Finite Group Databasebeta

← #37549021

Subgroups — #37549021

Order 23168.

312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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#26042298C211yesmaximal, characteristic, complemented
2#26042297C211yesmaximal, characteristic, complemented
3#26042127C212yesmaximal, complemented
4D4⋊#13089685C212yesmaximal, complemented
5C4×D4×D181C211yesmaximal, characteristic
6#19153883—21no—
7C4⋊#13089685C2212yescomplemented
8#19153873—21no—
9#19153873—21no—
10C4×#13089685—21no—
11C4×#13089685C2212yescomplemented
12C2×D4×D181C411yescharacteristic
13C22×C4×D181—21no—
14C4×D724C411yescharacteristic
15D4×Dic181C2211yescharacteristic
16#19153778C2211yescharacteristic
17C4×C22⋊D181—21no—
18#19153776—21no—
19C4⋊C4×D181C411yescharacteristic
20C22⋊C4×D181—21no—
21C42×D181C2211yescharacteristic
22C4×D4×C181C411yescharacteristic
23C2×#13089685—22no—
24C2×#13089685—22no—
25C23×D181—21no—
26C2×D724C2×C411yescharacteristic
27C2×C22⋊D181—21no—
28D4×D181—22no—
29D4×D181C814yescomplemented
30C22×Dic181—21no—
31C2×C4×D181—21no—
32C2×C4×D181—21no—
33C2×C4×D181—21no—
34C2×C4×D181—44no—
35C2×C4×D181C2×C411yescharacteristic
36C2×C4×D181D411yescharacteristic
37C2×C4×D181D411yescharacteristic
38C4⋊Dic181C2×C411yescharacteristic
39#15668428—21no—
40C22⋊Dic181—21no—
41#15668426—21no—
42#15668426—21no—
43C4×Dic181D411yescharacteristic
44C4×Dic181D411yescharacteristic
45C4×Dic181C2311yescharacteristic
46C2×D4×C181C2×C411yescharacteristic
47C22×C4×C181—21no—
48C4⋊C4×C181C2×C411yescharacteristic
49C22⋊C4×C181—21no—
50C42×C181C2×C411yescharacteristic
51#13089685—42no—
52#13089685—42no—
53C22×D181—21no—
54C22×D181—24no—
55C22×D181—42no—
56C22×D181—42no—
57C22×D181C22⋊C411yescharacteristic
58D724—21no—
59D724C2×C812yes—
60C22⋊D181—24no—
61C2×Dic181—21no—
62C2×Dic181—42no—
63C2×Dic181C22⋊C411yescharacteristic
64C2×Dic181C2×D411yescharacteristic
65C2×Dic181C2×D411yescharacteristic
66C4×D181—22no—
67C4×D181—41no—
68C4×D181—42no—
69C4×D181—42no—
70C4×D181—42no—
71C4×D181C2×C812yes—
72C4×D181M1612yes—
73C23×C181—21no—
74D4×C181—21no—
75D4×C181C2×C812yes—
76C2×C4×C181—21no—
77C2×C4×C181—42no—
78C2×C4×C181C22⋊C411yescharacteristic
79C2×C4×C181C22⋊C411yescharacteristic
80C2×C4×C181C22×C411yescharacteristic
81C22×C181—22no—
82C22×C181—41no—
83C22×C181—41no—
84C22×C181C2×C22⋊C411yescharacteristic
85C2×D181—21no—
86C2×D181—21no—
87C2×D181—22no—
88C2×D181—48no—
89C2×D181—41no—
90C2×D181—41no—
91C2×D181C22⋊C812yes—
92C4×C181—21no—
93C4×C181—21no—
94C4×C181—41no—
95C4×C181C22×C811yescharacteristic
96C4×C181C2×M1611yescharacteristic
97Dic181—21no—
98Dic181—41no—
99Dic181C22⋊C812yes—
100Dic181AGL(1,ℤ/8)12yes—
101C2×C181—42no—
102C2×C181C2×C22⋊C811yescharacteristic
103C2×C181#41811yescharacteristic
104C2×C181#42111yescharacteristic
105D181—22no—
106D181—42no—
107C181#147811yescharacteristic, complemented, Sylow
108#1478—1811nomaximal, Sylow
109C2×C4×D4—1811no—
110#431—1811no—
111#431—1811no—
112D4⋊C8—1812no—
113D4⋊C8—1812no—
114C22×D4—1811no—
115C23×C4—3621no—
116C4×D4—3621no—
117C4×D4—3621no—
118C4×D4—1811no—
119C4×D4—1811no—
120C4×D4—1811no—
121C4×D4#1062438211yescharacteristic
122C2×C4⋊C4—1811no—
123C2×C22⋊C4—3621no—
124C2×C42—1811no—
125C4⋊C8—3621no—
126C4⋊C8—1812no—
127C22⋊C8—3621no—
128C22⋊C8—3621no—
129C4×C8—3621no—
130C4×C8—1812no—
131C24—3621no—
132C2×D4—3622no—
133C2×D4—3621no—
134C2×D4—1814no—
135C2×D4—1811no—
136C2×D4C2×#1062438211yescharacteristic
137C22×C4—21no—
138C22×C4—3621no—
139C22×C4—3621no—
140C22×C4—3621no—
141C22×C4—3621no—
142C22×C4—1811no—
143C22×C4—1811no—
144C22×C4—1811no—
145C22×C4—7244no—
146C2×C8—3622no—
147C2×C8—3622no—
148C4⋊C4—3621no—
149C4⋊C4—1811no—
150C4⋊C4C2×#1062438211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3621no—
153C22⋊C4—3621no—
154C22⋊C4—3621no—
155C42—1811no—
156C42—1811no—
157C42—1811no—
158C42C2×#1062438211yescharacteristic
159C23—21no—
160C23—3624no—
161C23—3621no—
162C23—1811no—
163C23—7242no—
164C23—7242no—
165D4—21no—
166D4—3624no—
167D4—3621no—
168D4—1812no—
169D4D181⋊C812yes—
170C2×C4—21no—
171C2×C4—42no—
172C2×C4—3622no—
173C2×C4—3621no—
174C2×C4—1811no—
175C2×C4—1811no—
176C2×C4—1811no—
177C2×C4—1812no—
178C2×C4—1812no—
179C2×C4—7241no—
180C2×C4—7242no—
181C2×C4—7242no—
182C2×C4—7242no—
183C2×C4—7242no—
184C2×C4C22⋊#1062438211yescharacteristic
185C2×C4C22⋊#1062438211yescharacteristic
186C2×C4C22×#1062438211yescharacteristic
187C8—7242no—
188C8—7242no—
189C22—22no—
190C22—41no—
191C22—41no—
192C22—3621no—
193C22—3621no—
194C22—3622no—
195C22—1812no—
196C22—7248no—
197C22—7241no—
198C22—7241no—
199C22C2×C22⋊#1062438211yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—3621no—
204C4—1812no—
205C4—1812no—
206C4—7241no—
207C4C2×D181⋊C811yescharacteristic
208C4D181⋊M1611yescharacteristic
209C2—42no—
210C2—3622no—
211C2—7242no—
212C2D181⋊(C22⋊C8)11yescharacteristic
213C2#2604227111yescharacteristic
214C2#2604227611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC4×C181C22×C8
FrattiniC2×C4C22×#10624382
FittingC4×D4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC2×D4×D181C4
cosocleC4×Dic181C23
hypercenterC4×D4#10624382
hypocenterC181#1478
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26042298C2semidirect
2. #26042297C2semidirect
3. #26042127C2semidirect
4. D4⋊#13089685C2semidirect
7. C4⋊#13089685C22semidirect
11. C4×#13089685C22semidirect
29. D4×D181C8semidirect
107. C181#1478semidirect

Maximal subgroups

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

subgroupindex
#260422982
#260422972
#260421272
D4⋊#130896852
C4×D4×D1812
#1478181