Subgroups — #15777633

Order 3328.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117088	C₂	1	4	yes	maximal
2	#13114454	C₂	1	1	yes	maximal, characteristic
3	C₈×#6090	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1713	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#500	—	2	2	no	—
6	C₁₃×#494	C₂²	1	2	yes	—
7	C₂×#88069	—	2	8	no	—
8	#11718360	C₂²	1	2	yes	—
9	#11718343	—	2	2	no	—
10	C₈²×C₁₃	C₂²	1	1	yes	characteristic
11	C₄×#6090	C₂²	1	2	yes	—
12	C₂×C₁₃×Q₁₆	—	2	4	no	—
13	C₁₃×C₄⋊Q₈	—	2	2	no	—
14	C₂×Dic₅₂	—	2	4	no	—
15	#88123	—	2	2	no	—
16	C₁₃×#107	—	4	4	no	—
17	C₄×C₈×C₁₃	D₄	1	2	yes	—
18	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	#88069	—	4	16	no	—
20	#88058	—	4	4	no	—
21	C₂×#6090	D₄	1	4	yes	—
22	#12516	—	13	1	no	maximal, Sylow
23	C₂×Q₈×C₁₃	—	4	2	no	—
24	C₂×Dic₂₆	—	4	2	no	—
25	C₁₃×Q₁₆	—	4	8	no	—
26	C₂×C₈×C₁₃	D₈	1	4	yes	—
27	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
28	C₁₃×C₄⋊C₄	—	4	4	no	—
29	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₄⋊Dic₁₃	—	4	4	no	—
31	Dic₅₂	—	4	8	no	—
32	#6090	D₈	1	8	yes	—
33	#2247	—	13	4	no	—
34	#1713	—	13	1	no	—
35	#1713	D₁₃	1	1	yes	characteristic
36	C₈×C₁₆	—	13	1	no	—
37	Q₈×C₁₃	—	8	4	no	—
38	C₂×C₄×C₁₃	—	8	2	no	—
39	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
40	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
41	C₂×Dic₁₃	—	8	2	no	—
42	Dic₂₆	—	8	4	no	—
43	C₈×C₁₃	Q₃₂	1	8	yes	complemented
44	C₈×C₁₃	C₂×D₈	1	4	yes	—
45	C₂×Q₃₂	—	26	8	no	—
46	#500	—	2	2	no	—
47	#500	—	26	2	no	—
48	#494	—	13	2	no	—
49	#494	C₂×D₁₃	1	2	yes	—
50	C₄×C₁₆	—	13	2	no	—
51	C₈²	C₂×D₁₃	1	1	yes	characteristic
52	C₂²×C₁₃	#493	1	1	yes	characteristic
53	C₄×C₁₃	—	16	2	no	—
54	C₄×C₁₃	#493	1	2	yes	—
55	C₄×C₁₃	C₂×Q₃₂	1	4	yes	—
56	Dic₁₃	—	16	2	no	—
57	C₂×Q₁₆	—	2	4	no	—
58	C₂×Q₁₆	—	26	4	no	—
59	C₄⋊Q₈	—	2	2	no	—
60	C₄⋊Q₈	—	26	2	no	—
61	Q₃₂	—	52	16	no	—
62	C₂×C₁₆	—	13	4	no	—
63	#107	—	4	4	no	—
64	#107	—	52	4	no	—
65	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
66	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
67	C₂×C₁₃	#1712	1	1	yes	characteristic
68	C₂×C₁₃	#2247	1	2	yes	—
69	C₂×Q₈	—	4	2	no	—
70	C₂×Q₈	—	52	2	no	—
71	Q₁₆	—	4	8	no	—
72	Q₁₆	—	52	8	no	—
73	C₂×C₈	#6104	1	4	yes	—
74	C₂×C₈	D₄×D₁₃	1	2	yes	—
75	C₄⋊C₄	—	4	4	no	—
76	C₄⋊C₄	—	52	4	no	—
77	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
78	C₁₆	—	13	8	no	—
79	C₁₃	#12516	1	1	yes	characteristic, complemented, Sylow
80	Q₈	—	8	4	no	—
81	Q₈	—	104	4	no	—
82	C₂×C₄	—	8	2	no	—
83	C₂×C₄	—	104	2	no	—
84	C₂×C₄	C₂×#6104	1	2	yes	—
85	C₂×C₄	#88194	1	1	yes	characteristic
86	C₈	#88069	1	8	yes	complemented
87	C₈	D₈×D₁₃	1	4	yes	—
88	C₂²	#11718734	1	1	yes	characteristic
89	C₄	—	16	2	no	—
90	C₄	—	208	2	no	—
91	C₄	#11718812	1	2	yes	—
92	C₄	C₂×#88069	1	4	yes	—
93	C₂	#13114450	1	1	yes	characteristic
94	C₂	#13117088	1	2	yes	—

	subgroup	G/H
center	C₂²	#11718734
commutator, cosocle	C₄×C₈×C₁₃	C₂³
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₁₃×#1713	C₂
socle, prime radical	C₂²×C₁₃	#493
hypercenter	#1713	D₁₃
hypocenter	C₁₃	#12516
LCS	G ▷ C₄×C₈×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1713

Complements

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

N	H ≅ G/N	type
43. C₈×C₁₃	Q₃₂	semidirect
79. C₁₃	#12516	semidirect
86. C₈	#88069	semidirect

Maximal subgroups

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

subgroup	index
#13117088	2
#13114454	2
C₈×#6090	2
C₁₃×#1713	2
#12516	13