Finite Group Databasebeta

← #49120294

Subgroups — #49120294

Order 36224.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#31827062C211yesmaximal, characteristic
2#31826801C211yesmaximal, characteristic, complemented
3#31826784C211yesmaximal, characteristic
4#31826404C211yesmaximal, characteristic, complemented
5#31826203C211yesmaximal, characteristic, complemented
6#31826200C211yesmaximal, characteristic
7#324×C283C211yesmaximal, characteristic, complemented
8#22583605—21no—
9#22583600—21no—
10#22583595—21no—
11#22583593—21no—
12#22583589C2211yescharacteristic
13#22583588—21no—
14#22583584C2211yescharacteristic
15C4×C22⋊D283—21no—
16C2×C4⋊Dic283C2211yescharacteristic
17#22583544—21no—
18#22583542—21no—
19#22583535—21no—
20#22583532—21no—
21C283⋊#95—21no—
22C283⋊#95—21no—
23C283⋊#95C2211yescharacteristic
24C2×C4⋊C4×C283C2211yescharacteristic
25C22⋊C8×C283C2211yescharacteristic
26C22⋊C8×C283C2211yescharacteristic
27C2×Dic566D411yescharacteristic
28C2×D1132D411yescharacteristic
29C2×C22⋊D283—21no—
30C22×Dic283—21no—
31C22×Dic283—21no—
32C2×C4×D283—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283D411yescharacteristic
36C4⋊Dic283D411yescharacteristic
37Dic283⋊C4—21no—
38Dic283⋊C4—21no—
39Dic283⋊C4—21no—
40Dic283⋊C4—21no—
41C22⋊Dic283—21no—
42(C2×D283)⋊C4—21no—
43(C2×D283)⋊C4—21no—
44(C2×D283)⋊C4—21no—
45(C2×D283)⋊C4—21no—
46C4×Dic283—21no—
47C22×C4×C283D411yescharacteristic
48C22×C4×C283D411yescharacteristic
49C22×C4×C283C2311yescharacteristic
50C2×C8×C283—21no—
51C2×C8×C283—21no—
52C4⋊C4×C283—21no—
53C4⋊C4×C283—21no—
54C22×D283—21no—
55Dic566—41no—
56D1132—41no—
57C22⋊D283—41no—
58C22⋊D283—41no—
59C2×Dic283—21no—
60C2×Dic283—21no—
61C2×Dic283—21no—
62C2×Dic283—41no—
63C2×Dic283—41no—
64C2×Dic283—42no—
65C2×Dic283—41no—
66C2×Dic283—41no—
67C4×D283—81no—
68C23×C283C2×D411yescharacteristic
69C2×C4×C283—21no—
70C2×C4×C283—21no—
71C2×C4×C283—21no—
72C2×C4×C283—21no—
73C2×C4×C283—41no—
74C2×C4×C283—41no—
75C2×C4×C283C2×D411yescharacteristic
76C2×C4×C283C2×D411yescharacteristic
77C8×C283—41no—
78C8×C283—41no—
79C22×C283—21no—
80C22×C283—21no—
81C22×C283#12011yescharacteristic
82C22×C283#13511yescharacteristic
83C22×C283#13711yescharacteristic
84C2×D283—41no—
85C2×D283—41no—
86C2×D283—41no—
87C4×C283—21no—
88C4×C283—21no—
89C4×C283—41no—
90C4×C283—41no—
91Dic283—41no—
92Dic283—41no—
93Dic283—41no—
94Dic283—81no—
95Dic283—81no—
96C2×C283—21no—
97C2×C283—21no—
98C2×C283#45211yescharacteristic
99C2×C283#45411yescharacteristic
100C2×C283#45811yescharacteristic
101D283—81no—
102C283#161511yescharacteristic, complemented, Sylow
103#1615—2831nomaximal, Sylow
104#539—2831no—
105#484—2831no—
106#481—2831no—
107#400—2831no—
108#328—2831no—
109#327—2831no—
110#324D28311yescharacteristic, complemented
111#126—5661no—
112#125—5661no—
113#123—5661no—
114#123—5661no—
115C22⋊Q8—2831no—
116C22⋊Q8—5661no—
117#121—2831no—
118C4×D4—5661no—
119C2×C4⋊C4—2831no—
120C2×C4⋊C4C2×D28311yescharacteristic
121#107—5661no—
122#106—5661no—
123#103—5661no—
124#102—5661no—
125C22⋊C8C2×D28311yescharacteristic
126C22⋊C8C2×D28311yescharacteristic
127#95—2831no—
128#95—5661no—
129#95—5661no—
130C2×Q8—2831no—
131C2×D4—2831no—
132C2×D4—5661no—
133C22×C4—5661no—
134C22×C4—5661no—
135C22×C4—5661no—
136C22×C4D113211yescharacteristic
137C22×C4D113211yescharacteristic
138C22×C4C22×D28311yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2831no—
144C4⋊C4—2831no—
145C4⋊C4—5661no—
146C4⋊C4—5661no—
147C4⋊C4—5661no—
148C4⋊C4—5661no—
149C4⋊C4—5661no—
150C4⋊C4—5661no—
151C22⋊C4—5661no—
152C22⋊C4—5661no—
153C22⋊C4—5661no—
154C22⋊C4—5661no—
155C22⋊C4—5661no—
156C42—5661no—
157C23—5661no—
158C23C2×D113211yescharacteristic
159Q8—11321no—
160D4—11321no—
161D4—11321no—
162D4—11321no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—5661no—
170C2×C4—5661no—
171C2×C4—5661no—
172C2×C4—11321no—
173C2×C4—11321no—
174C2×C4—11322no—
175C2×C4—11321no—
176C2×C4—11321no—
177C2×C4—22641no—
178C2×C4D4×D28311yescharacteristic
179C2×C4D4×D28311yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—11321no—
185C22—11321no—
186C22—11321no—
187C22#2258358011yescharacteristic
188C22#2258363211yescharacteristic
189C22#2258364311yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—11321no—
195C4—11321no—
196C4—11321no—
197C4—22641no—
198C4—22641no—
199C2—21no—
200C2—21no—
201C2—22641no—
202C2#3182662911yescharacteristic
203C2#3182664011yescharacteristic
204C2#3182665611yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#324×C283C2
socleC22×C283#120
prime radical#22583584C22
hypercenter#324D283
hypocenterC283#1615
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #31826801C2semidirect
4. #31826404C2semidirect
5. #31826203C2semidirect
7. #324×C283C2semidirect
102. C283#1615semidirect
110. #324D283semidirect

Maximal subgroups

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

subgroupindex
#318270622
#318268012
#318267842
#318264042
#318262032
#318262002
#324×C2832
#1615283