Finite Group Databasebeta

← #49097299

Subgroups — #49097299

Order 35968.

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

normal subgroups only

This group has 246 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#31823652C212yesmaximal, complemented
2#31823630C211yesmaximal, characteristic
3#31823256C211yesmaximal, characteristic, complemented
4#31823253C212yesmaximal, complemented
5#559×C281C211yesmaximal, characteristic, complemented
6#22582924C2211yescharacteristic
7#22582905—21no—
8#22582862—22no—
9#22582807—21no—
10#22582796C2211yescharacteristic
11#22582794C2212yes—
12#22582793—22no—
13#127×C281C2211yescharacteristic
14#124×C281—22no—
15#123×C281—21no—
16#123×C281C2212yes—
17C4×Q8×C281—21no—
18C4×D4×C281—22no—
19#17985138—21no—
20#17985137—41no—
21C2×C22⋊D281—22no—
22D4×D281—41no—
23#17985126—41no—
24#17985123—41no—
25#17985122—21no—
26#17985117—42no—
27C22⋊Dic281—22no—
28#17985115—42no—
29C2×Q8×C281—21no—
30C2×D4×C281—22no—
31C2×D4×C281D411yescharacteristic
32C2×D4×C281C2311yescharacteristic
33C22×C4×C281—21no—
34C22×C4×C281D412yes—
35C4⋊C4×C281—21no—
36C4⋊C4×C281—22no—
37C22⋊C4×C281—22no—
38C22⋊C4×C281—21no—
39C22⋊C4×C281—22no—
40C22⋊C4×C281D412yes—
41C42×C281—22no—
42C42×C281D411yescharacteristic
43C22×D281—22no—
44Dic562—21no—
45D1124—21no—
46C22⋊D281—42no—
47C22⋊D281—41no—
48C2×Dic281—22no—
49C2×Dic281—42no—
50C4×D281—41no—
51#14555886—41no—
52C23×C281—21no—
53C23×C281C2×D412yes—
54Q8×C281—42no—
55D4×C281—41no—
56D4×C281—41no—
57D4×C281—44no—
58C2×C4×C281—21no—
59C2×C4×C281—22no—
60C2×C4×C281—22no—
61C2×C4×C281—42no—
62C2×C4×C281—81no—
63C2×C4×C281C2×D411yescharacteristic
64C22×C281—22no—
65C22×C281—42no—
66C22×C281—42no—
67C22×C281—41no—
68C22×C281#12011yescharacteristic
69C2×D281—41no—
70C2×D281—82no—
71C4×C281—22no—
72C4×C281—21no—
73C4×C281—42no—
74C4×C281—42no—
75Dic281—41no—
76Dic281—82no—
77C2×C281—21no—
78C2×C281—42no—
79C2×C281—81no—
80C2×C281B(4,𝔽2)11yescharacteristic
81D281—81no—
82C281#219811yescharacteristic, complemented, Sylow
83#2198—2811nomaximal, Sylow
84#559D28111yescharacteristic, complemented
85#458—2812no—
86#453—2811no—
87#353—2811no—
88#352—2812no—
89H(5,𝔽2)—2811no—
90AGL(1,ℤ/8)—5621no—
91#127C2×D28111yescharacteristic
92#124—22no—
93#123—21no—
94#123—5622no—
95#123C2×D28112yes—
96C4×Q8—21no—
97C4×D4—22no—
98#104—5621no—
99#100—2811no—
100#99—2812no—
101#99—5622no—
102#41—5621no—
103#41—11241no—
104C2×Q8—21no—
105C2×D4—22no—
106C2×D4—5622no—
107C2×D4—11241no—
108C2×D4C22⋊D28111yescharacteristic
109C2×D4C22×D28111yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D28112yes—
112SD16—11241no—
113D8—11241no—
114M16—5621no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C4⋊C4—11242no—
118C22⋊C4—22no—
119C22⋊C4—21no—
120C22⋊C4—22no—
121C22⋊C4—5622no—
122C22⋊C4—11242no—
123C22⋊C4C22⋊D28112yes—
124C42—22no—
125C42C22⋊D28111yescharacteristic
126C23—21no—
127C23—5622no—
128C23C2×C22⋊D28112yes—
129Q8—42no—
130Q8—5621no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—5621no—
135D4—11242no—
136D4—11241no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—81no—
142C2×C4—5622no—
143C2×C4—11241no—
144C2×C4—11242no—
145C2×C4C2×C22⋊D28111yescharacteristic
146C8—11241no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—11241no—
152C22—22482no—
153C22#2258284811yescharacteristic
154C4—22no—
155C4—21no—
156C4—42no—
157C4—42no—
158C4—11241no—
159C4—22482no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—22481no—
164C2#3182365011yescharacteristic
subgroupG/H
centerC2#31823650
commutator, cosocleC2×D4×C281C23
FrattiniC2×D4C22×D281
Fitting#559×C281C2
socleC2×C281B(4,𝔽2)
prime radical#31823630C2
hypercenter#559D281
hypocenterC281#2198
LCSG ▷ C2×D4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #31823652C2semidirect
3. #31823256C2semidirect
4. #31823253C2semidirect
5. #559×C281C2semidirect
82. C281#2198semidirect
84. #559D281semidirect

Maximal subgroups

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

subgroupindex
#318236522
#318236302
#318232562
#318232532
#559×C2812
#2198281