Subgroups — C₂×C₁₇×#3355 #16918992

Order 4352.

1962 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#553	C₂	1	2	yes	maximal, complemented
2	C₁₇×#3355	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₇×#480	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₇×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₇×#469	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×D₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₇×#428	C₂	1	2	yes	maximal, complemented
11	C₂²×D₈×C₁₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₇	C₂²	1	2	yes	—
13	C₁₇×#553	—	2	8	no	—
14	C₁₇×#553	C₂²	1	16	yes	complemented
15	C₂×C₁₇×#126	—	2	2	no	—
16	C₂×C₁₇×#125	C₂²	1	2	yes	—
17	C₂×C₁₇×#123	—	2	2	no	—
18	C₂×C₁₇×#121	—	2	2	no	—
19	C₂×C₁₇×#121	C₂²	1	2	yes	—
20	C₂×C₁₇×#121	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₇	—	2	2	no	—
22	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#117	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
26	C₁₇×#499	C₂²	1	8	yes	complemented
27	C₁₇×#482	C₂²	1	16	yes	complemented
28	C₁₇×#480	C₂²	1	16	yes	complemented
29	C₁₇×#478	C₂²	1	16	yes	complemented
30	C₁₇×#469	C₂²	1	16	yes	complemented
31	C₄×D₈×C₁₇	C₂²	1	8	yes	complemented
32	C₁₇×#436	C₂²	1	8	yes	complemented
33	C₁₇×#428	C₂²	1	16	yes	complemented
34	C₂×C₁₇×#107	C₂²	1	2	yes	—
35	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
37	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
38	C₂×C₁₇×#106	C₂²	1	2	yes	—
39	C₂×C₁₇×#106	C₂²	1	2	yes	—
40	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₇×#102	C₂²	1	2	yes	—
42	C₂×C₁₇×#102	C₂²	1	2	yes	—
43	C₂×C₁₇×#102	C₂²	1	2	yes	—
44	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
46	C₂²×D₄×C₁₇	—	2	2	no	—
47	C₂²×D₄×C₁₇	—	2	2	no	—
48	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₇	—	2	2	no	—
51	C₂³×C₄×C₁₇	—	2	2	no	—
52	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
53	C₂×D₈×C₁₇	—	2	4	no	—
54	C₂×D₈×C₁₇	C₂³	1	4	yes	—
55	C₂×M₁₆×C₁₇	—	2	8	no	—
56	C₂×M₁₆×C₁₇	C₂³	1	8	yes	—
57	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
60	C₁₇×#126	—	2	16	no	—
61	C₁₇×#125	—	2	4	no	—
62	C₁₇×#125	C₂³	1	8	yes	—
63	C₁₇×#123	—	2	16	no	—
64	C₁₇×#121	—	2	16	no	—
65	C₁₇×#121	—	2	4	no	—
66	C₁₇×#121	—	2	4	no	—
67	C₁₇×#121	C₂³	1	8	yes	—
68	C₁₇×#121	C₂³	1	8	yes	—
69	C₄×D₄×C₁₇	—	2	16	no	—
70	C₄×D₄×C₁₇	—	2	4	no	—
71	C₄×D₄×C₁₇	D₄	1	4	yes	—
72	C₄×D₄×C₁₇	C₂³	1	8	yes	—
73	C₄×D₄×C₁₇	C₂³	1	4	yes	—
74	C₁₇×#117	—	2	4	no	—
75	C₁₇×#117	C₂³	1	8	yes	—
76	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
78	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
84	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
90	C₂×C₄²×C₁₇	—	2	2	no	—
91	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
92	C₁₇×#107	C₂³	1	4	yes	—
93	C₁₇×#107	C₂³	1	4	yes	—
94	C₁₇×#107	C₂³	1	4	yes	—
95	C₁₇×#107	C₂³	1	8	yes	—
96	C₁₇×#106	C₂³	1	8	yes	—
97	C₁₇×#106	C₂³	1	8	yes	—
98	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
99	C₁₇×#102	C₂³	1	8	yes	—
100	C₁₇×#102	C₂³	1	8	yes	—
101	C₁₇×#102	C₂³	1	8	yes	—
102	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
103	C₄×C₈×C₁₇	C₂³	1	4	yes	—
104	C₂⁴×C₁₇	—	2	2	no	—
105	C₂⁴×C₁₇	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₁₇	—	2	8	no	—
107	C₂×D₄×C₁₇	—	2	8	no	—
108	C₂×D₄×C₁₇	—	2	2	no	—
109	C₂×D₄×C₁₇	—	2	4	no	—
110	C₂×D₄×C₁₇	—	2	4	no	—
111	C₂×D₄×C₁₇	—	4	2	no	—
112	C₂×D₄×C₁₇	—	4	8	no	—
113	C₂×D₄×C₁₇	—	8	4	no	—
114	C₂×D₄×C₁₇	C₂×D₄	1	4	yes	—
115	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₁₇	—	2	4	no	—
117	C₂²×C₄×C₁₇	—	2	4	no	—
118	C₂²×C₄×C₁₇	—	2	2	no	—
119	C₂²×C₄×C₁₇	—	2	2	no	—
120	C₂²×C₄×C₁₇	—	2	2	no	—
121	C₂²×C₄×C₁₇	—	2	8	no	—
122	C₂²×C₄×C₁₇	—	2	8	no	—
123	C₂²×C₄×C₁₇	—	8	4	no	—
124	C₂²×C₄×C₁₇	—	8	4	no	—
125	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
131	D₈×C₁₇	—	2	8	no	—
132	M₁₆×C₁₇	—	2	16	no	—
133	C₂×C₈×C₁₇	—	2	4	no	—
134	C₂×C₈×C₁₇	—	2	2	no	—
135	C₂×C₈×C₁₇	#41	1	4	yes	—
136	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
137	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
138	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
139	C₄⋊C₄×C₁₇	—	2	8	no	—
140	C₄⋊C₄×C₁₇	—	2	8	no	—
141	C₄⋊C₄×C₁₇	—	2	2	no	—
142	C₄⋊C₄×C₁₇	—	2	2	no	—
143	C₄⋊C₄×C₁₇	—	2	8	no	—
144	C₄⋊C₄×C₁₇	—	2	2	no	—
145	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
146	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
147	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
148	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
149	C₂²⋊C₄×C₁₇	—	2	8	no	—
150	C₂²⋊C₄×C₁₇	—	2	8	no	—
151	C₂²⋊C₄×C₁₇	—	2	8	no	—
152	C₂²⋊C₄×C₁₇	—	2	8	no	—
153	C₂²⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
154	C₄²×C₁₇	—	2	8	no	—
155	C₄²×C₁₇	C₂×D₄	1	2	yes	—
156	C₄²×C₁₇	C₂⁴	1	2	yes	—
157	C₂×#3355	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₁₇	—	2	4	no	—
159	C₂³×C₁₇	—	2	4	no	—
160	C₂³×C₁₇	—	2	4	no	—
161	C₂³×C₁₇	—	2	4	no	—
162	C₂³×C₁₇	—	4	4	no	—
163	C₂³×C₁₇	—	4	4	no	—
164	C₂³×C₁₇	—	4	4	no	—
165	C₂³×C₁₇	C₂²×D₄	1	4	yes	—
166	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
167	D₄×C₁₇	—	2	4	no	—
168	D₄×C₁₇	—	2	4	no	—
169	D₄×C₁₇	—	4	4	no	—
170	D₄×C₁₇	—	4	16	no	—
171	D₄×C₁₇	—	4	4	no	—
172	D₄×C₁₇	—	8	8	no	—
173	C₂×C₄×C₁₇	—	2	4	no	—
174	C₂×C₄×C₁₇	—	2	2	no	—
175	C₂×C₄×C₁₇	—	2	2	no	—
176	C₂×C₄×C₁₇	—	2	8	no	—
177	C₂×C₄×C₁₇	—	2	4	no	—
178	C₂×C₄×C₁₇	—	2	4	no	—
179	C₂×C₄×C₁₇	—	2	4	no	—
180	C₂×C₄×C₁₇	—	2	4	no	—
181	C₂×C₄×C₁₇	—	2	4	no	—
182	C₂×C₄×C₁₇	—	4	4	no	—
183	C₂×C₄×C₁₇	—	4	4	no	—
184	C₂×C₄×C₁₇	—	4	4	no	—
185	C₂×C₄×C₁₇	—	8	8	no	—
186	C₂×C₄×C₁₇	—	8	8	no	—
187	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
188	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
192	C₂×C₄×C₁₇	2₋¹⁺⁴	1	2	yes	—
193	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
194	C₈×C₁₇	—	2	4	no	—
195	C₈×C₁₇	—	2	2	no	—
196	C₈×C₁₇	C₂×#41	1	4	yes	—
197	C₂×#553	C₂×C₁₇	1	2	yes	complemented
198	#3355	C₂×C₁₇	1	16	yes	direct product factor
199	C₂×#499	C₂×C₁₇	1	1	yes	characteristic, complemented
200	C₂×#482	C₂×C₁₇	1	2	yes	complemented
201	C₂×#480	C₂×C₁₇	1	2	yes	complemented
202	C₂×#478	C₂×C₁₇	1	2	yes	complemented
203	C₂×#469	C₂×C₁₇	1	2	yes	complemented
204	C₂×C₄×D₈	C₂×C₁₇	1	1	yes	characteristic, complemented
205	C₂×#436	C₂×C₁₇	1	1	yes	characteristic, complemented
206	C₂×#428	C₂×C₁₇	1	2	yes	complemented
207	C₂²×C₁₇	—	2	4	no	—
208	C₂²×C₁₇	—	2	4	no	—
209	C₂²×C₁₇	—	2	4	no	—
210	C₂²×C₁₇	—	4	8	no	—
211	C₂²×C₁₇	—	4	4	no	—
212	C₂²×C₁₇	—	4	4	no	—
213	C₂²×C₁₇	—	4	4	no	—
214	C₂²×C₁₇	—	8	8	no	—
215	C₂²×C₁₇	#547	1	2	yes	—
216	C₂²×C₁₇	#575	1	2	yes	—
217	C₂²×C₁₇	#576	1	2	yes	—
218	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
219	C₄×C₁₇	—	2	4	no	—
220	C₄×C₁₇	—	2	2	no	—
221	C₄×C₁₇	—	2	2	no	—
222	C₄×C₁₇	—	4	4	no	—
223	C₄×C₁₇	—	4	4	no	—
224	C₄×C₁₇	—	4	4	no	—
225	C₄×C₁₇	#547	1	2	yes	—
226	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
227	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
228	C₂²×D₈	C₂²×C₁₇	1	1	yes	characteristic
229	C₂²×M₁₆	C₂²×C₁₇	1	2	yes	—
230	#553	—	2	8	no	—
231	#553	C₂²×C₁₇	1	16	yes	complemented
232	C₂×#126	—	2	2	no	—
233	C₂×#125	C₂²×C₁₇	1	2	yes	—
234	C₂×#123	—	2	2	no	—
235	C₂×#121	—	2	2	no	—
236	C₂×#121	C₂²×C₁₇	1	2	yes	—
237	C₂×#121	C₂²×C₁₇	1	2	yes	—
238	C₂×C₄×D₄	—	2	2	no	—
239	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
240	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
241	C₂×#117	C₂²×C₁₇	1	2	yes	—
242	C₂²×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
243	#499	C₂²×C₁₇	1	8	yes	complemented
244	#482	C₂²×C₁₇	1	16	yes	complemented
245	#480	C₂²×C₁₇	1	16	yes	complemented
246	#478	C₂²×C₁₇	1	16	yes	complemented
247	#469	C₂²×C₁₇	1	16	yes	complemented
248	C₄×D₈	C₂²×C₁₇	1	8	yes	complemented
249	#436	C₂²×C₁₇	1	8	yes	complemented
250	#428	C₂²×C₁₇	1	16	yes	complemented
251	C₂×#107	C₂²×C₁₇	1	2	yes	—
252	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
253	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
254	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
255	C₂×#106	C₂²×C₁₇	1	2	yes	—
256	C₂×#106	C₂²×C₁₇	1	2	yes	—
257	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
258	C₂×#102	C₂²×C₁₇	1	2	yes	—
259	C₂×#102	C₂²×C₁₇	1	2	yes	—
260	C₂×#102	C₂²×C₁₇	1	2	yes	—
261	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	—
262	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
263	C₂×C₁₇	—	4	4	no	—
264	C₂×C₁₇	—	8	4	no	—
265	C₂×C₁₇	#3355	1	4	yes	direct product factor
266	C₂×C₁₇	C₂×#547	1	1	yes	characteristic
267	C₂×C₁₇	C₂×#575	1	1	yes	characteristic
268	C₂×C₁₇	C₂×#576	1	1	yes	characteristic
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
272	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
273	C₂³×C₄	—	2	2	no	—
274	C₂³×C₄	—	2	2	no	—
275	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
276	C₂×D₈	—	2	4	no	—
277	C₂×D₈	C₂³×C₁₇	1	4	yes	—
278	C₂×M₁₆	—	2	8	no	—
279	C₂×M₁₆	C₂³×C₁₇	1	8	yes	—
280	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
281	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
283	#126	—	2	16	no	—
284	#125	—	2	4	no	—
285	#125	C₂³×C₁₇	1	8	yes	—
286	#123	—	2	16	no	—
287	#121	—	2	16	no	—
288	#121	—	2	4	no	—
289	#121	—	2	4	no	—
290	#121	C₂³×C₁₇	1	8	yes	—
291	#121	C₂³×C₁₇	1	8	yes	—
292	C₄×D₄	—	2	16	no	—
293	C₄×D₄	—	2	4	no	—
294	C₄×D₄	D₄×C₁₇	1	4	yes	—
295	C₄×D₄	C₂³×C₁₇	1	8	yes	—
296	C₄×D₄	C₂³×C₁₇	1	4	yes	—
297	#117	—	2	4	no	—
298	#117	C₂³×C₁₇	1	8	yes	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
315	#107	C₂³×C₁₇	1	4	yes	—
316	#107	C₂³×C₁₇	1	8	yes	—
317	#107	C₂³×C₁₇	1	4	yes	—
318	#107	C₂³×C₁₇	1	4	yes	—
319	#106	C₂³×C₁₇	1	8	yes	—
320	#106	C₂³×C₁₇	1	8	yes	—
321	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
322	#102	C₂³×C₁₇	1	8	yes	—
323	#102	C₂³×C₁₇	1	8	yes	—
324	#102	C₂³×C₁₇	1	8	yes	—
325	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
326	C₄×C₈	C₂³×C₁₇	1	4	yes	—
327	C₁₇	C₂×#3355	1	1	yes	characteristic, direct product factor, Sylow
328	C₂⁴	—	2	2	no	—
329	C₂⁴	C₂×D₄×C₁₇	1	2	yes	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	8	no	—
337	C₂×D₄	—	8	4	no	—
338	C₂×D₄	C₂×D₄×C₁₇	1	4	yes	—
339	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	8	4	no	—
348	C₂²×C₄	—	8	4	no	—
349	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
353	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
354	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
355	D₈	—	2	8	no	—
356	M₁₆	—	2	16	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	#41×C₁₇	1	4	yes	—
360	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
361	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
362	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	8	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
370	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
371	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
372	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	—	2	8	no	—
377	C₂²⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
378	C₄²	—	2	8	no	—
379	C₄²	C₂×D₄×C₁₇	1	2	yes	—
380	C₄²	C₂⁴×C₁₇	1	2	yes	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	C₂²×D₄×C₁₇	1	4	yes	—
389	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
390	D₄	—	2	4	no	—
391	D₄	—	2	4	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	16	no	—
394	D₄	—	4	4	no	—
395	D₄	—	8	8	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	8	8	no	—
409	C₂×C₄	—	8	8	no	—
410	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
411	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
412	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
413	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
415	C₂×C₄	C₁₇×2₋¹⁺⁴	1	2	yes	—
416	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
417	C₈	—	2	4	no	—
418	C₈	—	2	2	no	—
419	C₈	C₂×#41×C₁₇	1	4	yes	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	8	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	8	8	no	—
428	C₂²	C₁₇×#547	1	2	yes	—
429	C₂²	C₁₇×#575	1	2	yes	—
430	C₂²	C₁₇×#576	1	2	yes	—
431	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
432	C₄	—	2	4	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	4	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	4	no	—
438	C₄	C₁₇×#547	1	2	yes	—
439	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
440	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂	—	4	4	no	—
442	C₂	—	8	4	no	—
443	C₂	C₁₇×#3355	1	4	yes	direct product factor
444	C₂	C₂×C₁₇×#547	1	1	yes	characteristic
445	C₂	C₂×C₁₇×#575	1	1	yes	characteristic
446	C₂	C₂×C₁₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#553	C₂	semidirect
2. C₁₇×#3355	C₂	direct (N × H)
3. C₂×C₁₇×#499	C₂	semidirect
4. C₂×C₁₇×#482	C₂	semidirect
5. C₂×C₁₇×#480	C₂	semidirect
6. C₂×C₁₇×#478	C₂	semidirect
7. C₂×C₁₇×#469	C₂	semidirect
8. C₂×C₄×D₈×C₁₇	C₂	semidirect
9. C₂×C₁₇×#436	C₂	semidirect
10. C₂×C₁₇×#428	C₂	semidirect
14. C₁₇×#553	C₂²	semidirect
26. C₁₇×#499	C₂²	semidirect
27. C₁₇×#482	C₂²	semidirect
28. C₁₇×#480	C₂²	semidirect
29. C₁₇×#478	C₂²	semidirect
30. C₁₇×#469	C₂²	semidirect
31. C₄×D₈×C₁₇	C₂²	semidirect
32. C₁₇×#436	C₂²	semidirect
33. C₁₇×#428	C₂²	semidirect
157. C₂×#3355	C₁₇	direct (N × H)
197. C₂×#553	C₂×C₁₇	semidirect
198. #3355	C₂×C₁₇	direct (N × H)
199. C₂×#499	C₂×C₁₇	semidirect
200. C₂×#482	C₂×C₁₇	semidirect
201. C₂×#480	C₂×C₁₇	semidirect
202. C₂×#478	C₂×C₁₇	semidirect
203. C₂×#469	C₂×C₁₇	semidirect
204. C₂×C₄×D₈	C₂×C₁₇	semidirect
205. C₂×#436	C₂×C₁₇	semidirect
206. C₂×#428	C₂×C₁₇	semidirect
231. #553	C₂²×C₁₇	semidirect
243. #499	C₂²×C₁₇	semidirect
244. #482	C₂²×C₁₇	semidirect
245. #480	C₂²×C₁₇	semidirect
246. #478	C₂²×C₁₇	semidirect
247. #469	C₂²×C₁₇	semidirect
248. C₄×D₈	C₂²×C₁₇	semidirect
249. #436	C₂²×C₁₇	semidirect
250. #428	C₂²×C₁₇	semidirect
265. C₂×C₁₇	#3355	direct (N × H)
327. C₁₇	C₂×#3355	direct (N × H)
443. C₂	C₁₇×#3355	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×#553	2
C₁₇×#3355	2
C₂×C₁₇×#499	2
C₂×C₁₇×#482	2
C₂×C₁₇×#480	2
C₂×C₁₇×#478	2
C₂×C₁₇×#469	2
C₂×C₄×D₈×C₁₇	2
C₂×C₁₇×#436	2
C₂×C₁₇×#428	2
C₂×#3355	17

Subgroups — C2×C17×#3355 #16918992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#3355 #16918992