Subgroups — C₁₇×#60238 #16917982

Order 4352.

2090 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3449	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2978	C₂	1	4	yes	maximal, complemented
3	C₁₇×#2977	C₂	1	4	yes	maximal, complemented
4	C₁₇×#2976	C₂	1	8	yes	maximal, complemented
5	C₁₇×#2935	C₂	1	4	yes	maximal, complemented
6	C₁₇×#2932	C₂	1	2	yes	maximal, complemented
7	C₁₇×#2931	C₂	1	2	yes	maximal, complemented
8	C₁₇×#2921	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2880	C₂	1	4	yes	maximal, complemented
11	C₂²×#41×C₁₇	C₂²	1	2	yes	—
12	C₂×C₁₇×#131	C₂²	1	4	yes	complemented
13	C₂×C₁₇×#131	C₂²	1	4	yes	complemented
14	C₁₇×#537	C₄	1	4	yes	—
15	C₁₇×#536	C₄	1	4	yes	—
16	C₁₇×#535	C₄	1	4	yes	—
17	C₁₇×#534	C₄	1	4	yes	—
18	C₁₇×#532	C₂²	1	2	yes	—
19	C₁₇×#532	C₂²	1	2	yes	—
20	C₁₇×#525	C₂²	1	4	yes	—
21	C₁₇×#525	C₂²	1	4	yes	—
22	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
23	C₁₇×#436	C₂²	1	4	yes	complemented
24	C₁₇×#436	C₂²	1	8	yes	complemented
25	C₁₇×#436	C₂²	1	4	yes	complemented
26	C₁₇×#435	C₂²	1	8	yes	complemented
27	C₁₇×#435	C₂²	1	8	yes	complemented
28	C₁₇×#435	C₂²	1	8	yes	complemented
29	C₁₇×#435	C₂²	1	8	yes	complemented
30	C₈×D₄×C₁₇	C₂²	1	4	yes	complemented
31	C₈×D₄×C₁₇	C₂²	1	8	yes	complemented
32	C₈×D₄×C₁₇	C₂²	1	4	yes	complemented
33	C₁₇×#433	C₂²	1	4	yes	complemented
34	C₁₇×#433	C₂²	1	4	yes	complemented
35	C₁₇×#433	C₂²	1	2	yes	complemented
36	C₁₇×#433	C₂²	1	4	yes	complemented
37	C₁₇×#433	C₂²	1	2	yes	complemented
38	C₁₇×#423	C₂²	1	2	yes	complemented
39	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	complemented
40	C₁₇×#408	C₂²	1	8	yes	—
41	C₁₇×#408	C₂²	1	8	yes	—
42	C₁₇×#408	C₂²	1	4	yes	complemented
43	C₁₇×#408	C₂²	1	4	yes	complemented
44	C₁₇×#407	C₂²	1	2	yes	—
45	C₁₇×#407	C₂²	1	8	yes	complemented
46	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
47	C₂×C₁₇×C₂²⋊C₈	C₂²	1	8	yes	complemented
48	C₄×M₁₆×C₁₇	C₂²	1	2	yes	complemented
49	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
51	C₂×#41×C₁₇	—	4	8	no	—
52	C₂×#41×C₁₇	C₂×C₄	1	4	yes	—
53	C₂×#41×C₁₇	C₂×C₄	1	4	yes	—
54	C₂×#41×C₁₇	C₂³	1	4	yes	—
55	C₂×#41×C₁₇	C₂³	1	4	yes	—
56	C₂²×Q₈×C₁₇	C₂×C₄	1	2	yes	—
57	C₂²×D₄×C₁₇	C₂×C₄	1	4	yes	—
58	C₂²×D₄×C₁₇	C₂×C₄	1	2	yes	—
59	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
61	C₁₇×#131	—	4	8	no	—
62	C₁₇×#131	—	4	8	no	—
63	C₂×M₁₆×C₁₇	C₂³	1	4	yes	—
64	C₂×M₁₆×C₁₇	C₂³	1	8	yes	—
65	C₂×M₁₆×C₁₇	C₂³	1	8	yes	—
66	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₇	C₂³	1	8	yes	—
69	C₂²×C₈×C₁₇	C₂³	1	8	yes	—
70	C₁₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
71	C₁₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
72	C₁₇×#127	C₂×C₄	1	2	yes	—
73	C₁₇×#127	C₂×C₄	1	2	yes	—
74	C₁₇×#124	C₂×C₄	1	4	yes	—
75	C₁₇×#124	C₂×C₄	1	4	yes	—
76	C₁₇×#123	C₂×C₄	1	8	yes	—
77	C₁₇×#123	C₂×C₄	1	8	yes	—
78	C₁₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
79	C₁₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
80	C₁₇×#121	C₂×C₄	1	8	yes	—
81	C₁₇×#121	C₂×C₄	1	8	yes	—
82	C₁₇×#121	C₂×C₄	1	4	yes	—
83	C₁₇×#121	C₂×C₄	1	4	yes	—
84	C₁₇×#121	C₂×C₄	1	8	yes	—
85	C₁₇×#120	C₂×C₄	1	8	yes	—
86	C₁₇×#120	C₂×C₄	1	8	yes	—
87	C₄×D₄×C₁₇	C₂³	1	4	yes	—
88	C₄×D₄×C₁₇	C₂³	1	8	yes	—
89	C₄×D₄×C₁₇	C₂³	1	4	yes	—
90	C₁₇×#117	C₂×C₄	1	4	yes	—
91	C₁₇×#117	C₂³	1	2	yes	—
92	C₁₇×#117	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
94	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
95	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
97	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
98	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
99	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
100	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
101	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
102	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
103	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
104	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
105	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
106	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
107	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₁₇×#97	C₂³	1	2	yes	—
109	C₁₇×#97	C₂³	1	2	yes	—
110	C₁₇×#97	C₂³	1	4	yes	—
111	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₁₇	C₂³	1	2	yes	—
113	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
114	C₄×C₈×C₁₇	C₂³	1	4	yes	—
115	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
116	C₂⁴×C₁₇	C₂²×C₄	1	4	yes	—
117	#41×C₁₇	—	2	8	no	—
118	#41×C₁₇	—	2	8	no	—
119	#41×C₁₇	—	4	8	no	—
120	#41×C₁₇	—	4	8	no	—
121	#41×C₁₇	—	4	8	no	—
122	C₂×Q₈×C₁₇	—	4	4	no	—
123	C₂×Q₈×C₁₇	C₂²×C₄	1	4	yes	—
124	C₂×Q₈×C₁₇	C₂²×C₄	1	4	yes	—
125	C₂×D₄×C₁₇	—	4	4	no	—
126	C₂×D₄×C₁₇	—	4	8	no	—
127	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
128	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
129	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
130	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
131	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
132	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
133	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₁₇	—	2	4	no	—
135	C₂²×C₄×C₁₇	—	4	8	no	—
136	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
139	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
143	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
145	M₁₆×C₁₇	—	2	8	no	—
146	M₁₆×C₁₇	—	4	8	no	—
147	M₁₆×C₁₇	—	4	8	no	—
148	C₂×C₈×C₁₇	—	2	4	no	—
149	C₂×C₈×C₁₇	—	2	4	no	—
150	C₂×C₈×C₁₇	—	4	8	no	—
151	C₂×C₈×C₁₇	—	4	8	no	—
152	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
153	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
154	C₂×C₈×C₁₇	C₂⁴	1	8	yes	—
155	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
156	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
157	C₄⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
158	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
159	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
160	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
161	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
162	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
163	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
164	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
165	C₂²⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
166	C₂²⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
167	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
168	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
169	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
170	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
171	C₄²×C₁₇	C₂⁴	1	2	yes	—
172	#60238	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₇	—	2	2	no	—
174	C₂³×C₁₇	—	4	4	no	—
175	C₂³×C₁₇	—	4	2	no	—
176	C₂³×C₁₇	—	4	8	no	—
177	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
178	C₂³×C₁₇	C₂³×C₄	1	8	yes	—
179	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
180	Q₈×C₁₇	—	2	8	no	—
181	Q₈×C₁₇	—	4	4	no	—
182	D₄×C₁₇	—	2	16	no	—
183	D₄×C₁₇	—	2	8	no	—
184	D₄×C₁₇	—	4	4	no	—
185	D₄×C₁₇	—	4	8	no	—
186	D₄×C₁₇	—	4	4	no	—
187	D₄×C₁₇	—	4	4	no	—
188	D₄×C₁₇	—	4	8	no	—
189	C₂×C₄×C₁₇	—	2	2	no	—
190	C₂×C₄×C₁₇	—	2	4	no	—
191	C₂×C₄×C₁₇	—	2	8	no	—
192	C₂×C₄×C₁₇	—	2	8	no	—
193	C₂×C₄×C₁₇	—	2	4	no	—
194	C₂×C₄×C₁₇	—	4	4	no	—
195	C₂×C₄×C₁₇	—	4	8	no	—
196	C₂×C₄×C₁₇	—	4	2	no	—
197	C₂×C₄×C₁₇	—	4	2	no	—
198	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
199	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
200	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
201	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
202	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
203	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₇	H(5,𝔽₂)	1	4	yes	—
205	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
206	C₈×C₁₇	—	2	2	no	—
207	C₈×C₁₇	—	2	4	no	—
208	C₈×C₁₇	—	2	2	no	—
209	C₈×C₁₇	—	2	8	no	—
210	#3449	C₂×C₁₇	1	1	yes	characteristic
211	#2978	C₂×C₁₇	1	4	yes	complemented
212	#2977	C₂×C₁₇	1	4	yes	complemented
213	#2976	C₂×C₁₇	1	8	yes	complemented
214	#2935	C₂×C₁₇	1	4	yes	complemented
215	#2932	C₂×C₁₇	1	2	yes	complemented
216	#2931	C₂×C₁₇	1	2	yes	complemented
217	#2921	C₂×C₁₇	1	1	yes	characteristic, complemented
218	C₂×#433	C₂×C₁₇	1	1	yes	characteristic, complemented
219	#2880	C₂×C₁₇	1	4	yes	complemented
220	C₂²×C₁₇	—	2	2	no	—
221	C₂²×C₁₇	—	2	2	no	—
222	C₂²×C₁₇	—	2	8	no	—
223	C₂²×C₁₇	—	2	8	no	—
224	C₂²×C₁₇	—	2	8	no	—
225	C₂²×C₁₇	—	2	4	no	—
226	C₂²×C₁₇	—	8	2	no	—
227	C₂²×C₁₇	—	8	8	no	—
228	C₂²×C₁₇	#518	1	2	yes	—
229	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
230	C₄×C₁₇	—	2	2	no	—
231	C₄×C₁₇	—	2	8	no	—
232	C₄×C₁₇	—	2	2	no	—
233	C₄×C₁₇	—	2	2	no	—
234	C₄×C₁₇	—	2	4	no	—
235	C₄×C₁₇	#518	1	2	yes	—
236	C₄×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
237	C₂²×#41	C₂²×C₁₇	1	2	yes	—
238	C₂×#131	C₂²×C₁₇	1	4	yes	complemented
239	C₂×#131	C₂²×C₁₇	1	4	yes	complemented
240	#537	C₄×C₁₇	1	4	yes	—
241	#536	C₄×C₁₇	1	4	yes	—
242	#535	C₄×C₁₇	1	4	yes	—
243	#534	C₄×C₁₇	1	4	yes	—
244	#532	C₂²×C₁₇	1	2	yes	—
245	#532	C₂²×C₁₇	1	2	yes	—
246	#525	C₂²×C₁₇	1	4	yes	—
247	#525	C₂²×C₁₇	1	4	yes	—
248	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
249	#436	C₂²×C₁₇	1	4	yes	complemented
250	#436	C₂²×C₁₇	1	4	yes	complemented
251	#436	C₂²×C₁₇	1	8	yes	complemented
252	#435	C₂²×C₁₇	1	8	yes	complemented
253	#435	C₂²×C₁₇	1	8	yes	complemented
254	#435	C₂²×C₁₇	1	8	yes	complemented
255	#435	C₂²×C₁₇	1	8	yes	complemented
256	C₈×D₄	C₂²×C₁₇	1	4	yes	complemented
257	C₈×D₄	C₂²×C₁₇	1	4	yes	complemented
258	C₈×D₄	C₂²×C₁₇	1	8	yes	complemented
259	#433	C₂²×C₁₇	1	4	yes	complemented
260	#433	C₂²×C₁₇	1	2	yes	complemented
261	#433	C₂²×C₁₇	1	2	yes	complemented
262	#433	C₂²×C₁₇	1	4	yes	complemented
263	#433	C₂²×C₁₇	1	4	yes	complemented
264	#423	C₂²×C₁₇	1	2	yes	complemented
265	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	complemented
266	#408	C₂²×C₁₇	1	8	yes	—
267	#408	C₂²×C₁₇	1	8	yes	—
268	#408	C₂²×C₁₇	1	4	yes	complemented
269	#408	C₂²×C₁₇	1	4	yes	complemented
270	#407	C₂²×C₁₇	1	2	yes	—
271	#407	C₂²×C₁₇	1	8	yes	complemented
272	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	—
273	C₂×C₂²⋊C₈	C₂²×C₁₇	1	8	yes	complemented
274	C₄×M₁₆	C₂²×C₁₇	1	2	yes	complemented
275	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic, complemented
276	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
277	C₂×C₁₇	—	2	2	no	—
278	C₂×C₁₇	—	4	8	no	—
279	C₂×C₁₇	—	4	2	no	—
280	C₂×C₁₇	C₂×#518	1	1	yes	characteristic
281	C₂×C₁₇	#3573	1	2	yes	—
282	C₂×#41	—	4	8	no	—
283	C₂×#41	C₂×C₄×C₁₇	1	4	yes	—
284	C₂×#41	C₂×C₄×C₁₇	1	4	yes	—
285	C₂×#41	C₂³×C₁₇	1	4	yes	—
286	C₂×#41	C₂³×C₁₇	1	4	yes	—
287	C₂²×Q₈	C₂×C₄×C₁₇	1	2	yes	—
288	C₂²×D₄	C₂×C₄×C₁₇	1	4	yes	—
289	C₂²×D₄	C₂×C₄×C₁₇	1	2	yes	—
290	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
292	#131	—	4	8	no	—
293	#131	—	4	8	no	—
294	C₂×M₁₆	C₂³×C₁₇	1	4	yes	—
295	C₂×M₁₆	C₂³×C₁₇	1	8	yes	—
296	C₂×M₁₆	C₂³×C₁₇	1	8	yes	—
297	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
298	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
299	C₂²×C₈	C₂³×C₁₇	1	8	yes	—
300	C₂²×C₈	C₂³×C₁₇	1	8	yes	—
301	C₄⋊Q₈	C₂×C₄×C₁₇	1	2	yes	—
302	C₄⋊Q₈	C₂×C₄×C₁₇	1	2	yes	—
303	#127	C₂×C₄×C₁₇	1	2	yes	—
304	#127	C₂×C₄×C₁₇	1	2	yes	—
305	#124	C₂×C₄×C₁₇	1	4	yes	—
306	#124	C₂×C₄×C₁₇	1	4	yes	—
307	#123	C₂×C₄×C₁₇	1	8	yes	—
308	#123	C₂×C₄×C₁₇	1	8	yes	—
309	C₂²⋊Q₈	C₂×C₄×C₁₇	1	8	yes	—
310	C₂²⋊Q₈	C₂×C₄×C₁₇	1	8	yes	—
311	#121	C₂×C₄×C₁₇	1	8	yes	—
312	#121	C₂×C₄×C₁₇	1	8	yes	—
313	#121	C₂×C₄×C₁₇	1	4	yes	—
314	#121	C₂×C₄×C₁₇	1	4	yes	—
315	#121	C₂×C₄×C₁₇	1	8	yes	—
316	#120	C₂×C₄×C₁₇	1	8	yes	—
317	#120	C₂×C₄×C₁₇	1	8	yes	—
318	C₄×D₄	C₂³×C₁₇	1	4	yes	—
319	C₄×D₄	C₂³×C₁₇	1	8	yes	—
320	C₄×D₄	C₂³×C₁₇	1	4	yes	—
321	#117	C₂×C₄×C₁₇	1	4	yes	—
322	#117	C₂³×C₁₇	1	2	yes	—
323	#117	C₂³×C₁₇	1	2	yes	—
324	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
326	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
328	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
329	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
330	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
331	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
332	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
333	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
334	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
335	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
336	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
337	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
338	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
339	#97	C₂³×C₁₇	1	2	yes	—
340	#97	C₂³×C₁₇	1	2	yes	—
341	#97	C₂³×C₁₇	1	4	yes	—
342	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
343	C₄×C₈	C₂³×C₁₇	1	2	yes	—
344	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
345	C₄×C₈	C₂³×C₁₇	1	4	yes	—
346	C₁₇	#60238	1	1	yes	characteristic, direct product factor, Sylow
347	C₂⁴	C₂²×C₄×C₁₇	1	1	yes	characteristic
348	C₂⁴	C₂²×C₄×C₁₇	1	4	yes	—
349	#41	—	2	8	no	—
350	#41	—	2	8	no	—
351	#41	—	4	8	no	—
352	#41	—	4	8	no	—
353	#41	—	4	8	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×Q₈	C₂²×C₄×C₁₇	1	4	yes	—
356	C₂×Q₈	C₂²×C₄×C₁₇	1	4	yes	—
357	C₂×D₄	—	4	4	no	—
358	C₂×D₄	—	4	8	no	—
359	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
360	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
361	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
362	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
363	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
364	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
365	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	4	8	no	—
368	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
369	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
370	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
371	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
372	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
373	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
376	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
377	M₁₆	—	2	8	no	—
378	M₁₆	—	4	8	no	—
379	M₁₆	—	4	8	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	2	4	no	—
382	C₂×C₈	—	4	8	no	—
383	C₂×C₈	—	4	8	no	—
384	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
385	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
386	C₂×C₈	C₂⁴×C₁₇	1	8	yes	—
387	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
388	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
389	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
390	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
391	C₄⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
392	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
393	C₂²⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
394	C₂²⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
395	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
396	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
397	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
398	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
399	C₄²	C₂²×C₄×C₁₇	1	2	yes	—
400	C₄²	C₂²×C₄×C₁₇	1	2	yes	—
401	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
402	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
403	C₄²	C₂⁴×C₁₇	1	2	yes	—
404	C₂³	—	2	2	no	—
405	C₂³	—	4	4	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	8	no	—
408	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
409	C₂³	C₂³×C₄×C₁₇	1	8	yes	—
410	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
411	Q₈	—	2	8	no	—
412	Q₈	—	4	4	no	—
413	D₄	—	2	16	no	—
414	D₄	—	2	8	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	8	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	8	no	—
419	D₄	—	4	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
430	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
431	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
432	C₂×C₄	C₂³×C₄×C₁₇	1	8	yes	—
433	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
434	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
435	C₂×C₄	C₁₇×H(5,𝔽₂)	1	4	yes	—
436	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	2	4	no	—
439	C₈	—	2	2	no	—
440	C₈	—	2	8	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	8	no	—
443	C₂²	—	2	8	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	8	no	—
449	C₂²	C₁₇×#518	1	2	yes	—
450	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	4	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	8	no	—
456	C₄	C₁₇×#518	1	2	yes	—
457	C₄	C₂×C₁₇×H(5,𝔽₂)	1	2	yes	—
458	C₂	—	2	2	no	—
459	C₂	—	4	2	no	—
460	C₂	—	4	8	no	—
461	C₂	C₂×C₁₇×#518	1	1	yes	characteristic
462	C₂	C₁₇×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
socle	C₂²×C₁₇	C₂⁴×C₄
prime radical	C₁₇×#3449	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#2978	C₂	semidirect
3. C₁₇×#2977	C₂	semidirect
4. C₁₇×#2976	C₂	semidirect
5. C₁₇×#2935	C₂	semidirect
6. C₁₇×#2932	C₂	semidirect
7. C₁₇×#2931	C₂	semidirect
8. C₁₇×#2921	C₂	semidirect
9. C₂×C₁₇×#433	C₂	semidirect
10. C₁₇×#2880	C₂	semidirect
12. C₂×C₁₇×#131	C₂²	semidirect
13. C₂×C₁₇×#131	C₂²	semidirect
23. C₁₇×#436	C₂²	semidirect
24. C₁₇×#436	C₂²	semidirect
25. C₁₇×#436	C₂²	semidirect
26. C₁₇×#435	C₂²	semidirect
27. C₁₇×#435	C₂²	semidirect
28. C₁₇×#435	C₂²	semidirect
29. C₁₇×#435	C₂²	semidirect
30. C₈×D₄×C₁₇	C₂²	semidirect
31. C₈×D₄×C₁₇	C₂²	semidirect
32. C₈×D₄×C₁₇	C₂²	semidirect
33. C₁₇×#433	C₂²	semidirect
34. C₁₇×#433	C₂²	semidirect
35. C₁₇×#433	C₂²	semidirect
36. C₁₇×#433	C₂²	semidirect
37. C₁₇×#433	C₂²	semidirect
38. C₁₇×#423	C₂²	semidirect
39. C₂×C₁₇×C₄⋊C₈	C₂²	semidirect
42. C₁₇×#408	C₂²	semidirect
43. C₁₇×#408	C₂²	semidirect
45. C₁₇×#407	C₂²	semidirect
47. C₂×C₁₇×C₂²⋊C₈	C₂²	semidirect
48. C₄×M₁₆×C₁₇	C₂²	semidirect
49. C₂×C₁₇×#97	C₂²	semidirect
50. C₂×C₄×C₈×C₁₇	C₂²	semidirect
172. #60238	C₁₇	direct (N × H)
211. #2978	C₂×C₁₇	semidirect
212. #2977	C₂×C₁₇	semidirect
213. #2976	C₂×C₁₇	semidirect
214. #2935	C₂×C₁₇	semidirect
215. #2932	C₂×C₁₇	semidirect
216. #2931	C₂×C₁₇	semidirect
217. #2921	C₂×C₁₇	semidirect
218. C₂×#433	C₂×C₁₇	semidirect
219. #2880	C₂×C₁₇	semidirect
238. C₂×#131	C₂²×C₁₇	semidirect
239. C₂×#131	C₂²×C₁₇	semidirect
249. #436	C₂²×C₁₇	semidirect
250. #436	C₂²×C₁₇	semidirect
251. #436	C₂²×C₁₇	semidirect
252. #435	C₂²×C₁₇	semidirect
253. #435	C₂²×C₁₇	semidirect
254. #435	C₂²×C₁₇	semidirect
255. #435	C₂²×C₁₇	semidirect
256. C₈×D₄	C₂²×C₁₇	semidirect
257. C₈×D₄	C₂²×C₁₇	semidirect
258. C₈×D₄	C₂²×C₁₇	semidirect
259. #433	C₂²×C₁₇	semidirect
260. #433	C₂²×C₁₇	semidirect
261. #433	C₂²×C₁₇	semidirect
262. #433	C₂²×C₁₇	semidirect
263. #433	C₂²×C₁₇	semidirect
264. #423	C₂²×C₁₇	semidirect
265. C₂×C₄⋊C₈	C₂²×C₁₇	semidirect
268. #408	C₂²×C₁₇	semidirect
269. #408	C₂²×C₁₇	semidirect
271. #407	C₂²×C₁₇	semidirect
273. C₂×C₂²⋊C₈	C₂²×C₁₇	semidirect
274. C₄×M₁₆	C₂²×C₁₇	semidirect
275. C₂×#97	C₂²×C₁₇	semidirect
276. C₂×C₄×C₈	C₂²×C₁₇	semidirect
346. C₁₇	#60238	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#3449	2
C₁₇×#2978	2
C₁₇×#2977	2
C₁₇×#2976	2
C₁₇×#2935	2
C₁₇×#2932	2
C₁₇×#2931	2
C₁₇×#2921	2
C₂×C₁₇×#433	2
C₁₇×#2880	2
#60238	17

Subgroups — C17×#60238 #16917982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#60238 #16917982