Finite Group Databasebeta

← #49094615

Subgroups — #49094615

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#31823872C212yesmaximal, complemented
3#31823858C211yesmaximal, characteristic
4#31823204C212yesmaximal, complemented
5#329×C281C211yesmaximal, characteristic
6C2×#17985128—21no—
7C2×#17985126—21no—
8#22582879C2211yescharacteristic
9#22582877—21no—
10#22582872—22no—
11#22582871C2212yes—
12#22582860—21no—
13#22582856—22no—
14#22582813—22no—
15#22582811—22no—
16#22582790C2211yescharacteristic
17#124×C281C2211yescharacteristic
18#97×C281C2212yes—
19C2×Dic562—21no—
20C2×Dic562—21no—
21C22×Dic281—21no—
22#17985128—42no—
23#17985126—42no—
24C2×#14555886—21no—
25C4⋊Dic281—22no—
26C4⋊Dic281D412yes—
27C4⋊Dic281D412yes—
28#17985117—22no—
29#17985117—22no—
30#17985117—22no—
31C22⋊Dic281—22no—
32C22⋊Dic281—21no—
33C4×Dic281—21no—
34C2×Q8×C281D411yescharacteristic
35C2×D4×C281D411yescharacteristic
36C2×C8×C281—22no—
37C22⋊C4×C281—22no—
38C42×C281C2311yescharacteristic
39Dic562—41no—
40Dic562—41no—
41Dic562—81no—
42C2×Dic281—22no—
43C2×Dic281—22no—
44C2×Dic281—41no—
45C2×Dic281—81no—
46#14555886—22no—
47C23×C281—21no—
48Q8×C281—41no—
49D4×C281—41no—
50C2×C4×C281—21no—
51C2×C4×C281C2×D412yes—
52C2×C4×C281C2×D411yescharacteristic
53C8×C281—24no—
54C22×C281—41no—
55C22×C281—42no—
56C22×C281#12011yescharacteristic
57C4×C281—21no—
58C4×C281—22no—
59C4×C281—41no—
60Dic281—42no—
61Dic281—42no—
62Dic281—81no—
63C2×C281—81no—
64C2×C281#45311yescharacteristic
65C2×C281#45612yes—
66C281#166011yescharacteristic, complemented, Sylow
67#1660—2811nomaximal, Sylow
68#563—2811no—
69#501—2812no—
70#497—2811no—
71#330—2812no—
72#329D28111yescharacteristic
73C2×Q16—5621no—
74C2×SD16—5621no—
75C4⋊Q8—2811no—
76C4⋊Q8—5621no—
77#126—5622no—
78#125—2812no—
79#124C2×D28111yescharacteristic
80#123—5621no—
81C22⋊Q8—5622no—
82#107—5622no—
83#106—5622no—
84#97—2811no—
85#97C2×D28112yes—
86C2×Q8—5621no—
87C2×Q8—5621no—
88C2×Q8D112411yescharacteristic
89C2×D4D112411yescharacteristic
90C22×C4—5621no—
91Q16—11242no—
92SD16—11242no—
93C2×C8—22no—
94C2×C8—5621no—
95C4⋊C4—2812no—
96C4⋊C4—2812no—
97C4⋊C4—5622no—
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—11241no—
109Q8—11241no—
110Q8—22481no—
111D4—41no—
112C2×C4—21no—
113C2×C4—5622no—
114C2×C4—5622no—
115C2×C4—11241no—
116C2×C4—22481no—
117C2×C4D4×D28112yes—
118C2×C4C2×D112411yescharacteristic
119C8—24no—
120C8—5622no—
121C22—41no—
122C22—42no—
123C22#2258284911yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—11242no—
128C4—11242no—
129C4—22481no—
130C2—81no—
131C2#3182363311yescharacteristic
132C2#3182364712yes—
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#329×C281C2
socleC22×C281#120
prime radicalC2×D4×C281D4
hypercenter#329D281
hypocenterC281#1660
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31823872C2semidirect
4. #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
#318238722
#318238582
#318232042
#329×C2812
#1660281