Finite Group Databasebeta

← #49120182

Subgroups — #49120182

Order 36224.

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

normal subgroups only

This group has 316 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, complemented
2#31826616C211yesmaximal, characteristic, complemented
3#31826373C211yesmaximal, characteristic
4#31826203C211yesmaximal, characteristic, complemented
5#31826202C211yesmaximal, characteristic, complemented
6#31826188C211yesmaximal, characteristic, complemented
7#450×C283C211yesmaximal, characteristic, complemented
8C22×C22⋊D283—21no—
9C2×#17985380—21no—
10#22583590—21no—
11#22583589C2211yescharacteristic
12#22583588—21no—
13#22583588—21no—
14#22583587—21no—
15#22583586—21no—
16C2×C22⋊Dic283—21no—
17C2×(C2×D283)⋊C4C2211yescharacteristic
18C22⋊C4×D283—21no—
19#22583531—21no—
20C22⋊(C283⋊C8)C2211yescharacteristic
21C283⋊#95C2211yescharacteristic
22C22×D4×C283C2211yescharacteristic
23C2×SD16×C283—21no—
24C22⋊Q8×C283C2211yescharacteristic
25#102×C283—21no—
26C22⋊C8×C283C2211yescharacteristic
27C23×D283D411yescharacteristic
28C2×Dic566—21no—
29C2×Dic566D411yescharacteristic, complemented
30C2×C22⋊D283—42no—
31C2×C22⋊D283—42no—
32C2×C22⋊D283—42no—
33C22×Dic283—21no—
34C22×Dic283D411yescharacteristic
35C2×C4×D283—21no—
36C2×C4×D283—21no—
37#17985380—42no—
38C2×C283⋊C8—21no—
39C4⋊Dic283—21no—
40C4⋊Dic283D411yescharacteristic, complemented
41Dic283⋊C4—21no—
42Dic283⋊C4—21no—
43Dic283⋊C4—21no—
44C22⋊Dic283—21no—
45C22⋊Dic283—42no—
46(C2×D283)⋊C4—21no—
47(C2×D283)⋊C4—21no—
48(C2×D283)⋊C4—21no—
49(C2×D283)⋊C4—21no—
50C24×C283—21no—
51C2×Q8×C283D411yescharacteristic, complemented
52C2×D4×C283—21no—
53C2×D4×C283—21no—
54C2×D4×C283—42no—
55C22×C4×C283C2311yescharacteristic
56SD16×C283—42no—
57C2×C8×C283—21no—
58C4⋊C4×C283—21no—
59C4⋊C4×C283D411yescharacteristic, complemented
60C22⋊C4×C283—21no—
61C22×D283—21no—
62C22×D283—21no—
63C22×D283—41no—
64C22×D283—41no—
65C22×D283SD1612yescomplemented
66Dic566—41no—
67Dic566—81no—
68C22⋊D283—48no—
69C2×Dic283—22no—
70C2×Dic283—21no—
71C2×Dic283—21no—
72C2×Dic283—21no—
73C2×Dic283—41no—
74C2×Dic283—41no—
75C2×Dic283—41no—
76C4×D283—81no—
77C4×D283—81no—
78C283⋊C8—41no—
79C23×C283—22no—
80C23×C283—41no—
81C23×C283—41no—
82C23×C283—41no—
83C23×C283—41no—
84C23×C283—41no—
85C23×C283—41no—
86C23×C283C2×D411yescharacteristic
87Q8×C283—41no—
88D4×C283—22no—
89D4×C283—22no—
90D4×C283—41no—
91D4×C283—41no—
92C2×C4×C283—21no—
93C2×C4×C283—21no—
94C2×C4×C283—41no—
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2×D411yescharacteristic
97C8×C283—41no—
98C22×C283—21no—
99C22×C283—21no—
100C22×C283—42no—
101C22×C283—42no—
102C22×C283—42no—
103C22×C283—81no—
104C22×C283—81no—
105C22×C283—81no—
106C22×C283—81no—
107C22×C283#12011yescharacteristic
108C22×C283C2×SD1611yescharacteristic
109C22×C283#13711yescharacteristic
110C2×D283—22no—
111C2×D283—41no—
112C2×D283—41no—
113C2×D283—42no—
114C2×D283—81no—
115C4×C283—21no—
116C4×C283—21no—
117C4×C283—41no—
118C4×C283—41no—
119Dic283—42no—
120Dic283—41no—
121Dic283—41no—
122Dic283—41no—
123C2×C283—21no—
124C2×C283—21no—
125C2×C283—82no—
126C2×C283#44811yescharacteristic
127C2×C283#45311yescharacteristic
128C2×C283B(4,𝔽2)11yescharacteristic
129D283—42no—
130C283#159611yescharacteristic, complemented, Sylow
131#1596—2831nomaximal, Sylow
132#543—2831no—
133#450—2831no—
134#450D28311yescharacteristic, complemented
135#392—2831no—
136#328—2831no—
137#328—2831no—
138#323—2831no—
139C22×D4—5661no—
140C22×D4C2×D28311yescharacteristic
141C2×SD16—21no—
142C2×SD16—5661no—
143C22⋊Q8—2831no—
144C22⋊Q8—5661no—
145C22⋊Q8—5661no—
146C22⋊Q8—5661no—
147C22⋊Q8—5661no—
148C22⋊Q8—5661no—
149C22⋊Q8C2×D28311yescharacteristic
150C2×C22⋊C4—2831no—
151C2×C22⋊C4—5661no—
152C2×C22⋊C4—5661no—
153#102—21no—
154#102—5661no—
155C22⋊C8—2831no—
156C22⋊C8C2×D28311yescharacteristic
157#95—2831no—
158C24—21no—
159C24—2831no—
160C2×Q8—2831no—
161C2×Q8—5661no—
162C2×Q8C22⋊D28311yescharacteristic, complemented
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—42no—
166C2×D4—11322no—
167C2×D4—11322no—
168C2×D4—11322no—
169C22×C4—2831no—
170C22×C4—5661no—
171C22×C4—5661no—
172C22×C4—5661no—
173C22×C4C22×D28311yescharacteristic
174SD16—42no—
175SD16—11322no—
176C2×C8—21no—
177C2×C8—5661no—
178C4⋊C4—21no—
179C4⋊C4—2831no—
180C4⋊C4—5661no—
181C4⋊C4—5661no—
182C4⋊C4—5661no—
183C4⋊C4—5661no—
184C4⋊C4C22⋊D28311yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—5661no—
187C22⋊C4—5661no—
188C22⋊C4—5661no—
189C22⋊C4—5661no—
190C22⋊C4—5661no—
191C22⋊C4—11322no—
192C23—22no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23—41no—
197C23—41no—
198C23—41no—
199C23—2832no—
200C23—5661no—
201C23—5661no—
202C23—11321no—
203C23—11321no—
204C23D4×D28311yescharacteristic
205Q8—41no—
206Q8—11321no—
207Q8—22641no—
208D4—22no—
209D4—22no—
210D4—41no—
211D4—41no—
212D4—11328no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—5662no—
217C2×C4—5661no—
218C2×C4—5661no—
219C2×C4—5661no—
220C2×C4—11321no—
221C2×C4—11321no—
222C2×C4—11321no—
223C2×C4—22641no—
224C2×C4—22641no—
225C2×C4D4×D28311yescharacteristic
226C2×C4C2×C22⋊D28311yescharacteristic
227C8—41no—
228C8—11321no—
229C22—21no—
230C22—21no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—81no—
235C22—81no—
236C22—81no—
237C22—81no—
238C22—5662no—
239C22—11322no—
240C22—11321no—
241C22—11321no—
242C22—22641no—
243C22#2258357811yescharacteristic
244C22SD16×D28311yescharacteristic
245C22#2258363911yescharacteristic
246C4—21no—
247C4—21no—
248C4—41no—
249C4—41no—
250C4—11322no—
251C4—11321no—
252C4—11321no—
253C4—11321no—
254C2—21no—
255C2—21no—
256C2—82no—
257C2—11322no—
258C2#3182660211yescharacteristic
259C2#3182663111yescharacteristic
260C2#3182665111yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#450×C283C2
socleC22×C283#120
prime radical#31826373C2
hypercenter#450D283
hypocenterC283#1596
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #31827090C2semidirect
2. #31826616C2semidirect
4. #31826203C2semidirect
5. #31826202C2semidirect
6. #31826188C2semidirect
7. #450×C283C2semidirect
29. C2×Dic566D4semidirect
40. C4⋊Dic283D4semidirect
51. C2×Q8×C283D4semidirect
59. C4⋊C4×C283D4semidirect
65. C22×D283SD16semidirect
130. C283#1596semidirect
134. #450D283semidirect
162. C2×Q8C22⋊D283semidirect
184. C4⋊C4C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318270902
#318266162
#318263732
#318262032
#318262022
#318261882
#450×C2832
#1596283