Finite Group Databasebeta

← #49120213

Subgroups — #49120213

Order 36224.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#31826603C212yesmaximal, complemented
2#31826377C211yesmaximal, characteristic, complemented
3#31826199C212yesmaximal, complemented
4#31826189C211yesmaximal, characteristic, complemented
5#534×C283C211yesmaximal, characteristic
6C22×Dic566C2211yescharacteristic, complemented
7C2×#17985380—22no—
8C2×C22⋊Dic283—21no—
9#22583533—22no—
10C22⋊(C283⋊C8)C2212yescomplemented
11C283⋊#95—21no—
12C283⋊#95C2211yescharacteristic, complemented
13C22×D4×C283—21no—
14#123×C283—22no—
15#121×C283—21no—
16#121×C283C2212yes—
17#120×C283—22no—
18C2×C22⋊C4×C283C2211yescharacteristic
19C2×Dic566—22no—
20C2×Dic566—42no—
21C22×Dic283—21no—
22C22×Dic283—21no—
23#17985380—44no—
24C2×C283⋊C8—22no—
25C22⋊Dic283—42no—
26C24×C283—21no—
27C24×C283D411yescharacteristic
28C2×D4×C283—22no—
29C2×D4×C283—22no—
30C2×D4×C283—21no—
31C2×D4×C283—42no—
32C2×D4×C283—42no—
33C2×D4×C283D412yes—
34C22×C4×C283—21no—
35C22×C4×C283D411yescharacteristic
36C22×C4×C283C2311yescharacteristic
37C4⋊C4×C283—21no—
38C4⋊C4×C283D412yes—
39C22⋊C4×C283—22no—
40C22⋊C4×C283—22no—
41C22⋊C4×C283—22no—
42Dic566—24no—
43Dic566—42no—
44C2×Dic283—22no—
45C2×Dic283—41no—
46C2×Dic283—41no—
47C2×Dic283—41no—
48C2×Dic283—41no—
49C2×Dic283—41no—
50C283⋊C8—42no—
51C23×C283—21no—
52C23×C283—21no—
53C23×C283—22no—
54C23×C283—41no—
55C23×C283—41no—
56C23×C283—42no—
57C23×C283—81no—
58C23×C283—81no—
59C23×C283SD1612yescomplemented
60C23×C283C2×D411yescharacteristic
61D4×C283—42no—
62D4×C283—44no—
63D4×C283—42no—
64D4×C283—42no—
65D4×C283—81no—
66C2×C4×C283—21no—
67C2×C4×C283—22no—
68C2×C4×C283—41no—
69C2×C4×C283—42no—
70C2×C4×C283—41no—
71C2×C4×C283C2×D412yes—
72C22×C283—21no—
73C22×C283—21no—
74C22×C283—22no—
75C22×C283—42no—
76C22×C283—41no—
77C22×C283—41no—
78C22×C283—42no—
79C22×C283—42no—
80C22×C283—42no—
81C22×C283—81no—
82C22×C283—84no—
83C22×C283#12011yescharacteristic
84C22×C283C2×SD1611yescharacteristic
85C22×C283AGL(1,ℤ/8)11yescharacteristic
86C4×C283—22no—
87C4×C283—42no—
88C4×C283—41no—
89Dic283—42no—
90Dic283—81no—
91C2×C283—21no—
92C2×C283—21no—
93C2×C283—42no—
94C2×C283—82no—
95C2×C283#45011yescharacteristic
96C2×C283#45511yescharacteristic
97C2×C283B(4,𝔽2)11yescharacteristic
98C283#160111yescharacteristic, complemented, Sylow
99#1601—2831nomaximal, Sylow
100#534D28311yescharacteristic
101#448—2832no—
102#393—2831no—
103#327—2832no—
104#323—2831no—
105C22×Q8—2831no—
106C22×D4—21no—
107C2×SD16—5662no—
108#123—22no—
109#121—21no—
110#121C2×D28312yes—
111#120—22no—
112C2×C22⋊C4—5661no—
113C2×C22⋊C4C2×D28311yescharacteristic
114#103—5662no—
115C22⋊C8—2832no—
116#95—2831no—
117#95—5661no—
118C24—21no—
119C24C22⋊D28311yescharacteristic
120C2×Q8—5662no—
121C2×Q8—11322no—
122C2×D4—22no—
123C2×D4—22no—
124C2×D4—21no—
125C2×D4—42no—
126C2×D4—42no—
127C2×D4C22⋊D28312yes—
128C22×C4—21no—
129C22×C4—5661no—
130C22×C4—5661no—
131C22×C4C22⋊D28311yescharacteristic
132C22×C4C22×D28311yescharacteristic
133SD16—11324no—
134C2×C8—5662no—
135C4⋊C4—21no—
136C4⋊C4C22⋊D28312yes—
137C22⋊C4—22no—
138C22⋊C4—22no—
139C22⋊C4—22no—
140C22⋊C4—11322no—
141C23—21no—
142C23—21no—
143C23—22no—
144C23—41no—
145C23—41no—
146C23—42no—
147C23—81no—
148C23—81no—
149C23#1798538012yescomplemented
150C23C2×C22⋊D28311yescharacteristic
151Q8—5664no—
152Q8—11322no—
153D4—42no—
154D4—44no—
155D4—42no—
156D4—42no—
157D4—81no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—5662no—
164C2×C4—11321no—
165C2×C4—11321no—
166C2×C4—11321no—
167C2×C4—11321no—
168C2×C4—11321no—
169C2×C4C2×C22⋊D28312yes—
170C8—11322no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—42no—
178C22—42no—
179C22—42no—
180C22—81no—
181C22—84no—
182C22#2258357911yescharacteristic
183C22C2×#1798538011yescharacteristic
184C22#2258363611yescharacteristic
185C4—22no—
186C4—42no—
187C4—41no—
188C4—11322no—
189C4—22641no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—82no—
194C2#3182661611yescharacteristic
195C2#3182664311yescharacteristic
196C2#3182665211yescharacteristic
subgroupG/H
centerC22#22583579
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting, prime radical#534×C283C2
socleC22×C283#120
hypercenter#534D283
hypocenterC283#1601
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #31826603C2semidirect
2. #31826377C2semidirect
3. #31826199C2semidirect
4. #31826189C2semidirect
6. C22×Dic566C22semidirect
10. C22⋊(C283⋊C8)C22semidirect
12. C283⋊#95C22semidirect
59. C23×C283SD16semidirect
98. C283#1601semidirect
149. C23#17985380semidirect

Maximal subgroups

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

subgroupindex
#318266032
#318263772
#318261992
#318261892
#534×C2832
#1601283