Subgroups — C₂×C₁₇×#2992 #16918003

Order 4352.

1938 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2992	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₇×#446	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₇×#435	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₇×#435	C₂	1	2	yes	maximal, complemented
6	C₂×C₈×D₄×C₁₇	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₇×#433	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₇×#424	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×M₁₆×C₁₇	C₂²	1	2	yes	—
12	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₇	C₂²	1	2	yes	—
15	C₁₇×#529	C₄	1	8	yes	—
16	C₁₇×#529	C₂²	1	8	yes	—
17	C₂×C₁₇×#126	C₄	1	2	yes	—
18	C₂×C₁₇×#125	C₄	1	1	yes	characteristic
19	C₂×C₁₇×#124	C₄	1	1	yes	characteristic
20	C₂×C₁₇×#123	C₄	1	2	yes	—
21	C₂×C₁₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
22	C₂×C₁₇×#121	C₄	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#117	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
28	C₁₇×#446	C₂²	1	16	yes	complemented
29	C₁₇×#435	C₂²	1	16	yes	complemented
30	C₁₇×#435	C₂²	1	16	yes	complemented
31	C₈×D₄×C₁₇	C₂²	1	16	yes	complemented
32	C₁₇×#433	C₂²	1	16	yes	complemented
33	C₁₇×#432	C₂²	1	8	yes	complemented
34	C₁₇×#424	C₂²	1	16	yes	complemented
35	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
37	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
38	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
39	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₇×C₄⋊C₈	C₂²	1	8	yes	complemented
42	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
44	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₁₇×#97	C₂²	1	2	yes	—
46	C₂×C₁₇×#97	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
48	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₇	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
55	C₂×M₁₆×C₁₇	—	4	4	no	—
56	C₂×M₁₆×C₁₇	C₂³	1	8	yes	—
57	C₂²×C₈×C₁₇	—	4	2	no	—
58	C₂²×C₈×C₁₇	—	4	4	no	—
59	C₂²×C₈×C₁₇	—	4	2	no	—
60	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
65	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
66	C₂²×C₈×C₁₇	C₂³	1	8	yes	—
67	C₁₇×#126	C₂×C₄	1	16	yes	—
68	C₁₇×#125	C₂×C₄	1	8	yes	—
69	C₁₇×#124	C₂×C₄	1	8	yes	—
70	C₁₇×#123	C₂×C₄	1	16	yes	—
71	C₁₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
72	C₁₇×#121	C₂×C₄	1	8	yes	—
73	C₄×Q₈×C₁₇	C₂×C₄	1	4	yes	—
74	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
75	C₄×D₄×C₁₇	C₂×C₄	1	4	yes	—
76	C₄×D₄×C₁₇	C₂×C₄	1	8	yes	—
77	C₄×D₄×C₁₇	C₂³	1	8	yes	—
78	C₄×D₄×C₁₇	C₂³	1	4	yes	—
79	C₁₇×#117	C₂×C₄	1	8	yes	—
80	C₁₇×#117	C₂³	1	8	yes	—
81	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
88	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
90	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
91	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
92	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₇	C₂×C₄	1	4	yes	—
95	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
99	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
100	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
101	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
102	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
103	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
104	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
105	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
106	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
107	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₁₇×#97	C₂³	1	8	yes	—
109	C₁₇×#97	C₂³	1	8	yes	—
110	C₄×C₈×C₁₇	C₂³	1	8	yes	—
111	C₂⁴×C₁₇	C₂²×C₄	1	2	yes	—
112	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×Q₈×C₁₇	—	4	2	no	—
114	C₂×Q₈×C₁₇	C₂²×C₄	1	4	yes	—
115	C₂×D₄×C₁₇	—	2	8	no	—
116	C₂×D₄×C₁₇	—	4	2	no	—
117	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
118	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₇	—	2	4	no	—
120	C₂²×C₄×C₁₇	—	2	2	no	—
121	C₂²×C₄×C₁₇	—	2	4	no	—
122	C₂²×C₄×C₁₇	—	2	2	no	—
123	C₂²×C₄×C₁₇	—	2	4	no	—
124	C₂²×C₄×C₁₇	—	4	2	no	—
125	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
140	M₁₆×C₁₇	—	4	8	no	—
141	C₂×C₈×C₁₇	—	2	4	no	—
142	C₂×C₈×C₁₇	—	2	4	no	—
143	C₂×C₈×C₁₇	—	2	4	no	—
144	C₂×C₈×C₁₇	—	2	4	no	—
145	C₂×C₈×C₁₇	—	4	4	no	—
146	C₂×C₈×C₁₇	—	4	8	no	—
147	C₂×C₈×C₁₇	—	4	4	no	—
148	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
149	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
150	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
151	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
153	C₄⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
154	C₄⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
155	C₄⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
156	C₄⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
157	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
158	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
159	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
160	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
161	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
162	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
163	C₄²×C₁₇	C₂²×C₄	1	4	yes	—
164	C₄²×C₁₇	C₂²×C₄	1	4	yes	—
165	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
166	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
167	C₄²×C₁₇	C₂²×C₄	1	4	yes	—
168	C₄²×C₁₇	C₂⁴	1	4	yes	—
169	C₄²×C₁₇	C₂⁴	1	2	yes	—
170	C₄²×C₁₇	C₂⁴	1	2	yes	—
171	C₂×#2992	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₁₇	—	2	2	no	—
173	C₂³×C₁₇	—	2	2	no	—
174	C₂³×C₁₇	—	2	4	no	—
175	C₂³×C₁₇	—	2	4	no	—
176	C₂³×C₁₇	—	2	4	no	—
177	C₂³×C₁₇	#131	1	4	yes	—
178	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
179	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
180	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
181	Q₈×C₁₇	—	4	4	no	—
182	D₄×C₁₇	—	2	16	no	—
183	D₄×C₁₇	—	4	4	no	—
184	C₂×C₄×C₁₇	—	2	2	no	—
185	C₂×C₄×C₁₇	—	2	4	no	—
186	C₂×C₄×C₁₇	—	2	8	no	—
187	C₂×C₄×C₁₇	—	2	2	no	—
188	C₂×C₄×C₁₇	—	2	2	no	—
189	C₂×C₄×C₁₇	—	2	4	no	—
190	C₂×C₄×C₁₇	—	2	2	no	—
191	C₂×C₄×C₁₇	—	2	2	no	—
192	C₂×C₄×C₁₇	—	2	4	no	—
193	C₂×C₄×C₁₇	—	2	4	no	—
194	C₂×C₄×C₁₇	—	2	8	no	—
195	C₂×C₄×C₁₇	—	2	2	no	—
196	C₂×C₄×C₁₇	—	2	4	no	—
197	C₂×C₄×C₁₇	—	2	2	no	—
198	C₂×C₄×C₁₇	—	2	4	no	—
199	C₂×C₄×C₁₇	—	4	4	no	—
200	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
201	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
202	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
203	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
204	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
205	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
206	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
207	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
208	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
210	C₂×C₄×C₁₇	2₋¹⁺⁴	1	2	yes	—
211	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
212	C₈×C₁₇	—	2	4	no	—
213	C₈×C₁₇	—	2	4	no	—
214	C₈×C₁₇	—	2	4	no	—
215	C₈×C₁₇	—	2	4	no	—
216	C₂×#529	C₂×C₁₇	1	1	yes	characteristic
217	#2992	C₂×C₁₇	1	16	yes	direct product factor
218	C₂×#446	C₂×C₁₇	1	2	yes	complemented
219	C₂×#435	C₂×C₁₇	1	2	yes	complemented
220	C₂×#435	C₂×C₁₇	1	2	yes	complemented
221	C₂×C₈×D₄	C₂×C₁₇	1	2	yes	complemented
222	C₂×#433	C₂×C₁₇	1	2	yes	complemented
223	C₂×#432	C₂×C₁₇	1	1	yes	characteristic, complemented
224	C₂×#424	C₂×C₁₇	1	2	yes	complemented
225	C₂²×C₄⋊C₈	C₂×C₁₇	1	1	yes	characteristic, complemented
226	C₂²×C₁₇	—	2	2	no	—
227	C₂²×C₁₇	—	2	8	no	—
228	C₂²×C₁₇	—	2	2	no	—
229	C₂²×C₁₇	—	2	4	no	—
230	C₂²×C₁₇	—	2	4	no	—
231	C₂²×C₁₇	—	2	4	no	—
232	C₂²×C₁₇	—	4	8	no	—
233	C₂²×C₁₇	#520	1	2	yes	—
234	C₂²×C₁₇	C₂×#131	1	4	yes	—
235	C₂²×C₁₇	C₂×#131	1	2	yes	—
236	C₂²×C₁₇	#568	1	2	yes	—
237	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
238	C₄×C₁₇	—	2	2	no	—
239	C₄×C₁₇	—	2	4	no	—
240	C₄×C₁₇	—	2	2	no	—
241	C₄×C₁₇	—	2	2	no	—
242	C₄×C₁₇	—	2	4	no	—
243	C₄×C₁₇	—	2	2	no	—
244	C₄×C₁₇	—	2	2	no	—
245	C₄×C₁₇	—	2	4	no	—
246	C₄×C₁₇	#520	1	2	yes	—
247	C₄×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
248	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
249	C₂²×M₁₆	C₂²×C₁₇	1	2	yes	—
250	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
251	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
252	C₂³×C₈	C₂²×C₁₇	1	2	yes	—
253	#529	C₄×C₁₇	1	8	yes	—
254	#529	C₂²×C₁₇	1	8	yes	—
255	C₂×#126	C₄×C₁₇	1	2	yes	—
256	C₂×#125	C₄×C₁₇	1	1	yes	characteristic
257	C₂×#124	C₄×C₁₇	1	1	yes	characteristic
258	C₂×#123	C₄×C₁₇	1	2	yes	—
259	C₂×C₂²⋊Q₈	C₄×C₁₇	1	1	yes	characteristic
260	C₂×#121	C₄×C₁₇	1	1	yes	characteristic
261	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
263	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
264	C₂×#117	C₂²×C₁₇	1	2	yes	—
265	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
266	#446	C₂²×C₁₇	1	16	yes	complemented
267	#435	C₂²×C₁₇	1	16	yes	complemented
268	#435	C₂²×C₁₇	1	16	yes	complemented
269	C₈×D₄	C₂²×C₁₇	1	16	yes	complemented
270	#433	C₂²×C₁₇	1	16	yes	complemented
271	#432	C₂²×C₁₇	1	8	yes	complemented
272	#424	C₂²×C₁₇	1	16	yes	complemented
273	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
274	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
275	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
277	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
278	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂²×C₁₇	1	8	yes	complemented
280	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	—
281	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	—
282	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	—
283	C₂×#97	C₂²×C₁₇	1	2	yes	—
284	C₂×#97	C₂²×C₁₇	1	2	yes	—
285	C₂×C₄×C₈	C₂²×C₁₇	1	2	yes	—
286	C₂×C₁₇	—	2	4	no	—
287	C₂×C₁₇	—	4	4	no	—
288	C₂×C₁₇	#2992	1	4	yes	direct product factor
289	C₂×C₁₇	C₂×#520	1	1	yes	characteristic
290	C₂×C₁₇	C₂²×#131	1	1	yes	characteristic
291	C₂×C₁₇	C₂×#568	1	1	yes	characteristic
292	C₂²×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
293	C₂²×D₄	C₂×C₄×C₁₇	1	2	yes	—
294	C₂²×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
295	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
296	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
298	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
299	C₂×M₁₆	—	4	4	no	—
300	C₂×M₁₆	C₂³×C₁₇	1	8	yes	—
301	C₂²×C₈	—	4	2	no	—
302	C₂²×C₈	—	4	4	no	—
303	C₂²×C₈	—	4	2	no	—
304	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
305	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
306	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
307	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
308	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
309	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
310	C₂²×C₈	C₂³×C₁₇	1	8	yes	—
311	#126	C₂×C₄×C₁₇	1	16	yes	—
312	#125	C₂×C₄×C₁₇	1	8	yes	—
313	#124	C₂×C₄×C₁₇	1	8	yes	—
314	#123	C₂×C₄×C₁₇	1	16	yes	—
315	C₂²⋊Q₈	C₂×C₄×C₁₇	1	8	yes	—
316	#121	C₂×C₄×C₁₇	1	8	yes	—
317	C₄×Q₈	C₂×C₄×C₁₇	1	4	yes	—
318	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
319	C₄×D₄	C₂×C₄×C₁₇	1	4	yes	—
320	C₄×D₄	C₂×C₄×C₁₇	1	8	yes	—
321	C₄×D₄	C₂³×C₁₇	1	8	yes	—
322	C₄×D₄	C₂³×C₁₇	1	4	yes	—
323	#117	C₂×C₄×C₁₇	1	8	yes	—
324	#117	C₂³×C₁₇	1	8	yes	—
325	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
326	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
327	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
329	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
331	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
332	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
333	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
334	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
335	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
336	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
337	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
338	C₂×C₄²	C₂×C₄×C₁₇	1	4	yes	—
339	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
341	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
343	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
344	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
345	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
346	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
347	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
348	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
349	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
350	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
351	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
352	#97	C₂³×C₁₇	1	8	yes	—
353	#97	C₂³×C₁₇	1	8	yes	—
354	C₄×C₈	C₂³×C₁₇	1	8	yes	—
355	C₁₇	C₂×#2992	1	1	yes	characteristic, direct product factor, Sylow
356	C₂⁴	C₂²×C₄×C₁₇	1	2	yes	—
357	C₂⁴	C₂²×C₄×C₁₇	1	1	yes	characteristic
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	C₂²×C₄×C₁₇	1	4	yes	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
363	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
371	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
372	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
375	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
376	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
377	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
378	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
379	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
380	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
381	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
384	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
385	M₁₆	—	4	8	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	—	2	4	no	—
390	C₂×C₈	—	4	4	no	—
391	C₂×C₈	—	4	8	no	—
392	C₂×C₈	—	4	4	no	—
393	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
394	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
395	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
396	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
397	C₄⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
398	C₄⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
399	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
400	C₄⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
401	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
402	C₄⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
403	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
404	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
405	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
406	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
407	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
408	C₄²	C₂²×C₄×C₁₇	1	2	yes	—
409	C₄²	C₂²×C₄×C₁₇	1	2	yes	—
410	C₄²	C₂²×C₄×C₁₇	1	4	yes	—
411	C₄²	C₂²×C₄×C₁₇	1	4	yes	—
412	C₄²	C₂²×C₄×C₁₇	1	4	yes	—
413	C₄²	C₂⁴×C₁₇	1	4	yes	—
414	C₄²	C₂⁴×C₁₇	1	2	yes	—
415	C₄²	C₂⁴×C₁₇	1	2	yes	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	4	no	—
421	C₂³	C₁₇×#131	1	4	yes	—
422	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
423	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
424	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
425	Q₈	—	4	4	no	—
426	D₄	—	2	16	no	—
427	D₄	—	4	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	8	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
445	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
446	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
447	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
448	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
449	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
450	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
451	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
452	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
453	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
454	C₂×C₄	C₁₇×2₋¹⁺⁴	1	2	yes	—
455	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
456	C₈	—	2	4	no	—
457	C₈	—	2	4	no	—
458	C₈	—	2	4	no	—
459	C₈	—	2	4	no	—
460	C₂²	—	2	8	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	4	8	no	—
467	C₂²	C₁₇×#520	1	2	yes	—
468	C₂²	C₂×C₁₇×#131	1	4	yes	—
469	C₂²	C₂×C₁₇×#131	1	2	yes	—
470	C₂²	C₁₇×#568	1	2	yes	—
471	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	4	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	4	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	4	no	—
480	C₄	C₁₇×#520	1	2	yes	—
481	C₄	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
482	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
483	C₂	—	2	4	no	—
484	C₂	—	4	4	no	—
485	C₂	C₁₇×#2992	1	4	yes	direct product factor
486	C₂	C₂×C₁₇×#520	1	1	yes	characteristic
487	C₂	C₂²×C₁₇×#131	1	1	yes	characteristic
488	C₂	C₂×C₁₇×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
socle	C₂³×C₁₇	C₂³×C₄
prime radical	C₂×C₁₇×#121	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#2992	C₂	direct (N × H)
3. C₂×C₁₇×#446	C₂	semidirect
4. C₂×C₁₇×#435	C₂	semidirect
5. C₂×C₁₇×#435	C₂	semidirect
6. C₂×C₈×D₄×C₁₇	C₂	semidirect
7. C₂×C₁₇×#433	C₂	semidirect
8. C₂×C₁₇×#432	C₂	semidirect
9. C₂×C₁₇×#424	C₂	semidirect
10. C₂²×C₁₇×C₄⋊C₈	C₂	semidirect
28. C₁₇×#446	C₂²	semidirect
29. C₁₇×#435	C₂²	semidirect
30. C₁₇×#435	C₂²	semidirect
31. C₈×D₄×C₁₇	C₂²	semidirect
32. C₁₇×#433	C₂²	semidirect
33. C₁₇×#432	C₂²	semidirect
34. C₁₇×#424	C₂²	semidirect
41. C₂×C₁₇×C₄⋊C₈	C₂²	semidirect
171. C₂×#2992	C₁₇	direct (N × H)
217. #2992	C₂×C₁₇	direct (N × H)
218. C₂×#446	C₂×C₁₇	semidirect
219. C₂×#435	C₂×C₁₇	semidirect
220. C₂×#435	C₂×C₁₇	semidirect
221. C₂×C₈×D₄	C₂×C₁₇	semidirect
222. C₂×#433	C₂×C₁₇	semidirect
223. C₂×#432	C₂×C₁₇	semidirect
224. C₂×#424	C₂×C₁₇	semidirect
225. C₂²×C₄⋊C₈	C₂×C₁₇	semidirect
266. #446	C₂²×C₁₇	semidirect
267. #435	C₂²×C₁₇	semidirect
268. #435	C₂²×C₁₇	semidirect
269. C₈×D₄	C₂²×C₁₇	semidirect
270. #433	C₂²×C₁₇	semidirect
271. #432	C₂²×C₁₇	semidirect
272. #424	C₂²×C₁₇	semidirect
279. C₂×C₄⋊C₈	C₂²×C₁₇	semidirect
288. C₂×C₁₇	#2992	direct (N × H)
355. C₁₇	C₂×#2992	direct (N × H)
485. C₂	C₁₇×#2992	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×C₁₇×#529	2
C₁₇×#2992	2
C₂×C₁₇×#446	2
C₂×C₁₇×#435	2
C₂×C₈×D₄×C₁₇	2
C₂×C₁₇×#433	2
C₂×C₁₇×#432	2
C₂×C₁₇×#424	2
C₂²×C₁₇×C₄⋊C₈	2
C₂×#2992	17

Subgroups — C2×C17×#2992 #16918003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#2992 #16918003