Subgroups — #17004358

Order 4352.

624 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538849	C₂	1	1	yes	maximal, characteristic
2	C₈×#63252	C₂	1	1	yes	maximal, characteristic
3	#14527632	C₂	1	2	yes	maximal, complemented
4	#14527618	C₂	1	2	yes	maximal, complemented
5	#14527601	C₂	1	2	yes	maximal, complemented
6	#14527594	C₂	1	2	yes	maximal, complemented
7	#14527575	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527221	C₂	1	1	yes	maximal, characteristic
9	#14527205	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527073	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#63252	C₂²	1	1	yes	characteristic
13	#11763147	C₄	1	2	yes	—
14	#11763091	C₄	1	1	yes	characteristic
15	#11763086	C₄	1	1	yes	characteristic
16	#11763016	C₄	1	1	yes	characteristic
17	#11763011	C₄	1	1	yes	characteristic
18	#11762969	C₄	1	2	yes	—
19	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
20	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
21	C₄×#63231	C₂²	1	2	yes	—
22	C₄×#63230	C₂²	1	2	yes	—
23	C₈×D₆₈	C₂²	1	1	yes	characteristic
24	C₈×D₆₈	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₁₇	—	2	1	no	—
26	C₈×C₂²⋊D₁₇	—	2	1	no	—
27	#11762862	C₂²	1	1	yes	characteristic
28	#11762862	C₂²	1	1	yes	characteristic
29	#11762860	—	2	1	no	—
30	C₄×#63223	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₁₇	—	2	1	no	—
32	#11762561	C₂²	1	2	yes	—
33	#11762559	C₂²	1	2	yes	—
34	Q₈⋊#3622	C₂²	1	2	yes	—
35	Q₈⋊#3622	C₂²	1	2	yes	—
36	#11762539	C₂²	1	2	yes	—
37	#11762536	C₂²	1	2	yes	—
38	#11762531	C₂²	1	2	yes	—
39	#11762530	C₂²	1	2	yes	—
40	C₁₇×#533	C₂²	1	1	yes	characteristic
41	C₁₇×#446	—	2	1	no	—
42	C₁₇×#446	C₂²	1	2	yes	—
43	C₈×Q₈×C₁₇	—	2	1	no	—
44	C₈×Q₈×C₁₇	C₂²	1	2	yes	—
45	C₁₇×#424	—	2	1	no	—
46	C₁₇×#423	C₂²	1	1	yes	characteristic
47	C₁₇×#405	—	2	1	no	—
48	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
49	C₂×#63252	C₂×C₄	1	1	yes	characteristic
50	C₂×M₁₆×C₁₇	—	2	1	no	—
51	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
53	C₁₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₁₇×#125	—	2	1	no	—
56	C₁₇×C₂²⋊Q₈	—	2	1	no	—
57	C₁₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
58	C₄×Q₈×C₁₇	—	2	1	no	—
59	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
60	C₁₇×#117	—	2	1	no	—
61	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
62	C₂×#63231	C₂×C₄	1	2	yes	—
63	C₂×#63230	C₂×C₄	1	2	yes	—
64	C₄×C₂²⋊D₁₇	—	2	1	no	—
65	C₄×C₂²⋊D₁₇	—	2	1	no	—
66	#10587612	C₂×C₄	1	1	yes	characteristic
67	C₂×#63223	—	2	1	no	—
68	C₂×C₈×D₁₇	—	2	1	no	—
69	C₂×C₈×D₁₇	—	2	1	no	—
70	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
71	C₄×D₆₈	C₂³	1	1	yes	characteristic
72	#10587558	—	2	1	no	—
73	C₄²×D₁₇	—	2	1	no	—
74	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
76	C₁₇×C₄⋊C₈	—	2	2	no	—
77	C₁₇×C₄⋊C₈	—	2	2	no	—
78	C₁₇×C₄⋊C₈	—	2	1	no	—
79	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₇×#97	—	2	2	no	—
81	C₄×C₈×C₁₇	—	2	2	no	—
82	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
86	#10587506	C₂×C₄	1	2	yes	—
87	#10587506	C₂×C₄	1	2	yes	—
88	C₂²⋊#3622	—	2	1	no	—
89	C₂²⋊#3622	C₂×C₄	1	2	yes	—
90	#10587491	—	2	1	no	—
91	#10587491	—	2	1	no	—
92	#10587485	—	2	1	no	—
93	#10587485	—	2	1	no	—
94	C₈×Dic₁₇	—	2	1	no	—
95	C₈×Dic₁₇	—	2	1	no	—
96	#10587481	C₂×C₄	1	2	yes	—
97	#10587480	C₂×C₄	1	2	yes	—
98	#10587479	C₂×C₄	1	2	yes	—
99	#10587478	C₂×C₄	1	2	yes	—
100	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
101	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
102	C₄⋊#3622	C₂³	1	1	yes	characteristic
103	C₄⋊#3622	C₂³	1	1	yes	characteristic
104	#10587474	—	2	1	no	—
105	C₄×#3622	—	2	1	no	—
106	C₄×#3622	C₂³	1	2	yes	—
107	C₄×#3622	C₂³	1	2	yes	—
108	C₂×Q₈×C₁₇	—	2	1	no	—
109	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₁₇	—	2	1	no	—
114	#63252	—	2	2	no	—
115	#63252	—	2	2	no	—
116	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₇	—	2	1	no	—
118	C₂×C₄×D₁₇	—	2	1	no	—
119	C₂×C₄×D₁₇	—	2	1	no	—
120	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
121	M₁₆×C₁₇	—	4	2	no	—
122	C₂×C₈×C₁₇	—	2	2	no	—
123	C₂×C₈×C₁₇	—	2	2	no	—
124	C₂×C₈×C₁₇	—	4	1	no	—
125	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
129	C₄⋊C₄×C₁₇	—	2	1	no	—
130	C₄⋊C₄×C₁₇	—	2	2	no	—
131	C₄⋊C₄×C₁₇	—	2	1	no	—
132	C₄⋊C₄×C₁₇	—	2	1	no	—
133	C₄⋊C₄×C₁₇	—	2	2	no	—
134	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
135	C₂²⋊C₄×C₁₇	—	2	2	no	—
136	C₄²×C₁₇	—	2	2	no	—
137	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₇	#41	1	1	yes	characteristic
140	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
141	C₂²⋊Dic₁₇	—	2	1	no	—
142	#63231	—	2	4	no	—
143	#63230	—	2	4	no	—
144	#63227	—	2	1	no	—
145	#63227	—	2	1	no	—
146	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
148	#63225	—	2	1	no	—
149	#63225	—	2	1	no	—
150	C₄×Dic₁₇	—	2	1	no	—
151	C₄×Dic₁₇	—	2	1	no	—
152	C₄×Dic₁₇	—	2	1	no	—
153	#63223	—	4	2	no	—
154	C₂×#3622	—	2	1	no	—
155	C₂×#3622	—	2	1	no	—
156	C₂×#3622	—	2	2	no	—
157	C₂×#3622	C₂²×C₄	1	2	yes	—
158	C₂×#3622	C₂²×C₄	1	2	yes	—
159	C₈×D₁₇	—	4	2	no	—
160	C₈×D₁₇	—	4	2	no	—
161	#17916	—	17	1	no	maximal, Sylow
162	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
163	C₂²×D₁₇	—	2	1	no	—
164	Q₈×C₁₇	—	2	2	no	—
165	Q₈×C₁₇	—	2	2	no	—
166	Q₈×C₁₇	—	4	2	no	—
167	C₂×C₄×C₁₇	—	2	1	no	—
168	C₂×C₄×C₁₇	—	2	1	no	—
169	C₂×C₄×C₁₇	—	2	1	no	—
170	C₂×C₄×C₁₇	—	2	1	no	—
171	C₂×C₄×C₁₇	—	2	2	no	—
172	C₂×C₄×C₁₇	—	2	2	no	—
173	C₂×C₄×C₁₇	—	2	2	no	—
174	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₁₇	—	2	4	no	—
181	C₂×Dic₁₇	—	2	1	no	—
182	C₂×Dic₁₇	—	2	1	no	—
183	C₂×Dic₁₇	—	2	1	no	—
184	D₆₈	—	2	1	no	—
185	D₆₈	#131	1	2	yes	—
186	C₄×D₁₇	—	2	4	no	—
187	C₄×D₁₇	—	4	1	no	—
188	C₄×D₁₇	—	4	1	no	—
189	C₄×D₁₇	—	4	2	no	—
190	Dic₃₄	—	2	1	no	—
191	Dic₃₄	#131	1	2	yes	—
192	C₈×C₁₇	—	2	1	no	—
193	C₈×C₁₇	—	2	1	no	—
194	C₈×C₁₇	—	2	1	no	—
195	C₈×C₁₇	—	4	2	no	—
196	C₈×C₁₇	#137	1	2	yes	—
197	#3622	—	2	2	no	—
198	#3622	—	2	2	no	—
199	#3622	—	4	2	no	—
200	#3622	—	4	1	no	—
201	#3622	—	4	1	no	—
202	#3107	—	17	1	no	—
203	C₈×#41	—	17	1	no	—
204	#2960	D₁₇	1	1	yes	characteristic, complemented
205	#1584	—	17	2	no	—
206	#1582	—	17	2	no	—
207	#1579	—	17	2	no	—
208	SD₁₆⋊C₈	—	17	2	no	—
209	#1574	—	17	1	no	—
210	#1489	—	17	1	no	—
211	#1485	—	17	1	no	—
212	#1451	—	17	1	no	—
213	C₂²×C₁₇	—	2	1	no	—
214	C₂²×C₁₇	—	2	1	no	—
215	C₂²×C₁₇	—	2	1	no	—
216	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
217	C₂×D₁₇	—	2	2	no	—
218	C₂×D₁₇	—	4	1	no	—
219	C₂×D₁₇	—	4	1	no	—
220	C₄×C₁₇	—	2	1	no	—
221	C₄×C₁₇	—	2	1	no	—
222	C₄×C₁₇	—	2	1	no	—
223	C₄×C₁₇	—	4	2	no	—
224	C₄×C₁₇	—	4	2	no	—
225	C₄×C₁₇	#444	1	2	yes	—
226	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
227	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
228	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
229	C₄×C₁₇	#575	1	1	yes	characteristic
230	Dic₁₇	—	2	2	no	—
231	Dic₁₇	—	4	1	no	—
232	Dic₁₇	—	4	1	no	—
233	#533	C₂×D₁₇	1	1	yes	characteristic
234	C₄×#41	—	17	1	no	—
235	#485	—	17	2	no	—
236	#475	—	17	1	no	—
237	#474	—	17	1	no	—
238	#462	—	17	1	no	—
239	#461	—	17	1	no	—
240	#452	—	17	2	no	—
241	#446	—	2	1	no	—
242	#446	C₂×D₁₇	1	2	yes	—
243	C₈×Q₈	—	2	1	no	—
244	C₈×Q₈	—	17	1	no	—
245	C₈×Q₈	—	17	1	no	—
246	C₈×Q₈	C₂×D₁₇	1	2	yes	—
247	C₄×Q₁₆	—	17	2	no	—
248	C₄×SD₁₆	—	17	2	no	—
249	C₈×D₄	—	17	1	no	—
250	C₈×D₄	—	17	1	no	—
251	C₈×D₄	—	34	1	no	—
252	C₈×D₄	—	34	1	no	—
253	#431	—	17	1	no	—
254	#431	—	17	1	no	—
255	#431	—	34	1	no	—
256	#424	—	2	1	no	—
257	#423	C₂×D₁₇	1	1	yes	characteristic
258	#405	—	2	1	no	—
259	C₄×M₁₆	—	17	1	no	—
260	C₂×C₄×C₈	—	34	1	no	—
261	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
262	#335	—	17	2	no	—
263	#334	—	17	2	no	—
264	Q₈⋊C₈	—	17	2	no	—
265	Q₈⋊C₈	—	17	2	no	—
266	Q₈⋊C₈	—	17	2	no	—
267	D₄⋊C₈	—	17	2	no	—
268	#322	—	17	2	no	—
269	#322	—	17	2	no	—
270	C₂×C₁₇	—	4	1	no	—
271	C₂×C₁₇	#2929	1	1	yes	characteristic
272	C₂×C₁₇	C₄×#137	1	1	yes	characteristic
273	C₂×C₁₇	C₂×#444	1	1	yes	characteristic
274	D₁₇	—	4	2	no	—
275	C₂×#41	—	17	1	no	—
276	C₂×Q₁₆	—	17	2	no	—
277	C₂×SD₁₆	—	17	2	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	34	1	no	—
280	C₂²×C₈	—	34	1	no	—
281	C₂²×C₈	—	34	1	no	—
282	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
283	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
284	C₄⋊Q₈	C₄×D₁₇	1	1	yes	characteristic
285	C₄⋊Q₈	C₄×D₁₇	1	1	yes	characteristic
286	#125	—	2	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	C₂²⋊Q₈	C₄×D₁₇	1	2	yes	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	17	1	no	—
291	C₄×Q₈	—	17	1	no	—
292	C₄×Q₈	C₂²×D₁₇	1	2	yes	—
293	C₄×D₄	—	17	1	no	—
294	C₄×D₄	—	17	1	no	—
295	C₄×D₄	—	34	1	no	—
296	C₄×D₄	—	34	1	no	—
297	#117	—	2	1	no	—
298	#117	—	17	1	no	—
299	#117	—	34	1	no	—
300	C₂×C₄²	—	34	1	no	—
301	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
302	#107	—	17	2	no	—
303	#106	—	17	2	no	—
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	17	1	no	—
308	C₄⋊C₈	—	17	1	no	—
309	C₄⋊C₈	—	17	1	no	—
310	C₄⋊C₈	—	17	1	no	—
311	C₄⋊C₈	—	34	1	no	—
312	C₄⋊C₈	—	34	1	no	—
313	C₄⋊C₈	C₂²×D₁₇	1	2	yes	—
314	#103	—	17	2	no	—
315	#103	—	17	2	no	—
316	#103	—	17	2	no	—
317	#102	—	17	2	no	—
318	C₂²⋊C₈	—	17	2	no	—
319	C₂²⋊C₈	—	34	1	no	—
320	C₂²⋊C₈	—	34	1	no	—
321	C₂²⋊C₈	—	34	1	no	—
322	#97	—	2	2	no	—
323	#97	—	34	1	no	—
324	C₄×C₈	—	2	2	no	—
325	C₄×C₈	—	17	2	no	—
326	C₄×C₈	—	17	2	no	—
327	C₄×C₈	—	34	1	no	—
328	C₄×C₈	—	34	1	no	—
329	C₄×C₈	—	34	1	no	—
330	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
331	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
332	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
334	C₁₇	#17916	1	1	yes	characteristic, complemented, Sylow
335	#41	—	34	2	no	—
336	#41	—	34	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	17	1	no	—
339	C₂×Q₈	C₂×C₄×D₁₇	1	2	yes	—
340	C₂×D₄	—	17	1	no	—
341	C₂×D₄	—	34	1	no	—
342	C₂²×C₄	—	34	1	no	—
343	C₂²×C₄	—	34	1	no	—
344	C₂²×C₄	—	34	1	no	—
345	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
346	C₂²×C₄	#63252	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
348	Q₁₆	—	34	4	no	—
349	SD₁₆	—	34	4	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	—	68	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	17	2	no	—
356	C₂×C₈	—	17	2	no	—
357	C₂×C₈	—	34	2	no	—
358	C₂×C₈	—	34	1	no	—
359	C₂×C₈	—	34	1	no	—
360	C₂×C₈	—	68	2	no	—
361	C₂×C₈	—	68	2	no	—
362	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
363	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
364	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
365	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	17	1	no	—
372	C₄⋊C₄	—	17	1	no	—
373	C₄⋊C₄	—	34	1	no	—
374	C₄⋊C₄	—	34	1	no	—
375	C₄⋊C₄	C₂×C₄×D₁₇	1	2	yes	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	34	1	no	—
378	C₂²⋊C₄	—	34	1	no	—
379	C₂²⋊C₄	—	34	1	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	34	1	no	—
382	C₄²	—	34	1	no	—
383	C₄²	—	34	1	no	—
384	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
385	C₄²	#63252	1	1	yes	characteristic
386	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
387	C₄²	C₂³×D₁₇	1	1	yes	characteristic
388	C₂³	—	34	1	no	—
389	C₂³	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	17	2	no	—
394	Q₈	—	34	1	no	—
395	D₄	—	17	2	no	—
396	D₄	—	34	4	no	—
397	D₄	—	34	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	34	4	no	—
406	C₂×C₄	—	34	1	no	—
407	C₂×C₄	—	34	1	no	—
408	C₂×C₄	—	34	1	no	—
409	C₂×C₄	—	68	1	no	—
410	C₂×C₄	—	68	1	no	—
411	C₂×C₄	—	68	2	no	—
412	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
413	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
414	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
416	C₂×C₄	C₂×#63252	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	34	2	no	—
423	C₈	—	34	2	no	—
424	C₈	—	68	2	no	—
425	C₈	—	68	1	no	—
426	C₈	—	68	1	no	—
427	C₈	#10587628	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	34	2	no	—
432	C₂²	—	68	1	no	—
433	C₂²	—	68	1	no	—
434	C₂²	C₂×C₄×C₂²⋊D₁₇	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	34	2	no	—
441	C₄	—	68	1	no	—
442	C₄	—	68	1	no	—
443	C₄	#11762929	1	2	yes	—
444	C₄	#131×D₁₇	1	1	yes	characteristic
445	C₄	#131×D₁₇	1	1	yes	characteristic
446	C₄	C₂×#10587628	1	1	yes	characteristic
447	C₄	#11763607	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	68	2	no	—
450	C₂	#14537476	1	1	yes	characteristic
451	C₂	C₄×#10587628	1	1	yes	characteristic
452	C₂	C₂×#11762929	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×#2960	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂×#63252	C₂×C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#2960	D₁₇
hypocenter	C₁₇	#17916
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #14527632	C₂	semidirect
4. #14527618	C₂	semidirect
5. #14527601	C₂	semidirect
6. #14527594	C₂	semidirect
7. #14527575	C₂	semidirect
9. #14527205	C₂	semidirect
10. #14527073	C₂	semidirect
11. C₁₇×#2960	C₂	semidirect
204. #2960	D₁₇	semidirect
334. C₁₇	#17916	semidirect

Maximal subgroups

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

subgroup	index
#14538849	2
C₈×#63252	2
#14527632	2
#14527618	2
#14527601	2
#14527594	2
#14527575	2
#14527221	2
#14527205	2
#14527073	2
C₁₇×#2960	2
#17916	17