Finite Group Databasebeta

← #49094624

Subgroups — #49094624

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#31823825C212yesmaximal, complemented
3#31823205C211yesmaximal, characteristic, complemented
4#31823202C212yesmaximal, complemented
5#491×C281C211yesmaximal, characteristic, complemented
6#22582867C2212yes—
7#22582864—22no—
8#22582857—22no—
9#22582854—22no—
10#22582802—22no—
11#22582799—22no—
12#22582790C2212yes—
13C4⋊Q8×C281C2211yescharacteristic
14#125×C281C2211yescharacteristic
15#103×C281—22no—
16#97×C281C2211yescharacteristic
17C2×Dic562D412yes—
18C2×D1124—22no—
19C2×D1124D412yes—
20C2×C4×D281—22no—
21C2×#14555886—22no—
22#17985117—22no—
23#17985115—22no—
24#17985115—22no—
25#17985115—22no—
26C2×Q8×C281—21no—
27C2×C8×C281—21no—
28C4⋊C4×C281—22no—
29C4⋊C4×C281—22no—
30C4⋊C4×C281D412yes—
31C42×C281C2311yescharacteristic
32C22×D281—22no—
33Dic562—42no—
34D1124—42no—
35D1124—82no—
36C2×Dic281—22no—
37C4×D281—82no—
38#14555886—42no—
39Q8×C281—42no—
40C2×C4×C281—22no—
41C2×C4×C281—41no—
42C2×C4×C281C2×D412yes—
43C2×C4×C281C2×D411yescharacteristic
44C8×C281—41no—
45C22×C281#12011yescharacteristic
46C2×D281—42no—
47C2×D281—42no—
48C2×D281—42no—
49C4×C281—21no—
50C4×C281—22no—
51C4×C281—42no—
52C4×C281—81no—
53Dic281—42no—
54C2×C281#45411yescharacteristic
55C2×C281#45512yes—
56D281—82no—
57C281#166211yescharacteristic, complemented, Sylow
58#1662—2811nomaximal, Sylow
59#562—2811no—
60#491D28111yescharacteristic, complemented
61#489—2812no—
62#330—2811no—
63#329—2812no—
64C4⋊Q8C2×D28111yescharacteristic
65#125C2×D28111yescharacteristic
66#124—2812no—
67#123—5622no—
68C22⋊Q8—5622no—
69#121—5622no—
70#103—22no—
71#103—5622no—
72#102—5622no—
73#97—2812no—
74#97C2×D28111yescharacteristic
75C2×Q8—21no—
76C2×Q8—2812no—
77C2×D4—2812no—
78C2×D4—5622no—
79C22×C4—5622no—
80C2×C8—21no—
81C2×C8—5622no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—5622no—
85C4⋊C4C22⋊D28112yes—
86C22⋊C4—5622no—
87C22⋊C4—5622no—
88C22⋊C4—5622no—
89C42C22×D28111yescharacteristic
90C23—5622no—
91Q8—42no—
92Q8—11242no—
93D4—11242no—
94D4—22482no—
95C2×C4—22no—
96C2×C4—41no—
97C2×C4—5622no—
98C2×C4—22482no—
99C2×C4D4×D28112yes—
100C2×C4C2×C22⋊D28111yescharacteristic
101C8—41no—
102C8—11242no—
103C22—11242no—
104C22—11242no—
105C22—11242no—
106C22#2258284711yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—81no—
111C4—11242no—
112C2—22482no—
113C2#3182363511yescharacteristic
114C2#3182363912yes—
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#491×C281C2
socleC22×C281#120
prime radical#31824211C2
hypercenter#491D281
hypocenterC281#1662
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #31823825C2semidirect
3. #31823205C2semidirect
4. #31823202C2semidirect
5. #491×C281C2semidirect
57. C281#1662semidirect
60. #491D281semidirect

Maximal subgroups

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

subgroupindex
#318242112
#318238252
#318232052
#318232022
#491×C2812
#1662281