Finite Group Databasebeta

← #37549485

Subgroups — #37549485

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×#19153881C212yesmaximal
2C4×#15668459C211yesmaximal, characteristic, complemented
3#26042215C211yesmaximal, characteristic, complemented
4#26042149C212yesmaximal, complemented
5C4×#15668450C211yesmaximal, characteristic
6C2×#15668459C2212yes—
7C2×C4×#10624382C2212yes—
8#19153881C418yescomplemented
9#19153871—21no—
10C4×#13089685—21no—
11(C2×#10624382)⋊C4—21no—
12(C2×#10624382)⋊C4—21no—
13C2×#15668450C2211yescharacteristic
14Q8×Dic181C411yescharacteristic, complemented
15C4×D724—21no—
16C4×D724C411yescharacteristic, complemented
17#19153778—21no—
18#19153778C411yescharacteristic, complemented
19#19153774—21no—
20#19153774C2211yescharacteristic
21C42×D181—21no—
22C42×D181C2211yescharacteristic
23C4×Q8×C181C411yescharacteristic, complemented
24C22×#10624382—22no—
25#15668459—22no—
26#15668459C2×C414yescomplemented
27C2×#13089685—22no—
28C4×#10624382—22no—
29C4×#10624382C2×C414yescomplemented
30#15668450—22no—
31#15668450C2×C414yes—
32C2×D724—21no—
33C2×D724C2×C411yescharacteristic
34C2×C4×D181—21no—
35C2×C4×D181—21no—
36C2×C4×D181—21no—
37C2×C4×D181D411yescharacteristic
38C2×C4×D181D411yescharacteristic
39C2×C4×D181C2311yescharacteristic
40C4⋊Dic181—21no—
41C4⋊Dic181C2×C411yescharacteristic
42#15668426—21no—
43#15668426—21no—
44#15668426—21no—
45C4×Dic181—21no—
46C4×Dic181—21no—
47C4×Dic181C2×C411yescharacteristic
48C4×Dic181D411yescharacteristic
49C4×Dic181D411yescharacteristic
50C2×Q8×C181C2×C411yescharacteristic
51C4⋊C4×C181—21no—
52C4⋊C4×C181C2×C411yescharacteristic
53C42×C181—21no—
54C42×C181C2×C411yescharacteristic
55C2×#10624382—24no—
56C2×#10624382—42no—
57C2×#10624382—42no—
58#13089685—24no—
59C22×D181—21no—
60C22×D181C2×D411yescharacteristic
61D724—24no—
62D724—21no—
63D724C4212yes—
64C2×Dic181—21no—
65C2×Dic181C22⋊C411yescharacteristic
66C2×Dic181C22⋊C411yescharacteristic
67C2×Dic181C2×D411yescharacteristic
68C4×D181—24no—
69C4×D181—41no—
70C4×D181—41no—
71C4×D181—42no—
72C4×D181—42no—
73C4×D181C22×C412yes—
74C4×D181#4112yes—
75Q8×C181—21no—
76Q8×C181C4212yes—
77C2×C4×C181—21no—
78C2×C4×C181—21no—
79C2×C4×C181C22⋊C411yescharacteristic
80C2×C4×C181C22⋊C411yescharacteristic
81C2×C4×C181C22×C411yescharacteristic
82C22×C181C2×C22⋊C411yescharacteristic
83C2×D181—21no—
84C2×D181—21no—
85C2×D181—22no—
86C2×D181—41no—
87C2×D181—41no—
88C2×D181C4×D412yes—
89#10624382—44no—
90C4×C181—22no—
91C4×C181—21no—
92C4×C181—21no—
93C4×C181—41no—
94C4×C181C2×C4211yescharacteristic
95C4×C181#11711yescharacteristic
96Dic181—21no—
97Dic181—21no—
98Dic181—41no—
99Dic181C4×D412yes—
100C2×C181C4×C22⋊C411yescharacteristic
101C2×C181#42111yescharacteristic
102C2×C181#42111yescharacteristic
103D181—22no—
104D181—42no—
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#1062438211yescharacteristic, complemented
116C4×D4—3621no—
117C4×D4—3621no—
118C4×D4—1811no—
119C4×D4—1811no—
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×Q8C2×#1062438211yescharacteristic
133C2×D4—3621no—
134C2×D4—1811no—
135C22×C4—3621no—
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—21no—
146C4⋊C4—3621no—
147C4⋊C4—1811no—
148C4⋊C4C2×#1062438211yescharacteristic
149C22⋊C4—3621no—
150C22⋊C4—3621no—
151C22⋊C4—3621no—
152C42—21no—
153C42—3621no—
154C42—3621no—
155C42—3622no—
156C42—1814no—
157C42—1811no—
158C42—1811no—
159C42—1811no—
160C42C2×#1062438211yescharacteristic
161C23—3621no—
162C23—1811no—
163Q8—21no—
164Q8C4×#1062438212yes—
165D4—3624no—
166D4—3621no—
167D4—1812no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—3624no—
171C2×C4—3624no—
172C2×C4—3621no—
173C2×C4—1811no—
174C2×C4—1811no—
175C2×C4—1811no—
176C2×C4—1812no—
177C2×C4—1812no—
178C2×C4—7241no—
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—3624no—
188C22—3621no—
189C22—3621no—
190C22—3622no—
191C22—1812no—
192C22—7241no—
193C22—7241no—
194C22C2×C22⋊#1062438211yescharacteristic
195C4—22no—
196C4—21no—
197C4—21no—
198C4—41no—
199C4—3621no—
200C4—3621no—
201C4—1812no—
202C4—7244no—
203C4—7241no—
204C4C2×C4×#1062438211yescharacteristic
205C4#1915389511yescharacteristic
206C2—3622no—
207C2—7242no—
208C2C4×C22⋊#1062438211yescharacteristic
209C2#2604227611yescharacteristic
210C2#2604227811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC4×C181C2×C42
FrattiniC2×C4C22×#10624382
FittingC4×Q8×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC2×#15668450C22
cosocleC2×C4×D181C23
hypercenterC4×Q8#10624382
hypocenterC181#1759
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C4×#15668459C2semidirect
3. #26042215C2semidirect
4. #26042149C2semidirect
8. #19153881C4semidirect
14. Q8×Dic181C4semidirect
16. C4×D724C4semidirect
18. #19153778C4semidirect
23. C4×Q8×C181C4semidirect
26. #15668459C2×C4semidirect
29. C4×#10624382C2×C4semidirect
105. C181#1759semidirect
115. C4×Q8#10624382semidirect

Maximal subgroups

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

subgroupindex
C2×#191538812
C4×#156684592
#260422152
#260421492
C4×#156684502
#1759181