Subgroups — #34037163

Order 18752.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989812	C₂	1	2	yes	maximal, complemented
2	C₄⋊#14556880	C₂	1	1	yes	maximal, characteristic, complemented
3	#22627681	C₂	1	2	yes	maximal, complemented
4	C₄×#14556880	C₂	1	1	yes	maximal, characteristic, complemented
5	#22627586	C₂	1	1	yes	maximal, characteristic
6	#17989812	—	2	4	no	—
7	C₂×#14556880	C₂²	1	1	yes	characteristic
8	C₂×#14556880	C₂²	1	2	yes	—
9	C₂×#14556880	C₂²	1	1	yes	characteristic
10	C₂×D₁₁₇₂	C₄	1	1	yes	characteristic
11	C₂×C₄×D₂₉₃	C₂²	1	2	yes	—
12	#17989779	C₄	1	2	yes	—
13	C₄×Dic₂₉₃	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₂₉₃	C₄	1	1	yes	characteristic
15	#14556880	—	2	2	no	—
16	#14556880	—	2	1	no	—
17	#14556880	D₄	1	2	yes	complemented
18	C₂²×D₂₉₃	C₂×C₄	1	2	yes	—
19	D₁₁₇₂	—	2	2	no	—
20	C₂×Dic₂₉₃	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₂₉₃	C₂³	1	1	yes	characteristic
22	C₄×D₂₉₃	—	2	2	no	—
23	C₄×D₂₉₃	—	2	2	no	—
24	C₂×C₄×C₂₉₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₂₉₃	—	2	2	no	—
28	C₂×D₂₉₃	—	2	2	no	—
29	C₂×D₂₉₃	—	2	2	no	—
30	C₄×C₂₉₃	—	2	2	no	—
31	C₄×C₂₉₃	M₁₆	1	2	yes	complemented
32	Dic₂₉₃	—	2	1	no	—
33	Dic₂₉₃	C₂×D₄	1	1	yes	characteristic
34	Dic₂₉₃	#41	1	1	yes	characteristic
35	C₂×C₂₉₃	C₄×D₄	1	1	yes	characteristic
36	C₂×C₂₉₃	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₂₉₃	#131	1	1	yes	characteristic
38	D₂₉₃	—	4	2	no	—
39	C₂₉₃	#436	1	1	yes	characteristic, complemented, Sylow
40	#436	—	293	1	no	maximal, Sylow
41	C₂×M₁₆	—	293	2	no	—
42	C₄×D₄	—	293	1	no	—
43	C₄⋊C₈	—	293	1	no	—
44	C₂²⋊C₈	—	293	2	no	—
45	C₄×C₈	—	293	1	no	—
46	C₂×D₄	—	293	1	no	—
47	C₂²×C₄	—	293	2	no	—
48	M₁₆	—	586	4	no	—
49	C₂×C₈	—	293	1	no	—
50	C₂×C₈	—	293	1	no	—
51	C₂×C₈	—	293	2	no	—
52	C₄⋊C₄	#11924078	1	1	yes	characteristic
53	C₂²⋊C₄	—	293	2	no	—
54	C₄²	—	293	1	no	—
55	C₂³	—	293	2	no	—
56	D₄	—	586	2	no	—
57	C₂×C₄	—	293	1	no	—
58	C₂×C₄	—	293	1	no	—
59	C₂×C₄	—	586	2	no	—
60	C₂×C₄	—	586	2	no	—
61	C₂×C₄	C₂×#11924078	1	2	yes	—
62	C₂×C₄	C₂×#11924078	1	1	yes	characteristic
63	C₈	—	293	2	no	—
64	C₈	—	586	2	no	—
65	C₈	—	586	1	no	—
66	C₂²	—	586	2	no	—
67	C₂²	—	586	2	no	—
68	C₂²	—	586	2	no	—
69	C₂²	C₂²×#11924078	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	293	1	no	—
72	C₄	—	293	1	no	—
73	C₄	—	586	1	no	—
74	C₄	#17989812	1	2	yes	complemented
75	C₂	—	1172	2	no	—
76	C₂	D₄×#11924078	1	1	yes	characteristic
77	C₂	C₂×#17989812	1	1	yes	characteristic
78	C₂	#22627712	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#11924078
commutator, socle	C₂²×C₂₉₃	C₂²×C₄
Fitting	C₄⋊C₄×C₂₉₃	C₄
prime radical	C₂×D₁₁₇₂	C₄
cosocle	C₂×Dic₂₉₃	C₂³
hypercenter	C₄⋊C₄	#11924078
hypocenter	C₂₉₃	#436
LCS	G ▷ C₂²×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#17989812	C₂	semidirect
2. C₄⋊#14556880	C₂	semidirect
3. #22627681	C₂	semidirect
4. C₄×#14556880	C₂	semidirect
17. #14556880	D₄	semidirect
31. C₄×C₂₉₃	M₁₆	semidirect
39. C₂₉₃	#436	semidirect
74. C₄	#17989812	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989812	2
C₄⋊#14556880	2
#22627681	2
C₄×#14556880	2
#22627586	2
#436	293