Subgroups — #34036259

Order 18752.

94 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	C₄⋊#14556873	C₂	1	1	yes	maximal, characteristic
3	#22627553	C₂	1	2	yes	maximal
4	#22627534	C₂	1	2	yes	maximal
5	C₄×C₈×C₂₉₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₅₈₆	C₄	1	1	yes	characteristic
7	C₂×#14556873	C₂²	1	2	yes	—
8	C₄⋊Dic₂₉₃	C₄	1	1	yes	characteristic
9	#17989781	C₄	1	2	yes	—
10	C₄×Dic₂₉₃	C₂²	1	2	yes	—
11	C₂×C₈×C₂₉₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₂₉₃	C₂²	1	1	yes	characteristic
13	C₄²×C₂₉₃	C₂²	1	1	yes	characteristic
14	Dic₅₈₆	—	2	2	no	—
15	C₂×Dic₂₉₃	C₂×C₄	1	2	yes	—
16	C₂×Dic₂₉₃	C₂×C₄	1	2	yes	—
17	#14556873	—	2	2	no	—
18	C₂×C₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉₃	C₂³	1	1	yes	characteristic
21	C₈×C₂₉₃	—	2	1	no	—
22	C₈×C₂₉₃	Q₈	1	2	yes	complemented
23	C₂²×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₂₉₃	—	2	1	no	—
25	C₄×C₂₉₃	M₁₆	1	2	yes	—
26	C₄×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
27	C₄×C₂₉₃	#41	1	1	yes	characteristic
28	Dic₂₉₃	—	2	2	no	—
29	Dic₂₉₃	—	2	2	no	—
30	C₂×C₂₉₃	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₂₉₃	C₂×M₁₆	1	1	yes	characteristic
32	C₂×C₂₉₃	#131	1	1	yes	characteristic
33	C₂₉₃	#446	1	1	yes	characteristic, complemented, Sylow
34	#446	—	293	1	no	maximal, Sylow
35	C₄×Q₈	—	293	1	no	—
36	C₄⋊C₈	—	293	2	no	—
37	C₄⋊C₈	—	293	1	no	—
38	#97	—	293	2	no	—
39	C₄×C₈	D₂₉₃	1	1	yes	characteristic
40	C₂×Q₈	—	293	1	no	—
41	C₂×C₈	—	293	2	no	—
42	C₂×C₈	C₂×D₂₉₃	1	1	yes	characteristic
43	C₂×C₈	C₂×D₂₉₃	1	1	yes	characteristic
44	C₄⋊C₄	—	293	2	no	—
45	C₄⋊C₄	—	293	1	no	—
46	C₄²	—	293	2	no	—
47	C₄²	C₂×D₂₉₃	1	1	yes	characteristic
48	Q₈	—	586	2	no	—
49	C₂×C₄	—	293	2	no	—
50	C₂×C₄	—	293	2	no	—
51	C₂×C₄	C₄×D₂₉₃	1	1	yes	characteristic
52	C₂×C₄	C₄×D₂₉₃	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₂₉₃	1	1	yes	characteristic
54	C₈	—	2	1	no	—
55	C₈	—	586	2	no	—
56	C₈	Dic₅₈₆	1	2	yes	complemented
57	C₂²	C₂×C₄×D₂₉₃	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	586	2	no	—
60	C₄	—	586	2	no	—
61	C₄	#17989785	1	2	yes	—
62	C₄	C₂×Dic₅₈₆	1	1	yes	characteristic
63	C₄	#17989802	1	1	yes	characteristic
64	C₂	C₄×Dic₅₈₆	1	1	yes	characteristic
65	C₂	C₂×#17989785	1	1	yes	characteristic
66	C₂	#22627630	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉₃
commutator, socle, prime radical	C₂²×C₂₉₃	C₂²×C₄
Fitting	C₄×C₈×C₂₉₃	C₂
cosocle	C₂×C₄×C₂₉₃	C₂³
hypercenter	C₄×C₈	D₂₉₃
hypocenter	C₂₉₃	#446
LCS	G ▷ C₂²×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
22. C₈×C₂₉₃	Q₈	semidirect
33. C₂₉₃	#446	semidirect
56. C₈	Dic₅₈₆	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
C₄⋊#14556873	2
#22627553	2
#22627534	2
C₄×C₈×C₂₉₃	2
#446	293