Finite Group Databasebeta

← #37549057

Subgroups — #37549057

Order 23168.

266 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 70 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#26042283C211yesmaximal, characteristic, complemented
2C4×#15668459C211yesmaximal, characteristic, complemented
3#26042129C212yesmaximal, complemented
4D4⋊#13089685C212yesmaximal, complemented
5C4×#15668448C211yesmaximal, characteristic
6C2×#15668459—21no—
7C2×#15668459—21no—
8C4⋊#13089685—21no—
9C4⋊#13089685C2212yes—
10#19153871—21no—
11C4×#13089685C2212yes—
12C2×#15668448C411yescharacteristic
13C4×Dic362C411yescharacteristic
14#19153781C2211yescharacteristic
15D4×Dic181C2211yescharacteristic
16C4×C22⋊D181—21no—
17#19153776—21no—
18#19153774C411yescharacteristic
19#19153772—21no—
20C2×C4×Dic181—21no—
21C42×D181C2211yescharacteristic
22C4×D4×C181C411yescharacteristic
23#15668459—24no—
24#15668459—42no—
25C2×#13089685—22no—
26C2×#13089685—22no—
27#15668448—22no—
28#15668448—22no—
29C2×Dic362C2×C411yescharacteristic
30C2×C22⋊D181—21no—
31C22×Dic181—21no—
32C22×Dic181—21no—
33C2×C4×D181C2×C411yescharacteristic
34C2×C4×D181D411yescharacteristic
35C2×C4×D181D411yescharacteristic
36C4⋊Dic181C2×C411yescharacteristic
37#15668428—21no—
38#15668428—21no—
39C22⋊Dic181—21no—
40#15668426—21no—
41C4×Dic181—21no—
42C4×Dic181—21no—
43C4×Dic181—21no—
44C4×Dic181D411yescharacteristic
45C4×Dic181D411yescharacteristic
46C4×Dic181C2311yescharacteristic
47C2×D4×C181C2×C411yescharacteristic
48C22×C4×C181—21no—
49C4⋊C4×C181C2×C411yescharacteristic
50C22⋊C4×C181—21no—
51C42×C181C2×C411yescharacteristic
52#13089685—24no—
53#13089685—42no—
54C22×D181C22⋊C411yescharacteristic
55Dic362—21no—
56Dic362M1612yescomplemented
57C22⋊D181—24no—
58C2×Dic181—24no—
59C2×Dic181—21no—
60C2×Dic181—21no—
61C2×Dic181—41no—
62C2×Dic181—41no—
63C2×Dic181C22⋊C411yescharacteristic
64C2×Dic181C2×D411yescharacteristic
65C2×Dic181C2×D411yescharacteristic
66C4×D181—22no—
67C4×D181—21no—
68C4×D181—21no—
69C4×D181—21no—
70C4×D181—21no—
71C23×C181—21no—
72D4×C181—21no—
73D4×C181M1612yescomplemented
74C2×C4×C181—21no—
75C2×C4×C181—42no—
76C2×C4×C181C22⋊C411yescharacteristic
77C2×C4×C181C22⋊C411yescharacteristic
78C2×C4×C181C22×C411yescharacteristic
79C22×C181—22no—
80C22×C181—41no—
81C22×C181—41no—
82C22×C181C2×C22⋊C411yescharacteristic
83C2×D181—21no—
84C2×D181—21no—
85C2×D181—21no—
86C4×C181—21no—
87C4×C181—41no—
88C4×C181#10412yes—
89C4×C181C2×M1611yescharacteristic
90C4×C181C2×M1611yescharacteristic
91Dic181—21no—
92Dic181—22no—
93Dic181—21no—
94Dic181—41no—
95Dic181AGL(1,ℤ/8)11yescharacteristic
96Dic181#13711yescharacteristic
97C2×C181—42no—
98C2×C181#40711yescharacteristic
99C2×C181#41711yescharacteristic
100C2×C181C2×#10411yescharacteristic
101D181—41no—
102C181#148911yescharacteristic, complemented, Sylow
103#1489—1811nomaximal, Sylow
104C4×#41—1811no—
105#423—1811no—
106C4×M16—1811no—
107Q8⋊C8—1812no—
108D4⋊C8—1812no—
109C2×#41—1811no—
110C2×M16—3621no—
111C2×M16—3621no—
112C4×Q8—1811no—
113C4×Q8—1811no—
114C4×D4—3621no—
115C4×D4—3621no—
116C4×D4—1811no—
117C4×D4#1062438211yescharacteristic
118#117—3621no—
119#117—1811no—
120C2×C42—3621no—
121C2×C42—1811no—
122C4⋊C8—3621no—
123C4⋊C8—1812no—
124#97—3621no—
125C4×C8—1812no—
126#41—3622no—
127#41—3622no—
128C2×Q8—1811no—
129C2×D4—3621no—
130C2×D4C2×#1062438211yescharacteristic
131C22×C4—21no—
132C22×C4—3621no—
133C22×C4—3621no—
134C22×C4—1811no—
135C22×C4—1811no—
136C22×C4—1811no—
137M16—3624no—
138M16—7242no—
139C2×C8—3622no—
140C2×C8—3622no—
141C4⋊C4—3621no—
142C4⋊C4—3621no—
143C4⋊C4—1811no—
144C4⋊C4C2×#1062438211yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—3621no—
147C22⋊C4—3621no—
148C42—3621no—
149C42—3621no—
150C42—3621no—
151C42—1811no—
152C42—1811no—
153C42—1811no—
154C42C2×#1062438211yescharacteristic
155C23—21no—
156C23—1811no—
157Q8—3621no—
158Q8—1812no—
159D4—21no—
160D4—3624no—
161D4#1566845912yescomplemented
162C2×C4—21no—
163C2×C4—42no—
164C2×C4—3621no—
165C2×C4—3621no—
166C2×C4—3624no—
167C2×C4—3621no—
168C2×C4—3622no—
169C2×C4—3621no—
170C2×C4—3621no—
171C2×C4—3621no—
172C2×C4—1811no—
173C2×C4—1811no—
174C2×C4—1811no—
175C2×C4—7241no—
176C2×C4—7241no—
177C2×C4C22⋊#1062438211yescharacteristic
178C2×C4C22⋊#1062438211yescharacteristic
179C2×C4C22×#1062438211yescharacteristic
180C8—3624no—
181C8—7242no—
182C22—22no—
183C22—41no—
184C22—41no—
185C22—3621no—
186C22—3621no—
187C22—3621no—
188C22C2×C22⋊#1062438211yescharacteristic
189C4—21no—
190C4—41no—
191C4—3621no—
192C4—3622no—
193C4—3621no—
194C4—1811no—
195C4—1811no—
196C4—7241no—
197C4#1915388012yes—
198C4D181⋊M1611yescharacteristic
199C4C2×#1566845911yescharacteristic
200C2—42no—
201C2—7241no—
202C2#2604225011yescharacteristic
203C2#2604227011yescharacteristic
204C2C2×#1915388011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×D4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC2×#15668448C4
cosocleC4×Dic181C23
hypercenterC4×D4#10624382
hypocenterC181#1489
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26042283C2semidirect
2. C4×#15668459C2semidirect
3. #26042129C2semidirect
4. D4⋊#13089685C2semidirect
56. Dic362M16semidirect
73. D4×C181M16semidirect
102. C181#1489semidirect
161. D4#15668459semidirect

Maximal subgroups

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

subgroupindex
#260422832
C4×#156684592
#260421292
D4⋊#130896852
C4×#156684482
#1489181