Finite Group Databasebeta

← #37549257

Subgroups — #37549257

Order 23168.

202 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 58 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#26042299C211yesmaximal, characteristic
2#26042282C211yesmaximal, characteristic
3#26042139C212yesmaximal, complemented
4#26042138C212yesmaximal, complemented
5#26041831C211yesmaximal, characteristic
6C2×#15668458—21no—
7#19153883C2212yes—
8#19153883C2212yes—
9C4⋊#13089685—21no—
10C22⋊#13089685—21no—
11#19153871—21no—
12#19153815C2211yescharacteristic
13#19153814C2211yescharacteristic
14#19153806—21no—
15#19153795C411yescharacteristic
16#19153793—21no—
17Q8×Dic181C411yescharacteristic
18#19153781—21no—
19#19153781C411yescharacteristic
20#19153772—21no—
21C2×C4×Dic181C2211yescharacteristic
22C22⋊Q8×C181C411yescharacteristic
23#15668458—42no—
24C2×#13089685—22no—
25C2×#13089685—22no—
26C2×Dic362—21no—
27C2×Dic362C2×C411yescharacteristic
28C22×Dic181D411yescharacteristic
29C22×Dic181D411yescharacteristic
30C4⋊Dic181—21no—
31C4⋊Dic181C2×C411yescharacteristic
32#15668428—21no—
33#15668428—21no—
34#15668428—21no—
35#15668428—21no—
36#15668428—21no—
37C22⋊Dic181—21no—
38C4×Dic181—21no—
39C4×Dic181—21no—
40C4×Dic181C2×C411yescharacteristic
41C4×Dic181D411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181C2311yescharacteristic
44C2×Q8×C181C2×C411yescharacteristic
45C22×C4×C181C2×C411yescharacteristic
46C4⋊C4×C181—21no—
47C4⋊C4×C181C2×C411yescharacteristic
48C22⋊C4×C181—21no—
49#13089685—42no—
50#13089685—42no—
51Dic362—41no—
52Dic362—41no—
53Dic362—41no—
54C2×Dic181—21no—
55C2×Dic181—21no—
56C2×Dic181—22no—
57C2×Dic181—21no—
58C2×Dic181—21no—
59C2×Dic181C22⋊C411yescharacteristic
60C2×Dic181C22⋊C411yescharacteristic
61C2×Dic181C2×D411yescharacteristic
62C2×Dic181C2×D411yescharacteristic
63C23×C181C22⋊C411yescharacteristic
64Q8×C181—41no—
65C2×C4×C181—21no—
66C2×C4×C181—21no—
67C2×C4×C181—41no—
68C2×C4×C181C22⋊C411yescharacteristic
69C2×C4×C181C22×C411yescharacteristic
70C22×C181—21no—
71C22×C181—21no—
72C22×C181—21no—
73C22×C181C2×C22⋊C411yescharacteristic
74C4×C181—21no—
75C4×C181—21no—
76C4×C181—41no—
77C4×C181—41no—
78Dic181—21no—
79Dic181—21no—
80Dic181—41no—
81Dic181—41no—
82Dic181AGL(1,ℤ/8)11yescharacteristic
83Dic181#13711yescharacteristic
84Dic181#13712yes—
85C2×C181—41no—
86C2×C181#41311yescharacteristic
87C2×C181#41711yescharacteristic
88C2×C181#41911yescharacteristic
89C181#155911yescharacteristic, complemented, Sylow
90#1559—1811nomaximal, Sylow
91#533—1811no—
92#432—1811no—
93#423—1811no—
94#333—1812no—
95#332—1812no—
96C2×M16—3621no—
97C4⋊Q8—1811no—
98C4⋊Q8—1811no—
99#125—3621no—
100C22⋊Q8—3621no—
101C22⋊Q8—1811no—
102C22⋊Q8#1062438211yescharacteristic
103C4×Q8—3621no—
104C4×Q8—1811no—
105C4×Q8—1811no—
106#117—3621no—
107C2×C42—1811no—
108C4⋊C8—3621no—
109C4⋊C8—1812no—
110C4⋊C8—1812no—
111C22⋊C8—3621no—
112#97—3621no—
113C2×Q8—3621no—
114C2×Q8—1811no—
115C2×Q8C2×#1062438211yescharacteristic
116C22×C4—1811no—
117C22×C4—1811no—
118C22×C4C2×#1062438211yescharacteristic
119M16—7242no—
120C2×C8—3622no—
121C2×C8—3622no—
122C4⋊C4—21no—
123C4⋊C4—3621no—
124C4⋊C4—3621no—
125C4⋊C4—3621no—
126C4⋊C4—3621no—
127C4⋊C4—3621no—
128C4⋊C4—3621no—
129C4⋊C4—1811no—
130C4⋊C4C2×#1062438211yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—3621no—
133C42—3621no—
134C42—3621no—
135C42—1811no—
136C42—1811no—
137C42—1811no—
138C42—1811no—
139C23C22⋊#1062438211yescharacteristic
140Q8—41no—
141Q8—7241no—
142Q8—7241no—
143Q8—7241no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—3621no—
148C2×C4—3621no—
149C2×C4—3622no—
150C2×C4—3621no—
151C2×C4—3621no—
152C2×C4—1811no—
153C2×C4—1811no—
154C2×C4—1811no—
155C2×C4—1811no—
156C2×C4C22⋊#1062438211yescharacteristic
157C2×C4C22×#1062438211yescharacteristic
158C8—7242no—
159C8—7242no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22C2×C22⋊#1062438211yescharacteristic
164C4—21no—
165C4—21no—
166C4—41no—
167C4—41no—
168C4—3621no—
169C4—3621no—
170C4—1811no—
171C4—1811no—
172C4—1812no—
173C4—7241no—
174C4—7241no—
175C2—41no—
176C2#2604226611yescharacteristic
177C2#2604227011yescharacteristic
178C2#2604227211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC22⋊Q8×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC23×C181C22⋊C4
cosocleC4×Dic181C23
hypercenterC22⋊Q8#10624382
hypocenterC181#1559
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #26042139C2semidirect
4. #26042138C2semidirect
89. C181#1559semidirect

Maximal subgroups

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

subgroupindex
#260422992
#260422822
#260421392
#260421382
#260418312
#1559181