Finite Group Databasebeta

← #37545167

Subgroups — #37545167

Order 23168.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#26041891C211yesmaximal, characteristic, complemented
2#26041583C212yesmaximal, complemented
3#26041579C212yesmaximal, complemented
4#26041523C212yesmaximal, complemented
5#26041506C212yesmaximal, complemented
6#26041484C212yesmaximal, complemented
7#26041476C212yesmaximal, complemented
8#26041306C211yesmaximal, characteristic, complemented
9#540×C181C211yesmaximal, characteristic
10C2×#15668437C2212yes—
11C2×#15668437C2212yes—
12C2×#15668433C2211yescharacteristic
13C22×#13089678C2211yescharacteristic
14#19153816C2211yescharacteristic
15#19153809—22no—
16#19153808C2211yescharacteristic
17#19153806—22no—
18#19153795C2212yes—
19C4×Dic362C2212yes—
20#19153749C2212yes—
21#19153747C2212yes—
22C4⋊#13089678C2212yes—
23C4⋊#13089678C2212yes—
24#19153739C2212yes—
25#19153739C2212yes—
26#19153737C2212yes—
27#19153737C2212yes—
28#127×C181C2211yescharacteristic
29#125×C181C2211yescharacteristic
30#123×C181—22no—
31#121×C181—22no—
32#121×C181C2212yes—
33C4×D4×C181C2212yes—
34#117×C181C2211yescharacteristic
35C2×Dic362C2312yes—
36#15668437—42no—
37#15668437—42no—
38#15668433—41no—
39C2×#13089678—41no—
40C2×#13089678C2312yes—
41C2×#13089678C2312yes—
42C4⋊Dic181—22no—
43C4⋊Dic181C2312yes—
44#15668428—22no—
45#15668428—22no—
46#15668428—22no—
47C22⋊Dic181—22no—
48C4×Dic181—22no—
49C2×D4×C181—22no—
50C2×D4×C181—22no—
51C2×D4×C181C2312yes—
52C22×C4×C181—22no—
53C22×C4×C181C2311yescharacteristic
54C4⋊C4×C181—22no—
55C4⋊C4×C181D412yes—
56C4⋊C4×C181C2312yes—
57C22⋊C4×C181—22no—
58C22⋊C4×C181—22no—
59C22⋊C4×C181D412yes—
60C42×C181C2311yescharacteristic
61C42×C181C2311yescharacteristic
62Dic362—22no—
63Dic362—22no—
64C2×Dic181—22no—
65C2×Dic181—22no—
66#13089678—22no—
67#13089678—22no—
68C23×C181—22no—
69C23×C181C2×D411yescharacteristic
70D4×C181—22no—
71D4×C181—22no—
72D4×C181—82no—
73D4×C181—82no—
74C2×C4×C181—21no—
75C2×C4×C181—21no—
76C2×C4×C181—22no—
77C2×C4×C181—82no—
78C2×C4×C181C2×D412yes—
79C2×C4×C181C2×D412yes—
80C2×C4×C181C2×D411yescharacteristic
81C2×C4×C181C2411yescharacteristic
82C22×C181—21no—
83C22×C181—22no—
84C22×C181—42no—
85C22×C181—42no—
86C22×C181—42no—
87C22×C181C22×D411yescharacteristic
88C4×C181—21no—
89C4×C181—22no—
90C4×C181—22no—
91C4×C181—42no—
92C4×C181H(5,𝔽2)11yescharacteristic
93C4×C1812−1+411yescharacteristic
94Dic181—42no—
95Dic181—42no—
96C2×C181—41no—
97C2×C181—82no—
98C2×C181#53711yescharacteristic
99C2×C181#57712yes—
100C181#326011yescharacteristic, complemented, Sylow
101#3260—1811nomaximal, Sylow
102#541—1811no—
103#540D18111yescharacteristic
104#479—1812no—
105#478—1812no—
106#468—1812no—
107#465—1812no—
108#461—1812no—
109#460—1812no—
110#424—1811no—
111C2×SD16—1812no—
112C2×SD16—1812no—
113C2×M16—1811no—
114C22×C8—1811no—
115C4⋊Q8—1811no—
116#127C2×D18111yescharacteristic
117#126—3622no—
118#125—3622no—
119#125—1811no—
120#125C2×D18111yescharacteristic
121#123—22no—
122C22⋊Q8—1812no—
123#121—22no—
124#121C2×D18112yes—
125C4×Q8—1812no—
126C4×D4C2×D18112yes—
127#117C2×D18111yescharacteristic
128#107—1812no—
129#106—1812no—
130C4⋊C8—1812no—
131C4⋊C8—1812no—
132#103—1812no—
133#103—1812no—
134#102—1812no—
135#102—1812no—
136C2×Q8—1812no—
137C2×D4—22no—
138C2×D4—22no—
139C2×D4C22×D18112yes—
140C22×C4—22no—
141C22×C4C22×D18111yescharacteristic
142SD16—7242no—
143SD16—7242no—
144M16—7241no—
145C2×C8—1812no—
146C2×C8—1812no—
147C2×C8—7241no—
148C4⋊C4—22no—
149C4⋊C4—3622no—
150C4⋊C4—3622no—
151C4⋊C4—3622no—
152C4⋊C4—3622no—
153C4⋊C4—1812no—
154C4⋊C4C22⋊D18112yes—
155C4⋊C4C22×D18112yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—3622no—
159C22⋊C4C22⋊D18112yes—
160C42—3622no—
161C42C22×D18111yescharacteristic
162C42C22×D18111yescharacteristic
163C23—22no—
164C23C2×C22⋊D18111yescharacteristic
165Q8—3622no—
166Q8—3622no—
167D4—22no—
168D4—22no—
169D4—82no—
170D4—82no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—82no—
175C2×C4—3622no—
176C2×C4—3622no—
177C2×C4C2×C22⋊D18112yes—
178C2×C4C2×C22⋊D18112yes—
179C2×C4C2×C22⋊D18111yescharacteristic
180C2×C4C23×D18111yescharacteristic
181C8—3622no—
182C8—3622no—
183C22—21no—
184C22—22no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22C22×C22⋊D18111yescharacteristic
189C4—21no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—7242no—
194C4—7242no—
195C4#1915386211yescharacteristic
196C4#1915386311yescharacteristic
197C2—41no—
198C2—82no—
199C2#2604185711yescharacteristic
200C2#2604209012yes—
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting, prime radical#540×C181C2
socleC22×C181C22×D4
hypercenter#540D181
hypocenterC181#3260
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. #26041891C2semidirect
2. #26041583C2semidirect
3. #26041579C2semidirect
4. #26041523C2semidirect
5. #26041506C2semidirect
6. #26041484C2semidirect
7. #26041476C2semidirect
8. #26041306C2semidirect
100. C181#3260semidirect

Maximal subgroups

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

subgroupindex
#260418912
#260415832
#260415792
#260415232
#260415062
#260414842
#260414762
#260413062
#540×C1812
#3260181