Finite Group Databasebeta

← #49097323

Subgroups — #49097323

Order 35968.

216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 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, complemented
2#31823646C212yesmaximal, complemented
3#31823261C212yesmaximal, complemented
4#31823260C211yesmaximal, characteristic, complemented
5#454×C281C211yesmaximal, characteristic
6#22582909—22no—
7#22582877C2212yes—
8#22582872—22no—
9#22582871—21no—
10#22582860—21no—
11#22582856—22no—
12#22582806—22no—
13#22582798C2212yes—
142−1+4×C281C2211yescharacteristic
15AGL(1,ℤ/8)×C281—21no—
16#124×C281C2211yescharacteristic
17#104×C281—21no—
18#101×C281C2211yescharacteristic
19C2×Dic562D412yes—
20C22×Dic281—21no—
21#17985128—42no—
22#17985126—42no—
23#17985122—22no—
24C4⋊Dic281—21no—
25C4⋊Dic281—21no—
26#17985117—22no—
27#17985117—22no—
28#17985117—22no—
29C22⋊Dic281—22no—
30C22⋊Dic281—21no—
31C4×Dic281D412yes—
32#41×C281—22no—
33#41×C281—21no—
34#41×C281—41no—
35C2×Q8×C281—41no—
36C2×Q8×C281C2311yescharacteristic
37C2×D4×C281D411yescharacteristic
38SD16×C281—41no—
39D8×C281—41no—
40M16×C281—21no—
41C22⋊C4×C281—22no—
42C42×C281D411yescharacteristic
43Dic562—42no—
44C2×Dic281—22no—
45C2×Dic281—22no—
46C2×Dic281—81no—
47#14555886—42no—
48C23×C281—21no—
49Q8×C281—21no—
50Q8×C281—22no—
51Q8×C281—41no—
52D4×C281—21no—
53D4×C281—22no—
54D4×C281—41no—
55D4×C281—41no—
56C2×C4×C281—21no—
57C2×C4×C281—41no—
58C2×C4×C281—42no—
59C2×C4×C281C2×D412yes—
60C2×C4×C281C2×D411yescharacteristic
61C8×C281—41no—
62C22×C281—42no—
63C22×C281—41no—
64C22×C281—41no—
65C22×C281#12011yescharacteristic
66C4×C281—21no—
67C4×C281—22no—
68C4×C281—41no—
69C4×C281—41no—
70Dic281—42no—
71Dic281—42no—
72C2×C281—21no—
73C2×C281—81no—
74C2×C281—81no—
75C2×C281B(4,𝔽2)11yescharacteristic
76C281#220311yescharacteristic, complemented, Sylow
77#2203—2811nomaximal, Sylow
78#563—2811no—
79#456—2812no—
80#454D28111yescharacteristic
81#356—2812no—
82#355—2811no—
832−1+4C2×D28111yescharacteristic
84#137—5622no—
85AGL(1,ℤ/8)—21no—
86C4⋊Q8—2812no—
87#126—5622no—
88#125—5621no—
89#124C2×D28111yescharacteristic
90#123—5621no—
91C22⋊Q8—5622no—
92#104—21no—
93#104—5622no—
94#101—2812no—
95#101C2×D28111yescharacteristic
96#41—22no—
97#41—21no—
98#41—41no—
99C2×Q8—41no—
100C2×Q8—2812no—
101C2×Q8C22×D28111yescharacteristic
102C2×D4C22⋊D28111yescharacteristic
103C22×C4—5621no—
104Q16—11242no—
105SD16—41no—
106SD16—11242no—
107D8—41no—
108M16—21no—
109M16—5622no—
110C4⋊C4—5622no—
111C4⋊C4—5621no—
112C4⋊C4—5621no—
113C4⋊C4—5622no—
114C4⋊C4—5622no—
115C22⋊C4—22no—
116C22⋊C4—5622no—
117C22⋊C4—5621no—
118C42—2812no—
119C42C22⋊D28111yescharacteristic
120C23—21no—
121Q8—21no—
122Q8—22no—
123Q8—41no—
124Q8—11242no—
125D4—21no—
126D4—22no—
127D4—41no—
128D4—41no—
129C2×C4—21no—
130C2×C4—41no—
131C2×C4—42no—
132C2×C4—5622no—
133C2×C4—5622no—
134C2×C4—22481no—
135C2×C4D4×D28112yes—
136C2×C4C2×C22⋊D28111yescharacteristic
137C8—41no—
138C8—11242no—
139C22—42no—
140C22—41no—
141C22—41no—
142C22#2258284711yescharacteristic
143C4—21no—
144C4—22no—
145C4—41no—
146C4—41no—
147C4—11242no—
148C4—11242no—
149C2—21no—
150C2—81no—
151C2—81no—
152C2#3182364911yescharacteristic
subgroupG/H
centerC2#31823649
commutator, cosocleC2×Q8×C281C23
FrattiniC2×Q8C22×D281
Fitting, prime radical#454×C281C2
socleC2×C281B(4,𝔽2)
hypercenter#454D281
hypocenterC281#2203
LCSG ▷ C2×Q8×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #31824213C2semidirect
2. #31823646C2semidirect
3. #31823261C2semidirect
4. #31823260C2semidirect
76. C281#2203semidirect

Maximal subgroups

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

subgroupindex
#318242132
#318236462
#318232612
#318232602
#454×C2812
#2203281