Subgroups — #44507042

Order 30848.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29508122	C₂	1	1	yes	maximal, characteristic
2	#29508115	C₂	1	2	yes	maximal
3	#29508097	C₂	1	1	yes	maximal, characteristic
4	#29508068	C₂	1	2	yes	maximal
5	C₈²×C₂₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₆₄	—	2	2	no	—
7	#21440642	C₂²	1	2	yes	—
8	#21440642	C₂²	1	2	yes	—
9	#21440576	—	2	2	no	—
10	#21440574	—	2	4	no	—
11	#21440567	—	2	4	no	—
12	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₈₂	—	2	2	no	—
16	C₂×Dic₄₈₂	—	2	2	no	—
17	Dic₉₆₄	—	4	4	no	—
18	C₄⋊Dic₂₄₁	—	2	2	no	—
19	C₄⋊Dic₂₄₁	—	2	2	no	—
20	C₄⋊Dic₂₄₁	—	2	2	no	—
21	C₄⋊Dic₂₄₁	—	2	2	no	—
22	C₂×C₈×C₂₄₁	D₄	1	2	yes	—
23	C₂×C₈×C₂₄₁	D₄	1	2	yes	—
24	C₂×C₈×C₂₄₁	D₄	1	2	yes	—
25	C₄²×C₂₄₁	C₂³	1	1	yes	characteristic
26	Dic₄₈₂	—	4	4	no	—
27	Dic₄₈₂	—	4	4	no	—
28	C₂×Dic₂₄₁	—	4	2	no	—
29	C₂×Dic₂₄₁	—	4	2	no	—
30	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
33	C₈×C₂₄₁	—	2	2	no	—
34	C₈×C₂₄₁	SD₁₆	1	4	yes	—
35	C₈×C₂₄₁	Q₁₆	1	4	yes	complemented
36	C₂²×C₂₄₁	#127	1	1	yes	characteristic
37	C₄×C₂₄₁	C₂×SD₁₆	1	2	yes	—
38	C₄×C₂₄₁	C₂×Q₁₆	1	2	yes	—
39	C₄×C₂₄₁	#135	1	2	yes	—
40	Dic₂₄₁	—	8	2	no	—
41	Dic₂₄₁	—	8	2	no	—
42	C₂×C₂₄₁	#492	1	1	yes	characteristic
43	C₂×C₂₄₁	#494	1	1	yes	characteristic
44	C₂×C₂₄₁	#495	1	1	yes	characteristic
45	C₂₄₁	#1707	1	1	yes	characteristic, complemented, Sylow
46	#1707	—	241	1	no	maximal, Sylow
47	#500	—	241	1	no	—
48	#498	—	241	2	no	—
49	#494	—	241	1	no	—
50	#487	—	241	2	no	—
51	C₈²	D₂₄₁	1	1	yes	characteristic
52	C₂×Q₁₆	—	482	2	no	—
53	C₄⋊Q₈	—	241	2	no	—
54	C₄⋊Q₈	—	241	2	no	—
55	#107	—	482	2	no	—
56	#106	—	482	4	no	—
57	#103	—	482	4	no	—
58	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
59	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
60	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
61	C₂×Q₈	—	482	2	no	—
62	C₂×Q₈	—	482	2	no	—
63	Q₁₆	—	964	4	no	—
64	C₂×C₈	D₉₆₄	1	2	yes	—
65	C₂×C₈	D₉₆₄	1	2	yes	—
66	C₂×C₈	D₉₆₄	1	2	yes	—
67	C₄⋊C₄	—	482	2	no	—
68	C₄⋊C₄	—	482	2	no	—
69	C₄⋊C₄	—	482	2	no	—
70	C₄⋊C₄	—	482	2	no	—
71	C₄²	C₂²×D₂₄₁	1	1	yes	characteristic
72	Q₈	—	964	4	no	—
73	Q₈	—	964	4	no	—
74	C₂×C₄	—	964	2	no	—
75	C₂×C₄	—	964	2	no	—
76	C₂×C₄	C₂×D₉₆₄	1	1	yes	characteristic
77	C₂×C₄	C₂×D₉₆₄	1	1	yes	characteristic
78	C₂×C₄	C₂×D₉₆₄	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	#16838759	1	4	yes	—
81	C₈	Dic₉₆₄	1	4	yes	complemented
82	C₂²	#21440639	1	1	yes	characteristic
83	C₄	—	1928	2	no	—
84	C₄	—	1928	2	no	—
85	C₄	C₂×#16838759	1	2	yes	—
86	C₄	C₂×Dic₉₆₄	1	2	yes	—
87	C₄	#21440664	1	2	yes	—
88	C₂	#29508090	1	1	yes	characteristic
89	C₂	#29508097	1	1	yes	characteristic
90	C₂	#29508101	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#21440639
commutator, cosocle	C₄²×C₂₄₁	C₂³
Frattini	C₄²	C₂²×D₂₄₁
Fitting	C₈²×C₂₄₁	C₂
socle, prime radical	C₂²×C₂₄₁	#127
hypercenter	C₈²	D₂₄₁
hypocenter	C₂₄₁	#1707
LCS	G ▷ C₄²×C₂₄₁ ▷ C₂²×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
35. C₈×C₂₄₁	Q₁₆	semidirect
45. C₂₄₁	#1707	semidirect
81. C₈	Dic₉₆₄	semidirect

Maximal subgroups

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

subgroup	index
#29508122	2
#29508115	2
#29508097	2
#29508068	2
C₈²×C₂₄₁	2
#1707	241