4×C103—41no—
57C2×C4×C103—21no—
58C2×C4×C103—21no—
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×C4×C103C2×D411yescharacteristic
62C2×Dic103—21no—
63C2×Dic103—21no—
64C2×Dic103—22no—
65Dic206—21no—
66Dic206—41no—
67Dic206—41no—
68Dic206SD1612yescomplemented
69C8×C103—41no—
70C103⋊C8—41no—
71C103⋊C8—41no—
72C22×C103—81no—
73C22×C103—81no—
74C22×C103—81no—
75C22×C103#12011yescharacteristic
76C4×C103—21no—
77C4×C103—41no—
78C4×C103—41no—
79C4×C103C2×SD1611yescharacteristic
80C4×C103#13511yescharacteristic
81C4×C103AGL(1,ℤ/8)11yescharacteristic
82C4×C103#13711yescharacteristic
83Dic103—22no—
84Dic103—42no—
85Dic103—41no—
86C2×C103—161no—
87C2×C103#44811yescharacteristic
88C2×C103#44911yescharacteristic
89C2×C103#45411yescharacteristic
90#1626—1031nomaximal, Sylow
91C103#162611yescharacteristic, complemented, Sylow
92#557—1031no—
93#486—1031no—
94#460—1031no—
95#460D10311yescharacteristic
96#332—1031no—
97Q8⋊C8—1031no—
98Q8⋊C8—1031no—
99C2×SD16—21no—
100C2×SD16—2061no—
101C4⋊Q8—1031no—
102C4⋊Q8—2061no—
103#127C2×D10311yescharacteristic
104#125—2061no—
105#125—2062no—
106C4×Q8—1031no—
107C4×Q8—2061no—
108C4×Q8—2061no—
109C4×Q8C2×D10311yescharacteristic
110C4⋊C8—1031no—
111C4⋊C8C2×D10311yescharacteristic
112#102—21no—
113#102—2061no—
114#102—2062no—
115C4×C8—1031no—
116C2×Q8—1031no—
117C2×Q8—2061no—
118C2×Q8C22⋊D10311yescharacteristic
119C2×D4—21no—
120C2×D4—21no—
121C2×D4—21no—
122SD16—42no—
123SD16—4122no—
124C2×C8—21no—
125C2×C8—2061no—
126C2×C8—2061no—
127C4⋊C4—21no—
128C4⋊C4—1031no—
129C4⋊C4—1032no—
130C4⋊C4—2062no—
131C4⋊C4—2062no—
132C4⋊C4—2062no—
133C4⋊C4—2061no—
134C4⋊C4—2061no—
135C4⋊C4C22⋊D10311yescharacteristic
136C42—21no—
137C42—2062no—
138C42—2061no—
139C42C22×D10311yescharacteristic
140C23—41no—
141Q8—21no—
142Q8—21no—
143Q8—1032no—
144Q8—4121no—
145Q8—4121no—
146Q8—2061no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—2061no—
155C2×C4—2062no—
156C2×C4—2061no—
157C2×C4D4×D10311yescharacteristic
158C2×C4D4×D10311yescharacteristic
159C2×C4C2×C22⋊D10311yescharacteristic
160C8—41no—
161C8—4121no—
162C8—4121no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22#1569298911yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—4122no—
171C4—4121no—
172C4—2062no—
173C4SD16×D10311yescharacteristic
174C4#1569304111yescharacteristic
175C4#1569304711yescharacteristic
176C4#1569305011yescharacteristic
177C2—161no—
178C2#2026792811yescharacteristic
179C2#2026793411yescharacteristic
180C2#2026796211yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#460×C103C2
socleC22×C103#120
prime radical#127×C103C22
hypercenter#460D103
hypocenterC103#1626
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #20268519C2semidirect
4. #20267538C2semidirect
5. Q8⋊(C103⋊C8)C2semidirect
6. #20267521C2semidirect
68. Dic206SD16semidirect
91. C103#1626semidirect

Maximal subgroups

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

subgroupindex
#202685192
#202681372
#202679882
#202675382
Q8⋊(C103⋊C8)2
#202675212
#460×C1032
#1626103