Subgroups — C₈×#10587542 #17950268

Order 4352.

606 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14544499	C₂	1	1	yes	maximal, characteristic
2	C₄×#10587542	C₂	1	1	yes	maximal, characteristic
3	C₂×#11763651	C₂	1	2	yes	maximal
4	C₂×C₈×#3624	C₂	1	2	yes	maximal
5	C₄×C₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587542	C₄	1	4	yes	—
7	C₂×C₄×#3624	C₂²	1	2	yes	—
8	C₂×C₄×#3624	C₂²	1	2	yes	—
9	#11763675	C₄	1	4	yes	—
10	#11763651	C₄	1	8	yes	complemented
11	C₈×#3624	C₄	1	8	yes	complemented
12	C₂×C₄×#3622	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
14	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
15	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
16	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
17	C₄²×Dic₁₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
19	C₂²×#3624	C₂×C₄	1	4	yes	—
20	C₂²×#3624	C₂×C₄	1	4	yes	—
21	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×Dic₁₇	C₂×C₄	1	2	yes	—
26	C₂×C₄×Dic₁₇	C₂×C₄	1	2	yes	—
27	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
28	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
29	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
30	#10587542	C₈	1	16	yes	direct product factor
31	C₄×#3624	C₂×C₄	1	4	yes	—
32	C₄×#3624	C₂×C₄	1	4	yes	—
33	C₄×#3624	C₂×C₄	1	4	yes	—
34	C₄×#3624	C₂×C₄	1	4	yes	—
35	C₄×C₈×C₁₇	—	2	2	no	—
36	C₈×Dic₁₇	—	2	2	no	—
37	C₈×Dic₁₇	—	2	2	no	—
38	C₈×Dic₁₇	C₂×C₄	1	4	yes	—
39	C₈×Dic₁₇	C₂×C₄	1	4	yes	—
40	C₄×#3622	—	2	2	no	—
41	C₂²×C₄×C₁₇	C₄²	1	2	yes	—
42	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
43	C₂²×Dic₁₇	C₄²	1	2	yes	—
44	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
45	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
46	C₂×#3624	—	2	8	no	—
47	C₂×#3624	C₄²	1	8	yes	—
48	C₂×#3624	C₄²	1	8	yes	—
49	C₂×#3624	C₂×C₈	1	16	yes	—
50	C₂×C₈×C₁₇	—	2	1	no	—
51	C₂×C₈×C₁₇	—	2	1	no	—
52	C₂×C₈×C₁₇	C₄²	1	2	yes	—
53	C₂×C₈×C₁₇	C₄²	1	2	yes	—
54	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
55	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
56	C₄²×C₁₇	—	2	1	no	—
57	C₄²×C₁₇	—	2	1	no	—
58	C₄×Dic₁₇	—	2	1	no	—
59	C₄×Dic₁₇	—	2	1	no	—
60	C₄×Dic₁₇	—	2	4	no	—
61	C₄×Dic₁₇	C₂×C₈	1	8	yes	—
62	C₄×Dic₁₇	C₂²×C₄	1	2	yes	—
63	C₄×Dic₁₇	C₂²×C₄	1	2	yes	—
64	C₂×#3622	—	2	1	no	—
65	C₂×#3622	—	2	1	no	—
66	C₂×#3622	C₄²	1	2	yes	—
67	C₂×#3622	C₄²	1	2	yes	—
68	C₂×#3622	M₁₆	1	2	yes	—
69	C₂×#3622	M₁₆	1	2	yes	—
70	C₈×#97	—	17	1	no	maximal, Sylow
71	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
72	C₂×C₄×C₁₇	—	2	2	no	—
73	C₂×C₄×C₁₇	—	2	2	no	—
74	C₂×C₄×C₁₇	C₄×C₈	1	4	yes	—
75	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
76	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
77	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
78	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
79	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
81	C₂×Dic₁₇	—	2	2	no	—
82	C₂×Dic₁₇	—	2	2	no	—
83	C₂×Dic₁₇	C₄×C₈	1	4	yes	—
84	C₂×Dic₁₇	C₂×C₄²	1	2	yes	—
85	C₂×Dic₁₇	C₂×C₄²	1	2	yes	—
86	C₂×Dic₁₇	C₂²×C₈	1	4	yes	—
87	C₂×Dic₁₇	#131	1	4	yes	—
88	#3624	—	2	8	no	—
89	#3624	C₄×C₈	1	16	yes	complemented
90	C₈×C₁₇	—	2	2	no	—
91	C₈×C₁₇	#97	1	4	yes	complemented
92	#3622	—	2	2	no	—
93	#3622	#97	1	4	yes	complemented
94	#1744	—	17	1	no	—
95	C₄×#97	—	17	1	no	—
96	C₄²×C₈	—	17	1	no	—
97	C₂×#322	—	17	2	no	—
98	C₂×C₈²	—	17	2	no	—
99	C₂²×C₁₇	C₄³	1	1	yes	characteristic
100	C₂²×C₁₇	C₂×C₄×C₈	1	2	yes	—
101	C₂²×C₁₇	C₄×M₁₆	1	1	yes	characteristic
102	C₂²×C₁₇	C₄×M₁₆	1	1	yes	characteristic
103	C₂²×C₁₇	#405	1	2	yes	—
104	C₄×C₁₇	—	2	4	no	—
105	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
106	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
107	C₄×C₁₇	C₄×M₁₆	1	1	yes	characteristic
108	C₄×C₁₇	C₄×M₁₆	1	1	yes	characteristic
109	Dic₁₇	—	2	4	no	—
110	Dic₁₇	C₂×C₄×C₈	1	4	yes	—
111	Dic₁₇	#405	1	4	yes	—
112	C₂×#97	—	17	4	no	—
113	C₂×C₄×C₈	—	17	2	no	—
114	C₂×C₄×C₈	—	17	2	no	—
115	C₂×C₄×C₈	—	17	1	no	—
116	C₂×C₄×C₈	—	17	1	no	—
117	C₂×C₄×C₈	—	17	1	no	—
118	C₂×C₄×C₈	—	17	1	no	—
119	C₂×C₄×C₈	—	17	1	no	—
120	C₂×C₄×C₈	#595	1	1	yes	characteristic
121	C₄³	—	17	1	no	—
122	#336	—	17	4	no	—
123	#322	—	17	8	no	—
124	C₈²	—	17	8	no	—
125	C₂×C₁₇	C₈×M₁₆	1	2	yes	—
126	C₂×C₁₇	C₈×M₁₆	1	2	yes	—
127	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
128	C₂×C₁₇	C₄×#97	1	1	yes	characteristic
129	C₂×C₁₇	#1726	1	1	yes	characteristic
130	C₂²×C₈	—	17	4	no	—
131	C₂²×C₈	—	17	1	no	—
132	C₂²×C₈	—	17	4	no	—
133	C₂²×C₈	—	17	1	no	—
134	C₂²×C₈	C₂×#595	1	1	yes	characteristic
135	C₂²×C₈	C₂×#595	1	1	yes	characteristic
136	C₂×C₄²	—	17	2	no	—
137	C₂×C₄²	—	17	1	no	—
138	C₂×C₄²	—	17	2	no	—
139	C₂×C₄²	—	17	1	no	—
140	C₂×C₄²	C₂×#595	1	1	yes	characteristic
141	#97	—	17	16	no	—
142	C₄×C₈	—	2	2	no	—
143	C₄×C₈	—	17	4	no	—
144	C₄×C₈	—	17	4	no	—
145	C₄×C₈	—	17	4	no	—
146	C₄×C₈	—	17	4	no	—
147	C₄×C₈	—	17	4	no	—
148	C₄×C₈	—	17	4	no	—
149	C₄×C₈	—	34	2	no	—
150	C₄×C₈	—	34	2	no	—
151	C₄×C₈	—	34	2	no	—
152	C₁₇	C₈×#97	1	1	yes	characteristic, complemented, Sylow
153	C₂²×C₄	—	17	1	no	—
154	C₂²×C₄	—	17	1	no	—
155	C₂²×C₄	—	17	2	no	—
156	C₂²×C₄	C₄×#595	1	2	yes	—
157	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
158	C₂×C₈	—	2	1	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	17	8	no	—
161	C₂×C₈	—	17	16	no	—
162	C₂×C₈	—	17	2	no	—
163	C₂×C₈	—	17	2	no	—
164	C₂×C₈	—	17	2	no	—
165	C₂×C₈	—	17	8	no	—
166	C₂×C₈	—	17	2	no	—
167	C₂×C₈	—	34	8	no	—
168	C₂×C₈	—	34	1	no	—
169	C₂×C₈	—	34	1	no	—
170	C₂×C₈	#63243	1	2	yes	—
171	C₂×C₈	C₄×#595	1	2	yes	—
172	C₂×C₈	C₄×#595	1	2	yes	—
173	C₂×C₈	#63247	1	2	yes	—
174	C₄²	—	2	1	no	—
175	C₄²	—	2	1	no	—
176	C₄²	—	17	2	no	—
177	C₄²	—	17	2	no	—
178	C₄²	—	17	8	no	—
179	C₄²	—	34	4	no	—
180	C₄²	—	34	1	no	—
181	C₄²	—	34	1	no	—
182	C₂³	C₂×C₄×#595	1	1	yes	characteristic
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	17	2	no	—
186	C₂×C₄	—	17	2	no	—
187	C₂×C₄	—	17	4	no	—
188	C₂×C₄	—	17	4	no	—
189	C₂×C₄	—	17	4	no	—
190	C₂×C₄	—	34	2	no	—
191	C₂×C₄	—	34	2	no	—
192	C₂×C₄	C₈×#595	1	4	yes	—
193	C₂×C₄	C₂×#63243	1	1	yes	characteristic
194	C₂×C₄	D₁₇⋊M₁₆	1	1	yes	characteristic
195	C₂×C₄	D₁₇⋊M₁₆	1	1	yes	characteristic
196	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
197	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
198	C₂×C₄	C₂×#63247	1	1	yes	characteristic
199	C₈	—	2	2	no	—
200	C₈	—	17	16	no	—
201	C₈	—	17	4	no	—
202	C₈	—	34	8	no	—
203	C₈	—	34	2	no	—
204	C₈	#10587542	1	4	yes	direct product factor
205	C₂²	C₄²×#595	1	1	yes	characteristic
206	C₂²	C₂×C₈×#595	1	2	yes	—
207	C₂²	C₄×#63247	1	1	yes	characteristic
208	C₂²	C₄×#63243	1	1	yes	characteristic
209	C₂²	#11763772	1	2	yes	—
210	C₄	—	2	4	no	—
211	C₄	—	17	4	no	—
212	C₄	—	17	4	no	—
213	C₄	—	34	4	no	—
214	C₄	C₂×#10587542	1	1	yes	characteristic
215	C₄	#11763768	1	1	yes	characteristic
216	C₄	C₄×#63247	1	1	yes	characteristic
217	C₄	C₄×#63243	1	1	yes	characteristic
218	C₂	C₈×#63247	1	2	yes	—
219	C₂	C₈×#63243	1	2	yes	—
220	C₂	C₄×C₈×#595	1	1	yes	characteristic
221	C₂	C₄×#10587542	1	1	yes	characteristic
222	C₂	#14544440	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×#595
commutator	C₂×C₁₇	C₄²×C₈
Frattini	C₂²×C₄	C₂²×#595
Fitting	C₂×C₄×C₈×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₂×C₄²
cosocle	C₂×C₄×Dic₁₇	C₂³
hypercenter	C₂×C₄×C₈	#595
hypocenter	C₁₇	C₈×#97
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
10. #11763651	C₄	semidirect
11. C₈×#3624	C₄	semidirect
30. #10587542	C₈	direct (N × H)
89. #3624	C₄×C₈	semidirect
91. C₈×C₁₇	#97	semidirect
93. #3622	#97	semidirect
152. C₁₇	C₈×#97	semidirect
204. C₈	#10587542	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14544499	2
C₄×#10587542	2
C₂×#11763651	2
C₂×C₈×#3624	2
C₄×C₈×Dic₁₇	2
C₈×#97	17

Subgroups — C8×#10587542 #17950268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#10587542 #17950268