Finite Group Databasebeta

← #49098492

Subgroups — #49098492

Order 35968.

456 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 173 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×#22582873C211yesmaximal, characteristic
2#31823360C213yesmaximal, complemented
3#31823355C213yesmaximal
4#31823350C213yesmaximal, complemented
5#31823337C213yesmaximal
6#31823333C211yesmaximal, characteristic, complemented
7#383×C281C211yesmaximal, characteristic, complemented
8C22×C4×D281C2211yescharacteristic
9#22582873C418yescomplemented
10C2×C4⋊Dic281C2213yes—
11C2×C4⋊Dic281C2213yes—
12C2×#17985117C2213yes—
13C2×#17985117C2213yes—
14C2×#17985115C2213yes—
15C2×#17985115C2213yes—
16C2×C4×Dic281C2213yes—
17#22582786C2213yes—
18#22582786C2213yes—
19C2×C42×C281C2211yescharacteristic
20#95×C281C2213yes—
21#95×C281C2213yes—
22C23×D281C2311yescharacteristic
23C22×Dic281C2311yescharacteristic
24C22×Dic281C2313yes—
25C22×Dic281C2313yes—
26C2×C4×D281—43no—
27C4⋊Dic281—43no—
28C4⋊Dic281—43no—
29#17985117—43no—
30#17985117C2×C4112yescomplemented
31#17985115—43no—
32#17985115C2×C4112yes—
33C4×Dic281—43no—
34C22×C4×C281C2313yes—
35C22×C4×C281C2311yescharacteristic
36C22×C4×C281C2313yes—
37C42×C281C2×C414yescomplemented
38C22×D281—23no—
39C22×D281—23no—
40C22×D281C22×C412yes—
41C2×Dic281—23no—
42C2×Dic281—23no—
43C2×Dic281—23no—
44C2×Dic281—23no—
45C2×Dic281—23no—
46C2×Dic281—23no—
47C2×Dic281C22×C416yes—
48C4×D281—44no—
49C23×C281C2411yescharacteristic
50C2×C4×C281—23no—
51C2×C4×C281—23no—
52C2×C4×C281—23no—
53C2×C4×C281—23no—
54C2×C4×C281—26no—
55C2×C4×C281C22×C416yes—
56C22×C281C23×C411yescharacteristic
57C22×C281H(5,𝔽2)13yes—
58C22×C2812−1+413yes—
59C2×D281—26no—
60C2×D281—41no—
61C2×D281—43no—
62C4×C281—26no—
63C4×C281—41no—
64C4×C281—43no—
65Dic281—26no—
66Dic281—41no—
67Dic281—43no—
68C2×C281#52013yes—
69C2×C281#56011yescharacteristic
70C2×C281#56313yes—
71D281—42no—
72C281#238311yescharacteristic, complemented, Sylow
73#2383—2811nomaximal, Sylow
74C2×#126—2811no—
75#389—2813no—
76#388—2813no—
77#387—2813no—
78#385—2813no—
79#384—2811no—
80#383D28111yescharacteristic, complemented
81C23×C4—2811no—
82#126—2818no—
83C2×C4⋊C4—2813no—
84C2×C4⋊C4—2813no—
85C2×C4⋊C4—2813no—
86C2×C4⋊C4—2813no—
87C2×C22⋊C4—2813no—
88C2×C22⋊C4—2813no—
89C2×C42—2813no—
90C2×C42C2×D28111yescharacteristic
91#95—2813no—
92#95—2813no—
93#95C2×D28113yes—
94#95C2×D28113yes—
95C24—2811no—
96C22×C4—2813no—
97C22×C4—2811no—
98C22×C4—2813no—
99C22×C4—11243no—
100C22×C4C22×D28113yes—
101C22×C4C22×D28111yescharacteristic
102C22×C4C22×D28113yes—
103C4⋊C4—28112no—
104C4⋊C4—11243no—
105C4⋊C4—11243no—
106C4⋊C4—11243no—
107C22⋊C4—28112no—
108C22⋊C4—11243no—
109C42—11243no—
110C42C4×D28114yescomplemented
111C23—2812no—
112C23—5623no—
113C23—5623no—
114C23C23×D28111yescharacteristic
115C2×C4—23no—
116C2×C4—23no—
117C2×C4—23no—
118C2×C4—23no—
119C2×C4—26no—
120C2×C4—2816no—
121C2×C4—5623no—
122C2×C4—5623no—
123C2×C4—5623no—
124C2×C4—5623no—
125C2×C4—5623no—
126C2×C4—5623no—
127C2×C4—11244no—
128C2×C4C2×C4×D28116yes—
129C22—5626no—
130C22—11241no—
131C22—11243no—
132C22C22×C4×D28111yescharacteristic
133C22#2258292513yes—
134C22#2258292613yes—
135C4—26no—
136C4—41no—
137C4—43no—
138C4—5626no—
139C4—11241no—
140C4—11243no—
141C2—11242no—
142C2#3182394313yes—
143C2#3182420411yescharacteristic
144C2#3182421513yes—
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#383×C281C2
socle, cosocleC23×C281C24
prime radicalC23×D281C23
hypercenter#383D281
hypocenterC281#2383
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #31823360C2semidirect
4. #31823350C2semidirect
6. #31823333C2semidirect
7. #383×C281C2semidirect
9. #22582873C4semidirect
30. #17985117C2×C4semidirect
37. C42×C281C2×C4semidirect
72. C281#2383semidirect
80. #383D281semidirect
110. C42C4×D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828732
#318233602
#318233552
#318233502
#318233372
#318233332
#383×C2812
#2383281