Finite Group Databasebeta

← #44535201

Subgroups — #44535201

Order 31347.

596 conjugacy classes of subgroups; only the 250 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 250 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
1#23782844C314yesmaximal, complemented
2#23782842C314yesmaximal, complemented
3#23782842C314yesmaximal, complemented
4#23782842C314yesmaximal, complemented
5#23782839C312yesmaximal, complemented
6#23782832C314yesmaximal, complemented
7#23782832C314yesmaximal, complemented
8#23782831C311yesmaximal, characteristic, complemented
9#23782824C314yesmaximal, complemented
10#23782823C314yesmaximal, complemented
11#23782796C312yesmaximal
12#23782795C312yesmaximal
13C43×#6896C311yesmaximal, characteristic, complemented
14C33×C43⋊C3C3211yescharacteristic
15C3×#11923958C3214yes—
16C3×#11923956C3212yes—
17C3×#11923956C3214yes—
18#16812500C3214yescomplemented
19#16812500C3214yescomplemented
20#16812499C3214yescomplemented
21#16812499C3214yescomplemented
22(C43⋊C9)⋊C9C3214yescomplemented
23(C43⋊C9)⋊C9C3214yescomplemented
24(C43⋊C9)⋊C9C3214yescomplemented
25(C43⋊C9)⋊C9C3214yescomplemented
26(C43⋊C9)⋊C9C3214yescomplemented
27(C43⋊C9)⋊C9C3214yescomplemented
28(C43⋊C9)⋊C9C3214yescomplemented
29(C43⋊C9)⋊C9C3214yescomplemented
30(C43⋊C9)⋊C9C3214yescomplemented
31(C43⋊C9)⋊C9C3214yescomplemented
32(C43⋊C9)⋊C9C3214yescomplemented
33(C43⋊C9)⋊C9C3214yescomplemented
34C32⋊(C43⋊C9)C3214yes—
35(C3×C43⋊C3)⋊C9C3212yes—
36(C3×C43⋊C3)⋊C9C3214yes—
37(C3×C43⋊C3)⋊C9C3212yes—
38(C3×C43⋊C3)⋊C9C3212yes—
39(C3×C43⋊C3)⋊C9C3214yes—
40(C3×C43⋊C3)⋊C9C3214yes—
41(C3×C43⋊C3)⋊C9C3212yes—
42(C3×C43⋊C3)⋊C9C3214yes—
43(C3×C43⋊C3)⋊C9C3212yes—
44(C3×C43⋊C3)⋊C9C3214yes—
45C9×C43⋊C9C3214yescomplemented
46C9×C43⋊C9C3214yescomplemented
47C3×3−1+2×C43C3212yes—
48C43×C9⋊C9C3214yescomplemented
49C43×C9⋊C9C3214yescomplemented
50C43×C32⋊C9C3212yes—
51C92×C43C3211yescharacteristic, complemented
52C32×C43⋊C3—92no—
53C32×C43⋊C3—92no—
54C32×C43⋊C3C3311yescharacteristic
55C32×C43⋊C3C3312yes—
56#11923958—94no—
57#11923956—92no—
58#11923956—94no—
59C3×C43⋊C9C3314yes—
60C3×C43⋊C9C3314yes—
61C3×C43⋊C9C3314yes—
62C3×C43⋊C9C3314yes—
63C3×C43⋊C9C3314yes—
64C3×C43⋊C9C3314yes—
65C33×C43C3311yescharacteristic
663−1+2×C43—92no—
67C3×C9×C43C3312yes—
68C3×C9×C43C3312yes—
69C3×C9×C43C3314yes—
70C3×C9×C43C3314yes—
71#10624911—431nomaximal, Sylow
72C32×C43—32no—
73C32×C43—32no—
74C32×C43C3411yescharacteristic
75C3×C43⋊C3—32no—
76C3×C43⋊C3—32no—
77C3×C43⋊C3—32no—
78C3×C43⋊C3—32no—
79C3×C43⋊C3—34no—
80C3×C43⋊C3—99no—
81C9×C43—32no—
82C9×C43—34no—
83C9×C43—32no—
84C9×C43—34no—
85C43⋊C9—34no—
86C43⋊C9—34no—
87C43⋊C9—34no—
88C43⋊C9—34no—
89C43⋊C9—34no—
90C43⋊C9—34no—
91#6899—434no—
92#6899—434no—
93#6899—434no—
94#6899—434no—
95#6899—432no—
96#6897—434no—
97#6897—434no—
98#6897—431no—
99#6896—434no—
100#6896—434no—
101#6896C43⋊C311yescharacteristic, complemented
102#6891—432no—
103#6891—432no—
104C3×C43—91no—
105C3×C433−1+412yes—
106C3×C433−1+412yes—
107C43⋊C3—92no—
108C43⋊C3—91no—
109C34—431no—
110C3×3−1+2—434no—
111C3×3−1+2—434no—
112C3×3−1+2—432no—
113C3×3−1+2C3×C43⋊C312yes—
114C9⋊C9—434no—
115C9⋊C9—434no—
116C9⋊C9—434no—
117C9⋊C9—434no—
118C9⋊C9—434no—
119C9⋊C9—434no—
120C9⋊C9—434no—
121C9⋊C9—434no—
122C9⋊C9—434no—
123C9⋊C9—434no—
124C9⋊C9—434no—
125C9⋊C9—434no—
126C9⋊C9—434no—
127C9⋊C9—434no—
128C9⋊C9—434no—
129C9⋊C9—434no—
130C9⋊C9C3×C43⋊C314yescomplemented
131C9⋊C9C3×C43⋊C314yescomplemented
132C32⋊C9—434no—
133C32⋊C9—434no—
134C32⋊C9—434no—
135C32⋊C9—432no—
136C32⋊C9—432no—
137C32⋊C9—434no—
138C32⋊C9—434no—
139C32⋊C9—434no—
140C32⋊C9—432no—
141C32⋊C9—432no—
142C32⋊C9—432no—
143C32⋊C9C3×C43⋊C312yes—
144C92—434no—
145C92—434no—
146C92C3×C43⋊C311yescharacteristic, complemented
147C43#1062491111yescharacteristic, complemented, Sylow
148C33—431no—
149C33—432no—
150C33—3872no—
151C33—3872no—
152C33C32×C43⋊C311yescharacteristic
1533−1+2—92no—
1543−1+2—3874no—
1553−1+2—3872no—
1563−1+2—3874no—
157C3×C9—434no—
158C3×C9—434no—
159C3×C9—434no—
160C3×C9—434no—
161C3×C9—434no—
162C3×C9—434no—
163C3×C9C32×C43⋊C314yes—
164C3×C9C32×C43⋊C314yes—
165C3×C9C32×C43⋊C312yes—
166C3×C9C32×C43⋊C312yes—
167C32—32no—
168C32—32no—
169C32—1292no—
170C32—1292no—
171C32—1292no—
172C32—1292no—
173C32—1294no—
174C32—3879no—
175C32C33×C43⋊C311yescharacteristic
176C9—34no—
177C9—32no—
178C9—34no—
179C9—32no—
180C9—1294no—
181C9—1294no—
182C9—1294no—
183C9—1294no—
184C9—1294no—
185C9—1294no—
186C3—91no—
187C3—3872no—
188C3—3871no—
189C3#2378292112yes—
190C3#2378292312yes—
subgroupG/H
center, FrattiniC32C33×C43⋊C3
commutator, socle, cosocleC32×C43C34
FittingC43×#6896C3
prime radicalC33×C43⋊C3C32
hypercenter#6896C43⋊C3
hypocenterC43#10624911
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C32 ◁ #6896

Complements

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

NH ≅ G/Ntype
1. #23782844C3semidirect
2. #23782842C3semidirect
3. #23782842C3semidirect
4. #23782842C3semidirect
5. #23782839C3semidirect
6. #23782832C3semidirect
7. #23782832C3semidirect
8. #23782831C3semidirect
9. #23782824C3semidirect
10. #23782823C3semidirect
13. C43×#6896C3semidirect
18. #16812500C32semidirect
19. #16812500C32semidirect
20. #16812499C32semidirect
21. #16812499C32semidirect
22. (C43⋊C9)⋊C9C32semidirect
23. (C43⋊C9)⋊C9C32semidirect
24. (C43⋊C9)⋊C9C32semidirect
25. (C43⋊C9)⋊C9C32semidirect
26. (C43⋊C9)⋊C9C32semidirect
27. (C43⋊C9)⋊C9C32semidirect
28. (C43⋊C9)⋊C9C32semidirect
29. (C43⋊C9)⋊C9C32semidirect
30. (C43⋊C9)⋊C9C32semidirect
31. (C43⋊C9)⋊C9C32semidirect
32. (C43⋊C9)⋊C9C32semidirect
33. (C43⋊C9)⋊C9C32semidirect
45. C9×C43⋊C9C32semidirect
46. C9×C43⋊C9C32semidirect
48. C43×C9⋊C9C32semidirect
49. C43×C9⋊C9C32semidirect
51. C92×C43C32semidirect
101. #6896C43⋊C3semidirect
130. C9⋊C9C3×C43⋊C3semidirect
131. C9⋊C9C3×C43⋊C3semidirect
146. C92C3×C43⋊C3semidirect
147. C43#10624911semidirect

Maximal subgroups

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

subgroupindex
#237828443
#237828423
#237828393
#237828323
#237828313
#237828243
#237828233
#237827963
#237827953
C43×#68963
#1062491143