Subgroups — C₁₇×#22102 #16879846

Order 4352.

814 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#431	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1939	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1924	C₂	1	2	yes	maximal
8	C₁₇×#1923	C₂	1	2	yes	maximal
9	C₁₇×#1917	C₂	1	2	yes	maximal, complemented
10	C₁₇×#1797	C₂	1	1	yes	maximal, characteristic
11	C₈×C₄⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
15	C₁₇×#446	—	2	4	no	—
16	C₁₇×#431	—	2	4	no	—
17	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₇×#97	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
30	C₁₇×#391	C₄	1	1	yes	characteristic
31	C₁₇×#389	C₄	1	1	yes	characteristic
32	C₁₇×#387	C₄	1	2	yes	—
33	C₁₇×#385	C₄	1	2	yes	—
34	C₁₇×#380	C₄	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
38	C₁₇×#336	C₂²	1	2	yes	—
39	C₁₇×#336	C₂²	1	2	yes	—
40	C₁₇×#336	C₂²	1	2	yes	—
41	C₁₇×#336	C₂²	1	2	yes	—
42	C₁₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
53	C₁₇×C₂²⋊Q₈	—	2	4	no	—
54	C₄×Q₈×C₁₇	—	2	2	no	—
55	C₄×Q₈×C₁₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₇	—	2	2	no	—
65	C₂×C₄²×C₁₇	—	2	2	no	—
66	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
72	C₁₇×C₄⋊C₈	—	2	2	no	—
73	C₁₇×C₄⋊C₈	—	2	2	no	—
74	C₁₇×C₄⋊C₈	—	2	4	no	—
75	C₁₇×C₄⋊C₈	—	2	2	no	—
76	C₁₇×C₄⋊C₈	—	2	2	no	—
77	C₁₇×C₄⋊C₈	—	4	2	no	—
78	C₁₇×C₂²⋊C₈	—	2	2	no	—
79	C₁₇×C₂²⋊C₈	—	2	2	no	—
80	C₁₇×C₂²⋊C₈	—	4	2	no	—
81	C₁₇×#97	—	2	4	no	—
82	C₄×C₈×C₁₇	—	2	2	no	—
83	C₄×C₈×C₁₇	—	4	2	no	—
84	C₄×C₈×C₁₇	D₄	1	4	yes	—
85	C₁₇×#95	C₂×C₄	1	2	yes	—
86	C₁₇×#95	C₂×C₄	1	2	yes	—
87	C₁₇×#95	C₂×C₄	1	2	yes	—
88	C₁₇×#95	C₂×C₄	1	2	yes	—
89	C₁₇×#95	C₂×C₄	1	2	yes	—
90	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
91	C₂×Q₈×C₁₇	—	2	2	no	—
92	C₂×Q₈×C₁₇	—	2	2	no	—
93	C₂×Q₈×C₁₇	—	2	2	no	—
94	C₂²×C₄×C₁₇	—	2	2	no	—
95	C₂²×C₄×C₁₇	—	2	2	no	—
96	C₂²×C₄×C₁₇	—	2	2	no	—
97	C₂²×C₄×C₁₇	—	2	2	no	—
98	C₂²×C₄×C₁₇	—	2	2	no	—
99	C₂²×C₄×C₁₇	—	2	2	no	—
100	C₂²×C₄×C₁₇	—	2	1	no	—
101	C₂²×C₄×C₁₇	—	2	1	no	—
102	C₂²×C₄×C₁₇	—	2	1	no	—
103	C₂²×C₄×C₁₇	—	2	1	no	—
104	C₂²×C₄×C₁₇	—	2	1	no	—
105	C₂²×C₄×C₁₇	—	2	1	no	—
106	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₁₇	—	2	1	no	—
117	C₂×C₈×C₁₇	—	2	1	no	—
118	C₂×C₈×C₁₇	—	2	1	no	—
119	C₂×C₈×C₁₇	—	2	1	no	—
120	C₂×C₈×C₁₇	—	2	1	no	—
121	C₂×C₈×C₁₇	—	2	1	no	—
122	C₂×C₈×C₁₇	—	2	2	no	—
123	C₂×C₈×C₁₇	—	2	2	no	—
124	C₂×C₈×C₁₇	—	2	2	no	—
125	C₂×C₈×C₁₇	—	2	2	no	—
126	C₂×C₈×C₁₇	—	2	1	no	—
127	C₂×C₈×C₁₇	—	2	1	no	—
128	C₂×C₈×C₁₇	—	2	1	no	—
129	C₂×C₈×C₁₇	—	2	1	no	—
130	C₂×C₈×C₁₇	—	2	2	no	—
131	C₂×C₈×C₁₇	—	2	2	no	—
132	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₁₇	—	2	2	no	—
135	C₄⋊C₄×C₁₇	—	2	4	no	—
136	C₄⋊C₄×C₁₇	—	2	4	no	—
137	C₄⋊C₄×C₁₇	—	2	4	no	—
138	C₄⋊C₄×C₁₇	—	2	2	no	—
139	C₄⋊C₄×C₁₇	M₁₆	1	4	yes	—
140	C₂²⋊C₄×C₁₇	—	2	4	no	—
141	C₂²⋊C₄×C₁₇	—	2	4	no	—
142	C₄²×C₁₇	—	2	2	no	—
143	C₄²×C₁₇	—	2	2	no	—
144	C₄²×C₁₇	—	2	2	no	—
145	C₄²×C₁₇	—	2	1	no	—
146	C₄²×C₁₇	—	2	1	no	—
147	C₄²×C₁₇	—	2	2	no	—
148	C₄²×C₁₇	—	2	2	no	—
149	C₄²×C₁₇	—	2	2	no	—
150	C₄²×C₁₇	C₂×D₄	1	2	yes	—
151	C₄²×C₁₇	#41	1	2	yes	—
152	#22102	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₁₇	—	2	1	no	—
154	C₂³×C₁₇	—	2	1	no	—
155	C₂³×C₁₇	—	2	1	no	—
156	C₂³×C₁₇	—	2	1	no	—
157	C₂³×C₁₇	—	2	1	no	—
158	C₂³×C₁₇	—	2	1	no	—
159	C₂³×C₁₇	#131	1	2	yes	—
160	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
161	Q₈×C₁₇	—	4	4	no	—
162	C₂×C₄×C₁₇	—	2	8	no	—
163	C₂×C₄×C₁₇	—	2	1	no	—
164	C₂×C₄×C₁₇	—	2	2	no	—
165	C₂×C₄×C₁₇	—	2	2	no	—
166	C₂×C₄×C₁₇	—	2	1	no	—
167	C₂×C₄×C₁₇	—	2	1	no	—
168	C₂×C₄×C₁₇	—	2	1	no	—
169	C₂×C₄×C₁₇	—	2	1	no	—
170	C₂×C₄×C₁₇	—	2	1	no	—
171	C₂×C₄×C₁₇	—	2	2	no	—
172	C₂×C₄×C₁₇	—	2	2	no	—
173	C₂×C₄×C₁₇	—	2	1	no	—
174	C₂×C₄×C₁₇	—	2	2	no	—
175	C₂×C₄×C₁₇	—	2	1	no	—
176	C₂×C₄×C₁₇	—	2	2	no	—
177	C₂×C₄×C₁₇	—	2	1	no	—
178	C₂×C₄×C₁₇	—	2	2	no	—
179	C₂×C₄×C₁₇	—	2	2	no	—
180	C₂×C₄×C₁₇	—	2	2	no	—
181	C₂×C₄×C₁₇	—	2	2	no	—
182	C₂×C₄×C₁₇	—	2	1	no	—
183	C₂×C₄×C₁₇	—	2	2	no	—
184	C₂×C₄×C₁₇	—	4	1	no	—
185	C₂×C₄×C₁₇	—	4	1	no	—
186	C₂×C₄×C₁₇	—	4	1	no	—
187	C₂×C₄×C₁₇	—	4	1	no	—
188	C₂×C₄×C₁₇	—	4	4	no	—
189	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₁₇	C₂×M₁₆	1	4	yes	—
192	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
193	C₂×C₄×C₁₇	#131	1	2	yes	—
194	C₂×C₄×C₁₇	#131	1	2	yes	—
195	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
199	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
200	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
201	C₈×C₁₇	—	2	2	no	—
202	C₈×C₁₇	—	2	2	no	—
203	C₈×C₁₇	—	4	1	no	—
204	C₈×C₁₇	—	4	1	no	—
205	C₈×C₁₇	—	4	2	no	—
206	C₈×C₁₇	—	4	2	no	—
207	C₂×#446	C₂×C₁₇	1	1	yes	characteristic, complemented
208	C₂×#431	C₂×C₁₇	1	1	yes	characteristic
209	C₄×C₂²⋊Q₈	C₂×C₁₇	1	1	yes	characteristic
210	#1984	C₂×C₁₇	1	1	yes	characteristic, complemented
211	#1939	C₂×C₁₇	1	2	yes	complemented
212	#1939	C₂×C₁₇	1	1	yes	characteristic, complemented
213	#1924	C₂×C₁₇	1	2	yes	—
214	#1923	C₂×C₁₇	1	2	yes	—
215	#1917	C₂×C₁₇	1	2	yes	complemented
216	#1797	C₂×C₁₇	1	1	yes	characteristic
217	C₈×C₄⋊C₄	C₂×C₁₇	1	1	yes	characteristic, complemented
218	C₂²×C₁₇	—	2	2	no	—
219	C₂²×C₁₇	—	2	2	no	—
220	C₂²×C₁₇	—	2	2	no	—
221	C₂²×C₁₇	—	4	1	no	—
222	C₂²×C₁₇	—	4	1	no	—
223	C₂²×C₁₇	—	4	1	no	—
224	C₂²×C₁₇	—	4	1	no	—
225	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
226	C₂²×C₁₇	#519	1	1	yes	characteristic
227	C₂²×C₁₇	#520	1	1	yes	characteristic
228	C₂²×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
229	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
230	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
231	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
232	C₄×C₁₇	—	2	2	no	—
233	C₄×C₁₇	—	2	2	no	—
234	C₄×C₁₇	—	2	4	no	—
235	C₄×C₁₇	—	4	1	no	—
236	C₄×C₁₇	—	4	1	no	—
237	C₄×C₁₇	—	4	2	no	—
238	C₄×C₁₇	—	4	2	no	—
239	C₄×C₁₇	—	4	2	no	—
240	C₄×C₁₇	#436	1	4	yes	—
241	C₄×C₁₇	#536	1	1	yes	characteristic
242	C₄×C₁₇	#537	1	1	yes	characteristic
243	C₄×C₁₇	#541	1	1	yes	characteristic
244	C₄×C₁₇	#542	1	1	yes	characteristic
245	C₂×C₂²⋊Q₈	C₄×C₁₇	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
247	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
248	#446	—	2	4	no	—
249	#431	—	2	4	no	—
250	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
255	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
256	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
257	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	—
259	C₂×#97	C₂²×C₁₇	1	2	yes	—
260	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₁₇	1	2	yes	—
262	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
263	#391	C₄×C₁₇	1	1	yes	characteristic
264	#389	C₄×C₁₇	1	1	yes	characteristic
265	#387	C₄×C₁₇	1	2	yes	—
266	#385	C₄×C₁₇	1	2	yes	—
267	#380	C₄×C₁₇	1	1	yes	characteristic
268	C₄×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
269	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
270	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
271	#336	C₂²×C₁₇	1	2	yes	—
272	#336	C₂²×C₁₇	1	2	yes	—
273	#336	C₂²×C₁₇	1	2	yes	—
274	#336	C₂²×C₁₇	1	2	yes	—
275	#336	C₂²×C₁₇	1	2	yes	—
276	C₂×C₁₇	—	4	2	no	—
277	C₂×C₁₇	#2323	1	1	yes	characteristic
278	C₂×C₁₇	C₂×#436	1	1	yes	characteristic
279	C₂×C₁₇	#2929	1	1	yes	characteristic
280	C₂×C₁₇	#2984	1	1	yes	characteristic
281	C₂×C₁₇	#2986	1	1	yes	characteristic
282	C₂×C₁₇	#2990	1	1	yes	characteristic
283	C₂×C₁₇	#2994	1	1	yes	characteristic
284	C₂²×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
285	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
286	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
290	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
292	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
294	C₂²⋊Q₈	—	2	4	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
299	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
300	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
302	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
308	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
310	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
311	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	2	no	—
315	C₄⋊C₈	—	2	4	no	—
316	C₄⋊C₈	—	2	2	no	—
317	C₄⋊C₈	—	2	2	no	—
318	C₄⋊C₈	—	4	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₂²⋊C₈	—	4	2	no	—
322	#97	—	2	4	no	—
323	C₄×C₈	—	2	2	no	—
324	C₄×C₈	—	4	2	no	—
325	C₄×C₈	D₄×C₁₇	1	4	yes	—
326	#95	C₂×C₄×C₁₇	1	2	yes	—
327	#95	C₂×C₄×C₁₇	1	2	yes	—
328	#95	C₂×C₄×C₁₇	1	2	yes	—
329	#95	C₂×C₄×C₁₇	1	2	yes	—
330	#95	C₂×C₄×C₁₇	1	2	yes	—
331	C₁₇	#22102	1	1	yes	characteristic, direct product factor, Sylow
332	C₂⁴	C₂²×C₄×C₁₇	1	1	yes	characteristic
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
350	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
353	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
354	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
375	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	M₁₆×C₁₇	1	4	yes	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	C₂×D₄×C₁₇	1	2	yes	—
393	C₄²	#41×C₁₇	1	2	yes	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	C₁₇×#131	1	2	yes	—
401	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
402	Q₈	—	4	4	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
431	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
432	C₂×C₄	C₂×M₁₆×C₁₇	1	4	yes	—
433	C₂×C₄	C₂×M₁₆×C₁₇	1	2	yes	—
434	C₂×C₄	C₁₇×#131	1	2	yes	—
435	C₂×C₄	C₁₇×#131	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
438	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
440	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	2	2	no	—
444	C₈	—	4	1	no	—
445	C₈	—	4	1	no	—
446	C₈	—	4	2	no	—
447	C₈	—	4	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
456	C₂²	C₁₇×#519	1	1	yes	characteristic
457	C₂²	C₁₇×#520	1	1	yes	characteristic
458	C₂²	C₂²×M₁₆×C₁₇	1	1	yes	characteristic
459	C₂²	C₂×C₁₇×#131	1	1	yes	characteristic
460	C₂²	C₂×C₁₇×#131	1	1	yes	characteristic
461	C₂²	C₂×C₁₇×#131	1	1	yes	characteristic
462	C₄	—	2	4	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	C₁₇×#436	1	4	yes	—
471	C₄	C₁₇×#536	1	1	yes	characteristic
472	C₄	C₁₇×#537	1	1	yes	characteristic
473	C₄	C₁₇×#541	1	1	yes	characteristic
474	C₄	C₁₇×#542	1	1	yes	characteristic
475	C₂	—	4	2	no	—
476	C₂	C₁₇×#2323	1	1	yes	characteristic
477	C₂	C₂×C₁₇×#436	1	1	yes	characteristic
478	C₂	C₁₇×#2929	1	1	yes	characteristic
479	C₂	C₁₇×#2984	1	1	yes	characteristic
480	C₂	C₁₇×#2986	1	1	yes	characteristic
481	C₂	C₁₇×#2990	1	1	yes	characteristic
482	C₂	C₁₇×#2994	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#446	C₂	semidirect
4. C₁₇×#1984	C₂	semidirect
5. C₁₇×#1939	C₂	semidirect
6. C₁₇×#1939	C₂	semidirect
9. C₁₇×#1917	C₂	semidirect
11. C₈×C₄⋊C₄×C₁₇	C₂	semidirect
152. #22102	C₁₇	direct (N × H)
207. C₂×#446	C₂×C₁₇	semidirect
210. #1984	C₂×C₁₇	semidirect
211. #1939	C₂×C₁₇	semidirect
212. #1939	C₂×C₁₇	semidirect
215. #1917	C₂×C₁₇	semidirect
217. C₈×C₄⋊C₄	C₂×C₁₇	semidirect
331. C₁₇	#22102	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×#446	2
C₂×C₁₇×#431	2
C₄×C₁₇×C₂²⋊Q₈	2
C₁₇×#1984	2
C₁₇×#1939	2
C₁₇×#1924	2
C₁₇×#1923	2
C₁₇×#1917	2
C₁₇×#1797	2
C₈×C₄⋊C₄×C₁₇	2
#22102	17

Subgroups — C17×#22102 #16879846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22102 #16879846