Finite Group Databasebeta

← #44400802

Subgroups — #44400802

Order 29056.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#28409832C211yesmaximal, characteristic, complemented
2#28409544C212yesmaximal, complemented
3#28409050C212yesmaximal, complemented
4#28408995C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C227C211yesmaximal, characteristic, complemented
6C2×#16813884C2212yes—
7C22×C4×D227C2211yescharacteristic
8#20300321—22no—
9#20300316—22no—
10#20300310—22no—
11C2×#16813868C2211yescharacteristic
12#20300272—22no—
13#20300268—22no—
14#20300263—22no—
15#20300258—22no—
16C4×D908—24no—
17#20300216—24no—
18(C2×D227)⋊C8—22no—
19C2×M16×C227C2211yescharacteristic
20#117×C227C2212yes—
21C23×D227D411yescharacteristic
22#16813884—22no—
23#16813884—22no—
24#16813884—22no—
25#16813884—22no—
26C2×Dic454D412yescomplemented
27C2×D908—24no—
28C2×D908D412yescomplemented
29C2×C22⋊D227—22no—
30C22×Dic227D411yescharacteristic
31C2×C4×D227—21no—
32C2×C4×D227—22no—
33C2×C4×D227—22no—
34C2×C4×D227—22no—
35C2×C4×D227—21no—
36Dic908—22no—
37#16813873—24no—
38D1816—22no—
39#16813868—22no—
40C2×C227⋊C8—21no—
41C4⋊Dic227—24no—
42(C2×D227)⋊C4—24no—
43(C2×D227)⋊C4—24no—
44C22×C4×C227C2311yescharacteristic
45M16×C227—22no—
46C2×C8×C227D412yescomplemented
47C4⋊C4×C227—22no—
48C22⋊C4×C227—22no—
49C42×C227D414yescomplemented
50C22×D227—22no—
51C22×D227—21no—
52C22×D227—22no—
53C22×D227—42no—
54Dic454—22no—
55Dic454—22no—
56D908—22no—
57D908—22no—
58D908—48no—
59C22⋊D227—42no—
60C22⋊D227—42no—
61C2×Dic227—22no—
62C2×Dic227—22no—
63C2×Dic227—21no—
64C4×D227—41no—
65C4×D227—42no—
66C4×D227—42no—
67C4×D227—41no—
68C4×D227—42no—
69C227⋊C8—41no—
70C23×C227C2×D411yescharacteristic
71C2×C4×C227—24no—
72C2×C4×C227C2×D412yes—
73C2×C4×C227C2×D411yescharacteristic
74C2×C4×C227C2×D412yes—
75C2×C4×C227#4111yescharacteristic
76C8×C227—22no—
77C22×C227—41no—
78C22×C227#12012yes—
79C22×C227#12111yescharacteristic
80C2×D227—24no—
81C2×D227—22no—
82C2×D227—42no—
83C2×D227—41no—
84C2×D227—41no—
85C2×D227—44no—
86C2×D227—42no—
87C4×C227—44no—
88C4×C227#12011yescharacteristic
89C4×C227#12112yes—
90C4×C227#12711yescharacteristic
91Dic227—41no—
92Dic227—42no—
93C2×C227—22no—
94C2×C227—21no—
95C2×C227#39211yescharacteristic
96D227—42no—
97D227—82no—
98C227#201011yescharacteristic, complemented, Sylow
99#2010—2271nomaximal, Sylow
100#575—2271no—
101#525—2272no—
102#421—2272no—
103#407—2271no—
104H(3,ℤ/4)D22711yescharacteristic, complemented
105C2×#41—2272no—
106C23×C4—2271no—
107#137—4542no—
108AGL(1,ℤ/8)—4542no—
109#135—4542no—
110C2×M16—2271no—
111C2×M16C2×D22711yescharacteristic
112#123—4542no—
113C22⋊Q8—4542no—
114#121—4542no—
115#120—4542no—
116C4×D4—4544no—
117#117C2×D22712yes—
118#104—4544no—
119C22⋊C8—4542no—
120C24—2271no—
121#41—4542no—
122#41—4542no—
123#41—4542no—
124#41—4542no—
125C2×Q8—2272no—
126C2×D4—4544no—
127C2×D4—4542no—
128C2×D4—2272no—
129C22×C4—4542no—
130C22×C4—4541no—
131C22×C4—4542no—
132C22×C4—4542no—
133C22×C4—4541no—
134C22×C4—2271no—
135C22×C4C22×D22711yescharacteristic
136Q16—4542no—
137SD16—4544no—
138D8—4542no—
139M16—22no—
140M16—4542no—
141C2×C8—4541no—
142C2×C8D90812yescomplemented
143C4⋊C4—22no—
144C4⋊C4—4544no—
145C22⋊C4—22no—
146C22⋊C4—4544no—
147C22⋊C4—4544no—
148C42D90814yescomplemented
149C23—9082no—
150C23—4542no—
151C23—4542no—
152C23—4541no—
153C23D4×D22711yescharacteristic
154Q8—4542no—
155Q8—4542no—
156D4—9088no—
157D4—9082no—
158D4—9082no—
159D4—4542no—
160D4—4542no—
161C2×C4—24no—
162C2×C4—9081no—
163C2×C4—9082no—
164C2×C4—9082no—
165C2×C4—9081no—
166C2×C4—9082no—
167C2×C4—4542no—
168C2×C4—4542no—
169C2×C4—4541no—
170C2×C4D4×D22712yes—
171C2×C4C2×D90811yescharacteristic
172C2×C4C2×D90812yes—
173C2×C4#1681388511yescharacteristic
174C8—22no—
175C8—9081no—
176C22—41no—
177C22—9084no—
178C22—9082no—
179C22—9081no—
180C22—9082no—
181C22—9081no—
182C22—4544no—
183C22—4542no—
184C22#2030025812yes—
185C22#2030026311yescharacteristic
186C4—44no—
187C4—9081no—
188C4—9082no—
189C4#2030025811yescharacteristic
190C4#2030026312yes—
191C4#2030028511yescharacteristic
192C2—22no—
193C2—21no—
194C2—18162no—
195C2—9082no—
196C2#2840894211yescharacteristic
subgroupG/H
centerC4#20300285
commutator, cosocleC22×C4×C227C23
FrattiniC22×C4C22×D227
FittingH(3,ℤ/4)×C227C2
socleC2×C227#392
hypercenterH(3,ℤ/4)D227
hypocenterC227#2010
LCSG ▷ C22×C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #28409832C2semidirect
2. #28409544C2semidirect
3. #28409050C2semidirect
4. #28408995C2semidirect
5. H(3,ℤ/4)×C227C2semidirect
26. C2×Dic454D4semidirect
28. C2×D908D4semidirect
46. C2×C8×C227D4semidirect
49. C42×C227D4semidirect
98. C227#2010semidirect
104. H(3,ℤ/4)D227semidirect
142. C2×C8D908semidirect
148. C42D908semidirect

Maximal subgroups

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

subgroupindex
#284098322
#284095442
#284090502
#284089952
H(3,ℤ/4)×C2272
#2010227