Subgroups — C₂×#14531063 #17189806

Order 4352.

494 conjugacy classes of subgroups.

The subgroup lattice has 148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763211	C₂	1	2	yes	maximal
2	#14531063	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11762637	C₂	1	2	yes	maximal
4	C₂×#11762635	C₂	1	2	yes	maximal
5	C₂×C₄×C₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587556	—	2	2	no	—
7	#11763211	—	2	4	no	—
8	#11763211	C₂²	1	8	yes	—
9	C₂×#10587489	C₂²	1	4	yes	—
10	C₂×#10587488	—	2	2	no	—
11	#11762637	C₂²	1	8	yes	—
12	#11762635	C₂²	1	8	yes	—
13	C₂²×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
14	C₂²×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
16	C₄×C₁₆×C₁₇	C₂²	1	4	yes	—
17	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₇	—	2	4	no	—
21	C₂×#63225	—	4	4	no	—
22	#10587556	—	2	8	no	—
23	#10587556	—	4	4	no	—
24	C₂×C₁₆×C₁₇	Q₈	1	4	yes	—
25	C₂×C₁₆×C₁₇	Q₈	1	4	yes	—
26	C₂×C₁₆×C₁₇	C₂³	1	2	yes	—
27	C₂×C₁₆×C₁₇	C₂³	1	2	yes	—
28	C₄×C₈×C₁₇	D₄	1	2	yes	—
29	C₄×C₈×C₁₇	C₂³	1	2	yes	—
30	#10587489	—	2	4	no	—
31	#10587489	C₂³	1	8	yes	—
32	#10587488	—	2	8	no	—
33	C₂²×C₄×C₁₇	D₈	1	2	yes	—
34	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
35	C₂²×Dic₁₇	—	4	4	no	—
36	C₂×C₈×C₁₇	Q₁₆	1	4	yes	—
37	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
39	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
40	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
41	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
42	C₄²×C₁₇	D₈	1	2	yes	—
43	C₄²×C₁₇	C₂×D₄	1	2	yes	—
44	C₄⋊Dic₁₇	—	2	8	no	—
45	C₄⋊Dic₁₇	—	4	4	no	—
46	#63225	—	4	16	no	—
47	C₁₆×C₁₇	C₂×Q₈	1	4	yes	—
48	C₁₆×C₁₇	C₂×Q₈	1	4	yes	—
49	C₂×#2253	—	17	1	no	maximal, Sylow
50	C₂³×C₁₇	C₂×D₈	1	1	yes	characteristic
51	C₂×C₄×C₁₇	—	2	4	no	—
52	C₂×C₄×C₁₇	C₄⋊Q₈	1	2	yes	—
53	C₂×C₄×C₁₇	C₂×D₈	1	4	yes	—
54	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
55	C₂×C₄×C₁₇	C₂×Q₁₆	1	2	yes	—
56	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
57	C₂×Dic₁₇	—	4	8	no	—
58	C₂×Dic₁₇	—	8	8	no	—
59	C₈×C₁₇	C₄⋊Q₈	1	2	yes	—
60	C₈×C₁₇	C₂×Q₁₆	1	4	yes	—
61	C₈×C₁₇	C₂²×Q₈	1	1	yes	characteristic
62	C₈×C₁₇	C₂²×Q₈	1	1	yes	characteristic
63	C₂×#499	—	17	2	no	—
64	#2253	—	17	8	no	—
65	C₂×#367	—	17	2	no	—
66	C₂×#366	—	17	2	no	—
67	C₂×C₄×C₁₆	D₁₇	1	1	yes	characteristic
68	C₂²×C₁₇	#500	1	2	yes	—
69	C₂²×C₁₇	#508	1	4	yes	—
70	C₂²×C₁₇	C₂²×D₈	1	1	yes	characteristic
71	C₄×C₁₇	—	2	4	no	—
72	C₄×C₁₇	#500	1	2	yes	—
73	C₄×C₁₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
74	C₄×C₁₇	C₂²×Q₁₆	1	1	yes	characteristic
75	Dic₁₇	—	8	8	no	—
76	C₂×#125	—	34	2	no	—
77	C₂²×C₁₆	C₂×D₁₇	1	1	yes	characteristic
78	C₂²×C₁₆	C₂×D₁₇	1	1	yes	characteristic
79	#499	—	17	8	no	—
80	#499	—	34	4	no	—
81	C₂×#107	—	17	4	no	—
82	C₂×#106	—	34	2	no	—
83	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
84	#367	—	17	8	no	—
85	#366	—	17	8	no	—
86	C₄×C₁₆	C₂×D₁₇	1	4	yes	—
87	C₂×C₁₇	#2253	1	4	yes	complemented
88	C₂×C₁₇	C₂×#500	1	1	yes	characteristic
89	C₂×C₁₇	C₂×#508	1	2	yes	—
90	C₂²×C₈	D₆₈	1	1	yes	characteristic
91	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
92	#125	—	34	8	no	—
93	#125	—	68	4	no	—
94	C₂×C₄⋊C₄	—	34	4	no	—
95	C₂×C₄⋊C₄	—	68	4	no	—
96	C₂×C₄²	D₆₈	1	1	yes	characteristic
97	C₂×C₁₆	Dic₃₄	1	4	yes	—
98	C₂×C₁₆	Dic₃₄	1	4	yes	—
99	C₂×C₁₆	C₂²×D₁₇	1	2	yes	—
100	C₂×C₁₆	C₂²×D₁₇	1	2	yes	—
101	#107	—	17	8	no	—
102	#107	—	34	4	no	—
103	#106	—	34	8	no	—
104	C₄×C₈	D₆₈	1	2	yes	—
105	C₄×C₈	C₂²×D₁₇	1	2	yes	—
106	C₁₇	C₂×#2253	1	1	yes	characteristic, complemented, Sylow
107	C₂²×C₄	—	68	4	no	—
108	C₂²×C₄	D₁₃₆	1	2	yes	—
109	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
110	C₂×C₈	Dic₆₈	1	4	yes	—
111	C₂×C₈	C₂×Dic₃₄	1	2	yes	—
112	C₂×C₈	C₂×Dic₃₄	1	2	yes	—
113	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
114	C₂×C₈	C₂×D₆₈	1	2	yes	—
115	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
116	C₄⋊C₄	—	34	8	no	—
117	C₄⋊C₄	—	68	4	no	—
118	C₄⋊C₄	—	68	16	no	—
119	C₄²	D₁₃₆	1	2	yes	—
120	C₄²	C₂×D₆₈	1	2	yes	—
121	C₁₆	C₂×Dic₃₄	1	4	yes	—
122	C₁₆	C₂×Dic₃₄	1	4	yes	—
123	C₂³	C₂×D₁₃₆	1	1	yes	characteristic
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	68	8	no	—
126	C₂×C₄	—	136	8	no	—
127	C₂×C₄	#10587555	1	2	yes	—
128	C₂×C₄	C₂×D₁₃₆	1	4	yes	—
129	C₂×C₄	C₂×D₁₃₆	1	1	yes	characteristic
130	C₂×C₄	C₂×Dic₆₈	1	2	yes	—
131	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
132	C₈	#10587555	1	2	yes	—
133	C₈	C₂×Dic₆₈	1	4	yes	—
134	C₈	C₂²×Dic₃₄	1	1	yes	characteristic
135	C₈	C₂²×Dic₃₄	1	1	yes	characteristic
136	C₂²	#11763214	1	2	yes	—
137	C₂²	#11763241	1	4	yes	—
138	C₂²	C₂²×D₁₃₆	1	1	yes	characteristic
139	C₄	—	2	4	no	—
140	C₄	—	136	8	no	—
141	C₄	#11763214	1	2	yes	—
142	C₄	C₂×#10587555	1	1	yes	characteristic
143	C₄	C₂²×Dic₆₈	1	1	yes	characteristic
144	C₂	#14531063	1	4	yes	direct product factor
145	C₂	C₂×#11763214	1	1	yes	characteristic
146	C₂	C₂×#11763241	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₁₃₆
commutator, cosocle	C₂×C₈×C₁₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₇
Fitting	C₂×C₄×C₁₆×C₁₇	C₂
socle, prime radical	C₂³×C₁₇	C₂×D₈
hypercenter	C₂×C₄×C₁₆	D₁₇
hypocenter	C₁₇	C₂×#2253
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. #14531063	C₂	direct (N × H)
87. C₂×C₁₇	#2253	semidirect
106. C₁₇	C₂×#2253	semidirect
144. C₂	#14531063	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×#11763211	2
#14531063	2
C₂×#11762637	2
C₂×#11762635	2
C₂×C₄×C₁₆×C₁₇	2
C₂×#2253	17

Subgroups — C2×#14531063 #17189806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14531063 #17189806