Subgroups — C₈×#10587635 #17003736

Order 4352.

802 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10587635	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#14527606	C₂	1	2	yes	maximal, complemented
4	#14527594	C₂	1	2	yes	maximal, complemented
5	C₈×#63230	C₂	1	2	yes	maximal, complemented
6	C₈×#63228	C₂	1	2	yes	maximal, complemented
7	#14527537	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527174	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527171	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#63223	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10587635	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₁₇	—	2	1	no	—
14	C₂×C₄×D₆₈	C₂²	1	1	yes	characteristic
15	#11762919	C₄	1	2	yes	—
16	#11762907	C₄	1	2	yes	—
17	C₄×#63230	C₂²	1	2	yes	—
18	C₄×#63228	C₂²	1	2	yes	—
19	C₈×D₆₈	—	2	1	no	—
20	C₈×D₆₈	—	2	1	no	—
21	C₈×D₆₈	C₂²	1	2	yes	—
22	C₈×D₆₈	C₂²	1	2	yes	—
23	#11762862	C₂²	1	1	yes	characteristic
24	#11762852	C₄	1	1	yes	characteristic
25	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
26	#11762813	C₄	1	1	yes	characteristic
27	#11762810	C₄	1	1	yes	characteristic
28	C₂×#10587491	—	2	1	no	—
29	C₄×#63223	C₂²	1	1	yes	characteristic
30	#11762561	C₂²	1	2	yes	complemented
31	#11762559	C₂²	1	2	yes	complemented
32	Q₈⋊#3622	C₂²	1	2	yes	complemented
33	D₄⋊#3622	C₂²	1	2	yes	complemented
34	#11762536	C₂²	1	2	yes	—
35	#11762536	C₂²	1	2	yes	—
36	#11762531	C₂²	1	2	yes	complemented
37	C₈×#3622	C₂²	1	2	yes	complemented
38	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
39	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
40	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
41	C₈×D₄×C₁₇	—	2	1	no	—
42	C₈×D₄×C₁₇	—	2	1	no	—
43	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
44	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
45	C₁₇×#431	—	2	1	no	—
46	C₁₇×#431	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₁₇	—	2	1	no	—
48	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
49	C₂×#41×C₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₆₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₁₇	—	2	1	no	—
52	C₂²×C₈×C₁₇	—	2	1	no	—
53	C₂²×C₈×C₁₇	—	2	1	no	—
54	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
56	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
57	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
58	C₄×D₄×C₁₇	—	2	1	no	—
59	C₄×D₄×C₁₇	—	2	1	no	—
60	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
61	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
62	C₁₇×#117	—	2	1	no	—
63	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₇	—	2	1	no	—
65	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
66	#10587635	C₈	1	8	yes	direct product factor
67	C₂×#63230	C₂×C₄	1	2	yes	—
68	C₂×#63228	C₂×C₄	1	2	yes	—
69	C₂×#63227	—	2	1	no	—
70	C₂×C₄⋊Dic₁₇	C₂×C₄	1	1	yes	characteristic
71	C₂×#63223	C₂×C₄	1	1	yes	characteristic
72	C₂×#63223	C₂×C₄	1	1	yes	characteristic
73	C₂²×#3622	—	2	1	no	—
74	C₂×C₈×D₁₇	—	2	2	no	—
75	C₂×C₈×D₁₇	—	2	2	no	—
76	C₂×C₈×D₁₇	—	4	4	no	—
77	C₄×D₆₈	—	2	1	no	—
78	C₄×D₆₈	—	2	1	no	—
79	C₄×D₆₈	C₂×C₄	1	2	yes	—
80	C₄×D₆₈	C₂³	1	2	yes	—
81	C₁₇×C₄⋊C₈	—	2	1	no	—
82	C₁₇×C₄⋊C₈	—	2	1	no	—
83	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₇×C₂²⋊C₈	—	2	1	no	—
86	C₁₇×C₂²⋊C₈	—	2	1	no	—
87	C₁₇×C₂²⋊C₈	—	2	1	no	—
88	C₄×C₈×C₁₇	—	2	1	no	—
89	C₄×C₈×C₁₇	—	2	1	no	—
90	C₄×C₈×C₁₇	—	2	1	no	—
91	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
92	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
93	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
95	#10587506	C₂×C₄	1	2	yes	—
96	#10587503	C₂×C₄	1	2	yes	—
97	C₂²⋊#3622	—	2	1	no	—
98	#10587491	—	2	2	no	—
99	#10587491	—	2	2	no	—
100	#10587480	C₂×C₄	1	2	yes	—
101	#10587480	C₂×C₄	1	2	yes	—
102	#10587479	C₂×C₄	1	2	yes	—
103	#10587478	C₂×C₄	1	2	yes	—
104	C₄⋊#3622	—	2	1	no	—
105	C₄⋊#3622	—	2	1	no	—
106	C₄⋊#3622	C₂³	1	2	yes	—
107	#10587474	C₂×C₄	1	2	yes	—
108	C₄×#3622	C₂³	1	2	yes	—
109	C₄×#3622	C₂³	1	2	yes	—
110	C₂³×D₁₇	—	2	1	no	—
111	#41×C₁₇	—	2	2	no	—
112	#41×C₁₇	C₂×C₈	1	4	yes	complemented
113	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₁₇	—	2	1	no	—
115	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₇	—	2	1	no	—
117	C₂²×C₄×C₁₇	—	2	1	no	—
118	C₂²×C₄×C₁₇	—	2	1	no	—
119	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
122	C₂²×Dic₁₇	—	2	1	no	—
123	C₂×D₆₈	—	2	1	no	—
124	C₂×D₆₈	—	2	2	no	—
125	C₂×D₆₈	C₂×C₈	1	4	yes	complemented
126	C₂×D₆₈	C₂²×C₄	1	2	yes	—
127	C₂×C₄×D₁₇	—	2	2	no	—
128	C₂×C₄×D₁₇	—	2	2	no	—
129	C₂×C₄×D₁₇	—	4	2	no	—
130	C₂×C₄×D₁₇	—	4	2	no	—
131	C₂×C₈×C₁₇	—	2	2	no	—
132	C₂×C₈×C₁₇	—	2	1	no	—
133	C₂×C₈×C₁₇	—	2	1	no	—
134	C₂×C₈×C₁₇	—	4	1	no	—
135	C₂×C₈×C₁₇	—	4	2	no	—
136	C₂×C₈×C₁₇	—	4	2	no	—
137	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₁₇	—	2	1	no	—
142	C₄⋊C₄×C₁₇	—	2	1	no	—
143	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
144	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²⋊C₄×C₁₇	—	2	1	no	—
146	C₂²⋊C₄×C₁₇	—	2	1	no	—
147	C₂²⋊C₄×C₁₇	—	2	1	no	—
148	C₄²×C₁₇	—	2	1	no	—
149	C₄²×C₁₇	—	2	1	no	—
150	C₄²×C₁₇	—	2	1	no	—
151	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₇	#41	1	1	yes	characteristic
154	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
155	#63230	C₂×C₈	1	8	yes	complemented
156	#63228	C₂×C₈	1	8	yes	complemented
157	#63227	—	2	2	no	—
158	#63227	—	2	2	no	—
159	C₄⋊Dic₁₇	—	2	1	no	—
160	C₄⋊Dic₁₇	C₂²×C₄	1	2	yes	—
161	#63223	—	2	2	no	—
162	#63223	C₂×C₈	1	4	yes	complemented
163	C₂×#3622	—	2	2	no	—
164	C₂×#3622	—	2	2	no	—
165	C₂×#3622	—	4	2	no	—
166	C₂×#3622	C₂²×C₄	1	2	yes	—
167	C₂×#3622	C₂²×C₄	1	2	yes	—
168	C₈×D₁₇	—	4	4	no	—
169	C₈×D₁₇	—	4	4	no	—
170	C₈×AGL(1,ℤ/8)	—	17	1	no	maximal, Sylow
171	C₂³×C₁₇	—	2	1	no	—
172	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
173	C₂²×D₁₇	—	2	2	no	—
174	C₂²×D₁₇	—	2	4	no	—
175	C₂²×D₁₇	—	4	2	no	—
176	C₂²×D₁₇	—	4	2	no	—
177	Q₈×C₁₇	—	2	1	no	—
178	Q₈×C₁₇	C₂²×C₈	1	2	yes	complemented
179	D₄×C₁₇	—	2	4	no	—
180	D₄×C₁₇	—	2	1	no	—
181	D₄×C₁₇	C₂²×C₈	1	2	yes	complemented
182	C₂×C₄×C₁₇	—	2	1	no	—
183	C₂×C₄×C₁₇	—	2	1	no	—
184	C₂×C₄×C₁₇	—	2	1	no	—
185	C₂×C₄×C₁₇	—	2	4	no	—
186	C₂×C₄×C₁₇	—	2	1	no	—
187	C₂×C₄×C₁₇	—	2	1	no	—
188	C₂×C₄×C₁₇	—	4	1	no	—
189	C₂×C₄×C₁₇	—	4	2	no	—
190	C₂×C₄×C₁₇	—	4	1	no	—
191	C₂×C₄×C₁₇	—	4	1	no	—
192	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
196	C₂×C₄×C₁₇	#131	1	2	yes	—
197	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
200	C₂×Dic₁₇	—	2	2	no	—
201	C₂×Dic₁₇	—	4	2	no	—
202	D₆₈	—	2	2	no	—
203	D₆₈	—	2	4	no	—
204	D₆₈	C₂²×C₈	1	4	yes	—
205	C₄×D₁₇	—	4	4	no	—
206	C₄×D₁₇	—	4	2	no	—
207	C₄×D₁₇	—	4	2	no	—
208	C₈×C₁₇	—	2	1	no	—
209	C₈×C₁₇	—	2	1	no	—
210	C₈×C₁₇	—	2	1	no	—
211	C₈×C₁₇	—	4	1	no	—
212	C₈×C₁₇	—	4	1	no	—
213	C₈×C₁₇	AGL(1,ℤ/8)	1	2	yes	complemented
214	#3622	—	2	2	no	—
215	#3622	—	4	2	no	—
216	#3622	—	4	2	no	—
217	#3622	C₂²×C₈	1	4	yes	complemented
218	C₈×#41	D₁₇	1	1	yes	characteristic, complemented
219	C₄×AGL(1,ℤ/8)	—	17	1	no	—
220	C₂×C₈×D₄	—	17	1	no	—
221	#1580	—	17	2	no	—
222	SD₁₆⋊C₈	—	17	2	no	—
223	C₈×SD₁₆	—	17	2	no	—
224	C₈×D₈	—	17	2	no	—
225	#1565	—	17	1	no	—
226	#1478	—	17	1	no	—
227	#1477	—	17	1	no	—
228	C₈×M₁₆	—	17	1	no	—
229	C₂²×C₁₇	—	2	1	no	—
230	C₂²×C₁₇	—	2	1	no	—
231	C₂²×C₁₇	—	2	2	no	—
232	C₂²×C₁₇	—	4	1	no	—
233	C₂²×C₁₇	—	4	1	no	—
234	C₂²×C₁₇	C₈×D₄	1	2	yes	—
235	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
236	C₂×D₁₇	—	2	4	no	—
237	C₂×D₁₇	—	4	8	no	—
238	C₂×D₁₇	—	4	2	no	—
239	C₂×D₁₇	—	4	2	no	—
240	C₄×C₁₇	—	2	2	no	—
241	C₄×C₁₇	—	2	1	no	—
242	C₄×C₁₇	—	2	1	no	—
243	C₄×C₁₇	—	2	1	no	—
244	C₄×C₁₇	—	4	1	no	—
245	C₄×C₁₇	—	4	1	no	—
246	C₄×C₁₇	C₈×D₄	1	2	yes	—
247	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
248	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
249	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₄×C₁₇	#575	1	1	yes	characteristic
251	Dic₁₇	—	4	2	no	—
252	C₂×AGL(1,ℤ/8)	—	17	1	no	—
253	C₂³×C₈	—	34	1	no	—
254	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
255	C₂×C₄×D₄	—	17	1	no	—
256	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
257	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
258	#442	—	17	2	no	—
259	#440	—	17	2	no	—
260	C₄×SD₁₆	—	17	2	no	—
261	C₄×D₈	—	17	2	no	—
262	C₈×D₄	—	2	1	no	—
263	C₈×D₄	—	2	1	no	—
264	C₈×D₄	—	17	2	no	—
265	C₈×D₄	—	17	2	no	—
266	C₈×D₄	—	34	1	no	—
267	C₈×D₄	—	34	1	no	—
268	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
269	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
270	#431	—	2	1	no	—
271	#431	—	17	1	no	—
272	#431	C₂×D₁₇	1	1	yes	characteristic
273	#428	—	17	1	no	—
274	C₂×C₄⋊C₈	—	17	1	no	—
275	#418	—	17	1	no	—
276	#417	—	17	1	no	—
277	C₂×C₂²⋊C₈	—	34	1	no	—
278	C₄×M₁₆	—	17	1	no	—
279	C₂×C₄×C₈	—	2	1	no	—
280	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
281	#335	—	17	2	no	—
282	#334	—	17	2	no	—
283	Q₈⋊C₈	—	17	2	no	—
284	D₄⋊C₈	—	17	2	no	—
285	D₄⋊C₈	—	17	2	no	—
286	D₄⋊C₈	—	17	2	no	—
287	#322	—	17	2	no	—
288	C₈²	—	17	2	no	—
289	C₂×C₁₇	—	2	2	no	—
290	C₂×C₁₇	—	4	2	no	—
291	C₂×C₁₇	C₂×C₈×D₄	1	1	yes	characteristic
292	C₂×C₁₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
293	C₂×C₁₇	#2955	1	1	yes	characteristic
294	D₁₇	—	4	4	no	—
295	C₂×#41	C₄×D₁₇	1	1	yes	characteristic
296	C₂²×D₄	—	17	1	no	—
297	C₂³×C₄	—	34	1	no	—
298	AGL(1,ℤ/8)	—	17	8	no	—
299	C₂×SD₁₆	—	17	2	no	—
300	C₂×D₈	—	17	2	no	—
301	C₂×M₁₆	—	17	1	no	—
302	C₂×M₁₆	—	17	1	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	34	1	no	—
306	C₂²×C₈	—	34	2	no	—
307	C₂²×C₈	—	34	2	no	—
308	C₂²×C₈	—	68	4	no	—
309	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
310	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
311	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
312	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	17	2	no	—
316	C₄×D₄	—	17	2	no	—
317	C₄×D₄	—	34	1	no	—
318	C₄×D₄	—	34	1	no	—
319	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
320	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
321	#117	—	2	1	no	—
322	#117	C₄×D₁₇	1	1	yes	characteristic
323	C₂×C₄⋊C₄	—	17	1	no	—
324	C₂×C₂²⋊C₄	—	34	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
327	#107	—	17	2	no	—
328	#106	—	17	2	no	—
329	C₄⋊C₈	—	2	1	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	17	2	no	—
332	C₄⋊C₈	—	34	1	no	—
333	C₄⋊C₈	—	34	1	no	—
334	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
335	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
336	#103	—	17	2	no	—
337	#102	—	17	2	no	—
338	#102	—	17	2	no	—
339	#102	—	17	2	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	34	1	no	—
344	C₂²⋊C₈	—	34	2	no	—
345	C₂²⋊C₈	—	34	2	no	—
346	#97	—	17	2	no	—
347	C₄×C₈	—	2	1	no	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	—	17	2	no	—
351	C₄×C₈	—	17	2	no	—
352	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
353	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
354	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
355	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
356	C₁₇	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
357	C₂⁴	—	34	1	no	—
358	#41	—	2	2	no	—
359	#41	C₈×D₁₇	1	4	yes	complemented
360	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	17	2	no	—
363	C₂×D₄	—	17	4	no	—
364	C₂×D₄	—	34	2	no	—
365	C₂×D₄	—	34	1	no	—
366	C₂×D₄	C₂×C₄×D₁₇	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	34	1	no	—
371	C₂²×C₄	—	34	2	no	—
372	C₂²×C₄	—	34	2	no	—
373	C₂²×C₄	—	68	2	no	—
374	C₂²×C₄	—	68	2	no	—
375	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
376	C₂²×C₄	#63252	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
378	SD₁₆	—	17	8	no	—
379	D₈	—	17	8	no	—
380	M₁₆	—	17	4	no	—
381	M₁₆	—	34	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	4	1	no	—
386	C₂×C₈	—	4	2	no	—
387	C₂×C₈	—	4	2	no	—
388	C₂×C₈	—	17	2	no	—
389	C₂×C₈	—	17	2	no	—
390	C₂×C₈	—	34	2	no	—
391	C₂×C₈	—	34	2	no	—
392	C₂×C₈	—	68	4	no	—
393	C₂×C₈	—	68	2	no	—
394	C₂×C₈	—	68	4	no	—
395	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
396	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
397	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
398	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	17	2	no	—
402	C₄⋊C₄	—	34	1	no	—
403	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
404	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	34	2	no	—
409	C₂²⋊C₄	—	34	2	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
414	C₄²	#63252	1	1	yes	characteristic
415	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
416	C₄²	C₂³×D₁₇	1	1	yes	characteristic
417	C₂³	—	2	1	no	—
418	C₂³	—	34	2	no	—
419	C₂³	—	34	4	no	—
420	C₂³	—	68	2	no	—
421	C₂³	—	68	2	no	—
422	C₂³	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	C₂×C₈×D₁₇	1	2	yes	complemented
425	D₄	—	2	4	no	—
426	D₄	—	2	1	no	—
427	D₄	—	17	4	no	—
428	D₄	—	34	2	no	—
429	D₄	—	34	4	no	—
430	D₄	C₂×C₈×D₁₇	1	2	yes	complemented
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	34	2	no	—
442	C₂×C₄	—	68	4	no	—
443	C₂×C₄	—	68	2	no	—
444	C₂×C₄	—	68	2	no	—
445	C₂×C₄	—	68	2	no	—
446	C₂×C₄	C₂×C₈×D₁₇	1	2	yes	—
447	C₂×C₄	#10587587	1	2	yes	—
448	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
449	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
450	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
452	C₂×C₄	C₂×#63252	1	1	yes	characteristic
453	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	4	1	no	—
459	C₈	—	17	4	no	—
460	C₈	—	34	2	no	—
461	C₈	—	68	2	no	—
462	C₈	—	68	2	no	—
463	C₈	#10587635	1	2	yes	direct product factor
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	34	4	no	—
470	C₂²	—	68	8	no	—
471	C₂²	—	68	2	no	—
472	C₂²	—	68	2	no	—
473	C₂²	C₈×C₂²⋊D₁₇	1	2	yes	—
474	C₂²	C₂×C₄×C₂²⋊D₁₇	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	68	2	no	—
482	C₄	C₈×C₂²⋊D₁₇	1	2	yes	—
483	C₄	C₂²×C₈×D₁₇	1	1	yes	characteristic
484	C₄	C₂×#10587587	1	1	yes	characteristic
485	C₄	C₂×#10587635	1	1	yes	characteristic
486	C₄	#11763607	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	2	no	—
489	C₂	—	68	4	no	—
490	C₂	C₂×C₈×C₂²⋊D₁₇	1	1	yes	characteristic
491	C₂	C₄×#10587635	1	1	yes	characteristic
492	C₂	#14537685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₁₇
commutator	C₄×C₁₇	C₂³×C₈
Frattini	C₄²	C₂³×D₁₇
Fitting	C₈×#41×C₁₇	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂×#10587635	C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	C₈×#41	D₁₇
hypocenter	C₁₇	C₈×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×D₆₈	C₂	semidirect
3. #14527606	C₂	semidirect
4. #14527594	C₂	semidirect
5. C₈×#63230	C₂	semidirect
6. C₈×#63228	C₂	semidirect
7. #14527537	C₂	semidirect
8. #14527174	C₂	semidirect
9. #14527171	C₂	semidirect
10. C₈×#63223	C₂	semidirect
11. C₈×#41×C₁₇	C₂	semidirect
30. #11762561	C₂²	semidirect
31. #11762559	C₂²	semidirect
32. Q₈⋊#3622	C₂²	semidirect
33. D₄⋊#3622	C₂²	semidirect
36. #11762531	C₂²	semidirect
37. C₈×#3622	C₂²	semidirect
39. C₈×Q₈×C₁₇	C₂²	semidirect
40. C₈×Q₈×C₁₇	C₂²	semidirect
43. C₈×D₄×C₁₇	C₂²	semidirect
44. C₈×D₄×C₁₇	C₂²	semidirect
66. #10587635	C₈	direct (N × H)
112. #41×C₁₇	C₂×C₈	semidirect
125. C₂×D₆₈	C₂×C₈	semidirect
155. #63230	C₂×C₈	semidirect
156. #63228	C₂×C₈	semidirect
162. #63223	C₂×C₈	semidirect
178. Q₈×C₁₇	C₂²×C₈	semidirect
181. D₄×C₁₇	C₂²×C₈	semidirect
213. C₈×C₁₇	AGL(1,ℤ/8)	semidirect
217. #3622	C₂²×C₈	semidirect
218. C₈×#41	D₁₇	semidirect
256. C₈×Q₈	C₂×D₁₇	semidirect
257. C₈×Q₈	C₂×D₁₇	semidirect
268. C₈×D₄	C₂×D₁₇	semidirect
269. C₈×D₄	C₂×D₁₇	semidirect
356. C₁₇	C₈×AGL(1,ℤ/8)	semidirect
359. #41	C₈×D₁₇	semidirect
424. Q₈	C₂×C₈×D₁₇	semidirect
430. D₄	C₂×C₈×D₁₇	semidirect
463. C₈	#10587635	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#10587635	2
C₂×C₈×D₆₈	2
#14527606	2
#14527594	2
C₈×#63230	2
C₈×#63228	2
#14527537	2
#14527174	2
#14527171	2
C₈×#63223	2
C₈×#41×C₁₇	2
C₈×AGL(1,ℤ/8)	17

Subgroups — C8×#10587635 #17003736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#10587635 #17003736