Finite Group Databasebeta

← #37532727

Subgroups — #37532727

Order 23168.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#26041908C211yesmaximal, characteristic
2#26041609C211yesmaximal, characteristic
3#26041210C211yesmaximal, characteristic
4#26041017C211yesmaximal, characteristic
5#26041016C211yesmaximal, characteristic
6#26041004C211yesmaximal, characteristic
7#483×C181C211yesmaximal, characteristic
8#19153815—21no—
9#19153814—21no—
10#19153806—21no—
11#19153806—21no—
12#19153795C2211yescharacteristic
13#19153793—21no—
14#19153772—21no—
15C2×#15668428—21no—
16C2×#15668428C2211yescharacteristic
17#19153747—21no—
18#19153739—21no—
19C22⋊#13089678C2211yescharacteristic
20#19153723—21no—
21#19153723C2211yescharacteristic
22C22⋊Q8×C181C2211yescharacteristic
23C2×C4⋊C4×C181C2211yescharacteristic
24#106×C181—21no—
25#103×C181—21no—
26C22⋊C8×C181C2211yescharacteristic
27C2×Dic362—21no—
28C2×Dic362D411yescharacteristic
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—
40#15668428—21no—
41#15668428—21no—
42#15668428—42no—
43C22⋊Dic181—21no—
44C4×Dic181—21no—
45C4×Dic181—21no—
46C2×Q8×C181D411yescharacteristic
47C22×C4×C181—21no—
48C22×C4×C181C2311yescharacteristic
49C2×C8×C181—21no—
50C4⋊C4×C181—21no—
51C4⋊C4×C181—21no—
52C4⋊C4×C181—21no—
53C4⋊C4×C181D411yescharacteristic
54C22⋊C4×C181—21no—
55Dic362—41no—
56Dic362—81no—
57C2×Dic181—21no—
58C2×Dic181—21no—
59C2×Dic181—22no—
60C2×Dic181—21no—
61C2×Dic181—21no—
62C2×Dic181—21no—
63C2×Dic181—41no—
64C2×Dic181—41no—
65C2×Dic181—41no—
66C2×Dic181SD1612yes—
67#13089678—41no—
68C23×C181C2×D411yescharacteristic
69Q8×C181—41no—
70C2×C4×C181—21no—
71C2×C4×C181—21no—
72C2×C4×C181—41no—
73C2×C4×C181—41no—
74C2×C4×C181—41no—
75C2×C4×C181—41no—
76C2×C4×C181C2×D411yescharacteristic
77C2×C4×C181C2×D411yescharacteristic
78C8×C181—41no—
79C22×C181—21no—
80C22×C181—21no—
81C22×C181#12011yescharacteristic
82C22×C181C2×SD1611yescharacteristic
83C22×C181#13711yescharacteristic
84C4×C181—21no—
85C4×C181—21no—
86C4×C181—41no—
87C4×C181—41no—
88C4×C181—81no—
89Dic181—22no—
90Dic181—42no—
91Dic181—41no—
92Dic181—41no—
93Dic181—41no—
94C2×C181—21no—
95C2×C181—21no—
96C2×C181#44811yescharacteristic
97C2×C181#45611yescharacteristic
98C2×C181#45811yescharacteristic
99C181#161111yescharacteristic, complemented, Sylow
100#1611—1811nomaximal, Sylow
101#544—1811no—
102#483—1811no—
103#483D18111yescharacteristic
104#398—1811no—
105#328—1811no—
106#328—1811no—
107#324—1811no—
108C4⋊Q8—3621no—
109C4⋊Q8—3621no—
110#125—3621no—
111#125—3621no—
112C22⋊Q8—3621no—
113C22⋊Q8—1811no—
114C22⋊Q8C2×D18111yescharacteristic
115#117—3621no—
116C2×C4⋊C4—3621no—
117C2×C4⋊C4—1811no—
118C2×C4⋊C4C2×D18111yescharacteristic
119#106—21no—
120#106—3621no—
121#103—21no—
122#103—3621no—
123C22⋊C8—1811no—
124C22⋊C8C2×D18111yescharacteristic
125#95—3621no—
126#95—1811no—
127C2×Q8—3621no—
128C2×Q8—1811no—
129C2×Q8C22⋊D18111yescharacteristic
130C22×C4—21no—
131C22×C4—3621no—
132C22×C4—1811no—
133C22×C4—1811no—
134C22×C4C22×D18111yescharacteristic
135C2×C8—21no—
136C2×C8—3621no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—3621no—
141C4⋊C4—3621no—
142C4⋊C4—3621no—
143C4⋊C4—3621no—
144C4⋊C4—3621no—
145C4⋊C4—3621no—
146C4⋊C4—3621no—
147C4⋊C4—3621no—
148C4⋊C4—1811no—
149C4⋊C4—7242no—
150C4⋊C4C22⋊D18111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3621no—
153C42—3621no—
154C42—3621no—
155C23D4×D18111yescharacteristic
156Q8—41no—
157Q8—14481no—
158Q8—7241no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—3621no—
166C2×C4—3621no—
167C2×C4—3622no—
168C2×C4—3621no—
169C2×C4—3621no—
170C2×C4—3621no—
171C2×C4—1812no—
172C2×C4—7241no—
173C2×C4—7241no—
174C2×C4—7241no—
175C2×C4D4×D18111yescharacteristic
176C2×C4C2×C22⋊D18111yescharacteristic
177C8—41no—
178C8—7241no—
179C22—21no—
180C22—21no—
181C22#1915378411yescharacteristic
182C22SD16×D18111yescharacteristic
183C22#1915384511yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—81no—
189C4—3622no—
190C4—7242no—
191C4—7241no—
192C4—7241no—
193C4—7241no—
194C2—21no—
195C2—21no—
196C2#2604141611yescharacteristic
197C2#2604146011yescharacteristic
198C2#2604146811yescharacteristic
subgroupG/H
centerC22#19153784
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#483×C181C2
socleC22×C181#120
prime radicalC23×C181C2×D4
hypercenter#483D181
hypocenterC181#1611
LCSG ▷ C22×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
99. C181#1611semidirect

Maximal subgroups

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

subgroupindex
#260419082
#260416092
#260412102
#260410172
#260410162
#260410042
#483×C1812
#1611181