Finite Group Databasebeta

← #37548415

Subgroups — #37548415

Order 23168.

958 conjugacy classes of subgroups; only the 449 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 449 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#26042029C213yesmaximal, complemented
2#26041998C216yesmaximal, complemented
3#26041960C216yesmaximal, complemented
4#26041893C216yesmaximal, complemented
5#26041864C216yesmaximal, complemented
6#26041808C213yesmaximal, complemented
7H(3,𝔽4)×C181C211yesmaximal, characteristic, complemented
8#19153814C2216yescomplemented
9#19153810C2212yescomplemented
10#19153809C2216yescomplemented
11#19153809C2216yescomplemented
12#19153809C2216yescomplemented
13#19153809C2216yescomplemented
14#19153808C2213yescomplemented
15#19153803C2216yes—
16#19153802C2216yescomplemented
17#19153798C2216yescomplemented
18#19153797C2216yes—
19#19153797C2216yes—
20#19153793C2216yescomplemented
21#19153793C2216yescomplemented
22#19153793C2216yescomplemented
23#19153792C2213yescomplemented
24#19153788C2216yes—
25#19153787C2213yes—
26#19153785C2212yescomplemented
27Q8×Dic181C2213yescomplemented
28C4×Dic362C2216yescomplemented
29D4×Dic181C2216yes—
30D4×Dic181C2213yes—
31#19153776C2216yescomplemented
32#19153772C2216yescomplemented
33#19153772C2216yescomplemented
34C2×C22⋊Dic181C2216yescomplemented
35C42×D181C2211yescharacteristic, complemented
36#124×C181C2216yes—
37#124×C181C2213yes—
38#120×C181C2216yes—
39C2×Dic362C2316yes—
40C2×C22⋊D181C2316yes—
41C22×Dic181C2316yes—
42C22×Dic181C2316yes—
43C2×C4×D181C2313yes—
44C4⋊Dic181C2316yes—
45C4⋊Dic181C2313yes—
46C4⋊Dic181C2313yes—
47#15668428C2316yes—
48#15668428C2316yes—
49#15668428C2316yes—
50#15668428C2316yes—
51#15668428C2316yes—
52C22⋊Dic181C2316yes—
53C22⋊Dic181C2316yes—
54C22⋊Dic181C2316yes—
55C22⋊Dic181C2316yes—
56C22⋊Dic181C2316yes—
57#15668426C2316yes—
58C4×Dic181C2313yes—
59C4×Dic181C2316yes—
60C4×Dic181C2316yes—
61C24×C181C2312yes—
62C2×Q8×C181C2313yes—
63C2×D4×C181C2313yes—
64C2×D4×C181C2316yes—
65C22⋊C4×C181C2316yes—
66C22⋊C4×C181C2316yes—
67C22⋊C4×C181C2316yes—
68C42×C181C2311yescharacteristic
69C42×C181C2312yes—
70C22×D181C2411yescharacteristic
71Dic362—46no—
72C22⋊D181—46no—
73C2×Dic181—46no—
74C2×Dic181—46no—
75C2×Dic181C2413yes—
76C2×Dic181C2416yes—
77C2×Dic181C2416yes—
78C4×D181—43no—
79C23×C181—46no—
80C23×C181C2416yes—
81Q8×C181—43no—
82D4×C181—43no—
83D4×C181—46no—
84C2×C4×C181C2416yes—
85C2×C4×C181C2413yes—
86C22×C181—26no—
87C22×C181—26no—
88C22×C181—26no—
89C22×C181—84no—
90C22×C181C2511yescharacteristic
91C2×D181—23no—
92C4×C181—23no—
93C4×C181—26no—
94Dic181—23no—
95Dic181—26no—
96Dic181—26no—
97C2×C181—46no—
98C2×C181#58513yes—
99D181—41no—
100C181#356811yescharacteristic, complemented, Sylow
101#3568—1811nomaximal, Sylow
102#563—1813no—
103H(3,𝔽4)D18111yescharacteristic, complemented
104#556—1816no—
105#551—1816no—
106#542—1816no—
107#538—1816no—
108#529—1813no—
109C4⋊Q8—1816no—
110#126—1816no—
111#126—1816no—
112#126—1816no—
113#126—1816no—
114#126—1812no—
115#125—1813no—
116#124—1816no—
117#124—1816no—
118#124C2×D18113yes—
119#124C2×D18116yes—
120#123—1816no—
121#123—1816no—
122#123—1816no—
123C22⋊Q8—1813no—
124C22⋊Q8—1816no—
125C22⋊Q8—1816no—
126C22⋊Q8—1816no—
127#121—1813no—
128#121—1816no—
129#120—1812no—
130#120C2×D18116yes—
131C4×Q8—1813no—
132C4×Q8—1816no—
133C4×D4—1813no—
134C4×D4—1816no—
135C4×D4—1816no—
136#117—1816no—
137#117—1816no—
138C2×C22⋊C4—1816no—
139C2×C42—1811no—
140C24C22×D18112yes—
141C2×Q8—1816no—
142C2×Q8C22×D18113yes—
143C2×D4—1816no—
144C2×D4C22×D18113yes—
145C2×D4C22×D18116yes—
146C22×C4—1816no—
147C22×C4—1816no—
148C22×C4—1813no—
149C4⋊C4—1816no—
150C4⋊C4—1816no—
151C4⋊C4—1816no—
152C4⋊C4—1816no—
153C4⋊C4—1813no—
154C4⋊C4—1816no—
155C4⋊C4—1813no—
156C4⋊C4—1816no—
157C22⋊C4—1816no—
158C22⋊C4—1816no—
159C22⋊C4—1816no—
160C22⋊C4—1816no—
161C22⋊C4—1816no—
162C22⋊C4—1816no—
163C22⋊C4C22×D18116yes—
164C22⋊C4C22×D18116yes—
165C22⋊C4C22×D18116yes—
166C42—1813no—
167C42—1816no—
168C42—1816no—
169C42C22×D18111yescharacteristic
170C42C22×D18112yes—
171C23—46no—
172C23—1811no—
173C23C23×D18116yes—
174Q8—43no—
175Q8—7246no—
176D4—43no—
177D4—46no—
178D4—7246no—
179C2×C4—1813no—
180C2×C4—1816no—
181C2×C4—1816no—
182C2×C4—7243no—
183C2×C4—7246no—
184C2×C4—7246no—
185C2×C4C23×D18116yes—
186C2×C4C23×D18113yes—
187C22—26no—
188C22—26no—
189C22—26no—
190C22—84no—
191C22—3623no—
192C22C24×D18111yescharacteristic
193C4—23no—
194C4—26no—
195C4—3623no—
196C4—3626no—
197C4—3626no—
198C2—46no—
199C2—7241no—
200C2#2604211413yes—
subgroupG/H
center, FrattiniC22C24×D181
commutator, socle, cosocleC22×C181C25
FittingH(3,𝔽4)×C181C2
hypercenterH(3,𝔽4)D181
hypocenterC181#3568
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #26042029C2semidirect
2. #26041998C2semidirect
3. #26041960C2semidirect
4. #26041893C2semidirect
5. #26041864C2semidirect
6. #26041808C2semidirect
7. H(3,𝔽4)×C181C2semidirect
8. #19153814C22semidirect
9. #19153810C22semidirect
10. #19153809C22semidirect
11. #19153809C22semidirect
12. #19153809C22semidirect
13. #19153809C22semidirect
14. #19153808C22semidirect
16. #19153802C22semidirect
17. #19153798C22semidirect
20. #19153793C22semidirect
21. #19153793C22semidirect
22. #19153793C22semidirect
23. #19153792C22semidirect
26. #19153785C22semidirect
27. Q8×Dic181C22semidirect
28. C4×Dic362C22semidirect
31. #19153776C22semidirect
32. #19153772C22semidirect
33. #19153772C22semidirect
34. C2×C22⋊Dic181C22semidirect
35. C42×D181C22semidirect
100. C181#3568semidirect
103. H(3,𝔽4)D181semidirect

Maximal subgroups

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

subgroupindex
#260420292
#260419982
#260419602
#260418932
#260418642
#260418082
H(3,𝔽4)×C1812
#3568181