Finite Group Databasebeta

← #37549153

Subgroups — #37549153

Order 23168.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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#26042297C211yesmaximal, characteristic
2#26042223C211yesmaximal, characteristic
3#26042132C214yesmaximal
4#26041834C211yesmaximal, characteristic
5C2×C4⋊#10624382—21no—
6#19153883—21no—
7#19153873C2212yes—
8C4×#13089685—21no—
9(C2×#10624382)⋊C4—21no—
10(C2×#10624382)⋊C4C2212yes—
11#19153816C411yescharacteristic, complemented
12#19153807—21no—
13#19153796C2212yes—
14#19153792—21no—
15Q8×Dic181—21no—
16#19153781C412yescomplemented
17#19153774—21no—
18C42×D181C2211yescharacteristic
19C4⋊Q8×C181C411yescharacteristic, complemented
20C22×#10624382—22no—
21C2×#13089685—22no—
22C4⋊#10624382—42no—
23C2×Dic362C2×C412yes—
24C2×C4×D181D411yescharacteristic
25C2×C4×D181D411yescharacteristic
26C2×C4×D181C2311yescharacteristic
27C4⋊Dic181—22no—
28C4⋊Dic181—21no—
29C4⋊Dic181—21no—
30#15668428—22no—
31#15668426—22no—
32C4×Dic181—22no—
33C4×Dic181C2×C411yescharacteristic
34C4×Dic181D411yescharacteristic
35C4×Dic181D411yescharacteristic
36C2×Q8×C181—21no—
37C4⋊C4×C181—21no—
38C4⋊C4×C181C2×C412yes—
39C42×C181C2×C411yescharacteristic
40C2×#10624382—42no—
41C2×#10624382—42no—
42C2×#10624382—42no—
43#13089685—42no—
44C22×D181C2×D411yescharacteristic
45Dic362—42no—
46C2×Dic181—22no—
47C2×Dic181C22⋊C411yescharacteristic
48C2×Dic181C22⋊C411yescharacteristic
49C2×Dic181C2×D411yescharacteristic
50C4×D181—41no—
51C4×D181—41no—
52C4×D181SD1612yes—
53C4×D181Q1612yes—
54Q8×C181—42no—
55C2×C4×C181—22no—
56C2×C4×C181C22⋊C411yescharacteristic
57C2×C4×C181C22⋊C411yescharacteristic
58C2×C4×C181C22×C411yescharacteristic
59C22×C181C2×C22⋊C411yescharacteristic
60C2×D181—21no—
61C2×D181—21no—
62C2×D181C2×SD1611yescharacteristic
63C2×D181C2×Q1611yescharacteristic
64#10624382—82no—
65C4×C181—21no—
66C4×C181—21no—
67C4×C181—42no—
68C4×C181#10312yes—
69Dic181—21no—
70Dic181—21no—
71Dic181—42no—
72Dic181#10312yes—
73C2×C181#41011yescharacteristic
74C2×C181C2×#10311yescharacteristic
75C2×C181#42111yescharacteristic
76D181—21no—
77D181—21no—
78C181#151811yescharacteristic, complemented, Sylow
79#1518—1811nomaximal, Sylow
80#533—1811no—
81#431—1811no—
82#382—1811no—
83#328—1814no—
84C4⋊Q8—1811no—
85C4⋊Q8#1062438211yescharacteristic, complemented
86#125—3621no—
87C22⋊Q8—3621no—
88C22⋊Q8—1812no—
89C4×Q8—3621no—
90C4×Q8—1812no—
91#117—3621no—
92C2×C4⋊C4—3621no—
93C2×C42—1811no—
94C4⋊C8—3621no—
95C22⋊C8—1812no—
96C4×C8—3621no—
97#95—3621no—
98#95—1812no—
99C2×Q8—21no—
100C2×Q8—1812no—
101C22×C4—3622no—
102C22×C4—1811no—
103C22×C4—1811no—
104C22×C4—1811no—
105C2×C8—3622no—
106C4⋊C4—21no—
107C4⋊C4—3622no—
108C4⋊C4—3622no—
109C4⋊C4—3621no—
110C4⋊C4—3621no—
111C4⋊C4—7242no—
112C4⋊C4C2×#1062438212yes—
113C22⋊C4—3622no—
114C42—3622no—
115C42—1811no—
116C42—1811no—
117C42—1811no—
118C42C2×#1062438211yescharacteristic
119C23—1811no—
120Q8—42no—
121Q8—7242no—
122C2×C4—22no—
123C2×C4—3622no—
124C2×C4—1811no—
125C2×C4—1811no—
126C2×C4—1811no—
127C2×C4—1812no—
128C2×C4—1812no—
129C2×C4—7241no—
130C2×C4—7241no—
131C2×C4—7242no—
132C2×C4—7242no—
133C2×C4—7242no—
134C2×C4C22⋊#1062438211yescharacteristic
135C2×C4C22⋊#1062438211yescharacteristic
136C2×C4C22×#1062438211yescharacteristic
137C8—7242no—
138C22—3621no—
139C22—3621no—
140C22—1811no—
141C22—1811no—
142C22C2×C22⋊#1062438211yescharacteristic
143C4—21no—
144C4—21no—
145C4—42no—
146C4—3621no—
147C4—3621no—
148C4—14482no—
149C4—1812no—
150C4—7242no—
151C4#1915387912yes—
152C2—3621no—
153C2—3621no—
154C2#2604226011yescharacteristic
155C2C2×#1915387911yescharacteristic
156C2#2604227711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4⋊Q8×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC22×D181C2×D4
cosocleC2×C4×D181C23
hypercenterC4⋊Q8#10624382
hypocenterC181#1518
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #19153816C4semidirect
16. #19153781C4semidirect
19. C4⋊Q8×C181C4semidirect
78. C181#1518semidirect
85. C4⋊Q8#10624382semidirect

Maximal subgroups

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

subgroupindex
#260422972
#260422232
#260421322
#260418342
#1518181