Subgroups — C₂×#27131472 #37566254

Order 24276.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₇²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#27131472	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇⋊(C₁₇⋊D₁₇)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₁₇²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇⋊(C₁₇⋊D₁₇)	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₁₇²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×(C₁₇⋊D₁₇)⋊C₃	—	7	1	no	maximal, Hall
8	C₇×C₁₇²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₇²⋊C₃	D₇	1	1	yes	characteristic, complemented
10	(C₁₇⋊D₁₇)⋊C₃	—	7	2	no	—
11	C₂×C₁₇⋊D₁₇	—	7	1	no	Hall
12	C₁₇²⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₇²	C₃×D₇	1	1	yes	characteristic, complemented
14	C₁₇⋊D₁₇	—	7	2	no	—
15	C₂×D₁₁₉	—	51	6	no	—
16	C₁₇²	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₇×C₁₇	—	3	6	no	—
18	D₁₁₉	—	51	12	no	—
19	C₇×C₁₇	—	3	6	no	—
20	C₂×C₃×D₇	—	289	1	no	maximal, Hall
21	C₂×D₁₇	—	357	6	no	—
22	C₂×C₃×C₇	—	578	1	no	—
23	C₃×D₇	—	289	2	no	—
24	C₂×C₁₇	—	3	6	no	—
25	D₁₇	—	357	12	no	—
26	C₂×D₇	—	289	1	no	Hall
27	C₃×C₇	—	578	1	no	Hall
28	C₁₇	—	3	6	no	—
29	C₂×C₇	(C₁₇⋊D₁₇)⋊C₃	1	1	yes	characteristic, complemented
30	D₇	—	289	2	no	—
31	C₂²×C₃	—	2023	1	no	Hall
32	C₇	C₂×(C₁₇⋊D₁₇)⋊C₃	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃	—	578	1	no	—
34	C₂×C₃	—	2023	2	no	—
35	C₂²	—	2023	1	no	Sylow
36	C₃	—	578	1	no	Sylow
37	C₂	—	2023	2	no	—
38	C₂	#27131472	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#27131472
commutator, cosocle, hypocenter	C₇×C₁₇²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₇²	C₂×C₃
LCS	G ▷ C₇×C₁₇²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×C₁₇²⋊C₃	C₂	semidirect
2. #27131472	C₂	direct (N × H)
3. C₂×C₇⋊(C₁₇⋊D₁₇)	C₃	semidirect
4. C₇×C₁₇²⋊C₃	C₂²	semidirect
5. C₇⋊(C₁₇⋊D₁₇)	C₂×C₃	semidirect
6. C₂×C₇×C₁₇²	C₂×C₃	semidirect
8. C₇×C₁₇²	C₂²×C₃	semidirect
9. C₂×C₁₇²⋊C₃	D₇	semidirect
12. C₁₇²⋊C₃	C₂×D₇	semidirect
13. C₂×C₁₇²	C₃×D₇	semidirect
16. C₁₇²	C₂×C₃×D₇	semidirect
29. C₂×C₇	(C₁₇⋊D₁₇)⋊C₃	semidirect
32. C₇	C₂×(C₁₇⋊D₁₇)⋊C₃	semidirect
38. C₂	#27131472	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×C₇×C₁₇²⋊C₃	2
#27131472	2
C₂×C₇⋊(C₁₇⋊D₁₇)	3
C₂×(C₁₇⋊D₁₇)⋊C₃	7
C₂×C₃×D₇	289

Subgroups — C2×#27131472 #37566254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27131472 #37566254