Subgroups — #34036285

Order 18752.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989792	C₂	1	2	yes	maximal, complemented
2	#22627603	C₂	1	1	yes	maximal, characteristic
3	#22627548	C₂	1	2	yes	maximal, complemented
4	C₂²⋊#14556873	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₂₉₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₅₈₆	C₂²	1	1	yes	characteristic
7	#17989792	—	2	4	no	—
8	C₂×#14556873	C₂²	1	2	yes	—
9	C₄⋊Dic₂₉₃	C₂²	1	1	yes	characteristic
10	#17989781	—	2	1	no	—
11	C₂²⋊Dic₂₉₃	—	2	1	no	—
12	C₂×Q₈×C₂₉₃	—	2	4	no	—
13	C₂×Q₈×C₂₉₃	—	2	1	no	—
14	C₂×Q₈×C₂₉₃	C₂²	1	2	yes	—
15	C₂²×C₄×C₂₉₃	—	2	1	no	—
16	C₂²×C₄×C₂₉₃	C₂²	1	1	yes	characteristic
17	Dic₅₈₆	—	2	2	no	—
18	C₂×Dic₂₉₃	—	2	1	no	—
19	C₂×Dic₂₉₃	—	2	1	no	—
20	#14556873	—	2	2	no	—
21	C₂³×C₂₉₃	D₄	1	1	yes	characteristic
22	Q₈×C₂₉₃	—	2	4	no	—
23	Q₈×C₂₉₃	—	2	2	no	—
24	Q₈×C₂₉₃	D₄	1	4	yes	—
25	C₂×C₄×C₂₉₃	—	2	4	no	—
26	C₂×C₄×C₂₉₃	—	2	2	no	—
27	C₂×C₄×C₂₉₃	—	2	2	no	—
28	C₂×C₄×C₂₉₃	D₄	1	1	yes	characteristic
29	C₂×C₄×C₂₉₃	C₂³	1	1	yes	characteristic
30	C₂²×C₂₉₃	—	2	1	no	—
31	C₂²×C₂₉₃	—	2	1	no	—
32	C₂²×C₂₉₃	Q₁₆	1	2	yes	complemented
33	C₂²×C₂₉₃	C₂×D₄	1	1	yes	characteristic
34	C₄×C₂₉₃	—	2	4	no	—
35	C₄×C₂₉₃	—	2	1	no	—
36	C₄×C₂₉₃	C₂×D₄	1	2	yes	—
37	Dic₂₉₃	—	4	1	no	—
38	Dic₂₉₃	—	4	1	no	—
39	C₂×C₂₉₃	—	2	2	no	—
40	C₂×C₂₉₃	#120	1	1	yes	characteristic
41	C₂×C₂₉₃	C₂×Q₁₆	1	1	yes	characteristic
42	C₂×C₂₉₃	#137	1	1	yes	characteristic
43	C₂₉₃	#451	1	1	yes	characteristic, complemented, Sylow
44	#451	—	293	1	no	maximal, Sylow
45	C₂²×Q₈	D₂₉₃	1	1	yes	characteristic
46	C₂×Q₁₆	—	293	2	no	—
47	C₂²⋊Q₈	—	293	1	no	—
48	#103	—	293	2	no	—
49	C₂²⋊C₈	—	293	1	no	—
50	C₂×Q₈	—	2	4	no	—
51	C₂×Q₈	—	2	1	no	—
52	C₂×Q₈	—	293	1	no	—
53	C₂×Q₈	C₂×D₂₉₃	1	2	yes	—
54	C₂²×C₄	—	2	1	no	—
55	C₂²×C₄	C₂×D₂₉₃	1	1	yes	characteristic
56	Q₁₆	—	586	4	no	—
57	C₂×C₈	—	293	2	no	—
58	C₄⋊C₄	—	293	1	no	—
59	C₄⋊C₄	—	586	1	no	—
60	C₂²⋊C₄	—	586	1	no	—
61	C₂³	C₂²⋊D₂₉₃	1	1	yes	characteristic
62	Q₈	—	2	4	no	—
63	Q₈	—	2	2	no	—
64	Q₈	—	586	2	no	—
65	Q₈	C₂²⋊D₂₉₃	1	4	yes	—
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	—	586	1	no	—
70	C₂×C₄	—	586	1	no	—
71	C₂×C₄	C₂²⋊D₂₉₃	1	1	yes	characteristic
72	C₂×C₄	C₂²×D₂₉₃	1	1	yes	characteristic
73	C₈	—	586	2	no	—
74	C₂²	—	2	1	no	—
75	C₂²	—	2	1	no	—
76	C₂²	#17989792	1	2	yes	complemented
77	C₂²	C₂×C₂²⋊D₂₉₃	1	1	yes	characteristic
78	C₄	—	2	4	no	—
79	C₄	—	2	1	no	—
80	C₄	—	1172	1	no	—
81	C₄	—	1172	1	no	—
82	C₄	C₂×C₂²⋊D₂₉₃	1	2	yes	—
83	C₂	—	2	2	no	—
84	C₂	#22627593	1	1	yes	characteristic
85	C₂	C₂×#17989792	1	1	yes	characteristic
86	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	C₂²×Q₈×C₂₉₃	C₂
socle	C₂²×C₂₉₃	C₂×D₄
prime radical	C₂³×C₂₉₃	D₄
hypercenter	C₂²×Q₈	D₂₉₃
hypocenter	C₂₉₃	#451
LCS	G ▷ C₂×C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#17989792	C₂	semidirect
3. #22627548	C₂	semidirect
32. C₂²×C₂₉₃	Q₁₆	semidirect
43. C₂₉₃	#451	semidirect
76. C₂²	#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
#22627603	2
#22627548	2
C₂²⋊#14556873	2
C₂²×Q₈×C₂₉₃	2
#451	293