Finite Group Databasebeta

← #37543964

Subgroups — #37543964

Order 23168.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#26041884C211yesmaximal, characteristic, complemented
2#26041603C212yesmaximal, complemented
3#26041579C212yesmaximal, complemented
4#26041474C212yesmaximal, complemented
5#26041413C212yesmaximal, complemented
6#26041389C212yesmaximal, complemented
7C4×#15668434C212yesmaximal, complemented
8#26041340C211yesmaximal, characteristic, complemented
9#518×C181C211yesmaximal, characteristic, complemented
10C2×#15668434C2212yes—
11C2×#15668434C2212yes—
12#19153813C2211yescharacteristic, complemented
13#19153808C2211yescharacteristic, complemented
14#19153801—22no—
15#19153790C2212yes—
16#19153789—22no—
17C4×D724C2212yescomplemented
18#19153749C2212yescomplemented
19#19153747C2212yescomplemented
20C4⋊#13089678C2212yescomplemented
21#19153737C2212yes—
22#19153737C2212yes—
23#19153736C2212yescomplemented
24#19153736C2212yescomplemented
25C22⋊#13089678C2212yes—
26#19153727C2211yescharacteristic, complemented
27C4×#13089678C2211yescharacteristic, complemented
28C22×D4×C181C2211yescharacteristic
29C4×D4×C181—22no—
30C4×D4×C181C2212yes—
31C4×D4×C181C2212yes—
32#117×C181C2211yescharacteristic
33#117×C181C2211yescharacteristic
34C2×C22⋊C4×C181—22no—
35C2×D724—22no—
36C2×D724C2312yes—
37C2×C22⋊D181—22no—
38C2×C4×D181—22no—
39#15668434—24no—
40#15668434—24no—
41C2×#13089678C2312yes—
42C2×#13089678C2312yes—
43C4⋊Dic181C2312yes—
44#15668428—22no—
45#15668426—22no—
46#15668426—22no—
47C24×C181—21no—
48C2×D4×C181—24no—
49C2×D4×C181—21no—
50C2×D4×C181C2312yes—
51C22×C4×C181—22no—
52C22×C4×C181—22no—
53C22×C4×C181C2311yescharacteristic
54C4⋊C4×C181D412yes—
55C4⋊C4×C181C2312yes—
56C22⋊C4×C181—21no—
57C22⋊C4×C181—22no—
58C22⋊C4×C181—22no—
59C22⋊C4×C181D412yes—
60C42×C181—21no—
61C42×C181C2311yescharacteristic
62C42×C181C2311yescharacteristic
63C22×D181—22no—
64D724—22no—
65D724—22no—
66D724—82no—
67C22⋊D181—82no—
68C2×Dic181—22no—
69C4×D181—82no—
70#13089678—22no—
71#13089678—22no—
72C23×C181—24no—
73C23×C181—22no—
74C23×C181—82no—
75C23×C181C2×D411yescharacteristic
76D4×C181—24no—
77D4×C181—22no—
78D4×C181#4114yes—
79C2×C4×C181—22no—
80C2×C4×C181—22no—
81C2×C4×C181—82no—
82C2×C4×C181—82no—
83C2×C4×C181C2×D411yescharacteristic
84C2×C4×C181C2×D412yes—
85C2×C4×C181C2×D412yes—
86C2×C4×C181C2411yescharacteristic
87C22×C181—21no—
88C22×C181—24no—
89C22×C181—22no—
90C22×C181—42no—
91C22×C181—42no—
92C22×C181—84no—
93C22×C181C22×D411yescharacteristic
94C2×D181—42no—
95C2×D181—42no—
96C2×D181—42no—
97C4×C181—21no—
98C4×C181—22no—
99C4×C181—22no—
100C4×C181—42no—
101C4×C181C2×#4112yes—
102Dic181—42no—
103C2×C181—41no—
104C2×C181—44no—
105C2×C181#52511yescharacteristic
106C2×C181#57612yes—
107D181—82no—
108C181#312211yescharacteristic, complemented, Sylow
109#3122—1811nomaximal, Sylow
110#540—1811no—
111#518D18111yescharacteristic, complemented
112#482—1812no—
113#478—1812no—
114#459—1812no—
115#447—1812no—
116#442—1812no—
117C4×D8—1812no—
118#433—1811no—
119C22×D4C2×D18111yescharacteristic
120C2×D8—1812no—
121C2×D8—1812no—
122#127—1811no—
123#125—1811no—
124#123—3622no—
125#121—3622no—
126#121—1812no—
127C4×D4—22no—
128C4×D4—1812no—
129C4×D4C2×D18112yes—
130C4×D4C2×D18112yes—
131#117C2×D18111yescharacteristic
132#117C2×D18111yescharacteristic
133C2×C22⋊C4—22no—
134#107—1812no—
135#106—1812no—
136C4⋊C8—1812no—
137#102—1812no—
138#102—1812no—
139#102—1812no—
140#102—1812no—
141C22⋊C8—1812no—
142#97—1811no—
143C4×C8—1811no—
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—3622no—
148C2×D4—3622no—
149C2×D4—1812no—
150C2×D4C22×D18112yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—3622no—
154C22×C4C22×D18111yescharacteristic
155D8—3624no—
156D8—3624no—
157C2×C8—1812no—
158C2×C8—1812no—
159C4⋊C4—3622no—
160C4⋊C4—1812no—
161C4⋊C4C22⋊D18112yes—
162C4⋊C4C22×D18112yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—3622no—
167C22⋊C4—3622no—
168C22⋊C4C22⋊D18112yes—
169C42—21no—
170C42C22×D18111yescharacteristic
171C42C22×D18111yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—3622no—
176C23C2×C22⋊D18111yescharacteristic
177D4—24no—
178D4—22no—
179D4—3622no—
180D4—3622no—
181D4—14482no—
182D4—14482no—
183D4#1566844914yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—3622no—
189C2×C4—14482no—
190C2×C4C2×C22⋊D18111yescharacteristic
191C2×C4C2×C22⋊D18112yes—
192C2×C4C2×C22⋊D18112yes—
193C2×C4C23×D18111yescharacteristic
194C8—3622no—
195C8—3622no—
196C22—21no—
197C22—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—7242no—
203C22—7242no—
204C22—7242no—
205C22C22×C22⋊D18111yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—7242no—
211C4C2×#1566844912yes—
212C2—41no—
213C2—44no—
214C2—14482no—
215C2#2604179011yescharacteristic
216C2#2604208212yes—
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#518×C181C2
socleC22×C181C22×D4
hypercenter#518D181
hypocenterC181#3122
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #26041884C2semidirect
2. #26041603C2semidirect
3. #26041579C2semidirect
4. #26041474C2semidirect
5. #26041413C2semidirect
6. #26041389C2semidirect
7. C4×#15668434C2semidirect
8. #26041340C2semidirect
9. #518×C181C2semidirect
12. #19153813C22semidirect
13. #19153808C22semidirect
17. C4×D724C22semidirect
18. #19153749C22semidirect
19. #19153747C22semidirect
20. C4⋊#13089678C22semidirect
23. #19153736C22semidirect
24. #19153736C22semidirect
26. #19153727C22semidirect
27. C4×#13089678C22semidirect
108. C181#3122semidirect
111. #518D181semidirect

Maximal subgroups

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

subgroupindex
#260418842
#260416032
#260415792
#260414742
#260414132
#260413892
C4×#156684342
#260413402
#518×C1812
#3122181