Finite Group Databasebeta

← #43244117

Subgroups — #43244117

Order 28096.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#20296330C211yesmaximal, characteristic, complemented
2C22×C4×D439C211yesmaximal, characteristic, complemented
3#28380728C212yesmaximal, complemented
4#28380719C211yesmaximal, characteristic, complemented
5#28380718C211yesmaximal, characteristic, complemented
6#28380717C211yesmaximal, characteristic, complemented
7#28380713C212yesmaximal, complemented
8#28380705C212yesmaximal, complemented
9(C22⋊D439)⋊C4C212yesmaximal, complemented
10#28380701C211yesmaximal, characteristic, complemented
11C22⋊Q8×C439C211yesmaximal, characteristic, complemented
12C23×D439C2211yescharacteristic
13#20296330—24no—
14C2×D1756C2212yes—
15C2×D1756C2212yes—
16C2×D1756C2211yescharacteristic, complemented
17C2×C22⋊D439C2212yes—
18C22×Dic439C2211yescharacteristic
19C2×C4×D439—24no—
20C2×C4×D439C2211yescharacteristic
21C2×C4×D439C2211yescharacteristic
22C2×C4×D439C2211yescharacteristic
23C2×C4×D439C2211yescharacteristic
24C2×C4×D439C2212yescomplemented
25C4⋊Dic439C2211yescharacteristic, complemented
26Dic439⋊C4C2212yescomplemented
27(C2×D439)⋊C4C2212yes—
28(C2×D439)⋊C4C2212yes—
29(C2×D439)⋊C4C2212yescomplemented
30(C2×D439)⋊C4C2212yescomplemented
31C4×Dic439C2212yescomplemented
32C2×Q8×C439C2211yescharacteristic, complemented
33C22×C4×C439C2211yescharacteristic
34C4⋊C4×C439C2211yescharacteristic, complemented
35C4⋊C4×C439C2212yescomplemented
36C22⋊C4×C439C2212yes—
37C22×D439—22no—
38C22×D439—22no—
39C22×D439—22no—
40C22×D439C2312yes—
41C22×D439C2311yescharacteristic
42C22×D439C2311yescharacteristic
43D1756—24no—
44D1756—24no—
45D1756—22no—
46C22⋊D439—24no—
47C2×Dic439—22no—
48C2×Dic439C2312yes—
49C2×Dic439C2311yescharacteristic
50C2×Dic439C2311yescharacteristic
51C4×D439—22no—
52C4×D439—22no—
53C4×D439—22no—
54C4×D439—24no—
55C4×D439D414yescomplemented
56C23×C439C2311yescharacteristic
57Q8×C439—22no—
58C2×C4×C439—22no—
59C2×C4×C439C2312yes—
60C2×C4×C439C2312yes—
61C2×C4×C439C2311yescharacteristic
62C2×C4×C439C2311yescharacteristic
63C22×C439—21no—
64C22×C439—21no—
65C22×C439#4112yescomplemented
66C22×C439C2411yescharacteristic
67C2×D439—28no—
68C2×D439—21no—
69C2×D439—21no—
70C2×D439—21no—
71C2×D439—21no—
72C2×D439—22no—
73C2×D439—22no—
74C2×D439—22no—
75C2×D439C2×D412yes—
76C2×D439#4112yescomplemented
77C4×C439—21no—
78C4×C439—22no—
79C4×C439—22no—
80C4×C439C2×D412yes—
81Dic439—21no—
82Dic439—22no—
83Dic439C2×D412yes—
84C2×C439—22no—
85C2×C439C22×D411yescharacteristic
86C2×C439C2×#4111yescharacteristic
87C2×C439C2×#4111yescharacteristic
88D439—22no—
89D439—22no—
90D439—42no—
91C439#52511yescharacteristic, complemented, Sylow
92#525—4391nomaximal, Sylow
93C2×#41—4391no—
94C23×C4—4391no—
95#123—4392no—
96C22⋊Q8—4391no—
97C22⋊Q8D43911yescharacteristic, complemented
98#121—4391no—
99#121—4391no—
100#120—4392no—
101C4×D4—4392no—
102C4×D4—4392no—
103#117—4391no—
104C24—4391no—
105#41—8784no—
106C2×Q8C2×D43911yescharacteristic, complemented
107C2×D4—4392no—
108C2×D4—4392no—
109C2×D4—4392no—
110C2×D4—4391no—
111C22×C4—8784no—
112C22×C4—4391no—
113C22×C4—4391no—
114C22×C4—4392no—
115C22×C4—4391no—
116C22×C4—4391no—
117C22×C4—4391no—
118C22×C4C2×D43911yescharacteristic
119C4⋊C4—4392no—
120C4⋊C4—4391no—
121C4⋊C4C2×D43911yescharacteristic, complemented
122C4⋊C4C2×D43912yescomplemented
123C22⋊C4—4392no—
124C22⋊C4—4392no—
125C22⋊C4—4392no—
126C22⋊C4—4392no—
127C22⋊C4C2×D43912yes—
128C42—4392no—
129C23—8782no—
130C23—8782no—
131C23—8782no—
132C23—4392no—
133C23—4391no—
134C23—4391no—
135C23C22×D43911yescharacteristic
136Q8—22no—
137D4—8784no—
138D4—8784no—
139D4—8784no—
140D4—8782no—
141C2×C4—22no—
142C2×C4—8782no—
143C2×C4—8782no—
144C2×C4—8784no—
145C2×C4—8782no—
146C2×C4—8782no—
147C2×C4—4392no—
148C2×C4—4391no—
149C2×C4—4391no—
150C2×C4—4394no—
151C2×C4C22×D43912yes—
152C2×C4C22×D43911yescharacteristic
153C2×C4C22×D43912yes—
154C2×C4C22×D43911yescharacteristic
155C22—21no—
156C22—21no—
157C22—8788no—
158C22—8781no—
159C22—8781no—
160C22—8781no—
161C22—8781no—
162C22—8782no—
163C22—8782no—
164C22—8782no—
165C22—4392no—
166C22—4392no—
167C22#2029633012yescomplemented
168C22C23×D43911yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—8781no—
173C4—8782no—
174C4—4392no—
175C4D4×D43912yes—
176C2—22no—
177C2—8782no—
178C2—8782no—
179C2—17562no—
180C2C2×D4×D43911yescharacteristic
181C2#41×D43911yescharacteristic
182C2C2×#2029633011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D439
commutator, socle, cosocleC22×C439C24
FittingC22⋊Q8×C439C2
hypercenterC22⋊Q8D439
hypocenterC439#525
LCSG ▷ C22×C439 ▷ C439
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#20296330C2semidirect
2. C22×C4×D439C2semidirect
3. #28380728C2semidirect
4. #28380719C2semidirect
5. #28380718C2semidirect
6. #28380717C2semidirect
7. #28380713C2semidirect
8. #28380705C2semidirect
9. (C22⋊D439)⋊C4C2semidirect
10. #28380701C2semidirect
11. C22⋊Q8×C439C2semidirect
16. C2×D1756C22semidirect
24. C2×C4×D439C22semidirect
25. C4⋊Dic439C22semidirect
26. Dic439⋊C4C22semidirect
29. (C2×D439)⋊C4C22semidirect
30. (C2×D439)⋊C4C22semidirect
31. C4×Dic439C22semidirect
32. C2×Q8×C439C22semidirect
34. C4⋊C4×C439C22semidirect
35. C4⋊C4×C439C22semidirect
55. C4×D439D4semidirect
65. C22×C439#41semidirect
76. C2×D439#41semidirect
91. C439#525semidirect
97. C22⋊Q8D439semidirect
106. C2×Q8C2×D439semidirect
121. C4⋊C4C2×D439semidirect
122. C4⋊C4C2×D439semidirect
167. C22#20296330semidirect

Maximal subgroups

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

subgroupindex
C2×#202963302
C22×C4×D4392
#283807282
#283807192
#283807182
#283807172
#283807132
#283807052
(C22⋊D439)⋊C42
#283807012
C22⋊Q8×C4392
#525439