Subgroups — #49158916

Order 37504.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34035995	C₂	1	2	yes	maximal
2	#34035892	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₂₉₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₂₉₃	C₂²	1	4	yes	—
5	#22627531	—	2	4	no	—
6	C₂²×C₈×C₂₉₃	C₂²	1	2	yes	—
7	C₂×C₄²×C₂₉₃	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₂₉₃	C₄	1	4	yes	complemented
9	C₂²×Dic₂₉₃	—	2	4	no	—
10	C₄⋊Dic₂₉₃	—	2	8	no	—
11	C₂²×C₄×C₂₉₃	D₄	1	2	yes	—
12	C₂²×C₄×C₂₉₃	C₂³	1	1	yes	characteristic
13	C₂×C₈×C₂₉₃	—	2	4	no	—
14	C₂×C₈×C₂₉₃	C₂×C₄	1	4	yes	—
15	C₄²×C₂₉₃	C₂×C₄	1	2	yes	—
16	C₄²×C₂₉₃	Q₈	1	2	yes	—
17	C₂×Dic₂₉₃	—	4	4	no	—
18	C₂×Dic₂₉₃	—	4	8	no	—
19	C₂³×C₂₉₃	C₂×D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉₃	—	2	4	no	—
21	C₂×C₄×C₂₉₃	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₂₉₃	#41	1	4	yes	—
25	C₈×C₂₉₃	—	2	4	no	—
26	C₂²×C₂₉₃	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₂₉₃	#124	1	2	yes	—
28	C₂²×C₂₉₃	#135	1	4	yes	—
29	C₄×C₂₉₃	—	2	4	no	—
30	C₄×C₂₉₃	#117	1	2	yes	—
31	C₄×C₂₉₃	#125	1	2	yes	—
32	Dic₂₉₃	—	8	4	no	—
33	C₂×C₂₉₃	#382	1	1	yes	characteristic
34	C₂×C₂₉₃	#427	1	2	yes	—
35	C₂×C₂₉₃	#488	1	4	yes	—
36	C₂₉₃	#1835	1	1	yes	characteristic, complemented, Sylow
37	#1835	—	293	1	no	maximal, Sylow
38	C₂×C₄×C₈	D₂₉₃	1	1	yes	characteristic
39	#382	—	293	2	no	—
40	#340	—	293	4	no	—
41	C₂²×C₈	C₂×D₂₉₃	1	2	yes	—
42	C₂×C₄⋊C₄	—	293	4	no	—
43	C₂×C₄²	C₂×D₂₉₃	1	1	yes	characteristic
44	C₄×C₈	Dic₂₉₃	1	4	yes	complemented
45	#95	—	586	4	no	—
46	C₂²×C₄	—	586	4	no	—
47	C₂²×C₄	D₁₁₇₂	1	2	yes	—
48	C₂²×C₄	C₂²×D₂₉₃	1	1	yes	characteristic
49	C₂×C₈	—	2	4	no	—
50	C₂×C₈	C₂×Dic₂₉₃	1	4	yes	—
51	C₄⋊C₄	—	586	8	no	—
52	C₄²	C₂×Dic₂₉₃	1	2	yes	—
53	C₄²	Dic₅₈₆	1	2	yes	—
54	C₂³	C₂×D₁₁₇₂	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	1172	4	no	—
57	C₂×C₄	—	1172	8	no	—
58	C₂×C₄	C₄⋊Dic₂₉₃	1	4	yes	—
59	C₂×C₄	C₂²×Dic₂₉₃	1	1	yes	characteristic
60	C₂×C₄	C₂×Dic₅₈₆	1	1	yes	characteristic
61	C₂×C₄	#17989802	1	4	yes	—
62	C₈	—	2	4	no	—
63	C₂²	C₂×C₄⋊Dic₂₉₃	1	1	yes	characteristic
64	C₂²	#22627612	1	2	yes	—
65	C₂²	#22627646	1	4	yes	—
66	C₄	—	2	4	no	—
67	C₄	—	2344	4	no	—
68	C₄	#22627583	1	2	yes	—
69	C₄	#22627616	1	2	yes	—
70	C₂	#34035995	1	1	yes	characteristic
71	C₂	#34036167	1	2	yes	—
72	C₂	#34036484	1	4	yes	—

	subgroup	G/H
center	C₂³	C₂×D₁₁₇₂
commutator	C₂×C₄×C₂₉₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉₃
Fitting	C₂×C₄×C₈×C₂₉₃	C₂
socle, prime radical	C₂³×C₂₉₃	C₂×D₄
cosocle	C₂²×C₄×C₂₉₃	C₂³
hypercenter	C₂×C₄×C₈	D₂₉₃
hypocenter	C₂₉₃	#1835
LCS	G ▷ C₂×C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. C₄×C₈×C₂₉₃	C₄	semidirect
36. C₂₉₃	#1835	semidirect
44. C₄×C₈	Dic₂₉₃	semidirect

Maximal subgroups

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

subgroup	index
#34035995	2
#34035892	2
C₂×C₄×C₈×C₂₉₃	2
#1835	293