Subgroups — C₂×#14531058 #17189800

Order 4352.

558 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763213	C₂	1	2	yes	maximal
2	#14531058	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11762635	C₂	1	1	yes	maximal, characteristic
4	C₂×#11762634	C₂	1	2	yes	maximal
5	C₂×C₁₆×Dic₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₇×#366	C₂	1	1	yes	maximal, characteristic
7	C₂×#10587574	—	2	2	no	—
8	C₂²×#63214	C₂²	1	1	yes	characteristic
9	#11763213	—	2	4	no	—
10	#11763213	C₂²	1	8	yes	—
11	C₂×#10587489	C₂²	1	2	yes	—
12	C₂×#10587478	—	2	2	no	—
13	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
14	#11762635	C₂²	1	4	yes	—
15	#11762634	C₂²	1	8	yes	—
16	C₁₆×Dic₁₇	C₂²	1	4	yes	—
17	C₂²×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×#107	C₂²	1	2	yes	—
19	C₁₇×#366	C₂²	1	4	yes	—
20	C₂²×Dic₃₄	—	4	2	no	—
21	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
23	C₂×C₄⋊Dic₁₇	—	2	2	no	—
24	C₂×#63225	—	4	2	no	—
25	C₂×C₄×Dic₁₇	D₄	1	1	yes	characteristic
26	C₂²×#3622	D₄	1	1	yes	characteristic
27	#10587574	—	2	8	no	—
28	#10587574	—	4	4	no	—
29	C₂×C₁₆×C₁₇	Q₈	1	4	yes	complemented
30	C₂×C₁₆×C₁₇	C₂³	1	2	yes	—
31	C₁₇×#107	—	2	2	no	—
32	C₁₇×#107	C₂³	1	4	yes	—
33	#10587489	—	2	2	no	—
34	#10587489	C₂³	1	4	yes	—
35	C₈×Dic₁₇	D₄	1	2	yes	—
36	C₈×Dic₁₇	C₂³	1	2	yes	—
37	C₂×#63214	Q₈	1	4	yes	complemented
38	C₂×#63214	C₂³	1	2	yes	—
39	#10587478	—	2	8	no	—
40	C₂²×C₄×C₁₇	—	4	2	no	—
41	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
42	C₂²×Dic₁₇	—	4	2	no	—
43	C₂²×Dic₁₇	D₈	1	1	yes	characteristic
44	C₂²×Dic₁₇	D₈	1	1	yes	characteristic
45	C₂×Dic₃₄	—	4	8	no	—
46	C₂×Dic₃₄	—	8	8	no	—
47	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
48	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
49	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
50	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
51	C₄⋊C₄×C₁₇	—	2	4	no	—
52	C₄⋊C₄×C₁₇	—	4	2	no	—
53	C₄⋊Dic₁₇	—	2	4	no	—
54	C₄⋊Dic₁₇	—	4	2	no	—
55	#63225	—	4	8	no	—
56	C₄×Dic₁₇	D₈	1	2	yes	—
57	C₄×Dic₁₇	C₂×D₄	1	2	yes	—
58	C₂×#3622	Q₁₆	1	4	yes	—
59	C₂×#3622	C₂×D₄	1	2	yes	—
60	C₁₆×C₁₇	C₂×Q₈	1	4	yes	complemented
61	#63214	C₂×Q₈	1	4	yes	complemented
62	C₂×#2252	—	17	1	no	maximal, Sylow
63	C₂³×C₁₇	C₂×D₈	1	1	yes	characteristic
64	C₂×C₄×C₁₇	—	4	4	no	—
65	C₂×C₄×C₁₇	—	8	4	no	—
66	C₂×C₄×C₁₇	C₄⋊Q₈	1	2	yes	—
67	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₁₇	C₂×Q₁₆	1	2	yes	—
69	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
70	C₂×Dic₁₇	—	4	4	no	—
71	C₂×Dic₁₇	—	8	4	no	—
72	C₂×Dic₁₇	D₁₆	1	4	yes	—
73	C₂×Dic₁₇	Q₃₂	1	4	yes	—
74	C₂×Dic₁₇	C₂×D₈	1	2	yes	—
75	C₂×Dic₁₇	C₂×D₈	1	2	yes	—
76	Dic₃₄	—	8	16	no	—
77	C₈×C₁₇	C₄⋊Q₈	1	2	yes	—
78	C₈×C₁₇	C₂²×Q₈	1	1	yes	characteristic
79	C₈×C₁₇	C₂²×Q₈	1	1	yes	characteristic
80	#3622	C₂×Q₁₆	1	4	yes	—
81	C₂×#500	—	17	2	no	—
82	#2252	—	17	8	no	—
83	C₂×#366	—	17	1	no	—
84	C₂×#366	—	17	2	no	—
85	C₂×#366	D₁₇	1	1	yes	characteristic
86	C₂×C₄×C₁₆	—	17	1	no	—
87	C₂²×C₁₇	#500	1	2	yes	—
88	C₂²×C₁₇	C₂×D₁₆	1	2	yes	—
89	C₂²×C₁₇	C₂×Q₃₂	1	2	yes	—
90	C₂²×C₁₇	C₂²×D₈	1	1	yes	characteristic
91	C₄×C₁₇	—	8	4	no	—
92	C₄×C₁₇	#500	1	2	yes	—
93	C₄×C₁₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
94	C₄×C₁₇	C₂²×Q₁₆	1	1	yes	characteristic
95	Dic₁₇	—	8	4	no	—
96	Dic₁₇	C₂×D₁₆	1	4	yes	—
97	Dic₁₇	C₂×Q₃₂	1	4	yes	—
98	C₂×C₄⋊Q₈	—	34	2	no	—
99	C₂²×C₁₆	—	17	1	no	—
100	C₂²×C₁₆	C₂×D₁₇	1	1	yes	characteristic
101	#500	—	17	8	no	—
102	#500	—	34	4	no	—
103	C₂×#107	—	17	2	no	—
104	C₂×#107	—	34	2	no	—
105	C₂×#107	C₂×D₁₇	1	2	yes	—
106	C₂×C₄×C₈	—	17	1	no	—
107	#366	—	17	4	no	—
108	#366	—	17	8	no	—
109	#366	C₂×D₁₇	1	4	yes	—
110	C₄×C₁₆	—	17	4	no	—
111	C₂×C₁₇	#2252	1	4	yes	complemented
112	C₂×C₁₇	C₂×#500	1	1	yes	characteristic
113	C₂×C₁₇	C₂²×D₁₆	1	1	yes	characteristic
114	C₂×C₁₇	C₂²×Q₃₂	1	1	yes	characteristic
115	C₂²×Q₈	—	68	2	no	—
116	C₂²×C₈	—	17	1	no	—
117	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
118	C₄⋊Q₈	—	34	8	no	—
119	C₄⋊Q₈	—	68	4	no	—
120	C₂×C₄⋊C₄	—	2	2	no	—
121	C₂×C₄⋊C₄	—	34	2	no	—
122	C₂×C₄⋊C₄	—	68	2	no	—
123	C₂×C₄²	—	17	1	no	—
124	C₂×C₁₆	—	17	4	no	—
125	C₂×C₁₆	—	17	2	no	—
126	C₂×C₁₆	Dic₃₄	1	4	yes	complemented
127	C₂×C₁₆	C₂²×D₁₇	1	2	yes	—
128	#107	—	2	2	no	—
129	#107	—	17	4	no	—
130	#107	—	34	8	no	—
131	#107	—	34	2	no	—
132	#107	C₂²×D₁₇	1	4	yes	—
133	C₄×C₈	—	17	2	no	—
134	C₄×C₈	—	17	2	no	—
135	C₁₇	C₂×#2252	1	1	yes	characteristic, complemented, Sylow
136	C₂×Q₈	—	68	8	no	—
137	C₂×Q₈	—	136	8	no	—
138	C₂²×C₄	—	4	2	no	—
139	C₂²×C₄	—	17	1	no	—
140	C₂²×C₄	—	17	1	no	—
141	C₂²×C₄	—	68	2	no	—
142	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
143	C₂×C₈	—	17	2	no	—
144	C₂×C₈	—	17	4	no	—
145	C₂×C₈	C₂×Dic₃₄	1	2	yes	—
146	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
147	C₂×C₈	Q₈×D₁₇	1	2	yes	—
148	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
149	C₄⋊C₄	—	2	4	no	—
150	C₄⋊C₄	—	4	2	no	—
151	C₄⋊C₄	—	34	4	no	—
152	C₄⋊C₄	—	68	8	no	—
153	C₄⋊C₄	—	68	2	no	—
154	C₄²	—	17	2	no	—
155	C₄²	—	17	2	no	—
156	C₁₆	—	17	4	no	—
157	C₁₆	C₂×Dic₃₄	1	4	yes	complemented
158	C₂³	D₈×D₁₇	1	1	yes	characteristic
159	Q₈	—	136	16	no	—
160	C₂×C₄	—	4	4	no	—
161	C₂×C₄	—	8	4	no	—
162	C₂×C₄	—	17	4	no	—
163	C₂×C₄	—	17	4	no	—
164	C₂×C₄	—	17	2	no	—
165	C₂×C₄	—	17	2	no	—
166	C₂×C₄	—	68	4	no	—
167	C₂×C₄	—	136	4	no	—
168	C₂×C₄	#10587574	1	2	yes	—
169	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
170	C₂×C₄	Q₁₆×D₁₇	1	2	yes	—
171	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
172	C₈	—	17	4	no	—
173	C₈	#10587574	1	2	yes	—
174	C₈	C₂²×Dic₃₄	1	1	yes	characteristic
175	C₈	C₂×Q₈×D₁₇	1	1	yes	characteristic
176	C₂²	#11763213	1	2	yes	—
177	C₂²	D₁₆×D₁₇	1	2	yes	—
178	C₂²	Q₃₂×D₁₇	1	2	yes	—
179	C₂²	C₂×D₈×D₁₇	1	1	yes	characteristic
180	C₄	—	8	4	no	—
181	C₄	—	17	4	no	—
182	C₄	—	17	4	no	—
183	C₄	—	136	4	no	—
184	C₄	#11763213	1	2	yes	—
185	C₄	C₂×#10587574	1	1	yes	characteristic
186	C₄	C₂×Q₁₆×D₁₇	1	1	yes	characteristic
187	C₂	#14531058	1	4	yes	direct product factor
188	C₂	C₂×#11763213	1	1	yes	characteristic
189	C₂	C₂×D₁₆×D₁₇	1	1	yes	characteristic
190	C₂	C₂×Q₃₂×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈×D₁₇
commutator, cosocle	C₂×C₈×C₁₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₇
Fitting	C₂×C₁₇×#366	C₂
socle, prime radical	C₂³×C₁₇	C₂×D₈
hypercenter	C₂×#366	D₁₇
hypocenter	C₁₇	C₂×#2252
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

Complements

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

N	H ≅ G/N	type
2. #14531058	C₂	direct (N × H)
29. C₂×C₁₆×C₁₇	Q₈	semidirect
37. C₂×#63214	Q₈	semidirect
60. C₁₆×C₁₇	C₂×Q₈	semidirect
61. #63214	C₂×Q₈	semidirect
111. C₂×C₁₇	#2252	semidirect
126. C₂×C₁₆	Dic₃₄	semidirect
135. C₁₇	C₂×#2252	semidirect
157. C₁₆	C₂×Dic₃₄	semidirect
187. C₂	#14531058	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×#11763213	2
#14531058	2
C₂×#11762635	2
C₂×#11762634	2
C₂×C₁₆×Dic₁₇	2
C₂×C₁₇×#366	2
C₂×#2252	17

Subgroups — C2×#14531058 #17189800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14531058 #17189800