Finite Group Databasebeta

← #44398745

Subgroups — #44398745

Order 29056.

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#28409619C211yesmaximal, characteristic
2#28409362C211yesmaximal, characteristic, complemented
3#28408958C211yesmaximal, characteristic, complemented
4#28408770C211yesmaximal, characteristic, complemented
5#28408766C211yesmaximal, characteristic, complemented
6#28408755C211yesmaximal, characteristic, complemented
7#480×C227C211yesmaximal, characteristic, complemented
8#20300283—21no—
9#20300274—21no—
10#20300272—21no—
11#20300267C2211yescharacteristic
12#20300260—21no—
13#20300256—21no—
14D4×Dic227—21no—
15C2×(C2×D227)⋊C4—21no—
16C2×(C2×D227)⋊C4C2211yescharacteristic
17#20300219—21no—
18#20300211—21no—
19C22⋊(C227⋊C8)C2211yescharacteristic
20C227⋊#95—21no—
21C227⋊#95C2211yescharacteristic
22#121×C227C2211yescharacteristic
23C2×C4⋊C4×C227C2211yescharacteristic
24#107×C227—21no—
25#102×C227—21no—
26C22⋊C8×C227C2211yescharacteristic
27C23×D227D411yescharacteristic
28C2×Dic454D411yescharacteristic
29C2×C22⋊D227—21no—
30C2×C22⋊D227—21no—
31C22×Dic227—21no—
32C22×Dic227—21no—
33C22×Dic227D411yescharacteristic
34C2×C227⋊C8—21no—
35C4⋊Dic227—21no—
36C4⋊Dic227D411yescharacteristic
37Dic227⋊C4—21no—
38C22⋊Dic227—21no—
39C22⋊Dic227—21no—
40(C2×D227)⋊C4—21no—
41(C2×D227)⋊C4—21no—
42(C2×D227)⋊C4—21no—
43(C2×D227)⋊C4—21no—
44(C2×D227)⋊C4—42no—
45C4×Dic227—21no—
46C2×D4×C227—21no—
47C2×D4×C227D411yescharacteristic
48C22×C4×C227—21no—
49C22×C4×C227C2311yescharacteristic
50C2×C8×C227—21no—
51C4⋊C4×C227—21no—
52C4⋊C4×C227—21no—
53C4⋊C4×C227D411yescharacteristic
54C22⋊C4×C227—21no—
55C22×D227—21no—
56C22×D227—21no—
57C22×D227—21no—
58C22×D227—41no—
59C22×D227—41no—
60Dic454—41no—
61C22⋊D227—81no—
62C22⋊D227—81no—
63C2×Dic227—21no—
64C2×Dic227—21no—
65C2×Dic227—21no—
66C2×Dic227—41no—
67C2×Dic227—41no—
68C2×Dic227—41no—
69C2×Dic227—41no—
70C2×Dic227—81no—
71C227⋊C8—41no—
72C23×C227—21no—
73C23×C227C2×D411yescharacteristic
74D4×C227—41no—
75D4×C227—41no—
76D4×C227—41no—
77C2×C4×C227—21no—
78C2×C4×C227—41no—
79C2×C4×C227—41no—
80C2×C4×C227—41no—
81C2×C4×C227—41no—
82C2×C4×C227C2×D411yescharacteristic
83C2×C4×C227C2×D411yescharacteristic
84C8×C227—41no—
85C22×C227—21no—
86C22×C227—21no—
87C22×C227—41no—
88C22×C227—41no—
89C22×C227—41no—
90C22×C227#12011yescharacteristic
91C22×C227#13511yescharacteristic
92C22×C227AGL(1,ℤ/8)11yescharacteristic
93C2×D227—42no—
94C2×D227—41no—
95C2×D227—41no—
96C2×D227—41no—
97C2×D227—81no—
98C4×C227—21no—
99C4×C227—21no—
100C4×C227—41no—
101C4×C227—81no—
102Dic227—41no—
103Dic227—41no—
104Dic227—41no—
105Dic227—81no—
106C2×C227—21no—
107C2×C227—21no—
108C2×C227—81no—
109C2×C227#44911yescharacteristic
110C2×C227#45511yescharacteristic
111C2×C227#45811yescharacteristic
112D227—81no—
113C227#161211yescharacteristic, complemented, Sylow
114#1612—2271nomaximal, Sylow
115#538—2271no—
116#483—2271no—
117#480D22711yescharacteristic, complemented
118#397—2271no—
119#328—2271no—
120#327—2271no—
121#323—2271no—
122#126—4541no—
123#124—4541no—
124#123—4541no—
125C22⋊Q8—2271no—
126#121—4541no—
127#121C2×D22711yescharacteristic
128#120—4541no—
129C4×D4—4541no—
130C2×C4⋊C4C2×D22711yescharacteristic
131C2×C22⋊C4—4541no—
132C2×C22⋊C4—2271no—
133#107—21no—
134#106—4541no—
135#103—4541no—
136#102—21no—
137C22⋊C8—2271no—
138C22⋊C8C2×D22711yescharacteristic
139#95—4541no—
140#95—2271no—
141C24—2271no—
142C2×Q8—2271no—
143C2×D4—21no—
144C2×D4—4541no—
145C2×D4—4541no—
146C2×D4C22⋊D22711yescharacteristic
147C22×C4—21no—
148C22×C4—4541no—
149C22×C4—4541no—
150C22×C4—2271no—
151C22×C4C22×D22711yescharacteristic
152C2×C8—21no—
153C2×C8—4541no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—4541no—
157C4⋊C4—4541no—
158C4⋊C4—2271no—
159C4⋊C4C22⋊D22711yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—9082no—
162C22⋊C4—4541no—
163C22⋊C4—4541no—
164C22⋊C4—4541no—
165C22⋊C4—4541no—
166C22⋊C4—4541no—
167C22⋊C4—4541no—
168C42—4541no—
169C23—21no—
170C23—9081no—
171C23—9081no—
172C23—4541no—
173C23—4541no—
174C23—4541no—
175C23D4×D22711yescharacteristic
176Q8—9081no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—18161no—
181D4—18161no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—18161no—
188C2×C4—9081no—
189C2×C4—9081no—
190C2×C4—9081no—
191C2×C4—9081no—
192C2×C4—4541no—
193C2×C4—4541no—
194C2×C4—4541no—
195C2×C4D4×D22711yescharacteristic
196C2×C4C2×C22⋊D22711yescharacteristic
197C8—41no—
198C8—9081no—
199C22—21no—
200C22—21no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—18161no—
205C22—9082no—
206C22—9081no—
207C22—9081no—
208C22—9081no—
209C22#2030025611yescharacteristic
210C22#2030030711yescharacteristic
211C22#2030031211yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—18161no—
217C4—9081no—
218C4—9081no—
219C4—9081no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—18161no—
224C2#2840917411yescharacteristic
225C2#2840920811yescharacteristic
226C2#2840922111yescharacteristic
subgroupG/H
centerC22#20300256
commutator, cosocleC22×C4×C227C23
FrattiniC22×C4C22×D227
Fitting#480×C227C2
socleC22×C227#120
prime radical#28409619C2
hypercenter#480D227
hypocenterC227#1612
LCSG ▷ C22×C4×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #28409362C2semidirect
3. #28408958C2semidirect
4. #28408770C2semidirect
5. #28408766C2semidirect
6. #28408755C2semidirect
7. #480×C227C2semidirect
113. C227#1612semidirect
117. #480D227semidirect

Maximal subgroups

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

subgroupindex
#284096192
#284093622
#284089582
#284087702
#284087662
#284087552
#480×C2272
#1612227