Subgroups — #49119433

Order 36224.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31826833	C₂	1	1	yes	maximal, characteristic
2	#31826264	C₂	1	1	yes	maximal, characteristic
3	#356×C₂₈₃	C₂	1	1	yes	maximal, characteristic
4	#22583602	C₄	1	1	yes	characteristic
5	#22583534	—	2	1	no	—
6	#22583534	—	2	1	no	—
7	#22583529	—	2	1	no	—
8	#22583521	C₄	1	1	yes	characteristic
9	C₄⋊Q₈×C₂₈₃	C₂²	1	1	yes	characteristic
10	#101×C₂₈₃	—	2	1	no	—
11	#17985376	—	4	1	no	—
12	C₂×C₂₈₃⋊C₈	—	2	1	no	—
13	C₄⋊Dic₂₈₃	—	2	1	no	—
14	Dic₂₈₃⋊C₄	—	4	1	no	—
15	C₂×Q₈×C₂₈₃	D₄	1	1	yes	characteristic
16	C₂×Q₈×C₂₈₃	D₄	1	1	yes	characteristic
17	M₁₆×C₂₈₃	—	4	1	no	—
18	C₄⋊C₄×C₂₈₃	—	4	1	no	—
19	C₄²×C₂₈₃	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₂₈₃	—	4	1	no	—
21	C₂₈₃⋊C₈	—	4	1	no	—
22	C₂₈₃⋊C₈	—	8	1	no	—
23	Q₈×C₂₈₃	—	4	1	no	—
24	Q₈×C₂₈₃	—	4	1	no	—
25	C₂×C₄×C₂₈₃	—	2	1	no	—
26	C₂×C₄×C₂₈₃	—	2	1	no	—
27	C₂×C₄×C₂₈₃	—	2	1	no	—
28	C₂×C₄×C₂₈₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₈×C₂₈₃	—	8	1	no	—
30	C₂²×C₂₈₃	#99	1	1	yes	characteristic
31	C₄×C₂₈₃	—	2	1	no	—
32	C₄×C₂₈₃	—	4	1	no	—
33	C₄×C₂₈₃	—	4	1	no	—
34	C₄×C₂₈₃	—	4	1	no	—
35	Dic₂₈₃	—	8	1	no	—
36	C₂×C₂₈₃	—	2	1	no	—
37	C₂×C₂₈₃	#354	1	1	yes	characteristic
38	C₂₈₃	#1413	1	1	yes	characteristic, complemented, Sylow
39	#1413	—	283	1	no	maximal, Sylow
40	#491	—	283	1	no	—
41	#356	—	283	1	no	—
42	#356	D₂₈₃	1	1	yes	characteristic
43	C₄⋊Q₈	C₂×D₂₈₃	1	1	yes	characteristic
44	#125	—	283	1	no	—
45	#103	—	566	1	no	—
46	#103	—	566	1	no	—
47	#101	—	2	1	no	—
48	#101	—	566	1	no	—
49	#97	—	283	1	no	—
50	C₂×Q₈	C₂²⋊D₂₈₃	1	1	yes	characteristic
51	C₂×Q₈	D₁₁₃₂	1	1	yes	characteristic
52	M₁₆	—	4	1	no	—
53	M₁₆	—	1132	1	no	—
54	C₂×C₈	—	566	1	no	—
55	C₄⋊C₄	—	4	1	no	—
56	C₄⋊C₄	—	566	1	no	—
57	C₄⋊C₄	—	1132	1	no	—
58	C₄²	C₄×D₂₈₃	1	1	yes	characteristic
59	Q₈	—	4	1	no	—
60	Q₈	—	4	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	1132	1	no	—
65	C₂×C₄	(C₂×D₂₈₃)⋊C₄	1	1	yes	characteristic
66	C₈	—	8	1	no	—
67	C₈	—	1132	1	no	—
68	C₈	—	2264	1	no	—
69	C₂²	#22583524	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	4	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	2264	1	no	—
75	C₂	—	2	1	no	—
76	C₂	#31826259	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31826259
commutator	C₄²×C₂₈₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₂₈₃
Fitting	#356×C₂₈₃	C₂
socle	C₂×C₂₈₃	#354
prime radical	C₂²×C₂₈₃	#99
cosocle	C₄⋊Q₈×C₂₈₃	C₂²
hypercenter	#356	D₂₈₃
hypocenter	C₂₈₃	#1413
LCS	G ▷ C₄²×C₂₈₃ ▷ C₂×C₄×C₂₈₃ ▷ C₂²×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
38. C₂₈₃	#1413	semidirect

Maximal subgroups

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

subgroup	index
#31826833	2
#31826264	2
#356×C₂₈₃	2
#1413	283