Subgroups — #34036459

Order 18752.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627603	C₂	1	1	yes	maximal, characteristic
2	#22627555	C₂	1	2	yes	maximal, complemented
3	#22627547	C₂	1	2	yes	maximal, complemented
4	C₂²⋊#14556873	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₄×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	C₂²⋊Dic₂₉₃	—	2	1	no	—
11	C₂²×C₄×C₂₉₃	—	2	1	no	—
12	C₂²×C₄×C₂₉₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₂₉₃	—	2	1	no	—
14	C₄⋊C₄×C₂₉₃	C₂²	1	2	yes	—
15	Dic₅₈₆	—	2	2	no	—
16	C₂×Dic₂₉₃	—	2	1	no	—
17	C₂×Dic₂₉₃	—	2	1	no	—
18	#14556873	—	2	2	no	—
19	C₂³×C₂₉₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉₃	—	2	2	no	—
21	C₂×C₄×C₂₉₃	—	2	2	no	—
22	C₂×C₄×C₂₉₃	—	4	2	no	—
23	C₂×C₄×C₂₉₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₉₃	C₂³	1	1	yes	characteristic
25	C₂²×C₂₉₃	—	2	1	no	—
26	C₂²×C₂₉₃	—	2	1	no	—
27	C₂²×C₂₉₃	SD₁₆	1	2	yes	—
28	C₂²×C₂₉₃	C₂×D₄	1	1	yes	characteristic
29	C₄×C₂₉₃	—	2	1	no	—
30	C₄×C₂₉₃	—	4	2	no	—
31	C₄×C₂₉₃	#41	1	2	yes	—
32	Dic₂₉₃	—	4	1	no	—
33	Dic₂₉₃	—	4	1	no	—
34	C₂×C₂₉₃	—	2	2	no	—
35	C₂×C₂₉₃	#123	1	1	yes	characteristic
36	C₂×C₂₉₃	C₂×SD₁₆	1	1	yes	characteristic
37	C₂×C₂₉₃	#137	1	1	yes	characteristic
38	C₂₉₃	#483	1	1	yes	characteristic, complemented, Sylow
39	#483	—	293	1	no	maximal, Sylow
40	C₂²⋊Q₈	—	293	1	no	—
41	C₂×C₄⋊C₄	D₂₉₃	1	1	yes	characteristic
42	#106	—	293	2	no	—
43	#103	—	293	2	no	—
44	C₂²⋊C₈	—	293	1	no	—
45	C₂×Q₈	—	293	1	no	—
46	C₂²×C₄	—	2	1	no	—
47	C₂²×C₄	C₂×D₂₉₃	1	1	yes	characteristic
48	C₂×C₈	—	293	2	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	293	1	no	—
51	C₄⋊C₄	—	586	1	no	—
52	C₄⋊C₄	C₂×D₂₉₃	1	2	yes	—
53	C₂²⋊C₄	—	586	1	no	—
54	C₂³	C₂²⋊D₂₉₃	1	1	yes	characteristic
55	Q₈	—	586	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	4	2	no	—
59	C₂×C₄	—	586	1	no	—
60	C₂×C₄	—	586	1	no	—
61	C₂×C₄	C₂²⋊D₂₉₃	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₂₉₃	1	1	yes	characteristic
63	C₈	—	586	2	no	—
64	C₂²	—	2	1	no	—
65	C₂²	—	2	1	no	—
66	C₂²	#17989790	1	2	yes	—
67	C₂²	C₂×C₂²⋊D₂₉₃	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	4	2	no	—
70	C₄	—	1172	1	no	—
71	C₄	—	1172	1	no	—
72	C₄	#17989802	1	2	yes	—
73	C₂	—	2	2	no	—
74	C₂	#22627607	1	1	yes	characteristic
75	C₂	C₂×#17989790	1	1	yes	characteristic
76	C₂	#22627655	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₂₉₃
commutator, cosocle	C₂×C₄×C₂₉₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₉₃
Fitting	C₂×C₄⋊C₄×C₂₉₃	C₂
socle	C₂²×C₂₉₃	C₂×D₄
prime radical	C₂³×C₂₉₃	D₄
hypercenter	C₂×C₄⋊C₄	D₂₉₃
hypocenter	C₂₉₃	#483
LCS	G ▷ C₂×C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #22627555	C₂	semidirect
3. #22627547	C₂	semidirect
38. C₂₉₃	#483	semidirect

Maximal subgroups

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

subgroup	index
#22627603	2
#22627555	2
#22627547	2
C₂²⋊#14556873	2
C₂×C₄⋊C₄×C₂₉₃	2
#483	293