Finite Group Databasebeta

← #49097324

Subgroups — #49097324

Order 35968.

216 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 216 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#31823645C212yesmaximal, complemented
2#31823635C211yesmaximal, characteristic
3#31823262C212yesmaximal, complemented
4#31823260C211yesmaximal, characteristic, complemented
5#563×C281C211yesmaximal, characteristic, complemented
6#22582927C2211yescharacteristic
7#22582910—22no—
8#22582905—21no—
9#22582807—21no—
10#22582807—22no—
11#22582798C2211yescharacteristic
12#22582798C2212yes—
13C4⋊Q8×C281C2212yes—
14#126×C281—22no—
15#125×C281—21no—
16#124×C281C2211yescharacteristic
17#123×C281—21no—
18C22⋊Q8×C281—22no—
19#17985139—41no—
20#17985138—21no—
21#17985138—22no—
22Q8×D281—41no—
23#17985128—42no—
24#17985126—41no—
25#17985125—42no—
26#17985123—41no—
27#17985122—21no—
28#17985122—22no—
29C2×Q8×C281D412yes—
30C2×Q8×C281C2311yescharacteristic
31C2×D4×C281D411yescharacteristic
32C22×C4×C281—21no—
33C4⋊C4×C281—21no—
34C4⋊C4×C281—22no—
35C4⋊C4×C281—21no—
36C4⋊C4×C281—22no—
37C4⋊C4×C281—22no—
38C22⋊C4×C281—22no—
39C22⋊C4×C281—21no—
40C22⋊C4×C281—22no—
41C42×C281D411yescharacteristic
42C42×C281D412yes—
43Dic562—21no—
44Dic562—22no—
45D1124—21no—
46D1124—22no—
47C22⋊D281—41no—
48C4×D281—41no—
49C4×D281—42no—
50#14555886—41no—
51#14555886—42no—
52C23×C281—21no—
53Q8×C281—41no—
54Q8×C281—42no—
55D4×C281—41no—
56C2×C4×C281—21no—
57C2×C4×C281—22no—
58C2×C4×C281—22no—
59C2×C4×C281—81no—
60C2×C4×C281C2×D412yes—
61C2×C4×C281C2×D411yescharacteristic
62C22×C281—42no—
63C22×C281—41no—
64C22×C281#12011yescharacteristic
65C2×D281—41no—
66C4×C281—21no—
67C4×C281—22no—
68C4×C281—41no—
69C4×C281—42no—
70C4×C281—42no—
71Dic281—41no—
72C2×C281—21no—
73C2×C281—81no—
74C2×C281B(4,𝔽2)11yescharacteristic
75D281—81no—
76C281#220311yescharacteristic, complemented, Sylow
77#2203—2811nomaximal, Sylow
78#563D28111yescharacteristic, complemented
79#456—2812no—
80#454—2811no—
81#356—2812no—
82#355—2811no—
832−1+4—2811no—
84#137—5622no—
85AGL(1,ℤ/8)—5621no—
86C4⋊Q8C2×D28112yes—
87#126—22no—
88#125—21no—
89#124C2×D28111yescharacteristic
90#123—21no—
91C22⋊Q8—22no—
92#104—5621no—
93#104—5622no—
94#101—2812no—
95#101—2811no—
96#41—5621no—
97#41—5622no—
98#41—11241no—
99C2×Q8—11241no—
100C2×Q8C22⋊D28112yes—
101C2×Q8C22×D28111yescharacteristic
102C2×D4C22⋊D28111yescharacteristic
103C22×C4—21no—
104Q16—11242no—
105SD16—11241no—
106SD16—11242no—
107D8—11241no—
108M16—5621no—
109M16—5622no—
110C4⋊C4—21no—
111C4⋊C4—22no—
112C4⋊C4—21no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C22⋊C4—22no—
116C22⋊C4—21no—
117C22⋊C4—22no—
118C42C22⋊D28111yescharacteristic
119C42C22⋊D28112yes—
120C23—21no—
121Q8—41no—
122Q8—42no—
123Q8—5621no—
124Q8—5622no—
125D4—41no—
126D4—5621no—
127D4—5622no—
128D4—11241no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—81no—
133C2×C4—11241no—
134C2×C4—11242no—
135C2×C4C2×C22⋊D28112yes—
136C2×C4C2×C22⋊D28111yescharacteristic
137C8—11241no—
138C8—11242no—
139C22—42no—
140C22—41no—
141C22—11241no—
142C22#2258284811yescharacteristic
143C4—21no—
144C4—22no—
145C4—41no—
146C4—42no—
147C4—42no—
148C4—11241no—
149C2—21no—
150C2—81no—
151C2—22481no—
152C2#3182365011yescharacteristic
subgroupG/H
centerC2#31823650
commutator, cosocleC2×Q8×C281C23
FrattiniC2×Q8C22×D281
Fitting#563×C281C2
socleC2×C281B(4,𝔽2)
prime radical#31823635C2
hypercenter#563D281
hypocenterC281#2203
LCSG ▷ C2×Q8×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #31823645C2semidirect
3. #31823262C2semidirect
4. #31823260C2semidirect
5. #563×C281C2semidirect
76. C281#2203semidirect
78. #563D281semidirect

Maximal subgroups

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

subgroupindex
#318236452
#318236352
#318232622
#318232602
#563×C2812
#2203281