Subgroups — C₄×#22576777 #46855471

Order 35008.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22576777	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₅₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₂₁₈₈	C₂	1	3	yes	maximal, complemented
4	#31775964	C₂	1	3	yes	maximal, complemented
5	#31775960	C₂	1	3	yes	maximal, complemented
6	C₄²×D₅₄₇	C₂	1	3	yes	maximal, complemented
7	C₄×Q₈×C₅₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#22576777	C₄	1	8	yes	direct product factor
9	C₂×D₂₁₈₈	C₂²	1	3	yes	—
10	C₂×C₄×D₅₄₇	C₂²	1	3	yes	—
11	C₂×C₄×D₅₄₇	C₂²	1	3	yes	—
12	C₂×C₄×D₅₄₇	C₂²	1	3	yes	—
13	C₄⋊Dic₅₄₇	C₂²	1	3	yes	—
14	(C₂×D₅₄₇)⋊C₄	C₂²	1	6	yes	—
15	C₄×Dic₅₄₇	C₂²	1	1	yes	characteristic
16	C₄×Dic₅₄₇	C₂²	1	3	yes	—
17	C₄×Dic₅₄₇	C₂²	1	3	yes	—
18	C₂×Q₈×C₅₄₇	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₅₄₇	C₂²	1	3	yes	—
20	C₄²×C₅₄₇	C₂²	1	3	yes	—
21	C₂²×D₅₄₇	C₂³	1	3	yes	—
22	D₂₁₈₈	C₂×C₄	1	12	yes	complemented
23	C₂×Dic₅₄₇	C₂³	1	3	yes	—
24	C₂×Dic₅₄₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₅₄₇	C₂³	1	1	yes	characteristic
26	C₄×D₅₄₇	—	2	6	no	—
27	C₄×D₅₄₇	—	2	6	no	—
28	C₄×D₅₄₇	C₂×C₄	1	12	yes	complemented
29	Q₈×C₅₄₇	C₂×C₄	1	4	yes	complemented
30	C₂×C₄×C₅₄₇	C₂³	1	3	yes	—
31	C₂×C₄×C₅₄₇	C₂³	1	3	yes	—
32	C₂×C₄×C₅₄₇	C₂³	1	1	yes	characteristic
33	C₂²×C₅₄₇	C₂⁴	1	1	yes	characteristic
34	C₂×D₅₄₇	—	2	3	no	—
35	C₂×D₅₄₇	—	2	3	no	—
36	C₂×D₅₄₇	C₂²×C₄	1	6	yes	—
37	C₄×C₅₄₇	—	2	3	no	—
38	C₄×C₅₄₇	C₂²×C₄	1	6	yes	—
39	C₄×C₅₄₇	#41	1	2	yes	complemented
40	Dic₅₄₇	—	2	3	no	—
41	Dic₅₄₇	C₂²×C₄	1	2	yes	—
42	Dic₅₄₇	#41	1	2	yes	complemented
43	C₂×C₅₄₇	C₂³×C₄	1	1	yes	characteristic
44	C₂×C₅₄₇	C₂×#41	1	1	yes	characteristic
45	C₂×C₅₄₇	C₂×#41	1	1	yes	characteristic
46	D₅₄₇	—	2	6	no	—
47	C₅₄₇	C₄×#41	1	1	yes	characteristic, complemented, Sylow
48	C₄×#41	—	547	1	no	maximal, Sylow
49	C₂×#41	—	547	1	no	—
50	C₄×Q₈	—	547	1	no	—
51	C₄×Q₈	D₅₄₇	1	1	yes	characteristic, complemented
52	C₄×D₄	—	547	3	no	—
53	C₄×D₄	—	547	3	no	—
54	#117	—	547	3	no	—
55	C₂×C₄²	—	547	3	no	—
56	#41	—	547	8	no	—
57	C₂×Q₈	C₂×D₅₄₇	1	1	yes	characteristic
58	C₂×D₄	—	547	3	no	—
59	C₂²×C₄	—	547	3	no	—
60	C₂²×C₄	—	547	3	no	—
61	C₂²×C₄	—	547	3	no	—
62	C₄⋊C₄	—	547	3	no	—
63	C₄⋊C₄	C₂×D₅₄₇	1	3	yes	—
64	C₂²⋊C₄	—	547	6	no	—
65	C₄²	—	547	3	no	—
66	C₄²	—	547	3	no	—
67	C₄²	—	547	1	no	—
68	C₄²	C₂×D₅₄₇	1	3	yes	—
69	C₂³	—	547	3	no	—
70	Q₈	C₄×D₅₄₇	1	4	yes	complemented
71	D₄	—	547	12	no	—
72	C₂×C₄	—	547	1	no	—
73	C₂×C₄	—	547	1	no	—
74	C₂×C₄	—	547	12	no	—
75	C₂×C₄	—	547	3	no	—
76	C₂×C₄	—	1094	6	no	—
77	C₂×C₄	—	1094	6	no	—
78	C₂×C₄	C₂²×D₅₄₇	1	3	yes	—
79	C₂×C₄	C₂²×D₅₄₇	1	3	yes	—
80	C₂×C₄	C₂²×D₅₄₇	1	1	yes	characteristic
81	C₂²	—	547	6	no	—
82	C₂²	—	1094	3	no	—
83	C₂²	—	1094	3	no	—
84	C₂²	C₂³×D₅₄₇	1	1	yes	characteristic
85	C₄	—	2	3	no	—
86	C₄	—	547	2	no	—
87	C₄	—	547	2	no	—
88	C₄	—	1094	3	no	—
89	C₄	C₂×C₄×D₅₄₇	1	6	yes	—
90	C₄	#22576777	1	2	yes	direct product factor
91	C₂	—	1094	6	no	—
92	C₂	C₂²×C₄×D₅₄₇	1	1	yes	characteristic
93	C₂	#41×D₅₄₇	1	1	yes	characteristic
94	C₂	C₂×#22576777	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₄₇
commutator	C₂×C₅₄₇	C₂³×C₄
Frattini	C₂²	C₂³×D₅₄₇
Fitting	C₄×Q₈×C₅₄₇	C₂
socle, cosocle	C₂²×C₅₄₇	C₂⁴
prime radical	C₂×#22576777	C₂
hypercenter	C₄×Q₈	D₅₄₇
hypocenter	C₅₄₇	C₄×#41
LCS	G ▷ C₂×C₅₄₇ ▷ C₅₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×Dic₅₄₇	C₂	semidirect
3. C₄×D₂₁₈₈	C₂	semidirect
4. #31775964	C₂	semidirect
5. #31775960	C₂	semidirect
6. C₄²×D₅₄₇	C₂	semidirect
7. C₄×Q₈×C₅₄₇	C₂	semidirect
8. #22576777	C₄	direct (N × H)
22. D₂₁₈₈	C₂×C₄	semidirect
28. C₄×D₅₄₇	C₂×C₄	semidirect
29. Q₈×C₅₄₇	C₂×C₄	semidirect
39. C₄×C₅₄₇	#41	semidirect
42. Dic₅₄₇	#41	semidirect
47. C₅₄₇	C₄×#41	semidirect
51. C₄×Q₈	D₅₄₇	semidirect
70. Q₈	C₄×D₅₄₇	semidirect
90. C₄	#22576777	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×#22576777	2
Q₈×Dic₅₄₇	2
C₄×D₂₁₈₈	2
#31775964	2
#31775960	2
C₄²×D₅₄₇	2
C₄×Q₈×C₅₄₇	2
C₄×#41	547

Subgroups — C4×#22576777 #46855471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#22576777 #46855471