Subgroups — C₄×#19153199 #37524385

Order 22932.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19153199	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₇²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	#19153199	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic
5	C₄×#11717942	—	7	8	no	maximal
6	C₄×C₇²×C₁₃	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic
8	C₄×#89204	—	13	1	no	maximal, Hall
9	C₂×#11717942	—	7	8	no	—
10	C₂×C₇²×C₁₃	C₂×C₉	1	1	yes	characteristic
11	C₃×C₄×C₇×C₁₃	ΓL(1,𝔽₈)	1	8	yes	—
12	C₂×#89204	—	13	1	no	—
13	#11717942	—	7	8	no	—
14	C₇²×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₄×C₇²	C₁₃⋊C₃	1	1	yes	characteristic
16	C₂×C₃×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	8	yes	—
17	C₄×C₁₃⋊C₉	—	49	1	no	Hall
18	#89204	—	13	1	no	Hall
19	C₄×C₇×C₁₃	C₇⋊C₉	1	8	yes	complemented
20	C₂×C₃×C₇²	C₂×C₁₃⋊C₃	1	1	yes	characteristic
21	C₃×C₇×C₁₃	C₄×ΓL(1,𝔽₈)	1	8	yes	—
22	C₄×C₇⋊C₉	—	91	8	no	—
23	C₂×C₁₃⋊C₉	—	49	1	no	—
24	C₄×C₇²	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₁₃	C₂×C₇⋊C₉	1	8	yes	—
26	C₃×C₄×C₁₃	#3861	1	1	yes	characteristic
27	C₃×C₇²	C₄×C₁₃⋊C₃	1	1	yes	characteristic
28	C₂×C₇⋊C₉	—	91	8	no	—
29	C₁₃⋊C₉	—	49	1	no	Hall
30	C₂×C₇²	C₂×C₁₃⋊C₉	1	1	yes	characteristic
31	C₇×C₁₃	C₄×C₇⋊C₉	1	8	yes	complemented
32	C₃×C₄×C₇	#63271	1	8	yes	—
33	C₂×C₃×C₁₃	C₂×#3861	1	1	yes	characteristic
34	C₇⋊C₉	—	91	8	no	—
35	C₄×C₁₃	#89204	1	1	yes	characteristic, complemented, Hall
36	C₇²	C₄×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₇	C₂×#63271	1	8	yes	—
38	C₃×C₁₃	C₄×#3861	1	1	yes	characteristic
39	C₄×C₉	—	637	1	no	Hall
40	C₄×C₇	#11717942	1	8	yes	complemented
41	C₂×C₁₃	C₂×#89204	1	1	yes	characteristic
42	C₃×C₇	C₄×#63271	1	8	yes	—
43	C₂×C₉	—	637	1	no	—
44	C₂×C₇	C₂×#11717942	1	8	yes	—
45	C₁₃	C₄×#89204	1	1	yes	characteristic, complemented, Sylow
46	C₃×C₄	#14274262	1	1	yes	characteristic
47	C₉	—	637	1	no	Sylow
48	C₇	C₄×#11717942	1	8	yes	complemented
49	C₂×C₃	C₂×#14274262	1	1	yes	characteristic
50	C₄	#19153199	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₄×#14274262	1	1	yes	characteristic
52	C₂	C₂×#19153199	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	#14274262
commutator, hypocenter	C₇²×C₁₃	C₄×C₉
Frattini	C₂×C₃	C₂×#14274262
Fitting	C₃×C₄×C₇²×C₁₃	C₃
socle, prime radical, cosocle	C₂×C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
3. #19153199	C₄	direct (N × H)
6. C₄×C₇²×C₁₃	C₉	semidirect
14. C₇²×C₁₃	C₄×C₉	semidirect
19. C₄×C₇×C₁₃	C₇⋊C₉	semidirect
24. C₄×C₇²	C₁₃⋊C₉	semidirect
31. C₇×C₁₃	C₄×C₇⋊C₉	semidirect
35. C₄×C₁₃	#89204	semidirect
36. C₇²	C₄×C₁₃⋊C₉	semidirect
40. C₄×C₇	#11717942	semidirect
45. C₁₃	C₄×#89204	semidirect
48. C₇	C₄×#11717942	semidirect
50. C₄	#19153199	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×#19153199	2
C₃×C₄×C₇²×C₁₃	3
C₄×#11717942	7
C₄×#89204	13

Subgroups — C4×#19153199 #37524385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19153199 #37524385