Finite Group Databasebeta

← #37549175

Subgroups — #37549175

Order 23168.

270 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C4×#15668458C212yesmaximal, complemented
2#26042135C212yesmaximal, complemented
3#26042134C212yesmaximal, complemented
4#26041825C211yesmaximal, characteristic
5C2×#15668458—22no—
6#19153871C2214yes—
7C4×#13089685—22no—
8C2×#15668449C411yescharacteristic
9#19153814C411yescharacteristic
10#19153812C411yescharacteristic
11#19153805C2211yescharacteristic
12#19153803C2211yescharacteristic
13#19153788—22no—
14C4×C22⋊D181—22no—
15C2×C4×Dic181C2211yescharacteristic
16C2×#41×C181C411yescharacteristic
17#15668458—28no—
18C2×#13089685—24no—
19#15668449—42no—
20C2×Dic362C2×C411yescharacteristic
21C2×D724C2×C411yescharacteristic
22C2×C22⋊D181—22no—
23C2×C22⋊D181—21no—
24C22×Dic181D412yes—
25C2×C4×D181—21no—
26#15668428—22no—
27C22⋊Dic181—22no—
28#15668426—22no—
29C4×Dic181C2×C411yescharacteristic
30C4×Dic181D412yes—
31C4×Dic181C2311yescharacteristic
32#41×C181—42no—
33C2×Q8×C181C2×C411yescharacteristic
34C2×D4×C181—21no—
35C2×D4×C181C2×C411yescharacteristic
36C22×C4×C181—21no—
37C22×C4×C181C2×C411yescharacteristic
38#13089685—28no—
39C22×D181—21no—
40Dic362—41no—
41D724—41no—
42C22⋊D181—42no—
43C22⋊D181—44no—
44C2×Dic181—24no—
45C2×Dic181—21no—
46C2×Dic181C22⋊C412yes—
47C2×Dic181C2×D412yes—
48C4×D181—42no—
49C23×C181—21no—
50C23×C181C22⋊C411yescharacteristic
51Q8×C181—41no—
52D4×C181—41no—
53D4×C181—42no—
54C2×C4×C181—22no—
55C2×C4×C181—21no—
56C2×C4×C181—42no—
57C2×C4×C181C22⋊C411yescharacteristic
58C2×C4×C181C22×C411yescharacteristic
59C22×C181—21no—
60C22×C181—22no—
61C22×C181—41no—
62C22×C181—42no—
63C22×C181C2×C22⋊C411yescharacteristic
64C2×D181—41no—
65C2×D181—42no—
66C4×C181—21no—
67C4×C181—41no—
68C4×C181#10012yes—
69Dic181—22no—
70Dic181—41no—
71Dic181#10414yes—
72C2×C181—41no—
73C2×C181—81no—
74C2×C181C2×#10011yescharacteristic
75C2×C181C2×#10412yes—
76D181—81no—
77C181#152511yescharacteristic, complemented, Sylow
78#1525—1811nomaximal, Sylow
79#532—1811no—
80C4×M16—1812no—
81#329—1812no—
82#329—1812no—
83C2×#41—1811no—
84C2×#41#1062438211yescharacteristic
85C2×M16—3622no—
86C4⋊Q8—1811no—
87#127—1811no—
88#124—1811no—
89#124—1811no—
90#121—3622no—
91C4×D4—3622no—
92C2×C42—1811no—
93#97—1814no—
94C4×C8—3622no—
95#41—42no—
96#41—7242no—
97C2×Q8—1811no—
98C2×Q8C2×#1062438211yescharacteristic
99C2×D4—21no—
100C2×D4—3621no—
101C2×D4—3622no—
102C2×D4—1811no—
103C2×D4C2×#1062438211yescharacteristic
104C22×C4—21no—
105C22×C4—3621no—
106C22×C4—1812no—
107C22×C4C2×#1062438211yescharacteristic
108M16—3628no—
109C2×C8—3624no—
110C4⋊C4—3622no—
111C22⋊C4—3622no—
112C22⋊C4—3622no—
113C42—1812no—
114C42—1811no—
115C42—1811no—
116C23—21no—
117C23—3621no—
118C23C22⋊#1062438211yescharacteristic
119Q8—41no—
120Q8—7241no—
121D4—41no—
122D4—42no—
123D4—7241no—
124D4—7244no—
125D4—7242no—
126C2×C4—22no—
127C2×C4—21no—
128C2×C4—42no—
129C2×C4—3624no—
130C2×C4—3621no—
131C2×C4—1812no—
132C2×C4—1812no—
133C2×C4—7242no—
134C2×C4C22⋊#1062438211yescharacteristic
135C2×C4C22×#1062438211yescharacteristic
136C8—3628no—
137C22—21no—
138C22—22no—
139C22—41no—
140C22—42no—
141C22—7241no—
142C22—7242no—
143C22C2×C22⋊#1062438211yescharacteristic
144C4—21no—
145C4—41no—
146C4—3622no—
147C4—1814no—
148C4—7241no—
149C4#1915387612yes—
150C2—41no—
151C2—81no—
152C2—14481no—
153C2C2×#1915387611yescharacteristic
154C2D181⋊#10412yes—
subgroupG/H
centerC2×C4C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×#41×C181C4
socleC22×C181C2×C22⋊C4
prime radical#26041825C2
cosocleC4×Dic181C23
hypercenterC2×#41#10624382
hypocenterC181#1525
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C4×#15668458C2semidirect
2. #26042135C2semidirect
3. #26042134C2semidirect
77. C181#1525semidirect

Maximal subgroups

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

subgroupindex
C4×#156684582
#260421352
#260421342
#260418252
#1525181