Subgroups — #443×#595 #17968826

Order 4352.

1046 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇⋊#443	C₂	1	1	yes	maximal, characteristic
2	#135×#595	C₂	1	1	yes	maximal, characteristic
3	#131×#595	C₂	1	2	yes	maximal, complemented
4	#108×#595	C₂	1	1	yes	maximal, characteristic, complemented
5	#14544589	C₂	1	1	yes	maximal, characteristic, complemented
6	#14544586	C₂	1	1	yes	maximal, characteristic, complemented
7	#14544560	C₂	1	2	yes	maximal, complemented
8	#14544558	C₂	1	2	yes	maximal, complemented
9	#104×#595	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×#595	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₇×#443	C₂	1	1	yes	maximal, characteristic
12	D₁₇⋊#131	C₂²	1	2	yes	—
13	#41×#595	C₂²	1	2	yes	—
14	#11763853	C₄	1	2	yes	complemented
15	#11763852	C₄	1	4	yes	complemented
16	#11763851	C₄	1	2	yes	complemented
17	Q₁₆×#595	C₄	1	2	yes	complemented
18	SD₁₆×#595	C₄	1	4	yes	complemented
19	D₈×#595	C₄	1	2	yes	complemented
20	D₁₇⋊#108	C₂²	1	1	yes	characteristic
21	#11763819	C₂²	1	1	yes	characteristic
22	D₁₇⋊#104	C₂²	1	2	yes	—
23	#11763799	C₂²	1	2	yes	—
24	#11763775	—	2	2	no	—
25	#11763775	C₂²	1	2	yes	—
26	#11763772	—	2	2	no	—
27	#11763772	C₂²	1	2	yes	—
28	M₁₆×#595	—	2	2	no	—
29	M₁₆×#595	C₂²	1	2	yes	—
30	C₄×#63242	C₂²	1	1	yes	characteristic
31	C₂×C₈×#595	—	2	2	no	—
32	C₂×C₈×#595	C₂²	1	1	yes	characteristic
33	C₂×C₈×#595	C₂²	1	1	yes	characteristic
34	C₂×C₈×#595	C₂²	1	1	yes	characteristic
35	C₂×C₈×#595	C₂²	1	1	yes	characteristic
36	C₄²×#595	C₂²	1	1	yes	characteristic
37	#11763684	C₂²	1	2	yes	—
38	#11763681	C₂²	1	2	yes	—
39	#11763680	C₂²	1	2	yes	—
40	#135×D₁₇	C₂²	1	1	yes	characteristic
41	#131×D₁₇	C₂²	1	2	yes	—
42	#11762927	C₄	1	1	yes	characteristic, complemented
43	#11762926	C₄	1	1	yes	characteristic, complemented
44	#11762925	C₄	1	1	yes	characteristic, complemented
45	#11762924	C₄	1	2	yes	complemented
46	#11762923	C₄	1	2	yes	complemented
47	#108×D₁₇	C₂²	1	1	yes	characteristic
48	#104×D₁₇	C₂²	1	2	yes	—
49	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
50	C₁₇×#443	C₄	1	1	yes	characteristic, complemented
51	#41×D₁₇	C₂³	1	2	yes	—
52	Q₈×#595	C₂×C₄	1	4	yes	—
53	#10587680	C₂×C₄	1	4	yes	complemented
54	D₄×#595	—	2	4	no	—
55	D₄×#595	C₂×C₄	1	4	yes	—
56	#10587678	—	2	4	no	—
57	#10587678	C₂×C₄	1	4	yes	complemented
58	#10587677	—	2	2	no	—
59	#10587677	C₂³	1	2	yes	—
60	C₂×C₄×#595	—	2	2	no	—
61	C₂×C₄×#595	—	2	2	no	—
62	C₂×C₄×#595	C₂³	1	1	yes	characteristic
63	C₂×C₄×#595	C₂³	1	1	yes	characteristic
64	D₁₇⋊M₁₆	—	2	2	no	—
65	D₁₇⋊M₁₆	C₂³	1	2	yes	—
66	C₂×#63242	—	2	2	no	—
67	C₂×#63242	C₂³	1	1	yes	characteristic
68	C₂×#63242	C₂³	1	1	yes	characteristic
69	C₁₇×#135	C₂×C₄	1	1	yes	characteristic
70	C₁₇×#131	C₂×C₄	1	2	yes	complemented
71	#10587636	C₂×C₄	1	2	yes	—
72	#10587634	C₂×C₄	1	2	yes	complemented
73	#10587605	C₂×C₄	1	1	yes	characteristic
74	Q₁₆×D₁₇	C₂×C₄	1	1	yes	characteristic
75	#10587602	C₂×C₄	1	2	yes	—
76	SD₁₆×D₁₇	C₂×C₄	1	2	yes	—
77	#10587598	C₂×C₄	1	1	yes	characteristic
78	D₈×D₁₇	C₂×C₄	1	1	yes	characteristic
79	#10587593	—	2	2	no	—
80	#10587593	C₂×C₄	1	2	yes	complemented
81	M₁₆×D₁₇	—	2	2	no	—
82	M₁₆×D₁₇	C₂³	1	2	yes	—
83	#10587590	C₂×C₄	1	1	yes	characteristic
84	#10587587	—	2	2	no	—
85	#10587587	C₂×C₄	1	2	yes	complemented
86	C₂×C₈×D₁₇	—	2	2	no	—
87	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
88	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
89	C₄²×D₁₇	C₂³	1	1	yes	characteristic
90	#10587550	C₂×C₄	1	4	yes	complemented
91	#10587549	C₂×C₄	1	4	yes	—
92	#10587548	C₂×C₄	1	4	yes	complemented
93	#10587547	C₂×C₄	1	4	yes	—
94	C₄×#3624	—	2	2	no	—
95	#10587536	C₂×C₄	1	2	yes	complemented
96	#10587535	C₂×C₄	1	2	yes	complemented
97	#10587534	C₂×C₄	1	2	yes	—
98	#10587533	C₂×C₄	1	2	yes	—
99	#10587532	—	2	2	no	—
100	#10587532	—	2	2	no	—
101	#10587532	—	2	2	no	—
102	C₈×#595	—	2	2	no	—
103	C₈×#595	—	2	1	no	—
104	C₈×#595	—	2	1	no	—
105	C₈×#595	—	2	2	no	—
106	C₈×#595	—	2	2	no	—
107	C₈×#595	C₂×C₄	1	2	yes	—
108	C₈×#595	C₂×C₄	1	2	yes	—
109	C₈×#595	C₂×C₄	1	2	yes	complemented
110	C₈×#595	C₂×C₄	1	2	yes	complemented
111	C₈×#595	D₄	1	1	yes	characteristic
112	C₈×#595	D₄	1	1	yes	characteristic
113	C₈×#595	D₄	1	1	yes	characteristic
114	C₈×#595	D₄	1	1	yes	characteristic
115	C₁₇×#108	C₂×C₄	1	1	yes	characteristic, complemented
116	C₁₇×#104	C₂×C₄	1	2	yes	complemented
117	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic, complemented
118	#10587508	C₂×C₄	1	2	yes	complemented
119	#10587496	C₂×C₄	1	2	yes	complemented
120	#10587493	C₂×C₄	1	2	yes	complemented
121	#10587490	C₂×C₄	1	1	yes	characteristic, complemented
122	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic, complemented
123	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic, complemented
124	#10587476	C₂×C₄	1	2	yes	complemented
125	C₄×#3622	C₂×C₄	1	1	yes	characteristic, complemented
126	C₂²×#595	—	2	1	no	—
127	C₂²×#595	—	2	4	no	—
128	C₂²×#595	#41	1	2	yes	—
129	#41×C₁₇	C₂²×C₄	1	2	yes	—
130	#63256	C₂²×C₄	1	2	yes	—
131	Q₈×D₁₇	C₂²×C₄	1	2	yes	—
132	#63254	—	2	2	no	—
133	#63254	C₂²×C₄	1	2	yes	—
134	D₄×D₁₇	—	2	2	no	—
135	D₄×D₁₇	C₂²×C₄	1	2	yes	—
136	#63252	—	2	2	no	—
137	#63252	C₂²×C₄	1	2	yes	—
138	C₂×C₄×D₁₇	—	2	1	no	—
139	C₂×C₄×D₁₇	—	2	2	no	—
140	C₂×C₄×D₁₇	C₂⁴	1	1	yes	characteristic
141	C₂²⋊#595	—	2	2	no	—
142	C₂²⋊#595	—	2	4	no	—
143	#63247	—	2	2	no	—
144	#63247	—	2	4	no	—
145	C₂×#3624	—	2	1	no	—
146	C₂×#3624	—	2	4	no	—
147	C₂×#3624	#41	1	2	yes	—
148	C₄⋊#595	—	2	4	no	—
149	C₄⋊#595	C₂²×C₄	1	4	yes	—
150	C₄×#595	—	2	8	no	—
151	C₄×#595	—	2	4	no	—
152	C₄×#595	—	2	2	no	—
153	C₄×#595	—	2	1	no	—
154	C₄×#595	C₂²×C₄	1	2	yes	—
155	C₄×#595	C₂²×C₄	1	2	yes	—
156	C₄×#595	C₂×D₄	1	1	yes	characteristic
157	C₄×#595	C₂×D₄	1	1	yes	characteristic
158	#63243	—	2	4	no	—
159	#63243	C₂²×C₄	1	4	yes	—
160	#63242	—	2	2	no	—
161	#63242	—	2	1	no	—
162	#63242	—	2	4	no	—
163	#63242	C₂²×C₄	1	2	yes	—
164	#63242	C₂²×C₄	1	2	yes	—
165	#63242	C₂×D₄	1	1	yes	characteristic
166	#63242	C₂×D₄	1	1	yes	characteristic
167	Q₁₆×C₁₇	C₄²	1	1	yes	characteristic, complemented
168	SD₁₆×C₁₇	C₄²	1	2	yes	complemented
169	D₈×C₁₇	C₄²	1	1	yes	characteristic, complemented
170	M₁₆×C₁₇	—	2	2	no	—
171	M₁₆×C₁₇	C₂²×C₄	1	2	yes	—
172	C₂×C₈×C₁₇	—	2	2	no	—
173	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
176	#63231	C₄²	1	2	yes	complemented
177	#63230	C₄²	1	2	yes	complemented
178	#63229	C₄²	1	2	yes	complemented
179	#63228	C₄²	1	2	yes	complemented
180	C₄×Dic₁₇	—	2	1	no	—
181	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
182	#63223	—	2	2	no	—
183	#63223	C₂²×C₄	1	2	yes	—
184	C₂×#3622	—	2	2	no	—
185	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
186	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
187	Dic₆₈	C₄²	1	1	yes	characteristic, complemented
188	D₁₃₆	C₄²	1	1	yes	characteristic, complemented
189	#63219	C₄²	1	2	yes	complemented
190	#63218	—	2	2	no	—
191	#63218	—	2	2	no	—
192	#63218	—	2	2	no	—
193	C₈×D₁₇	—	2	2	no	—
194	C₈×D₁₇	—	2	2	no	—
195	C₈×D₁₇	—	2	2	no	—
196	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
197	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
198	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
199	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
200	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
201	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
202	C₈×D₁₇	#41	1	1	yes	characteristic
203	C₈×D₁₇	#41	1	1	yes	characteristic
204	C₄×#443	—	17	1	no	maximal, Sylow
205	C₂²×D₁₇	—	2	2	no	—
206	C₂²×D₁₇	C₂×#41	1	1	yes	characteristic
207	C₂×#595	—	2	4	no	—
208	C₂×#595	—	2	2	no	—
209	C₂×#595	—	2	4	no	—
210	C₂×#595	—	2	4	no	—
211	C₂×#595	—	4	8	no	—
212	C₂×#595	C₄×D₄	1	2	yes	—
213	C₂×#595	C₄×D₄	1	2	yes	—
214	Q₈×C₁₇	C₂×C₄²	1	2	yes	—
215	D₄×C₁₇	—	2	2	no	—
216	D₄×C₁₇	C₂×C₄²	1	2	yes	—
217	C₂×C₄×C₁₇	—	2	1	no	—
218	C₂×C₄×C₁₇	—	2	2	no	—
219	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
220	C₂²⋊D₁₇	—	2	2	no	—
221	C₂²⋊D₁₇	—	2	2	no	—
222	C₂²⋊D₁₇	—	2	2	no	—
223	C₂×Dic₁₇	—	2	1	no	—
224	C₂×Dic₁₇	—	2	2	no	—
225	C₂×Dic₁₇	C₂×#41	1	1	yes	characteristic
226	D₆₈	—	2	2	no	—
227	D₆₈	C₂×C₄²	1	2	yes	—
228	C₄×D₁₇	—	2	4	no	—
229	C₄×D₁₇	—	2	2	no	—
230	C₄×D₁₇	—	2	2	no	—
231	C₄×D₁₇	—	2	2	no	—
232	C₄×D₁₇	C₂³×C₄	1	1	yes	characteristic
233	C₄×D₁₇	C₂³×C₄	1	1	yes	characteristic
234	C₄×D₁₇	C₂²×D₄	1	1	yes	characteristic
235	C₄×D₁₇	C₂×#41	1	1	yes	characteristic
236	Dic₃₄	—	2	2	no	—
237	Dic₃₄	C₂×C₄²	1	2	yes	—
238	#3624	—	2	4	no	—
239	#3624	—	2	2	no	—
240	#3624	C₄×D₄	1	2	yes	—
241	#3624	C₄×D₄	1	2	yes	—
242	C₈×C₁₇	—	2	2	no	—
243	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
244	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
245	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
246	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
247	#3622	—	2	2	no	—
248	#3622	C₂×C₄²	1	1	yes	characteristic
249	#3622	C₂×C₄²	1	1	yes	characteristic
250	#3622	C₄×D₄	1	1	yes	characteristic
251	#3622	C₄×D₄	1	1	yes	characteristic
252	C₂×#443	—	17	1	no	—
253	C₂×#443	—	17	1	no	—
254	C₄×#135	—	17	1	no	—
255	C₄×#131	—	17	2	no	—
256	C₄×#108	—	17	1	no	—
257	#1772	—	17	1	no	—
258	#1772	—	17	1	no	—
259	#1764	—	17	2	no	—
260	#1764	—	17	2	no	—
261	C₄×#104	—	17	2	no	—
262	C₄²×C₈	—	17	1	no	—
263	C₂²×C₁₇	—	2	2	no	—
264	C₂²×C₁₇	C₄×#41	1	1	yes	characteristic
265	C₂×D₁₇	—	2	2	no	—
266	C₂×D₁₇	—	2	2	no	—
267	C₂×D₁₇	—	4	4	no	—
268	C₂×D₁₇	C₂×C₄×D₄	1	1	yes	characteristic
269	C₂×D₁₇	C₄×#41	1	1	yes	characteristic
270	#595	—	2	4	no	—
271	#595	—	2	2	no	—
272	#595	—	4	4	no	—
273	#595	#443	1	4	yes	direct product factor
274	C₄×C₁₇	—	2	2	no	—
275	C₄×C₁₇	—	2	2	no	—
276	C₄×C₁₇	C₂²×C₄²	1	1	yes	characteristic
277	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
278	Dic₁₇	—	2	2	no	—
279	Dic₁₇	—	2	2	no	—
280	Dic₁₇	C₂×C₄×D₄	1	1	yes	characteristic
281	Dic₁₇	C₄×#41	1	1	yes	characteristic
282	C₂×#135	—	17	1	no	—
283	C₂×#131	—	17	2	no	—
284	C₂×#131	—	17	2	no	—
285	C₄×#41	—	17	2	no	—
286	#443	—	17	2	no	—
287	#443	—	17	4	no	—
288	#443	—	17	2	no	—
289	#443	—	17	1	no	—
290	#443	—	17	2	no	—
291	#443	—	17	1	no	—
292	#443	—	17	2	no	—
293	#443	—	17	1	no	—
294	#443	#595	1	1	yes	characteristic, direct product factor
295	C₄×Q₁₆	—	17	2	no	—
296	C₄×SD₁₆	—	17	4	no	—
297	C₄×D₈	—	17	2	no	—
298	C₂×#108	—	17	1	no	—
299	C₂×#108	—	17	1	no	—
300	#427	—	17	1	no	—
301	C₂×#104	—	17	2	no	—
302	C₂×#104	—	17	2	no	—
303	#416	—	17	2	no	—
304	#405	—	17	2	no	—
305	#405	—	17	2	no	—
306	#405	—	34	2	no	—
307	#405	—	34	2	no	—
308	C₄×M₁₆	—	17	2	no	—
309	C₄×M₁₆	—	34	2	no	—
310	C₂×C₄×C₈	—	17	1	no	—
311	C₂×C₄×C₈	—	17	1	no	—
312	C₂×C₄×C₈	—	17	1	no	—
313	C₂×C₄×C₈	—	17	1	no	—
314	C₂×C₄×C₈	—	17	1	no	—
315	C₂×C₄×C₈	—	17	1	no	—
316	C₂×C₄×C₈	—	34	2	no	—
317	C₄³	—	17	1	no	—
318	#341	—	17	2	no	—
319	#339	—	17	2	no	—
320	#339	—	17	2	no	—
321	C₂×C₁₇	—	2	1	no	—
322	C₂×C₁₇	—	4	2	no	—
323	C₂×C₁₇	C₄²×D₄	1	1	yes	characteristic
324	D₁₇	—	2	1	no	—
325	D₁₇	—	4	2	no	—
326	D₁₇	C₂×#443	1	2	yes	—
327	C₂×#41	—	17	2	no	—
328	#135	—	17	2	no	—
329	#135	—	17	1	no	—
330	#135	—	17	2	no	—
331	#135	—	17	1	no	—
332	#135	—	17	1	no	—
333	#135	C₂×#595	1	1	yes	characteristic
334	C₂×Q₁₆	—	17	1	no	—
335	C₂×SD₁₆	—	17	2	no	—
336	C₂×D₈	—	17	1	no	—
337	#131	—	17	4	no	—
338	#131	—	17	4	no	—
339	#131	—	17	2	no	—
340	#131	—	17	2	no	—
341	#131	—	17	2	no	—
342	#131	—	34	2	no	—
343	#131	—	34	2	no	—
344	#131	—	34	4	no	—
345	#131	C₂×#595	1	2	yes	complemented
346	C₂×M₁₆	—	17	2	no	—
347	C₂×M₁₆	—	17	2	no	—
348	C₂×M₁₆	—	34	2	no	—
349	C₂×M₁₆	—	34	2	no	—
350	C₂²×C₈	—	17	1	no	—
351	C₂²×C₈	—	17	1	no	—
352	C₂²×C₈	—	17	1	no	—
353	C₂²×C₈	—	17	1	no	—
354	C₂²×C₈	—	34	2	no	—
355	C₂²×C₈	—	34	2	no	—
356	C₄×Q₈	—	17	4	no	—
357	C₄×D₄	—	17	4	no	—
358	C₄×D₄	—	34	4	no	—
359	#117	—	17	2	no	—
360	#117	—	34	2	no	—
361	C₂×C₄²	—	17	1	no	—
362	C₂×C₄²	—	17	1	no	—
363	C₂×C₄²	—	17	1	no	—
364	C₂×C₄²	—	34	2	no	—
365	C₂×C₄²	—	34	2	no	—
366	#108	—	17	2	no	—
367	#108	—	17	2	no	—
368	#108	—	17	2	no	—
369	#108	—	17	1	no	—
370	#108	C₂×#595	1	1	yes	characteristic, complemented
371	#107	—	17	2	no	—
372	#106	—	17	2	no	—
373	#104	—	17	4	no	—
374	#104	—	17	4	no	—
375	#104	—	17	2	no	—
376	#104	—	17	2	no	—
377	#104	—	17	2	no	—
378	#104	C₂×#595	1	2	yes	complemented
379	#103	—	17	4	no	—
380	#102	—	17	4	no	—
381	#97	—	34	2	no	—
382	#97	—	34	2	no	—
383	#97	—	34	2	no	—
384	C₄×C₈	—	17	2	no	—
385	C₄×C₈	—	17	2	no	—
386	C₄×C₈	—	17	2	no	—
387	C₄×C₈	—	17	2	no	—
388	C₄×C₈	—	17	1	no	—
389	C₄×C₈	—	17	1	no	—
390	C₄×C₈	—	17	1	no	—
391	C₄×C₈	—	17	1	no	—
392	C₄×C₈	—	17	1	no	—
393	C₄×C₈	—	17	1	no	—
394	C₄×C₈	—	17	1	no	—
395	C₄×C₈	—	34	2	no	—
396	C₄×C₈	—	34	1	no	—
397	C₄×C₈	—	34	1	no	—
398	C₄×C₈	—	34	2	no	—
399	C₄×C₈	—	34	2	no	—
400	C₄×C₈	—	34	2	no	—
401	C₄×C₈	C₂×#595	1	1	yes	characteristic, complemented
402	C₁₇	C₄×#443	1	1	yes	characteristic, complemented, Sylow
403	#41	—	17	2	no	—
404	#41	—	17	2	no	—
405	#41	—	17	2	no	—
406	#41	—	34	2	no	—
407	#41	—	34	2	no	—
408	#41	C₂²×#595	1	2	yes	—
409	C₂×Q₈	—	17	2	no	—
410	C₂×D₄	—	17	2	no	—
411	C₂×D₄	—	34	2	no	—
412	C₂²×C₄	—	17	1	no	—
413	C₂²×C₄	—	17	2	no	—
414	C₂²×C₄	—	34	2	no	—
415	C₂²×C₄	—	34	1	no	—
416	C₂²×C₄	—	34	4	no	—
417	C₂²×C₄	—	34	1	no	—
418	Q₁₆	—	17	2	no	—
419	Q₁₆	—	17	1	no	—
420	Q₁₆	C₄×#595	1	1	yes	characteristic, complemented
421	SD₁₆	—	17	2	no	—
422	SD₁₆	—	17	2	no	—
423	SD₁₆	—	17	2	no	—
424	SD₁₆	C₄×#595	1	2	yes	complemented
425	D₈	—	17	2	no	—
426	D₈	—	17	1	no	—
427	D₈	C₄×#595	1	1	yes	characteristic, complemented
428	M₁₆	—	2	2	no	—
429	M₁₆	—	17	4	no	—
430	M₁₆	—	17	2	no	—
431	M₁₆	—	34	2	no	—
432	M₁₆	—	34	2	no	—
433	M₁₆	—	34	2	no	—
434	M₁₆	—	34	4	no	—
435	M₁₆	—	34	4	no	—
436	M₁₆	—	34	2	no	—
437	M₁₆	—	34	2	no	—
438	M₁₆	C₂²×#595	1	2	yes	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	17	2	no	—
441	C₂×C₈	—	17	1	no	—
442	C₂×C₈	—	17	1	no	—
443	C₂×C₈	—	17	2	no	—
444	C₂×C₈	—	17	1	no	—
445	C₂×C₈	—	17	1	no	—
446	C₂×C₈	—	17	1	no	—
447	C₂×C₈	—	17	1	no	—
448	C₂×C₈	—	17	1	no	—
449	C₂×C₈	—	17	1	no	—
450	C₂×C₈	—	17	1	no	—
451	C₂×C₈	—	17	1	no	—
452	C₂×C₈	—	17	1	no	—
453	C₂×C₈	—	17	1	no	—
454	C₂×C₈	—	17	2	no	—
455	C₂×C₈	—	34	2	no	—
456	C₂×C₈	—	34	2	no	—
457	C₂×C₈	—	34	2	no	—
458	C₂×C₈	—	34	4	no	—
459	C₂×C₈	—	34	4	no	—
460	C₂×C₈	—	34	2	no	—
461	C₂×C₈	—	34	1	no	—
462	C₂×C₈	—	34	1	no	—
463	C₂×C₈	—	34	2	no	—
464	C₂×C₈	C₂²×#595	1	1	yes	characteristic
465	C₂×C₈	C₂²×#595	1	1	yes	characteristic
466	C₄⋊C₄	—	17	4	no	—
467	C₄⋊C₄	—	34	4	no	—
468	C₂²⋊C₄	—	34	4	no	—
469	C₂²⋊C₄	—	34	2	no	—
470	C₄²	—	17	2	no	—
471	C₄²	—	17	1	no	—
472	C₄²	—	17	1	no	—
473	C₄²	—	17	2	no	—
474	C₄²	—	17	1	no	—
475	C₄²	—	34	1	no	—
476	C₄²	—	34	2	no	—
477	C₄²	—	34	1	no	—
478	C₄²	—	34	4	no	—
479	C₄²	—	34	8	no	—
480	C₄²	C₂²×#595	1	1	yes	characteristic
481	C₂³	—	17	1	no	—
482	C₂³	—	34	2	no	—
483	Q₈	—	17	2	no	—
484	Q₈	—	34	2	no	—
485	Q₈	C₂×C₄×#595	1	2	yes	—
486	D₄	—	2	2	no	—
487	D₄	—	17	2	no	—
488	D₄	—	34	2	no	—
489	D₄	—	34	2	no	—
490	D₄	—	34	2	no	—
491	D₄	—	34	2	no	—
492	D₄	C₂×C₄×#595	1	2	yes	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	17	2	no	—
496	C₂×C₄	—	17	1	no	—
497	C₂×C₄	—	17	1	no	—
498	C₂×C₄	—	17	1	no	—
499	C₂×C₄	—	17	1	no	—
500	C₂×C₄	—	17	1	no	—
501	C₂×C₄	—	17	2	no	—
502	C₂×C₄	—	34	2	no	—
503	C₂×C₄	—	34	2	no	—
504	C₂×C₄	—	34	4	no	—
505	C₂×C₄	—	34	2	no	—
506	C₂×C₄	—	34	4	no	—
507	C₂×C₄	—	34	2	no	—
508	C₂×C₄	—	34	4	no	—
509	C₂×C₄	—	34	1	no	—
510	C₂×C₄	—	34	2	no	—
511	C₂×C₄	—	34	4	no	—
512	C₂×C₄	—	68	8	no	—
513	C₂×C₄	C₂³×#595	1	1	yes	characteristic
514	C₈	—	2	2	no	—
515	C₈	—	17	2	no	—
516	C₈	—	17	2	no	—
517	C₈	—	17	1	no	—
518	C₈	—	17	1	no	—
519	C₈	—	17	1	no	—
520	C₈	—	17	1	no	—
521	C₈	—	34	2	no	—
522	C₈	—	34	4	no	—
523	C₈	—	34	2	no	—
524	C₈	C₂×C₄×#595	1	1	yes	characteristic
525	C₈	C₂×C₄×#595	1	1	yes	characteristic
526	C₈	D₄×#595	1	1	yes	characteristic
527	C₈	D₄×#595	1	1	yes	characteristic
528	C₂²	—	2	2	no	—
529	C₂²	—	17	1	no	—
530	C₂²	—	17	1	no	—
531	C₂²	—	34	2	no	—
532	C₂²	—	34	2	no	—
533	C₂²	—	68	4	no	—
534	C₂²	#41×#595	1	1	yes	characteristic
535	C₄	—	2	2	no	—
536	C₄	—	2	2	no	—
537	C₄	—	17	4	no	—
538	C₄	—	17	1	no	—
539	C₄	—	17	1	no	—
540	C₄	—	34	2	no	—
541	C₄	—	34	2	no	—
542	C₄	—	34	4	no	—
543	C₄	—	34	2	no	—
544	C₄	—	68	4	no	—
545	C₄	C₂²×C₄×#595	1	1	yes	characteristic
546	C₄	C₂×D₄×#595	1	1	yes	characteristic
547	C₂	—	2	1	no	—
548	C₂	—	4	2	no	—
549	C₂	—	17	2	no	—
550	C₂	—	34	1	no	—
551	C₂	—	68	2	no	—
552	C₂	C₄×D₄×#595	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₄×#595
commutator	C₄×C₁₇	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#595
Fitting	C₁₇×#443	C₄
socle	C₂×C₁₇	C₄²×D₄
prime radical	#135×D₁₇	C₂²
cosocle	C₂×C₄×D₁₇	C₂⁴
hypercenter	#443	#595
hypocenter	C₁₇	C₄×#443
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #443

Complements

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

N	H ≅ G/N	type
3. #131×#595	C₂	semidirect
4. #108×#595	C₂	semidirect
5. #14544589	C₂	semidirect
6. #14544586	C₂	semidirect
7. #14544560	C₂	semidirect
8. #14544558	C₂	semidirect
9. #104×#595	C₂	semidirect
10. C₄×C₈×#595	C₂	semidirect
14. #11763853	C₄	semidirect
15. #11763852	C₄	semidirect
16. #11763851	C₄	semidirect
17. Q₁₆×#595	C₄	semidirect
18. SD₁₆×#595	C₄	semidirect
19. D₈×#595	C₄	semidirect
42. #11762927	C₄	semidirect
43. #11762926	C₄	semidirect
44. #11762925	C₄	semidirect
45. #11762924	C₄	semidirect
46. #11762923	C₄	semidirect
50. C₁₇×#443	C₄	semidirect
53. #10587680	C₂×C₄	semidirect
57. #10587678	C₂×C₄	semidirect
70. C₁₇×#131	C₂×C₄	semidirect
72. #10587634	C₂×C₄	semidirect
80. #10587593	C₂×C₄	semidirect
85. #10587587	C₂×C₄	semidirect
90. #10587550	C₂×C₄	semidirect
92. #10587548	C₂×C₄	semidirect
95. #10587536	C₂×C₄	semidirect
96. #10587535	C₂×C₄	semidirect
109. C₈×#595	C₂×C₄	semidirect
110. C₈×#595	C₂×C₄	semidirect
115. C₁₇×#108	C₂×C₄	semidirect
116. C₁₇×#104	C₂×C₄	semidirect
117. C₄×C₈×C₁₇	C₂×C₄	semidirect
118. #10587508	C₂×C₄	semidirect
119. #10587496	C₂×C₄	semidirect
120. #10587493	C₂×C₄	semidirect
121. #10587490	C₂×C₄	semidirect
122. C₈×Dic₁₇	C₂×C₄	semidirect
123. C₈×Dic₁₇	C₂×C₄	semidirect
124. #10587476	C₂×C₄	semidirect
125. C₄×#3622	C₂×C₄	semidirect
167. Q₁₆×C₁₇	C₄²	semidirect
168. SD₁₆×C₁₇	C₄²	semidirect
169. D₈×C₁₇	C₄²	semidirect
176. #63231	C₄²	semidirect
177. #63230	C₄²	semidirect
178. #63229	C₄²	semidirect
179. #63228	C₄²	semidirect
187. Dic₆₈	C₄²	semidirect
188. D₁₃₆	C₄²	semidirect
189. #63219	C₄²	semidirect
273. #595	#443	direct (N × H)
294. #443	#595	direct (N × H)
345. #131	C₂×#595	semidirect
370. #108	C₂×#595	semidirect
378. #104	C₂×#595	semidirect
401. C₄×C₈	C₂×#595	semidirect
402. C₁₇	C₄×#443	semidirect
420. Q₁₆	C₄×#595	semidirect
424. SD₁₆	C₄×#595	semidirect
427. D₈	C₄×#595	semidirect

Maximal subgroups

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

subgroup	index
D₁₇⋊#443	2
#135×#595	2
#131×#595	2
#108×#595	2
#14544589	2
#14544586	2
#14544560	2
#14544558	2
#104×#595	2
C₄×C₈×#595	2
D₁₇×#443	2
C₄×#443	17