Finite Group Databasebeta

← #44401396

Subgroups — #44401396

Order 29056.

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

normal subgroups only

This group has 258 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#28409580C211yesmaximal, characteristic
2#28409004C212yesmaximal, complemented
3#28408826C212yesmaximal, complemented
4#28408825C211yesmaximal, characteristic, complemented
5#353×C227C211yesmaximal, characteristic, complemented
6C2×#16813883C411yescharacteristic, complemented
7C2×#16813883C2211yescharacteristic
8#20300288C411yescharacteristic, complemented
9#20300275C411yescharacteristic, complemented
10#20300275C2211yescharacteristic
11#20300259—22no—
12D4×Dic227—22no—
13#20300244—22no—
14C42×D227C411yescharacteristic, complemented
15#20300203C2212yes—
16#20300202—22no—
17#127×C227C2211yescharacteristic
18#99×C227C2212yes—
19#16813883—41no—
20#16813883—41no—
21#16813883—41no—
22#16813883—41no—
23C2×Dic454C2×C411yescharacteristic
24C2×Dic454C2×C411yescharacteristic
25C2×C22⋊D227—21no—
26C2×C22⋊D227D412yes—
27C22×Dic227—21no—
28C22×Dic227D412yes—
29C2×C4×D227—21no—
30C2×C4×D227C2×C411yescharacteristic
31C4⋊Dic227—22no—
32Dic227⋊C4—42no—
33C22⋊Dic227—22no—
34C22⋊Dic227—22no—
35C22⋊Dic227—22no—
36C4×Dic227—21no—
37C4×Dic227—42no—
38C4×Dic227C2×C411yescharacteristic
39C2×D4×C227—22no—
40C2×D4×C227C2×C411yescharacteristic
41C2×D4×C227C2311yescharacteristic
42C22⋊C4×C227—22no—
43C42×C227C2×C411yescharacteristic
44C22×D227C22⋊C411yescharacteristic
45Dic454—41no—
46Dic454—41no—
47C22⋊D227—42no—
48C22⋊D227—42no—
49C2×Dic227—22no—
50C2×Dic227—22no—
51C2×Dic227—21no—
52C2×Dic227—21no—
53C2×Dic227—41no—
54C2×Dic227—41no—
55C2×Dic227—42no—
56C2×Dic227C22⋊C412yes—
57C2×Dic227C22⋊C411yescharacteristic
58C4×D227—21no—
59C4×D227—21no—
60C4×D227—42no—
61C23×C227—21no—
62C23×C227C2×D412yes—
63D4×C227—41no—
64D4×C227—44no—
65D4×C227—41no—
66C2×C4×C227—21no—
67C2×C4×C227—42no—
68C2×C4×C227C22×C411yescharacteristic
69C22×C227—22no—
70C22×C227—42no—
71C22×C227—42no—
72C22×C227—41no—
73C22×C227C2×C22⋊C411yescharacteristic
74C2×D227—21no—
75C2×D227—41no—
76C4×C227—22no—
77C4×C227—21no—
78C4×C227—82no—
79Dic227—22no—
80Dic227—41no—
81Dic227—41no—
82Dic227—82no—
83Dic227#9911yescharacteristic
84Dic227#9911yescharacteristic
85C2×C227—21no—
86C2×C227—42no—
87C2×C227—81no—
88C2×C227C2×#9911yescharacteristic
89D227—41no—
90C227#212611yescharacteristic, complemented, Sylow
91#2126—2271nomaximal, Sylow
92#532—2271no—
93#410—2272no—
94#354—2272no—
95#353—2271no—
96#353D22711yescharacteristic, complemented
97C2×#41—2271no—
98C2×#41—2271no—
99C4⋊Q8—2271no—
100#127C2×D22711yescharacteristic
101#124—2271no—
102#124—2271no—
103#121—4542no—
104C4×D4—4542no—
105#117—4542no—
106C2×C42—2271no—
107#99—4542no—
108#99—2272no—
109#99C2×D22712yes—
110#41—9081no—
111#41—9081no—
112#41—9081no—
113#41—9081no—
114C2×Q8—2271no—
115C2×Q8—2271no—
116C2×D4—22no—
117C2×D4—4541no—
118C2×D4—2272no—
119C2×D4C4×D22711yescharacteristic
120C2×D4C22×D22711yescharacteristic
121C22×C4—4541no—
122C22×C4—4541no—
123C22×C4—2272no—
124C22×C4—2271no—
125C4⋊C4—9082no—
126C4⋊C4—4542no—
127C22⋊C4—22no—
128C22⋊C4—4542no—
129C22⋊C4—4542no—
130C22⋊C4—4542no—
131C42—9082no—
132C42—4541no—
133C42—2271no—
134C42C4×D22711yescharacteristic
135C23—21no—
136C23—2271no—
137C23D4×D22712yes—
138Q8—9081no—
139Q8—9081no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—9082no—
144D4—9082no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—9082no—
148C2×C4—9082no—
149C2×C4—9081no—
150C2×C4—9081no—
151C2×C4—4541no—
152C2×C4—4541no—
153C2×C4—4541no—
154C2×C4—4541no—
155C2×C4—4542no—
156C2×C4—4542no—
157C2×C4—2272no—
158C2×C4—2271no—
159C2×C4C2×C4×D22711yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—9081no—
165C22—4541no—
166C22C22⋊C4×D22711yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—18162no—
171C4—9081no—
172C4—9081no—
173C4—4542no—
174C4—2271no—
175C4—2271no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—9081no—
180C2#99×D22711yescharacteristic
subgroupG/H
centerC2#99×D227
commutatorC2×C4×C227C22×C4
FrattiniC2×D4C22×D227
Fitting#353×C227C2
socleC2×C227C2×#99
prime radical#28409580C2
cosocleC2×D4×C227C23
hypercenter#353D227
hypocenterC227#2126
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. #28408826C2semidirect
4. #28408825C2semidirect
5. #353×C227C2semidirect
6. C2×#16813883C4semidirect
8. #20300288C4semidirect
9. #20300275C4semidirect
14. C42×D227C4semidirect
90. C227#2126semidirect
96. #353D227semidirect

Maximal subgroups

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

subgroupindex
#284095802
#284090042
#284088262
#284088252
#353×C2272
#2126227