Finite Group Databasebeta

← #37534113

Subgroups — #37534113

Order 23168.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#19153816C211yesmaximal, characteristic
2#26041756C211yesmaximal, characteristic
3#26041289C211yesmaximal, characteristic
4#26041287C211yesmaximal, characteristic
5C2×#19153734C211yesmaximal, characteristic
6#26041039C211yesmaximal, characteristic
7#339×C181C211yesmaximal, characteristic
8C22×Dic362C2211yescharacteristic
9C22×Dic362C2211yescharacteristic
10C2×#15668433C2211yescharacteristic
11#19153816—22no—
12#19153816C414yescomplemented
13C4×Dic362—22no—
14#19153781—22no—
15#19153775C2211yescharacteristic
16#19153772—22no—
17C2×C4⋊Dic181—22no—
18#19153741—22no—
19#19153739—22no—
20#19153734—22no—
21C2×M16×C181C2211yescharacteristic
22#117×C181C2211yescharacteristic
23C2×C42×C181C2211yescharacteristic
24C2×Dic362—21no—
25C2×Dic362—21no—
26C2×Dic362—21no—
27C2×Dic362—21no—
28C2×Dic362—21no—
29C2×Dic362—21no—
30C2×Dic362—21no—
31C2×Dic362—21no—
32C2×Dic362—21no—
33C2×Dic362C2×C412yes—
34C2×Dic362C2×C412yes—
35C2×Dic362D412yes—
36C22×Dic181—21no—
37C22×Dic181D412yes—
38#15668433—21no—
39#15668433—21no—
40C2×#13089678—21no—
41C4⋊Dic181—28no—
42C4⋊Dic181D412yes—
43#15668428—24no—
44C22⋊Dic181—21no—
45C4×Dic181—24no—
46C4×Dic181—21no—
47C22×C4×C181—21no—
48C22×C4×C181C2311yescharacteristic
49M16×C181—21no—
50M16×C181—21no—
51C2×C8×C181—21no—
52C4⋊C4×C181D412yes—
53C22⋊C4×C181—21no—
54C42×C181—21no—
55C42×C181—21no—
56C42×C181C2×C412yes—
57Dic362—22no—
58Dic362—22no—
59Dic362—22no—
60Dic362—22no—
61Dic362—22no—
62Dic362—22no—
63Dic362—41no—
64Dic362—41no—
65C2×Dic181—22no—
66C2×Dic181—22no—
67C2×Dic181—22no—
68C2×Dic181—22no—
69C2×Dic181—41no—
70C2×Dic181—41no—
71C2×Dic181C22⋊C414yes—
72#13089678—41no—
73C23×C181C2×D411yescharacteristic
74C2×C4×C181—24no—
75C2×C4×C181—22no—
76C2×C4×C181—22no—
77C2×C4×C181C22×C411yescharacteristic
78C2×C4×C181C2×D411yescharacteristic
79C2×C4×C181C2×D411yescharacteristic
80C2×C4×C181C2×D411yescharacteristic
81C2×C4×C181#4111yescharacteristic
82C2×C4×C181#4111yescharacteristic
83C8×C181—41no—
84C22×C181—22no—
85C22×C181C2×C22⋊C411yescharacteristic
86C22×C181#12011yescharacteristic
87C22×C181#12311yescharacteristic
88C4×C181—24no—
89C4×C181—42no—
90C4×C181C4×D411yescharacteristic
91C4×C181C4×D411yescharacteristic
92C4×C181#12111yescharacteristic
93C4×C181#12111yescharacteristic
94Dic181—24no—
95Dic181—42no—
96Dic181—42no—
97C2×C181—21no—
98C2×C181—21no—
99C2×C181#38611yescharacteristic
100C2×C181#45612yes—
101C181#188611yescharacteristic, complemented, Sylow
102#1886—1811nomaximal, Sylow
103C2×C4⋊Q8—1811no—
104#519—1811no—
105#419—1811no—
106#419—1811no—
107C2×#101—1811no—
108#339—1811no—
109#339D18111yescharacteristic
110C22×Q8—1811no—
111C22×Q8—1811no—
112C2×M16—1811no—
113C2×M16C2×D18111yescharacteristic
114C4⋊Q8—3622no—
115C4⋊Q8—1814no—
116C4×Q8—3622no—
117C4×Q8—3622no—
118#117—3622no—
119#117—1811no—
120#117C2×D18111yescharacteristic
121C2×C4⋊C4—3622no—
122C2×C42C2×D18111yescharacteristic
123#103—3622no—
124#103—3622no—
125#101—3622no—
126C2×Q8—3621no—
127C2×Q8—3621no—
128C2×Q8—3621no—
129C2×Q8—3621no—
130C2×Q8—3621no—
131C2×Q8—3621no—
132C2×Q8—3621no—
133C2×Q8—3621no—
134C2×Q8—3621no—
135C2×Q8—1812no—
136C2×Q8—1812no—
137C2×Q8—1812no—
138C22×C4—21no—
139C22×C4—3621no—
140C22×C4—1812no—
141C22×C4C22×D18111yescharacteristic
142M16—21no—
143M16—21no—
144M16—3621no—
145M16—3621no—
146C2×C8—21no—
147C2×C8—3621no—
148C4⋊C4—3624no—
149C4⋊C4—3628no—
150C4⋊C4—1812no—
151C4⋊C4D72412yes—
152C22⋊C4—21no—
153C22⋊C4—3621no—
154C42—21no—
155C42—21no—
156C42—3624no—
157C42—3621no—
158C42C4×D18112yes—
159C23D4×D18111yescharacteristic
160Q8—3622no—
161Q8—3622no—
162Q8—3622no—
163Q8—3622no—
164Q8—3622no—
165Q8—3622no—
166Q8—7241no—
167Q8—7241no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—3622no—
172C2×C4—3622no—
173C2×C4—3622no—
174C2×C4—3622no—
175C2×C4—1814no—
176C2×C4—7241no—
177C2×C4—7241no—
178C2×C4C2×C4×D18111yescharacteristic
179C2×C4D4×D18111yescharacteristic
180C2×C4D4×D18111yescharacteristic
181C2×C4C2×D72411yescharacteristic
182C2×C4#1566844911yescharacteristic
183C2×C4#1566845011yescharacteristic
184C8—41no—
185C8—7241no—
186C22—22no—
187C22C22⋊C4×D18111yescharacteristic
188C22#1915378611yescharacteristic
189C22#1915380111yescharacteristic
190C4—24no—
191C4—42no—
192C4—3624no—
193C4—7242no—
194C4—7242no—
195C4#1915377811yescharacteristic
196C4C4×D72411yescharacteristic
197C4#1915378911yescharacteristic
198C4#1915379111yescharacteristic
199C2—21no—
200C2—21no—
201C2#2604115711yescharacteristic
202C2#2604146312yes—
subgroupG/H
centerC22#19153786
commutatorC2×C4×C181C22×C4
FrattiniC22×C4C22×D181
Fitting#339×C181C2
socleC22×C181#120
prime radicalC23×C181C2×D4
cosocleC22×C4×C181C23
hypercenter#339D181
hypocenterC181#1886
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #19153816C4semidirect
101. C181#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#191538162
#260417562
#260412892
#260412872
C2×#191537342
#260410392
#339×C1812
#1886181