Subgroups — #17957132

Order 4352.

714 conjugacy classes of subgroups.

The subgroup lattice has 492 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×#11763772	C₂	1	1	yes	maximal, characteristic
3	#14544488	C₂	1	2	yes	maximal
4	D₁₇⋊#338	C₂	1	2	yes	maximal
5	C₂×#108×D₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×D₁₇⋊M₁₆	C₂²	1	2	yes	—
7	C₂×D₁₇⋊M₁₆	C₂²	1	1	yes	characteristic
8	C₂×#10587677	C₂²	1	1	yes	characteristic
9	C₂×#10587536	—	2	1	no	—
10	D₁₇⋊#108	—	2	1	no	—
11	D₁₇⋊#108	—	2	1	no	—
12	D₁₇⋊#108	C₄	1	2	yes	complemented
13	D₁₇⋊#108	C₄	1	2	yes	complemented
14	C₂×#10587535	—	2	1	no	—
15	#11763772	—	2	1	no	—
16	#11763772	—	2	1	no	—
17	#11763772	—	2	1	no	—
18	#11763772	—	2	1	no	—
19	C₂×#10587532	C₄	1	2	yes	—
20	C₂×C₈×#595	C₄	1	2	yes	—
21	#11763688	—	2	4	no	—
22	#11763678	—	2	4	no	—
23	C₂×M₁₆×D₁₇	C₂²	1	2	yes	—
24	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
25	C₂×#10587490	C₄	1	1	yes	characteristic, complemented
26	C₂×#10587493	C₄	1	2	yes	complemented
27	#108×D₁₇	—	2	1	no	—
28	#108×D₁₇	—	2	1	no	—
29	#108×D₁₇	—	2	1	no	—
30	#108×D₁₇	—	2	1	no	—
31	C₂×C₁₇×#108	C₄	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₁₇	C₂³	1	1	yes	characteristic
33	C₂×C₂²⋊#595	Q₈	1	2	yes	—
34	C₂×#63247	—	2	1	no	—
35	C₂×#63247	—	2	2	no	—
36	#10587677	—	2	1	no	—
37	#10587677	—	2	1	no	—
38	#10587677	—	2	1	no	—
39	#10587677	—	2	1	no	—
40	C₂×C₄⋊#595	D₄	1	2	yes	—
41	C₂×C₄×#595	C₂×C₄	1	2	yes	—
42	D₁₇⋊M₁₆	—	2	1	no	—
43	D₁₇⋊M₁₆	—	2	1	no	—
44	D₁₇⋊M₁₆	—	2	2	no	—
45	D₁₇⋊M₁₆	—	2	2	no	—
46	D₁₇⋊M₁₆	—	2	2	no	—
47	D₁₇⋊M₁₆	C₂×C₄	1	4	yes	—
48	D₁₇⋊M₁₆	D₄	1	2	yes	—
49	D₁₇⋊M₁₆	Q₈	1	2	yes	—
50	C₂×#63243	—	2	1	no	—
51	C₂×#63243	—	2	2	no	—
52	C₂×#63242	—	2	2	no	—
53	C₂×#63242	C₂×C₄	1	2	yes	—
54	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
55	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂×#63223	C₂×C₄	1	2	yes	—
57	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
58	M₁₆×D₁₇	—	2	2	no	—
59	M₁₆×D₁₇	—	2	2	no	—
60	M₁₆×D₁₇	—	2	2	no	—
61	M₁₆×D₁₇	—	2	2	no	—
62	C₂×#63218	—	2	2	no	—
63	C₂×C₈×D₁₇	—	2	2	no	—
64	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
69	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
70	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
71	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
72	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
73	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
74	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
75	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
76	#10587536	—	2	2	no	—
77	#10587536	—	2	2	no	—
78	#10587535	—	2	2	no	—
79	#10587535	—	2	2	no	—
80	#10587532	—	2	2	no	—
81	#10587532	—	2	2	no	—
82	C₈×#595	—	2	2	no	—
83	C₈×#595	—	2	2	no	—
84	C₁₇×#108	—	2	1	no	—
85	C₁₇×#108	—	2	1	no	—
86	#10587493	—	2	2	no	—
87	#10587493	—	2	2	no	—
88	#10587490	—	2	1	no	—
89	#10587490	—	2	1	no	—
90	C₂³×D₁₇	C₂×Q₈	1	1	yes	characteristic
91	C₂²×#595	C₄⋊C₄	1	4	yes	—
92	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₁₇	#41	1	1	yes	characteristic
94	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
99	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
102	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
104	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
105	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
106	C₂²⋊#595	—	2	2	no	—
107	C₂²⋊#595	—	2	2	no	—
108	#63247	—	2	2	no	—
109	#63247	—	2	2	no	—
110	#63247	—	2	4	no	—
111	#63247	—	4	2	no	—
112	C₂×#3624	—	2	2	no	—
113	C₂×#3624	—	4	2	no	—
114	C₄⋊#595	—	2	2	no	—
115	C₄⋊#595	—	2	2	no	—
116	C₄×#595	—	2	2	no	—
117	C₄×#595	—	2	2	no	—
118	#63243	—	2	2	no	—
119	#63243	—	2	2	no	—
120	#63243	—	2	4	no	—
121	#63243	—	4	2	no	—
122	#63242	—	2	2	no	—
123	#63242	—	2	4	no	—
124	#63242	—	4	2	no	—
125	#63242	C₄⋊C₄	1	4	yes	—
126	M₁₆×C₁₇	—	2	2	no	—
127	M₁₆×C₁₇	—	2	2	no	—
128	C₂×C₈×C₁₇	—	2	2	no	—
129	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
130	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
131	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
135	#63223	—	2	2	no	—
136	#63223	—	2	2	no	—
137	C₂×#3622	—	2	2	no	—
138	C₂×#3622	C₄²	1	1	yes	characteristic
139	C₂×#3622	C₄²	1	1	yes	characteristic
140	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
141	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
142	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
143	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
144	#63218	—	4	2	no	—
145	#63218	—	4	2	no	—
146	C₈×D₁₇	—	4	2	no	—
147	C₈×D₁₇	—	4	2	no	—
148	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
149	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
150	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
152	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
153	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
154	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
155	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
156	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
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	#10867	—	17	1	no	maximal, Sylow
165	C₂³×C₁₇	C₄×Q₈	1	1	yes	characteristic
166	C₂²×D₁₇	—	4	2	no	—
167	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂²×D₁₇	C₄×Q₈	1	1	yes	characteristic
169	C₂²×D₁₇	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂²×D₁₇	C₂²⋊Q₈	1	1	yes	characteristic
171	C₂²×D₁₇	C₄⋊Q₈	1	1	yes	characteristic
172	C₂²×D₁₇	C₄⋊Q₈	1	1	yes	characteristic
173	C₂×#595	—	2	4	no	—
174	C₂×#595	—	4	4	no	—
175	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
176	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
181	C₂×Dic₁₇	#117	1	1	yes	characteristic
182	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
183	C₂×Dic₁₇	#121	1	1	yes	characteristic
184	C₂×Dic₁₇	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×Dic₁₇	#124	1	1	yes	characteristic
186	C₂×Dic₁₇	#125	1	1	yes	characteristic
187	C₄×D₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₄×D₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₄×D₁₇	#117	1	1	yes	characteristic
193	C₄×D₁₇	C₄×D₄	1	1	yes	characteristic
194	C₄×D₁₇	C₄×Q₈	1	1	yes	characteristic
195	C₄×D₁₇	#121	1	1	yes	characteristic
196	C₄×D₁₇	#121	1	1	yes	characteristic
197	C₄×D₁₇	#121	1	1	yes	characteristic
198	C₄×D₁₇	C₂²⋊Q₈	1	1	yes	characteristic
199	C₄×D₁₇	#124	1	1	yes	characteristic
200	C₄×D₁₇	#125	1	1	yes	characteristic
201	C₄×D₁₇	#127	1	1	yes	characteristic
202	C₄×D₁₇	C₄⋊Q₈	1	1	yes	characteristic
203	#3624	—	2	4	no	—
204	#3624	—	4	4	no	—
205	C₈×C₁₇	—	4	2	no	—
206	C₈×C₁₇	#95	1	1	yes	characteristic
207	C₈×C₁₇	#95	1	1	yes	characteristic
208	C₈×C₁₇	#95	1	1	yes	characteristic
209	C₈×C₁₇	#95	1	1	yes	characteristic
210	#3622	—	4	2	no	—
211	#3622	#95	1	1	yes	characteristic
212	#3622	#95	1	1	yes	characteristic
213	#3622	#95	1	1	yes	characteristic
214	#3622	#95	1	1	yes	characteristic
215	C₂²×#108	—	17	1	no	—
216	C₂²×#108	—	17	1	no	—
217	C₂×#405	—	17	1	no	—
218	#1742	—	17	2	no	—
219	C₂×#338	—	17	2	no	—
220	C₂²×C₁₇	—	4	1	no	—
221	C₂²×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
222	C₂²×C₁₇	#389	1	1	yes	characteristic
223	C₂²×C₁₇	#391	1	1	yes	characteristic
224	C₂×D₁₇	—	2	2	no	—
225	C₂×D₁₇	—	2	2	no	—
226	C₂×D₁₇	—	2	2	no	—
227	C₂×D₁₇	—	4	1	no	—
228	C₂×D₁₇	—	4	1	no	—
229	C₂×D₁₇	—	4	1	no	—
230	C₂×D₁₇	#380	1	1	yes	characteristic
231	C₂×D₁₇	#384	1	1	yes	characteristic
232	C₂×D₁₇	#389	1	1	yes	characteristic
233	C₂×D₁₇	#391	1	1	yes	characteristic
234	#595	—	4	4	no	—
235	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
236	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
237	C₄×C₁₇	#389	1	1	yes	characteristic
238	C₄×C₁₇	#390	1	1	yes	characteristic
239	Dic₁₇	#380	1	1	yes	characteristic
240	Dic₁₇	#382	1	1	yes	characteristic
241	Dic₁₇	#389	1	1	yes	characteristic
242	Dic₁₇	#390	1	1	yes	characteristic
243	C₂²×M₁₆	—	17	1	no	—
244	C₂²×M₁₆	—	17	2	no	—
245	C₂²×M₁₆	—	17	2	no	—
246	C₂³×C₈	—	17	1	no	—
247	C₂×#117	—	17	1	no	—
248	C₂×#108	—	17	2	no	—
249	C₂×#108	—	17	2	no	—
250	C₂×#108	—	17	2	no	—
251	C₂×#108	—	17	1	no	—
252	C₂×#108	—	34	1	no	—
253	C₂×#108	—	34	1	no	—
254	C₂×#108	—	34	1	no	—
255	C₂×#108	—	34	1	no	—
256	C₂×#108	—	34	1	no	—
257	C₂×#108	—	34	1	no	—
258	C₂×#108	—	34	1	no	—
259	C₂×#108	—	34	1	no	—
260	C₂×#108	#595	1	1	yes	characteristic, complemented
261	#405	—	34	1	no	—
262	#405	—	34	1	no	—
263	#405	—	34	1	no	—
264	#405	—	34	1	no	—
265	C₂×#97	—	17	2	no	—
266	C₂×C₄×C₈	—	17	2	no	—
267	#343	—	34	4	no	—
268	#338	—	34	4	no	—
269	C₂×C₁₇	—	2	1	no	—
270	C₂×C₁₇	—	2	1	no	—
271	C₂×C₁₇	—	2	1	no	—
272	C₂×C₁₇	C₄⋊#95	1	1	yes	characteristic
273	D₁₇	—	2	1	no	—
274	D₁₇	—	2	1	no	—
275	D₁₇	—	2	1	no	—
276	D₁₇	#1813	1	2	yes	—
277	C₂³×C₄	—	17	1	no	—
278	C₂×M₁₆	—	17	2	no	—
279	C₂×M₁₆	—	17	2	no	—
280	C₂×M₁₆	—	17	4	no	—
281	C₂×M₁₆	—	17	2	no	—
282	C₂×M₁₆	—	34	2	no	—
283	C₂×M₁₆	—	34	1	no	—
284	C₂×M₁₆	—	34	1	no	—
285	C₂×M₁₆	—	34	1	no	—
286	C₂×M₁₆	—	34	1	no	—
287	C₂×M₁₆	—	34	2	no	—
288	C₂×M₁₆	—	34	2	no	—
289	C₂×M₁₆	—	34	2	no	—
290	C₂×M₁₆	—	34	2	no	—
291	C₂×M₁₆	—	34	2	no	—
292	C₂×M₁₆	—	34	2	no	—
293	C₂×M₁₆	—	34	2	no	—
294	C₂×M₁₆	—	34	2	no	—
295	C₂×M₁₆	—	34	2	no	—
296	C₂×M₁₆	C₂×#595	1	2	yes	—
297	C₂²×C₈	—	17	1	no	—
298	C₂²×C₈	—	17	1	no	—
299	C₂²×C₈	—	17	1	no	—
300	C₂²×C₈	—	17	1	no	—
301	C₂²×C₈	—	17	1	no	—
302	C₂²×C₈	—	17	1	no	—
303	C₂²×C₈	—	17	1	no	—
304	C₂²×C₈	—	17	1	no	—
305	C₂²×C₈	—	17	1	no	—
306	C₂²×C₈	—	17	1	no	—
307	C₂²×C₈	—	17	1	no	—
308	C₂²×C₈	—	17	1	no	—
309	C₂²×C₈	—	17	1	no	—
310	C₂²×C₈	—	17	2	no	—
311	C₂²×C₈	—	34	2	no	—
312	C₂²×C₈	—	34	2	no	—
313	C₂²×C₈	C₂×#595	1	1	yes	characteristic
314	#117	—	34	1	no	—
315	#117	—	34	1	no	—
316	#117	—	34	1	no	—
317	#117	—	34	1	no	—
318	C₂×C₄⋊C₄	—	17	2	no	—
319	C₂×C₂²⋊C₄	—	17	2	no	—
320	C₂×C₄²	—	17	2	no	—
321	#108	—	2	1	no	—
322	#108	—	2	1	no	—
323	#108	—	34	2	no	—
324	#108	—	34	2	no	—
325	#108	—	34	2	no	—
326	#108	—	34	2	no	—
327	#108	—	34	2	no	—
328	#108	—	34	2	no	—
329	#108	—	34	1	no	—
330	#108	—	34	1	no	—
331	#97	—	34	2	no	—
332	#97	—	34	2	no	—
333	C₄×C₈	—	34	2	no	—
334	C₄×C₈	—	34	2	no	—
335	C₁₇	#10867	1	1	yes	characteristic, complemented, Sylow
336	C₂⁴	—	17	1	no	—
337	C₂²×C₄	—	17	1	no	—
338	C₂²×C₄	—	17	1	no	—
339	C₂²×C₄	—	17	1	no	—
340	C₂²×C₄	—	17	1	no	—
341	C₂²×C₄	—	17	1	no	—
342	C₂²×C₄	—	17	1	no	—
343	C₂²×C₄	—	17	1	no	—
344	C₂²×C₄	—	17	1	no	—
345	C₂²×C₄	—	17	1	no	—
346	C₂²×C₄	—	17	1	no	—
347	C₂²×C₄	—	17	1	no	—
348	C₂²×C₄	—	17	1	no	—
349	C₂²×C₄	—	17	1	no	—
350	C₂²×C₄	—	17	4	no	—
351	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
352	M₁₆	—	2	2	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	34	2	no	—
355	M₁₆	—	34	2	no	—
356	M₁₆	—	34	2	no	—
357	M₁₆	—	34	2	no	—
358	M₁₆	—	34	4	no	—
359	M₁₆	—	34	4	no	—
360	M₁₆	—	34	2	no	—
361	M₁₆	—	34	2	no	—
362	M₁₆	—	68	2	no	—
363	M₁₆	—	68	2	no	—
364	M₁₆	—	68	2	no	—
365	M₁₆	—	68	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	17	1	no	—
368	C₂×C₈	—	17	1	no	—
369	C₂×C₈	—	17	1	no	—
370	C₂×C₈	—	17	1	no	—
371	C₂×C₈	—	17	1	no	—
372	C₂×C₈	—	17	1	no	—
373	C₂×C₈	—	17	1	no	—
374	C₂×C₈	—	17	1	no	—
375	C₂×C₈	—	17	1	no	—
376	C₂×C₈	—	17	1	no	—
377	C₂×C₈	—	17	1	no	—
378	C₂×C₈	—	17	1	no	—
379	C₂×C₈	—	17	1	no	—
380	C₂×C₈	—	17	1	no	—
381	C₂×C₈	—	17	1	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	4	no	—
390	C₂×C₈	—	34	2	no	—
391	C₂×C₈	—	34	2	no	—
392	C₂×C₈	—	34	4	no	—
393	C₂×C₈	—	34	2	no	—
394	C₂×C₈	—	68	2	no	—
395	C₂×C₈	—	68	2	no	—
396	C₂×C₈	—	68	2	no	—
397	C₂×C₈	—	68	2	no	—
398	C₂×C₈	C₄×#595	1	1	yes	characteristic
399	C₂×C₈	C₄×#595	1	1	yes	characteristic
400	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
401	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
402	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
403	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
404	C₄⋊C₄	—	34	2	no	—
405	C₄⋊C₄	—	34	2	no	—
406	C₂²⋊C₄	—	34	2	no	—
407	C₂²⋊C₄	—	34	2	no	—
408	C₄²	—	34	2	no	—
409	C₄²	—	34	2	no	—
410	C₂³	—	17	1	no	—
411	C₂³	—	17	1	no	—
412	C₂³	—	17	1	no	—
413	C₂³	—	17	1	no	—
414	C₂³	—	17	1	no	—
415	C₂³	—	17	1	no	—
416	C₂³	—	68	2	no	—
417	C₂³	Q₈×#595	1	1	yes	characteristic
418	C₂×C₄	—	17	1	no	—
419	C₂×C₄	—	17	1	no	—
420	C₂×C₄	—	17	1	no	—
421	C₂×C₄	—	17	1	no	—
422	C₂×C₄	—	17	1	no	—
423	C₂×C₄	—	17	1	no	—
424	C₂×C₄	—	17	1	no	—
425	C₂×C₄	—	17	1	no	—
426	C₂×C₄	—	17	1	no	—
427	C₂×C₄	—	17	1	no	—
428	C₂×C₄	—	17	1	no	—
429	C₂×C₄	—	17	1	no	—
430	C₂×C₄	—	17	1	no	—
431	C₂×C₄	—	17	1	no	—
432	C₂×C₄	—	17	1	no	—
433	C₂×C₄	—	17	1	no	—
434	C₂×C₄	—	17	1	no	—
435	C₂×C₄	—	17	1	no	—
436	C₂×C₄	—	17	1	no	—
437	C₂×C₄	—	17	1	no	—
438	C₂×C₄	—	17	1	no	—
439	C₂×C₄	—	17	1	no	—
440	C₂×C₄	—	34	4	no	—
441	C₂×C₄	—	68	4	no	—
442	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
443	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
444	C₂×C₄	D₄×#595	1	1	yes	characteristic
445	C₂×C₄	D₄×#595	1	1	yes	characteristic
446	C₂×C₄	Q₈×#595	1	1	yes	characteristic
447	C₂×C₄	C₂×C₂²⋊#595	1	1	yes	characteristic
448	C₈	—	4	2	no	—
449	C₈	—	17	1	no	—
450	C₈	—	17	1	no	—
451	C₈	—	17	1	no	—
452	C₈	—	17	1	no	—
453	C₈	—	34	4	no	—
454	C₈	—	68	4	no	—
455	C₈	—	68	2	no	—
456	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
457	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
458	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
459	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
460	C₂²	—	4	1	no	—
461	C₂²	—	17	1	no	—
462	C₂²	—	17	1	no	—
463	C₂²	—	17	1	no	—
464	C₂²	—	17	1	no	—
465	C₂²	—	34	2	no	—
466	C₂²	—	34	2	no	—
467	C₂²	—	34	2	no	—
468	C₂²	—	68	1	no	—
469	C₂²	—	68	1	no	—
470	C₂²	—	68	1	no	—
471	C₂²	C₄⋊C₄×#595	1	1	yes	characteristic
472	C₂²	#11763760	1	1	yes	characteristic
473	C₂²	(C₂×#595)⋊Q₈	1	1	yes	characteristic
474	C₄	—	17	1	no	—
475	C₄	—	17	1	no	—
476	C₄	—	17	1	no	—
477	C₄	—	17	1	no	—
478	C₄	—	68	4	no	—
479	C₄	C₂×(C₂×#595)⋊C₄	1	1	yes	characteristic
480	C₄	C₄⋊C₄×#595	1	1	yes	characteristic
481	C₄	#11763760	1	1	yes	characteristic
482	C₄	#11763761	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	—	17	2	no	—
487	C₂	—	34	1	no	—
488	C₂	—	34	1	no	—
489	C₂	—	34	1	no	—
490	C₂	#14543961	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊C₄×#595
commutator	C₂×C₄×C₁₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#595
Fitting	C₂×C₁₇×#108	C₄
socle	C₂×C₁₇	C₄⋊#95
prime radical	C₂³×D₁₇	C₂×Q₈
cosocle	C₂²×C₄×D₁₇	C₂³
hypercenter	C₂×#108	#595
hypocenter	C₁₇	#10867
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
12. D₁₇⋊#108	C₄	semidirect
13. D₁₇⋊#108	C₄	semidirect
25. C₂×#10587490	C₄	semidirect
26. C₂×#10587493	C₄	semidirect
31. C₂×C₁₇×#108	C₄	semidirect
260. C₂×#108	#595	semidirect
335. C₁₇	#10867	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×#11763772	2
#14544488	2
D₁₇⋊#338	2
C₂×#108×D₁₇	2
#10867	17