Finite Group Databasebeta

← #49094612

Subgroups — #49094612

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#31824213C211yesmaximal, characteristic
2#31823869C212yesmaximal, complemented
3#31823204C212yesmaximal, complemented
4#31823203C211yesmaximal, characteristic
5#497×C281C211yesmaximal, characteristic
6#22582877—21no—
7#22582872—22no—
8#22582871C2212yes—
9#22582860—21no—
10#22582856—22no—
11#22582812—22no—
12#22582810—22no—
13#22582790C2212yes—
14C2×Q16×C281—21no—
15C2×SD16×C281—21no—
16C4⋊Q8×C281C2211yescharacteristic
17#124×C281C2211yescharacteristic
18#97×C281C2211yescharacteristic
19C2×Dic562—21no—
20C22×Dic281—21no—
21C2×#14555886—22no—
22C4⋊Dic281D412yes—
23C4⋊Dic281D412yes—
24#17985117—22no—
25#17985117—22no—
26#17985117—22no—
27C22⋊Dic281—22no—
28C22⋊Dic281—21no—
29C4×Dic281—21no—
30C2×Q8×C281—21no—
31C2×Q8×C281D411yescharacteristic
32C2×D4×C281D411yescharacteristic
33Q16×C281—42no—
34SD16×C281—42no—
35C2×C8×C281—21no—
36C4⋊C4×C281—22no—
37C22⋊C4×C281—22no—
38C42×C281C2311yescharacteristic
39Dic562—81no—
40C2×Dic281—22no—
41C2×Dic281—22no—
42C2×Dic281—81no—
43#14555886—24no—
44C23×C281—21no—
45Q8×C281—41no—
46Q8×C281—41no—
47Q8×C281—41no—
48D4×C281—41no—
49C2×C4×C281—21no—
50C2×C4×C281—41no—
51C2×C4×C281C2×D412yes—
52C2×C4×C281C2×D411yescharacteristic
53C8×C281—22no—
54C22×C281—41no—
55C22×C281—42no—
56C22×C281#12011yescharacteristic
57C4×C281—21no—
58C4×C281—22no—
59C4×C281—41no—
60C4×C281—81no—
61Dic281—42no—
62Dic281—42no—
63C2×C281—81no—
64C2×C281#45311yescharacteristic
65C2×C281#45612yes—
66C281#166011yescharacteristic, complemented, Sylow
67#1660—2811nomaximal, Sylow
68#563—2811no—
69#501—2812no—
70#497D28111yescharacteristic
71#330—2812no—
72#329—2811no—
73C2×Q16—21no—
74C2×SD16—21no—
75C4⋊Q8—5621no—
76C4⋊Q8C2×D28111yescharacteristic
77#126—5622no—
78#125—2812no—
79#124C2×D28111yescharacteristic
80#123—5621no—
81C22⋊Q8—5622no—
82#107—5622no—
83#106—5622no—
84#97—2812no—
85#97C2×D28111yescharacteristic
86C2×Q8—21no—
87C2×Q8—5621no—
88C2×Q8C22⋊D28111yescharacteristic
89C2×D4C22⋊D28111yescharacteristic
90C22×C4—5621no—
91Q16—42no—
92SD16—42no—
93C2×C8—21no—
94C2×C8—5622no—
95C4⋊C4—22no—
96C4⋊C4—2812no—
97C4⋊C4—2812no—
98C4⋊C4—5622no—
99C4⋊C4—5622no—
100C4⋊C4—5622no—
101C22⋊C4—22no—
102C22⋊C4—5622no—
103C22⋊C4—5621no—
104C42—5621no—
105C42C22×D28111yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—41no—
109Q8—41no—
110Q8—22481no—
111D4—41no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—5622no—
115C2×C4—5622no—
116C2×C4—22481no—
117C2×C4D4×D28112yes—
118C2×C4C2×C22⋊D28111yescharacteristic
119C8—22no—
120C8—5624no—
121C22—41no—
122C22—42no—
123C22#2258284711yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—81no—
128C4—11242no—
129C4—11242no—
130C2—81no—
131C2#3182363011yescharacteristic
132C2#3182364412yes—
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#497×C281C2
socleC22×C281#120
prime radicalC2×D4×C281D4
hypercenter#497D281
hypocenterC281#1660
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #31823869C2semidirect
3. #31823204C2semidirect
66. C281#1660semidirect

Maximal subgroups

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

subgroupindex
#318242132
#318238692
#318232042
#318232032
#497×C2812
#1660281