Finite Group Databasebeta

← #46830647

Subgroups — #46830647

Order 34624.

338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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×D4×D541C211yesmaximal, characteristic
2C4×D2164C211yesmaximal, characteristic, complemented
3D4×Dic541C211yesmaximal, characteristic, complemented
4#31772590C211yesmaximal, characteristic, complemented
5C4×C22⋊D541C212yesmaximal, complemented
6#31772588C212yesmaximal, complemented
7#31772586C211yesmaximal, characteristic, complemented
8#31772585C211yesmaximal, characteristic, complemented
9C2×#22575813C212yesmaximal, complemented
10C22⋊C4×D541C212yesmaximal, complemented
11C4×D4×C541C211yesmaximal, characteristic, complemented
12C23×D541C2212yes—
13C2×D2164C2211yescharacteristic
14C2×C22⋊D541C2212yes—
15D4×D541C418yescomplemented
16C22×Dic541C2212yescomplemented
17C2×C4×D541C2211yescharacteristic
18C2×C4×D541C2212yescomplemented
19C2×C4×D541C2212yescomplemented
20C4⋊Dic541C2211yescharacteristic, complemented
21#22575815C2211yescharacteristic, complemented
22#22575815C2211yescharacteristic, complemented
23C22⋊Dic541C2212yescomplemented
24#22575813C2211yescharacteristic
25#22575813C2212yes—
26#22575813C2211yescharacteristic
27#22575813C2212yescomplemented
28#22575813C2212yescomplemented
29C4×Dic541C2211yescharacteristic, complemented
30C4×Dic541C2212yescomplemented
31C2×D4×C541C2211yescharacteristic
32C22×C4×C541C2212yescomplemented
33C4⋊C4×C541C2211yescharacteristic, complemented
34C22⋊C4×C541C2212yescomplemented
35C42×C541C2211yescharacteristic, complemented
36C22×D541—42no—
37C22×D541—42no—
38C22×D541C2×C418yescomplemented
39C22×D541C2311yescharacteristic
40C22×D541C2312yes—
41D2164C2×C414yescomplemented
42C22⋊D541C2×C418yescomplemented
43C2×Dic541—42no—
44C2×Dic541C2311yescharacteristic
45C2×Dic541C2312yes—
46C2×Dic541C2311yescharacteristic
47C2×Dic541C2311yescharacteristic
48C4×D541—42no—
49C4×D541—42no—
50C4×D541C2×C414yescomplemented
51C23×C541C2312yes—
52D4×C541C2×C414yescomplemented
53C2×C4×C541—42no—
54C2×C4×C541C2311yescharacteristic
55C2×C4×C541C2311yescharacteristic
56C2×C4×C541C2312yes—
57C2×C4×C541C2311yescharacteristic
58C22×C541—22no—
59C22×C541—22no—
60C22×C541C22×C414yes—
61C22×C541C2411yescharacteristic
62C2×D541—22no—
63C2×D541—22no—
64C2×D541—21no—
65C2×D541—21no—
66C2×D541—48no—
67C2×D541C22×C412yes—
68C2×D541C22×C414yes—
69C4×C541—21no—
70C4×C541—22no—
71C4×C541—21no—
72C4×C541C22×C412yes—
73Dic541—21no—
74Dic541—22no—
75Dic541—21no—
76Dic541C22×C412yes—
77C2×C541—24no—
78C2×C541C23×C411yescharacteristic
79C2×C541H(5,𝔽2)11yescharacteristic
80C2×C541H(5,𝔽2)11yescharacteristic
81D541—22no—
82D541—24no—
83C541#51811yescharacteristic, complemented, Sylow
84#518—5411nomaximal, Sylow
85C22×D4—5411no—
86C4×D4—5411no—
87C4×D4—5412no—
88C4×D4—5411no—
89C4×D4—5412no—
90C4×D4—5411no—
91C4×D4D54111yescharacteristic, complemented
92#117—5411no—
93#117—5411no—
94C2×C22⋊C4—5412no—
95C2×C22⋊C4—5412no—
96C24—5412no—
97C2×D4—5412no—
98C2×D4—5418no—
99C2×D4—5411no—
100C2×D4C2×D54111yescharacteristic
101C22×C4—5411no—
102C22×C4—5412no—
103C22×C4—5412no—
104C22×C4—5412no—
105C22×C4C2×D54112yescomplemented
106C4⋊C4—5411no—
107C4⋊C4—5411no—
108C4⋊C4—5411no—
109C4⋊C4C2×D54111yescharacteristic, complemented
110C22⋊C4—5412no—
111C22⋊C4—5412no—
112C22⋊C4—5411no—
113C22⋊C4—5411no—
114C22⋊C4—5412no—
115C22⋊C4—5412no—
116C22⋊C4C2×D54112yescomplemented
117C42—5412no—
118C42—5411no—
119C42C2×D54111yescharacteristic, complemented
120C23—5411no—
121C23—5412no—
122C23—5418no—
123C23—21642no—
124C23—21642no—
125C23C22×D54112yes—
126D4—5418no—
127D4—5414no—
128D4C4×D54114yescomplemented
129C2×C4—42no—
130C2×C4—5411no—
131C2×C4—5414no—
132C2×C4—5411no—
133C2×C4—5411no—
134C2×C4—5412no—
135C2×C4—21642no—
136C2×C4—21642no—
137C2×C4—21642no—
138C2×C4C22×D54112yes—
139C2×C4C22×D54111yescharacteristic
140C2×C4C22×D54111yescharacteristic
141C2×C4C22×D54111yescharacteristic
142C22—22no—
143C22—22no—
144C22—5412no—
145C22—5414no—
146C22—10822no—
147C22—10821no—
148C22—10822no—
149C22—10821no—
150C22—21648no—
151C22C2×C4×D54114yes—
152C22C23×D54111yescharacteristic
153C4—21no—
154C4—22no—
155C4—21no—
156C4—5412no—
157C4—10821no—
158C4—10822no—
159C4—10821no—
160C4C2×C4×D54112yes—
161C2—24no—
162C2—10822no—
163C2—10824no—
164C2C22×C4×D54111yescharacteristic
165C2#3177267311yescharacteristic
166C2#3177267411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D541
commutatorC2×C541C23×C4
FittingC4×D4×C541C2
socle, cosocleC22×C541C24
prime radicalC2×D4×D541C2
hypercenterC4×D4D541
hypocenterC541#518
LCSG ▷ C2×C541 ▷ C541
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D2164C2semidirect
3. D4×Dic541C2semidirect
4. #31772590C2semidirect
5. C4×C22⋊D541C2semidirect
6. #31772588C2semidirect
7. #31772586C2semidirect
8. #31772585C2semidirect
9. C2×#22575813C2semidirect
10. C22⋊C4×D541C2semidirect
11. C4×D4×C541C2semidirect
15. D4×D541C4semidirect
16. C22×Dic541C22semidirect
18. C2×C4×D541C22semidirect
19. C2×C4×D541C22semidirect
20. C4⋊Dic541C22semidirect
21. #22575815C22semidirect
22. #22575815C22semidirect
23. C22⋊Dic541C22semidirect
27. #22575813C22semidirect
28. #22575813C22semidirect
29. C4×Dic541C22semidirect
30. C4×Dic541C22semidirect
32. C22×C4×C541C22semidirect
33. C4⋊C4×C541C22semidirect
34. C22⋊C4×C541C22semidirect
35. C42×C541C22semidirect
38. C22×D541C2×C4semidirect
41. D2164C2×C4semidirect
42. C22⋊D541C2×C4semidirect
50. C4×D541C2×C4semidirect
52. D4×C541C2×C4semidirect
83. C541#518semidirect
91. C4×D4D541semidirect
105. C22×C4C2×D541semidirect
109. C4⋊C4C2×D541semidirect
116. C22⋊C4C2×D541semidirect
119. C42C2×D541semidirect
128. D4C4×D541semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D5412
C4×D21642
D4×Dic5412
#317725902
C4×C22⋊D5412
#317725882
#317725862
#317725852
C2×#225758132
C22⋊C4×D5412
C4×D4×C5412
#518541