Finite Group Databasebeta

← #49094595

Subgroups — #49094595

Order 35968.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#31824211C211yesmaximal, characteristic, complemented
2#31823850C212yesmaximal, complemented
3#31823205C211yesmaximal, characteristic, complemented
4#31823202C212yesmaximal, complemented
5#490×C281C211yesmaximal, characteristic, complemented
6C2×#17985126—22no—
7C2×#17985123—22no—
8#22582867C2212yes—
9#22582864—22no—
10#22582857—22no—
11#22582854—22no—
12#22582790C2212yes—
13#127×C281C2211yescharacteristic
14#125×C281C2211yescharacteristic
15#102×C281—22no—
16#97×C281C2211yescharacteristic
17C2×Dic562D412yes—
18C2×D1124—22no—
19C2×D1124D412yes—
20C2×C4×D281—22no—
21#17985126—44no—
22#17985123—44no—
23C2×#14555886—22no—
24#17985117—22no—
25#17985115—22no—
26#17985115—22no—
27#17985115—22no—
28C2×D4×C281—22no—
29C2×D4×C281—21no—
30C2×C8×C281—21no—
31C4⋊C4×C281—22no—
32C4⋊C4×C281D412yes—
33C42×C281C2311yescharacteristic
34C22×D281—22no—
35Dic562—42no—
36D1124—42no—
37D1124—82no—
38C2×Dic281—22no—
39C4×D281—82no—
40#14555886—24no—
41C23×C281—41no—
42D4×C281—42no—
43D4×C281—42no—
44D4×C281—42no—
45C2×C4×C281—22no—
46C2×C4×C281C2×D412yes—
47C2×C4×C281C2×D411yescharacteristic
48C8×C281—41no—
49C22×C281—82no—
50C22×C281—81no—
51C22×C281#12011yescharacteristic
52C2×D281—42no—
53C2×D281—42no—
54C2×D281—42no—
55C4×C281—22no—
56C4×C281—21no—
57C4×C281—42no—
58Dic281—42no—
59C2×C281—161no—
60C2×C281#45312yes—
61C2×C281#45411yescharacteristic
62D281—82no—
63C281#165611yescharacteristic, complemented, Sylow
64#1656—2811nomaximal, Sylow
65#562—2811no—
66#496—2812no—
67#490D28111yescharacteristic, complemented
68#330—2811no—
69#329—2812no—
70C2×SD16—5622no—
71C2×D8—5622no—
72#127C2×D28111yescharacteristic
73#125C2×D28111yescharacteristic
74#124—2812no—
75#123—5622no—
76C22⋊Q8—5622no—
77#121—5622no—
78#102—22no—
79#97—2812no—
80#97C2×D28111yescharacteristic
81C2×Q8—2812no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—2812no—
85C2×D4—5622no—
86C22×C4—5622no—
87SD16—11244no—
88D8—11244no—
89C2×C8—21no—
90C2×C8—5622no—
91C4⋊C4—22no—
92C4⋊C4—5622no—
93C4⋊C4C22⋊D28112yes—
94C22⋊C4—5622no—
95C22⋊C4—5622no—
96C22⋊C4—5622no—
97C42C22×D28111yescharacteristic
98C23—41no—
99C23—5622no—
100Q8—11242no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—11242no—
105D4—22482no—
106C2×C4—22no—
107C2×C4—5622no—
108C2×C4—22482no—
109C2×C4D4×D28112yes—
110C2×C4C2×C22⋊D28111yescharacteristic
111C8—41no—
112C8—5624no—
113C22—82no—
114C22—81no—
115C22—11242no—
116C22—11242no—
117C22—11242no—
118C22#2258284711yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—11242no—
123C2—161no—
124C2—22482no—
125C2#3182362912yes—
126C2#3182363511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#490×C281C2
socleC22×C281#120
hypercenter#490D281
hypocenterC281#1656
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #31824211C2semidirect
2. #31823850C2semidirect
3. #31823205C2semidirect
4. #31823202C2semidirect
5. #490×C281C2semidirect
63. C281#1656semidirect
67. #490D281semidirect

Maximal subgroups

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

subgroupindex
#318242112
#318238502
#318232052
#318232022
#490×C2812
#1656281