Finite Group Databasebeta

← #37549242

Subgroups — #37549242

Order 23168.

208 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 62 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#26042299C211yesmaximal, characteristic
2C2×#19153883C211yesmaximal, characteristic
3#26042138C212yesmaximal, complemented
4#26042138C212yesmaximal, complemented
5#26041832C211yesmaximal, characteristic
6C22×#13089685—21no—
7#19153883—21no—
8#19153883C2212yes—
9#19153883C2212yes—
10C22⋊#13089685—21no—
11#19153871—21no—
12#19153815C2211yescharacteristic
13#19153815C2211yescharacteristic
14#19153807C411yescharacteristic
15#19153807C411yescharacteristic
16#19153793—21no—
17#19153793—21no—
18C4×Dic362—21no—
19C4×Dic362—21no—
20#19153775C411yescharacteristic
21C2×C4×Dic181C2211yescharacteristic
22#117×C181C411yescharacteristic
23C2×#13089685—22no—
24C2×#13089685—22no—
25C2×#13089685—42no—
26C2×Dic362—21no—
27C2×Dic362—21no—
28C22×Dic181D411yescharacteristic
29C22×Dic181D411yescharacteristic
30C4⋊Dic181—21no—
31C4⋊Dic181—21no—
32C4⋊Dic181C2×C411yescharacteristic
33C4⋊Dic181C2×C411yescharacteristic
34#15668428—21no—
35#15668428—21no—
36#15668428—21no—
37#15668428—21no—
38C22⋊Dic181—21no—
39C4×Dic181—21no—
40C4×Dic181C2×C411yescharacteristic
41C4×Dic181D411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181C2311yescharacteristic
44C22×C4×C181C2×C411yescharacteristic
45C4⋊C4×C181C2×C411yescharacteristic
46C4⋊C4×C181C2×C411yescharacteristic
47C22⋊C4×C181—21no—
48C42×C181—21no—
49#13089685—42no—
50#13089685—42no—
51Dic362—42no—
52Dic362—41no—
53Dic362—41no—
54C2×Dic181—22no—
55C2×Dic181—21no—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C2×Dic181—21no—
59C2×Dic181C22⋊C411yescharacteristic
60C2×Dic181C22⋊C411yescharacteristic
61C2×Dic181C2×D411yescharacteristic
62C2×Dic181C2×D411yescharacteristic
63C23×C181C22⋊C411yescharacteristic
64C2×C4×C181—22no—
65C2×C4×C181—21no—
66C2×C4×C181—21no—
67C2×C4×C181C22⋊C411yescharacteristic
68C2×C4×C181C22×C411yescharacteristic
69C22×C181—21no—
70C22×C181—21no—
71C22×C181#10112yes—
72C22×C181C2×C22⋊C411yescharacteristic
73C4×C181—21no—
74C4×C181—21no—
75C4×C181—41no—
76C4×C181—41no—
77Dic181—21no—
78Dic181—21no—
79Dic181—41no—
80Dic181—41no—
81Dic181#13512yes—
82Dic181AGL(1,ℤ/8)11yescharacteristic
83Dic181#13711yescharacteristic
84C2×C181—22no—
85C2×C181C2×#10111yescharacteristic
86C2×C181#41611yescharacteristic
87C2×C181#41711yescharacteristic
88C181#155211yescharacteristic, complemented, Sylow
89#1552—1811nomaximal, Sylow
90#533—1811no—
91#432—1811no—
92C2×C4⋊C8—1811no—
93#332—1812no—
94#332—1812no—
95C22×C8—3621no—
96C4⋊Q8—1811no—
97C4⋊Q8—1811no—
98#125—1811no—
99#125—1811no—
100C22⋊Q8—3621no—
101C22⋊Q8—3621no—
102C4×Q8—3621no—
103C4×Q8—3621no—
104#117—1811no—
105#117#1062438211yescharacteristic
106C2×C42—1811no—
107C4⋊C8—3621no—
108C4⋊C8—1812no—
109C4⋊C8—1812no—
110C22⋊C8—3621no—
111#97—3621no—
112C2×Q8—3621no—
113C2×Q8—3621no—
114C22×C4—1811no—
115C22×C4—1811no—
116C22×C4C2×#1062438211yescharacteristic
117C2×C8—3622no—
118C2×C8—3622no—
119C2×C8—7242no—
120C4⋊C4—3621no—
121C4⋊C4—3621no—
122C4⋊C4—3621no—
123C4⋊C4—3621no—
124C4⋊C4—3621no—
125C4⋊C4—3621no—
126C4⋊C4—1811no—
127C4⋊C4—1811no—
128C4⋊C4C2×#1062438211yescharacteristic
129C4⋊C4C2×#1062438211yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—3621no—
132C42—21no—
133C42—3621no—
134C42—1811no—
135C42—1811no—
136C42—1811no—
137C42—1811no—
138C23C22⋊#1062438211yescharacteristic
139Q8—7242no—
140Q8—7241no—
141Q8—7241no—
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—3621no—
146C2×C4—3622no—
147C2×C4—3621no—
148C2×C4—3621no—
149C2×C4—3621no—
150C2×C4—1811no—
151C2×C4—1811no—
152C2×C4—1811no—
153C2×C4—1811no—
154C2×C4C22⋊#1062438211yescharacteristic
155C2×C4C22×#1062438211yescharacteristic
156C8—7242no—
157C8—7242no—
158C22—21no—
159C22—21no—
160C22#1915387712yes—
161C22C2×C22⋊#1062438211yescharacteristic
162C4—21no—
163C4—21no—
164C4—41no—
165C4—41no—
166C4—3621no—
167C4—3621no—
168C4—1812no—
169C4—1811no—
170C4—1811no—
171C4—7241no—
172C4—7241no—
173C2—22no—
174C2C2×#1915387711yescharacteristic
175C2#2604226911yescharacteristic
176C2#2604227011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#117×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC23×C181C22⋊C4
cosocleC4×Dic181C23
hypercenter#117#10624382
hypocenterC181#1552
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #26042138C2semidirect
4. #26042138C2semidirect
88. C181#1552semidirect

Maximal subgroups

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

subgroupindex
#260422992
C2×#191538832
#260421382
#260418322
#1552181