Subgroups — #49175182

Order 37504.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×#11924078	C₂	1	2	yes	maximal
2	#34037056	C₂	1	1	yes	maximal, characteristic
3	#34037042	C₂	1	2	yes	maximal
4	#34037016	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×D₂₉₃	C₂	1	1	yes	maximal, characteristic
6	Q₈×#11924078	—	2	2	no	—
7	D₂₉₃⋊C₁₆	C₂²	1	1	yes	characteristic
8	#22627693	C₂²	1	2	yes	—
9	#22627687	—	2	2	no	—
10	C₈×#11924078	C₂²	1	1	yes	characteristic
11	Q₁₆×D₂₉₃	C₂²	1	2	yes	—
12	Dic₂₃₄₄	C₄	1	1	yes	characteristic, complemented
13	#22627570	C₄	1	2	yes	complemented
14	C₁₆×D₂₉₃	C₂²	1	1	yes	characteristic
15	Q₃₂×C₂₉₃	C₄	1	1	yes	characteristic, complemented
16	D₂₉₃⋊C₈	D₄	1	1	yes	characteristic
17	C₄⋊#11924078	—	2	2	no	—
18	C₄⋊#11924078	—	4	2	no	—
19	C₄×#11924078	—	4	2	no	—
20	C₄×#11924078	D₄	1	1	yes	characteristic
21	#17989805	—	2	1	no	—
22	Q₈×D₂₉₃	—	2	2	no	—
23	Dic₁₁₇₂	C₂×C₄	1	2	yes	—
24	#17989792	—	2	2	no	—
25	C₈×D₂₉₃	C₂³	1	1	yes	characteristic
26	#17989777	C₂×C₄	1	1	yes	characteristic
27	Q₁₆×C₂₉₃	C₂×C₄	1	2	yes	—
28	C₁₆×C₂₉₃	C₂×C₄	1	1	yes	characteristic
29	C₂×#11924078	—	4	2	no	—
30	C₂×#11924078	D₈	1	2	yes	—
31	#14556880	—	2	1	no	—
32	Dic₅₈₆	—	2	2	no	—
33	Dic₅₈₆	—	4	2	no	—
34	C₄×D₂₉₃	—	4	2	no	—
35	C₄×D₂₉₃	C₂×D₄	1	1	yes	characteristic
36	#14556873	#41	1	1	yes	characteristic
37	Q₈×C₂₉₃	—	2	2	no	—
38	C₈×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×D₂₉₃	C₂×D₈	1	1	yes	characteristic
40	#11924078	—	2	2	no	—
41	#11924078	—	8	2	no	—
42	C₄×C₂₉₃	—	4	2	no	—
43	C₄×C₂₉₃	C₄×D₄	1	1	yes	characteristic
44	Dic₂₉₃	—	4	2	no	—
45	Dic₂₉₃	#135	1	1	yes	characteristic
46	C₂×C₂₉₃	C₄×D₈	1	1	yes	characteristic
47	D₂₉₃	#510	1	2	yes	—
48	C₂₉₃	#2176	1	1	yes	characteristic, complemented, Sylow
49	#2176	—	293	1	no	maximal, Sylow
50	C₂×Q₃₂	—	293	1	no	—
51	C₄×Q₁₆	—	293	2	no	—
52	#367	—	293	1	no	—
53	#358	—	293	2	no	—
54	#346	—	293	1	no	—
55	C₂×Q₁₆	—	293	2	no	—
56	C₄×Q₈	—	586	2	no	—
57	Q₃₂	—	293	2	no	—
58	Q₃₂	—	293	1	no	—
59	Q₃₂	#11924078	1	1	yes	characteristic, complemented
60	C₂×C₁₆	—	293	1	no	—
61	C₂×C₁₆	—	293	1	no	—
62	#107	—	293	2	no	—
63	#103	—	586	2	no	—
64	C₄×C₈	—	293	1	no	—
65	C₂×Q₈	—	586	2	no	—
66	Q₁₆	—	293	2	no	—
67	Q₁₆	—	586	2	no	—
68	Q₁₆	C₂×#11924078	1	2	yes	—
69	C₂×C₈	—	293	1	no	—
70	C₂×C₈	—	293	1	no	—
71	C₄⋊C₄	—	586	2	no	—
72	C₄⋊C₄	—	1172	2	no	—
73	C₄²	—	293	1	no	—
74	C₄²	—	1172	2	no	—
75	C₁₆	—	293	1	no	—
76	C₁₆	—	586	1	no	—
77	C₁₆	C₂×#11924078	1	1	yes	characteristic
78	Q₈	—	2	2	no	—
79	Q₈	—	586	2	no	—
80	Q₈	—	1172	2	no	—
81	C₂×C₄	—	293	1	no	—
82	C₂×C₄	—	293	2	no	—
83	C₂×C₄	—	1172	2	no	—
84	C₂×C₄	—	1172	2	no	—
85	C₈	—	293	1	no	—
86	C₈	—	586	1	no	—
87	C₈	C₂²×#11924078	1	1	yes	characteristic
88	C₂²	—	293	1	no	—
89	C₄	—	4	2	no	—
90	C₄	—	293	1	no	—
91	C₄	—	2344	2	no	—
92	C₄	—	586	2	no	—
93	C₄	—	1172	2	no	—
94	C₄	D₄×#11924078	1	1	yes	characteristic
95	C₂	—	293	2	no	—
96	C₂	D₈×#11924078	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×#11924078
commutator	C₈×C₂₉₃	C₂²×C₄
Frattini	C₈	C₂²×#11924078
Fitting	Q₃₂×C₂₉₃	C₄
socle	C₂×C₂₉₃	C₄×D₈
prime radical	C₂×D₂₉₃	C₂×D₈
cosocle	C₈×D₂₉₃	C₂³
hypercenter	Q₃₂	#11924078
hypocenter	C₂₉₃	#2176
LCS	G ▷ C₈×C₂₉₃ ▷ C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
12. Dic₂₃₄₄	C₄	semidirect
13. #22627570	C₄	semidirect
15. Q₃₂×C₂₉₃	C₄	semidirect
48. C₂₉₃	#2176	semidirect
59. Q₃₂	#11924078	semidirect

Maximal subgroups

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

subgroup	index
Q₁₆×#11924078	2
#34037056	2
#34037042	2
#34037016	2
Q₃₂×D₂₉₃	2
#2176	293