Subgroups — D₁₇⋊#1833 #17969569

Order 4352.

786 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₇⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#11763819	C₂	1	1	yes	maximal, characteristic
3	#14544704	C₂	1	4	yes	maximal, complemented
4	#14544703	C₂	1	4	yes	maximal, complemented
5	#14544494	C₂	1	2	yes	maximal
6	#14544454	C₂	1	2	yes	maximal
7	D₁₇×#405	C₂	1	1	yes	maximal, characteristic
8	C₂×D₁₇⋊M₁₆	C₂²	1	2	yes	—
9	C₂×#10587677	C₂²	1	2	yes	—
10	C₂×#10587536	—	2	1	no	—
11	D₁₇⋊#108	—	2	1	no	—
12	D₁₇⋊#108	—	2	1	no	—
13	D₁₇⋊#108	C₂²	1	2	yes	—
14	D₁₇⋊#108	C₂²	1	2	yes	—
15	C₂×#10587535	—	2	1	no	—
16	#11763819	—	2	1	no	—
17	#11763819	—	2	1	no	—
18	#11763819	C₂²	1	2	yes	—
19	#11763819	C₂²	1	2	yes	—
20	C₂×#10587534	—	2	1	no	—
21	C₂×#10587533	—	2	1	no	—
22	#11763691	C₂²	1	8	yes	—
23	#11763676	C₂²	1	8	yes	—
24	C₂×M₁₆×D₁₇	C₂²	1	1	yes	characteristic
25	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
26	#117×D₁₇	C₂²	1	1	yes	characteristic
27	#11762767	C₄	1	1	yes	characteristic, complemented
28	#11762766	C₂²	1	2	yes	—
29	#11762765	C₄	1	1	yes	characteristic, complemented
30	#11762764	C₄	1	1	yes	characteristic, complemented
31	#11762763	C₂²	1	2	yes	—
32	#97×D₁₇	C₄	1	2	yes	complemented
33	C₄×C₈×D₁₇	C₄	1	2	yes	complemented
34	C₁₇×#405	C₄	1	1	yes	characteristic, complemented
35	C₂²×C₄×D₁₇	C₂³	1	1	yes	characteristic
36	C₂×C₂²⋊#595	—	2	2	no	—
37	C₂×#63247	—	2	2	no	—
38	#10587677	—	2	2	no	—
39	#10587677	—	2	2	no	—
40	#10587677	—	2	2	no	—
41	#10587677	C₂³	1	4	yes	—
42	C₂×C₄⋊#595	—	2	2	no	—
43	C₂×C₄×#595	—	2	2	no	—
44	D₁₇⋊M₁₆	—	2	2	no	—
45	D₁₇⋊M₁₆	—	2	2	no	—
46	D₁₇⋊M₁₆	—	2	2	no	—
47	D₁₇⋊M₁₆	C₂³	1	4	yes	—
48	C₂×#63243	—	2	2	no	—
49	C₂×#63242	—	2	2	no	—
50	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
52	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
53	#10587612	C₂×C₄	1	1	yes	characteristic
54	C₂×#63223	C₂×C₄	1	1	yes	characteristic
55	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
56	M₁₆×D₁₇	—	2	1	no	—
57	M₁₆×D₁₇	—	2	1	no	—
58	M₁₆×D₁₇	—	2	1	no	—
59	M₁₆×D₁₇	—	2	1	no	—
60	C₂×#63218	C₂³	1	2	yes	—
61	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
62	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
65	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
66	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
67	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
68	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
69	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
70	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
71	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
72	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
73	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
74	#10587578	—	2	1	no	—
75	C₄⋊C₄×D₁₇	—	2	1	no	—
76	C₂²⋊C₄×D₁₇	—	2	1	no	—
77	#10587563	—	2	1	no	—
78	#10587558	C₂³	1	2	yes	—
79	C₄²×D₁₇	C₂×C₄	1	2	yes	—
80	#10587536	—	2	2	no	—
81	#10587536	—	2	2	no	—
82	#10587535	—	2	2	no	—
83	#10587535	—	2	2	no	—
84	#10587534	—	2	2	no	—
85	#10587534	—	2	2	no	—
86	#10587533	—	2	2	no	—
87	#10587533	—	2	2	no	—
88	C₁₇×#97	C₂×C₄	1	2	yes	complemented
89	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	complemented
90	#10587486	C₂×C₄	1	2	yes	complemented
91	#10587486	C₂×C₄	1	2	yes	complemented
92	C₈×Dic₁₇	C₂×C₄	1	2	yes	complemented
93	C₈×Dic₁₇	C₂×C₄	1	2	yes	complemented
94	#10587474	C₂×C₄	1	2	yes	complemented
95	C₄×#3622	C₂×C₄	1	2	yes	complemented
96	C₂³×D₁₇	#41	1	1	yes	characteristic
97	C₂²×#595	—	4	2	no	—
98	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×Dic₁₇	#41	1	1	yes	characteristic
100	C₂×C₄×D₁₇	—	2	2	no	—
101	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
105	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
107	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
108	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
109	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
110	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
111	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
112	C₂×C₄×D₁₇	C₂⁴	1	1	yes	characteristic
113	C₂²⋊#595	—	2	4	no	—
114	C₂²⋊#595	—	4	2	no	—
115	#63247	—	2	4	no	—
116	#63247	—	4	2	no	—
117	C₂×#3624	—	4	2	no	—
118	C₄⋊#595	—	2	4	no	—
119	C₄⋊#595	—	4	2	no	—
120	C₄×#595	—	2	4	no	—
121	C₄×#595	—	4	2	no	—
122	#63243	—	2	4	no	—
123	#63243	—	4	2	no	—
124	#63242	—	2	4	no	—
125	#63242	—	4	2	no	—
126	M₁₆×C₁₇	—	2	1	no	—
127	M₁₆×C₁₇	—	2	1	no	—
128	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
135	C₄⋊C₄×C₁₇	—	2	1	no	—
136	C₂²⋊C₄×C₁₇	—	2	1	no	—
137	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
138	C₂²⋊Dic₁₇	—	2	1	no	—
139	#63227	—	2	2	no	—
140	C₄⋊Dic₁₇	—	2	1	no	—
141	#63225	—	2	2	no	—
142	C₄×Dic₁₇	—	2	2	no	—
143	C₄×Dic₁₇	C₂²×C₄	1	2	yes	—
144	#63223	—	2	1	no	—
145	#63223	—	2	1	no	—
146	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
147	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
148	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
149	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
150	C₂×#3622	C₂²×C₄	1	2	yes	—
151	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
152	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
153	#63218	—	2	2	no	—
154	#63218	—	2	2	no	—
155	C₈×D₁₇	—	2	2	no	—
156	C₈×D₁₇	—	2	2	no	—
157	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
158	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
159	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
160	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
161	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
162	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
163	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
164	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
165	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
166	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
167	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
168	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
169	C₈×D₁₇	C₂×Q₈	1	1	yes	characteristic
170	C₈×D₁₇	C₂×Q₈	1	1	yes	characteristic
171	C₈×D₁₇	C₂×Q₈	1	1	yes	characteristic
172	C₈×D₁₇	C₂×Q₈	1	1	yes	characteristic
173	C₂×#1833	—	17	1	no	maximal, Sylow
174	C₂³×C₁₇	#117	1	1	yes	characteristic
175	C₂²×D₁₇	—	4	2	no	—
176	C₂²×D₁₇	#117	1	1	yes	characteristic
177	C₂²×D₁₇	#124	1	1	yes	characteristic
178	C₂²×D₁₇	#124	1	1	yes	characteristic
179	C₂²×D₁₇	#125	1	1	yes	characteristic
180	C₂²×D₁₇	#125	1	1	yes	characteristic
181	C₂²×D₁₇	C₂×#41	1	1	yes	characteristic
182	C₂×#595	—	4	4	no	—
183	C₂×#595	—	8	4	no	—
184	C₂×C₄×C₁₇	—	2	2	no	—
185	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
188	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
189	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
190	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
191	C₂×Dic₁₇	—	2	2	no	—
192	C₂×Dic₁₇	#117	1	1	yes	characteristic
193	C₂×Dic₁₇	#124	1	1	yes	characteristic
194	C₂×Dic₁₇	#124	1	1	yes	characteristic
195	C₂×Dic₁₇	#125	1	1	yes	characteristic
196	C₂×Dic₁₇	#125	1	1	yes	characteristic
197	C₂×Dic₁₇	C₂×#41	1	1	yes	characteristic
198	C₄×D₁₇	—	4	4	no	—
199	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₄×D₁₇	#117	1	1	yes	characteristic
202	C₄×D₁₇	#117	1	1	yes	characteristic
203	C₄×D₁₇	#124	1	1	yes	characteristic
204	C₄×D₁₇	#124	1	1	yes	characteristic
205	C₄×D₁₇	#124	1	1	yes	characteristic
206	C₄×D₁₇	#124	1	1	yes	characteristic
207	C₄×D₁₇	#125	1	1	yes	characteristic
208	C₄×D₁₇	#125	1	1	yes	characteristic
209	C₄×D₁₇	#125	1	1	yes	characteristic
210	C₄×D₁₇	#125	1	1	yes	characteristic
211	C₄×D₁₇	C₂²×D₄	1	1	yes	characteristic
212	C₄×D₁₇	C₂²×Q₈	1	1	yes	characteristic
213	C₄×D₁₇	C₂×#41	1	1	yes	characteristic
214	C₄×D₁₇	C₂×#41	1	1	yes	characteristic
215	#3624	—	4	4	no	—
216	C₈×C₁₇	—	2	2	no	—
217	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
221	#3622	—	2	2	no	—
222	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
223	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
224	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
225	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂²×#108	—	17	1	no	—
227	C₂×#427	—	17	1	no	—
228	C₂×#405	—	17	1	no	—
229	#1833	—	17	4	no	—
230	#1833	—	17	4	no	—
231	C₂×#344	—	17	2	no	—
232	C₂×H(3,ℤ/4)	—	17	2	no	—
233	C₂²×C₁₇	—	4	1	no	—
234	C₂²×C₁₇	#382	1	1	yes	characteristic
235	C₂²×C₁₇	#382	1	1	yes	characteristic
236	C₂²×C₁₇	C₂×#117	1	1	yes	characteristic
237	C₂×D₁₇	—	2	2	no	—
238	C₂×D₁₇	—	2	2	no	—
239	C₂×D₁₇	—	2	2	no	—
240	C₂×D₁₇	—	4	1	no	—
241	C₂×D₁₇	—	4	1	no	—
242	C₂×D₁₇	—	4	1	no	—
243	C₂×D₁₇	#382	1	1	yes	characteristic
244	C₂×D₁₇	#382	1	1	yes	characteristic
245	C₂×D₁₇	C₂×#124	1	1	yes	characteristic
246	C₂×D₁₇	C₂×#125	1	1	yes	characteristic
247	#595	—	8	4	no	—
248	C₄×C₁₇	—	4	2	no	—
249	C₄×C₁₇	#382	1	1	yes	characteristic
250	C₄×C₁₇	#382	1	1	yes	characteristic
251	C₄×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
252	C₄×C₁₇	C₂×#117	1	1	yes	characteristic
253	Dic₁₇	—	4	2	no	—
254	Dic₁₇	#382	1	1	yes	characteristic
255	Dic₁₇	#382	1	1	yes	characteristic
256	Dic₁₇	C₂×#124	1	1	yes	characteristic
257	Dic₁₇	C₂×#125	1	1	yes	characteristic
258	C₂²×M₁₆	—	17	1	no	—
259	C₂²×M₁₆	—	17	2	no	—
260	C₂³×C₈	—	17	1	no	—
261	C₂×#117	—	17	1	no	—
262	C₂×#117	—	17	2	no	—
263	C₂×#108	—	17	2	no	—
264	C₂×#108	—	17	2	no	—
265	C₂×#108	—	34	1	no	—
266	C₂×#108	—	34	1	no	—
267	C₂×#108	—	34	1	no	—
268	C₂×#108	—	34	1	no	—
269	#427	—	17	2	no	—
270	#427	—	17	2	no	—
271	#427	—	34	1	no	—
272	#427	—	34	1	no	—
273	C₂×#107	—	34	1	no	—
274	C₂×#106	—	34	1	no	—
275	#405	—	17	1	no	—
276	#405	—	17	1	no	—
277	#405	—	17	1	no	—
278	#405	—	17	2	no	—
279	#405	—	17	2	no	—
280	#405	#595	1	1	yes	characteristic, complemented
281	C₂×#97	—	17	2	no	—
282	C₂×C₄×C₈	—	17	2	no	—
283	#344	—	17	8	no	—
284	H(3,ℤ/4)	—	17	8	no	—
285	C₂×C₁₇	—	2	1	no	—
286	C₂×C₁₇	—	2	1	no	—
287	C₂×C₁₇	—	2	1	no	—
288	C₂×C₁₇	C₂×#382	1	1	yes	characteristic
289	D₁₇	—	2	1	no	—
290	D₁₇	—	2	1	no	—
291	D₁₇	—	2	1	no	—
292	D₁₇	#1833	1	2	yes	complemented
293	C₂³×C₄	—	17	1	no	—
294	C₂×M₁₆	—	17	1	no	—
295	C₂×M₁₆	—	17	2	no	—
296	C₂×M₁₆	—	17	4	no	—
297	C₂×M₁₆	—	34	1	no	—
298	C₂×M₁₆	—	34	1	no	—
299	C₂×M₁₆	—	34	1	no	—
300	C₂×M₁₆	—	34	1	no	—
301	C₂×M₁₆	—	34	2	no	—
302	C₂×M₁₆	—	34	2	no	—
303	C₂×M₁₆	—	34	2	no	—
304	C₂×M₁₆	—	34	2	no	—
305	C₂×M₁₆	—	34	2	no	—
306	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
307	C₂²×C₈	—	17	1	no	—
308	C₂²×C₈	—	17	1	no	—
309	C₂²×C₈	—	17	1	no	—
310	C₂²×C₈	—	17	1	no	—
311	C₂²×C₈	—	17	1	no	—
312	C₂²×C₈	—	17	1	no	—
313	C₂²×C₈	—	17	1	no	—
314	C₂²×C₈	—	17	1	no	—
315	C₂²×C₈	—	17	1	no	—
316	C₂²×C₈	—	17	1	no	—
317	C₂²×C₈	—	17	1	no	—
318	C₂²×C₈	—	17	1	no	—
319	C₂²×C₈	—	17	1	no	—
320	C₂²×C₈	—	17	2	no	—
321	C₂²×C₈	—	34	2	no	—
322	C₂²×C₈	C₂×#595	1	1	yes	characteristic
323	#117	—	17	1	no	—
324	#117	—	17	2	no	—
325	#117	—	17	4	no	—
326	#117	—	34	1	no	—
327	#117	—	34	1	no	—
328	#117	—	34	2	no	—
329	#117	—	34	2	no	—
330	#117	—	34	2	no	—
331	#117	C₂×#595	1	1	yes	characteristic
332	C₂×C₄⋊C₄	—	34	1	no	—
333	C₂×C₄⋊C₄	—	34	2	no	—
334	C₂×C₂²⋊C₄	—	34	1	no	—
335	C₂×C₂²⋊C₄	—	34	2	no	—
336	C₂×C₄²	—	17	2	no	—
337	C₂×C₄²	—	34	2	no	—
338	#108	—	34	2	no	—
339	#108	—	34	2	no	—
340	#108	—	34	2	no	—
341	#108	—	34	2	no	—
342	#107	—	34	2	no	—
343	#107	—	34	2	no	—
344	#106	—	34	2	no	—
345	#106	—	34	2	no	—
346	#97	—	17	2	no	—
347	#97	—	17	2	no	—
348	#97	—	17	2	no	—
349	#97	C₂×#595	1	2	yes	complemented
350	C₄×C₈	—	17	2	no	—
351	C₄×C₈	—	17	2	no	—
352	C₄×C₈	—	17	2	no	—
353	C₄×C₈	C₂×#595	1	2	yes	complemented
354	C₁₇	C₂×#1833	1	1	yes	characteristic, complemented, Sylow
355	C₂⁴	—	17	1	no	—
356	C₂²×C₄	—	17	1	no	—
357	C₂²×C₄	—	17	1	no	—
358	C₂²×C₄	—	17	1	no	—
359	C₂²×C₄	—	17	1	no	—
360	C₂²×C₄	—	17	1	no	—
361	C₂²×C₄	—	17	1	no	—
362	C₂²×C₄	—	17	1	no	—
363	C₂²×C₄	—	17	1	no	—
364	C₂²×C₄	—	17	1	no	—
365	C₂²×C₄	—	17	1	no	—
366	C₂²×C₄	—	17	1	no	—
367	C₂²×C₄	—	17	1	no	—
368	C₂²×C₄	—	17	1	no	—
369	C₂²×C₄	—	34	2	no	—
370	C₂²×C₄	—	68	2	no	—
371	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
372	M₁₆	—	2	1	no	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	34	2	no	—
375	M₁₆	—	34	2	no	—
376	M₁₆	—	34	1	no	—
377	M₁₆	—	34	1	no	—
378	M₁₆	—	34	4	no	—
379	M₁₆	—	34	4	no	—
380	M₁₆	—	68	2	no	—
381	M₁₆	—	68	2	no	—
382	C₂×C₈	—	17	1	no	—
383	C₂×C₈	—	17	1	no	—
384	C₂×C₈	—	17	1	no	—
385	C₂×C₈	—	17	1	no	—
386	C₂×C₈	—	17	1	no	—
387	C₂×C₈	—	17	1	no	—
388	C₂×C₈	—	17	1	no	—
389	C₂×C₈	—	17	1	no	—
390	C₂×C₈	—	17	1	no	—
391	C₂×C₈	—	17	1	no	—
392	C₂×C₈	—	17	1	no	—
393	C₂×C₈	—	17	1	no	—
394	C₂×C₈	—	17	1	no	—
395	C₂×C₈	—	17	1	no	—
396	C₂×C₈	—	17	1	no	—
397	C₂×C₈	—	17	1	no	—
398	C₂×C₈	—	17	1	no	—
399	C₂×C₈	—	17	1	no	—
400	C₂×C₈	—	17	1	no	—
401	C₂×C₈	—	17	1	no	—
402	C₂×C₈	—	17	1	no	—
403	C₂×C₈	—	17	1	no	—
404	C₂×C₈	—	17	2	no	—
405	C₂×C₈	—	34	2	no	—
406	C₂×C₈	—	34	2	no	—
407	C₂×C₈	—	34	4	no	—
408	C₂×C₈	—	68	2	no	—
409	C₂×C₈	—	68	2	no	—
410	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
411	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
412	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
413	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
414	C₂×C₈	C₂²×#595	1	2	yes	—
415	C₂×C₈	C₂²×#595	1	1	yes	characteristic
416	C₂×C₈	C₂²×#595	1	1	yes	characteristic
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	34	2	no	—
419	C₄⋊C₄	—	34	4	no	—
420	C₄⋊C₄	—	34	1	no	—
421	C₄⋊C₄	—	68	2	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	34	2	no	—
424	C₂²⋊C₄	—	34	1	no	—
425	C₂²⋊C₄	—	34	4	no	—
426	C₂²⋊C₄	—	68	2	no	—
427	C₄²	—	17	2	no	—
428	C₄²	—	34	2	no	—
429	C₄²	—	34	4	no	—
430	C₄²	—	68	2	no	—
431	C₄²	C₂²×#595	1	2	yes	—
432	C₂³	—	17	1	no	—
433	C₂³	—	17	1	no	—
434	C₂³	—	17	1	no	—
435	C₂³	—	17	1	no	—
436	C₂³	—	17	1	no	—
437	C₂³	—	17	1	no	—
438	C₂³	—	68	2	no	—
439	C₂³	#10587677	1	1	yes	characteristic
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	17	1	no	—
442	C₂×C₄	—	17	1	no	—
443	C₂×C₄	—	17	1	no	—
444	C₂×C₄	—	17	1	no	—
445	C₂×C₄	—	17	1	no	—
446	C₂×C₄	—	17	1	no	—
447	C₂×C₄	—	17	1	no	—
448	C₂×C₄	—	17	1	no	—
449	C₂×C₄	—	17	1	no	—
450	C₂×C₄	—	17	1	no	—
451	C₂×C₄	—	17	1	no	—
452	C₂×C₄	—	17	1	no	—
453	C₂×C₄	—	17	1	no	—
454	C₂×C₄	—	17	1	no	—
455	C₂×C₄	—	17	1	no	—
456	C₂×C₄	—	17	1	no	—
457	C₂×C₄	—	17	1	no	—
458	C₂×C₄	—	17	1	no	—
459	C₂×C₄	—	17	1	no	—
460	C₂×C₄	—	17	1	no	—
461	C₂×C₄	—	17	1	no	—
462	C₂×C₄	—	17	1	no	—
463	C₂×C₄	—	34	2	no	—
464	C₂×C₄	—	68	4	no	—
465	C₂×C₄	—	68	4	no	—
466	C₂×C₄	—	136	4	no	—
467	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
468	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
469	C₂×C₄	#10587677	1	1	yes	characteristic
470	C₂×C₄	#10587677	1	1	yes	characteristic
471	C₂×C₄	#10587677	1	1	yes	characteristic
472	C₂×C₄	C₂³×#595	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	17	1	no	—
475	C₈	—	17	1	no	—
476	C₈	—	17	1	no	—
477	C₈	—	17	1	no	—
478	C₈	—	34	2	no	—
479	C₈	—	68	4	no	—
480	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
481	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
482	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
483	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
484	C₂²	—	4	1	no	—
485	C₂²	—	17	1	no	—
486	C₂²	—	17	1	no	—
487	C₂²	—	17	1	no	—
488	C₂²	—	17	1	no	—
489	C₂²	—	34	2	no	—
490	C₂²	—	34	2	no	—
491	C₂²	—	34	2	no	—
492	C₂²	—	68	1	no	—
493	C₂²	—	68	1	no	—
494	C₂²	—	68	1	no	—
495	C₂²	#11763753	1	1	yes	characteristic
496	C₂²	#11763753	1	1	yes	characteristic
497	C₂²	C₂×#10587677	1	1	yes	characteristic
498	C₄	—	4	2	no	—
499	C₄	—	17	1	no	—
500	C₄	—	17	1	no	—
501	C₄	—	17	1	no	—
502	C₄	—	17	1	no	—
503	C₄	—	68	2	no	—
504	C₄	—	136	4	no	—
505	C₄	#11763753	1	1	yes	characteristic
506	C₄	#11763753	1	1	yes	characteristic
507	C₄	C₂²×C₄⋊#595	1	1	yes	characteristic
508	C₄	C₂×#10587677	1	1	yes	characteristic
509	C₂	—	2	1	no	—
510	C₂	—	2	1	no	—
511	C₂	—	2	1	no	—
512	C₂	—	17	2	no	—
513	C₂	—	34	1	no	—
514	C₂	—	34	1	no	—
515	C₂	—	34	1	no	—
516	C₂	C₂×#11763753	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#10587677
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×#595
Fitting	C₁₇×#405	C₄
socle	C₂×C₁₇	C₂×#382
prime radical	C₂³×D₁₇	#41
cosocle	C₂×C₄×D₁₇	C₂⁴
hypercenter	#405	#595
hypocenter	C₁₇	C₂×#1833
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
3. #14544704	C₂	semidirect
4. #14544703	C₂	semidirect
27. #11762767	C₄	semidirect
29. #11762765	C₄	semidirect
30. #11762764	C₄	semidirect
32. #97×D₁₇	C₄	semidirect
33. C₄×C₈×D₁₇	C₄	semidirect
34. C₁₇×#405	C₄	semidirect
88. C₁₇×#97	C₂×C₄	semidirect
89. C₄×C₈×C₁₇	C₂×C₄	semidirect
90. #10587486	C₂×C₄	semidirect
91. #10587486	C₂×C₄	semidirect
92. C₈×Dic₁₇	C₂×C₄	semidirect
93. C₈×Dic₁₇	C₂×C₄	semidirect
94. #10587474	C₂×C₄	semidirect
95. C₄×#3622	C₂×C₄	semidirect
280. #405	#595	semidirect
292. D₁₇	#1833	semidirect
349. #97	C₂×#595	semidirect
353. C₄×C₈	C₂×#595	semidirect
354. C₁₇	C₂×#1833	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₇⋊#108	2
C₂×#11763819	2
#14544704	2
#14544703	2
#14544494	2
#14544454	2
D₁₇×#405	2
C₂×#1833	17

Subgroups — D17⋊#1833 #17969569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇⋊#1833 #17969569