Subgroups — #16999978

Order 4352.

836 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14537412	C₂	1	1	yes	maximal, characteristic
2	D₁₇×#431	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
4	#14527081	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527079	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527079	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527072	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527072	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527070	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527070	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527063	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527063	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#63218	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#63218	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×M₁₆×D₁₇	C₄	1	2	yes	—
17	C₂×C₄²×D₁₇	C₂²	1	1	yes	characteristic
18	#11762865	C₄	1	2	yes	—
19	#11762863	C₄	1	2	yes	—
20	#11762862	C₂²	1	1	yes	characteristic
21	#11762862	C₂²	1	1	yes	characteristic
22	#11762861	C₄	1	2	yes	—
23	#11762860	C₂²	1	1	yes	characteristic
24	#11762860	C₂²	1	1	yes	characteristic
25	#11762860	C₂²	1	1	yes	characteristic
26	#11762860	C₂²	1	1	yes	characteristic
27	#11762859	C₄	1	2	yes	—
28	#11762831	C₄	1	2	yes	—
29	C₄⋊C₈×D₁₇	C₄	1	2	yes	—
30	#11762771	C₄	1	2	yes	—
31	C₂²⋊C₈×D₁₇	C₄	1	2	yes	—
32	C₄×#63223	C₂²	1	1	yes	characteristic
33	#11762761	C₄	1	2	yes	—
34	M₁₆×Dic₁₇	C₄	1	2	yes	—
35	C₄×#63218	C₂²	1	1	yes	characteristic
36	C₄×#63218	C₂²	1	1	yes	characteristic
37	C₄×#63218	C₂²	1	1	yes	characteristic
38	C₄×#63218	C₂²	1	1	yes	characteristic
39	#97×D₁₇	C₄	1	2	yes	—
40	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
42	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
44	#11762531	C₂²	1	1	yes	characteristic, complemented
45	#11762531	C₂²	1	1	yes	characteristic, complemented
46	#11762531	C₂²	1	1	yes	characteristic, complemented
47	#11762531	C₂²	1	1	yes	characteristic, complemented
48	#11762531	C₂²	1	1	yes	characteristic, complemented
49	#11762531	C₂²	1	1	yes	characteristic, complemented
50	#11762530	C₂²	1	1	yes	characteristic, complemented
51	#11762530	C₂²	1	1	yes	characteristic, complemented
52	#11762530	C₂²	1	1	yes	characteristic, complemented
53	C₈×#3622	C₂²	1	1	yes	characteristic, complemented
54	C₈×#3622	C₂²	1	1	yes	characteristic, complemented
55	C₈×#3622	C₂²	1	1	yes	characteristic, complemented
56	C₁₇×#431	C₂²	1	1	yes	characteristic
57	C₁₇×#431	C₂²	1	1	yes	characteristic
58	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
59	C₁₇×#322	C₂²	1	1	yes	characteristic, complemented
60	C₁₇×#322	C₂²	1	1	yes	characteristic, complemented
61	C₁₇×#322	C₂²	1	1	yes	characteristic, complemented
62	C₈²×C₁₇	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
66	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
71	C₂×#63223	C₂×C₄	1	2	yes	—
72	M₁₆×D₁₇	—	2	8	no	—
73	C₂×#63218	C₂×C₄	1	2	yes	—
74	C₂×#63218	C₂×C₄	1	2	yes	—
75	C₂×#63218	C₂×C₄	1	2	yes	—
76	C₂×#63218	C₂×C₄	1	2	yes	—
77	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
78	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
79	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
80	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
81	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
83	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
84	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
85	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
86	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
87	C₄²×D₁₇	C₂³	1	1	yes	characteristic
88	C₄²×D₁₇	C₂³	1	1	yes	characteristic
89	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
90	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
92	C₁₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₇×#97	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
100	C₂²⋊#3622	C₂×C₄	1	2	yes	—
101	C₂²⋊#3622	C₂×C₄	1	2	yes	—
102	#10587491	C₂×C₄	1	2	yes	—
103	#10587491	C₂×C₄	1	2	yes	—
104	#10587491	C₂×C₄	1	2	yes	—
105	#10587491	C₂×C₄	1	2	yes	—
106	#10587486	C₂×C₄	1	2	yes	—
107	#10587486	C₂×C₄	1	2	yes	—
108	#10587486	C₂×C₄	1	2	yes	—
109	#10587486	C₂×C₄	1	2	yes	—
110	#10587485	C₂×C₄	1	2	yes	—
111	#10587485	C₂×C₄	1	2	yes	—
112	#10587485	C₂×C₄	1	2	yes	—
113	#10587485	C₂×C₄	1	2	yes	—
114	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
115	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
116	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
117	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
118	C₄⋊#3622	C₂×C₄	1	2	yes	—
119	C₄⋊#3622	C₂×C₄	1	2	yes	—
120	#10587474	C₂×C₄	1	2	yes	—
121	C₄×#3622	C₂³	1	1	yes	characteristic
122	C₄×#3622	C₂³	1	1	yes	characteristic
123	C₄×#3622	C₂³	1	1	yes	characteristic
124	C₄×#3622	C₂³	1	1	yes	characteristic
125	C₄×#3622	C₂³	1	1	yes	characteristic
126	C₄×#3622	C₂³	1	1	yes	characteristic
127	C₂³×D₁₇	C₄²	1	1	yes	characteristic
128	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₁₇	C₄²	1	1	yes	characteristic
132	C₂²×Dic₁₇	C₄²	1	1	yes	characteristic
133	C₂²×Dic₁₇	C₄²	1	1	yes	characteristic
134	C₂×C₄×D₁₇	—	2	4	no	—
135	C₂×C₄×D₁₇	—	2	4	no	—
136	C₂×C₄×D₁₇	—	4	2	no	—
137	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
138	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
139	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
140	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
141	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
142	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
143	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
149	M₁₆×C₁₇	—	2	4	no	—
150	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
156	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
160	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
161	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
162	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
163	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
164	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
165	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
166	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
167	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
169	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
170	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
171	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
172	#63223	—	2	4	no	—
173	C₂×#3622	C₂²×C₄	1	2	yes	—
174	C₂×#3622	C₂²×C₄	1	2	yes	—
175	C₂×#3622	C₂²×C₄	1	2	yes	—
176	C₂×#3622	C₂²×C₄	1	2	yes	—
177	C₂×#3622	C₂²×C₄	1	2	yes	—
178	C₂×#3622	C₂²×C₄	1	2	yes	—
179	#63218	—	2	4	no	—
180	#63218	—	2	4	no	—
181	#63218	—	2	4	no	—
182	#63218	M₁₆	1	8	yes	complemented
183	C₈×D₁₇	—	2	4	no	—
184	C₈×D₁₇	—	2	4	no	—
185	C₈×D₁₇	—	4	2	no	—
186	C₈×D₁₇	—	4	2	no	—
187	#17327	—	17	1	no	maximal, Sylow
188	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
189	C₂²×D₁₇	—	2	2	no	—
190	C₂²×D₁₇	—	2	2	no	—
191	C₂²×D₁₇	—	4	1	no	—
192	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
193	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
194	C₂×C₄×C₁₇	—	2	2	no	—
195	C₂×C₄×C₁₇	—	2	2	no	—
196	C₂×C₄×C₁₇	—	2	2	no	—
197	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
198	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
199	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
200	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
203	C₂×Dic₁₇	—	2	2	no	—
204	C₂×Dic₁₇	—	2	2	no	—
205	C₂×Dic₁₇	—	4	1	no	—
206	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
207	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
208	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
209	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
210	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
211	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
212	C₄×D₁₇	—	2	2	no	—
213	C₄×D₁₇	—	2	2	no	—
214	C₄×D₁₇	—	2	2	no	—
215	C₄×D₁₇	—	2	2	no	—
216	C₄×D₁₇	—	2	2	no	—
217	C₄×D₁₇	—	2	2	no	—
218	C₄×D₁₇	—	2	2	no	—
219	C₄×D₁₇	—	2	2	no	—
220	C₄×D₁₇	—	4	1	no	—
221	C₄×D₁₇	—	4	1	no	—
222	C₄×D₁₇	C₂×M₁₆	1	4	yes	—
223	C₄×D₁₇	#131	1	4	yes	—
224	C₈×C₁₇	—	2	2	no	—
225	C₈×C₁₇	—	2	2	no	—
226	C₈×C₁₇	—	2	2	no	—
227	C₈×C₁₇	—	2	2	no	—
228	C₈×C₁₇	—	2	2	no	—
229	C₈×C₁₇	C₂×M₁₆	1	4	yes	—
230	#3622	—	2	2	no	—
231	#3622	—	2	2	no	—
232	#3622	—	2	2	no	—
233	#3622	—	2	2	no	—
234	#3622	—	2	2	no	—
235	#3622	C₂×M₁₆	1	4	yes	—
236	#2920	—	17	1	no	—
237	C₂×#431	—	17	1	no	—
238	C₂×C₄×M₁₆	—	17	1	no	—
239	#1453	—	17	1	no	—
240	#1453	—	17	1	no	—
241	#1453	—	17	1	no	—
242	#1453	D₁₇	1	1	yes	characteristic, complemented
243	#1451	—	17	1	no	—
244	#1451	—	17	1	no	—
245	#1451	—	17	1	no	—
246	#1451	—	17	1	no	—
247	C₈×M₁₆	—	17	1	no	—
248	C₈×M₁₆	—	17	1	no	—
249	C₈×M₁₆	—	17	1	no	—
250	C₈×M₁₆	—	17	1	no	—
251	C₂²×C₁₇	—	2	1	no	—
252	C₂²×C₁₇	—	2	1	no	—
253	C₂²×C₁₇	—	2	1	no	—
254	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
255	C₂×D₁₇	—	2	1	no	—
256	C₂×D₁₇	—	2	1	no	—
257	C₂×D₁₇	—	2	1	no	—
258	C₂×D₁₇	—	2	1	no	—
259	C₂×D₁₇	—	4	4	no	—
260	C₂×D₁₇	C₄×M₁₆	1	2	yes	—
261	C₂×D₁₇	#405	1	2	yes	—
262	C₄×C₁₇	—	2	1	no	—
263	C₄×C₁₇	—	2	1	no	—
264	C₄×C₁₇	—	2	1	no	—
265	C₄×C₁₇	C₂²×M₁₆	1	2	yes	—
266	C₄×C₁₇	C₂×#131	1	2	yes	—
267	C₄×C₁₇	#568	1	2	yes	—
268	Dic₁₇	—	2	1	no	—
269	Dic₁₇	—	2	1	no	—
270	Dic₁₇	—	2	1	no	—
271	Dic₁₇	—	2	1	no	—
272	Dic₁₇	C₄×M₁₆	1	2	yes	—
273	Dic₁₇	#405	1	2	yes	—
274	C₂²×M₁₆	—	17	2	no	—
275	C₂²×C₄²	—	17	1	no	—
276	#432	—	17	2	no	—
277	#432	—	17	2	no	—
278	#431	—	17	1	no	—
279	#431	—	17	1	no	—
280	#431	—	17	2	no	—
281	#431	—	17	2	no	—
282	#431	—	17	1	no	—
283	#431	—	17	1	no	—
284	#431	—	17	1	no	—
285	#431	—	17	1	no	—
286	#431	C₂×D₁₇	1	1	yes	characteristic
287	#431	C₂×D₁₇	1	1	yes	characteristic
288	#423	—	17	2	no	—
289	C₂×C₄⋊C₈	—	17	2	no	—
290	#407	—	17	2	no	—
291	C₂×C₂²⋊C₈	—	17	2	no	—
292	C₄×M₁₆	—	17	2	no	—
293	C₄×M₁₆	—	17	1	no	—
294	C₄×M₁₆	—	17	2	no	—
295	C₄×M₁₆	—	17	1	no	—
296	C₄×M₁₆	—	17	1	no	—
297	C₄×M₁₆	—	17	1	no	—
298	C₄×M₁₆	—	17	1	no	—
299	C₄×M₁₆	C₂×D₁₇	1	1	yes	characteristic
300	C₂×#97	—	17	2	no	—
301	C₂×C₄×C₈	—	17	1	no	—
302	C₂×C₄×C₈	—	17	1	no	—
303	C₂×C₄×C₈	—	17	1	no	—
304	C₂×C₄×C₈	—	17	1	no	—
305	#322	—	17	1	no	—
306	#322	—	17	1	no	—
307	#322	—	17	1	no	—
308	#322	—	17	1	no	—
309	#322	—	17	1	no	—
310	#322	—	17	1	no	—
311	#322	—	17	1	no	—
312	#322	—	17	1	no	—
313	#322	—	17	1	no	—
314	#322	C₂×D₁₇	1	1	yes	characteristic, complemented
315	#322	C₂×D₁₇	1	1	yes	characteristic, complemented
316	#322	C₂×D₁₇	1	1	yes	characteristic, complemented
317	C₈²	—	17	1	no	—
318	C₈²	—	17	1	no	—
319	C₈²	—	17	1	no	—
320	C₈²	C₂×D₁₇	1	1	yes	characteristic, complemented
321	C₂×C₁₇	—	4	1	no	—
322	C₂×C₁₇	C₂×C₄×M₁₆	1	1	yes	characteristic
323	C₂×C₁₇	C₂×#405	1	1	yes	characteristic
324	C₂×C₁₇	#2873	1	1	yes	characteristic
325	D₁₇	—	2	2	no	—
326	D₁₇	—	2	2	no	—
327	C₂³×C₄	—	17	1	no	—
328	C₂³×C₄	—	17	1	no	—
329	C₂³×C₄	—	17	1	no	—
330	C₂×M₁₆	—	17	2	no	—
331	C₂×M₁₆	—	17	2	no	—
332	C₂×M₁₆	—	17	2	no	—
333	C₂×M₁₆	—	17	2	no	—
334	C₂×M₁₆	—	17	2	no	—
335	C₂×M₁₆	—	34	8	no	—
336	C₂×M₁₆	C₄×D₁₇	1	2	yes	—
337	C₂²×C₈	—	17	2	no	—
338	C₂²×C₈	—	17	2	no	—
339	C₂²×C₈	—	17	2	no	—
340	C₂²×C₈	—	17	2	no	—
341	C₂×C₄²	—	17	1	no	—
342	C₂×C₄²	—	17	1	no	—
343	C₂×C₄²	—	17	1	no	—
344	C₂×C₄²	—	17	1	no	—
345	C₂×C₄²	—	17	1	no	—
346	C₂×C₄²	—	17	1	no	—
347	C₂×C₄²	—	17	1	no	—
348	C₂×C₄²	—	17	1	no	—
349	C₂×C₄²	—	17	1	no	—
350	C₂×C₄²	—	17	1	no	—
351	C₂×C₄²	—	17	1	no	—
352	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
353	C₄⋊C₈	—	17	2	no	—
354	C₄⋊C₈	—	17	2	no	—
355	C₄⋊C₈	—	17	2	no	—
356	C₄⋊C₈	—	17	2	no	—
357	C₄⋊C₈	—	17	2	no	—
358	C₄⋊C₈	—	17	2	no	—
359	C₄⋊C₈	C₄×D₁₇	1	2	yes	—
360	C₄⋊C₈	C₄×D₁₇	1	2	yes	—
361	C₂²⋊C₈	—	17	2	no	—
362	C₂²⋊C₈	—	17	2	no	—
363	C₂²⋊C₈	—	17	2	no	—
364	C₂²⋊C₈	—	17	2	no	—
365	C₂²⋊C₈	—	17	2	no	—
366	C₂²⋊C₈	—	17	2	no	—
367	C₂²⋊C₈	C₄×D₁₇	1	2	yes	—
368	C₂²⋊C₈	C₄×D₁₇	1	2	yes	—
369	#97	—	17	2	no	—
370	#97	—	17	2	no	—
371	#97	—	17	2	no	—
372	#97	—	17	2	no	—
373	#97	—	17	2	no	—
374	#97	C₄×D₁₇	1	2	yes	—
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	1	no	—
380	C₄×C₈	—	17	1	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	C₂²×D₁₇	1	1	yes	characteristic
386	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
387	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
388	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
389	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
390	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
391	C₁₇	#17327	1	1	yes	characteristic, complemented, Sylow
392	C₂⁴	—	17	1	no	—
393	C₂²×C₄	—	17	1	no	—
394	C₂²×C₄	—	17	1	no	—
395	C₂²×C₄	—	17	1	no	—
396	C₂²×C₄	—	17	1	no	—
397	C₂²×C₄	—	17	1	no	—
398	C₂²×C₄	—	17	1	no	—
399	C₂²×C₄	—	17	1	no	—
400	C₂²×C₄	—	17	1	no	—
401	C₂²×C₄	—	17	1	no	—
402	C₂²×C₄	—	17	1	no	—
403	C₂²×C₄	—	17	1	no	—
404	C₂²×C₄	—	17	1	no	—
405	C₂²×C₄	—	17	1	no	—
406	C₂²×C₄	—	17	1	no	—
407	C₂²×C₄	—	17	1	no	—
408	C₂²×C₄	—	34	4	no	—
409	C₂²×C₄	—	34	4	no	—
410	C₂²×C₄	—	68	2	no	—
411	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
412	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
413	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
414	M₁₆	—	2	4	no	—
415	M₁₆	—	17	8	no	—
416	M₁₆	—	34	4	no	—
417	M₁₆	—	34	4	no	—
418	M₁₆	—	34	4	no	—
419	M₁₆	—	34	4	no	—
420	C₂×C₈	—	17	2	no	—
421	C₂×C₈	—	17	2	no	—
422	C₂×C₈	—	17	2	no	—
423	C₂×C₈	—	17	2	no	—
424	C₂×C₈	—	17	2	no	—
425	C₂×C₈	—	17	2	no	—
426	C₂×C₈	—	34	4	no	—
427	C₂×C₈	—	34	4	no	—
428	C₂×C₈	—	68	2	no	—
429	C₂×C₈	—	68	2	no	—
430	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
431	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
432	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
433	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
434	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
435	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
436	C₄²	—	17	1	no	—
437	C₄²	—	17	1	no	—
438	C₄²	—	17	1	no	—
439	C₄²	—	17	1	no	—
440	C₄²	—	17	1	no	—
441	C₄²	—	17	1	no	—
442	C₄²	—	17	1	no	—
443	C₄²	—	17	1	no	—
444	C₄²	—	17	1	no	—
445	C₄²	—	17	1	no	—
446	C₄²	—	17	1	no	—
447	C₄²	—	17	1	no	—
448	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
449	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
450	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
451	C₄²	C₂³×D₁₇	1	1	yes	characteristic
452	C₂³	—	17	1	no	—
453	C₂³	—	17	1	no	—
454	C₂³	—	34	2	no	—
455	C₂³	—	34	2	no	—
456	C₂³	—	68	1	no	—
457	C₂³	C₄²×D₁₇	1	1	yes	characteristic
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	17	1	no	—
462	C₂×C₄	—	17	1	no	—
463	C₂×C₄	—	17	4	no	—
464	C₂×C₄	—	17	4	no	—
465	C₂×C₄	—	17	1	no	—
466	C₂×C₄	—	17	1	no	—
467	C₂×C₄	—	17	1	no	—
468	C₂×C₄	—	17	1	no	—
469	C₂×C₄	—	34	2	no	—
470	C₂×C₄	—	34	2	no	—
471	C₂×C₄	—	34	2	no	—
472	C₂×C₄	—	34	2	no	—
473	C₂×C₄	—	34	2	no	—
474	C₂×C₄	—	34	2	no	—
475	C₂×C₄	—	34	2	no	—
476	C₂×C₄	—	34	2	no	—
477	C₂×C₄	—	34	2	no	—
478	C₂×C₄	—	34	2	no	—
479	C₂×C₄	—	68	1	no	—
480	C₂×C₄	—	68	1	no	—
481	C₂×C₄	—	68	1	no	—
482	C₂×C₄	C₄²×D₁₇	1	1	yes	characteristic
483	C₂×C₄	C₄²×D₁₇	1	1	yes	characteristic
484	C₂×C₄	C₄²×D₁₇	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
487	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
488	C₈	—	2	2	no	—
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	—	17	4	no	—
494	C₈	—	34	2	no	—
495	C₈	—	34	2	no	—
496	C₈	—	34	2	no	—
497	C₈	—	34	2	no	—
498	C₈	—	34	2	no	—
499	C₈	M₁₆×D₁₇	1	4	yes	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	17	2	no	—
504	C₂²	—	17	2	no	—
505	C₂²	—	34	1	no	—
506	C₂²	—	34	1	no	—
507	C₂²	—	34	1	no	—
508	C₂²	—	34	1	no	—
509	C₂²	—	68	4	no	—
510	C₂²	C₂×C₄²×D₁₇	1	1	yes	characteristic
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	17	2	no	—
515	C₄	—	17	2	no	—
516	C₄	—	34	1	no	—
517	C₄	—	34	1	no	—
518	C₄	—	34	1	no	—
519	C₄	—	34	1	no	—
520	C₄	C₂×M₁₆×D₁₇	1	2	yes	—
521	C₄	#131×D₁₇	1	2	yes	—
522	C₄	#11763574	1	2	yes	—
523	C₂	—	4	1	no	—
524	C₂	—	34	2	no	—
525	C₂	—	34	2	no	—
526	C₂	C₄×M₁₆×D₁₇	1	1	yes	characteristic
527	C₂	D₁₇×#405	1	1	yes	characteristic
528	C₂	#14537200	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₇
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₁₇×#1453	C₂
prime radical	C₂³×D₁₇	C₄²
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1453	D₁₇
hypocenter	C₁₇	#17327
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ #1453

Complements

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

N	H ≅ G/N	type
4. #14527081	C₂	semidirect
5. #14527079	C₂	semidirect
6. #14527079	C₂	semidirect
7. #14527072	C₂	semidirect
8. #14527072	C₂	semidirect
9. #14527070	C₂	semidirect
10. #14527070	C₂	semidirect
11. #14527063	C₂	semidirect
12. #14527063	C₂	semidirect
13. C₈×#63218	C₂	semidirect
14. C₈×#63218	C₂	semidirect
15. C₁₇×#1453	C₂	semidirect
44. #11762531	C₂²	semidirect
45. #11762531	C₂²	semidirect
46. #11762531	C₂²	semidirect
47. #11762531	C₂²	semidirect
48. #11762531	C₂²	semidirect
49. #11762531	C₂²	semidirect
50. #11762530	C₂²	semidirect
51. #11762530	C₂²	semidirect
52. #11762530	C₂²	semidirect
53. C₈×#3622	C₂²	semidirect
54. C₈×#3622	C₂²	semidirect
55. C₈×#3622	C₂²	semidirect
59. C₁₇×#322	C₂²	semidirect
60. C₁₇×#322	C₂²	semidirect
61. C₁₇×#322	C₂²	semidirect
62. C₈²×C₁₇	C₂²	semidirect
182. #63218	M₁₆	semidirect
242. #1453	D₁₇	semidirect
314. #322	C₂×D₁₇	semidirect
315. #322	C₂×D₁₇	semidirect
316. #322	C₂×D₁₇	semidirect
320. C₈²	C₂×D₁₇	semidirect
391. C₁₇	#17327	semidirect

Maximal subgroups

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

subgroup	index
#14537412	2
D₁₇×#431	2
C₄×M₁₆×D₁₇	2
#14527081	2
#14527079	2
#14527072	2
#14527070	2
#14527063	2
C₈×#63218	2
C₁₇×#1453	2
#17327	17