Subgroups — #11928997

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₇₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#10597671	C₂	1	4	yes	maximal, complemented
4	C₄×Dic₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#88190	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₃	C₂²	1	2	yes	—
7	C₃×D₄×C₁₃	—	2	2	no	—
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₉	C₂²	1	2	yes	—
10	C₂×Dic₃₉	C₂²	1	2	yes	—
11	Dic₇₈	—	2	2	no	—
12	C₂×D₄×C₁₃	D₃	1	1	yes	characteristic
13	C₂×Dic₂₆	—	3	1	no	—
14	C₂²⋊Dic₁₃	—	3	4	no	—
15	C₄×Dic₁₃	—	3	1	no	—
16	C₂²×C₃×C₁₃	—	2	2	no	—
17	C₂²×C₃×C₁₃	—	2	4	no	—
18	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
19	C₃×C₄×C₁₃	D₄	1	2	yes	—
20	Dic₃₉	—	2	2	no	—
21	Dic₃₉	—	2	2	no	—
22	C₂³×C₁₃	C₂×D₃	1	2	yes	—
23	D₄×C₁₃	—	2	2	no	—
24	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
25	C₂×Dic₁₃	—	3	2	no	—
26	C₂×Dic₁₃	—	3	2	no	—
27	Dic₂₆	—	6	2	no	—
28	#936	—	13	1	no	maximal, Hall
29	C₂×C₃×C₁₃	—	4	2	no	—
30	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₃×C₁₃	#41	1	2	yes	—
32	C₂²×C₁₃	—	2	4	no	—
33	C₂²×C₁₃	—	2	2	no	—
34	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
35	C₄×C₁₃	#67	1	2	yes	—
36	Dic₁₃	—	6	2	no	—
37	Dic₁₃	—	6	2	no	—
38	C₂×C₃×D₄	D₁₃	1	1	yes	characteristic
39	C₂×Dic₆	—	13	1	no	—
40	#217	—	13	4	no	—
41	C₄×Dic₃	—	13	1	no	—
42	C₃×C₁₃	#124	1	1	yes	characteristic, complemented, Hall
43	#124	—	39	1	no	Sylow
44	C₂×C₁₃	—	4	2	no	—
45	C₂×C₁₃	#237	1	2	yes	—
46	C₂×C₁₃	C₂×#67	1	1	yes	characteristic
47	C₂³×C₃	C₂×D₁₃	1	2	yes	—
48	C₃×D₄	—	2	2	no	—
49	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
50	C₂×Dic₃	—	13	2	no	—
51	C₂×Dic₃	—	13	2	no	—
52	Dic₆	—	26	2	no	—
53	C₂×Q₈	—	39	1	no	—
54	C₂×D₄	D₃₉	1	1	yes	characteristic
55	C₂²⋊C₄	—	39	4	no	—
56	C₄²	—	39	1	no	—
57	C₁₃	#936	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₃	—	2	4	no	—
59	C₂²×C₃	—	2	2	no	—
60	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
61	C₃×C₄	C₂²⋊D₁₃	1	2	yes	—
62	Dic₃	—	26	2	no	—
63	Dic₃	—	26	2	no	—
64	C₂³	C₂×D₃₉	1	2	yes	—
65	Q₈	—	78	2	no	—
66	D₄	—	2	2	no	—
67	C₂×C₄	—	39	2	no	—
68	C₂×C₄	—	39	2	no	—
69	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
70	C₂×C₃	—	4	2	no	—
71	C₂×C₃	#6129	1	2	yes	—
72	C₂×C₃	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
73	C₂²	—	2	4	no	—
74	C₂²	—	2	2	no	—
75	C₂²	C₂²×D₃₉	1	1	yes	characteristic
76	C₄	—	78	2	no	—
77	C₄	—	78	2	no	—
78	C₄	#64625	1	2	yes	—
79	C₃	#88190	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	4	2	no	—
81	C₂	#10597792	1	2	yes	—
82	C₂	C₂×#64625	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃₉
commutator, socle, cosocle	C₂²×C₃×C₁₃	C₂³
Fitting, prime radical	C₂×C₃×D₄×C₁₃	C₂
hypercenter	C₂×D₄	D₃₉
hypocenter	C₃×C₁₃	#124
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₇₈	C₂	semidirect
3. #10597671	C₂	semidirect
4. C₄×Dic₃₉	C₂	semidirect
42. C₃×C₁₃	#124	semidirect
57. C₁₃	#936	semidirect
79. C₃	#88190	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄×C₁₃	2
C₂×Dic₇₈	2
#10597671	2
C₄×Dic₃₉	2
#88190	3
#936	13