Finite Group Databasebeta

← #37543851

Subgroups — #37543851

Order 23168.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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#26041836C211yesmaximal, characteristic
2#26041609C212yesmaximal
3#26041564C212yesmaximal, complemented
4#26041489C212yesmaximal, complemented
5#26041435C212yesmaximal
6#26041384C214yesmaximal, complemented
7#26041336C211yesmaximal, characteristic
8C2×C4×Q8×C181C211yesmaximal, characteristic
9C2×#15668439C2214yes—
10#19153816C2211yescharacteristic
11#19153816C2211yescharacteristic
12#19153808—21no—
13#19153795—21no—
14#19153795C2212yes—
15C4×Dic362—21no—
16C4×Dic362C2212yes—
17#19153775—21no—
18#19153747C2214yes—
19C4⋊#13089678C2212yes—
20#19153740C2214yes—
21#19153739C2214yes—
22C22⋊#13089678C2212yes—
23#19153727C2212yes—
24C22×Q8×C181C2211yescharacteristic
25C4×Q8×C181—21no—
26C4×Q8×C181—21no—
27C4×Q8×C181C2212yes—
28C4×Q8×C181C2212yes—
29C2×C4⋊C4×C181—21no—
30C2×C4⋊C4×C181C2211yescharacteristic
31C2×C42×C181—21no—
32C2×C42×C181C2211yescharacteristic
33C2×Dic362—21no—
34C2×Dic362C2312yes—
35#15668439—28no—
36C2×#13089678C2314yes—
37C4⋊Dic181—21no—
38C4⋊Dic181—21no—
39C4⋊Dic181—21no—
40C4⋊Dic181C2312yes—
41#15668428—22no—
42#15668428—22no—
43C22⋊Dic181—22no—
44C4×Dic181—22no—
45C2×Q8×C181—24no—
46C2×Q8×C181—21no—
47C2×Q8×C181C2312yes—
48C22×C4×C181—21no—
49C22×C4×C181—21no—
50C22×C4×C181D411yescharacteristic
51C22×C4×C181D411yescharacteristic
52C22×C4×C181C2311yescharacteristic
53C4⋊C4×C181—22no—
54C4⋊C4×C181—22no—
55C4⋊C4×C181—21no—
56C4⋊C4×C181C2312yes—
57C42×C181—22no—
58C42×C181—22no—
59C42×C181D411yescharacteristic
60C42×C181D411yescharacteristic
61C42×C181C2311yescharacteristic
62C42×C181C2311yescharacteristic
63Dic362—24no—
64Dic362—42no—
65C2×Dic181—22no—
66C2×Dic181—22no—
67#13089678—24no—
68C23×C181C2×D411yescharacteristic
69Q8×C181—24no—
70Q8×C181—22no—
71Q8×C181#4114yes—
72C2×C4×C181—24no—
73C2×C4×C181—22no—
74C2×C4×C181—22no—
75C2×C4×C181—22no—
76C2×C4×C181—22no—
77C2×C4×C181—22no—
78C2×C4×C181—42no—
79C2×C4×C181C2×D411yescharacteristic
80C2×C4×C181C2×D411yescharacteristic
81C2×C4×C181C2×D411yescharacteristic
82C2×C4×C181C2×D411yescharacteristic
83C2×C4×C181C2×D411yescharacteristic
84C2×C4×C181C2411yescharacteristic
85C22×C181—21no—
86C22×C181—21no—
87C22×C181#13712yes—
88C22×C181C22×D411yescharacteristic
89C4×C181—24no—
90C4×C181—21no—
91C4×C181—21no—
92C4×C181—21no—
93C4×C181—21no—
94C4×C181—42no—
95C4×C181#13712yes—
96C4×C181C2×#4112yes—
97Dic181—42no—
98Dic181—42no—
99C2×C181—22no—
100C2×C181#52511yescharacteristic
101C2×C181C2×#13711yescharacteristic
102C2×C181C2×#13711yescharacteristic
103C181#311311yescharacteristic, complemented, Sylow
104#3113—1811nomaximal, Sylow
105#533—1811no—
106C2×C4×Q8D18111yescharacteristic
107#483—1812no—
108#475—1812no—
109#462—1812no—
110#451—1812no—
111#441—1814no—
112#432—1811no—
113C22×Q8C2×D18111yescharacteristic
114C2×Q16—1814no—
115C4⋊Q8—1811no—
116C4⋊Q8—1811no—
117#125—3621no—
118C22⋊Q8—3621no—
119C22⋊Q8—1812no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—3621no—
123C4×Q8—1812no—
124C4×Q8C2×D18112yes—
125C4×Q8C2×D18112yes—
126#117—3621no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D18111yescharacteristic
129C2×C42—21no—
130C2×C42C2×D18111yescharacteristic
131#106—1814no—
132C4⋊C8—1812no—
133#103—1814no—
134#103—1814no—
135C22⋊C8—1812no—
136#97—1812no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—3621no—
140C2×Q8—1812no—
141C2×Q8C22×D18112yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D18111yescharacteristic
145C22×C4C22⋊D18111yescharacteristic
146C22×C4C22×D18111yescharacteristic
147Q16—3628no—
148C2×C8—1814no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—3621no—
153C4⋊C4—3621no—
154C4⋊C4—3621no—
155C4⋊C4—3622no—
156C4⋊C4—3622no—
157C4⋊C4—1812no—
158C4⋊C4C22×D18112yes—
159C22⋊C4—3622no—
160C42—22no—
161C42—22no—
162C42—3622no—
163C42C22⋊D18111yescharacteristic
164C42C22⋊D18111yescharacteristic
165C42C22×D18111yescharacteristic
166C42C22×D18111yescharacteristic
167C23C2×C22⋊D18111yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—3624no—
171Q8—7242no—
172Q8#1566844914yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—3622no—
181C2×C4—3622no—
182C2×C4C2×C22⋊D18111yescharacteristic
183C2×C4C2×C22⋊D18111yescharacteristic
184C2×C4C2×C22⋊D18111yescharacteristic
185C2×C4C2×C22⋊D18111yescharacteristic
186C2×C4C2×C22⋊D18111yescharacteristic
187C2×C4C23×D18111yescharacteristic
188C8—3624no—
189C22—21no—
190C22—21no—
191C22#1915384612yes—
192C22C22×C22⋊D18111yescharacteristic
193C4—24no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—7242no—
200C4—7242no—
201C4#1915384712yes—
202C4C2×#1566844912yes—
203C2—22no—
204C2#2604179011yescharacteristic
205C2C2×#1915384611yescharacteristic
206C2C2×#1915384711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×C4×Q8×C181C2
socleC22×C181C22×D4
prime radicalC23×C181C2×D4
hypercenterC2×C4×Q8D181
hypocenterC181#3113
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #26041564C2semidirect
4. #26041489C2semidirect
6. #26041384C2semidirect
103. C181#3113semidirect

Maximal subgroups

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

subgroupindex
#260418362
#260416092
#260415642
#260414892
#260414352
#260413842
#260413362
C2×C4×Q8×C1812
#3113181