Finite Group Databasebeta

← #44398781

Subgroups — #44398781

Order 29056.

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

normal subgroups only

This group has 240 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#28409622C211yesmaximal, characteristic
2#28409350C211yesmaximal, characteristic, complemented
3#28408967C211yesmaximal, characteristic, complemented
4#28408769C211yesmaximal, characteristic, complemented
5#28408767C211yesmaximal, characteristic, complemented
6#28408755C211yesmaximal, characteristic, complemented
7#484×C227C211yesmaximal, characteristic, complemented
8#20300283—21no—
9#20300277—21no—
10#20300273—21no—
11#20300263—21no—
12#20300262C2211yescharacteristic
13#20300258—21no—
14(C22⋊D227)⋊C4—21no—
15C2×Dic227⋊C4—21no—
16C2×(C2×D227)⋊C4—21no—
17C2×(C2×D227)⋊C4C2211yescharacteristic
18#20300219—21no—
19#20300208—21no—
20C22⋊(C227⋊C8)C2211yescharacteristic
21C227⋊#95C2211yescharacteristic
22C22⋊Q8×C227C2211yescharacteristic
23C2×C4⋊C4×C227C2211yescharacteristic
24#107×C227—21no—
25#103×C227—21no—
26C22⋊C8×C227C2211yescharacteristic
27C23×D227D411yescharacteristic
28C2×D908—21no—
29C2×D908—21no—
30C2×D908D411yescharacteristic
31C2×C22⋊D227—21no—
32C22×Dic227—21no—
33C22×Dic227D411yescharacteristic
34C2×C4×D227—21no—
35C2×C227⋊C8—21no—
36C4⋊Dic227D411yescharacteristic
37Dic227⋊C4—21no—
38Dic227⋊C4—42no—
39(C2×D227)⋊C4—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—21no—
45(C2×D227)⋊C4—42no—
46C4×Dic227—21no—
47C2×Q8×C227D411yescharacteristic
48C22×C4×C227—21no—
49C22×C4×C227C2311yescharacteristic
50C2×C8×C227—21no—
51C4⋊C4×C227—21no—
52C4⋊C4×C227—21no—
53C4⋊C4×C227—21no—
54C4⋊C4×C227D411yescharacteristic
55C22⋊C4×C227—21no—
56C22×D227—21no—
57C22×D227—21no—
58C22×D227—21no—
59C22×D227—21no—
60C22×D227—41no—
61C22×D227—41no—
62D908—41no—
63D908—81no—
64D908—81no—
65C22⋊D227—41no—
66C22⋊D227—41no—
67C2×Dic227—22no—
68C2×Dic227—21no—
69C2×Dic227—21no—
70C2×Dic227—41no—
71C2×Dic227—41no—
72C2×Dic227—41no—
73C4×D227—81no—
74C227⋊C8—41no—
75C23×C227C2×D411yescharacteristic
76Q8×C227—41no—
77C2×C4×C227—21no—
78C2×C4×C227—21no—
79C2×C4×C227—41no—
80C2×C4×C227—41no—
81C2×C4×C227—41no—
82C2×C4×C227—41no—
83C2×C4×C227C2×D411yescharacteristic
84C2×C4×C227C2×D411yescharacteristic
85C8×C227—41no—
86C22×C227—21no—
87C22×C227—21no—
88C22×C227#12011yescharacteristic
89C22×C227#13511yescharacteristic
90C22×C227#13711yescharacteristic
91C2×D227—42no—
92C2×D227—41no—
93C2×D227—41no—
94C2×D227—41no—
95C2×D227—41no—
96C2×D227—41no—
97C2×D227—41no—
98C2×D227—81no—
99C4×C227—21no—
100C4×C227—21no—
101C4×C227—41no—
102C4×C227—41no—
103C4×C227—81no—
104Dic227—42no—
105Dic227—41no—
106Dic227—41no—
107C2×C227—21no—
108C2×C227—21no—
109C2×C227#45211yescharacteristic
110C2×C227#45311yescharacteristic
111C2×C227#45811yescharacteristic
112D227—81no—
113D227—81no—
114C227#161811yescharacteristic, complemented, Sylow
115#1618—2271nomaximal, Sylow
116#538—2271no—
117#484D22711yescharacteristic, complemented
118#481—2271no—
119#399—2271no—
120#328—2271no—
121#327—2271no—
122#323—2271no—
123#126—4541no—
124#124—4541no—
125#123—4541no—
126C22⋊Q8C2×D22711yescharacteristic
127#121—4541no—
128#121—2271no—
129#120—4541no—
130C4×D4—4541no—
131C2×C4⋊C4—4541no—
132C2×C4⋊C4C2×D22711yescharacteristic
133C2×C22⋊C4—4541no—
134C2×C22⋊C4—2271no—
135#107—21no—
136#106—4541no—
137#103—21no—
138#102—4541no—
139C22⋊C8—2271no—
140C22⋊C8C2×D22711yescharacteristic
141#95—2271no—
142C24—2271no—
143C2×Q8C22⋊D22711yescharacteristic
144C2×D4—4541no—
145C2×D4—4541no—
146C2×D4—4541no—
147C2×D4—2271no—
148C22×C4—21no—
149C22×C4—4541no—
150C22×C4—4541no—
151C22×C4—2271no—
152C22×C4C22×D22711yescharacteristic
153C2×C8—21no—
154C2×C8—4541no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—9082no—
159C4⋊C4—4541no—
160C4⋊C4—2271no—
161C4⋊C4C22⋊D22711yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—9082no—
164C22⋊C4—4541no—
165C22⋊C4—4541no—
166C22⋊C4—4541no—
167C22⋊C4—4541no—
168C22⋊C4—4541no—
169C22⋊C4—4541no—
170C42—4541no—
171C23—9081no—
172C23—9081no—
173C23—4541no—
174C23—4541no—
175C23—4541no—
176C23—4541no—
177C23D4×D22711yescharacteristic
178Q8—41no—
179D4—18161no—
180D4—18161no—
181D4—9081no—
182D4—9081no—
183D4—9081no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—18161no—
191C2×C4—9081no—
192C2×C4—9081no—
193C2×C4—9081no—
194C2×C4—4542no—
195C2×C4—4541no—
196C2×C4—4541no—
197C2×C4D4×D22711yescharacteristic
198C2×C4C2×C22⋊D22711yescharacteristic
199C8—41no—
200C8—9081no—
201C22—21no—
202C22—21no—
203C22—18161no—
204C22—9082no—
205C22—9081no—
206C22—9081no—
207C22—9081no—
208C22—9081no—
209C22—9081no—
210C22—9081no—
211C22#2030025611yescharacteristic
212C22#2030031111yescharacteristic
213C22#2030032011yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—9082no—
220C4—9081no—
221C4—9081no—
222C2—21no—
223C2—21no—
224C2—18161no—
225C2—18161no—
226C2#2840919311yescharacteristic
227C2#2840919811yescharacteristic
228C2#2840922111yescharacteristic
subgroupG/H
centerC22#20300256
commutator, cosocleC22×C4×C227C23
FrattiniC22×C4C22×D227
Fitting#484×C227C2
socleC22×C227#120
prime radical#28409622C2
hypercenter#484D227
hypocenterC227#1618
LCSG ▷ C22×C4×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #28409350C2semidirect
3. #28408967C2semidirect
4. #28408769C2semidirect
5. #28408767C2semidirect
6. #28408755C2semidirect
7. #484×C227C2semidirect
114. C227#1618semidirect
117. #484D227semidirect

Maximal subgroups

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

subgroupindex
#284096222
#284093502
#284089672
#284087692
#284087672
#284087552
#484×C2272
#1618227