Finite Group Databasebeta

← #37549205

Subgroups — #37549205

Order 23168.

200 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 54 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#26042302C211yesmaximal, characteristic, complemented
2#26042301C211yesmaximal, characteristic, complemented
3#26042136C212yesmaximal, complemented
4#26042134C212yesmaximal, complemented
5#26041811C211yesmaximal, characteristic
6#19153883—21no—
7C4⋊#13089685—21no—
8#19153873—21no—
9#19153873—21no—
10#19153871C2212yes—
11#19153871C2212yes—
12#19153809—21no—
13#19153807C2211yescharacteristic
14#19153803C2211yescharacteristic
15#19153798—21no—
16#19153796C411yescharacteristic
17#19153787C411yescharacteristic
18C4×Dic362C411yescharacteristic
19C4×C22⋊D181—21no—
20#19153775—21no—
21C42×D181C2211yescharacteristic
22C4×D4×C181C411yescharacteristic
23C2×#13089685—22no—
24C2×#13089685—22no—
25C2×Dic362C2×C411yescharacteristic
26C2×C22⋊D181—21no—
27C2×C4×D181C2×C411yescharacteristic
28C2×C4×D181D411yescharacteristic
29C2×C4×D181D411yescharacteristic
30C4⋊Dic181—21no—
31C4⋊Dic181—21no—
32C4⋊Dic181C2×C411yescharacteristic
33#15668428—21no—
34#15668428—21no—
35C22⋊Dic181—21no—
36C22⋊Dic181—21no—
37C22⋊Dic181—21no—
38#15668426—21no—
39C4×Dic181—21no—
40C4×Dic181D411yescharacteristic
41C4×Dic181D411yescharacteristic
42C4×Dic181C2311yescharacteristic
43C2×D4×C181C2×C411yescharacteristic
44C22×C4×C181—21no—
45C4⋊C4×C181C2×C411yescharacteristic
46C22⋊C4×C181—21no—
47C42×C181C2×C411yescharacteristic
48#13089685—42no—
49#13089685—42no—
50C22×D181C22⋊C411yescharacteristic
51Dic362—41no—
52C22⋊D181—42no—
53C2×Dic181—21no—
54C2×Dic181—21no—
55C2×Dic181C22⋊C411yescharacteristic
56C2×Dic181C2×D411yescharacteristic
57C2×Dic181C2×D411yescharacteristic
58C4×D181—41no—
59C4×D181—41no—
60C4×D181—41no—
61C23×C181—21no—
62D4×C181—41no—
63C2×C4×C181—21no—
64C2×C4×C181—42no—
65C2×C4×C181C22⋊C411yescharacteristic
66C2×C4×C181C22⋊C411yescharacteristic
67C2×C4×C181C22×C411yescharacteristic
68C22×C181—41no—
69C22×C181—41no—
70C22×C181—41no—
71C22×C181C2×C22⋊C411yescharacteristic
72C2×D181—21no—
73C2×D181—21no—
74C2×D181—21no—
75C4×C181—21no—
76C4×C181—21no—
77C4×C181—21no—
78C4×C181—41no—
79Dic181—21no—
80Dic181—21no—
81Dic181—21no—
82Dic181—41no—
83Dic181—41no—
84C2×C181—81no—
85C2×C181#41311yescharacteristic
86C2×C181#42111yescharacteristic
87C2×C181#42111yescharacteristic
88D181—41no—
89C181#153511yescharacteristic, complemented, Sylow
90#1535—1811nomaximal, Sylow
91#529—1811no—
92#432—1811no—
93#432—1811no—
94#330—1812no—
95#329—1812no—
96#126—3621no—
97#125—1811no—
98#124—1811no—
99#123—3621no—
100C22⋊Q8—1811no—
101#121—1811no—
102C4×Q8—1811no—
103C4×D4—3621no—
104C4×D4#1062438211yescharacteristic
105#117—3621no—
106C2×C42—1811no—
107C4⋊C8—3621no—
108C4⋊C8—3621no—
109C22⋊C8—3621no—
110C22⋊C8—3621no—
111#97—1812no—
112#97—1812no—
113C2×Q8—1811no—
114C2×D4—3621no—
115C2×D4C2×#1062438211yescharacteristic
116C22×C4—21no—
117C22×C4—1811no—
118C22×C4—1811no—
119C22×C4—1811no—
120C2×C8—3622no—
121C2×C8—3622no—
122C4⋊C4—3621no—
123C4⋊C4—3621no—
124C4⋊C4—3621no—
125C4⋊C4—3621no—
126C4⋊C4—1811no—
127C4⋊C4C2×#1062438211yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—3621no—
130C22⋊C4—3621no—
131C22⋊C4—3621no—
132C22⋊C4—3621no—
133C42—3621no—
134C42—1811no—
135C42—1811no—
136C42—1811no—
137C42C2×#1062438211yescharacteristic
138C23—21no—
139C23—1811no—
140Q8—7241no—
141D4—41no—
142D4—7242no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—3621no—
146C2×C4—3621no—
147C2×C4—1811no—
148C2×C4—1811no—
149C2×C4—1811no—
150C2×C4—7241no—
151C2×C4—7241no—
152C2×C4—7241no—
153C2×C4C22⋊#1062438211yescharacteristic
154C2×C4C22⋊#1062438211yescharacteristic
155C2×C4C22×#1062438211yescharacteristic
156C8—7242no—
157C8—7242no—
158C22—41no—
159C22—41no—
160C22—41no—
161C22—3621no—
162C22—3621no—
163C22—3621no—
164C22C2×C22⋊#1062438211yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—41no—
169C4—3621no—
170C4—3621no—
171C4—3621no—
172C4—7241no—
173C4—7241no—
174C2—81no—
175C2—7241no—
176C2#2604226511yescharacteristic
177C2#2604227611yescharacteristic
178C2#2604227711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×D4×C181C4
socleC22×C181C2×C22⋊C4
prime radical#19153787C4
cosocleC4×Dic181C23
hypercenterC4×D4#10624382
hypocenterC181#1535
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26042302C2semidirect
2. #26042301C2semidirect
3. #26042136C2semidirect
4. #26042134C2semidirect
89. C181#1535semidirect

Maximal subgroups

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

subgroupindex
#260423022
#260423012
#260421362
#260421342
#260418112
#1535181