Finite Group Databasebeta

← #37545112

Subgroups — #37545112

Order 23168.

342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 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#26041564C212yesmaximal, complemented
3#26041561C212yesmaximal, complemented
4#26041535C214yesmaximal
5#26041489C212yesmaximal, complemented
6#26041486C212yesmaximal, complemented
7#26041303C211yesmaximal, characteristic
8#533×C181C211yesmaximal, characteristic
9C2×#15668439C2214yes—
10C2×#15668433C2212yes—
11#19153816C2211yescharacteristic
12#19153816C2211yescharacteristic
13#19153808—21no—
14#19153795—21no—
15#19153795C2212yes—
16C4×Dic362—21no—
17C4×Dic362C2212yes—
18#19153775—21no—
19#19153747C2214yes—
20C4⋊#13089678C2212yes—
21C4⋊#13089678C2212yes—
22#19153740C2214yes—
23#19153739C2214yes—
24C4⋊Q8×C181C2211yescharacteristic
25C4⋊Q8×C181C2211yescharacteristic
26#125×C181—21no—
27C22⋊Q8×C181—21no—
28C22⋊Q8×C181C2212yes—
29C4×Q8×C181—21no—
30C4×Q8×C181C2212yes—
31#117×C181—21no—
32C2×C42×C181C2211yescharacteristic
33C2×Dic362—21no—
34C2×Dic362C2312yes—
35#15668439—44no—
36#15668433—42no—
37C2×#13089678C2314yes—
38C4⋊Dic181—21no—
39C4⋊Dic181—21no—
40C4⋊Dic181—21no—
41C4⋊Dic181C2312yes—
42#15668428—22no—
43#15668428—22no—
44C22⋊Dic181—22no—
45C4×Dic181—22no—
46C2×Q8×C181—21no—
47C2×Q8×C181C2312yes—
48C22×C4×C181D411yescharacteristic
49C22×C4×C181D411yescharacteristic
50C22×C4×C181C2311yescharacteristic
51C4⋊C4×C181—21no—
52C4⋊C4×C181—21no—
53C4⋊C4×C181—21no—
54C4⋊C4×C181—22no—
55C4⋊C4×C181—22no—
56C4⋊C4×C181C2312yes—
57C22⋊C4×C181—22no—
58C42×C181—22no—
59C42×C181D411yescharacteristic
60C42×C181D411yescharacteristic
61C42×C181C2311yescharacteristic
62C42×C181C2311yescharacteristic
63Dic362—22no—
64Dic362—22no—
65Dic362—42no—
66C2×Dic181—22no—
67C2×Dic181—22no—
68#13089678—24no—
69C23×C181C2×D411yescharacteristic
70Q8×C181—22no—
71Q8×C181—22no—
72Q8×C181—42no—
73C2×C4×C181—22no—
74C2×C4×C181—22no—
75C2×C4×C181—21no—
76C2×C4×C181—21no—
77C2×C4×C181—22no—
78C2×C4×C181—22no—
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—21no—
88C22×C181C22×D411yescharacteristic
89C4×C181—21no—
90C4×C181—21no—
91C4×C181—21no—
92C4×C181—42no—
93C4×C181—42no—
94C4×C181#13712yes—
95C4×C181#13712yes—
96C4×C181H(5,𝔽2)11yescharacteristic
97C4×C1812−1+411yescharacteristic
98Dic181—42no—
99Dic181—42no—
100C2×C181—41no—
101C2×C181#53711yescharacteristic
102C2×C181C2×#13711yescharacteristic
103C2×C181C2×#13711yescharacteristic
104C181#325511yescharacteristic, complemented, Sylow
105#3255—1811nomaximal, Sylow
106#533—1811no—
107#533D18111yescharacteristic
108#475—1812no—
109#475—1812no—
110#470—1814no—
111#462—1812no—
112#462—1812no—
113#423—1811no—
114C2×Q16—1814no—
115C2×M16—1812no—
116C4⋊Q8—1811no—
117C4⋊Q8—1811no—
118C4⋊Q8C2×D18111yescharacteristic
119C4⋊Q8C2×D18111yescharacteristic
120#125—21no—
121#125—3621no—
122C22⋊Q8—21no—
123C22⋊Q8—3621no—
124C22⋊Q8—1812no—
125C22⋊Q8C2×D18112yes—
126C4×Q8—21no—
127C4×Q8—3621no—
128C4×Q8—1812no—
129C4×Q8C2×D18112yes—
130#117—21no—
131#117—3621no—
132C2×C42C2×D18111yescharacteristic
133#106—1814no—
134C4⋊C8—1812no—
135C4⋊C8—1812no—
136#103—1814no—
137#103—1814no—
138C2×Q8—21no—
139C2×Q8—3621no—
140C2×Q8—1812no—
141C2×Q8C22×D18112yes—
142C22×C4C22⋊D18111yescharacteristic
143C22×C4C22⋊D18111yescharacteristic
144C22×C4C22×D18111yescharacteristic
145Q16—7244no—
146M16—7242no—
147C2×C8—1814no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—3621no—
154C4⋊C4—3621no—
155C4⋊C4—3621no—
156C4⋊C4—3622no—
157C4⋊C4—3622no—
158C4⋊C4—1812no—
159C4⋊C4C22×D18112yes—
160C22⋊C4—22no—
161C22⋊C4—3622no—
162C42—22no—
163C42—3622no—
164C42C22⋊D18111yescharacteristic
165C42C22⋊D18111yescharacteristic
166C42C22×D18111yescharacteristic
167C42C22×D18111yescharacteristic
168C23C2×C22⋊D18111yescharacteristic
169Q8—22no—
170Q8—22no—
171Q8—42no—
172Q8—3622no—
173Q8—3622no—
174Q8—7242no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—3622no—
182C2×C4—3622no—
183C2×C4C2×C22⋊D18111yescharacteristic
184C2×C4C2×C22⋊D18111yescharacteristic
185C2×C4C2×C22⋊D18111yescharacteristic
186C2×C4C2×C22⋊D18111yescharacteristic
187C2×C4C2×C22⋊D18111yescharacteristic
188C2×C4C23×D18111yescharacteristic
189C8—3624no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22C22×C22⋊D18111yescharacteristic
194C4—21no—
195C4—21no—
196C4—21no—
197C4—42no—
198C4—42no—
199C4—7242no—
200C4—7242no—
201C4#1915384612yes—
202C4#1915384712yes—
203C4#1915386211yescharacteristic
204C4#1915386311yescharacteristic
205C2—41no—
206C2#2604185711yescharacteristic
207C2C2×#1915384611yescharacteristic
208C2C2×#1915384711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#533×C181C2
socleC22×C181C22×D4
prime radicalC23×C181C2×D4
hypercenter#533D181
hypocenterC181#3255
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #26041564C2semidirect
3. #26041561C2semidirect
5. #26041489C2semidirect
6. #26041486C2semidirect
104. C181#3255semidirect

Maximal subgroups

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

subgroupindex
#260418362
#260415642
#260415612
#260415352
#260414892
#260414862
#260413032
#533×C1812
#3255181