Finite Group Databasebeta

← #49094614

Subgroups — #49094614

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#31823873C212yesmaximal, complemented
2#31823858C211yesmaximal, characteristic
3#31823205C212yesmaximal, complemented
4#31823203C211yesmaximal, characteristic
5#563×C281C211yesmaximal, characteristic
6C2×#17985128—21no—
7C2×#17985126—21no—
8#22582879C2211yescharacteristic
9#22582812—22no—
10#22582810—22no—
11#22582790C2212yes—
12#22582790C2211yescharacteristic
13C4⋊Q8×C281—21no—
14#126×C281—22no—
15#125×C281C2212yes—
16#124×C281C2211yescharacteristic
17#123×C281—21no—
18C22⋊Q8×C281—22no—
19C2×Dic562—21no—
20#17985128—42no—
21#17985126—42no—
22C2×#14555886—22no—
23C2×#14555886—21no—
24C4⋊Dic281—22no—
25C2×Q8×C281—21no—
26C2×Q8×C281D411yescharacteristic
27C2×D4×C281D411yescharacteristic
28C22×C4×C281—21no—
29C4⋊C4×C281—22no—
30C4⋊C4×C281—22no—
31C4⋊C4×C281—22no—
32C4⋊C4×C281D412yes—
33C4⋊C4×C281D412yes—
34C22⋊C4×C281—22no—
35C22⋊C4×C281—21no—
36C22⋊C4×C281—22no—
37C42×C281—21no—
38C42×C281C2311yescharacteristic
39Dic562—41no—
40Dic562—41no—
41C2×Dic281—41no—
42#14555886—24no—
43#14555886—22no—
44C23×C281—21no—
45Q8×C281—41no—
46Q8×C281—81no—
47D4×C281—41no—
48C2×C4×C281—22no—
49C2×C4×C281—21no—
50C2×C4×C281—22no—
51C2×C4×C281—81no—
52C2×C4×C281C2×D412yes—
53C2×C4×C281C2×D411yescharacteristic
54C22×C281—41no—
55C22×C281—42no—
56C22×C281#12011yescharacteristic
57C4×C281—21no—
58C4×C281—22no—
59C4×C281—42no—
60C4×C281—41no—
61C4×C281—42no—
62Dic281—81no—
63C2×C281—81no—
64C2×C281#45311yescharacteristic
65C2×C281#45612yes—
66C281#166011yescharacteristic, complemented, Sylow
67#1660—2811nomaximal, Sylow
68#563D28111yescharacteristic
69#501—2812no—
70#497—2811no—
71#330—2812no—
72#329—2811no—
73C2×Q16—5621no—
74C2×SD16—5621no—
75C4⋊Q8—21no—
76C4⋊Q8—2811no—
77#126—22no—
78#125C2×D28112yes—
79#124C2×D28111yescharacteristic
80#123—21no—
81C22⋊Q8—22no—
82#107—5622no—
83#106—5622no—
84#97—2812no—
85#97—2811no—
86C2×Q8—21no—
87C2×Q8—5621no—
88C2×Q8C22⋊D28111yescharacteristic
89C2×D4C22⋊D28111yescharacteristic
90C22×C4—21no—
91Q16—11242no—
92SD16—11242no—
93C2×C8—5622no—
94C2×C8—5621no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4—5622no—
99C4⋊C4C22⋊D28112yes—
100C4⋊C4C22⋊D28112yes—
101C22⋊C4—22no—
102C22⋊C4—21no—
103C22⋊C4—22no—
104C42—21no—
105C42C22×D28111yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—81no—
109Q8—11241no—
110Q8—11241no—
111D4—41no—
112C2×C4—22no—
113C2×C4—21no—
114C2×C4—22no—
115C2×C4—81no—
116C2×C4—11241no—
117C2×C4C2×C22⋊D28112yes—
118C2×C4C2×C22⋊D28111yescharacteristic
119C8—5622no—
120C8—5624no—
121C22—41no—
122C22—42no—
123C22#2258284811yescharacteristic
124C4—21no—
125C4—22no—
126C4—42no—
127C4—41no—
128C4—42no—
129C4—22481no—
130C2—81no—
131C2#3182363111yescharacteristic
132C2#3182364612yes—
subgroupG/H
centerC22#22582848
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#563×C281C2
socleC22×C281#120
prime radicalC2×D4×C281D4
hypercenter#563D281
hypocenterC281#1660
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #31823873C2semidirect
3. #31823205C2semidirect
66. C281#1660semidirect

Maximal subgroups

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

subgroupindex
#318238732
#318238582
#318232052
#318232032
#563×C2812
#1660281