Finite Group Databasebeta

← #37532764

Subgroups — #37532764

Order 23168.

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

normal subgroups only

This group has 202 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#26041615C211yesmaximal, characteristic
3#26041612C211yesmaximal, characteristic
4#26041219C211yesmaximal, characteristic
5#26041015C211yesmaximal, characteristic
6#26041004C211yesmaximal, characteristic
7#328×C181C211yesmaximal, characteristic
8#19153815—21no—
9#19153814—21no—
10#19153806—21no—
11#19153806—21no—
12#19153795C2211yescharacteristic
13#19153793—21no—
14#19153772—21no—
15C2×C4⋊Dic181C2211yescharacteristic
16C2×#15668428C2211yescharacteristic
17#19153750—21no—
18#19153749—21no—
19#19153741—21no—
20#19153740—21no—
21C22⋊#13089678C2211yescharacteristic
22#19153723—21no—
23#19153723—21no—
24C22⋊Q8×C181C2211yescharacteristic
25C22⋊C8×C181C2211yescharacteristic
26#95×C181C2211yescharacteristic
27C2×Dic362—21no—
28C2×Dic362D411yescharacteristic
29C22×Dic181—21no—
30C22×Dic181D411yescharacteristic
31C22×Dic181D411yescharacteristic
32C2×#13089678—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181—21no—
35C4⋊Dic181—21no—
36C4⋊Dic181D411yescharacteristic
37#15668428—21no—
38#15668428—21no—
39#15668428—21no—
40#15668428—21no—
41#15668428—21no—
42#15668428—21no—
43#15668428—21no—
44C22⋊Dic181—21no—
45C4×Dic181—21no—
46C4×Dic181—21no—
47C2×Q8×C181D411yescharacteristic
48C22×C4×C181—21no—
49C22×C4×C181C2311yescharacteristic
50C2×C8×C181—21no—
51C4⋊C4×C181—21no—
52C4⋊C4×C181D411yescharacteristic
53C22⋊C4×C181—21no—
54Dic362—41no—
55Dic362—81no—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C2×Dic181—21no—
59C2×Dic181—21no—
60C2×Dic181—21no—
61C2×Dic181—41no—
62C2×Dic181—42no—
63C2×Dic181—41no—
64C2×Dic181Q1612yes—
65#13089678—41no—
66C23×C181C2×D411yescharacteristic
67Q8×C181—41no—
68C2×C4×C181—21no—
69C2×C4×C181—21no—
70C2×C4×C181—41no—
71C2×C4×C181—41no—
72C2×C4×C181—41no—
73C2×C4×C181—41no—
74C2×C4×C181C2×D411yescharacteristic
75C2×C4×C181C2×D411yescharacteristic
76C8×C181—41no—
77C22×C181—21no—
78C22×C181—21no—
79C22×C181#12011yescharacteristic
80C22×C181C2×Q1611yescharacteristic
81C22×C181#13711yescharacteristic
82C4×C181—21no—
83C4×C181—21no—
84C4×C181—41no—
85C4×C181—41no—
86C4×C181—81no—
87Dic181—22no—
88Dic181—41no—
89Dic181—41no—
90Dic181—41no—
91Dic181—81no—
92C2×C181—21no—
93C2×C181—21no—
94C2×C181#45111yescharacteristic
95C2×C181#45411yescharacteristic
96C2×C181#45811yescharacteristic
97C181#161711yescharacteristic, complemented, Sylow
98#1617—1811nomaximal, Sylow
99#544—1811no—
100#484—1811no—
101#484—1811no—
102#400—1811no—
103#328—1811no—
104#328D18111yescharacteristic
105#324—1811no—
106C4⋊Q8—3621no—
107C4⋊Q8—3621no—
108#125—3621no—
109#125—3621no—
110C22⋊Q8—3621no—
111C22⋊Q8—1811no—
112C22⋊Q8C2×D18111yescharacteristic
113#117—3621no—
114C2×C4⋊C4—1811no—
115C2×C4⋊C4—1811no—
116#107—3621no—
117#107—3621no—
118#103—3621no—
119#103—3621no—
120C22⋊C8—1811no—
121C22⋊C8C2×D18111yescharacteristic
122#95—3621no—
123#95—3621no—
124#95C2×D18111yescharacteristic
125C2×Q8—3621no—
126C2×Q8—1811no—
127C2×Q8D72411yescharacteristic
128C22×C4—21no—
129C22×C4—3621no—
130C22×C4—1811no—
131C22×C4—1811no—
132C22×C4C22×D18111yescharacteristic
133C2×C8—21no—
134C2×C8—3621no—
135C4⋊C4—21no—
136C4⋊C4—3621no—
137C4⋊C4—3621no—
138C4⋊C4—3621no—
139C4⋊C4—3621no—
140C4⋊C4—3621no—
141C4⋊C4—3621no—
142C4⋊C4—3621no—
143C4⋊C4—3621no—
144C4⋊C4—3621no—
145C4⋊C4—3621no—
146C4⋊C4—1811no—
147C4⋊C4D72411yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—3621no—
150C42—3621no—
151C42—3621no—
152C23D4×D18111yescharacteristic
153Q8—41no—
154Q8—14481no—
155Q8—7241no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—3621no—
163C2×C4—3621no—
164C2×C4—3621no—
165C2×C4—3621no—
166C2×C4—3621no—
167C2×C4—1812no—
168C2×C4—7242no—
169C2×C4—7241no—
170C2×C4—7241no—
171C2×C4D4×D18111yescharacteristic
172C2×C4C2×D72411yescharacteristic
173C8—41no—
174C8—7241no—
175C22—21no—
176C22—21no—
177C22#1915378611yescharacteristic
178C22Q16×D18111yescharacteristic
179C22#1915384511yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—3622no—
186C4—14481no—
187C4—7241no—
188C4—7241no—
189C4—7241no—
190C2—21no—
191C2—21no—
192C2#2604143611yescharacteristic
193C2#2604145311yescharacteristic
194C2#2604147011yescharacteristic
subgroupG/H
centerC22#19153786
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#328×C181C2
socleC22×C181#120
prime radicalC23×C181C2×D4
hypercenter#328D181
hypocenterC181#1617
LCSG ▷ C22×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
97. C181#1617semidirect

Maximal subgroups

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

subgroupindex
#260419082
#260416152
#260416122
#260412192
#260410152
#260410042
#328×C1812
#1617181