Finite Group Databasebeta

← #49094627

Subgroups — #49094627

Order 35968.

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

normal subgroups only

This group has 196 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
2#31823833C211yesmaximal, characteristic, complemented
3#31823823C212yesmaximal, complemented
4#31823202C212yesmaximal, complemented
5#330×C281C211yesmaximal, characteristic, complemented
6#22582879C2211yescharacteristic
7#22582867C2212yes—
8#22582864—22no—
9#22582857—22no—
10#22582854—22no—
11#22582804—22no—
12#22582802—22no—
13#22582801—22no—
14#22582790C2211yescharacteristic
15#125×C281C2211yescharacteristic
16#97×C281C2212yes—
17C2×Dic562—21no—
18C2×Dic562D412yes—
19C2×D1124—22no—
20C2×D1124D412yes—
21C2×C4×D281—22no—
22C2×#14555886—21no—
23C4⋊Dic281—22no—
24#17985117—22no—
25#17985115—22no—
26#17985115—22no—
27#17985115—22no—
28C2×C8×C281—22no—
29C4⋊C4×C281—22no—
30C4⋊C4×C281D412yes—
31C42×C281C2311yescharacteristic
32C22×D281—22no—
33Dic562—42no—
34Dic562—42no—
35D1124—42no—
36D1124—82no—
37C2×Dic281—22no—
38C2×Dic281—41no—
39C4×D281—82no—
40#14555886—41no—
41C2×C4×C281—22no—
42C2×C4×C281C2×D412yes—
43C2×C4×C281C2×D411yescharacteristic
44C8×C281—42no—
45C22×C281#12011yescharacteristic
46C2×D281—42no—
47C2×D281—42no—
48C2×D281—42no—
49C4×C281—21no—
50C4×C281—22no—
51C4×C281—42no—
52Dic281—42no—
53Dic281—81no—
54C2×C281#45411yescharacteristic
55C2×C281#45512yes—
56D281—82no—
57C281#166211yescharacteristic, complemented, Sylow
58#1662—2811nomaximal, Sylow
59#562—2811no—
60#491—2811no—
61#489—2812no—
62#330D28111yescharacteristic, complemented
63#329—2812no—
64C4⋊Q8—2811no—
65#125C2×D28111yescharacteristic
66#124—2812no—
67#123—5622no—
68C22⋊Q8—5622no—
69#121—5622no—
70#103—5622no—
71#103—5622no—
72#102—5622no—
73#97—2811no—
74#97C2×D28112yes—
75C2×Q8—2812no—
76C2×Q8—5621no—
77C2×D4—2812no—
78C2×D4—5622no—
79C22×C4—5622no—
80C2×C8—22no—
81C2×C8—5621no—
82C4⋊C4—22no—
83C4⋊C4—5622no—
84C4⋊C4—5622no—
85C4⋊C4D112412yes—
86C22⋊C4—5622no—
87C22⋊C4—5622no—
88C22⋊C4—5622no—
89C42C22×D28111yescharacteristic
90C23—5622no—
91Q8—11242no—
92Q8—11242no—
93D4—11242no—
94D4—22482no—
95C2×C4—22no—
96C2×C4—5622no—
97C2×C4—11241no—
98C2×C4—22482no—
99C2×C4D4×D28112yes—
100C2×C4C2×D112411yescharacteristic
101C8—42no—
102C8—11241no—
103C22—11242no—
104C22—11242no—
105C22—11242no—
106C22#2258284911yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—11242no—
111C4—22481no—
112C2—22482no—
113C2#3182363811yescharacteristic
114C2#3182364212yes—
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#330×C281C2
socleC22×C281#120
prime radical#31824211C2
hypercenter#330D281
hypocenterC281#1662
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #31823833C2semidirect
3. #31823823C2semidirect
4. #31823202C2semidirect
5. #330×C281C2semidirect
57. C281#1662semidirect
62. #330D281semidirect

Maximal subgroups

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

subgroupindex
#318242112
#318238332
#318238232
#318232022
#330×C2812
#1662281