Subgroups — C₄×C₁₇×#576 #16917915

Order 4352.

2826 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#576	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₇×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
3	C₁₇×#2951	C₂	1	3	yes	maximal, complemented
4	C₁₇×#2948	C₂	1	3	yes	maximal, complemented
5	C₁₇×#2946	C₂	1	6	yes	maximal, complemented
6	C₄×C₁₇×AGL(1,ℤ/8)	C₂	1	6	yes	maximal, complemented
7	C₄×C₁₇×#135	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×D₈×C₁₇	C₂	1	3	yes	maximal, complemented
9	C₁₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2897	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₇×H(5,𝔽₂)	C₂²	1	2	yes	—
13	C₁₇×#576	C₄	1	16	yes	direct product factor
14	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	6	yes	—
15	C₂×C₁₇×#135	C₂²	1	3	yes	—
16	C₂²×D₈×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	2	no	—
20	C₁₇×#520	C₂²	1	2	yes	—
21	C₁₇×#520	C₂²	1	6	yes	complemented
22	C₁₇×#518	—	2	6	no	—
23	C₁₇×#518	C₂²	1	6	yes	complemented
24	C₄×#41×C₁₇	—	2	2	no	—
25	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
26	C₄×#41×C₁₇	C₂²	1	6	yes	complemented
27	C₂×C₄×D₄×C₁₇	—	2	6	no	—
28	C₂×C₄×D₄×C₁₇	C₂²	1	6	yes	complemented
29	C₁₇×#442	C₂²	1	12	yes	complemented
30	C₁₇×#440	C₂²	1	12	yes	complemented
31	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	complemented
32	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
33	C₄×SD₁₆×C₁₇	C₂²	1	6	yes	complemented
34	C₄×SD₁₆×C₁₇	C₂²	1	6	yes	complemented
35	C₄×D₈×C₁₇	C₂²	1	6	yes	complemented
36	C₄×D₈×C₁₇	C₂²	1	3	yes	complemented
37	C₄×D₈×C₁₇	C₂²	1	6	yes	complemented
38	C₄×D₈×C₁₇	C₂²	1	3	yes	complemented
39	C₄×D₈×C₁₇	C₂²	1	6	yes	complemented
40	C₁₇×#428	C₂²	1	6	yes	complemented
41	C₁₇×#427	C₂²	1	3	yes	complemented
42	C₂×C₁₇×#107	C₂²	1	3	yes	complemented
43	C₁₇×#418	C₂²	1	6	yes	complemented
44	C₁₇×#417	C₂²	1	6	yes	complemented
45	C₁₇×#416	C₂²	1	6	yes	complemented
46	C₂×C₁₇×#102	C₂²	1	6	yes	complemented
47	C₁₇×#405	C₂²	1	3	yes	complemented
48	C₁₇×#405	C₂²	1	3	yes	complemented
49	C₄×M₁₆×C₁₇	C₂²	1	3	yes	complemented
50	C₂×C₄×C₈×C₁₇	C₂²	1	3	yes	complemented
51	C₁₇×H(5,𝔽₂)	—	2	8	no	—
52	C₁₇×H(5,𝔽₂)	C₂×C₄	1	16	yes	complemented
53	C₂×#41×C₁₇	—	2	2	no	—
54	C₂×#41×C₁₇	C₂³	1	6	yes	—
55	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₇	—	2	6	no	—
57	C₂²×D₄×C₁₇	C₂³	1	6	yes	—
58	C₂³×C₄×C₁₇	—	2	6	no	—
59	C₁₇×AGL(1,ℤ/8)	C₂×C₄	1	48	yes	complemented
60	C₁₇×#135	C₂×C₄	1	24	yes	complemented
61	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
62	C₂×SD₁₆×C₁₇	C₂³	1	6	yes	—
63	C₂×D₈×C₁₇	C₂×C₄	1	24	yes	complemented
64	C₂×D₈×C₁₇	C₂³	1	3	yes	—
65	C₂×D₈×C₁₇	C₂³	1	6	yes	—
66	C₁₇×#131	—	2	4	no	—
67	C₁₇×#131	C₂×C₄	1	8	yes	complemented
68	C₂×M₁₆×C₁₇	C₂³	1	3	yes	—
69	C₂×M₁₆×C₁₇	C₂³	1	3	yes	—
70	C₂²×C₈×C₁₇	C₂³	1	3	yes	—
71	C₂²×C₈×C₁₇	C₂³	1	3	yes	—
72	C₄×Q₈×C₁₇	—	2	2	no	—
73	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
74	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
75	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
76	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
77	C₄×D₄×C₁₇	—	2	6	no	—
78	C₄×D₄×C₁₇	—	2	6	no	—
79	C₄×D₄×C₁₇	—	2	6	no	—
80	C₄×D₄×C₁₇	—	2	6	no	—
81	C₄×D₄×C₁₇	—	2	6	no	—
82	C₄×D₄×C₁₇	—	2	12	no	—
83	C₄×D₄×C₁₇	—	2	6	no	—
84	C₄×D₄×C₁₇	—	2	6	no	—
85	C₄×D₄×C₁₇	D₄	1	3	yes	—
86	C₄×D₄×C₁₇	D₄	1	3	yes	—
87	C₄×D₄×C₁₇	C₂³	1	6	yes	—
88	C₄×D₄×C₁₇	C₂³	1	12	yes	—
89	C₄×D₄×C₁₇	C₂³	1	6	yes	—
90	C₁₇×#117	—	2	6	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	C₂³	1	6	yes	—
96	C₂×C₂²⋊C₄×C₁₇	—	2	6	no	—
97	C₂×C₂²⋊C₄×C₁₇	—	2	12	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	2	yes	—
105	C₁₇×#103	C₂³	1	6	yes	—
106	C₁₇×#102	C₂³	1	6	yes	—
107	C₁₇×#102	C₂³	1	12	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	C₂⁴×C₁₇	—	2	6	no	—
115	#41×C₁₇	—	2	16	no	—
116	#41×C₁₇	—	2	12	no	—
117	#41×C₁₇	C₂²×C₄	1	4	yes	—
118	#41×C₁₇	C₂²×C₄	1	24	yes	complemented
119	#41×C₁₇	#41	1	4	yes	—
120	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
121	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
122	C₂×D₄×C₁₇	—	2	6	no	—
123	C₂×D₄×C₁₇	—	2	48	no	—
124	C₂×D₄×C₁₇	—	2	6	no	—
125	C₂×D₄×C₁₇	—	2	12	no	—
126	C₂×D₄×C₁₇	C₂²×C₄	1	24	yes	complemented
127	C₂×D₄×C₁₇	C₂×D₄	1	3	yes	—
128	C₂×D₄×C₁₇	C₂⁴	1	6	yes	—
129	C₂²×C₄×C₁₇	—	2	6	no	—
130	C₂²×C₄×C₁₇	—	2	6	no	—
131	C₂²×C₄×C₁₇	—	2	6	no	—
132	C₂²×C₄×C₁₇	—	2	12	no	—
133	C₂²×C₄×C₁₇	—	2	6	no	—
134	C₂²×C₄×C₁₇	—	8	12	no	—
135	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
136	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
137	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
138	Q₁₆×C₁₇	C₂²×C₄	1	4	yes	complemented
139	SD₁₆×C₁₇	C₂²×C₄	1	24	yes	complemented
140	D₈×C₁₇	C₂²×C₄	1	12	yes	complemented
141	D₈×C₁₇	C₂²×C₄	1	24	yes	complemented
142	M₁₆×C₁₇	—	2	6	no	—
143	M₁₆×C₁₇	C₂²×C₄	1	12	yes	complemented
144	C₂×C₈×C₁₇	—	2	6	no	—
145	C₂×C₈×C₁₇	C₂²×C₄	1	12	yes	complemented
146	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
147	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
148	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
149	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
150	C₄⋊C₄×C₁₇	—	2	6	no	—
151	C₄⋊C₄×C₁₇	—	2	6	no	—
152	C₄⋊C₄×C₁₇	—	2	2	no	—
153	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
154	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
155	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
156	C₄⋊C₄×C₁₇	C₂⁴	1	6	yes	—
157	C₂²⋊C₄×C₁₇	—	2	6	no	—
158	C₂²⋊C₄×C₁₇	—	2	6	no	—
159	C₂²⋊C₄×C₁₇	—	2	12	no	—
160	C₂²⋊C₄×C₁₇	—	2	6	no	—
161	C₂²⋊C₄×C₁₇	C₂×D₄	1	6	yes	—
162	C₄²×C₁₇	—	2	6	no	—
163	C₄²×C₁₇	—	2	6	no	—
164	C₄²×C₁₇	—	2	2	no	—
165	C₄²×C₁₇	C₂×D₄	1	3	yes	—
166	C₄²×C₁₇	C₂×D₄	1	3	yes	—
167	C₄²×C₁₇	C₂⁴	1	3	yes	—
168	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
169	C₄×#576	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₁₇	—	2	6	no	—
171	C₂³×C₁₇	—	2	24	no	—
172	C₂³×C₁₇	—	8	6	no	—
173	C₂³×C₁₇	—	8	6	no	—
174	C₂³×C₁₇	C₂²×D₄	1	3	yes	—
175	Q₈×C₁₇	—	2	2	no	—
176	Q₈×C₁₇	C₄×D₄	1	4	yes	—
177	Q₈×C₁₇	C₂³×C₄	1	4	yes	—
178	D₄×C₁₇	—	2	24	no	—
179	D₄×C₁₇	—	2	24	no	—
180	D₄×C₁₇	—	2	6	no	—
181	D₄×C₁₇	C₄×D₄	1	12	yes	—
182	D₄×C₁₇	C₂³×C₄	1	12	yes	—
183	C₂×C₄×C₁₇	—	2	2	no	—
184	C₂×C₄×C₁₇	—	2	24	no	—
185	C₂×C₄×C₁₇	—	2	6	no	—
186	C₂×C₄×C₁₇	—	2	2	no	—
187	C₂×C₄×C₁₇	—	2	6	no	—
188	C₂×C₄×C₁₇	—	4	3	no	—
189	C₂×C₄×C₁₇	—	4	12	no	—
190	C₂×C₄×C₁₇	—	8	6	no	—
191	C₂×C₄×C₁₇	—	8	12	no	—
192	C₂×C₄×C₁₇	—	8	6	no	—
193	C₂×C₄×C₁₇	C₂³×C₄	1	6	yes	—
194	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
195	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
197	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
198	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₇	C₂×#41	1	6	yes	—
200	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
201	C₈×C₁₇	—	2	1	no	—
202	C₈×C₁₇	—	2	3	no	—
203	C₈×C₁₇	C₂³×C₄	1	2	yes	—
204	C₈×C₁₇	C₂³×C₄	1	6	yes	—
205	C₂×#576	C₂×C₁₇	1	1	yes	characteristic
206	C₄×H(5,𝔽₂)	C₂×C₁₇	1	2	yes	complemented
207	#2951	C₂×C₁₇	1	3	yes	complemented
208	#2948	C₂×C₁₇	1	3	yes	complemented
209	#2946	C₂×C₁₇	1	6	yes	complemented
210	C₄×AGL(1,ℤ/8)	C₂×C₁₇	1	6	yes	complemented
211	C₄×#135	C₂×C₁₇	1	3	yes	complemented
212	C₂×C₄×D₈	C₂×C₁₇	1	3	yes	complemented
213	#2913	C₂×C₁₇	1	1	yes	characteristic, complemented
214	#2897	C₂×C₁₇	1	2	yes	complemented
215	C₄×#131	C₂×C₁₇	1	1	yes	characteristic, complemented
216	C₂²×C₁₇	—	2	3	no	—
217	C₂²×C₁₇	—	2	3	no	—
218	C₂²×C₁₇	—	2	12	no	—
219	C₂²×C₁₇	—	4	6	no	—
220	C₂²×C₁₇	—	4	6	no	—
221	C₂²×C₁₇	—	8	24	no	—
222	C₂²×C₁₇	C₂×C₄×D₄	1	6	yes	—
223	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
224	C₄×C₁₇	—	2	1	no	—
225	C₄×C₁₇	—	2	3	no	—
226	C₄×C₁₇	—	2	4	no	—
227	C₄×C₁₇	—	2	3	no	—
228	C₄×C₁₇	—	4	2	no	—
229	C₄×C₁₇	—	4	6	no	—
230	C₄×C₁₇	C₂×C₄×D₄	1	6	yes	—
231	C₄×C₁₇	#576	1	2	yes	direct product factor
232	C₄×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
233	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
234	C₂×H(5,𝔽₂)	C₂²×C₁₇	1	2	yes	—
235	#576	C₄×C₁₇	1	16	yes	direct product factor
236	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	6	yes	—
237	C₂×#135	C₂²×C₁₇	1	3	yes	—
238	C₂²×D₈	C₂²×C₁₇	1	3	yes	—
239	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
240	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
241	#520	—	2	2	no	—
242	#520	C₂²×C₁₇	1	2	yes	—
243	#520	C₂²×C₁₇	1	6	yes	complemented
244	#518	—	2	6	no	—
245	#518	C₂²×C₁₇	1	6	yes	complemented
246	C₄×#41	—	2	2	no	—
247	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
248	C₄×#41	C₂²×C₁₇	1	6	yes	complemented
249	C₂×C₄×D₄	—	2	6	no	—
250	C₂×C₄×D₄	C₂²×C₁₇	1	6	yes	complemented
251	#442	C₂²×C₁₇	1	12	yes	complemented
252	#440	C₂²×C₁₇	1	12	yes	complemented
253	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic, complemented
254	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	complemented
255	C₄×SD₁₆	C₂²×C₁₇	1	6	yes	complemented
256	C₄×SD₁₆	C₂²×C₁₇	1	6	yes	complemented
257	C₄×D₈	C₂²×C₁₇	1	3	yes	complemented
258	C₄×D₈	C₂²×C₁₇	1	6	yes	complemented
259	C₄×D₈	C₂²×C₁₇	1	6	yes	complemented
260	C₄×D₈	C₂²×C₁₇	1	6	yes	complemented
261	C₄×D₈	C₂²×C₁₇	1	3	yes	complemented
262	#428	C₂²×C₁₇	1	6	yes	complemented
263	#427	C₂²×C₁₇	1	3	yes	complemented
264	C₂×#107	C₂²×C₁₇	1	3	yes	complemented
265	#418	C₂²×C₁₇	1	6	yes	complemented
266	#417	C₂²×C₁₇	1	6	yes	complemented
267	#416	C₂²×C₁₇	1	6	yes	complemented
268	C₂×#102	C₂²×C₁₇	1	6	yes	complemented
269	#405	C₂²×C₁₇	1	3	yes	complemented
270	#405	C₂²×C₁₇	1	3	yes	complemented
271	C₄×M₁₆	C₂²×C₁₇	1	3	yes	complemented
272	C₂×C₄×C₈	C₂²×C₁₇	1	3	yes	complemented
273	C₂×C₁₇	—	2	6	no	—
274	C₂×C₁₇	—	4	12	no	—
275	C₂×C₁₇	C₂²×C₄×D₄	1	1	yes	characteristic
276	C₂×C₁₇	C₂×#576	1	1	yes	characteristic
277	C₂×C₁₇	#3584	1	1	yes	characteristic
278	H(5,𝔽₂)	—	2	8	no	—
279	H(5,𝔽₂)	C₂×C₄×C₁₇	1	16	yes	complemented
280	C₂×#41	—	2	2	no	—
281	C₂×#41	C₂³×C₁₇	1	6	yes	—
282	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
283	C₂²×D₄	—	2	6	no	—
284	C₂²×D₄	C₂³×C₁₇	1	6	yes	—
285	C₂³×C₄	—	2	6	no	—
286	AGL(1,ℤ/8)	C₂×C₄×C₁₇	1	48	yes	complemented
287	#135	C₂×C₄×C₁₇	1	24	yes	complemented
288	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
289	C₂×SD₁₆	C₂³×C₁₇	1	6	yes	—
290	C₂×D₈	C₂×C₄×C₁₇	1	24	yes	complemented
291	C₂×D₈	C₂³×C₁₇	1	3	yes	—
292	C₂×D₈	C₂³×C₁₇	1	6	yes	—
293	#131	—	2	4	no	—
294	#131	C₂×C₄×C₁₇	1	8	yes	complemented
295	C₂×M₁₆	C₂³×C₁₇	1	3	yes	—
296	C₂×M₁₆	C₂³×C₁₇	1	3	yes	—
297	C₂²×C₈	C₂³×C₁₇	1	3	yes	—
298	C₂²×C₈	C₂³×C₁₇	1	3	yes	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
301	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
302	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
303	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
304	C₄×D₄	—	2	6	no	—
305	C₄×D₄	—	2	6	no	—
306	C₄×D₄	—	2	6	no	—
307	C₄×D₄	—	2	6	no	—
308	C₄×D₄	—	2	6	no	—
309	C₄×D₄	—	2	12	no	—
310	C₄×D₄	—	2	6	no	—
311	C₄×D₄	—	2	6	no	—
312	C₄×D₄	D₄×C₁₇	1	3	yes	—
313	C₄×D₄	D₄×C₁₇	1	3	yes	—
314	C₄×D₄	C₂³×C₁₇	1	6	yes	—
315	C₄×D₄	C₂³×C₁₇	1	12	yes	—
316	C₄×D₄	C₂³×C₁₇	1	6	yes	—
317	#117	—	2	6	no	—
318	#117	—	2	6	no	—
319	#117	C₂³×C₁₇	1	6	yes	—
320	#117	C₂³×C₁₇	1	3	yes	—
321	C₂×C₄⋊C₄	—	2	6	no	—
322	C₂×C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
323	C₂×C₂²⋊C₄	—	2	6	no	—
324	C₂×C₂²⋊C₄	—	2	12	no	—
325	C₂×C₄²	—	2	6	no	—
326	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
327	#107	C₂³×C₁₇	1	3	yes	—
328	#107	C₂³×C₁₇	1	6	yes	—
329	#107	C₂³×C₁₇	1	1	yes	characteristic
330	#106	C₂³×C₁₇	1	6	yes	—
331	#103	C₂³×C₁₇	1	2	yes	—
332	#103	C₂³×C₁₇	1	6	yes	—
333	#102	C₂³×C₁₇	1	6	yes	—
334	#102	C₂³×C₁₇	1	12	yes	—
335	#102	C₂³×C₁₇	1	6	yes	—
336	#97	C₂³×C₁₇	1	6	yes	—
337	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
338	C₄×C₈	C₂³×C₁₇	1	3	yes	—
339	C₄×C₈	C₂³×C₁₇	1	3	yes	—
340	C₄×C₈	C₂³×C₁₇	1	3	yes	—
341	C₁₇	C₄×#576	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁴	—	2	6	no	—
343	#41	—	2	16	no	—
344	#41	—	2	12	no	—
345	#41	C₂²×C₄×C₁₇	1	4	yes	—
346	#41	C₂²×C₄×C₁₇	1	24	yes	complemented
347	#41	#41×C₁₇	1	4	yes	—
348	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
349	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
350	C₂×D₄	—	2	6	no	—
351	C₂×D₄	—	2	48	no	—
352	C₂×D₄	—	2	6	no	—
353	C₂×D₄	—	2	12	no	—
354	C₂×D₄	C₂²×C₄×C₁₇	1	24	yes	complemented
355	C₂×D₄	C₂×D₄×C₁₇	1	3	yes	—
356	C₂×D₄	C₂⁴×C₁₇	1	6	yes	—
357	C₂²×C₄	—	2	6	no	—
358	C₂²×C₄	—	2	6	no	—
359	C₂²×C₄	—	2	6	no	—
360	C₂²×C₄	—	2	6	no	—
361	C₂²×C₄	—	2	12	no	—
362	C₂²×C₄	—	8	12	no	—
363	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
364	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
365	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
366	Q₁₆	C₂²×C₄×C₁₇	1	4	yes	complemented
367	SD₁₆	C₂²×C₄×C₁₇	1	24	yes	complemented
368	D₈	C₂²×C₄×C₁₇	1	12	yes	complemented
369	D₈	C₂²×C₄×C₁₇	1	24	yes	complemented
370	M₁₆	—	2	6	no	—
371	M₁₆	C₂²×C₄×C₁₇	1	12	yes	complemented
372	C₂×C₈	—	2	6	no	—
373	C₂×C₈	C₂²×C₄×C₁₇	1	12	yes	complemented
374	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
375	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
376	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
377	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
378	C₄⋊C₄	—	2	6	no	—
379	C₄⋊C₄	—	2	6	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
382	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
383	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
384	C₄⋊C₄	C₂⁴×C₁₇	1	6	yes	—
385	C₂²⋊C₄	—	2	6	no	—
386	C₂²⋊C₄	—	2	6	no	—
387	C₂²⋊C₄	—	2	12	no	—
388	C₂²⋊C₄	—	2	6	no	—
389	C₂²⋊C₄	C₂×D₄×C₁₇	1	6	yes	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	6	no	—
392	C₄²	—	2	6	no	—
393	C₄²	C₂×D₄×C₁₇	1	3	yes	—
394	C₄²	C₂×D₄×C₁₇	1	3	yes	—
395	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
396	C₄²	C₂⁴×C₁₇	1	3	yes	—
397	C₂³	—	2	6	no	—
398	C₂³	—	2	24	no	—
399	C₂³	—	8	6	no	—
400	C₂³	—	8	6	no	—
401	C₂³	C₂²×D₄×C₁₇	1	3	yes	—
402	Q₈	—	2	2	no	—
403	Q₈	C₄×D₄×C₁₇	1	4	yes	—
404	Q₈	C₂³×C₄×C₁₇	1	4	yes	—
405	D₄	—	2	24	no	—
406	D₄	—	2	24	no	—
407	D₄	—	2	6	no	—
408	D₄	C₄×D₄×C₁₇	1	12	yes	—
409	D₄	C₂³×C₄×C₁₇	1	12	yes	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	24	no	—
412	C₂×C₄	—	2	6	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	6	no	—
415	C₂×C₄	—	4	3	no	—
416	C₂×C₄	—	4	12	no	—
417	C₂×C₄	—	8	12	no	—
418	C₂×C₄	—	8	6	no	—
419	C₂×C₄	—	8	6	no	—
420	C₂×C₄	C₂³×C₄×C₁₇	1	6	yes	—
421	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
422	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
424	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
425	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₁₇	1	6	yes	—
427	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	3	no	—
430	C₈	C₂³×C₄×C₁₇	1	2	yes	—
431	C₈	C₂³×C₄×C₁₇	1	6	yes	—
432	C₂²	—	2	3	no	—
433	C₂²	—	2	3	no	—
434	C₂²	—	2	12	no	—
435	C₂²	—	4	6	no	—
436	C₂²	—	4	6	no	—
437	C₂²	—	8	24	no	—
438	C₂²	C₂×C₄×D₄×C₁₇	1	6	yes	—
439	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
440	C₄	—	2	3	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	3	no	—
443	C₄	—	2	4	no	—
444	C₄	—	4	6	no	—
445	C₄	—	4	2	no	—
446	C₄	C₂×C₄×D₄×C₁₇	1	6	yes	—
447	C₄	C₁₇×#576	1	2	yes	direct product factor
448	C₄	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
449	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
450	C₂	—	2	6	no	—
451	C₂	—	4	12	no	—
452	C₂	C₂²×C₄×D₄×C₁₇	1	1	yes	characteristic
453	C₂	C₂×C₁₇×#576	1	1	yes	characteristic
454	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×#576	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×H(5,𝔽₂)	C₂	semidirect
3. C₁₇×#2951	C₂	semidirect
4. C₁₇×#2948	C₂	semidirect
5. C₁₇×#2946	C₂	semidirect
6. C₄×C₁₇×AGL(1,ℤ/8)	C₂	semidirect
7. C₄×C₁₇×#135	C₂	semidirect
8. C₂×C₄×D₈×C₁₇	C₂	semidirect
9. C₁₇×#2913	C₂	semidirect
10. C₁₇×#2897	C₂	semidirect
11. C₄×C₁₇×#131	C₂	semidirect
13. C₁₇×#576	C₄	direct (N × H)
21. C₁₇×#520	C₂²	semidirect
23. C₁₇×#518	C₂²	semidirect
26. C₄×#41×C₁₇	C₂²	semidirect
28. C₂×C₄×D₄×C₁₇	C₂²	semidirect
29. C₁₇×#442	C₂²	semidirect
30. C₁₇×#440	C₂²	semidirect
31. C₄×Q₁₆×C₁₇	C₂²	semidirect
32. C₄×Q₁₆×C₁₇	C₂²	semidirect
33. C₄×SD₁₆×C₁₇	C₂²	semidirect
34. C₄×SD₁₆×C₁₇	C₂²	semidirect
35. C₄×D₈×C₁₇	C₂²	semidirect
36. C₄×D₈×C₁₇	C₂²	semidirect
37. C₄×D₈×C₁₇	C₂²	semidirect
38. C₄×D₈×C₁₇	C₂²	semidirect
39. C₄×D₈×C₁₇	C₂²	semidirect
40. C₁₇×#428	C₂²	semidirect
41. C₁₇×#427	C₂²	semidirect
42. C₂×C₁₇×#107	C₂²	semidirect
43. C₁₇×#418	C₂²	semidirect
44. C₁₇×#417	C₂²	semidirect
45. C₁₇×#416	C₂²	semidirect
46. C₂×C₁₇×#102	C₂²	semidirect
47. C₁₇×#405	C₂²	semidirect
48. C₁₇×#405	C₂²	semidirect
49. C₄×M₁₆×C₁₇	C₂²	semidirect
50. C₂×C₄×C₈×C₁₇	C₂²	semidirect
52. C₁₇×H(5,𝔽₂)	C₂×C₄	semidirect
59. C₁₇×AGL(1,ℤ/8)	C₂×C₄	semidirect
60. C₁₇×#135	C₂×C₄	semidirect
63. C₂×D₈×C₁₇	C₂×C₄	semidirect
67. C₁₇×#131	C₂×C₄	semidirect
118. #41×C₁₇	C₂²×C₄	semidirect
126. C₂×D₄×C₁₇	C₂²×C₄	semidirect
138. Q₁₆×C₁₇	C₂²×C₄	semidirect
139. SD₁₆×C₁₇	C₂²×C₄	semidirect
140. D₈×C₁₇	C₂²×C₄	semidirect
141. D₈×C₁₇	C₂²×C₄	semidirect
143. M₁₆×C₁₇	C₂²×C₄	semidirect
145. C₂×C₈×C₁₇	C₂²×C₄	semidirect
169. C₄×#576	C₁₇	direct (N × H)
206. C₄×H(5,𝔽₂)	C₂×C₁₇	semidirect
207. #2951	C₂×C₁₇	semidirect
208. #2948	C₂×C₁₇	semidirect
209. #2946	C₂×C₁₇	semidirect
210. C₄×AGL(1,ℤ/8)	C₂×C₁₇	semidirect
211. C₄×#135	C₂×C₁₇	semidirect
212. C₂×C₄×D₈	C₂×C₁₇	semidirect
213. #2913	C₂×C₁₇	semidirect
214. #2897	C₂×C₁₇	semidirect
215. C₄×#131	C₂×C₁₇	semidirect
231. C₄×C₁₇	#576	direct (N × H)
235. #576	C₄×C₁₇	direct (N × H)
243. #520	C₂²×C₁₇	semidirect
245. #518	C₂²×C₁₇	semidirect
248. C₄×#41	C₂²×C₁₇	semidirect
250. C₂×C₄×D₄	C₂²×C₁₇	semidirect
251. #442	C₂²×C₁₇	semidirect
252. #440	C₂²×C₁₇	semidirect
253. C₄×Q₁₆	C₂²×C₁₇	semidirect
254. C₄×Q₁₆	C₂²×C₁₇	semidirect
255. C₄×SD₁₆	C₂²×C₁₇	semidirect
256. C₄×SD₁₆	C₂²×C₁₇	semidirect
257. C₄×D₈	C₂²×C₁₇	semidirect
258. C₄×D₈	C₂²×C₁₇	semidirect
259. C₄×D₈	C₂²×C₁₇	semidirect
260. C₄×D₈	C₂²×C₁₇	semidirect
261. C₄×D₈	C₂²×C₁₇	semidirect
262. #428	C₂²×C₁₇	semidirect
263. #427	C₂²×C₁₇	semidirect
264. C₂×#107	C₂²×C₁₇	semidirect
265. #418	C₂²×C₁₇	semidirect
266. #417	C₂²×C₁₇	semidirect
267. #416	C₂²×C₁₇	semidirect
268. C₂×#102	C₂²×C₁₇	semidirect
269. #405	C₂²×C₁₇	semidirect
270. #405	C₂²×C₁₇	semidirect
271. C₄×M₁₆	C₂²×C₁₇	semidirect
272. C₂×C₄×C₈	C₂²×C₁₇	semidirect
279. H(5,𝔽₂)	C₂×C₄×C₁₇	semidirect
286. AGL(1,ℤ/8)	C₂×C₄×C₁₇	semidirect
287. #135	C₂×C₄×C₁₇	semidirect
290. C₂×D₈	C₂×C₄×C₁₇	semidirect
294. #131	C₂×C₄×C₁₇	semidirect
341. C₁₇	C₄×#576	direct (N × H)
346. #41	C₂²×C₄×C₁₇	semidirect
354. C₂×D₄	C₂²×C₄×C₁₇	semidirect
366. Q₁₆	C₂²×C₄×C₁₇	semidirect
367. SD₁₆	C₂²×C₄×C₁₇	semidirect
368. D₈	C₂²×C₄×C₁₇	semidirect
369. D₈	C₂²×C₄×C₁₇	semidirect
371. M₁₆	C₂²×C₄×C₁₇	semidirect
373. C₂×C₈	C₂²×C₄×C₁₇	semidirect
447. C₄	C₁₇×#576	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×#576	2
C₄×C₁₇×H(5,𝔽₂)	2
C₁₇×#2951	2
C₁₇×#2948	2
C₁₇×#2946	2
C₄×C₁₇×AGL(1,ℤ/8)	2
C₄×C₁₇×#135	2
C₂×C₄×D₈×C₁₇	2
C₁₇×#2913	2
C₁₇×#2897	2
C₄×C₁₇×#131	2
C₄×#576	17

Subgroups — C4×C17×#576 #16917915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₇×#576 #16917915