Subgroups — C₂×#14545205 #17978837

Order 4352.

502 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763742	C₂	1	2	yes	maximal, complemented
2	#14545205	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11763741	C₂	1	2	yes	maximal, complemented
4	C₂×#11763740	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
6	#11763742	C₂²	1	8	yes	complemented
7	#11763741	C₂²	1	8	yes	complemented
8	#11763740	C₂²	1	8	yes	complemented
9	C₂×#10587467	C₂²	1	4	yes	complemented
10	C₂²×C₈×D₁₇	C₄	1	1	yes	characteristic
11	C₂²×#63214	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×D₁₇	C₄	1	4	yes	—
13	C₂×C₁₆×D₁₇	C₄	1	1	yes	characteristic
14	C₂×C₁₆×D₁₇	C₄	1	1	yes	characteristic
15	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×D₁₇	C₂²	1	4	yes	—
17	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
18	C₂²×C₁₆×C₁₇	C₄	1	1	yes	characteristic
19	C₂²×C₄×D₁₇	C₈	1	1	yes	characteristic
20	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂²×#3622	C₈	1	1	yes	characteristic
22	C₂×C₈×D₁₇	C₈	1	4	yes	—
23	C₂×C₈×D₁₇	C₈	1	1	yes	characteristic
24	C₂×C₈×D₁₇	C₈	1	1	yes	characteristic
25	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×D₁₇	C₂×C₄	1	4	yes	—
27	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₁₆×C₁₇	C₂×C₄	1	4	yes	—
29	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
30	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
31	C₂×#63214	C₂×C₄	1	2	yes	—
32	C₂×#63214	C₂×C₄	1	1	yes	characteristic
33	C₂×#63214	C₂³	1	1	yes	characteristic
34	C₂×#63214	C₂³	1	2	yes	—
35	C₁₆×D₁₇	C₂×C₄	1	2	yes	—
36	C₁₆×D₁₇	C₂×C₄	1	4	yes	—
37	C₁₆×D₁₇	C₂×C₄	1	4	yes	—
38	C₁₆×D₁₇	C₂×C₄	1	2	yes	—
39	C₁₆×D₁₇	C₂³	1	2	yes	—
40	C₁₆×D₁₇	C₂³	1	2	yes	—
41	#10587467	C₂³	1	8	yes	complemented
42	C₂³×D₁₇	C₁₆	1	1	yes	characteristic
43	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
44	C₂²×Dic₁₇	C₁₆	1	1	yes	characteristic
45	C₂×C₄×D₁₇	C₁₆	1	1	yes	characteristic
46	C₂×C₄×D₁₇	C₁₆	1	4	yes	—
47	C₂×C₄×D₁₇	C₁₆	1	1	yes	characteristic
48	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
49	C₂×C₄×D₁₇	C₂×C₈	1	4	yes	—
50	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
51	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
52	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
53	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
54	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
55	C₂×#3622	C₂×C₈	1	4	yes	—
56	C₂×#3622	C₂×C₈	1	1	yes	characteristic
57	C₂×#3622	C₂×C₈	1	1	yes	characteristic
58	C₈×D₁₇	C₂×C₈	1	4	yes	—
59	C₈×D₁₇	C₂×C₈	1	2	yes	—
60	C₈×D₁₇	C₂×C₈	1	2	yes	—
61	C₈×D₁₇	C₂×C₈	1	4	yes	—
62	C₈×D₁₇	C₂²×C₄	1	2	yes	—
63	C₈×D₁₇	C₂²×C₄	1	2	yes	—
64	C₁₆×C₁₇	C₂²×C₄	1	2	yes	—
65	C₁₆×C₁₇	C₂²×C₄	1	2	yes	—
66	#63214	C₂²×C₄	1	1	yes	characteristic
67	#63214	C₂²×C₄	1	2	yes	—
68	#63214	C₂⁴	1	1	yes	characteristic
69	C₂²×M₆₄	—	17	1	no	maximal, Sylow
70	C₂³×C₁₇	C₂×C₁₆	1	1	yes	characteristic
71	C₂²×D₁₇	—	2	4	no	—
72	C₂²×D₁₇	C₂×C₁₆	1	1	yes	characteristic
73	C₂²×D₁₇	C₂×C₁₆	1	4	yes	—
74	C₂²×D₁₇	C₂×C₁₆	1	1	yes	characteristic
75	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
76	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
77	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
78	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
79	C₂×Dic₁₇	C₂×C₁₆	1	4	yes	—
80	C₂×Dic₁₇	C₂×C₁₆	1	1	yes	characteristic
81	C₂×Dic₁₇	C₂×C₁₆	1	1	yes	characteristic
82	C₄×D₁₇	C₂×C₁₆	1	4	yes	—
83	C₄×D₁₇	C₂×C₁₆	1	2	yes	—
84	C₄×D₁₇	C₂×C₁₆	1	2	yes	—
85	C₄×D₁₇	C₂×C₁₆	1	4	yes	—
86	C₄×D₁₇	C₂²×C₈	1	2	yes	—
87	C₄×D₁₇	C₂²×C₈	1	2	yes	—
88	C₈×C₁₇	C₂²×C₈	1	2	yes	—
89	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
90	C₈×C₁₇	C₂³×C₄	1	1	yes	characteristic
91	#3622	C₂²×C₈	1	2	yes	—
92	#3622	C₂²×C₈	1	2	yes	—
93	C₂³×C₁₆	—	17	1	no	—
94	C₂×M₆₄	—	17	2	no	—
95	C₂×M₆₄	—	17	8	no	—
96	C₂×M₆₄	—	17	2	no	—
97	C₂²×C₃₂	—	17	2	no	—
98	C₂²×C₁₇	—	2	2	no	—
99	C₂²×C₁₇	C₂²×C₁₆	1	2	yes	—
100	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
101	C₂×D₁₇	—	2	2	no	—
102	C₂×D₁₇	—	2	8	no	—
103	C₂×D₁₇	M₆₄	1	4	yes	complemented
104	C₂×D₁₇	C₂²×C₁₆	1	2	yes	—
105	C₂×D₁₇	C₂²×C₁₆	1	2	yes	—
106	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
107	C₄×C₁₇	C₂²×C₁₆	1	2	yes	—
108	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
109	Dic₁₇	C₂²×C₁₆	1	2	yes	—
110	Dic₁₇	C₂²×C₁₆	1	2	yes	—
111	C₂³×C₈	—	17	1	no	—
112	C₂²×C₁₆	—	17	1	no	—
113	C₂²×C₁₆	—	17	4	no	—
114	C₂²×C₁₆	—	17	1	no	—
115	C₂²×C₁₆	—	17	1	no	—
116	C₂²×C₁₆	—	17	4	no	—
117	C₂²×C₁₆	—	17	1	no	—
118	C₂²×C₁₆	—	17	1	no	—
119	C₂²×C₁₆	#595	1	1	yes	characteristic
120	M₆₄	—	17	8	no	—
121	M₆₄	—	17	8	no	—
122	C₂×C₃₂	—	17	4	no	—
123	C₂×C₃₂	—	17	8	no	—
124	C₂×C₁₇	—	2	2	no	—
125	C₂×C₁₇	C₂×M₆₄	1	2	yes	complemented
126	C₂×C₁₇	C₂³×C₁₆	1	1	yes	characteristic
127	D₁₇	—	2	2	no	—
128	D₁₇	C₂×M₆₄	1	4	yes	complemented
129	C₂³×C₄	—	17	1	no	—
130	C₂²×C₈	—	17	1	no	—
131	C₂²×C₈	—	17	1	no	—
132	C₂²×C₈	—	17	4	no	—
133	C₂²×C₈	—	17	1	no	—
134	C₂²×C₈	—	17	4	no	—
135	C₂²×C₈	—	17	1	no	—
136	C₂²×C₈	—	17	1	no	—
137	C₂²×C₈	C₂×#595	1	1	yes	characteristic
138	C₂×C₁₆	—	17	2	no	—
139	C₂×C₁₆	—	17	1	no	—
140	C₂×C₁₆	—	17	1	no	—
141	C₂×C₁₆	—	17	2	no	—
142	C₂×C₁₆	—	17	2	no	—
143	C₂×C₁₆	—	17	4	no	—
144	C₂×C₁₆	—	17	2	no	—
145	C₂×C₁₆	—	17	4	no	—
146	C₂×C₁₆	—	17	2	no	—
147	C₂×C₁₆	—	17	2	no	—
148	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
149	C₂×C₁₆	C₂×#595	1	4	yes	—
150	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
151	C₃₂	—	17	8	no	—
152	C₁₇	C₂²×M₆₄	1	1	yes	characteristic, complemented, Sylow
153	C₂⁴	—	17	1	no	—
154	C₂²×C₄	—	17	1	no	—
155	C₂²×C₄	—	17	1	no	—
156	C₂²×C₄	—	17	4	no	—
157	C₂²×C₄	—	17	1	no	—
158	C₂²×C₄	—	17	1	no	—
159	C₂²×C₄	—	17	4	no	—
160	C₂²×C₄	—	17	1	no	—
161	C₂²×C₄	#63242	1	1	yes	characteristic
162	C₂×C₈	—	17	4	no	—
163	C₂×C₈	—	17	1	no	—
164	C₂×C₈	—	17	1	no	—
165	C₂×C₈	—	17	4	no	—
166	C₂×C₈	—	17	4	no	—
167	C₂×C₈	—	17	2	no	—
168	C₂×C₈	—	17	2	no	—
169	C₂×C₈	—	17	2	no	—
170	C₂×C₈	—	17	2	no	—
171	C₂×C₈	#63242	1	1	yes	characteristic
172	C₂×C₈	#63242	1	2	yes	—
173	C₂×C₈	C₂²×#595	1	2	yes	—
174	C₂×C₈	C₂²×#595	1	1	yes	characteristic
175	C₁₆	—	17	1	no	—
176	C₁₆	—	17	1	no	—
177	C₁₆	—	17	2	no	—
178	C₁₆	C₂²×#595	1	2	yes	—
179	C₁₆	C₂²×#595	1	2	yes	—
180	C₂³	—	17	1	no	—
181	C₂³	—	17	4	no	—
182	C₂³	—	17	1	no	—
183	C₂³	—	34	4	no	—
184	C₂³	#10587529	1	1	yes	characteristic
185	C₂×C₄	—	17	4	no	—
186	C₂×C₄	—	17	1	no	—
187	C₂×C₄	—	17	1	no	—
188	C₂×C₄	—	17	2	no	—
189	C₂×C₄	—	17	4	no	—
190	C₂×C₄	—	17	2	no	—
191	C₂×C₄	—	17	4	no	—
192	C₂×C₄	—	17	2	no	—
193	C₂×C₄	—	17	2	no	—
194	C₂×C₄	#10587529	1	2	yes	—
195	C₂×C₄	#10587529	1	1	yes	characteristic
196	C₂×C₄	C₂×#63242	1	2	yes	—
197	C₂×C₄	C₂×#63242	1	1	yes	characteristic
198	C₈	—	17	2	no	—
199	C₈	—	17	2	no	—
200	C₈	C₂×#63242	1	2	yes	—
201	C₈	C₂×#63242	1	1	yes	characteristic
202	C₈	C₂³×#595	1	1	yes	characteristic
203	C₂²	—	2	2	no	—
204	C₂²	—	17	4	no	—
205	C₂²	—	17	2	no	—
206	C₂²	—	17	2	no	—
207	C₂²	—	34	8	no	—
208	C₂²	—	34	2	no	—
209	C₂²	C₂×#10587529	1	2	yes	—
210	C₂²	C₂×#10587529	1	1	yes	characteristic
211	C₄	—	17	2	no	—
212	C₄	—	17	2	no	—
213	C₄	C₂×#10587529	1	2	yes	—
214	C₄	C₂×#10587529	1	1	yes	characteristic
215	C₄	C₂²×#63242	1	1	yes	characteristic
216	C₂	—	2	2	no	—
217	C₂	—	17	4	no	—
218	C₂	—	34	2	no	—
219	C₂	#14545205	1	2	yes	direct product factor
220	C₂	C₂²×#10587529	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×#595
commutator	C₂×C₁₇	C₂³×C₁₆
Frattini	C₈	C₂³×#595
Fitting	C₂²×C₁₆×C₁₇	C₄
socle	C₂²×C₁₇	C₂²×C₁₆
prime radical	C₂³×D₁₇	C₁₆
cosocle	#63214	C₂⁴
hypercenter	C₂²×C₁₆	#595
hypocenter	C₁₇	C₂²×M₆₄
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#11763742	C₂	semidirect
2. #14545205	C₂	direct (N × H)
3. C₂×#11763741	C₂	semidirect
4. C₂×#11763740	C₂	semidirect
6. #11763742	C₂²	semidirect
7. #11763741	C₂²	semidirect
8. #11763740	C₂²	semidirect
9. C₂×#10587467	C₂²	semidirect
41. #10587467	C₂³	semidirect
103. C₂×D₁₇	M₆₄	semidirect
125. C₂×C₁₇	C₂×M₆₄	semidirect
128. D₁₇	C₂×M₆₄	semidirect
152. C₁₇	C₂²×M₆₄	semidirect
219. C₂	#14545205	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×#11763742	2
#14545205	2
C₂×#11763741	2
C₂×#11763740	2
C₂²×C₁₆×D₁₇	2
C₂²×M₆₄	17

Subgroups — C2×#14545205 #17978837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14545205 #17978837