Finite Group Databasebeta

← #49097298

Subgroups — #49097298

Order 35968.

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

normal subgroups only

This group has 246 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#31824199C211yesmaximal, characteristic, complemented
2#31823653C212yesmaximal, complemented
3#31823256C211yesmaximal, characteristic, complemented
4#31823254C212yesmaximal, complemented
5#453×C281C211yesmaximal, characteristic
6#22582866—22no—
7#22582860—22no—
8#22582860—21no—
9#22582860C2212yes—
10C4×Dic562—21no—
11D4×Dic281—22no—
12#22582794—22no—
13#22582794C2212yes—
14H(5,𝔽2)×C281C2211yescharacteristic
15AGL(1,ℤ/8)×C281—21no—
16#127×C281C2211yescharacteristic
17#104×C281—21no—
18#100×C281C2211yescharacteristic
19C2×Dic562—21no—
20C22×Dic281—21no—
21C22×Dic281D412yes—
22C4⋊Dic281—21no—
23#17985117—22no—
24#17985117—42no—
25C22⋊Dic281—22no—
26C22⋊Dic281—21no—
27C22⋊Dic281—22no—
28C22⋊Dic281—22no—
29C22⋊Dic281—42no—
30C22⋊Dic281D412yes—
31C4×Dic281—22no—
32#41×C281—21no—
33#41×C281—41no—
34C2×D4×C281—22no—
35C2×D4×C281—22no—
36C2×D4×C281—41no—
37C2×D4×C281D411yescharacteristic
38C2×D4×C281C2311yescharacteristic
39SD16×C281—41no—
40D8×C281—41no—
41M16×C281—21no—
42C42×C281D411yescharacteristic
43Dic562—42no—
44C2×Dic281—22no—
45C2×Dic281—22no—
46C2×Dic281—42no—
47C2×Dic281—42no—
48C2×Dic281—81no—
49C23×C281—22no—
50C23×C281—21no—
51C23×C281C2×D412yes—
52Q8×C281—21no—
53D4×C281—21no—
54D4×C281—41no—
55D4×C281—41no—
56D4×C281—44no—
57D4×C281—42no—
58D4×C281—41no—
59C2×C4×C281—21no—
60C2×C4×C281—22no—
61C2×C4×C281—41no—
62C2×C4×C281C2×D411yescharacteristic
63C8×C281—41no—
64C22×C281—22no—
65C22×C281—42no—
66C22×C281—42no—
67C22×C281—41no—
68C22×C281—41no—
69C22×C281—82no—
70C22×C281#12011yescharacteristic
71C4×C281—22no—
72C4×C281—21no—
73C4×C281—41no—
74Dic281—42no—
75Dic281—42no—
76Dic281—82no—
77C2×C281—21no—
78C2×C281—42no—
79C2×C281—81no—
80C2×C281—81no—
81C2×C281B(4,𝔽2)11yescharacteristic
82C281#219811yescharacteristic, complemented, Sylow
83#2198—2811nomaximal, Sylow
84#559—2811no—
85#458—2812no—
86#453D28111yescharacteristic
87#353—2811no—
88#352—2812no—
89H(5,𝔽2)C2×D28111yescharacteristic
90AGL(1,ℤ/8)—21no—
91#127C2×D28111yescharacteristic
92#124—5622no—
93#123—2812no—
94#123—5621no—
95#123—5622no—
96C4×Q8—5621no—
97C4×D4—5622no—
98#104—21no—
99#100C2×D28111yescharacteristic
100#99—2812no—
101#99—5622no—
102#41—21no—
103#41—41no—
104C2×Q8—5621no—
105C2×D4—22no—
106C2×D4—22no—
107C2×D4—41no—
108C2×D4C22⋊D28111yescharacteristic
109C2×D4C22×D28111yescharacteristic
110C22×C4—2812no—
111C22×C4—5621no—
112SD16—41no—
113D8—41no—
114M16—21no—
115C4⋊C4—5621no—
116C4⋊C4—5622no—
117C4⋊C4—11242no—
118C22⋊C4—2812no—
119C22⋊C4—5622no—
120C22⋊C4—5621no—
121C22⋊C4—5622no—
122C22⋊C4—5622no—
123C22⋊C4—11242no—
124C42—5622no—
125C42C22⋊D28111yescharacteristic
126C23—22no—
127C23—21no—
128C23D4×D28112yes—
129Q8—21no—
130Q8—11242no—
131D4—21no—
132D4—41no—
133D4—41no—
134D4—44no—
135D4—42no—
136D4—41no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—41no—
140C2×C4—5622no—
141C2×C4—5622no—
142C2×C4—11242no—
143C2×C4—11242no—
144C2×C4—22481no—
145C2×C4C2×C22⋊D28111yescharacteristic
146C8—41no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—41no—
152C22—82no—
153C22#2258284711yescharacteristic
154C4—22no—
155C4—21no—
156C4—41no—
157C4—11242no—
158C4—11242no—
159C4—22482no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—81no—
164C2#3182364911yescharacteristic
subgroupG/H
centerC2#31823649
commutator, cosocleC2×D4×C281C23
FrattiniC2×D4C22×D281
Fitting, prime radical#453×C281C2
socleC2×C281B(4,𝔽2)
hypercenter#453D281
hypocenterC281#2198
LCSG ▷ C2×D4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #31824199C2semidirect
2. #31823653C2semidirect
3. #31823256C2semidirect
4. #31823254C2semidirect
82. C281#2198semidirect

Maximal subgroups

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

subgroupindex
#318241992
#318236532
#318232562
#318232542
#453×C2812
#2198281