Subgroups — C₂×#22579941 #31800986

Order 17728.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17984572	C₂	1	2	yes	maximal
2	#22579941	C₂	1	4	yes	maximal, direct product factor
3	C₂²×Dic₅₅₄	C₂	1	1	yes	maximal, characteristic
4	#17984572	—	2	2	no	—
5	#17984572	C₂²	1	4	yes	—
6	C₂×#14555667	—	2	2	no	—
7	C₂×Dic₅₅₄	—	2	2	no	—
8	C₂×Dic₅₅₄	—	2	2	no	—
9	C₂×Dic₅₅₄	C₄	1	2	yes	—
10	C₂×Dic₅₅₄	C₂²	1	2	yes	—
11	C₂²×Dic₂₇₇	C₄	1	1	yes	characteristic
12	C₂²×Dic₂₇₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₂₇₇	C₄	1	1	yes	characteristic
14	#14555667	—	2	4	no	—
15	Dic₅₅₄	—	2	4	no	—
16	Dic₅₅₄	—	2	4	no	—
17	C₂×Dic₂₇₇	—	2	1	no	—
18	C₂×Dic₂₇₇	—	2	1	no	—
19	C₂×Dic₂₇₇	C₂×C₄	1	2	yes	—
20	C₂×Dic₂₇₇	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₂₇₇	D₄	1	2	yes	—
22	C₂×Dic₂₇₇	D₄	1	2	yes	—
23	C₂×Dic₂₇₇	C₂³	1	1	yes	characteristic
24	C₂³×C₂₇₇	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₇₇	—	2	1	no	—
26	C₂×C₄×C₂₇₇	—	2	1	no	—
27	C₂×C₄×C₂₇₇	C₂×C₄	1	2	yes	—
28	C₂²×C₂₇₇	—	2	2	no	—
29	C₂²×C₂₇₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₂₇₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₂₇₇	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₂₇₇	—	2	2	no	—
33	Dic₂₇₇	—	2	2	no	—
34	Dic₂₇₇	C₂²⋊C₄	1	2	yes	—
35	Dic₂₇₇	C₂×D₄	1	2	yes	—
36	C₂×C₂₇₇	—	2	1	no	—
37	C₂×C₂₇₇	—	2	1	no	—
38	C₂×C₂₇₇	#101	1	2	yes	complemented
39	C₂×C₂₇₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂₇₇	C₂×#101	1	1	yes	characteristic, complemented, Sylow
41	C₂×#101	—	277	1	no	maximal, Sylow
42	C₂²×Q₈	—	277	1	no	—
43	C₂×M₁₆	—	277	2	no	—
44	#101	—	277	4	no	—
45	C₂×Q₈	—	277	2	no	—
46	C₂×Q₈	—	277	2	no	—
47	C₂×Q₈	—	554	2	no	—
48	C₂×Q₈	—	554	2	no	—
49	C₂²×C₄	—	277	1	no	—
50	C₂²×C₄	—	277	1	no	—
51	C₂²×C₄	#11764308	1	1	yes	characteristic
52	M₁₆	—	277	4	no	—
53	M₁₆	—	554	2	no	—
54	C₂×C₈	—	554	2	no	—
55	C₂³	C₂×#11764308	1	1	yes	characteristic
56	Q₈	—	554	4	no	—
57	Q₈	—	554	4	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	277	2	no	—
61	C₂×C₄	—	277	2	no	—
62	C₂×C₄	—	277	1	no	—
63	C₂×C₄	—	277	1	no	—
64	C₂×C₄	—	277	2	no	—
65	C₂×C₄	—	554	1	no	—
66	C₂×C₄	—	554	1	no	—
67	C₂×C₄	C₂×#11764308	1	2	yes	—
68	C₈	—	554	4	no	—
69	C₂²	—	2	2	no	—
70	C₂²	C₂²⋊#11764308	1	1	yes	characteristic
71	C₂²	C₂²⋊#11764308	1	1	yes	characteristic
72	C₂²	C₂²×#11764308	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	277	2	no	—
75	C₄	—	277	2	no	—
76	C₄	—	554	2	no	—
77	C₂	—	2	1	no	—
78	C₂	—	2	1	no	—
79	C₂	#22579941	1	2	yes	direct product factor
80	C₂	C₂×C₂²⋊#11764308	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#11764308
commutator	C₂²×C₂₇₇	C₂²×C₄
Frattini	C₂²	C₂²×#11764308
Fitting	C₂²×C₄×C₂₇₇	C₄
socle	C₂²×C₂₇₇	C₂²⋊C₄
prime radical	C₂³×C₂₇₇	C₂×C₄
cosocle	C₂×Dic₂₇₇	C₂³
hypercenter	C₂²×C₄	#11764308
hypocenter	C₂₇₇	C₂×#101
LCS	G ▷ C₂²×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. #22579941	C₂	direct (N × H)
38. C₂×C₂₇₇	#101	semidirect
40. C₂₇₇	C₂×#101	semidirect
79. C₂	#22579941	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#17984572	2
#22579941	2
C₂²×Dic₅₅₄	2
C₂×#101	277

Subgroups — C2×#22579941 #31800986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22579941 #31800986