Subgroups — #17003355

Order 4352.

712 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14537414	C₂	1	1	yes	maximal, characteristic
2	D₁₇×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#63218	C₂	1	1	yes	maximal, characteristic
4	#14527550	C₂	1	2	yes	maximal, complemented
5	#14527548	C₂	1	2	yes	maximal, complemented
6	#14527547	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527545	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527545	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527535	C₂	1	2	yes	maximal, complemented
10	#14527533	C₂	1	2	yes	maximal, complemented
11	C₁₇×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#63218	C₄	1	1	yes	characteristic
13	C₂²×#63218	C₄	1	1	yes	characteristic
14	C₂×C₄²×D₁₇	C₂²	1	1	yes	characteristic
15	#11762866	C₂²	1	1	yes	characteristic
16	#11762866	C₂²	1	1	yes	characteristic
17	#11762865	C₂²	1	2	yes	—
18	#11762864	—	2	1	no	—
19	#11762864	—	2	1	no	—
20	#11762863	—	2	1	no	—
21	#11762861	C₂²	1	2	yes	—
22	#11762859	—	2	1	no	—
23	#11762831	C₂²	1	2	yes	—
24	C₄⋊C₈×D₁₇	C₂²	1	2	yes	—
25	#11762771	—	2	1	no	—
26	C₂²⋊C₈×D₁₇	—	2	1	no	—
27	#11762761	—	2	1	no	—
28	C₄×#63218	C₄	1	1	yes	characteristic
29	C₄×#63218	C₄	1	1	yes	characteristic
30	C₄×#63218	C₄	1	1	yes	characteristic
31	C₄×#63218	C₄	1	1	yes	characteristic
32	C₄×#63218	C₂²	1	1	yes	characteristic
33	C₄×#63218	C₂²	1	1	yes	characteristic
34	C₄×#63218	C₂²	1	1	yes	characteristic
35	C₄×#63218	C₂²	1	1	yes	characteristic
36	C₂×#10587486	C₄	1	1	yes	characteristic
37	C₂×#10587486	C₄	1	1	yes	characteristic
38	#97×D₁₇	—	2	1	no	—
39	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
40	#11762562	C₂²	1	2	yes	complemented
41	#11762561	C₂²	1	2	yes	complemented
42	#11762561	C₂²	1	2	yes	complemented
43	#11762560	C₂²	1	2	yes	complemented
44	#11762559	C₂²	1	2	yes	complemented
45	#11762559	C₂²	1	2	yes	complemented
46	C₁₇×#432	C₂²	1	1	yes	characteristic
47	C₁₇×#432	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
49	C₁₇×#335	C₂²	1	2	yes	complemented
50	C₁₇×#334	C₂²	1	2	yes	complemented
51	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄×D₁₇	D₄	1	1	yes	characteristic
53	C₂²×C₄×D₁₇	Q₈	1	1	yes	characteristic
54	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₇	D₄	1	1	yes	characteristic
59	C₂×C₄×Dic₁₇	Q₈	1	1	yes	characteristic
60	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
61	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
62	C₂×#63218	—	2	4	no	—
63	C₂×#63218	—	2	4	no	—
64	C₂×#63218	—	2	2	no	—
65	C₂×#63218	C₂×C₄	1	1	yes	characteristic
66	C₂×#63218	C₂×C₄	1	1	yes	characteristic
67	C₂×#63218	C₂×C₄	1	1	yes	characteristic
68	C₂×#63218	C₂×C₄	1	1	yes	characteristic
69	C₂×#63218	C₂×C₄	1	1	yes	characteristic
70	C₂×#63218	C₂×C₄	1	1	yes	characteristic
71	C₂×#63218	C₂×C₄	1	1	yes	characteristic
72	C₂×#63218	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₁₇	—	2	2	no	—
74	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₁₇	D₄	1	1	yes	characteristic
77	C₄²×D₁₇	D₄	1	1	yes	characteristic
78	C₄²×D₁₇	Q₈	1	1	yes	characteristic
79	C₄²×D₁₇	Q₈	1	1	yes	characteristic
80	C₄²×D₁₇	C₂³	1	1	yes	characteristic
81	C₄²×D₁₇	C₂³	1	1	yes	characteristic
82	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
83	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₇×C₂²⋊C₈	—	2	1	no	—
85	C₁₇×C₂²⋊C₈	—	2	1	no	—
86	C₁₇×#97	—	2	1	no	—
87	C₁₇×#97	—	2	1	no	—
88	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
92	C₂²⋊#3622	—	2	1	no	—
93	C₂²⋊#3622	—	2	1	no	—
94	#10587491	—	2	2	no	—
95	#10587491	—	2	2	no	—
96	#10587486	—	2	2	no	—
97	#10587486	C₂×C₄	1	1	yes	characteristic
98	#10587486	C₂×C₄	1	1	yes	characteristic
99	#10587486	C₂×C₄	1	1	yes	characteristic
100	#10587486	C₂×C₄	1	1	yes	characteristic
101	#10587486	C₂×C₄	1	1	yes	characteristic
102	#10587486	C₂×C₄	1	1	yes	characteristic
103	#10587486	C₂×C₄	1	1	yes	characteristic
104	#10587486	C₂×C₄	1	1	yes	characteristic
105	#10587485	—	2	2	no	—
106	#10587485	—	2	2	no	—
107	C₈×Dic₁₇	—	2	2	no	—
108	C₄⋊#3622	C₂³	1	2	yes	—
109	C₄⋊#3622	C₂³	1	2	yes	—
110	#10587474	—	2	1	no	—
111	#10587474	—	2	1	no	—
112	C₄×#3622	C₂×C₄	1	1	yes	characteristic
113	C₄×#3622	C₂×C₄	1	1	yes	characteristic
114	C₄×#3622	C₂³	1	1	yes	characteristic
115	C₄×#3622	C₂³	1	1	yes	characteristic
116	C₂³×D₁₇	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
120	C₂²×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
122	C₂²×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×D₁₇	—	2	2	no	—
124	C₂×C₄×D₁₇	—	2	2	no	—
125	C₂×C₄×D₁₇	—	4	2	no	—
126	C₂×C₄×D₁₇	—	4	2	no	—
127	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
138	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
139	C₂×C₈×C₁₇	—	2	2	no	—
140	C₂×C₈×C₁₇	—	2	2	no	—
141	C₂×C₈×C₁₇	—	2	2	no	—
142	C₂×C₈×C₁₇	—	2	2	no	—
143	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
150	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
151	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
152	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
153	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
154	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
155	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
156	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
157	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
159	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
160	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
161	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
162	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
163	C₂×#3622	—	2	2	no	—
164	C₂×#3622	—	2	2	no	—
165	C₂×#3622	—	2	2	no	—
166	C₂×#3622	—	2	2	no	—
167	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
168	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
169	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
170	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
171	#63218	—	2	2	no	—
172	#63218	—	2	2	no	—
173	#63218	—	2	2	no	—
174	#63218	—	2	2	no	—
175	#63218	—	2	2	no	—
176	#63218	—	2	2	no	—
177	#63218	—	4	4	no	—
178	#63218	M₁₆	1	4	yes	complemented
179	#63218	M₁₆	1	4	yes	complemented
180	C₈×D₁₇	—	4	4	no	—
181	#17797	—	17	1	no	maximal, Sylow
182	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×D₁₇	—	2	2	no	—
184	C₂²×D₁₇	—	2	2	no	—
185	C₂²×D₁₇	—	4	1	no	—
186	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₇	—	2	2	no	—
189	C₂×C₄×C₁₇	—	2	1	no	—
190	C₂×C₄×C₁₇	—	2	1	no	—
191	C₂×C₄×C₁₇	—	2	2	no	—
192	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
198	C₂×Dic₁₇	—	2	2	no	—
199	C₂×Dic₁₇	—	2	2	no	—
200	C₂×Dic₁₇	—	4	1	no	—
201	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₄×D₁₇	—	2	2	no	—
208	C₄×D₁₇	—	2	1	no	—
209	C₄×D₁₇	—	2	1	no	—
210	C₄×D₁₇	—	2	2	no	—
211	C₄×D₁₇	—	2	2	no	—
212	C₄×D₁₇	—	2	2	no	—
213	C₄×D₁₇	—	4	1	no	—
214	C₄×D₁₇	—	4	1	no	—
215	C₄×D₁₇	—	4	1	no	—
216	C₄×D₁₇	—	4	1	no	—
217	C₄×D₁₇	—	4	1	no	—
218	C₄×D₁₇	—	4	1	no	—
219	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
220	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
221	C₈×C₁₇	—	2	1	no	—
222	C₈×C₁₇	—	2	1	no	—
223	C₈×C₁₇	—	4	2	no	—
224	C₈×C₁₇	—	4	2	no	—
225	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
226	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
227	#3622	—	2	1	no	—
228	#3622	—	2	1	no	—
229	#3622	—	4	2	no	—
230	#3622	—	4	2	no	—
231	#3622	C₂×M₁₆	1	2	yes	—
232	#3622	C₂×M₁₆	1	2	yes	—
233	#2920	—	17	1	no	—
234	C₂×#432	—	17	1	no	—
235	C₂×C₄×M₁₆	—	17	1	no	—
236	#1569	—	17	2	no	—
237	#1569	—	17	2	no	—
238	#1568	—	17	1	no	—
239	#1568	—	17	1	no	—
240	#1568	—	17	1	no	—
241	#1568	D₁₇	1	1	yes	characteristic, complemented
242	#1565	—	17	2	no	—
243	#1565	—	17	2	no	—
244	C₂²×C₁₇	—	2	1	no	—
245	C₂²×C₁₇	—	2	1	no	—
246	C₂²×C₁₇	#430	1	2	yes	—
247	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
248	C₂×D₁₇	—	2	1	no	—
249	C₂×D₁₇	—	2	1	no	—
250	C₂×D₁₇	—	2	1	no	—
251	C₂×D₁₇	—	2	1	no	—
252	C₂×D₁₇	—	2	1	no	—
253	C₂×D₁₇	—	4	4	no	—
254	C₂×D₁₇	#423	1	2	yes	—
255	C₄×C₁₇	—	2	1	no	—
256	C₄×C₁₇	—	2	1	no	—
257	C₄×C₁₇	—	2	1	no	—
258	C₄×C₁₇	—	2	1	no	—
259	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
260	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
261	C₄×C₁₇	#575	1	2	yes	—
262	Dic₁₇	—	2	1	no	—
263	Dic₁₇	—	2	1	no	—
264	Dic₁₇	—	2	1	no	—
265	Dic₁₇	—	2	1	no	—
266	Dic₁₇	—	2	1	no	—
267	Dic₁₇	#423	1	2	yes	—
268	C₂²×M₁₆	—	17	1	no	—
269	C₂²×M₁₆	—	17	1	no	—
270	C₂²×C₄²	—	17	1	no	—
271	#432	—	17	1	no	—
272	#432	—	17	1	no	—
273	#432	—	17	2	no	—
274	#432	—	34	1	no	—
275	#432	—	34	1	no	—
276	#432	—	34	1	no	—
277	#432	C₂×D₁₇	1	1	yes	characteristic
278	#432	C₂×D₁₇	1	1	yes	characteristic
279	#431	—	17	2	no	—
280	#431	—	34	1	no	—
281	#423	—	17	2	no	—
282	C₂×C₄⋊C₈	—	17	2	no	—
283	#407	—	34	1	no	—
284	C₂×C₂²⋊C₈	—	34	1	no	—
285	C₄×M₁₆	—	17	1	no	—
286	C₄×M₁₆	—	17	1	no	—
287	C₄×M₁₆	—	17	1	no	—
288	C₄×M₁₆	—	17	1	no	—
289	C₄×M₁₆	—	17	1	no	—
290	C₄×M₁₆	—	17	1	no	—
291	C₄×M₁₆	—	17	1	no	—
292	C₄×M₁₆	—	17	1	no	—
293	C₄×M₁₆	—	34	1	no	—
294	C₂×#97	—	17	1	no	—
295	C₂×#97	—	17	1	no	—
296	C₂×#97	—	34	1	no	—
297	C₂×C₄×C₈	—	17	1	no	—
298	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
299	#335	—	17	2	no	—
300	#335	—	17	2	no	—
301	#335	—	17	2	no	—
302	#335	C₂×D₁₇	1	2	yes	complemented
303	#334	—	17	2	no	—
304	#334	—	17	2	no	—
305	#334	—	17	2	no	—
306	#334	C₂×D₁₇	1	2	yes	complemented
307	C₂×C₁₇	—	2	2	no	—
308	C₂×C₁₇	C₂×#423	1	1	yes	characteristic
309	C₂×C₁₇	#2911	1	1	yes	characteristic
310	C₂×C₁₇	C₂×#430	1	1	yes	characteristic
311	D₁₇	—	2	2	no	—
312	D₁₇	—	4	1	no	—
313	C₂³×C₄	—	17	1	no	—
314	C₂³×C₄	—	17	1	no	—
315	C₂³×C₄	—	17	1	no	—
316	C₂×M₁₆	—	17	1	no	—
317	C₂×M₁₆	—	17	1	no	—
318	C₂×M₁₆	—	17	1	no	—
319	C₂×M₁₆	—	17	1	no	—
320	C₂×M₁₆	—	17	1	no	—
321	C₂×M₁₆	—	17	1	no	—
322	C₂×M₁₆	—	17	1	no	—
323	C₂×M₁₆	—	17	1	no	—
324	C₂×M₁₆	—	34	4	no	—
325	C₂×M₁₆	—	34	4	no	—
326	C₂×M₁₆	—	34	2	no	—
327	C₂²×C₈	—	17	1	no	—
328	C₂²×C₈	—	17	1	no	—
329	C₂²×C₈	—	34	2	no	—
330	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
331	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
332	C₂×C₄²	—	17	1	no	—
333	C₂×C₄²	—	17	1	no	—
334	C₂×C₄²	—	17	1	no	—
335	C₂×C₄²	—	17	1	no	—
336	C₂×C₄²	—	17	1	no	—
337	C₂×C₄²	—	17	1	no	—
338	C₂×C₄²	—	17	1	no	—
339	C₂×C₄²	—	17	1	no	—
340	C₂×C₄²	—	17	1	no	—
341	C₂×C₄²	—	17	1	no	—
342	C₂×C₄²	—	17	1	no	—
343	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
344	C₄⋊C₈	—	17	2	no	—
345	C₄⋊C₈	—	17	2	no	—
346	C₄⋊C₈	—	34	2	no	—
347	C₄⋊C₈	—	34	2	no	—
348	C₄⋊C₈	C₂²×D₁₇	1	2	yes	—
349	C₄⋊C₈	C₂²×D₁₇	1	2	yes	—
350	C₂²⋊C₈	—	2	1	no	—
351	C₂²⋊C₈	—	2	1	no	—
352	C₂²⋊C₈	—	34	2	no	—
353	C₂²⋊C₈	—	34	2	no	—
354	C₂²⋊C₈	—	34	1	no	—
355	C₂²⋊C₈	—	34	1	no	—
356	#97	—	2	1	no	—
357	#97	—	2	1	no	—
358	#97	—	17	1	no	—
359	#97	—	17	1	no	—
360	#97	—	17	1	no	—
361	#97	—	17	1	no	—
362	#97	—	17	1	no	—
363	#97	—	17	1	no	—
364	#97	—	17	1	no	—
365	#97	—	17	1	no	—
366	#97	—	34	2	no	—
367	#97	—	34	1	no	—
368	#97	—	34	1	no	—
369	C₄×C₈	—	17	1	no	—
370	C₄×C₈	—	17	1	no	—
371	C₄×C₈	—	17	1	no	—
372	C₄×C₈	—	17	1	no	—
373	C₄×C₈	—	34	2	no	—
374	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
375	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
376	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
377	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
378	C₁₇	#17797	1	1	yes	characteristic, complemented, Sylow
379	C₂⁴	—	17	1	no	—
380	C₂²×C₄	—	17	1	no	—
381	C₂²×C₄	—	17	1	no	—
382	C₂²×C₄	—	17	1	no	—
383	C₂²×C₄	—	17	1	no	—
384	C₂²×C₄	—	17	1	no	—
385	C₂²×C₄	—	17	1	no	—
386	C₂²×C₄	—	17	1	no	—
387	C₂²×C₄	—	17	1	no	—
388	C₂²×C₄	—	17	1	no	—
389	C₂²×C₄	—	17	1	no	—
390	C₂²×C₄	—	17	1	no	—
391	C₂²×C₄	—	17	1	no	—
392	C₂²×C₄	—	17	1	no	—
393	C₂²×C₄	—	17	1	no	—
394	C₂²×C₄	—	17	1	no	—
395	C₂²×C₄	—	34	2	no	—
396	C₂²×C₄	—	34	2	no	—
397	C₂²×C₄	—	68	2	no	—
398	C₂²×C₄	—	68	2	no	—
399	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
400	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
401	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
402	M₁₆	—	17	4	no	—
403	M₁₆	—	17	4	no	—
404	M₁₆	—	34	2	no	—
405	M₁₆	—	34	2	no	—
406	M₁₆	—	34	2	no	—
407	M₁₆	—	34	2	no	—
408	M₁₆	—	34	2	no	—
409	M₁₆	—	34	2	no	—
410	M₁₆	—	68	4	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	17	1	no	—
416	C₂×C₈	—	17	1	no	—
417	C₂×C₈	—	17	1	no	—
418	C₂×C₈	—	17	1	no	—
419	C₂×C₈	—	34	2	no	—
420	C₂×C₈	—	34	2	no	—
421	C₂×C₈	—	34	2	no	—
422	C₂×C₈	—	34	2	no	—
423	C₂×C₈	—	68	4	no	—
424	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
425	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
426	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
427	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
428	C₄²	—	17	1	no	—
429	C₄²	—	17	1	no	—
430	C₄²	—	17	1	no	—
431	C₄²	—	17	1	no	—
432	C₄²	—	17	1	no	—
433	C₄²	—	17	1	no	—
434	C₄²	—	17	1	no	—
435	C₄²	—	17	1	no	—
436	C₄²	—	17	1	no	—
437	C₄²	—	17	1	no	—
438	C₄²	—	17	1	no	—
439	C₄²	—	17	1	no	—
440	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
441	C₄²	D₄×D₁₇	1	1	yes	characteristic
442	C₄²	Q₈×D₁₇	1	1	yes	characteristic
443	C₄²	C₂³×D₁₇	1	1	yes	characteristic
444	C₂³	—	17	1	no	—
445	C₂³	—	17	1	no	—
446	C₂³	—	34	2	no	—
447	C₂³	—	34	2	no	—
448	C₂³	—	68	1	no	—
449	C₂³	C₄⋊C₄×D₁₇	1	1	yes	characteristic
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	17	1	no	—
455	C₂×C₄	—	17	2	no	—
456	C₂×C₄	—	17	2	no	—
457	C₂×C₄	—	17	1	no	—
458	C₂×C₄	—	17	1	no	—
459	C₂×C₄	—	17	1	no	—
460	C₂×C₄	—	17	1	no	—
461	C₂×C₄	—	17	1	no	—
462	C₂×C₄	—	34	2	no	—
463	C₂×C₄	—	34	2	no	—
464	C₂×C₄	—	34	2	no	—
465	C₂×C₄	—	34	2	no	—
466	C₂×C₄	—	34	1	no	—
467	C₂×C₄	—	34	1	no	—
468	C₂×C₄	—	34	2	no	—
469	C₂×C₄	—	34	2	no	—
470	C₂×C₄	—	68	1	no	—
471	C₂×C₄	—	68	1	no	—
472	C₂×C₄	—	68	1	no	—
473	C₂×C₄	—	68	1	no	—
474	C₂×C₄	—	68	1	no	—
475	C₂×C₄	—	68	1	no	—
476	C₂×C₄	—	68	1	no	—
477	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
478	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
479	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
480	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
481	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
482	C₂×C₄	C₂×Q₈×D₁₇	1	1	yes	characteristic
483	C₈	—	2	1	no	—
484	C₈	—	2	1	no	—
485	C₈	—	4	2	no	—
486	C₈	—	4	2	no	—
487	C₈	—	17	2	no	—
488	C₈	—	17	2	no	—
489	C₈	—	34	1	no	—
490	C₈	—	34	1	no	—
491	C₈	—	68	2	no	—
492	C₈	—	68	2	no	—
493	C₈	M₁₆×D₁₇	1	2	yes	—
494	C₈	M₁₆×D₁₇	1	2	yes	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	17	2	no	—
498	C₂²	—	34	1	no	—
499	C₂²	—	34	1	no	—
500	C₂²	—	34	1	no	—
501	C₂²	—	34	1	no	—
502	C₂²	—	34	1	no	—
503	C₂²	—	68	4	no	—
504	C₂²	#11762856	1	2	yes	—
505	C₂²	C₂×C₄⋊C₄×D₁₇	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	17	2	no	—
511	C₄	—	34	1	no	—
512	C₄	—	34	1	no	—
513	C₄	—	34	1	no	—
514	C₄	—	34	1	no	—
515	C₄	—	34	1	no	—
516	C₄	C₂×M₁₆×D₁₇	1	1	yes	characteristic
517	C₄	C₂×M₁₆×D₁₇	1	1	yes	characteristic
518	C₄	#11763606	1	2	yes	—
519	C₂	—	2	2	no	—
520	C₂	—	34	2	no	—
521	C₂	—	68	1	no	—
522	C₂	D₁₇×#423	1	1	yes	characteristic
523	C₂	#14537372	1	1	yes	characteristic
524	C₂	C₂×#11762856	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×#1568	C₂
socle	C₂²×C₁₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₇	C₄⋊C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1568	D₁₇
hypocenter	C₁₇	#17797
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
4. #14527550	C₂	semidirect
5. #14527548	C₂	semidirect
6. #14527547	C₂	semidirect
7. #14527545	C₂	semidirect
8. #14527545	C₂	semidirect
9. #14527535	C₂	semidirect
10. #14527533	C₂	semidirect
11. C₁₇×#1568	C₂	semidirect
40. #11762562	C₂²	semidirect
41. #11762561	C₂²	semidirect
42. #11762561	C₂²	semidirect
43. #11762560	C₂²	semidirect
44. #11762559	C₂²	semidirect
45. #11762559	C₂²	semidirect
49. C₁₇×#335	C₂²	semidirect
50. C₁₇×#334	C₂²	semidirect
178. #63218	M₁₆	semidirect
179. #63218	M₁₆	semidirect
241. #1568	D₁₇	semidirect
302. #335	C₂×D₁₇	semidirect
306. #334	C₂×D₁₇	semidirect
378. C₁₇	#17797	semidirect

Maximal subgroups

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

subgroup	index
#14537414	2
D₁₇×#432	2
C₂×C₄×#63218	2
#14527550	2
#14527548	2
#14527547	2
#14527545	2
#14527535	2
#14527533	2
C₁₇×#1568	2
#17797	17