Finite Group Databasebeta

← #49120274

Subgroups — #49120274

Order 36224.

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

normal subgroups only

This group has 232 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#31827055C211yesmaximal, characteristic
2#31826778C211yesmaximal, characteristic, complemented
3#31826391C211yesmaximal, characteristic, complemented
4#31826202C211yesmaximal, characteristic, complemented
5#31826200C211yesmaximal, characteristic, complemented
6#31826188C211yesmaximal, characteristic, complemented
7#483×C283C211yesmaximal, characteristic, complemented
8#22583605—21no—
9#22583599—21no—
10#22583595—21no—
11#22583585—21no—
12#22583584C2211yescharacteristic
13#22583580—21no—
14(C22⋊D283)⋊C4—21no—
15C2×(C2×D283)⋊C4—21no—
16C2×(C2×D283)⋊C4C2211yescharacteristic
17#22583543—21no—
18#22583530—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×D1132—21no—
29C2×D1132—21no—
30C2×D1132D411yescharacteristic
31C2×C22⋊D283—21no—
32C22×Dic283—21no—
33C22×Dic283D411yescharacteristic
34C2×C4×D283—21no—
35C2×C283⋊C8—21no—
36C4⋊Dic283D411yescharacteristic
37Dic283⋊C4—21no—
38(C2×D283)⋊C4—21no—
39(C2×D283)⋊C4—21no—
40(C2×D283)⋊C4—21no—
41(C2×D283)⋊C4—21no—
42(C2×D283)⋊C4—21no—
43(C2×D283)⋊C4—21no—
44(C2×D283)⋊C4—42no—
45C4×Dic283—21no—
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—21no—
58C22×D283—21no—
59C22×D283—41no—
60C22×D283—41no—
61D1132—41no—
62D1132—81no—
63D1132—81no—
64C22⋊D283—41no—
65C22⋊D283—41no—
66C2×Dic283—21no—
67C2×Dic283—21no—
68C2×Dic283—41no—
69C2×Dic283—41no—
70C2×Dic283—41no—
71C2×Dic283—41no—
72C4×D283—81no—
73C283⋊C8—41no—
74C23×C283C2×D411yescharacteristic
75Q8×C283—41no—
76C2×C4×C283—21no—
77C2×C4×C283—21no—
78C2×C4×C283—41no—
79C2×C4×C283—41no—
80C2×C4×C283—41no—
81C2×C4×C283—41no—
82C2×C4×C283C2×D411yescharacteristic
83C2×C4×C283C2×D411yescharacteristic
84C8×C283—41no—
85C22×C283—21no—
86C22×C283—21no—
87C22×C283#12011yescharacteristic
88C22×C283#13511yescharacteristic
89C22×C283AGL(1,ℤ/8)11yescharacteristic
90C2×D283—42no—
91C2×D283—41no—
92C2×D283—41no—
93C2×D283—41no—
94C2×D283—41no—
95C2×D283—41no—
96C2×D283—41no—
97C2×D283—81no—
98C4×C283—21no—
99C4×C283—21no—
100C4×C283—41no—
101C4×C283—41no—
102C4×C283—81no—
103Dic283—41no—
104Dic283—41no—
105Dic283—81no—
106C2×C283—21no—
107C2×C283—21no—
108C2×C283#44911yescharacteristic
109C2×C283#45511yescharacteristic
110C2×C283#45811yescharacteristic
111D283—81no—
112D283—81no—
113C283#161211yescharacteristic, complemented, Sylow
114#1612—2831nomaximal, Sylow
115#538—2831no—
116#483D28311yescharacteristic, complemented
117#480—2831no—
118#397—2831no—
119#328—2831no—
120#327—2831no—
121#323—2831no—
122#126—5661no—
123#124—5661no—
124#123—5661no—
125C22⋊Q8C2×D28311yescharacteristic
126#121—2831no—
127#121—5661no—
128#120—5661no—
129C4×D4—5661no—
130C2×C4⋊C4C2×D28311yescharacteristic
131C2×C22⋊C4—2831no—
132C2×C22⋊C4—5661no—
133#107—5661no—
134#106—21no—
135#103—21no—
136#102—5661no—
137C22⋊C8—2831no—
138C22⋊C8C2×D28311yescharacteristic
139#95—2831no—
140#95—5661no—
141C24—2831no—
142C2×Q8C22⋊D28311yescharacteristic
143C2×D4—2831no—
144C2×D4—5661no—
145C2×D4—5661no—
146C2×D4—5661no—
147C22×C4—21no—
148C22×C4—2831no—
149C22×C4—5661no—
150C22×C4—5661no—
151C22×C4C22×D28311yescharacteristic
152C2×C8—21no—
153C2×C8—5661no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—2831no—
158C4⋊C4—5661no—
159C4⋊C4C22⋊D28311yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—5661no—
162C22⋊C4—5661no—
163C22⋊C4—5661no—
164C22⋊C4—5661no—
165C22⋊C4—5661no—
166C22⋊C4—5661no—
167C22⋊C4—11322no—
168C42—5661no—
169C23—5661no—
170C23—5661no—
171C23—5661no—
172C23—5661no—
173C23—11321no—
174C23—11321no—
175C23D4×D28311yescharacteristic
176Q8—41no—
177D4—11321no—
178D4—11321no—
179D4—11321no—
180D4—22641no—
181D4—22641no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—5661no—
189C2×C4—5661no—
190C2×C4—11321no—
191C2×C4—11321no—
192C2×C4—11321no—
193C2×C4—11321no—
194C2×C4—22641no—
195C2×C4D4×D28311yescharacteristic
196C2×C4C2×C22⋊D28311yescharacteristic
197C8—41no—
198C8—11321no—
199C22—21no—
200C22—21no—
201C22—11322no—
202C22—11321no—
203C22—11321no—
204C22—11321no—
205C22—11321no—
206C22—11321no—
207C22—11321no—
208C22—22641no—
209C22#2258357811yescharacteristic
210C22#2258363111yescharacteristic
211C22#2258363711yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—11321no—
218C4—11321no—
219C4—22641no—
220C2—21no—
221C2—21no—
222C2—22641no—
223C2—22641no—
224C2#3182660911yescharacteristic
225C2#3182664111yescharacteristic
226C2#3182665411yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#483×C283C2
socleC22×C283#120
prime radical#31827055C2
hypercenter#483D283
hypocenterC283#1612
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. #31826778C2semidirect
3. #31826391C2semidirect
4. #31826202C2semidirect
5. #31826200C2semidirect
6. #31826188C2semidirect
7. #483×C283C2semidirect
113. C283#1612semidirect
116. #483D283semidirect

Maximal subgroups

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

subgroupindex
#318270552
#318267782
#318263912
#318262022
#318262002
#318261882
#483×C2832
#1612283