Subgroups — C₂²×#19153200 #37524610

Order 22932.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19153200	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	#19153200	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	3	yes	—
5	C₂²×#11717941	—	7	8	no	maximal
6	C₂²×C₇²×C₁₃	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic
8	C₂²×#89204	—	13	1	no	maximal, Hall
9	C₂×#11717941	—	7	24	no	—
10	C₂×C₇²×C₁₃	C₂×C₉	1	3	yes	complemented
11	C₂²×C₃×C₇×C₁₃	ΓL(1,𝔽₈)	1	8	yes	—
12	C₂×#89204	—	13	3	no	—
13	#11717941	—	7	8	no	—
14	C₇²×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₃×C₇²	C₁₃⋊C₃	1	1	yes	characteristic
16	C₂×C₃×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	24	yes	—
17	C₂²×C₁₃⋊C₉	—	49	1	no	Hall
18	#89204	—	13	1	no	Hall
19	C₂²×C₇×C₁₃	C₇⋊C₉	1	8	yes	complemented
20	C₂×C₃×C₇²	C₂×C₁₃⋊C₃	1	3	yes	—
21	C₃×C₇×C₁₃	C₂²×ΓL(1,𝔽₈)	1	8	yes	—
22	C₂²×C₇⋊C₉	—	91	8	no	—
23	C₂×C₁₃⋊C₉	—	49	3	no	—
24	C₂²×C₇²	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₁₃	C₂×C₇⋊C₉	1	24	yes	complemented
26	C₂²×C₃×C₁₃	#3861	1	1	yes	characteristic
27	C₃×C₇²	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
28	C₂×C₇⋊C₉	—	91	24	no	—
29	C₁₃⋊C₉	—	49	1	no	Hall
30	C₂×C₇²	C₂×C₁₃⋊C₉	1	3	yes	complemented
31	C₇×C₁₃	C₂²×C₇⋊C₉	1	8	yes	complemented
32	C₂²×C₃×C₇	#63270	1	8	yes	—
33	C₂×C₃×C₁₃	C₂×#3861	1	3	yes	—
34	C₇⋊C₉	—	91	8	no	—
35	C₂²×C₁₃	#89204	1	1	yes	characteristic, complemented, Hall
36	C₇²	C₂²×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₇	C₂×#63270	1	24	yes	—
38	C₃×C₁₃	C₂²×#3861	1	1	yes	characteristic
39	C₂²×C₉	—	637	1	no	Hall
40	C₂²×C₇	#11717941	1	8	yes	complemented
41	C₂×C₁₃	C₂×#89204	1	3	yes	complemented
42	C₃×C₇	C₂²×#63270	1	8	yes	—
43	C₂×C₉	—	637	3	no	—
44	C₂×C₇	C₂×#11717941	1	24	yes	complemented
45	C₁₃	C₂²×#89204	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₃	#14274263	1	1	yes	characteristic
47	C₉	—	637	1	no	Sylow
48	C₇	C₂²×#11717941	1	8	yes	complemented
49	C₂×C₃	C₂×#14274263	1	3	yes	—
50	C₂²	#19153200	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₂²×#14274263	1	1	yes	characteristic
52	C₂	C₂×#19153200	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	#14274263
commutator, hypocenter	C₇²×C₁₃	C₂²×C₉
Frattini	C₃	C₂²×#14274263
Fitting, socle, prime radical	C₂²×C₃×C₇²×C₁₃	C₃
cosocle	C₃×C₇²×C₁₃	C₂²×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×#19153200	C₂	direct (N × H)
3. #19153200	C₂²	direct (N × H)
6. C₂²×C₇²×C₁₃	C₉	semidirect
10. C₂×C₇²×C₁₃	C₂×C₉	semidirect
14. C₇²×C₁₃	C₂²×C₉	semidirect
19. C₂²×C₇×C₁₃	C₇⋊C₉	semidirect
24. C₂²×C₇²	C₁₃⋊C₉	semidirect
25. C₂×C₇×C₁₃	C₂×C₇⋊C₉	semidirect
30. C₂×C₇²	C₂×C₁₃⋊C₉	semidirect
31. C₇×C₁₃	C₂²×C₇⋊C₉	semidirect
35. C₂²×C₁₃	#89204	semidirect
36. C₇²	C₂²×C₁₃⋊C₉	semidirect
40. C₂²×C₇	#11717941	semidirect
41. C₂×C₁₃	C₂×#89204	semidirect
44. C₂×C₇	C₂×#11717941	semidirect
45. C₁₃	C₂²×#89204	semidirect
48. C₇	C₂²×#11717941	semidirect
50. C₂²	#19153200	direct (N × H)
52. C₂	C₂×#19153200	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19153200	2
C₂²×C₃×C₇²×C₁₃	3
C₂²×#11717941	7
C₂²×#89204	13

Subgroups — C22×#19153200 #37524610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19153200 #37524610