Finite Group Databasebeta

← #1483×C181 #37529426

Subgroups — #1483×C181 #37529426

Order 23168.

234 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 96 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
2C2×C4⋊C8×C181C211yesmaximal, characteristic, complemented
3C4×M16×C181C211yesmaximal, characteristic, complemented
4Q8⋊C8×C181C212yesmaximal, complemented
5D4⋊C8×C181C212yesmaximal, complemented
6C2×M16×C181—21no—
7C22×C8×C181—21no—
8#126×C181—21no—
9#125×C181C411yescharacteristic
10#124×C181C411yescharacteristic
11#123×C181—21no—
12C22⋊Q8×C181C411yescharacteristic
13#121×C181C411yescharacteristic
14C4×Q8×C181C2211yescharacteristic
15C4×D4×C181—21no—
16C4×D4×C181C2211yescharacteristic
17#117×C181—21no—
18C2×C42×C181C2211yescharacteristic
19C4⋊C8×C181—21no—
20C4⋊C8×C181C2212yes—
21#97×C181—21no—
22C4×C8×C181C2212yes—
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—22no—
32C2×C8×C181—22no—
33C2×C8×C181—42no—
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—22no—
53D4×C181—22no—
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—21no—
61C2×C4×C181—21no—
62C2×C4×C181—41no—
63C2×C4×C181—41no—
64C2×C4×C181C22⋊C411yescharacteristic
65C2×C4×C181C22⋊C411yescharacteristic
66C2×C4×C181C22⋊C411yescharacteristic
67C2×C4×C181C22×C411yescharacteristic
68C2×C4×C181C2×D411yescharacteristic
69C2×C4×C181C2×D411yescharacteristic
70C8×C181—24no—
71C8×C181—42no—
72C22×C181—21no—
73C22×C181—21no—
74C22×C181—41no—
75C22×C181—41no—
76C22×C181—41no—
77C22×C181#10412yes—
78C22×C181C2×C22⋊C411yescharacteristic
79C4×C181—21no—
80C4×C181—21no—
81C4×C181—21no—
82C4×C181—21no—
83C4×C181—41no—
84C4×C181—41no—
85C4×C181—41no—
86C4×C181#13112yes—
87C4×C181AGL(1,ℤ/8)11yescharacteristic
88C4×C181#13711yescharacteristic
89C2×C181—22no—
90C2×C181—81no—
91C2×C181#40811yescharacteristic
92C2×C181#41711yescharacteristic
93C2×C181C2×#10411yescharacteristic
94C181#148311yescharacteristic, direct product factor, Sylow
95#1483C18111yesmaximal, characteristic, direct product factor, Sylow
96#529C2×C18111yescharacteristic
97C2×C4⋊C8C2×C18111yescharacteristic, complemented
98C4×M16C2×C18111yescharacteristic, complemented
99Q8⋊C8C2×C18112yescomplemented
100D4⋊C8C2×C18112yescomplemented
101C2×M16—21no—
102C22×C8—21no—
103#126—21no—
104#125C4×C18111yescharacteristic
105#124C4×C18111yescharacteristic
106#123—21no—
107C22⋊Q8C4×C18111yescharacteristic
108#121C4×C18111yescharacteristic
109C4×Q8C22×C18111yescharacteristic
110C4×D4—21no—
111C4×D4C22×C18111yescharacteristic
112#117—21no—
113C2×C42C22×C18111yescharacteristic
114C4⋊C8—21no—
115C4⋊C8C22×C18112yes—
116#97—21no—
117C4×C8C22×C18112yes—
118C2×Q8C2×C4×C18111yescharacteristic
119C2×D4—21no—
120C2×D4C2×C4×C18111yescharacteristic
121C22×C4—21no—
122C22×C4C2×C4×C18111yescharacteristic
123C22×C4D4×C18111yescharacteristic
124C22×C4D4×C18111yescharacteristic
125M16—24no—
126C2×C8—22no—
127C2×C8—22no—
128C2×C8—42no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4C2×C4×C18111yescharacteristic
134C4⋊C4C2×C4×C18111yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—21no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C42—21no—
141C42C2×C4×C18111yescharacteristic
142C42D4×C18111yescharacteristic
143C42D4×C18111yescharacteristic
144C42C23×C18111yescharacteristic
145C23—21no—
146C23C22⋊C4×C18111yescharacteristic
147Q8—22no—
148D4—22no—
149D4—42no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4C22⋊C4×C18111yescharacteristic
160C2×C4C22⋊C4×C18111yescharacteristic
161C2×C4C22⋊C4×C18111yescharacteristic
162C2×C4C22×C4×C18111yescharacteristic
163C2×C4C2×D4×C18111yescharacteristic
164C2×C4C2×D4×C18111yescharacteristic
165C8—24no—
166C8—42no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#104×C18112yes—
173C22C2×C22⋊C4×C18111yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—41no—
179C4—41no—
180C4—41no—
181C4#131×C18112yes—
182C4AGL(1,ℤ/8)×C18111yescharacteristic
183C4#137×C18111yescharacteristic
184C2—22no—
185C2—81no—
186C2#408×C18111yescharacteristic
187C2#417×C18111yescharacteristic
188C2C2×#104×C18111yescharacteristic
subgroupG/H
centerC2×C4×C181C2×D4
commutatorC2×C4C22×C4×C181
Frattini, cosocleC42C23×C181
socleC22×C181C2×C22⋊C4
prime radical#121×C181C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C181 ◁ C2×C42×C181 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×C181C2semidirect
3. C4×M16×C181C2semidirect
4. Q8⋊C8×C181C2semidirect
5. D4⋊C8×C181C2semidirect
94. C181#1483direct (N × H)
95. #1483C181direct (N × H)
97. C2×C4⋊C8C2×C181semidirect
98. C4×M16C2×C181semidirect
99. Q8⋊C8C2×C181semidirect
100. D4⋊C8C2×C181semidirect

Maximal subgroups

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

subgroupindex
#529×C1812
C2×C4⋊C8×C1812
C4×M16×C1812
Q8⋊C8×C1812
D4⋊C8×C1812
#1483181