Subgroups — C₄×C₁₇×#578 #16917917

Order 4352.

2658 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#578	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₇×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
3	C₁₇×#2951	C₂	1	3	yes	maximal, complemented
4	C₁₇×#2950	C₂	1	3	yes	maximal, complemented
5	C₁₇×#2947	C₂	1	6	yes	maximal, complemented
6	C₄×C₁₇×#137	C₂	1	6	yes	maximal, complemented
7	C₄×C₁₇×#135	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×Q₁₆×C₁₇	C₂	1	3	yes	maximal, complemented
9	C₁₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2898	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₇×2₋¹⁺⁴	C₂²	1	2	yes	—
13	C₁₇×#578	C₄	1	16	yes	direct product factor
14	C₂×C₁₇×#137	C₂²	1	6	yes	—
15	C₂×C₁₇×#135	C₂²	1	3	yes	—
16	C₂²×Q₁₆×C₁₇	C₂²	1	3	yes	—
17	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
19	C₁₇×#520	—	2	6	no	—
20	C₁₇×#520	C₂²	1	6	yes	—
21	C₁₇×#520	C₂²	1	2	yes	—
22	C₁₇×#519	—	2	2	no	—
23	C₁₇×#519	C₂²	1	6	yes	—
24	C₄×#41×C₁₇	—	2	6	no	—
25	C₄×#41×C₁₇	C₂²	1	6	yes	—
26	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₇	—	2	2	no	—
28	C₂×C₄×Q₈×C₁₇	C₂²	1	6	yes	—
29	C₁₇×#441	C₂²	1	12	yes	—
30	C₁₇×#440	C₂²	1	12	yes	—
31	C₄×Q₁₆×C₁₇	C₂²	1	6	yes	—
32	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
33	C₄×Q₁₆×C₁₇	C₂²	1	6	yes	—
34	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
35	C₄×Q₁₆×C₁₇	C₂²	1	6	yes	—
36	C₄×SD₁₆×C₁₇	C₂²	1	6	yes	—
37	C₄×SD₁₆×C₁₇	C₂²	1	6	yes	—
38	C₄×D₈×C₁₇	C₂²	1	3	yes	—
39	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
40	C₁₇×#428	C₂²	1	6	yes	—
41	C₁₇×#427	C₂²	1	3	yes	—
42	C₂×C₁₇×#107	C₂²	1	3	yes	—
43	C₁₇×#419	C₂²	1	6	yes	—
44	C₁₇×#417	C₂²	1	6	yes	—
45	C₁₇×#416	C₂²	1	6	yes	—
46	C₂×C₁₇×#103	C₂²	1	6	yes	—
47	C₁₇×#405	C₂²	1	3	yes	—
48	C₁₇×#405	C₂²	1	3	yes	—
49	C₄×M₁₆×C₁₇	C₂²	1	3	yes	—
50	C₂×C₄×C₈×C₁₇	C₂²	1	3	yes	—
51	C₁₇×2₋¹⁺⁴	—	2	8	no	—
52	C₁₇×2₋¹⁺⁴	C₂×C₄	1	16	yes	complemented
53	C₂×#41×C₁₇	—	2	6	no	—
54	C₂×#41×C₁₇	C₂³	1	6	yes	—
55	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₁₇	—	2	2	no	—
57	C₂²×Q₈×C₁₇	C₂³	1	6	yes	—
58	C₁₇×#137	C₂×C₄	1	48	yes	complemented
59	C₁₇×#135	C₂×C₄	1	24	yes	complemented
60	C₂×Q₁₆×C₁₇	C₂×C₄	1	24	yes	complemented
61	C₂×Q₁₆×C₁₇	C₂³	1	3	yes	—
62	C₂×Q₁₆×C₁₇	C₂³	1	6	yes	—
63	C₂×SD₁₆×C₁₇	C₂³	1	6	yes	—
64	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
65	C₁₇×#131	—	2	4	no	—
66	C₁₇×#131	C₂×C₄	1	8	yes	complemented
67	C₂×M₁₆×C₁₇	C₂³	1	3	yes	—
68	C₂×M₁₆×C₁₇	C₂³	1	3	yes	—
69	C₂²×C₈×C₁₇	C₂³	1	3	yes	—
70	C₂²×C₈×C₁₇	C₂³	1	3	yes	—
71	C₄×Q₈×C₁₇	—	2	2	no	—
72	C₄×Q₈×C₁₇	—	2	6	no	—
73	C₄×Q₈×C₁₇	—	2	6	no	—
74	C₄×Q₈×C₁₇	—	2	6	no	—
75	C₄×Q₈×C₁₇	—	2	6	no	—
76	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
77	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
79	C₄×Q₈×C₁₇	C₂³	1	12	yes	—
80	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
81	C₄×D₄×C₁₇	—	2	6	no	—
82	C₄×D₄×C₁₇	—	2	6	no	—
83	C₄×D₄×C₁₇	—	2	6	no	—
84	C₄×D₄×C₁₇	—	2	12	no	—
85	C₄×D₄×C₁₇	D₄	1	3	yes	—
86	C₄×D₄×C₁₇	D₄	1	3	yes	—
87	C₄×D₄×C₁₇	C₂³	1	2	yes	—
88	C₄×D₄×C₁₇	C₂³	1	6	yes	—
89	C₁₇×#117	—	2	6	no	—
90	C₁₇×#117	—	2	12	no	—
91	C₁₇×#117	—	2	6	no	—
92	C₁₇×#117	C₂³	1	6	yes	—
93	C₁₇×#117	C₂³	1	3	yes	—
94	C₂×C₄⋊C₄×C₁₇	—	2	6	no	—
95	C₂×C₄⋊C₄×C₁₇	—	2	6	no	—
96	C₂×C₄⋊C₄×C₁₇	C₂³	1	6	yes	—
97	C₂×C₄²×C₁₇	—	2	6	no	—
98	C₂×C₄²×C₁₇	—	2	6	no	—
99	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
100	C₁₇×#107	C₂³	1	3	yes	—
101	C₁₇×#107	C₂³	1	6	yes	—
102	C₁₇×#107	C₂³	1	1	yes	characteristic
103	C₁₇×#106	C₂³	1	6	yes	—
104	C₁₇×#103	C₂³	1	6	yes	—
105	C₁₇×#103	C₂³	1	12	yes	—
106	C₁₇×#103	C₂³	1	6	yes	—
107	C₁₇×#102	C₂³	1	2	yes	—
108	C₁₇×#102	C₂³	1	6	yes	—
109	C₁₇×#97	C₂³	1	6	yes	—
110	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₇	C₂³	1	3	yes	—
112	C₄×C₈×C₁₇	C₂³	1	3	yes	—
113	C₄×C₈×C₁₇	C₂³	1	3	yes	—
114	#41×C₁₇	—	2	48	no	—
115	#41×C₁₇	—	2	12	no	—
116	#41×C₁₇	C₂²×C₄	1	24	yes	—
117	#41×C₁₇	C₂²×C₄	1	4	yes	—
118	#41×C₁₇	#41	1	4	yes	—
119	C₂×Q₈×C₁₇	—	2	16	no	—
120	C₂×Q₈×C₁₇	—	2	6	no	—
121	C₂×Q₈×C₁₇	—	2	12	no	—
122	C₂×Q₈×C₁₇	C₂²×C₄	1	24	yes	—
123	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
124	C₂×Q₈×C₁₇	C₂⁴	1	6	yes	—
125	C₂×D₄×C₁₇	—	2	6	no	—
126	C₂×D₄×C₁₇	C₂×D₄	1	3	yes	—
127	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₁₇	—	2	6	no	—
129	C₂²×C₄×C₁₇	—	2	6	no	—
130	C₂²×C₄×C₁₇	—	2	6	no	—
131	C₂²×C₄×C₁₇	—	2	2	no	—
132	C₂²×C₄×C₁₇	—	2	6	no	—
133	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
134	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
135	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
136	Q₁₆×C₁₇	C₂²×C₄	1	12	yes	—
137	Q₁₆×C₁₇	C₂²×C₄	1	24	yes	—
138	SD₁₆×C₁₇	C₂²×C₄	1	24	yes	—
139	D₈×C₁₇	C₂²×C₄	1	4	yes	—
140	M₁₆×C₁₇	—	2	6	no	—
141	M₁₆×C₁₇	C₂²×C₄	1	12	yes	—
142	C₂×C₈×C₁₇	—	2	6	no	—
143	C₂×C₈×C₁₇	C₂²×C₄	1	12	yes	—
144	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
145	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
146	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
147	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
148	C₄⋊C₄×C₁₇	—	2	12	no	—
149	C₄⋊C₄×C₁₇	—	2	6	no	—
150	C₄⋊C₄×C₁₇	—	2	6	no	—
151	C₄⋊C₄×C₁₇	—	2	6	no	—
152	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
153	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
154	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
155	C₄⋊C₄×C₁₇	C₂⁴	1	6	yes	—
156	C₂²⋊C₄×C₁₇	—	2	6	no	—
157	C₂²⋊C₄×C₁₇	—	2	2	no	—
158	C₂²⋊C₄×C₁₇	—	2	6	no	—
159	C₂²⋊C₄×C₁₇	C₂×D₄	1	6	yes	—
160	C₄²×C₁₇	—	2	6	no	—
161	C₄²×C₁₇	—	2	12	no	—
162	C₄²×C₁₇	—	2	6	no	—
163	C₄²×C₁₇	—	2	6	no	—
164	C₄²×C₁₇	C₂×D₄	1	3	yes	—
165	C₄²×C₁₇	C₂×D₄	1	3	yes	—
166	C₄²×C₁₇	C₂⁴	1	3	yes	—
167	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
168	C₄×#578	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₁₇	—	2	2	no	—
170	C₂³×C₁₇	C₂²×D₄	1	3	yes	—
171	Q₈×C₁₇	—	2	24	no	—
172	Q₈×C₁₇	—	2	6	no	—
173	Q₈×C₁₇	C₄×D₄	1	4	yes	—
174	Q₈×C₁₇	C₂³×C₄	1	12	yes	—
175	D₄×C₁₇	—	2	24	no	—
176	D₄×C₁₇	—	2	2	no	—
177	D₄×C₁₇	C₄×D₄	1	12	yes	—
178	D₄×C₁₇	C₂³×C₄	1	4	yes	—
179	C₂×C₄×C₁₇	—	2	24	no	—
180	C₂×C₄×C₁₇	—	2	6	no	—
181	C₂×C₄×C₁₇	—	2	24	no	—
182	C₂×C₄×C₁₇	—	2	6	no	—
183	C₂×C₄×C₁₇	—	2	2	no	—
184	C₂×C₄×C₁₇	—	2	6	no	—
185	C₂×C₄×C₁₇	—	4	3	no	—
186	C₂×C₄×C₁₇	—	4	4	no	—
187	C₂×C₄×C₁₇	—	8	6	no	—
188	C₂×C₄×C₁₇	—	8	6	no	—
189	C₂×C₄×C₁₇	C₂³×C₄	1	6	yes	—
190	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
191	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
192	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
194	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₇	C₂×#41	1	6	yes	—
196	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
197	C₈×C₁₇	—	2	1	no	—
198	C₈×C₁₇	—	2	3	no	—
199	C₈×C₁₇	C₂³×C₄	1	2	yes	—
200	C₈×C₁₇	C₂³×C₄	1	6	yes	—
201	C₂×#578	C₂×C₁₇	1	1	yes	characteristic
202	C₄×2₋¹⁺⁴	C₂×C₁₇	1	2	yes	complemented
203	#2951	C₂×C₁₇	1	3	yes	complemented
204	#2950	C₂×C₁₇	1	3	yes	complemented
205	#2947	C₂×C₁₇	1	6	yes	complemented
206	C₄×#137	C₂×C₁₇	1	6	yes	complemented
207	C₄×#135	C₂×C₁₇	1	3	yes	complemented
208	C₂×C₄×Q₁₆	C₂×C₁₇	1	3	yes	complemented
209	#2913	C₂×C₁₇	1	1	yes	characteristic, complemented
210	#2898	C₂×C₁₇	1	2	yes	complemented
211	C₄×#131	C₂×C₁₇	1	1	yes	characteristic, complemented
212	C₂²×C₁₇	—	2	3	no	—
213	C₂²×C₁₇	—	2	3	no	—
214	C₂²×C₁₇	—	2	4	no	—
215	C₂²×C₁₇	—	4	2	no	—
216	C₂²×C₁₇	—	4	2	no	—
217	C₂²×C₁₇	C₂×C₄×D₄	1	6	yes	—
218	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
219	C₄×C₁₇	—	2	1	no	—
220	C₄×C₁₇	—	2	3	no	—
221	C₄×C₁₇	—	2	12	no	—
222	C₄×C₁₇	—	2	3	no	—
223	C₄×C₁₇	—	4	6	no	—
224	C₄×C₁₇	—	4	2	no	—
225	C₄×C₁₇	C₂×C₄×D₄	1	6	yes	—
226	C₄×C₁₇	#578	1	2	yes	direct product factor
227	C₄×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
228	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
229	C₂×2₋¹⁺⁴	C₂²×C₁₇	1	2	yes	—
230	#578	C₄×C₁₇	1	16	yes	direct product factor
231	C₂×#137	C₂²×C₁₇	1	6	yes	—
232	C₂×#135	C₂²×C₁₇	1	3	yes	—
233	C₂²×Q₁₆	C₂²×C₁₇	1	3	yes	—
234	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
235	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
236	#520	—	2	6	no	—
237	#520	C₂²×C₁₇	1	6	yes	—
238	#520	C₂²×C₁₇	1	2	yes	—
239	#519	—	2	2	no	—
240	#519	C₂²×C₁₇	1	6	yes	—
241	C₄×#41	—	2	6	no	—
242	C₄×#41	C₂²×C₁₇	1	6	yes	—
243	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
244	C₂×C₄×Q₈	—	2	2	no	—
245	C₂×C₄×Q₈	C₂²×C₁₇	1	6	yes	—
246	#441	C₂²×C₁₇	1	12	yes	—
247	#440	C₂²×C₁₇	1	12	yes	—
248	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
249	C₄×Q₁₆	C₂²×C₁₇	1	6	yes	—
250	C₄×Q₁₆	C₂²×C₁₇	1	6	yes	—
251	C₄×Q₁₆	C₂²×C₁₇	1	6	yes	—
252	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
253	C₄×SD₁₆	C₂²×C₁₇	1	6	yes	—
254	C₄×SD₁₆	C₂²×C₁₇	1	6	yes	—
255	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
256	C₄×D₈	C₂²×C₁₇	1	3	yes	—
257	#428	C₂²×C₁₇	1	6	yes	—
258	#427	C₂²×C₁₇	1	3	yes	—
259	C₂×#107	C₂²×C₁₇	1	3	yes	—
260	#419	C₂²×C₁₇	1	6	yes	—
261	#417	C₂²×C₁₇	1	6	yes	—
262	#416	C₂²×C₁₇	1	6	yes	—
263	C₂×#103	C₂²×C₁₇	1	6	yes	—
264	#405	C₂²×C₁₇	1	3	yes	—
265	#405	C₂²×C₁₇	1	3	yes	—
266	C₄×M₁₆	C₂²×C₁₇	1	3	yes	—
267	C₂×C₄×C₈	C₂²×C₁₇	1	3	yes	—
268	C₂×C₁₇	—	2	6	no	—
269	C₂×C₁₇	—	4	4	no	—
270	C₂×C₁₇	C₂²×C₄×D₄	1	1	yes	characteristic
271	C₂×C₁₇	C₂×#578	1	1	yes	characteristic
272	C₂×C₁₇	#3584	1	1	yes	characteristic
273	2₋¹⁺⁴	—	2	8	no	—
274	2₋¹⁺⁴	C₂×C₄×C₁₇	1	16	yes	complemented
275	C₂×#41	—	2	6	no	—
276	C₂×#41	C₂³×C₁₇	1	6	yes	—
277	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
278	C₂²×Q₈	—	2	2	no	—
279	C₂²×Q₈	C₂³×C₁₇	1	6	yes	—
280	#137	C₂×C₄×C₁₇	1	48	yes	complemented
281	#135	C₂×C₄×C₁₇	1	24	yes	complemented
282	C₂×Q₁₆	C₂×C₄×C₁₇	1	24	yes	complemented
283	C₂×Q₁₆	C₂³×C₁₇	1	3	yes	—
284	C₂×Q₁₆	C₂³×C₁₇	1	6	yes	—
285	C₂×SD₁₆	C₂³×C₁₇	1	6	yes	—
286	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
287	#131	—	2	4	no	—
288	#131	C₂×C₄×C₁₇	1	8	yes	complemented
289	C₂×M₁₆	C₂³×C₁₇	1	3	yes	—
290	C₂×M₁₆	C₂³×C₁₇	1	3	yes	—
291	C₂²×C₈	C₂³×C₁₇	1	3	yes	—
292	C₂²×C₈	C₂³×C₁₇	1	3	yes	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	6	no	—
295	C₄×Q₈	—	2	6	no	—
296	C₄×Q₈	—	2	6	no	—
297	C₄×Q₈	—	2	6	no	—
298	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
299	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
300	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
301	C₄×Q₈	C₂³×C₁₇	1	12	yes	—
302	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
303	C₄×D₄	—	2	6	no	—
304	C₄×D₄	—	2	6	no	—
305	C₄×D₄	—	2	6	no	—
306	C₄×D₄	—	2	12	no	—
307	C₄×D₄	D₄×C₁₇	1	3	yes	—
308	C₄×D₄	D₄×C₁₇	1	3	yes	—
309	C₄×D₄	C₂³×C₁₇	1	2	yes	—
310	C₄×D₄	C₂³×C₁₇	1	6	yes	—
311	#117	—	2	6	no	—
312	#117	—	2	12	no	—
313	#117	—	2	6	no	—
314	#117	C₂³×C₁₇	1	6	yes	—
315	#117	C₂³×C₁₇	1	3	yes	—
316	C₂×C₄⋊C₄	—	2	6	no	—
317	C₂×C₄⋊C₄	—	2	6	no	—
318	C₂×C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
319	C₂×C₄²	—	2	6	no	—
320	C₂×C₄²	—	2	6	no	—
321	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
322	#107	C₂³×C₁₇	1	3	yes	—
323	#107	C₂³×C₁₇	1	6	yes	—
324	#107	C₂³×C₁₇	1	1	yes	characteristic
325	#106	C₂³×C₁₇	1	6	yes	—
326	#103	C₂³×C₁₇	1	6	yes	—
327	#103	C₂³×C₁₇	1	12	yes	—
328	#103	C₂³×C₁₇	1	6	yes	—
329	#102	C₂³×C₁₇	1	2	yes	—
330	#102	C₂³×C₁₇	1	6	yes	—
331	#97	C₂³×C₁₇	1	6	yes	—
332	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
333	C₄×C₈	C₂³×C₁₇	1	3	yes	—
334	C₄×C₈	C₂³×C₁₇	1	3	yes	—
335	C₄×C₈	C₂³×C₁₇	1	3	yes	—
336	C₁₇	C₄×#578	1	1	yes	characteristic, direct product factor, Sylow
337	#41	—	2	48	no	—
338	#41	—	2	12	no	—
339	#41	C₂²×C₄×C₁₇	1	24	yes	—
340	#41	C₂²×C₄×C₁₇	1	4	yes	—
341	#41	#41×C₁₇	1	4	yes	—
342	C₂×Q₈	—	2	16	no	—
343	C₂×Q₈	—	2	6	no	—
344	C₂×Q₈	—	2	12	no	—
345	C₂×Q₈	C₂²×C₄×C₁₇	1	24	yes	—
346	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
347	C₂×Q₈	C₂⁴×C₁₇	1	6	yes	—
348	C₂×D₄	—	2	6	no	—
349	C₂×D₄	C₂×D₄×C₁₇	1	3	yes	—
350	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
351	C₂²×C₄	—	2	6	no	—
352	C₂²×C₄	—	2	6	no	—
353	C₂²×C₄	—	2	6	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	6	no	—
356	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
357	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
358	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
359	Q₁₆	C₂²×C₄×C₁₇	1	12	yes	—
360	Q₁₆	C₂²×C₄×C₁₇	1	24	yes	—
361	SD₁₆	C₂²×C₄×C₁₇	1	24	yes	—
362	D₈	C₂²×C₄×C₁₇	1	4	yes	—
363	M₁₆	—	2	6	no	—
364	M₁₆	C₂²×C₄×C₁₇	1	12	yes	—
365	C₂×C₈	—	2	6	no	—
366	C₂×C₈	C₂²×C₄×C₁₇	1	12	yes	—
367	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
368	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
369	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
370	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
371	C₄⋊C₄	—	2	12	no	—
372	C₄⋊C₄	—	2	6	no	—
373	C₄⋊C₄	—	2	6	no	—
374	C₄⋊C₄	—	2	6	no	—
375	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
376	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
377	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
378	C₄⋊C₄	C₂⁴×C₁₇	1	6	yes	—
379	C₂²⋊C₄	—	2	6	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	6	no	—
382	C₂²⋊C₄	C₂×D₄×C₁₇	1	6	yes	—
383	C₄²	—	2	6	no	—
384	C₄²	—	2	6	no	—
385	C₄²	—	2	12	no	—
386	C₄²	—	2	6	no	—
387	C₄²	C₂×D₄×C₁₇	1	3	yes	—
388	C₄²	C₂×D₄×C₁₇	1	3	yes	—
389	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
390	C₄²	C₂⁴×C₁₇	1	3	yes	—
391	C₂³	—	2	2	no	—
392	C₂³	C₂²×D₄×C₁₇	1	3	yes	—
393	Q₈	—	2	24	no	—
394	Q₈	—	2	6	no	—
395	Q₈	C₄×D₄×C₁₇	1	4	yes	—
396	Q₈	C₂³×C₄×C₁₇	1	12	yes	—
397	D₄	—	2	24	no	—
398	D₄	—	2	2	no	—
399	D₄	C₄×D₄×C₁₇	1	12	yes	—
400	D₄	C₂³×C₄×C₁₇	1	4	yes	—
401	C₂×C₄	—	2	24	no	—
402	C₂×C₄	—	2	6	no	—
403	C₂×C₄	—	2	24	no	—
404	C₂×C₄	—	2	6	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	6	no	—
407	C₂×C₄	—	4	3	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	8	6	no	—
410	C₂×C₄	—	8	6	no	—
411	C₂×C₄	C₂³×C₄×C₁₇	1	6	yes	—
412	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
413	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
414	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
416	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₁₇	1	6	yes	—
418	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	3	no	—
421	C₈	C₂³×C₄×C₁₇	1	2	yes	—
422	C₈	C₂³×C₄×C₁₇	1	6	yes	—
423	C₂²	—	2	3	no	—
424	C₂²	—	2	3	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	C₂×C₄×D₄×C₁₇	1	6	yes	—
429	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
430	C₄	—	2	3	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	3	no	—
433	C₄	—	2	12	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	6	no	—
436	C₄	C₂×C₄×D₄×C₁₇	1	6	yes	—
437	C₄	C₁₇×#578	1	2	yes	direct product factor
438	C₄	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
439	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
440	C₂	—	2	6	no	—
441	C₂	—	4	4	no	—
442	C₂	C₂²×C₄×D₄×C₁₇	1	1	yes	characteristic
443	C₂	C₂×C₁₇×#578	1	1	yes	characteristic
444	C₂	C₁₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
socle	C₂²×C₁₇	C₂³×D₄
prime radical	C₂×C₁₇×#578	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₄×#41×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₇×2₋¹⁺⁴	C₂	semidirect
3. C₁₇×#2951	C₂	semidirect
4. C₁₇×#2950	C₂	semidirect
5. C₁₇×#2947	C₂	semidirect
6. C₄×C₁₇×#137	C₂	semidirect
7. C₄×C₁₇×#135	C₂	semidirect
8. C₂×C₄×Q₁₆×C₁₇	C₂	semidirect
9. C₁₇×#2913	C₂	semidirect
10. C₁₇×#2898	C₂	semidirect
11. C₄×C₁₇×#131	C₂	semidirect
13. C₁₇×#578	C₄	direct (N × H)
52. C₁₇×2₋¹⁺⁴	C₂×C₄	semidirect
58. C₁₇×#137	C₂×C₄	semidirect
59. C₁₇×#135	C₂×C₄	semidirect
60. C₂×Q₁₆×C₁₇	C₂×C₄	semidirect
66. C₁₇×#131	C₂×C₄	semidirect
168. C₄×#578	C₁₇	direct (N × H)
202. C₄×2₋¹⁺⁴	C₂×C₁₇	semidirect
203. #2951	C₂×C₁₇	semidirect
204. #2950	C₂×C₁₇	semidirect
205. #2947	C₂×C₁₇	semidirect
206. C₄×#137	C₂×C₁₇	semidirect
207. C₄×#135	C₂×C₁₇	semidirect
208. C₂×C₄×Q₁₆	C₂×C₁₇	semidirect
209. #2913	C₂×C₁₇	semidirect
210. #2898	C₂×C₁₇	semidirect
211. C₄×#131	C₂×C₁₇	semidirect
226. C₄×C₁₇	#578	direct (N × H)
230. #578	C₄×C₁₇	direct (N × H)
274. 2₋¹⁺⁴	C₂×C₄×C₁₇	semidirect
280. #137	C₂×C₄×C₁₇	semidirect
281. #135	C₂×C₄×C₁₇	semidirect
282. C₂×Q₁₆	C₂×C₄×C₁₇	semidirect
288. #131	C₂×C₄×C₁₇	semidirect
336. C₁₇	C₄×#578	direct (N × H)
437. C₄	C₁₇×#578	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#578	2
C₄×C₁₇×2₋¹⁺⁴	2
C₁₇×#2951	2
C₁₇×#2950	2
C₁₇×#2947	2
C₄×C₁₇×#137	2
C₄×C₁₇×#135	2
C₂×C₄×Q₁₆×C₁₇	2
C₁₇×#2913	2
C₁₇×#2898	2
C₄×C₁₇×#131	2
C₄×#578	17

Subgroups — C4×C17×#578 #16917917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₇×#578 #16917917