Finite Group Databasebeta

← #49094626

Subgroups — #49094626

Order 35968.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#31823833C211yesmaximal, characteristic, complemented
2#31823822C212yesmaximal, complemented
3#31823205C211yesmaximal, characteristic, complemented
4#31823203C212yesmaximal, complemented
5#562×C281C211yesmaximal, characteristic
6#22582879C2211yescharacteristic
7#22582803—22no—
8#22582802—22no—
9#22582800—22no—
10#22582790C2211yescharacteristic
11#22582790C2212yes—
12#125×C281C2211yescharacteristic
13#124×C281C2212yes—
14#123×C281—22no—
15C22⋊Q8×C281—22no—
16#121×C281—22no—
17C2×Dic562—21no—
18C2×#14555886—22no—
19C2×#14555886—21no—
20C4⋊Dic281—22no—
21C2×Q8×C281D412yes—
22C2×D4×C281—22no—
23C2×D4×C281D412yes—
24C22×C4×C281—22no—
25C4⋊C4×C281—22no—
26C4⋊C4×C281—22no—
27C4⋊C4×C281D412yes—
28C22⋊C4×C281—22no—
29C22⋊C4×C281—22no—
30C22⋊C4×C281—22no—
31C42×C281C2311yescharacteristic
32Dic562—42no—
33C2×Dic281—41no—
34#14555886—41no—
35#14555886—42no—
36C23×C281—22no—
37Q8×C281—42no—
38D4×C281—42no—
39D4×C281—82no—
40C2×C4×C281—22no—
41C2×C4×C281—22no—
42C2×C4×C281—82no—
43C2×C4×C281C2×D411yescharacteristic
44C2×C4×C281C2×D412yes—
45C22×C281—42no—
46C22×C281—42no—
47C22×C281—42no—
48C22×C281#12011yescharacteristic
49C4×C281—21no—
50C4×C281—22no—
51C4×C281—42no—
52C4×C281—42no—
53Dic281—81no—
54C2×C281—82no—
55C2×C281#45411yescharacteristic
56C2×C281#45512yes—
57C281#166211yescharacteristic, complemented, Sylow
58#1662—2811nomaximal, Sylow
59#562D28111yescharacteristic
60#491—2811no—
61#489—2812no—
62#330—2811no—
63#329—2812no—
64C4⋊Q8—2811no—
65#125C2×D28111yescharacteristic
66#124C2×D28112yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—5622no—
71#103—5622no—
72#102—5622no—
73#97—2811no—
74#97—2812no—
75C2×Q8—5621no—
76C2×Q8C22⋊D28112yes—
77C2×D4—22no—
78C2×D4C22⋊D28112yes—
79C22×C4—22no—
80C2×C8—5622no—
81C2×C8—5621no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—5622no—
85C4⋊C4C22⋊D28112yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D28111yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—11242no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—11241no—
99C2×C4C2×C22⋊D28111yescharacteristic
100C2×C4C2×C22⋊D28112yes—
101C8—11241no—
102C8—11242no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#2258284811yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—22481no—
112C2—82no—
113C2#3182363611yescharacteristic
114C2#3182364112yes—
subgroupG/H
centerC22#22582848
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting, prime radical#562×C281C2
socleC22×C281#120
hypercenter#562D281
hypocenterC281#1662
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #31823833C2semidirect
2. #31823822C2semidirect
3. #31823205C2semidirect
4. #31823203C2semidirect
57. C281#1662semidirect

Maximal subgroups

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

subgroupindex
#318238332
#318238222
#318232052
#318232032
#562×C2812
#1662281