Subgroups — #17004397

Order 4352.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538866	C₂	1	1	yes	maximal, characteristic
2	#14537929	C₂	1	1	yes	maximal, characteristic
3	#14537864	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527661	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527654	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527633	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527626	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527602	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527595	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527590	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527583	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527212	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527190	C₂	1	1	yes	maximal, characteristic
14	#14527084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1574	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763343	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₃₄	C₂²	1	1	yes	characteristic
18	#11763140	C₄	1	1	yes	characteristic
19	#11763123	C₄	1	1	yes	characteristic
20	#11763117	C₄	1	1	yes	characteristic
21	#11763117	C₄	1	1	yes	characteristic
22	#11763032	C₄	1	1	yes	characteristic
23	#11763032	C₄	1	1	yes	characteristic
24	#11762967	C₄	1	1	yes	characteristic
25	#11762950	C₄	1	1	yes	characteristic
26	#11762936	C₂²	1	1	yes	characteristic
27	C₈×Dic₃₄	—	2	1	no	—
28	C₈×Dic₃₄	—	2	1	no	—
29	#11762933	C₂²	1	1	yes	characteristic
30	#11762933	C₂²	1	1	yes	characteristic
31	#11762933	C₂²	1	1	yes	characteristic
32	#11762933	C₂²	1	1	yes	characteristic
33	#11762933	C₂²	1	1	yes	characteristic
34	C₄×Dic₆₈	C₂²	1	1	yes	characteristic
35	C₄×Dic₆₈	C₂²	1	1	yes	characteristic
36	C₄×#63219	C₂²	1	1	yes	characteristic
37	C₄×#63219	C₂²	1	1	yes	characteristic
38	#11762886	C₂²	1	1	yes	characteristic
39	#11762885	—	2	1	no	—
40	#11762878	—	2	1	no	—
41	#11762874	C₂²	1	1	yes	characteristic
42	#11762869	—	2	1	no	—
43	#11762862	C₂²	1	1	yes	characteristic
44	#11762862	C₂²	1	1	yes	characteristic
45	#11762859	—	2	1	no	—
46	#11762859	—	2	1	no	—
47	#11762834	—	2	1	no	—
48	#11762539	C₂²	1	1	yes	characteristic
49	#11762539	C₂²	1	1	yes	characteristic
50	#11762539	C₂²	1	1	yes	characteristic
51	#11762539	C₂²	1	1	yes	characteristic
52	#11762539	C₂²	1	1	yes	characteristic
53	#11762539	C₂²	1	1	yes	characteristic
54	#11762536	C₂²	1	1	yes	characteristic
55	#11762536	C₂²	1	1	yes	characteristic
56	#11762531	C₂²	1	1	yes	characteristic
57	#11762531	C₂²	1	1	yes	characteristic
58	#11762530	C₂²	1	1	yes	characteristic
59	C₈×#3622	C₂²	1	1	yes	characteristic
60	C₁₇×#431	C₂²	1	1	yes	characteristic
61	C₁₇×#431	C₂²	1	1	yes	characteristic
62	C₁₇×#423	C₂²	1	1	yes	characteristic
63	C₁₇×#335	C₂²	1	1	yes	characteristic
64	C₁₇×#335	C₂²	1	1	yes	characteristic
65	C₁₇×#334	C₂²	1	1	yes	characteristic
66	C₁₇×#334	C₂²	1	1	yes	characteristic
67	C₂²×Dic₃₄	C₂×C₄	1	1	yes	characteristic
68	C₂×M₁₆×C₁₇	—	2	1	no	—
69	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
70	#10587616	C₂×C₄	1	1	yes	characteristic
71	#10587615	—	2	1	no	—
72	C₄×C₂²⋊D₁₇	—	2	1	no	—
73	C₂×C₄⋊Dic₁₇	C₂×C₄	1	1	yes	characteristic
74	#10587610	C₂×C₄	1	1	yes	characteristic
75	C₂×#63225	—	2	1	no	—
76	C₂×C₄×Dic₁₇	—	2	1	no	—
77	C₂×Dic₆₈	C₂×C₄	1	1	yes	characteristic
78	C₂×Dic₆₈	C₂×C₄	1	1	yes	characteristic
79	C₂×#63219	C₂×C₄	1	1	yes	characteristic
80	C₂×#63219	C₂×C₄	1	1	yes	characteristic
81	C₂×#63218	—	2	1	no	—
82	C₂×C₈×D₁₇	—	2	1	no	—
83	#10587562	—	2	1	no	—
84	#10587561	C₂×C₄	1	1	yes	characteristic
85	C₄×D₆₈	C₂³	1	1	yes	characteristic
86	#10587558	—	2	1	no	—
87	#10587556	C₂×C₄	1	1	yes	characteristic
88	C₄×Dic₃₄	—	2	1	no	—
89	C₄×Dic₃₄	—	2	1	no	—
90	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
91	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
92	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
93	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
94	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
95	C₁₇×C₄⋊C₈	—	2	1	no	—
96	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₁₇×C₂²⋊C₈	—	2	1	no	—
103	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
104	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
105	C₄×C₈×C₁₇	—	2	1	no	—
106	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
108	C₂²⋊#3622	—	2	1	no	—
109	C₂²⋊#3622	D₄	1	1	yes	characteristic
110	C₂²⋊#3622	D₄	1	1	yes	characteristic
111	#10587492	C₂×C₄	1	1	yes	characteristic
112	#10587492	C₂×C₄	1	1	yes	characteristic
113	#10587491	—	2	1	no	—
114	#10587491	—	2	1	no	—
115	#10587489	C₂×C₄	1	1	yes	characteristic
116	#10587489	C₂×C₄	1	1	yes	characteristic
117	#10587488	C₂×C₄	1	1	yes	characteristic
118	#10587488	C₂×C₄	1	1	yes	characteristic
119	#10587487	C₂×C₄	1	1	yes	characteristic
120	#10587487	C₂×C₄	1	1	yes	characteristic
121	#10587487	C₂×C₄	1	1	yes	characteristic
122	#10587487	C₂×C₄	1	1	yes	characteristic
123	#10587487	C₂×C₄	1	1	yes	characteristic
124	#10587487	C₂×C₄	1	1	yes	characteristic
125	#10587486	—	2	1	no	—
126	#10587485	—	2	1	no	—
127	#10587485	—	2	1	no	—
128	#10587485	—	2	1	no	—
129	#10587485	—	2	1	no	—
130	#10587485	—	2	1	no	—
131	#10587485	—	2	1	no	—
132	C₈×Dic₁₇	—	2	1	no	—
133	C₈×Dic₁₇	—	2	1	no	—
134	C₈×Dic₁₇	—	2	1	no	—
135	C₈×Dic₁₇	—	2	1	no	—
136	C₈×Dic₁₇	—	2	1	no	—
137	C₄⋊#3622	—	2	1	no	—
138	C₄⋊#3622	D₄	1	1	yes	characteristic
139	C₄⋊#3622	D₄	1	1	yes	characteristic
140	C₄×#3622	C₂³	1	1	yes	characteristic
141	C₄×#3622	C₂³	1	1	yes	characteristic
142	C₄×#3622	C₂³	1	1	yes	characteristic
143	C₄×#3622	C₂³	1	1	yes	characteristic
144	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
147	C₂×C₂²⋊D₁₇	—	2	1	no	—
148	C₂²×Dic₁₇	—	2	1	no	—
149	C₂²×Dic₁₇	—	2	1	no	—
150	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₁₇	—	2	1	no	—
152	C₂×Dic₃₄	—	2	1	no	—
153	C₂×Dic₃₄	—	2	2	no	—
154	C₂×Dic₃₄	—	2	2	no	—
155	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
156	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
157	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
158	M₁₆×C₁₇	—	8	1	no	—
159	C₂×C₈×C₁₇	—	2	1	no	—
160	C₂×C₈×C₁₇	—	2	1	no	—
161	C₂×C₈×C₁₇	—	2	1	no	—
162	C₂×C₈×C₁₇	—	2	1	no	—
163	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₇	#41	1	1	yes	characteristic
170	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
171	C₂²⋊Dic₁₇	—	2	1	no	—
172	#63227	—	2	1	no	—
173	#63227	—	2	1	no	—
174	#63227	—	2	1	no	—
175	#63227	—	2	1	no	—
176	C₄⋊Dic₁₇	—	2	1	no	—
177	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
178	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
181	#63225	—	2	1	no	—
182	#63225	—	2	1	no	—
183	#63225	—	2	1	no	—
184	#63225	—	2	1	no	—
185	#63225	—	2	1	no	—
186	#63225	—	2	1	no	—
187	#63225	—	2	1	no	—
188	#63225	—	2	1	no	—
189	C₄×Dic₁₇	—	2	1	no	—
190	C₄×Dic₁₇	—	2	1	no	—
191	C₄×Dic₁₇	—	2	1	no	—
192	C₄×Dic₁₇	—	2	1	no	—
193	C₄×Dic₁₇	—	2	1	no	—
194	C₂×#3622	—	2	1	no	—
195	C₂×#3622	—	2	1	no	—
196	C₂×#3622	C₂×D₄	1	1	yes	characteristic
197	C₂×#3622	C₂×D₄	1	1	yes	characteristic
198	C₂×#3622	C₂×D₄	1	1	yes	characteristic
199	C₂×#3622	C₂×D₄	1	1	yes	characteristic
200	Dic₆₈	—	2	2	no	—
201	Dic₆₈	—	2	2	no	—
202	#63219	—	2	2	no	—
203	#63219	—	2	2	no	—
204	#63218	—	8	1	no	—
205	C₈×D₁₇	—	8	1	no	—
206	#17919	—	17	1	no	maximal, Sylow
207	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
208	C₂²×D₁₇	—	2	1	no	—
209	C₂×C₄×C₁₇	—	2	1	no	—
210	C₂×C₄×C₁₇	—	2	1	no	—
211	C₂×C₄×C₁₇	—	2	1	no	—
212	C₂×C₄×C₁₇	—	2	1	no	—
213	C₂×C₄×C₁₇	—	4	1	no	—
214	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
220	C₂²⋊D₁₇	—	8	1	no	—
221	C₂×Dic₁₇	—	2	4	no	—
222	C₂×Dic₁₇	—	2	1	no	—
223	C₂×Dic₁₇	—	2	1	no	—
224	C₂×Dic₁₇	—	2	1	no	—
225	C₂×Dic₁₇	—	2	1	no	—
226	C₂×Dic₁₇	—	2	1	no	—
227	C₂×Dic₁₇	—	2	1	no	—
228	C₂×Dic₁₇	—	2	1	no	—
229	C₂×Dic₁₇	—	8	1	no	—
230	D₆₈	—	2	1	no	—
231	D₆₈	—	2	1	no	—
232	C₄×D₁₇	—	4	1	no	—
233	C₄×D₁₇	—	4	1	no	—
234	Dic₃₄	—	2	4	no	—
235	Dic₃₄	—	2	1	no	—
236	Dic₃₄	—	2	1	no	—
237	Dic₃₄	—	2	1	no	—
238	Dic₃₄	—	2	1	no	—
239	Dic₃₄	#131	1	2	yes	—
240	Dic₃₄	#131	1	2	yes	—
241	C₈×C₁₇	—	2	1	no	—
242	C₈×C₁₇	—	2	1	no	—
243	C₈×C₁₇	—	2	1	no	—
244	C₈×C₁₇	—	2	1	no	—
245	C₈×C₁₇	—	4	1	no	—
246	C₈×C₁₇	—	4	1	no	—
247	C₈×C₁₇	—	4	1	no	—
248	C₈×C₁₇	—	4	1	no	—
249	#3622	—	2	1	no	—
250	#3622	—	2	1	no	—
251	#3622	—	2	1	no	—
252	#3622	—	2	1	no	—
253	#3622	—	4	1	no	—
254	#3622	—	4	1	no	—
255	#3108	—	17	1	no	—
256	#2993	—	17	1	no	—
257	#2982	—	17	1	no	—
258	#1588	—	17	1	no	—
259	#1587	—	17	1	no	—
260	#1584	—	17	1	no	—
261	#1583	—	17	1	no	—
262	#1579	—	17	1	no	—
263	SD₁₆⋊C₈	—	17	1	no	—
264	C₈×Q₁₆	—	17	1	no	—
265	C₈×SD₁₆	—	17	1	no	—
266	#1574	D₁₇	1	1	yes	characteristic, complemented
267	#1487	—	17	1	no	—
268	#1482	—	17	1	no	—
269	#1454	—	17	1	no	—
270	C₂²×C₁₇	—	2	1	no	—
271	C₂²×C₁₇	—	2	1	no	—
272	C₂²×C₁₇	—	2	1	no	—
273	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
274	C₂×D₁₇	—	4	1	no	—
275	C₂×D₁₇	—	4	1	no	—
276	C₂×D₁₇	—	4	1	no	—
277	C₄×C₁₇	—	2	1	no	—
278	C₄×C₁₇	—	2	1	no	—
279	C₄×C₁₇	—	2	1	no	—
280	C₄×C₁₇	—	2	1	no	—
281	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
282	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
283	C₄×C₁₇	#577	1	1	yes	characteristic
284	C₄×C₁₇	#578	1	1	yes	characteristic
285	Dic₁₇	—	2	2	no	—
286	Dic₁₇	—	2	2	no	—
287	Dic₁₇	—	4	1	no	—
288	Dic₁₇	—	4	1	no	—
289	Dic₁₇	—	4	1	no	—
290	Dic₁₇	—	4	1	no	—
291	Dic₁₇	—	4	1	no	—
292	#529	—	17	1	no	—
293	C₂×C₄×Q₈	—	17	1	no	—
294	#483	—	17	1	no	—
295	#480	—	17	1	no	—
296	#479	—	17	1	no	—
297	#479	—	17	1	no	—
298	#464	—	17	1	no	—
299	#464	—	17	1	no	—
300	#451	—	17	1	no	—
301	#448	—	17	1	no	—
302	#446	—	17	1	no	—
303	C₈×Q₈	—	17	1	no	—
304	C₈×Q₈	—	17	1	no	—
305	C₈×Q₈	—	17	1	no	—
306	C₈×Q₈	—	17	1	no	—
307	C₈×Q₈	—	17	1	no	—
308	C₈×Q₈	—	34	1	no	—
309	C₈×Q₈	—	34	1	no	—
310	C₄×Q₁₆	—	17	1	no	—
311	C₄×Q₁₆	—	17	1	no	—
312	C₄×SD₁₆	—	17	1	no	—
313	C₄×SD₁₆	—	17	1	no	—
314	#436	—	17	1	no	—
315	#436	—	34	1	no	—
316	#435	—	34	1	no	—
317	C₈×D₄	—	17	1	no	—
318	#433	—	34	1	no	—
319	#431	—	17	1	no	—
320	#431	—	17	1	no	—
321	#431	—	34	1	no	—
322	#431	—	34	1	no	—
323	#431	C₂×D₁₇	1	1	yes	characteristic
324	#431	C₂×D₁₇	1	1	yes	characteristic
325	#424	—	34	1	no	—
326	#423	C₂×D₁₇	1	1	yes	characteristic
327	#335	C₂×D₁₇	1	1	yes	characteristic
328	#335	C₂×D₁₇	1	1	yes	characteristic
329	#334	C₂×D₁₇	1	1	yes	characteristic
330	#334	C₂×D₁₇	1	1	yes	characteristic
331	Q₈⋊C₈	—	17	1	no	—
332	Q₈⋊C₈	—	17	1	no	—
333	Q₈⋊C₈	—	17	1	no	—
334	Q₈⋊C₈	—	17	1	no	—
335	Q₈⋊C₈	—	17	1	no	—
336	Q₈⋊C₈	—	17	1	no	—
337	D₄⋊C₈	—	17	1	no	—
338	D₄⋊C₈	—	17	1	no	—
339	#322	—	17	1	no	—
340	#322	—	17	1	no	—
341	#322	—	17	1	no	—
342	C₈²	—	17	1	no	—
343	C₂×C₁₇	—	4	1	no	—
344	C₂×C₁₇	#2929	1	1	yes	characteristic
345	C₂×C₁₇	#2947	1	1	yes	characteristic
346	C₂×C₁₇	#2957	1	1	yes	characteristic
347	D₁₇	—	8	1	no	—
348	C₂²×Q₈	—	17	1	no	—
349	C₂×Q₁₆	—	17	1	no	—
350	C₂×Q₁₆	—	17	1	no	—
351	C₂×SD₁₆	—	17	1	no	—
352	C₂×SD₁₆	—	17	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	34	1	no	—
355	C₂²×C₈	—	34	1	no	—
356	#126	—	34	1	no	—
357	#125	—	17	1	no	—
358	#124	—	17	1	no	—
359	#123	—	34	1	no	—
360	C₂²⋊Q₈	—	17	1	no	—
361	#121	—	17	1	no	—
362	C₄×Q₈	—	17	1	no	—
363	C₄×Q₈	—	17	1	no	—
364	C₄×Q₈	—	17	1	no	—
365	C₄×Q₈	—	17	1	no	—
366	C₄×Q₈	—	17	1	no	—
367	C₄×Q₈	—	34	1	no	—
368	C₄×Q₈	—	34	1	no	—
369	C₄×D₄	—	17	1	no	—
370	C₄×D₄	—	34	1	no	—
371	#117	—	34	1	no	—
372	C₂×C₄⋊C₄	—	17	1	no	—
373	C₂×C₄⋊C₄	—	34	1	no	—
374	C₂×C₄²	—	34	1	no	—
375	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
376	#107	—	17	1	no	—
377	#107	—	17	1	no	—
378	#106	—	17	1	no	—
379	#106	—	17	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	17	1	no	—
382	C₄⋊C₈	—	17	1	no	—
383	C₄⋊C₈	—	34	1	no	—
384	C₄⋊C₈	—	34	1	no	—
385	C₄⋊C₈	—	34	1	no	—
386	C₄⋊C₈	—	34	1	no	—
387	C₄⋊C₈	—	34	1	no	—
388	C₄⋊C₈	—	34	1	no	—
389	C₄⋊C₈	—	34	1	no	—
390	C₄⋊C₈	C₄×D₁₇	1	1	yes	characteristic
391	C₄⋊C₈	C₄×D₁₇	1	1	yes	characteristic
392	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
396	#103	—	17	1	no	—
397	#103	—	17	1	no	—
398	#103	—	17	1	no	—
399	#103	—	17	1	no	—
400	#103	—	17	1	no	—
401	#103	—	17	1	no	—
402	#102	—	17	1	no	—
403	#102	—	17	1	no	—
404	C₂²⋊C₈	—	2	1	no	—
405	C₂²⋊C₈	—	17	1	no	—
406	C₂²⋊C₈	—	17	1	no	—
407	C₂²⋊C₈	—	34	1	no	—
408	C₂²⋊C₈	—	34	1	no	—
409	C₂²⋊C₈	—	34	1	no	—
410	C₂²⋊C₈	C₄×D₁₇	1	1	yes	characteristic
411	C₂²⋊C₈	C₄×D₁₇	1	1	yes	characteristic
412	#97	—	34	1	no	—
413	C₄×C₈	—	2	1	no	—
414	C₄×C₈	—	17	1	no	—
415	C₄×C₈	—	17	1	no	—
416	C₄×C₈	—	17	1	no	—
417	C₄×C₈	—	17	1	no	—
418	C₄×C₈	—	34	1	no	—
419	C₄×C₈	—	34	1	no	—
420	C₄×C₈	—	34	1	no	—
421	C₄×C₈	—	34	1	no	—
422	C₄×C₈	—	34	1	no	—
423	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
425	C₁₇	#17919	1	1	yes	characteristic, complemented, Sylow
426	C₂×Q₈	—	17	1	no	—
427	C₂×Q₈	—	17	1	no	—
428	C₂×Q₈	—	17	1	no	—
429	C₂×Q₈	—	34	2	no	—
430	C₂×Q₈	—	34	2	no	—
431	C₂×Q₈	—	34	1	no	—
432	C₂×D₄	—	17	1	no	—
433	C₂×D₄	—	34	1	no	—
434	C₂²×C₄	—	34	1	no	—
435	C₂²×C₄	—	34	1	no	—
436	C₂²×C₄	—	34	1	no	—
437	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
438	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
439	C₂²×C₄	#63256	1	1	yes	characteristic
440	Q₁₆	—	34	2	no	—
441	Q₁₆	—	34	2	no	—
442	SD₁₆	—	34	2	no	—
443	SD₁₆	—	34	2	no	—
444	M₁₆	—	8	1	no	—
445	M₁₆	—	136	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	17	1	no	—
451	C₂×C₈	—	17	1	no	—
452	C₂×C₈	—	17	1	no	—
453	C₂×C₈	—	17	1	no	—
454	C₂×C₈	—	34	1	no	—
455	C₂×C₈	—	34	1	no	—
456	C₂×C₈	—	136	1	no	—
457	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
458	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
459	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
460	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
461	C₄⋊C₄	—	17	1	no	—
462	C₄⋊C₄	—	17	1	no	—
463	C₄⋊C₄	—	17	1	no	—
464	C₄⋊C₄	—	17	1	no	—
465	C₄⋊C₄	—	34	1	no	—
466	C₄⋊C₄	—	34	1	no	—
467	C₄⋊C₄	—	34	1	no	—
468	C₄⋊C₄	—	34	1	no	—
469	C₄⋊C₄	—	34	1	no	—
470	C₄⋊C₄	—	34	1	no	—
471	C₄⋊C₄	—	34	1	no	—
472	C₄⋊C₄	—	34	1	no	—
473	C₄⋊C₄	—	34	1	no	—
474	C₂²⋊C₄	—	34	1	no	—
475	C₂²⋊C₄	—	34	1	no	—
476	C₂²⋊C₄	—	34	1	no	—
477	C₂²⋊C₄	—	34	1	no	—
478	C₂²⋊C₄	—	34	1	no	—
479	C₄²	—	34	1	no	—
480	C₄²	—	34	1	no	—
481	C₄²	—	34	1	no	—
482	C₄²	—	34	1	no	—
483	C₄²	—	34	1	no	—
484	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
485	C₄²	D₄×D₁₇	1	1	yes	characteristic
486	C₄²	#63256	1	1	yes	characteristic
487	C₄²	C₂³×D₁₇	1	1	yes	characteristic
488	C₂³	—	34	1	no	—
489	C₂³	#10587579	1	1	yes	characteristic
490	Q₈	—	17	2	no	—
491	Q₈	—	17	2	no	—
492	Q₈	—	34	4	no	—
493	Q₈	—	34	1	no	—
494	Q₈	—	34	1	no	—
495	Q₈	—	34	1	no	—
496	Q₈	—	34	1	no	—
497	D₄	—	34	1	no	—
498	D₄	—	34	1	no	—
499	D₄	—	136	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	34	4	no	—
506	C₂×C₄	—	34	1	no	—
507	C₂×C₄	—	34	1	no	—
508	C₂×C₄	—	34	1	no	—
509	C₂×C₄	—	34	1	no	—
510	C₂×C₄	—	34	1	no	—
511	C₂×C₄	—	34	1	no	—
512	C₂×C₄	—	34	1	no	—
513	C₂×C₄	—	68	1	no	—
514	C₂×C₄	—	68	1	no	—
515	C₂×C₄	—	136	1	no	—
516	C₂×C₄	#10587579	1	1	yes	characteristic
517	C₂×C₄	#10587579	1	1	yes	characteristic
518	C₂×C₄	#10587579	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
521	C₂×C₄	C₂×#63256	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	34	1	no	—
531	C₈	—	34	1	no	—
532	C₈	—	34	1	no	—
533	C₈	—	34	1	no	—
534	C₈	—	68	1	no	—
535	C₈	—	68	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	68	1	no	—
540	C₂²	—	68	1	no	—
541	C₂²	—	68	1	no	—
542	C₂²	C₂×#10587579	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	34	2	no	—
548	C₄	—	34	2	no	—
549	C₄	—	68	1	no	—
550	C₄	—	68	1	no	—
551	C₄	—	68	1	no	—
552	C₄	—	68	1	no	—
553	C₄	—	68	1	no	—
554	C₄	#131×D₁₇	1	1	yes	characteristic
555	C₄	#131×D₁₇	1	1	yes	characteristic
556	C₄	#11763619	1	1	yes	characteristic
557	C₄	#11763625	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	136	1	no	—
560	C₂	#14537477	1	1	yes	characteristic
561	C₂	#14537625	1	1	yes	characteristic
562	C₂	#14537700	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×#1574	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#10587616	C₂×C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1574	D₁₇
hypocenter	C₁₇	#17919
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1574

Complements

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

N	H ≅ G/N	type
3. #14537864	C₂	semidirect
4. #14527661	C₂	semidirect
5. #14527654	C₂	semidirect
6. #14527633	C₂	semidirect
7. #14527626	C₂	semidirect
8. #14527602	C₂	semidirect
9. #14527595	C₂	semidirect
10. #14527590	C₂	semidirect
11. #14527583	C₂	semidirect
12. #14527212	C₂	semidirect
14. #14527084	C₂	semidirect
15. C₁₇×#1574	C₂	semidirect
266. #1574	D₁₇	semidirect
425. C₁₇	#17919	semidirect

Maximal subgroups

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

subgroup	index
#14538866	2
#14537929	2
#14537864	2
#14527661	2
#14527654	2
#14527633	2
#14527626	2
#14527602	2
#14527595	2
#14527590	2
#14527583	2
#14527212	2
#14527190	2
#14527084	2
C₁₇×#1574	2
#17919	17