Subgroups — #49160656

Order 37504.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×Dic₂₉₃	C₂	1	2	yes	maximal
2	#34035957	C₂	1	1	yes	maximal, characteristic
3	#34035933	C₂	1	2	yes	maximal
4	#34035904	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₃₂×C₂₉₃	C₂	1	1	yes	maximal, characteristic
6	Q₈×Dic₂₉₃	—	2	2	no	—
7	C₂×#17989777	C₂²	1	1	yes	characteristic
8	#22627558	C₂²	1	2	yes	—
9	#22627548	—	2	2	no	—
10	C₈×Dic₂₉₃	C₂²	1	1	yes	characteristic
11	C₂×Q₁₆×C₂₉₃	C₂²	1	2	yes	—
12	Q₃₂×C₂₉₃	C₄	1	4	yes	complemented
13	C₂×C₁₆×C₂₉₃	C₂²	1	1	yes	characteristic
14	C₂×#14556873	D₄	1	1	yes	characteristic
15	C₄⋊Dic₂₉₃	—	2	2	no	—
16	C₄⋊Dic₂₉₃	—	4	2	no	—
17	C₄×Dic₂₉₃	—	4	2	no	—
18	C₄×Dic₂₉₃	D₄	1	1	yes	characteristic
19	#17989777	—	2	1	no	—
20	C₂×Q₈×C₂₉₃	—	2	2	no	—
21	Q₁₆×C₂₉₃	—	2	2	no	—
22	Q₁₆×C₂₉₃	C₂×C₄	1	4	yes	—
23	C₂×C₈×C₂₉₃	C₂³	1	1	yes	characteristic
24	C₁₆×C₂₉₃	C₂×C₄	1	2	yes	—
25	C₂×Dic₂₉₃	—	4	2	no	—
26	C₂×Dic₂₉₃	D₈	1	2	yes	—
27	#14556873	—	2	1	no	—
28	Q₈×C₂₉₃	—	2	4	no	—
29	Q₈×C₂₉₃	—	4	2	no	—
30	C₂×C₄×C₂₉₃	—	4	2	no	—
31	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
32	C₈×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₂₉₃	#41	1	1	yes	characteristic
34	C₂²×C₂₉₃	C₂×D₈	1	1	yes	characteristic
35	C₄×C₂₉₃	—	4	4	no	—
36	C₄×C₂₉₃	C₄×D₄	1	1	yes	characteristic
37	C₄×C₂₉₃	#135	1	1	yes	characteristic
38	Dic₂₉₃	—	2	2	no	—
39	Dic₂₉₃	—	8	2	no	—
40	C₂×C₂₉₃	C₄×D₈	1	1	yes	characteristic
41	C₂×C₂₉₃	#510	1	2	yes	—
42	C₂₉₃	#2176	1	1	yes	characteristic, complemented, Sylow
43	#2176	—	293	1	no	maximal, Sylow
44	C₂×Q₃₂	D₂₉₃	1	1	yes	characteristic
45	C₄×Q₁₆	—	293	2	no	—
46	#367	—	293	1	no	—
47	#358	—	293	2	no	—
48	#346	—	293	1	no	—
49	C₂×Q₁₆	C₂×D₂₉₃	1	2	yes	—
50	C₄×Q₈	—	586	2	no	—
51	Q₃₂	Dic₂₉₃	1	4	yes	complemented
52	C₂×C₁₆	—	293	1	no	—
53	C₂×C₁₆	C₂×D₂₉₃	1	1	yes	characteristic
54	#107	—	293	2	no	—
55	#103	—	586	2	no	—
56	C₄×C₈	—	293	1	no	—
57	C₂×Q₈	—	2	2	no	—
58	Q₁₆	—	2	2	no	—
59	Q₁₆	C₂×Dic₂₉₃	1	4	yes	—
60	C₂×C₈	—	293	1	no	—
61	C₂×C₈	C₂²×D₂₉₃	1	1	yes	characteristic
62	C₄⋊C₄	—	586	2	no	—
63	C₄⋊C₄	—	1172	2	no	—
64	C₄²	—	293	1	no	—
65	C₄²	—	1172	2	no	—
66	C₁₆	—	586	1	no	—
67	C₁₆	C₂×Dic₂₉₃	1	2	yes	—
68	Q₈	—	2	4	no	—
69	Q₈	—	4	2	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	293	2	no	—
72	C₂×C₄	—	1172	2	no	—
73	C₂×C₄	D₄×D₂₉₃	1	1	yes	characteristic
74	C₈	—	586	1	no	—
75	C₈	C₂²×Dic₂₉₃	1	1	yes	characteristic
76	C₈	#17989801	1	1	yes	characteristic
77	C₂²	D₈×D₂₉₃	1	1	yes	characteristic
78	C₄	—	4	4	no	—
79	C₄	—	2344	2	no	—
80	C₄	—	586	2	no	—
81	C₄	D₄×Dic₂₉₃	1	1	yes	characteristic
82	C₄	#22627643	1	1	yes	characteristic
83	C₂	D₈×Dic₂₉₃	1	1	yes	characteristic
84	C₂	#34036571	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
12. Q₃₂×C₂₉₃	C₄	semidirect
42. C₂₉₃	#2176	semidirect
51. Q₃₂	Dic₂₉₃	semidirect

Maximal subgroups

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

subgroup	index
Q₁₆×Dic₂₉₃	2
#34035957	2
#34035933	2
#34035904	2
C₂×Q₃₂×C₂₉₃	2
#2176	293