Subgroups — #17004233

Order 4352.

634 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538798	C₂	1	1	yes	maximal, characteristic
2	#14537762	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#63254	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527636	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527625	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527620	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527590	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527587	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527587	C₂	1	1	yes	maximal, characteristic, complemented
10	D₈×#3622	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527563	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527215	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527189	C₂	1	1	yes	maximal, characteristic, complemented
14	#14527069	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1581	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763341	C₂²	1	1	yes	characteristic
17	C₄×#63254	C₂²	1	1	yes	characteristic
18	#11763152	C₄	1	1	yes	characteristic
19	#11763131	C₄	1	1	yes	characteristic
20	#11763115	C₄	1	1	yes	characteristic
21	#11763107	C₄	1	1	yes	characteristic
22	#11763030	C₄	1	1	yes	characteristic
23	#11763022	C₄	1	1	yes	characteristic
24	#11762972	C₄	1	1	yes	characteristic
25	#11762951	C₄	1	1	yes	characteristic
26	#11762939	C₂²	1	1	yes	characteristic
27	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
28	#11762933	C₂²	1	1	yes	characteristic
29	#11762933	C₂²	1	1	yes	characteristic
30	C₄×Dic₆₈	C₂²	1	1	yes	characteristic
31	C₄×#63229	C₂²	1	1	yes	characteristic
32	C₄×#63229	C₂²	1	1	yes	characteristic
33	#11762878	—	2	1	no	—
34	D₄×#3622	C₂²	1	1	yes	characteristic
35	D₄×#3622	C₂²	1	1	yes	characteristic
36	C₈×C₂²⋊D₁₇	—	2	1	no	—
37	#11762872	—	2	1	no	—
38	#11762872	—	2	1	no	—
39	#11762867	—	2	1	no	—
40	#11762865	C₂²	1	1	yes	characteristic
41	#11762861	C₂²	1	1	yes	characteristic
42	#11762860	C₂²	1	1	yes	characteristic
43	#11762860	C₂²	1	1	yes	characteristic
44	#11762859	—	2	1	no	—
45	#11762767	—	2	1	no	—
46	C₂×C₈×Dic₁₇	—	2	1	no	—
47	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
48	#11762562	C₂²	1	1	yes	characteristic
49	#11762559	C₂²	1	1	yes	characteristic
50	#11762559	C₂²	1	1	yes	characteristic
51	#11762541	C₂²	1	1	yes	characteristic
52	#11762541	C₂²	1	1	yes	characteristic
53	#11762539	C₂²	1	1	yes	characteristic
54	#11762539	C₂²	1	1	yes	characteristic
55	D₄⋊#3622	C₂²	1	1	yes	characteristic
56	D₄⋊#3622	C₂²	1	1	yes	characteristic
57	#11762530	C₂²	1	1	yes	characteristic
58	C₈×#3622	C₂²	1	1	yes	characteristic
59	C₈×#3622	C₂²	1	1	yes	characteristic
60	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
61	C₁₇×#436	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
63	C₁₇×#335	C₂²	1	1	yes	characteristic
64	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₇×#322	C₂²	1	1	yes	characteristic
67	C₂×#63254	C₂×C₄	1	1	yes	characteristic
68	C₂×D₈×C₁₇	C₂×C₄	1	1	yes	characteristic
69	C₂×M₁₆×C₁₇	—	2	1	no	—
70	C₂²×C₈×C₁₇	—	2	1	no	—
71	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
72	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
73	#10587624	C₂×C₄	1	1	yes	characteristic
74	#10587622	C₂×C₄	1	1	yes	characteristic
75	D₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
76	C₂×#63229	C₂×C₄	1	1	yes	characteristic
77	C₂×#63229	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₁₇	—	2	1	no	—
79	C₄×C₂²⋊D₁₇	—	2	1	no	—
80	#10587612	—	2	1	no	—
81	C₂×C₄×Dic₁₇	—	2	1	no	—
82	C₂²×#3622	—	2	1	no	—
83	C₂²×#3622	—	2	1	no	—
84	C₂×Dic₆₈	C₂×C₄	1	1	yes	characteristic
85	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
86	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
87	#10587583	C₂×C₄	1	1	yes	characteristic
88	#10587578	C₂×C₄	1	1	yes	characteristic
89	#10587576	C₂×C₄	1	1	yes	characteristic
90	#10587573	C₂×C₄	1	1	yes	characteristic
91	#10587569	—	2	1	no	—
92	#10587567	—	2	1	no	—
93	#10587565	—	2	1	no	—
94	#10587563	—	2	1	no	—
95	C₄²×D₁₇	C₂³	1	1	yes	characteristic
96	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
97	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
98	C₁₇×#107	C₂×C₄	1	1	yes	characteristic
99	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
102	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
103	C₁₇×C₂²⋊C₈	—	2	1	no	—
104	C₁₇×C₂²⋊C₈	—	2	1	no	—
105	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
106	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
108	#10587503	C₂×C₄	1	1	yes	characteristic
109	#10587503	C₂×C₄	1	1	yes	characteristic
110	C₂²⋊#3622	—	2	1	no	—
111	C₂²⋊#3622	—	2	1	no	—
112	#10587491	—	2	1	no	—
113	#10587491	—	2	1	no	—
114	#10587491	—	2	1	no	—
115	#10587491	C₂×C₄	1	1	yes	characteristic
116	#10587491	C₂×C₄	1	1	yes	characteristic
117	#10587489	C₂×C₄	1	1	yes	characteristic
118	#10587487	C₂×C₄	1	1	yes	characteristic
119	#10587487	C₂×C₄	1	1	yes	characteristic
120	#10587486	—	2	1	no	—
121	#10587486	—	2	1	no	—
122	#10587485	—	2	1	no	—
123	#10587485	—	2	1	no	—
124	#10587485	—	2	1	no	—
125	#10587485	—	2	1	no	—
126	#10587485	—	2	1	no	—
127	#10587485	C₂×C₄	1	1	yes	characteristic
128	#10587485	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₁₇	—	2	1	no	—
130	C₈×Dic₁₇	—	2	1	no	—
131	C₈×Dic₁₇	—	2	1	no	—
132	C₈×Dic₁₇	—	2	1	no	—
133	C₈×Dic₁₇	D₄	1	1	yes	characteristic
134	C₈×Dic₁₇	D₄	1	1	yes	characteristic
135	#10587481	C₂×C₄	1	1	yes	characteristic
136	#10587481	C₂×C₄	1	1	yes	characteristic
137	#10587479	C₂×C₄	1	1	yes	characteristic
138	#10587479	C₂×C₄	1	1	yes	characteristic
139	C₄⋊#3622	C₂³	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	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₇	—	2	1	no	—
147	C₂²×C₄×C₁₇	—	2	1	no	—
148	C₂×C₂²⋊D₁₇	—	2	1	no	—
149	C₂×C₂²⋊D₁₇	—	2	1	no	—
150	C₂²×Dic₁₇	—	2	1	no	—
151	C₂²×Dic₁₇	—	2	1	no	—
152	#63254	—	2	2	no	—
153	#63254	—	2	2	no	—
154	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
157	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
158	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
159	D₈×C₁₇	—	2	2	no	—
160	M₁₆×C₁₇	—	4	2	no	—
161	C₂×C₈×C₁₇	—	2	1	no	—
162	C₂×C₈×C₁₇	—	2	1	no	—
163	C₂×C₈×C₁₇	—	2	1	no	—
164	C₂×C₈×C₁₇	—	4	2	no	—
165	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
169	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
170	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
171	C₂²⋊C₄×C₁₇	—	2	1	no	—
172	C₂²⋊C₄×C₁₇	—	2	1	no	—
173	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
174	C₂²⋊Dic₁₇	—	2	1	no	—
175	C₂²⋊Dic₁₇	—	2	1	no	—
176	C₂²⋊Dic₁₇	—	2	1	no	—
177	C₂²⋊Dic₁₇	—	2	1	no	—
178	#63229	—	2	2	no	—
179	#63229	—	2	2	no	—
180	#63227	—	2	1	no	—
181	#63227	—	2	1	no	—
182	C₄⋊Dic₁₇	—	2	1	no	—
183	C₄⋊Dic₁₇	—	2	1	no	—
184	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
185	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
186	#63225	—	2	1	no	—
187	#63225	—	2	1	no	—
188	#63225	—	2	1	no	—
189	#63225	—	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	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
195	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
196	C₄×Dic₁₇	#41	1	1	yes	characteristic
197	C₂×#3622	—	2	1	no	—
198	C₂×#3622	—	2	1	no	—
199	C₂×#3622	—	2	1	no	—
200	C₂×#3622	—	4	2	no	—
201	C₂×#3622	—	4	2	no	—
202	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
203	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
204	C₂×#3622	C₂×D₄	1	1	yes	characteristic
205	C₂×#3622	C₂×D₄	1	1	yes	characteristic
206	Dic₆₈	—	2	2	no	—
207	C₈×D₁₇	—	2	2	no	—
208	C₈×D₁₇	—	2	2	no	—
209	#17904	—	17	1	no	maximal, Sylow
210	C₂³×C₁₇	—	2	1	no	—
211	C₂³×C₁₇	—	2	1	no	—
212	C₂²×D₁₇	C₄×D₄	1	1	yes	characteristic
213	D₄×C₁₇	—	2	1	no	—
214	D₄×C₁₇	—	2	1	no	—
215	D₄×C₁₇	—	2	1	no	—
216	D₄×C₁₇	#131	1	2	yes	—
217	C₂×C₄×C₁₇	—	2	1	no	—
218	C₂×C₄×C₁₇	—	2	1	no	—
219	C₂×C₄×C₁₇	—	4	1	no	—
220	C₂×C₄×C₁₇	—	4	1	no	—
221	C₂×C₄×C₁₇	—	4	1	no	—
222	C₂×C₄×C₁₇	—	4	1	no	—
223	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
226	C₂²⋊D₁₇	—	2	4	no	—
227	C₂²⋊D₁₇	—	4	2	no	—
228	C₂×Dic₁₇	—	2	4	no	—
229	C₂×Dic₁₇	—	2	1	no	—
230	C₂×Dic₁₇	—	2	1	no	—
231	C₂×Dic₁₇	—	2	1	no	—
232	C₂×Dic₁₇	—	2	1	no	—
233	C₂×Dic₁₇	—	4	2	no	—
234	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
235	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
236	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
237	C₄×D₁₇	—	2	1	no	—
238	C₄×D₁₇	—	2	1	no	—
239	C₄×D₁₇	—	2	1	no	—
240	C₄×D₁₇	—	2	1	no	—
241	C₄×D₁₇	—	4	1	no	—
242	Dic₃₄	—	2	1	no	—
243	Dic₃₄	—	2	1	no	—
244	Dic₃₄	—	2	1	no	—
245	Dic₃₄	#131	1	2	yes	—
246	C₈×C₁₇	—	2	1	no	—
247	C₈×C₁₇	—	2	1	no	—
248	C₈×C₁₇	—	2	1	no	—
249	C₈×C₁₇	—	4	1	no	—
250	C₈×C₁₇	—	4	1	no	—
251	C₈×C₁₇	—	4	1	no	—
252	C₈×C₁₇	#135	1	2	yes	—
253	#3622	—	2	1	no	—
254	#3622	—	2	1	no	—
255	#3622	—	2	1	no	—
256	#3622	—	4	1	no	—
257	#3622	—	4	1	no	—
258	#3622	—	4	1	no	—
259	#3622	#135	1	2	yes	—
260	#3102	—	17	1	no	—
261	#2966	—	17	1	no	—
262	C₈×#41	—	17	1	no	—
263	#1584	—	17	1	no	—
264	#1583	—	17	1	no	—
265	#1582	—	17	1	no	—
266	#1581	D₁₇	1	1	yes	characteristic, complemented
267	C₈×Q₁₆	—	17	1	no	—
268	C₈×SD₁₆	—	17	1	no	—
269	C₈×SD₁₆	—	17	1	no	—
270	C₈×D₈	—	17	1	no	—
271	#1572	—	17	1	no	—
272	#1488	—	17	1	no	—
273	#1482	—	17	1	no	—
274	#1450	—	17	1	no	—
275	C₂²×C₁₇	—	2	2	no	—
276	C₂²×C₁₇	—	4	1	no	—
277	C₂²×C₁₇	—	4	1	no	—
278	C₂²×C₁₇	—	4	1	no	—
279	C₂²×C₁₇	—	4	1	no	—
280	C₂²×C₁₇	—	4	1	no	—
281	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
282	C₂×D₁₇	—	2	1	no	—
283	C₂×D₁₇	—	2	1	no	—
284	C₂×D₁₇	—	2	1	no	—
285	C₄×C₁₇	—	2	1	no	—
286	C₄×C₁₇	—	4	1	no	—
287	C₄×C₁₇	—	4	1	no	—
288	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
289	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
290	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
291	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
292	Dic₁₇	—	2	2	no	—
293	Dic₁₇	—	2	1	no	—
294	Dic₁₇	—	2	1	no	—
295	Dic₁₇	—	2	1	no	—
296	Dic₁₇	—	4	1	no	—
297	Dic₁₇	—	4	1	no	—
298	Dic₁₇	—	4	1	no	—
299	#529	—	17	1	no	—
300	C₄×#41	—	17	1	no	—
301	#485	—	17	1	no	—
302	#482	—	17	1	no	—
303	#479	—	17	1	no	—
304	#478	—	17	1	no	—
305	#464	—	17	1	no	—
306	#463	—	17	1	no	—
307	#452	—	17	1	no	—
308	#449	—	17	1	no	—
309	#446	—	17	1	no	—
310	C₈×Q₈	—	17	1	no	—
311	C₈×Q₈	—	17	1	no	—
312	C₈×Q₈	—	17	1	no	—
313	C₄×Q₁₆	—	17	1	no	—
314	C₄×SD₁₆	—	17	1	no	—
315	C₄×SD₁₆	—	17	1	no	—
316	C₄×D₈	C₂×D₁₇	1	1	yes	characteristic
317	#436	C₂×D₁₇	1	1	yes	characteristic
318	#435	—	34	1	no	—
319	C₈×D₄	—	17	1	no	—
320	C₈×D₄	—	17	1	no	—
321	C₈×D₄	—	34	1	no	—
322	C₈×D₄	—	34	1	no	—
323	C₈×D₄	—	34	1	no	—
324	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
325	#433	—	34	1	no	—
326	#432	—	17	1	no	—
327	#431	—	17	1	no	—
328	#431	—	17	1	no	—
329	#431	—	17	1	no	—
330	#431	—	34	1	no	—
331	#405	—	34	1	no	—
332	C₂×C₄×C₈	—	17	1	no	—
333	C₂×C₄×C₈	—	34	1	no	—
334	#335	—	17	1	no	—
335	#335	C₂×D₁₇	1	1	yes	characteristic
336	#334	—	17	1	no	—
337	#334	—	17	1	no	—
338	Q₈⋊C₈	—	17	1	no	—
339	Q₈⋊C₈	—	17	1	no	—
340	Q₈⋊C₈	—	17	1	no	—
341	Q₈⋊C₈	—	17	1	no	—
342	D₄⋊C₈	—	17	1	no	—
343	D₄⋊C₈	—	17	1	no	—
344	D₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
345	D₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
346	#322	—	17	1	no	—
347	#322	C₂×D₁₇	1	1	yes	characteristic
348	C₈²	—	17	1	no	—
349	C₈²	—	17	1	no	—
350	C₂×C₁₇	—	4	2	no	—
351	C₂×C₁₇	—	8	1	no	—
352	C₂×C₁₇	#2929	1	1	yes	characteristic
353	C₂×C₁₇	C₄×#135	1	1	yes	characteristic
354	C₂×C₁₇	#2955	1	1	yes	characteristic
355	D₁₇	—	4	1	no	—
356	C₂×#41	—	17	1	no	—
357	C₂×Q₁₆	—	17	1	no	—
358	C₂×SD₁₆	—	17	1	no	—
359	C₂×SD₁₆	—	17	1	no	—
360	C₂×D₈	C₄×D₁₇	1	1	yes	characteristic
361	C₂×M₁₆	—	2	1	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₂²×C₈	—	17	1	no	—
364	C₂²×C₈	—	17	1	no	—
365	C₂²×C₈	—	34	1	no	—
366	C₂²×C₈	—	34	1	no	—
367	#126	—	34	1	no	—
368	#125	—	17	1	no	—
369	#124	—	17	1	no	—
370	#123	—	34	1	no	—
371	C₂²⋊Q₈	—	17	1	no	—
372	#121	—	17	1	no	—
373	C₄×Q₈	—	17	1	no	—
374	C₄×Q₈	—	17	1	no	—
375	C₄×Q₈	—	17	1	no	—
376	C₄×D₄	—	17	1	no	—
377	C₄×D₄	—	34	1	no	—
378	C₄×D₄	—	34	1	no	—
379	C₄×D₄	—	34	1	no	—
380	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
381	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
382	#117	—	17	1	no	—
383	#117	—	34	1	no	—
384	#117	—	34	1	no	—
385	C₂×C₄²	—	17	1	no	—
386	C₂×C₄²	—	34	1	no	—
387	#107	—	17	1	no	—
388	#107	C₄×D₁₇	1	1	yes	characteristic
389	#106	—	17	1	no	—
390	#106	—	17	1	no	—
391	C₄⋊C₈	—	17	1	no	—
392	C₄⋊C₈	—	17	1	no	—
393	C₄⋊C₈	—	17	1	no	—
394	C₄⋊C₈	—	17	1	no	—
395	C₄⋊C₈	—	34	1	no	—
396	C₄⋊C₈	—	34	1	no	—
397	C₄⋊C₈	—	34	1	no	—
398	C₄⋊C₈	—	34	1	no	—
399	C₄⋊C₈	—	34	1	no	—
400	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
401	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
402	#103	—	17	1	no	—
403	#103	—	17	1	no	—
404	#103	—	17	1	no	—
405	#103	—	17	1	no	—
406	#102	—	17	1	no	—
407	#102	—	17	1	no	—
408	#102	C₄×D₁₇	1	1	yes	characteristic
409	#102	C₄×D₁₇	1	1	yes	characteristic
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	17	1	no	—
413	C₂²⋊C₈	—	17	1	no	—
414	C₂²⋊C₈	—	34	1	no	—
415	C₂²⋊C₈	—	34	1	no	—
416	C₂²⋊C₈	—	34	1	no	—
417	C₂²⋊C₈	—	34	1	no	—
418	C₂²⋊C₈	—	34	1	no	—
419	#97	—	34	1	no	—
420	#97	—	34	1	no	—
421	C₄×C₈	—	17	1	no	—
422	C₄×C₈	—	17	1	no	—
423	C₄×C₈	—	17	1	no	—
424	C₄×C₈	—	17	1	no	—
425	C₄×C₈	—	17	1	no	—
426	C₄×C₈	—	34	1	no	—
427	C₄×C₈	—	34	1	no	—
428	C₄×C₈	—	34	1	no	—
429	C₄×C₈	—	34	1	no	—
430	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
431	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
432	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
433	C₁₇	#17904	1	1	yes	characteristic, complemented, Sylow
434	#41	—	34	2	no	—
435	#41	—	34	2	no	—
436	C₂×Q₈	—	17	1	no	—
437	C₂×Q₈	—	17	1	no	—
438	C₂×D₄	—	34	1	no	—
439	C₂×D₄	—	34	1	no	—
440	C₂×D₄	C₂×C₄×D₁₇	1	1	yes	characteristic
441	C₂×D₄	C₂×C₄×D₁₇	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	17	1	no	—
445	C₂²×C₄	—	17	1	no	—
446	C₂²×C₄	—	17	1	no	—
447	C₂²×C₄	—	34	1	no	—
448	C₂²×C₄	—	34	1	no	—
449	Q₁₆	—	34	2	no	—
450	SD₁₆	—	34	2	no	—
451	SD₁₆	—	34	2	no	—
452	D₈	—	2	2	no	—
453	M₁₆	—	4	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	4	2	no	—
458	C₂×C₈	—	17	1	no	—
459	C₂×C₈	—	17	1	no	—
460	C₂×C₈	—	17	1	no	—
461	C₂×C₈	—	17	1	no	—
462	C₂×C₈	—	34	2	no	—
463	C₂×C₈	—	34	2	no	—
464	C₂×C₈	—	34	1	no	—
465	C₂×C₈	—	34	1	no	—
466	C₂×C₈	—	34	1	no	—
467	C₂×C₈	—	68	2	no	—
468	C₂×C₈	—	68	2	no	—
469	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
470	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
471	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
472	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
473	C₄⋊C₄	—	17	1	no	—
474	C₄⋊C₄	—	17	1	no	—
475	C₄⋊C₄	—	34	1	no	—
476	C₄⋊C₄	—	34	1	no	—
477	C₄⋊C₄	—	34	1	no	—
478	C₄⋊C₄	—	34	1	no	—
479	C₄⋊C₄	—	34	1	no	—
480	C₄⋊C₄	—	34	1	no	—
481	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
482	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	34	1	no	—
486	C₂²⋊C₄	—	34	1	no	—
487	C₂²⋊C₄	—	34	1	no	—
488	C₂²⋊C₄	—	34	1	no	—
489	C₂²⋊C₄	—	34	1	no	—
490	C₂²⋊C₄	—	34	1	no	—
491	C₄²	—	17	1	no	—
492	C₄²	—	17	1	no	—
493	C₄²	—	17	1	no	—
494	C₄²	—	34	1	no	—
495	C₄²	—	34	1	no	—
496	C₄²	—	34	1	no	—
497	C₄²	—	34	1	no	—
498	C₄²	C₂³×D₁₇	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	17	1	no	—
502	Q₈	—	17	2	no	—
503	Q₈	—	34	1	no	—
504	Q₈	—	34	1	no	—
505	Q₈	—	34	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	34	4	no	—
510	D₄	—	68	2	no	—
511	D₄	#10587593	1	2	yes	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	17	1	no	—
519	C₂×C₄	—	17	1	no	—
520	C₂×C₄	—	17	1	no	—
521	C₂×C₄	—	34	4	no	—
522	C₂×C₄	—	34	1	no	—
523	C₂×C₄	—	34	1	no	—
524	C₂×C₄	—	34	1	no	—
525	C₂×C₄	—	34	1	no	—
526	C₂×C₄	—	34	1	no	—
527	C₂×C₄	—	34	1	no	—
528	C₂×C₄	—	34	1	no	—
529	C₂×C₄	—	34	1	no	—
530	C₂×C₄	—	68	1	no	—
531	C₂×C₄	—	68	2	no	—
532	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
534	C₂×C₄	#41×D₁₇	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	17	2	no	—
542	C₈	—	34	1	no	—
543	C₈	—	34	1	no	—
544	C₈	—	34	1	no	—
545	C₈	—	68	1	no	—
546	C₈	—	68	1	no	—
547	C₈	—	68	1	no	—
548	C₈	#10587598	1	2	yes	—
549	C₂²	—	2	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	34	1	no	—
556	C₂²	—	34	1	no	—
557	C₂²	—	34	1	no	—
558	C₂²	C₄×D₄×D₁₇	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	34	1	no	—
563	C₄	—	34	2	no	—
564	C₄	—	34	1	no	—
565	C₄	—	34	1	no	—
566	C₄	—	68	1	no	—
567	C₄	—	68	1	no	—
568	C₄	—	68	1	no	—
569	C₄	#131×D₁₇	1	1	yes	characteristic
570	C₄	C₂×#10587593	1	1	yes	characteristic
571	C₄	#135×D₁₇	1	1	yes	characteristic
572	C₄	C₂×#10587598	1	1	yes	characteristic
573	C₂	—	4	2	no	—
574	C₂	—	8	1	no	—
575	C₂	—	68	1	no	—
576	C₂	#14537475	1	1	yes	characteristic
577	C₂	C₄×#10587598	1	1	yes	characteristic
578	C₂	#14537684	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×#1581	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#11762951	C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1581	D₁₇
hypocenter	C₁₇	#17904
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1581

Complements

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

N	H ≅ G/N	type
2. #14537762	C₂	semidirect
3. C₈×#63254	C₂	semidirect
4. #14527636	C₂	semidirect
5. #14527625	C₂	semidirect
6. #14527620	C₂	semidirect
7. #14527590	C₂	semidirect
8. #14527587	C₂	semidirect
9. #14527587	C₂	semidirect
10. D₈×#3622	C₂	semidirect
11. #14527563	C₂	semidirect
12. #14527215	C₂	semidirect
13. #14527189	C₂	semidirect
14. #14527069	C₂	semidirect
15. C₁₇×#1581	C₂	semidirect
266. #1581	D₁₇	semidirect
433. C₁₇	#17904	semidirect

Maximal subgroups

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

subgroup	index
#14538798	2
#14537762	2
C₈×#63254	2
#14527636	2
#14527625	2
#14527620	2
#14527590	2
#14527587	2
D₈×#3622	2
#14527563	2
#14527215	2
#14527189	2
#14527069	2
C₁₇×#1581	2
#17904	17