Finite Group Databasebeta

← #37549993

Subgroups — #37549993

Order 23168.

258 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 52 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#26042260C212yesmaximal, complemented
2#26042186C212yesmaximal, complemented
3#26042183C212yesmaximal, complemented
4#26041828C211yesmaximal, characteristic
5#19153895—22no—
6#19153875—22no—
7#19153875C2214yes—
8C2×#15668450C2211yescharacteristic
9C2×#15668448C411yescharacteristic, complemented
10#19153814C411yescharacteristic, complemented
11#19153812C2211yescharacteristic
12#19153804C2211yescharacteristic
13#19153789—22no—
14#19153776—22no—
15C42×D181C411yescharacteristic, complemented
16#124×C181C411yescharacteristic, complemented
17C4⋊#10624382—42no—
18C22⋊#10624382—24no—
19C4×#10624382—42no—
20#15668450—41no—
21#15668450—41no—
22#15668448—41no—
23#15668448—41no—
24C2×Dic362C2×C411yescharacteristic
25C2×D724D412yes—
26C2×D724C2311yescharacteristic
27C2×C22⋊D181—21no—
28C2×C22⋊D181—22no—
29C22×Dic181—21no—
30C2×C4×D181—21no—
31C2×C4×D181C2×C411yescharacteristic
32C2×C4×D181D412yes—
33#15668428—22no—
34#15668426—22no—
35C4×Dic181—21no—
36C4×Dic181C2×C411yescharacteristic
37C2×Q8×C181C2×C411yescharacteristic
38C2×D4×C181C2×C411yescharacteristic
39C22⋊C4×C181—22no—
40C42×C181C2×C411yescharacteristic
41C2×#10624382—44no—
42C22×D181C22⋊C411yescharacteristic
43C22×D181C2×D412yes—
44Dic362—41no—
45D724—42no—
46D724—41no—
47C22⋊D181—44no—
48C22⋊D181—42no—
49C2×Dic181—21no—
50C2×Dic181—21no—
51C2×Dic181—41no—
52C2×Dic181—41no—
53C2×Dic181C22⋊C411yescharacteristic
54C4×D181—21no—
55C4×D181—21no—
56C4×D181—22no—
57C4×D181—22no—
58C4×D181—42no—
59C23×C181—21no—
60Q8×C181—41no—
61D4×C181—41no—
62C2×C4×C181—21no—
63C2×C4×C181C22⋊C412yes—
64C2×C4×C181C22×C411yescharacteristic
65C22×C181—42no—
66C22×C181—41no—
67C22×C181C2×C22⋊C411yescharacteristic
68C2×D181—21no—
69C2×D181—22no—
70C2×D181—41no—
71C2×D181—42no—
72#10624382—84no—
73C4×C181—22no—
74C4×C181—21no—
75C4×C181—41no—
76Dic181—22no—
77Dic181—41no—
78Dic181#9911yescharacteristic
79Dic181#9911yescharacteristic
80C2×C181—21no—
81C2×C181—81no—
82C2×C181C2×#9911yescharacteristic
83D181—42no—
84D181—41no—
85C181#212611yescharacteristic, complemented, Sylow
86#2126—1811nomaximal, Sylow
87#532—1811no—
88#410—1812no—
89#354—1812no—
90#353—1812no—
91C2×#41—1811no—
92C2×#41—1811no—
93C4⋊Q8—1811no—
94#127—1811no—
95#124—1811no—
96#124#1062438211yescharacteristic, complemented
97#121—3622no—
98C4×D4—3622no—
99#117—3622no—
100C2×C42—1811no—
101#99—3622no—
102#99—1814no—
103#41—7241no—
104#41—7241no—
105#41—7241no—
106#41—7241no—
107C2×Q8—1811no—
108C2×Q8C2×#1062438211yescharacteristic
109C2×D4—3622no—
110C2×D4—3621no—
111C2×D4—1812no—
112C2×D4—1811no—
113C2×D4C2×#1062438211yescharacteristic
114C22×C4—3621no—
115C22×C4—3621no—
116C22×C4—1812no—
117C22×C4—1811no—
118C4⋊C4—3622no—
119C4⋊C4—7242no—
120C22⋊C4—22no—
121C22⋊C4—3622no—
122C22⋊C4—3624no—
123C42—3621no—
124C42—1811no—
125C42—7242no—
126C42C2×#1062438211yescharacteristic
127C23—21no—
128C23—1812no—
129C23—1811no—
130Q8—41no—
131Q8—7241no—
132D4—41no—
133D4—7242no—
134D4—7241no—
135D4—7244no—
136D4—7242no—
137C2×C4—21no—
138C2×C4—3622no—
139C2×C4—3622no—
140C2×C4—3621no—
141C2×C4—3621no—
142C2×C4—3621no—
143C2×C4—3621no—
144C2×C4—1811no—
145C2×C4—7242no—
146C2×C4—7244no—
147C2×C4—7241no—
148C2×C4—7241no—
149C2×C4C22⋊#1062438212yes—
150C2×C4C22×#1062438211yescharacteristic
151C22—42no—
152C22—41no—
153C22—3622no—
154C22—3621no—
155C22—7241no—
156C22—7242no—
157C22C2×C22⋊#1062438211yescharacteristic
158C4—22no—
159C4—21no—
160C4—41no—
161C4—3622no—
162C4—14484no—
163C4—1811no—
164C4—1811no—
165C4—7241no—
166C2—21no—
167C2—81no—
168C2—7242no—
169C2—7241no—
170C2D181⋊#9911yescharacteristic
subgroupG/H
centerC2D181⋊#99
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#124×C181C4
socleC2×C181C2×#99
prime radical#26041828C2
cosocleC2×D724C23
hypercenter#124#10624382
hypocenterC181#2126
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #26042260C2semidirect
2. #26042186C2semidirect
3. #26042183C2semidirect
9. C2×#15668448C4semidirect
10. #19153814C4semidirect
15. C42×D181C4semidirect
16. #124×C181C4semidirect
85. C181#2126semidirect
96. #124#10624382semidirect

Maximal subgroups

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

subgroupindex
#260422602
#260421862
#260421832
#260418282
#2126181