Subgroups — C₁₇×#22693 #16880437

Order 4352.

850 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#444	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2952	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2951	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2912	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1951	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1860	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1860	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1859	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1859	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1847	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1816	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1815	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1773	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
17	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
19	C₁₇×#520	C₂²	1	1	yes	characteristic
20	C₁₇×#520	C₂²	1	1	yes	characteristic
21	C₁₇×#520	C₂²	1	1	yes	characteristic
22	C₁₇×#520	C₂²	1	1	yes	characteristic
23	C₁₇×#444	C₄	1	8	yes	complemented
24	C₁₇×#442	—	2	1	no	—
25	C₁₇×#441	—	2	1	no	—
26	C₁₇×#440	—	2	1	no	—
27	C₁₇×#440	—	2	1	no	—
28	C₄×Q₁₆×C₁₇	—	2	1	no	—
29	C₄×SD₁₆×C₁₇	—	2	1	no	—
30	C₄×SD₁₆×C₁₇	—	2	1	no	—
31	C₄×D₈×C₁₇	—	2	1	no	—
32	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
33	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
34	C₁₇×#428	—	2	1	no	—
35	C₁₇×#428	—	2	1	no	—
36	C₁₇×#428	—	2	1	no	—
37	C₁₇×#428	—	2	1	no	—
38	C₁₇×#428	C₂²	1	1	yes	characteristic
39	C₁₇×#428	C₂²	1	1	yes	characteristic
40	C₁₇×#428	C₂²	1	1	yes	characteristic
41	C₁₇×#428	C₂²	1	1	yes	characteristic
42	C₁₇×#427	—	2	1	no	—
43	C₁₇×#427	—	2	1	no	—
44	C₁₇×#427	C₂²	1	1	yes	characteristic
45	C₂×C₁₇×#107	—	2	1	no	—
46	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
47	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
48	C₂×C₁₇×#106	—	2	1	no	—
49	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
50	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
51	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
52	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
53	C₁₇×#417	C₂²	1	1	yes	characteristic
54	C₁₇×#417	C₂²	1	1	yes	characteristic
55	C₁₇×#417	C₂²	1	1	yes	characteristic
56	C₁₇×#417	C₂²	1	1	yes	characteristic
57	C₁₇×#405	C₂²	1	1	yes	characteristic
58	C₁₇×#405	C₂²	1	1	yes	characteristic
59	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
60	C₁₇×#384	C₂²	1	1	yes	characteristic
61	C₁₇×#382	C₂²	1	1	yes	characteristic
62	C₁₇×#343	C₂²	1	1	yes	characteristic
63	C₁₇×#343	C₂²	1	1	yes	characteristic
64	C₁₇×#343	C₂²	1	1	yes	characteristic
65	C₁₇×#343	C₂²	1	1	yes	characteristic
66	C₁₇×#339	C₂²	1	1	yes	characteristic
67	C₁₇×#339	C₂²	1	1	yes	characteristic
68	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
69	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
70	C₁₇×#135	C₂×C₄	1	4	yes	—
71	C₁₇×#135	Q₈	1	4	yes	—
72	C₂×Q₁₆×C₁₇	D₄	1	1	yes	characteristic
73	C₂×SD₁₆×C₁₇	D₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₁₇	D₄	1	1	yes	characteristic
75	C₂×D₈×C₁₇	D₄	1	1	yes	characteristic
76	C₁₇×#131	—	2	2	no	—
77	C₁₇×#131	—	2	2	no	—
78	C₁₇×#131	C₂×C₄	1	4	yes	complemented
79	C₁₇×#131	C₂×C₄	1	4	yes	complemented
80	C₂×M₁₆×C₁₇	—	2	1	no	—
81	C₂×M₁₆×C₁₇	—	2	1	no	—
82	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₇	—	2	1	no	—
87	C₂²×C₈×C₁₇	—	2	1	no	—
88	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
90	C₄×Q₈×C₁₇	—	2	1	no	—
91	C₄×Q₈×C₁₇	—	2	1	no	—
92	C₄×Q₈×C₁₇	—	2	1	no	—
93	C₄×Q₈×C₁₇	—	2	1	no	—
94	C₄×D₄×C₁₇	—	2	1	no	—
95	C₄×D₄×C₁₇	—	2	1	no	—
96	C₄×D₄×C₁₇	—	2	1	no	—
97	C₄×D₄×C₁₇	—	2	1	no	—
98	C₄×D₄×C₁₇	—	4	1	no	—
99	C₄×D₄×C₁₇	—	4	1	no	—
100	C₄×D₄×C₁₇	—	4	1	no	—
101	C₄×D₄×C₁₇	—	4	1	no	—
102	C₁₇×#117	—	2	1	no	—
103	C₁₇×#117	—	2	1	no	—
104	C₁₇×#117	—	2	1	no	—
105	C₁₇×#117	—	2	1	no	—
106	C₁₇×#117	C₂³	1	1	yes	characteristic
107	C₁₇×#117	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₇	—	4	1	no	—
113	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
118	C₁₇×#108	—	2	2	no	—
119	C₁₇×#108	C₂×C₄	1	4	yes	complemented
120	C₁₇×#107	—	2	1	no	—
121	C₁₇×#107	—	2	1	no	—
122	C₁₇×#107	—	2	1	no	—
123	C₁₇×#107	—	2	1	no	—
124	C₁₇×#107	—	2	1	no	—
125	C₁₇×#107	—	2	1	no	—
126	C₁₇×#107	—	2	1	no	—
127	C₁₇×#107	—	2	1	no	—
128	C₁₇×#107	D₄	1	1	yes	characteristic
129	C₁₇×#107	D₄	1	1	yes	characteristic
130	C₁₇×#106	—	2	1	no	—
131	C₁₇×#106	—	2	1	no	—
132	C₁₇×#106	—	2	1	no	—
133	C₁₇×#106	—	2	1	no	—
134	C₁₇×#106	—	2	1	no	—
135	C₁₇×#106	—	2	1	no	—
136	C₁₇×#106	—	2	1	no	—
137	C₁₇×#106	—	2	1	no	—
138	C₁₇×#106	D₄	1	1	yes	characteristic
139	C₁₇×#106	D₄	1	1	yes	characteristic
140	C₁₇×#104	C₂×C₄	1	4	yes	complemented
141	C₁₇×#104	C₂×C₄	1	4	yes	complemented
142	C₁₇×#103	—	2	1	no	—
143	C₁₇×#103	—	2	1	no	—
144	C₁₇×#103	—	2	1	no	—
145	C₁₇×#103	—	2	1	no	—
146	C₁₇×#102	—	2	1	no	—
147	C₁₇×#102	—	2	1	no	—
148	C₁₇×#102	—	2	1	no	—
149	C₁₇×#102	—	2	1	no	—
150	C₁₇×#97	—	2	1	no	—
151	C₁₇×#97	—	2	1	no	—
152	C₁₇×#97	C₂×C₄	1	4	yes	complemented
153	C₄×C₈×C₁₇	—	2	1	no	—
154	C₄×C₈×C₁₇	—	2	1	no	—
155	C₁₇×#95	—	4	1	no	—
156	#41×C₁₇	—	2	1	no	—
157	#41×C₁₇	—	2	1	no	—
158	#41×C₁₇	—	2	1	no	—
159	#41×C₁₇	—	2	1	no	—
160	#41×C₁₇	C₂²×C₄	1	2	yes	—
161	#41×C₁₇	C₂²×C₄	1	2	yes	—
162	#41×C₁₇	C₂×Q₈	1	2	yes	—
163	#41×C₁₇	C₂×Q₈	1	2	yes	—
164	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
165	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₁₇	—	2	1	no	—
167	C₂×D₄×C₁₇	—	2	1	no	—
168	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
169	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₇	—	2	1	no	—
171	C₂²×C₄×C₁₇	—	2	1	no	—
172	C₂²×C₄×C₁₇	—	2	1	no	—
173	C₂²×C₄×C₁₇	—	2	1	no	—
174	C₂²×C₄×C₁₇	—	2	1	no	—
175	C₂²×C₄×C₁₇	—	2	1	no	—
176	C₂²×C₄×C₁₇	—	2	1	no	—
177	C₂²×C₄×C₁₇	—	4	1	no	—
178	C₂²×C₄×C₁₇	—	4	1	no	—
179	C₂²×C₄×C₁₇	—	4	1	no	—
180	C₂²×C₄×C₁₇	—	4	1	no	—
181	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
182	Q₁₆×C₁₇	C₄⋊C₄	1	4	yes	complemented
183	SD₁₆×C₁₇	C₄⋊C₄	1	4	yes	complemented
184	SD₁₆×C₁₇	C₄⋊C₄	1	4	yes	complemented
185	D₈×C₁₇	C₄⋊C₄	1	4	yes	complemented
186	M₁₆×C₁₇	—	2	1	no	—
187	M₁₆×C₁₇	—	2	1	no	—
188	M₁₆×C₁₇	—	2	4	no	—
189	M₁₆×C₁₇	—	2	4	no	—
190	M₁₆×C₁₇	—	2	1	no	—
191	M₁₆×C₁₇	—	2	1	no	—
192	M₁₆×C₁₇	—	2	1	no	—
193	M₁₆×C₁₇	—	2	1	no	—
194	M₁₆×C₁₇	C₂²×C₄	1	2	yes	—
195	M₁₆×C₁₇	C₂²×C₄	1	2	yes	—
196	C₂×C₈×C₁₇	—	2	1	no	—
197	C₂×C₈×C₁₇	—	2	1	no	—
198	C₂×C₈×C₁₇	—	2	4	no	—
199	C₂×C₈×C₁₇	—	2	4	no	—
200	C₂×C₈×C₁₇	—	2	1	no	—
201	C₂×C₈×C₁₇	—	2	1	no	—
202	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
203	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
204	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
205	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
206	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
209	C₂×C₈×C₁₇	#41	1	2	yes	—
210	C₄⋊C₄×C₁₇	—	2	1	no	—
211	C₄⋊C₄×C₁₇	—	2	1	no	—
212	C₄⋊C₄×C₁₇	—	2	1	no	—
213	C₄⋊C₄×C₁₇	—	2	1	no	—
214	C₄⋊C₄×C₁₇	—	2	1	no	—
215	C₄⋊C₄×C₁₇	—	2	1	no	—
216	C₄⋊C₄×C₁₇	—	2	1	no	—
217	C₄⋊C₄×C₁₇	—	2	1	no	—
218	C₄⋊C₄×C₁₇	—	4	1	no	—
219	C₄⋊C₄×C₁₇	—	4	1	no	—
220	C₄⋊C₄×C₁₇	—	4	1	no	—
221	C₄⋊C₄×C₁₇	—	4	1	no	—
222	C₄⋊C₄×C₁₇	—	8	2	no	—
223	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
224	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
225	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
226	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
227	C₂²⋊C₄×C₁₇	—	2	1	no	—
228	C₂²⋊C₄×C₁₇	—	2	1	no	—
229	C₂²⋊C₄×C₁₇	—	4	1	no	—
230	C₂²⋊C₄×C₁₇	—	4	1	no	—
231	C₂²⋊C₄×C₁₇	—	4	1	no	—
232	C₂²⋊C₄×C₁₇	—	4	1	no	—
233	C₄²×C₁₇	—	2	1	no	—
234	C₄²×C₁₇	—	2	1	no	—
235	C₄²×C₁₇	—	2	1	no	—
236	C₄²×C₁₇	—	4	1	no	—
237	C₄²×C₁₇	—	4	1	no	—
238	C₄²×C₁₇	—	4	1	no	—
239	C₄²×C₁₇	—	4	1	no	—
240	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
241	#22693	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂³×C₁₇	—	2	1	no	—
243	C₂³×C₁₇	—	2	1	no	—
244	C₂³×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
245	Q₈×C₁₇	—	2	1	no	—
246	Q₈×C₁₇	—	2	1	no	—
247	Q₈×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
248	Q₈×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
249	D₄×C₁₇	—	2	2	no	—
250	D₄×C₁₇	—	2	2	no	—
251	D₄×C₁₇	—	2	2	no	—
252	D₄×C₁₇	—	2	2	no	—
253	D₄×C₁₇	—	2	1	no	—
254	D₄×C₁₇	—	2	1	no	—
255	D₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
256	D₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
257	C₂×C₄×C₁₇	—	2	1	no	—
258	C₂×C₄×C₁₇	—	2	1	no	—
259	C₂×C₄×C₁₇	—	2	2	no	—
260	C₂×C₄×C₁₇	—	2	2	no	—
261	C₂×C₄×C₁₇	—	2	2	no	—
262	C₂×C₄×C₁₇	—	2	2	no	—
263	C₂×C₄×C₁₇	—	2	2	no	—
264	C₂×C₄×C₁₇	—	2	1	no	—
265	C₂×C₄×C₁₇	—	2	1	no	—
266	C₂×C₄×C₁₇	—	2	1	no	—
267	C₂×C₄×C₁₇	—	2	1	no	—
268	C₂×C₄×C₁₇	—	4	1	no	—
269	C₂×C₄×C₁₇	—	4	1	no	—
270	C₂×C₄×C₁₇	—	4	1	no	—
271	C₂×C₄×C₁₇	—	4	1	no	—
272	C₂×C₄×C₁₇	—	4	1	no	—
273	C₂×C₄×C₁₇	—	4	1	no	—
274	C₂×C₄×C₁₇	—	8	1	no	—
275	C₂×C₄×C₁₇	—	8	1	no	—
276	C₂×C₄×C₁₇	—	8	1	no	—
277	C₂×C₄×C₁₇	—	8	1	no	—
278	C₂×C₄×C₁₇	—	16	1	no	—
279	C₂×C₄×C₁₇	—	16	1	no	—
280	C₂×C₄×C₁₇	—	16	1	no	—
281	C₂×C₄×C₁₇	—	16	1	no	—
282	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
283	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
286	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
288	C₈×C₁₇	—	2	2	no	—
289	C₈×C₁₇	—	2	2	no	—
290	C₈×C₁₇	—	4	1	no	—
291	C₈×C₁₇	—	4	1	no	—
292	C₈×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
293	C₈×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
294	C₈×C₁₇	C₄×D₄	1	2	yes	—
295	C₈×C₁₇	C₄×D₄	1	2	yes	—
296	C₂×#444	C₂×C₁₇	1	1	yes	characteristic
297	#2952	C₂×C₁₇	1	1	yes	characteristic
298	#2951	C₂×C₁₇	1	1	yes	characteristic
299	#2913	C₂×C₁₇	1	1	yes	characteristic, complemented
300	#2912	C₂×C₁₇	1	1	yes	characteristic, complemented
301	#1952	C₂×C₁₇	1	1	yes	characteristic, complemented
302	#1951	C₂×C₁₇	1	1	yes	characteristic, complemented
303	#1860	C₂×C₁₇	1	1	yes	characteristic, complemented
304	#1860	C₂×C₁₇	1	1	yes	characteristic, complemented
305	#1859	C₂×C₁₇	1	1	yes	characteristic, complemented
306	#1859	C₂×C₁₇	1	1	yes	characteristic, complemented
307	#1847	C₂×C₁₇	1	1	yes	characteristic, complemented
308	#1816	C₂×C₁₇	1	1	yes	characteristic, complemented
309	#1815	C₂×C₁₇	1	1	yes	characteristic, complemented
310	#1773	C₂×C₁₇	1	1	yes	characteristic, complemented
311	C₂²×C₁₇	—	2	1	no	—
312	C₂²×C₁₇	—	2	1	no	—
313	C₂²×C₁₇	—	2	2	no	—
314	C₂²×C₁₇	—	2	2	no	—
315	C₂²×C₁₇	—	4	1	no	—
316	C₂²×C₁₇	—	4	1	no	—
317	C₂²×C₁₇	—	4	1	no	—
318	C₂²×C₁₇	—	4	1	no	—
319	C₂²×C₁₇	#520	1	1	yes	characteristic
320	C₂²×C₁₇	D₄²	1	1	yes	characteristic
321	C₂²×C₁₇	#554	1	1	yes	characteristic
322	C₄×C₁₇	—	2	2	no	—
323	C₄×C₁₇	—	2	2	no	—
324	C₄×C₁₇	—	4	2	no	—
325	C₄×C₁₇	—	4	1	no	—
326	C₄×C₁₇	—	4	1	no	—
327	C₄×C₁₇	—	4	1	no	—
328	C₄×C₁₇	—	4	1	no	—
329	C₄×C₁₇	—	8	1	no	—
330	C₄×C₁₇	—	8	1	no	—
331	C₄×C₁₇	—	8	1	no	—
332	C₄×C₁₇	—	8	1	no	—
333	C₄×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
334	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
335	C₄×C₁₇	#547	1	1	yes	characteristic
336	C₄×C₁₇	D₄×Q₈	1	1	yes	characteristic
337	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
338	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
339	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
340	#520	C₂²×C₁₇	1	1	yes	characteristic
341	#520	C₂²×C₁₇	1	1	yes	characteristic
342	#520	C₂²×C₁₇	1	1	yes	characteristic
343	#520	C₂²×C₁₇	1	1	yes	characteristic
344	#444	C₄×C₁₇	1	8	yes	complemented
345	#442	—	2	1	no	—
346	#441	—	2	1	no	—
347	#440	—	2	1	no	—
348	#440	—	2	1	no	—
349	C₄×Q₁₆	—	2	1	no	—
350	C₄×SD₁₆	—	2	1	no	—
351	C₄×SD₁₆	—	2	1	no	—
352	C₄×D₈	—	2	1	no	—
353	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
354	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
355	#428	—	2	1	no	—
356	#428	—	2	1	no	—
357	#428	—	2	1	no	—
358	#428	—	2	1	no	—
359	#428	C₂²×C₁₇	1	1	yes	characteristic
360	#428	C₂²×C₁₇	1	1	yes	characteristic
361	#428	C₂²×C₁₇	1	1	yes	characteristic
362	#428	C₂²×C₁₇	1	1	yes	characteristic
363	#427	—	2	1	no	—
364	#427	—	2	1	no	—
365	#427	C₂²×C₁₇	1	1	yes	characteristic
366	C₂×#107	—	2	1	no	—
367	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
368	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
369	C₂×#106	—	2	1	no	—
370	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
371	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
372	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
373	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
374	#417	C₂²×C₁₇	1	1	yes	characteristic
375	#417	C₂²×C₁₇	1	1	yes	characteristic
376	#417	C₂²×C₁₇	1	1	yes	characteristic
377	#417	C₂²×C₁₇	1	1	yes	characteristic
378	#405	C₂²×C₁₇	1	1	yes	characteristic
379	#405	C₂²×C₁₇	1	1	yes	characteristic
380	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
381	#384	C₂²×C₁₇	1	1	yes	characteristic
382	#382	C₂²×C₁₇	1	1	yes	characteristic
383	#343	C₂²×C₁₇	1	1	yes	characteristic
384	#343	C₂²×C₁₇	1	1	yes	characteristic
385	#343	C₂²×C₁₇	1	1	yes	characteristic
386	#343	C₂²×C₁₇	1	1	yes	characteristic
387	#339	C₂²×C₁₇	1	1	yes	characteristic
388	#339	C₂²×C₁₇	1	1	yes	characteristic
389	C₂×C₁₇	—	2	1	no	—
390	C₂×C₁₇	—	2	1	no	—
391	C₂×C₁₇	—	4	2	no	—
392	C₂×C₁₇	—	4	2	no	—
393	C₂×C₁₇	D₄×C₄⋊C₄	1	1	yes	characteristic
394	C₂×C₁₇	#3288	1	1	yes	characteristic
395	C₂×C₁₇	#3289	1	1	yes	characteristic
396	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
397	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
398	#135	C₂×C₄×C₁₇	1	4	yes	—
399	#135	Q₈×C₁₇	1	4	yes	—
400	C₂×Q₁₆	D₄×C₁₇	1	1	yes	characteristic
401	C₂×SD₁₆	D₄×C₁₇	1	1	yes	characteristic
402	C₂×SD₁₆	D₄×C₁₇	1	1	yes	characteristic
403	C₂×D₈	D₄×C₁₇	1	1	yes	characteristic
404	#131	—	2	2	no	—
405	#131	—	2	2	no	—
406	#131	C₂×C₄×C₁₇	1	4	yes	complemented
407	#131	C₂×C₄×C₁₇	1	4	yes	complemented
408	C₂×M₁₆	—	2	1	no	—
409	C₂×M₁₆	—	2	1	no	—
410	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
411	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
412	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
413	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
414	C₂²×C₈	—	2	1	no	—
415	C₂²×C₈	—	2	1	no	—
416	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
418	C₄×Q₈	—	2	1	no	—
419	C₄×Q₈	—	2	1	no	—
420	C₄×Q₈	—	2	1	no	—
421	C₄×Q₈	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	—	2	1	no	—
425	C₄×D₄	—	2	1	no	—
426	C₄×D₄	—	4	1	no	—
427	C₄×D₄	—	4	1	no	—
428	C₄×D₄	—	4	1	no	—
429	C₄×D₄	—	4	1	no	—
430	#117	—	2	1	no	—
431	#117	—	2	1	no	—
432	#117	—	2	1	no	—
433	#117	—	2	1	no	—
434	#117	C₂³×C₁₇	1	1	yes	characteristic
435	#117	C₂³×C₁₇	1	1	yes	characteristic
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	—	4	1	no	—
441	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
446	#108	—	2	2	no	—
447	#108	C₂×C₄×C₁₇	1	4	yes	complemented
448	#107	—	2	1	no	—
449	#107	—	2	1	no	—
450	#107	—	2	1	no	—
451	#107	—	2	1	no	—
452	#107	—	2	1	no	—
453	#107	—	2	1	no	—
454	#107	—	2	1	no	—
455	#107	—	2	1	no	—
456	#107	D₄×C₁₇	1	1	yes	characteristic
457	#107	D₄×C₁₇	1	1	yes	characteristic
458	#106	—	2	1	no	—
459	#106	—	2	1	no	—
460	#106	—	2	1	no	—
461	#106	—	2	1	no	—
462	#106	—	2	1	no	—
463	#106	—	2	1	no	—
464	#106	—	2	1	no	—
465	#106	—	2	1	no	—
466	#106	D₄×C₁₇	1	1	yes	characteristic
467	#106	D₄×C₁₇	1	1	yes	characteristic
468	#104	C₂×C₄×C₁₇	1	4	yes	complemented
469	#104	C₂×C₄×C₁₇	1	4	yes	complemented
470	#103	—	2	1	no	—
471	#103	—	2	1	no	—
472	#103	—	2	1	no	—
473	#103	—	2	1	no	—
474	#102	—	2	1	no	—
475	#102	—	2	1	no	—
476	#102	—	2	1	no	—
477	#102	—	2	1	no	—
478	#97	—	2	1	no	—
479	#97	—	2	1	no	—
480	#97	C₂×C₄×C₁₇	1	4	yes	complemented
481	C₄×C₈	—	2	1	no	—
482	C₄×C₈	—	2	1	no	—
483	#95	—	4	1	no	—
484	C₁₇	#22693	1	1	yes	characteristic, direct product factor, Sylow
485	#41	—	2	1	no	—
486	#41	—	2	1	no	—
487	#41	—	2	1	no	—
488	#41	—	2	1	no	—
489	#41	C₂²×C₄×C₁₇	1	2	yes	—
490	#41	C₂²×C₄×C₁₇	1	2	yes	—
491	#41	C₂×Q₈×C₁₇	1	2	yes	—
492	#41	C₂×Q₈×C₁₇	1	2	yes	—
493	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
494	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
498	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	4	1	no	—
507	C₂²×C₄	—	4	1	no	—
508	C₂²×C₄	—	4	1	no	—
509	C₂²×C₄	—	4	1	no	—
510	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
511	Q₁₆	C₄⋊C₄×C₁₇	1	4	yes	complemented
512	SD₁₆	C₄⋊C₄×C₁₇	1	4	yes	complemented
513	SD₁₆	C₄⋊C₄×C₁₇	1	4	yes	complemented
514	D₈	C₄⋊C₄×C₁₇	1	4	yes	complemented
515	M₁₆	—	2	1	no	—
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	4	no	—
518	M₁₆	—	2	4	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	C₂²×C₄×C₁₇	1	2	yes	—
524	M₁₆	C₂²×C₄×C₁₇	1	2	yes	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	4	no	—
528	C₂×C₈	—	2	4	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
532	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
533	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
534	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
535	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
536	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
537	C₂×C₈	C₂×Q₈×C₁₇	1	2	yes	—
538	C₂×C₈	#41×C₁₇	1	2	yes	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	4	1	no	—
548	C₄⋊C₄	—	4	1	no	—
549	C₄⋊C₄	—	4	1	no	—
550	C₄⋊C₄	—	4	1	no	—
551	C₄⋊C₄	—	8	2	no	—
552	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
553	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
554	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
555	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
556	C₂²⋊C₄	—	2	1	no	—
557	C₂²⋊C₄	—	2	1	no	—
558	C₂²⋊C₄	—	4	1	no	—
559	C₂²⋊C₄	—	4	1	no	—
560	C₂²⋊C₄	—	4	1	no	—
561	C₂²⋊C₄	—	4	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	4	1	no	—
566	C₄²	—	4	1	no	—
567	C₄²	—	4	1	no	—
568	C₄²	—	4	1	no	—
569	C₄²	C₂²×C₄×C₁₇	1	2	yes	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
573	Q₈	—	2	1	no	—
574	Q₈	—	2	1	no	—
575	Q₈	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
576	Q₈	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	1	no	—
582	D₄	—	2	1	no	—
583	D₄	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
584	D₄	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	8	1	no	—
603	C₂×C₄	—	8	1	no	—
604	C₂×C₄	—	8	1	no	—
605	C₂×C₄	—	8	1	no	—
606	C₂×C₄	—	16	1	no	—
607	C₂×C₄	—	16	1	no	—
608	C₂×C₄	—	16	1	no	—
609	C₂×C₄	—	16	1	no	—
610	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
611	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
612	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
613	C₂×C₄	C₂²×Q₈×C₁₇	1	1	yes	characteristic
614	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
615	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
616	C₈	—	2	2	no	—
617	C₈	—	2	2	no	—
618	C₈	—	4	1	no	—
619	C₈	—	4	1	no	—
620	C₈	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
621	C₈	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
622	C₈	C₄×D₄×C₁₇	1	2	yes	—
623	C₈	C₄×D₄×C₁₇	1	2	yes	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	C₁₇×#520	1	1	yes	characteristic
633	C₂²	D₄²×C₁₇	1	1	yes	characteristic
634	C₂²	C₁₇×#554	1	1	yes	characteristic
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	8	1	no	—
643	C₄	—	8	1	no	—
644	C₄	—	8	1	no	—
645	C₄	—	8	1	no	—
646	C₄	C₂²×C₄⋊C₄×C₁₇	1	1	yes	characteristic
647	C₄	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
648	C₄	C₁₇×#547	1	1	yes	characteristic
649	C₄	D₄×Q₈×C₁₇	1	1	yes	characteristic
650	C₂	—	2	1	no	—
651	C₂	—	2	1	no	—
652	C₂	—	4	2	no	—
653	C₂	—	4	2	no	—
654	C₂	D₄×C₄⋊C₄×C₁₇	1	1	yes	characteristic
655	C₂	C₁₇×#3288	1	1	yes	characteristic
656	C₂	C₁₇×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₇×#2913	C₂	semidirect
5. C₁₇×#2912	C₂	semidirect
6. C₁₇×#1952	C₂	semidirect
7. C₁₇×#1951	C₂	semidirect
8. C₁₇×#1860	C₂	semidirect
9. C₁₇×#1860	C₂	semidirect
10. C₁₇×#1859	C₂	semidirect
11. C₁₇×#1859	C₂	semidirect
12. C₁₇×#1847	C₂	semidirect
13. C₁₇×#1816	C₂	semidirect
14. C₁₇×#1815	C₂	semidirect
15. C₁₇×#1773	C₂	semidirect
23. C₁₇×#444	C₄	semidirect
78. C₁₇×#131	C₂×C₄	semidirect
79. C₁₇×#131	C₂×C₄	semidirect
119. C₁₇×#108	C₂×C₄	semidirect
140. C₁₇×#104	C₂×C₄	semidirect
141. C₁₇×#104	C₂×C₄	semidirect
152. C₁₇×#97	C₂×C₄	semidirect
182. Q₁₆×C₁₇	C₄⋊C₄	semidirect
183. SD₁₆×C₁₇	C₄⋊C₄	semidirect
184. SD₁₆×C₁₇	C₄⋊C₄	semidirect
185. D₈×C₁₇	C₄⋊C₄	semidirect
241. #22693	C₁₇	direct (N × H)
299. #2913	C₂×C₁₇	semidirect
300. #2912	C₂×C₁₇	semidirect
301. #1952	C₂×C₁₇	semidirect
302. #1951	C₂×C₁₇	semidirect
303. #1860	C₂×C₁₇	semidirect
304. #1860	C₂×C₁₇	semidirect
305. #1859	C₂×C₁₇	semidirect
306. #1859	C₂×C₁₇	semidirect
307. #1847	C₂×C₁₇	semidirect
308. #1816	C₂×C₁₇	semidirect
309. #1815	C₂×C₁₇	semidirect
310. #1773	C₂×C₁₇	semidirect
344. #444	C₄×C₁₇	semidirect
406. #131	C₂×C₄×C₁₇	semidirect
407. #131	C₂×C₄×C₁₇	semidirect
447. #108	C₂×C₄×C₁₇	semidirect
468. #104	C₂×C₄×C₁₇	semidirect
469. #104	C₂×C₄×C₁₇	semidirect
480. #97	C₂×C₄×C₁₇	semidirect
484. C₁₇	#22693	direct (N × H)
511. Q₁₆	C₄⋊C₄×C₁₇	semidirect
512. SD₁₆	C₄⋊C₄×C₁₇	semidirect
513. SD₁₆	C₄⋊C₄×C₁₇	semidirect
514. D₈	C₄⋊C₄×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#444	2
C₁₇×#2952	2
C₁₇×#2951	2
C₁₇×#2913	2
C₁₇×#2912	2
C₁₇×#1952	2
C₁₇×#1951	2
C₁₇×#1860	2
C₁₇×#1859	2
C₁₇×#1847	2
C₁₇×#1816	2
C₁₇×#1815	2
C₁₇×#1773	2
#22693	17

Subgroups — C17×#22693 #16880437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22693 #16880437