Finite Group Databasebeta

← #1524×C181 #37529467

Subgroups — #1524×C181 #37529467

Order 23168.

234 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 92 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#529×C181C211yesmaximal, characteristic
2C4×M16×C181C211yesmaximal, characteristic, complemented
3C2×#97×C181C211yesmaximal, characteristic, complemented
4#330×C181C212yesmaximal, complemented
5#329×C181C212yesmaximal, complemented
6C2×M16×C181—21no—
7C22×C8×C181—21no—
8#126×C181—21no—
9#125×C181C2211yescharacteristic
10#124×C181C2211yescharacteristic
11#123×C181—21no—
12C22⋊Q8×C181C411yescharacteristic
13#121×C181C411yescharacteristic
14C4×Q8×C181C411yescharacteristic
15C4×D4×C181—21no—
16C4×D4×C181C411yescharacteristic
17#117×C181—21no—
18C2×C42×C181C2211yescharacteristic
19#97×C181—21no—
20#97×C181C2212yes—
21#97×C181C2212yes—
22C4×C8×C181—21no—
23C2×Q8×C181C2×C411yescharacteristic
24C2×D4×C181—21no—
25C2×D4×C181C2×C411yescharacteristic
26C22×C4×C181—21no—
27C22×C4×C181C2×C411yescharacteristic
28C22×C4×C181D411yescharacteristic
29C22×C4×C181D411yescharacteristic
30M16×C181—24no—
31C2×C8×C181—24no—
32C2×C8×C181—22no—
33C2×C8×C181—22no—
34C4⋊C4×C181—21no—
35C4⋊C4×C181—21no—
36C4⋊C4×C181—21no—
37C4⋊C4×C181—21no—
38C4⋊C4×C181C2×C411yescharacteristic
39C4⋊C4×C181C2×C411yescharacteristic
40C22⋊C4×C181—21no—
41C22⋊C4×C181—21no—
42C22⋊C4×C181—21no—
43C22⋊C4×C181—21no—
44C22⋊C4×C181—21no—
45C42×C181—21no—
46C42×C181C2×C411yescharacteristic
47C42×C181D411yescharacteristic
48C42×C181D411yescharacteristic
49C42×C181C2311yescharacteristic
50C23×C181—21no—
51C23×C181C22⋊C411yescharacteristic
52Q8×C181—41no—
53D4×C181—41no—
54D4×C181—42no—
55C2×C4×C181—22no—
56C2×C4×C181—22no—
57C2×C4×C181—21no—
58C2×C4×C181—21no—
59C2×C4×C181—21no—
60C2×C4×C181—41no—
61C2×C4×C181—42no—
62C2×C4×C181C22⋊C411yescharacteristic
63C2×C4×C181C22⋊C411yescharacteristic
64C2×C4×C181C22⋊C411yescharacteristic
65C2×C4×C181C22×C411yescharacteristic
66C2×C4×C181C2×D411yescharacteristic
67C2×C4×C181C2×D411yescharacteristic
68C8×C181—24no—
69C8×C181—24no—
70C22×C181—21no—
71C22×C181—21no—
72C22×C181—41no—
73C22×C181—41no—
74C22×C181—41no—
75C22×C181#10412yes—
76C22×C181C2×C22⋊C411yescharacteristic
77C4×C181—21no—
78C4×C181—21no—
79C4×C181—21no—
80C4×C181—21no—
81C4×C181—21no—
82C4×C181—41no—
83C4×C181—41no—
84C4×C181—41no—
85C4×C181#10412yes—
86C2×C181—22no—
87C2×C181—81no—
88C2×C181#41311yescharacteristic
89C2×C181C2×#10411yescharacteristic
90C2×C181C2×#10411yescharacteristic
91C181#152411yescharacteristic, direct product factor, Sylow
92#1524C18111yesmaximal, characteristic, direct product factor, Sylow
93#529C2×C18111yescharacteristic
94C4×M16C2×C18111yescharacteristic, complemented
95C2×#97C2×C18111yescharacteristic, complemented
96#330C2×C18112yescomplemented
97#329C2×C18112yescomplemented
98C2×M16—21no—
99C22×C8—21no—
100#126—21no—
101#125C22×C18111yescharacteristic
102#124C22×C18111yescharacteristic
103#123—21no—
104C22⋊Q8C4×C18111yescharacteristic
105#121C4×C18111yescharacteristic
106C4×Q8C4×C18111yescharacteristic
107C4×D4—21no—
108C4×D4C4×C18111yescharacteristic
109#117—21no—
110C2×C42C22×C18111yescharacteristic
111#97—21no—
112#97C22×C18112yes—
113#97C22×C18112yes—
114C4×C8—21no—
115C2×Q8C2×C4×C18111yescharacteristic
116C2×D4—21no—
117C2×D4C2×C4×C18111yescharacteristic
118C22×C4—21no—
119C22×C4C2×C4×C18111yescharacteristic
120C22×C4D4×C18111yescharacteristic
121C22×C4D4×C18111yescharacteristic
122M16—24no—
123C2×C8—24no—
124C2×C8—22no—
125C2×C8—22no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4C2×C4×C18111yescharacteristic
131C4⋊C4C2×C4×C18111yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C42—21no—
138C42C2×C4×C18111yescharacteristic
139C42D4×C18111yescharacteristic
140C42D4×C18111yescharacteristic
141C42C23×C18111yescharacteristic
142C23—21no—
143C23C22⋊C4×C18111yescharacteristic
144Q8—41no—
145D4—41no—
146D4—42no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4C22⋊C4×C18111yescharacteristic
155C2×C4C22⋊C4×C18111yescharacteristic
156C2×C4C22⋊C4×C18111yescharacteristic
157C2×C4C22×C4×C18111yescharacteristic
158C2×C4C2×D4×C18111yescharacteristic
159C2×C4C2×D4×C18111yescharacteristic
160C8—24no—
161C8—24no—
162C22—21no—
163C22—21no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22#104×C18112yes—
168C22C2×C22⋊C4×C18111yescharacteristic
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—41no—
175C4—41no—
176C4—41no—
177C4#104×C18112yes—
178C2—22no—
179C2—81no—
180C2#413×C18111yescharacteristic
181C2C2×#104×C18111yescharacteristic
182C2C2×#104×C18111yescharacteristic
subgroupG/H
centerC2×C4×C181C22⋊C4
commutatorC2×C4C22×C4×C181
Frattini, cosocleC42C23×C181
socleC22×C181C2×C22⋊C4
prime radical#121×C181C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C181 ◁ C2×C42×C181 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×M16×C181C2semidirect
3. C2×#97×C181C2semidirect
4. #330×C181C2semidirect
5. #329×C181C2semidirect
91. C181#1524direct (N × H)
92. #1524C181direct (N × H)
94. C4×M16C2×C181semidirect
95. C2×#97C2×C181semidirect
96. #330C2×C181semidirect
97. #329C2×C181semidirect

Maximal subgroups

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

subgroupindex
#529×C1812
C4×M16×C1812
C2×#97×C1812
#330×C1812
#329×C1812
#1524181