Finite Group Databasebeta

← #37549092

Subgroups — #37549092

Order 23168.

238 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 60 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#26042298C211yesmaximal, characteristic, complemented
2#26042215C211yesmaximal, characteristic, complemented
3#26042132C212yesmaximal, complemented
4#26042130C212yesmaximal
5#26041811C211yesmaximal, characteristic
6C2×C4×#10624382—21no—
7C4⋊#13089685—21no—
8#19153873C2212yes—
9C4×#13089685—21no—
10(C2×#10624382)⋊C4—21no—
11(C2×#10624382)⋊C4C2212yes—
12#19153809—21no—
13#19153807C411yescharacteristic, complemented
14#19153803C411yescharacteristic, complemented
15#19153798—21no—
16#19153796C2211yescharacteristic
17#19153787C2211yescharacteristic
18C4×Dic362C411yescharacteristic, complemented
19C4×C22⋊D181—21no—
20#19153775—21no—
21C42×D181C2211yescharacteristic
22C4×D4×C181C411yescharacteristic, complemented
23C22×#10624382—22no—
24C2×#13089685—22no—
25C4×#10624382—24no—
26C2×Dic362C2×C411yescharacteristic
27C2×C22⋊D181—21no—
28C2×C4×D181D411yescharacteristic
29C2×C4×D181D411yescharacteristic
30C2×C4×D181C2311yescharacteristic
31C4⋊Dic181—21no—
32C4⋊Dic181—21no—
33C4⋊Dic181C2×C411yescharacteristic
34#15668428—21no—
35#15668428—21no—
36C22⋊Dic181—21no—
37C22⋊Dic181—21no—
38C22⋊Dic181—21no—
39#15668426—21no—
40C4×Dic181—21no—
41C4×Dic181C2×C411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181D411yescharacteristic
44C2×D4×C181C2×C411yescharacteristic
45C22×C4×C181—21no—
46C4⋊C4×C181C2×C411yescharacteristic
47C22⋊C4×C181—21no—
48C42×C181C2×C411yescharacteristic
49C2×#10624382—24no—
50C2×#10624382—42no—
51C2×#10624382—42no—
52#13089685—42no—
53C22×D181C2×D411yescharacteristic
54Dic362—41no—
55C22⋊D181—42no—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C2×Dic181C22⋊C411yescharacteristic
59C2×Dic181C22⋊C411yescharacteristic
60C2×Dic181C2×D411yescharacteristic
61C4×D181—22no—
62C4×D181—22no—
63C4×D181—41no—
64C23×C181—21no—
65D4×C181—41no—
66C2×C4×C181—21no—
67C2×C4×C181—42no—
68C2×C4×C181C22⋊C411yescharacteristic
69C2×C4×C181C22⋊C411yescharacteristic
70C2×C4×C181C22×C411yescharacteristic
71C22×C181—41no—
72C22×C181—41no—
73C22×C181—41no—
74C22×C181C2×C22⋊C411yescharacteristic
75C2×D181—21no—
76C2×D181—21no—
77C2×D181#13512yes—
78#10624382—44no—
79C4×C181—21no—
80C4×C181—21no—
81C4×C181—41no—
82C4×C181#10412yes—
83Dic181—21no—
84Dic181—21no—
85Dic181—21no—
86Dic181—41no—
87Dic181—41no—
88C2×C181—81no—
89C2×C181#41011yescharacteristic
90C2×C181#41611yescharacteristic
91C2×C181C2×#10411yescharacteristic
92D181—22no—
93C181#150011yescharacteristic, complemented, Sylow
94#1500—1811nomaximal, Sylow
95#529—1811no—
96#431—1811no—
97#376—1811no—
98#328—1812no—
99#327—1812no—
100#126—3621no—
101#125—1811no—
102#124—1811no—
103#123—3621no—
104C22⋊Q8—1811no—
105#121—1811no—
106C4×Q8—1811no—
107C4×D4—3621no—
108C4×D4#1062438211yescharacteristic, complemented
109#117—3621no—
110C2×C42—3621no—
111C2×C42—1811no—
112C4⋊C8—3621no—
113C22⋊C8—1812no—
114C4×C8—3621no—
115#95—3621no—
116#95—1812no—
117C2×Q8—1811no—
118C2×D4—3621no—
119C2×D4C2×#1062438211yescharacteristic
120C22×C4—21no—
121C22×C4—3622no—
122C22×C4—1811no—
123C22×C4—1811no—
124C22×C4—1811no—
125C2×C8—3622no—
126C4⋊C4—3621no—
127C4⋊C4—3621no—
128C4⋊C4—3621no—
129C4⋊C4—3621no—
130C4⋊C4—1811no—
131C4⋊C4C2×#1062438211yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—3621no—
134C22⋊C4—3621no—
135C22⋊C4—3621no—
136C22⋊C4—3621no—
137C42—3624no—
138C42—3621no—
139C42—1811no—
140C42—1811no—
141C42—1811no—
142C42C2×#1062438211yescharacteristic
143C23—21no—
144C23—1811no—
145Q8—7241no—
146D4—41no—
147D4—7242no—
148C2×C4—21no—
149C2×C4—42no—
150C2×C4—3622no—
151C2×C4—3622no—
152C2×C4—3624no—
153C2×C4—3621no—
154C2×C4—3621no—
155C2×C4—1811no—
156C2×C4—1811no—
157C2×C4—1811no—
158C2×C4—7241no—
159C2×C4—7242no—
160C2×C4—7242no—
161C2×C4C22⋊#1062438211yescharacteristic
162C2×C4C22⋊#1062438211yescharacteristic
163C2×C4C22×#1062438211yescharacteristic
164C8—7242no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—3621no—
169C22—3621no—
170C22—1812no—
171C22C2×C22⋊#1062438211yescharacteristic
172C4—21no—
173C4—21no—
174C4—41no—
175C4—3621no—
176C4—3621no—
177C4—3621no—
178C4—7244no—
179C4—7241no—
180C4—7241no—
181C4#1915388012yes—
182C2—81no—
183C2—3622no—
184C2#2604225811yescharacteristic
185C2#2604226911yescharacteristic
186C2C2×#1915388011yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×D4×C181C4
socleC22×C181C2×C22⋊C4
prime radical#19153787C22
cosocleC2×C4×D181C23
hypercenterC4×D4#10624382
hypocenterC181#1500
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26042298C2semidirect
2. #26042215C2semidirect
3. #26042132C2semidirect
13. #19153807C4semidirect
14. #19153803C4semidirect
18. C4×Dic362C4semidirect
22. C4×D4×C181C4semidirect
93. C181#1500semidirect
108. C4×D4#10624382semidirect

Maximal subgroups

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

subgroupindex
#260422982
#260422152
#260421322
#260421302
#260418112
#1500181