Subgroups — C₁₇×#24986 #16882730

Order 4352.

642 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3067	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#2080	C₂	1	2	yes	maximal, complemented
4	C₁₇×#2053	C₂	1	2	yes	maximal, complemented
5	C₁₇×#1976	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1906	C₂	1	2	yes	maximal, complemented
8	C₁₇×#1833	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1827	C₂	1	2	yes	maximal, complemented
10	C₁₇×#1812	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1765	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#575	C₂²	1	2	yes	—
13	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
14	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
15	C₄×#41×C₁₇	C₂²	1	2	yes	—
16	C₁₇×#473	—	2	1	no	—
17	C₁₇×#472	—	2	1	no	—
18	C₁₇×#471	—	2	2	no	—
19	C₁₇×#442	—	2	1	no	—
20	C₁₇×#441	—	2	1	no	—
21	C₁₇×#440	—	2	2	no	—
22	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
23	C₁₇×#427	C₂²	1	1	yes	characteristic
24	C₁₇×#427	C₂²	1	1	yes	characteristic
25	C₁₇×#424	C₂²	1	2	yes	—
26	C₁₇×#421	C₂²	1	2	yes	—
27	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
28	C₁₇×#416	C₂²	1	1	yes	characteristic
29	C₁₇×#416	C₂²	1	2	yes	—
30	C₁₇×#413	C₂²	1	2	yes	—
31	C₁₇×#410	C₂²	1	2	yes	—
32	C₁₇×#410	C₂²	1	2	yes	—
33	C₁₇×#405	C₂²	1	1	yes	characteristic
34	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
35	C₁₇×#344	C₂²	1	2	yes	—
36	C₁₇×#341	C₂²	1	1	yes	characteristic
37	C₁₇×#339	C₂²	1	2	yes	—
38	C₁₇×#339	C₂²	1	1	yes	characteristic
39	C₁₇×H(3,ℤ/4)	C₂²	1	2	yes	—
40	C₁₇×H(3,ℤ/4)	C₂²	1	2	yes	—
41	C₂×#41×C₁₇	C₂³	1	2	yes	—
42	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
43	C₁₇×#137	—	2	2	no	—
44	C₁₇×#137	—	2	2	no	—
45	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
46	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
47	C₁₇×#135	—	2	1	no	—
48	C₁₇×#135	—	2	1	no	—
49	C₁₇×#135	—	2	1	no	—
50	C₁₇×#135	—	2	1	no	—
51	C₁₇×#135	—	4	2	no	—
52	C₂×Q₁₆×C₁₇	D₄	1	1	yes	characteristic
53	C₂×SD₁₆×C₁₇	D₄	1	2	yes	—
54	C₂×D₈×C₁₇	D₄	1	1	yes	characteristic
55	C₁₇×#131	—	2	1	no	—
56	C₁₇×#131	—	2	1	no	—
57	C₁₇×#131	—	2	1	no	—
58	C₁₇×#131	—	2	1	no	—
59	C₂×M₁₆×C₁₇	—	2	1	no	—
60	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
62	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₇	—	2	1	no	—
64	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
66	C₄×Q₈×C₁₇	—	2	2	no	—
67	C₄×D₄×C₁₇	—	2	2	no	—
68	C₄×D₄×C₁₇	—	4	2	no	—
69	C₁₇×#117	—	2	2	no	—
70	C₁₇×#117	C₂³	1	2	yes	—
71	C₁₇×#117	C₂³	1	1	yes	characteristic
72	C₁₇×#117	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₇	—	2	2	no	—
74	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
75	C₁₇×#108	—	2	1	no	—
76	C₁₇×#108	—	2	1	no	—
77	C₁₇×#107	—	2	1	no	—
78	C₁₇×#107	—	2	1	no	—
79	C₁₇×#106	—	2	1	no	—
80	C₁₇×#106	—	2	1	no	—
81	C₁₇×C₄⋊C₈	—	4	2	no	—
82	C₁₇×#104	—	2	2	no	—
83	C₁₇×#104	—	4	2	no	—
84	C₁₇×#103	—	2	2	no	—
85	C₁₇×#103	—	2	1	no	—
86	C₁₇×#102	—	2	2	no	—
87	C₁₇×#102	—	2	1	no	—
88	C₁₇×#101	—	2	2	no	—
89	C₁₇×#100	—	2	2	no	—
90	C₁₇×#99	—	4	2	no	—
91	C₁₇×#99	—	4	2	no	—
92	C₁₇×#97	—	2	1	no	—
93	C₁₇×#97	—	2	1	no	—
94	C₁₇×#97	—	2	1	no	—
95	C₄×C₈×C₁₇	—	2	1	no	—
96	#41×C₁₇	—	2	1	no	—
97	#41×C₁₇	—	2	1	no	—
98	#41×C₁₇	—	2	2	no	—
99	#41×C₁₇	—	2	2	no	—
100	#41×C₁₇	—	2	2	no	—
101	#41×C₁₇	—	2	1	no	—
102	#41×C₁₇	—	2	1	no	—
103	#41×C₁₇	—	2	2	no	—
104	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
105	C₂×Q₈×C₁₇	#41	1	1	yes	characteristic
106	C₂×D₄×C₁₇	—	2	1	no	—
107	C₂×D₄×C₁₇	—	2	2	no	—
108	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₁₇	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₇	—	2	1	no	—
111	C₂²×C₄×C₁₇	—	2	1	no	—
112	C₂²×C₄×C₁₇	—	2	2	no	—
113	C₂²×C₄×C₁₇	—	4	2	no	—
114	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
115	Q₁₆×C₁₇	—	2	1	no	—
116	Q₁₆×C₁₇	—	2	1	no	—
117	Q₁₆×C₁₇	—	4	2	no	—
118	SD₁₆×C₁₇	—	2	2	no	—
119	SD₁₆×C₁₇	—	2	2	no	—
120	SD₁₆×C₁₇	—	4	2	no	—
121	SD₁₆×C₁₇	—	4	2	no	—
122	D₈×C₁₇	—	2	1	no	—
123	D₈×C₁₇	—	2	1	no	—
124	D₈×C₁₇	—	4	2	no	—
125	M₁₆×C₁₇	—	2	1	no	—
126	M₁₆×C₁₇	—	2	2	no	—
127	M₁₆×C₁₇	—	2	1	no	—
128	M₁₆×C₁₇	—	2	2	no	—
129	M₁₆×C₁₇	—	2	1	no	—
130	M₁₆×C₁₇	—	2	1	no	—
131	M₁₆×C₁₇	—	4	1	no	—
132	M₁₆×C₁₇	—	4	1	no	—
133	C₂×C₈×C₁₇	—	2	1	no	—
134	C₂×C₈×C₁₇	—	2	1	no	—
135	C₂×C₈×C₁₇	—	2	1	no	—
136	C₂×C₈×C₁₇	—	2	1	no	—
137	C₂×C₈×C₁₇	—	2	1	no	—
138	C₂×C₈×C₁₇	—	2	2	no	—
139	C₂×C₈×C₁₇	—	4	1	no	—
140	C₂×C₈×C₁₇	—	4	1	no	—
141	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
144	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
145	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
146	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
147	C₄⋊C₄×C₁₇	—	2	2	no	—
148	C₄⋊C₄×C₁₇	—	2	1	no	—
149	C₄⋊C₄×C₁₇	—	2	2	no	—
150	C₄⋊C₄×C₁₇	—	4	2	no	—
151	C₂²⋊C₄×C₁₇	—	2	2	no	—
152	C₂²⋊C₄×C₁₇	—	2	1	no	—
153	C₂²⋊C₄×C₁₇	—	2	2	no	—
154	C₂²⋊C₄×C₁₇	—	4	2	no	—
155	C₄²×C₁₇	—	2	1	no	—
156	C₄²×C₁₇	—	2	1	no	—
157	C₄²×C₁₇	—	2	2	no	—
158	C₄²×C₁₇	—	2	2	no	—
159	C₄²×C₁₇	—	4	2	no	—
160	C₄²×C₁₇	#41	1	2	yes	—
161	#24986	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₁₇	—	2	2	no	—
163	C₂³×C₁₇	—	2	1	no	—
164	C₂³×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
165	Q₈×C₁₇	—	2	2	no	—
166	Q₈×C₁₇	—	2	1	no	—
167	Q₈×C₁₇	—	2	1	no	—
168	Q₈×C₁₇	—	2	2	no	—
169	D₄×C₁₇	—	2	2	no	—
170	D₄×C₁₇	—	2	1	no	—
171	D₄×C₁₇	—	2	1	no	—
172	D₄×C₁₇	—	2	2	no	—
173	D₄×C₁₇	—	4	1	no	—
174	D₄×C₁₇	—	4	2	no	—
175	D₄×C₁₇	—	4	1	no	—
176	D₄×C₁₇	—	4	2	no	—
177	C₂×C₄×C₁₇	—	2	2	no	—
178	C₂×C₄×C₁₇	—	2	2	no	—
179	C₂×C₄×C₁₇	—	2	1	no	—
180	C₂×C₄×C₁₇	—	4	1	no	—
181	C₂×C₄×C₁₇	—	4	2	no	—
182	C₂×C₄×C₁₇	—	4	1	no	—
183	C₂×C₄×C₁₇	—	4	2	no	—
184	C₂×C₄×C₁₇	—	4	2	no	—
185	C₂×C₄×C₁₇	—	4	2	no	—
186	C₂×C₄×C₁₇	—	4	1	no	—
187	C₂×C₄×C₁₇	—	8	1	no	—
188	C₂×C₄×C₁₇	—	8	4	no	—
189	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
195	C₈×C₁₇	—	4	1	no	—
196	C₈×C₁₇	—	4	1	no	—
197	C₈×C₁₇	—	4	2	no	—
198	C₈×C₁₇	—	4	1	no	—
199	C₈×C₁₇	#123	1	1	yes	characteristic
200	C₈×C₁₇	#123	1	1	yes	characteristic
201	C₈×C₁₇	#123	1	1	yes	characteristic
202	C₈×C₁₇	#123	1	1	yes	characteristic
203	#3067	C₂×C₁₇	1	1	yes	characteristic
204	#2943	C₂×C₁₇	1	1	yes	characteristic, complemented
205	#2080	C₂×C₁₇	1	2	yes	complemented
206	#2053	C₂×C₁₇	1	2	yes	complemented
207	#1976	C₂×C₁₇	1	1	yes	characteristic, complemented
208	#1946	C₂×C₁₇	1	1	yes	characteristic, complemented
209	#1906	C₂×C₁₇	1	2	yes	complemented
210	#1833	C₂×C₁₇	1	1	yes	characteristic, complemented
211	#1827	C₂×C₁₇	1	2	yes	complemented
212	#1812	C₂×C₁₇	1	1	yes	characteristic, complemented
213	#1765	C₂×C₁₇	1	1	yes	characteristic, complemented
214	C₂²×C₁₇	—	4	1	no	—
215	C₂²×C₁₇	—	4	1	no	—
216	C₂²×C₁₇	—	4	2	no	—
217	C₂²×C₁₇	—	8	2	no	—
218	C₂²×C₁₇	—	8	1	no	—
219	C₂²×C₁₇	#540	1	1	yes	characteristic
220	C₂²×C₁₇	#546	1	1	yes	characteristic
221	C₂²×C₁₇	#553	1	1	yes	characteristic
222	C₄×C₁₇	—	4	2	no	—
223	C₄×C₁₇	—	4	2	no	—
224	C₄×C₁₇	—	4	1	no	—
225	C₄×C₁₇	—	8	2	no	—
226	C₄×C₁₇	—	8	1	no	—
227	C₄×C₁₇	—	8	2	no	—
228	C₄×C₁₇	C₂×#123	1	1	yes	characteristic
229	C₄×C₁₇	#529	1	1	yes	characteristic
230	C₄×C₁₇	#546	1	1	yes	characteristic
231	C₄×C₁₇	#555	1	1	yes	characteristic
232	#575	C₂²×C₁₇	1	2	yes	—
233	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
234	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
235	C₄×#41	C₂²×C₁₇	1	2	yes	—
236	#473	—	2	1	no	—
237	#472	—	2	1	no	—
238	#471	—	2	2	no	—
239	#442	—	2	1	no	—
240	#441	—	2	1	no	—
241	#440	—	2	2	no	—
242	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
243	#427	C₂²×C₁₇	1	1	yes	characteristic
244	#427	C₂²×C₁₇	1	1	yes	characteristic
245	#424	C₂²×C₁₇	1	2	yes	—
246	#421	C₂²×C₁₇	1	2	yes	—
247	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
248	#416	C₂²×C₁₇	1	1	yes	characteristic
249	#416	C₂²×C₁₇	1	2	yes	—
250	#413	C₂²×C₁₇	1	2	yes	—
251	#410	C₂²×C₁₇	1	2	yes	—
252	#410	C₂²×C₁₇	1	2	yes	—
253	#405	C₂²×C₁₇	1	1	yes	characteristic
254	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
255	#344	C₂²×C₁₇	1	2	yes	—
256	#341	C₂²×C₁₇	1	1	yes	characteristic
257	#339	C₂²×C₁₇	1	1	yes	characteristic
258	#339	C₂²×C₁₇	1	2	yes	—
259	H(3,ℤ/4)	C₂²×C₁₇	1	2	yes	—
260	H(3,ℤ/4)	C₂²×C₁₇	1	2	yes	—
261	C₂×C₁₇	—	2	1	no	—
262	C₂×C₁₇	—	2	1	no	—
263	C₂×C₁₇	—	2	1	no	—
264	C₂×C₁₇	—	8	2	no	—
265	C₂×C₁₇	—	8	1	no	—
266	C₂×C₁₇	#2420	1	1	yes	characteristic
267	C₂×#41	C₂³×C₁₇	1	2	yes	—
268	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
269	#137	—	2	2	no	—
270	#137	—	2	2	no	—
271	AGL(1,ℤ/8)	—	2	2	no	—
272	AGL(1,ℤ/8)	—	2	2	no	—
273	#135	—	2	1	no	—
274	#135	—	2	1	no	—
275	#135	—	2	1	no	—
276	#135	—	2	1	no	—
277	#135	—	4	2	no	—
278	C₂×Q₁₆	D₄×C₁₇	1	1	yes	characteristic
279	C₂×SD₁₆	D₄×C₁₇	1	2	yes	—
280	C₂×D₈	D₄×C₁₇	1	1	yes	characteristic
281	#131	—	2	1	no	—
282	#131	—	2	1	no	—
283	#131	—	2	1	no	—
284	#131	—	2	1	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
287	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
288	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
292	C₄×Q₈	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	4	2	no	—
295	#117	—	2	2	no	—
296	#117	C₂³×C₁₇	1	2	yes	—
297	#117	C₂³×C₁₇	1	1	yes	characteristic
298	#117	C₂³×C₁₇	1	2	yes	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
301	#108	—	2	1	no	—
302	#108	—	2	1	no	—
303	#107	—	2	1	no	—
304	#107	—	2	1	no	—
305	#106	—	2	1	no	—
306	#106	—	2	1	no	—
307	C₄⋊C₈	—	4	2	no	—
308	#104	—	2	2	no	—
309	#104	—	4	2	no	—
310	#103	—	2	2	no	—
311	#103	—	2	1	no	—
312	#102	—	2	2	no	—
313	#102	—	2	1	no	—
314	#101	—	2	2	no	—
315	#100	—	2	2	no	—
316	#99	—	4	2	no	—
317	#99	—	4	2	no	—
318	#97	—	2	1	no	—
319	#97	—	2	1	no	—
320	#97	—	2	1	no	—
321	C₄×C₈	—	2	1	no	—
322	C₁₇	#24986	1	1	yes	characteristic, direct product factor, Sylow
323	#41	—	2	1	no	—
324	#41	—	2	1	no	—
325	#41	—	2	1	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	2	1	no	—
331	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
332	C₂×Q₈	#41×C₁₇	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
336	C₂×D₄	#41×C₁₇	1	1	yes	characteristic
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
342	Q₁₆	—	2	1	no	—
343	Q₁₆	—	2	1	no	—
344	Q₁₆	—	4	2	no	—
345	SD₁₆	—	2	2	no	—
346	SD₁₆	—	2	2	no	—
347	SD₁₆	—	4	2	no	—
348	SD₁₆	—	4	2	no	—
349	D₈	—	2	1	no	—
350	D₈	—	2	1	no	—
351	D₈	—	4	2	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	4	1	no	—
359	M₁₆	—	4	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
370	C₂×C₈	#41×C₁₇	1	1	yes	characteristic
371	C₂×C₈	#41×C₁₇	1	1	yes	characteristic
372	C₂×C₈	#41×C₁₇	1	1	yes	characteristic
373	C₂×C₈	#41×C₁₇	1	1	yes	characteristic
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	4	2	no	—
387	C₄²	#41×C₁₇	1	2	yes	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	1	no	—
390	C₂³	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	1	no	—
393	Q₈	—	2	1	no	—
394	Q₈	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	1	no	—
397	D₄	—	2	1	no	—
398	D₄	—	2	2	no	—
399	D₄	—	4	1	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	1	no	—
402	D₄	—	4	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	8	4	no	—
415	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
420	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₈	C₁₇×#123	1	1	yes	characteristic
426	C₈	C₁₇×#123	1	1	yes	characteristic
427	C₈	C₁₇×#123	1	1	yes	characteristic
428	C₈	C₁₇×#123	1	1	yes	characteristic
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	1	no	—
434	C₂²	C₁₇×#540	1	1	yes	characteristic
435	C₂²	C₁₇×#546	1	1	yes	characteristic
436	C₂²	C₁₇×#553	1	1	yes	characteristic
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	1	no	—
443	C₄	C₂×C₁₇×#123	1	1	yes	characteristic
444	C₄	C₁₇×#529	1	1	yes	characteristic
445	C₄	C₁₇×#546	1	1	yes	characteristic
446	C₄	C₁₇×#555	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	8	2	no	—
451	C₂	—	8	1	no	—
452	C₂	C₁₇×#2420	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₇	#555
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
socle	C₂×C₁₇	#2420
prime radical	C₁₇×#3067	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#2943	C₂	semidirect
3. C₁₇×#2080	C₂	semidirect
4. C₁₇×#2053	C₂	semidirect
5. C₁₇×#1976	C₂	semidirect
6. C₁₇×#1946	C₂	semidirect
7. C₁₇×#1906	C₂	semidirect
8. C₁₇×#1833	C₂	semidirect
9. C₁₇×#1827	C₂	semidirect
10. C₁₇×#1812	C₂	semidirect
11. C₁₇×#1765	C₂	semidirect
161. #24986	C₁₇	direct (N × H)
204. #2943	C₂×C₁₇	semidirect
205. #2080	C₂×C₁₇	semidirect
206. #2053	C₂×C₁₇	semidirect
207. #1976	C₂×C₁₇	semidirect
208. #1946	C₂×C₁₇	semidirect
209. #1906	C₂×C₁₇	semidirect
210. #1833	C₂×C₁₇	semidirect
211. #1827	C₂×C₁₇	semidirect
212. #1812	C₂×C₁₇	semidirect
213. #1765	C₂×C₁₇	semidirect
322. C₁₇	#24986	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×#3067	2
C₁₇×#2943	2
C₁₇×#2080	2
C₁₇×#2053	2
C₁₇×#1976	2
C₁₇×#1946	2
C₁₇×#1906	2
C₁₇×#1833	2
C₁₇×#1827	2
C₁₇×#1812	2
C₁₇×#1765	2
#24986	17

Subgroups — C17×#24986 #16882730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#24986 #16882730