Subgroups — C₁₇×#61562 #16919306

Order 4352.

2370 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3496	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3298	C₂	1	8	yes	maximal, complemented
4	D₄×SD₁₆×C₁₇	C₂	1	8	yes	maximal, complemented
5	C₁₇×#3206	C₂	1	2	yes	maximal, complemented
6	C₁₇×#3187	C₂	1	4	yes	maximal, complemented
7	C₁₇×#3103	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₇×#448	C₂	1	4	yes	maximal, complemented
9	C₁₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₇×H(5,𝔽₂)	—	2	1	no	—
11	C₂³×Q₈×C₁₇	C₂²	1	2	yes	complemented
12	C₂²×SD₁₆×C₁₇	C₂²	1	8	yes	complemented
13	D₄×Q₈×C₁₇	—	2	4	no	—
14	D₄×Q₈×C₁₇	C₂²	1	8	yes	complemented
15	C₁₇×#547	C₂²	1	4	yes	—
16	C₁₇×#546	—	2	4	no	—
17	D₄²×C₁₇	C₂²	1	4	yes	—
18	C₁₇×#537	—	2	1	no	—
19	C₁₇×#534	—	2	2	no	—
20	C₁₇×#532	C₂²	1	2	yes	—
21	C₂×C₁₇×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₇×C₂²⋊Q₈	—	2	2	no	—
24	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₁₇×#121	C₂²	1	4	yes	—
26	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×D₄×C₁₇	—	2	1	no	—
28	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
29	C₁₇×#492	C₂²	1	4	yes	complemented
30	C₁₇×#487	C₂²	1	4	yes	complemented
31	C₁₇×#483	C₂²	1	8	yes	complemented
32	C₁₇×#481	C₂²	1	4	yes	complemented
33	C₁₇×#475	C₂²	1	4	yes	complemented
34	C₁₇×#465	C₂²	1	16	yes	complemented
35	C₁₇×#461	C₂²	1	8	yes	complemented
36	C₁₇×#460	C₂²	1	4	yes	complemented
37	C₁₇×#450	C₂²	1	8	yes	complemented
38	C₁₇×#448	C₂²	1	8	yes	complemented
39	C₁₇×#448	C₂²	1	4	yes	complemented
40	C₁₇×#448	C₂²	1	16	yes	complemented
41	C₄×SD₁₆×C₁₇	C₂²	1	8	yes	complemented
42	C₈×D₄×C₁₇	C₂²	1	8	yes	complemented
43	C₁₇×#431	C₂²	1	2	yes	complemented
44	C₂×C₁₇×#103	C₂²	1	8	yes	complemented
45	C₂×C₁₇×C₂²⋊C₈	C₂²	1	4	yes	complemented
46	C₁₇×H(5,𝔽₂)	—	4	8	no	—
47	C₂×#41×C₁₇	—	2	4	no	—
48	C₂×#41×C₁₇	—	2	2	no	—
49	C₂²×Q₈×C₁₇	—	2	2	no	—
50	C₂²×Q₈×C₁₇	—	2	4	no	—
51	C₂²×Q₈×C₁₇	—	4	8	no	—
52	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₁₇	C₂³	1	8	yes	—
54	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
55	C₂²×D₄×C₁₇	—	2	4	no	—
56	C₂²×D₄×C₁₇	—	2	4	no	—
57	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₇	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₇	—	2	2	no	—
60	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
61	C₂×SD₁₆×C₁₇	—	4	16	no	—
62	C₂×SD₁₆×C₁₇	C₂³	1	8	yes	—
63	C₂×SD₁₆×C₁₇	C₂³	1	16	yes	—
64	C₂²×C₈×C₁₇	C₂³	1	8	yes	—
65	C₁₇×C₄⋊Q₈	—	2	8	no	—
66	C₁₇×C₄⋊Q₈	—	2	2	no	—
67	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
68	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₇×#127	C₂³	1	2	yes	—
70	C₁₇×#124	—	2	2	no	—
71	C₁₇×#123	—	2	8	no	—
72	C₁₇×C₂²⋊Q₈	—	2	4	no	—
73	C₁₇×C₂²⋊Q₈	—	2	4	no	—
74	C₁₇×C₂²⋊Q₈	—	2	16	no	—
75	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
76	C₁₇×#121	—	2	4	no	—
77	C₁₇×#121	—	2	4	no	—
78	C₁₇×#121	—	2	2	no	—
79	C₁₇×#121	—	2	4	no	—
80	C₁₇×#121	C₂³	1	4	yes	—
81	C₁₇×#121	C₂³	1	8	yes	—
82	C₁₇×#120	—	2	8	no	—
83	C₄×Q₈×C₁₇	—	2	2	no	—
84	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
85	C₄×D₄×C₁₇	—	2	8	no	—
86	C₄×D₄×C₁₇	—	2	2	no	—
87	C₄×D₄×C₁₇	D₄	1	4	yes	—
88	C₄×D₄×C₁₇	C₂³	1	4	yes	—
89	C₄×D₄×C₁₇	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
94	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
99	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
100	C₂×C₄²×C₁₇	—	2	1	no	—
101	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
102	C₁₇×#106	C₂³	1	8	yes	—
103	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
104	C₁₇×#103	C₂³	1	8	yes	—
105	C₁₇×#103	C₂³	1	16	yes	—
106	C₁₇×#102	C₂³	1	8	yes	—
107	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
108	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
109	C₄×C₈×C₁₇	C₂³	1	4	yes	—
110	C₂⁴×C₁₇	—	2	4	no	—
111	C₂⁴×C₁₇	C₂×D₄	1	2	yes	—
112	#41×C₁₇	—	4	16	no	—
113	#41×C₁₇	—	4	8	no	—
114	C₂×Q₈×C₁₇	—	2	4	no	—
115	C₂×Q₈×C₁₇	—	2	1	no	—
116	C₂×Q₈×C₁₇	—	2	2	no	—
117	C₂×Q₈×C₁₇	—	2	8	no	—
118	C₂×Q₈×C₁₇	—	2	2	no	—
119	C₂×Q₈×C₁₇	—	2	16	no	—
120	C₂×Q₈×C₁₇	—	4	8	no	—
121	C₂×Q₈×C₁₇	—	4	4	no	—
122	C₂×Q₈×C₁₇	—	4	8	no	—
123	C₂×Q₈×C₁₇	—	4	16	no	—
124	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
125	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
126	C₂×D₄×C₁₇	—	2	8	no	—
127	C₂×D₄×C₁₇	—	2	4	no	—
128	C₂×D₄×C₁₇	—	2	2	no	—
129	C₂×D₄×C₁₇	—	2	2	no	—
130	C₂×D₄×C₁₇	—	2	4	no	—
131	C₂×D₄×C₁₇	—	4	8	no	—
132	C₂×D₄×C₁₇	—	4	16	no	—
133	C₂×D₄×C₁₇	—	4	16	no	—
134	C₂×D₄×C₁₇	SD₁₆	1	8	yes	complemented
135	C₂×D₄×C₁₇	C₂×D₄	1	4	yes	—
136	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₇	—	2	1	no	—
138	C₂²×C₄×C₁₇	—	2	8	no	—
139	C₂²×C₄×C₁₇	—	2	4	no	—
140	C₂²×C₄×C₁₇	—	2	2	no	—
141	C₂²×C₄×C₁₇	—	2	1	no	—
142	C₂²×C₄×C₁₇	—	2	4	no	—
143	C₂²×C₄×C₁₇	—	4	4	no	—
144	C₂²×C₄×C₁₇	—	4	8	no	—
145	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
151	SD₁₆×C₁₇	—	2	16	no	—
152	SD₁₆×C₁₇	—	4	16	no	—
153	C₂×C₈×C₁₇	—	4	8	no	—
154	C₂×C₈×C₁₇	C₂⁴	1	8	yes	—
155	C₄⋊C₄×C₁₇	—	2	4	no	—
156	C₄⋊C₄×C₁₇	—	2	4	no	—
157	C₄⋊C₄×C₁₇	—	2	1	no	—
158	C₄⋊C₄×C₁₇	—	2	8	no	—
159	C₄⋊C₄×C₁₇	—	2	4	no	—
160	C₄⋊C₄×C₁₇	—	2	2	no	—
161	C₄⋊C₄×C₁₇	—	2	4	no	—
162	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
163	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
164	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
165	C₂²⋊C₄×C₁₇	—	2	8	no	—
166	C₂²⋊C₄×C₁₇	—	2	8	no	—
167	C₂²⋊C₄×C₁₇	—	2	4	no	—
168	C₂²⋊C₄×C₁₇	—	2	4	no	—
169	C₂²⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
170	C₄²×C₁₇	—	2	4	no	—
171	C₄²×C₁₇	C₂×D₄	1	2	yes	—
172	C₄²×C₁₇	C₂⁴	1	2	yes	—
173	#61562	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₁₇	—	2	4	no	—
175	C₂³×C₁₇	—	4	2	no	—
176	C₂³×C₁₇	—	4	2	no	—
177	C₂³×C₁₇	—	4	8	no	—
178	C₂³×C₁₇	—	8	4	no	—
179	C₂³×C₁₇	—	8	4	no	—
180	C₂³×C₁₇	C₂×SD₁₆	1	8	yes	complemented
181	C₂³×C₁₇	C₂²×D₄	1	4	yes	—
182	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₇	—	2	4	no	—
184	Q₈×C₁₇	—	2	2	no	—
185	Q₈×C₁₇	—	2	8	no	—
186	Q₈×C₁₇	—	4	16	no	—
187	Q₈×C₁₇	—	4	4	no	—
188	Q₈×C₁₇	—	4	4	no	—
189	Q₈×C₁₇	H(5,𝔽₂)	1	4	yes	complemented
190	D₄×C₁₇	—	2	8	no	—
191	D₄×C₁₇	—	4	16	no	—
192	D₄×C₁₇	—	4	8	no	—
193	D₄×C₁₇	—	4	4	no	—
194	D₄×C₁₇	—	8	2	no	—
195	D₄×C₁₇	—	8	4	no	—
196	D₄×C₁₇	C₂×SD₁₆	1	16	yes	complemented
197	C₂×C₄×C₁₇	—	2	4	no	—
198	C₂×C₄×C₁₇	—	2	2	no	—
199	C₂×C₄×C₁₇	—	2	8	no	—
200	C₂×C₄×C₁₇	—	2	2	no	—
201	C₂×C₄×C₁₇	—	2	2	no	—
202	C₂×C₄×C₁₇	—	2	4	no	—
203	C₂×C₄×C₁₇	—	2	4	no	—
204	C₂×C₄×C₁₇	—	4	4	no	—
205	C₂×C₄×C₁₇	—	4	2	no	—
206	C₂×C₄×C₁₇	—	4	1	no	—
207	C₂×C₄×C₁₇	—	4	16	no	—
208	C₂×C₄×C₁₇	—	4	2	no	—
209	C₂×C₄×C₁₇	—	4	4	no	—
210	C₂×C₄×C₁₇	—	4	8	no	—
211	C₂×C₄×C₁₇	—	4	8	no	—
212	C₂×C₄×C₁₇	C₂×SD₁₆	1	4	yes	complemented
213	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
216	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
218	C₈×C₁₇	—	2	8	no	—
219	#3496	C₂×C₁₇	1	1	yes	characteristic
220	C₂×D₄×Q₈	C₂×C₁₇	1	1	yes	characteristic, complemented
221	#3298	C₂×C₁₇	1	8	yes	complemented
222	D₄×SD₁₆	C₂×C₁₇	1	8	yes	complemented
223	#3206	C₂×C₁₇	1	2	yes	complemented
224	#3187	C₂×C₁₇	1	4	yes	complemented
225	#3103	C₂×C₁₇	1	2	yes	complemented
226	C₂×#448	C₂×C₁₇	1	4	yes	complemented
227	#2972	C₂×C₁₇	1	1	yes	characteristic, complemented
228	C₂²×C₁₇	—	2	1	no	—
229	C₂²×C₁₇	—	2	4	no	—
230	C₂²×C₁₇	—	2	1	no	—
231	C₂²×C₁₇	—	2	4	no	—
232	C₂²×C₁₇	—	4	8	no	—
233	C₂²×C₁₇	—	4	4	no	—
234	C₂²×C₁₇	—	4	4	no	—
235	C₂²×C₁₇	—	4	4	no	—
236	C₂²×C₁₇	—	16	8	no	—
237	C₂²×C₁₇	C₂²×SD₁₆	1	8	yes	—
238	C₂²×C₁₇	C₂²×SD₁₆	1	2	yes	—
239	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
240	C₄×C₁₇	—	2	2	no	—
241	C₄×C₁₇	—	2	4	no	—
242	C₄×C₁₇	—	2	1	no	—
243	C₄×C₁₇	—	2	4	no	—
244	C₄×C₁₇	—	4	2	no	—
245	C₄×C₁₇	—	4	4	no	—
246	C₄×C₁₇	—	4	4	no	—
247	C₄×C₁₇	C₂²×SD₁₆	1	4	yes	—
248	C₄×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
249	C₂×H(5,𝔽₂)	—	2	1	no	—
250	C₂³×Q₈	C₂²×C₁₇	1	2	yes	complemented
251	C₂²×SD₁₆	C₂²×C₁₇	1	8	yes	complemented
252	D₄×Q₈	—	2	4	no	—
253	D₄×Q₈	C₂²×C₁₇	1	8	yes	complemented
254	#547	C₂²×C₁₇	1	4	yes	—
255	#546	—	2	4	no	—
256	D₄²	C₂²×C₁₇	1	4	yes	—
257	#537	—	2	1	no	—
258	#534	—	2	2	no	—
259	#532	C₂²×C₁₇	1	2	yes	—
260	C₂×C₄⋊Q₈	—	2	1	no	—
261	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
262	C₂×C₂²⋊Q₈	—	2	2	no	—
263	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	2	yes	complemented
264	C₂×#121	C₂²×C₁₇	1	4	yes	—
265	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
268	#492	C₂²×C₁₇	1	4	yes	complemented
269	#487	C₂²×C₁₇	1	4	yes	complemented
270	#483	C₂²×C₁₇	1	8	yes	complemented
271	#481	C₂²×C₁₇	1	4	yes	complemented
272	#475	C₂²×C₁₇	1	4	yes	complemented
273	#465	C₂²×C₁₇	1	16	yes	complemented
274	#461	C₂²×C₁₇	1	8	yes	complemented
275	#460	C₂²×C₁₇	1	4	yes	complemented
276	#450	C₂²×C₁₇	1	8	yes	complemented
277	#448	C₂²×C₁₇	1	4	yes	complemented
278	#448	C₂²×C₁₇	1	8	yes	complemented
279	#448	C₂²×C₁₇	1	16	yes	complemented
280	C₄×SD₁₆	C₂²×C₁₇	1	8	yes	complemented
281	C₈×D₄	C₂²×C₁₇	1	8	yes	complemented
282	#431	C₂²×C₁₇	1	2	yes	complemented
283	C₂×#103	C₂²×C₁₇	1	8	yes	complemented
284	C₂×C₂²⋊C₈	C₂²×C₁₇	1	4	yes	complemented
285	C₂×C₁₇	—	2	2	no	—
286	C₂×C₁₇	—	2	8	no	—
287	C₂×C₁₇	—	8	4	no	—
288	C₂×C₁₇	#3484	1	1	yes	characteristic
289	C₂×C₁₇	C₂³×SD₁₆	1	1	yes	characteristic
290	C₂×C₁₇	#3586	1	1	yes	characteristic
291	H(5,𝔽₂)	—	4	8	no	—
292	C₂×#41	—	2	4	no	—
293	C₂×#41	—	2	2	no	—
294	C₂²×Q₈	—	2	2	no	—
295	C₂²×Q₈	—	2	4	no	—
296	C₂²×Q₈	—	4	8	no	—
297	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
298	C₂²×Q₈	C₂³×C₁₇	1	8	yes	—
299	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
300	C₂²×D₄	—	2	4	no	—
301	C₂²×D₄	—	2	4	no	—
302	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
303	C₂²×D₄	C₂³×C₁₇	1	4	yes	—
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
306	C₂×SD₁₆	—	4	16	no	—
307	C₂×SD₁₆	C₂³×C₁₇	1	8	yes	—
308	C₂×SD₁₆	C₂³×C₁₇	1	16	yes	—
309	C₂²×C₈	C₂³×C₁₇	1	8	yes	—
310	C₄⋊Q₈	—	2	8	no	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
313	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
314	#127	C₂³×C₁₇	1	2	yes	—
315	#124	—	2	2	no	—
316	#123	—	2	8	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	16	no	—
320	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
321	#121	—	2	4	no	—
322	#121	—	2	4	no	—
323	#121	—	2	2	no	—
324	#121	—	2	4	no	—
325	#121	C₂³×C₁₇	1	4	yes	—
326	#121	C₂³×C₁₇	1	8	yes	—
327	#120	—	2	8	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
330	C₄×D₄	—	2	8	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	D₄×C₁₇	1	4	yes	—
333	C₄×D₄	C₂³×C₁₇	1	4	yes	—
334	C₄×D₄	C₂³×C₁₇	1	4	yes	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	4	no	—
344	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
347	#106	C₂³×C₁₇	1	8	yes	—
348	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
349	#103	C₂³×C₁₇	1	8	yes	—
350	#103	C₂³×C₁₇	1	16	yes	—
351	#102	C₂³×C₁₇	1	8	yes	—
352	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
353	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
354	C₄×C₈	C₂³×C₁₇	1	4	yes	—
355	C₁₇	#61562	1	1	yes	characteristic, direct product factor, Sylow
356	C₂⁴	—	2	4	no	—
357	C₂⁴	C₂×D₄×C₁₇	1	2	yes	—
358	#41	—	4	16	no	—
359	#41	—	4	8	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	8	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	16	no	—
366	C₂×Q₈	—	4	8	no	—
367	C₂×Q₈	—	4	4	no	—
368	C₂×Q₈	—	4	8	no	—
369	C₂×Q₈	—	4	16	no	—
370	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
371	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	4	8	no	—
378	C₂×D₄	—	4	16	no	—
379	C₂×D₄	—	4	16	no	—
380	C₂×D₄	SD₁₆×C₁₇	1	8	yes	complemented
381	C₂×D₄	C₂×D₄×C₁₇	1	4	yes	—
382	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	8	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	—	4	8	no	—
391	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
393	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
397	SD₁₆	—	2	16	no	—
398	SD₁₆	—	4	16	no	—
399	C₂×C₈	—	4	8	no	—
400	C₂×C₈	C₂⁴×C₁₇	1	8	yes	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
409	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
410	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
416	C₄²	—	2	4	no	—
417	C₄²	C₂×D₄×C₁₇	1	2	yes	—
418	C₄²	C₂⁴×C₁₇	1	2	yes	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	8	no	—
423	C₂³	—	8	4	no	—
424	C₂³	—	8	4	no	—
425	C₂³	C₂×SD₁₆×C₁₇	1	8	yes	complemented
426	C₂³	C₂²×D₄×C₁₇	1	4	yes	—
427	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
428	Q₈	—	2	4	no	—
429	Q₈	—	2	2	no	—
430	Q₈	—	2	8	no	—
431	Q₈	—	4	16	no	—
432	Q₈	—	4	4	no	—
433	Q₈	—	4	4	no	—
434	Q₈	C₁₇×H(5,𝔽₂)	1	4	yes	complemented
435	D₄	—	2	8	no	—
436	D₄	—	4	16	no	—
437	D₄	—	4	8	no	—
438	D₄	—	4	4	no	—
439	D₄	—	8	4	no	—
440	D₄	—	8	2	no	—
441	D₄	C₂×SD₁₆×C₁₇	1	16	yes	complemented
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	16	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	C₂×SD₁₆×C₁₇	1	4	yes	complemented
458	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
461	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
462	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
463	C₈	—	2	8	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	16	8	no	—
473	C₂²	C₂²×SD₁₆×C₁₇	1	8	yes	—
474	C₂²	C₂²×SD₁₆×C₁₇	1	2	yes	—
475	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
476	C₄	—	2	4	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	2	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	4	no	—
482	C₄	—	4	2	no	—
483	C₄	C₂²×SD₁₆×C₁₇	1	4	yes	—
484	C₄	C₂×C₁₇×H(5,𝔽₂)	1	2	yes	—
485	C₂	—	2	2	no	—
486	C₂	—	2	8	no	—
487	C₂	—	8	4	no	—
488	C₂	C₁₇×#3484	1	1	yes	characteristic
489	C₂	C₂³×SD₁₆×C₁₇	1	1	yes	characteristic
490	C₂	C₁₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×D₄×Q₈×C₁₇	C₂	semidirect
3. C₁₇×#3298	C₂	semidirect
4. D₄×SD₁₆×C₁₇	C₂	semidirect
5. C₁₇×#3206	C₂	semidirect
6. C₁₇×#3187	C₂	semidirect
7. C₁₇×#3103	C₂	semidirect
8. C₂×C₁₇×#448	C₂	semidirect
9. C₁₇×#2972	C₂	semidirect
11. C₂³×Q₈×C₁₇	C₂²	semidirect
12. C₂²×SD₁₆×C₁₇	C₂²	semidirect
14. D₄×Q₈×C₁₇	C₂²	semidirect
22. C₂×C₁₇×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₁₇×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
29. C₁₇×#492	C₂²	semidirect
30. C₁₇×#487	C₂²	semidirect
31. C₁₇×#483	C₂²	semidirect
32. C₁₇×#481	C₂²	semidirect
33. C₁₇×#475	C₂²	semidirect
34. C₁₇×#465	C₂²	semidirect
35. C₁₇×#461	C₂²	semidirect
36. C₁₇×#460	C₂²	semidirect
37. C₁₇×#450	C₂²	semidirect
38. C₁₇×#448	C₂²	semidirect
39. C₁₇×#448	C₂²	semidirect
40. C₁₇×#448	C₂²	semidirect
41. C₄×SD₁₆×C₁₇	C₂²	semidirect
42. C₈×D₄×C₁₇	C₂²	semidirect
43. C₁₇×#431	C₂²	semidirect
44. C₂×C₁₇×#103	C₂²	semidirect
45. C₂×C₁₇×C₂²⋊C₈	C₂²	semidirect
134. C₂×D₄×C₁₇	SD₁₆	semidirect
173. #61562	C₁₇	direct (N × H)
180. C₂³×C₁₇	C₂×SD₁₆	semidirect
189. Q₈×C₁₇	H(5,𝔽₂)	semidirect
196. D₄×C₁₇	C₂×SD₁₆	semidirect
212. C₂×C₄×C₁₇	C₂×SD₁₆	semidirect
220. C₂×D₄×Q₈	C₂×C₁₇	semidirect
221. #3298	C₂×C₁₇	semidirect
222. D₄×SD₁₆	C₂×C₁₇	semidirect
223. #3206	C₂×C₁₇	semidirect
224. #3187	C₂×C₁₇	semidirect
225. #3103	C₂×C₁₇	semidirect
226. C₂×#448	C₂×C₁₇	semidirect
227. #2972	C₂×C₁₇	semidirect
250. C₂³×Q₈	C₂²×C₁₇	semidirect
251. C₂²×SD₁₆	C₂²×C₁₇	semidirect
253. D₄×Q₈	C₂²×C₁₇	semidirect
261. C₂×C₄⋊Q₈	C₂²×C₁₇	semidirect
263. C₂×C₂²⋊Q₈	C₂²×C₁₇	semidirect
265. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
268. #492	C₂²×C₁₇	semidirect
269. #487	C₂²×C₁₇	semidirect
270. #483	C₂²×C₁₇	semidirect
271. #481	C₂²×C₁₇	semidirect
272. #475	C₂²×C₁₇	semidirect
273. #465	C₂²×C₁₇	semidirect
274. #461	C₂²×C₁₇	semidirect
275. #460	C₂²×C₁₇	semidirect
276. #450	C₂²×C₁₇	semidirect
277. #448	C₂²×C₁₇	semidirect
278. #448	C₂²×C₁₇	semidirect
279. #448	C₂²×C₁₇	semidirect
280. C₄×SD₁₆	C₂²×C₁₇	semidirect
281. C₈×D₄	C₂²×C₁₇	semidirect
282. #431	C₂²×C₁₇	semidirect
283. C₂×#103	C₂²×C₁₇	semidirect
284. C₂×C₂²⋊C₈	C₂²×C₁₇	semidirect
355. C₁₇	#61562	direct (N × H)
380. C₂×D₄	SD₁₆×C₁₇	semidirect
425. C₂³	C₂×SD₁₆×C₁₇	semidirect
434. Q₈	C₁₇×H(5,𝔽₂)	semidirect
441. D₄	C₂×SD₁₆×C₁₇	semidirect
457. C₂×C₄	C₂×SD₁₆×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3496	2
C₂×D₄×Q₈×C₁₇	2
C₁₇×#3298	2
D₄×SD₁₆×C₁₇	2
C₁₇×#3206	2
C₁₇×#3187	2
C₁₇×#3103	2
C₂×C₁₇×#448	2
C₁₇×#2972	2
#61562	17

Subgroups — C17×#61562 #16919306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61562 #16919306