Subgroups — C₁₇×#62860 #16920604

Order 4352.

6866 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3510	C₂	1	8	yes	maximal, complemented
2	C₁₇×#3509	C₂	1	8	yes	maximal, complemented
3	C₁₇×#3507	C₂	1	8	yes	maximal, complemented
4	C₁₇×#3495	C₂	1	16	yes	maximal, complemented
5	C₁₇×#3491	C₂	1	8	yes	maximal, complemented
6	C₁₇×#3461	C₂	1	8	yes	maximal, complemented
7	C₁₇×#3458	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#3449	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₇×#536	C₂	1	2	yes	maximal, complemented
10	C₁₇×#3428	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₇	C₂²	1	2	yes	—
13	C₂³×Q₈×C₁₇	C₂²	1	1	yes	characteristic
14	C₁₇×#559	C₂²	1	16	yes	complemented
15	C₁₇×#557	C₂²	1	16	yes	complemented
16	C₁₇×#556	C₂²	1	16	yes	complemented
17	C₁₇×#556	C₂²	1	32	yes	complemented
18	C₁₇×#554	C₂²	1	16	yes	complemented
19	C₁₇×#552	C₂²	1	64	yes	complemented
20	C₁₇×#552	C₂²	1	32	yes	complemented
21	C₁₇×#551	C₂²	1	64	yes	complemented
22	C₁₇×#544	C₂²	1	4	yes	complemented
23	C₁₇×#544	C₂²	1	8	yes	complemented
24	C₁₇×#543	C₂²	1	4	yes	—
25	C₁₇×#542	C₂²	1	32	yes	complemented
26	C₁₇×#541	C₂²	1	32	yes	complemented
27	C₁₇×#539	C₂²	1	32	yes	complemented
28	C₁₇×#537	C₂²	1	4	yes	—
29	C₁₇×#536	C₂²	1	8	yes	—
30	C₁₇×#536	C₂²	1	4	yes	—
31	C₁₇×#536	C₂²	1	8	yes	—
32	C₁₇×#536	C₂²	1	8	yes	complemented
33	C₁₇×#536	C₂²	1	8	yes	complemented
34	C₁₇×#535	C₂²	1	4	yes	—
35	C₁₇×#534	C₂²	1	4	yes	—
36	C₁₇×#533	C₂²	1	4	yes	complemented
37	C₁₇×#533	C₂²	1	8	yes	complemented
38	C₁₇×#533	C₂²	1	32	yes	complemented
39	C₁₇×#532	C₂²	1	4	yes	—
40	C₂×C₁₇×C₄⋊Q₈	C₂²	1	4	yes	complemented
41	C₁₇×#529	C₂²	1	32	yes	complemented
42	C₁₇×#529	C₂²	1	32	yes	complemented
43	C₂×C₁₇×#124	C₂²	1	4	yes	complemented
44	C₁₇×#525	C₂²	1	8	yes	—
45	C₂×C₁₇×#123	C₂²	1	8	yes	—
46	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
47	C₁₇×#520	C₂²	1	8	yes	—
48	C₁₇×#520	C₂²	1	8	yes	complemented
49	C₁₇×#519	C₂²	1	8	yes	complemented
50	C₁₇×#519	C₂²	1	4	yes	complemented
51	C₁₇×#519	C₂²	1	8	yes	complemented
52	C₁₇×#518	C₂²	1	8	yes	—
53	C₁₇×#518	C₂²	1	4	yes	complemented
54	C₄×#41×C₁₇	C₂²	1	8	yes	—
55	C₄×#41×C₁₇	C₂²	1	8	yes	complemented
56	C₂×C₄×Q₈×C₁₇	C₂²	1	4	yes	complemented
57	C₂×C₄×Q₈×C₁₇	C₂²	1	4	yes	complemented
58	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
59	C₂×C₁₇×#117	C₂²	1	2	yes	—
60	C₂×C₁₇×#117	C₂²	1	4	yes	—
61	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
62	C₂×C₁₇×#117	C₂²	1	8	yes	complemented
63	C₂×#41×C₁₇	—	2	16	no	—
64	C₂×#41×C₁₇	C₂³	1	4	yes	—
65	C₂×#41×C₁₇	C₂³	1	4	yes	—
66	C₂×#41×C₁₇	C₂³	1	4	yes	—
67	C₂×#41×C₁₇	C₂³	1	4	yes	—
68	C₂²×Q₈×C₁₇	—	2	8	no	—
69	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
70	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
71	C₂²×Q₈×C₁₇	C₂³	1	4	yes	—
72	C₂²×Q₈×C₁₇	C₂³	1	4	yes	—
73	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
74	C₂²×D₄×C₁₇	C₂³	1	4	yes	—
75	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
79	C₁₇×C₄⋊Q₈	C₂³	1	16	yes	—
80	C₁₇×C₄⋊Q₈	C₂³	1	16	yes	—
81	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
82	C₁₇×C₄⋊Q₈	C₂³	1	16	yes	—
83	C₁₇×C₄⋊Q₈	C₂³	1	8	yes	—
84	C₁₇×#127	C₂³	1	4	yes	—
85	C₁₇×#126	C₂³	1	64	yes	—
86	C₁₇×#126	C₂³	1	64	yes	—
87	C₁₇×#125	C₂³	1	16	yes	—
88	C₁₇×#125	C₂³	1	32	yes	—
89	C₁₇×#125	C₂³	1	64	yes	—
90	C₁₇×#125	C₂³	1	8	yes	—
91	C₁₇×#124	C₂³	1	16	yes	—
92	C₁₇×#124	C₂³	1	16	yes	—
93	C₁₇×#124	C₂³	1	32	yes	—
94	C₁₇×#124	C₂³	1	8	yes	—
95	C₁₇×#123	C₂³	1	32	yes	—
96	C₁₇×#123	C₂³	1	32	yes	—
97	C₁₇×#123	C₂³	1	16	yes	—
98	C₁₇×#123	C₂³	1	64	yes	—
99	C₁₇×C₂²⋊Q₈	C₂³	1	32	yes	—
100	C₁₇×C₂²⋊Q₈	C₂³	1	32	yes	—
101	C₁₇×C₂²⋊Q₈	C₂³	1	16	yes	—
102	C₁₇×C₂²⋊Q₈	C₂³	1	16	yes	—
103	C₁₇×C₂²⋊Q₈	C₂³	1	64	yes	—
104	C₁₇×C₂²⋊Q₈	C₂³	1	32	yes	—
105	C₁₇×#121	C₂³	1	16	yes	—
106	C₁₇×#121	C₂³	1	16	yes	—
107	C₁₇×#120	C₂³	1	16	yes	—
108	C₄×Q₈×C₁₇	C₂³	1	32	yes	—
109	C₄×Q₈×C₁₇	C₂³	1	16	yes	—
110	C₄×Q₈×C₁₇	C₂³	1	16	yes	—
111	C₄×Q₈×C₁₇	C₂³	1	16	yes	—
112	C₄×Q₈×C₁₇	C₂³	1	16	yes	—
113	C₄×Q₈×C₁₇	C₂³	1	32	yes	—
114	C₄×Q₈×C₁₇	C₂³	1	16	yes	—
115	C₄×D₄×C₁₇	C₂³	1	32	yes	—
116	C₄×D₄×C₁₇	C₂³	1	16	yes	—
117	C₄×D₄×C₁₇	C₂³	1	32	yes	—
118	C₄×D₄×C₁₇	C₂³	1	16	yes	—
119	C₄×D₄×C₁₇	C₂³	1	16	yes	—
120	C₄×D₄×C₁₇	C₂³	1	32	yes	—
121	C₁₇×#117	C₂³	1	4	yes	—
122	C₁₇×#117	C₂³	1	4	yes	—
123	C₁₇×#117	C₂³	1	4	yes	—
124	C₁₇×#117	C₂³	1	4	yes	—
125	C₁₇×#117	C₂³	1	4	yes	—
126	C₁₇×#117	C₂³	1	4	yes	—
127	C₁₇×#117	C₂³	1	4	yes	—
128	C₁₇×#117	C₂³	1	32	yes	—
129	C₁₇×#117	C₂³	1	4	yes	—
130	C₁₇×#117	C₂³	1	16	yes	—
131	C₁₇×#117	C₂³	1	16	yes	—
132	C₁₇×#117	C₂³	1	16	yes	—
133	C₁₇×#117	C₂³	1	64	yes	—
134	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
137	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₁₇	C₂³	1	16	yes	—
139	C₂×C₄⋊C₄×C₁₇	C₂³	1	16	yes	—
140	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₇	C₂³	1	16	yes	—
144	C₂×C₂²⋊C₄×C₁₇	C₂³	1	16	yes	—
145	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₇	C₂³	1	8	yes	—
147	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
149	C₂×C₄²×C₁₇	C₂³	1	16	yes	—
150	C₂⁴×C₁₇	C₂⁴	1	4	yes	—
151	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
152	#41×C₁₇	—	2	16	no	—
153	#41×C₁₇	—	2	16	no	—
154	#41×C₁₇	—	2	16	no	—
155	#41×C₁₇	—	2	16	no	—
156	C₂×Q₈×C₁₇	—	2	16	no	—
157	C₂×Q₈×C₁₇	—	2	16	no	—
158	C₂×Q₈×C₁₇	—	2	8	no	—
159	C₂×Q₈×C₁₇	—	2	8	no	—
160	C₂×Q₈×C₁₇	—	2	8	no	—
161	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
162	C₂×Q₈×C₁₇	C₂⁴	1	8	yes	—
163	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
164	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
165	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
166	C₂×Q₈×C₁₇	C₂⁴	1	16	yes	—
167	C₂×D₄×C₁₇	—	2	16	no	—
168	C₂×D₄×C₁₇	—	2	8	no	—
169	C₂×D₄×C₁₇	C₂⁴	1	8	yes	—
170	C₂×D₄×C₁₇	C₂⁴	1	8	yes	—
171	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
172	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
173	C₂×D₄×C₁₇	C₂⁴	1	16	yes	—
174	C₂²×C₄×C₁₇	—	2	8	no	—
175	C₂²×C₄×C₁₇	—	2	16	no	—
176	C₂²×C₄×C₁₇	#41	1	8	yes	—
177	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
178	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
179	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
182	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
184	C₂²×C₄×C₁₇	C₂⁴	1	32	yes	—
185	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
190	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
191	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
192	C₄⋊C₄×C₁₇	C₂⁴	1	32	yes	—
193	C₄⋊C₄×C₁₇	C₂⁴	1	64	yes	—
194	C₄⋊C₄×C₁₇	C₂⁴	1	16	yes	—
195	C₄⋊C₄×C₁₇	C₂⁴	1	16	yes	—
196	C₄⋊C₄×C₁₇	C₂⁴	1	32	yes	—
197	C₄⋊C₄×C₁₇	C₂⁴	1	32	yes	—
198	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
199	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
200	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
201	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
202	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
203	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
204	C₂²⋊C₄×C₁₇	C₂⁴	1	64	yes	—
205	C₂²⋊C₄×C₁₇	C₂⁴	1	32	yes	—
206	C₂²⋊C₄×C₁₇	C₂⁴	1	32	yes	—
207	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
208	C₄²×C₁₇	C₂⁴	1	8	yes	—
209	C₄²×C₁₇	C₂⁴	1	4	yes	—
210	C₄²×C₁₇	C₂⁴	1	8	yes	—
211	C₄²×C₁₇	C₂⁴	1	32	yes	—
212	C₄²×C₁₇	C₂⁴	1	32	yes	—
213	C₄²×C₁₇	C₂⁴	1	4	yes	—
214	C₄²×C₁₇	C₂⁴	1	8	yes	—
215	#62860	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₁₇	—	2	8	no	—
217	C₂³×C₁₇	—	4	2	no	—
218	C₂³×C₁₇	—	4	8	no	—
219	C₂³×C₁₇	C₂×#41	1	4	yes	—
220	C₂³×C₁₇	C₂⁵	1	8	yes	—
221	C₂³×C₁₇	C₂⁵	1	2	yes	—
222	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
223	Q₈×C₁₇	—	2	8	no	—
224	Q₈×C₁₇	—	2	16	no	—
225	Q₈×C₁₇	—	2	8	no	—
226	Q₈×C₁₇	—	2	8	no	—
227	Q₈×C₁₇	—	2	8	no	—
228	Q₈×C₁₇	—	4	16	no	—
229	D₄×C₁₇	—	2	16	no	—
230	D₄×C₁₇	—	2	16	no	—
231	D₄×C₁₇	—	2	8	no	—
232	D₄×C₁₇	—	2	8	no	—
233	D₄×C₁₇	—	4	16	no	—
234	C₂×C₄×C₁₇	—	2	8	no	—
235	C₂×C₄×C₁₇	—	2	16	no	—
236	C₂×C₄×C₁₇	—	2	8	no	—
237	C₂×C₄×C₁₇	—	2	16	no	—
238	C₂×C₄×C₁₇	—	2	16	no	—
239	C₂×C₄×C₁₇	—	4	4	no	—
240	C₂×C₄×C₁₇	—	4	32	no	—
241	C₂×C₄×C₁₇	—	4	8	no	—
242	C₂×C₄×C₁₇	—	4	4	no	—
243	C₂×C₄×C₁₇	C₂×#41	1	8	yes	—
244	C₂×C₄×C₁₇	C₂×#41	1	8	yes	—
245	C₂×C₄×C₁₇	C₂×#41	1	4	yes	—
246	C₂×C₄×C₁₇	C₂×#41	1	4	yes	—
247	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
248	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
249	C₂×C₄×C₁₇	C₂⁵	1	16	yes	—
250	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
251	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
252	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
253	C₂×C₄×C₁₇	C₂⁵	1	2	yes	—
254	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
255	#3510	C₂×C₁₇	1	8	yes	complemented
256	#3509	C₂×C₁₇	1	8	yes	complemented
257	#3507	C₂×C₁₇	1	8	yes	complemented
258	#3495	C₂×C₁₇	1	16	yes	complemented
259	#3491	C₂×C₁₇	1	8	yes	complemented
260	#3461	C₂×C₁₇	1	8	yes	complemented
261	#3458	C₂×C₁₇	1	1	yes	characteristic, complemented
262	#3449	C₂×C₁₇	1	1	yes	characteristic
263	C₂×#536	C₂×C₁₇	1	2	yes	complemented
264	#3428	C₂×C₁₇	1	2	yes	complemented
265	C₂×#519	C₂×C₁₇	1	1	yes	characteristic, complemented
266	C₂²×C₁₇	—	2	2	no	—
267	C₂²×C₁₇	—	2	4	no	—
268	C₂²×C₁₇	—	2	8	no	—
269	C₂²×C₁₇	—	2	16	no	—
270	C₂²×C₁₇	—	4	4	no	—
271	C₂²×C₁₇	—	8	8	no	—
272	C₂²×C₁₇	C₂²×#41	1	4	yes	—
273	C₂²×C₁₇	C₂²×#41	1	2	yes	—
274	C₂²×C₁₇	C₂⁶	1	1	yes	characteristic
275	C₄×C₁₇	—	2	8	no	—
276	C₄×C₁₇	—	2	8	no	—
277	C₄×C₁₇	—	2	8	no	—
278	C₄×C₁₇	—	2	16	no	—
279	C₄×C₁₇	—	2	8	no	—
280	C₄×C₁₇	C₂²×#41	1	2	yes	—
281	C₄×C₁₇	C₂²×#41	1	4	yes	—
282	C₄×C₁₇	C₂²×#41	1	2	yes	—
283	C₂²×#41	C₂²×C₁₇	1	2	yes	—
284	C₂³×Q₈	C₂²×C₁₇	1	1	yes	characteristic
285	#559	C₂²×C₁₇	1	16	yes	complemented
286	#557	C₂²×C₁₇	1	16	yes	complemented
287	#556	C₂²×C₁₇	1	16	yes	complemented
288	#556	C₂²×C₁₇	1	32	yes	complemented
289	#554	C₂²×C₁₇	1	16	yes	complemented
290	#552	C₂²×C₁₇	1	64	yes	complemented
291	#552	C₂²×C₁₇	1	32	yes	complemented
292	#551	C₂²×C₁₇	1	64	yes	complemented
293	#544	C₂²×C₁₇	1	4	yes	complemented
294	#544	C₂²×C₁₇	1	8	yes	complemented
295	#543	C₂²×C₁₇	1	4	yes	—
296	#542	C₂²×C₁₇	1	32	yes	complemented
297	#541	C₂²×C₁₇	1	32	yes	complemented
298	#539	C₂²×C₁₇	1	32	yes	complemented
299	#537	C₂²×C₁₇	1	4	yes	—
300	#536	C₂²×C₁₇	1	8	yes	—
301	#536	C₂²×C₁₇	1	8	yes	—
302	#536	C₂²×C₁₇	1	4	yes	—
303	#536	C₂²×C₁₇	1	8	yes	complemented
304	#536	C₂²×C₁₇	1	8	yes	complemented
305	#535	C₂²×C₁₇	1	4	yes	—
306	#534	C₂²×C₁₇	1	4	yes	—
307	#533	C₂²×C₁₇	1	4	yes	complemented
308	#533	C₂²×C₁₇	1	8	yes	complemented
309	#533	C₂²×C₁₇	1	32	yes	complemented
310	#532	C₂²×C₁₇	1	4	yes	—
311	C₂×C₄⋊Q₈	C₂²×C₁₇	1	4	yes	complemented
312	#529	C₂²×C₁₇	1	32	yes	complemented
313	#529	C₂²×C₁₇	1	32	yes	complemented
314	C₂×#124	C₂²×C₁₇	1	4	yes	complemented
315	#525	C₂²×C₁₇	1	8	yes	—
316	C₂×#123	C₂²×C₁₇	1	8	yes	—
317	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	8	yes	complemented
318	#520	C₂²×C₁₇	1	8	yes	—
319	#520	C₂²×C₁₇	1	8	yes	complemented
320	#519	C₂²×C₁₇	1	8	yes	complemented
321	#519	C₂²×C₁₇	1	8	yes	complemented
322	#519	C₂²×C₁₇	1	4	yes	complemented
323	#518	C₂²×C₁₇	1	8	yes	—
324	#518	C₂²×C₁₇	1	4	yes	complemented
325	C₄×#41	C₂²×C₁₇	1	8	yes	—
326	C₄×#41	C₂²×C₁₇	1	8	yes	complemented
327	C₂×C₄×Q₈	C₂²×C₁₇	1	4	yes	complemented
328	C₂×C₄×Q₈	C₂²×C₁₇	1	4	yes	complemented
329	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
330	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
331	C₂×#117	C₂²×C₁₇	1	4	yes	—
332	C₂×#117	C₂²×C₁₇	1	2	yes	—
333	C₂×#117	C₂²×C₁₇	1	8	yes	complemented
334	C₂×C₁₇	—	2	4	no	—
335	C₂×C₁₇	—	2	2	no	—
336	C₂×C₁₇	—	4	8	no	—
337	C₂×C₁₇	C₂³×#41	1	1	yes	characteristic
338	C₂×C₁₇	2₋¹⁺⁶	1	2	yes	—
339	C₂×#41	—	2	16	no	—
340	C₂×#41	C₂³×C₁₇	1	4	yes	—
341	C₂×#41	C₂³×C₁₇	1	4	yes	—
342	C₂×#41	C₂³×C₁₇	1	4	yes	—
343	C₂×#41	C₂³×C₁₇	1	4	yes	—
344	C₂²×Q₈	—	2	8	no	—
345	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
346	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
347	C₂²×Q₈	C₂³×C₁₇	1	4	yes	—
348	C₂²×Q₈	C₂³×C₁₇	1	4	yes	—
349	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
350	C₂²×D₄	C₂³×C₁₇	1	4	yes	—
351	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
352	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
353	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
354	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₁₇	1	16	yes	—
356	C₄⋊Q₈	C₂³×C₁₇	1	16	yes	—
357	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
358	C₄⋊Q₈	C₂³×C₁₇	1	16	yes	—
359	C₄⋊Q₈	C₂³×C₁₇	1	8	yes	—
360	#127	C₂³×C₁₇	1	4	yes	—
361	#126	C₂³×C₁₇	1	64	yes	—
362	#126	C₂³×C₁₇	1	64	yes	—
363	#125	C₂³×C₁₇	1	16	yes	—
364	#125	C₂³×C₁₇	1	32	yes	—
365	#125	C₂³×C₁₇	1	64	yes	—
366	#125	C₂³×C₁₇	1	8	yes	—
367	#124	C₂³×C₁₇	1	16	yes	—
368	#124	C₂³×C₁₇	1	16	yes	—
369	#124	C₂³×C₁₇	1	32	yes	—
370	#124	C₂³×C₁₇	1	8	yes	—
371	#123	C₂³×C₁₇	1	32	yes	—
372	#123	C₂³×C₁₇	1	32	yes	—
373	#123	C₂³×C₁₇	1	16	yes	—
374	#123	C₂³×C₁₇	1	64	yes	—
375	C₂²⋊Q₈	C₂³×C₁₇	1	32	yes	—
376	C₂²⋊Q₈	C₂³×C₁₇	1	32	yes	—
377	C₂²⋊Q₈	C₂³×C₁₇	1	16	yes	—
378	C₂²⋊Q₈	C₂³×C₁₇	1	16	yes	—
379	C₂²⋊Q₈	C₂³×C₁₇	1	64	yes	—
380	C₂²⋊Q₈	C₂³×C₁₇	1	32	yes	—
381	#121	C₂³×C₁₇	1	16	yes	—
382	#121	C₂³×C₁₇	1	16	yes	—
383	#120	C₂³×C₁₇	1	16	yes	—
384	C₄×Q₈	C₂³×C₁₇	1	32	yes	—
385	C₄×Q₈	C₂³×C₁₇	1	16	yes	—
386	C₄×Q₈	C₂³×C₁₇	1	16	yes	—
387	C₄×Q₈	C₂³×C₁₇	1	16	yes	—
388	C₄×Q₈	C₂³×C₁₇	1	16	yes	—
389	C₄×Q₈	C₂³×C₁₇	1	32	yes	—
390	C₄×Q₈	C₂³×C₁₇	1	16	yes	—
391	C₄×D₄	C₂³×C₁₇	1	32	yes	—
392	C₄×D₄	C₂³×C₁₇	1	16	yes	—
393	C₄×D₄	C₂³×C₁₇	1	32	yes	—
394	C₄×D₄	C₂³×C₁₇	1	16	yes	—
395	C₄×D₄	C₂³×C₁₇	1	16	yes	—
396	C₄×D₄	C₂³×C₁₇	1	32	yes	—
397	#117	C₂³×C₁₇	1	4	yes	—
398	#117	C₂³×C₁₇	1	4	yes	—
399	#117	C₂³×C₁₇	1	4	yes	—
400	#117	C₂³×C₁₇	1	4	yes	—
401	#117	C₂³×C₁₇	1	4	yes	—
402	#117	C₂³×C₁₇	1	4	yes	—
403	#117	C₂³×C₁₇	1	4	yes	—
404	#117	C₂³×C₁₇	1	32	yes	—
405	#117	C₂³×C₁₇	1	4	yes	—
406	#117	C₂³×C₁₇	1	16	yes	—
407	#117	C₂³×C₁₇	1	16	yes	—
408	#117	C₂³×C₁₇	1	16	yes	—
409	#117	C₂³×C₁₇	1	64	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₇	1	16	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₇	1	16	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₇	1	16	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₇	1	16	yes	—
421	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
422	C₂×C₄²	C₂³×C₁₇	1	8	yes	—
423	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
425	C₂×C₄²	C₂³×C₁₇	1	16	yes	—
426	C₁₇	#62860	1	1	yes	characteristic, direct product factor, Sylow
427	C₂⁴	C₂⁴×C₁₇	1	4	yes	—
428	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
429	#41	—	2	16	no	—
430	#41	—	2	16	no	—
431	#41	—	2	16	no	—
432	#41	—	2	16	no	—
433	C₂×Q₈	—	2	16	no	—
434	C₂×Q₈	—	2	16	no	—
435	C₂×Q₈	—	2	8	no	—
436	C₂×Q₈	—	2	8	no	—
437	C₂×Q₈	—	2	8	no	—
438	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
439	C₂×Q₈	C₂⁴×C₁₇	1	8	yes	—
440	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
441	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
442	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
443	C₂×Q₈	C₂⁴×C₁₇	1	16	yes	—
444	C₂×D₄	—	2	16	no	—
445	C₂×D₄	—	2	8	no	—
446	C₂×D₄	C₂⁴×C₁₇	1	8	yes	—
447	C₂×D₄	C₂⁴×C₁₇	1	8	yes	—
448	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
449	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
450	C₂×D₄	C₂⁴×C₁₇	1	16	yes	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	16	no	—
453	C₂²×C₄	#41×C₁₇	1	8	yes	—
454	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
456	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
457	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
459	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
460	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
462	C₂²×C₄	C₂⁴×C₁₇	1	32	yes	—
463	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
464	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
467	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
468	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
469	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
471	C₄⋊C₄	C₂⁴×C₁₇	1	32	yes	—
472	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
473	C₄⋊C₄	C₂⁴×C₁₇	1	32	yes	—
474	C₄⋊C₄	C₂⁴×C₁₇	1	64	yes	—
475	C₄⋊C₄	C₂⁴×C₁₇	1	32	yes	—
476	C₄⋊C₄	C₂⁴×C₁₇	1	16	yes	—
477	C₄⋊C₄	C₂⁴×C₁₇	1	16	yes	—
478	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
479	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
480	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
481	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
482	C₂²⋊C₄	C₂⁴×C₁₇	1	32	yes	—
483	C₂²⋊C₄	C₂⁴×C₁₇	1	64	yes	—
484	C₂²⋊C₄	C₂⁴×C₁₇	1	32	yes	—
485	C₄²	C₂⁴×C₁₇	1	8	yes	—
486	C₄²	C₂⁴×C₁₇	1	8	yes	—
487	C₄²	C₂⁴×C₁₇	1	32	yes	—
488	C₄²	C₂⁴×C₁₇	1	32	yes	—
489	C₄²	C₂⁴×C₁₇	1	4	yes	—
490	C₄²	C₂⁴×C₁₇	1	8	yes	—
491	C₄²	C₂⁴×C₁₇	1	4	yes	—
492	C₂³	—	2	8	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	8	no	—
495	C₂³	C₂×#41×C₁₇	1	4	yes	—
496	C₂³	C₂⁵×C₁₇	1	8	yes	—
497	C₂³	C₂⁵×C₁₇	1	2	yes	—
498	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
499	Q₈	—	2	8	no	—
500	Q₈	—	2	16	no	—
501	Q₈	—	2	8	no	—
502	Q₈	—	2	8	no	—
503	Q₈	—	2	8	no	—
504	Q₈	—	4	16	no	—
505	D₄	—	2	16	no	—
506	D₄	—	2	16	no	—
507	D₄	—	2	8	no	—
508	D₄	—	2	8	no	—
509	D₄	—	4	16	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	2	16	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	16	no	—
514	C₂×C₄	—	2	16	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	32	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	C₂×#41×C₁₇	1	8	yes	—
520	C₂×C₄	C₂×#41×C₁₇	1	8	yes	—
521	C₂×C₄	C₂×#41×C₁₇	1	4	yes	—
522	C₂×C₄	C₂×#41×C₁₇	1	4	yes	—
523	C₂×C₄	C₂⁵×C₁₇	1	8	yes	—
524	C₂×C₄	C₂⁵×C₁₇	1	8	yes	—
525	C₂×C₄	C₂⁵×C₁₇	1	16	yes	—
526	C₂×C₄	C₂⁵×C₁₇	1	8	yes	—
527	C₂×C₄	C₂⁵×C₁₇	1	8	yes	—
528	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
529	C₂×C₄	C₂⁵×C₁₇	1	2	yes	—
530	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
531	C₂²	—	2	2	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	8	no	—
534	C₂²	—	2	16	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	8	8	no	—
537	C₂²	C₂²×#41×C₁₇	1	4	yes	—
538	C₂²	C₂²×#41×C₁₇	1	2	yes	—
539	C₂²	C₂⁶×C₁₇	1	1	yes	characteristic
540	C₄	—	2	8	no	—
541	C₄	—	2	8	no	—
542	C₄	—	2	8	no	—
543	C₄	—	2	16	no	—
544	C₄	—	2	8	no	—
545	C₄	C₂²×#41×C₁₇	1	2	yes	—
546	C₄	C₂²×#41×C₁₇	1	4	yes	—
547	C₄	C₂²×#41×C₁₇	1	2	yes	—
548	C₂	—	2	4	no	—
549	C₂	—	2	2	no	—
550	C₂	—	4	8	no	—
551	C₂	C₂³×#41×C₁₇	1	1	yes	characteristic
552	C₂	C₁₇×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₇
prime radical	C₁₇×#3449	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3510	C₂	semidirect
2. C₁₇×#3509	C₂	semidirect
3. C₁₇×#3507	C₂	semidirect
4. C₁₇×#3495	C₂	semidirect
5. C₁₇×#3491	C₂	semidirect
6. C₁₇×#3461	C₂	semidirect
7. C₁₇×#3458	C₂	semidirect
9. C₂×C₁₇×#536	C₂	semidirect
10. C₁₇×#3428	C₂	semidirect
11. C₂×C₁₇×#519	C₂	semidirect
14. C₁₇×#559	C₂²	semidirect
15. C₁₇×#557	C₂²	semidirect
16. C₁₇×#556	C₂²	semidirect
17. C₁₇×#556	C₂²	semidirect
18. C₁₇×#554	C₂²	semidirect
19. C₁₇×#552	C₂²	semidirect
20. C₁₇×#552	C₂²	semidirect
21. C₁₇×#551	C₂²	semidirect
22. C₁₇×#544	C₂²	semidirect
23. C₁₇×#544	C₂²	semidirect
25. C₁₇×#542	C₂²	semidirect
26. C₁₇×#541	C₂²	semidirect
27. C₁₇×#539	C₂²	semidirect
32. C₁₇×#536	C₂²	semidirect
33. C₁₇×#536	C₂²	semidirect
36. C₁₇×#533	C₂²	semidirect
37. C₁₇×#533	C₂²	semidirect
38. C₁₇×#533	C₂²	semidirect
40. C₂×C₁₇×C₄⋊Q₈	C₂²	semidirect
41. C₁₇×#529	C₂²	semidirect
42. C₁₇×#529	C₂²	semidirect
43. C₂×C₁₇×#124	C₂²	semidirect
46. C₂×C₁₇×C₂²⋊Q₈	C₂²	semidirect
48. C₁₇×#520	C₂²	semidirect
49. C₁₇×#519	C₂²	semidirect
50. C₁₇×#519	C₂²	semidirect
51. C₁₇×#519	C₂²	semidirect
53. C₁₇×#518	C₂²	semidirect
55. C₄×#41×C₁₇	C₂²	semidirect
56. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
57. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
62. C₂×C₁₇×#117	C₂²	semidirect
215. #62860	C₁₇	direct (N × H)
255. #3510	C₂×C₁₇	semidirect
256. #3509	C₂×C₁₇	semidirect
257. #3507	C₂×C₁₇	semidirect
258. #3495	C₂×C₁₇	semidirect
259. #3491	C₂×C₁₇	semidirect
260. #3461	C₂×C₁₇	semidirect
261. #3458	C₂×C₁₇	semidirect
263. C₂×#536	C₂×C₁₇	semidirect
264. #3428	C₂×C₁₇	semidirect
265. C₂×#519	C₂×C₁₇	semidirect
285. #559	C₂²×C₁₇	semidirect
286. #557	C₂²×C₁₇	semidirect
287. #556	C₂²×C₁₇	semidirect
288. #556	C₂²×C₁₇	semidirect
289. #554	C₂²×C₁₇	semidirect
290. #552	C₂²×C₁₇	semidirect
291. #552	C₂²×C₁₇	semidirect
292. #551	C₂²×C₁₇	semidirect
293. #544	C₂²×C₁₇	semidirect
294. #544	C₂²×C₁₇	semidirect
296. #542	C₂²×C₁₇	semidirect
297. #541	C₂²×C₁₇	semidirect
298. #539	C₂²×C₁₇	semidirect
303. #536	C₂²×C₁₇	semidirect
304. #536	C₂²×C₁₇	semidirect
307. #533	C₂²×C₁₇	semidirect
308. #533	C₂²×C₁₇	semidirect
309. #533	C₂²×C₁₇	semidirect
311. C₂×C₄⋊Q₈	C₂²×C₁₇	semidirect
312. #529	C₂²×C₁₇	semidirect
313. #529	C₂²×C₁₇	semidirect
314. C₂×#124	C₂²×C₁₇	semidirect
317. C₂×C₂²⋊Q₈	C₂²×C₁₇	semidirect
319. #520	C₂²×C₁₇	semidirect
320. #519	C₂²×C₁₇	semidirect
321. #519	C₂²×C₁₇	semidirect
322. #519	C₂²×C₁₇	semidirect
324. #518	C₂²×C₁₇	semidirect
326. C₄×#41	C₂²×C₁₇	semidirect
327. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
328. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
333. C₂×#117	C₂²×C₁₇	semidirect
426. C₁₇	#62860	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×#3510	2
C₁₇×#3509	2
C₁₇×#3507	2
C₁₇×#3495	2
C₁₇×#3491	2
C₁₇×#3461	2
C₁₇×#3458	2
C₁₇×#3449	2
C₂×C₁₇×#536	2
C₁₇×#3428	2
C₂×C₁₇×#519	2
#62860	17

Subgroups — C17×#62860 #16920604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#62860 #16920604