Finite Group Databasebeta

← #37544007

Subgroups — #37544007

Order 23168.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#26041756C211yesmaximal, characteristic, complemented
2#26041600C212yesmaximal, complemented
3#26041583C212yesmaximal, complemented
4#26041476C212yesmaximal, complemented
5#26041417C212yesmaximal, complemented
6#26041379C212yesmaximal, complemented
7C4×#15668437C212yesmaximal, complemented
8#26041340C211yesmaximal, characteristic, complemented
9#540×C181C211yesmaximal, characteristic
10C22×Dic362C2211yescharacteristic
11C2×#15668437C2212yes—
12C2×#15668437C2212yes—
13C4×Dic362C2212yes—
14C4×Dic362C2212yes—
15#19153781—22no—
16#19153775C2211yescharacteristic
17#19153772—22no—
18#19153749C2212yes—
19#19153747C2212yes—
20C4⋊#13089678C2212yes—
21#19153739C2212yes—
22#19153739C2212yes—
23#19153737C2212yes—
24#19153737C2212yes—
25C22⋊#13089678C2212yes—
26#19153727C2211yescharacteristic
27C4×#13089678C2211yescharacteristic
28#127×C181C2211yescharacteristic
29#125×C181C2211yescharacteristic
30#123×C181—22no—
31#121×C181—22no—
32#121×C181C2212yes—
33C4×D4×C181C2212yes—
34#117×C181C2211yescharacteristic
35C2×Dic362—24no—
36C2×Dic362—21no—
37C2×Dic362C2312yes—
38C22×Dic181—21no—
39#15668437—24no—
40#15668437—24no—
41C2×#13089678C2312yes—
42C2×#13089678C2312yes—
43C4⋊Dic181C2312yes—
44#15668428—22no—
45#15668428—22no—
46C22⋊Dic181—21no—
47C4×Dic181—22no—
48C4×Dic181—22no—
49C4×Dic181—21no—
50C2×D4×C181—22no—
51C2×D4×C181—22no—
52C2×D4×C181C2312yes—
53C22×C4×C181—22no—
54C22×C4×C181C2311yescharacteristic
55C4⋊C4×C181—22no—
56C4⋊C4×C181D412yes—
57C4⋊C4×C181C2312yes—
58C22⋊C4×C181—22no—
59C22⋊C4×C181—22no—
60C22⋊C4×C181D412yes—
61C42×C181C2311yescharacteristic
62C42×C181C2311yescharacteristic
63Dic362—24no—
64Dic362—22no—
65Dic362#4114yes—
66C2×Dic181—24no—
67C2×Dic181—22no—
68C2×Dic181—22no—
69#13089678—22no—
70#13089678—22no—
71C23×C181—22no—
72C23×C181C2×D411yescharacteristic
73D4×C181—22no—
74D4×C181—22no—
75D4×C181—82no—
76D4×C181—82no—
77C2×C4×C181—22no—
78C2×C4×C181—22no—
79C2×C4×C181—82no—
80C2×C4×C181C2×D412yes—
81C2×C4×C181C2×D412yes—
82C2×C4×C181C2×D411yescharacteristic
83C2×C4×C181C2411yescharacteristic
84C22×C181—21no—
85C22×C181—22no—
86C22×C181—42no—
87C22×C181—42no—
88C22×C181—42no—
89C22×C181C22×D411yescharacteristic
90C4×C181—21no—
91C4×C181—22no—
92C4×C181—22no—
93C4×C181—42no—
94C4×C181C2×#4112yes—
95Dic181—24no—
96Dic181—42no—
97C2×C181—41no—
98C2×C181—82no—
99C2×C181#52511yescharacteristic
100C2×C181#57712yes—
101C181#312611yescharacteristic, complemented, Sylow
102#3126—1811nomaximal, Sylow
103#540D18111yescharacteristic
104#519—1811no—
105#482—1812no—
106#479—1812no—
107#460—1812no—
108#448—1812no—
109#440—1812no—
110C4×SD16—1812no—
111#433—1811no—
112C22×Q8—1811no—
113C2×SD16—1812no—
114C2×SD16—1812no—
115#127C2×D18111yescharacteristic
116#125C2×D18111yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D18112yes—
120C4×Q8—3622no—
121C4×Q8—1812no—
122C4×Q8—1812no—
123C4×D4C2×D18112yes—
124#117—3622no—
125#117—1811no—
126#117C2×D18111yescharacteristic
127#107—1812no—
128#106—1812no—
129C4⋊C8—1812no—
130#103—1812no—
131#103—1812no—
132#102—1812no—
133#102—1812no—
134C22⋊C8—1812no—
135#97—1811no—
136C4×C8—1811no—
137C2×Q8—3624no—
138C2×Q8—3621no—
139C2×Q8—1812no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D18112yes—
143C22×C4—22no—
144C22×C4—3621no—
145C22×C4C22×D18111yescharacteristic
146SD16—3624no—
147SD16—3624no—
148C2×C8—1812no—
149C2×C8—1812no—
150C4⋊C4—22no—
151C4⋊C4—3622no—
152C4⋊C4—3622no—
153C4⋊C4—1812no—
154C4⋊C4C22⋊D18112yes—
155C4⋊C4C22×D18112yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—3621no—
159C22⋊C4C22⋊D18112yes—
160C42—3622no—
161C42—3622no—
162C42—3621no—
163C42C22×D18111yescharacteristic
164C42C22×D18111yescharacteristic
165C23—22no—
166C23C2×C22⋊D18111yescharacteristic
167Q8—3624no—
168Q8—3622no—
169Q8—1814no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—3624no—
178C2×C4—3622no—
179C2×C4—3622no—
180C2×C4C2×C22⋊D18112yes—
181C2×C4C2×C22⋊D18112yes—
182C2×C4C2×C22⋊D18111yescharacteristic
183C2×C4C23×D18111yescharacteristic
184C8—3622no—
185C8—3622no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D18111yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—3624no—
197C4—7242no—
198C4#41×D18112yes—
199C2—41no—
200C2—82no—
201C2#2604178611yescharacteristic
202C2#2604209012yes—
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting, prime radical#540×C181C2
socleC22×C181C22×D4
hypercenter#540D181
hypocenterC181#3126
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #26041756C2semidirect
2. #26041600C2semidirect
3. #26041583C2semidirect
4. #26041476C2semidirect
5. #26041417C2semidirect
6. #26041379C2semidirect
7. C4×#15668437C2semidirect
8. #26041340C2semidirect
101. C181#3126semidirect

Maximal subgroups

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

subgroupindex
#260417562
#260416002
#260415832
#260414762
#260414172
#260413792
C4×#156684372
#260413402
#540×C1812
#3126181