Subgroups — #49148827

Order 36928.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊#14556313	C₂	1	2	yes	maximal
2	C₂×#22604395	C₂	1	1	yes	maximal, characteristic
3	C₂²×#14556313	—	2	2	no	—
4	C₂²⋊#14556313	—	2	2	no	—
5	C₂²⋊#14556313	C₄	1	4	yes	complemented
6	C₂³×D₅₇₇	C₂²	1	1	yes	characteristic
7	C₂²×Dic₅₇₇	C₄	1	1	yes	characteristic, complemented
8	#22604395	—	2	2	no	—
9	C₂²×C₄×C₅₇₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#14556313	—	2	4	no	—
11	C₂×#14556313	—	4	2	no	—
12	C₂×#14556313	—	4	2	no	—
13	C₂²×D₅₇₇	—	4	1	no	—
14	C₂²×D₅₇₇	—	4	1	no	—
15	C₂²×D₅₇₇	C₂×C₄	1	2	yes	—
16	C₂²×D₅₇₇	D₄	1	2	yes	—
17	C₂²×D₅₇₇	D₄	1	1	yes	characteristic
18	C₂²×D₅₇₇	Q₈	1	1	yes	characteristic
19	C₂×Dic₅₇₇	—	2	1	no	—
20	C₂×Dic₅₇₇	—	4	1	no	—
21	C₂³×C₅₇₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₅₇₇	—	2	1	no	—
23	C₂×C₄×C₅₇₇	—	4	1	no	—
24	C₂²×C₅₇₇	—	2	1	no	—
25	C₂²×C₅₇₇	—	2	1	no	—
26	C₂²×C₅₇₇	C₄²	1	1	yes	characteristic
27	C₂²×C₅₇₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²×C₅₇₇	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₅₇₇	—	2	2	no	—
30	C₂×D₅₇₇	—	2	2	no	—
31	C₂×D₅₇₇	—	4	2	no	—
32	C₂×D₅₇₇	—	4	1	no	—
33	C₂×D₅₇₇	—	4	1	no	—
34	C₂×D₅₇₇	C₂²⋊C₄	1	2	yes	—
35	C₂×D₅₇₇	C₄⋊C₄	1	2	yes	—
36	#14556313	—	4	4	no	—
37	C₄×C₅₇₇	—	4	1	no	—
38	Dic₅₇₇	—	4	1	no	—
39	C₂×C₅₇₇	—	2	1	no	—
40	C₂×C₅₇₇	—	2	1	no	—
41	C₂×C₅₇₇	#95	1	1	yes	characteristic
42	C₂×C₅₇₇	#99	1	1	yes	characteristic
43	C₂×C₅₇₇	#99	1	1	yes	characteristic
44	D₅₇₇	—	2	2	no	—
45	D₅₇₇	—	2	2	no	—
46	C₅₇₇	#342	1	1	yes	characteristic, complemented, Sylow
47	#342	—	577	1	no	maximal, Sylow
48	C₂×C₂²⋊C₄	—	577	2	no	—
49	C₂×C₂²⋊C₄	—	577	1	no	—
50	C₂⁴	—	577	1	no	—
51	C₂²×C₄	—	577	1	no	—
52	C₂²×C₄	—	1154	2	no	—
53	C₂²×C₄	#14556313	1	1	yes	characteristic, complemented
54	C₂²⋊C₄	—	577	4	no	—
55	C₂²⋊C₄	—	1154	2	no	—
56	C₂²⋊C₄	—	1154	2	no	—
57	C₂³	—	2308	1	no	—
58	C₂³	—	2308	1	no	—
59	C₂³	—	577	2	no	—
60	C₂³	—	577	1	no	—
61	C₂³	—	577	1	no	—
62	C₂³	—	577	2	no	—
63	C₂³	C₂×#14556313	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	4	1	no	—
66	C₂×C₄	—	2308	2	no	—
67	C₂×C₄	—	2308	2	no	—
68	C₂×C₄	—	2308	1	no	—
69	C₂×C₄	—	1154	4	no	—
70	C₂×C₄	—	1154	1	no	—
71	C₂²	—	2	1	no	—
72	C₂²	—	2	1	no	—
73	C₂²	—	2308	2	no	—
74	C₂²	—	2308	1	no	—
75	C₂²	—	2308	1	no	—
76	C₂²	—	577	2	no	—
77	C₂²	—	577	2	no	—
78	C₂²	—	1154	2	no	—
79	C₂²	—	1154	2	no	—
80	C₂²	C₄×#14556313	1	1	yes	characteristic
81	C₂²	C₂²⋊#14556313	1	1	yes	characteristic
82	C₂²	C₄⋊#14556313	1	1	yes	characteristic
83	C₄	—	4	1	no	—
84	C₄	—	2308	4	no	—
85	C₄	—	2308	1	no	—
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	—	1154	2	no	—
89	C₂	—	1154	2	no	—
90	C₂	(C₂×#14556313)⋊C₄	1	1	yes	characteristic
91	C₂	#32914722	1	1	yes	characteristic
92	C₂	#32914723	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#14556313
commutator	C₂²×C₅₇₇	C₄²
Frattini	C₂³	C₂×#14556313
Fitting	C₂²×C₄×C₅₇₇	C₄
socle	C₂²×C₅₇₇	C₂²⋊C₄
prime radical, cosocle	C₂³×D₅₇₇	C₂²
hypercenter	C₂²×C₄	#14556313
hypocenter	C₅₇₇	#342
LCS	G ▷ C₂²×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
5. C₂²⋊#14556313	C₄	semidirect
7. C₂²×Dic₅₇₇	C₄	semidirect
9. C₂²×C₄×C₅₇₇	C₄	semidirect
46. C₅₇₇	#342	semidirect
53. C₂²×C₄	#14556313	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂²⋊#14556313	2
C₂×#22604395	2
#342	577