Subgroups — #17978155

Order 4352.

738 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763865	C₂	1	1	yes	maximal, characteristic
2	C₂×#11763772	C₂	1	1	yes	maximal, characteristic
3	#14545004	C₂	1	4	yes	maximal, complemented
4	#14545003	C₂	1	4	yes	maximal, complemented
5	#14544999	C₂	1	4	yes	maximal, complemented
6	C₂×M₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
7	C₂×D₁₇⋊M₁₆	C₄	1	1	yes	characteristic
8	C₂×#10587677	C₄	1	1	yes	characteristic
9	C₂×#10587530	C₂²	1	2	yes	—
10	#11763865	C₄	1	2	yes	complemented
11	#11763865	C₄	1	2	yes	complemented
12	#11763865	C₂²	1	2	yes	—
13	#11763865	C₂²	1	2	yes	—
14	C₂×#10587538	C₄	1	2	yes	complemented
15	C₂×#10587529	C₄	1	2	yes	complemented
16	#11763772	C₄	1	2	yes	—
17	#11763772	C₄	1	2	yes	—
18	#11763772	C₂²	1	2	yes	—
19	#11763772	C₂²	1	2	yes	—
20	C₂×#10587532	C₂²	1	2	yes	—
21	C₂×C₈×#595	C₄	1	2	yes	—
22	#11763700	C₂²	1	8	yes	complemented
23	#11763699	C₂²	1	8	yes	complemented
24	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
25	C₂×#10587483	C₄	1	1	yes	characteristic, complemented
26	C₂×#10587469	C₂²	1	2	yes	—
27	M₃₂×D₁₇	C₄	1	2	yes	complemented
28	M₃₂×D₁₇	C₄	1	2	yes	complemented
29	M₃₂×D₁₇	C₂²	1	2	yes	—
30	M₃₂×D₁₇	C₂²	1	2	yes	—
31	C₂×C₁₆×D₁₇	C₄	1	2	yes	complemented
32	C₂×C₁₇×M₃₂	C₄	1	1	yes	characteristic, complemented
33	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
34	C₂×C₂²⋊#595	—	2	1	no	—
35	C₂×#63247	—	2	1	no	—
36	#10587677	—	2	1	no	—
37	#10587677	—	2	1	no	—
38	#10587677	C₂×C₄	1	2	yes	—
39	#10587677	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊#595	—	2	1	no	—
41	C₂×C₄×#595	C₂×C₄	1	2	yes	—
42	D₁₇⋊M₁₆	—	2	1	no	—
43	D₁₇⋊M₁₆	—	2	1	no	—
44	D₁₇⋊M₁₆	C₂×C₄	1	2	yes	—
45	D₁₇⋊M₁₆	C₂×C₄	1	2	yes	—
46	C₂×#63243	—	2	1	no	—
47	C₂×#63242	C₂×C₄	1	2	yes	—
48	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
49	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
60	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
62	#10587538	C₂×C₄	1	4	yes	—
63	#10587538	C₂×C₄	1	4	yes	complemented
64	C₂×#63216	C₂×C₄	1	4	yes	complemented
65	#10587532	C₂×C₄	1	4	yes	—
66	#10587532	C₂³	1	4	yes	—
67	C₈×#595	C₂×C₄	1	4	yes	—
68	C₈×#595	C₂×C₄	1	4	yes	—
69	#10587530	C₂×C₄	1	4	yes	complemented
70	#10587530	C₂³	1	4	yes	—
71	#10587529	C₂×C₄	1	4	yes	—
72	#10587529	C₂×C₄	1	4	yes	complemented
73	C₁₇×M₃₂	C₂×C₄	1	2	yes	—
74	C₁₇×M₃₂	C₂×C₄	1	2	yes	complemented
75	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	complemented
76	#10587483	C₂×C₄	1	2	yes	—
77	#10587483	C₂×C₄	1	2	yes	complemented
78	C₂×#63214	C₂×C₄	1	2	yes	complemented
79	#10587469	C₂×C₄	1	4	yes	complemented
80	#10587469	C₂³	1	4	yes	—
81	C₁₆×D₁₇	C₂×C₄	1	4	yes	—
82	C₁₆×D₁₇	C₂×C₄	1	4	yes	complemented
83	C₂³×D₁₇	M₁₆	1	1	yes	characteristic
84	C₂²×#595	—	2	2	no	—
85	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
86	C₂²×Dic₁₇	M₁₆	1	1	yes	characteristic
87	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
88	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
89	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
91	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
92	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
93	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
94	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
95	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
96	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²⋊#595	—	2	2	no	—
100	C₂²⋊#595	—	2	2	no	—
101	#63247	—	2	2	no	—
102	#63247	—	2	2	no	—
103	C₂×#3624	—	2	2	no	—
104	C₄⋊#595	—	2	2	no	—
105	C₄⋊#595	—	2	2	no	—
106	C₄×#595	—	2	2	no	—
107	C₄×#595	C₂²×C₄	1	4	yes	—
108	#63243	—	2	2	no	—
109	#63243	—	2	2	no	—
110	#63242	—	2	2	no	—
111	#63242	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
113	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
114	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
115	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×#3622	C₄²	1	1	yes	characteristic
119	C₂×#3622	C₄²	1	1	yes	characteristic
120	C₂×#3622	C₄²	1	1	yes	characteristic
121	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
122	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
123	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
124	C₈×D₁₇	C₄²	1	1	yes	characteristic
125	C₈×D₁₇	C₄²	1	1	yes	characteristic
126	C₈×D₁₇	C₄²	1	1	yes	characteristic
127	C₈×D₁₇	C₄²	1	1	yes	characteristic
128	C₈×D₁₇	C₄²	1	1	yes	characteristic
129	C₈×D₁₇	C₄²	1	1	yes	characteristic
130	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
131	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
135	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
136	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
137	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
139	C₈×D₁₇	C₂⁴	1	1	yes	characteristic
140	#63216	C₂²×C₄	1	8	yes	—
141	C₁₆×C₁₇	C₂²×C₄	1	4	yes	—
142	#63214	C₂²×C₄	1	4	yes	—
143	C₂×#2110	—	17	1	no	maximal, Sylow
144	C₂³×C₁₇	#97	1	1	yes	characteristic
145	C₂²×D₁₇	—	4	2	no	—
146	C₂²×D₁₇	#97	1	1	yes	characteristic
147	C₂²×D₁₇	#97	1	1	yes	characteristic
148	C₂²×D₁₇	#97	1	1	yes	characteristic
149	C₂²×D₁₇	C₂×M₁₆	1	1	yes	characteristic
150	C₂²×D₁₇	C₂×M₁₆	1	1	yes	characteristic
151	C₂²×D₁₇	C₂×M₁₆	1	1	yes	characteristic
152	C₂×#595	—	2	4	no	—
153	C₂×#595	—	4	4	no	—
154	C₂×C₄×C₁₇	#97	1	1	yes	characteristic
155	C₂×C₄×C₁₇	#97	1	1	yes	characteristic
156	C₂×C₄×C₁₇	#97	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
160	C₂×Dic₁₇	#97	1	1	yes	characteristic
161	C₂×Dic₁₇	#97	1	1	yes	characteristic
162	C₂×Dic₁₇	#97	1	1	yes	characteristic
163	C₂×Dic₁₇	C₂×M₁₆	1	1	yes	characteristic
164	C₂×Dic₁₇	C₂×M₁₆	1	1	yes	characteristic
165	C₂×Dic₁₇	C₂×M₁₆	1	1	yes	characteristic
166	C₄×D₁₇	#97	1	1	yes	characteristic
167	C₄×D₁₇	#97	1	1	yes	characteristic
168	C₄×D₁₇	#97	1	1	yes	characteristic
169	C₄×D₁₇	#97	1	1	yes	characteristic
170	C₄×D₁₇	#97	1	1	yes	characteristic
171	C₄×D₁₇	#97	1	1	yes	characteristic
172	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
173	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
174	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
175	C₄×D₁₇	C₂×M₁₆	1	1	yes	characteristic
176	C₄×D₁₇	C₂×M₁₆	1	1	yes	characteristic
177	C₄×D₁₇	C₂×M₁₆	1	1	yes	characteristic
178	C₄×D₁₇	C₂×M₁₆	1	1	yes	characteristic
179	C₄×D₁₇	C₂×M₁₆	1	1	yes	characteristic
180	C₄×D₁₇	C₂×M₁₆	1	1	yes	characteristic
181	C₄×D₁₇	C₂³×C₄	1	1	yes	characteristic
182	#3624	—	2	4	no	—
183	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
184	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
185	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
186	C₈×C₁₇	C₂³×C₄	1	1	yes	characteristic
187	#3622	C₂×C₄²	1	1	yes	characteristic
188	#3622	C₂×C₄²	1	1	yes	characteristic
189	#3622	C₂×C₄²	1	1	yes	characteristic
190	#3622	C₂³×C₄	1	1	yes	characteristic
191	C₂²×M₃₂	—	17	1	no	—
192	C₂²×M₃₂	—	17	1	no	—
193	C₂×#405	—	17	1	no	—
194	#2110	—	17	4	no	—
195	#2110	—	17	4	no	—
196	C₂×#347	—	17	4	no	—
197	C₂²×C₁₇	—	4	1	no	—
198	C₂²×C₁₇	C₂×#97	1	1	yes	characteristic
199	C₂²×C₁₇	C₂×#97	1	1	yes	characteristic
200	C₂²×C₁₇	C₂×#97	1	1	yes	characteristic
201	C₂×D₁₇	—	2	2	no	—
202	C₂×D₁₇	—	2	2	no	—
203	C₂×D₁₇	—	2	2	no	—
204	C₂×D₁₇	—	4	1	no	—
205	C₂×D₁₇	—	4	1	no	—
206	C₂×D₁₇	—	4	1	no	—
207	C₂×D₁₇	C₂×#97	1	1	yes	characteristic
208	C₂×D₁₇	C₂×#97	1	1	yes	characteristic
209	C₂×D₁₇	C₂×#97	1	1	yes	characteristic
210	C₂×D₁₇	C₂²×M₁₆	1	1	yes	characteristic
211	#595	—	4	4	no	—
212	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
213	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
214	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
215	C₄×C₁₇	C₂²×C₄²	1	1	yes	characteristic
216	Dic₁₇	C₂×#97	1	1	yes	characteristic
217	Dic₁₇	C₂×#97	1	1	yes	characteristic
218	Dic₁₇	C₂×#97	1	1	yes	characteristic
219	Dic₁₇	C₂²×M₁₆	1	1	yes	characteristic
220	C₂²×M₁₆	—	17	1	no	—
221	C₂³×C₈	—	17	1	no	—
222	C₂×#117	—	17	1	no	—
223	C₂×M₃₂	—	17	2	no	—
224	C₂×M₃₂	—	17	2	no	—
225	C₂×M₃₂	—	17	2	no	—
226	C₂×M₃₂	—	17	2	no	—
227	C₂×M₃₂	—	17	2	no	—
228	C₂×M₃₂	—	17	2	no	—
229	C₂×M₃₂	—	17	1	no	—
230	C₂×M₃₂	—	17	2	no	—
231	C₂×M₃₂	—	17	2	no	—
232	C₂×M₃₂	—	17	2	no	—
233	C₂×M₃₂	—	17	2	no	—
234	C₂×M₃₂	—	17	2	no	—
235	C₂×M₃₂	#595	1	1	yes	characteristic, complemented
236	C₂²×C₁₆	—	17	2	no	—
237	C₂²×C₁₆	—	17	2	no	—
238	#405	—	17	2	no	—
239	#405	—	17	2	no	—
240	#405	—	17	2	no	—
241	#405	—	17	2	no	—
242	C₂×#97	—	17	2	no	—
243	C₂×C₄×C₈	—	17	2	no	—
244	#347	—	17	8	no	—
245	#347	—	17	8	no	—
246	C₂×C₁₇	—	2	1	no	—
247	C₂×C₁₇	—	2	1	no	—
248	C₂×C₁₇	—	2	1	no	—
249	C₂×C₁₇	C₂²×#97	1	1	yes	characteristic
250	D₁₇	—	2	1	no	—
251	D₁₇	—	2	1	no	—
252	D₁₇	—	2	1	no	—
253	D₁₇	#2110	1	2	yes	complemented
254	C₂³×C₄	—	17	1	no	—
255	C₂×M₁₆	—	17	2	no	—
256	C₂×M₁₆	—	17	2	no	—
257	C₂×M₁₆	—	34	1	no	—
258	C₂×M₁₆	—	34	1	no	—
259	C₂×M₁₆	—	34	1	no	—
260	C₂×M₁₆	—	34	1	no	—
261	C₂²×C₈	—	17	1	no	—
262	C₂²×C₈	—	17	1	no	—
263	C₂²×C₈	—	17	1	no	—
264	C₂²×C₈	—	17	1	no	—
265	C₂²×C₈	—	17	1	no	—
266	C₂²×C₈	—	17	1	no	—
267	C₂²×C₈	—	17	1	no	—
268	C₂²×C₈	—	17	1	no	—
269	C₂²×C₈	—	17	1	no	—
270	C₂²×C₈	—	17	1	no	—
271	C₂²×C₈	—	17	1	no	—
272	C₂²×C₈	—	17	1	no	—
273	C₂²×C₈	—	17	1	no	—
274	C₂²×C₈	—	17	2	no	—
275	C₂²×C₈	C₂×#595	1	1	yes	characteristic
276	#117	—	17	2	no	—
277	#117	—	17	2	no	—
278	#117	—	34	1	no	—
279	#117	—	34	1	no	—
280	C₂×C₄⋊C₄	—	34	1	no	—
281	C₂×C₂²⋊C₄	—	34	1	no	—
282	C₂×C₄²	—	17	2	no	—
283	M₃₂	—	17	4	no	—
284	M₃₂	—	17	4	no	—
285	M₃₂	—	17	4	no	—
286	M₃₂	—	17	4	no	—
287	M₃₂	—	17	2	no	—
288	M₃₂	—	17	2	no	—
289	M₃₂	—	17	4	no	—
290	M₃₂	—	17	4	no	—
291	M₃₂	C₂×#595	1	2	yes	—
292	M₃₂	C₂×#595	1	2	yes	complemented
293	C₂×C₁₆	—	17	4	no	—
294	C₂×C₁₆	—	17	4	no	—
295	C₂×C₁₆	—	17	4	no	—
296	C₂×C₁₆	—	17	2	no	—
297	C₂×C₁₆	—	17	4	no	—
298	C₂×C₁₆	—	17	4	no	—
299	C₂×C₁₆	C₂×#595	1	2	yes	complemented
300	#97	—	17	4	no	—
301	#97	—	17	4	no	—
302	C₄×C₈	—	17	4	no	—
303	C₄×C₈	—	17	4	no	—
304	C₁₇	C₂×#2110	1	1	yes	characteristic, complemented, Sylow
305	C₂⁴	—	17	1	no	—
306	C₂²×C₄	—	17	1	no	—
307	C₂²×C₄	—	17	1	no	—
308	C₂²×C₄	—	17	1	no	—
309	C₂²×C₄	—	17	1	no	—
310	C₂²×C₄	—	17	1	no	—
311	C₂²×C₄	—	17	1	no	—
312	C₂²×C₄	—	17	1	no	—
313	C₂²×C₄	—	17	1	no	—
314	C₂²×C₄	—	17	1	no	—
315	C₂²×C₄	—	17	1	no	—
316	C₂²×C₄	—	17	1	no	—
317	C₂²×C₄	—	17	1	no	—
318	C₂²×C₄	—	17	1	no	—
319	C₂²×C₄	—	34	2	no	—
320	C₂²×C₄	C₄×#595	1	1	yes	characteristic
321	M₁₆	—	34	2	no	—
322	M₁₆	—	34	2	no	—
323	M₁₆	—	34	2	no	—
324	M₁₆	—	34	2	no	—
325	C₂×C₈	—	17	1	no	—
326	C₂×C₈	—	17	1	no	—
327	C₂×C₈	—	17	1	no	—
328	C₂×C₈	—	17	1	no	—
329	C₂×C₈	—	17	1	no	—
330	C₂×C₈	—	17	1	no	—
331	C₂×C₈	—	17	1	no	—
332	C₂×C₈	—	17	1	no	—
333	C₂×C₈	—	17	1	no	—
334	C₂×C₈	—	17	1	no	—
335	C₂×C₈	—	17	1	no	—
336	C₂×C₈	—	17	1	no	—
337	C₂×C₈	—	17	1	no	—
338	C₂×C₈	—	17	1	no	—
339	C₂×C₈	—	17	1	no	—
340	C₂×C₈	—	17	1	no	—
341	C₂×C₈	—	17	1	no	—
342	C₂×C₈	—	17	1	no	—
343	C₂×C₈	—	17	1	no	—
344	C₂×C₈	—	17	1	no	—
345	C₂×C₈	—	17	1	no	—
346	C₂×C₈	—	17	1	no	—
347	C₂×C₈	—	17	4	no	—
348	C₂×C₈	—	34	2	no	—
349	C₂×C₈	—	34	2	no	—
350	C₂×C₈	C₄×#595	1	1	yes	characteristic
351	C₂×C₈	C₄×#595	1	1	yes	characteristic
352	C₂×C₈	C₄×#595	1	1	yes	characteristic
353	C₂×C₈	C₂²×#595	1	1	yes	characteristic
354	C₂×C₈	C₂²×#595	1	1	yes	characteristic
355	C₂×C₈	C₂²×#595	1	1	yes	characteristic
356	C₄⋊C₄	—	34	2	no	—
357	C₄⋊C₄	—	34	2	no	—
358	C₂²⋊C₄	—	34	2	no	—
359	C₂²⋊C₄	—	34	2	no	—
360	C₄²	—	17	4	no	—
361	C₄²	—	34	2	no	—
362	C₁₆	—	17	8	no	—
363	C₁₆	—	17	4	no	—
364	C₁₆	C₂²×#595	1	4	yes	—
365	C₂³	—	17	1	no	—
366	C₂³	—	17	1	no	—
367	C₂³	—	17	1	no	—
368	C₂³	—	17	1	no	—
369	C₂³	—	17	1	no	—
370	C₂³	—	17	1	no	—
371	C₂³	—	68	2	no	—
372	C₂³	#10587532	1	1	yes	characteristic
373	C₂×C₄	—	17	1	no	—
374	C₂×C₄	—	17	1	no	—
375	C₂×C₄	—	17	1	no	—
376	C₂×C₄	—	17	1	no	—
377	C₂×C₄	—	17	1	no	—
378	C₂×C₄	—	17	1	no	—
379	C₂×C₄	—	17	1	no	—
380	C₂×C₄	—	17	1	no	—
381	C₂×C₄	—	17	1	no	—
382	C₂×C₄	—	17	1	no	—
383	C₂×C₄	—	17	1	no	—
384	C₂×C₄	—	17	1	no	—
385	C₂×C₄	—	17	1	no	—
386	C₂×C₄	—	17	1	no	—
387	C₂×C₄	—	17	1	no	—
388	C₂×C₄	—	17	1	no	—
389	C₂×C₄	—	17	1	no	—
390	C₂×C₄	—	17	1	no	—
391	C₂×C₄	—	17	1	no	—
392	C₂×C₄	—	17	1	no	—
393	C₂×C₄	—	17	1	no	—
394	C₂×C₄	—	17	1	no	—
395	C₂×C₄	—	34	4	no	—
396	C₂×C₄	—	68	4	no	—
397	C₂×C₄	#10587532	1	1	yes	characteristic
398	C₂×C₄	#10587532	1	1	yes	characteristic
399	C₂×C₄	#10587532	1	1	yes	characteristic
400	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
401	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
403	C₈	—	17	1	no	—
404	C₈	—	17	1	no	—
405	C₈	—	17	1	no	—
406	C₈	—	17	1	no	—
407	C₈	—	34	4	no	—
408	C₈	C₂×C₄×#595	1	1	yes	characteristic
409	C₈	C₂×C₄×#595	1	1	yes	characteristic
410	C₈	C₂×C₄×#595	1	1	yes	characteristic
411	C₈	C₂³×#595	1	1	yes	characteristic
412	C₂²	—	4	1	no	—
413	C₂²	—	17	1	no	—
414	C₂²	—	17	1	no	—
415	C₂²	—	17	1	no	—
416	C₂²	—	17	1	no	—
417	C₂²	—	34	2	no	—
418	C₂²	—	34	2	no	—
419	C₂²	—	34	2	no	—
420	C₂²	—	68	1	no	—
421	C₂²	—	68	1	no	—
422	C₂²	—	68	1	no	—
423	C₂²	C₂×#10587532	1	1	yes	characteristic
424	C₂²	C₂×#10587532	1	1	yes	characteristic
425	C₂²	C₂×#10587532	1	1	yes	characteristic
426	C₄	—	17	1	no	—
427	C₄	—	17	1	no	—
428	C₄	—	17	1	no	—
429	C₄	—	17	1	no	—
430	C₄	—	68	4	no	—
431	C₄	C₂×#10587532	1	1	yes	characteristic
432	C₄	C₂×#10587532	1	1	yes	characteristic
433	C₄	C₂×#10587532	1	1	yes	characteristic
434	C₄	C₂²×C₄×#595	1	1	yes	characteristic
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	17	2	no	—
439	C₂	—	34	1	no	—
440	C₂	—	34	1	no	—
441	C₂	—	34	1	no	—
442	C₂	C₂²×#10587532	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×C₄×#595
commutator	C₄×C₁₇	C₂²×C₄²
Frattini	C₈	C₂³×#595
Fitting	C₂×C₁₇×M₃₂	C₄
socle	C₂×C₁₇	C₂²×#97
prime radical	C₂³×D₁₇	M₁₆
cosocle	C₈×D₁₇	C₂⁴
hypercenter	C₂×M₃₂	#595
hypocenter	C₁₇	C₂×#2110
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #14545004	C₂	semidirect
4. #14545003	C₂	semidirect
5. #14544999	C₂	semidirect
10. #11763865	C₄	semidirect
11. #11763865	C₄	semidirect
14. C₂×#10587538	C₄	semidirect
15. C₂×#10587529	C₄	semidirect
22. #11763700	C₂²	semidirect
23. #11763699	C₂²	semidirect
25. C₂×#10587483	C₄	semidirect
27. M₃₂×D₁₇	C₄	semidirect
28. M₃₂×D₁₇	C₄	semidirect
31. C₂×C₁₆×D₁₇	C₄	semidirect
32. C₂×C₁₇×M₃₂	C₄	semidirect
63. #10587538	C₂×C₄	semidirect
64. C₂×#63216	C₂×C₄	semidirect
69. #10587530	C₂×C₄	semidirect
72. #10587529	C₂×C₄	semidirect
74. C₁₇×M₃₂	C₂×C₄	semidirect
75. C₂×C₁₆×C₁₇	C₂×C₄	semidirect
77. #10587483	C₂×C₄	semidirect
78. C₂×#63214	C₂×C₄	semidirect
79. #10587469	C₂×C₄	semidirect
82. C₁₆×D₁₇	C₂×C₄	semidirect
235. C₂×M₃₂	#595	semidirect
253. D₁₇	#2110	semidirect
292. M₃₂	C₂×#595	semidirect
299. C₂×C₁₆	C₂×#595	semidirect
304. C₁₇	C₂×#2110	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763865	2
C₂×#11763772	2
#14545004	2
#14545003	2
#14544999	2
C₂×M₃₂×D₁₇	2
C₂×#2110	17