Finite Group Databasebeta

← #37549121

Subgroups — #37549121

Order 23168.

294 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 64 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#26042250C211yesmaximal, characteristic
2C4×C22⋊#10624382C211yesmaximal, characteristic
3#26042133C214yesmaximal, complemented
4C2×#19153792C211yesmaximal, characteristic
5C2×#15668459—21no—
6C2×C22⋊#10624382—21no—
7C2×C4×#10624382—21no—
8#19153873C2212yes—
9C22⋊#13089685—21no—
10(C2×#10624382)⋊C4C2212yes—
11C22×C4×D181C2211yescharacteristic
12#19153792—21no—
13#19153792—21no—
14#19153792C412yescomplemented
15#19153792C2212yes—
16C2×C4⋊Dic181C411yescharacteristic, complemented
17C2×#15668428—21no—
18C2×#15668426—21no—
19C22×Q8×C181C411yescharacteristic, complemented
20C22×#10624382—22no—
21#15668459—42no—
22C2×#13089685—22no—
23C22⋊#10624382—24no—
24C4×#10624382—42no—
25C23×D181D411yescharacteristic
26C22×Dic181—21no—
27C22×Dic181D411yescharacteristic
28C2×C4×D181—42no—
29C2×C4×D181C2×C411yescharacteristic
30C2×C4×D181D411yescharacteristic
31C2×C4×D181D411yescharacteristic
32C2×C4×D181C2311yescharacteristic
33C4⋊Dic181—21no—
34C4⋊Dic181C2×C412yes—
35#15668428—22no—
36#15668428—22no—
37#15668426—22no—
38#15668426—22no—
39C2×Q8×C181—21no—
40C2×Q8×C181—42no—
41C2×Q8×C181C2×C412yes—
42C22×C4×C181—21no—
43C22×C4×C181C2×C411yescharacteristic
44C2×#10624382—24no—
45C2×#10624382—42no—
46C2×#10624382—42no—
47#13089685—42no—
48C22×D181—22no—
49C22×D181—22no—
50C22×D181—41no—
51C22×D181C22⋊C411yescharacteristic
52C22×D181C2×D411yescharacteristic
53C2×Dic181—22no—
54C2×Dic181—41no—
55C2×Dic181—42no—
56C2×Dic181C22⋊C411yescharacteristic
57C2×Dic181C2×D411yescharacteristic
58C4×D181—22no—
59C4×D181—22no—
60C4×D181—41no—
61C4×D181—41no—
62C23×C181C22⋊C411yescharacteristic
63Q8×C181—42no—
64Q8×C181—42no—
65C2×C4×C181—22no—
66C2×C4×C181—22no—
67C2×C4×C181—42no—
68C2×C4×C181C22⋊C411yescharacteristic
69C2×C4×C181C22×C411yescharacteristic
70C22×C181—21no—
71C22×C181—21no—
72C22×C181#10412yes—
73C22×C181C2×C22⋊C411yescharacteristic
74C2×D181—21no—
75C2×D181—21no—
76C2×D181—21no—
77C2×D181—21no—
78C2×D181—21no—
79C2×D181—44no—
80C2×D181#13712yes—
81#10624382—44no—
82C4×C181—21no—
83C4×C181—42no—
84C4×C181#9912yes—
85Dic181—21no—
86Dic181—21no—
87Dic181—42no—
88C2×C181—22no—
89C2×C181C2×#9911yescharacteristic
90C2×C181#41911yescharacteristic
91C2×C181C2×#10411yescharacteristic
92D181—22no—
93D181—41no—
94C181#150811yescharacteristic, complemented, Sylow
95#1508—1811nomaximal, Sylow
96C2×C22⋊Q8—1811no—
97#407—1811no—
98C4×C22⋊C4—1811no—
99#328—1814no—
100C22×Q8#1062438211yescharacteristic, complemented
101C23×C4—1811no—
102C2×M16—3621no—
103C22⋊Q8—3621no—
104C22⋊Q8—3621no—
105C22⋊Q8—1812no—
106C22⋊Q8—1812no—
107C2×C4⋊C4—3621no—
108C2×C4⋊C4—1811no—
109C2×C22⋊C4—3621no—
110C2×C22⋊C4—3621no—
111C2×C42—3621no—
112C22⋊C8—3621no—
113C22⋊C8—1812no—
114#95—1812no—
115C24—1811no—
116C2×Q8—21no—
117C2×Q8—42no—
118C2×Q8C2×#1062438212yes—
119C22×C4—21no—
120C22×C4—3622no—
121C22×C4—3621no—
122C22×C4—1811no—
123C22×C4—1811no—
124C22×C4—1811no—
125C22×C4—1811no—
126C22×C4—1811no—
127C22×C4—7242no—
128C22×C4C2×#1062438211yescharacteristic
129M16—7242no—
130C2×C8—3622no—
131C4⋊C4—3622no—
132C4⋊C4—3622no—
133C4⋊C4—3621no—
134C4⋊C4—1812no—
135C22⋊C4—3622no—
136C22⋊C4—3622no—
137C22⋊C4—3624no—
138C42—7242no—
139C23—3622no—
140C23—3622no—
141C23—1811no—
142C23—1811no—
143C23—7241no—
144C23C22⋊#1062438211yescharacteristic
145Q8—42no—
146Q8—42no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—42no—
150C2×C4—3622no—
151C2×C4—3622no—
152C2×C4—3624no—
153C2×C4—3622no—
154C2×C4—1811no—
155C2×C4—1811no—
156C2×C4—7241no—
157C2×C4—7241no—
158C2×C4—7241no—
159C2×C4—7242no—
160C2×C4—7242no—
161C2×C4—7242no—
162C2×C4C22⋊#1062438211yescharacteristic
163C2×C4C22×#1062438211yescharacteristic
164C8—7242no—
165C22—21no—
166C22—21no—
167C22—3621no—
168C22—3621no—
169C22—3621no—
170C22—3621no—
171C22—3621no—
172C22—1812no—
173C22—7244no—
174C22#1915388112yes—
175C22C2×C22⋊#1062438211yescharacteristic
176C4—21no—
177C4—42no—
178C4—3621no—
179C4—3621no—
180C4—7244no—
181C4—7242no—
182C4#1915387412yes—
183C2—22no—
184C2—3622no—
185C2—7241no—
186C2C2×#1915387411yescharacteristic
187C2#2604227211yescharacteristic
188C2C2×#1915388111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC22×Q8×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC23×D181D4
cosocleC2×C4×D181C23
hypercenterC22×Q8#10624382
hypocenterC181#1508
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #26042133C2semidirect
14. #19153792C4semidirect
16. C2×C4⋊Dic181C4semidirect
19. C22×Q8×C181C4semidirect
94. C181#1508semidirect
100. C22×Q8#10624382semidirect

Maximal subgroups

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

subgroupindex
#260422502
C4×C22⋊#106243822
#260421332
C2×#191537922
#1508181