Subgroups — #34036339

Order 18752.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989792	C₂	1	2	yes	maximal
2	#22627624	C₂	1	1	yes	maximal, characteristic
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	2	yes	—
7	#17989792	—	2	4	no	—
8	C₂×#14556873	C₂²	1	2	yes	—
9	C₄⋊Dic₂₉₃	—	2	1	no	—
10	C₄⋊Dic₂₉₃	—	2	1	no	—
11	C₂×Q₈×C₂₉₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₂₉₃	—	2	1	no	—
13	C₄⋊C₄×C₂₉₃	C₂²	1	1	yes	characteristic
14	C₄²×C₂₉₃	—	2	1	no	—
15	C₄²×C₂₉₃	C₂²	1	1	yes	characteristic
16	Dic₅₈₆	—	2	2	no	—
17	Dic₅₈₆	—	2	2	no	—
18	C₂×Dic₂₉₃	—	2	2	no	—
19	#14556873	—	2	2	no	—
20	Q₈×C₂₉₃	—	2	1	no	—
21	Q₈×C₂₉₃	D₄	1	2	yes	—
22	C₂×C₄×C₂₉₃	—	2	1	no	—
23	C₂×C₄×C₂₉₃	—	2	1	no	—
24	C₂×C₄×C₂₉₃	D₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉₃	D₄	1	1	yes	characteristic
26	C₂×C₄×C₂₉₃	C₂³	1	1	yes	characteristic
27	C₂²×C₂₉₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₂₉₃	—	2	2	no	—
29	C₄×C₂₉₃	—	2	1	no	—
30	C₄×C₂₉₃	—	4	1	no	—
31	C₄×C₂₉₃	Q₁₆	1	2	yes	complemented
32	C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₉₃	#41	1	1	yes	characteristic
34	Dic₂₉₃	—	4	2	no	—
35	C₂×C₂₉₃	#121	1	1	yes	characteristic
36	C₂×C₂₉₃	C₂×Q₁₆	1	1	yes	characteristic
37	C₂×C₂₉₃	#137	1	1	yes	characteristic
38	C₂₉₃	#462	1	1	yes	characteristic, complemented, Sylow
39	#462	—	293	1	no	maximal, Sylow
40	C₂×Q₁₆	—	293	2	no	—
41	C₄⋊Q₈	—	293	1	no	—
42	C₄×Q₈	D₂₉₃	1	1	yes	characteristic
43	C₄⋊C₈	—	293	1	no	—
44	#103	—	293	2	no	—
45	C₂×Q₈	—	293	2	no	—
46	C₂×Q₈	C₂×D₂₉₃	1	1	yes	characteristic
47	Q₁₆	—	586	4	no	—
48	C₂×C₈	—	293	2	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	586	1	no	—
51	C₄⋊C₄	—	586	1	no	—
52	C₄⋊C₄	C₂×D₂₉₃	1	1	yes	characteristic
53	C₄²	—	2	1	no	—
54	C₄²	C₂×D₂₉₃	1	1	yes	characteristic
55	Q₈	—	2	1	no	—
56	Q₈	—	586	2	no	—
57	Q₈	—	586	2	no	—
58	Q₈	D₁₁₇₂	1	2	yes	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	586	2	no	—
62	C₂×C₄	C₂²⋊D₂₉₃	1	1	yes	characteristic
63	C₂×C₄	C₂²⋊D₂₉₃	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₂₉₃	1	1	yes	characteristic
65	C₈	—	586	2	no	—
66	C₂²	C₂×C₂²⋊D₂₉₃	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	2	1	no	—
69	C₄	—	4	1	no	—
70	C₄	—	1172	2	no	—
71	C₄	#17989792	1	2	yes	complemented
72	C₄	C₂×D₁₁₇₂	1	1	yes	characteristic
73	C₄	#17989802	1	1	yes	characteristic
74	C₂	#22627598	1	1	yes	characteristic
75	C₂	C₂×#17989792	1	1	yes	characteristic
76	C₂	#22627654	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	#462
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
31. C₄×C₂₉₃	Q₁₆	semidirect
38. C₂₉₃	#462	semidirect
71. C₄	#17989792	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989792	2
#22627624	2
C₄⋊#14556873	2
#22627547	2
C₄×Q₈×C₂₉₃	2
#462	293