Subgroups — C₄₁×#7317 #23783518

Order 10496.

432 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#1784	C₂	1	3	yes	maximal
2	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
3	C₂×#101×C₄₁	—	2	6	no	—
4	C₄₁×#407	C₄	1	6	yes	—
5	C₂²×Q₈×C₄₁	—	4	6	no	—
6	C₂²×Q₈×C₄₁	D₄	1	3	yes	—
7	C₂²×Q₈×C₄₁	Q₈	1	1	yes	characteristic
8	C₂³×C₄×C₄₁	C₂×C₄	1	3	yes	—
9	C₂×M₁₆×C₄₁	—	2	6	no	—
10	#101×C₄₁	—	4	12	no	—
11	C₂²⋊C₈×C₄₁	—	4	6	no	—
12	C₂⁴×C₄₁	C₄²	1	1	yes	characteristic
13	C₂×Q₈×C₄₁	—	2	12	no	—
14	C₂×Q₈×C₄₁	—	4	3	no	—
15	C₂×Q₈×C₄₁	—	4	3	no	—
16	C₂×Q₈×C₄₁	—	4	16	no	—
17	C₂²×C₄×C₄₁	—	2	6	no	—
18	C₂²×C₄×C₄₁	—	4	6	no	—
19	C₂²×C₄×C₄₁	C₂²⋊C₄	1	3	yes	—
20	C₂²×C₄×C₄₁	C₄⋊C₄	1	3	yes	—
21	M₁₆×C₄₁	—	4	12	no	—
22	C₂×C₈×C₄₁	—	4	6	no	—
23	C₂³×C₄₁	—	2	3	no	—
24	C₂³×C₄₁	—	4	2	no	—
25	C₂³×C₄₁	#95	1	1	yes	characteristic
26	Q₈×C₄₁	—	4	12	no	—
27	Q₈×C₄₁	—	4	4	no	—
28	C₂×C₄×C₄₁	—	2	6	no	—
29	C₂×C₄×C₄₁	—	2	3	no	—
30	C₂×C₄×C₄₁	—	2	6	no	—
31	C₂×C₄×C₄₁	—	4	12	no	—
32	C₂×C₄×C₄₁	#99	1	6	yes	—
33	C₈×C₄₁	—	8	6	no	—
34	#7317	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₄₁	—	2	6	no	—
36	C₂²×C₄₁	—	4	1	no	—
37	C₂²×C₄₁	—	4	3	no	—
38	C₂²×C₄₁	—	4	1	no	—
39	C₂²×C₄₁	#342	1	3	yes	—
40	C₄×C₄₁	—	2	6	no	—
41	C₄×C₄₁	—	4	3	no	—
42	#1784	C₂×C₄₁	1	3	yes	—
43	C₂×C₄₁	—	2	3	no	—
44	C₂×C₄₁	—	4	2	no	—
45	C₂×C₄₁	#1304	1	1	yes	characteristic
46	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
47	C₂×#101	—	2	6	no	—
48	#407	C₄×C₄₁	1	6	yes	—
49	C₄₁	#7317	1	1	yes	characteristic, direct product factor, Sylow
50	C₂²×Q₈	—	4	6	no	—
51	C₂²×Q₈	D₄×C₄₁	1	3	yes	—
52	C₂²×Q₈	Q₈×C₄₁	1	1	yes	characteristic
53	C₂³×C₄	C₂×C₄×C₄₁	1	3	yes	—
54	C₂×M₁₆	—	2	6	no	—
55	#101	—	4	12	no	—
56	C₂²⋊C₈	—	4	6	no	—
57	C₂⁴	C₄²×C₄₁	1	1	yes	characteristic
58	C₂×Q₈	—	2	12	no	—
59	C₂×Q₈	—	4	3	no	—
60	C₂×Q₈	—	4	3	no	—
61	C₂×Q₈	—	4	16	no	—
62	C₂²×C₄	—	2	6	no	—
63	C₂²×C₄	—	4	6	no	—
64	C₂²×C₄	C₂²⋊C₄×C₄₁	1	3	yes	—
65	C₂²×C₄	C₄⋊C₄×C₄₁	1	3	yes	—
66	M₁₆	—	4	12	no	—
67	C₂×C₈	—	4	6	no	—
68	C₂³	—	2	3	no	—
69	C₂³	—	4	2	no	—
70	C₂³	#95×C₄₁	1	1	yes	characteristic
71	Q₈	—	4	12	no	—
72	Q₈	—	4	4	no	—
73	C₂×C₄	—	2	6	no	—
74	C₂×C₄	—	2	3	no	—
75	C₂×C₄	—	2	6	no	—
76	C₂×C₄	—	4	12	no	—
77	C₂×C₄	#99×C₄₁	1	6	yes	—
78	C₈	—	8	6	no	—
79	C₂²	—	2	6	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	4	3	no	—
82	C₂²	—	4	1	no	—
83	C₂²	C₄₁×#342	1	3	yes	—
84	C₄	—	2	6	no	—
85	C₄	—	4	3	no	—
86	C₂	—	2	3	no	—
87	C₂	—	4	2	no	—
88	C₂	C₄₁×#1304	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₁	#1304
commutator	C₂⁴	C₄²×C₄₁
Frattini, cosocle	C₂³×Q₈	C₂²×C₄₁
prime radical	C₂⁴×C₄₁	C₄²
LCS	G ▷ C₂⁴ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₁ ◁ C₂³×C₄₁ ◁ C₂³×Q₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
34. #7317	C₄₁	direct (N × H)
49. C₄₁	#7317	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#1784	2
#7317	41

Subgroups — C41×#7317 #23783518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#7317 #23783518