Finite Group Databasebeta

← #49097326

Subgroups — #49097326

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#31823648C212yesmaximal, complemented
3#31823635C211yesmaximal, characteristic
4#31823261C212yesmaximal, complemented
5#355×C281C211yesmaximal, characteristic, complemented
6#22582927C2211yescharacteristic
7#22582912—22no—
8#22582905—21no—
9#22582877C2212yes—
10#22582872—22no—
11#22582871—21no—
12#22582860—21no—
13#22582856—22no—
14#22582807—21no—
15#22582805—22no—
16#22582798C2211yescharacteristic
17#124×C281C2211yescharacteristic
18#101×C281C2212yes—
19#17985139—41no—
20#17985138—22no—
21#17985138—21no—
22C2×Dic562D412yes—
23Q8×D281—41no—
24C22×Dic281—21no—
25Dic1124—42no—
26#17985127—42no—
27#17985126—41no—
28#17985123—41no—
29#17985122—21no—
30C4⋊Dic281—21no—
31C4⋊Dic281—21no—
32#17985117—22no—
33#17985117—22no—
34#17985117—22no—
35C22⋊Dic281—22no—
36C22⋊Dic281—21no—
37C4×Dic281D412yes—
38C2×Q8×C281C2311yescharacteristic
39C2×D4×C281D411yescharacteristic
40M16×C281—22no—
41C22⋊C4×C281—22no—
42C42×C281D411yescharacteristic
43Dic562—21no—
44Dic562—22no—
45Dic562—42no—
46D1124—21no—
47D1124—22no—
48C22⋊D281—41no—
49C2×Dic281—22no—
50C2×Dic281—22no—
51C2×Dic281—81no—
52C4×D281—42no—
53C4×D281—41no—
54#14555886—41no—
55C23×C281—21no—
56Q8×C281—41no—
57D4×C281—41no—
58C2×C4×C281—21no—
59C2×C4×C281C2×D412yes—
60C2×C4×C281C2×D411yescharacteristic
61C8×C281—42no—
62C22×C281—42no—
63C22×C281—41no—
64C22×C281#12011yescharacteristic
65C2×D281—41no—
66C4×C281—22no—
67C4×C281—21no—
68C4×C281—41no—
69Dic281—42no—
70Dic281—41no—
71Dic281—42no—
72C2×C281—21no—
73C2×C281—81no—
74C2×C281B(4,𝔽2)11yescharacteristic
75D281—81no—
76C281#220311yescharacteristic, complemented, Sylow
77#2203—2811nomaximal, Sylow
78#563—2811no—
79#456—2812no—
80#454—2811no—
81#356—2812no—
82#355D28111yescharacteristic, complemented
832−1+4—2811no—
84#137—5622no—
85AGL(1,ℤ/8)—5621no—
86C4⋊Q8—2812no—
87#126—5622no—
88#125—5621no—
89#124C2×D28111yescharacteristic
90#123—5621no—
91C22⋊Q8—5622no—
92#104—5622no—
93#104—5621no—
94#101—2811no—
95#101C2×D28112yes—
96#41—5622no—
97#41—5621no—
98#41—11241no—
99C2×Q8—2812no—
100C2×Q8—11241no—
101C2×Q8C22×D28111yescharacteristic
102C2×D4D112411yescharacteristic
103C22×C4—5621no—
104Q16—11242no—
105SD16—11242no—
106SD16—11241no—
107D8—11241no—
108M16—22no—
109M16—5621no—
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—
119C42D112411yescharacteristic
120C23—21no—
121Q8—41no—
122Q8—5621no—
123Q8—5622no—
124Q8—11242no—
125D4—41no—
126D4—5621no—
127D4—5622no—
128D4—11241no—
129C2×C4—21no—
130C2×C4—5622no—
131C2×C4—5622no—
132C2×C4—11242no—
133C2×C4—11241no—
134C2×C4—22481no—
135C2×C4D4×D28112yes—
136C2×C4C2×D112411yescharacteristic
137C8—42no—
138C8—11241no—
139C22—42no—
140C22—41no—
141C22—11241no—
142C22#2258284911yescharacteristic
143C4—22no—
144C4—21no—
145C4—41no—
146C4—11242no—
147C4—11242no—
148C4—11241no—
149C2—21no—
150C2—81no—
151C2—22481no—
152C2#3182365111yescharacteristic
subgroupG/H
centerC2#31823651
commutator, cosocleC2×Q8×C281C23
FrattiniC2×Q8C22×D281
Fitting#355×C281C2
socleC2×C281B(4,𝔽2)
prime radical#31823635C2
hypercenter#355D281
hypocenterC281#2203
LCSG ▷ C2×Q8×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
1. #31824213C2semidirect
2. #31823648C2semidirect
4. #31823261C2semidirect
5. #355×C281C2semidirect
76. C281#2203semidirect
82. #355D281semidirect

Maximal subgroups

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

subgroupindex
#318242132
#318236482
#318236352
#318232612
#355×C2812
#2203281