Subgroups — #17187412

Order 4352.

598 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10587587	C₂	1	1	yes	maximal, characteristic
2	#14530590	C₂	1	2	yes	maximal, complemented
3	#14530588	C₂	1	2	yes	maximal, complemented
4	#14530583	C₂	1	1	yes	maximal, characteristic, complemented
5	#14530581	C₂	1	1	yes	maximal, characteristic, complemented
6	#14530581	C₂	1	1	yes	maximal, characteristic, complemented
7	#14530541	C₂	1	2	yes	maximal, complemented
8	#14530396	C₂	1	2	yes	maximal
9	C₄×#10587469	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10587587	C₄	1	1	yes	characteristic
13	C₂×#10587587	C₂²	1	1	yes	characteristic
14	C₄×#63252	C₄	1	1	yes	characteristic
15	C₂×#10587469	C₂²	1	2	yes	—
16	C₂×C₁₆×D₁₇	C₂²	1	2	yes	—
17	#11762764	C₄	1	1	yes	characteristic
18	#11762764	C₂²	1	1	yes	characteristic
19	#11762763	C₄	1	1	yes	characteristic
20	#11762763	C₄	1	1	yes	characteristic
21	#11762763	C₂²	1	1	yes	characteristic
22	#11762763	C₂²	1	1	yes	characteristic
23	C₄×#63223	C₄	1	1	yes	characteristic
24	C₄×#63218	C₄	1	1	yes	characteristic
25	C₄×#63218	C₄	1	1	yes	characteristic
26	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
28	C₄⋊#63214	C₂²	1	2	yes	—
29	#11762627	C₂²	1	2	yes	—
30	#11762627	C₂²	1	2	yes	—
31	C₂²⋊#63214	C₂²	1	2	yes	—
32	#11762588	C₂²	1	2	yes	—
33	#11762588	C₂²	1	2	yes	—
34	#11762584	C₂²	1	2	yes	—
35	C₄×#63214	C₂²	1	1	yes	characteristic
36	C₄×#63214	C₂²	1	1	yes	characteristic
37	C₁₆×Dic₁₇	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
39	C₁₇×C₄⋊C₁₆	C₂²	1	2	yes	—
40	C₁₇×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
43	C₂×#63252	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₇	C₈	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₇	C₈	1	1	yes	characteristic
49	C₄×C₂²⋊D₁₇	C₈	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₇	C₈	1	1	yes	characteristic
51	#10587612	C₂×C₄	1	1	yes	characteristic
52	C₂×#63223	C₂×C₄	1	1	yes	characteristic
53	C₂×#63223	C₂×C₄	1	1	yes	characteristic
54	#10587587	—	2	4	no	—
55	#10587587	—	2	4	no	—
56	C₂×#63218	C₂×C₄	1	1	yes	characteristic
57	C₂×#63218	C₂×C₄	1	1	yes	characteristic
58	C₂×#63218	C₂×C₄	1	1	yes	characteristic
59	C₂×#63218	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
64	C₄×D₆₈	C₈	1	1	yes	characteristic
65	C₄×D₆₈	C₈	1	1	yes	characteristic
66	#10587558	C₂×C₄	1	1	yes	characteristic
67	#10587558	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₃₄	C₈	1	1	yes	characteristic
71	C₄×Dic₃₄	C₈	1	1	yes	characteristic
72	C₂×C₁₆×C₁₇	C₂³	1	2	yes	—
73	C₂×C₁₆×C₁₇	C₂³	1	2	yes	—
74	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
78	#10587486	C₂×C₄	1	1	yes	characteristic
79	#10587486	C₂×C₄	1	1	yes	characteristic
80	#10587486	C₂×C₄	1	1	yes	characteristic
81	#10587486	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
85	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
86	C₂×#63214	C₂³	1	2	yes	—
87	C₂×#63214	C₂³	1	2	yes	—
88	#10587474	C₂×C₄	1	1	yes	characteristic
89	#10587474	C₂×C₄	1	1	yes	characteristic
90	C₄×#3622	C₂×C₄	1	1	yes	characteristic
91	C₄×#3622	C₂×C₄	1	1	yes	characteristic
92	#10587469	—	2	4	no	—
93	C₁₆×D₁₇	—	2	4	no	—
94	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
98	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
99	#63252	—	2	2	no	—
100	#63252	—	2	2	no	—
101	C₂×D₆₈	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×Dic₃₄	C₂×C₈	1	1	yes	characteristic
109	C₂×C₈×C₁₇	—	2	2	no	—
110	C₂×C₈×C₁₇	—	2	2	no	—
111	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
115	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
116	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
117	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
120	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
121	#63227	C₂×C₈	1	1	yes	characteristic
122	#63227	C₂×C₈	1	1	yes	characteristic
123	#63227	C₂×C₈	1	1	yes	characteristic
124	#63227	C₂×C₈	1	1	yes	characteristic
125	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
127	#63225	C₂×C₈	1	1	yes	characteristic
128	#63225	C₂×C₈	1	1	yes	characteristic
129	#63225	C₂×C₈	1	1	yes	characteristic
130	#63225	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
137	#63223	—	2	2	no	—
138	#63223	—	2	2	no	—
139	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
140	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
141	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
142	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
143	#63218	—	2	2	no	—
144	#63218	—	2	2	no	—
145	#63218	—	2	2	no	—
146	#63218	—	2	2	no	—
147	C₈×D₁₇	—	2	2	no	—
148	C₈×D₁₇	—	2	2	no	—
149	C₈×D₁₇	M₁₆	1	4	yes	—
150	C₈×D₁₇	#41	1	4	yes	—
151	C₁₆×C₁₇	—	2	2	no	—
152	C₁₆×C₁₇	—	2	2	no	—
153	#63214	—	2	2	no	—
154	#63214	—	2	2	no	—
155	#33420	—	17	1	no	maximal, Sylow
156	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
157	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
158	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₁₇	—	2	1	no	—
160	C₂×C₄×C₁₇	—	2	1	no	—
161	C₂×C₄×C₁₇	—	2	2	no	—
162	C₂×C₄×C₁₇	—	2	2	no	—
163	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
164	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
169	C₂²⋊D₁₇	—	2	2	no	—
170	C₂²⋊D₁₇	—	2	2	no	—
171	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
172	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
173	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
174	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
177	D₆₈	—	2	2	no	—
178	C₄×D₁₇	—	2	1	no	—
179	C₄×D₁₇	—	2	1	no	—
180	C₄×D₁₇	—	2	2	no	—
181	C₄×D₁₇	—	2	2	no	—
182	C₄×D₁₇	—	2	2	no	—
183	C₄×D₁₇	—	2	2	no	—
184	C₄×D₁₇	#117	1	2	yes	—
185	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
186	Dic₃₄	—	2	2	no	—
187	C₈×C₁₇	—	2	1	no	—
188	C₈×C₁₇	—	2	1	no	—
189	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
190	C₈×C₁₇	C₂×#41	1	2	yes	—
191	#3622	—	2	1	no	—
192	#3622	—	2	1	no	—
193	#3622	#117	1	2	yes	—
194	#3622	C₂×M₁₆	1	2	yes	—
195	C₄×#131	—	17	1	no	—
196	#2164	—	17	2	no	—
197	#2164	—	17	2	no	—
198	#2162	—	17	1	no	—
199	#2162	—	17	1	no	—
200	#2162	—	17	1	no	—
201	#2162	D₁₇	1	1	yes	characteristic, complemented
202	#2151	—	17	2	no	—
203	#2113	—	17	2	no	—
204	C₄×M₃₂	—	17	1	no	—
205	C₂×C₄×C₁₆	—	17	1	no	—
206	C₂²×C₁₇	—	2	1	no	—
207	C₂²×C₁₇	—	2	1	no	—
208	C₂²×C₁₇	—	2	1	no	—
209	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
210	C₂×D₁₇	—	2	1	no	—
211	C₂×D₁₇	—	2	1	no	—
212	C₂×D₁₇	—	2	1	no	—
213	C₂×D₁₇	—	2	1	no	—
214	C₂×D₁₇	—	2	1	no	—
215	C₂×D₁₇	#431	1	2	yes	—
216	C₄×C₁₇	—	2	1	no	—
217	C₄×C₁₇	—	2	1	no	—
218	C₄×C₁₇	—	2	1	no	—
219	C₄×C₁₇	#504	1	2	yes	—
220	C₄×C₁₇	#504	1	2	yes	—
221	C₄×C₁₇	C₂×#117	1	1	yes	characteristic
222	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
223	Dic₁₇	—	2	1	no	—
224	Dic₁₇	—	2	1	no	—
225	Dic₁₇	—	2	1	no	—
226	Dic₁₇	—	2	1	no	—
227	Dic₁₇	—	2	1	no	—
228	Dic₁₇	#431	1	2	yes	—
229	C₂×#131	—	17	1	no	—
230	C₂×#131	—	17	1	no	—
231	C₄×#41	—	17	1	no	—
232	C₂×M₃₂	—	17	2	no	—
233	C₂²×C₁₆	—	17	2	no	—
234	#405	—	17	1	no	—
235	#405	—	17	1	no	—
236	#405	—	17	1	no	—
237	#405	—	17	1	no	—
238	#405	—	17	1	no	—
239	#405	—	17	1	no	—
240	C₄×M₁₆	—	17	1	no	—
241	C₄×M₁₆	—	17	1	no	—
242	C₄×M₁₆	—	17	1	no	—
243	C₂×C₄×C₈	—	17	1	no	—
244	C₂×C₄×C₈	—	17	1	no	—
245	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
246	C₄⋊C₁₆	—	17	2	no	—
247	C₄⋊C₁₆	—	17	2	no	—
248	C₄⋊C₁₆	—	17	2	no	—
249	C₄⋊C₁₆	C₂×D₁₇	1	2	yes	—
250	C₂²⋊C₁₆	—	17	2	no	—
251	C₂²⋊C₁₆	—	17	2	no	—
252	C₂²⋊C₁₆	—	17	2	no	—
253	C₂²⋊C₁₆	C₂×D₁₇	1	2	yes	—
254	#346	—	17	2	no	—
255	C₄×C₁₆	—	17	2	no	—
256	C₄×C₁₆	—	17	1	no	—
257	C₄×C₁₆	—	17	1	no	—
258	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic
259	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic
260	C₂×C₁₇	—	4	1	no	—
261	C₂×C₁₇	C₂×#431	1	1	yes	characteristic
262	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
263	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
264	D₁₇	—	2	2	no	—
265	D₁₇	—	4	1	no	—
266	C₂×#41	—	17	1	no	—
267	#131	—	34	4	no	—
268	#131	—	34	4	no	—
269	C₂×M₁₆	—	17	1	no	—
270	C₂×M₁₆	—	17	1	no	—
271	C₂×M₁₆	—	17	1	no	—
272	C₂×M₁₆	—	17	1	no	—
273	C₂×M₁₆	—	17	1	no	—
274	C₂×M₁₆	—	17	1	no	—
275	C₂²×C₈	—	17	1	no	—
276	C₂²×C₈	—	17	1	no	—
277	C₂²×C₈	—	17	1	no	—
278	C₂²×C₈	—	17	1	no	—
279	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
280	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
281	C₄×Q₈	—	17	1	no	—
282	C₄×Q₈	—	17	1	no	—
283	C₄×D₄	—	17	1	no	—
284	C₄×D₄	—	17	1	no	—
285	C₄×D₄	—	17	1	no	—
286	C₄×D₄	—	17	1	no	—
287	C₄×D₄	—	17	1	no	—
288	C₄×D₄	—	17	1	no	—
289	#117	—	17	1	no	—
290	#117	—	17	1	no	—
291	#117	—	17	1	no	—
292	C₂×C₄²	—	17	1	no	—
293	C₂×C₄²	—	17	1	no	—
294	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
295	M₃₂	—	34	4	no	—
296	C₂×C₁₆	—	17	2	no	—
297	C₂×C₁₆	—	17	2	no	—
298	C₂×C₁₆	—	34	4	no	—
299	C₂×C₁₆	C₂²×D₁₇	1	2	yes	—
300	C₂×C₁₆	C₂²×D₁₇	1	2	yes	—
301	#97	—	17	1	no	—
302	#97	—	17	1	no	—
303	#97	—	17	1	no	—
304	#97	—	17	1	no	—
305	#97	—	17	1	no	—
306	#97	—	17	1	no	—
307	C₄×C₈	—	17	1	no	—
308	C₄×C₈	—	17	1	no	—
309	C₄×C₈	—	17	1	no	—
310	C₄×C₈	—	17	1	no	—
311	C₄×C₈	—	17	1	no	—
312	C₄×C₈	—	17	1	no	—
313	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
314	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
317	C₁₇	#33420	1	1	yes	characteristic, complemented, Sylow
318	#41	—	34	2	no	—
319	#41	—	34	2	no	—
320	C₂×Q₈	—	17	1	no	—
321	C₂×D₄	—	17	1	no	—
322	C₂×D₄	—	17	1	no	—
323	C₂×D₄	—	17	1	no	—
324	C₂²×C₄	—	17	1	no	—
325	C₂²×C₄	—	17	1	no	—
326	C₂²×C₄	—	17	1	no	—
327	C₂²×C₄	—	17	1	no	—
328	C₂²×C₄	—	17	1	no	—
329	C₂²×C₄	—	17	1	no	—
330	C₂²×C₄	C₈×D₁₇	1	1	yes	characteristic
331	C₂²×C₄	C₈×D₁₇	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
333	M₁₆	—	34	2	no	—
334	M₁₆	—	34	2	no	—
335	M₁₆	—	34	2	no	—
336	M₁₆	—	34	2	no	—
337	M₁₆	—	34	2	no	—
338	M₁₆	—	34	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	17	1	no	—
342	C₂×C₈	—	17	1	no	—
343	C₂×C₈	—	17	4	no	—
344	C₂×C₈	—	17	4	no	—
345	C₂×C₈	—	17	1	no	—
346	C₂×C₈	—	17	1	no	—
347	C₂×C₈	—	34	2	no	—
348	C₂×C₈	—	34	2	no	—
349	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
350	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
351	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
352	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
353	C₄⋊C₄	—	17	1	no	—
354	C₄⋊C₄	—	17	1	no	—
355	C₄⋊C₄	—	17	1	no	—
356	C₄⋊C₄	—	17	1	no	—
357	C₄⋊C₄	—	17	1	no	—
358	C₄⋊C₄	—	17	1	no	—
359	C₂²⋊C₄	—	17	1	no	—
360	C₂²⋊C₄	—	17	1	no	—
361	C₂²⋊C₄	—	17	1	no	—
362	C₂²⋊C₄	—	17	1	no	—
363	C₂²⋊C₄	—	17	1	no	—
364	C₂²⋊C₄	—	17	1	no	—
365	C₄²	—	17	1	no	—
366	C₄²	—	17	1	no	—
367	C₄²	—	17	1	no	—
368	C₄²	—	17	1	no	—
369	C₄²	—	17	1	no	—
370	C₄²	—	17	1	no	—
371	C₄²	C₈×D₁₇	1	1	yes	characteristic
372	C₄²	C₈×D₁₇	1	1	yes	characteristic
373	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
374	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
375	C₁₆	—	2	2	no	—
376	C₁₆	—	2	2	no	—
377	C₁₆	—	34	2	no	—
378	C₁₆	—	34	2	no	—
379	C₂³	—	17	1	no	—
380	C₂³	—	17	1	no	—
381	C₂³	C₂×C₈×D₁₇	1	1	yes	characteristic
382	Q₈	—	34	2	no	—
383	D₄	—	34	2	no	—
384	D₄	—	34	2	no	—
385	D₄	—	34	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	17	1	no	—
391	C₂×C₄	—	17	2	no	—
392	C₂×C₄	—	17	2	no	—
393	C₂×C₄	—	17	1	no	—
394	C₂×C₄	—	17	1	no	—
395	C₂×C₄	—	17	1	no	—
396	C₂×C₄	—	17	1	no	—
397	C₂×C₄	—	17	1	no	—
398	C₂×C₄	—	34	2	no	—
399	C₂×C₄	—	34	2	no	—
400	C₂×C₄	—	34	2	no	—
401	C₂×C₄	—	34	2	no	—
402	C₂×C₄	—	34	1	no	—
403	C₂×C₄	—	34	1	no	—
404	C₂×C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
405	C₂×C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
406	C₂×C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
407	C₂×C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
408	C₂×C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
409	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	17	2	no	—
413	C₈	—	17	2	no	—
414	C₈	—	34	1	no	—
415	C₈	—	34	1	no	—
416	C₈	M₁₆×D₁₇	1	2	yes	—
417	C₈	#41×D₁₇	1	2	yes	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	17	2	no	—
422	C₂²	—	34	1	no	—
423	C₂²	—	34	1	no	—
424	C₂²	—	34	1	no	—
425	C₂²	—	34	1	no	—
426	C₂²	—	34	1	no	—
427	C₂²	C₂²×C₈×D₁₇	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	17	2	no	—
432	C₄	—	34	1	no	—
433	C₄	—	34	1	no	—
434	C₄	—	34	1	no	—
435	C₄	—	34	1	no	—
436	C₄	—	34	1	no	—
437	C₄	#11763225	1	2	yes	—
438	C₄	#11763227	1	2	yes	—
439	C₄	#117×D₁₇	1	1	yes	characteristic
440	C₄	C₂×M₁₆×D₁₇	1	1	yes	characteristic
441	C₂	—	4	1	no	—
442	C₂	—	34	2	no	—
443	C₂	—	68	1	no	—
444	C₂	D₁₇×#431	1	1	yes	characteristic
445	C₂	C₂×#11763225	1	1	yes	characteristic
446	C₂	C₂×#11763227	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₁₇
commutator, socle	C₂²×C₁₇	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₇
Fitting	C₁₇×#2162	C₂
prime radical	C₂×#63252	C₂×C₄
cosocle	C₂×C₈×C₁₇	C₂⁴
hypercenter	#2162	D₁₇
hypocenter	C₁₇	#33420
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄×C₈ ◁ #2162

Complements

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

N	H ≅ G/N	type
2. #14530590	C₂	semidirect
3. #14530588	C₂	semidirect
4. #14530583	C₂	semidirect
5. #14530581	C₂	semidirect
6. #14530581	C₂	semidirect
7. #14530541	C₂	semidirect
9. C₄×#10587469	C₂	semidirect
10. C₄×C₁₆×D₁₇	C₂	semidirect
11. C₁₇×#2162	C₂	semidirect
201. #2162	D₁₇	semidirect
317. C₁₇	#33420	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10587587	2
#14530590	2
#14530588	2
#14530583	2
#14530581	2
#14530541	2
#14530396	2
C₄×#10587469	2
C₄×C₁₆×D₁₇	2
C₁₇×#2162	2
#33420	17