Subgroups — #49160670

Order 37504.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34036561	C₂	1	1	yes	maximal, characteristic
2	#34036245	C₂	1	2	yes	maximal, complemented
3	#34035935	C₂	1	2	yes	maximal, complemented
4	#34035904	C₂	1	1	yes	maximal, characteristic, complemented
5	#368×C₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#22627646	C₂²	1	2	yes	—
7	#22627632	—	2	2	no	—
8	Dic₂₃₄₄	C₄	1	1	yes	characteristic, complemented
9	#22627569	C₄	1	2	yes	complemented
10	D₄₆₈₈	C₄	1	1	yes	characteristic, complemented
11	C₂×#17989777	C₂²	1	1	yes	characteristic
12	#22627550	—	2	2	no	—
13	C₈×Dic₂₉₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₂₉₃	C₂²	1	1	yes	characteristic
15	#108×C₂₉₃	C₂²	1	2	yes	—
16	#17989802	—	2	2	no	—
17	Dic₁₁₇₂	C₂×C₄	1	2	yes	—
18	#17989791	—	2	2	no	—
19	D₂₃₄₄	C₂×C₄	1	2	yes	—
20	#17989785	—	4	2	no	—
21	C₂×#14556873	D₄	1	1	yes	characteristic
22	C₈×D₂₉₃	—	4	2	no	—
23	C₄×Dic₂₉₃	D₄	1	1	yes	characteristic
24	#17989777	—	2	1	no	—
25	M₁₆×C₂₉₃	—	2	2	no	—
26	C₂×C₈×C₂₉₃	C₂³	1	1	yes	characteristic
27	C₁₆×C₂₉₃	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₂₉₃	C₂×C₄	1	1	yes	characteristic
29	Dic₅₈₆	—	2	2	no	—
30	D₁₁₇₂	—	2	2	no	—
31	C₂²⋊D₂₉₃	—	4	2	no	—
32	C₂×Dic₂₉₃	—	2	1	no	—
33	C₄×D₂₉₃	—	4	2	no	—
34	#14556873	D₈	1	2	yes	—
35	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
36	C₈×C₂₉₃	—	4	2	no	—
37	C₈×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₂₉₃	#41	1	1	yes	characteristic
39	C₂²×C₂₉₃	#135	1	1	yes	characteristic
40	C₂×D₂₉₃	—	4	2	no	—
41	C₄×C₂₉₃	C₄×D₄	1	1	yes	characteristic
42	C₄×C₂₉₃	C₂×D₈	1	1	yes	characteristic
43	Dic₂₉₃	—	4	1	no	—
44	Dic₂₉₃	—	4	2	no	—
45	C₂×C₂₉₃	—	2	1	no	—
46	C₂×C₂₉₃	C₄×D₈	1	1	yes	characteristic
47	D₂₉₃	—	8	2	no	—
48	C₂₉₃	#2179	1	1	yes	characteristic, complemented, Sylow
49	#2179	—	293	1	no	maximal, Sylow
50	#508	—	293	1	no	—
51	#443	—	293	2	no	—
52	#368	D₂₉₃	1	1	yes	characteristic, complemented
53	#359	—	293	2	no	—
54	#346	—	293	1	no	—
55	#135	—	293	2	no	—
56	#131	—	586	2	no	—
57	Q₃₂	—	293	1	no	—
58	SD₃₂	—	293	2	no	—
59	D₁₆	—	293	1	no	—
60	C₂×C₁₆	—	293	1	no	—
61	C₂×C₁₆	C₂×D₂₉₃	1	1	yes	characteristic
62	#108	C₂×D₂₉₃	1	2	yes	—
63	#104	—	586	2	no	—
64	C₄×C₈	—	293	1	no	—
65	#41	—	586	2	no	—
66	Q₁₆	—	293	2	no	—
67	SD₁₆	—	586	2	no	—
68	D₈	—	293	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	1172	2	no	—
71	C₂×C₈	—	293	1	no	—
72	C₂×C₈	—	1172	2	no	—
73	C₂×C₈	C₂²×D₂₉₃	1	1	yes	characteristic
74	C₄²	—	293	1	no	—
75	C₁₆	—	586	1	no	—
76	C₁₆	C₄×D₂₉₃	1	1	yes	characteristic
77	C₁₆	C₄×D₂₉₃	1	1	yes	characteristic
78	Q₈	—	586	2	no	—
79	D₄	—	586	2	no	—
80	D₄	—	1172	2	no	—
81	C₂×C₄	—	586	1	no	—
82	C₂×C₄	—	1172	2	no	—
83	C₂×C₄	D₄×D₂₉₃	1	1	yes	characteristic
84	C₈	—	4	2	no	—
85	C₈	—	293	2	no	—
86	C₈	C₂×C₄×D₂₉₃	1	1	yes	characteristic
87	C₈	#17989803	1	1	yes	characteristic
88	C₂²	—	1172	2	no	—
89	C₂²	#22627647	1	1	yes	characteristic
90	C₄	—	1172	1	no	—
91	C₄	—	1172	2	no	—
92	C₄	#22627586	1	1	yes	characteristic
93	C₄	D₈×D₂₉₃	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	2344	2	no	—
96	C₂	#34036211	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₂₉₃
commutator	C₈×C₂₉₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₉₃
Fitting	#368×C₂₉₃	C₂
socle	C₂×C₂₉₃	C₄×D₈
prime radical	#34036561	C₂
cosocle	C₂×C₈×C₂₉₃	C₂³
hypercenter	#368	D₂₉₃
hypocenter	C₂₉₃	#2179
LCS	G ▷ C₈×C₂₉₃ ▷ C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

Complements

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

N	H ≅ G/N	type
2. #34036245	C₂	semidirect
3. #34035935	C₂	semidirect
4. #34035904	C₂	semidirect
5. #368×C₂₉₃	C₂	semidirect
8. Dic₂₃₄₄	C₄	semidirect
9. #22627569	C₄	semidirect
10. D₄₆₈₈	C₄	semidirect
48. C₂₉₃	#2179	semidirect
52. #368	D₂₉₃	semidirect

Maximal subgroups

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

subgroup	index
#34036561	2
#34036245	2
#34035935	2
#34035904	2
#368×C₂₉₃	2
#2179	293