Subgroups — #17004285

Order 4352.

626 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	#14538804	C₂	1	1	yes	maximal, characteristic
2	#14537759	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#63252	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527664	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527657	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527650	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527643	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527609	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527604	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527598	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527598	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527564	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527219	C₂	1	1	yes	maximal, characteristic, complemented
14	#14527193	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1452	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763343	C₂²	1	1	yes	characteristic
17	C₄×#63252	C₂²	1	1	yes	characteristic
18	#11763151	C₄	1	1	yes	characteristic
19	#11763134	C₄	1	1	yes	characteristic
20	#11763117	C₄	1	1	yes	characteristic
21	#11763110	C₄	1	1	yes	characteristic
22	#11763032	C₄	1	1	yes	characteristic
23	#11763025	C₄	1	1	yes	characteristic
24	#11762973	C₄	1	1	yes	characteristic
25	#11762956	C₄	1	1	yes	characteristic
26	#11762939	C₂²	1	1	yes	characteristic
27	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
28	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
29	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
30	C₄×Dic₆₈	C₂²	1	1	yes	characteristic
31	C₄×#63219	C₂²	1	1	yes	characteristic
32	C₄×#63219	C₂²	1	1	yes	characteristic
33	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
34	#11762888	C₂²	1	1	yes	characteristic
35	#11762880	—	2	1	no	—
36	C₈×D₆₈	C₂²	1	1	yes	characteristic
37	C₈×D₆₈	C₂²	1	1	yes	characteristic
38	C₈×D₆₈	C₂²	1	1	yes	characteristic
39	C₈×C₂²⋊D₁₇	—	2	1	no	—
40	C₈×C₂²⋊D₁₇	—	2	1	no	—
41	C₈×C₂²⋊D₁₇	—	2	1	no	—
42	#11762868	—	2	1	no	—
43	#11762866	C₂²	1	1	yes	characteristic
44	#11762862	C₂²	1	1	yes	characteristic
45	#11762860	—	2	1	no	—
46	#11762763	—	2	1	no	—
47	C₄×C₈×D₁₇	—	2	1	no	—
48	#11762562	C₂²	1	1	yes	characteristic
49	#11762562	C₂²	1	1	yes	characteristic
50	#11762560	C₂²	1	1	yes	characteristic
51	#11762560	C₂²	1	1	yes	characteristic
52	#11762541	C₂²	1	1	yes	characteristic
53	#11762541	C₂²	1	1	yes	characteristic
54	#11762541	C₂²	1	1	yes	characteristic
55	#11762541	C₂²	1	1	yes	characteristic
56	#11762538	C₂²	1	1	yes	characteristic
57	#11762538	C₂²	1	1	yes	characteristic
58	#11762538	C₂²	1	1	yes	characteristic
59	#11762538	C₂²	1	1	yes	characteristic
60	C₁₇×#431	C₂²	1	1	yes	characteristic
61	C₁₇×#431	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
63	C₁₇×#322	C₂²	1	1	yes	characteristic
64	C₁₇×#322	C₂²	1	1	yes	characteristic
65	C₁₇×#322	C₂²	1	1	yes	characteristic
66	C₁₇×#322	C₂²	1	1	yes	characteristic
67	C₂×#63252	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
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	C₄×C₂²⋊D₁₇	—	2	1	no	—
75	C₄×C₂²⋊D₁₇	—	2	1	no	—
76	#10587612	C₂×C₄	1	1	yes	characteristic
77	#10587610	C₂×C₄	1	1	yes	characteristic
78	C₂×Dic₆₈	C₂×C₄	1	1	yes	characteristic
79	C₂×D₁₃₆	C₂×C₄	1	1	yes	characteristic
80	C₂×#63219	C₂×C₄	1	1	yes	characteristic
81	C₂×#63219	C₂×C₄	1	1	yes	characteristic
82	C₂×#63218	—	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	#10587562	—	2	1	no	—
87	#10587561	C₂×C₄	1	1	yes	characteristic
88	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
89	C₄×D₆₈	C₂³	1	1	yes	characteristic
90	C₄×D₆₈	C₂³	1	1	yes	characteristic
91	#10587558	—	2	1	no	—
92	#10587558	—	2	1	no	—
93	C₄²×D₁₇	—	2	1	no	—
94	#10587556	C₂×C₄	1	1	yes	characteristic
95	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
96	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
97	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
98	C₁₇×C₄⋊C₈	—	2	1	no	—
99	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₁₇×C₂²⋊C₈	—	2	1	no	—
102	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
103	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
104	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
105	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
114	#10587492	C₂×C₄	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	#10587491	—	2	1	no	—
119	#10587491	—	2	1	no	—
120	#10587491	—	2	1	no	—
121	#10587491	—	2	1	no	—
122	#10587489	C₂×C₄	1	1	yes	characteristic
123	#10587489	C₂×C₄	1	1	yes	characteristic
124	#10587488	C₂×C₄	1	1	yes	characteristic
125	#10587488	C₂×C₄	1	1	yes	characteristic
126	#10587487	C₂×C₄	1	1	yes	characteristic
127	#10587487	C₂×C₄	1	1	yes	characteristic
128	#10587487	C₂×C₄	1	1	yes	characteristic
129	#10587487	C₂×C₄	1	1	yes	characteristic
130	#10587486	—	2	1	no	—
131	#10587485	—	2	1	no	—
132	#10587485	—	2	1	no	—
133	#10587485	—	2	1	no	—
134	#10587485	—	2	1	no	—
135	C₈×Dic₁₇	—	2	1	no	—
136	C₈×Dic₁₇	—	2	1	no	—
137	C₈×Dic₁₇	—	2	1	no	—
138	C₄⋊#3622	C₂³	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	#10587474	—	2	1	no	—
143	C₄×#3622	—	2	1	no	—
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	C₂×C₂²⋊D₁₇	—	2	1	no	—
149	#63252	—	2	2	no	—
150	#63252	—	2	2	no	—
151	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₁₇	—	2	1	no	—
154	C₂×C₄×D₁₇	—	2	1	no	—
155	C₂×C₄×D₁₇	—	2	1	no	—
156	C₂×C₄×D₁₇	—	2	1	no	—
157	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
158	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₁₇	—	2	1	no	—
160	C₂×C₈×C₁₇	—	2	1	no	—
161	C₂×C₈×C₁₇	—	4	1	no	—
162	C₂×C₈×C₁₇	—	4	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	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₇	#41	1	1	yes	characteristic
174	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
175	C₂²⋊Dic₁₇	—	2	1	no	—
176	C₂²⋊Dic₁₇	—	2	1	no	—
177	#63227	—	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	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
184	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
185	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
186	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
187	#63225	—	2	1	no	—
188	#63225	—	2	1	no	—
189	#63225	—	2	1	no	—
190	#63225	—	2	1	no	—
191	#63225	—	2	1	no	—
192	#63225	—	2	1	no	—
193	C₄×Dic₁₇	—	2	1	no	—
194	C₄×Dic₁₇	—	2	1	no	—
195	C₄×Dic₁₇	—	2	1	no	—
196	C₄×Dic₁₇	—	2	1	no	—
197	C₂×#3622	—	2	1	no	—
198	C₂×#3622	—	2	1	no	—
199	C₂×#3622	—	2	1	no	—
200	C₂×#3622	—	2	1	no	—
201	Dic₆₈	—	2	2	no	—
202	D₁₃₆	—	2	2	no	—
203	#63219	—	2	2	no	—
204	#63219	—	2	2	no	—
205	#63218	—	4	2	no	—
206	C₈×D₁₇	—	4	2	no	—
207	C₈×D₁₇	—	4	2	no	—
208	C₈×D₁₇	—	4	2	no	—
209	#17909	—	17	1	no	maximal, Sylow
210	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
211	C₂²×D₁₇	—	2	1	no	—
212	C₂²×D₁₇	—	2	1	no	—
213	C₂×C₄×C₁₇	—	2	1	no	—
214	C₂×C₄×C₁₇	—	2	1	no	—
215	C₂×C₄×C₁₇	—	2	1	no	—
216	C₂×C₄×C₁₇	—	2	1	no	—
217	C₂×C₄×C₁₇	—	4	1	no	—
218	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
224	C₂²⋊D₁₇	—	2	4	no	—
225	C₂²⋊D₁₇	—	4	2	no	—
226	C₂×Dic₁₇	—	2	1	no	—
227	C₂×Dic₁₇	—	2	1	no	—
228	C₂×Dic₁₇	—	2	1	no	—
229	C₂×Dic₁₇	—	2	1	no	—
230	C₂×Dic₁₇	—	2	1	no	—
231	C₂×Dic₁₇	—	2	1	no	—
232	D₆₈	—	2	1	no	—
233	D₆₈	—	2	1	no	—
234	D₆₈	—	2	1	no	—
235	D₆₈	#131	1	2	yes	—
236	C₄×D₁₇	—	2	4	no	—
237	C₄×D₁₇	—	4	2	no	—
238	C₄×D₁₇	—	4	1	no	—
239	C₄×D₁₇	—	4	1	no	—
240	C₄×D₁₇	—	4	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	—	2	1	no	—
250	C₈×C₁₇	—	2	1	no	—
251	C₈×C₁₇	—	2	1	no	—
252	C₈×C₁₇	—	2	1	no	—
253	C₈×C₁₇	—	2	1	no	—
254	C₈×C₁₇	—	4	1	no	—
255	C₈×C₁₇	—	4	1	no	—
256	#3622	—	4	1	no	—
257	#3622	—	4	1	no	—
258	#3622	—	4	1	no	—
259	#3622	—	4	1	no	—
260	#3102	—	17	1	no	—
261	#2966	—	17	1	no	—
262	C₈×#41	—	17	1	no	—
263	#1588	—	17	1	no	—
264	#1587	—	17	1	no	—
265	#1586	—	17	1	no	—
266	#1585	—	17	1	no	—
267	#1580	—	17	1	no	—
268	#1579	—	17	1	no	—
269	SD₁₆⋊C₈	—	17	1	no	—
270	SD₁₆⋊C₈	—	17	1	no	—
271	#1572	—	17	1	no	—
272	#1488	—	17	1	no	—
273	#1482	—	17	1	no	—
274	#1452	D₁₇	1	1	yes	characteristic, complemented
275	C₂²×C₁₇	—	2	1	no	—
276	C₂²×C₁₇	—	2	1	no	—
277	C₂²×C₁₇	—	2	1	no	—
278	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂×D₁₇	—	2	2	no	—
280	C₂×D₁₇	—	4	1	no	—
281	C₂×D₁₇	—	4	1	no	—
282	C₂×D₁₇	—	4	1	no	—
283	C₂×D₁₇	—	4	1	no	—
284	C₂×D₁₇	—	4	1	no	—
285	C₄×C₁₇	—	2	1	no	—
286	C₄×C₁₇	—	2	1	no	—
287	C₄×C₁₇	—	2	1	no	—
288	C₄×C₁₇	—	2	1	no	—
289	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
290	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
291	C₄×C₁₇	#575	1	1	yes	characteristic
292	C₄×C₁₇	#575	1	1	yes	characteristic
293	Dic₁₇	—	2	2	no	—
294	Dic₁₇	—	4	1	no	—
295	Dic₁₇	—	4	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	—	17	1	no	—
317	#436	—	17	1	no	—
318	#435	—	34	1	no	—
319	C₈×D₄	—	17	1	no	—
320	C₈×D₄	—	17	1	no	—
321	C₈×D₄	—	17	1	no	—
322	C₈×D₄	—	34	1	no	—
323	C₈×D₄	—	34	1	no	—
324	C₈×D₄	—	34	1	no	—
325	#433	—	34	1	no	—
326	#432	—	17	1	no	—
327	#431	—	17	1	no	—
328	#431	—	34	1	no	—
329	#431	C₂×D₁₇	1	1	yes	characteristic
330	#431	C₂×D₁₇	1	1	yes	characteristic
331	#405	—	34	1	no	—
332	C₂×C₄×C₈	—	34	1	no	—
333	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
334	#335	—	17	1	no	—
335	#335	—	17	1	no	—
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	—	17	1	no	—
345	D₄⋊C₈	—	17	1	no	—
346	#322	C₂×D₁₇	1	1	yes	characteristic
347	#322	C₂×D₁₇	1	1	yes	characteristic
348	#322	C₂×D₁₇	1	1	yes	characteristic
349	#322	C₂×D₁₇	1	1	yes	characteristic
350	C₂×C₁₇	—	4	1	no	—
351	C₂×C₁₇	#2929	1	1	yes	characteristic
352	C₂×C₁₇	#2943	1	1	yes	characteristic
353	C₂×C₁₇	#2955	1	1	yes	characteristic
354	D₁₇	—	4	2	no	—
355	D₁₇	—	8	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	—	17	1	no	—
361	C₂×M₁₆	—	34	1	no	—
362	C₂²×C₈	—	34	1	no	—
363	C₂²×C₈	—	34	1	no	—
364	C₂²×C₈	—	34	1	no	—
365	C₂²×C₈	D₆₈	1	1	yes	characteristic
366	C₂²×C₈	D₆₈	1	1	yes	characteristic
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	—	17	1	no	—
378	C₄×D₄	—	17	1	no	—
379	C₄×D₄	—	34	1	no	—
380	C₄×D₄	—	34	1	no	—
381	C₄×D₄	—	34	1	no	—
382	#117	—	17	1	no	—
383	#117	—	34	1	no	—
384	#117	—	34	1	no	—
385	C₂×C₄²	—	34	1	no	—
386	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
387	#107	—	17	1	no	—
388	#107	—	17	1	no	—
389	#106	—	17	1	no	—
390	#106	—	17	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	17	1	no	—
393	C₄⋊C₈	—	17	1	no	—
394	C₄⋊C₈	—	17	1	no	—
395	C₄⋊C₈	—	17	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	C₄×D₁₇	1	1	yes	characteristic
401	C₄⋊C₈	C₄×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	—	17	1	no	—
409	#102	—	17	1	no	—
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	34	1	no	—
412	C₂²⋊C₈	—	34	1	no	—
413	C₂²⋊C₈	—	34	1	no	—
414	C₂²⋊C₈	—	34	1	no	—
415	C₂²⋊C₈	—	34	1	no	—
416	C₂²⋊C₈	—	34	1	no	—
417	C₂²⋊C₈	C₄×D₁₇	1	1	yes	characteristic
418	C₂²⋊C₈	C₄×D₁₇	1	1	yes	characteristic
419	#97	—	34	1	no	—
420	#97	—	34	1	no	—
421	C₄×C₈	—	34	1	no	—
422	C₄×C₈	—	34	1	no	—
423	C₄×C₈	—	34	1	no	—
424	C₄×C₈	—	34	1	no	—
425	C₄×C₈	D₆₈	1	1	yes	characteristic
426	C₄×C₈	D₆₈	1	1	yes	characteristic
427	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
428	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
429	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
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	#17909	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	—	17	1	no	—
439	C₂×D₄	—	17	1	no	—
440	C₂×D₄	—	34	1	no	—
441	C₂×D₄	—	34	1	no	—
442	C₂²×C₄	—	34	1	no	—
443	C₂²×C₄	—	34	1	no	—
444	C₂²×C₄	—	34	1	no	—
445	C₂²×C₄	—	34	1	no	—
446	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
448	C₂²×C₄	#63252	1	1	yes	characteristic
449	Q₁₆	—	34	2	no	—
450	SD₁₆	—	34	2	no	—
451	SD₁₆	—	34	2	no	—
452	D₈	—	34	2	no	—
453	M₁₆	—	68	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	4	1	no	—
457	C₂×C₈	—	4	1	no	—
458	C₂×C₈	—	34	1	no	—
459	C₂×C₈	—	34	1	no	—
460	C₂×C₈	—	34	1	no	—
461	C₂×C₈	—	34	1	no	—
462	C₂×C₈	—	68	2	no	—
463	C₂×C₈	—	68	2	no	—
464	C₂×C₈	—	68	2	no	—
465	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
466	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
467	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
468	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
469	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
470	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
471	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
472	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
473	C₄⋊C₄	—	17	1	no	—
474	C₄⋊C₄	—	17	1	no	—
475	C₄⋊C₄	—	17	1	no	—
476	C₄⋊C₄	—	17	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	—	34	1	no	—
482	C₄⋊C₄	—	34	1	no	—
483	C₂²⋊C₄	—	34	1	no	—
484	C₂²⋊C₄	—	34	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	—	34	1	no	—
492	C₄²	—	34	1	no	—
493	C₄²	—	34	1	no	—
494	C₄²	—	34	1	no	—
495	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
496	C₄²	C₂×D₆₈	1	1	yes	characteristic
497	C₄²	#63252	1	1	yes	characteristic
498	C₄²	C₂³×D₁₇	1	1	yes	characteristic
499	C₂³	—	34	1	no	—
500	C₂³	—	34	1	no	—
501	C₂³	C₄×D₆₈	1	1	yes	characteristic
502	Q₈	—	17	2	no	—
503	Q₈	—	34	1	no	—
504	Q₈	—	34	1	no	—
505	Q₈	—	34	1	no	—
506	D₄	—	17	2	no	—
507	D₄	—	34	4	no	—
508	D₄	—	34	1	no	—
509	D₄	—	34	1	no	—
510	D₄	—	34	1	no	—
511	D₄	—	68	2	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	34	4	no	—
518	C₂×C₄	—	34	1	no	—
519	C₂×C₄	—	34	1	no	—
520	C₂×C₄	—	34	1	no	—
521	C₂×C₄	—	34	1	no	—
522	C₂×C₄	—	34	1	no	—
523	C₂×C₄	—	34	1	no	—
524	C₂×C₄	—	68	2	no	—
525	C₂×C₄	—	68	1	no	—
526	C₂×C₄	—	68	1	no	—
527	C₂×C₄	—	68	1	no	—
528	C₂×C₄	—	68	1	no	—
529	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
530	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
531	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
534	C₂×C₄	C₂×#63252	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	68	1	no	—
546	C₈	—	68	1	no	—
547	C₈	—	68	1	no	—
548	C₈	—	68	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	34	2	no	—
553	C₂²	—	68	1	no	—
554	C₂²	—	68	1	no	—
555	C₂²	—	68	1	no	—
556	C₂²	—	68	1	no	—
557	C₂²	—	68	1	no	—
558	C₂²	C₂×C₄×D₆₈	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	34	2	no	—
564	C₄	—	68	1	no	—
565	C₄	—	68	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	#131×D₁₇	1	1	yes	characteristic
571	C₄	#11763609	1	1	yes	characteristic
572	C₄	#11763609	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	68	2	no	—
575	C₂	—	136	1	no	—
576	C₂	#14537480	1	1	yes	characteristic
577	C₂	#14537586	1	1	yes	characteristic
578	C₂	#14537688	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₆₈
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×#1452	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#11762956	C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1452	D₁₇
hypocenter	C₁₇	#17909
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1452

Complements

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

N	H ≅ G/N	type
2. #14537759	C₂	semidirect
3. C₈×#63252	C₂	semidirect
4. #14527664	C₂	semidirect
5. #14527657	C₂	semidirect
6. #14527650	C₂	semidirect
7. #14527643	C₂	semidirect
8. #14527609	C₂	semidirect
9. #14527604	C₂	semidirect
10. #14527598	C₂	semidirect
11. #14527598	C₂	semidirect
12. #14527564	C₂	semidirect
13. #14527219	C₂	semidirect
14. #14527193	C₂	semidirect
15. C₁₇×#1452	C₂	semidirect
274. #1452	D₁₇	semidirect
433. C₁₇	#17909	semidirect

Maximal subgroups

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

subgroup	index
#14538804	2
#14537759	2
C₈×#63252	2
#14527664	2
#14527657	2
#14527650	2
#14527643	2
#14527609	2
#14527604	2
#14527598	2
#14527564	2
#14527219	2
#14527193	2
C₁₇×#1452	2
#17909	17