Subgroups — C₁₇×#61412 #16919156

Order 4352.

1886 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3510	C₂	1	2	yes	maximal, complemented
2	C₁₇×#3403	C₂	1	4	yes	maximal, complemented
3	C₁₇×#3402	C₂	1	4	yes	maximal, complemented
4	C₁₇×#3394	C₂	1	8	yes	maximal, complemented
5	C₁₇×#3154	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#3044	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3041	C₂	1	2	yes	maximal, complemented
9	C₁₇×#3040	C₂	1	2	yes	maximal, complemented
10	C₁₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#2949	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₇×#137	C₂²	1	2	yes	—
14	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
15	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
16	C₂²×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₇	C₂²	1	2	yes	—
18	C₂²×D₈×C₁₇	C₂²	1	1	yes	characteristic
19	C₁₇×#559	C₂²	1	8	yes	complemented
20	C₁₇×#556	C₂²	1	8	yes	complemented
21	C₁₇×#551	—	2	8	no	—
22	C₁₇×#542	—	2	4	no	—
23	C₁₇×#536	C₂²	1	2	yes	—
24	C₁₇×#535	C₂²	1	2	yes	—
25	C₁₇×#533	C₂²	1	1	yes	characteristic
26	C₁₇×#529	—	2	4	no	—
27	C₂×C₁₇×#124	C₂²	1	2	yes	—
28	C₁₇×#519	C₂²	1	2	yes	—
29	C₁₇×#518	C₂²	1	2	yes	—
30	C₄×#41×C₁₇	C₂²	1	2	yes	—
31	C₁₇×#497	C₂²	1	4	yes	complemented
32	C₁₇×#496	C₂²	1	4	yes	complemented
33	C₁₇×#495	C₂²	1	4	yes	—
34	C₁₇×#495	C₂²	1	4	yes	—
35	C₁₇×#495	C₂²	1	4	yes	complemented
36	C₁₇×#492	C₂²	1	4	yes	complemented
37	C₁₇×#464	C₂²	1	8	yes	complemented
38	C₁₇×#464	C₂²	1	8	yes	complemented
39	C₁₇×#463	C₂²	1	8	yes	—
40	C₁₇×#463	C₂²	1	8	yes	complemented
41	C₁₇×#462	C₂²	1	8	yes	complemented
42	C₁₇×#459	C₂²	1	8	yes	—
43	C₁₇×#446	C₂²	1	4	yes	complemented
44	C₈×Q₈×C₁₇	C₂²	1	4	yes	complemented
45	C₁₇×#440	C₂²	1	8	yes	complemented
46	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	complemented
47	C₄×SD₁₆×C₁₇	C₂²	1	8	yes	complemented
48	C₄×SD₁₆×C₁₇	C₂²	1	4	yes	complemented
49	C₄×D₈×C₁₇	C₂²	1	2	yes	complemented
50	C₁₇×#427	C₂²	1	1	yes	characteristic
51	C₁₇×#424	C₂²	1	2	yes	—
52	C₁₇×#423	C₂²	1	1	yes	characteristic
53	C₁₇×#419	C₂²	1	2	yes	—
54	C₁₇×#418	C₂²	1	2	yes	—
55	C₁₇×#416	C₂²	1	2	yes	—
56	C₁₇×#405	C₂²	1	2	yes	—
57	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
58	C₂×#41×C₁₇	C₂³	1	2	yes	—
59	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
61	C₁₇×#137	—	4	4	no	—
62	C₁₇×AGL(1,ℤ/8)	—	4	4	no	—
63	C₁₇×#135	—	2	4	no	—
64	C₂×Q₁₆×C₁₇	—	4	2	no	—
65	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
66	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
67	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
68	C₂×SD₁₆×C₁₇	—	2	8	no	—
69	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
70	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
71	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
72	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
73	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
74	C₂×D₈×C₁₇	—	4	2	no	—
75	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
76	C₂×D₈×C₁₇	C₂³	1	4	yes	—
77	C₂×D₈×C₁₇	C₂³	1	4	yes	—
78	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
79	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
81	C₁₇×C₄⋊Q₈	D₄	1	2	yes	—
82	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
83	C₁₇×#127	C₂³	1	4	yes	—
84	C₁₇×#126	—	2	8	no	—
85	C₁₇×#126	—	2	8	no	—
86	C₁₇×#125	D₄	1	2	yes	—
87	C₁₇×#124	—	2	8	no	—
88	C₁₇×#124	—	2	2	no	—
89	C₁₇×#124	—	2	2	no	—
90	C₁₇×#124	C₂³	1	8	yes	—
91	C₁₇×#124	C₂³	1	4	yes	—
92	C₁₇×#124	C₂³	1	4	yes	—
93	C₁₇×#123	—	2	8	no	—
94	C₁₇×#123	—	2	8	no	—
95	C₁₇×#123	—	2	4	no	—
96	C₁₇×C₂²⋊Q₈	—	2	8	no	—
97	C₁₇×C₂²⋊Q₈	—	2	4	no	—
98	C₁₇×C₂²⋊Q₈	D₄	1	4	yes	—
99	C₁₇×#121	—	2	4	no	—
100	C₁₇×#120	—	2	4	no	—
101	C₄×Q₈×C₁₇	—	2	4	no	—
102	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
103	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
104	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
105	C₄×D₄×C₁₇	—	2	4	no	—
106	C₄×D₄×C₁₇	—	2	4	no	—
107	C₄×D₄×C₁₇	—	2	8	no	—
108	C₄×D₄×C₁₇	C₂³	1	4	yes	—
109	C₄×D₄×C₁₇	C₂³	1	8	yes	—
110	C₁₇×#117	—	2	8	no	—
111	C₁₇×#117	—	2	4	no	—
112	C₁₇×#117	—	2	2	no	—
113	C₁₇×#117	C₂³	1	2	yes	—
114	C₁₇×#117	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
116	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
117	C₂×C₄²×C₁₇	—	2	2	no	—
118	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
119	C₁₇×#107	C₂³	1	2	yes	—
120	C₁₇×#106	C₂³	1	2	yes	—
121	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
122	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
123	C₁₇×#103	C₂³	1	4	yes	—
124	C₁₇×#103	C₂³	1	8	yes	—
125	C₁₇×#102	C₂³	1	4	yes	—
126	C₁₇×#102	C₂³	1	8	yes	—
127	C₁₇×#97	C₂³	1	4	yes	—
128	C₄×C₈×C₁₇	C₂³	1	4	yes	—
129	C₄×C₈×C₁₇	C₂³	1	2	yes	—
130	C₄×C₈×C₁₇	C₂³	1	2	yes	—
131	C₂⁴×C₁₇	—	2	2	no	—
132	#41×C₁₇	—	2	4	no	—
133	#41×C₁₇	—	2	4	no	—
134	C₂×Q₈×C₁₇	—	2	2	no	—
135	C₂×Q₈×C₁₇	—	2	4	no	—
136	C₂×Q₈×C₁₇	—	2	4	no	—
137	C₂×Q₈×C₁₇	C₂×D₄	1	4	yes	—
138	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
139	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
140	C₂×D₄×C₁₇	—	2	2	no	—
141	C₂×D₄×C₁₇	—	2	2	no	—
142	C₂×D₄×C₁₇	—	2	8	no	—
143	C₂×D₄×C₁₇	—	2	4	no	—
144	C₂×D₄×C₁₇	—	2	4	no	—
145	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
146	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₇	—	2	2	no	—
148	C₂²×C₄×C₁₇	—	2	2	no	—
149	C₂²×C₄×C₁₇	—	2	8	no	—
150	C₂²×C₄×C₁₇	—	2	4	no	—
151	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
153	Q₁₆×C₁₇	—	2	2	no	—
154	Q₁₆×C₁₇	—	4	4	no	—
155	Q₁₆×C₁₇	—	4	4	no	—
156	SD₁₆×C₁₇	—	2	8	no	—
157	SD₁₆×C₁₇	—	2	8	no	—
158	SD₁₆×C₁₇	—	2	4	no	—
159	SD₁₆×C₁₇	—	4	4	no	—
160	SD₁₆×C₁₇	—	4	4	no	—
161	D₈×C₁₇	—	2	2	no	—
162	D₈×C₁₇	—	4	4	no	—
163	D₈×C₁₇	—	4	4	no	—
164	M₁₆×C₁₇	—	2	4	no	—
165	C₂×C₈×C₁₇	—	2	2	no	—
166	C₂×C₈×C₁₇	#41	1	4	yes	—
167	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
168	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
169	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
171	C₄⋊C₄×C₁₇	—	2	8	no	—
172	C₄⋊C₄×C₁₇	—	2	4	no	—
173	C₄⋊C₄×C₁₇	—	2	8	no	—
174	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
175	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
176	C₄⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
177	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
178	C₂²⋊C₄×C₁₇	—	2	2	no	—
179	C₂²⋊C₄×C₁₇	—	2	8	no	—
180	C₂²⋊C₄×C₁₇	—	2	8	no	—
181	C₂²⋊C₄×C₁₇	—	2	8	no	—
182	C₂²⋊C₄×C₁₇	—	2	4	no	—
183	C₂²⋊C₄×C₁₇	—	2	8	no	—
184	C₂²⋊C₄×C₁₇	—	2	8	no	—
185	C₂²⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
186	C₄²×C₁₇	—	2	8	no	—
187	C₄²×C₁₇	—	2	4	no	—
188	C₄²×C₁₇	—	2	2	no	—
189	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₇	C₂⁴	1	2	yes	—
192	C₄²×C₁₇	C₂⁴	1	4	yes	—
193	#61412	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂³×C₁₇	—	2	4	no	—
195	C₂³×C₁₇	—	2	2	no	—
196	C₂³×C₁₇	—	4	4	no	—
197	C₂³×C₁₇	—	8	4	no	—
198	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
199	Q₈×C₁₇	—	2	4	no	—
200	Q₈×C₁₇	—	2	2	no	—
201	Q₈×C₁₇	—	2	2	no	—
202	Q₈×C₁₇	—	2	4	no	—
203	Q₈×C₁₇	—	4	4	no	—
204	Q₈×C₁₇	—	4	4	no	—
205	D₄×C₁₇	—	2	2	no	—
206	D₄×C₁₇	—	2	4	no	—
207	D₄×C₁₇	—	2	4	no	—
208	D₄×C₁₇	—	2	2	no	—
209	D₄×C₁₇	—	4	4	no	—
210	D₄×C₁₇	—	4	4	no	—
211	D₄×C₁₇	—	8	8	no	—
212	C₂×C₄×C₁₇	—	2	4	no	—
213	C₂×C₄×C₁₇	—	2	4	no	—
214	C₂×C₄×C₁₇	—	2	2	no	—
215	C₂×C₄×C₁₇	—	4	2	no	—
216	C₂×C₄×C₁₇	—	4	4	no	—
217	C₂×C₄×C₁₇	—	4	4	no	—
218	C₂×C₄×C₁₇	—	8	4	no	—
219	C₂×C₄×C₁₇	—	8	8	no	—
220	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₁₇	C₂²×D₄	1	8	yes	—
222	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
225	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
227	C₈×C₁₇	—	2	2	no	—
228	C₈×C₁₇	—	2	4	no	—
229	C₈×C₁₇	C₂×#41	1	2	yes	—
230	C₈×C₁₇	C₂×#41	1	2	yes	—
231	#3510	C₂×C₁₇	1	2	yes	complemented
232	#3403	C₂×C₁₇	1	4	yes	complemented
233	#3402	C₂×C₁₇	1	4	yes	complemented
234	#3394	C₂×C₁₇	1	8	yes	complemented
235	#3154	C₂×C₁₇	1	2	yes	complemented
236	C₂×#495	C₂×C₁₇	1	1	yes	characteristic, complemented
237	#3044	C₂×C₁₇	1	2	yes	complemented
238	#3041	C₂×C₁₇	1	2	yes	complemented
239	#3040	C₂×C₁₇	1	2	yes	complemented
240	#2960	C₂×C₁₇	1	1	yes	characteristic, complemented
241	#2949	C₂×C₁₇	1	2	yes	complemented
242	C₄×#135	C₂×C₁₇	1	1	yes	characteristic, complemented
243	C₂²×C₁₇	—	2	2	no	—
244	C₂²×C₁₇	—	4	4	no	—
245	C₂²×C₁₇	—	4	8	no	—
246	C₂²×C₁₇	—	4	2	no	—
247	C₂²×C₁₇	—	4	4	no	—
248	C₂²×C₁₇	—	16	4	no	—
249	C₂²×C₁₇	#550	1	2	yes	—
250	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
251	C₄×C₁₇	—	2	2	no	—
252	C₄×C₁₇	—	2	2	no	—
253	C₄×C₁₇	—	2	8	no	—
254	C₄×C₁₇	—	4	4	no	—
255	C₄×C₁₇	—	4	2	no	—
256	C₄×C₁₇	—	4	4	no	—
257	C₄×C₁₇	#550	1	2	yes	—
258	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
259	C₄×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×#137	C₂²×C₁₇	1	2	yes	—
261	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	2	yes	—
262	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
263	C₂²×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
264	C₂²×SD₁₆	C₂²×C₁₇	1	2	yes	—
265	C₂²×D₈	C₂²×C₁₇	1	1	yes	characteristic
266	#559	C₂²×C₁₇	1	8	yes	complemented
267	#556	C₂²×C₁₇	1	8	yes	complemented
268	#551	—	2	8	no	—
269	#542	—	2	4	no	—
270	#536	C₂²×C₁₇	1	2	yes	—
271	#535	C₂²×C₁₇	1	2	yes	—
272	#533	C₂²×C₁₇	1	1	yes	characteristic
273	#529	—	2	4	no	—
274	C₂×#124	C₂²×C₁₇	1	2	yes	—
275	#519	C₂²×C₁₇	1	2	yes	—
276	#518	C₂²×C₁₇	1	2	yes	—
277	C₄×#41	C₂²×C₁₇	1	2	yes	—
278	#497	C₂²×C₁₇	1	4	yes	complemented
279	#496	C₂²×C₁₇	1	4	yes	complemented
280	#495	C₂²×C₁₇	1	4	yes	—
281	#495	C₂²×C₁₇	1	4	yes	—
282	#495	C₂²×C₁₇	1	4	yes	complemented
283	#492	C₂²×C₁₇	1	4	yes	complemented
284	#464	C₂²×C₁₇	1	8	yes	complemented
285	#464	C₂²×C₁₇	1	8	yes	complemented
286	#463	C₂²×C₁₇	1	8	yes	—
287	#463	C₂²×C₁₇	1	8	yes	complemented
288	#462	C₂²×C₁₇	1	8	yes	complemented
289	#459	C₂²×C₁₇	1	8	yes	—
290	#446	C₂²×C₁₇	1	4	yes	complemented
291	C₈×Q₈	C₂²×C₁₇	1	4	yes	complemented
292	#440	C₂²×C₁₇	1	8	yes	complemented
293	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	complemented
294	C₄×SD₁₆	C₂²×C₁₇	1	4	yes	complemented
295	C₄×SD₁₆	C₂²×C₁₇	1	8	yes	complemented
296	C₄×D₈	C₂²×C₁₇	1	2	yes	complemented
297	#427	C₂²×C₁₇	1	1	yes	characteristic
298	#424	C₂²×C₁₇	1	2	yes	—
299	#423	C₂²×C₁₇	1	1	yes	characteristic
300	#419	C₂²×C₁₇	1	2	yes	—
301	#418	C₂²×C₁₇	1	2	yes	—
302	#416	C₂²×C₁₇	1	2	yes	—
303	#405	C₂²×C₁₇	1	2	yes	—
304	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
305	C₂×C₁₇	—	2	2	no	—
306	C₂×C₁₇	—	8	2	no	—
307	C₂×C₁₇	—	8	4	no	—
308	C₂×C₁₇	C₂×#550	1	1	yes	characteristic
309	C₂×C₁₇	#3584	1	2	yes	—
310	C₂×#41	C₂³×C₁₇	1	2	yes	—
311	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
312	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
313	#137	—	4	4	no	—
314	AGL(1,ℤ/8)	—	4	4	no	—
315	#135	—	2	4	no	—
316	C₂×Q₁₆	—	4	2	no	—
317	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
318	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
319	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
320	C₂×SD₁₆	—	2	8	no	—
321	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
322	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
323	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
324	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
325	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
326	C₂×D₈	—	4	2	no	—
327	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
328	C₂×D₈	C₂³×C₁₇	1	4	yes	—
329	C₂×D₈	C₂³×C₁₇	1	4	yes	—
330	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
331	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
333	C₄⋊Q₈	D₄×C₁₇	1	2	yes	—
334	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
335	#127	C₂³×C₁₇	1	4	yes	—
336	#126	—	2	8	no	—
337	#126	—	2	8	no	—
338	#125	D₄×C₁₇	1	2	yes	—
339	#124	—	2	8	no	—
340	#124	—	2	2	no	—
341	#124	—	2	2	no	—
342	#124	C₂³×C₁₇	1	8	yes	—
343	#124	C₂³×C₁₇	1	4	yes	—
344	#124	C₂³×C₁₇	1	4	yes	—
345	#123	—	2	8	no	—
346	#123	—	2	8	no	—
347	#123	—	2	4	no	—
348	C₂²⋊Q₈	—	2	8	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	D₄×C₁₇	1	4	yes	—
351	#121	—	2	4	no	—
352	#120	—	2	4	no	—
353	C₄×Q₈	—	2	4	no	—
354	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
355	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
356	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
357	C₄×D₄	—	2	4	no	—
358	C₄×D₄	—	2	4	no	—
359	C₄×D₄	—	2	8	no	—
360	C₄×D₄	C₂³×C₁₇	1	4	yes	—
361	C₄×D₄	C₂³×C₁₇	1	8	yes	—
362	#117	—	2	8	no	—
363	#117	—	2	4	no	—
364	#117	—	2	2	no	—
365	#117	C₂³×C₁₇	1	2	yes	—
366	#117	C₂³×C₁₇	1	2	yes	—
367	C₂×C₂²⋊C₄	—	2	4	no	—
368	C₂×C₂²⋊C₄	—	2	4	no	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
371	#107	C₂³×C₁₇	1	2	yes	—
372	#106	C₂³×C₁₇	1	2	yes	—
373	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
374	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
375	#103	C₂³×C₁₇	1	4	yes	—
376	#103	C₂³×C₁₇	1	8	yes	—
377	#102	C₂³×C₁₇	1	4	yes	—
378	#102	C₂³×C₁₇	1	8	yes	—
379	#97	C₂³×C₁₇	1	4	yes	—
380	C₄×C₈	C₂³×C₁₇	1	2	yes	—
381	C₄×C₈	C₂³×C₁₇	1	2	yes	—
382	C₄×C₈	C₂³×C₁₇	1	4	yes	—
383	C₁₇	#61412	1	1	yes	characteristic, direct product factor, Sylow
384	C₂⁴	—	2	2	no	—
385	#41	—	2	4	no	—
386	#41	—	2	4	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	C₂×D₄×C₁₇	1	4	yes	—
391	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
392	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
399	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	8	no	—
404	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
406	Q₁₆	—	2	2	no	—
407	Q₁₆	—	4	4	no	—
408	Q₁₆	—	4	4	no	—
409	SD₁₆	—	2	8	no	—
410	SD₁₆	—	2	8	no	—
411	SD₁₆	—	2	4	no	—
412	SD₁₆	—	4	4	no	—
413	SD₁₆	—	4	4	no	—
414	D₈	—	2	2	no	—
415	D₈	—	4	4	no	—
416	D₈	—	4	4	no	—
417	M₁₆	—	2	4	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	#41×C₁₇	1	4	yes	—
420	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
421	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
422	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
423	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	8	no	—
426	C₄⋊C₄	—	2	8	no	—
427	C₄⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
428	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
429	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
430	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₂²⋊C₄	—	2	8	no	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
439	C₄²	—	2	4	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	8	no	—
442	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
443	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
444	C₄²	C₂⁴×C₁₇	1	2	yes	—
445	C₄²	C₂⁴×C₁₇	1	4	yes	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	8	4	no	—
450	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
451	Q₈	—	2	4	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	2	4	no	—
455	Q₈	—	4	4	no	—
456	Q₈	—	4	4	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	2	no	—
461	D₄	—	4	4	no	—
462	D₄	—	4	4	no	—
463	D₄	—	8	8	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	8	4	no	—
471	C₂×C₄	—	8	8	no	—
472	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₇	1	8	yes	—
474	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
475	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
476	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
477	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
478	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
479	C₈	—	2	2	no	—
480	C₈	—	2	4	no	—
481	C₈	C₂×#41×C₁₇	1	2	yes	—
482	C₈	C₂×#41×C₁₇	1	2	yes	—
483	C₂²	—	2	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	8	no	—
488	C₂²	—	16	4	no	—
489	C₂²	C₁₇×#550	1	2	yes	—
490	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	8	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	4	no	—
497	C₄	C₁₇×#550	1	2	yes	—
498	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
499	C₄	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂	—	2	2	no	—
501	C₂	—	8	4	no	—
502	C₂	—	8	2	no	—
503	C₂	C₂×C₁₇×#550	1	1	yes	characteristic
504	C₂	C₁₇×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₁₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3510	C₂	semidirect
2. C₁₇×#3403	C₂	semidirect
3. C₁₇×#3402	C₂	semidirect
4. C₁₇×#3394	C₂	semidirect
5. C₁₇×#3154	C₂	semidirect
6. C₂×C₁₇×#495	C₂	semidirect
7. C₁₇×#3044	C₂	semidirect
8. C₁₇×#3041	C₂	semidirect
9. C₁₇×#3040	C₂	semidirect
10. C₁₇×#2960	C₂	semidirect
11. C₁₇×#2949	C₂	semidirect
12. C₄×C₁₇×#135	C₂	semidirect
19. C₁₇×#559	C₂²	semidirect
20. C₁₇×#556	C₂²	semidirect
31. C₁₇×#497	C₂²	semidirect
32. C₁₇×#496	C₂²	semidirect
35. C₁₇×#495	C₂²	semidirect
36. C₁₇×#492	C₂²	semidirect
37. C₁₇×#464	C₂²	semidirect
38. C₁₇×#464	C₂²	semidirect
40. C₁₇×#463	C₂²	semidirect
41. C₁₇×#462	C₂²	semidirect
43. C₁₇×#446	C₂²	semidirect
44. C₈×Q₈×C₁₇	C₂²	semidirect
45. C₁₇×#440	C₂²	semidirect
46. C₄×Q₁₆×C₁₇	C₂²	semidirect
47. C₄×SD₁₆×C₁₇	C₂²	semidirect
48. C₄×SD₁₆×C₁₇	C₂²	semidirect
49. C₄×D₈×C₁₇	C₂²	semidirect
193. #61412	C₁₇	direct (N × H)
231. #3510	C₂×C₁₇	semidirect
232. #3403	C₂×C₁₇	semidirect
233. #3402	C₂×C₁₇	semidirect
234. #3394	C₂×C₁₇	semidirect
235. #3154	C₂×C₁₇	semidirect
236. C₂×#495	C₂×C₁₇	semidirect
237. #3044	C₂×C₁₇	semidirect
238. #3041	C₂×C₁₇	semidirect
239. #3040	C₂×C₁₇	semidirect
240. #2960	C₂×C₁₇	semidirect
241. #2949	C₂×C₁₇	semidirect
242. C₄×#135	C₂×C₁₇	semidirect
266. #559	C₂²×C₁₇	semidirect
267. #556	C₂²×C₁₇	semidirect
278. #497	C₂²×C₁₇	semidirect
279. #496	C₂²×C₁₇	semidirect
282. #495	C₂²×C₁₇	semidirect
283. #492	C₂²×C₁₇	semidirect
284. #464	C₂²×C₁₇	semidirect
285. #464	C₂²×C₁₇	semidirect
287. #463	C₂²×C₁₇	semidirect
288. #462	C₂²×C₁₇	semidirect
290. #446	C₂²×C₁₇	semidirect
291. C₈×Q₈	C₂²×C₁₇	semidirect
292. #440	C₂²×C₁₇	semidirect
293. C₄×Q₁₆	C₂²×C₁₇	semidirect
294. C₄×SD₁₆	C₂²×C₁₇	semidirect
295. C₄×SD₁₆	C₂²×C₁₇	semidirect
296. C₄×D₈	C₂²×C₁₇	semidirect
383. C₁₇	#61412	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×#3510	2
C₁₇×#3403	2
C₁₇×#3402	2
C₁₇×#3394	2
C₁₇×#3154	2
C₂×C₁₇×#495	2
C₁₇×#3044	2
C₁₇×#3041	2
C₁₇×#3040	2
C₁₇×#2960	2
C₁₇×#2949	2
C₄×C₁₇×#135	2
#61412	17

Subgroups — C17×#61412 #16919156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61412 #16919156