Finite Group Databasebeta

← #37532945

Subgroups — #37532945

Order 23168.

200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×Dic362C211yesmaximal, characteristic
2#26041630C211yesmaximal, characteristic
3#26041564C211yesmaximal, characteristic
4#26041490C211yesmaximal, characteristic
5#26041027C211yesmaximal, characteristic
6#26041011C211yesmaximal, characteristic
7Q8⋊C8×C181C211yesmaximal, characteristic
8C2×Dic724—21no—
9#19153816—21no—
10#19153816C2211yescharacteristic
11#19153816C2211yescharacteristic
12#19153815—22no—
13#19153815—21no—
14Q8×Dic181—21no—
15C4×Dic362—21no—
16C4×Dic362C2211yescharacteristic
17#19153747—21no—
18C4⋊#13089678C2211yescharacteristic
19#19153741—22no—
20#19153741—21no—
21#19153740—21no—
22C4×Q8×C181C2211yescharacteristic
23C4⋊C8×C181C2211yescharacteristic
24C4×C8×C181C2211yescharacteristic
25C2×Dic362—22no—
26C2×Dic362—21no—
27C2×Dic362D411yescharacteristic
28C2×Dic362D412yes—
29Dic724—42no—
30C2×#13089678—21no—
31C4⋊Dic181—22no—
32C4⋊Dic181—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181—21no—
35C4⋊Dic181—21no—
36C4⋊Dic181D411yescharacteristic
37#15668428—22no—
38#15668428—21no—
39C4×Dic181—22no—
40C4×Dic181—21no—
41C2×Q8×C181D411yescharacteristic
42C2×C8×C181—21no—
43C2×C8×C181—21no—
44C4⋊C4×C181—21no—
45C4⋊C4×C181D411yescharacteristic
46C42×C181—21no—
47C42×C181C2311yescharacteristic
48Dic362—21no—
49Dic362—42no—
50Dic362—41no—
51Dic362—41no—
52Dic362—82no—
53Dic362SD1612yes—
54C2×Dic181—21no—
55C2×Dic181—22no—
56C2×Dic181—21no—
57C2×Dic181—41no—
58#13089678—41no—
59Q8×C181—21no—
60Q8×C181Q1612yescomplemented
61C2×C4×C181—21no—
62C2×C4×C181—21no—
63C2×C4×C181C2×D411yescharacteristic
64C2×C4×C181C2×D411yescharacteristic
65C2×C4×C181C2×D411yescharacteristic
66C8×C181—41no—
67C8×C181—41no—
68C22×C181#12011yescharacteristic
69C4×C181—22no—
70C4×C181—21no—
71C4×C181—41no—
72C4×C181C2×SD1611yescharacteristic
73C4×C181C2×Q1611yescharacteristic
74C4×C181#13711yescharacteristic
75C4×C181#13711yescharacteristic
76Dic181—22no—
77Dic181—42no—
78Dic181—41no—
79Dic181—81no—
80C2×C181#44811yescharacteristic
81C2×C181#45111yescharacteristic
82C2×C181#45511yescharacteristic
83C181#164511yescharacteristic, complemented, Sylow
84#1645—1811nomaximal, Sylow
85Q82—1811no—
86#487—1811no—
87#475—1811no—
88#462—1811no—
89#333—1811no—
90Q8⋊C8—1811no—
91Q8⋊C8D18111yescharacteristic
92C2×Q16—3621no—
93C4⋊Q8—3621no—
94C4⋊Q8—3622no—
95C4⋊Q8—3621no—
96C4⋊Q8—1811no—
97C4⋊Q8—1811no—
98C4×Q8—3621no—
99C4×Q8—3621no—
100C4×Q8—1811no—
101C4×Q8C2×D18111yescharacteristic
102#106—3621no—
103C4⋊C8—1811no—
104C4⋊C8C2×D18111yescharacteristic
105#103—3622no—
106#103—3621no—
107#103—3621no—
108C4×C8C2×D18111yescharacteristic
109C2×Q8—3622no—
110C2×Q8—3621no—
111C2×Q8—1811no—
112C2×Q8—1812no—
113C2×Q8D72411yescharacteristic
114Q16—7242no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—3621no—
118C4⋊C4—21no—
119C4⋊C4—3622no—
120C4⋊C4—3622no—
121C4⋊C4—3621no—
122C4⋊C4—3621no—
123C4⋊C4—3621no—
124C4⋊C4—3621no—
125C4⋊C4—3621no—
126C4⋊C4—1811no—
127C4⋊C4D72411yescharacteristic
128C42—21no—
129C42—3622no—
130C42—3621no—
131C42C22×D18111yescharacteristic
132Q8—21no—
133Q8—3621no—
134Q8—14482no—
135Q8—1812no—
136Q8—7242no—
137Q8—7241no—
138Q8—7241no—
139Q8Dic72412yescomplemented
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—3621no—
143C2×C4—3622no—
144C2×C4—3621no—
145C2×C4—7241no—
146C2×C4D4×D18111yescharacteristic
147C2×C4D4×D18111yescharacteristic
148C2×C4C2×D72411yescharacteristic
149C8—41no—
150C8—41no—
151C8—7241no—
152C22#1915378611yescharacteristic
153C4—22no—
154C4—21no—
155C4—41no—
156C4—3622no—
157C4—14481no—
158C4—7241no—
159C4—7242no—
160C4SD16×D18111yescharacteristic
161C4C2×Dic72411yescharacteristic
162C4#1915384811yescharacteristic
163C4#1915384911yescharacteristic
164C2#2604141911yescharacteristic
165C2#2604143711yescharacteristic
166C2#2604145811yescharacteristic
subgroupG/H
centerC22#19153786
commutator, cosocleC42×C181C23
FrattiniC42C22×D181
FittingQ8⋊C8×C181C2
socle, prime radicalC22×C181#120
hypercenterQ8⋊C8D181
hypocenterC181#1645
LCSG ▷ C42×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
60. Q8×C181Q16semidirect
83. C181#1645semidirect
139. Q8Dic724semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic3622
#260416302
#260415642
#260414902
#260410272
#260410112
Q8⋊C8×C1812
#1645181