Finite Group Databasebeta

← C4×D4×D541 #46830632

Subgroups — C4×D4×D541 #46830632

Order 34624.

426 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 169 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
2C22×C4×D541C212yesmaximal, complemented
3C4×D2164C211yesmaximal, characteristic, complemented
4D4×Dic541C211yesmaximal, characteristic, complemented
5#31772590C211yesmaximal, characteristic, complemented
6C4×C22⋊D541C212yesmaximal, complemented
7#31772588C212yesmaximal, complemented
8C4⋊C4×D541C211yesmaximal, characteristic, complemented
9C22⋊C4×D541C212yesmaximal, complemented
10C42×D541C211yesmaximal, characteristic, complemented
11C4×D4×C541C211yesmaximal, characteristic, complemented
12C23×D541C2212yes—
13C2×D2164C2211yescharacteristic
14C2×C22⋊D541C2212yes—
15D4×D541C418yesdirect product factor
16C22×Dic541C2212yescomplemented
17C2×C4×D541—28no—
18C2×C4×D541C2211yescharacteristic
19C2×C4×D541C2212yes—
20C2×C4×D541C2211yescharacteristic
21C2×C4×D541C2211yescharacteristic
22C2×C4×D541C2212yescomplemented
23C2×C4×D541C2212yescomplemented
24C4⋊Dic541C2211yescharacteristic, complemented
25#22575815C2212yescomplemented
26C22⋊Dic541C2212yescomplemented
27#22575813C2212yescomplemented
28#22575813C2212yescomplemented
29C4×Dic541C2211yescharacteristic, complemented
30C4×Dic541C2211yescharacteristic, complemented
31C4×Dic541C2211yescharacteristic, complemented
32C2×D4×C541C2211yescharacteristic
33C22×C4×C541C2212yescomplemented
34C4⋊C4×C541C2211yescharacteristic, complemented
35C22⋊C4×C541C2212yescomplemented
36C42×C541C2211yescharacteristic, complemented
37C22×D541—24no—
38C22×D541—24no—
39C22×D541C2×C418yescomplemented
40C22×D541C2312yes—
41C22×D541C2311yescharacteristic
42D2164C2×C414yescomplemented
43C22⋊D541C2×C418yescomplemented
44C2×Dic541—24no—
45C2×Dic541C2311yescharacteristic
46C2×Dic541C2312yes—
47C2×Dic541C2311yescharacteristic
48C2×Dic541C2311yescharacteristic
49C4×D541—24no—
50C4×D541—22no—
51C4×D541—24no—
52C4×D541—24no—
53C4×D541C2×C414yescomplemented
54C4×D541D414yesdirect product factor
55C23×C541C2312yes—
56D4×C541C2×C414yescomplemented
57C2×C4×C541—24no—
58C2×C4×C541C2311yescharacteristic
59C2×C4×C541C2312yes—
60C2×C4×C541C2311yescharacteristic
61C2×C4×C541C2311yescharacteristic
62C22×C541—22no—
63C22×C541—22no—
64C22×C541C22×C414yescomplemented
65C22×C541C2411yescharacteristic
66C2×D541—22no—
67C2×D541—22no—
68C2×D541—216no—
69C2×D541C22×C412yes—
70C2×D541C22×C414yescomplemented
71C2×D541C2×D412yes—
72C2×D541#4112yes—
73C4×C541—22no—
74C4×C541—21no—
75C4×C541C22×C412yescomplemented
76C4×C541C2×D412yescomplemented
77Dic541—22no—
78Dic541—21no—
79Dic541C22×C412yescomplemented
80Dic541C2×D412yescomplemented
81C2×C541—24no—
82C2×C541C23×C411yescharacteristic
83C2×C541C22×D411yescharacteristic
84C2×C541C2×#4111yescharacteristic
85D541—24no—
86D541C4×D414yesdirect product factor
87C541C2×C4×D411yescharacteristic, complemented, Sylow
88C2×C4×D4—5411nomaximal, Sylow
89C22×D4—5411no—
90C23×C4—5412no—
91C4×D4—5411no—
92C4×D4—5412no—
93C4×D4—5411no—
94C4×D4—5412no—
95C4×D4—5411no—
96C4×D4D54111yescharacteristic, direct product factor
97C2×C4⋊C4—5411no—
98C2×C22⋊C4—5412no—
99C2×C42—5411no—
100C24—5412no—
101C2×D4—5412no—
102C2×D4—5418no—
103C2×D4—5411no—
104C2×D4C2×D54111yescharacteristic
105C22×C4—5411no—
106C22×C4—5411no—
107C22×C4—5412no—
108C22×C4—5411no—
109C22×C4—5412no—
110C22×C4—5412no—
111C22×C4—5412no—
112C22×C4—10828no—
113C22×C4C2×D54112yescomplemented
114C4⋊C4—5412no—
115C4⋊C4—5411no—
116C4⋊C4C2×D54111yescharacteristic, complemented
117C22⋊C4—5412no—
118C22⋊C4—5412no—
119C22⋊C4—5412no—
120C22⋊C4C2×D54112yescomplemented
121C42—5411no—
122C42—5411no—
123C42—5411no—
124C42C2×D54111yescharacteristic, complemented
125C23—5411no—
126C23—5418no—
127C23—5412no—
128C23—10824no—
129C23—10824no—
130C23C22×D54112yes—
131D4—5418no—
132D4—5414no—
133D4C4×D54114yesdirect product factor
134C2×C4—24no—
135C2×C4—5411no—
136C2×C4—5411no—
137C2×C4—5414no—
138C2×C4—5414no—
139C2×C4—5411no—
140C2×C4—5412no—
141C2×C4—10824no—
142C2×C4—10822no—
143C2×C4—10824no—
144C2×C4—10824no—
145C2×C4—10824no—
146C2×C4C22×D54111yescharacteristic
147C2×C4C22×D54112yes—
148C2×C4C22×D54111yescharacteristic
149C2×C4C22×D54111yescharacteristic
150C22—22no—
151C22—22no—
152C22—5412no—
153C22—5412no—
154C22—5412no—
155C22—5414no—
156C22—108216no—
157C22—10822no—
158C22—10822no—
159C22C2×C4×D54114yescomplemented
160C22C23×D54111yescharacteristic
161C4—22no—
162C4—21no—
163C4—5412no—
164C4—5412no—
165C4—10822no—
166C4—10821no—
167C4C2×C4×D54112yescomplemented
168C4D4×D54112yesdirect product factor
169C2—24no—
170C2—5414no—
171C2—10824no—
172C2C22×C4×D54111yescharacteristic
173C2C2×D4×D54111yescharacteristic
174C2#41×D54111yescharacteristic
subgroupG/H
centerC2×C4C22×D541
commutatorC2×C541C23×C4
FrattiniC22C23×D541
FittingC4×D4×C541C2
socle, cosocleC22×C541C24
prime radicalC2×D4×D541C2
hypercenterC4×D4D541
hypocenterC541C2×C4×D4
LCSG ▷ C2×C541 ▷ C541
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D541C2semidirect
3. C4×D2164C2semidirect
4. D4×Dic541C2semidirect
5. #31772590C2semidirect
6. C4×C22⋊D541C2semidirect
7. #31772588C2semidirect
8. C4⋊C4×D541C2semidirect
9. C22⋊C4×D541C2semidirect
10. C42×D541C2semidirect
11. C4×D4×C541C2semidirect
15. D4×D541C4direct (N × H)
16. C22×Dic541C22semidirect
22. C2×C4×D541C22semidirect
23. C2×C4×D541C22semidirect
24. C4⋊Dic541C22semidirect
25. #22575815C22semidirect
26. C22⋊Dic541C22semidirect
27. #22575813C22semidirect
28. #22575813C22semidirect
29. C4×Dic541C22semidirect
30. C4×Dic541C22semidirect
31. C4×Dic541C22semidirect
33. C22×C4×C541C22semidirect
34. C4⋊C4×C541C22semidirect
35. C22⋊C4×C541C22semidirect
36. C42×C541C22semidirect
39. C22×D541C2×C4semidirect
42. D2164C2×C4semidirect
43. C22⋊D541C2×C4semidirect
53. C4×D541C2×C4semidirect
54. C4×D541D4direct (N × H)
56. D4×C541C2×C4semidirect
64. C22×C541C22×C4semidirect
70. C2×D541C22×C4semidirect
75. C4×C541C22×C4semidirect
76. C4×C541C2×D4semidirect
79. Dic541C22×C4semidirect
80. Dic541C2×D4semidirect
86. D541C4×D4direct (N × H)
87. C541C2×C4×D4semidirect
96. C4×D4D541direct (N × H)
113. C22×C4C2×D541semidirect
116. C4⋊C4C2×D541semidirect
120. C22⋊C4C2×D541semidirect
124. C42C2×D541semidirect
133. D4C4×D541direct (N × H)
159. C22C2×C4×D541semidirect
167. C4C2×C4×D541semidirect
168. C4D4×D541direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D5412
C22×C4×D5412
C4×D21642
D4×Dic5412
#317725902
C4×C22⋊D5412
#317725882
C4⋊C4×D5412
C22⋊C4×D5412
C42×D5412
C4×D4×C5412
C2×C4×D4541