Finite Group Databasebeta

← #37549763

Subgroups — #37549763

Order 23168.

312 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 66 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#26042359C211yesmaximal, characteristic
2#26042272C212yesmaximal, complemented
3#26042260C211yesmaximal, characteristic
4#26042146C212yesmaximal, complemented
5#26041854C211yesmaximal, characteristic
6#19153904—24no—
7D181⋊M16—22no—
8D181⋊M16C2212yes—
9#19153895C2212yes—
10#19153879—24no—
11#19153875—22no—
12C2×#15668450C2211yescharacteristic
13C2×Q8×D181C2211yescharacteristic
14#19153814C411yescharacteristic, complemented
15#19153805C411yescharacteristic, complemented
16#19153804C411yescharacteristic, complemented
17#19153801—22no—
18#19153794—22no—
19#19153773C2211yescharacteristic
20C4⋊Q8×C181C411yescharacteristic, complemented
21#15668459—24no—
22#15668459—22no—
23#15668458—22no—
24D181⋊C8—24no—
25D181⋊C8D414yes—
26C4⋊#10624382—22no—
27C22⋊#10624382—22no—
28C4×#10624382—22no—
29#15668450—22no—
30#15668450—22no—
31C2×Dic362—21no—
32C2×Dic362C2×C411yescharacteristic
33Q8×D181—22no—
34Q8×D181—22no—
35C2×D724C2×C411yescharacteristic
36C2×D724D412yes—
37C2×C4×D181—21no—
38C2×C4×D181D412yes—
39C2×C4×D181C2311yescharacteristic
40#15668428—21no—
41#15668428—22no—
42#15668426—22no—
43#15668426—22no—
44#15668426—21no—
45C4×Dic181C2×C411yescharacteristic
46C2×Q8×C181C2×C411yescharacteristic
47C2×Q8×C181C2×C411yescharacteristic
48C4⋊C4×C181—22no—
49C42×C181C2×C411yescharacteristic
50C2×#10624382—42no—
51#13089685—24no—
52C22×D181C22⋊C412yes—
53C22×D181C2×D411yescharacteristic
54Dic362—22no—
55Dic362—41no—
56Dic362—41no—
57D724—24no—
58D724—22no—
59C2×Dic181—21no—
60C2×Dic181—21no—
61C2×Dic181C2×D411yescharacteristic
62C4×D181—22no—
63C4×D181—22no—
64C4×D181—42no—
65C4×D181C2×D412yes—
66C4×D181#4112yes—
67Q8×C181—22no—
68Q8×C181—22no—
69C2×C4×C181—21no—
70C2×C4×C181—21no—
71C2×C4×C181C22⋊C412yes—
72C2×C4×C181C22×C411yescharacteristic
73C22×C181C2×C22⋊C411yescharacteristic
74C2×D181—22no—
75C2×D181—41no—
76C2×D181—42no—
77C2×D181#12112yes—
78#10624382—82no—
79C4×C181—22no—
80C4×C181—41no—
81C4×C181—41no—
82C4×C181C4×D412yes—
83Dic181—41no—
84Dic181—41no—
85Dic181#12011yescharacteristic
86Dic181#12311yescharacteristic
87C2×C181—21no—
88C2×C181#38611yescharacteristic
89D181—22no—
90D181—42no—
91C181#190911yescharacteristic, complemented, Sylow
92#1909—1811nomaximal, Sylow
93#568—1811no—
94#536—1811no—
95#419—1812no—
96#410—1811no—
97H(3,ℤ/4)—1812no—
98C2×#41—1811no—
99C22×Q8—1811no—
100#131—3624no—
101C2×M16—3622no—
102C2×M16—1812no—
103C4⋊Q8—1811no—
104C4⋊Q8#1062438211yescharacteristic, complemented
105#124—1811no—
106#124—1811no—
107#123—3622no—
108C22⋊Q8—3622no—
109#117—1812no—
110#117—1811no—
111#103—3624no—
112#99—3622no—
113#41—3622no—
114#41—3622no—
115C2×Q8—3621no—
116C2×Q8—3622no—
117C2×Q8—3622no—
118C2×Q8—1811no—
119C2×Q8C2×#1062438211yescharacteristic
120C2×Q8C2×#1062438211yescharacteristic
121C2×D4—1812no—
122C2×D4—1811no—
123C22×C4—3621no—
124C22×C4—1812no—
125C22×C4—1811no—
126M16—3624no—
127M16—3622no—
128M16—3622no—
129C2×C8—3624no—
130C2×C8—1814no—
131C4⋊C4—22no—
132C4⋊C4—3621no—
133C4⋊C4—3622no—
134C4⋊C4—3622no—
135C22⋊C4—3621no—
136C22⋊C4—3622no—
137C22⋊C4—3622no—
138C22⋊C4—3622no—
139C42—3622no—
140C42—1811no—
141C42C2×#1062438211yescharacteristic
142C23—1812no—
143C23—1811no—
144Q8—22no—
145Q8—22no—
146Q8—3622no—
147Q8—7241no—
148Q8—7241no—
149D4—3624no—
150D4—3622no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—3622no—
154C2×C4—3622no—
155C2×C4—3621no—
156C2×C4—3621no—
157C2×C4—1811no—
158C2×C4—1812no—
159C2×C4—1812no—
160C2×C4—7242no—
161C2×C4—7242no—
162C2×C4C22⋊#1062438212yes—
163C2×C4C22×#1062438211yescharacteristic
164C8—3624no—
165C22—3622no—
166C22—1812no—
167C22—7241no—
168C22—7242no—
169C22C2×C22⋊#1062438211yescharacteristic
170C4—22no—
171C4—41no—
172C4—41no—
173C4—14482no—
174C4—1811no—
175C4—1811no—
176C4—7241no—
177C4—7241no—
178C4D4×#1062438212yes—
179C2—21no—
180C2—3622no—
181C2—7242no—
182C2#2604222711yescharacteristic
subgroupG/H
centerC2#26042227
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4⋊Q8×C181C4
socleC2×C181#386
prime radicalC2×#15668450C22
cosocleC2×C4×D181C23
hypercenterC4⋊Q8#10624382
hypocenterC181#1909
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #26042272C2semidirect
4. #26042146C2semidirect
14. #19153814C4semidirect
15. #19153805C4semidirect
16. #19153804C4semidirect
20. C4⋊Q8×C181C4semidirect
91. C181#1909semidirect
104. C4⋊Q8#10624382semidirect

Maximal subgroups

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

subgroupindex
#260423592
#260422722
#260422602
#260421462
#260418542
#1909181