Subgroups — C₁₇×#21784 #16879528

Order 4352.

1278 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3500	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2888	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#2883	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#1911	C₂	1	2	yes	maximal, complemented
5	C₁₇×#1909	C₂	1	2	yes	maximal, complemented
6	C₁₇×#1885	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1884	C₂	1	2	yes	maximal, complemented
8	C₁₇×#1827	C₂	1	2	yes	maximal, complemented
9	C₁₇×#1796	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
11	C₂×C₁₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
12	C₁₇×#568	C₂²	1	2	yes	—
13	C₁₇×#548	—	2	2	no	—
14	C₁₇×#546	—	2	4	no	—
15	C₁₇×#546	—	2	2	no	—
16	C₁₇×#536	C₄	1	2	yes	complemented
17	C₁₇×#536	C₂²	1	1	yes	characteristic
18	C₁₇×#535	C₄	1	2	yes	complemented
19	C₁₇×#535	C₂²	1	1	yes	characteristic
20	C₁₇×#532	C₄	1	2	yes	complemented
21	C₁₇×#532	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×#124	C₄	1	2	yes	complemented
23	C₂×C₁₇×#124	C₂²	1	1	yes	characteristic
24	C₁₇×#518	C₂²	1	2	yes	—
25	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
26	C₁₇×#421	C₂²	1	4	yes	complemented
27	C₁₇×#419	C₂²	1	4	yes	complemented
28	C₁₇×#413	—	2	2	no	—
29	C₁₇×#413	C₂²	1	2	yes	—
30	C₂×C₁₇×#100	—	2	2	no	—
31	C₂×C₁₇×#100	C₂²	1	2	yes	—
32	C₁₇×#410	C₂²	1	2	yes	—
33	C₁₇×#410	C₂²	1	2	yes	—
34	C₂×C₁₇×#99	—	2	4	no	—
35	C₁₇×#339	C₂²	1	4	yes	complemented
36	C₁₇×H(3,ℤ/4)	C₂²	1	4	yes	complemented
37	C₁₇×2₋¹⁺⁴	—	4	4	no	—
38	C₁₇×H(5,𝔽₂)	—	4	4	no	—
39	C₂×#41×C₁₇	—	2	1	no	—
40	C₂×#41×C₁₇	—	2	2	no	—
41	C₂×#41×C₁₇	C₂×C₄	1	2	yes	—
42	C₂×#41×C₁₇	C₂×C₄	1	2	yes	complemented
43	C₂×#41×C₁₇	D₄	1	2	yes	—
44	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
45	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
46	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₁₇	—	2	1	no	—
48	C₂²×Q₈×C₁₇	C₂×C₄	1	2	yes	complemented
49	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₇	C₂×C₄	1	2	yes	—
51	C₂²×D₄×C₁₇	D₄	1	4	yes	—
52	C₂²×D₄×C₁₇	D₄	1	2	yes	—
53	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
54	C₁₇×#131	—	4	4	no	—
55	C₂×M₁₆×C₁₇	—	2	4	no	—
56	C₂×M₁₆×C₁₇	C₂³	1	4	yes	—
57	C₁₇×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
58	C₁₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
59	C₁₇×#127	C₂×C₄	1	2	yes	—
60	C₁₇×#127	C₂×C₄	1	1	yes	characteristic, complemented
61	C₁₇×#124	—	2	4	no	—
62	C₁₇×#124	—	2	2	no	—
63	C₁₇×#124	C₂×C₄	1	2	yes	—
64	C₁₇×#124	C₂×C₄	1	2	yes	—
65	C₁₇×#124	C₂×C₄	1	2	yes	—
66	C₁₇×#124	C₂×C₄	1	1	yes	characteristic, complemented
67	C₁₇×#124	C₂×C₄	1	2	yes	complemented
68	C₁₇×#124	C₂×C₄	1	1	yes	characteristic, complemented
69	C₁₇×#123	—	2	4	no	—
70	C₁₇×#123	—	2	2	no	—
71	C₁₇×C₂²⋊Q₈	—	2	4	no	—
72	C₁₇×C₂²⋊Q₈	—	2	2	no	—
73	C₁₇×#121	—	2	4	no	—
74	C₁₇×#121	—	2	4	no	—
75	C₁₇×#121	—	2	2	no	—
76	C₁₇×#121	—	2	2	no	—
77	C₁₇×#120	—	2	4	no	—
78	C₁₇×#120	—	2	2	no	—
79	C₄×Q₈×C₁₇	—	2	1	no	—
80	C₄×D₄×C₁₇	—	2	2	no	—
81	C₄×D₄×C₁₇	—	2	1	no	—
82	C₄×D₄×C₁₇	—	2	4	no	—
83	C₄×D₄×C₁₇	—	2	2	no	—
84	C₄×D₄×C₁₇	—	4	4	no	—
85	C₁₇×#117	C₂×C₄	1	2	yes	complemented
86	C₁₇×#117	C₂³	1	4	yes	—
87	C₁₇×#117	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
91	C₂×C₄²×C₁₇	C₂×C₄	1	2	yes	complemented
92	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
93	C₁₇×#104	—	4	4	no	—
94	C₁₇×#103	—	4	4	no	—
95	C₁₇×#101	—	2	2	no	—
96	C₁₇×#100	—	2	2	no	—
97	C₁₇×#100	—	2	4	no	—
98	C₁₇×#99	—	2	4	no	—
99	C₁₇×#99	—	2	4	no	—
100	C₂⁴×C₁₇	C₂²⋊C₄	1	4	yes	—
101	C₂⁴×C₁₇	C₂×D₄	1	2	yes	—
102	#41×C₁₇	—	2	4	no	—
103	#41×C₁₇	—	2	4	no	—
104	#41×C₁₇	—	2	4	no	—
105	#41×C₁₇	—	4	4	no	—
106	#41×C₁₇	—	4	4	no	—
107	#41×C₁₇	—	4	4	no	—
108	#41×C₁₇	—	4	8	no	—
109	#41×C₁₇	—	4	4	no	—
110	C₂×Q₈×C₁₇	—	2	2	no	—
111	C₂×Q₈×C₁₇	—	2	1	no	—
112	C₂×Q₈×C₁₇	—	2	4	no	—
113	C₂×Q₈×C₁₇	—	4	4	no	—
114	C₂×Q₈×C₁₇	—	4	4	no	—
115	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
117	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₁₇	—	2	2	no	—
120	C₂×D₄×C₁₇	—	2	1	no	—
121	C₂×D₄×C₁₇	—	2	4	no	—
122	C₂×D₄×C₁₇	—	2	2	no	—
123	C₂×D₄×C₁₇	—	2	4	no	—
124	C₂×D₄×C₁₇	—	4	4	no	—
125	C₂×D₄×C₁₇	—	4	4	no	—
126	C₂×D₄×C₁₇	—	4	8	no	—
127	C₂×D₄×C₁₇	C₂²⋊C₄	1	4	yes	—
128	C₂×D₄×C₁₇	C₂²⋊C₄	1	4	yes	—
129	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
131	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₇	—	2	2	no	—
137	C₂²×C₄×C₁₇	—	2	1	no	—
138	C₂²×C₄×C₁₇	—	2	2	no	—
139	C₂²×C₄×C₁₇	—	2	1	no	—
140	C₂²×C₄×C₁₇	—	2	2	no	—
141	C₂²×C₄×C₁₇	—	2	1	no	—
142	C₂²×C₄×C₁₇	—	4	4	no	—
143	C₂²×C₄×C₁₇	C₂²⋊C₄	1	4	yes	—
144	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
147	M₁₆×C₁₇	—	2	4	no	—
148	M₁₆×C₁₇	—	2	4	no	—
149	M₁₆×C₁₇	—	4	4	no	—
150	C₂×C₈×C₁₇	—	2	4	no	—
151	C₂×C₈×C₁₇	—	4	4	no	—
152	C₄⋊C₄×C₁₇	—	2	2	no	—
153	C₄⋊C₄×C₁₇	—	2	4	no	—
154	C₄⋊C₄×C₁₇	—	2	2	no	—
155	C₄⋊C₄×C₁₇	—	2	1	no	—
156	C₄⋊C₄×C₁₇	—	2	4	no	—
157	C₂²⋊C₄×C₁₇	—	2	4	no	—
158	C₂²⋊C₄×C₁₇	—	2	4	no	—
159	C₂²⋊C₄×C₁₇	—	2	4	no	—
160	C₂²⋊C₄×C₁₇	—	2	2	no	—
161	C₂²⋊C₄×C₁₇	—	2	4	no	—
162	C₂²⋊C₄×C₁₇	—	2	2	no	—
163	C₂²⋊C₄×C₁₇	—	2	1	no	—
164	C₂²⋊C₄×C₁₇	—	2	2	no	—
165	C₂²⋊C₄×C₁₇	—	2	4	no	—
166	C₂²⋊C₄×C₁₇	—	4	4	no	—
167	C₄²×C₁₇	—	2	2	no	—
168	C₄²×C₁₇	—	2	1	no	—
169	C₄²×C₁₇	—	2	4	no	—
170	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
173	#21784	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₁₇	—	2	4	no	—
175	C₂³×C₁₇	—	2	1	no	—
176	C₂³×C₁₇	—	4	4	no	—
177	C₂³×C₁₇	—	8	2	no	—
178	C₂³×C₁₇	—	8	4	no	—
179	C₂³×C₁₇	C₂×C₂²⋊C₄	1	4	yes	—
180	C₂³×C₁₇	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂³×C₁₇	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₇	—	2	2	no	—
184	Q₈×C₁₇	—	2	2	no	—
185	Q₈×C₁₇	—	2	4	no	—
186	Q₈×C₁₇	—	2	2	no	—
187	Q₈×C₁₇	—	4	4	no	—
188	Q₈×C₁₇	—	4	2	no	—
189	D₄×C₁₇	—	2	4	no	—
190	D₄×C₁₇	—	2	4	no	—
191	D₄×C₁₇	—	2	4	no	—
192	D₄×C₁₇	—	2	2	no	—
193	D₄×C₁₇	—	2	2	no	—
194	D₄×C₁₇	—	2	4	no	—
195	D₄×C₁₇	—	2	2	no	—
196	D₄×C₁₇	—	4	4	no	—
197	D₄×C₁₇	—	4	4	no	—
198	D₄×C₁₇	—	4	4	no	—
199	D₄×C₁₇	—	4	2	no	—
200	D₄×C₁₇	—	8	4	no	—
201	D₄×C₁₇	—	8	2	no	—
202	C₂×C₄×C₁₇	—	2	4	no	—
203	C₂×C₄×C₁₇	—	2	4	no	—
204	C₂×C₄×C₁₇	—	2	1	no	—
205	C₂×C₄×C₁₇	—	2	2	no	—
206	C₂×C₄×C₁₇	—	2	1	no	—
207	C₂×C₄×C₁₇	—	2	1	no	—
208	C₂×C₄×C₁₇	—	2	2	no	—
209	C₂×C₄×C₁₇	—	4	4	no	—
210	C₂×C₄×C₁₇	—	4	4	no	—
211	C₂×C₄×C₁₇	—	4	4	no	—
212	C₂×C₄×C₁₇	—	4	2	no	—
213	C₂×C₄×C₁₇	—	4	2	no	—
214	C₂×C₄×C₁₇	—	4	4	no	—
215	C₂×C₄×C₁₇	—	8	1	no	—
216	C₂×C₄×C₁₇	—	8	2	no	—
217	C₂×C₄×C₁₇	—	16	4	no	—
218	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₇	H(5,𝔽₂)	1	4	yes	—
223	C₈×C₁₇	—	4	4	no	—
224	#3500	C₂×C₁₇	1	1	yes	characteristic
225	#2888	C₂×C₁₇	1	1	yes	characteristic, complemented
226	#2883	C₂×C₁₇	1	1	yes	characteristic, complemented
227	#1911	C₂×C₁₇	1	2	yes	complemented
228	#1909	C₂×C₁₇	1	2	yes	complemented
229	#1885	C₂×C₁₇	1	2	yes	complemented
230	#1884	C₂×C₁₇	1	2	yes	complemented
231	#1827	C₂×C₁₇	1	2	yes	complemented
232	#1796	C₂×C₁₇	1	2	yes	complemented
233	C₂²×C₁₇	—	2	2	no	—
234	C₂²×C₁₇	—	2	2	no	—
235	C₂²×C₁₇	—	2	4	no	—
236	C₂²×C₁₇	—	4	1	no	—
237	C₂²×C₁₇	—	4	2	no	—
238	C₂²×C₁₇	—	4	4	no	—
239	C₂²×C₁₇	—	4	2	no	—
240	C₂²×C₁₇	—	4	2	no	—
241	C₂²×C₁₇	—	4	1	no	—
242	C₂²×C₁₇	—	8	4	no	—
243	C₂²×C₁₇	—	16	4	no	—
244	C₂²×C₁₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₁₇	#534	1	2	yes	—
246	C₄×C₁₇	—	2	2	no	—
247	C₄×C₁₇	—	2	2	no	—
248	C₄×C₁₇	—	4	1	no	—
249	C₄×C₁₇	—	4	2	no	—
250	C₄×C₁₇	—	4	1	no	—
251	C₄×C₁₇	—	4	2	no	—
252	C₄×C₁₇	—	4	1	no	—
253	C₄×C₁₇	—	8	4	no	—
254	C₄×C₁₇	#518	1	2	yes	—
255	C₄×C₁₇	#534	1	2	yes	—
256	C₂×2₋¹⁺⁴	C₂²×C₁₇	1	1	yes	characteristic
257	C₂×H(5,𝔽₂)	C₂²×C₁₇	1	1	yes	characteristic
258	#568	C₂²×C₁₇	1	2	yes	—
259	#548	—	2	2	no	—
260	#546	—	2	2	no	—
261	#546	—	2	4	no	—
262	#536	C₄×C₁₇	1	2	yes	complemented
263	#536	C₂²×C₁₇	1	1	yes	characteristic
264	#535	C₄×C₁₇	1	2	yes	complemented
265	#535	C₂²×C₁₇	1	1	yes	characteristic
266	#532	C₄×C₁₇	1	2	yes	complemented
267	#532	C₂²×C₁₇	1	1	yes	characteristic
268	C₂×#124	C₄×C₁₇	1	2	yes	complemented
269	C₂×#124	C₂²×C₁₇	1	1	yes	characteristic
270	#518	C₂²×C₁₇	1	2	yes	—
271	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
272	#421	C₂²×C₁₇	1	4	yes	complemented
273	#419	C₂²×C₁₇	1	4	yes	complemented
274	#413	—	2	2	no	—
275	#413	C₂²×C₁₇	1	2	yes	—
276	C₂×#100	—	2	2	no	—
277	C₂×#100	C₂²×C₁₇	1	2	yes	—
278	#410	C₂²×C₁₇	1	2	yes	—
279	#410	C₂²×C₁₇	1	2	yes	—
280	C₂×#99	—	2	4	no	—
281	#339	C₂²×C₁₇	1	4	yes	complemented
282	H(3,ℤ/4)	C₂²×C₁₇	1	4	yes	complemented
283	C₂×C₁₇	—	2	1	no	—
284	C₂×C₁₇	—	2	2	no	—
285	C₂×C₁₇	—	4	4	no	—
286	C₂×C₁₇	—	4	2	no	—
287	C₂×C₁₇	—	4	2	no	—
288	C₂×C₁₇	—	8	1	no	—
289	C₂×C₁₇	#2308	1	1	yes	characteristic
290	2₋¹⁺⁴	—	4	4	no	—
291	H(5,𝔽₂)	—	4	4	no	—
292	C₂×#41	—	2	2	no	—
293	C₂×#41	—	2	1	no	—
294	C₂×#41	C₂×C₄×C₁₇	1	2	yes	—
295	C₂×#41	C₂×C₄×C₁₇	1	2	yes	complemented
296	C₂×#41	D₄×C₁₇	1	2	yes	—
297	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
298	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
299	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
300	C₂²×Q₈	—	2	1	no	—
301	C₂²×Q₈	C₂×C₄×C₁₇	1	2	yes	complemented
302	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
303	C₂²×D₄	C₂×C₄×C₁₇	1	2	yes	—
304	C₂²×D₄	D₄×C₁₇	1	4	yes	—
305	C₂²×D₄	D₄×C₁₇	1	2	yes	—
306	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
307	#131	—	4	4	no	—
308	C₂×M₁₆	—	2	4	no	—
309	C₂×M₁₆	C₂³×C₁₇	1	4	yes	—
310	C₄⋊Q₈	C₂×C₄×C₁₇	1	2	yes	complemented
311	C₄⋊Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic, complemented
312	#127	C₂×C₄×C₁₇	1	2	yes	—
313	#127	C₂×C₄×C₁₇	1	1	yes	characteristic, complemented
314	#124	—	2	4	no	—
315	#124	—	2	2	no	—
316	#124	C₂×C₄×C₁₇	1	2	yes	—
317	#124	C₂×C₄×C₁₇	1	2	yes	—
318	#124	C₂×C₄×C₁₇	1	2	yes	—
319	#124	C₂×C₄×C₁₇	1	1	yes	characteristic, complemented
320	#124	C₂×C₄×C₁₇	1	2	yes	complemented
321	#124	C₂×C₄×C₁₇	1	1	yes	characteristic, complemented
322	#123	—	2	4	no	—
323	#123	—	2	2	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	#121	—	2	4	no	—
327	#121	—	2	4	no	—
328	#121	—	2	2	no	—
329	#121	—	2	2	no	—
330	#120	—	2	4	no	—
331	#120	—	2	2	no	—
332	C₄×Q₈	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	4	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	—	4	4	no	—
338	#117	C₂×C₄×C₁₇	1	2	yes	complemented
339	#117	C₂³×C₁₇	1	4	yes	—
340	#117	C₂³×C₁₇	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	2	4	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	4	no	—
344	C₂×C₄²	C₂×C₄×C₁₇	1	2	yes	complemented
345	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
346	#104	—	4	4	no	—
347	#103	—	4	4	no	—
348	#101	—	2	2	no	—
349	#100	—	2	2	no	—
350	#100	—	2	4	no	—
351	#99	—	2	4	no	—
352	#99	—	2	4	no	—
353	C₁₇	#21784	1	1	yes	characteristic, direct product factor, Sylow
354	C₂⁴	C₂²⋊C₄×C₁₇	1	4	yes	—
355	C₂⁴	C₂×D₄×C₁₇	1	2	yes	—
356	#41	—	2	4	no	—
357	#41	—	2	4	no	—
358	#41	—	2	4	no	—
359	#41	—	4	4	no	—
360	#41	—	4	4	no	—
361	#41	—	4	4	no	—
362	#41	—	4	8	no	—
363	#41	—	4	4	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	4	4	no	—
368	C₂×Q₈	—	4	4	no	—
369	C₂×Q₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
370	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
371	C₂×Q₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
372	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	8	no	—
381	C₂×D₄	C₂²⋊C₄×C₁₇	1	4	yes	—
382	C₂×D₄	C₂²⋊C₄×C₁₇	1	4	yes	—
383	C₂×D₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
384	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
385	C₂×D₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
386	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
387	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
388	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
389	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	4	no	—
397	C₂²×C₄	C₂²⋊C₄×C₁₇	1	4	yes	—
398	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
401	M₁₆	—	2	4	no	—
402	M₁₆	—	2	4	no	—
403	M₁₆	—	4	4	no	—
404	C₂×C₈	—	2	4	no	—
405	C₂×C₈	—	4	4	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	4	no	—
424	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
425	C₄²	C₂²×C₄×C₁₇	1	2	yes	—
426	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
427	C₂³	—	2	4	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	8	2	no	—
431	C₂³	—	8	4	no	—
432	C₂³	C₂×C₂²⋊C₄×C₁₇	1	4	yes	—
433	C₂³	C₂×C₂²⋊C₄×C₁₇	1	2	yes	—
434	C₂³	C₂×C₂²⋊C₄×C₁₇	1	2	yes	—
435	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	4	no	—
439	Q₈	—	2	2	no	—
440	Q₈	—	4	4	no	—
441	Q₈	—	4	2	no	—
442	D₄	—	2	4	no	—
443	D₄	—	2	4	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	4	no	—
448	D₄	—	2	2	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	4	no	—
451	D₄	—	4	4	no	—
452	D₄	—	4	2	no	—
453	D₄	—	8	4	no	—
454	D₄	—	8	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	8	1	no	—
469	C₂×C₄	—	8	2	no	—
470	C₂×C₄	—	16	4	no	—
471	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	2	yes	—
472	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	2	yes	—
473	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
475	C₂×C₄	C₁₇×H(5,𝔽₂)	1	4	yes	—
476	C₈	—	4	4	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	8	4	no	—
487	C₂²	—	16	4	no	—
488	C₂²	C₂²×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
489	C₂²	C₁₇×#534	1	2	yes	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	8	4	no	—
498	C₄	C₁₇×#518	1	2	yes	—
499	C₄	C₁₇×#534	1	2	yes	—
500	C₂	—	2	1	no	—
501	C₂	—	2	2	no	—
502	C₂	—	4	4	no	—
503	C₂	—	4	2	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	1	no	—
506	C₂	C₁₇×#2308	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₇	#2308
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#2888	C₂	semidirect
3. C₁₇×#2883	C₂	semidirect
4. C₁₇×#1911	C₂	semidirect
5. C₁₇×#1909	C₂	semidirect
6. C₁₇×#1885	C₂	semidirect
7. C₁₇×#1884	C₂	semidirect
8. C₁₇×#1827	C₂	semidirect
9. C₁₇×#1796	C₂	semidirect
16. C₁₇×#536	C₄	semidirect
18. C₁₇×#535	C₄	semidirect
20. C₁₇×#532	C₄	semidirect
22. C₂×C₁₇×#124	C₄	semidirect
26. C₁₇×#421	C₂²	semidirect
27. C₁₇×#419	C₂²	semidirect
35. C₁₇×#339	C₂²	semidirect
36. C₁₇×H(3,ℤ/4)	C₂²	semidirect
42. C₂×#41×C₁₇	C₂×C₄	semidirect
48. C₂²×Q₈×C₁₇	C₂×C₄	semidirect
57. C₁₇×C₄⋊Q₈	C₂×C₄	semidirect
58. C₁₇×C₄⋊Q₈	C₂×C₄	semidirect
60. C₁₇×#127	C₂×C₄	semidirect
66. C₁₇×#124	C₂×C₄	semidirect
67. C₁₇×#124	C₂×C₄	semidirect
68. C₁₇×#124	C₂×C₄	semidirect
85. C₁₇×#117	C₂×C₄	semidirect
91. C₂×C₄²×C₁₇	C₂×C₄	semidirect
173. #21784	C₁₇	direct (N × H)
225. #2888	C₂×C₁₇	semidirect
226. #2883	C₂×C₁₇	semidirect
227. #1911	C₂×C₁₇	semidirect
228. #1909	C₂×C₁₇	semidirect
229. #1885	C₂×C₁₇	semidirect
230. #1884	C₂×C₁₇	semidirect
231. #1827	C₂×C₁₇	semidirect
232. #1796	C₂×C₁₇	semidirect
262. #536	C₄×C₁₇	semidirect
264. #535	C₄×C₁₇	semidirect
266. #532	C₄×C₁₇	semidirect
268. C₂×#124	C₄×C₁₇	semidirect
272. #421	C₂²×C₁₇	semidirect
273. #419	C₂²×C₁₇	semidirect
281. #339	C₂²×C₁₇	semidirect
282. H(3,ℤ/4)	C₂²×C₁₇	semidirect
295. C₂×#41	C₂×C₄×C₁₇	semidirect
301. C₂²×Q₈	C₂×C₄×C₁₇	semidirect
310. C₄⋊Q₈	C₂×C₄×C₁₇	semidirect
311. C₄⋊Q₈	C₂×C₄×C₁₇	semidirect
313. #127	C₂×C₄×C₁₇	semidirect
319. #124	C₂×C₄×C₁₇	semidirect
320. #124	C₂×C₄×C₁₇	semidirect
321. #124	C₂×C₄×C₁₇	semidirect
338. #117	C₂×C₄×C₁₇	semidirect
344. C₂×C₄²	C₂×C₄×C₁₇	semidirect
353. C₁₇	#21784	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#3500	2
C₁₇×#2888	2
C₁₇×#2883	2
C₁₇×#1911	2
C₁₇×#1909	2
C₁₇×#1885	2
C₁₇×#1884	2
C₁₇×#1827	2
C₁₇×#1796	2
#21784	17

Subgroups — C17×#21784 #16879528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#21784 #16879528