Finite Group Databasebeta

← #49097332

Subgroups — #49097332

Order 35968.

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

normal subgroups only

This group has 224 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#31824193C211yesmaximal, characteristic, complemented
2#31823646C212yesmaximal
3#31823262C211yesmaximal, characteristic, complemented
4#31823261C212yesmaximal, complemented
5#456×C281C211yesmaximal, characteristic
6#22582909—22no—
7#22582878—22no—
8#22582877—21no—
9#22582877C2212yes—
10C4×Dic562—21no—
11#22582844—22no—
12#22582806—22no—
13#22582798C2212yes—
142−1+4×C281C2211yescharacteristic
15#137×C281—21no—
16C4⋊Q8×C281C2211yescharacteristic
17#104×C281—21no—
18#101×C281C2211yescharacteristic
19C2×Dic562—21no—
20C2×Dic562—21no—
21C2×Dic562D412yes—
22#17985128—42no—
23#17985126—42no—
24#17985122—22no—
25C4⋊Dic281—21no—
26#17985117—22no—
27#17985117—22no—
28#17985117—22no—
29C4×Dic281—21no—
30C4×Dic281—22no—
31C4×Dic281D412yes—
32#41×C281—22no—
33#41×C281—21no—
34#41×C281—41no—
35C2×Q8×C281—41no—
36C2×Q8×C281D411yescharacteristic
37C2×Q8×C281C2311yescharacteristic
38Q16×C281—41no—
39SD16×C281—41no—
40M16×C281—21no—
41C4⋊C4×C281—22no—
42C42×C281D411yescharacteristic
43Dic562—24no—
44Dic562—42no—
45Dic562—81no—
46C2×Dic281—22no—
47C2×Dic281—22no—
48#14555886—42no—
49Q8×C281—21no—
50Q8×C281—22no—
51Q8×C281—41no—
52Q8×C281—41no—
53D4×C281—21no—
54D4×C281—22no—
55D4×C281—41no—
56C2×C4×C281—21no—
57C2×C4×C281—21no—
58C2×C4×C281—41no—
59C2×C4×C281—42no—
60C2×C4×C281C2×D412yes—
61C2×C4×C281C2×D411yescharacteristic
62C8×C281—41no—
63C22×C281—41no—
64C22×C281#12011yescharacteristic
65C4×C281—22no—
66C4×C281—21no—
67C4×C281—22no—
68C4×C281—41no—
69C4×C281—41no—
70Dic281—24no—
71Dic281—42no—
72C2×C281—21no—
73C2×C281—81no—
74C2×C281B(4,𝔽2)11yescharacteristic
75C281#220511yescharacteristic, complemented, Sylow
76#2205—2811nomaximal, Sylow
77Q82—2811no—
78#456—2812no—
79#456D28111yescharacteristic
80#356—2811no—
81#356—2812no—
822−1+4C2×D28111yescharacteristic
83#137—21no—
84#137—5622no—
85C4⋊Q8—2812no—
86C4⋊Q8—5622no—
87C4⋊Q8—5621no—
88C4⋊Q8C2×D28111yescharacteristic
89C4×Q8—5622no—
90C4×Q8—5621no—
91#104—21no—
92#104—5622no—
93#101—2812no—
94#101C2×D28111yescharacteristic
95#41—22no—
96#41—21no—
97#41—41no—
98C2×Q8—41no—
99C2×Q8—2812no—
100C2×Q8—5621no—
101C2×Q8—5621no—
102C2×Q8C22⋊D28111yescharacteristic
103C2×Q8C22×D28111yescharacteristic
104Q16—41no—
105Q16—11242no—
106SD16—41no—
107SD16—11242no—
108M16—21no—
109M16—5622no—
110C4⋊C4—22no—
111C4⋊C4—5622no—
112C4⋊C4—5621no—
113C4⋊C4—5622no—
114C4⋊C4—5622no—
115C42—2812no—
116C42—5622no—
117C42—5621no—
118C42C22⋊D28111yescharacteristic
119Q8—21no—
120Q8—22no—
121Q8—41no—
122Q8—41no—
123Q8—5624no—
124Q8—11242no—
125Q8—22481no—
126D4—21no—
127D4—22no—
128D4—41no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—42no—
133C2×C4—5622no—
134C2×C4—5622no—
135C2×C4D4×D28112yes—
136C2×C4C2×C22⋊D28111yescharacteristic
137C8—41no—
138C8—11242no—
139C22—41no—
140C22#2258284711yescharacteristic
141C4—22no—
142C4—21no—
143C4—22no—
144C4—41no—
145C4—41no—
146C4—5624no—
147C4—11242no—
148C2—21no—
149C2—81no—
150C2#3182364911yescharacteristic
subgroupG/H
centerC2#31823649
commutator, cosocleC2×Q8×C281C23
FrattiniC2×Q8C22×D281
Fitting#456×C281C2
socleC2×C281B(4,𝔽2)
prime radical2−1+4×C281C22
hypercenter#456D281
hypocenterC281#2205
LCSG ▷ C2×Q8×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #31824193C2semidirect
3. #31823262C2semidirect
4. #31823261C2semidirect
75. C281#2205semidirect

Maximal subgroups

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

subgroupindex
#318241932
#318236462
#318232622
#318232612
#456×C2812
#2205281