Finite Group Databasebeta

← #37549693

Subgroups — #37549693

Order 23168.

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

normal subgroups only

This group has 260 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#26042357C211yesmaximal, characteristic
2#26042285C212yesmaximal, complemented
3#26042252C211yesmaximal, characteristic
4#26042160C212yesmaximal, complemented
5#26041251C211yesmaximal, characteristic
6#19153903—22no—
7#19153903—22no—
8D181⋊M16—21no—
9C2×#15668458—21no—
10C2×#15668458C2211yescharacteristic
11C2×#15668458C2212yes—
12C22×#13089685C2211yescharacteristic
13#19153883—22no—
14C4⋊#13089685—22no—
15#19153873—21no—
16C22⋊#13089685—21no—
17C2×#15668448C2211yescharacteristic
18#19153772C2212yes—
19#19153731C411yescharacteristic
20#19153730C412yes—
21#99×C181C411yescharacteristic
22#15668459—21no—
23#15668459—21no—
24#15668458—22no—
25#15668458—22no—
26#15668458—22no—
27#15668458—22no—
28D181⋊C8—22no—
29C2×#13089685—21no—
30C2×#13089685—21no—
31C2×#13089685—21no—
32C2×#13089685—21no—
33C2×#13089685—22no—
34C2×#13089685D412yes—
35C2×#13089685D412yes—
36#15668448—22no—
37#15668448—22no—
38C2×Dic362Q811yescharacteristic
39C2×C22⋊D181C2×C411yescharacteristic
40C2×C22⋊D181Q811yescharacteristic
41C22×Dic181D411yescharacteristic
42C22×Dic181C2311yescharacteristic
43C2×C4×D181D411yescharacteristic
44#15668428—22no—
45C22⋊Dic181C2×C412yes—
46C4×Dic181—22no—
47C2×D4×C181C2×C411yescharacteristic
48C22⋊C4×C181C2×C412yes—
49#13089685—22no—
50#13089685—22no—
51#13089685—41no—
52#13089685—41no—
53C22×D181C4⋊C411yescharacteristic
54Dic362—22no—
55C22⋊D181—22no—
56C22⋊D181—22no—
57C2×Dic181—21no—
58C2×Dic181—21no—
59C2×Dic181—22no—
60C2×Dic181C4⋊C411yescharacteristic
61C2×Dic181C2×D412yes—
62C2×Dic181C2×D411yescharacteristic
63C2×Dic181C2×Q811yescharacteristic
64C2×Dic181#4112yes—
65C4×D181—21no—
66C4×D181—21no—
67C23×C181C4⋊C411yescharacteristic
68C23×C181C22×C411yescharacteristic
69D4×C181—22no—
70C2×C4×C181—22no—
71C2×C4×C181C4⋊C411yescharacteristic
72C22×C181—21no—
73C22×C181—41no—
74C22×C181—41no—
75C22×C181C2×C4⋊C411yescharacteristic
76C22×C181C4×D412yes—
77C2×D181—21no—
78C2×D181—41no—
79C4×C181—21no—
80C4×C181—42no—
81Dic181—21no—
82Dic181—42no—
83Dic181#12011yescharacteristic
84Dic181C22⋊Q812yes—
85Dic181#12311yescharacteristic
86C2×C181—22no—
87C2×C181—21no—
88C2×C181—41no—
89C2×C181#38511yescharacteristic
90D181—41no—
91C181#186811yescharacteristic, complemented, Sylow
92#1868—1811nomaximal, Sylow
93#568—1811no—
94#424—1812no—
95#410—1811no—
96#408—1811no—
97#344—1812no—
98C2×#41—1811no—
99#131—3622no—
100#131—3622no—
101C2×M16—3621no—
102C2×M16—3621no—
103C2×M16—1811no—
104C2×M16—1812no—
105C22×C8—1811no—
106#117—1812no—
107C4⋊C8—3622no—
108C4⋊C8—3622no—
109#99—1811no—
110#99—1812no—
111#99#1062438211yescharacteristic
112C22⋊C8—3621no—
113C22⋊C8—3621no—
114#41—3622no—
115#41—3622no—
116C2×Q8—1811no—
117C2×D4—1811no—
118C2×D4—1811no—
119C2×D4C2×#1062438211yescharacteristic
120C22×C4—1811no—
121C22×C4—1811no—
122C22×C4—1811no—
123M16—3622no—
124M16—3621no—
125M16—3621no—
126M16—3622no—
127M16—3622no—
128M16—3622no—
129C2×C8—3621no—
130C2×C8—3621no—
131C2×C8—3622no—
132C2×C8—3621no—
133C2×C8—3621no—
134C2×C8—3622no—
135C2×C8—1812no—
136C2×C8—1812no—
137C4⋊C4—3622no—
138C22⋊C4—1812no—
139C22⋊C4C2×#1062438212yes—
140C42—3622no—
141C23—1811no—
142C23C4⋊#1062438211yescharacteristic
143C23C22×#1062438211yescharacteristic
144Q8—3622no—
145D4—22no—
146D4—3622no—
147D4—3622no—
148C2×C4—22no—
149C2×C4—3621no—
150C2×C4—3621no—
151C2×C4—3621no—
152C2×C4—3621no—
153C2×C4—3622no—
154C2×C4—1811no—
155C2×C4—1811no—
156C2×C4—1811no—
157C2×C4—1812no—
158C2×C4—1812no—
159C2×C4C4⋊#1062438211yescharacteristic
160C8—3622no—
161C8—3622no—
162C8—7241no—
163C8—7241no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—3621no—
168C22—7241no—
169C22C2×C4⋊#1062438211yescharacteristic
170C22D4×#1062438212yes—
171C4—21no—
172C4—42no—
173C4—3621no—
174C4—1811no—
175C4—1811no—
176C4—1812no—
177C4—7242no—
178C2—22no—
179C2—21no—
180C2—41no—
181C2—7241no—
182C2#2604222611yescharacteristic
subgroupG/H
centerC2#26042226
commutatorC23×C181C22×C4
FrattiniC23C22×#10624382
Fitting#99×C181C4
socleC2×C181#385
prime radicalC2×#15668448C22
cosocleC22×Dic181C23
hypercenter#99#10624382
hypocenterC181#1868
LCSG ▷ C23×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #26042285C2semidirect
4. #26042160C2semidirect
91. C181#1868semidirect

Maximal subgroups

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

subgroupindex
#260423572
#260422852
#260422522
#260421602
#260412512
#1868181