Subgroups — C₄×#108×C₄₁ #19105557

Order 5248.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108×C₄₁	C₂	1	2	yes	maximal
2	C₄×M₁₆×C₄₁	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#341	C₂	1	2	yes	maximal
5	C₂×M₁₆×C₄₁	C₂²	1	4	yes	—
6	C₂²×C₈×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₄₁	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₄₁	C₂²	1	1	yes	characteristic
9	#108×C₄₁	C₄	1	8	yes	direct product factor
10	#97×C₄₁	—	2	2	no	—
11	C₄×C₈×C₄₁	—	2	2	no	—
12	C₄×C₈×C₄₁	C₄	1	4	yes	—
13	C₂²×C₄×C₄₁	Q₈	1	2	yes	—
14	C₂²×C₄×C₄₁	C₂³	1	1	yes	characteristic
15	M₁₆×C₄₁	—	2	4	no	—
16	M₁₆×C₄₁	C₂×C₄	1	8	yes	—
17	C₂×C₈×C₄₁	—	2	4	no	—
18	C₂×C₈×C₄₁	—	2	2	no	—
19	C₂×C₈×C₄₁	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₄₁	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₄₁	C₂×C₄	1	4	yes	—
22	C₄²×C₄₁	C₂×C₄	1	2	yes	—
23	C₄²×C₄₁	D₄	1	1	yes	characteristic
24	C₄²×C₄₁	D₄	1	1	yes	characteristic
25	C₂³×C₄₁	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₄×C₄₁	—	2	4	no	—
27	C₂×C₄×C₄₁	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₄₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₁	C₂²×C₄	1	2	yes	—
31	C₂×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₁	#41	1	2	yes	—
33	C₈×C₄₁	—	2	2	no	—
34	C₈×C₄₁	—	2	8	no	—
35	C₈×C₄₁	C₄²	1	4	yes	—
36	C₂²×C₄₁	—	2	2	no	—
37	C₂²×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₄₁	C₄×Q₈	1	2	yes	—
39	C₄×C₄₁	—	2	2	no	—
40	C₄×C₄₁	#108	1	4	yes	direct product factor
41	C₄×C₄₁	C₂×C₄²	1	1	yes	characteristic
42	C₄×C₄₁	#117	1	1	yes	characteristic
43	C₄×C₄₁	C₄×D₄	1	2	yes	—
44	C₄×#108	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×C₄₁	—	2	2	no	—
46	C₂×C₄₁	C₄×C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₄₁	C₂×#108	1	2	yes	—
48	C₂×#108	C₂×C₄₁	1	2	yes	—
49	C₄×M₁₆	C₂×C₄₁	1	2	yes	—
50	C₂×C₄×C₈	C₂×C₄₁	1	1	yes	characteristic
51	#341	C₂×C₄₁	1	2	yes	—
52	C₄₁	C₄×#108	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×M₁₆	C₂²×C₄₁	1	4	yes	—
54	C₂²×C₈	C₂²×C₄₁	1	1	yes	characteristic
55	C₂²×C₈	C₂²×C₄₁	1	1	yes	characteristic
56	C₂×C₄²	C₂²×C₄₁	1	1	yes	characteristic
57	#108	C₄×C₄₁	1	8	yes	direct product factor
58	#97	—	2	2	no	—
59	C₄×C₈	—	2	2	no	—
60	C₄×C₈	C₄×C₄₁	1	4	yes	—
61	C₂²×C₄	Q₈×C₄₁	1	2	yes	—
62	C₂²×C₄	C₂³×C₄₁	1	1	yes	characteristic
63	M₁₆	—	2	4	no	—
64	M₁₆	C₂×C₄×C₄₁	1	8	yes	—
65	C₂×C₈	—	2	4	no	—
66	C₂×C₈	—	2	2	no	—
67	C₂×C₈	C₂×C₄×C₄₁	1	2	yes	—
68	C₂×C₈	C₂×C₄×C₄₁	1	2	yes	—
69	C₂×C₈	C₂×C₄×C₄₁	1	4	yes	—
70	C₄²	C₂×C₄×C₄₁	1	2	yes	—
71	C₄²	D₄×C₄₁	1	1	yes	characteristic
72	C₄²	D₄×C₄₁	1	1	yes	characteristic
73	C₂³	C₂×Q₈×C₄₁	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄⋊C₄×C₄₁	1	2	yes	—
76	C₂×C₄	C₄⋊C₄×C₄₁	1	2	yes	—
77	C₂×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
78	C₂×C₄	C₂²×C₄×C₄₁	1	2	yes	—
79	C₂×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
80	C₂×C₄	#41×C₄₁	1	2	yes	—
81	C₈	—	2	2	no	—
82	C₈	—	2	8	no	—
83	C₈	C₄²×C₄₁	1	4	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
86	C₂²	C₄×Q₈×C₄₁	1	2	yes	—
87	C₄	—	2	2	no	—
88	C₄	#108×C₄₁	1	4	yes	direct product factor
89	C₄	C₂×C₄²×C₄₁	1	1	yes	characteristic
90	C₄	#117×C₄₁	1	1	yes	characteristic
91	C₄	C₄×D₄×C₄₁	1	2	yes	—
92	C₂	—	2	2	no	—
93	C₂	C₄×C₄⋊C₄×C₄₁	1	1	yes	characteristic
94	C₂	C₂×#108×C₄₁	1	2	yes	—

	subgroup	G/H
center	C₄²×C₄₁	D₄
commutator	C₄	C₂×C₄²×C₄₁
Frattini, cosocle	C₂²×C₄	C₂³×C₄₁
socle	C₂²×C₄₁	C₂×C₄⋊C₄
prime radical	C₂³×C₄₁	C₂×Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
9. #108×C₄₁	C₄	direct (N × H)
40. C₄×C₄₁	#108	direct (N × H)
44. C₄×#108	C₄₁	direct (N × H)
52. C₄₁	C₄×#108	direct (N × H)
57. #108	C₄×C₄₁	direct (N × H)
88. C₄	#108×C₄₁	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×#108×C₄₁	2
C₄×M₁₆×C₄₁	2
C₂×C₄×C₈×C₄₁	2
C₄₁×#341	2
C₄×#108	41

Subgroups — C4×#108×C41 #19105557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#108×C₄₁ #19105557