Subgroups — C₂×#14543827 #17960467

Order 4352.

670 conjugacy classes of subgroups.

The subgroup lattice has 442 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	C₂²×C₈×#595	C₂	1	1	yes	maximal, characteristic
3	#14543827	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#63242	C₄	1	1	yes	characteristic
6	C₂²×C₄×#595	C₄	1	1	yes	characteristic
7	C₂×#10587530	—	2	1	no	—
8	#11763865	—	2	1	no	—
9	#11763865	—	2	1	no	—
10	#11763865	C₄	1	2	yes	complemented
11	#11763865	C₂²	1	2	yes	—
12	C₂×#10587538	C₄	1	2	yes	complemented
13	C₂×#10587529	—	2	1	no	—
14	C₂×C₈×#595	—	2	1	no	—
15	C₂×C₈×#595	—	2	1	no	—
16	C₂×C₈×#595	—	2	1	no	—
17	C₂×C₈×#595	—	2	1	no	—
18	C₂×C₈×#595	C₄	1	2	yes	—
19	C₂×C₈×#595	C₂²	1	2	yes	—
20	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
21	C₂×#10587483	C₄	1	1	yes	characteristic, complemented
22	C₂×#10587469	—	2	1	no	—
23	M₃₂×D₁₇	—	2	1	no	—
24	M₃₂×D₁₇	—	2	1	no	—
25	M₃₂×D₁₇	C₄	1	2	yes	complemented
26	M₃₂×D₁₇	C₂²	1	2	yes	—
27	C₂×C₁₆×D₁₇	—	2	1	no	—
28	C₂×C₁₇×M₃₂	C₄	1	1	yes	characteristic, complemented
29	C₂³×#595	—	2	1	no	—
30	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
31	C₂²×#3624	—	2	1	no	—
32	C₂×C₄×#595	—	2	1	no	—
33	C₂×C₄×#595	—	2	1	no	—
34	C₂×C₄×#595	—	2	1	no	—
35	C₂×C₄×#595	C₈	1	2	yes	—
36	C₂×C₄×#595	C₈	1	2	yes	—
37	C₂×C₄×#595	C₂×C₄	1	2	yes	—
38	C₂×#63242	—	2	1	no	—
39	C₂×#63242	—	2	1	no	—
40	C₂×#63242	—	2	1	no	—
41	C₂×#63242	C₈	1	2	yes	—
42	C₂×#63242	C₈	1	2	yes	—
43	C₂×#63242	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
50	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
51	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
52	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
53	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
54	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
55	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
56	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
57	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
58	#10587538	—	2	2	no	—
59	#10587538	C₂×C₄	1	4	yes	complemented
60	C₂×#63216	—	2	2	no	—
61	C₈×#595	—	2	2	no	—
62	C₈×#595	—	2	2	no	—
63	C₈×#595	—	2	2	no	—
64	C₈×#595	—	2	2	no	—
65	#10587530	—	2	2	no	—
66	#10587530	—	2	2	no	—
67	#10587529	—	2	2	no	—
68	#10587529	—	2	2	no	—
69	C₁₇×M₃₂	—	2	1	no	—
70	C₁₇×M₃₂	C₂×C₄	1	2	yes	complemented
71	C₂×C₁₆×C₁₇	—	2	1	no	—
72	#10587483	—	2	1	no	—
73	#10587483	C₂×C₄	1	2	yes	complemented
74	C₂×#63214	—	2	1	no	—
75	#10587469	—	2	2	no	—
76	#10587469	—	2	2	no	—
77	C₁₆×D₁₇	—	2	2	no	—
78	C₁₆×D₁₇	—	2	2	no	—
79	C₂³×D₁₇	M₁₆	1	1	yes	characteristic
80	C₂²×#595	—	2	8	no	—
81	C₂²×#595	—	2	2	no	—
82	C₂²×#595	—	2	2	no	—
83	C₂²×#595	—	2	2	no	—
84	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
85	C₂²×Dic₁₇	M₁₆	1	1	yes	characteristic
86	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
87	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
96	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
97	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
98	C₂×#3624	—	2	2	no	—
99	C₂×#3624	—	2	2	no	—
100	C₂×#3624	—	2	2	no	—
101	C₄×#595	—	2	2	no	—
102	C₄×#595	—	2	2	no	—
103	C₄×#595	—	2	2	no	—
104	C₄×#595	C₂×C₈	1	4	yes	—
105	#63242	—	2	2	no	—
106	#63242	—	2	2	no	—
107	#63242	—	2	2	no	—
108	#63242	C₂×C₈	1	4	yes	—
109	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
110	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×#3622	C₄²	1	1	yes	characteristic
116	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
119	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
120	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
121	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
122	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
123	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
124	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
126	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
127	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
128	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
130	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
131	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
132	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
133	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
134	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
135	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
136	C₈×D₁₇	C₂×Q₈	1	1	yes	characteristic
137	#63216	—	2	4	no	—
138	C₁₆×C₁₇	—	2	2	no	—
139	#63214	—	2	2	no	—
140	C₂×#1376	—	17	1	no	maximal, Sylow
141	C₂³×C₁₇	#97	1	1	yes	characteristic
142	C₂²×D₁₇	—	2	4	no	—
143	C₂²×D₁₇	#97	1	1	yes	characteristic
144	C₂²×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
145	C₂²×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
146	C₂²×D₁₇	C₄⋊C₈	1	1	yes	characteristic
147	C₂²×D₁₇	C₄⋊C₈	1	1	yes	characteristic
148	C₂²×D₁₇	C₂×M₁₆	1	1	yes	characteristic
149	C₂×#595	—	2	8	no	—
150	C₂×#595	—	2	8	no	—
151	C₂×#595	—	2	8	no	—
152	C₂×#595	—	2	4	no	—
153	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
154	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
155	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
156	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
157	C₂×C₄×C₁₇	#97	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
159	C₂×Dic₁₇	#97	1	1	yes	characteristic
160	C₂×Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
161	C₂×Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
162	C₂×Dic₁₇	C₄⋊C₈	1	1	yes	characteristic
163	C₂×Dic₁₇	C₄⋊C₈	1	1	yes	characteristic
164	C₂×Dic₁₇	C₂×M₁₆	1	1	yes	characteristic
165	C₄×D₁₇	#95	1	1	yes	characteristic
166	C₄×D₁₇	#95	1	1	yes	characteristic
167	C₄×D₁₇	C₄×C₈	1	1	yes	characteristic
168	C₄×D₁₇	C₄×C₈	1	1	yes	characteristic
169	C₄×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
170	C₄×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
171	C₄×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
172	C₄×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
173	C₄×D₁₇	C₄⋊C₈	1	1	yes	characteristic
174	C₄×D₁₇	C₄⋊C₈	1	1	yes	characteristic
175	C₄×D₁₇	C₄⋊C₈	1	1	yes	characteristic
176	C₄×D₁₇	C₄⋊C₈	1	1	yes	characteristic
177	C₄×D₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
180	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
181	#3624	—	2	4	no	—
182	C₈×C₁₇	#95	1	1	yes	characteristic
183	C₈×C₁₇	#95	1	1	yes	characteristic
184	C₈×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
186	#3622	#95	1	1	yes	characteristic
187	#3622	#95	1	1	yes	characteristic
188	#3622	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂²×M₃₂	—	17	1	no	—
191	C₂²×M₃₂	—	17	1	no	—
192	C₂²×C₄×C₈	—	17	1	no	—
193	#1376	—	17	4	no	—
194	C₂²×C₁₇	—	2	2	no	—
195	C₂²×C₁₇	#336	1	1	yes	characteristic
196	C₂²×C₁₇	#336	1	1	yes	characteristic
197	C₂²×C₁₇	C₂×#97	1	1	yes	characteristic
198	C₂×D₁₇	—	2	2	no	—
199	C₂×D₁₇	—	2	2	no	—
200	C₂×D₁₇	—	2	2	no	—
201	C₂×D₁₇	—	2	2	no	—
202	C₂×D₁₇	—	2	2	no	—
203	C₂×D₁₇	#336	1	1	yes	characteristic
204	C₂×D₁₇	#336	1	1	yes	characteristic
205	C₂×D₁₇	#364	1	4	yes	—
206	C₂×D₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
207	C₂×D₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
208	#595	—	2	8	no	—
209	C₄×C₁₇	#336	1	1	yes	characteristic
210	C₄×C₁₇	#336	1	1	yes	characteristic
211	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
212	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
213	Dic₁₇	#336	1	1	yes	characteristic
214	Dic₁₇	#336	1	1	yes	characteristic
215	Dic₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
216	Dic₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
217	C₂³×C₈	—	17	1	no	—
218	C₂³×C₈	—	17	1	no	—
219	C₂²×C₄²	—	17	1	no	—
220	C₂×M₃₂	—	17	2	no	—
221	C₂×M₃₂	—	17	2	no	—
222	C₂×M₃₂	—	17	2	no	—
223	C₂×M₃₂	—	17	1	no	—
224	C₂×M₃₂	—	17	2	no	—
225	C₂×M₃₂	—	17	2	no	—
226	C₂×M₃₂	—	34	1	no	—
227	C₂×M₃₂	—	34	1	no	—
228	C₂×M₃₂	—	34	1	no	—
229	C₂×M₃₂	—	34	1	no	—
230	C₂×M₃₂	—	34	1	no	—
231	C₂×M₃₂	—	34	1	no	—
232	C₂×M₃₂	#595	1	1	yes	characteristic, complemented
233	C₂²×C₁₆	—	34	1	no	—
234	C₂²×C₁₆	—	34	1	no	—
235	C₂×C₄×C₈	—	17	2	no	—
236	C₂×C₄×C₈	—	17	2	no	—
237	C₂×C₄×C₈	—	34	1	no	—
238	C₂×C₄×C₈	—	34	1	no	—
239	C₂×C₄×C₈	—	34	1	no	—
240	C₂×C₄×C₈	—	34	1	no	—
241	C₂×C₁₇	—	2	1	no	—
242	C₂×C₁₇	—	2	1	no	—
243	C₂×C₁₇	#1376	1	2	yes	complemented
244	C₂×C₁₇	C₂×#336	1	1	yes	characteristic
245	D₁₇	—	2	1	no	—
246	D₁₇	—	2	1	no	—
247	D₁₇	#1376	1	2	yes	complemented
248	D₁₇	C₂×#364	1	2	yes	—
249	C₂³×C₄	—	17	1	no	—
250	C₂³×C₄	—	34	1	no	—
251	C₂²×C₈	—	17	1	no	—
252	C₂²×C₈	—	17	1	no	—
253	C₂²×C₈	—	17	1	no	—
254	C₂²×C₈	—	17	1	no	—
255	C₂²×C₈	—	17	1	no	—
256	C₂²×C₈	—	17	1	no	—
257	C₂²×C₈	—	17	1	no	—
258	C₂²×C₈	—	17	1	no	—
259	C₂²×C₈	—	17	1	no	—
260	C₂²×C₈	—	17	1	no	—
261	C₂²×C₈	—	17	1	no	—
262	C₂²×C₈	—	17	1	no	—
263	C₂²×C₈	—	17	1	no	—
264	C₂²×C₈	—	17	2	no	—
265	C₂²×C₈	—	17	2	no	—
266	C₂²×C₈	—	17	2	no	—
267	C₂²×C₈	—	34	1	no	—
268	C₂²×C₈	—	34	1	no	—
269	C₂²×C₈	—	34	1	no	—
270	C₂²×C₈	—	34	1	no	—
271	C₂²×C₈	C₂×#595	1	1	yes	characteristic
272	C₂×C₄²	—	17	2	no	—
273	C₂×C₄²	—	17	2	no	—
274	C₂×C₄²	—	17	2	no	—
275	C₂×C₄²	—	34	1	no	—
276	C₂×C₄²	—	34	1	no	—
277	C₂×C₄²	—	34	1	no	—
278	M₃₂	—	2	1	no	—
279	M₃₂	—	17	4	no	—
280	M₃₂	—	17	2	no	—
281	M₃₂	—	34	2	no	—
282	M₃₂	—	34	2	no	—
283	M₃₂	—	34	2	no	—
284	M₃₂	—	34	2	no	—
285	M₃₂	—	34	2	no	—
286	M₃₂	—	34	1	no	—
287	M₃₂	C₂×#595	1	2	yes	complemented
288	C₂×C₁₆	—	2	1	no	—
289	C₂×C₁₆	—	34	2	no	—
290	C₂×C₁₆	—	34	2	no	—
291	C₂×C₁₆	—	34	2	no	—
292	C₂×C₁₆	—	34	2	no	—
293	C₂×C₁₆	—	34	2	no	—
294	C₂×C₁₆	—	34	1	no	—
295	C₄×C₈	—	34	2	no	—
296	C₄×C₈	—	34	2	no	—
297	C₄×C₈	—	34	2	no	—
298	C₄×C₈	—	34	2	no	—
299	C₁₇	C₂×#1376	1	1	yes	characteristic, complemented, Sylow
300	C₂⁴	—	17	1	no	—
301	C₂²×C₄	—	17	1	no	—
302	C₂²×C₄	—	17	1	no	—
303	C₂²×C₄	—	17	1	no	—
304	C₂²×C₄	—	17	1	no	—
305	C₂²×C₄	—	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	—	34	2	no	—
315	C₂²×C₄	—	34	2	no	—
316	C₂²×C₄	—	34	2	no	—
317	C₂²×C₄	—	34	8	no	—
318	C₂²×C₄	C₄×#595	1	1	yes	characteristic
319	C₂×C₈	—	17	1	no	—
320	C₂×C₈	—	17	1	no	—
321	C₂×C₈	—	17	1	no	—
322	C₂×C₈	—	17	1	no	—
323	C₂×C₈	—	17	1	no	—
324	C₂×C₈	—	17	1	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	4	no	—
342	C₂×C₈	—	34	2	no	—
343	C₂×C₈	—	34	2	no	—
344	C₂×C₈	—	34	2	no	—
345	C₂×C₈	—	34	2	no	—
346	C₂×C₈	—	34	2	no	—
347	C₂×C₈	—	34	2	no	—
348	C₂×C₈	C₄×#595	1	1	yes	characteristic
349	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
350	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
351	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
352	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
353	C₂×C₈	C₂²×#595	1	1	yes	characteristic
354	C₄²	—	17	4	no	—
355	C₄²	—	34	2	no	—
356	C₄²	—	34	2	no	—
357	C₄²	—	34	2	no	—
358	C₁₆	—	2	2	no	—
359	C₁₆	—	34	4	no	—
360	C₁₆	—	34	2	no	—
361	C₂³	—	17	1	no	—
362	C₂³	—	17	1	no	—
363	C₂³	—	17	1	no	—
364	C₂³	—	17	1	no	—
365	C₂³	—	17	1	no	—
366	C₂³	—	17	1	no	—
367	C₂³	—	34	4	no	—
368	C₂³	#10587532	1	1	yes	characteristic
369	C₂×C₄	—	17	1	no	—
370	C₂×C₄	—	17	1	no	—
371	C₂×C₄	—	17	1	no	—
372	C₂×C₄	—	17	1	no	—
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	—	34	4	no	—
392	C₂×C₄	—	34	8	no	—
393	C₂×C₄	—	34	8	no	—
394	C₂×C₄	—	34	8	no	—
395	C₂×C₄	C₈×#595	1	1	yes	characteristic
396	C₂×C₄	C₈×#595	1	1	yes	characteristic
397	C₂×C₄	#10587532	1	1	yes	characteristic
398	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
399	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
400	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
401	C₈	—	17	1	no	—
402	C₈	—	17	1	no	—
403	C₈	—	17	1	no	—
404	C₈	—	17	1	no	—
405	C₈	—	34	4	no	—
406	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
407	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
408	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
409	C₈	C₂×C₂²⋊#595	1	1	yes	characteristic
410	C₂²	—	2	2	no	—
411	C₂²	—	17	1	no	—
412	C₂²	—	17	1	no	—
413	C₂²	—	17	4	no	—
414	C₂²	—	17	1	no	—
415	C₂²	—	17	1	no	—
416	C₂²	—	34	2	no	—
417	C₂²	—	34	2	no	—
418	C₂²	—	34	2	no	—
419	C₂²	—	34	2	no	—
420	C₂²	—	34	2	no	—
421	C₂²	#11763674	1	1	yes	characteristic
422	C₂²	#11763674	1	1	yes	characteristic
423	C₂²	C₂×#10587532	1	1	yes	characteristic
424	C₄	—	17	1	no	—
425	C₄	—	17	1	no	—
426	C₄	—	17	1	no	—
427	C₄	—	17	1	no	—
428	C₄	—	34	8	no	—
429	C₄	#11763674	1	1	yes	characteristic
430	C₄	#11763674	1	1	yes	characteristic
431	C₄	C₂×(C₂×#595)⋊C₄	1	1	yes	characteristic
432	C₄	C₂×C₈×#595	1	1	yes	characteristic
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	17	2	no	—
436	C₂	—	17	2	no	—
437	C₂	—	34	1	no	—
438	C₂	—	34	1	no	—
439	C₂	#14543827	1	2	yes	direct product factor
440	C₂	C₂×#11763674	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊#595
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×#595
Fitting	C₂×C₁₇×M₃₂	C₄
socle	C₂²×C₁₇	#336
prime radical	C₂³×D₁₇	M₁₆
cosocle	C₂×C₈×D₁₇	C₂³
hypercenter	C₂×M₃₂	#595
hypocenter	C₁₇	C₂×#1376
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #14543827	C₂	direct (N × H)
10. #11763865	C₄	semidirect
12. C₂×#10587538	C₄	semidirect
21. C₂×#10587483	C₄	semidirect
25. M₃₂×D₁₇	C₄	semidirect
28. C₂×C₁₇×M₃₂	C₄	semidirect
59. #10587538	C₂×C₄	semidirect
70. C₁₇×M₃₂	C₂×C₄	semidirect
73. #10587483	C₂×C₄	semidirect
232. C₂×M₃₂	#595	semidirect
243. C₂×C₁₇	#1376	semidirect
247. D₁₇	#1376	semidirect
287. M₃₂	C₂×#595	semidirect
299. C₁₇	C₂×#1376	semidirect
439. C₂	#14543827	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11763865	2
C₂²×C₈×#595	2
#14543827	2
C₂×M₃₂×D₁₇	2
C₂×#1376	17

Subgroups — C2×#14543827 #17960467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14543827 #17960467