Subgroups — C₁₇×#18647 #16876391

Order 4352.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1638	C₂	1	4	yes	maximal, complemented
6	C₁₇×#1635	C₂	1	4	yes	maximal, complemented
7	C₁₇×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#556	C₂²	1	2	yes	—
11	C₁₇×#555	—	2	1	no	—
12	C₁₇×#554	—	2	1	no	—
13	C₁₇×#553	—	2	2	no	—
14	C₁₇×#548	—	2	2	no	—
15	C₁₇×#547	C₂²	1	2	yes	—
16	C₁₇×#542	—	2	2	no	—
17	C₁₇×#537	—	2	1	no	—
18	C₁₇×#533	—	2	1	no	—
19	C₁₇×#532	—	2	1	no	—
20	C₁₇×#532	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₇×#520	—	2	1	no	—
24	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
25	C₁₇×#498	—	2	1	no	—
26	C₁₇×#487	—	2	2	no	—
27	C₁₇×#487	C₂²	1	4	yes	—
28	C₁₇×#486	—	2	1	no	—
29	C₁₇×#481	—	2	2	no	—
30	C₁₇×#477	C₂²	1	2	yes	—
31	C₁₇×#476	C₂²	1	4	yes	—
32	C₁₇×#476	C₂²	1	2	yes	—
33	C₁₇×#475	—	2	1	no	—
34	C₁₇×#474	—	2	1	no	—
35	C₁₇×#431	C₂²	1	1	yes	characteristic
36	C₁₇×#428	—	2	1	no	—
37	C₁₇×#423	C₂²	1	1	yes	characteristic
38	C₁₇×#417	—	2	1	no	—
39	C₂×C₁₇×#103	—	2	2	no	—
40	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
41	C₁₇×#332	C₂²	1	4	yes	—
42	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₇×D₄⋊C₈	C₂²	1	2	yes	—
44	C₁₇×D₄⋊C₈	C₂²	1	4	yes	—
45	C₂×#41×C₁₇	—	2	2	no	—
46	C₂×#41×C₁₇	—	2	1	no	—
47	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₇	—	2	1	no	—
49	C₂²×Q₈×C₁₇	—	2	1	no	—
50	C₂×M₁₆×C₁₇	—	2	1	no	—
51	C₂²×C₈×C₁₇	—	2	1	no	—
52	C₁₇×C₄⋊Q₈	—	2	1	no	—
53	C₁₇×C₄⋊Q₈	—	2	1	no	—
54	C₁₇×C₄⋊Q₈	—	2	1	no	—
55	C₁₇×C₄⋊Q₈	—	2	1	no	—
56	C₁₇×C₄⋊Q₈	—	2	1	no	—
57	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₇×C₄⋊Q₈	D₄	1	2	yes	—
59	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₇×#127	D₄	1	1	yes	characteristic
62	C₁₇×#126	—	2	4	no	—
63	C₁₇×#125	—	2	2	no	—
64	C₁₇×#124	—	2	4	no	—
65	C₁₇×#124	—	2	2	no	—
66	C₁₇×#124	—	2	1	no	—
67	C₁₇×#123	—	2	4	no	—
68	C₁₇×C₂²⋊Q₈	—	2	2	no	—
69	C₁₇×C₂²⋊Q₈	—	2	4	no	—
70	C₁₇×C₂²⋊Q₈	—	2	2	no	—
71	C₁₇×C₂²⋊Q₈	—	2	2	no	—
72	C₁₇×#121	—	2	2	no	—
73	C₁₇×#121	—	2	2	no	—
74	C₁₇×#121	—	2	4	no	—
75	C₁₇×#121	—	2	2	no	—
76	C₁₇×#121	—	2	1	no	—
77	C₁₇×#121	D₄	1	2	yes	—
78	C₄×Q₈×C₁₇	—	2	2	no	—
79	C₄×Q₈×C₁₇	—	2	2	no	—
80	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
81	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
82	C₄×D₄×C₁₇	—	2	2	no	—
83	C₄×D₄×C₁₇	—	2	4	no	—
84	C₄×D₄×C₁₇	—	2	2	no	—
85	C₄×D₄×C₁₇	—	2	1	no	—
86	C₄×D₄×C₁₇	—	2	1	no	—
87	C₄×D₄×C₁₇	—	2	1	no	—
88	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
89	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
90	C₄×D₄×C₁₇	C₂³	1	2	yes	—
91	C₁₇×#117	—	2	2	no	—
92	C₁₇×#117	—	2	2	no	—
93	C₁₇×#117	—	2	1	no	—
94	C₁₇×#117	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
97	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
100	C₂×C₄²×C₁₇	—	2	1	no	—
101	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
102	C₁₇×#107	—	2	2	no	—
103	C₁₇×#106	—	2	4	no	—
104	C₁₇×#106	—	2	2	no	—
105	C₁₇×C₄⋊C₈	—	2	1	no	—
106	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
107	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
108	C₁₇×#103	—	2	2	no	—
109	C₁₇×#103	—	2	8	no	—
110	C₁₇×#102	—	2	2	no	—
111	C₁₇×#102	—	2	4	no	—
112	C₁₇×C₂²⋊C₈	—	2	1	no	—
113	C₄×C₈×C₁₇	—	2	1	no	—
114	C₄×C₈×C₁₇	—	2	1	no	—
115	C₄×C₈×C₁₇	C₂³	1	2	yes	—
116	#41×C₁₇	—	2	2	no	—
117	#41×C₁₇	—	2	2	no	—
118	#41×C₁₇	—	4	2	no	—
119	#41×C₁₇	—	4	2	no	—
120	#41×C₁₇	—	8	4	no	—
121	C₂×Q₈×C₁₇	—	2	1	no	—
122	C₂×Q₈×C₁₇	—	2	2	no	—
123	C₂×Q₈×C₁₇	—	2	2	no	—
124	C₂×Q₈×C₁₇	—	2	2	no	—
125	C₂×Q₈×C₁₇	—	4	4	no	—
126	C₂×Q₈×C₁₇	—	4	1	no	—
127	C₂×Q₈×C₁₇	—	8	2	no	—
128	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
129	C₂×D₄×C₁₇	—	2	2	no	—
130	C₂×D₄×C₁₇	—	2	1	no	—
131	C₂×D₄×C₁₇	—	2	4	no	—
132	C₂×D₄×C₁₇	—	2	1	no	—
133	C₂×D₄×C₁₇	—	2	1	no	—
134	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₇	—	2	4	no	—
137	C₂²×C₄×C₁₇	—	2	2	no	—
138	C₂²×C₄×C₁₇	—	2	1	no	—
139	C₂²×C₄×C₁₇	—	2	1	no	—
140	C₂²×C₄×C₁₇	—	2	1	no	—
141	C₂²×C₄×C₁₇	—	2	2	no	—
142	C₂²×C₄×C₁₇	—	4	1	no	—
143	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
146	M₁₆×C₁₇	—	4	2	no	—
147	C₂×C₈×C₁₇	—	2	2	no	—
148	C₂×C₈×C₁₇	—	2	2	no	—
149	C₂×C₈×C₁₇	—	2	2	no	—
150	C₂×C₈×C₁₇	—	4	2	no	—
151	C₄⋊C₄×C₁₇	—	2	4	no	—
152	C₄⋊C₄×C₁₇	—	2	4	no	—
153	C₄⋊C₄×C₁₇	—	2	1	no	—
154	C₄⋊C₄×C₁₇	—	2	2	no	—
155	C₄⋊C₄×C₁₇	—	2	1	no	—
156	C₄⋊C₄×C₁₇	—	2	2	no	—
157	C₄⋊C₄×C₁₇	—	2	2	no	—
158	C₄⋊C₄×C₁₇	—	2	1	no	—
159	C₄⋊C₄×C₁₇	—	2	2	no	—
160	C₄⋊C₄×C₁₇	—	2	2	no	—
161	C₄⋊C₄×C₁₇	—	4	1	no	—
162	C₄⋊C₄×C₁₇	—	4	1	no	—
163	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
165	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
166	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
167	C₂²⋊C₄×C₁₇	—	2	4	no	—
168	C₂²⋊C₄×C₁₇	—	2	4	no	—
169	C₂²⋊C₄×C₁₇	—	2	4	no	—
170	C₂²⋊C₄×C₁₇	—	2	1	no	—
171	C₂²⋊C₄×C₁₇	—	2	2	no	—
172	C₂²⋊C₄×C₁₇	—	2	1	no	—
173	C₂²⋊C₄×C₁₇	—	2	1	no	—
174	C₂²⋊C₄×C₁₇	—	2	2	no	—
175	C₄²×C₁₇	—	2	4	no	—
176	C₄²×C₁₇	—	2	1	no	—
177	C₄²×C₁₇	—	2	1	no	—
178	C₄²×C₁₇	—	2	1	no	—
179	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
183	#18647	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂³×C₁₇	—	2	1	no	—
185	C₂³×C₁₇	—	2	2	no	—
186	C₂³×C₁₇	#120	1	1	yes	characteristic
187	Q₈×C₁₇	—	2	1	no	—
188	Q₈×C₁₇	—	2	1	no	—
189	Q₈×C₁₇	—	4	4	no	—
190	Q₈×C₁₇	—	4	4	no	—
191	Q₈×C₁₇	—	4	2	no	—
192	Q₈×C₁₇	—	8	2	no	—
193	Q₈×C₁₇	—	8	2	no	—
194	D₄×C₁₇	—	2	1	no	—
195	D₄×C₁₇	—	2	1	no	—
196	D₄×C₁₇	—	2	4	no	—
197	D₄×C₁₇	—	4	2	no	—
198	D₄×C₁₇	—	4	4	no	—
199	D₄×C₁₇	—	4	2	no	—
200	D₄×C₁₇	—	4	2	no	—
201	D₄×C₁₇	—	8	4	no	—
202	C₂×C₄×C₁₇	—	2	2	no	—
203	C₂×C₄×C₁₇	—	2	2	no	—
204	C₂×C₄×C₁₇	—	2	1	no	—
205	C₂×C₄×C₁₇	—	2	1	no	—
206	C₂×C₄×C₁₇	—	2	2	no	—
207	C₂×C₄×C₁₇	—	2	1	no	—
208	C₂×C₄×C₁₇	—	2	4	no	—
209	C₂×C₄×C₁₇	—	4	2	no	—
210	C₂×C₄×C₁₇	—	4	2	no	—
211	C₂×C₄×C₁₇	—	4	2	no	—
212	C₂×C₄×C₁₇	—	4	2	no	—
213	C₂×C₄×C₁₇	—	4	2	no	—
214	C₂×C₄×C₁₇	—	4	2	no	—
215	C₂×C₄×C₁₇	—	8	2	no	—
216	C₂×C₄×C₁₇	—	8	4	no	—
217	C₂×C₄×C₁₇	—	8	2	no	—
218	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
219	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
220	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
221	C₂×C₄×C₁₇	#135	1	2	yes	—
222	C₂×C₄×C₁₇	#137	1	2	yes	—
223	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
226	C₈×C₁₇	—	4	2	no	—
227	C₈×C₁₇	—	4	2	no	—
228	C₈×C₁₇	—	4	2	no	—
229	#3511	C₂×C₁₇	1	1	yes	characteristic
230	#3227	C₂×C₁₇	1	1	yes	characteristic, complemented
231	C₂×#487	C₂×C₁₇	1	1	yes	characteristic, complemented
232	#3079	C₂×C₁₇	1	1	yes	characteristic, complemented
233	#1638	C₂×C₁₇	1	4	yes	complemented
234	#1635	C₂×C₁₇	1	4	yes	complemented
235	#1549	C₂×C₁₇	1	1	yes	characteristic, complemented
236	#1492	C₂×C₁₇	1	1	yes	characteristic, complemented
237	#1476	C₂×C₁₇	1	1	yes	characteristic, complemented
238	C₂²×C₁₇	—	2	1	no	—
239	C₂²×C₁₇	—	2	1	no	—
240	C₂²×C₁₇	—	4	1	no	—
241	C₂²×C₁₇	—	4	2	no	—
242	C₂²×C₁₇	—	4	1	no	—
243	C₂²×C₁₇	—	4	2	no	—
244	C₂²×C₁₇	—	4	1	no	—
245	C₂²×C₁₇	—	4	2	no	—
246	C₂²×C₁₇	#452	1	2	yes	—
247	C₂²×C₁₇	C₂×#120	1	1	yes	characteristic
248	C₄×C₁₇	—	2	1	no	—
249	C₄×C₁₇	—	2	1	no	—
250	C₄×C₁₇	—	4	1	no	—
251	C₄×C₁₇	—	4	2	no	—
252	C₄×C₁₇	—	4	1	no	—
253	C₄×C₁₇	—	4	4	no	—
254	C₄×C₁₇	—	4	1	no	—
255	C₄×C₁₇	—	8	2	no	—
256	C₄×C₁₇	#452	1	2	yes	—
257	C₄×C₁₇	#454	1	2	yes	—
258	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
259	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
260	C₄×C₁₇	#577	1	2	yes	—
261	#556	C₂²×C₁₇	1	2	yes	—
262	#555	—	2	1	no	—
263	#554	—	2	1	no	—
264	#553	—	2	2	no	—
265	#548	—	2	2	no	—
266	#547	C₂²×C₁₇	1	2	yes	—
267	#542	—	2	2	no	—
268	#537	—	2	1	no	—
269	#533	—	2	1	no	—
270	#532	—	2	1	no	—
271	#532	C₂²×C₁₇	1	1	yes	characteristic
272	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
274	#520	—	2	1	no	—
275	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
276	#498	—	2	1	no	—
277	#487	—	2	2	no	—
278	#487	C₂²×C₁₇	1	4	yes	—
279	#486	—	2	1	no	—
280	#481	—	2	2	no	—
281	#477	C₂²×C₁₇	1	2	yes	—
282	#476	C₂²×C₁₇	1	2	yes	—
283	#476	C₂²×C₁₇	1	4	yes	—
284	#475	—	2	1	no	—
285	#474	—	2	1	no	—
286	#431	C₂²×C₁₇	1	1	yes	characteristic
287	#428	—	2	1	no	—
288	#423	C₂²×C₁₇	1	1	yes	characteristic
289	#417	—	2	1	no	—
290	C₂×#103	—	2	2	no	—
291	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
292	#332	C₂²×C₁₇	1	4	yes	—
293	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	—
294	D₄⋊C₈	C₂²×C₁₇	1	2	yes	—
295	D₄⋊C₈	C₂²×C₁₇	1	4	yes	—
296	C₂×C₁₇	—	2	2	no	—
297	C₂×C₁₇	—	8	1	no	—
298	C₂×C₁₇	—	8	2	no	—
299	C₂×C₁₇	C₂×#452	1	1	yes	characteristic
300	C₂×C₁₇	#3009	1	1	yes	characteristic
301	C₂×C₁₇	C₂×#454	1	1	yes	characteristic
302	C₂×#41	—	2	2	no	—
303	C₂×#41	—	2	1	no	—
304	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
305	C₂²×Q₈	—	2	1	no	—
306	C₂²×Q₈	—	2	1	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	D₄×C₁₇	1	2	yes	—
315	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
316	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
317	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
318	#127	D₄×C₁₇	1	1	yes	characteristic
319	#126	—	2	4	no	—
320	#125	—	2	2	no	—
321	#124	—	2	4	no	—
322	#124	—	2	2	no	—
323	#124	—	2	1	no	—
324	#123	—	2	4	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	—	2	4	no	—
327	C₂²⋊Q₈	—	2	2	no	—
328	C₂²⋊Q₈	—	2	2	no	—
329	#121	—	2	2	no	—
330	#121	—	2	2	no	—
331	#121	—	2	4	no	—
332	#121	—	2	2	no	—
333	#121	—	2	1	no	—
334	#121	D₄×C₁₇	1	2	yes	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
338	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
346	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
347	C₄×D₄	C₂³×C₁₇	1	2	yes	—
348	#117	—	2	2	no	—
349	#117	—	2	2	no	—
350	#117	—	2	1	no	—
351	#117	D₄×C₁₇	1	1	yes	characteristic
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
359	#107	—	2	2	no	—
360	#106	—	2	2	no	—
361	#106	—	2	4	no	—
362	C₄⋊C₈	—	2	1	no	—
363	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
364	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
365	#103	—	2	2	no	—
366	#103	—	2	8	no	—
367	#102	—	2	2	no	—
368	#102	—	2	4	no	—
369	C₂²⋊C₈	—	2	1	no	—
370	C₄×C₈	—	2	1	no	—
371	C₄×C₈	—	2	1	no	—
372	C₄×C₈	C₂³×C₁₇	1	2	yes	—
373	C₁₇	#18647	1	1	yes	characteristic, direct product factor, Sylow
374	#41	—	2	2	no	—
375	#41	—	2	2	no	—
376	#41	—	4	2	no	—
377	#41	—	4	2	no	—
378	#41	—	8	4	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	4	4	no	—
384	C₂×Q₈	—	4	1	no	—
385	C₂×Q₈	—	8	2	no	—
386	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
393	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
404	M₁₆	—	4	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	4	2	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	—	4	1	no	—
421	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
422	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
423	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
424	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₄²	—	2	4	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
438	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
439	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
440	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
441	C₂³	—	2	1	no	—
442	C₂³	—	2	2	no	—
443	C₂³	C₁₇×#120	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	4	4	no	—
447	Q₈	—	4	4	no	—
448	Q₈	—	4	2	no	—
449	Q₈	—	8	2	no	—
450	Q₈	—	8	2	no	—
451	D₄	—	2	1	no	—
452	D₄	—	2	1	no	—
453	D₄	—	2	4	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	4	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	8	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	8	2	no	—
473	C₂×C₄	—	8	4	no	—
474	C₂×C₄	—	8	2	no	—
475	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
476	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
477	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
478	C₂×C₄	C₁₇×#135	1	2	yes	—
479	C₂×C₄	C₁₇×#137	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
483	C₈	—	4	2	no	—
484	C₈	—	4	2	no	—
485	C₈	—	4	2	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	2	no	—
494	C₂²	C₁₇×#452	1	2	yes	—
495	C₂²	C₂×C₁₇×#120	1	1	yes	characteristic
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	1	no	—
503	C₄	—	8	2	no	—
504	C₄	C₁₇×#452	1	2	yes	—
505	C₄	C₁₇×#454	1	2	yes	—
506	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
507	C₄	C₂×C₁₇×#137	1	1	yes	characteristic
508	C₄	C₁₇×#577	1	2	yes	—
509	C₂	—	2	2	no	—
510	C₂	—	8	1	no	—
511	C₂	—	8	2	no	—
512	C₂	C₂×C₁₇×#452	1	1	yes	characteristic
513	C₂	C₁₇×#3009	1	1	yes	characteristic
514	C₂	C₂×C₁₇×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#3511	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#3227	C₂	semidirect
3. C₂×C₁₇×#487	C₂	semidirect
4. C₁₇×#3079	C₂	semidirect
5. C₁₇×#1638	C₂	semidirect
6. C₁₇×#1635	C₂	semidirect
7. C₁₇×#1549	C₂	semidirect
8. C₁₇×#1492	C₂	semidirect
9. C₁₇×#1476	C₂	semidirect
183. #18647	C₁₇	direct (N × H)
230. #3227	C₂×C₁₇	semidirect
231. C₂×#487	C₂×C₁₇	semidirect
232. #3079	C₂×C₁₇	semidirect
233. #1638	C₂×C₁₇	semidirect
234. #1635	C₂×C₁₇	semidirect
235. #1549	C₂×C₁₇	semidirect
236. #1492	C₂×C₁₇	semidirect
237. #1476	C₂×C₁₇	semidirect
373. C₁₇	#18647	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×#3511	2
C₁₇×#3227	2
C₂×C₁₇×#487	2
C₁₇×#3079	2
C₁₇×#1638	2
C₁₇×#1635	2
C₁₇×#1549	2
C₁₇×#1492	2
C₁₇×#1476	2
#18647	17

Subgroups — C17×#18647 #16876391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#18647 #16876391