Finite Group Databasebeta

← #37549484

Subgroups — #37549484

Order 23168.

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C2×#19153880C212yesmaximal
2C4×#15668459C211yesmaximal, characteristic, complemented
3#26042215C211yesmaximal, characteristic, complemented
4#26042149C212yesmaximal, complemented
5C4×#15668448C211yesmaximal, characteristic
6C2×#15668459C2212yes—
7C2×C4×#10624382C2212yes—
8#19153880C418yescomplemented
9#19153871—21no—
10C4×#13089685—21no—
11(C2×#10624382)⋊C4—21no—
12(C2×#10624382)⋊C4—21no—
13C2×#15668448C2211yescharacteristic
14C4×Dic362C411yescharacteristic, complemented
15#19153781C411yescharacteristic, complemented
16D4×Dic181C411yescharacteristic, complemented
17C4×C22⋊D181—21no—
18#19153776—21no—
19#19153774C2211yescharacteristic
20#19153772—21no—
21C2×C4×Dic181—21no—
22C42×D181C2211yescharacteristic
23C4×D4×C181C411yescharacteristic, complemented
24C22×#10624382—22no—
25#15668459—22no—
26#15668459C2×C414yescomplemented
27C2×#13089685—22no—
28C4×#10624382—22no—
29C4×#10624382C2×C414yescomplemented
30#15668448—22no—
31#15668448C2×C414yes—
32C2×Dic362C2×C411yescharacteristic
33C2×C22⋊D181—21no—
34C22×Dic181—21no—
35C22×Dic181—21no—
36C2×C4×D181D411yescharacteristic
37C2×C4×D181D411yescharacteristic
38C2×C4×D181C2311yescharacteristic
39C4⋊Dic181C2×C411yescharacteristic
40#15668428—21no—
41#15668428—21no—
42C22⋊Dic181—21no—
43#15668426—21no—
44C4×Dic181—21no—
45C4×Dic181—21no—
46C4×Dic181—21no—
47C4×Dic181C2×C411yescharacteristic
48C4×Dic181D411yescharacteristic
49C4×Dic181D411yescharacteristic
50C2×D4×C181C2×C411yescharacteristic
51C22×C4×C181—21no—
52C4⋊C4×C181C2×C411yescharacteristic
53C22⋊C4×C181—21no—
54C42×C181C2×C411yescharacteristic
55C2×#10624382—24no—
56C2×#10624382—42no—
57C2×#10624382—42no—
58#13089685—24no—
59C22×D181C2×D411yescharacteristic
60Dic362—21no—
61Dic362C4212yes—
62C22⋊D181—24no—
63C2×Dic181—21no—
64C2×Dic181—24no—
65C2×Dic181—21no—
66C2×Dic181—42no—
67C2×Dic181C22⋊C411yescharacteristic
68C2×Dic181C22⋊C411yescharacteristic
69C2×Dic181C2×D411yescharacteristic
70C4×D181—41no—
71C4×D181—41no—
72C4×D181C22×C412yes—
73C4×D181#4112yes—
74C23×C181—21no—
75D4×C181—21no—
76D4×C181C4212yes—
77C2×C4×C181—21no—
78C2×C4×C181—42no—
79C2×C4×C181C22⋊C411yescharacteristic
80C2×C4×C181C22⋊C411yescharacteristic
81C2×C4×C181C22×C411yescharacteristic
82C22×C181—22no—
83C22×C181—41no—
84C22×C181—41no—
85C22×C181C2×C22⋊C411yescharacteristic
86C2×D181—21no—
87C2×D181—21no—
88C2×D181C4×D412yes—
89#10624382—44no—
90C4×C181—21no—
91C4×C181—21no—
92C4×C181—41no—
93C4×C181C2×C4211yescharacteristic
94C4×C181#11711yescharacteristic
95Dic181—22no—
96Dic181—21no—
97Dic181—21no—
98Dic181—41no—
99Dic181C4×D412yes—
100C2×C181—42no—
101C2×C181C4×C22⋊C411yescharacteristic
102C2×C181#42111yescharacteristic
103C2×C181#42111yescharacteristic
104D181—22no—
105C181#175911yescharacteristic, complemented, Sylow
106#1759—1811nomaximal, Sylow
107C4×#41—1811no—
108C2×#104—1812no—
109C4×M16—1811no—
110#376—1811no—
111#339—1812no—
112C2×#41—1811no—
113C2×M16—1812no—
114C4×Q8—1811no—
115C4×Q8—1811no—
116C4×D4—3621no—
117C4×D4—3621no—
118C4×D4—1811no—
119C4×D4#1062438211yescharacteristic, complemented
120#117—3621no—
121#117—1811no—
122C2×C42—3621no—
123C2×C42—1812no—
124C2×C42—1811no—
125#104—1818no—
126#97—3621no—
127C4×C8—3621no—
128#95—3621no—
129#95—3621no—
130#41—3622no—
131#41—1814no—
132C2×Q8—1811no—
133C2×D4—3621no—
134C2×D4C2×#1062438211yescharacteristic
135C22×C4—21no—
136C22×C4—3621no—
137C22×C4—3622no—
138C22×C4—3621no—
139C22×C4—1811no—
140C22×C4—1811no—
141C22×C4—1811no—
142M16—3622no—
143M16—1814no—
144C2×C8—3622no—
145C4⋊C4—3621no—
146C4⋊C4—3621no—
147C4⋊C4—1811no—
148C4⋊C4C2×#1062438211yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—3621no—
151C22⋊C4—3621no—
152C42—3621no—
153C42—3621no—
154C42—3622no—
155C42—3621no—
156C42—1814no—
157C42—1811no—
158C42—1811no—
159C42—1811no—
160C42C2×#1062438211yescharacteristic
161C23—21no—
162C23—1811no—
163Q8—3621no—
164Q8—1812no—
165D4—21no—
166D4—3624no—
167D4C4×#1062438212yes—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—3621no—
171C2×C4—3624no—
172C2×C4—3624no—
173C2×C4—3621no—
174C2×C4—1811no—
175C2×C4—1811no—
176C2×C4—1811no—
177C2×C4—1812no—
178C2×C4—1812no—
179C2×C4—7241no—
180C2×C4—7241no—
181C2×C4—7242no—
182C2×C4—7242no—
183C2×C4—7242no—
184C2×C4C22⋊#1062438211yescharacteristic
185C2×C4C22⋊#1062438211yescharacteristic
186C2×C4C22×#1062438211yescharacteristic
187C8—3624no—
188C22—22no—
189C22—41no—
190C22—41no—
191C22—3621no—
192C22—3621no—
193C22—1812no—
194C22C2×C22⋊#1062438211yescharacteristic
195C4—21no—
196C4—21no—
197C4—41no—
198C4—3622no—
199C4—3621no—
200C4—3621no—
201C4—1812no—
202C4—7244no—
203C4—7241no—
204C4C2×C4×#1062438211yescharacteristic
205C4#1915389511yescharacteristic
206C2—42no—
207C2—3622no—
208C2C4×C22⋊#1062438211yescharacteristic
209C2#2604227611yescharacteristic
210C2#2604227711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC4×C181C2×C42
FrattiniC2×C4C22×#10624382
FittingC4×D4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC2×#15668448C22
cosocleC2×C4×D181C23
hypercenterC4×D4#10624382
hypocenterC181#1759
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
2. C4×#15668459C2semidirect
3. #26042215C2semidirect
4. #26042149C2semidirect
8. #19153880C4semidirect
14. C4×Dic362C4semidirect
15. #19153781C4semidirect
16. D4×Dic181C4semidirect
23. C4×D4×C181C4semidirect
26. #15668459C2×C4semidirect
29. C4×#10624382C2×C4semidirect
105. C181#1759semidirect
119. C4×D4#10624382semidirect

Maximal subgroups

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

subgroupindex
C2×#191538802
C4×#156684592
#260422152
#260421492
C4×#156684482
#1759181