Finite Group Databasebeta

← #37532283

Subgroups — #37532283

Order 23168.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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#26041831C211yesmaximal, characteristic
2#26041329C211yesmaximal, characteristic
3#26041143C211yesmaximal, characteristic
4#26041017C211yesmaximal, characteristic
5#26041016C211yesmaximal, characteristic
6#26041015C211yesmaximal, characteristic
7#328×C181C211yesmaximal, characteristic
8#19153815C411yescharacteristic, complemented
9#19153814C411yescharacteristic, complemented
10#19153806—21no—
11#19153795C2211yescharacteristic
12#19153793—21no—
13Q8×Dic181C411yescharacteristic, complemented
14#19153781—21no—
15#19153781C411yescharacteristic, complemented
16#19153772—21no—
17C2×#15668428—21no—
18C2×C4×Dic181C2211yescharacteristic
19#19153745—21no—
20C22⋊#13089678C2211yescharacteristic
21C8×Dic181—21no—
22#19153723—21no—
23#19153723C2211yescharacteristic
24C22⋊Q8×C181C2211yescharacteristic
25C22⋊C8×C181C2211yescharacteristic
26#95×C181C2211yescharacteristic
27C2×Dic362—21no—
28C2×Dic362C2×C411yescharacteristic
29C22×Dic181—21no—
30C22×Dic181D411yescharacteristic
31C22×Dic181D411yescharacteristic
32C2×#13089678—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181C2×C411yescharacteristic
35#15668428—21no—
36#15668428—21no—
37#15668428—21no—
38#15668428—21no—
39#15668428—21no—
40#15668428—42no—
41C22⋊Dic181—21no—
42C4×Dic181—21no—
43C4×Dic181—21no—
44C4×Dic181C2×C411yescharacteristic
45C4×Dic181C2×C411yescharacteristic
46C4×Dic181D411yescharacteristic
47C4×Dic181D411yescharacteristic
48C2×Q8×C181C2×C411yescharacteristic
49C22×C4×C181—21no—
50C22×C4×C181C2311yescharacteristic
51C2×C8×C181—21no—
52C4⋊C4×C181—21no—
53C4⋊C4×C181C2×C411yescharacteristic
54C22⋊C4×C181—21no—
55Dic362—42no—
56Dic362—41no—
57C2×Dic181—21no—
58C2×Dic181—21no—
59C2×Dic181—41no—
60C2×Dic181—41no—
61C2×Dic181—41no—
62C2×Dic181—41no—
63C2×Dic181C22⋊C411yescharacteristic
64C2×Dic181C22⋊C411yescharacteristic
65C2×Dic181C22⋊C411yescharacteristic
66C2×Dic181C22⋊C411yescharacteristic
67C2×Dic181SD1612yes—
68C2×Dic181Q1612yes—
69#13089678—41no—
70C23×C181C2×D411yescharacteristic
71Q8×C181—41no—
72C2×C4×C181—21no—
73C2×C4×C181—21no—
74C2×C4×C181—41no—
75C2×C4×C181—41no—
76C2×C4×C181—41no—
77C2×C4×C181—41no—
78C2×C4×C181C22×C411yescharacteristic
79C2×C4×C181C2×D411yescharacteristic
80C8×C181—41no—
81C22×C181—21no—
82C22×C181—21no—
83C22×C181C2×C22⋊C411yescharacteristic
84C22×C181C2×SD1611yescharacteristic
85C22×C181C2×Q1611yescharacteristic
86C4×C181—21no—
87C4×C181—21no—
88C4×C181—41no—
89C4×C181—41no—
90C4×C181—81no—
91Dic181—21no—
92Dic181—21no—
93Dic181—41no—
94Dic181—41no—
95Dic181—81no—
96Dic181#10312yes—
97Dic181#10312yes—
98C2×C181—21no—
99C2×C181—21no—
100C2×C181#41011yescharacteristic
101C2×C181C2×#10311yescharacteristic
102C2×C181#42111yescharacteristic
103C181#151811yescharacteristic, complemented, Sylow
104#1518—1811nomaximal, Sylow
105#533—1811no—
106#431—1811no—
107#382—1811no—
108#328—1811no—
109#328—1811no—
110#328—1811no—
111#328D18111yescharacteristic
112C4⋊Q8—1811no—
113C4⋊Q8—1811no—
114#125—3621no—
115C22⋊Q8—3621no—
116C22⋊Q8—1811no—
117C22⋊Q8C2×D18111yescharacteristic
118C4×Q8—3621no—
119C4×Q8—1811no—
120C4×Q8—1811no—
121#117—3621no—
122C2×C4⋊C4—3621no—
123C2×C42—1811no—
124C4⋊C8—3621no—
125C22⋊C8—1811no—
126C22⋊C8C2×D18111yescharacteristic
127C4×C8—3621no—
128#95—3621no—
129#95—1811no—
130#95C2×D18111yescharacteristic
131C2×Q8—3621no—
132C2×Q8—1811no—
133C2×Q8C4×D18111yescharacteristic
134C22×C4—21no—
135C22×C4—3621no—
136C22×C4—1811no—
137C22×C4—1811no—
138C22×C4C22×D18111yescharacteristic
139C2×C8—21no—
140C2×C8—3621no—
141C4⋊C4—21no—
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⋊C4C4×D18111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3621no—
153C42—3621no—
154C42—3621no—
155C42—1811no—
156C42—1811no—
157C42—1811no—
158C42—1811no—
159C23D4×D18111yescharacteristic
160Q8—41no—
161Q8—7241no—
162Q8—7242no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3621no—
170C2×C4—3621no—
171C2×C4—1811no—
172C2×C4—1811no—
173C2×C4—1811no—
174C2×C4—1811no—
175C2×C4—1812no—
176C2×C4—1812no—
177C2×C4—7241no—
178C2×C4—7241no—
179C2×C4—7241no—
180C2×C4—7241no—
181C2×C4C2×C4×D18111yescharacteristic
182C2×C4D4×D18111yescharacteristic
183C8—41no—
184C8—7241no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D18111yescharacteristic
188C22SD16×D18111yescharacteristic
189C22Q16×D18111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—3621no—
196C4—3621no—
197C4—14481no—
198C4—1812no—
199C4—1812no—
200C4—7241no—
201C4—7241no—
202C2—21no—
203C2—21no—
204C2#2604125111yescharacteristic
205C2#103×D18111yescharacteristic
206C2#2604129411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D181
commutatorC2×C4×C181C22×C4
FrattiniC22×C4C22×D181
Fitting#328×C181C2
socleC22×C181C2×C22⋊C4
prime radicalC23×C181C2×D4
cosocleC22×C4×C181C23
hypercenter#328D181
hypocenterC181#1518
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #19153815C4semidirect
9. #19153814C4semidirect
13. Q8×Dic181C4semidirect
15. #19153781C4semidirect
103. C181#1518semidirect

Maximal subgroups

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

subgroupindex
#260418312
#260413292
#260411432
#260410172
#260410162
#260410152
#328×C1812
#1518181