Subgroups — #17964156

Order 4352.

798 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545595	C₂	1	1	yes	maximal, characteristic
2	#14545595	C₂	1	1	yes	maximal, characteristic
3	#14544008	C₂	1	1	yes	maximal, characteristic, complemented
4	#14544007	C₂	1	1	yes	maximal, characteristic, complemented
5	#14544004	C₂	1	1	yes	maximal, characteristic, complemented
6	#14544003	C₂	1	1	yes	maximal, characteristic, complemented
7	#14543998	C₂	1	1	yes	maximal, characteristic, complemented
8	#14543994	C₂	1	1	yes	maximal, characteristic, complemented
9	#14543993	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#63243	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#63247	C₂	1	1	yes	maximal, characteristic, complemented
12	#14543982	C₂	1	1	yes	maximal, characteristic, complemented
13	#14543982	C₂	1	1	yes	maximal, characteristic, complemented
14	#14543980	C₂	1	1	yes	maximal, characteristic, complemented
15	#14537206	C₂	1	1	yes	maximal, characteristic
16	#11763861	C₄	1	2	yes	—
17	#11763861	C₄	1	2	yes	—
18	#11763842	C₄	1	2	yes	—
19	#11763842	C₄	1	2	yes	—
20	#11763841	C₄	1	2	yes	—
21	#11763841	C₄	1	2	yes	—
22	#11763839	C₄	1	2	yes	—
23	#11763839	C₄	1	2	yes	—
24	#11763828	C₂²	1	1	yes	characteristic
25	#11763828	C₂²	1	1	yes	characteristic
26	#11763827	C₂²	1	1	yes	characteristic
27	#11763827	C₂²	1	1	yes	characteristic
28	#11763826	C₂²	1	1	yes	characteristic
29	#11763826	C₂²	1	1	yes	characteristic
30	C₄×#63243	C₂²	1	1	yes	characteristic
31	C₄×#63243	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	C₄×#63242	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	#11763650	C₂²	1	1	yes	characteristic
45	#11763650	C₂²	1	1	yes	characteristic
46	#11763650	C₂²	1	1	yes	characteristic
47	#11763650	C₂²	1	1	yes	characteristic
48	C₈×#3624	C₂²	1	1	yes	characteristic
49	C₈×#3624	C₂²	1	1	yes	characteristic
50	C₈×#3624	C₂²	1	1	yes	characteristic
51	C₈×#3624	C₂²	1	1	yes	characteristic
52	C₂×#10587593	C₄	1	1	yes	characteristic
53	C₂×#10587587	C₄	1	1	yes	characteristic
54	#11763277	C₂²	1	1	yes	characteristic
55	#11762766	C₄	1	1	yes	characteristic
56	#11762766	C₄	1	1	yes	characteristic
57	#11762765	C₄	1	1	yes	characteristic
58	#11762763	C₄	1	1	yes	characteristic
59	#11762763	C₄	1	1	yes	characteristic
60	#11762761	C₂²	1	1	yes	characteristic
61	#11762761	C₂²	1	1	yes	characteristic
62	M₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
63	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
64	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
65	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
66	C₁₇×#405	C₄	1	1	yes	characteristic
67	C₂×#63252	C₂×C₄	1	1	yes	characteristic
68	C₂×#63247	C₂×C₄	1	2	yes	—
69	C₂×#63247	C₂×C₄	1	2	yes	—
70	C₂×#63243	C₂×C₄	1	2	yes	—
71	C₂×#63243	C₂×C₄	1	2	yes	—
72	C₂×#63242	C₂×C₄	1	2	yes	—
73	C₂×#63242	C₂×C₄	1	2	yes	—
74	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
76	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
78	C₂×#63223	C₂×C₄	1	1	yes	characteristic
79	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
80	#10587593	—	2	4	no	—
81	#10587587	—	2	4	no	—
82	C₂×#63218	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	C₂×#63218	C₂×C₄	1	1	yes	characteristic
86	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
90	#10587579	C₂×C₄	1	1	yes	characteristic
91	#10587579	C₂×C₄	1	1	yes	characteristic
92	#10587573	C₂×C₄	1	1	yes	characteristic
93	#10587573	C₂×C₄	1	1	yes	characteristic
94	#10587567	C₂×C₄	1	1	yes	characteristic
95	#10587567	C₂×C₄	1	1	yes	characteristic
96	#10587567	C₂×C₄	1	1	yes	characteristic
97	#10587567	C₂×C₄	1	1	yes	characteristic
98	#10587558	C₂×C₄	1	1	yes	characteristic
99	#10587558	C₂×C₄	1	1	yes	characteristic
100	C₄²×D₁₇	C₂³	1	1	yes	characteristic
101	C₄²×D₁₇	C₂³	1	1	yes	characteristic
102	C₂²⋊#3624	C₂×C₄	1	2	yes	—
103	C₂²⋊#3624	C₂×C₄	1	2	yes	—
104	#10587544	C₂×C₄	1	2	yes	—
105	#10587544	C₂×C₄	1	2	yes	—
106	#10587544	C₂×C₄	1	2	yes	—
107	#10587544	C₂×C₄	1	2	yes	—
108	#10587543	C₂×C₄	1	2	yes	—
109	#10587543	C₂×C₄	1	2	yes	—
110	#10587543	C₂×C₄	1	2	yes	—
111	#10587543	C₂×C₄	1	2	yes	—
112	#10587542	C₂×C₄	1	2	yes	—
113	#10587542	C₂×C₄	1	2	yes	—
114	#10587542	C₂×C₄	1	2	yes	—
115	#10587542	C₂×C₄	1	2	yes	—
116	C₄⋊#3624	C₂×C₄	1	2	yes	—
117	C₄⋊#3624	C₂×C₄	1	2	yes	—
118	C₄×#3624	C₂×C₄	1	2	yes	—
119	C₄×#3624	C₂×C₄	1	2	yes	—
120	C₄×#3624	C₂³	1	1	yes	characteristic
121	C₄×#3624	C₂³	1	1	yes	characteristic
122	C₄×#3624	C₂³	1	1	yes	characteristic
123	C₄×#3624	C₂³	1	1	yes	characteristic
124	C₄×#3624	C₂³	1	1	yes	characteristic
125	C₄×#3624	C₂³	1	1	yes	characteristic
126	C₄×#3624	C₂³	1	1	yes	characteristic
127	C₄×#3624	C₂³	1	1	yes	characteristic
128	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
129	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
130	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
131	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
132	#10587486	C₂×C₄	1	1	yes	characteristic
133	#10587486	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	#10587474	C₂×C₄	1	1	yes	characteristic
141	#10587474	C₂×C₄	1	1	yes	characteristic
142	C₄×#3622	C₂×C₄	1	1	yes	characteristic
143	C₄×#3622	C₂×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	#63252	—	2	2	no	—
150	#63252	—	2	2	no	—
151	C₂×D₆₈	C₄²	1	1	yes	characteristic
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×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
158	C₂×Dic₃₄	C₄²	1	1	yes	characteristic
159	#63247	—	2	4	no	—
160	#63247	—	4	2	no	—
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	C₂×#3624	C₂²×C₄	1	2	yes	—
169	#63243	—	2	4	no	—
170	#63243	—	4	2	no	—
171	#63242	—	2	4	no	—
172	#63242	—	4	2	no	—
173	M₁₆×C₁₇	—	2	2	no	—
174	C₂×C₈×C₁₇	—	2	2	no	—
175	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
180	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
181	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
182	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
183	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
185	#63227	C₄²	1	1	yes	characteristic
186	#63227	C₄²	1	1	yes	characteristic
187	#63227	C₄²	1	1	yes	characteristic
188	#63227	C₄²	1	1	yes	characteristic
189	#63225	C₄²	1	1	yes	characteristic
190	#63225	C₄²	1	1	yes	characteristic
191	#63225	C₄²	1	1	yes	characteristic
192	#63225	C₄²	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	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
198	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
199	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₁₇	C₂⁴	1	1	yes	characteristic
201	#63223	—	2	2	no	—
202	C₂×#3622	—	2	2	no	—
203	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
204	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
205	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
206	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
207	#63218	—	2	2	no	—
208	#63218	—	2	2	no	—
209	#63218	M₁₆	1	4	yes	complemented
210	#63218	M₁₆	1	4	yes	complemented
211	C₈×D₁₇	—	2	2	no	—
212	C₈×D₁₇	—	2	2	no	—
213	C₈×D₁₇	—	2	2	no	—
214	C₈×D₁₇	—	2	2	no	—
215	#17337	—	17	1	no	maximal, Sylow
216	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
217	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
218	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
219	C₂×C₄×C₁₇	—	2	1	no	—
220	C₂×C₄×C₁₇	—	2	1	no	—
221	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
222	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
223	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
224	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
225	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
226	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
227	C₂²⋊D₁₇	—	2	2	no	—
228	C₂²⋊D₁₇	—	2	2	no	—
229	C₂×Dic₁₇	—	2	2	no	—
230	C₂×Dic₁₇	—	2	2	no	—
231	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
232	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
233	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
234	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
235	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
236	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
237	D₆₈	—	2	2	no	—
238	C₄×D₁₇	—	2	1	no	—
239	C₄×D₁₇	—	2	1	no	—
240	C₄×D₁₇	—	2	2	no	—
241	C₄×D₁₇	—	2	2	no	—
242	C₄×D₁₇	—	2	2	no	—
243	C₄×D₁₇	—	2	2	no	—
244	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
245	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
246	Dic₃₄	—	2	2	no	—
247	#3624	—	2	2	no	—
248	#3624	—	2	2	no	—
249	#3624	—	2	2	no	—
250	#3624	—	2	2	no	—
251	#3624	—	2	2	no	—
252	#3624	—	2	2	no	—
253	#3624	—	2	2	no	—
254	#3624	#131	1	4	yes	complemented
255	C₈×C₁₇	—	2	1	no	—
256	C₈×C₁₇	—	2	1	no	—
257	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
258	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
259	#3622	—	2	1	no	—
260	#3622	—	2	1	no	—
261	#3622	C₂×M₁₆	1	2	yes	—
262	#3622	C₂×M₁₆	1	2	yes	—
263	#2965	—	17	1	no	—
264	#2965	—	17	1	no	—
265	C₄×#131	—	17	1	no	—
266	#1455	—	17	1	no	—
267	#1455	—	17	1	no	—
268	#1453	—	17	1	no	—
269	#1453	—	17	1	no	—
270	#1452	—	17	1	no	—
271	#1451	—	17	1	no	—
272	#1451	—	17	1	no	—
273	C₈×M₁₆	—	17	1	no	—
274	C₈×M₁₆	—	17	1	no	—
275	C₈×M₁₆	—	17	1	no	—
276	C₈×M₁₆	—	17	1	no	—
277	C₂×#322	—	17	1	no	—
278	C₂²×C₁₇	—	2	1	no	—
279	C₂²×C₁₇	—	2	1	no	—
280	C₂²×C₁₇	—	2	1	no	—
281	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
282	C₂×D₁₇	—	2	1	no	—
283	C₂×D₁₇	—	2	1	no	—
284	C₂×D₁₇	—	2	1	no	—
285	C₂×D₁₇	—	2	1	no	—
286	C₂×D₁₇	—	2	1	no	—
287	C₂×D₁₇	C₄×M₁₆	1	2	yes	—
288	C₄×C₁₇	—	2	1	no	—
289	C₄×C₁₇	—	2	1	no	—
290	C₄×C₁₇	—	2	1	no	—
291	C₄×C₁₇	—	2	1	no	—
292	C₄×C₁₇	—	2	1	no	—
293	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
294	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
295	Dic₁₇	—	2	1	no	—
296	Dic₁₇	—	2	1	no	—
297	Dic₁₇	—	2	1	no	—
298	Dic₁₇	C₄×M₁₆	1	2	yes	—
299	Dic₁₇	C₂×#131	1	2	yes	—
300	Dic₁₇	#568	1	2	yes	—
301	C₂×#131	—	17	1	no	—
302	C₂×#131	—	17	1	no	—
303	C₄×#41	—	17	1	no	—
304	#446	—	17	2	no	—
305	#446	—	17	2	no	—
306	#436	—	17	2	no	—
307	#436	—	17	2	no	—
308	#435	—	17	2	no	—
309	#435	—	17	2	no	—
310	#435	—	17	2	no	—
311	#435	—	17	2	no	—
312	#431	—	17	1	no	—
313	#431	—	17	1	no	—
314	#431	—	17	1	no	—
315	#431	—	17	1	no	—
316	#431	—	17	1	no	—
317	#431	—	17	1	no	—
318	#405	—	17	1	no	—
319	#405	—	17	1	no	—
320	#405	—	17	1	no	—
321	#405	—	17	1	no	—
322	#405	—	17	1	no	—
323	#405	#595	1	1	yes	characteristic
324	C₄×M₁₆	—	17	1	no	—
325	C₄×M₁₆	—	17	1	no	—
326	C₄×M₁₆	—	17	1	no	—
327	C₄×M₁₆	—	17	1	no	—
328	C₄×M₁₆	—	17	1	no	—
329	C₄×M₁₆	—	17	1	no	—
330	C₄×M₁₆	—	17	1	no	—
331	C₂×C₄×C₈	—	17	1	no	—
332	C₂×C₄×C₈	—	17	1	no	—
333	C₂×C₄×C₈	—	17	1	no	—
334	C₂×C₄×C₈	—	17	1	no	—
335	C₂×C₄×C₈	—	17	1	no	—
336	#322	—	17	1	no	—
337	#322	—	17	1	no	—
338	#322	—	17	1	no	—
339	#322	—	17	1	no	—
340	#322	—	17	1	no	—
341	#322	—	17	1	no	—
342	#322	—	17	1	no	—
343	#322	—	17	1	no	—
344	#322	—	17	1	no	—
345	#322	—	17	1	no	—
346	#322	—	17	1	no	—
347	#322	—	17	1	no	—
348	C₈²	—	17	1	no	—
349	C₈²	—	17	1	no	—
350	C₈²	—	17	1	no	—
351	C₈²	—	17	1	no	—
352	C₂×C₁₇	—	4	1	no	—
353	C₂×C₁₇	C₂×C₄×M₁₆	1	1	yes	characteristic
354	C₂×C₁₇	C₄×#131	1	1	yes	characteristic
355	C₂×C₁₇	#2875	1	1	yes	characteristic
356	D₁₇	—	2	2	no	—
357	D₁₇	—	4	1	no	—
358	C₂×#41	—	17	1	no	—
359	#131	—	34	4	no	—
360	#131	—	34	4	no	—
361	C₂×M₁₆	—	17	2	no	—
362	C₂×M₁₆	—	17	2	no	—
363	C₂×M₁₆	—	17	1	no	—
364	C₂×M₁₆	—	17	2	no	—
365	C₂×M₁₆	—	17	2	no	—
366	C₂×M₁₆	—	17	1	no	—
367	C₂×M₁₆	—	17	1	no	—
368	C₂×M₁₆	—	17	1	no	—
369	C₂×M₁₆	—	17	1	no	—
370	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
371	C₂²×C₈	—	17	2	no	—
372	C₂²×C₈	—	17	1	no	—
373	C₂²×C₈	—	17	2	no	—
374	C₂²×C₈	—	17	1	no	—
375	C₂²×C₈	—	17	1	no	—
376	C₂²×C₈	—	17	1	no	—
377	C₂²×C₈	—	17	1	no	—
378	C₂²×C₈	C₂×#595	1	1	yes	characteristic
379	C₄×Q₈	—	17	1	no	—
380	C₄×Q₈	—	17	1	no	—
381	C₄×D₄	—	17	1	no	—
382	C₄×D₄	—	17	1	no	—
383	C₄×D₄	—	17	1	no	—
384	C₄×D₄	—	17	1	no	—
385	C₄×D₄	—	17	1	no	—
386	C₄×D₄	—	17	1	no	—
387	#117	—	17	1	no	—
388	#117	—	17	1	no	—
389	#117	C₂×#595	1	1	yes	characteristic
390	C₂×C₄²	—	17	1	no	—
391	C₂×C₄²	—	17	1	no	—
392	C₂×C₄²	—	17	1	no	—
393	C₄⋊C₈	—	17	2	no	—
394	C₄⋊C₈	—	17	2	no	—
395	C₄⋊C₈	—	17	2	no	—
396	C₄⋊C₈	—	17	2	no	—
397	C₄⋊C₈	—	17	2	no	—
398	C₄⋊C₈	—	17	2	no	—
399	C₂²⋊C₈	—	17	2	no	—
400	C₂²⋊C₈	—	17	2	no	—
401	C₂²⋊C₈	—	17	2	no	—
402	C₂²⋊C₈	—	17	2	no	—
403	C₂²⋊C₈	—	17	2	no	—
404	C₂²⋊C₈	—	17	2	no	—
405	#97	—	17	2	no	—
406	#97	—	17	2	no	—
407	#97	—	17	2	no	—
408	#97	—	17	2	no	—
409	#97	—	17	1	no	—
410	#97	—	17	1	no	—
411	#97	—	17	1	no	—
412	#97	—	17	1	no	—
413	#97	C₂×#595	1	1	yes	characteristic
414	#97	C₂×#595	1	1	yes	characteristic
415	C₄×C₈	—	17	1	no	—
416	C₄×C₈	—	17	1	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	C₄×C₈	—	17	2	no	—
424	C₄×C₈	—	17	2	no	—
425	C₄×C₈	—	17	1	no	—
426	C₄×C₈	—	17	1	no	—
427	C₄×C₈	—	17	1	no	—
428	C₄×C₈	—	17	1	no	—
429	C₄×C₈	—	17	1	no	—
430	C₄×C₈	—	17	1	no	—
431	C₄×C₈	—	17	1	no	—
432	C₄×C₈	—	17	1	no	—
433	C₄×C₈	C₂×#595	1	1	yes	characteristic
434	C₄×C₈	C₂×#595	1	1	yes	characteristic
435	C₁₇	#17337	1	1	yes	characteristic, complemented, Sylow
436	#41	—	34	2	no	—
437	#41	—	34	2	no	—
438	C₂×Q₈	—	17	1	no	—
439	C₂×D₄	—	17	1	no	—
440	C₂×D₄	—	17	1	no	—
441	C₂×D₄	—	17	1	no	—
442	C₂²×C₄	—	17	1	no	—
443	C₂²×C₄	—	17	1	no	—
444	C₂²×C₄	—	17	1	no	—
445	C₂²×C₄	—	17	1	no	—
446	C₂²×C₄	—	17	1	no	—
447	C₂²×C₄	—	17	1	no	—
448	C₂²×C₄	—	17	1	no	—
449	C₂²×C₄	—	17	1	no	—
450	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
451	M₁₆	—	2	2	no	—
452	M₁₆	—	17	4	no	—
453	M₁₆	—	17	4	no	—
454	M₁₆	—	34	2	no	—
455	M₁₆	—	34	2	no	—
456	M₁₆	—	34	4	no	—
457	M₁₆	—	34	4	no	—
458	M₁₆	—	34	2	no	—
459	M₁₆	—	68	2	no	—
460	M₁₆	—	68	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	17	2	no	—
463	C₂×C₈	—	17	1	no	—
464	C₂×C₈	—	17	1	no	—
465	C₂×C₈	—	17	2	no	—
466	C₂×C₈	—	17	2	no	—
467	C₂×C₈	—	17	2	no	—
468	C₂×C₈	—	17	2	no	—
469	C₂×C₈	—	17	2	no	—
470	C₂×C₈	—	17	2	no	—
471	C₂×C₈	—	17	2	no	—
472	C₂×C₈	—	17	1	no	—
473	C₂×C₈	—	17	1	no	—
474	C₂×C₈	—	34	2	no	—
475	C₂×C₈	—	34	2	no	—
476	C₂×C₈	—	34	2	no	—
477	C₂×C₈	—	34	2	no	—
478	C₂×C₈	—	34	4	no	—
479	C₂×C₈	—	34	2	no	—
480	C₂×C₈	—	68	2	no	—
481	C₂×C₈	C₂²×#595	1	1	yes	characteristic
482	C₂×C₈	C₂²×#595	1	1	yes	characteristic
483	C₂×C₈	C₂²×#595	1	1	yes	characteristic
484	C₂×C₈	C₂²×#595	1	1	yes	characteristic
485	C₄⋊C₄	—	17	1	no	—
486	C₄⋊C₄	—	17	1	no	—
487	C₄⋊C₄	—	17	1	no	—
488	C₄⋊C₄	—	17	1	no	—
489	C₄⋊C₄	C₄×#595	1	1	yes	characteristic
490	C₄⋊C₄	C₄×#595	1	1	yes	characteristic
491	C₂²⋊C₄	—	17	1	no	—
492	C₂²⋊C₄	—	17	1	no	—
493	C₂²⋊C₄	—	17	1	no	—
494	C₂²⋊C₄	—	17	1	no	—
495	C₂²⋊C₄	C₄×#595	1	1	yes	characteristic
496	C₂²⋊C₄	C₄×#595	1	1	yes	characteristic
497	C₄²	—	17	1	no	—
498	C₄²	—	17	1	no	—
499	C₄²	—	17	1	no	—
500	C₄²	—	17	1	no	—
501	C₄²	—	17	1	no	—
502	C₄²	—	17	1	no	—
503	C₄²	—	17	1	no	—
504	C₄²	—	17	1	no	—
505	C₄²	C₂²×#595	1	1	yes	characteristic
506	C₄²	C₂²×#595	1	1	yes	characteristic
507	C₂³	—	17	1	no	—
508	C₂³	—	17	1	no	—
509	C₂³	C₂×C₄×#595	1	1	yes	characteristic
510	Q₈	—	34	2	no	—
511	D₄	—	34	2	no	—
512	D₄	—	34	2	no	—
513	D₄	—	34	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	17	1	no	—
517	C₂×C₄	—	17	1	no	—
518	C₂×C₄	—	17	1	no	—
519	C₂×C₄	—	17	2	no	—
520	C₂×C₄	—	17	2	no	—
521	C₂×C₄	—	17	1	no	—
522	C₂×C₄	—	17	1	no	—
523	C₂×C₄	—	17	1	no	—
524	C₂×C₄	—	34	2	no	—
525	C₂×C₄	—	34	2	no	—
526	C₂×C₄	—	34	2	no	—
527	C₂×C₄	—	34	2	no	—
528	C₂×C₄	—	34	2	no	—
529	C₂×C₄	—	34	2	no	—
530	C₂×C₄	—	34	1	no	—
531	C₂×C₄	—	34	1	no	—
532	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
533	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
534	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
535	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
536	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
537	C₂×C₄	C₂³×#595	1	1	yes	characteristic
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	17	4	no	—
541	C₈	—	17	2	no	—
542	C₈	—	17	2	no	—
543	C₈	—	34	2	no	—
544	C₈	—	34	2	no	—
545	C₈	—	34	2	no	—
546	C₈	—	34	2	no	—
547	C₈	—	34	2	no	—
548	C₈	—	34	2	no	—
549	C₈	—	34	2	no	—
550	C₈	—	34	1	no	—
551	C₈	—	34	1	no	—
552	C₈	D₁₇⋊M₁₆	1	2	yes	—
553	C₈	D₁₇⋊M₁₆	1	2	yes	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	17	2	no	—
558	C₂²	—	34	1	no	—
559	C₂²	—	34	1	no	—
560	C₂²	—	34	1	no	—
561	C₂²	—	34	1	no	—
562	C₂²	—	34	1	no	—
563	C₂²	C₂²×C₄×#595	1	1	yes	characteristic
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	17	2	no	—
570	C₄	—	17	2	no	—
571	C₄	—	17	2	no	—
572	C₄	—	34	1	no	—
573	C₄	—	34	1	no	—
574	C₄	—	34	1	no	—
575	C₄	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
576	C₄	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
577	C₂	—	4	1	no	—
578	C₂	—	34	2	no	—
579	C₂	—	68	1	no	—
580	C₂	C₄×D₁₇⋊M₁₆	1	1	yes	characteristic
581	C₂	#131×#595	1	1	yes	characteristic
582	C₂	#14545354	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₁₇×#405	C₄
prime radical	C₂×#63252	C₂×C₄
cosocle	C₄×Dic₁₇	C₂⁴
hypercenter	#405	#595
hypocenter	C₁₇	#17337
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #14544008	C₂	semidirect
4. #14544007	C₂	semidirect
5. #14544004	C₂	semidirect
6. #14544003	C₂	semidirect
7. #14543998	C₂	semidirect
8. #14543994	C₂	semidirect
9. #14543993	C₂	semidirect
10. C₈×#63243	C₂	semidirect
11. C₈×#63247	C₂	semidirect
12. #14543982	C₂	semidirect
13. #14543982	C₂	semidirect
14. #14543980	C₂	semidirect
209. #63218	M₁₆	semidirect
210. #63218	M₁₆	semidirect
254. #3624	#131	semidirect
435. C₁₇	#17337	semidirect

Maximal subgroups

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

subgroup	index
#14545595	2
#14544008	2
#14544007	2
#14544004	2
#14544003	2
#14543998	2
#14543994	2
#14543993	2
C₈×#63243	2
C₈×#63247	2
#14543982	2
#14543980	2
#14537206	2
#17337	17