Subgroups — C₁₇×#24801 #16882545

Order 4352.

866 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#471	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3057	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3045	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₇×#444	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#2038	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2037	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1946	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1883	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1882	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1816	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
22	C₁₇×#536	C₂²	1	1	yes	characteristic
23	C₁₇×#535	C₂²	1	1	yes	characteristic
24	C₁₇×#520	C₂²	1	1	yes	characteristic
25	C₁₇×#520	C₂²	1	1	yes	characteristic
26	C₁₇×#471	—	2	4	no	—
27	C₁₇×#468	—	2	1	no	—
28	C₁₇×#468	—	2	1	no	—
29	C₁₇×#465	—	2	1	no	—
30	C₁₇×#465	—	2	1	no	—
31	C₁₇×#464	—	2	1	no	—
32	C₁₇×#464	—	2	1	no	—
33	C₁₇×#463	—	2	1	no	—
34	C₁₇×#463	—	2	1	no	—
35	C₁₇×#462	—	2	1	no	—
36	C₁₇×#461	—	2	1	no	—
37	C₁₇×#460	—	2	1	no	—
38	C₁₇×#459	—	2	1	no	—
39	C₁₇×#444	—	2	4	no	—
40	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
41	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
42	C₁₇×#428	—	2	1	no	—
43	C₁₇×#428	—	2	1	no	—
44	C₁₇×#428	C₂²	1	1	yes	characteristic
45	C₁₇×#428	C₂²	1	1	yes	characteristic
46	C₁₇×#427	—	2	1	no	—
47	C₁₇×#427	C₂²	1	1	yes	characteristic
48	C₂×C₁₇×#107	—	2	1	no	—
49	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
50	C₁₇×#424	C₂²	1	1	yes	characteristic
51	C₁₇×#424	C₂²	1	1	yes	characteristic
52	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
53	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
54	C₁₇×#419	C₂²	1	1	yes	characteristic
55	C₁₇×#418	C₂²	1	1	yes	characteristic
56	C₁₇×#417	C₂²	1	1	yes	characteristic
57	C₁₇×#417	C₂²	1	1	yes	characteristic
58	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
59	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
60	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic
61	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
62	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
63	C₁₇×#391	C₂²	1	1	yes	characteristic
64	C₁₇×#390	C₂²	1	1	yes	characteristic
65	C₁₇×#343	C₂²	1	1	yes	characteristic
66	C₁₇×#343	C₂²	1	1	yes	characteristic
67	C₁₇×#339	C₂²	1	1	yes	characteristic
68	C₁₇×#339	C₂²	1	1	yes	characteristic
69	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
70	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
73	C₁₇×#137	—	2	2	no	—
74	C₁₇×#137	—	2	2	no	—
75	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
76	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
77	C₁₇×#135	—	2	2	no	—
78	C₁₇×#135	—	2	2	no	—
79	C₂×Q₁₆×C₁₇	—	2	1	no	—
80	C₂×Q₁₆×C₁₇	D₄	1	1	yes	characteristic
81	C₂×SD₁₆×C₁₇	—	2	1	no	—
82	C₂×SD₁₆×C₁₇	—	2	1	no	—
83	C₂×SD₁₆×C₁₇	—	2	1	no	—
84	C₂×SD₁₆×C₁₇	—	2	1	no	—
85	C₂×SD₁₆×C₁₇	—	2	2	no	—
86	C₂×SD₁₆×C₁₇	—	2	2	no	—
87	C₂×SD₁₆×C₁₇	D₄	1	1	yes	characteristic
88	C₂×SD₁₆×C₁₇	D₄	1	1	yes	characteristic
89	C₂×D₈×C₁₇	—	2	1	no	—
90	C₂×D₈×C₁₇	D₄	1	1	yes	characteristic
91	C₁₇×#131	—	2	2	no	—
92	C₁₇×#131	—	2	2	no	—
93	C₁₇×#131	—	2	2	no	—
94	C₁₇×#131	D₄	1	4	yes	complemented
95	C₂×M₁₆×C₁₇	—	2	1	no	—
96	C₂×M₁₆×C₁₇	—	2	1	no	—
97	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₁₇	—	2	1	no	—
102	C₂²×C₈×C₁₇	—	2	1	no	—
103	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
105	C₁₇×C₄⋊Q₈	—	2	1	no	—
106	C₁₇×#127	—	2	1	no	—
107	C₁₇×#124	—	2	1	no	—
108	C₁₇×#124	—	2	1	no	—
109	C₁₇×#123	—	4	1	no	—
110	C₁₇×C₂²⋊Q₈	—	2	1	no	—
111	C₁₇×C₂²⋊Q₈	—	2	1	no	—
112	C₁₇×#121	—	2	1	no	—
113	C₁₇×#121	—	2	1	no	—
114	C₁₇×#120	—	4	1	no	—
115	C₄×Q₈×C₁₇	—	2	1	no	—
116	C₄×Q₈×C₁₇	—	2	1	no	—
117	C₄×D₄×C₁₇	—	2	1	no	—
118	C₄×D₄×C₁₇	—	2	1	no	—
119	C₄×D₄×C₁₇	—	4	1	no	—
120	C₄×D₄×C₁₇	—	4	1	no	—
121	C₁₇×#117	—	2	1	no	—
122	C₁₇×#117	—	2	1	no	—
123	C₁₇×#117	C₂³	1	1	yes	characteristic
124	C₁₇×#117	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
126	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
127	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₁₇	—	4	1	no	—
130	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
131	C₁₇×#108	—	2	2	no	—
132	C₁₇×#108	—	2	2	no	—
133	C₁₇×#107	—	2	1	no	—
134	C₁₇×#107	—	2	1	no	—
135	C₁₇×#107	—	2	1	no	—
136	C₁₇×#107	—	2	1	no	—
137	C₁₇×#107	D₄	1	1	yes	characteristic
138	C₁₇×#107	D₄	1	1	yes	characteristic
139	C₁₇×#106	—	2	1	no	—
140	C₁₇×#106	—	2	1	no	—
141	C₁₇×#106	D₄	1	1	yes	characteristic
142	C₁₇×#106	D₄	1	1	yes	characteristic
143	C₁₇×C₄⋊C₈	—	2	1	no	—
144	C₁₇×C₄⋊C₈	—	2	1	no	—
145	C₁₇×C₄⋊C₈	—	2	1	no	—
146	C₁₇×C₄⋊C₈	—	2	1	no	—
147	C₁₇×#104	—	2	2	no	—
148	C₁₇×#104	—	2	2	no	—
149	C₁₇×#103	—	2	1	no	—
150	C₁₇×#103	—	2	1	no	—
151	C₁₇×#103	—	2	1	no	—
152	C₁₇×#103	—	2	1	no	—
153	C₁₇×#103	—	2	1	no	—
154	C₁₇×#103	—	2	1	no	—
155	C₁₇×#102	—	2	1	no	—
156	C₁₇×#102	—	2	1	no	—
157	C₁₇×#102	—	2	1	no	—
158	C₁₇×#102	—	2	1	no	—
159	C₁₇×#102	—	2	1	no	—
160	C₁₇×#102	—	2	1	no	—
161	C₁₇×#101	—	2	2	no	—
162	C₁₇×#100	—	2	2	no	—
163	C₁₇×#97	—	2	2	no	—
164	C₁₇×#95	—	4	1	no	—
165	C₂⁴×C₁₇	—	2	1	no	—
166	#41×C₁₇	—	2	1	no	—
167	#41×C₁₇	—	2	1	no	—
168	#41×C₁₇	—	2	1	no	—
169	#41×C₁₇	—	2	1	no	—
170	#41×C₁₇	—	2	1	no	—
171	#41×C₁₇	—	2	1	no	—
172	#41×C₁₇	C₂×D₄	1	2	yes	—
173	#41×C₁₇	#41	1	2	yes	—
174	C₂×Q₈×C₁₇	—	2	1	no	—
175	C₂×Q₈×C₁₇	—	2	1	no	—
176	C₂×Q₈×C₁₇	—	2	1	no	—
177	C₂×Q₈×C₁₇	—	2	1	no	—
178	C₂×Q₈×C₁₇	—	2	1	no	—
179	C₂×Q₈×C₁₇	—	2	1	no	—
180	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
181	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
182	C₂×D₄×C₁₇	—	2	1	no	—
183	C₂×D₄×C₁₇	—	2	1	no	—
184	C₂×D₄×C₁₇	—	2	1	no	—
185	C₂×D₄×C₁₇	—	2	1	no	—
186	C₂×D₄×C₁₇	—	2	1	no	—
187	C₂×D₄×C₁₇	—	2	1	no	—
188	C₂×D₄×C₁₇	—	2	1	no	—
189	C₂×D₄×C₁₇	—	2	1	no	—
190	C₂×D₄×C₁₇	—	4	1	no	—
191	C₂×D₄×C₁₇	—	4	1	no	—
192	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
193	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₇	—	2	1	no	—
195	C₂²×C₄×C₁₇	—	2	1	no	—
196	C₂²×C₄×C₁₇	—	2	1	no	—
197	C₂²×C₄×C₁₇	—	2	1	no	—
198	C₂²×C₄×C₁₇	—	2	1	no	—
199	C₂²×C₄×C₁₇	—	2	1	no	—
200	C₂²×C₄×C₁₇	—	4	1	no	—
201	C₂²×C₄×C₁₇	—	4	1	no	—
202	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
203	Q₁₆×C₁₇	—	2	2	no	—
204	Q₁₆×C₁₇	—	4	2	no	—
205	SD₁₆×C₁₇	—	2	2	no	—
206	SD₁₆×C₁₇	—	2	2	no	—
207	SD₁₆×C₁₇	—	4	2	no	—
208	SD₁₆×C₁₇	—	4	2	no	—
209	SD₁₆×C₁₇	—	4	2	no	—
210	SD₁₆×C₁₇	—	4	2	no	—
211	D₈×C₁₇	—	2	2	no	—
212	D₈×C₁₇	—	4	2	no	—
213	M₁₆×C₁₇	—	2	1	no	—
214	M₁₆×C₁₇	—	2	4	no	—
215	M₁₆×C₁₇	—	2	1	no	—
216	M₁₆×C₁₇	—	2	1	no	—
217	M₁₆×C₁₇	—	2	1	no	—
218	M₁₆×C₁₇	—	2	1	no	—
219	M₁₆×C₁₇	—	2	1	no	—
220	M₁₆×C₁₇	—	2	1	no	—
221	M₁₆×C₁₇	—	4	2	no	—
222	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
223	C₂×C₈×C₁₇	—	2	1	no	—
224	C₂×C₈×C₁₇	—	2	1	no	—
225	C₂×C₈×C₁₇	—	2	1	no	—
226	C₂×C₈×C₁₇	—	2	4	no	—
227	C₂×C₈×C₁₇	—	2	1	no	—
228	C₂×C₈×C₁₇	—	2	1	no	—
229	C₂×C₈×C₁₇	—	2	1	no	—
230	C₂×C₈×C₁₇	—	4	2	no	—
231	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
232	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
233	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
234	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
235	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
236	C₂×C₈×C₁₇	#41	1	2	yes	—
237	C₄⋊C₄×C₁₇	—	2	1	no	—
238	C₄⋊C₄×C₁₇	—	2	1	no	—
239	C₄⋊C₄×C₁₇	—	2	1	no	—
240	C₄⋊C₄×C₁₇	—	2	1	no	—
241	C₄⋊C₄×C₁₇	—	4	1	no	—
242	C₄⋊C₄×C₁₇	—	4	1	no	—
243	C₄⋊C₄×C₁₇	—	4	1	no	—
244	C₄⋊C₄×C₁₇	—	4	1	no	—
245	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
247	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
248	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
249	C₂²⋊C₄×C₁₇	—	2	1	no	—
250	C₂²⋊C₄×C₁₇	—	2	1	no	—
251	C₂²⋊C₄×C₁₇	—	4	1	no	—
252	C₂²⋊C₄×C₁₇	—	4	1	no	—
253	C₂²⋊C₄×C₁₇	—	4	1	no	—
254	C₂²⋊C₄×C₁₇	—	4	1	no	—
255	C₂²⋊C₄×C₁₇	—	4	1	no	—
256	C₂²⋊C₄×C₁₇	—	4	1	no	—
257	C₂²⋊C₄×C₁₇	—	8	2	no	—
258	C₄²×C₁₇	—	2	1	no	—
259	C₄²×C₁₇	—	2	1	no	—
260	C₄²×C₁₇	—	2	1	no	—
261	C₄²×C₁₇	—	2	1	no	—
262	C₄²×C₁₇	—	4	1	no	—
263	C₄²×C₁₇	—	4	1	no	—
264	#24801	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂³×C₁₇	—	2	1	no	—
266	C₂³×C₁₇	—	2	1	no	—
267	C₂³×C₁₇	—	4	1	no	—
268	C₂³×C₁₇	—	4	1	no	—
269	C₂³×C₁₇	—	4	1	no	—
270	C₂³×C₁₇	—	8	1	no	—
271	C₂³×C₁₇	—	8	1	no	—
272	C₂³×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
273	Q₈×C₁₇	—	2	1	no	—
274	Q₈×C₁₇	—	2	1	no	—
275	Q₈×C₁₇	—	2	1	no	—
276	Q₈×C₁₇	—	4	1	no	—
277	Q₈×C₁₇	—	4	1	no	—
278	Q₈×C₁₇	—	4	1	no	—
279	Q₈×C₁₇	—	4	1	no	—
280	Q₈×C₁₇	#121	1	2	yes	—
281	D₄×C₁₇	—	2	2	no	—
282	D₄×C₁₇	—	2	2	no	—
283	D₄×C₁₇	—	2	1	no	—
284	D₄×C₁₇	—	2	1	no	—
285	D₄×C₁₇	—	2	1	no	—
286	D₄×C₁₇	—	4	1	no	—
287	D₄×C₁₇	—	4	1	no	—
288	D₄×C₁₇	—	4	1	no	—
289	D₄×C₁₇	—	4	1	no	—
290	D₄×C₁₇	—	4	1	no	—
291	D₄×C₁₇	—	4	1	no	—
292	D₄×C₁₇	—	16	1	no	—
293	D₄×C₁₇	—	16	1	no	—
294	D₄×C₁₇	#121	1	2	yes	—
295	C₂×C₄×C₁₇	—	2	1	no	—
296	C₂×C₄×C₁₇	—	2	2	no	—
297	C₂×C₄×C₁₇	—	2	2	no	—
298	C₂×C₄×C₁₇	—	2	1	no	—
299	C₂×C₄×C₁₇	—	2	1	no	—
300	C₂×C₄×C₁₇	—	2	1	no	—
301	C₂×C₄×C₁₇	—	2	1	no	—
302	C₂×C₄×C₁₇	—	2	1	no	—
303	C₂×C₄×C₁₇	—	4	1	no	—
304	C₂×C₄×C₁₇	—	4	1	no	—
305	C₂×C₄×C₁₇	—	4	1	no	—
306	C₂×C₄×C₁₇	—	4	1	no	—
307	C₂×C₄×C₁₇	—	4	1	no	—
308	C₂×C₄×C₁₇	—	4	1	no	—
309	C₂×C₄×C₁₇	—	4	1	no	—
310	C₂×C₄×C₁₇	—	4	1	no	—
311	C₂×C₄×C₁₇	—	4	1	no	—
312	C₂×C₄×C₁₇	—	4	1	no	—
313	C₂×C₄×C₁₇	—	8	1	no	—
314	C₂×C₄×C₁₇	—	8	1	no	—
315	C₂×C₄×C₁₇	—	16	1	no	—
316	C₂×C₄×C₁₇	—	16	1	no	—
317	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
323	C₈×C₁₇	—	2	2	no	—
324	C₈×C₁₇	—	2	1	no	—
325	C₈×C₁₇	—	2	1	no	—
326	C₈×C₁₇	—	4	1	no	—
327	C₈×C₁₇	—	4	1	no	—
328	C₈×C₁₇	—	4	1	no	—
329	C₈×C₁₇	#121	1	2	yes	—
330	C₈×C₁₇	#121	1	2	yes	—
331	C₂×#471	C₂×C₁₇	1	1	yes	characteristic, complemented
332	#3057	C₂×C₁₇	1	1	yes	characteristic, complemented
333	#3046	C₂×C₁₇	1	1	yes	characteristic, complemented
334	#3045	C₂×C₁₇	1	1	yes	characteristic
335	C₂×#444	C₂×C₁₇	1	1	yes	characteristic, complemented
336	#2913	C₂×C₁₇	1	1	yes	characteristic, complemented
337	#2064	C₂×C₁₇	1	1	yes	characteristic, complemented
338	#2063	C₂×C₁₇	1	1	yes	characteristic, complemented
339	#2038	C₂×C₁₇	1	1	yes	characteristic, complemented
340	#2037	C₂×C₁₇	1	1	yes	characteristic, complemented
341	#1973	C₂×C₁₇	1	1	yes	characteristic, complemented
342	#1946	C₂×C₁₇	1	1	yes	characteristic, complemented
343	#1883	C₂×C₁₇	1	1	yes	characteristic, complemented
344	#1882	C₂×C₁₇	1	1	yes	characteristic, complemented
345	#1816	C₂×C₁₇	1	1	yes	characteristic, complemented
346	C₂²×C₁₇	—	2	1	no	—
347	C₂²×C₁₇	—	2	1	no	—
348	C₂²×C₁₇	—	2	2	no	—
349	C₂²×C₁₇	—	4	1	no	—
350	C₂²×C₁₇	—	4	1	no	—
351	C₂²×C₁₇	—	4	1	no	—
352	C₂²×C₁₇	—	4	1	no	—
353	C₂²×C₁₇	—	4	1	no	—
354	C₂²×C₁₇	—	8	2	no	—
355	C₂²×C₁₇	—	8	1	no	—
356	C₂²×C₁₇	—	8	1	no	—
357	C₂²×C₁₇	—	8	1	no	—
358	C₂²×C₁₇	—	16	1	no	—
359	C₂²×C₁₇	#537	1	1	yes	characteristic
360	C₂²×C₁₇	D₄²	1	1	yes	characteristic
361	C₂²×C₁₇	#553	1	1	yes	characteristic
362	C₄×C₁₇	—	2	2	no	—
363	C₄×C₁₇	—	4	1	no	—
364	C₄×C₁₇	—	4	1	no	—
365	C₄×C₁₇	—	4	1	no	—
366	C₄×C₁₇	—	4	1	no	—
367	C₄×C₁₇	—	4	1	no	—
368	C₄×C₁₇	—	8	1	no	—
369	C₄×C₁₇	—	8	1	no	—
370	C₄×C₁₇	—	8	1	no	—
371	C₄×C₁₇	—	8	1	no	—
372	C₄×C₁₇	C₂×#121	1	1	yes	characteristic
373	C₄×C₁₇	C₂×#121	1	1	yes	characteristic
374	C₄×C₁₇	#547	1	1	yes	characteristic
375	C₄×C₁₇	#548	1	1	yes	characteristic
376	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
377	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
378	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
379	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
380	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
381	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
382	#536	C₂²×C₁₇	1	1	yes	characteristic
383	#535	C₂²×C₁₇	1	1	yes	characteristic
384	#520	C₂²×C₁₇	1	1	yes	characteristic
385	#520	C₂²×C₁₇	1	1	yes	characteristic
386	#471	—	2	4	no	—
387	#468	—	2	1	no	—
388	#468	—	2	1	no	—
389	#465	—	2	1	no	—
390	#465	—	2	1	no	—
391	#464	—	2	1	no	—
392	#464	—	2	1	no	—
393	#463	—	2	1	no	—
394	#463	—	2	1	no	—
395	#462	—	2	1	no	—
396	#461	—	2	1	no	—
397	#460	—	2	1	no	—
398	#459	—	2	1	no	—
399	#444	—	2	4	no	—
400	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
401	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
402	#428	—	2	1	no	—
403	#428	—	2	1	no	—
404	#428	C₂²×C₁₇	1	1	yes	characteristic
405	#428	C₂²×C₁₇	1	1	yes	characteristic
406	#427	—	2	1	no	—
407	#427	C₂²×C₁₇	1	1	yes	characteristic
408	C₂×#107	—	2	1	no	—
409	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
410	#424	C₂²×C₁₇	1	1	yes	characteristic
411	#424	C₂²×C₁₇	1	1	yes	characteristic
412	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
413	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
414	#419	C₂²×C₁₇	1	1	yes	characteristic
415	#418	C₂²×C₁₇	1	1	yes	characteristic
416	#417	C₂²×C₁₇	1	1	yes	characteristic
417	#417	C₂²×C₁₇	1	1	yes	characteristic
418	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
419	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
420	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic
421	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
422	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
423	#391	C₂²×C₁₇	1	1	yes	characteristic
424	#390	C₂²×C₁₇	1	1	yes	characteristic
425	#343	C₂²×C₁₇	1	1	yes	characteristic
426	#343	C₂²×C₁₇	1	1	yes	characteristic
427	#339	C₂²×C₁₇	1	1	yes	characteristic
428	#339	C₂²×C₁₇	1	1	yes	characteristic
429	C₂×C₁₇	—	2	1	no	—
430	C₂×C₁₇	—	2	1	no	—
431	C₂×C₁₇	—	4	2	no	—
432	C₂×C₁₇	—	8	1	no	—
433	C₂×C₁₇	—	16	1	no	—
434	C₂×C₁₇	#2416	1	1	yes	characteristic
435	C₂×C₁₇	#3288	1	1	yes	characteristic
436	C₂×C₁₇	#3289	1	1	yes	characteristic
437	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
438	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
439	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
440	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
441	#137	—	2	2	no	—
442	#137	—	2	2	no	—
443	AGL(1,ℤ/8)	—	2	2	no	—
444	AGL(1,ℤ/8)	—	2	2	no	—
445	#135	—	2	2	no	—
446	#135	—	2	2	no	—
447	C₂×Q₁₆	—	2	1	no	—
448	C₂×Q₁₆	D₄×C₁₇	1	1	yes	characteristic
449	C₂×SD₁₆	—	2	1	no	—
450	C₂×SD₁₆	—	2	1	no	—
451	C₂×SD₁₆	—	2	1	no	—
452	C₂×SD₁₆	—	2	1	no	—
453	C₂×SD₁₆	—	2	2	no	—
454	C₂×SD₁₆	—	2	2	no	—
455	C₂×SD₁₆	D₄×C₁₇	1	1	yes	characteristic
456	C₂×SD₁₆	D₄×C₁₇	1	1	yes	characteristic
457	C₂×D₈	—	2	1	no	—
458	C₂×D₈	D₄×C₁₇	1	1	yes	characteristic
459	#131	—	2	2	no	—
460	#131	—	2	2	no	—
461	#131	—	2	2	no	—
462	#131	D₄×C₁₇	1	4	yes	complemented
463	C₂×M₁₆	—	2	1	no	—
464	C₂×M₁₆	—	2	1	no	—
465	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
466	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
467	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
468	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
469	C₂²×C₈	—	2	1	no	—
470	C₂²×C₈	—	2	1	no	—
471	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
473	C₄⋊Q₈	—	2	1	no	—
474	#127	—	2	1	no	—
475	#124	—	2	1	no	—
476	#124	—	2	1	no	—
477	#123	—	4	1	no	—
478	C₂²⋊Q₈	—	2	1	no	—
479	C₂²⋊Q₈	—	2	1	no	—
480	#121	—	2	1	no	—
481	#121	—	2	1	no	—
482	#120	—	4	1	no	—
483	C₄×Q₈	—	2	1	no	—
484	C₄×Q₈	—	2	1	no	—
485	C₄×D₄	—	2	1	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	—	4	1	no	—
488	C₄×D₄	—	4	1	no	—
489	#117	—	2	1	no	—
490	#117	—	2	1	no	—
491	#117	C₂³×C₁₇	1	1	yes	characteristic
492	#117	C₂³×C₁₇	1	1	yes	characteristic
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	—	4	1	no	—
498	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
499	#108	—	2	2	no	—
500	#108	—	2	2	no	—
501	#107	—	2	1	no	—
502	#107	—	2	1	no	—
503	#107	—	2	1	no	—
504	#107	—	2	1	no	—
505	#107	D₄×C₁₇	1	1	yes	characteristic
506	#107	D₄×C₁₇	1	1	yes	characteristic
507	#106	—	2	1	no	—
508	#106	—	2	1	no	—
509	#106	D₄×C₁₇	1	1	yes	characteristic
510	#106	D₄×C₁₇	1	1	yes	characteristic
511	C₄⋊C₈	—	2	1	no	—
512	C₄⋊C₈	—	2	1	no	—
513	C₄⋊C₈	—	2	1	no	—
514	C₄⋊C₈	—	2	1	no	—
515	#104	—	2	2	no	—
516	#104	—	2	2	no	—
517	#103	—	2	1	no	—
518	#103	—	2	1	no	—
519	#103	—	2	1	no	—
520	#103	—	2	1	no	—
521	#103	—	2	1	no	—
522	#103	—	2	1	no	—
523	#102	—	2	1	no	—
524	#102	—	2	1	no	—
525	#102	—	2	1	no	—
526	#102	—	2	1	no	—
527	#102	—	2	1	no	—
528	#102	—	2	1	no	—
529	#101	—	2	2	no	—
530	#100	—	2	2	no	—
531	#97	—	2	2	no	—
532	#95	—	4	1	no	—
533	C₁₇	#24801	1	1	yes	characteristic, direct product factor, Sylow
534	C₂⁴	—	2	1	no	—
535	#41	—	2	1	no	—
536	#41	—	2	1	no	—
537	#41	—	2	1	no	—
538	#41	—	2	1	no	—
539	#41	—	2	1	no	—
540	#41	—	2	1	no	—
541	#41	C₂×D₄×C₁₇	1	2	yes	—
542	#41	#41×C₁₇	1	2	yes	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
550	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	4	1	no	—
560	C₂×D₄	—	4	1	no	—
561	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
562	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	4	1	no	—
570	C₂²×C₄	—	4	1	no	—
571	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
572	Q₁₆	—	2	2	no	—
573	Q₁₆	—	4	2	no	—
574	SD₁₆	—	2	2	no	—
575	SD₁₆	—	2	2	no	—
576	SD₁₆	—	4	2	no	—
577	SD₁₆	—	4	2	no	—
578	SD₁₆	—	4	2	no	—
579	SD₁₆	—	4	2	no	—
580	D₈	—	2	2	no	—
581	D₈	—	4	2	no	—
582	M₁₆	—	2	1	no	—
583	M₁₆	—	2	4	no	—
584	M₁₆	—	2	1	no	—
585	M₁₆	—	2	1	no	—
586	M₁₆	—	2	1	no	—
587	M₁₆	—	2	1	no	—
588	M₁₆	—	2	1	no	—
589	M₁₆	—	2	1	no	—
590	M₁₆	—	4	2	no	—
591	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	4	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	4	2	no	—
600	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
601	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
602	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
603	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
604	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
605	C₂×C₈	#41×C₁₇	1	2	yes	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	4	1	no	—
611	C₄⋊C₄	—	4	1	no	—
612	C₄⋊C₄	—	4	1	no	—
613	C₄⋊C₄	—	4	1	no	—
614	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
615	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
616	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
617	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	4	1	no	—
621	C₂²⋊C₄	—	4	1	no	—
622	C₂²⋊C₄	—	4	1	no	—
623	C₂²⋊C₄	—	4	1	no	—
624	C₂²⋊C₄	—	4	1	no	—
625	C₂²⋊C₄	—	4	1	no	—
626	C₂²⋊C₄	—	8	2	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	—	2	1	no	—
630	C₄²	—	2	1	no	—
631	C₄²	—	4	1	no	—
632	C₄²	—	4	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	8	1	no	—
639	C₂³	—	8	1	no	—
640	C₂³	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
641	Q₈	—	2	1	no	—
642	Q₈	—	2	1	no	—
643	Q₈	—	2	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	4	1	no	—
647	Q₈	—	4	1	no	—
648	Q₈	C₁₇×#121	1	2	yes	—
649	D₄	—	2	2	no	—
650	D₄	—	2	2	no	—
651	D₄	—	2	1	no	—
652	D₄	—	2	1	no	—
653	D₄	—	2	1	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	4	1	no	—
658	D₄	—	4	1	no	—
659	D₄	—	4	1	no	—
660	D₄	—	16	1	no	—
661	D₄	—	16	1	no	—
662	D₄	C₁₇×#121	1	2	yes	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	8	1	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	—	16	1	no	—
684	C₂×C₄	—	16	1	no	—
685	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
688	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
689	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
690	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
691	C₈	—	2	2	no	—
692	C₈	—	2	1	no	—
693	C₈	—	2	1	no	—
694	C₈	—	4	1	no	—
695	C₈	—	4	1	no	—
696	C₈	—	4	1	no	—
697	C₈	C₁₇×#121	1	2	yes	—
698	C₈	C₁₇×#121	1	2	yes	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	8	2	no	—
708	C₂²	—	8	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	—	16	1	no	—
712	C₂²	C₁₇×#537	1	1	yes	characteristic
713	C₂²	D₄²×C₁₇	1	1	yes	characteristic
714	C₂²	C₁₇×#553	1	1	yes	characteristic
715	C₄	—	2	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	8	1	no	—
722	C₄	—	8	1	no	—
723	C₄	—	8	1	no	—
724	C₄	—	8	1	no	—
725	C₄	C₂×C₁₇×#121	1	1	yes	characteristic
726	C₄	C₂×C₁₇×#121	1	1	yes	characteristic
727	C₄	C₁₇×#547	1	1	yes	characteristic
728	C₄	C₁₇×#548	1	1	yes	characteristic
729	C₂	—	2	1	no	—
730	C₂	—	2	1	no	—
731	C₂	—	4	2	no	—
732	C₂	—	8	1	no	—
733	C₂	—	16	1	no	—
734	C₂	C₁₇×#2416	1	1	yes	characteristic
735	C₂	C₁₇×#3288	1	1	yes	characteristic
736	C₂	C₁₇×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#3045	C₂
LCS	G ▷ C₂²×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
1. C₂×C₁₇×#471	C₂	semidirect
2. C₁₇×#3057	C₂	semidirect
3. C₁₇×#3046	C₂	semidirect
5. C₂×C₁₇×#444	C₂	semidirect
6. C₁₇×#2913	C₂	semidirect
7. C₁₇×#2064	C₂	semidirect
8. C₁₇×#2063	C₂	semidirect
9. C₁₇×#2038	C₂	semidirect
10. C₁₇×#2037	C₂	semidirect
11. C₁₇×#1973	C₂	semidirect
12. C₁₇×#1946	C₂	semidirect
13. C₁₇×#1883	C₂	semidirect
14. C₁₇×#1882	C₂	semidirect
15. C₁₇×#1816	C₂	semidirect
94. C₁₇×#131	D₄	semidirect
264. #24801	C₁₇	direct (N × H)
331. C₂×#471	C₂×C₁₇	semidirect
332. #3057	C₂×C₁₇	semidirect
333. #3046	C₂×C₁₇	semidirect
335. C₂×#444	C₂×C₁₇	semidirect
336. #2913	C₂×C₁₇	semidirect
337. #2064	C₂×C₁₇	semidirect
338. #2063	C₂×C₁₇	semidirect
339. #2038	C₂×C₁₇	semidirect
340. #2037	C₂×C₁₇	semidirect
341. #1973	C₂×C₁₇	semidirect
342. #1946	C₂×C₁₇	semidirect
343. #1883	C₂×C₁₇	semidirect
344. #1882	C₂×C₁₇	semidirect
345. #1816	C₂×C₁₇	semidirect
462. #131	D₄×C₁₇	semidirect
533. C₁₇	#24801	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×#471	2
C₁₇×#3057	2
C₁₇×#3046	2
C₁₇×#3045	2
C₂×C₁₇×#444	2
C₁₇×#2913	2
C₁₇×#2064	2
C₁₇×#2063	2
C₁₇×#2038	2
C₁₇×#2037	2
C₁₇×#1973	2
C₁₇×#1946	2
C₁₇×#1883	2
C₁₇×#1882	2
C₁₇×#1816	2
#24801	17

Subgroups — C17×#24801 #16882545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#24801 #16882545