Subgroups — #17964192

Order 4352.

688 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545596	C₂	1	1	yes	maximal, characteristic
2	#14545467	C₂	1	1	yes	maximal, characteristic
3	#14544007	C₂	1	1	yes	maximal, characteristic, complemented
4	#14544006	C₂	1	1	yes	maximal, characteristic, complemented
5	#14544005	C₂	1	1	yes	maximal, characteristic, complemented
6	#14544004	C₂	1	1	yes	maximal, characteristic, complemented
7	#14544001	C₂	1	1	yes	maximal, characteristic, complemented
8	#14544001	C₂	1	1	yes	maximal, characteristic, complemented
9	#14544000	C₂	1	1	yes	maximal, characteristic, complemented
10	#14543997	C₂	1	1	yes	maximal, characteristic, complemented
11	#14543995	C₂	1	1	yes	maximal, characteristic, complemented
12	#14543993	C₂	1	1	yes	maximal, characteristic, complemented
13	#14543992	C₂	1	1	yes	maximal, characteristic, complemented
14	#14543991	C₂	1	1	yes	maximal, characteristic, complemented
15	#14537744	C₂	1	1	yes	maximal, characteristic
16	#11763859	C₄	1	2	yes	—
17	#11763844	C₄	1	2	yes	—
18	#11763841	C₄	1	2	yes	—
19	#11763841	C₄	1	2	yes	—
20	#11763834	C₄	1	2	yes	—
21	#11763833	C₄	1	2	yes	—
22	#11763828	C₂²	1	1	yes	characteristic
23	#11763828	C₂²	1	1	yes	characteristic
24	#11763827	C₂²	1	1	yes	characteristic
25	#11763826	C₂²	1	1	yes	characteristic
26	#11763825	C₂²	1	1	yes	characteristic
27	#11763825	C₂²	1	1	yes	characteristic
28	#11763825	C₂²	1	1	yes	characteristic
29	#11763815	C₄	1	2	yes	—
30	#11763782	C₄	1	2	yes	—
31	C₄×#63247	C₂²	1	1	yes	characteristic
32	C₄×#63247	C₂²	1	1	yes	characteristic
33	C₄×#63247	C₂²	1	1	yes	characteristic
34	C₄×#63242	C₂²	1	1	yes	characteristic
35	C₂×C₄×#3624	C₂²	1	1	yes	characteristic
36	#11763651	C₂²	1	1	yes	characteristic
37	#11763651	C₂²	1	1	yes	characteristic
38	#11763651	C₂²	1	1	yes	characteristic
39	#11763651	C₂²	1	1	yes	characteristic
40	#11763651	C₂²	1	1	yes	characteristic
41	#11763651	C₂²	1	1	yes	characteristic
42	#11763651	C₂²	1	1	yes	characteristic
43	#11763651	C₂²	1	1	yes	characteristic
44	#11763651	C₂²	1	1	yes	characteristic
45	#11763651	C₂²	1	1	yes	characteristic
46	#11763650	C₂²	1	1	yes	characteristic
47	#11763650	C₂²	1	1	yes	characteristic
48	#11763650	C₂²	1	1	yes	characteristic
49	#11763650	C₂²	1	1	yes	characteristic
50	C₈×#3624	C₂²	1	1	yes	characteristic
51	C₈×#3624	C₂²	1	1	yes	characteristic
52	C₄×#63254	C₂²	1	1	yes	characteristic
53	#11762938	C₄	1	1	yes	characteristic
54	#11762937	C₄	1	1	yes	characteristic
55	#11762885	C₄	1	1	yes	characteristic
56	#11762884	C₄	1	1	yes	characteristic
57	#11762881	C₄	1	1	yes	characteristic
58	#11762880	C₄	1	1	yes	characteristic
59	#11762877	C₄	1	1	yes	characteristic
60	#11762861	C₂²	1	1	yes	characteristic
61	#11762859	C₂²	1	1	yes	characteristic
62	#11762859	C₂²	1	1	yes	characteristic
63	#11762761	C₂²	1	1	yes	characteristic
64	M₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
65	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
66	C₁₇×#435	C₄	1	1	yes	characteristic
67	C₂×#63254	C₂×C₄	1	1	yes	characteristic
68	C₂×#63247	C₂×C₄	1	2	yes	—
69	C₂×#63247	C₂×C₄	1	2	yes	—
70	C₂×#63247	C₂×C₄	1	2	yes	—
71	C₂²×#3624	C₂×C₄	1	2	yes	—
72	C₂×#63242	C₂×C₄	1	2	yes	—
73	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
75	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
76	D₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
80	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
81	C₂×#63223	C₂×C₄	1	1	yes	characteristic
82	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
83	C₂×#63218	C₂×C₄	1	1	yes	characteristic
84	C₂×#63218	C₂×C₄	1	1	yes	characteristic
85	#10587578	C₂×C₄	1	1	yes	characteristic
86	#10587573	C₂×C₄	1	1	yes	characteristic
87	#10587567	C₂×C₄	1	1	yes	characteristic
88	#10587567	C₂×C₄	1	1	yes	characteristic
89	#10587563	C₂×C₄	1	1	yes	characteristic
90	#10587563	C₂×C₄	1	1	yes	characteristic
91	C₄²×D₁₇	C₂³	1	1	yes	characteristic
92	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊#3624	C₂×C₄	1	2	yes	—
94	C₂²⋊#3624	C₂×C₄	1	2	yes	—
95	C₂²⋊#3624	C₂×C₄	1	2	yes	—
96	C₂²⋊#3624	C₂×C₄	1	2	yes	—
97	#10587544	C₂×C₄	1	2	yes	—
98	#10587544	C₂×C₄	1	2	yes	—
99	#10587543	C₂×C₄	1	2	yes	—
100	#10587543	C₂×C₄	1	2	yes	—
101	#10587543	C₂×C₄	1	2	yes	—
102	#10587542	C₂×C₄	1	2	yes	—
103	#10587542	C₂×C₄	1	2	yes	—
104	#10587542	C₂×C₄	1	2	yes	—
105	C₄⋊#3624	C₂×C₄	1	2	yes	—
106	C₄⋊#3624	C₂×C₄	1	2	yes	—
107	C₄⋊#3624	C₂×C₄	1	2	yes	—
108	C₄⋊#3624	C₂×C₄	1	2	yes	—
109	C₄⋊#3624	C₂×C₄	1	2	yes	—
110	C₄×#3624	C₂×C₄	1	2	yes	—
111	C₄×#3624	C₂×C₄	1	2	yes	—
112	C₄×#3624	C₂³	1	1	yes	characteristic
113	C₄×#3624	C₂³	1	1	yes	characteristic
114	C₄×#3624	C₂³	1	1	yes	characteristic
115	C₄×#3624	C₂³	1	1	yes	characteristic
116	C₄×#3624	C₂³	1	1	yes	characteristic
117	C₄×#3624	C₂³	1	1	yes	characteristic
118	C₄×#3624	C₂³	1	1	yes	characteristic
119	C₄×#3624	C₂³	1	1	yes	characteristic
120	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
121	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
122	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
123	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
124	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
126	#10587491	C₂×C₄	1	1	yes	characteristic
127	#10587491	C₂×C₄	1	1	yes	characteristic
128	#10587486	C₂×C₄	1	1	yes	characteristic
129	#10587486	C₂×C₄	1	1	yes	characteristic
130	#10587485	C₂×C₄	1	1	yes	characteristic
131	#10587485	C₂×C₄	1	1	yes	characteristic
132	#10587485	C₂×C₄	1	1	yes	characteristic
133	#10587485	C₂×C₄	1	1	yes	characteristic
134	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
135	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
136	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
137	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
138	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
139	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
140	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
141	#10587474	C₂×C₄	1	1	yes	characteristic
142	C₂×D₄×C₁₇	C₄²	1	1	yes	characteristic
143	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₇	C₄²	1	1	yes	characteristic
146	C₂×C₂²⋊D₁₇	C₄²	1	1	yes	characteristic
147	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
151	#63254	—	4	2	no	—
152	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
155	C₂×Dic₃₄	C₄²	1	1	yes	characteristic
156	#63247	—	4	2	no	—
157	#63247	—	4	2	no	—
158	#63247	—	4	2	no	—
159	C₂×#3624	—	4	2	no	—
160	C₂×#3624	C₂²×C₄	1	2	yes	—
161	C₂×#3624	C₂²×C₄	1	2	yes	—
162	C₂×#3624	C₂²×C₄	1	2	yes	—
163	C₂×#3624	C₂²×C₄	1	2	yes	—
164	C₂×#3624	C₂²×C₄	1	2	yes	—
165	C₂×#3624	C₂²×C₄	1	2	yes	—
166	C₂×#3624	C₂²×C₄	1	2	yes	—
167	C₂×#3624	C₂²×C₄	1	2	yes	—
168	#63242	—	4	2	no	—
169	M₁₆×C₁₇	—	4	1	no	—
170	C₂×C₈×C₁₇	—	4	1	no	—
171	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
175	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
176	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
177	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
178	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²⋊Dic₁₇	C₄²	1	1	yes	characteristic
180	C₂²⋊Dic₁₇	C₄²	1	1	yes	characteristic
181	#63227	C₄²	1	1	yes	characteristic
182	#63227	C₄²	1	1	yes	characteristic
183	C₄⋊Dic₁₇	C₄²	1	1	yes	characteristic
184	#63225	C₄²	1	1	yes	characteristic
185	#63225	C₄²	1	1	yes	characteristic
186	#63225	C₄²	1	1	yes	characteristic
187	#63225	C₄²	1	1	yes	characteristic
188	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
189	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
190	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
191	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
192	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
195	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
196	C₄×Dic₁₇	C₂⁴	1	1	yes	characteristic
197	#63223	—	4	1	no	—
198	C₂×#3622	—	4	1	no	—
199	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
200	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
201	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
202	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
203	#63218	—	4	1	no	—
204	#63218	—	4	1	no	—
205	#17342	—	17	1	no	maximal, Sylow
206	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
207	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
208	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
209	D₄×C₁₇	—	4	1	no	—
210	C₂×C₄×C₁₇	—	2	1	no	—
211	C₂×C₄×C₁₇	—	2	1	no	—
212	C₂×C₄×C₁₇	—	2	1	no	—
213	C₂×C₄×C₁₇	—	2	1	no	—
214	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
215	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
216	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
217	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
218	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
219	C₂²⋊D₁₇	—	4	1	no	—
220	C₂²⋊D₁₇	—	4	1	no	—
221	C₂×Dic₁₇	—	2	2	no	—
222	C₂×Dic₁₇	—	2	2	no	—
223	C₂×Dic₁₇	—	2	2	no	—
224	C₂×Dic₁₇	—	2	2	no	—
225	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
226	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
227	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
228	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
229	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
230	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
231	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
232	C₄×D₁₇	—	2	1	no	—
233	C₄×D₁₇	—	2	1	no	—
234	C₄×D₁₇	—	2	2	no	—
235	C₄×D₁₇	—	2	2	no	—
236	Dic₃₄	—	4	1	no	—
237	#3624	—	2	2	no	—
238	#3624	—	2	2	no	—
239	#3624	—	2	2	no	—
240	#3624	—	2	2	no	—
241	#3624	—	2	2	no	—
242	#3624	—	2	2	no	—
243	#3624	—	2	2	no	—
244	#3624	—	2	2	no	—
245	C₈×C₁₇	—	2	1	no	—
246	C₈×C₁₇	—	2	1	no	—
247	C₈×C₁₇	—	2	1	no	—
248	C₈×C₁₇	—	2	1	no	—
249	#3622	—	2	1	no	—
250	#3622	—	2	1	no	—
251	#3622	—	2	1	no	—
252	#3622	—	2	1	no	—
253	#2965	—	17	1	no	—
254	#2965	—	17	1	no	—
255	#2922	—	17	1	no	—
256	#1455	—	17	1	no	—
257	#1454	—	17	1	no	—
258	#1454	—	17	1	no	—
259	#1453	—	17	1	no	—
260	#1453	—	17	1	no	—
261	#1453	—	17	1	no	—
262	#1452	—	17	1	no	—
263	#1452	—	17	1	no	—
264	#1451	—	17	1	no	—
265	#1451	—	17	1	no	—
266	#1451	—	17	1	no	—
267	#1451	—	17	1	no	—
268	C₂²×C₁₇	—	2	1	no	—
269	C₂²×C₁₇	—	2	1	no	—
270	C₂²×C₁₇	—	2	1	no	—
271	C₂²×C₁₇	—	2	1	no	—
272	C₂²×C₁₇	—	2	1	no	—
273	C₂²×C₁₇	—	2	1	no	—
274	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
275	C₂×D₁₇	—	2	1	no	—
276	C₂×D₁₇	—	2	1	no	—
277	C₂×D₁₇	—	2	1	no	—
278	C₄×C₁₇	—	2	1	no	—
279	C₄×C₁₇	—	2	1	no	—
280	C₄×C₁₇	—	2	1	no	—
281	C₄×C₁₇	—	2	1	no	—
282	C₄×C₁₇	#568	1	1	yes	characteristic
283	C₄×C₁₇	#568	1	1	yes	characteristic
284	Dic₁₇	—	2	1	no	—
285	Dic₁₇	—	2	1	no	—
286	Dic₁₇	—	2	1	no	—
287	Dic₁₇	—	2	1	no	—
288	Dic₁₇	—	2	1	no	—
289	Dic₁₇	#568	1	2	yes	—
290	Dic₁₇	#568	1	2	yes	—
291	C₄×#41	—	17	1	no	—
292	#446	—	17	2	no	—
293	#446	—	17	1	no	—
294	#446	—	17	1	no	—
295	#436	—	17	2	no	—
296	#436	—	17	1	no	—
297	#436	—	17	1	no	—
298	#435	—	17	2	no	—
299	#435	—	17	2	no	—
300	#435	—	17	1	no	—
301	#435	—	17	1	no	—
302	#435	—	17	1	no	—
303	#435	#595	1	1	yes	characteristic
304	#433	—	17	2	no	—
305	#433	—	17	2	no	—
306	#431	—	17	1	no	—
307	#431	—	17	1	no	—
308	#431	—	17	1	no	—
309	#431	—	17	1	no	—
310	#431	—	17	1	no	—
311	#431	—	17	1	no	—
312	#431	—	17	1	no	—
313	#431	—	17	1	no	—
314	#431	—	17	1	no	—
315	#431	—	17	1	no	—
316	#424	—	17	2	no	—
317	#408	—	17	2	no	—
318	C₄×M₁₆	—	17	1	no	—
319	C₄×M₁₆	—	17	1	no	—
320	C₄×M₁₆	—	17	1	no	—
321	C₄×M₁₆	—	17	1	no	—
322	C₄×M₁₆	—	17	1	no	—
323	C₂×C₄×C₈	—	17	1	no	—
324	C₂×C₄×C₈	—	17	1	no	—
325	C₂×C₄×C₈	—	17	1	no	—
326	#322	—	17	1	no	—
327	#322	—	17	1	no	—
328	#322	—	17	1	no	—
329	#322	—	17	1	no	—
330	#322	—	17	1	no	—
331	#322	—	17	1	no	—
332	#322	—	17	1	no	—
333	#322	—	17	1	no	—
334	#322	—	17	1	no	—
335	#322	—	17	1	no	—
336	#322	—	17	1	no	—
337	#322	—	17	1	no	—
338	#322	—	17	1	no	—
339	#322	—	17	1	no	—
340	C₈²	—	17	1	no	—
341	C₈²	—	17	1	no	—
342	C₂×C₁₇	—	4	1	no	—
343	C₂×C₁₇	—	4	1	no	—
344	C₂×C₁₇	#2873	1	1	yes	characteristic
345	C₂×C₁₇	#2875	1	1	yes	characteristic
346	C₂×C₁₇	#2875	1	1	yes	characteristic
347	D₁₇	—	4	1	no	—
348	C₂×#41	—	17	1	no	—
349	C₂×M₁₆	—	17	2	no	—
350	C₂×M₁₆	—	17	2	no	—
351	C₂×M₁₆	—	17	2	no	—
352	C₂×M₁₆	—	17	1	no	—
353	C₂×M₁₆	—	17	1	no	—
354	C₂×M₁₆	—	17	1	no	—
355	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
356	C₂²×C₈	—	17	2	no	—
357	C₂²×C₈	—	17	2	no	—
358	C₂²×C₈	—	17	1	no	—
359	C₂²×C₈	C₂×#595	1	1	yes	characteristic
360	C₄×Q₈	—	17	1	no	—
361	C₄×Q₈	—	17	1	no	—
362	C₄×D₄	—	17	1	no	—
363	C₄×D₄	—	17	1	no	—
364	C₄×D₄	—	17	1	no	—
365	C₄×D₄	—	17	1	no	—
366	C₄×D₄	—	17	1	no	—
367	C₄×D₄	C₂×#595	1	1	yes	characteristic
368	#117	—	17	1	no	—
369	#117	—	17	1	no	—
370	#117	—	17	1	no	—
371	C₂×C₄²	—	17	1	no	—
372	C₂×C₄²	—	17	1	no	—
373	C₂×C₄²	—	17	1	no	—
374	C₄⋊C₈	—	17	2	no	—
375	C₄⋊C₈	—	17	2	no	—
376	C₄⋊C₈	—	17	2	no	—
377	C₄⋊C₈	—	17	2	no	—
378	C₄⋊C₈	—	17	2	no	—
379	C₄⋊C₈	—	17	2	no	—
380	C₄⋊C₈	—	17	2	no	—
381	C₄⋊C₈	—	17	1	no	—
382	C₄⋊C₈	—	17	1	no	—
383	C₄⋊C₈	—	17	1	no	—
384	C₄⋊C₈	—	17	1	no	—
385	C₄⋊C₈	—	17	1	no	—
386	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
387	C₂²⋊C₈	—	17	2	no	—
388	C₂²⋊C₈	—	17	2	no	—
389	C₂²⋊C₈	—	17	2	no	—
390	C₂²⋊C₈	—	17	2	no	—
391	C₂²⋊C₈	—	17	2	no	—
392	C₂²⋊C₈	—	17	2	no	—
393	C₂²⋊C₈	—	17	2	no	—
394	C₂²⋊C₈	—	17	1	no	—
395	C₂²⋊C₈	—	17	1	no	—
396	C₂²⋊C₈	—	17	1	no	—
397	C₂²⋊C₈	—	17	1	no	—
398	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
399	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
400	#97	—	17	2	no	—
401	#97	—	17	2	no	—
402	#97	—	17	2	no	—
403	#97	—	17	1	no	—
404	#97	—	17	1	no	—
405	#97	—	17	1	no	—
406	#97	C₂×#595	1	1	yes	characteristic
407	C₄×C₈	—	17	1	no	—
408	C₄×C₈	—	17	1	no	—
409	C₄×C₈	—	17	1	no	—
410	C₄×C₈	—	17	1	no	—
411	C₄×C₈	—	17	1	no	—
412	C₄×C₈	—	17	1	no	—
413	C₄×C₈	—	17	1	no	—
414	C₄×C₈	—	17	1	no	—
415	C₄×C₈	—	17	2	no	—
416	C₄×C₈	—	17	2	no	—
417	C₄×C₈	—	17	1	no	—
418	C₄×C₈	—	17	1	no	—
419	C₄×C₈	—	17	1	no	—
420	C₄×C₈	—	17	1	no	—
421	C₄×C₈	—	17	1	no	—
422	C₄×C₈	—	17	1	no	—
423	C₁₇	#17342	1	1	yes	characteristic, complemented, Sylow
424	#41	—	68	2	no	—
425	C₂×Q₈	—	17	1	no	—
426	C₂×D₄	—	17	1	no	—
427	C₂×D₄	—	17	1	no	—
428	C₂×D₄	C₄×#595	1	1	yes	characteristic
429	C₂²×C₄	—	17	1	no	—
430	C₂²×C₄	—	17	1	no	—
431	C₂²×C₄	—	17	1	no	—
432	C₂²×C₄	—	17	1	no	—
433	C₂²×C₄	—	17	1	no	—
434	C₂²×C₄	—	17	1	no	—
435	C₂²×C₄	—	17	1	no	—
436	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
437	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
438	M₁₆	—	4	1	no	—
439	M₁₆	—	68	1	no	—
440	M₁₆	—	68	1	no	—
441	M₁₆	—	68	1	no	—
442	M₁₆	—	68	2	no	—
443	M₁₆	—	68	2	no	—
444	M₁₆	—	68	2	no	—
445	C₂×C₈	—	4	1	no	—
446	C₂×C₈	—	17	2	no	—
447	C₂×C₈	—	17	2	no	—
448	C₂×C₈	—	17	2	no	—
449	C₂×C₈	—	17	2	no	—
450	C₂×C₈	—	17	2	no	—
451	C₂×C₈	—	17	2	no	—
452	C₂×C₈	—	17	2	no	—
453	C₂×C₈	—	17	2	no	—
454	C₂×C₈	—	17	1	no	—
455	C₂×C₈	—	17	1	no	—
456	C₂×C₈	—	17	1	no	—
457	C₂×C₈	—	17	1	no	—
458	C₂×C₈	—	68	1	no	—
459	C₂×C₈	—	68	2	no	—
460	C₂×C₈	—	68	2	no	—
461	C₂×C₈	C₂²×#595	1	1	yes	characteristic
462	C₂×C₈	C₂²×#595	1	1	yes	characteristic
463	C₂×C₈	C₂²×#595	1	1	yes	characteristic
464	C₂×C₈	C₂²×#595	1	1	yes	characteristic
465	C₄⋊C₄	—	17	1	no	—
466	C₄⋊C₄	—	17	1	no	—
467	C₄⋊C₄	—	17	1	no	—
468	C₄⋊C₄	—	17	1	no	—
469	C₄⋊C₄	—	17	1	no	—
470	C₄⋊C₄	C₄×#595	1	1	yes	characteristic
471	C₂²⋊C₄	—	17	1	no	—
472	C₂²⋊C₄	—	17	1	no	—
473	C₂²⋊C₄	—	17	1	no	—
474	C₂²⋊C₄	—	17	1	no	—
475	C₂²⋊C₄	C₄×#595	1	1	yes	characteristic
476	C₂²⋊C₄	C₄×#595	1	1	yes	characteristic
477	C₄²	—	17	1	no	—
478	C₄²	—	17	1	no	—
479	C₄²	—	17	1	no	—
480	C₄²	—	17	1	no	—
481	C₄²	—	17	1	no	—
482	C₄²	—	17	1	no	—
483	C₄²	—	17	1	no	—
484	C₄²	—	17	1	no	—
485	C₄²	—	17	1	no	—
486	C₄²	C₂²×#595	1	1	yes	characteristic
487	C₂³	—	17	1	no	—
488	C₂³	C₂×C₄×#595	1	1	yes	characteristic
489	C₂³	C₂×C₄×#595	1	1	yes	characteristic
490	Q₈	—	68	1	no	—
491	D₄	—	4	1	no	—
492	D₄	—	68	1	no	—
493	D₄	—	68	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	17	1	no	—
499	C₂×C₄	—	17	1	no	—
500	C₂×C₄	—	17	1	no	—
501	C₂×C₄	—	17	1	no	—
502	C₂×C₄	—	17	1	no	—
503	C₂×C₄	—	17	1	no	—
504	C₂×C₄	—	17	1	no	—
505	C₂×C₄	—	34	2	no	—
506	C₂×C₄	—	34	2	no	—
507	C₂×C₄	—	34	2	no	—
508	C₂×C₄	—	34	2	no	—
509	C₂×C₄	—	34	2	no	—
510	C₂×C₄	—	34	2	no	—
511	C₂×C₄	—	34	1	no	—
512	C₂×C₄	—	34	1	no	—
513	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
514	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
515	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
516	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
517	C₂×C₄	C₂³×#595	1	1	yes	characteristic
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	34	2	no	—
523	C₈	—	34	2	no	—
524	C₈	—	34	2	no	—
525	C₈	—	34	2	no	—
526	C₈	—	34	2	no	—
527	C₈	—	34	2	no	—
528	C₈	—	34	2	no	—
529	C₈	—	34	2	no	—
530	C₈	—	34	1	no	—
531	C₈	—	34	1	no	—
532	C₈	—	34	1	no	—
533	C₈	—	34	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	34	1	no	—
541	C₂²	—	34	1	no	—
542	C₂²	—	34	1	no	—
543	C₂²	C₂²×C₄×#595	1	1	yes	characteristic
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	17	2	no	—
549	C₄	—	17	2	no	—
550	C₄	—	34	1	no	—
551	C₄	—	34	1	no	—
552	C₄	—	34	1	no	—
553	C₄	—	34	1	no	—
554	C₄	—	34	1	no	—
555	C₄	#11763887	1	1	yes	characteristic
556	C₄	#11763888	1	1	yes	characteristic
557	C₂	—	4	1	no	—
558	C₂	—	4	1	no	—
559	C₂	—	68	1	no	—
560	C₂	#14545347	1	1	yes	characteristic
561	C₂	#14545354	1	1	yes	characteristic
562	C₂	#14545355	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₁₇×#435	C₄
prime radical	C₂×#63254	C₂×C₄
cosocle	C₄×Dic₁₇	C₂⁴
hypercenter	#435	#595
hypocenter	C₁₇	#17342
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
3. #14544007	C₂	semidirect
4. #14544006	C₂	semidirect
5. #14544005	C₂	semidirect
6. #14544004	C₂	semidirect
7. #14544001	C₂	semidirect
8. #14544001	C₂	semidirect
9. #14544000	C₂	semidirect
10. #14543997	C₂	semidirect
11. #14543995	C₂	semidirect
12. #14543993	C₂	semidirect
13. #14543992	C₂	semidirect
14. #14543991	C₂	semidirect
423. C₁₇	#17342	semidirect

Maximal subgroups

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

subgroup	index
#14545596	2
#14545467	2
#14544007	2
#14544006	2
#14544005	2
#14544004	2
#14544001	2
#14544000	2
#14543997	2
#14543995	2
#14543993	2
#14543992	2
#14543991	2
#14537744	2
#17342	17