Subgroups — #17005521

Order 4352.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 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	#14537946	C₂	1	1	yes	maximal, characteristic
3	#14537871	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527682	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527676	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527664	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527657	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527657	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527643	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×Dic₆₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#63219	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527569	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527245	C₂	1	1	yes	maximal, characteristic
14	C₂×#11762541	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1450	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	#11762939	C₂²	1	1	yes	characteristic
27	#11762939	C₂²	1	1	yes	characteristic
28	#11762939	C₂²	1	1	yes	characteristic
29	#11762938	—	2	1	no	—
30	#11762938	—	2	1	no	—
31	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
32	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
33	C₈×Dic₃₄	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	#11762888	C₂²	1	1	yes	characteristic
39	#11762877	—	2	1	no	—
40	C₈×D₆₈	C₂²	1	1	yes	characteristic
41	#11762872	—	2	1	no	—
42	#11762869	—	2	1	no	—
43	#11762866	C₂²	1	1	yes	characteristic
44	#11762863	—	2	1	no	—
45	#11762859	—	2	1	no	—
46	#11762834	—	2	1	no	—
47	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
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	#11762541	C₂²	1	1	yes	characteristic
57	#11762541	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	C₈²×C₁₇	C₂²	1	1	yes	characteristic
66	C₈²×C₁₇	C₂²	1	1	yes	characteristic
67	C₂²×Dic₃₄	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×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	C₂²×#3622	—	2	1	no	—
78	C₂×Dic₆₈	C₂×C₄	1	1	yes	characteristic
79	C₂×Dic₆₈	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	#10587562	—	2	1	no	—
85	#10587561	C₂×C₄	1	1	yes	characteristic
86	C₄×D₆₈	C₂³	1	1	yes	characteristic
87	#10587558	—	2	1	no	—
88	#10587556	C₂×C₄	1	1	yes	characteristic
89	C₄×Dic₃₄	—	2	1	no	—
90	C₄×Dic₃₄	—	2	1	no	—
91	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
92	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
93	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
94	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
95	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
96	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
99	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
100	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
103	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
104	C₄×C₈×C₁₇	—	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	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	C₂²⋊#3622	—	2	1	no	—
112	#10587492	C₂×C₄	1	1	yes	characteristic
113	#10587492	C₂×C₄	1	1	yes	characteristic
114	#10587491	—	2	1	no	—
115	#10587491	—	2	1	no	—
116	#10587489	C₂×C₄	1	1	yes	characteristic
117	#10587489	C₂×C₄	1	1	yes	characteristic
118	#10587488	C₂×C₄	1	1	yes	characteristic
119	#10587488	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	#10587487	C₂×C₄	1	1	yes	characteristic
126	#10587486	—	2	1	no	—
127	#10587486	—	2	1	no	—
128	#10587486	—	2	1	no	—
129	#10587485	—	2	1	no	—
130	#10587485	—	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	—	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	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	2	no	—
153	C₂×Dic₃₄	—	2	1	no	—
154	C₂×Dic₃₄	—	4	1	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	C₂×C₈×C₁₇	—	2	4	no	—
159	C₂×C₈×C₁₇	—	2	1	no	—
160	C₂×C₈×C₁₇	—	2	1	no	—
161	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₁₇	C₂×D₄	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	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₇	#41	1	1	yes	characteristic
172	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
173	C₂²⋊Dic₁₇	—	2	1	no	—
174	#63227	—	2	1	no	—
175	#63227	—	2	1	no	—
176	#63227	—	2	1	no	—
177	#63227	—	2	1	no	—
178	C₄⋊Dic₁₇	—	2	1	no	—
179	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
182	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
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	#63225	—	2	1	no	—
190	#63225	—	2	1	no	—
191	C₄×Dic₁₇	—	2	1	no	—
192	C₄×Dic₁₇	—	2	1	no	—
193	C₄×Dic₁₇	—	2	1	no	—
194	C₄×Dic₁₇	—	2	1	no	—
195	C₄×Dic₁₇	—	2	1	no	—
196	C₂×#3622	—	2	1	no	—
197	C₂×#3622	—	2	1	no	—
198	C₂×#3622	—	2	1	no	—
199	C₂×#3622	—	2	1	no	—
200	C₂×#3622	—	8	1	no	—
201	Dic₆₈	—	2	2	no	—
202	Dic₆₈	—	4	1	no	—
203	#63219	—	2	2	no	—
204	#63219	—	4	1	no	—
205	#63218	—	8	1	no	—
206	C₈×D₁₇	—	8	1	no	—
207	#18017	—	17	1	no	maximal, Sylow
208	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
209	C₂²×D₁₇	—	2	1	no	—
210	C₂×C₄×C₁₇	—	2	2	no	—
211	C₂×C₄×C₁₇	—	2	1	no	—
212	C₂×C₄×C₁₇	—	2	1	no	—
213	C₂×C₄×C₁₇	—	2	1	no	—
214	C₂×C₄×C₁₇	—	2	1	no	—
215	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
221	C₂²⋊D₁₇	—	4	2	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	—	4	2	no	—
230	C₂×Dic₁₇	—	4	2	no	—
231	D₆₈	—	2	1	no	—
232	D₆₈	—	2	1	no	—
233	C₄×D₁₇	—	4	1	no	—
234	C₄×D₁₇	—	4	1	no	—
235	Dic₃₄	—	2	1	no	—
236	Dic₃₄	—	2	1	no	—
237	Dic₃₄	—	2	1	no	—
238	Dic₃₄	—	2	1	no	—
239	Dic₃₄	—	2	1	no	—
240	Dic₃₄	—	4	2	no	—
241	Dic₃₄	#131	1	2	yes	—
242	C₈×C₁₇	—	2	2	no	—
243	C₈×C₁₇	—	2	2	no	—
244	C₈×C₁₇	—	2	1	no	—
245	C₈×C₁₇	—	2	1	no	—
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	#3622	—	4	1	no	—
253	#3622	—	4	1	no	—
254	#3622	—	4	1	no	—
255	#3622	—	4	1	no	—
256	#3108	—	17	1	no	—
257	#2994	—	17	1	no	—
258	#2984	—	17	1	no	—
259	#1591	—	17	1	no	—
260	#1590	—	17	1	no	—
261	#1588	—	17	1	no	—
262	#1587	—	17	1	no	—
263	#1587	—	17	1	no	—
264	#1585	—	17	1	no	—
265	C₈×Q₁₆	—	17	1	no	—
266	C₈×SD₁₆	—	17	1	no	—
267	#1573	—	17	1	no	—
268	#1494	—	17	1	no	—
269	C₂×Q₈⋊C₈	—	17	1	no	—
270	#1450	D₁₇	1	1	yes	characteristic, complemented
271	C₂²×C₁₇	—	2	1	no	—
272	C₂²×C₁₇	—	2	1	no	—
273	C₂²×C₁₇	#443	1	2	yes	—
274	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
275	C₂×D₁₇	—	4	1	no	—
276	C₂×D₁₇	—	4	1	no	—
277	C₂×D₁₇	—	4	1	no	—
278	C₄×C₁₇	—	2	1	no	—
279	C₄×C₁₇	—	2	1	no	—
280	C₄×C₁₇	—	2	1	no	—
281	C₄×C₁₇	—	2	1	no	—
282	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
283	C₄×C₁₇	#568	1	1	yes	characteristic
284	C₄×C₁₇	#577	1	1	yes	characteristic
285	C₄×C₁₇	#578	1	1	yes	characteristic
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	Dic₁₇	—	4	1	no	—
293	#529	—	17	1	no	—
294	C₂×C₄×Q₈	—	17	1	no	—
295	#483	—	17	1	no	—
296	#480	—	17	1	no	—
297	#479	—	17	1	no	—
298	#479	—	17	1	no	—
299	#464	—	17	1	no	—
300	#464	—	17	1	no	—
301	#451	—	17	1	no	—
302	#448	—	17	1	no	—
303	#446	—	17	1	no	—
304	#446	—	17	1	no	—
305	#446	—	17	1	no	—
306	#446	—	34	1	no	—
307	#446	—	34	1	no	—
308	C₈×Q₈	—	17	1	no	—
309	C₈×Q₈	—	17	1	no	—
310	C₈×Q₈	—	17	1	no	—
311	C₄×Q₁₆	—	17	1	no	—
312	C₄×Q₁₆	—	17	1	no	—
313	C₄×SD₁₆	—	17	1	no	—
314	C₄×SD₁₆	—	17	1	no	—
315	#436	—	17	1	no	—
316	#435	—	34	1	no	—
317	C₈×D₄	—	17	1	no	—
318	C₈×D₄	—	34	1	no	—
319	#433	—	34	1	no	—
320	#432	—	17	1	no	—
321	#432	—	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	C₂×C₄⋊C₈	—	17	1	no	—
327	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
328	#335	—	17	1	no	—
329	#335	—	17	1	no	—
330	#334	—	17	1	no	—
331	#334	—	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	Q₈⋊C₈	—	17	1	no	—
338	D₄⋊C₈	—	17	1	no	—
339	D₄⋊C₈	—	17	1	no	—
340	#322	C₂×D₁₇	1	1	yes	characteristic
341	#322	C₂×D₁₇	1	1	yes	characteristic
342	C₈²	C₂×D₁₇	1	1	yes	characteristic
343	C₈²	C₂×D₁₇	1	1	yes	characteristic
344	C₂×C₁₇	—	2	2	no	—
345	C₂×C₁₇	#2933	1	1	yes	characteristic
346	C₂×C₁₇	#2947	1	1	yes	characteristic
347	C₂×C₁₇	C₂×#443	1	1	yes	characteristic
348	D₁₇	—	8	1	no	—
349	C₂²×Q₈	—	17	1	no	—
350	C₂×Q₁₆	—	17	1	no	—
351	C₂×Q₁₆	—	17	1	no	—
352	C₂×SD₁₆	—	17	1	no	—
353	C₂×SD₁₆	—	17	1	no	—
354	C₂×M₁₆	—	34	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	34	1	no	—
357	C₂²×C₈	—	34	1	no	—
358	#126	—	34	1	no	—
359	#125	—	17	1	no	—
360	#124	—	17	1	no	—
361	#123	—	34	1	no	—
362	C₂²⋊Q₈	—	17	1	no	—
363	#121	—	17	1	no	—
364	C₄×Q₈	—	17	1	no	—
365	C₄×Q₈	—	17	1	no	—
366	C₄×Q₈	—	17	1	no	—
367	C₄×Q₈	—	17	1	no	—
368	C₄×Q₈	—	17	1	no	—
369	C₄×Q₈	—	34	1	no	—
370	C₄×Q₈	—	34	1	no	—
371	C₄×D₄	—	17	1	no	—
372	C₄×D₄	—	34	1	no	—
373	#117	—	34	1	no	—
374	C₂×C₄⋊C₄	—	17	1	no	—
375	C₂×C₄⋊C₄	—	34	1	no	—
376	C₂×C₄²	—	34	1	no	—
377	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
378	#107	—	17	1	no	—
379	#107	—	17	1	no	—
380	#106	—	17	1	no	—
381	#106	—	17	1	no	—
382	C₄⋊C₈	—	17	1	no	—
383	C₄⋊C₈	—	17	1	no	—
384	C₄⋊C₈	—	17	1	no	—
385	C₄⋊C₈	—	17	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	—	34	1	no	—
391	C₄⋊C₈	—	34	1	no	—
392	C₄⋊C₈	—	34	1	no	—
393	C₄⋊C₈	C₄×D₁₇	1	1	yes	characteristic
394	C₄⋊C₈	C₄×D₁₇	1	1	yes	characteristic
395	C₄⋊C₈	D₆₈	1	1	yes	characteristic
396	C₄⋊C₈	D₆₈	1	1	yes	characteristic
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	#103	—	17	1	no	—
403	#102	—	17	1	no	—
404	#102	—	17	1	no	—
405	C₂²⋊C₈	—	34	1	no	—
406	C₂²⋊C₈	—	34	1	no	—
407	C₂²⋊C₈	—	34	1	no	—
408	C₂²⋊C₈	C₄×D₁₇	1	1	yes	characteristic
409	C₂²⋊C₈	C₄×D₁₇	1	1	yes	characteristic
410	C₂²⋊C₈	D₆₈	1	1	yes	characteristic
411	C₂²⋊C₈	D₆₈	1	1	yes	characteristic
412	#97	—	34	1	no	—
413	#97	—	34	1	no	—
414	#97	—	34	1	no	—
415	#97	—	34	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	34	1	no	—
418	C₄×C₈	—	34	1	no	—
419	C₄×C₈	—	34	1	no	—
420	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
421	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
422	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
423	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
426	C₁₇	#18017	1	1	yes	characteristic, complemented, Sylow
427	C₂×Q₈	—	17	1	no	—
428	C₂×Q₈	—	17	1	no	—
429	C₂×Q₈	—	17	1	no	—
430	C₂×Q₈	—	34	2	no	—
431	C₂×Q₈	—	34	1	no	—
432	C₂×Q₈	—	68	1	no	—
433	C₂×D₄	—	17	1	no	—
434	C₂×D₄	—	34	1	no	—
435	C₂²×C₄	—	34	1	no	—
436	C₂²×C₄	—	34	1	no	—
437	C₂²×C₄	—	34	1	no	—
438	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
440	C₂²×C₄	#63252	1	1	yes	characteristic
441	Q₁₆	—	34	2	no	—
442	Q₁₆	—	68	1	no	—
443	SD₁₆	—	34	2	no	—
444	SD₁₆	—	68	1	no	—
445	M₁₆	—	136	1	no	—
446	C₂×C₈	—	2	4	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	34	1	no	—
450	C₂×C₈	—	34	1	no	—
451	C₂×C₈	—	34	1	no	—
452	C₂×C₈	—	34	1	no	—
453	C₂×C₈	—	136	1	no	—
454	C₂×C₈	—	136	1	no	—
455	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
456	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
457	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
458	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
459	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
460	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
461	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
462	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
463	C₄⋊C₄	—	17	1	no	—
464	C₄⋊C₄	—	17	1	no	—
465	C₄⋊C₄	—	17	1	no	—
466	C₄⋊C₄	—	17	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	C₄⋊C₄	—	34	1	no	—
475	C₄⋊C₄	—	34	1	no	—
476	C₂²⋊C₄	—	34	1	no	—
477	C₂²⋊C₄	—	34	1	no	—
478	C₂²⋊C₄	—	34	1	no	—
479	C₂²⋊C₄	—	34	1	no	—
480	C₂²⋊C₄	—	34	1	no	—
481	C₄²	—	34	1	no	—
482	C₄²	—	34	1	no	—
483	C₄²	—	34	1	no	—
484	C₄²	—	34	1	no	—
485	C₄²	—	34	1	no	—
486	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
487	C₄²	C₂×D₆₈	1	1	yes	characteristic
488	C₄²	#63252	1	1	yes	characteristic
489	C₄²	C₂³×D₁₇	1	1	yes	characteristic
490	C₂³	—	34	1	no	—
491	C₂³	C₄×D₆₈	1	1	yes	characteristic
492	Q₈	—	17	2	no	—
493	Q₈	—	34	1	no	—
494	Q₈	—	34	1	no	—
495	Q₈	—	34	1	no	—
496	Q₈	—	34	1	no	—
497	Q₈	—	34	1	no	—
498	Q₈	—	68	2	no	—
499	D₄	—	34	1	no	—
500	D₄	—	34	1	no	—
501	D₄	—	68	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	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	—	34	1	no	—
514	C₂×C₄	—	68	2	no	—
515	C₂×C₄	—	68	2	no	—
516	C₂×C₄	—	68	1	no	—
517	C₂×C₄	—	68	1	no	—
518	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
519	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
520	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
521	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
523	C₂×C₄	C₂×#63252	1	1	yes	characteristic
524	C₈	—	2	2	no	—
525	C₈	—	2	2	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	68	1	no	—
535	C₈	—	68	1	no	—
536	C₈	—	68	1	no	—
537	C₈	—	68	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	68	1	no	—
541	C₂²	—	68	1	no	—
542	C₂²	—	68	1	no	—
543	C₂²	#11762927	1	2	yes	—
544	C₂²	C₂×C₄×D₆₈	1	1	yes	characteristic
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	34	2	no	—
550	C₄	—	68	1	no	—
551	C₄	—	68	1	no	—
552	C₄	—	68	1	no	—
553	C₄	—	68	1	no	—
554	C₄	—	68	1	no	—
555	C₄	—	68	1	no	—
556	C₄	#131×D₁₇	1	1	yes	characteristic
557	C₄	#11763574	1	1	yes	characteristic
558	C₄	#11763621	1	1	yes	characteristic
559	C₄	#11763626	1	1	yes	characteristic
560	C₂	—	2	2	no	—
561	C₂	—	136	1	no	—
562	C₂	#14537512	1	1	yes	characteristic
563	C₂	#14537629	1	1	yes	characteristic
564	C₂	C₂×#11762927	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₆₈
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×#1450	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#10587616	C₂×C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1450	D₁₇
hypocenter	C₁₇	#18017
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1450

Complements

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

N	H ≅ G/N	type
3. #14537871	C₂	semidirect
4. #14527682	C₂	semidirect
5. #14527676	C₂	semidirect
6. #14527664	C₂	semidirect
7. #14527657	C₂	semidirect
8. #14527657	C₂	semidirect
9. #14527643	C₂	semidirect
10. C₈×Dic₆₈	C₂	semidirect
11. C₈×#63219	C₂	semidirect
12. #14527569	C₂	semidirect
14. C₂×#11762541	C₂	semidirect
15. C₁₇×#1450	C₂	semidirect
270. #1450	D₁₇	semidirect
426. C₁₇	#18017	semidirect

Maximal subgroups

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

subgroup	index
#14538866	2
#14537946	2
#14537871	2
#14527682	2
#14527676	2
#14527664	2
#14527657	2
#14527643	2
C₈×Dic₆₈	2
C₈×#63219	2
#14527569	2
#14527245	2
C₂×#11762541	2
C₁₇×#1450	2
#18017	17