Subgroups — #34036421

Order 18752.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₅₈₆	C₂	1	1	yes	maximal, characteristic
2	#22627557	C₂	1	2	yes	maximal
3	C₄⋊#14556873	C₂	1	1	yes	maximal, characteristic
4	#22627547	C₂	1	2	yes	maximal
5	C₄⋊Q₈×C₂₉₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₅₈₆	C₂²	1	1	yes	characteristic
7	C₂×#14556873	C₂²	1	2	yes	—
8	C₄⋊Dic₂₉₃	C₂²	1	1	yes	characteristic
9	#17989781	—	2	1	no	—
10	C₄×Dic₂₉₃	—	2	1	no	—
11	C₂×Q₈×C₂₉₃	—	2	1	no	—
12	C₄⋊C₄×C₂₉₃	—	2	1	no	—
13	C₄⋊C₄×C₂₉₃	C₂²	1	2	yes	—
14	C₄²×C₂₉₃	C₂²	1	1	yes	characteristic
15	Dic₅₈₆	—	2	1	no	—
16	Dic₅₈₆	Q₈	1	2	yes	complemented
17	C₂×Dic₂₉₃	—	2	1	no	—
18	C₂×Dic₂₉₃	—	2	1	no	—
19	#14556873	—	2	2	no	—
20	Q₈×C₂₉₃	—	4	2	no	—
21	C₂×C₄×C₂₉₃	—	2	2	no	—
22	C₂×C₄×C₂₉₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₂₉₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₉₃	C₂³	1	1	yes	characteristic
25	C₂²×C₂₉₃	C₂×D₄	1	1	yes	characteristic
26	C₄×C₂₉₃	—	2	1	no	—
27	C₄×C₂₉₃	—	4	2	no	—
28	C₄×C₂₉₃	Q₁₆	1	2	yes	—
29	C₄×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
30	C₄×C₂₉₃	#41	1	1	yes	characteristic
31	Dic₂₉₃	—	2	2	no	—
32	Dic₂₉₃	—	4	1	no	—
33	C₂×C₂₉₃	C₂²⋊Q₈	1	1	yes	characteristic
34	C₂×C₂₉₃	C₂×Q₁₆	1	1	yes	characteristic
35	C₂×C₂₉₃	AGL(1,ℤ/8)	1	1	yes	characteristic
36	C₂₉₃	#477	1	1	yes	characteristic, complemented, Sylow
37	#477	—	293	1	no	maximal, Sylow
38	C₄⋊Q₈	D₂₉₃	1	1	yes	characteristic
39	C₄×Q₈	—	293	1	no	—
40	#107	—	293	2	no	—
41	C₄⋊C₈	—	293	1	no	—
42	#103	—	293	2	no	—
43	C₂×Q₈	—	2	1	no	—
44	C₂×Q₈	—	293	1	no	—
45	C₂×C₈	—	293	2	no	—
46	C₄⋊C₄	—	2	1	no	—
47	C₄⋊C₄	—	293	1	no	—
48	C₄⋊C₄	—	586	1	no	—
49	C₄⋊C₄	C₂×D₂₉₃	1	2	yes	—
50	C₄²	—	586	1	no	—
51	C₄²	C₂×D₂₉₃	1	1	yes	characteristic
52	Q₈	—	4	2	no	—
53	Q₈	—	293	2	no	—
54	Q₈	—	586	1	no	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	586	1	no	—
57	C₂×C₄	—	586	1	no	—
58	C₂×C₄	C₂²⋊D₂₉₃	1	1	yes	characteristic
59	C₂×C₄	C₂²⋊D₂₉₃	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₂₉₃	1	1	yes	characteristic
61	C₈	—	586	2	no	—
62	C₂²	C₂×C₂²⋊D₂₉₃	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	—	4	2	no	—
65	C₄	—	586	2	no	—
66	C₄	—	1172	1	no	—
67	C₄	#17989792	1	2	yes	—
68	C₄	Q₈×D₂₉₃	1	1	yes	characteristic
69	C₄	#17989803	1	1	yes	characteristic
70	C₂	#22627600	1	1	yes	characteristic
71	C₂	C₂×#17989792	1	1	yes	characteristic
72	C₂	#22627650	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₂₉₃
commutator, cosocle	C₂×C₄×C₂₉₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₉₃
Fitting	C₄⋊Q₈×C₂₉₃	C₂
socle, prime radical	C₂²×C₂₉₃	C₂×D₄
hypercenter	C₄⋊Q₈	D₂₉₃
hypocenter	C₂₉₃	#477
LCS	G ▷ C₂×C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
16. Dic₅₈₆	Q₈	semidirect
36. C₂₉₃	#477	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₅₈₆	2
#22627557	2
C₄⋊#14556873	2
#22627547	2
C₄⋊Q₈×C₂₉₃	2
#477	293