Finite Group Databasebeta

← #44400801

Subgroups — #44400801

Order 29056.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#28409543C212yesmaximal, complemented
3#28409048C212yesmaximal, complemented
4#28408789C211yesmaximal, characteristic, complemented
5#407×C227C211yesmaximal, characteristic, complemented
6C2×#16813884C2212yes—
7#20300321—22no—
8#20300316—22no—
9#20300310—22no—
10#20300271—22no—
11#20300267—22no—
12#20300262—22no—
13#20300257—22no—
14C4×C22⋊D227—24no—
15#20300247C2212yes—
16#20300214—24no—
17C23×C4×C227C2211yescharacteristic
18C2×M16×C227C2211yescharacteristic
19C2×M16×C227C2211yescharacteristic
20C22⋊C8×C227—22no—
21#16813884—22no—
22#16813884—22no—
23#16813884—22no—
24#16813884—22no—
25C2×Dic454D412yescomplemented
26C2×D908D412yescomplemented
27C2×C22⋊D227—24no—
28C2×C22⋊D227—22no—
29C2×C4×D227—22no—
30Dic908—22no—
31#16813873—24no—
32D1816—22no—
33C4⋊Dic227—22no—
34Dic227⋊C4—24no—
35C22⋊Dic227—24no—
36C22⋊Dic227—22no—
37(C2×D227)⋊C4—24no—
38C4×Dic227D414yescomplemented
39C24×C227D411yescharacteristic
40C22×C4×C227—21no—
41C22×C4×C227—22no—
42C22×C4×C227—22no—
43C22×C4×C227—21no—
44C22×C4×C227D411yescharacteristic
45C22×C4×C227C2311yescharacteristic
46M16×C227—22no—
47M16×C227—22no—
48C2×C8×C227—21no—
49C2×C8×C227D412yescomplemented
50C22×D227—22no—
51Dic454—22no—
52Dic454—22no—
53D908—22no—
54D908—22no—
55C22⋊D227—48no—
56C22⋊D227—42no—
57C22⋊D227—42no—
58C2×Dic227—24no—
59C2×Dic227—22no—
60C4×D227—42no—
61C4×D227—42no—
62C23×C227—22no—
63C23×C227—21no—
64C23×C227—42no—
65C23×C227C2×D411yescharacteristic
66C2×C4×C227—22no—
67C2×C4×C227—21no—
68C2×C4×C227—41no—
69C2×C4×C227—42no—
70C2×C4×C227—41no—
71C2×C4×C227C2×D412yes—
72C2×C4×C227C2×D411yescharacteristic
73C2×C4×C227C2×D412yes—
74C2×C4×C227#4111yescharacteristic
75C8×C227—22no—
76C8×C227—41no—
77C22×C227—22no—
78C22×C227—24no—
79C22×C227—41no—
80C22×C227—42no—
81C22×C227—41no—
82C22×C227—41no—
83C22×C227#12012yes—
84C22×C227#12111yescharacteristic
85C2×D227—44no—
86C2×D227—42no—
87C4×C227—41no—
88C4×C227#12011yescharacteristic
89C4×C227#12112yes—
90C4×C227#12711yescharacteristic
91Dic227—44no—
92Dic227—42no—
93C2×C227—22no—
94C2×C227—21no—
95C2×C227—42no—
96C2×C227#39211yescharacteristic
97D227—82no—
98C227#201011yescharacteristic, complemented, Sylow
99#2010—2271nomaximal, Sylow
100#575—2271no—
101#525—2272no—
102#421—2272no—
103#407D22711yescharacteristic, complemented
104H(3,ℤ/4)—2271no—
105C2×#41—2272no—
106C23×C4C2×D22711yescharacteristic
107#137—4542no—
108AGL(1,ℤ/8)—4542no—
109#135—4542no—
110C2×M16C2×D22711yescharacteristic
111C2×M16C2×D22711yescharacteristic
112#123—4542no—
113C22⋊Q8—4542no—
114#121—4542no—
115#120—4542no—
116C4×D4—4544no—
117#117—2272no—
118#104—4544no—
119C22⋊C8—22no—
120C24D90811yescharacteristic
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—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—4542no—
134C22×C4D90811yescharacteristic
135C22×C4C22×D22711yescharacteristic
136Q16—4542no—
137SD16—4544no—
138D8—4542no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D22712yescomplemented
143C4⋊C4—4544no—
144C4⋊C4—4542no—
145C22⋊C4—4544no—
146C22⋊C4—4544no—
147C22⋊C4—4542no—
148C42—2274no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—4542no—
153C23C2×D90811yescharacteristic
154Q8—4542no—
155Q8—4542no—
156D4—9088no—
157D4—9082no—
158D4—9082no—
159D4—4542no—
160D4—4542no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—9082no—
167C2×C4—9082no—
168C2×C4—4544no—
169C2×C4—4542no—
170C2×C4D4×D22712yes—
171C2×C4D4×D22712yes—
172C2×C4C2×C22⋊D22711yescharacteristic
173C2×C4#1681388411yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—9084no—
183C22—9082no—
184C22#2030025812yes—
185C22#2030026211yescharacteristic
186C4—41no—
187C4—9084no—
188C4—9082no—
189C4#2030025611yescharacteristic
190C4#2030026112yes—
191C4#2030028411yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—18162no—
196C2#2840894111yescharacteristic
subgroupG/H
centerC4#20300284
commutator, cosocleC22×C4×C227C23
FrattiniC22×C4C22×D227
Fitting#407×C227C2
socleC2×C227#392
hypercenter#407D227
hypocenterC227#2010
LCSG ▷ C22×C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #28409832C2semidirect
2. #28409543C2semidirect
3. #28409048C2semidirect
4. #28408789C2semidirect
5. #407×C227C2semidirect
25. C2×Dic454D4semidirect
26. C2×D908D4semidirect
38. C4×Dic227D4semidirect
49. C2×C8×C227D4semidirect
98. C227#2010semidirect
103. #407D227semidirect
142. C2×C8C22⋊D227semidirect

Maximal subgroups

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

subgroupindex
#284098322
#284095432
#284090482
#284087892
#407×C2272
#2010227