Finite Group Databasebeta

← #37545191

Subgroups — #37545191

Order 23168.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#26041896C212yesmaximal, complemented
2#26041567C212yesmaximal, complemented
3#26041563C212yesmaximal, complemented
4#26041537C211yesmaximal, characteristic, complemented
5#26041506C212yesmaximal, complemented
6#26041500C212yesmaximal, complemented
7#26041492C212yesmaximal, complemented
8#26041307C211yesmaximal, characteristic, complemented
9#469×C181C211yesmaximal, characteristic
10C2×Dic724C2211yescharacteristic
11C2×#15668437C2212yes—
12C22×#13089678C2211yescharacteristic
13#19153815C2212yes—
14#19153809—22no—
15#19153803—22no—
16#19153803C2212yes—
17#19153797—22no—
18#19153795C2212yes—
19#19153793—22no—
20#19153781C2212yes—
21D4×Dic181C2212yes—
22#19153775C2211yescharacteristic
23#19153748C2211yescharacteristic
24#19153747C2212yes—
25#19153745C2212yes—
26#19153745C2212yes—
27#19153741C2212yes—
28#19153739C2212yes—
29#19153737C2212yes—
30C2×D8×C181C2211yescharacteristic
31C2×M16×C181C2211yescharacteristic
32#121×C181C2212yes—
33#106×C181C2211yescharacteristic
34#102×C181C2212yes—
35C2×Dic362—22no—
36C2×Dic362C2312yes—
37C22×Dic181—22no—
38Dic724—41no—
39#15668437—42no—
40C2×#13089678—41no—
41C2×#13089678C2312yes—
42C4⋊Dic181D412yes—
43C4⋊Dic181C2312yes—
44#15668428—22no—
45#15668428—22no—
46#15668428—22no—
47C22⋊Dic181—22no—
48C22⋊Dic181—22no—
49C22⋊Dic181—22no—
50C22⋊Dic181—22no—
51C22⋊Dic181D411yescharacteristic
52C22⋊Dic181D411yescharacteristic
53C4×Dic181—22no—
54C4×Dic181C2312yes—
55C2×D4×C181—22no—
56C2×D4×C181C2312yes—
57C22×C4×C181C2311yescharacteristic
58D8×C181—41no—
59M16×C181—41no—
60C2×C8×C181C2311yescharacteristic
61C2×C8×C181C2311yescharacteristic
62C4⋊C4×C181C2312yes—
63C22⋊C4×C181—22no—
64Dic362—22no—
65Dic362—22no—
66Dic362—82no—
67C2×Dic181—22no—
68C2×Dic181—22no—
69C2×Dic181—82no—
70C2×Dic181C2×D412yes—
71C2×Dic181C2×D412yes—
72#13089678—22no—
73C23×C181—22no—
74C23×C181C2×D411yescharacteristic
75D4×C181—22no—
76D4×C181—22no—
77D4×C181—82no—
78C2×C4×C181—21no—
79C2×C4×C181—21no—
80C2×C4×C181—22no—
81C2×C4×C181C2×D411yescharacteristic
82C2×C4×C181C2411yescharacteristic
83C8×C181—21no—
84C8×C181—21no—
85C22×C181—21no—
86C22×C181—22no—
87C22×C181—42no—
88C22×C181—42no—
89C22×C181—42no—
90C22×C181C22×D411yescharacteristic
91C4×C181—21no—
92C4×C181—42no—
93C4×C181H(5,𝔽2)11yescharacteristic
94C4×C1812−1+411yescharacteristic
95Dic181—22no—
96Dic181—22no—
97Dic181—42no—
98Dic181—42no—
99C2×C181—41no—
100C2×C181—82no—
101C2×C181#53711yescharacteristic
102C2×C181#57712yes—
103C181#326311yescharacteristic, complemented, Sylow
104#3263—1811nomaximal, Sylow
105#542—1812no—
106#476—1812no—
107#475—1812no—
108#470—1811no—
109#469D18111yescharacteristic
110#465—1812no—
111#464—1812no—
112#463—1812no—
113#424—1811no—
114C2×Q16—1811no—
115C2×SD16—1812no—
116C2×D8C2×D18111yescharacteristic
117C2×M16C2×D18111yescharacteristic
118C22×C8—1811no—
119C4⋊Q8—1812no—
120#126—3622no—
121#124—3622no—
122#124—1812no—
123#123—3622no—
124C22⋊Q8—3622no—
125C22⋊Q8—1812no—
126#121C2×D18112yes—
127C4×Q8—1812no—
128C4×D4—1812no—
129#117—1811no—
130#106—1811no—
131#106—1812no—
132#106C2×D18111yescharacteristic
133C4⋊C8—1812no—
134C4⋊C8—1812no—
135#103—1812no—
136#103—1812no—
137#102—1812no—
138#102C2×D18112yes—
139C2×Q8—3622no—
140C2×Q8—1812no—
141C2×D4—22no—
142C2×D4C22×D18112yes—
143C22×C4—3622no—
144C22×C4C22×D18111yescharacteristic
145Q16—7241no—
146SD16—7242no—
147D8—41no—
148M16—41no—
149C2×C8—1812no—
150C2×C8—7241no—
151C2×C8C22×D18111yescharacteristic
152C2×C8C22×D18111yescharacteristic
153C4⋊C4—3622no—
154C4⋊C4—3622no—
155C4⋊C4—3622no—
156C4⋊C4—1812no—
157C4⋊C4—1812no—
158C4⋊C4C22×D18112yes—
159C22⋊C4—22no—
160C22⋊C4—3622no—
161C22⋊C4—3622no—
162C22⋊C4—3622no—
163C22⋊C4—3622no—
164C22⋊C4—1811no—
165C22⋊C4—1811no—
166C42—3622no—
167C42—1812no—
168C23—22no—
169C23D4×D18111yescharacteristic
170Q8—3622no—
171Q8—3622no—
172Q8—14482no—
173D4—22no—
174D4—22no—
175D4—82no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—3622no—
180C2×C4—3622no—
181C2×C4—14482no—
182C2×C4—1812no—
183C2×C4—1812no—
184C2×C4D4×D18111yescharacteristic
185C2×C4C23×D18111yescharacteristic
186C8—21no—
187C8—21no—
188C8—3622no—
189C22—21no—
190C22—22no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D18111yescharacteristic
195C4—21no—
196C4—42no—
197C4—3622no—
198C4—3622no—
199C4—7242no—
200C4—7242no—
201C4#1915386111yescharacteristic
202C4#1915386311yescharacteristic
203C2—41no—
204C2—82no—
205C2#2604185611yescharacteristic
206C2#2604208912yes—
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting, prime radical#469×C181C2
socleC22×C181C22×D4
hypercenter#469D181
hypocenterC181#3263
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #26041896C2semidirect
2. #26041567C2semidirect
3. #26041563C2semidirect
4. #26041537C2semidirect
5. #26041506C2semidirect
6. #26041500C2semidirect
7. #26041492C2semidirect
8. #26041307C2semidirect
103. C181#3263semidirect

Maximal subgroups

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

subgroupindex
#260418962
#260415672
#260415632
#260415372
#260415062
#260415002
#260414922
#260413072
#469×C1812
#3263181