Finite Group Databasebeta

← #49120186

Subgroups — #49120186

Order 36224.

316 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 53 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#31827091C211yesmaximal, characteristic, complemented
2#31826618C212yesmaximal, complemented
3#31826374C211yesmaximal, characteristic
4#31826203C212yesmaximal, complemented
5#323×C283C211yesmaximal, characteristic, complemented
6C22×D1132C2211yescharacteristic
7C22×C22⋊D283—21no—
8C2×#17985381—22no—
9#22583589—21no—
10#22583589C2212yes—
11#22583587—22no—
12#22583587—22no—
13C2×C22⋊Dic283—21no—
14C2×(C2×D283)⋊C4—21no—
15#22583532—22no—
16C283⋊#95C2211yescharacteristic
17C2×C22⋊C4×C283C2211yescharacteristic
18C22⋊C8×C283C2212yes—
19C23×D283—21no—
20C2×Dic566—21no—
21C2×Dic566D412yescomplemented
22C2×D1132—22no—
23C2×D1132—42no—
24C2×C22⋊D283—42no—
25C2×C22⋊D283—42no—
26C2×C22⋊D283—42no—
27C22×Dic283—21no—
28C22×Dic283—21no—
29C22×Dic283—21no—
30#17985381—44no—
31C4⋊Dic283—21no—
32C4⋊Dic283D412yescomplemented
33Dic283⋊C4—22no—
34Dic283⋊C4—22no—
35C22⋊Dic283—22no—
36C22⋊Dic283—22no—
37(C2×D283)⋊C4—42no—
38C24×C283D411yescharacteristic
39C22×C4×C283D411yescharacteristic
40C22×C4×C283C2311yescharacteristic
41C2×C8×C283—22no—
42C22⋊C4×C283—22no—
43C22×D283—22no—
44C22×D283—41no—
45C22×D283—41no—
46C22×D283—41no—
47C22×D283—41no—
48C22×D283—41no—
49C22×D283—41no—
50Dic566—42no—
51Dic566—81no—
52D1132—24no—
53D1132—42no—
54C22⋊D283—48no—
55C2×Dic283—22no—
56C2×Dic283—22no—
57C2×Dic283—22no—
58C2×Dic283—41no—
59C2×Dic283—41no—
60C2×Dic283—81no—
61C2×Dic283—81no—
62C23×C283—21no—
63C23×C283—21no—
64C23×C283—41no—
65C23×C283—41no—
66C23×C283SD1612yescomplemented
67C23×C283C2×D411yescharacteristic
68C2×C4×C283—21no—
69C2×C4×C283—41no—
70C2×C4×C283—41no—
71C2×C4×C283C2×D412yes—
72C8×C283—42no—
73C22×C283—21no—
74C22×C283—21no—
75C22×C283—22no—
76C22×C283—42no—
77C22×C283—41no—
78C22×C283—41no—
79C22×C283—81no—
80C22×C283#12011yescharacteristic
81C22×C283C2×SD1611yescharacteristic
82C22×C283#13711yescharacteristic
83C2×D283—42no—
84C2×D283—42no—
85C2×D283—42no—
86C2×D283—81no—
87C2×D283—81no—
88C2×D283—81no—
89C2×D283—81no—
90C4×C283—22no—
91C4×C283—41no—
92Dic283—42no—
93Dic283—42no—
94Dic283—42no—
95C2×C283—21no—
96C2×C283—21no—
97C2×C283—42no—
98C2×C283#44811yescharacteristic
99C2×C283#45311yescharacteristic
100C2×C283B(4,𝔽2)11yescharacteristic
101D283—82no—
102C283#159611yescharacteristic, complemented, Sylow
103#1596—2831nomaximal, Sylow
104#543—2831no—
105#450—2832no—
106#392—2831no—
107#328—2832no—
108#323D28311yescharacteristic, complemented
109C22×D4—2831no—
110C22×D4—5661no—
111C2×SD16—5662no—
112C22⋊Q8—2832no—
113C22⋊Q8—5662no—
114C22⋊Q8—5662no—
115C22⋊Q8—5661no—
116C2×C22⋊C4—5661no—
117C2×C22⋊C4—5661no—
118C2×C22⋊C4C2×D28311yescharacteristic
119#102—5662no—
120C22⋊C8C2×D28312yes—
121#95—2831no—
122C24—5661no—
123C24D113211yescharacteristic
124C2×Q8—2832no—
125C2×Q8—5661no—
126C2×D4—5662no—
127C2×D4—11322no—
128C2×D4—11322no—
129C2×D4—11322no—
130C2×D4—11322no—
131C22×C4—5661no—
132C22×C4—5661no—
133C22×C4—5661no—
134C22×C4D113211yescharacteristic
135C22×C4C22×D28311yescharacteristic
136SD16—11324no—
137C2×C8—22no—
138C4⋊C4—2832no—
139C4⋊C4—5662no—
140C4⋊C4—5661no—
141C4⋊C4—5662no—
142C22⋊C4—22no—
143C22⋊C4—5662no—
144C22⋊C4—5662no—
145C22⋊C4—11322no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—5662no—
151C23—11321no—
152C23—11321no—
153C23—11321no—
154C23—11321no—
155C23—11321no—
156C23—11321no—
157C23#1798538112yescomplemented
158C23C2×D113211yescharacteristic
159Q8—11322no—
160Q8—22641no—
161D4—5664no—
162D4—11322no—
163D4—11328no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—5662no—
168C2×C4—5662no—
169C2×C4—5662no—
170C2×C4—11321no—
171C2×C4—11321no—
172C2×C4—22641no—
173C2×C4—22641no—
174C2×C4D4×D28312yes—
175C8—42no—
176C22—21no—
177C22—21no—
178C22—22no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—11322no—
184C22—11322no—
185C22—11322no—
186C22—22641no—
187C22—22641no—
188C22—22641no—
189C22—22641no—
190C22#2258358011yescharacteristic
191C22C2×#1798538111yescharacteristic
192C22#2258364311yescharacteristic
193C4—22no—
194C4—41no—
195C4—11322no—
196C4—11322no—
197C4—11322no—
198C2—21no—
199C2—21no—
200C2—42no—
201C2—22642no—
202C2#3182660611yescharacteristic
203C2#3182663511yescharacteristic
204C2#3182665311yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#323×C283C2
socleC22×C283#120
prime radical#31826374C2
hypercenter#323D283
hypocenterC283#1596
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
1. #31827091C2semidirect
2. #31826618C2semidirect
4. #31826203C2semidirect
5. #323×C283C2semidirect
21. C2×Dic566D4semidirect
32. C4⋊Dic283D4semidirect
66. C23×C283SD16semidirect
102. C283#1596semidirect
108. #323D283semidirect
157. C23#17985381semidirect

Maximal subgroups

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

subgroupindex
#318270912
#318266182
#318263742
#318262032
#323×C2832
#1596283