Subgroups — C₁₇×#24835 #16882579

Order 4352.

988 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₇×#121	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#2086	C₂	1	2	yes	maximal, complemented
6	C₁₇×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1893	C₂	1	2	yes	maximal
10	C₁₇×#1808	C₂	1	2	yes	maximal, complemented
11	C₁₇×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₇	C₂²	1	2	yes	—
13	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₇×#121	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₇	—	2	1	no	—
17	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
19	C₁₇×#474	—	2	4	no	—
20	C₂×C₁₇×#107	C₂²	1	2	yes	—
21	C₂×C₁₇×#107	C₂²	1	2	yes	—
22	C₂×C₁₇×C₄⋊C₈	—	2	4	no	—
23	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#102	C₂²	1	2	yes	—
27	C₂×C₁₇×#102	C₂²	1	2	yes	—
28	C₁₇×#391	—	2	1	no	—
29	C₁₇×#390	C₂²	1	1	yes	characteristic
30	C₁₇×#389	—	2	1	no	—
31	C₁₇×#389	C₂²	1	1	yes	characteristic
32	C₁₇×#389	C₂²	1	2	yes	—
33	C₁₇×#388	—	2	1	no	—
34	C₁₇×#386	—	2	1	no	—
35	C₁₇×#384	C₂²	1	1	yes	characteristic
36	C₁₇×#380	—	2	1	no	—
37	C₁₇×#380	C₂²	1	1	yes	characteristic
38	C₁₇×#380	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₁₇	—	2	1	no	—
41	C₁₇×#340	C₂²	1	2	yes	—
42	C₁₇×#340	C₂²	1	2	yes	—
43	C₁₇×#340	C₂²	1	2	yes	—
44	C₁₇×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₇	—	2	1	no	—
46	C₂²×D₄×C₁₇	—	2	1	no	—
47	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₇	—	2	1	no	—
49	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₇	—	2	4	no	—
53	C₂²×C₈×C₁₇	—	2	4	no	—
54	C₂²×C₈×C₁₇	—	4	2	no	—
55	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
57	C₁₇×C₄⋊Q₈	—	2	2	no	—
58	C₁₇×C₄⋊Q₈	—	2	2	no	—
59	C₁₇×C₂²⋊Q₈	—	4	4	no	—
60	C₁₇×#121	—	2	2	no	—
61	C₁₇×#121	Q₈	1	4	yes	complemented
62	C₄×D₄×C₁₇	—	2	2	no	—
63	C₄×D₄×C₁₇	—	2	2	no	—
64	C₄×D₄×C₁₇	—	4	4	no	—
65	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
81	C₂×C₄²×C₁₇	—	2	2	no	—
82	C₂×C₄²×C₁₇	—	2	2	no	—
83	C₂×C₄²×C₁₇	—	2	1	no	—
84	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
88	C₁₇×#107	—	2	4	no	—
89	C₁₇×#107	—	4	2	no	—
90	C₁₇×C₄⋊C₈	—	2	4	no	—
91	C₁₇×C₄⋊C₈	—	2	2	no	—
92	C₁₇×C₄⋊C₈	D₄	1	4	yes	complemented
93	C₁₇×#102	—	2	4	no	—
94	C₁₇×#102	—	4	2	no	—
95	C₁₇×#95	—	2	1	no	—
96	C₁₇×#95	—	2	1	no	—
97	C₁₇×#95	—	2	1	no	—
98	C₁₇×#95	—	2	2	no	—
99	C₁₇×#95	—	2	2	no	—
100	C₂⁴×C₁₇	—	2	1	no	—
101	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
102	C₂×Q₈×C₁₇	—	4	2	no	—
103	C₂×Q₈×C₁₇	—	4	2	no	—
104	C₂×Q₈×C₁₇	—	4	2	no	—
105	C₂×D₄×C₁₇	—	2	4	no	—
106	C₂×D₄×C₁₇	—	2	1	no	—
107	C₂×D₄×C₁₇	—	2	1	no	—
108	C₂×D₄×C₁₇	—	2	1	no	—
109	C₂×D₄×C₁₇	—	2	1	no	—
110	C₂×D₄×C₁₇	—	2	1	no	—
111	C₂×D₄×C₁₇	—	4	2	no	—
112	C₂×D₄×C₁₇	—	4	2	no	—
113	C₂×D₄×C₁₇	C₂×Q₈	1	2	yes	—
114	C₂²×C₄×C₁₇	—	2	2	no	—
115	C₂²×C₄×C₁₇	—	2	2	no	—
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	—	2	1	no	—
120	C₂²×C₄×C₁₇	—	2	2	no	—
121	C₂²×C₄×C₁₇	—	2	1	no	—
122	C₂²×C₄×C₁₇	—	2	2	no	—
123	C₂²×C₄×C₁₇	—	2	1	no	—
124	C₂²×C₄×C₁₇	—	2	2	no	—
125	C₂²×C₄×C₁₇	—	2	1	no	—
126	C₂²×C₄×C₁₇	—	2	2	no	—
127	C₂²×C₄×C₁₇	—	4	1	no	—
128	C₂²×C₄×C₁₇	—	4	2	no	—
129	C₂²×C₄×C₁₇	—	4	2	no	—
130	C₂²×C₄×C₁₇	—	4	2	no	—
131	C₂²×C₄×C₁₇	D₈	1	4	yes	—
132	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₇	C₂×Q₈	1	2	yes	—
138	C₂²×C₄×C₁₇	#41	1	2	yes	—
139	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
140	C₂×C₈×C₁₇	—	2	2	no	—
141	C₂×C₈×C₁₇	—	2	2	no	—
142	C₂×C₈×C₁₇	—	2	2	no	—
143	C₂×C₈×C₁₇	—	2	2	no	—
144	C₂×C₈×C₁₇	—	2	2	no	—
145	C₂×C₈×C₁₇	—	4	8	no	—
146	C₂×C₈×C₁₇	C₂×D₄	1	4	yes	—
147	C₄⋊C₄×C₁₇	—	2	1	no	—
148	C₄⋊C₄×C₁₇	—	2	2	no	—
149	C₄⋊C₄×C₁₇	—	2	1	no	—
150	C₄⋊C₄×C₁₇	—	2	2	no	—
151	C₄⋊C₄×C₁₇	—	2	1	no	—
152	C₄⋊C₄×C₁₇	—	2	2	no	—
153	C₄⋊C₄×C₁₇	—	2	1	no	—
154	C₄⋊C₄×C₁₇	—	2	1	no	—
155	C₄⋊C₄×C₁₇	—	2	2	no	—
156	C₄⋊C₄×C₁₇	—	4	2	no	—
157	C₄⋊C₄×C₁₇	—	4	2	no	—
158	C₄⋊C₄×C₁₇	—	4	2	no	—
159	C₄⋊C₄×C₁₇	—	4	4	no	—
160	C₄⋊C₄×C₁₇	—	4	2	no	—
161	C₄⋊C₄×C₁₇	C₂×Q₈	1	2	yes	—
162	C₂²⋊C₄×C₁₇	—	2	4	no	—
163	C₂²⋊C₄×C₁₇	—	4	2	no	—
164	C₂²⋊C₄×C₁₇	—	4	4	no	—
165	C₂²⋊C₄×C₁₇	—	4	2	no	—
166	C₂²⋊C₄×C₁₇	—	4	2	no	—
167	C₂²⋊C₄×C₁₇	—	4	2	no	—
168	C₄²×C₁₇	—	2	2	no	—
169	C₄²×C₁₇	—	2	2	no	—
170	C₄²×C₁₇	—	2	1	no	—
171	C₄²×C₁₇	—	2	1	no	—
172	C₄²×C₁₇	—	4	2	no	—
173	C₄²×C₁₇	C₂×D₄	1	2	yes	—
174	C₄²×C₁₇	#41	1	2	yes	—
175	#24835	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₁₇	—	2	1	no	—
177	C₂³×C₁₇	—	2	1	no	—
178	C₂³×C₁₇	—	2	1	no	—
179	C₂³×C₁₇	—	2	1	no	—
180	C₂³×C₁₇	—	2	2	no	—
181	C₂³×C₁₇	—	4	1	no	—
182	C₂³×C₁₇	—	4	1	no	—
183	C₂³×C₁₇	—	4	1	no	—
184	C₂³×C₁₇	—	4	1	no	—
185	C₂³×C₁₇	—	4	1	no	—
186	C₂³×C₁₇	—	4	1	no	—
187	C₂³×C₁₇	C₂²⋊Q₈	1	2	yes	—
188	C₂³×C₁₇	C₂×D₈	1	2	yes	—
189	C₂³×C₁₇	#137	1	2	yes	—
190	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₁₇	—	8	4	no	—
192	D₄×C₁₇	—	2	2	no	—
193	D₄×C₁₇	—	2	2	no	—
194	D₄×C₁₇	—	4	8	no	—
195	D₄×C₁₇	—	4	1	no	—
196	D₄×C₁₇	—	4	1	no	—
197	C₂×C₄×C₁₇	—	2	1	no	—
198	C₂×C₄×C₁₇	—	2	1	no	—
199	C₂×C₄×C₁₇	—	2	1	no	—
200	C₂×C₄×C₁₇	—	2	1	no	—
201	C₂×C₄×C₁₇	—	2	1	no	—
202	C₂×C₄×C₁₇	—	2	1	no	—
203	C₂×C₄×C₁₇	—	2	2	no	—
204	C₂×C₄×C₁₇	—	2	2	no	—
205	C₂×C₄×C₁₇	—	2	2	no	—
206	C₂×C₄×C₁₇	—	2	2	no	—
207	C₂×C₄×C₁₇	—	2	8	no	—
208	C₂×C₄×C₁₇	—	2	1	no	—
209	C₂×C₄×C₁₇	—	2	2	no	—
210	C₂×C₄×C₁₇	—	2	1	no	—
211	C₂×C₄×C₁₇	—	2	1	no	—
212	C₂×C₄×C₁₇	—	4	4	no	—
213	C₂×C₄×C₁₇	—	4	1	no	—
214	C₂×C₄×C₁₇	—	4	1	no	—
215	C₂×C₄×C₁₇	—	4	1	no	—
216	C₂×C₄×C₁₇	—	4	2	no	—
217	C₂×C₄×C₁₇	—	4	2	no	—
218	C₂×C₄×C₁₇	—	4	1	no	—
219	C₂×C₄×C₁₇	—	4	1	no	—
220	C₂×C₄×C₁₇	—	4	2	no	—
221	C₂×C₄×C₁₇	—	4	1	no	—
222	C₂×C₄×C₁₇	—	4	2	no	—
223	C₂×C₄×C₁₇	—	4	1	no	—
224	C₂×C₄×C₁₇	—	4	2	no	—
225	C₂×C₄×C₁₇	—	4	1	no	—
226	C₂×C₄×C₁₇	—	4	2	no	—
227	C₂×C₄×C₁₇	—	8	4	no	—
228	C₂×C₄×C₁₇	#121	1	2	yes	—
229	C₂×C₄×C₁₇	#121	1	2	yes	—
230	C₂×C₄×C₁₇	C₂²⋊Q₈	1	2	yes	—
231	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
232	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
233	C₂×C₄×C₁₇	#135	1	2	yes	—
234	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
236	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
240	C₈×C₁₇	—	2	4	no	—
241	C₈×C₁₇	—	4	2	no	—
242	C₂×#474	C₂×C₁₇	1	1	yes	characteristic, complemented
243	C₂²×C₄⋊C₈	C₂×C₁₇	1	1	yes	characteristic, complemented
244	#2857	C₂×C₁₇	1	1	yes	characteristic, complemented
245	C₄×#121	C₂×C₁₇	1	1	yes	characteristic
246	#2086	C₂×C₁₇	1	2	yes	complemented
247	#2067	C₂×C₁₇	1	2	yes	complemented
248	#1988	C₂×C₁₇	1	1	yes	characteristic, complemented
249	#1947	C₂×C₁₇	1	1	yes	characteristic, complemented
250	#1893	C₂×C₁₇	1	2	yes	—
251	#1808	C₂×C₁₇	1	2	yes	complemented
252	#1802	C₂×C₁₇	1	1	yes	characteristic, complemented
253	C₂²×C₁₇	—	2	2	no	—
254	C₂²×C₁₇	—	2	2	no	—
255	C₂²×C₁₇	—	2	2	no	—
256	C₂²×C₁₇	—	2	2	no	—
257	C₂²×C₁₇	—	2	2	no	—
258	C₂²×C₁₇	—	2	2	no	—
259	C₂²×C₁₇	—	4	2	no	—
260	C₂²×C₁₇	—	4	2	no	—
261	C₂²×C₁₇	—	4	2	no	—
262	C₂²×C₁₇	—	8	1	no	—
263	C₂²×C₁₇	—	8	1	no	—
264	C₂²×C₁₇	—	8	1	no	—
265	C₂²×C₁₇	—	8	1	no	—
266	C₂²×C₁₇	#474	1	4	yes	complemented
267	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
268	C₂²×C₁₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
269	C₂²×C₁₇	#537	1	1	yes	characteristic
270	C₂²×C₁₇	C₂²×D₈	1	1	yes	characteristic
271	C₂²×C₁₇	C₂×#135	1	1	yes	characteristic
272	C₂²×C₁₇	C₂×#137	1	1	yes	characteristic
273	C₂²×C₁₇	#575	1	1	yes	characteristic
274	C₄×C₁₇	—	2	2	no	—
275	C₄×C₁₇	—	2	2	no	—
276	C₄×C₁₇	—	2	2	no	—
277	C₄×C₁₇	—	4	1	no	—
278	C₄×C₁₇	—	4	2	no	—
279	C₄×C₁₇	—	8	1	no	—
280	C₄×C₁₇	—	8	2	no	—
281	C₄×C₁₇	—	8	1	no	—
282	C₄×C₁₇	—	8	2	no	—
283	C₄×C₁₇	#466	1	4	yes	—
284	C₄×C₁₇	#546	1	1	yes	characteristic
285	C₄×C₁₇	D₄×Q₈	1	1	yes	characteristic
286	C₄×C₁₇	#552	1	1	yes	characteristic
287	C₄×C₁₇	#554	1	1	yes	characteristic
288	C₂³×C₈	C₂²×C₁₇	1	2	yes	—
289	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
290	C₂×C₂²⋊Q₈	—	2	1	no	—
291	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
292	C₂×C₄×D₄	—	2	1	no	—
293	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
294	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
295	#474	—	2	4	no	—
296	C₂×#107	C₂²×C₁₇	1	2	yes	—
297	C₂×#107	C₂²×C₁₇	1	2	yes	—
298	C₂×C₄⋊C₈	—	2	4	no	—
299	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
300	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
301	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
302	C₂×#102	C₂²×C₁₇	1	2	yes	—
303	C₂×#102	C₂²×C₁₇	1	2	yes	—
304	#391	—	2	1	no	—
305	#390	C₂²×C₁₇	1	1	yes	characteristic
306	#389	—	2	1	no	—
307	#389	C₂²×C₁₇	1	2	yes	—
308	#389	C₂²×C₁₇	1	1	yes	characteristic
309	#388	—	2	1	no	—
310	#386	—	2	1	no	—
311	#384	C₂²×C₁₇	1	1	yes	characteristic
312	#380	—	2	1	no	—
313	#380	C₂²×C₁₇	1	1	yes	characteristic
314	#380	C₂²×C₁₇	1	2	yes	—
315	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
316	C₄×C₂²⋊C₄	—	2	1	no	—
317	#340	C₂²×C₁₇	1	2	yes	—
318	#340	C₂²×C₁₇	1	2	yes	—
319	#340	C₂²×C₁₇	1	2	yes	—
320	#340	C₂²×C₁₇	1	2	yes	—
321	C₂×C₁₇	—	2	4	no	—
322	C₂×C₁₇	—	8	2	no	—
323	C₂×C₁₇	#2417	1	1	yes	characteristic
324	C₂×C₁₇	C₂×#466	1	1	yes	characteristic
325	C₂×C₁₇	#3056	1	1	yes	characteristic
326	C₂×C₁₇	C₂×#474	1	1	yes	characteristic
327	C₂×C₁₇	#3076	1	1	yes	characteristic
328	C₂×C₁₇	#3245	1	1	yes	characteristic
329	C₂×C₁₇	#3248	1	1	yes	characteristic
330	C₂²×Q₈	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
335	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
337	C₂²×C₈	—	2	4	no	—
338	C₂²×C₈	—	2	4	no	—
339	C₂²×C₈	—	4	2	no	—
340	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
341	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	—	2	2	no	—
344	C₂²⋊Q₈	—	4	4	no	—
345	#121	—	2	2	no	—
346	#121	Q₈×C₁₇	1	4	yes	complemented
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	4	4	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	2	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
370	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
373	#107	—	2	4	no	—
374	#107	—	4	2	no	—
375	C₄⋊C₈	—	2	4	no	—
376	C₄⋊C₈	—	2	2	no	—
377	C₄⋊C₈	D₄×C₁₇	1	4	yes	complemented
378	#102	—	2	4	no	—
379	#102	—	4	2	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	2	no	—
384	#95	—	2	2	no	—
385	C₁₇	#24835	1	1	yes	characteristic, direct product factor, Sylow
386	C₂⁴	—	2	1	no	—
387	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
388	C₂×Q₈	—	4	2	no	—
389	C₂×Q₈	—	4	2	no	—
390	C₂×Q₈	—	4	2	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	C₂×Q₈×C₁₇	1	2	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	4	1	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	D₈×C₁₇	1	4	yes	—
418	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
423	C₂²×C₄	C₂×Q₈×C₁₇	1	2	yes	—
424	C₂²×C₄	#41×C₁₇	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	4	8	no	—
432	C₂×C₈	C₂×D₄×C₁₇	1	4	yes	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	4	4	no	—
446	C₄⋊C₄	—	4	2	no	—
447	C₄⋊C₄	C₂×Q₈×C₁₇	1	2	yes	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	4	2	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	4	2	no	—
459	C₄²	C₂×D₄×C₁₇	1	2	yes	—
460	C₄²	#41×C₁₇	1	2	yes	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	C₁₇×C₂²⋊Q₈	1	2	yes	—
473	C₂³	C₂×D₈×C₁₇	1	2	yes	—
474	C₂³	C₁₇×#137	1	2	yes	—
475	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
476	Q₈	—	8	4	no	—
477	D₄	—	2	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	1	no	—
481	D₄	—	4	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	4	no	—
513	C₂×C₄	C₁₇×#121	1	2	yes	—
514	C₂×C₄	C₁₇×#121	1	2	yes	—
515	C₂×C₄	C₁₇×C₂²⋊Q₈	1	2	yes	—
516	C₂×C₄	C₂×D₈×C₁₇	1	2	yes	—
517	C₂×C₄	C₂×D₈×C₁₇	1	2	yes	—
518	C₂×C₄	C₁₇×#135	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
520	C₂×C₄	C₂²×Q₈×C₁₇	1	1	yes	characteristic
521	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
522	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
523	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
525	C₈	—	2	4	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	C₁₇×#474	1	4	yes	complemented
541	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
542	C₂²	C₂×C₁₇×C₂²⋊Q₈	1	1	yes	characteristic
543	C₂²	C₁₇×#537	1	1	yes	characteristic
544	C₂²	C₂²×D₈×C₁₇	1	1	yes	characteristic
545	C₂²	C₂×C₁₇×#135	1	1	yes	characteristic
546	C₂²	C₂×C₁₇×#137	1	1	yes	characteristic
547	C₂²	C₁₇×#575	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	2	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	2	no	—
557	C₄	C₁₇×#466	1	4	yes	—
558	C₄	C₁₇×#546	1	1	yes	characteristic
559	C₄	D₄×Q₈×C₁₇	1	1	yes	characteristic
560	C₄	C₁₇×#552	1	1	yes	characteristic
561	C₄	C₁₇×#554	1	1	yes	characteristic
562	C₂	—	2	4	no	—
563	C₂	—	8	2	no	—
564	C₂	C₁₇×#2417	1	1	yes	characteristic
565	C₂	C₂×C₁₇×#466	1	1	yes	characteristic
566	C₂	C₁₇×#3056	1	1	yes	characteristic
567	C₂	C₂×C₁₇×#474	1	1	yes	characteristic
568	C₂	C₁₇×#3076	1	1	yes	characteristic
569	C₂	C₁₇×#3245	1	1	yes	characteristic
570	C₂	C₁₇×#3248	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂²×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#474	C₂	semidirect
2. C₂²×C₁₇×C₄⋊C₈	C₂	semidirect
3. C₁₇×#2857	C₂	semidirect
5. C₁₇×#2086	C₂	semidirect
6. C₁₇×#2067	C₂	semidirect
7. C₁₇×#1988	C₂	semidirect
8. C₁₇×#1947	C₂	semidirect
10. C₁₇×#1808	C₂	semidirect
11. C₁₇×#1802	C₂	semidirect
61. C₁₇×#121	Q₈	semidirect
92. C₁₇×C₄⋊C₈	D₄	semidirect
175. #24835	C₁₇	direct (N × H)
242. C₂×#474	C₂×C₁₇	semidirect
243. C₂²×C₄⋊C₈	C₂×C₁₇	semidirect
244. #2857	C₂×C₁₇	semidirect
246. #2086	C₂×C₁₇	semidirect
247. #2067	C₂×C₁₇	semidirect
248. #1988	C₂×C₁₇	semidirect
249. #1947	C₂×C₁₇	semidirect
251. #1808	C₂×C₁₇	semidirect
252. #1802	C₂×C₁₇	semidirect
266. C₂²×C₁₇	#474	semidirect
346. #121	Q₈×C₁₇	semidirect
377. C₄⋊C₈	D₄×C₁₇	semidirect
385. C₁₇	#24835	direct (N × H)
540. C₂²	C₁₇×#474	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#474	2
C₂²×C₁₇×C₄⋊C₈	2
C₁₇×#2857	2
C₄×C₁₇×#121	2
C₁₇×#2086	2
C₁₇×#2067	2
C₁₇×#1988	2
C₁₇×#1947	2
C₁₇×#1893	2
C₁₇×#1808	2
C₁₇×#1802	2
#24835	17

Subgroups — C17×#24835 #16882579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#24835 #16882579