Finite Group Databasebeta

← #44401404

Subgroups — #44401404

Order 29056.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#28409595C211yesmaximal, characteristic
2#28409004C212yesmaximal, complemented
3#28408825C211yesmaximal, characteristic, complemented
4#28408824C212yesmaximal, complemented
5#353×C227C211yesmaximal, characteristic, complemented
6C2×#16813883C2211yescharacteristic
7C2×D4×D227C411yescharacteristic, complemented
8#20300284C2211yescharacteristic
9#20300276C411yescharacteristic, complemented
10#20300275C411yescharacteristic, complemented
11#20300260—22no—
12#20300256—22no—
13#20300245C411yescharacteristic, complemented
14#20300244—22no—
15#20300203C2212yescomplemented
16#20300202—22no—
17#127×C227C2211yescharacteristic
18#99×C227C2212yescomplemented
19C23×D227—21no—
20#16813883—42no—
21C2×Dic454C2×C411yescharacteristic
22C2×D908C2×C411yescharacteristic
23C2×C22⋊D227—21no—
24C2×C22⋊D227—22no—
25C2×C22⋊D227D412yes—
26D4×D227—42no—
27C22×Dic227D412yes—
28C2×C4×D227C2×C411yescharacteristic
29Dic227⋊C4—21no—
30Dic227⋊C4—42no—
31C22⋊Dic227—22no—
32C22⋊Dic227—22no—
33(C2×D227)⋊C4—21no—
34(C2×D227)⋊C4—22no—
35C4×Dic227—42no—
36C4×Dic227C2×C411yescharacteristic
37C2×D4×C227—22no—
38C2×D4×C227C2×C411yescharacteristic
39C2×D4×C227C2311yescharacteristic
40C22⋊C4×C227—22no—
41C42×C227C2×C411yescharacteristic
42C22×D227—21no—
43C22×D227—42no—
44C22×D227—82no—
45C22×D227C22⋊C411yescharacteristic
46Dic454—41no—
47D908—41no—
48C22⋊D227—42no—
49C22⋊D227—42no—
50C22⋊D227—82no—
51C2×Dic227—22no—
52C2×Dic227—22no—
53C2×Dic227—21no—
54C2×Dic227—42no—
55C2×Dic227C22⋊C412yes—
56C2×Dic227C22⋊C411yescharacteristic
57C4×D227—22no—
58C23×C227—21no—
59C23×C227C2×D412yes—
60D4×C227—41no—
61D4×C227—41no—
62D4×C227—82no—
63C2×C4×C227—21no—
64C2×C4×C227—42no—
65C2×C4×C227C22×C411yescharacteristic
66C22×C227—22no—
67C22×C227—42no—
68C22×C227—42no—
69C22×C227—41no—
70C22×C227C2×C22⋊C411yescharacteristic
71C2×D227—21no—
72C2×D227—41no—
73C2×D227—42no—
74C2×D227—41no—
75C2×D227—84no—
76C4×C227—21no—
77C4×C227—41no—
78C4×C227—82no—
79Dic227—22no—
80Dic227—41no—
81Dic227—82no—
82Dic227#9912yes—
83C2×C227—21no—
84C2×C227—42no—
85C2×C227—81no—
86C2×C227C2×#9911yescharacteristic
87D227—41no—
88D227—81no—
89C227#212811yescharacteristic, complemented, Sylow
90#2128—2271nomaximal, Sylow
91#535—2271no—
92#410—2272no—
93#353—2271no—
94#353—2272no—
95#353D22711yescharacteristic, complemented
96C2×#41—2271no—
97C22×D4—2271no—
98#127—2271no—
99#127C2×D22711yescharacteristic
100#124—2271no—
101#124—2271no—
102#121—4542no—
103#120—4542no—
104#117—4542no—
105#117—2271no—
106#99—4542no—
107#99—2272no—
108#99C2×D22712yescomplemented
109C24—4541no—
110#41—9082no—
111C2×Q8—2271no—
112C2×D4—22no—
113C2×D4—9082no—
114C2×D4—4542no—
115C2×D4—4541no—
116C2×D4—2272no—
117C2×D4—2271no—
118C2×D4C4×D22711yescharacteristic
119C2×D4C22×D22711yescharacteristic
120C22×C4—2272no—
121C22×C4—2271no—
122C4⋊C4—9082no—
123C4⋊C4—4541no—
124C22⋊C4—22no—
125C22⋊C4—4541no—
126C22⋊C4—4542no—
127C22⋊C4—4542no—
128C22⋊C4—4542no—
129C42—9082no—
130C42—2271no—
131C42C4×D22711yescharacteristic
132C23—21no—
133C23—18162no—
134C23—9082no—
135C23—4541no—
136C23—2271no—
137C23D4×D22712yes—
138Q8—9081no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—18162no—
143D4—9081no—
144D4—9082no—
145D4—9082no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—9082no—
149C2×C4—4542no—
150C2×C4—4541no—
151C2×C4—4542no—
152C2×C4—4542no—
153C2×C4—2272no—
154C2×C4—2271no—
155C2×C4C2×C4×D22711yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—18164no—
161C22—9082no—
162C22—9081no—
163C22—9081no—
164C22—4541no—
165C22C22⋊C4×D22711yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—18162no—
170C4—9081no—
171C4—4542no—
172C4—2272no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—18161no—
177C2—9081no—
178C2#99×D22711yescharacteristic
subgroupG/H
centerC2#99×D227
commutatorC2×C4×C227C22×C4
FrattiniC2×D4C22×D227
Fitting#353×C227C2
socleC2×C227C2×#99
prime radical#28409595C2
cosocleC2×D4×C227C23
hypercenter#353D227
hypocenterC227#2128
LCSG ▷ C2×C4×C227 ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #28409004C2semidirect
3. #28408825C2semidirect
4. #28408824C2semidirect
5. #353×C227C2semidirect
7. C2×D4×D227C4semidirect
9. #20300276C4semidirect
10. #20300275C4semidirect
13. #20300245C4semidirect
15. #20300203C22semidirect
18. #99×C227C22semidirect
89. C227#2128semidirect
95. #353D227semidirect
108. #99C2×D227semidirect

Maximal subgroups

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

subgroupindex
#284095952
#284090042
#284088252
#284088242
#353×C2272
#2128227