Finite Group Databasebeta

← #37549093

Subgroups — #37549093

Order 23168.

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

normal subgroups only

This group has 238 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#26042297C211yesmaximal, characteristic, complemented
2#26042215C211yesmaximal, characteristic, complemented
3#26042133C212yesmaximal, complemented
4#26042130C212yesmaximal
5#26041808C211yesmaximal, characteristic
6C2×C4×#10624382—21no—
7#19153883—21no—
8#19153873C2212yes—
9C4×#13089685—21no—
10(C2×#10624382)⋊C4—21no—
11(C2×#10624382)⋊C4C2212yes—
12#19153809—21no—
13#19153808C411yescharacteristic, complemented
14#19153798—21no—
15#19153792C2211yescharacteristic
16#19153787C2211yescharacteristic
17Q8×Dic181C411yescharacteristic, complemented
18D4×Dic181C411yescharacteristic, complemented
19#19153776—21no—
20#19153772—21no—
21C42×D181C2211yescharacteristic
22#124×C181C411yescharacteristic, complemented
23C22×#10624382—22no—
24C2×#13089685—22no—
25C4×#10624382—24no—
26C2×C22⋊D181—21no—
27C22×Dic181—21no—
28C2×C4×D181D411yescharacteristic
29C2×C4×D181D411yescharacteristic
30C2×C4×D181C2311yescharacteristic
31C4⋊Dic181—21no—
32C4⋊Dic181C2×C411yescharacteristic
33C4⋊Dic181C2×C411yescharacteristic
34#15668428—21no—
35#15668428—21no—
36#15668428—21no—
37C22⋊Dic181—21no—
38C22⋊Dic181—21no—
39#15668426—21no—
40C4×Dic181—21no—
41C4×Dic181C2×C411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181D411yescharacteristic
44C2×Q8×C181C2×C411yescharacteristic
45C2×D4×C181C2×C411yescharacteristic
46C22⋊C4×C181—21no—
47C22⋊C4×C181—21no—
48C42×C181C2×C411yescharacteristic
49C2×#10624382—24no—
50C2×#10624382—42no—
51C2×#10624382—42no—
52#13089685—42no—
53C22×D181C2×D411yescharacteristic
54C22⋊D181—42no—
55C2×Dic181—21no—
56C2×Dic181—21no—
57C2×Dic181—42no—
58C2×Dic181C22⋊C411yescharacteristic
59C2×Dic181C22⋊C411yescharacteristic
60C2×Dic181C2×D411yescharacteristic
61C4×D181—22no—
62C4×D181—22no—
63C4×D181—41no—
64C23×C181—21no—
65Q8×C181—41no—
66D4×C181—41no—
67C2×C4×C181—21no—
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—21no—
82C4×C181—41no—
83Dic181—21no—
84Dic181—21no—
85Dic181—41no—
86Dic181—41no—
87Dic181#10412yes—
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#1062438211yescharacteristic, complemented
103#123—3621no—
104C22⋊Q8—1811no—
105#121—1811no—
106C4×Q8—1811no—
107C4×D4—3621no—
108C4×D4—1811no—
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×Q8C2×#1062438211yescharacteristic
118C2×D4—3621no—
119C2×D4C2×#1062438211yescharacteristic
120C22×C4—3622no—
121C22×C4—3621no—
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⋊C4—1811no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—3621no—
135C22⋊C4—3621no—
136C22⋊C4—3621no—
137C42—3621no—
138C42—3624no—
139C42—1811no—
140C42—1811no—
141C42—1811no—
142C42C2×#1062438211yescharacteristic
143C23—21no—
144C23—1811no—
145Q8—41no—
146D4—41no—
147D4—7242no—
148C2×C4—21no—
149C2×C4—3622no—
150C2×C4—3622no—
151C2×C4—3624no—
152C2×C4—3621no—
153C2×C4—3621no—
154C2×C4—1811no—
155C2×C4—1811no—
156C2×C4—1811no—
157C2×C4—7241no—
158C2×C4—7242no—
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—21no—
175C4—41no—
176C4—3621no—
177C4—3621no—
178C4—1812no—
179C4—7244no—
180C4—7241no—
181C4—7241no—
182C2—81no—
183C2—3622no—
184C2#2604225911yescharacteristic
185C2#2604226911yescharacteristic
186C2D181⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#124×C181C4
socleC22×C181C2×C22⋊C4
prime radical#19153787C22
cosocleC2×C4×D181C23
hypercenter#124#10624382
hypocenterC181#1500
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #26042297C2semidirect
2. #26042215C2semidirect
3. #26042133C2semidirect
13. #19153808C4semidirect
17. Q8×Dic181C4semidirect
18. D4×Dic181C4semidirect
22. #124×C181C4semidirect
93. C181#1500semidirect
102. #124#10624382semidirect

Maximal subgroups

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

subgroupindex
#260422972
#260422152
#260421332
#260421302
#260418082
#1500181