Subgroups — C₄×#10587490 #14528686

Order 2176.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587490	C₂	1	2	yes	maximal
2	C₄×#63223	C₂	1	2	yes	maximal
3	#11762574	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₁₇	C₂²	1	1	yes	characteristic
6	C₂²×C₈×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
8	C₂×#63223	C₂²	1	4	yes	—
9	C₄×C₈×C₁₇	C₄	1	4	yes	—
10	#10587490	C₄	1	8	yes	direct product factor
11	#10587474	—	2	2	no	—
12	C₄×#3622	—	2	2	no	—
13	C₂²×C₄×C₁₇	Q₈	1	2	yes	—
14	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
15	C₂×C₈×C₁₇	—	2	2	no	—
16	C₂×C₈×C₁₇	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
19	C₄²×C₁₇	C₂×C₄	1	2	yes	—
20	C₄²×C₁₇	D₄	1	1	yes	characteristic
21	C₄²×C₁₇	D₄	1	1	yes	characteristic
22	#63223	—	2	4	no	—
23	#63223	C₂×C₄	1	8	yes	—
24	C₂×#3622	—	2	4	no	—
25	C₂³×C₁₇	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₄×C₁₇	—	2	4	no	—
27	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₇	C₂²×C₄	1	2	yes	—
30	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₁₇	#41	1	2	yes	—
33	C₈×C₁₇	—	2	2	no	—
34	C₈×C₁₇	C₄²	1	4	yes	—
35	#3622	—	2	8	no	—
36	C₄×#108	—	17	1	no	maximal, Sylow
37	C₂²×C₁₇	—	2	2	no	—
38	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₁₇	C₄×Q₈	1	2	yes	—
40	C₄×C₁₇	—	2	2	no	—
41	C₄×C₁₇	#108	1	4	yes	complemented
42	C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
43	C₄×C₁₇	#117	1	1	yes	characteristic
44	C₄×C₁₇	C₄×D₄	1	2	yes	—
45	C₂×#108	—	17	2	no	—
46	C₄×M₁₆	—	17	2	no	—
47	C₂×C₄×C₈	D₁₇	1	1	yes	characteristic
48	#341	—	17	2	no	—
49	C₂×C₁₇	—	2	2	no	—
50	C₂×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₁₇	C₂×#108	1	2	yes	—
52	C₂×M₁₆	—	17	4	no	—
53	C₂²×C₈	C₂×D₁₇	1	1	yes	characteristic
54	C₂²×C₈	C₂×D₁₇	1	1	yes	characteristic
55	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
56	#108	—	17	8	no	—
57	#97	—	34	2	no	—
58	C₄×C₈	—	34	2	no	—
59	C₄×C₈	Dic₁₇	1	4	yes	—
60	C₁₇	C₄×#108	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	Dic₃₄	1	2	yes	—
62	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
63	M₁₆	—	17	8	no	—
64	M₁₆	—	34	4	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	—	34	4	no	—
67	C₂×C₈	C₄×D₁₇	1	4	yes	—
68	C₂×C₈	C₂×Dic₁₇	1	2	yes	—
69	C₂×C₈	C₂×Dic₁₇	1	2	yes	—
70	C₄²	D₆₈	1	1	yes	characteristic
71	C₄²	D₆₈	1	1	yes	characteristic
72	C₄²	C₂×Dic₁₇	1	2	yes	—
73	C₂³	C₂×Dic₃₄	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄⋊Dic₁₇	1	2	yes	—
76	C₂×C₄	C₄⋊Dic₁₇	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₁₇	1	2	yes	—
78	C₂×C₄	C₂×D₆₈	1	1	yes	characteristic
79	C₂×C₄	#63252	1	2	yes	—
80	C₂×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	34	8	no	—
83	C₈	C₄×Dic₁₇	1	4	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	C₄×Dic₃₄	1	2	yes	—
86	C₂²	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
87	C₄	—	2	2	no	—
88	C₄	#10587490	1	4	yes	direct product factor
89	C₄	C₄×D₆₈	1	2	yes	—
90	C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
91	C₄	#10587612	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	C₄×C₄⋊Dic₁₇	1	1	yes	characteristic
94	C₂	C₂×#10587490	1	2	yes	—

	subgroup	G/H
center	C₄²	D₆₈
commutator	C₄×C₁₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₇
Fitting	C₂×C₄×C₈×C₁₇	C₂
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂³×C₁₇	C₂×Q₈
cosocle	C₂²×C₄×C₁₇	C₂³
hypercenter	C₂×C₄×C₈	D₁₇
hypocenter	C₁₇	C₄×#108
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
10. #10587490	C₄	direct (N × H)
41. C₄×C₁₇	#108	semidirect
60. C₁₇	C₄×#108	semidirect
88. C₄	#10587490	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×#10587490	2
C₄×#63223	2
#11762574	2
C₂×C₄×C₈×C₁₇	2
C₄×#108	17

Subgroups — C4×#10587490 #14528686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10587490 #14528686