Subgroups — #34035932

Order 18752.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₇₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989777	C₂	1	1	yes	maximal, characteristic
3	#107×C₂₉₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₅₈₆	—	2	1	no	—
5	Dic₁₁₇₂	—	2	1	no	—
6	Dic₁₁₇₂	C₄	1	2	yes	complemented
7	#17989777	—	2	1	no	—
8	C₂×C₈×C₂₉₃	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₂₉₃	—	2	1	no	—
10	Dic₅₈₆	—	2	2	no	—
11	Dic₅₈₆	—	4	1	no	—
12	C₂×Dic₂₉₃	—	4	1	no	—
13	C₂×C₄×C₂₉₃	—	4	1	no	—
14	C₂×C₄×C₂₉₃	D₄	1	1	yes	characteristic
15	C₈×C₂₉₃	C₂×C₄	1	1	yes	characteristic
16	C₈×C₂₉₃	D₄	1	1	yes	characteristic
17	C₂²×C₂₉₃	D₈	1	1	yes	characteristic
18	C₄×C₂₉₃	—	8	1	no	—
19	C₄×C₂₉₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₂₉₃	SD₁₆	1	1	yes	characteristic
21	Dic₂₉₃	—	4	2	no	—
22	C₂×C₂₉₃	#102	1	1	yes	characteristic
23	C₂×C₂₉₃	SD₃₂	1	1	yes	characteristic
24	C₂×C₂₉₃	Q₃₂	1	1	yes	characteristic
25	C₂₉₃	#358	1	1	yes	characteristic, complemented, Sylow
26	#358	—	293	1	no	maximal, Sylow
27	C₂×Q₁₆	—	293	1	no	—
28	C₂×C₁₆	—	293	1	no	—
29	#107	D₂₉₃	1	1	yes	characteristic
30	C₂×Q₈	—	586	1	no	—
31	Q₁₆	—	293	2	no	—
32	Q₁₆	—	586	1	no	—
33	C₂×C₈	C₂×D₂₉₃	1	1	yes	characteristic
34	C₄⋊C₄	—	2	1	no	—
35	C₁₆	—	586	1	no	—
36	Q₈	—	586	2	no	—
37	Q₈	—	1172	1	no	—
38	C₂×C₄	—	4	1	no	—
39	C₂×C₄	—	1172	1	no	—
40	C₂×C₄	C₂²⋊D₂₉₃	1	1	yes	characteristic
41	C₈	C₄×D₂₉₃	1	1	yes	characteristic
42	C₈	D₁₁₇₂	1	1	yes	characteristic
43	C₂²	#17989787	1	1	yes	characteristic
44	C₄	—	8	1	no	—
45	C₄	—	1172	2	no	—
46	C₄	#17989779	1	1	yes	characteristic
47	C₄	#17989789	1	1	yes	characteristic
48	C₂	#22627544	1	1	yes	characteristic
49	C₂	#22627568	1	1	yes	characteristic
50	C₂	#22627570	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#17989787
commutator	C₈×C₂₉₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₂₉₃
Fitting	#107×C₂₉₃	C₂
socle, prime radical	C₂²×C₂₉₃	D₈
cosocle	C₂×C₈×C₂₉₃	C₂²
hypercenter	#107	D₂₉₃
hypocenter	C₂₉₃	#358
LCS	G ▷ C₈×C₂₉₃ ▷ C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
6. Dic₁₁₇₂	C₄	semidirect
25. C₂₉₃	#358	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₁₇₂	2
C₂×#17989777	2
#107×C₂₉₃	2
#358	293