Subgroups — #41×#3866 #14558599

Order 2368.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#3866	C₂	1	2	yes	maximal, complemented
2	D₄×#3866	C₂	1	6	yes	maximal, complemented
3	#11924615	C₂	1	3	yes	maximal, complemented
4	C₂×C₄×#3866	C₂	1	3	yes	maximal, complemented
5	#41×D₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#3866	C₂²	1	6	yes	—
7	#41×C₃₇	C₄	1	1	yes	characteristic, complemented
8	#10596966	C₄	1	1	yes	characteristic, complemented
9	Q₈×D₃₇	C₂²	1	1	yes	characteristic
10	#10596964	C₄	1	3	yes	complemented
11	D₄×D₃₇	C₂²	1	3	yes	—
12	#10596962	C₄	1	3	yes	complemented
13	C₂×C₄×D₃₇	C₂²	1	3	yes	—
14	C₂²⋊#3866	C₂²	1	6	yes	—
15	C₄⋊#3866	C₂²	1	6	yes	—
16	C₄×#3866	C₂²	1	1	yes	characteristic
17	C₄×#3866	C₂²	1	3	yes	—
18	C₄×#3866	C₂²	1	6	yes	—
19	C₂²×D₃₇	C₂³	1	3	yes	—
20	C₂×#3866	—	2	12	no	—
21	C₂×#3866	C₂³	1	6	yes	—
22	C₂×#3866	C₂³	1	2	yes	—
23	Q₈×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
24	D₄×C₃₇	C₂×C₄	1	3	yes	complemented
25	C₂×C₄×C₃₇	C₂×C₄	1	3	yes	complemented
26	C₂²⋊D₃₇	C₂×C₄	1	6	yes	complemented
27	C₂×Dic₃₇	C₂×C₄	1	3	yes	complemented
28	D₁₄₈	C₂×C₄	1	3	yes	complemented
29	C₄×D₃₇	C₂×C₄	1	3	yes	complemented
30	C₄×D₃₇	C₂×C₄	1	3	yes	complemented
31	C₄×D₃₇	C₂³	1	1	yes	characteristic
32	C₄×D₃₇	C₂³	1	3	yes	—
33	Dic₇₄	C₂×C₄	1	3	yes	complemented
34	C₂²×C₃₇	C₂²×C₄	1	3	yes	—
35	C₂×D₃₇	—	2	6	no	—
36	C₂×D₃₇	C₂²×C₄	1	3	yes	—
37	C₂×D₃₇	C₂⁴	1	1	yes	characteristic
38	#3866	—	2	6	no	—
39	#3866	#41	1	4	yes	direct product factor
40	C₄×C₃₇	C₂²×C₄	1	3	yes	—
41	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
42	Dic₃₇	C₂²×C₄	1	3	yes	—
43	Dic₃₇	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₃₇	—	2	3	no	—
45	C₂×C₃₇	C₂³×C₄	1	1	yes	characteristic
46	D₃₇	—	2	3	no	—
47	D₃₇	C₂×#41	1	2	yes	—
48	C₄×#41	—	37	1	no	maximal, Sylow
49	C₃₇	C₄×#41	1	1	yes	characteristic, complemented, Sylow
50	C₂×#41	—	37	1	no	—
51	C₄×Q₈	—	37	2	no	—
52	C₄×D₄	—	37	6	no	—
53	#117	—	37	3	no	—
54	C₂×C₄²	—	37	3	no	—
55	#41	—	37	1	no	—
56	#41	—	37	3	no	—
57	#41	—	37	3	no	—
58	#41	#3866	1	1	yes	characteristic, direct product factor
59	C₂×Q₈	—	37	1	no	—
60	C₂×D₄	—	37	3	no	—
61	C₂²×C₄	—	37	3	no	—
62	C₂²×C₄	—	37	6	no	—
63	C₄⋊C₄	—	37	6	no	—
64	C₂²⋊C₄	—	37	6	no	—
65	C₄²	—	37	1	no	—
66	C₄²	—	37	3	no	—
67	C₄²	—	37	6	no	—
68	C₂³	—	37	3	no	—
69	Q₈	—	37	3	no	—
70	Q₈	C₂×#3866	1	1	yes	characteristic, complemented
71	D₄	—	37	6	no	—
72	D₄	—	37	3	no	—
73	D₄	C₂×#3866	1	3	yes	complemented
74	C₂×C₄	—	37	2	no	—
75	C₂×C₄	—	37	3	no	—
76	C₂×C₄	—	37	3	no	—
77	C₂×C₄	—	37	3	no	—
78	C₂×C₄	—	37	1	no	—
79	C₂×C₄	—	37	3	no	—
80	C₂×C₄	—	37	6	no	—
81	C₂×C₄	—	74	12	no	—
82	C₂×C₄	C₂×#3866	1	3	yes	complemented
83	C₂²	—	37	1	no	—
84	C₂²	—	37	3	no	—
85	C₂²	—	74	6	no	—
86	C₂²	C₂²×#3866	1	3	yes	—
87	C₄	—	37	4	no	—
88	C₄	—	37	1	no	—
89	C₄	—	37	3	no	—
90	C₄	—	74	6	no	—
91	C₄	C₂²×#3866	1	3	yes	—
92	C₄	C₂²×#3866	1	1	yes	characteristic
93	C₂	—	2	3	no	—
94	C₂	—	37	2	no	—
95	C₂	—	74	3	no	—
96	C₂	C₂³×#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×#3866
commutator, socle	C₂×C₃₇	C₂³×C₄
Frattini	C₂	C₂³×#3866
Fitting	#41×C₃₇	C₄
prime radical	#41×D₃₇	C₂
cosocle	C₂×D₃₇	C₂⁴
hypercenter	#41	#3866
hypocenter	C₃₇	C₄×#41
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. Q₈×#3866	C₂	semidirect
2. D₄×#3866	C₂	semidirect
3. #11924615	C₂	semidirect
4. C₂×C₄×#3866	C₂	semidirect
7. #41×C₃₇	C₄	semidirect
8. #10596966	C₄	semidirect
10. #10596964	C₄	semidirect
12. #10596962	C₄	semidirect
23. Q₈×C₃₇	C₂×C₄	semidirect
24. D₄×C₃₇	C₂×C₄	semidirect
25. C₂×C₄×C₃₇	C₂×C₄	semidirect
26. C₂²⋊D₃₇	C₂×C₄	semidirect
27. C₂×Dic₃₇	C₂×C₄	semidirect
28. D₁₄₈	C₂×C₄	semidirect
29. C₄×D₃₇	C₂×C₄	semidirect
30. C₄×D₃₇	C₂×C₄	semidirect
33. Dic₇₄	C₂×C₄	semidirect
39. #3866	#41	direct (N × H)
49. C₃₇	C₄×#41	semidirect
58. #41	#3866	direct (N × H)
70. Q₈	C₂×#3866	semidirect
73. D₄	C₂×#3866	semidirect
82. C₂×C₄	C₂×#3866	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#3866	2
D₄×#3866	2
#11924615	2
C₂×C₄×#3866	2
#41×D₃₇	2
C₄×#41	37