Finite Group Databasebeta

← #14580980

Subgroups — #14580980

Order 2624.

334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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×#10620308C211yesmaximal, characteristic, complemented
2#13050151C211yesmaximal, characteristic, complemented
3#13050145C212yesmaximal, complemented
4#13050143C211yesmaximal, characteristic, complemented
5#13050136C212yesmaximal, complemented
6#13050135C211yesmaximal, characteristic, complemented
7#13050133C212yesmaximal, complemented
8D4×Dic41C211yesmaximal, characteristic, complemented
9C4×C22⋊D41C211yesmaximal, characteristic, complemented
10C2×C22⋊Dic41C212yesmaximal, complemented
11C22×D4×C41C211yesmaximal, characteristic, complemented
12C24×C41C2212yes—
13C2×D4×C41—24no—
14C2×D4×C41C2211yescharacteristic
15C2×D4×C41C2212yes—
16C2×D4×C41C2211yescharacteristic
17C22×C4×C41C2211yescharacteristic
18C2×C22⋊D41C2211yescharacteristic
19C2×C22⋊D41C2212yescomplemented
20C2×C22⋊D41C2212yescomplemented
21C22×Dic41C2212yescomplemented
22C22×Dic41C2212yescomplemented
23#10620308—24no—
24C2×C4×D41C2211yescharacteristic, complemented
25C2×Dic82C2211yescharacteristic, complemented
26C22⋊Dic41C2211yescharacteristic
27C22⋊Dic41C2212yes—
28C22⋊Dic41C2212yescomplemented
29C22⋊Dic41C2212yescomplemented
30C22⋊Dic41C2212yescomplemented
31C22⋊Dic41C2212yescomplemented
32#10620281C2211yescharacteristic, complemented
33C4⋊Dic41C2211yescharacteristic, complemented
34#10620279C2211yescharacteristic, complemented
35#10620279C2212yescomplemented
36C4×Dic41C2211yescharacteristic, complemented
37C23×C41—24no—
38C23×C41—24no—
39C23×C41—42no—
40C23×C41C2312yes—
41C23×C41C2312yes—
42C23×C41C2311yescharacteristic
43C22×D41C2311yescharacteristic
44D4×C41—24no—
45D4×C41—22no—
46D4×C41D414yescomplemented
47C2×C4×C41—22no—
48C2×C4×C41C2311yescharacteristic
49C2×C4×C41C2311yescharacteristic
50C22⋊D41—24no—
51C22⋊D41—22no—
52C22⋊D41—42no—
53C2×Dic41—24no—
54C2×Dic41—42no—
55C2×Dic41C2311yescharacteristic
56C2×Dic41C2311yescharacteristic
57C2×Dic41C2312yes—
58C2×Dic41C2312yes—
59C2×Dic41C2311yescharacteristic
60C4×D41—22no—
61Dic82—22no—
62C22×C41—21no—
63C22×C41—22no—
64C22×C41—22no—
65C22×C41—21no—
66C22×C41—22no—
67C22×C41—22no—
68C22×C41—22no—
69C22×C41—48no—
70C22×C41C2×D414yes—
71C22×C41#4112yescomplemented
72C22×C41C2411yescharacteristic
73C2×D41—21no—
74C2×D41—21no—
75C2×D41—21no—
76C4×C41—21no—
77C4×C41C2×D412yes—
78Dic41—22no—
79Dic41—21no—
80Dic41—21no—
81Dic41—21no—
82Dic41—22no—
83C2×C41—22no—
84C2×C41—24no—
85C2×C41—42no—
86C2×C41C22×D411yescharacteristic
87C2×C41C2×#4111yescharacteristic
88C2×C41H(5,𝔽2)11yescharacteristic
89D41—41no—
90#546—411nomaximal, Sylow
91C41#54611yescharacteristic, complemented, Sylow
92C2×#41—411no—
93C22×D4D4111yescharacteristic, complemented
94#124—411no—
95#123—412no—
96C22⋊Q8—411no—
97#121—411no—
98#121—412no—
99#120—412no—
100C4×D4—411no—
101C4×D4—411no—
102C2×C22⋊C4—412no—
103C24C2×D4112yes—
104#41—824no—
105C2×Q8—411no—
106C2×D4—24no—
107C2×D4—411no—
108C2×D4—412no—
109C2×D4—412no—
110C2×D4C2×D4112yes—
111C2×D4C2×D4111yescharacteristic
112C2×D4C2×D4111yescharacteristic
113C22×C4—412no—
114C22×C4—412no—
115C22×C4—411no—
116C22×C4C2×D4111yescharacteristic
117C4⋊C4—411no—
118C4⋊C4—411no—
119C4⋊C4—412no—
120C22⋊C4—411no—
121C22⋊C4—412no—
122C22⋊C4—412no—
123C22⋊C4—412no—
124C22⋊C4—412no—
125C22⋊C4—412no—
126C22⋊C4—411no—
127C42—411no—
128C23—24no—
129C23—24no—
130C23—42no—
131C23—411no—
132C23C22×D4112yes—
133C23C22×D4111yescharacteristic
134C23C22×D4112yes—
135Q8—822no—
136D4—24no—
137D4—22no—
138D4—822no—
139D4—824no—
140D4—1642no—
141D4C22⋊D4114yescomplemented
142C2×C4—22no—
143C2×C4—411no—
144C2×C4—411no—
145C2×C4—412no—
146C2×C4—411no—
147C2×C4—412no—
148C2×C4—824no—
149C2×C4—822no—
150C2×C4—1642no—
151C2×C4C22×D4111yescharacteristic
152C2×C4C22×D4111yescharacteristic
153C22—21no—
154C22—22no—
155C22—22no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—48no—
161C22—821no—
162C22—821no—
163C22—821no—
164C22#1062030812yescomplemented
165C22C2×C22⋊D4114yes—
166C22C23×D4111yescharacteristic
167C4—21no—
168C4—821no—
169C4—822no—
170C4—821no—
171C4—821no—
172C4—822no—
173C4C2×C22⋊D4112yes—
174C2—22no—
175C2—24no—
176C2—42no—
177C2—1641no—
178C2C22×C22⋊D4111yescharacteristic
179C2C2×#1062030811yescharacteristic
180C2#1305020911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
FittingC22×D4×C41C2
hypercenterC22×D4D41
hypocenterC41#546
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10620308C2semidirect
2. #13050151C2semidirect
3. #13050145C2semidirect
4. #13050143C2semidirect
5. #13050136C2semidirect
6. #13050135C2semidirect
7. #13050133C2semidirect
8. D4×Dic41C2semidirect
9. C4×C22⋊D41C2semidirect
10. C2×C22⋊Dic41C2semidirect
11. C22×D4×C41C2semidirect
19. C2×C22⋊D41C22semidirect
20. C2×C22⋊D41C22semidirect
21. C22×Dic41C22semidirect
22. C22×Dic41C22semidirect
24. C2×C4×D41C22semidirect
25. C2×Dic82C22semidirect
28. C22⋊Dic41C22semidirect
29. C22⋊Dic41C22semidirect
30. C22⋊Dic41C22semidirect
31. C22⋊Dic41C22semidirect
32. #10620281C22semidirect
33. C4⋊Dic41C22semidirect
34. #10620279C22semidirect
35. #10620279C22semidirect
36. C4×Dic41C22semidirect
46. D4×C41D4semidirect
71. C22×C41#41semidirect
91. C41#546semidirect
93. C22×D4D41semidirect
141. D4C22⋊D41semidirect
164. C22#10620308semidirect

Maximal subgroups

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

subgroupindex
C2×#106203082
#130501512
#130501452
#130501432
#130501362
#130501352
#130501332
D4×Dic412
C4×C22⋊D412
C2×C22⋊Dic412
C22×D4×C412
#54641