Subgroups — #17004382

Order 4352.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538833	C₂	1	1	yes	maximal, characteristic
2	#14537929	C₂	1	1	yes	maximal, characteristic, complemented
3	#14537807	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527647	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527640	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527619	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527612	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527607	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527595	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527583	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527578	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527208	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527190	C₂	1	1	yes	maximal, characteristic, complemented
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×D₆₈	C₂²	1	1	yes	characteristic
18	#11763145	C₄	1	1	yes	characteristic
19	#11763128	C₄	1	1	yes	characteristic
20	#11763110	C₄	1	1	yes	characteristic
21	#11763110	C₄	1	1	yes	characteristic
22	#11763025	C₄	1	1	yes	characteristic
23	#11763025	C₄	1	1	yes	characteristic
24	#11762962	C₄	1	1	yes	characteristic
25	#11762945	C₄	1	1	yes	characteristic
26	#11762936	C₂²	1	1	yes	characteristic, complemented
27	#11762933	C₂²	1	1	yes	characteristic, complemented
28	C₄×#63219	C₂²	1	1	yes	characteristic
29	C₄×#63219	C₂²	1	1	yes	characteristic
30	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
31	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
32	#11762886	C₂²	1	1	yes	characteristic, complemented
33	#11762885	—	2	1	no	—
34	#11762878	—	2	1	no	—
35	C₈×D₆₈	—	2	1	no	—
36	C₈×D₆₈	—	2	1	no	—
37	#11762874	C₂²	1	1	yes	characteristic
38	#11762874	C₂²	1	1	yes	characteristic
39	#11762874	C₂²	1	1	yes	characteristic
40	#11762874	C₂²	1	1	yes	characteristic
41	#11762874	C₂²	1	1	yes	characteristic, complemented
42	#11762869	—	2	1	no	—
43	#11762862	C₂²	1	1	yes	characteristic
44	#11762862	C₂²	1	1	yes	characteristic
45	#11762834	—	2	1	no	—
46	C₂²⋊C₈×D₁₇	—	2	1	no	—
47	C₂²⋊C₈×D₁₇	—	2	1	no	—
48	#11762539	C₂²	1	1	yes	characteristic, complemented
49	#11762539	C₂²	1	1	yes	characteristic, complemented
50	#11762536	C₂²	1	1	yes	characteristic
51	#11762536	C₂²	1	1	yes	characteristic
52	#11762536	C₂²	1	1	yes	characteristic
53	#11762536	C₂²	1	1	yes	characteristic
54	#11762536	C₂²	1	1	yes	characteristic, complemented
55	#11762536	C₂²	1	1	yes	characteristic, complemented
56	#11762531	C₂²	1	1	yes	characteristic, complemented
57	#11762531	C₂²	1	1	yes	characteristic, complemented
58	#11762530	C₂²	1	1	yes	characteristic, complemented
59	C₈×#3622	C₂²	1	1	yes	characteristic, complemented
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, complemented
64	C₁₇×#335	C₂²	1	1	yes	characteristic, complemented
65	C₁₇×#334	C₂²	1	1	yes	characteristic, complemented
66	C₁₇×#334	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₆₈	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₄×D₁₇	—	2	1	no	—
69	C₂×M₁₆×C₁₇	—	2	1	no	—
70	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
71	#10587616	C₂×C₄	1	1	yes	characteristic
72	#10587615	—	2	1	no	—
73	C₄×C₂²⋊D₁₇	—	2	1	no	—
74	C₂×#63227	—	2	1	no	—
75	C₂×C₄⋊Dic₁₇	C₂×C₄	1	1	yes	characteristic
76	#10587610	C₂×C₄	1	1	yes	characteristic
77	C₂×D₁₃₆	C₂×C₄	1	1	yes	characteristic
78	C₂×D₁₃₆	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	C₂×C₈×D₁₇	—	2	1	no	—
84	C₂×C₈×D₁₇	—	2	1	no	—
85	C₂×C₈×D₁₇	—	2	1	no	—
86	C₂×C₈×D₁₇	—	2	1	no	—
87	#10587562	—	2	1	no	—
88	#10587561	C₂×C₄	1	1	yes	characteristic
89	C₄×D₆₈	—	2	1	no	—
90	C₄×D₆₈	—	2	1	no	—
91	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
92	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
93	C₄×D₆₈	C₂³	1	1	yes	characteristic
94	C₄×D₆₈	C₂³	1	1	yes	characteristic
95	C₄×D₆₈	C₂³	1	1	yes	characteristic
96	#10587558	—	2	1	no	—
97	#10587556	C₂×C₄	1	1	yes	characteristic
98	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
99	C₁₇×C₄⋊C₈	—	2	1	no	—
100	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₁₇×C₂²⋊C₈	—	2	1	no	—
107	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
109	C₄×C₈×C₁₇	—	2	1	no	—
110	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
112	C₂²⋊#3622	—	2	1	no	—
113	C₂²⋊#3622	D₄	1	1	yes	characteristic
114	C₂²⋊#3622	D₄	1	1	yes	characteristic
115	#10587492	C₂×C₄	1	1	yes	characteristic
116	#10587492	C₂×C₄	1	1	yes	characteristic
117	#10587492	C₂×C₄	1	1	yes	characteristic
118	#10587492	C₂×C₄	1	1	yes	characteristic
119	#10587492	C₂×C₄	1	1	yes	characteristic
120	#10587492	C₂×C₄	1	1	yes	characteristic
121	#10587491	—	2	1	no	—
122	#10587491	—	2	1	no	—
123	#10587491	—	2	1	no	—
124	#10587491	—	2	1	no	—
125	#10587491	—	2	1	no	—
126	#10587491	—	2	1	no	—
127	#10587489	C₂×C₄	1	1	yes	characteristic
128	#10587489	C₂×C₄	1	1	yes	characteristic
129	#10587488	C₂×C₄	1	1	yes	characteristic
130	#10587488	C₂×C₄	1	1	yes	characteristic
131	#10587487	C₂×C₄	1	1	yes	characteristic
132	#10587487	C₂×C₄	1	1	yes	characteristic
133	#10587486	—	2	1	no	—
134	#10587485	—	2	1	no	—
135	#10587485	—	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	C₂³×D₁₇	—	2	1	no	—
145	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₇	—	2	1	no	—
149	C₂²×Dic₁₇	—	2	1	no	—
150	C₂×D₆₈	—	2	1	no	—
151	C₂×D₆₈	—	2	2	no	—
152	C₂×D₆₈	—	2	2	no	—
153	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
154	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
155	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×D₁₇	—	2	1	no	—
157	C₂×C₄×D₁₇	—	2	1	no	—
158	C₂×C₄×D₁₇	—	2	1	no	—
159	C₂×C₄×D₁₇	—	2	1	no	—
160	C₂×C₄×D₁₇	—	2	1	no	—
161	C₂×C₄×D₁₇	—	8	1	no	—
162	C₂×C₄×D₁₇	—	8	1	no	—
163	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
164	M₁₆×C₁₇	—	8	1	no	—
165	C₂×C₈×C₁₇	—	2	1	no	—
166	C₂×C₈×C₁₇	—	2	1	no	—
167	C₂×C₈×C₁₇	—	2	1	no	—
168	C₂×C₈×C₁₇	—	2	1	no	—
169	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₇	#41	1	1	yes	characteristic
176	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
177	C₂²⋊Dic₁₇	—	2	1	no	—
178	#63227	—	2	1	no	—
179	#63227	—	2	1	no	—
180	#63227	—	2	1	no	—
181	#63227	—	2	1	no	—
182	#63227	—	2	1	no	—
183	#63227	—	2	1	no	—
184	#63227	—	2	1	no	—
185	#63227	—	2	1	no	—
186	C₄⋊Dic₁₇	—	2	1	no	—
187	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
188	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
189	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
190	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
191	#63225	—	2	1	no	—
192	#63225	—	2	1	no	—
193	#63225	—	2	1	no	—
194	#63225	—	2	1	no	—
195	C₄×Dic₁₇	—	2	1	no	—
196	C₂×#3622	—	2	1	no	—
197	C₂×#3622	—	2	1	no	—
198	C₂×#3622	C₂×D₄	1	1	yes	characteristic
199	C₂×#3622	C₂×D₄	1	1	yes	characteristic
200	C₂×#3622	C₂×D₄	1	1	yes	characteristic
201	C₂×#3622	C₂×D₄	1	1	yes	characteristic
202	D₁₃₆	—	2	2	no	—
203	D₁₃₆	—	2	2	no	—
204	#63219	—	2	2	no	—
205	#63219	—	2	2	no	—
206	#63218	—	8	1	no	—
207	C₈×D₁₇	—	8	1	no	—
208	C₈×D₁₇	—	8	1	no	—
209	C₈×D₁₇	—	8	1	no	—
210	C₈×D₁₇	—	8	1	no	—
211	C₈×D₁₇	—	8	1	no	—
212	#17918	—	17	1	no	maximal, Sylow
213	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
214	C₂²×D₁₇	—	2	1	no	—
215	C₂²×D₁₇	—	2	1	no	—
216	C₂²×D₁₇	—	2	4	no	—
217	C₂²×D₁₇	—	2	1	no	—
218	C₂²×D₁₇	—	8	1	no	—
219	C₂²×D₁₇	—	8	1	no	—
220	C₂×C₄×C₁₇	—	2	1	no	—
221	C₂×C₄×C₁₇	—	2	1	no	—
222	C₂×C₄×C₁₇	—	2	1	no	—
223	C₂×C₄×C₁₇	—	2	1	no	—
224	C₂×C₄×C₁₇	—	4	1	no	—
225	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
231	C₂²⋊D₁₇	—	8	1	no	—
232	C₂×Dic₁₇	—	2	1	no	—
233	C₂×Dic₁₇	—	2	1	no	—
234	C₂×Dic₁₇	—	2	1	no	—
235	C₂×Dic₁₇	—	2	1	no	—
236	C₂×Dic₁₇	—	2	1	no	—
237	C₂×Dic₁₇	—	8	1	no	—
238	D₆₈	—	2	4	no	—
239	D₆₈	—	2	1	no	—
240	D₆₈	—	2	1	no	—
241	D₆₈	—	2	1	no	—
242	D₆₈	—	2	1	no	—
243	D₆₈	#131	1	2	yes	—
244	D₆₈	#131	1	2	yes	—
245	C₄×D₁₇	—	4	1	no	—
246	C₄×D₁₇	—	4	1	no	—
247	C₄×D₁₇	—	4	1	no	—
248	C₄×D₁₇	—	4	1	no	—
249	C₄×D₁₇	—	4	1	no	—
250	C₄×D₁₇	—	4	1	no	—
251	C₄×D₁₇	—	8	1	no	—
252	C₄×D₁₇	—	8	1	no	—
253	Dic₃₄	—	2	1	no	—
254	Dic₃₄	—	2	1	no	—
255	C₈×C₁₇	—	2	1	no	—
256	C₈×C₁₇	—	2	1	no	—
257	C₈×C₁₇	—	2	1	no	—
258	C₈×C₁₇	—	2	1	no	—
259	C₈×C₁₇	—	4	1	no	—
260	C₈×C₁₇	—	4	1	no	—
261	C₈×C₁₇	—	4	1	no	—
262	C₈×C₁₇	—	4	1	no	—
263	#3622	—	2	1	no	—
264	#3622	—	2	1	no	—
265	#3622	—	2	1	no	—
266	#3622	—	2	1	no	—
267	#3622	—	4	1	no	—
268	#3622	—	4	1	no	—
269	#3105	—	17	1	no	—
270	#2993	—	17	1	no	—
271	#2972	—	17	1	no	—
272	#1586	—	17	1	no	—
273	#1585	—	17	1	no	—
274	#1582	—	17	1	no	—
275	#1581	—	17	1	no	—
276	#1580	—	17	1	no	—
277	SD₁₆⋊C₈	—	17	1	no	—
278	C₈×SD₁₆	—	17	1	no	—
279	C₈×D₈	—	17	1	no	—
280	#1574	D₁₇	1	1	yes	characteristic, complemented
281	#1486	—	17	1	no	—
282	#1482	—	17	1	no	—
283	#1454	—	17	1	no	—
284	C₂²×C₁₇	—	2	1	no	—
285	C₂²×C₁₇	—	2	1	no	—
286	C₂²×C₁₇	—	2	1	no	—
287	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
288	C₂×D₁₇	—	2	2	no	—
289	C₂×D₁₇	—	2	2	no	—
290	C₂×D₁₇	—	4	1	no	—
291	C₂×D₁₇	—	4	1	no	—
292	C₂×D₁₇	—	4	1	no	—
293	C₂×D₁₇	—	4	1	no	—
294	C₂×D₁₇	—	4	1	no	—
295	C₂×D₁₇	—	4	1	no	—
296	C₂×D₁₇	—	4	1	no	—
297	C₂×D₁₇	—	8	4	no	—
298	C₄×C₁₇	—	2	1	no	—
299	C₄×C₁₇	—	2	1	no	—
300	C₄×C₁₇	—	2	1	no	—
301	C₄×C₁₇	—	2	1	no	—
302	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
303	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
304	C₄×C₁₇	#576	1	1	yes	characteristic
305	C₄×C₁₇	#577	1	1	yes	characteristic
306	Dic₁₇	—	4	1	no	—
307	Dic₁₇	—	4	1	no	—
308	Dic₁₇	—	4	1	no	—
309	Dic₁₇	—	4	1	no	—
310	Dic₁₇	—	4	1	no	—
311	#529	—	17	1	no	—
312	C₂×C₄×D₄	—	17	1	no	—
313	#484	—	17	1	no	—
314	#481	—	17	1	no	—
315	#478	—	17	1	no	—
316	#478	—	17	1	no	—
317	#463	—	17	1	no	—
318	#463	—	17	1	no	—
319	#450	—	17	1	no	—
320	#447	—	17	1	no	—
321	#446	—	17	1	no	—
322	C₈×Q₈	—	17	1	no	—
323	C₄×SD₁₆	—	17	1	no	—
324	C₄×SD₁₆	—	17	1	no	—
325	C₄×D₈	—	17	1	no	—
326	C₄×D₈	—	17	1	no	—
327	#436	—	17	1	no	—
328	#436	—	34	1	no	—
329	#435	—	34	1	no	—
330	C₈×D₄	—	17	1	no	—
331	C₈×D₄	—	17	1	no	—
332	C₈×D₄	—	17	1	no	—
333	C₈×D₄	—	17	1	no	—
334	C₈×D₄	—	17	1	no	—
335	C₈×D₄	—	34	1	no	—
336	C₈×D₄	—	34	1	no	—
337	#433	—	34	1	no	—
338	#431	—	17	1	no	—
339	#431	—	17	1	no	—
340	#431	C₂×D₁₇	1	1	yes	characteristic
341	#431	C₂×D₁₇	1	1	yes	characteristic
342	#424	—	34	1	no	—
343	#423	C₂×D₁₇	1	1	yes	characteristic
344	C₂×C₂²⋊C₈	—	34	1	no	—
345	C₂×C₂²⋊C₈	—	34	1	no	—
346	#335	C₂×D₁₇	1	1	yes	characteristic, complemented
347	#335	C₂×D₁₇	1	1	yes	characteristic, complemented
348	#334	C₂×D₁₇	1	1	yes	characteristic, complemented
349	#334	C₂×D₁₇	1	1	yes	characteristic, complemented
350	Q₈⋊C₈	—	17	1	no	—
351	Q₈⋊C₈	—	17	1	no	—
352	D₄⋊C₈	—	17	1	no	—
353	D₄⋊C₈	—	17	1	no	—
354	D₄⋊C₈	—	17	1	no	—
355	D₄⋊C₈	—	17	1	no	—
356	D₄⋊C₈	—	17	1	no	—
357	D₄⋊C₈	—	17	1	no	—
358	#322	—	17	1	no	—
359	#322	—	17	1	no	—
360	#322	—	17	1	no	—
361	C₈²	—	17	1	no	—
362	C₂×C₁₇	—	4	1	no	—
363	C₂×C₁₇	#2929	1	1	yes	characteristic
364	C₂×C₁₇	#2946	1	1	yes	characteristic
365	C₂×C₁₇	#2957	1	1	yes	characteristic
366	D₁₇	—	4	2	no	—
367	D₁₇	—	4	2	no	—
368	D₁₇	—	8	1	no	—
369	C₂²×D₄	—	17	1	no	—
370	C₂³×C₄	—	34	1	no	—
371	C₂×SD₁₆	—	17	1	no	—
372	C₂×SD₁₆	—	17	1	no	—
373	C₂×D₈	—	17	1	no	—
374	C₂×D₈	—	17	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	34	1	no	—
377	C₂²×C₈	—	34	1	no	—
378	C₂²×C₈	—	34	1	no	—
379	C₂²×C₈	—	34	1	no	—
380	C₂²×C₈	—	34	1	no	—
381	C₂²×C₈	—	34	1	no	—
382	#126	—	34	1	no	—
383	#125	—	17	1	no	—
384	#124	—	17	1	no	—
385	#123	—	34	1	no	—
386	C₂²⋊Q₈	—	17	1	no	—
387	#121	—	17	1	no	—
388	C₄×Q₈	—	17	1	no	—
389	C₄×D₄	—	17	1	no	—
390	C₄×D₄	—	17	1	no	—
391	C₄×D₄	—	17	1	no	—
392	C₄×D₄	—	17	1	no	—
393	C₄×D₄	—	17	1	no	—
394	C₄×D₄	—	34	1	no	—
395	C₄×D₄	—	34	1	no	—
396	C₄×D₄	—	34	1	no	—
397	#117	—	34	1	no	—
398	C₂×C₄⋊C₄	—	17	1	no	—
399	C₂×C₂²⋊C₄	—	34	1	no	—
400	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
401	#107	—	17	1	no	—
402	#107	—	17	1	no	—
403	#106	—	17	1	no	—
404	#106	—	17	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	17	1	no	—
407	C₄⋊C₈	—	17	1	no	—
408	C₄⋊C₈	—	34	1	no	—
409	C₄⋊C₈	—	34	1	no	—
410	C₄⋊C₈	—	34	1	no	—
411	C₄⋊C₈	C₄×D₁₇	1	1	yes	characteristic
412	C₄⋊C₈	C₄×D₁₇	1	1	yes	characteristic
413	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
414	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
415	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
416	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
417	#103	—	17	1	no	—
418	#103	—	17	1	no	—
419	#102	—	17	1	no	—
420	#102	—	17	1	no	—
421	#102	—	17	1	no	—
422	#102	—	17	1	no	—
423	#102	—	17	1	no	—
424	#102	—	17	1	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	17	1	no	—
427	C₂²⋊C₈	—	17	1	no	—
428	C₂²⋊C₈	—	34	1	no	—
429	C₂²⋊C₈	—	34	1	no	—
430	C₂²⋊C₈	—	34	1	no	—
431	C₂²⋊C₈	—	34	1	no	—
432	C₂²⋊C₈	—	34	1	no	—
433	C₂²⋊C₈	—	34	1	no	—
434	C₂²⋊C₈	—	34	1	no	—
435	C₂²⋊C₈	C₄×D₁₇	1	1	yes	characteristic
436	C₂²⋊C₈	C₄×D₁₇	1	1	yes	characteristic
437	#97	—	34	1	no	—
438	C₄×C₈	—	2	1	no	—
439	C₄×C₈	—	17	1	no	—
440	C₄×C₈	—	17	1	no	—
441	C₄×C₈	—	17	1	no	—
442	C₄×C₈	—	17	1	no	—
443	C₄×C₈	—	34	1	no	—
444	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
445	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
446	C₁₇	#17918	1	1	yes	characteristic, complemented, Sylow
447	C₂⁴	—	34	1	no	—
448	C₂×Q₈	—	17	1	no	—
449	C₂×D₄	—	17	1	no	—
450	C₂×D₄	—	17	1	no	—
451	C₂×D₄	—	17	1	no	—
452	C₂×D₄	—	34	2	no	—
453	C₂×D₄	—	34	2	no	—
454	C₂×D₄	—	34	1	no	—
455	C₂×D₄	—	34	1	no	—
456	C₂²×C₄	—	34	1	no	—
457	C₂²×C₄	—	34	1	no	—
458	C₂²×C₄	—	34	1	no	—
459	C₂²×C₄	—	34	1	no	—
460	C₂²×C₄	—	34	1	no	—
461	C₂²×C₄	—	34	1	no	—
462	C₂²×C₄	—	136	1	no	—
463	C₂²×C₄	—	136	1	no	—
464	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
465	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
466	C₂²×C₄	#63256	1	1	yes	characteristic
467	SD₁₆	—	34	2	no	—
468	SD₁₆	—	34	2	no	—
469	D₈	—	34	2	no	—
470	D₈	—	34	2	no	—
471	M₁₆	—	8	1	no	—
472	M₁₆	—	136	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	17	1	no	—
478	C₂×C₈	—	17	1	no	—
479	C₂×C₈	—	17	1	no	—
480	C₂×C₈	—	17	1	no	—
481	C₂×C₈	—	34	1	no	—
482	C₂×C₈	—	34	1	no	—
483	C₂×C₈	—	136	1	no	—
484	C₂×C₈	—	136	1	no	—
485	C₂×C₈	—	136	1	no	—
486	C₂×C₈	—	136	1	no	—
487	C₂×C₈	—	136	1	no	—
488	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
489	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
490	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
491	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
492	C₄⋊C₄	—	17	1	no	—
493	C₄⋊C₄	—	17	1	no	—
494	C₄⋊C₄	—	17	1	no	—
495	C₄⋊C₄	—	17	1	no	—
496	C₄⋊C₄	—	34	1	no	—
497	C₄⋊C₄	—	34	1	no	—
498	C₄⋊C₄	—	34	1	no	—
499	C₄⋊C₄	—	34	1	no	—
500	C₄⋊C₄	—	34	1	no	—
501	C₂²⋊C₄	—	34	1	no	—
502	C₂²⋊C₄	—	34	1	no	—
503	C₂²⋊C₄	—	34	1	no	—
504	C₂²⋊C₄	—	34	1	no	—
505	C₂²⋊C₄	—	34	1	no	—
506	C₂²⋊C₄	—	34	1	no	—
507	C₂²⋊C₄	—	34	1	no	—
508	C₂²⋊C₄	—	34	1	no	—
509	C₂²⋊C₄	—	34	1	no	—
510	C₄²	—	34	1	no	—
511	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
512	C₄²	D₄×D₁₇	1	1	yes	characteristic
513	C₄²	#63256	1	1	yes	characteristic
514	C₄²	C₂³×D₁₇	1	1	yes	characteristic
515	C₂³	—	34	4	no	—
516	C₂³	—	34	1	no	—
517	C₂³	—	34	1	no	—
518	C₂³	—	34	1	no	—
519	C₂³	—	136	1	no	—
520	C₂³	—	136	1	no	—
521	C₂³	#10587579	1	1	yes	characteristic
522	Q₈	—	34	1	no	—
523	Q₈	—	34	1	no	—
524	D₄	—	17	2	no	—
525	D₄	—	17	2	no	—
526	D₄	—	34	4	no	—
527	D₄	—	34	1	no	—
528	D₄	—	34	1	no	—
529	D₄	—	34	1	no	—
530	D₄	—	34	1	no	—
531	D₄	—	136	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	34	1	no	—
538	C₂×C₄	—	34	1	no	—
539	C₂×C₄	—	34	1	no	—
540	C₂×C₄	—	34	1	no	—
541	C₂×C₄	—	34	1	no	—
542	C₂×C₄	—	68	1	no	—
543	C₂×C₄	—	68	1	no	—
544	C₂×C₄	—	68	1	no	—
545	C₂×C₄	—	68	1	no	—
546	C₂×C₄	—	68	1	no	—
547	C₂×C₄	—	68	1	no	—
548	C₂×C₄	—	136	1	no	—
549	C₂×C₄	—	136	1	no	—
550	C₂×C₄	—	136	1	no	—
551	C₂×C₄	#10587579	1	1	yes	characteristic
552	C₂×C₄	#10587579	1	1	yes	characteristic
553	C₂×C₄	#10587579	1	1	yes	characteristic
554	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
555	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
556	C₂×C₄	C₂×#63256	1	1	yes	characteristic
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	34	1	no	—
566	C₈	—	34	1	no	—
567	C₈	—	34	1	no	—
568	C₈	—	34	1	no	—
569	C₈	—	68	1	no	—
570	C₈	—	68	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	34	2	no	—
575	C₂²	—	34	2	no	—
576	C₂²	—	68	1	no	—
577	C₂²	—	68	1	no	—
578	C₂²	—	68	1	no	—
579	C₂²	—	68	1	no	—
580	C₂²	—	68	1	no	—
581	C₂²	—	68	1	no	—
582	C₂²	—	68	1	no	—
583	C₂²	—	136	4	no	—
584	C₂²	C₂×#10587579	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	68	1	no	—
590	C₄	—	68	1	no	—
591	C₄	—	68	1	no	—
592	C₄	—	68	1	no	—
593	C₄	—	68	1	no	—
594	C₄	#131×D₁₇	1	1	yes	characteristic
595	C₄	#131×D₁₇	1	1	yes	characteristic
596	C₄	#11763613	1	1	yes	characteristic
597	C₄	#11763618	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	68	2	no	—
600	C₂	—	68	2	no	—
601	C₂	—	136	1	no	—
602	C₂	#14537477	1	1	yes	characteristic
603	C₂	#14537614	1	1	yes	characteristic
604	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	#11762945	C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1574	D₁₇
hypocenter	C₁₇	#17918
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
2. #14537929	C₂	semidirect
3. #14537807	C₂	semidirect
4. #14527647	C₂	semidirect
5. #14527640	C₂	semidirect
6. #14527619	C₂	semidirect
7. #14527612	C₂	semidirect
8. #14527607	C₂	semidirect
9. #14527595	C₂	semidirect
10. #14527583	C₂	semidirect
11. #14527578	C₂	semidirect
12. #14527208	C₂	semidirect
13. #14527190	C₂	semidirect
14. #14527084	C₂	semidirect
15. C₁₇×#1574	C₂	semidirect
26. #11762936	C₂²	semidirect
27. #11762933	C₂²	semidirect
32. #11762886	C₂²	semidirect
41. #11762874	C₂²	semidirect
48. #11762539	C₂²	semidirect
49. #11762539	C₂²	semidirect
54. #11762536	C₂²	semidirect
55. #11762536	C₂²	semidirect
56. #11762531	C₂²	semidirect
57. #11762531	C₂²	semidirect
58. #11762530	C₂²	semidirect
59. C₈×#3622	C₂²	semidirect
63. C₁₇×#335	C₂²	semidirect
64. C₁₇×#335	C₂²	semidirect
65. C₁₇×#334	C₂²	semidirect
66. C₁₇×#334	C₂²	semidirect
280. #1574	D₁₇	semidirect
346. #335	C₂×D₁₇	semidirect
347. #335	C₂×D₁₇	semidirect
348. #334	C₂×D₁₇	semidirect
349. #334	C₂×D₁₇	semidirect
446. C₁₇	#17918	semidirect

Maximal subgroups

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

subgroup	index
#14538833	2
#14537929	2
#14537807	2
#14527647	2
#14527640	2
#14527619	2
#14527612	2
#14527607	2
#14527595	2
#14527583	2
#14527578	2
#14527208	2
#14527190	2
#14527084	2
C₁₇×#1574	2
#17918	17