Subgroups — #34176131

Order 20224.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761569	C₂	1	2	yes	maximal, complemented
2	C₇₉×#1709	C₂	1	1	yes	maximal, characteristic
3	#19098362	—	2	2	no	—
4	#494×C₇₉	C₂²	1	1	yes	characteristic
5	#493×C₇₉	C₄	1	1	yes	characteristic
6	#486×C₇₉	—	2	2	no	—
7	C₈²×C₇₉	C₄	1	1	yes	characteristic
8	#14579080	—	4	2	no	—
9	C₂×Q₁₆×C₇₉	—	4	1	no	—
10	C₂×D₈×C₇₉	—	4	1	no	—
11	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
12	#127×C₇₉	—	2	1	no	—
13	#102×C₇₉	—	4	4	no	—
14	C₄×C₈×C₇₉	—	2	1	no	—
15	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
16	#11929608	—	8	2	no	—
17	C₂×Q₈×C₇₉	—	2	2	no	—
18	C₂×D₄×C₇₉	—	4	2	no	—
19	C₂×D₄×C₇₉	—	4	1	no	—
20	Q₁₆×C₇₉	—	8	2	no	—
21	D₈×C₇₉	—	8	2	no	—
22	C₂×C₈×C₇₉	—	2	2	no	—
23	C₂×C₈×C₇₉	—	2	1	no	—
24	C₄⋊C₄×C₇₉	—	4	2	no	—
25	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂³×C₇₉	—	8	1	no	—
27	Q₈×C₇₉	—	8	2	no	—
28	D₄×C₇₉	—	8	2	no	—
29	D₄×C₇₉	—	8	4	no	—
30	C₂×C₄×C₇₉	—	2	1	no	—
31	C₂×C₄×C₇₉	—	4	2	no	—
32	C₂×C₄×C₇₉	#99	1	1	yes	characteristic
33	C₈×C₇₉	—	2	2	no	—
34	C₈×C₇₉	—	4	2	no	—
35	C₇₉⋊C₈	—	16	2	no	—
36	C₂²×C₇₉	—	16	2	no	—
37	C₂²×C₇₉	—	16	1	no	—
38	C₂²×C₇₉	#353	1	1	yes	characteristic
39	C₄×C₇₉	—	2	2	no	—
40	C₄×C₇₉	—	2	1	no	—
41	C₄×C₇₉	—	8	2	no	—
42	#7531	—	79	1	no	maximal, Sylow
43	C₂×C₇₉	—	2	1	no	—
44	C₂×C₇₉	—	32	1	no	—
45	C₂×C₇₉	#1408	1	1	yes	characteristic
46	#1709	D₇₉	1	1	yes	characteristic
47	#1411	—	79	2	no	—
48	C₇₉	#7531	1	1	yes	characteristic, complemented, Sylow
49	#494	C₂×D₇₉	1	1	yes	characteristic
50	#493	Dic₇₉	1	1	yes	characteristic
51	#486	—	2	2	no	—
52	#356	—	158	2	no	—
53	C₈²	Dic₇₉	1	1	yes	characteristic
54	C₂×Q₁₆	—	4	1	no	—
55	C₂×D₈	—	4	1	no	—
56	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
57	#127	—	2	1	no	—
58	#102	—	4	4	no	—
59	#101	—	316	2	no	—
60	C₄×C₈	—	2	1	no	—
61	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
62	C₂×Q₈	—	2	2	no	—
63	C₂×D₄	—	4	2	no	—
64	C₂×D₄	—	4	1	no	—
65	Q₁₆	—	8	2	no	—
66	D₈	—	8	2	no	—
67	M₁₆	—	632	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₄⋊C₄	—	4	2	no	—
71	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
72	C₂³	—	8	1	no	—
73	Q₈	—	8	2	no	—
74	D₄	—	8	2	no	—
75	D₄	—	8	4	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	4	2	no	—
78	C₂×C₄	#14579076	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	4	2	no	—
81	C₈	—	1264	2	no	—
82	C₂²	—	16	2	no	—
83	C₂²	—	16	1	no	—
84	C₂²	#19098356	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	—	2	1	no	—
87	C₄	—	8	2	no	—
88	C₂	—	2	1	no	—
89	C₂	—	32	1	no	—
90	C₂	#23761563	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23761563
commutator	C₄×C₈×C₇₉	C₂×C₄
Frattini	#494	C₂×D₇₉
Fitting	C₇₉×#1709	C₂
socle	C₂×C₇₉	#1408
prime radical	#493×C₇₉	C₄
cosocle	#494×C₇₉	C₂²
hypercenter	#1709	D₇₉
hypocenter	C₇₉	#7531
LCS	G ▷ C₄×C₈×C₇₉ ▷ C₄²×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #494 ◁ #1709

Complements

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

N	H ≅ G/N	type
1. #23761569	C₂	semidirect
48. C₇₉	#7531	semidirect

Maximal subgroups

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

subgroup	index
#23761569	2
C₇₉×#1709	2
#7531	79