Subgroups — #27136134

Order 12352.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₉₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#15690563	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₁₉₃	C₂	1	1	yes	maximal, characteristic
4	#15690565	C₄	1	2	yes	—
5	#15690564	—	2	1	no	—
6	#15690563	—	2	1	no	—
7	#15690563	—	2	1	no	—
8	#15690563	C₄	1	2	yes	—
9	C₂×#13095400	—	2	1	no	—
10	C₂×C₄×D₁₉₃	C₂²	1	1	yes	characteristic
11	#15690539	C₄	1	1	yes	characteristic
12	#15690538	—	2	1	no	—
13	C₈×D₁₉₃	—	2	1	no	—
14	M₁₆×C₁₉₃	C₄	1	1	yes	characteristic
15	#13095400	—	2	2	no	—
16	#13095400	—	2	2	no	—
17	C₂²×D₁₉₃	Q₈	1	1	yes	characteristic
18	C₂×Dic₁₉₃	D₄	1	1	yes	characteristic
19	C₄×D₁₉₃	C₂×C₄	1	1	yes	characteristic
20	C₄×D₁₉₃	C₂×C₄	1	1	yes	characteristic
21	C₄×D₁₉₃	D₄	1	1	yes	characteristic
22	C₄×D₁₉₃	D₄	1	1	yes	characteristic
23	#13095393	—	2	1	no	—
24	C₂×C₄×C₁₉₃	C₂×C₄	1	1	yes	characteristic
25	C₈×C₁₉₃	—	2	1	no	—
26	C₂²×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
27	C₂×D₁₉₃	—	2	2	no	—
28	C₂×D₁₉₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₁₉₃	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₁₉₃	C₄²	1	1	yes	characteristic
31	C₄×C₁₉₃	C₂²⋊C₄	1	1	yes	characteristic
32	Dic₁₉₃	C₂²⋊C₄	1	1	yes	characteristic
33	Dic₁₉₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₁₉₃	—	2	1	no	—
35	C₂×C₁₉₃	#95	1	1	yes	characteristic
36	D₁₉₃	—	2	1	no	—
37	D₁₉₃	#108	1	2	yes	—
38	C₁₉₃	#341	1	1	yes	characteristic, complemented, Sylow
39	#341	—	193	1	no	maximal, Sylow
40	C₂×M₁₆	—	193	1	no	—
41	C₂×M₁₆	—	193	1	no	—
42	C₂²×C₈	—	193	1	no	—
43	C₂²×C₄	—	193	1	no	—
44	M₁₆	—	386	1	no	—
45	M₁₆	—	386	1	no	—
46	M₁₆	—	193	2	no	—
47	M₁₆	—	193	1	no	—
48	M₁₆	#11715871	1	1	yes	characteristic
49	C₂×C₈	—	386	1	no	—
50	C₂×C₈	—	386	1	no	—
51	C₂×C₈	—	386	1	no	—
52	C₂×C₈	—	386	1	no	—
53	C₂×C₈	—	193	2	no	—
54	C₂³	—	193	1	no	—
55	C₂×C₄	—	193	1	no	—
56	C₂×C₄	—	193	1	no	—
57	C₂×C₄	—	193	1	no	—
58	C₂×C₄	—	193	1	no	—
59	C₂×C₄	—	193	1	no	—
60	C₂×C₄	C₂×#11715871	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	386	2	no	—
63	C₈	—	386	2	no	—
64	C₈	—	386	1	no	—
65	C₂²	—	386	2	no	—
66	C₂²	—	193	1	no	—
67	C₂²	—	193	1	no	—
68	C₂²	C₄⋊#11715871	1	1	yes	characteristic
69	C₄	—	193	1	no	—
70	C₄	—	193	1	no	—
71	C₄	C₄×#11715871	1	1	yes	characteristic
72	C₄	C₂²⋊#11715871	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	386	1	no	—
75	C₂	—	193	2	no	—
76	C₂	(C₂×#11715871)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#11715871
commutator	C₄×C₁₉₃	C₄²
Frattini	C₂×C₄	C₂×#11715871
Fitting	M₁₆×C₁₉₃	C₄
socle	C₂×C₁₉₃	#95
prime radical	C₂²×D₁₉₃	Q₈
cosocle	C₂×C₄×D₁₉₃	C₂²
hypercenter	M₁₆	#11715871
hypocenter	C₁₉₃	#341
LCS	G ▷ C₄×C₁₉₃ ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
38. C₁₉₃	#341	semidirect

Maximal subgroups

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

subgroup	index
D₁₉₃⋊M₁₆	2
C₂×#15690563	2
M₁₆×D₁₉₃	2
#341	193