Subgroups — D₂₉₃⋊#108 #34037142

Order 18752.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉₃⋊M₁₆	C₂	1	2	yes	maximal
2	#22627695	C₂	1	2	yes	maximal, complemented
3	#22627694	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₂₉₃	C₂	1	1	yes	maximal, characteristic
5	#17989812	C₂²	1	4	yes	—
6	#17989811	—	2	2	no	—
7	D₂₉₃⋊C₈	—	2	2	no	—
8	C₂×C₄×D₂₉₃	C₂²	1	1	yes	characteristic
9	C₂×#14556873	C₄	1	1	yes	characteristic
10	C₈×D₂₉₃	C₄	1	1	yes	characteristic
11	C₈×D₂₉₃	C₄	1	1	yes	characteristic
12	C₈×D₂₉₃	C₂²	1	1	yes	characteristic
13	C₈×D₂₉₃	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₂₉₃	C₄	1	1	yes	characteristic
15	#14556880	—	2	4	no	—
16	C₂²×D₂₉₃	Q₈	1	1	yes	characteristic
17	C₂×Dic₂₉₃	D₄	1	1	yes	characteristic
18	C₄×D₂₉₃	C₂×C₄	1	1	yes	characteristic
19	C₄×D₂₉₃	D₄	1	1	yes	characteristic
20	C₄×D₂₉₃	Q₈	1	1	yes	characteristic
21	C₄×D₂₉₃	C₂³	1	1	yes	characteristic
22	#14556873	C₂×C₄	1	1	yes	characteristic
23	#14556873	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
25	C₈×C₂₉₃	C₂×C₄	1	1	yes	characteristic
26	C₈×C₂₉₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₂₉₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₂₉₃	—	2	2	no	—
29	C₂×D₂₉₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₂₉₃	C₂×Q₈	1	1	yes	characteristic
31	C₄×C₂₉₃	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
33	Dic₂₉₃	C₄⋊C₄	1	1	yes	characteristic
34	Dic₂₉₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₂₉₃	—	2	1	no	—
36	C₂×C₂₉₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	D₂₉₃	—	2	1	no	—
38	D₂₉₃	#108	1	2	yes	complemented
39	C₂₉₃	C₂×#108	1	1	yes	characteristic, complemented, Sylow
40	C₂×#108	—	293	1	no	maximal, Sylow
41	C₂×M₁₆	—	293	2	no	—
42	C₂²×C₈	—	293	1	no	—
43	#108	—	293	2	no	—
44	#108	—	293	2	no	—
45	C₂²×C₄	—	293	1	no	—
46	M₁₆	—	293	4	no	—
47	M₁₆	—	586	2	no	—
48	C₂×C₈	—	293	1	no	—
49	C₂×C₈	—	293	1	no	—
50	C₂×C₈	—	293	1	no	—
51	C₂×C₈	—	293	1	no	—
52	C₂×C₈	—	293	1	no	—
53	C₂×C₈	—	586	2	no	—
54	C₂×C₈	#11924078	1	1	yes	characteristic
55	C₂³	—	293	1	no	—
56	C₂×C₄	—	293	1	no	—
57	C₂×C₄	—	293	1	no	—
58	C₂×C₄	—	293	1	no	—
59	C₂×C₄	—	293	1	no	—
60	C₂×C₄	—	293	1	no	—
61	C₂×C₄	C₂×#11924078	1	1	yes	characteristic
62	C₈	—	293	1	no	—
63	C₈	—	293	1	no	—
64	C₈	—	586	4	no	—
65	C₈	C₂×#11924078	1	1	yes	characteristic
66	C₈	C₂×#11924078	1	1	yes	characteristic
67	C₂²	—	293	1	no	—
68	C₂²	—	293	1	no	—
69	C₂²	—	586	2	no	—
70	C₂²	C₄⋊#11924078	1	1	yes	characteristic
71	C₄	—	293	1	no	—
72	C₄	—	293	1	no	—
73	C₄	C₄⋊#11924078	1	1	yes	characteristic
74	C₄	C₂²×#11924078	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	293	2	no	—
77	C₂	—	586	1	no	—
78	C₂	C₂×C₄⋊#11924078	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#11924078
commutator	C₄×C₂₉₃	C₂²×C₄
Frattini	C₄	C₂²×#11924078
Fitting	C₂×C₈×C₂₉₃	C₄
socle	C₂×C₂₉₃	C₂×C₄⋊C₄
prime radical	C₂²×D₂₉₃	Q₈
cosocle	C₄×D₂₉₃	C₂³
hypercenter	C₂×C₈	#11924078
hypocenter	C₂₉₃	C₂×#108
LCS	G ▷ C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #22627695	C₂	semidirect
3. #22627694	C₂	semidirect
38. D₂₉₃	#108	semidirect
39. C₂₉₃	C₂×#108	semidirect

Maximal subgroups

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

subgroup	index
D₂₉₃⋊M₁₆	2
#22627695	2
#22627694	2
C₂×C₈×D₂₉₃	2
C₂×#108	293

Subgroups — D293⋊#108 #34037142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉₃⋊#108 #34037142