Subgroups — C₈₃×#1558 #24903243

Order 10624.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Q₈×C₈₃	C₂	1	1	yes	maximal, characteristic
2	#432×C₈₃	C₂	1	2	yes	maximal
3	#333×C₈₃	C₂	1	4	yes	maximal, complemented
4	C₂²×Q₈×C₈₃	C₄	1	2	yes	—
5	C₄⋊Q₈×C₈₃	—	2	2	no	—
6	C₄⋊Q₈×C₈₃	C₄	1	2	yes	—
7	C₄⋊Q₈×C₈₃	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
9	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
10	C₄⋊C₈×C₈₃	C₂²	1	4	yes	—
11	C₂²⋊C₈×C₈₃	—	2	2	no	—
12	#97×C₈₃	—	2	2	no	—
13	C₂×Q₈×C₈₃	—	2	2	no	—
14	C₂×Q₈×C₈₃	—	4	4	no	—
15	C₂×Q₈×C₈₃	C₂×C₄	1	4	yes	—
16	C₂²×C₄×C₈₃	—	2	2	no	—
17	C₂²×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₈₃	D₄	1	2	yes	—
19	C₂×C₈×C₈₃	—	2	4	no	—
20	C₄⋊C₄×C₈₃	—	2	4	no	—
21	C₄⋊C₄×C₈₃	—	2	4	no	—
22	C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₈₃	D₄	1	2	yes	—
24	C₄²×C₈₃	C₂³	1	1	yes	characteristic
25	C₂³×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
26	Q₈×C₈₃	—	4	4	no	—
27	Q₈×C₈₃	—	4	4	no	—
28	C₂×C₄×C₈₃	—	2	2	no	—
29	C₂×C₄×C₈₃	—	2	4	no	—
30	C₂×C₄×C₈₃	—	2	4	no	—
31	C₂×C₄×C₈₃	—	4	4	no	—
32	C₂×C₄×C₈₃	C₂²⋊C₄	1	2	yes	—
33	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
36	C₈×C₈₃	—	4	4	no	—
37	C₂²×C₈₃	—	2	2	no	—
38	C₂²×C₈₃	#100	1	2	yes	—
39	C₂²×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₄×C₈₃	—	2	1	no	—
41	C₄×C₈₃	—	2	1	no	—
42	C₄×C₈₃	—	2	2	no	—
43	C₄×C₈₃	—	4	4	no	—
44	C₄×C₈₃	#137	1	4	yes	—
45	C₂×C₈₃	—	2	2	no	—
46	C₂×C₈₃	C₂×#100	1	1	yes	characteristic
47	C₂×C₈₃	#419	1	2	yes	—
48	#1558	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₈₃	#1558	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₄⋊Q₈	C₂×C₈₃	1	1	yes	characteristic
51	#432	C₂×C₈₃	1	2	yes	—
52	#333	C₂×C₈₃	1	4	yes	complemented
53	C₂²×Q₈	C₄×C₈₃	1	2	yes	—
54	C₄⋊Q₈	—	2	2	no	—
55	C₄⋊Q₈	C₄×C₈₃	1	2	yes	—
56	C₄⋊Q₈	C₂²×C₈₃	1	2	yes	—
57	C₂×C₄⋊C₄	—	2	2	no	—
58	C₂×C₄²	C₂²×C₈₃	1	1	yes	characteristic
59	C₄⋊C₈	C₂²×C₈₃	1	4	yes	—
60	C₂²⋊C₈	—	2	2	no	—
61	#97	—	2	2	no	—
62	C₂×Q₈	—	2	2	no	—
63	C₂×Q₈	—	4	4	no	—
64	C₂×Q₈	C₂×C₄×C₈₃	1	4	yes	—
65	C₂²×C₄	—	2	2	no	—
66	C₂²×C₄	C₂×C₄×C₈₃	1	1	yes	characteristic
67	C₂²×C₄	D₄×C₈₃	1	2	yes	—
68	C₂×C₈	—	2	4	no	—
69	C₄⋊C₄	—	2	4	no	—
70	C₄⋊C₄	—	2	4	no	—
71	C₄²	C₂×C₄×C₈₃	1	1	yes	characteristic
72	C₄²	D₄×C₈₃	1	2	yes	—
73	C₄²	C₂³×C₈₃	1	1	yes	characteristic
74	C₂³	C₂²⋊C₄×C₈₃	1	1	yes	characteristic
75	Q₈	—	4	4	no	—
76	Q₈	—	4	4	no	—
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	2	4	no	—
79	C₂×C₄	—	2	4	no	—
80	C₂×C₄	—	4	4	no	—
81	C₂×C₄	C₂²⋊C₄×C₈₃	1	2	yes	—
82	C₂×C₄	C₂²⋊C₄×C₈₃	1	1	yes	characteristic
83	C₂×C₄	C₂²×C₄×C₈₃	1	1	yes	characteristic
84	C₂×C₄	C₂×D₄×C₈₃	1	2	yes	—
85	C₈	—	4	4	no	—
86	C₂²	—	2	2	no	—
87	C₂²	#100×C₈₃	1	2	yes	—
88	C₂²	C₂×C₂²⋊C₄×C₈₃	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	2	1	no	—
91	C₄	—	2	2	no	—
92	C₄	—	4	4	no	—
93	C₄	#137×C₈₃	1	4	yes	—
94	C₂	—	2	2	no	—
95	C₂	C₂×#100×C₈₃	1	1	yes	characteristic
96	C₂	#419×C₈₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₈₃
Frattini, cosocle	C₄²	C₂³×C₈₃
prime radical	C₂³×C₈₃	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂×C₄²×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. #333×C₈₃	C₂	semidirect
48. #1558	C₈₃	direct (N × H)
49. C₈₃	#1558	direct (N × H)
52. #333	C₂×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Q₈×C₈₃	2
#432×C₈₃	2
#333×C₈₃	2
#1558	83

Subgroups — C83×#1558 #24903243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#1558 #24903243