Finite Group Databasebeta

← #44401398

Subgroups — #44401398

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#28409581C211yesmaximal, characteristic
2#28409004C212yesmaximal, complemented
3#28408827C211yesmaximal, characteristic, complemented
4#28408824C212yesmaximal, complemented
5#354×C227C211yesmaximal, characteristic, complemented
6C2×#16813885C411yescharacteristic, complemented
7C2×#16813883C2211yescharacteristic
8#20300286C411yescharacteristic, complemented
9#20300284C2211yescharacteristic
10#20300276C411yescharacteristic, complemented
11#20300261—22no—
12(C22⋊D227)⋊C4—22no—
13#20300244—22no—
14C42×D227C411yescharacteristic, complemented
15#20300203C2212yes—
16#20300202—22no—
17#124×C227C2211yescharacteristic
18#99×C227C2212yes—
19#16813885—41no—
20#16813885—41no—
21#16813883—41no—
22#16813883—41no—
23C2×Dic454C2×C411yescharacteristic
24C2×D908—21no—
25C2×D908C2×C411yescharacteristic
26C2×C22⋊D227—22no—
27C2×C22⋊D227D412yes—
28C22×Dic227D412yes—
29C2×C4×D227—21no—
30C2×C4×D227—21no—
31C2×C4×D227C2×C411yescharacteristic
32Dic227⋊C4—22no—
33Dic227⋊C4—42no—
34C22⋊Dic227—22no—
35(C2×D227)⋊C4—22no—
36C4×Dic227—21no—
37C4×Dic227—42no—
38C4×Dic227C2×C411yescharacteristic
39C2×Q8×C227C2×C411yescharacteristic
40C2×D4×C227C2311yescharacteristic
41C22⋊C4×C227—22no—
42C22⋊C4×C227—22no—
43C42×C227C2×C411yescharacteristic
44C22×D227—21no—
45C22×D227C22⋊C411yescharacteristic
46Dic454—41no—
47D908—41no—
48D908—42no—
49C22⋊D227—42no—
50C22⋊D227—44no—
51C2×Dic227—21no—
52C2×Dic227—22no—
53C2×Dic227—22no—
54C2×Dic227—42no—
55C2×Dic227C22⋊C412yes—
56C2×Dic227C22⋊C411yescharacteristic
57C4×D227—21no—
58C4×D227—21no—
59C4×D227—42no—
60C4×D227—41no—
61C4×D227—41no—
62C23×C227C2×D412yes—
63Q8×C227—41no—
64D4×C227—41no—
65C2×C4×C227—21no—
66C2×C4×C227—21no—
67C2×C4×C227—42no—
68C2×C4×C227C22×C411yescharacteristic
69C22×C227—22no—
70C22×C227—42no—
71C22×C227C2×C22⋊C411yescharacteristic
72C2×D227—21no—
73C2×D227—41no—
74C2×D227—42no—
75C2×D227—41no—
76C4×C227—21no—
77C4×C227—41no—
78C4×C227—41no—
79C4×C227—82no—
80Dic227—22no—
81Dic227—22no—
82Dic227—82no—
83Dic227#9911yescharacteristic
84Dic227#9911yescharacteristic
85C2×C227—21no—
86C2×C227—42no—
87C2×C227C2×#9911yescharacteristic
88D227—41no—
89D227—81no—
90C227#212611yescharacteristic, complemented, Sylow
91#2126—2271nomaximal, Sylow
92#532—2271no—
93#410—2272no—
94#354—2271no—
95#354D22711yescharacteristic, complemented
96#353—2272no—
97C2×#41—2271no—
98C2×#41—2271no—
99C4⋊Q8—2271no—
100#127—2271no—
101#124—2271no—
102#124C2×D22711yescharacteristic
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×Q8C4×D22711yescharacteristic
116C2×D4—4541no—
117C2×D4—4542no—
118C2×D4—2272no—
119C2×D4—2271no—
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—22no—
129C22⋊C4—4542no—
130C22⋊C4—4542no—
131C42—9082no—
132C42—4541no—
133C42—2271no—
134C42C4×D22711yescharacteristic
135C23—4541no—
136C23—2271no—
137C23D4×D22712yes—
138Q8—41no—
139Q8—9081no—
140D4—41no—
141D4—9081no—
142D4—9082no—
143D4—9082no—
144D4—9084no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—9082no—
149C2×C4—9081no—
150C2×C4—9081no—
151C2×C4—9082no—
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—9082no—
163C22—9081no—
164C22—9081no—
165C22—4541no—
166C22C22⋊C4×D22711yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—18162no—
172C4—4542no—
173C4—4542no—
174C4—2271no—
175C4—2271no—
176C2—21no—
177C2—42no—
178C2—18161no—
179C2—9081no—
180C2#99×D22711yescharacteristic
subgroupG/H
centerC2#99×D227
commutatorC2×C4×C227C22×C4
FrattiniC2×D4C22×D227
Fitting#354×C227C2
socleC2×C227C2×#99
prime radical#28409581C2
cosocleC2×D4×C227C23
hypercenter#354D227
hypocenterC227#2126
LCSG ▷ C2×C4×C227 ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #28409004C2semidirect
3. #28408827C2semidirect
4. #28408824C2semidirect
5. #354×C227C2semidirect
6. C2×#16813885C4semidirect
8. #20300286C4semidirect
10. #20300276C4semidirect
14. C42×D227C4semidirect
90. C227#2126semidirect
95. #354D227semidirect

Maximal subgroups

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

subgroupindex
#284095812
#284090042
#284088272
#284088242
#354×C2272
#2126227