Subgroups — C₁₇×#3484 #14526490

Order 2176.

1900 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#546	C₂	1	8	yes	maximal, complemented
4	D₄²×C₁₇	C₂	1	8	yes	maximal, complemented
5	C₁₇×#535	C₂	1	2	yes	maximal, complemented
6	C₁₇×#534	C₂	1	4	yes	maximal, complemented
7	C₁₇×#525	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₇×#120	C₂	1	4	yes	maximal, complemented
9	C₁₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁵×C₁₇	C₂²	1	2	yes	complemented
11	C₁₇×H(5,𝔽₂)	—	2	8	no	—
12	C₂×#41×C₁₇	C₂²	1	2	yes	complemented
13	C₂×#41×C₁₇	C₂²	1	4	yes	complemented
14	C₂²×D₄×C₁₇	—	2	8	no	—
15	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic
16	C₂²×D₄×C₁₇	C₂²	1	2	yes	complemented
17	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₄×C₁₇	C₂²	1	8	yes	complemented
19	C₂²×D₄×C₁₇	C₂²	1	4	yes	complemented
20	C₂²×D₄×C₁₇	C₂²	1	4	yes	complemented
21	C₂²×D₄×C₁₇	C₂²	1	8	yes	complemented
22	C₂³×C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
23	C₁₇×#127	C₂²	1	4	yes	complemented
24	C₁₇×#124	C₂²	1	4	yes	complemented
25	C₁₇×#123	C₂²	1	4	yes	complemented
26	C₁₇×#123	C₂²	1	8	yes	complemented
27	C₁₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
28	C₁₇×#121	C₂²	1	4	yes	complemented
29	C₁₇×#121	C₂²	1	16	yes	complemented
30	C₁₇×#121	C₂²	1	8	yes	complemented
31	C₁₇×#120	C₂²	1	4	yes	complemented
32	C₁₇×#120	C₂²	1	8	yes	complemented
33	C₁₇×#120	C₂²	1	16	yes	complemented
34	C₁₇×#120	C₂²	1	8	yes	complemented
35	C₄×D₄×C₁₇	C₂²	1	8	yes	complemented
36	C₄×D₄×C₁₇	C₂²	1	8	yes	complemented
37	C₁₇×#117	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	complemented
39	C₂×C₂²⋊C₄×C₁₇	C₂²	1	8	yes	complemented
40	C₂⁴×C₁₇	—	2	8	no	—
41	C₂⁴×C₁₇	—	4	8	no	—
42	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
43	C₂⁴×C₁₇	C₂³	1	8	yes	—
44	C₂⁴×C₁₇	C₂³	1	2	yes	—
45	C₂⁴×C₁₇	C₂³	1	2	yes	—
46	C₂⁴×C₁₇	C₂³	1	4	yes	complemented
47	#41×C₁₇	—	2	16	no	—
48	#41×C₁₇	—	2	8	no	—
49	C₂×Q₈×C₁₇	C₂³	1	2	yes	complemented
50	C₂×D₄×C₁₇	—	2	8	no	—
51	C₂×D₄×C₁₇	—	2	16	no	—
52	C₂×D₄×C₁₇	—	2	32	no	—
53	C₂×D₄×C₁₇	—	2	16	no	—
54	C₂×D₄×C₁₇	—	2	4	no	—
55	C₂×D₄×C₁₇	—	4	16	no	—
56	C₂×D₄×C₁₇	D₄	1	8	yes	complemented
57	C₂×D₄×C₁₇	C₂³	1	8	yes	—
58	C₂×D₄×C₁₇	C₂³	1	4	yes	—
59	C₂×D₄×C₁₇	C₂³	1	4	yes	—
60	C₂×D₄×C₁₇	C₂³	1	8	yes	—
61	C₂×D₄×C₁₇	C₂³	1	4	yes	—
62	C₂×D₄×C₁₇	C₂³	1	2	yes	complemented
63	C₂×D₄×C₁₇	C₂³	1	8	yes	complemented
64	C₂×D₄×C₁₇	C₂³	1	16	yes	complemented
65	C₂²×C₄×C₁₇	—	2	4	no	—
66	C₂²×C₄×C₁₇	C₂³	1	4	yes	—
67	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₇	C₂³	1	4	yes	complemented
70	C₂²×C₄×C₁₇	C₂³	1	4	yes	complemented
71	C₂²×C₄×C₁₇	C₂³	1	8	yes	complemented
72	C₄⋊C₄×C₁₇	C₂³	1	8	yes	complemented
73	C₄⋊C₄×C₁₇	C₂³	1	4	yes	complemented
74	C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
75	C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
76	C₂²⋊C₄×C₁₇	C₂³	1	16	yes	complemented
77	C₂²⋊C₄×C₁₇	C₂³	1	8	yes	complemented
78	C₂²⋊C₄×C₁₇	C₂³	1	8	yes	complemented
79	C₄²×C₁₇	C₂³	1	4	yes	complemented
80	C₂³×C₁₇	—	2	2	no	—
81	C₂³×C₁₇	—	2	4	no	—
82	C₂³×C₁₇	—	2	16	no	—
83	C₂³×C₁₇	—	2	4	no	—
84	C₂³×C₁₇	—	2	16	no	—
85	C₂³×C₁₇	—	2	8	no	—
86	C₂³×C₁₇	—	4	4	no	—
87	C₂³×C₁₇	—	4	8	no	—
88	C₂³×C₁₇	—	4	4	no	—
89	C₂³×C₁₇	—	4	8	no	—
90	C₂³×C₁₇	—	4	32	no	—
91	C₂³×C₁₇	C₂×D₄	1	8	yes	complemented
92	C₂³×C₁₇	C₂⁴	1	4	yes	—
93	C₂³×C₁₇	C₂⁴	1	4	yes	—
94	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
95	C₂³×C₁₇	C₂⁴	1	4	yes	—
96	C₂³×C₁₇	C₂⁴	1	2	yes	—
97	Q₈×C₁₇	—	2	4	no	—
98	D₄×C₁₇	—	2	16	no	—
99	D₄×C₁₇	—	2	8	no	—
100	D₄×C₁₇	—	2	16	no	—
101	D₄×C₁₇	—	2	16	no	—
102	D₄×C₁₇	—	2	8	no	—
103	D₄×C₁₇	—	2	4	no	—
104	D₄×C₁₇	—	4	16	no	—
105	D₄×C₁₇	C₂×D₄	1	16	yes	complemented
106	C₂×C₄×C₁₇	—	2	2	no	—
107	C₂×C₄×C₁₇	—	2	8	no	—
108	C₂×C₄×C₁₇	—	2	8	no	—
109	C₂×C₄×C₁₇	—	2	8	no	—
110	C₂×C₄×C₁₇	—	4	8	no	—
111	C₂×C₄×C₁₇	C₂×D₄	1	4	yes	complemented
112	C₂×C₄×C₁₇	C₂⁴	1	8	yes	—
113	C₂×C₄×C₁₇	C₂⁴	1	4	yes	—
114	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
115	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
116	#3484	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂²×C₁₇	—	2	8	no	—
118	C₂²×C₁₇	—	2	2	no	—
119	C₂²×C₁₇	—	2	8	no	—
120	C₂²×C₁₇	—	2	2	no	—
121	C₂²×C₁₇	—	2	2	no	—
122	C₂²×C₁₇	—	2	4	no	—
123	C₂²×C₁₇	—	2	4	no	—
124	C₂²×C₁₇	—	2	8	no	—
125	C₂²×C₁₇	—	2	8	no	—
126	C₂²×C₁₇	—	4	8	no	—
127	C₂²×C₁₇	—	4	32	no	—
128	C₂²×C₁₇	—	4	8	no	—
129	C₂²×C₁₇	—	8	8	no	—
130	C₂²×C₁₇	C₂²×D₄	1	2	yes	—
131	C₂²×C₁₇	C₂²×D₄	1	8	yes	—
132	C₂²×C₁₇	H(5,𝔽₂)	1	4	yes	complemented
133	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
134	C₄×C₁₇	—	2	2	no	—
135	C₄×C₁₇	—	2	4	no	—
136	C₄×C₁₇	—	2	8	no	—
137	C₄×C₁₇	C₂²×D₄	1	4	yes	—
138	C₂×H(5,𝔽₂)	C₂×C₁₇	1	1	yes	characteristic, complemented
139	C₂³×D₄	C₂×C₁₇	1	1	yes	characteristic, complemented
140	#546	C₂×C₁₇	1	8	yes	complemented
141	D₄²	C₂×C₁₇	1	8	yes	complemented
142	#535	C₂×C₁₇	1	2	yes	complemented
143	#534	C₂×C₁₇	1	4	yes	complemented
144	#525	C₂×C₁₇	1	2	yes	complemented
145	C₂×#120	C₂×C₁₇	1	4	yes	complemented
146	#518	C₂×C₁₇	1	1	yes	characteristic, complemented
147	C₂×C₁₇	—	2	2	no	—
148	C₂×C₁₇	—	2	4	no	—
149	C₂×C₁₇	—	2	8	no	—
150	C₂×C₁₇	—	4	4	no	—
151	C₂×C₁₇	—	4	4	no	—
152	C₂×C₁₇	C₂³×D₄	1	1	yes	characteristic
153	C₂×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
154	C₂⁵	C₂²×C₁₇	1	2	yes	complemented
155	H(5,𝔽₂)	—	2	8	no	—
156	C₂×#41	C₂²×C₁₇	1	2	yes	complemented
157	C₂×#41	C₂²×C₁₇	1	4	yes	complemented
158	C₂²×D₄	—	2	8	no	—
159	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic
160	C₂²×D₄	C₂²×C₁₇	1	2	yes	complemented
161	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
162	C₂²×D₄	C₂²×C₁₇	1	8	yes	complemented
163	C₂²×D₄	C₂²×C₁₇	1	4	yes	complemented
164	C₂²×D₄	C₂²×C₁₇	1	4	yes	complemented
165	C₂²×D₄	C₂²×C₁₇	1	8	yes	complemented
166	C₂³×C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
167	#127	C₂²×C₁₇	1	4	yes	complemented
168	#124	C₂²×C₁₇	1	4	yes	complemented
169	#123	C₂²×C₁₇	1	4	yes	complemented
170	#123	C₂²×C₁₇	1	8	yes	complemented
171	C₂²⋊Q₈	C₂²×C₁₇	1	4	yes	complemented
172	#121	C₂²×C₁₇	1	4	yes	complemented
173	#121	C₂²×C₁₇	1	16	yes	complemented
174	#121	C₂²×C₁₇	1	8	yes	complemented
175	#120	C₂²×C₁₇	1	4	yes	complemented
176	#120	C₂²×C₁₇	1	8	yes	complemented
177	#120	C₂²×C₁₇	1	16	yes	complemented
178	#120	C₂²×C₁₇	1	8	yes	complemented
179	C₄×D₄	C₂²×C₁₇	1	8	yes	complemented
180	C₄×D₄	C₂²×C₁₇	1	8	yes	complemented
181	#117	C₂²×C₁₇	1	2	yes	complemented
182	C₂×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	complemented
183	C₂×C₂²⋊C₄	C₂²×C₁₇	1	8	yes	complemented
184	C₁₇	#3484	1	1	yes	characteristic, direct product factor, Sylow
185	C₂⁴	—	2	8	no	—
186	C₂⁴	—	4	8	no	—
187	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
188	C₂⁴	C₂³×C₁₇	1	8	yes	—
189	C₂⁴	C₂³×C₁₇	1	2	yes	—
190	C₂⁴	C₂³×C₁₇	1	2	yes	—
191	C₂⁴	C₂³×C₁₇	1	4	yes	complemented
192	#41	—	2	16	no	—
193	#41	—	2	8	no	—
194	C₂×Q₈	C₂³×C₁₇	1	2	yes	complemented
195	C₂×D₄	—	2	8	no	—
196	C₂×D₄	—	2	16	no	—
197	C₂×D₄	—	2	32	no	—
198	C₂×D₄	—	2	16	no	—
199	C₂×D₄	—	2	4	no	—
200	C₂×D₄	—	4	16	no	—
201	C₂×D₄	D₄×C₁₇	1	8	yes	complemented
202	C₂×D₄	C₂³×C₁₇	1	8	yes	—
203	C₂×D₄	C₂³×C₁₇	1	4	yes	—
204	C₂×D₄	C₂³×C₁₇	1	8	yes	—
205	C₂×D₄	C₂³×C₁₇	1	4	yes	—
206	C₂×D₄	C₂³×C₁₇	1	4	yes	—
207	C₂×D₄	C₂³×C₁₇	1	8	yes	complemented
208	C₂×D₄	C₂³×C₁₇	1	2	yes	complemented
209	C₂×D₄	C₂³×C₁₇	1	16	yes	complemented
210	C₂²×C₄	—	2	4	no	—
211	C₂²×C₄	C₂³×C₁₇	1	4	yes	—
212	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
213	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
214	C₂²×C₄	C₂³×C₁₇	1	4	yes	complemented
215	C₂²×C₄	C₂³×C₁₇	1	4	yes	complemented
216	C₂²×C₄	C₂³×C₁₇	1	8	yes	complemented
217	C₄⋊C₄	C₂³×C₁₇	1	4	yes	complemented
218	C₄⋊C₄	C₂³×C₁₇	1	8	yes	complemented
219	C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
220	C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
221	C₂²⋊C₄	C₂³×C₁₇	1	8	yes	complemented
222	C₂²⋊C₄	C₂³×C₁₇	1	16	yes	complemented
223	C₂²⋊C₄	C₂³×C₁₇	1	8	yes	complemented
224	C₄²	C₂³×C₁₇	1	4	yes	complemented
225	C₂³	—	2	2	no	—
226	C₂³	—	2	4	no	—
227	C₂³	—	2	16	no	—
228	C₂³	—	2	4	no	—
229	C₂³	—	2	16	no	—
230	C₂³	—	2	8	no	—
231	C₂³	—	4	4	no	—
232	C₂³	—	4	8	no	—
233	C₂³	—	4	4	no	—
234	C₂³	—	4	8	no	—
235	C₂³	—	4	32	no	—
236	C₂³	C₂×D₄×C₁₇	1	8	yes	complemented
237	C₂³	C₂⁴×C₁₇	1	4	yes	—
238	C₂³	C₂⁴×C₁₇	1	4	yes	—
239	C₂³	C₂⁴×C₁₇	1	1	yes	characteristic
240	C₂³	C₂⁴×C₁₇	1	4	yes	—
241	C₂³	C₂⁴×C₁₇	1	2	yes	—
242	Q₈	—	2	4	no	—
243	D₄	—	2	16	no	—
244	D₄	—	2	8	no	—
245	D₄	—	2	16	no	—
246	D₄	—	2	16	no	—
247	D₄	—	2	8	no	—
248	D₄	—	2	4	no	—
249	D₄	—	4	16	no	—
250	D₄	C₂×D₄×C₁₇	1	16	yes	complemented
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	8	no	—
253	C₂×C₄	—	2	8	no	—
254	C₂×C₄	—	2	8	no	—
255	C₂×C₄	—	4	8	no	—
256	C₂×C₄	C₂×D₄×C₁₇	1	4	yes	complemented
257	C₂×C₄	C₂⁴×C₁₇	1	8	yes	—
258	C₂×C₄	C₂⁴×C₁₇	1	4	yes	—
259	C₂×C₄	C₂⁴×C₁₇	1	2	yes	—
260	C₂×C₄	C₂⁴×C₁₇	1	2	yes	—
261	C₂²	—	2	8	no	—
262	C₂²	—	2	2	no	—
263	C₂²	—	2	8	no	—
264	C₂²	—	2	2	no	—
265	C₂²	—	2	2	no	—
266	C₂²	—	2	4	no	—
267	C₂²	—	2	4	no	—
268	C₂²	—	2	8	no	—
269	C₂²	—	2	8	no	—
270	C₂²	—	4	8	no	—
271	C₂²	—	4	32	no	—
272	C₂²	—	4	8	no	—
273	C₂²	—	8	8	no	—
274	C₂²	C₂²×D₄×C₁₇	1	2	yes	—
275	C₂²	C₂²×D₄×C₁₇	1	8	yes	—
276	C₂²	C₁₇×H(5,𝔽₂)	1	4	yes	complemented
277	C₂²	C₂⁵×C₁₇	1	1	yes	characteristic
278	C₄	—	2	2	no	—
279	C₄	—	2	4	no	—
280	C₄	—	2	8	no	—
281	C₄	C₂²×D₄×C₁₇	1	4	yes	—
282	C₂	—	2	2	no	—
283	C₂	—	2	4	no	—
284	C₂	—	2	8	no	—
285	C₂	—	4	4	no	—
286	C₂	—	4	4	no	—
287	C₂	C₂³×D₄×C₁₇	1	1	yes	characteristic
288	C₂	C₂×C₁₇×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×H(5,𝔽₂)	C₂	semidirect
2. C₂³×D₄×C₁₇	C₂	semidirect
3. C₁₇×#546	C₂	semidirect
4. D₄²×C₁₇	C₂	semidirect
5. C₁₇×#535	C₂	semidirect
6. C₁₇×#534	C₂	semidirect
7. C₁₇×#525	C₂	semidirect
8. C₂×C₁₇×#120	C₂	semidirect
9. C₁₇×#518	C₂	semidirect
10. C₂⁵×C₁₇	C₂²	semidirect
12. C₂×#41×C₁₇	C₂²	semidirect
13. C₂×#41×C₁₇	C₂²	semidirect
16. C₂²×D₄×C₁₇	C₂²	semidirect
17. C₂²×D₄×C₁₇	C₂²	semidirect
18. C₂²×D₄×C₁₇	C₂²	semidirect
19. C₂²×D₄×C₁₇	C₂²	semidirect
20. C₂²×D₄×C₁₇	C₂²	semidirect
21. C₂²×D₄×C₁₇	C₂²	semidirect
22. C₂³×C₄×C₁₇	C₂²	semidirect
23. C₁₇×#127	C₂²	semidirect
24. C₁₇×#124	C₂²	semidirect
25. C₁₇×#123	C₂²	semidirect
26. C₁₇×#123	C₂²	semidirect
27. C₁₇×C₂²⋊Q₈	C₂²	semidirect
28. C₁₇×#121	C₂²	semidirect
29. C₁₇×#121	C₂²	semidirect
30. C₁₇×#121	C₂²	semidirect
31. C₁₇×#120	C₂²	semidirect
32. C₁₇×#120	C₂²	semidirect
33. C₁₇×#120	C₂²	semidirect
34. C₁₇×#120	C₂²	semidirect
35. C₄×D₄×C₁₇	C₂²	semidirect
36. C₄×D₄×C₁₇	C₂²	semidirect
37. C₁₇×#117	C₂²	semidirect
38. C₂×C₂²⋊C₄×C₁₇	C₂²	semidirect
39. C₂×C₂²⋊C₄×C₁₇	C₂²	semidirect
46. C₂⁴×C₁₇	C₂³	semidirect
49. C₂×Q₈×C₁₇	C₂³	semidirect
56. C₂×D₄×C₁₇	D₄	semidirect
62. C₂×D₄×C₁₇	C₂³	semidirect
63. C₂×D₄×C₁₇	C₂³	semidirect
64. C₂×D₄×C₁₇	C₂³	semidirect
69. C₂²×C₄×C₁₇	C₂³	semidirect
70. C₂²×C₄×C₁₇	C₂³	semidirect
71. C₂²×C₄×C₁₇	C₂³	semidirect
72. C₄⋊C₄×C₁₇	C₂³	semidirect
73. C₄⋊C₄×C₁₇	C₂³	semidirect
76. C₂²⋊C₄×C₁₇	C₂³	semidirect
77. C₂²⋊C₄×C₁₇	C₂³	semidirect
78. C₂²⋊C₄×C₁₇	C₂³	semidirect
79. C₄²×C₁₇	C₂³	semidirect
91. C₂³×C₁₇	C₂×D₄	semidirect
105. D₄×C₁₇	C₂×D₄	semidirect
111. C₂×C₄×C₁₇	C₂×D₄	semidirect
116. #3484	C₁₇	direct (N × H)
132. C₂²×C₁₇	H(5,𝔽₂)	semidirect
138. C₂×H(5,𝔽₂)	C₂×C₁₇	semidirect
139. C₂³×D₄	C₂×C₁₇	semidirect
140. #546	C₂×C₁₇	semidirect
141. D₄²	C₂×C₁₇	semidirect
142. #535	C₂×C₁₇	semidirect
143. #534	C₂×C₁₇	semidirect
144. #525	C₂×C₁₇	semidirect
145. C₂×#120	C₂×C₁₇	semidirect
146. #518	C₂×C₁₇	semidirect
154. C₂⁵	C₂²×C₁₇	semidirect
156. C₂×#41	C₂²×C₁₇	semidirect
157. C₂×#41	C₂²×C₁₇	semidirect
160. C₂²×D₄	C₂²×C₁₇	semidirect
161. C₂²×D₄	C₂²×C₁₇	semidirect
162. C₂²×D₄	C₂²×C₁₇	semidirect
163. C₂²×D₄	C₂²×C₁₇	semidirect
164. C₂²×D₄	C₂²×C₁₇	semidirect
165. C₂²×D₄	C₂²×C₁₇	semidirect
166. C₂³×C₄	C₂²×C₁₇	semidirect
167. #127	C₂²×C₁₇	semidirect
168. #124	C₂²×C₁₇	semidirect
169. #123	C₂²×C₁₇	semidirect
170. #123	C₂²×C₁₇	semidirect
171. C₂²⋊Q₈	C₂²×C₁₇	semidirect
172. #121	C₂²×C₁₇	semidirect
173. #121	C₂²×C₁₇	semidirect
174. #121	C₂²×C₁₇	semidirect
175. #120	C₂²×C₁₇	semidirect
176. #120	C₂²×C₁₇	semidirect
177. #120	C₂²×C₁₇	semidirect
178. #120	C₂²×C₁₇	semidirect
179. C₄×D₄	C₂²×C₁₇	semidirect
180. C₄×D₄	C₂²×C₁₇	semidirect
181. #117	C₂²×C₁₇	semidirect
182. C₂×C₂²⋊C₄	C₂²×C₁₇	semidirect
183. C₂×C₂²⋊C₄	C₂²×C₁₇	semidirect
184. C₁₇	#3484	direct (N × H)
191. C₂⁴	C₂³×C₁₇	semidirect
194. C₂×Q₈	C₂³×C₁₇	semidirect
201. C₂×D₄	D₄×C₁₇	semidirect
207. C₂×D₄	C₂³×C₁₇	semidirect
208. C₂×D₄	C₂³×C₁₇	semidirect
209. C₂×D₄	C₂³×C₁₇	semidirect
214. C₂²×C₄	C₂³×C₁₇	semidirect
215. C₂²×C₄	C₂³×C₁₇	semidirect
216. C₂²×C₄	C₂³×C₁₇	semidirect
217. C₄⋊C₄	C₂³×C₁₇	semidirect
218. C₄⋊C₄	C₂³×C₁₇	semidirect
221. C₂²⋊C₄	C₂³×C₁₇	semidirect
222. C₂²⋊C₄	C₂³×C₁₇	semidirect
223. C₂²⋊C₄	C₂³×C₁₇	semidirect
224. C₄²	C₂³×C₁₇	semidirect
236. C₂³	C₂×D₄×C₁₇	semidirect
250. D₄	C₂×D₄×C₁₇	semidirect
256. C₂×C₄	C₂×D₄×C₁₇	semidirect
276. C₂²	C₁₇×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×H(5,𝔽₂)	2
C₂³×D₄×C₁₇	2
C₁₇×#546	2
D₄²×C₁₇	2
C₁₇×#535	2
C₁₇×#534	2
C₁₇×#525	2
C₂×C₁₇×#120	2
C₁₇×#518	2
#3484	17

Subgroups — C17×#3484 #14526490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#3484 #14526490