Finite Group Databasebeta

← #37532749

Subgroups — #37532749

Order 23168.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#26041874C211yesmaximal, characteristic
2#26041614C211yesmaximal, characteristic, complemented
3#26041217C211yesmaximal, characteristic, complemented
4#26041017C211yesmaximal, characteristic, complemented
5#26041013C211yesmaximal, characteristic
6#26041004C211yesmaximal, characteristic, complemented
7#481×C181C211yesmaximal, characteristic
8#19153809—21no—
9#19153806—21no—
10#19153797—21no—
11#19153797—21no—
12#19153795C2211yescharacteristic
13#19153793—21no—
14D4×Dic181—21no—
15C2×#15668428C2211yescharacteristic
16#19153749—21no—
17#19153739—21no—
18C22⋊#13089678C2211yescharacteristic
19#19153723—21no—
20#19153723—21no—
21#19153723C2211yescharacteristic
22#121×C181C2211yescharacteristic
23C2×C4⋊C4×C181C2211yescharacteristic
24#106×C181—21no—
25#102×C181—21no—
26C22⋊C8×C181C2211yescharacteristic
27C2×Dic362D411yescharacteristic
28C22×Dic181—21no—
29C22×Dic181—21no—
30C22×Dic181D411yescharacteristic
31C22×Dic181D411yescharacteristic
32C2×#13089678—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181D411yescharacteristic
35#15668428—21no—
36#15668428—21no—
37#15668428—21no—
38#15668428—21no—
39#15668428—21no—
40C22⋊Dic181—21no—
41C22⋊Dic181—21no—
42C22⋊Dic181—21no—
43C22⋊Dic181—21no—
44C4×Dic181—21no—
45C2×D4×C181—21no—
46C2×D4×C181D411yescharacteristic
47C22×C4×C181—21no—
48C22×C4×C181C2311yescharacteristic
49C2×C8×C181—21no—
50C4⋊C4×C181—21no—
51C4⋊C4×C181—21no—
52C4⋊C4×C181D411yescharacteristic
53C22⋊C4×C181—21no—
54Dic362—41no—
55C2×Dic181—21no—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C2×Dic181—21no—
59C2×Dic181—21no—
60C2×Dic181—21no—
61C2×Dic181—41no—
62C2×Dic181—41no—
63C2×Dic181—41no—
64C2×Dic181—41no—
65C2×Dic181—81no—
66#13089678—41no—
67C23×C181—21no—
68C23×C181C2×D411yescharacteristic
69D4×C181—41no—
70D4×C181—41no—
71D4×C181—41no—
72C2×C4×C181—21no—
73C2×C4×C181—41no—
74C2×C4×C181—42no—
75C2×C4×C181—41no—
76C2×C4×C181C2×D411yescharacteristic
77C2×C4×C181C2×D411yescharacteristic
78C8×C181—41no—
79C22×C181—21no—
80C22×C181—21no—
81C22×C181—41no—
82C22×C181—41no—
83C22×C181—41no—
84C22×C181#12011yescharacteristic
85C22×C181#13511yescharacteristic
86C22×C181#13711yescharacteristic
87C4×C181—21no—
88C4×C181—21no—
89C4×C181—41no—
90C4×C181—81no—
91Dic181—41no—
92Dic181—41no—
93Dic181—41no—
94Dic181—41no—
95Dic181—81no—
96C2×C181—21no—
97C2×C181—21no—
98C2×C181—81no—
99C2×C181#45211yescharacteristic
100C2×C181#45411yescharacteristic
101C2×C181#45811yescharacteristic
102C181#161511yescharacteristic, complemented, Sylow
103#1615—1811nomaximal, Sylow
104#539—1811no—
105#484—1811no—
106#481D18111yescharacteristic
107#400—1811no—
108#328—1811no—
109#327—1811no—
110#324—1811no—
111#126—3621no—
112#125—3621no—
113#123—3621no—
114#123—3621no—
115C22⋊Q8—3621no—
116C22⋊Q8—1811no—
117#121C2×D18111yescharacteristic
118C4×D4—3621no—
119C2×C4⋊C4—1811no—
120C2×C4⋊C4C2×D18111yescharacteristic
121#107—3621no—
122#106—21no—
123#103—3621no—
124#102—21no—
125C22⋊C8—1811no—
126C22⋊C8C2×D18111yescharacteristic
127#95—3621no—
128#95—3621no—
129#95—1811no—
130C2×Q8—1811no—
131C2×D4—21no—
132C2×D4C22⋊D18111yescharacteristic
133C22×C4—21no—
134C22×C4—3621no—
135C22×C4—3621no—
136C22×C4—1811no—
137C22×C4—1811no—
138C22×C4C22×D18111yescharacteristic
139C2×C8—21no—
140C2×C8—3621no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—3621no—
144C4⋊C4—3621no—
145C4⋊C4—3621no—
146C4⋊C4—3621no—
147C4⋊C4—3621no—
148C4⋊C4—3621no—
149C4⋊C4—1811no—
150C4⋊C4C22⋊D18111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3621no—
153C22⋊C4—3621no—
154C22⋊C4—3621no—
155C22⋊C4—3621no—
156C42—3621no—
157C23—21no—
158C23D4×D18111yescharacteristic
159Q8—7241no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—3621no—
168C2×C4—3621no—
169C2×C4—3621no—
170C2×C4—3621no—
171C2×C4—3621no—
172C2×C4—3621no—
173C2×C4—14481no—
174C2×C4—7241no—
175C2×C4—7241no—
176C2×C4—7241no—
177C2×C4—7241no—
178C2×C4D4×D18111yescharacteristic
179C2×C4C2×C22⋊D18111yescharacteristic
180C8—41no—
181C8—7241no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#1915378411yescharacteristic
188C22#1915383711yescharacteristic
189C22#1915384511yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—81no—
194C4—14481no—
195C4—7241no—
196C4—7241no—
197C4—7241no—
198C4—7241no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#2604143811yescharacteristic
203C2#2604145011yescharacteristic
204C2#2604146811yescharacteristic
subgroupG/H
centerC22#19153784
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#481×C181C2
socleC22×C181#120
prime radical#121×C181C22
hypercenter#481D181
hypocenterC181#1615
LCSG ▷ C22×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #26041614C2semidirect
3. #26041217C2semidirect
4. #26041017C2semidirect
6. #26041004C2semidirect
102. C181#1615semidirect

Maximal subgroups

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

subgroupindex
#260418742
#260416142
#260412172
#260410172
#260410132
#260410042
#481×C1812
#1615181