Subgroups — C₄×#22576096 #46836266

Order 34688.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22576096	C₂	1	2	yes	maximal
2	C₄×#16864638	C₂	1	2	yes	maximal
3	#31773662	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₂₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#16864638	C₂²	1	4	yes	—
6	#22576096	C₄	1	8	yes	direct product factor
7	#22576071	—	2	2	no	—
8	C₄×C₂₇₁⋊C₈	—	2	2	no	—
9	C₂²×C₈×C₂₇₁	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₂₇₁	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₂₇₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₂₇₁	C₄	1	4	yes	—
13	#16864638	—	2	4	no	—
14	#16864638	C₂×C₄	1	8	yes	—
15	C₂×C₂₇₁⋊C₈	—	2	4	no	—
16	C₂²×C₄×C₂₇₁	Q₈	1	2	yes	—
17	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
18	C₂×C₈×C₂₇₁	—	2	2	no	—
19	C₂×C₈×C₂₇₁	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₂₇₁	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₂₇₁	C₂×C₄	1	2	yes	—
22	C₄²×C₂₇₁	C₂×C₄	1	2	yes	—
23	C₄²×C₂₇₁	D₄	1	1	yes	characteristic
24	C₄²×C₂₇₁	D₄	1	1	yes	characteristic
25	C₂₇₁⋊C₈	—	2	8	no	—
26	C₂³×C₂₇₁	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₄×C₂₇₁	—	2	4	no	—
28	C₂×C₄×C₂₇₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₂₇₁	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₂₇₁	C₂²×C₄	1	2	yes	—
31	C₂×C₄×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₇₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₂₇₁	#41	1	2	yes	—
34	C₈×C₂₇₁	—	2	2	no	—
35	C₈×C₂₇₁	C₄²	1	4	yes	—
36	C₂²×C₂₇₁	—	2	2	no	—
37	C₂²×C₂₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₂₇₁	C₄×Q₈	1	2	yes	—
39	C₄×C₂₇₁	—	2	2	no	—
40	C₄×C₂₇₁	#108	1	4	yes	complemented
41	C₄×C₂₇₁	C₂×C₄²	1	1	yes	characteristic
42	C₄×C₂₇₁	#117	1	1	yes	characteristic
43	C₄×C₂₇₁	C₄×D₄	1	2	yes	—
44	C₂×C₂₇₁	—	2	2	no	—
45	C₂×C₂₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₂₇₁	C₂×#108	1	2	yes	—
47	C₂₇₁	C₄×#108	1	1	yes	characteristic, complemented, Sylow
48	C₄×#108	—	271	1	no	maximal, Sylow
49	C₂×#108	—	271	2	no	—
50	C₄×M₁₆	—	271	2	no	—
51	C₂×C₄×C₈	D₂₇₁	1	1	yes	characteristic
52	#341	—	271	2	no	—
53	C₂×M₁₆	—	271	4	no	—
54	C₂²×C₈	C₂×D₂₇₁	1	1	yes	characteristic
55	C₂²×C₈	C₂×D₂₇₁	1	1	yes	characteristic
56	C₂×C₄²	C₂×D₂₇₁	1	1	yes	characteristic
57	#108	—	271	8	no	—
58	#97	—	542	2	no	—
59	C₄×C₈	—	542	2	no	—
60	C₄×C₈	Dic₂₇₁	1	4	yes	—
61	C₂²×C₄	Dic₅₄₂	1	2	yes	—
62	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
63	M₁₆	—	271	8	no	—
64	M₁₆	—	542	4	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	—	542	4	no	—
67	C₂×C₈	C₄×D₂₇₁	1	4	yes	—
68	C₂×C₈	C₂×Dic₂₇₁	1	2	yes	—
69	C₂×C₈	C₂×Dic₂₇₁	1	2	yes	—
70	C₄²	C₂×Dic₂₇₁	1	2	yes	—
71	C₄²	D₁₀₈₄	1	1	yes	characteristic
72	C₄²	D₁₀₈₄	1	1	yes	characteristic
73	C₂³	C₂×Dic₅₄₂	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄⋊Dic₂₇₁	1	2	yes	—
76	C₂×C₄	C₄⋊Dic₂₇₁	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₂₇₁	1	2	yes	—
78	C₂×C₄	C₂²×Dic₂₇₁	1	1	yes	characteristic
79	C₂×C₄	C₂×D₁₀₈₄	1	1	yes	characteristic
80	C₂×C₄	#16864654	1	2	yes	—
81	C₈	—	2	2	no	—
82	C₈	—	542	8	no	—
83	C₈	C₄×Dic₂₇₁	1	4	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄⋊Dic₂₇₁	1	1	yes	characteristic
86	C₂²	C₄×Dic₅₄₂	1	2	yes	—
87	C₄	—	2	2	no	—
88	C₄	#22576096	1	4	yes	direct product factor
89	C₄	C₂×C₄×Dic₂₇₁	1	1	yes	characteristic
90	C₄	#22576119	1	1	yes	characteristic
91	C₄	C₄×D₁₀₈₄	1	2	yes	—
92	C₂	—	2	2	no	—
93	C₂	C₄×C₄⋊Dic₂₇₁	1	1	yes	characteristic
94	C₂	C₂×#22576096	1	2	yes	—

	subgroup	G/H
center	C₄²	D₁₀₈₄
commutator	C₄×C₂₇₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₇₁
Fitting	C₂×C₄×C₈×C₂₇₁	C₂
socle	C₂²×C₂₇₁	C₂×C₄⋊C₄
prime radical	C₂³×C₂₇₁	C₂×Q₈
cosocle	C₂²×C₄×C₂₇₁	C₂³
hypercenter	C₂×C₄×C₈	D₂₇₁
hypocenter	C₂₇₁	C₄×#108
LCS	G ▷ C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #22576096	C₄	direct (N × H)
40. C₄×C₂₇₁	#108	semidirect
47. C₂₇₁	C₄×#108	semidirect
88. C₄	#22576096	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×#22576096	2
C₄×#16864638	2
#31773662	2
C₂×C₄×C₈×C₂₇₁	2
C₄×#108	271

Subgroups — C4×#22576096 #46836266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#22576096 #46836266