Finite Group Databasebeta

← #43244112

Subgroups — #43244112

Order 28096.

330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#20296328C211yesmaximal, characteristic, complemented
2C22×C4×D439C211yesmaximal, characteristic, complemented
3#28380726C211yesmaximal, characteristic, complemented
4#28380721C212yesmaximal, complemented
5#28380716C212yesmaximal, complemented
6#28380713C211yesmaximal, characteristic, complemented
7#28380711C211yesmaximal, characteristic, complemented
8#28380705C212yesmaximal, complemented
9(C22⋊D439)⋊C4C212yesmaximal, complemented
10#28380699C211yesmaximal, characteristic, complemented
11#123×C439C211yesmaximal, characteristic, complemented
12C23×D439C2211yescharacteristic
13#20296328—24no—
14C2×Dic878C2211yescharacteristic, complemented
15C2×D1756C2212yes—
16C2×C22⋊D439C2212yes—
17C2×C22⋊D439C2211yescharacteristic
18C2×C22⋊D439C2211yescharacteristic, complemented
19C22×Dic439C2211yescharacteristic
20C22×Dic439C2211yescharacteristic, complemented
21C2×C4×D439—24no—
22C2×C4×D439C2212yes—
23C2×C4×D439C2212yes—
24C2×C4×D439C2211yescharacteristic, complemented
25Dic439⋊C4C2212yescomplemented
26Dic439⋊C4C2212yescomplemented
27C22⋊Dic439C2211yescharacteristic
28(C2×D439)⋊C4C2212yes—
29(C2×D439)⋊C4C2212yes—
30(C2×D439)⋊C4C2212yescomplemented
31C4×Dic439C2212yescomplemented
32C2×D4×C439C2211yescharacteristic
33C22×C4×C439C2211yescharacteristic
34C4⋊C4×C439C2212yescomplemented
35C22⋊C4×C439C2211yescharacteristic
36C22⋊C4×C439C2212yescomplemented
37C22×D439—22no—
38C22×D439—24no—
39C22×D439C2311yescharacteristic
40C22×D439C2312yes—
41Dic878—22no—
42D1756—24no—
43C22⋊D439—22no—
44C22⋊D439—24no—
45C22⋊D439—22no—
46C2×Dic439—22no—
47C2×Dic439D414yescomplemented
48C2×Dic439C2312yes—
49C2×Dic439C2311yescharacteristic
50C2×Dic439C2311yescharacteristic
51C2×Dic439C2311yescharacteristic
52C4×D439—24no—
53C4×D439—24no—
54C4×D439—22no—
55C23×C439C2311yescharacteristic
56C23×C439C2311yescharacteristic
57D4×C439—22no—
58C2×C4×C439—22no—
59C2×C4×C439C2312yes—
60C2×C4×C439C2312yes—
61C2×C4×C439C2311yescharacteristic
62C22×C439—22no—
63C22×C439—21no—
64C22×C439—22no—
65C22×C439C2×D412yes—
66C22×C439C2411yescharacteristic
67C2×D439—28no—
68C2×D439—22no—
69C2×D439—22no—
70C2×D439—21no—
71C2×D439—22no—
72C2×D439#4114yescomplemented
73C4×C439—22no—
74C4×C439—21no—
75C4×C439—22no—
76Dic439—21no—
77Dic439—22no—
78Dic439C2×D412yes—
79Dic439C2×D412yes—
80C2×C439—22no—
81C2×C439—41no—
82C2×C439C22×D411yescharacteristic
83C2×C439C2×#4112yes—
84D439—24no—
85D439—41no—
86C439#52511yescharacteristic, complemented, Sylow
87#525—4391nomaximal, Sylow
88C2×#41—4391no—
89C23×C4—4391no—
90#123—4391no—
91#123D43911yescharacteristic, complemented
92C22⋊Q8—4392no—
93#121—4392no—
94#120—4391no—
95#120—4391no—
96C4×D4—4392no—
97C4×D4—4392no—
98#117—4391no—
99C24—4391no—
100#41—8784no—
101C2×Q8—4391no—
102C2×D4—4392no—
103C2×D4—4391no—
104C2×D4—4391no—
105C2×D4—4392no—
106C2×D4C2×D43911yescharacteristic
107C22×C4—8784no—
108C22×C4—4391no—
109C22×C4—4392no—
110C22×C4—4391no—
111C22×C4—4392no—
112C22×C4—4391no—
113C22×C4C2×D43911yescharacteristic
114C4⋊C4—4392no—
115C4⋊C4—4392no—
116C4⋊C4C2×D43912yescomplemented
117C22⋊C4—4391no—
118C22⋊C4—4392no—
119C22⋊C4—4392no—
120C22⋊C4—4392no—
121C22⋊C4C2×D43911yescharacteristic
122C22⋊C4C2×D43912yescomplemented
123C42—4392no—
124C23—8784no—
125C23—8782no—
126C23—4391no—
127C23—4392no—
128C23C22×D43911yescharacteristic
129C23C22×D43911yescharacteristic
130Q8—8782no—
131D4—22no—
132D4—8784no—
133D4—8784no—
134D4—8782no—
135D4—8782no—
136C2×C4—22no—
137C2×C4—8784no—
138C2×C4—8784no—
139C2×C4—8782no—
140C2×C4—8782no—
141C2×C4—4392no—
142C2×C4—4391no—
143C2×C4—4394no—
144C2×C4—4391no—
145C2×C4—4391no—
146C2×C4C22×D43912yes—
147C2×C4C22×D43911yescharacteristic
148C2×C4C22×D43912yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—8788no—
153C22—8782no—
154C22—8782no—
155C22—8781no—
156C22—8782no—
157C22—4394no—
158C22D4×D43912yes—
159C22C23×D43911yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—8781no—
164C4—8782no—
165C4—4392no—
166C4—4392no—
167C2—22no—
168C2—41no—
169C2—8784no—
170C2—17561no—
171C2C2×D4×D43911yescharacteristic
172C2#41×D43912yes—
subgroupG/H
center, FrattiniC22C23×D439
commutator, socle, cosocleC22×C439C24
Fitting#123×C439C2
hypercenter#123D439
hypocenterC439#525
LCSG ▷ C22×C439 ▷ C439
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#20296328C2semidirect
2. C22×C4×D439C2semidirect
3. #28380726C2semidirect
4. #28380721C2semidirect
5. #28380716C2semidirect
6. #28380713C2semidirect
7. #28380711C2semidirect
8. #28380705C2semidirect
9. (C22⋊D439)⋊C4C2semidirect
10. #28380699C2semidirect
11. #123×C439C2semidirect
14. C2×Dic878C22semidirect
18. C2×C22⋊D439C22semidirect
20. C22×Dic439C22semidirect
24. C2×C4×D439C22semidirect
25. Dic439⋊C4C22semidirect
26. Dic439⋊C4C22semidirect
30. (C2×D439)⋊C4C22semidirect
31. C4×Dic439C22semidirect
34. C4⋊C4×C439C22semidirect
36. C22⋊C4×C439C22semidirect
47. C2×Dic439D4semidirect
72. C2×D439#41semidirect
86. C439#525semidirect
91. #123D439semidirect
116. C4⋊C4C2×D439semidirect
122. C22⋊C4C2×D439semidirect

Maximal subgroups

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

subgroupindex
C2×#202963282
C22×C4×D4392
#283807262
#283807212
#283807162
#283807132
#283807112
#283807052
(C22⋊D439)⋊C42
#283806992
#123×C4392
#525439