Finite Group Databasebeta

← #49120250

Subgroups — #49120250

Order 36224.

228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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#31827090C211yesmaximal, characteristic
2#31826795C211yesmaximal, characteristic, complemented
3#31826391C211yesmaximal, characteristic
4#31826203C211yesmaximal, characteristic, complemented
5#31826202C211yesmaximal, characteristic, complemented
6#31826188C211yesmaximal, characteristic
7#483×C283C211yesmaximal, characteristic, complemented
8#22583590—21no—
9#22583589C2211yescharacteristic
10#22583588—21no—
11#22583588—21no—
12#22583587—21no—
13#22583586—21no—
14C2×(C2×D283)⋊C4—21no—
15C2×(C2×D283)⋊C4C2211yescharacteristic
16C22⋊C4×D283—21no—
17#22583541—21no—
18#22583533—21no—
19C22⋊(C283⋊C8)C2211yescharacteristic
20C283⋊#95—21no—
21C283⋊#95C2211yescharacteristic
22C22⋊Q8×C283C2211yescharacteristic
23C2×C4⋊C4×C283C2211yescharacteristic
24#106×C283—21no—
25#103×C283—21no—
26C22⋊C8×C283C2211yescharacteristic
27C23×D283D411yescharacteristic
28C2×Dic566—21no—
29C2×Dic566D411yescharacteristic
30C22×Dic283—21no—
31C22×Dic283D411yescharacteristic
32C2×C4×D283—21no—
33C2×C4×D283—21no—
34C2×C283⋊C8—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283D411yescharacteristic
37Dic283⋊C4—21no—
38Dic283⋊C4—21no—
39Dic283⋊C4—21no—
40C22⋊Dic283—21no—
41(C2×D283)⋊C4—21no—
42(C2×D283)⋊C4—21no—
43(C2×D283)⋊C4—21no—
44(C2×D283)⋊C4—21no—
45(C2×D283)⋊C4—42no—
46C2×Q8×C283D411yescharacteristic
47C22×C4×C283—21no—
48C22×C4×C283C2311yescharacteristic
49C2×C8×C283—21no—
50C4⋊C4×C283—21no—
51C4⋊C4×C283—21no—
52C4⋊C4×C283—21no—
53C4⋊C4×C283D411yescharacteristic
54C22⋊C4×C283—21no—
55C22×D283—21no—
56C22×D283—21no—
57C22×D283—41no—
58C22×D283—41no—
59C22×D283SD1612yes—
60Dic566—41no—
61Dic566—81no—
62C2×Dic283—21no—
63C2×Dic283—21no—
64C2×Dic283—21no—
65C2×Dic283—41no—
66C2×Dic283—41no—
67C2×Dic283—41no—
68C2×Dic283—41no—
69C4×D283—81no—
70C4×D283—81no—
71C283⋊C8—41no—
72C23×C283C2×D411yescharacteristic
73Q8×C283—41no—
74C2×C4×C283—21no—
75C2×C4×C283—21no—
76C2×C4×C283—41no—
77C2×C4×C283—41no—
78C2×C4×C283—41no—
79C2×C4×C283—41no—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D411yescharacteristic
82C8×C283—41no—
83C22×C283—21no—
84C22×C283—21no—
85C22×C283#12011yescharacteristic
86C22×C283C2×SD1611yescharacteristic
87C22×C283#13711yescharacteristic
88C2×D283—22no—
89C2×D283—41no—
90C2×D283—41no—
91C2×D283—42no—
92C2×D283—81no—
93C4×C283—21no—
94C4×C283—21no—
95C4×C283—41no—
96C4×C283—41no—
97C4×C283—81no—
98Dic283—41no—
99Dic283—41no—
100Dic283—41no—
101Dic283—81no—
102C2×C283—21no—
103C2×C283—21no—
104C2×C283#44811yescharacteristic
105C2×C283#45511yescharacteristic
106C2×C283#45811yescharacteristic
107D283—42no—
108C283#160811yescharacteristic, complemented, Sylow
109#1608—2831nomaximal, Sylow
110#543—2831no—
111#483—2831no—
112#483D28311yescharacteristic, complemented
113#397—2831no—
114#328—2831no—
115#328—2831no—
116#323—2831no—
117C22⋊Q8—2831no—
118C22⋊Q8—5661no—
119C22⋊Q8—5661no—
120C22⋊Q8—5661no—
121C22⋊Q8—5661no—
122C22⋊Q8—5661no—
123C22⋊Q8C2×D28311yescharacteristic
124C2×C4⋊C4C2×D28311yescharacteristic
125C2×C22⋊C4—2831no—
126C2×C22⋊C4—5661no—
127C2×C22⋊C4—5661no—
128#106—21no—
129#106—5661no—
130#103—21no—
131#103—5661no—
132C22⋊C8—2831no—
133C22⋊C8C2×D28311yescharacteristic
134#95—2831no—
135#95—5661no—
136C24—2831no—
137C2×Q8—2831no—
138C2×Q8—5661no—
139C2×Q8C22⋊D28311yescharacteristic
140C22×C4—21no—
141C22×C4—2831no—
142C22×C4—5661no—
143C22×C4—5661no—
144C22×C4—5661no—
145C22×C4C22×D28311yescharacteristic
146C2×C8—21no—
147C2×C8—5661no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—2831no—
152C4⋊C4—5661no—
153C4⋊C4—5661no—
154C4⋊C4—5661no—
155C4⋊C4—5661no—
156C4⋊C4C22⋊D28311yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—5661no—
159C22⋊C4—5661no—
160C22⋊C4—5661no—
161C22⋊C4—5661no—
162C22⋊C4—5661no—
163C22⋊C4—11322no—
164C23—2832no—
165C23—5661no—
166C23—5661no—
167C23—11321no—
168C23—11321no—
169C23D4×D28311yescharacteristic
170Q8—41no—
171Q8—11321no—
172Q8—22641no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—5661no—
180C2×C4—5661no—
181C2×C4—5661no—
182C2×C4—11321no—
183C2×C4—11321no—
184C2×C4—11321no—
185C2×C4—11321no—
186C2×C4—22641no—
187C2×C4—22641no—
188C2×C4D4×D28311yescharacteristic
189C2×C4C2×C22⋊D28311yescharacteristic
190C8—41no—
191C8—11321no—
192C22—21no—
193C22—21no—
194C22—5662no—
195C22—11322no—
196C22—11321no—
197C22—11321no—
198C22—22641no—
199C22#2258357811yescharacteristic
200C22SD16×D28311yescharacteristic
201C22#2258363911yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—11321no—
208C4—11321no—
209C4—11321no—
210C4—22641no—
211C2—21no—
212C2—21no—
213C2—11322no—
214C2#3182660211yescharacteristic
215C2#3182664111yescharacteristic
216C2#3182665411yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#483×C283C2
socleC22×C283#120
prime radicalC23×D283D4
hypercenter#483D283
hypocenterC283#1608
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #31826795C2semidirect
4. #31826203C2semidirect
5. #31826202C2semidirect
7. #483×C283C2semidirect
108. C283#1608semidirect
112. #483D283semidirect

Maximal subgroups

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

subgroupindex
#318270902
#318267952
#318263912
#318262032
#318262022
#318261882
#483×C2832
#1608283