Finite Group Databasebeta

← #14580979

Subgroups — #14580979

Order 2624.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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×#10620310C211yesmaximal, characteristic, complemented
2C2×D4×D41C211yesmaximal, characteristic, complemented
3#13050146C212yesmaximal, complemented
4#13050140C211yesmaximal, characteristic, complemented
5#13050137C212yesmaximal, complemented
6#13050135C211yesmaximal, characteristic, complemented
7#13050134C212yesmaximal, complemented
8C4×D164C211yesmaximal, characteristic, complemented
9C4×D164C211yesmaximal, characteristic, complemented
10C22⋊C4×D41C212yesmaximal, complemented
11#124×C41C211yesmaximal, characteristic, complemented
12C23×D41C2212yes—
13C2×Q8×C41C2211yescharacteristic, complemented
14C2×D4×C41C2211yescharacteristic
15C2×C22⋊D41C2212yes—
16C2×C22⋊D41C2212yescomplemented
17#10620310—24no—
18D4×D41—24no—
19C2×D164C2211yescharacteristic
20C2×D164C2211yescharacteristic
21C2×D164C2212yescomplemented
22C2×C4×D41C2211yescharacteristic
23C2×C4×D41C2212yescomplemented
24C2×C4×D41C2211yescharacteristic, complemented
25C2×C4×D41C2212yescomplemented
26C22⋊C4×C41C2212yescomplemented
27C22⋊C4×C41C2212yescomplemented
28C42×C41C2211yescharacteristic, complemented
29C22⋊Dic41C2212yescomplemented
30#10620281C2211yescharacteristic
31#10620281C2212yes—
32#10620281C2212yescomplemented
33#10620281C2211yescharacteristic, complemented
34C4⋊Dic41C2211yescharacteristic, complemented
35C4⋊Dic41C2211yescharacteristic, complemented
36#10620279C2212yescomplemented
37C23×C41C2312yes—
38C22×D41—24no—
39C22×D41—24no—
40C22×D41—42no—
41C22×D41C2311yescharacteristic
42C22×D41C2312yes—
43C22×D41C2311yescharacteristic
44Q8×C41—22no—
45D4×C41—22no—
46C2×C4×C41C2312yes—
47C2×C4×C41C2311yescharacteristic
48C2×C4×C41C2311yescharacteristic
49C2×C4×C41C2311yescharacteristic
50C22⋊D41—24no—
51C22⋊D41—42no—
52C2×Dic41C2311yescharacteristic
53C2×Dic41C2312yes—
54C2×Dic41C2311yescharacteristic
55D164—24no—
56D164—22no—
57D164D414yescomplemented
58C4×D41—24no—
59C4×D41—22no—
60C4×D41—22no—
61C4×D41—42no—
62C22×C41—22no—
63C22×C41—22no—
64C22×C41—22no—
65C22×C41C2411yescharacteristic
66C2×D41—21no—
67C2×D41—22no—
68C2×D41—22no—
69C2×D41—21no—
70C2×D41—21no—
71C2×D41—21no—
72C2×D41—21no—
73C2×D41—48no—
74C2×D41C2×D414yes—
75C2×D41#4112yescomplemented
76C4×C41—22no—
77C4×C41—21no—
78C4×C41—21no—
79C4×C41C2×D412yes—
80Dic41—21no—
81Dic41—21no—
82Dic41—22no—
83C2×C41—42no—
84C2×C41C22×D411yescharacteristic
85C2×C41C2×#4111yescharacteristic
86C2×C41H(5,𝔽2)11yescharacteristic
87D41—22no—
88D41—24no—
89D41—41no—
90#546—411nomaximal, Sylow
91C41#54611yescharacteristic, complemented, Sylow
92C2×#41—411no—
93C22×D4—411no—
94#124D4111yescharacteristic, complemented
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—
103C24—412no—
104#41—824no—
105C2×Q8C2×D4111yescharacteristic, complemented
106C2×D4—412no—
107C2×D4—412no—
108C2×D4—411no—
109C2×D4—411no—
110C2×D4—412no—
111C2×D4—824no—
112C2×D4C2×D4111yescharacteristic
113C22×C4—412no—
114C22×C4—411no—
115C22×C4—411no—
116C22×C4—412no—
117C4⋊C4—411no—
118C4⋊C4—411no—
119C4⋊C4—412no—
120C22⋊C4—412no—
121C22⋊C4—411no—
122C22⋊C4—412no—
123C22⋊C4—412no—
124C22⋊C4—411no—
125C22⋊C4C2×D4112yescomplemented
126C22⋊C4C2×D4112yescomplemented
127C42C2×D4111yescharacteristic, complemented
128C23—411no—
129C23—412no—
130C23—411no—
131C23—824no—
132C23—824no—
133C23—1642no—
134C23C22×D4112yes—
135Q8—22no—
136D4—22no—
137D4—414no—
138D4—824no—
139D4—822no—
140D4—824no—
141D4—1642no—
142C2×C4—412no—
143C2×C4—411no—
144C2×C4—411no—
145C2×C4—824no—
146C2×C4—822no—
147C2×C4—822no—
148C2×C4—1642no—
149C2×C4C22×D4111yescharacteristic
150C2×C4C22×D4111yescharacteristic
151C2×C4C22×D4112yes—
152C2×C4C22×D4111yescharacteristic
153C22—22no—
154C22—22no—
155C22—22no—
156C22—414no—
157C22—412no—
158C22—821no—
159C22—822no—
160C22—822no—
161C22—821no—
162C22—821no—
163C22—821no—
164C22—821no—
165C22—1648no—
166C22C23×D4111yescharacteristic
167C4—22no—
168C4—21no—
169C4—21no—
170C4—821no—
171C4—821no—
172C4—822no—
173C4D4×D4112yes—
174C2—42no—
175C2—822no—
176C2—824no—
177C2—1641no—
178C2C2×D4×D4111yescharacteristic
179C2#41×D4111yescharacteristic
180C2#1305021011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
Fitting#124×C41C2
hypercenter#124D41
hypocenterC41#546
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#10620310C2semidirect
2. C2×D4×D41C2semidirect
3. #13050146C2semidirect
4. #13050140C2semidirect
5. #13050137C2semidirect
6. #13050135C2semidirect
7. #13050134C2semidirect
8. C4×D164C2semidirect
9. C4×D164C2semidirect
10. C22⋊C4×D41C2semidirect
11. #124×C41C2semidirect
13. C2×Q8×C41C22semidirect
16. C2×C22⋊D41C22semidirect
21. C2×D164C22semidirect
23. C2×C4×D41C22semidirect
24. C2×C4×D41C22semidirect
25. C2×C4×D41C22semidirect
26. C22⋊C4×C41C22semidirect
27. C22⋊C4×C41C22semidirect
28. C42×C41C22semidirect
29. C22⋊Dic41C22semidirect
32. #10620281C22semidirect
33. #10620281C22semidirect
34. C4⋊Dic41C22semidirect
35. C4⋊Dic41C22semidirect
36. #10620279C22semidirect
57. D164D4semidirect
75. C2×D41#41semidirect
91. C41#546semidirect
94. #124D41semidirect
105. C2×Q8C2×D41semidirect
125. C22⋊C4C2×D41semidirect
126. C22⋊C4C2×D41semidirect
127. C42C2×D41semidirect

Maximal subgroups

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

subgroupindex
C2×#106203102
C2×D4×D412
#130501462
#130501402
#130501372
#130501352
#130501342
C4×D1642
C22⋊C4×D412
#124×C412
#54641