Finite Group Databasebeta

← #44401682

Subgroups — #44401682

Order 29056.

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

normal subgroups only

This group has 226 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#28409832C211yesmaximal, characteristic, complemented
2#28409470C212yesmaximal, complemented
3#28409285C211yesmaximal, characteristic, complemented
4#28408843C212yesmaximal, complemented
5#349×C227C211yesmaximal, characteristic, complemented
6C2×#16813884—21no—
7#20300321—22no—
8#20300316—22no—
9#20300310—21no—
10#20300310C2212yes—
11C2×D1816C2211yescharacteristic, complemented
12#20300262—21no—
13#20300233—22no—
14D3632—22no—
15#20300220C2211yescharacteristic, complemented
16#20300210—21no—
17C2×M16×C227C2211yescharacteristic
18M32×C227C2212yescomplemented
19#16813884—22no—
20#16813884—22no—
21#16813884—41no—
22#16813884—41no—
23C2×Dic454—21no—
24C2×D908—21no—
25C2×D908—21no—
26C2×C22⋊D227—41no—
27C2×C22⋊D227—41no—
28C2×C4×D227—41no—
29Dic908—21no—
30Dic908D412yescomplemented
31#16813873—22no—
32#16813873—22no—
33D1816—21no—
34D1816—22no—
35D1816D412yescomplemented
36C4⋊Dic227—21no—
37(C2×D227)⋊C4—41no—
38C22×C4×C227D411yescharacteristic
39M16×C227—22no—
40C2×C8×C227D411yescharacteristic
41C2×C8×C227C2311yescharacteristic
42C16×C227—22no—
43C22×D227—41no—
44C22×D227—41no—
45Dic454—22no—
46Dic454—41no—
47D908—22no—
48D908—41no—
49D908—41no—
50D908—41no—
51C22⋊D227—42no—
52C22⋊D227—42no—
53C22⋊D227—82no—
54C2×Dic227—41no—
55C2×Dic227—41no—
56C4×D227—42no—
57C4×D227—42no—
58C23×C227D811yescharacteristic
59C2×C4×C227—21no—
60C2×C4×C227—21no—
61C2×C4×C227D811yescharacteristic
62C2×C4×C227C2×D411yescharacteristic
63C8×C227—21no—
64C8×C227C2×D412yes—
65C22×C227—21no—
66C22×C227—41no—
67C22×C227C2×D811yescharacteristic
68C2×D227—42no—
69C2×D227—82no—
70C2×D227—81no—
71C2×D227—81no—
72C2×D227—81no—
73C4×C227—21no—
74C4×C227#12011yescharacteristic
75C4×C227AGL(1,ℤ/8)11yescharacteristic
76Dic227—42no—
77Dic227—81no—
78C2×C227—21no—
79C2×C227—41no—
80C2×C227#44711yescharacteristic
81D227—82no—
82D227—161no—
83C227#219011yescharacteristic, complemented, Sylow
84#2190—2271nomaximal, Sylow
85#575—2271no—
86#509—2272no—
87#469—2271no—
88#360—2272no—
89#349D22711yescharacteristic, complemented
90C2×#41—4541no—
91#137—4542no—
92AGL(1,ℤ/8)—4542no—
93#135—4541no—
94#135—2272no—
95C2×D8—2271no—
96C2×M16C2×D22711yescharacteristic
97#121—4541no—
98SD32—4542no—
99D16—4542no—
100M32C2×D22712yescomplemented
101#106—2271no—
102#102—4541no—
103#41—9081no—
104#41—9081no—
105#41—4542no—
106#41—4542no—
107C2×Q8—4541no—
108C2×D4—9081no—
109C2×D4—9081no—
110C2×D4—4541no—
111C2×D4—4541no—
112C22×C4—9081no—
113C22×C4D90811yescharacteristic
114Q16—4541no—
115Q16—2272no—
116SD16—4542no—
117SD16—4542no—
118D8—4541no—
119D8—4542no—
120D8—2272no—
121M16—22no—
122C2×C8D90811yescharacteristic
123C2×C8C22×D22711yescharacteristic
124C4⋊C4—4541no—
125C22⋊C4—9081no—
126C16—22no—
127C23—9081no—
128C23—9081no—
129C23D181611yescharacteristic
130Q8—9081no—
131Q8—4542no—
132D4—18162no—
133D4—9081no—
134D4—9082no—
135D4—9082no—
136D4—9081no—
137D4—9081no—
138D4—4542no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—9082no—
142C2×C4—9081no—
143C2×C4—9081no—
144C2×C4—9082no—
145C2×C4D181611yescharacteristic
146C2×C4C2×D90811yescharacteristic
147C8—21no—
148C8D4×D22712yes—
149C22—21no—
150C22—41no—
151C22—18161no—
152C22—18161no—
153C22—18162no—
154C22—18161no—
155C22—9082no—
156C22C2×D181611yescharacteristic
157C4—21no—
158C4—18161no—
159C4—9082no—
160C4#2030025811yescharacteristic
161C4#2030031611yescharacteristic
162C2—21no—
163C2—41no—
164C2—18162no—
165C2—36321no—
166C2#2840916811yescharacteristic
subgroupG/H
centerC2#28409168
commutator, cosocleC2×C8×C227C23
FrattiniC2×C8C22×D227
Fitting#349×C227C2
socleC2×C227#447
hypercenter#349D227
hypocenterC227#2190
LCSG ▷ C2×C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
1. #28409832C2semidirect
2. #28409470C2semidirect
3. #28409285C2semidirect
4. #28408843C2semidirect
5. #349×C227C2semidirect
11. C2×D1816C22semidirect
15. #20300220C22semidirect
18. M32×C227C22semidirect
30. Dic908D4semidirect
35. D1816D4semidirect
83. C227#2190semidirect
89. #349D227semidirect
100. M32C2×D227semidirect

Maximal subgroups

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

subgroupindex
#284098322
#284094702
#284092852
#284088432
#349×C2272
#2190227