Finite Group Databasebeta

← #37535383

Subgroups — #37535383

Order 23168.

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

normal subgroups only

This group has 258 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#26041827C211yesmaximal, characteristic
2#26041251C212yesmaximal, complemented
3#26041073C212yesmaximal, complemented
4#26041072C211yesmaximal, characteristic, complemented
5#353×C181C211yesmaximal, characteristic, complemented
6C2×#15668448C411yescharacteristic, complemented
7C2×#15668448C2211yescharacteristic
8#19153816C411yescharacteristic, complemented
9#19153803C411yescharacteristic, complemented
10#19153803C2211yescharacteristic
11#19153787—22no—
12D4×Dic181—22no—
13#19153772—22no—
14C42×D181C411yescharacteristic, complemented
15#19153731C2212yes—
16#19153730—22no—
17#127×C181C2211yescharacteristic
18#99×C181C2212yes—
19#15668448—41no—
20#15668448—41no—
21#15668448—41no—
22#15668448—41no—
23C2×Dic362C2×C411yescharacteristic
24C2×Dic362C2×C411yescharacteristic
25C2×C22⋊D181—21no—
26C2×C22⋊D181D412yes—
27C22×Dic181—21no—
28C22×Dic181D412yes—
29C2×C4×D181—21no—
30C2×C4×D181C2×C411yescharacteristic
31C4⋊Dic181—22no—
32#15668428—42no—
33C22⋊Dic181—22no—
34C22⋊Dic181—22no—
35C22⋊Dic181—22no—
36C4×Dic181—21no—
37C4×Dic181—42no—
38C4×Dic181C2×C411yescharacteristic
39C2×D4×C181—22no—
40C2×D4×C181C2×C411yescharacteristic
41C2×D4×C181C2311yescharacteristic
42C22⋊C4×C181—22no—
43C42×C181C2×C411yescharacteristic
44C22×D181C22⋊C411yescharacteristic
45Dic362—41no—
46Dic362—41no—
47C22⋊D181—42no—
48C22⋊D181—42no—
49C2×Dic181—22no—
50C2×Dic181—22no—
51C2×Dic181—21no—
52C2×Dic181—21no—
53C2×Dic181—41no—
54C2×Dic181—41no—
55C2×Dic181—42no—
56C2×Dic181C22⋊C412yes—
57C2×Dic181C22⋊C411yescharacteristic
58C4×D181—21no—
59C4×D181—21no—
60C4×D181—42no—
61C23×C181—21no—
62C23×C181C2×D412yes—
63D4×C181—41no—
64D4×C181—41no—
65D4×C181—44no—
66C2×C4×C181—21no—
67C2×C4×C181—42no—
68C2×C4×C181C22×C411yescharacteristic
69C22×C181—22no—
70C22×C181—42no—
71C22×C181—42no—
72C22×C181—41no—
73C22×C181C2×C22⋊C411yescharacteristic
74C2×D181—21no—
75C2×D181—41no—
76C4×C181—22no—
77C4×C181—21no—
78C4×C181—82no—
79Dic181—22no—
80Dic181—41no—
81Dic181—41no—
82Dic181—82no—
83Dic181#9911yescharacteristic
84Dic181#9911yescharacteristic
85C2×C181—21no—
86C2×C181—42no—
87C2×C181—81no—
88C2×C181C2×#9911yescharacteristic
89D181—41no—
90C181#212611yescharacteristic, complemented, Sylow
91#2126—1811nomaximal, Sylow
92#532—1811no—
93#410—1812no—
94#354—1812no—
95#353—1811no—
96#353D18111yescharacteristic, complemented
97C2×#41—1811no—
98C2×#41—1811no—
99C4⋊Q8—1811no—
100#127C2×D18111yescharacteristic
101#124—1811no—
102#124—1811no—
103#121—3622no—
104C4×D4—3622no—
105#117—3622no—
106C2×C42—1811no—
107#99—3622no—
108#99—1812no—
109#99C2×D18112yes—
110#41—7241no—
111#41—7241no—
112#41—7241no—
113#41—7241no—
114C2×Q8—1811no—
115C2×Q8—1811no—
116C2×D4—22no—
117C2×D4—3621no—
118C2×D4—1812no—
119C2×D4C4×D18111yescharacteristic
120C2×D4C22×D18111yescharacteristic
121C22×C4—3621no—
122C22×C4—3621no—
123C22×C4—1812no—
124C22×C4—1811no—
125C4⋊C4—3622no—
126C4⋊C4—7242no—
127C22⋊C4—22no—
128C22⋊C4—3622no—
129C22⋊C4—3622no—
130C22⋊C4—3622no—
131C42—3621no—
132C42—1811no—
133C42—7242no—
134C42C4×D18111yescharacteristic
135C23—21no—
136C23—1811no—
137C23D4×D18112yes—
138Q8—7241no—
139Q8—7241no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—7242no—
144D4—7242no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—3621no—
148C2×C4—3621no—
149C2×C4—3622no—
150C2×C4—3622no—
151C2×C4—3621no—
152C2×C4—3621no—
153C2×C4—1812no—
154C2×C4—1811no—
155C2×C4—7242no—
156C2×C4—7242no—
157C2×C4—7241no—
158C2×C4—7241no—
159C2×C4C2×C4×D18111yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—3621no—
165C22—7241no—
166C22C22⋊C4×D18111yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—3622no—
171C4—14482no—
172C4—1811no—
173C4—1811no—
174C4—7241no—
175C4—7241no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—7241no—
180C2#99×D18111yescharacteristic
subgroupG/H
centerC2#99×D181
commutatorC2×C4×C181C22×C4
FrattiniC2×D4C22×D181
Fitting#353×C181C2
socleC2×C181C2×#99
prime radical#26041827C2
cosocleC2×D4×C181C23
hypercenter#353D181
hypocenterC181#2126
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #26041251C2semidirect
3. #26041073C2semidirect
4. #26041072C2semidirect
5. #353×C181C2semidirect
6. C2×#15668448C4semidirect
8. #19153816C4semidirect
9. #19153803C4semidirect
14. C42×D181C4semidirect
90. C181#2126semidirect
96. #353D181semidirect

Maximal subgroups

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

subgroupindex
#260418272
#260412512
#260410732
#260410722
#353×C1812
#2126181