Subgroups — D₂₄₃₈₈ #72287828

Order 48776.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₄₈₄	—	7	1	no	maximal, Hall
2	D₁₈₇₆	—	13	1	no	maximal, Hall
3	C₂×D₆₀₉₇	C₂	1	2	yes	maximal, complemented
4	C₄×C₇×C₁₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₆₀₉₇	—	2	2	no	—
6	C₂×C₇×C₁₃×C₆₇	C₂²	1	1	yes	characteristic
7	C₇×C₁₃×C₆₇	D₄	1	1	yes	characteristic, complemented, Hall
8	C₂×D₈₇₁	—	7	2	no	—
9	C₄×C₁₃×C₆₇	D₇	1	1	yes	characteristic, complemented
10	C₂×D₄₆₉	—	13	2	no	—
11	C₄×C₇×C₆₇	D₁₃	1	1	yes	characteristic, complemented
12	C₂×C₁₃×C₆₇	C₂×D₇	1	1	yes	characteristic
13	D₈₇₁	—	14	2	no	—
14	C₂×C₇×C₆₇	C₂×D₁₃	1	1	yes	characteristic
15	D₄₆₉	—	26	2	no	—
16	C₁₃×C₆₇	D₂₈	1	1	yes	characteristic, complemented, Hall
17	D₃₆₄	—	67	1	no	maximal, Hall
18	D₂₆₈	—	91	1	no	Hall
19	C₇×C₆₇	D₅₂	1	1	yes	characteristic, complemented, Hall
20	C₂×D₉₁	—	67	2	no	—
21	C₄×C₇×C₁₃	D₆₇	1	1	yes	characteristic, complemented
22	C₂×D₆₇	—	91	2	no	—
23	C₄×C₆₇	D₉₁	1	1	yes	characteristic, complemented
24	C₂×C₇×C₁₃	C₂×D₆₇	1	1	yes	characteristic
25	D₉₁	—	134	2	no	—
26	C₂×C₆₇	C₂×D₉₁	1	1	yes	characteristic
27	D₆₇	—	182	2	no	—
28	D₅₂	—	469	1	no	Hall
29	C₇×C₁₃	D₂₆₈	1	1	yes	characteristic, complemented, Hall
30	C₆₇	D₃₆₄	1	1	yes	characteristic, complemented, Sylow
31	D₂₈	—	871	1	no	Hall
32	C₂×D₁₃	—	469	2	no	—
33	C₄×C₁₃	D₄₆₉	1	1	yes	characteristic, complemented
34	C₂×D₇	—	871	2	no	—
35	C₄×C₇	D₈₇₁	1	1	yes	characteristic, complemented
36	C₂×C₁₃	C₂×D₄₆₉	1	1	yes	characteristic
37	D₁₃	—	938	2	no	—
38	C₂×C₇	C₂×D₈₇₁	1	1	yes	characteristic
39	D₇	—	1742	2	no	—
40	C₁₃	D₁₈₇₆	1	1	yes	characteristic, complemented, Sylow
41	D₄	—	6097	1	no	Sylow
42	C₇	D₃₄₈₄	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	6097	2	no	—
44	C₄	D₆₀₉₇	1	1	yes	characteristic, complemented
45	C₂	—	12194	2	no	—
46	C₂	C₂×D₆₀₉₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₆₀₉₇
commutator, socle, cosocle	C₂×C₇×C₁₃×C₆₇	C₂²
Fitting	C₄×C₇×C₁₃×C₆₇	C₂
hypercenter	C₄	D₆₀₉₇
hypocenter	C₇×C₁₃×C₆₇	D₄
LCS	G ▷ C₂×C₇×C₁₃×C₆₇ ▷ C₇×C₁₃×C₆₇
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
3. C₂×D₆₀₉₇	C₂	semidirect
4. C₄×C₇×C₁₃×C₆₇	C₂	semidirect
7. C₇×C₁₃×C₆₇	D₄	semidirect
9. C₄×C₁₃×C₆₇	D₇	semidirect
11. C₄×C₇×C₆₇	D₁₃	semidirect
16. C₁₃×C₆₇	D₂₈	semidirect
19. C₇×C₆₇	D₅₂	semidirect
21. C₄×C₇×C₁₃	D₆₇	semidirect
23. C₄×C₆₇	D₉₁	semidirect
29. C₇×C₁₃	D₂₆₈	semidirect
30. C₆₇	D₃₆₄	semidirect
33. C₄×C₁₃	D₄₆₉	semidirect
35. C₄×C₇	D₈₇₁	semidirect
40. C₁₃	D₁₈₇₆	semidirect
42. C₇	D₃₄₈₄	semidirect
44. C₄	D₆₀₉₇	semidirect

Maximal subgroups

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

subgroup	index
D₃₄₈₄	7
D₁₈₇₆	13
C₂×D₆₀₉₇	2
C₄×C₇×C₁₃×C₆₇	2
D₃₆₄	67

Subgroups — D24388 #72287828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₄₃₈₈ #72287828