Subgroups — C₄×#16861145 #30638632

Order 16256.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861145	C₂	1	2	yes	maximal
2	C₄×#14523232	C₂	1	2	yes	maximal
3	#22549641	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#14523232	C₂²	1	4	yes	—
6	#16861145	C₄	1	8	yes	direct product factor
7	#16861120	—	2	2	no	—
8	C₄×C₁₂₇⋊C₈	—	2	2	no	—
9	C₂²×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₁₂₇	C₄	1	4	yes	—
13	#14523232	—	2	4	no	—
14	#14523232	C₂×C₄	1	8	yes	—
15	C₂×C₁₂₇⋊C₈	—	2	4	no	—
16	C₂²×C₄×C₁₂₇	Q₈	1	2	yes	—
17	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
18	C₂×C₈×C₁₂₇	—	2	2	no	—
19	C₂×C₈×C₁₂₇	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
22	C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
23	C₄²×C₁₂₇	D₄	1	1	yes	characteristic
24	C₄²×C₁₂₇	D₄	1	1	yes	characteristic
25	C₁₂₇⋊C₈	—	2	8	no	—
26	C₂³×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₄×C₁₂₇	—	2	4	no	—
28	C₂×C₄×C₁₂₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₂₇	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
31	C₂×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₁₂₇	#41	1	2	yes	—
34	C₈×C₁₂₇	—	2	2	no	—
35	C₈×C₁₂₇	C₄²	1	4	yes	—
36	C₂²×C₁₂₇	—	2	2	no	—
37	C₂²×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₁₂₇	C₄×Q₈	1	2	yes	—
39	C₄×C₁₂₇	—	2	2	no	—
40	C₄×C₁₂₇	#108	1	4	yes	complemented
41	C₄×C₁₂₇	C₂×C₄²	1	1	yes	characteristic
42	C₄×C₁₂₇	#117	1	1	yes	characteristic
43	C₄×C₁₂₇	C₄×D₄	1	2	yes	—
44	C₂×C₁₂₇	—	2	2	no	—
45	C₂×C₁₂₇	C₄×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₁₂₇	C₂×#108	1	2	yes	—
47	C₄×#108	—	127	1	no	maximal, Sylow
48	C₁₂₇	C₄×#108	1	1	yes	characteristic, complemented, Sylow
49	C₂×#108	—	127	2	no	—
50	C₄×M₁₆	—	127	2	no	—
51	C₂×C₄×C₈	D₁₂₇	1	1	yes	characteristic
52	#341	—	127	2	no	—
53	C₂×M₁₆	—	127	4	no	—
54	C₂²×C₈	C₂×D₁₂₇	1	1	yes	characteristic
55	C₂²×C₈	C₂×D₁₂₇	1	1	yes	characteristic
56	C₂×C₄²	C₂×D₁₂₇	1	1	yes	characteristic
57	#108	—	127	8	no	—
58	#97	—	254	2	no	—
59	C₄×C₈	—	254	2	no	—
60	C₄×C₈	Dic₁₂₇	1	4	yes	—
61	C₂²×C₄	Dic₂₅₄	1	2	yes	—
62	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
63	M₁₆	—	127	8	no	—
64	M₁₆	—	254	4	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	—	254	4	no	—
67	C₂×C₈	C₄×D₁₂₇	1	4	yes	—
68	C₂×C₈	C₂×Dic₁₂₇	1	2	yes	—
69	C₂×C₈	C₂×Dic₁₂₇	1	2	yes	—
70	C₄²	C₂×Dic₁₂₇	1	2	yes	—
71	C₄²	D₅₀₈	1	1	yes	characteristic
72	C₄²	D₅₀₈	1	1	yes	characteristic
73	C₂³	C₂×Dic₂₅₄	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄⋊Dic₁₂₇	1	2	yes	—
76	C₂×C₄	C₄⋊Dic₁₂₇	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₁₂₇	1	2	yes	—
78	C₂×C₄	C₂²×Dic₁₂₇	1	1	yes	characteristic
79	C₂×C₄	C₂×D₅₀₈	1	1	yes	characteristic
80	C₂×C₄	#14523248	1	2	yes	—
81	C₈	—	2	2	no	—
82	C₈	—	254	8	no	—
83	C₈	C₄×Dic₁₂₇	1	4	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄⋊Dic₁₂₇	1	1	yes	characteristic
86	C₂²	C₄×Dic₂₅₄	1	2	yes	—
87	C₄	—	2	2	no	—
88	C₄	#16861145	1	4	yes	direct product factor
89	C₄	C₂×C₄×Dic₁₂₇	1	1	yes	characteristic
90	C₄	#16861168	1	1	yes	characteristic
91	C₄	C₄×D₅₀₈	1	2	yes	—
92	C₂	—	2	2	no	—
93	C₂	C₄×C₄⋊Dic₁₂₇	1	1	yes	characteristic
94	C₂	C₂×#16861145	1	2	yes	—

	subgroup	G/H
center	C₄²	D₅₀₈
commutator	C₄×C₁₂₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₂₇
Fitting	C₂×C₄×C₈×C₁₂₇	C₂
socle	C₂²×C₁₂₇	C₂×C₄⋊C₄
prime radical	C₂³×C₁₂₇	C₂×Q₈
cosocle	C₂²×C₄×C₁₂₇	C₂³
hypercenter	C₂×C₄×C₈	D₁₂₇
hypocenter	C₁₂₇	C₄×#108
LCS	G ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
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. #16861145	C₄	direct (N × H)
40. C₄×C₁₂₇	#108	semidirect
48. C₁₂₇	C₄×#108	semidirect
88. C₄	#16861145	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×#16861145	2
C₄×#14523232	2
#22549641	2
C₂×C₄×C₈×C₁₂₇	2
C₄×#108	127

Subgroups — C4×#16861145 #30638632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16861145 #30638632