Finite Group Databasebeta

← #37535376

Subgroups — #37535376

Order 23168.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#26041850C211yesmaximal, characteristic
2#26041253C211yesmaximal, characteristic
3#26041070C214yesmaximal, complemented
4#413×C181C211yesmaximal, characteristic
5C22×Dic362C411yescharacteristic, complemented
6#19153814—21no—
7#19153803—21no—
8#19153797C412yescomplemented
9#19153797C2212yes—
10#19153795—21no—
11#19153795—21no—
12#19153775—21no—
13#19153775C411yescharacteristic, complemented
14#19153731—21no—
15#19153731C2212yes—
16C2×#41×C181C2211yescharacteristic
17C2×M16×C181—21no—
18#101×C181—21no—
19#100×C181C2212yes—
20C2×Dic362—21no—
21C2×Dic362—21no—
22C2×Dic362—41no—
23C2×Dic362—41no—
24C22×Dic181C2×C412yes—
25C4⋊Dic181—21no—
26C4⋊Dic181—41no—
27#15668428—22no—
28#15668428—22no—
29C22⋊Dic181—22no—
30C22⋊Dic181—22no—
31C22⋊Dic181—22no—
32C22⋊Dic181C2×C412yes—
33C4×Dic181—21no—
34C4×Dic181—41no—
35#41×C181—41no—
36#41×C181—41no—
37C2×Q8×C181D411yescharacteristic
38C2×D4×C181C2×C411yescharacteristic
39C2×D4×C181D411yescharacteristic
40C2×D4×C181C2311yescharacteristic
41C22×C4×C181C2×C411yescharacteristic
42C22×C4×C181D411yescharacteristic
43C22×C4×C181D411yescharacteristic
44M16×C181—22no—
45M16×C181—41no—
46C2×C8×C181—41no—
47Dic362—42no—
48Dic362—41no—
49Dic362—41no—
50C2×Dic181—22no—
51C2×Dic181—22no—
52C2×Dic181—42no—
53C2×Dic181—42no—
54C23×C181C22⋊C411yescharacteristic
55C23×C181C22×C411yescharacteristic
56C23×C181C2×D411yescharacteristic
57Q8×C181—41no—
58D4×C181—41no—
59D4×C181—41no—
60D4×C181—41no—
61C2×C4×C181—21no—
62C2×C4×C181—21no—
63C2×C4×C181—21no—
64C2×C4×C181—21no—
65C2×C4×C181—21no—
66C2×C4×C181—21no—
67C2×C4×C181C22⋊C411yescharacteristic
68C2×C4×C181C22⋊C411yescharacteristic
69C2×C4×C181C22⋊C411yescharacteristic
70C2×C4×C181C2×D411yescharacteristic
71C8×C181—42no—
72C22×C181—21no—
73C22×C181—21no—
74C22×C181—21no—
75C22×C181—41no—
76C22×C181—41no—
77C22×C181—41no—
78C22×C181C2×C22⋊C411yescharacteristic
79C4×C181—21no—
80C4×C181—21no—
81C4×C181—21no—
82C4×C181#9911yescharacteristic
83C4×C181#9911yescharacteristic
84Dic181—42no—
85Dic181—42no—
86Dic181—82no—
87C2×C181—21no—
88C2×C181—41no—
89C2×C181—41no—
90C2×C181—41no—
91C2×C181C2×#9911yescharacteristic
92C181#212311yescharacteristic, complemented, Sylow
93#2123—1811nomaximal, Sylow
94#536—1811no—
95#413D18111yescharacteristic
96#410—1811no—
97#352—1814no—
98C2×#41C2×D18111yescharacteristic
99C22×Q8—1811no—
100C2×M16—21no—
101C4⋊Q8—3621no—
102#124—3621no—
103#123—1812no—
104#123—1812no—
105C22⋊Q8—3621no—
106C22⋊Q8—3621no—
107#117—3621no—
108#117—1811no—
109#101—21no—
110#100C2×D18112yes—
111#99—3621no—
112#99—1812no—
113#41—41no—
114#41—41no—
115C2×Q8—3621no—
116C2×Q8—3621no—
117C2×Q8—7241no—
118C2×Q8—7241no—
119C2×Q8C22⋊D18111yescharacteristic
120C2×D4C4×D18111yescharacteristic
121C2×D4D72411yescharacteristic
122C2×D4C22×D18111yescharacteristic
123C22×C4—1812no—
124C22×C4C4×D18111yescharacteristic
125C22×C4C22⋊D18111yescharacteristic
126C22×C4D72411yescharacteristic
127M16—22no—
128M16—41no—
129C2×C8—41no—
130C4⋊C4—3622no—
131C4⋊C4—3621no—
132C4⋊C4—3622no—
133C4⋊C4—7241no—
134C22⋊C4—3622no—
135C22⋊C4—3622no—
136C22⋊C4—3622no—
137C22⋊C4—1812no—
138C42—3621no—
139C42—7241no—
140C23#1566842611yescharacteristic
141C23C2×C4×D18111yescharacteristic
142C23C2×D72411yescharacteristic
143Q8—41no—
144Q8—7242no—
145Q8—7241no—
146Q8—7241no—
147D4—41no—
148D4—41no—
149D4—41no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—3622no—
157C2×C4—3622no—
158C2×C4—7242no—
159C2×C4—7242no—
160C2×C4#1566842611yescharacteristic
161C2×C4#1566842611yescharacteristic
162C2×C4#1566842611yescharacteristic
163C2×C4C2×C22⋊D18111yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×#1566842611yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—14482no—
176C4—7242no—
177C4—7242no—
178C4#1915373011yescharacteristic
179C4#1915373011yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#1915373011yescharacteristic
subgroupG/H
centerC2C2×#19153730
commutatorC23×C181C22×C4
FrattiniC2×D4C22×D181
Fitting#413×C181C2
socleC2×C181C2×#99
prime radicalC2×#41×C181C22
cosocleC2×D4×C181C23
hypercenter#413D181
hypocenterC181#2123
LCSG ▷ C23×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #26041070C2semidirect
5. C22×Dic362C4semidirect
8. #19153797C4semidirect
13. #19153775C4semidirect
92. C181#2123semidirect

Maximal subgroups

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

subgroupindex
#260418502
#260412532
#260410702
#413×C1812
#2123181