Subgroups — #17004418

Order 4352.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538845	C₂	1	1	yes	maximal, characteristic
2	#14537892	C₂	1	1	yes	maximal, characteristic, complemented
3	#14537859	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527664	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527650	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527629	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527615	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527609	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527598	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#63219	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₁₃₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527569	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527219	C₂	1	1	yes	maximal, characteristic, complemented
14	#14527184	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763359	C₂²	1	1	yes	characteristic
17	C₄×#63252	C₂²	1	1	yes	characteristic
18	#11763134	C₄	1	1	yes	characteristic
19	#11763134	C₄	1	1	yes	characteristic
20	#11763105	C₄	1	1	yes	characteristic
21	#11763100	C₄	1	1	yes	characteristic
22	#11763010	C₄	1	1	yes	characteristic
23	#11763005	C₄	1	1	yes	characteristic
24	#11762956	C₄	1	1	yes	characteristic
25	#11762956	C₄	1	1	yes	characteristic
26	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
27	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
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	#11762888	C₂²	1	1	yes	characteristic
33	#11762888	C₂²	1	1	yes	characteristic
34	#11762879	—	2	1	no	—
35	#11762879	—	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×D₆₈	C₂²	1	1	yes	characteristic
40	#11762872	—	2	1	no	—
41	#11762872	—	2	1	no	—
42	#11762866	C₂²	1	1	yes	characteristic
43	#11762861	—	2	1	no	—
44	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
45	C₄⋊C₈×D₁₇	—	2	1	no	—
46	#11762774	—	2	1	no	—
47	#11762774	—	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	#11762538	C₂²	1	1	yes	characteristic
55	#11762538	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	C₁₇×#431	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	C₈²×C₁₇	C₂²	1	1	yes	characteristic
67	C₂×#63252	—	2	1	no	—
68	C₂×#63252	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
70	#10587616	—	2	1	no	—
71	#10587616	C₂×C₄	1	1	yes	characteristic
72	#10587616	C₂×C₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₇	—	2	1	no	—
74	C₄×C₂²⋊D₁₇	—	2	1	no	—
75	#10587612	C₂×C₄	1	1	yes	characteristic
76	C₂²×#3622	—	2	1	no	—
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×#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	C₂×C₈×D₁₇	—	2	1	no	—
87	#10587561	—	2	1	no	—
88	#10587560	C₂×C₄	1	1	yes	characteristic
89	C₄×D₆₈	—	2	1	no	—
90	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
91	C₄×D₆₈	C₂³	1	1	yes	characteristic
92	C₄×D₆₈	C₂³	1	1	yes	characteristic
93	C₄×D₆₈	C₂³	1	1	yes	characteristic
94	#10587558	—	2	1	no	—
95	C₄²×D₁₇	—	2	1	no	—
96	#10587555	C₂×C₄	1	1	yes	characteristic
97	C₄×Dic₃₄	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	D₄	1	1	yes	characteristic
103	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
104	C₁₇×C₂²⋊C₈	—	2	1	no	—
105	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
108	C₁₇×C₂²⋊C₈	D₄	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	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
114	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
115	C₂²⋊#3622	—	2	1	no	—
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	#10587492	C₂×C₄	1	1	yes	characteristic
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	#10587491	—	2	1	no	—
128	#10587489	C₂×C₄	1	1	yes	characteristic
129	#10587489	C₂×C₄	1	1	yes	characteristic
130	#10587488	C₂×C₄	1	1	yes	characteristic
131	#10587488	C₂×C₄	1	1	yes	characteristic
132	#10587487	C₂×C₄	1	1	yes	characteristic
133	#10587487	C₂×C₄	1	1	yes	characteristic
134	#10587485	—	2	1	no	—
135	#10587485	—	2	1	no	—
136	C₈×Dic₁₇	—	2	1	no	—
137	C₈×Dic₁₇	—	2	1	no	—
138	C₄⋊#3622	—	2	1	no	—
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	#10587474	—	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	C₂×C₂²⋊D₁₇	—	2	1	no	—
150	#63252	—	2	2	no	—
151	#63252	—	2	2	no	—
152	#63252	—	8	1	no	—
153	#63252	—	8	1	no	—
154	C₂×D₆₈	—	2	1	no	—
155	C₂×D₆₈	—	2	1	no	—
156	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₁₇	—	2	1	no	—
160	C₂×C₄×D₁₇	—	2	1	no	—
161	C₂×C₄×D₁₇	—	2	1	no	—
162	C₂×C₄×D₁₇	—	2	1	no	—
163	C₂×C₄×D₁₇	—	2	1	no	—
164	C₂×Dic₃₄	—	2	1	no	—
165	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₁₇	—	2	1	no	—
167	C₂×C₈×C₁₇	—	2	1	no	—
168	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₇	#41	1	1	yes	characteristic
179	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
180	C₂²⋊Dic₁₇	—	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	#63227	—	2	1	no	—
187	C₄⋊Dic₁₇	—	2	1	no	—
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	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
192	#63225	—	2	1	no	—
193	#63225	—	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	C₂×#3622	—	8	1	no	—
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	#63218	—	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	#17920	—	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	1	no	—
217	C₂×C₄×C₁₇	—	2	1	no	—
218	C₂×C₄×C₁₇	—	2	1	no	—
219	C₂×C₄×C₁₇	—	2	1	no	—
220	C₂×C₄×C₁₇	—	2	1	no	—
221	C₂×C₄×C₁₇	—	4	1	no	—
222	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
228	C₂²⋊D₁₇	—	2	4	no	—
229	C₂²⋊D₁₇	—	8	1	no	—
230	C₂²⋊D₁₇	—	8	1	no	—
231	C₂×Dic₁₇	—	2	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	D₆₈	—	2	1	no	—
237	D₆₈	—	2	1	no	—
238	D₆₈	—	2	1	no	—
239	D₆₈	—	2	1	no	—
240	D₆₈	—	2	1	no	—
241	D₆₈	—	8	1	no	—
242	D₆₈	—	8	1	no	—
243	D₆₈	#131	1	2	yes	—
244	C₄×D₁₇	—	2	4	no	—
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	Dic₃₄	—	2	1	no	—
253	Dic₃₄	—	8	1	no	—
254	Dic₃₄	#131	1	2	yes	—
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	—	2	1	no	—
260	C₈×C₁₇	—	2	1	no	—
261	C₈×C₁₇	—	2	1	no	—
262	C₈×C₁₇	—	2	1	no	—
263	C₈×C₁₇	—	4	1	no	—
264	C₈×C₁₇	—	4	1	no	—
265	#3622	—	4	1	no	—
266	#3622	—	4	1	no	—
267	#3622	—	4	1	no	—
268	#3622	—	4	1	no	—
269	#3106	—	17	1	no	—
270	#2988	—	17	1	no	—
271	#2981	—	17	1	no	—
272	#1588	—	17	1	no	—
273	#1586	—	17	1	no	—
274	#1583	—	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	#1573	—	17	1	no	—
281	#1488	—	17	1	no	—
282	#1480	—	17	1	no	—
283	#1454	D₁₇	1	1	yes	characteristic, complemented
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	—	4	1	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	C₄×C₁₇	—	2	1	no	—
298	C₄×C₁₇	—	2	1	no	—
299	C₄×C₁₇	—	2	1	no	—
300	C₄×C₁₇	—	2	1	no	—
301	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
302	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
303	C₄×C₁₇	#576	1	1	yes	characteristic
304	C₄×C₁₇	#577	1	1	yes	characteristic
305	Dic₁₇	—	2	2	no	—
306	Dic₁₇	—	4	1	no	—
307	Dic₁₇	—	4	1	no	—
308	Dic₁₇	—	4	1	no	—
309	Dic₁₇	—	4	1	no	—
310	#532	—	17	1	no	—
311	C₄×#41	—	17	1	no	—
312	#482	—	17	1	no	—
313	#482	—	17	1	no	—
314	#477	—	17	1	no	—
315	#476	—	17	1	no	—
316	#460	—	17	1	no	—
317	#459	—	17	1	no	—
318	#449	—	17	1	no	—
319	#449	—	17	1	no	—
320	C₈×Q₈	—	17	1	no	—
321	C₈×Q₈	—	17	1	no	—
322	C₄×SD₁₆	—	17	1	no	—
323	C₄×SD₁₆	—	17	1	no	—
324	C₄×D₈	—	17	1	no	—
325	C₄×D₈	—	17	1	no	—
326	#436	—	17	1	no	—
327	#436	—	17	1	no	—
328	#435	—	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	—	34	1	no	—
335	C₈×D₄	—	34	1	no	—
336	#432	—	17	1	no	—
337	#431	—	34	1	no	—
338	#431	C₂×D₁₇	1	1	yes	characteristic
339	#431	C₂×D₁₇	1	1	yes	characteristic
340	#431	C₂×D₁₇	1	1	yes	characteristic
341	C₂×C₄⋊C₈	—	17	1	no	—
342	C₂×C₄⋊C₈	—	34	1	no	—
343	#408	—	34	1	no	—
344	#408	—	34	1	no	—
345	#335	—	17	1	no	—
346	#335	—	17	1	no	—
347	#334	—	17	1	no	—
348	#334	—	17	1	no	—
349	Q₈⋊C₈	—	17	1	no	—
350	Q₈⋊C₈	—	17	1	no	—
351	D₄⋊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	#322	C₂×D₁₇	1	1	yes	characteristic
358	#322	C₂×D₁₇	1	1	yes	characteristic
359	#322	C₂×D₁₇	1	1	yes	characteristic
360	C₈²	C₂×D₁₇	1	1	yes	characteristic
361	C₂×C₁₇	—	4	1	no	—
362	C₂×C₁₇	#2929	1	1	yes	characteristic
363	C₂×C₁₇	#2946	1	1	yes	characteristic
364	C₂×C₁₇	#2957	1	1	yes	characteristic
365	D₁₇	—	4	2	no	—
366	D₁₇	—	8	1	no	—
367	D₁₇	—	8	1	no	—
368	C₂×#41	—	17	1	no	—
369	C₂×#41	—	34	1	no	—
370	C₂×SD₁₆	—	17	1	no	—
371	C₂×SD₁₆	—	17	1	no	—
372	C₂×D₈	—	17	1	no	—
373	C₂×D₈	—	17	1	no	—
374	C₂×M₁₆	—	34	1	no	—
375	C₂×M₁₆	—	34	1	no	—
376	C₂²×C₈	—	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	C₄⋊Q₈	—	17	1	no	—
382	#127	—	17	1	no	—
383	#124	—	34	1	no	—
384	#121	—	17	1	no	—
385	#121	—	17	1	no	—
386	#121	—	34	1	no	—
387	C₄×Q₈	—	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	—	34	1	no	—
394	C₄×D₄	—	34	1	no	—
395	C₄×D₄	—	34	1	no	—
396	#117	—	17	1	no	—
397	#117	—	34	1	no	—
398	C₂×C₄²	—	34	1	no	—
399	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
400	#107	—	17	1	no	—
401	#107	—	17	1	no	—
402	#106	—	17	1	no	—
403	#106	—	17	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	17	1	no	—
406	C₄⋊C₈	—	17	1	no	—
407	C₄⋊C₈	—	17	1	no	—
408	C₄⋊C₈	—	17	1	no	—
409	C₄⋊C₈	—	34	1	no	—
410	C₄⋊C₈	—	34	1	no	—
411	C₄⋊C₈	—	34	1	no	—
412	C₄⋊C₈	C₄×D₁₇	1	1	yes	characteristic
413	C₄⋊C₈	C₄×D₁₇	1	1	yes	characteristic
414	C₄⋊C₈	D₆₈	1	1	yes	characteristic
415	C₄⋊C₈	D₆₈	1	1	yes	characteristic
416	#103	—	17	1	no	—
417	#103	—	17	1	no	—
418	#102	—	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	C₂²⋊C₈	—	2	1	no	—
425	C₂²⋊C₈	—	34	1	no	—
426	C₂²⋊C₈	—	34	1	no	—
427	C₂²⋊C₈	—	34	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	C₄×D₁₇	1	1	yes	characteristic
433	C₂²⋊C₈	C₄×D₁₇	1	1	yes	characteristic
434	C₂²⋊C₈	D₆₈	1	1	yes	characteristic
435	C₂²⋊C₈	D₆₈	1	1	yes	characteristic
436	#97	—	34	1	no	—
437	C₄×C₈	—	34	1	no	—
438	C₄×C₈	—	34	1	no	—
439	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
440	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
441	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
442	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
443	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
444	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
445	C₁₇	#17920	1	1	yes	characteristic, complemented, Sylow
446	#41	—	34	2	no	—
447	#41	—	34	2	no	—
448	#41	—	136	1	no	—
449	#41	—	136	1	no	—
450	C₂×Q₈	—	17	1	no	—
451	C₂×Q₈	—	34	1	no	—
452	C₂×D₄	—	17	1	no	—
453	C₂×D₄	—	17	1	no	—
454	C₂×D₄	—	17	1	no	—
455	C₂×D₄	—	34	1	no	—
456	C₂×D₄	—	34	1	no	—
457	C₂×D₄	—	34	1	no	—
458	C₂×D₄	—	34	1	no	—
459	C₂×D₄	—	34	1	no	—
460	C₂²×C₄	—	34	1	no	—
461	C₂²×C₄	—	34	1	no	—
462	C₂²×C₄	—	34	1	no	—
463	C₂²×C₄	—	34	1	no	—
464	C₂²×C₄	—	34	1	no	—
465	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
467	C₂²×C₄	#63252	1	1	yes	characteristic
468	SD₁₆	—	34	2	no	—
469	SD₁₆	—	34	2	no	—
470	D₈	—	34	2	no	—
471	D₈	—	34	2	no	—
472	M₁₆	—	136	1	no	—
473	M₁₆	—	136	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	34	1	no	—
477	C₂×C₈	—	34	1	no	—
478	C₂×C₈	—	34	1	no	—
479	C₂×C₈	—	34	1	no	—
480	C₂×C₈	—	136	1	no	—
481	C₂×C₈	—	136	1	no	—
482	C₂×C₈	—	136	1	no	—
483	C₂×C₈	—	136	1	no	—
484	C₂×C₈	—	136	1	no	—
485	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
486	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
487	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
488	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
489	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
490	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
491	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
492	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
493	C₄⋊C₄	—	17	1	no	—
494	C₄⋊C₄	—	17	1	no	—
495	C₄⋊C₄	—	17	1	no	—
496	C₄⋊C₄	—	17	1	no	—
497	C₄⋊C₄	—	34	1	no	—
498	C₄⋊C₄	—	34	1	no	—
499	C₄⋊C₄	—	34	1	no	—
500	C₂²⋊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	C₄²	—	34	1	no	—
508	C₄²	—	34	1	no	—
509	C₄²	—	34	1	no	—
510	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
511	C₄²	C₂×D₆₈	1	1	yes	characteristic
512	C₄²	#63252	1	1	yes	characteristic
513	C₄²	C₂³×D₁₇	1	1	yes	characteristic
514	C₂³	—	34	1	no	—
515	C₂³	—	34	1	no	—
516	C₂³	—	34	1	no	—
517	C₂³	C₄×D₆₈	1	1	yes	characteristic
518	Q₈	—	17	2	no	—
519	Q₈	—	34	1	no	—
520	Q₈	—	136	1	no	—
521	D₄	—	17	2	no	—
522	D₄	—	34	4	no	—
523	D₄	—	34	1	no	—
524	D₄	—	34	1	no	—
525	D₄	—	34	1	no	—
526	D₄	—	34	1	no	—
527	D₄	—	34	1	no	—
528	D₄	—	136	1	no	—
529	D₄	—	136	1	no	—
530	D₄	—	136	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	4	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	—	34	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	—	68	1	no	—
549	C₂×C₄	—	136	1	no	—
550	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
551	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
552	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
553	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
555	C₂×C₄	C₂×#63252	1	1	yes	characteristic
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	68	1	no	—
567	C₈	—	68	1	no	—
568	C₈	—	68	1	no	—
569	C₈	—	68	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	34	2	no	—
574	C₂²	—	68	1	no	—
575	C₂²	—	68	1	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	C₂×C₄×D₆₈	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	34	2	no	—
588	C₄	—	68	1	no	—
589	C₄	—	68	1	no	—
590	C₄	—	68	1	no	—
591	C₄	—	68	1	no	—
592	C₄	#131×D₁₇	1	1	yes	characteristic
593	C₄	#131×D₁₇	1	1	yes	characteristic
594	C₄	#11763614	1	1	yes	characteristic
595	C₄	#11763621	1	1	yes	characteristic
596	C₂	—	4	1	no	—
597	C₂	—	68	2	no	—
598	C₂	—	136	1	no	—
599	C₂	—	136	1	no	—
600	C₂	#14537480	1	1	yes	characteristic
601	C₂	#14537618	1	1	yes	characteristic
602	C₂	#14537702	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₆₈
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×#1454	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#14538845	C₂
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1454	D₁₇
hypocenter	C₁₇	#17920
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1454

Complements

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

N	H ≅ G/N	type
2. #14537892	C₂	semidirect
3. #14537859	C₂	semidirect
4. #14527664	C₂	semidirect
5. #14527650	C₂	semidirect
6. #14527629	C₂	semidirect
7. #14527615	C₂	semidirect
8. #14527609	C₂	semidirect
9. #14527598	C₂	semidirect
10. C₈×#63219	C₂	semidirect
11. C₈×D₁₃₆	C₂	semidirect
12. #14527569	C₂	semidirect
13. #14527219	C₂	semidirect
14. #14527184	C₂	semidirect
15. C₁₇×#1454	C₂	semidirect
283. #1454	D₁₇	semidirect
445. C₁₇	#17920	semidirect

Maximal subgroups

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

subgroup	index
#14538845	2
#14537892	2
#14537859	2
#14527664	2
#14527650	2
#14527629	2
#14527615	2
#14527609	2
#14527598	2
C₈×#63219	2
C₈×D₁₃₆	2
#14527569	2
#14527219	2
#14527184	2
C₁₇×#1454	2
#17920	17