Subgroups — #23765272

Order 10112.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₃₂	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₃₁₆	C₂	1	2	yes	maximal
3	#19098391	C₂	1	1	yes	maximal, characteristic
4	#19098368	C₂	1	2	yes	maximal
5	#346×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₆	C₂²	1	2	yes	—
7	C₄×Dic₁₅₈	—	2	2	no	—
8	Dic₆₃₂	C₄	1	4	yes	complemented
9	#14579095	C₂²	1	2	yes	—
10	#14579086	—	2	2	no	—
11	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₅₈	—	2	2	no	—
15	Dic₃₁₆	—	2	2	no	—
16	Dic₃₁₆	C₂×C₄	1	4	yes	—
17	C₄⋊Dic₇₉	—	2	2	no	—
18	Dic₇₉⋊C₄	—	4	2	no	—
19	C₄×Dic₇₉	—	4	2	no	—
20	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
22	C₄²×C₇₉	D₄	1	1	yes	characteristic
23	C₁₆×C₇₉	—	2	1	no	—
24	C₁₆×C₇₉	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₇₉	D₈	1	2	yes	—
26	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₇₉	—	4	2	no	—
28	C₂×Dic₇₉	—	4	2	no	—
29	Dic₁₅₈	—	2	4	no	—
30	Dic₁₅₈	—	4	2	no	—
31	C₈×C₇₉	—	2	1	no	—
32	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₇₉	#41	1	1	yes	characteristic
34	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
35	C₄×C₇₉	—	2	2	no	—
36	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
37	C₄×C₇₉	#135	1	1	yes	characteristic
38	Dic₇₉	—	4	4	no	—
39	Dic₇₉	—	8	2	no	—
40	C₂×C₇₉	C₄×D₈	1	1	yes	characteristic
41	C₂×C₇₉	#510	1	2	yes	—
42	#2176	—	79	1	no	maximal, Sylow
43	C₇₉	#2176	1	1	yes	characteristic, complemented, Sylow
44	C₂×Q₃₂	—	79	1	no	—
45	C₄×Q₁₆	—	79	2	no	—
46	#367	—	79	1	no	—
47	#358	—	79	2	no	—
48	#346	D₇₉	1	1	yes	characteristic
49	C₂×Q₁₆	—	79	2	no	—
50	C₄×Q₈	—	158	2	no	—
51	Q₃₂	—	79	4	no	—
52	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
53	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
54	#107	—	79	2	no	—
55	#103	—	158	2	no	—
56	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
57	C₂×Q₈	—	158	2	no	—
58	Q₁₆	—	79	4	no	—
59	Q₁₆	—	158	2	no	—
60	C₂×C₈	D₃₁₆	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
62	C₄⋊C₄	—	316	2	no	—
63	C₄⋊C₄	—	158	2	no	—
64	C₄²	—	316	2	no	—
65	C₄²	D₃₁₆	1	1	yes	characteristic
66	C₁₆	—	2	1	no	—
67	C₁₆	C₄×D₇₉	1	2	yes	—
68	Q₈	—	316	2	no	—
69	Q₈	—	158	4	no	—
70	C₂×C₄	—	316	2	no	—
71	C₂×C₄	—	316	2	no	—
72	C₂×C₄	D₆₃₂	1	2	yes	—
73	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
76	C₈	#11929624	1	1	yes	characteristic
77	C₂²	C₂×D₆₃₂	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	316	4	no	—
80	C₄	—	632	2	no	—
81	C₄	C₄×D₃₁₆	1	1	yes	characteristic
82	C₄	#14579183	1	1	yes	characteristic
83	C₂	C₄×D₆₃₂	1	1	yes	characteristic
84	C₂	#19099006	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₆₃₂
commutator	C₈×C₇₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#346×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₂×D₈
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	#346	D₇₉
hypocenter	C₇₉	#2176
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
8. Dic₆₃₂	C₄	semidirect
43. C₇₉	#2176	semidirect