Subgroups — C₁₇×#34313 #16892057

Order 4352.

3276 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#520	C₂	1	2	yes	maximal, complemented
3	C₁₇×#2366	C₂	1	3	yes	maximal, complemented
4	C₁₇×#2361	C₂	1	6	yes	maximal, complemented
5	Q₈×C₄⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₄⋊C₄×C₁₇	C₂	1	3	yes	maximal, complemented
7	C₁₇×#2341	C₂	1	2	yes	maximal, complemented
8	C₁₇×#2324	C₂	1	6	yes	maximal, complemented
9	C₄×C₁₇×#127	C₂	1	3	yes	maximal, complemented
10	C₁₇×#2293	C₂	1	3	yes	maximal, complemented
11	C₄²×Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₇	C₂²	1	2	yes	—
13	C₁₇×#550	C₄	1	16	yes	complemented
14	C₂×C₁₇×#127	C₂²	1	3	yes	—
15	C₂×C₁₇×#121	C₂²	1	6	yes	—
16	C₁₇×#520	—	2	16	no	—
17	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₇	C₂²	1	6	yes	—
22	C₂×C₄×D₄×C₁₇	C₂²	1	6	yes	—
23	C₂×C₄×D₄×C₁₇	C₂²	1	6	yes	—
24	C₂×C₄×D₄×C₁₇	C₂²	1	6	yes	—
25	C₂×C₄×D₄×C₁₇	C₂²	1	3	yes	—
26	C₂×C₁₇×#117	C₂²	1	6	yes	—
27	C₂²×C₄⋊C₄×C₁₇	C₂²	1	6	yes	—
28	C₁₇×#390	C₂²	1	3	yes	—
29	C₁₇×#390	C₂²	1	3	yes	—
30	C₁₇×#390	C₂²	1	6	yes	—
31	C₁₇×#390	C₂²	1	6	yes	—
32	C₁₇×#390	C₂²	1	6	yes	—
33	C₁₇×#389	C₂²	1	1	yes	characteristic
34	C₁₇×#389	C₂²	1	3	yes	—
35	C₁₇×#389	C₂²	1	6	yes	—
36	C₁₇×#388	C₂²	1	6	yes	—
37	C₁₇×#388	C₂²	1	6	yes	—
38	C₁₇×#386	C₂²	1	12	yes	—
39	C₁₇×#385	C₂²	1	12	yes	—
40	C₁₇×#384	C₂²	1	3	yes	—
41	C₁₇×#380	C₂²	1	6	yes	—
42	C₄×C₄⋊C₄×C₁₇	C₂²	1	3	yes	—
43	C₄×C₄⋊C₄×C₁₇	C₂²	1	3	yes	—
44	C₄×C₄⋊C₄×C₁₇	C₂²	1	3	yes	—
45	C₄×C₄⋊C₄×C₁₇	C₂²	1	3	yes	—
46	C₄×C₂²⋊C₄×C₁₇	C₂²	1	6	yes	—
47	C₄³×C₁₇	C₂²	1	3	yes	—
48	C₂×#41×C₁₇	—	2	8	no	—
49	C₂×#41×C₁₇	—	2	8	no	—
50	C₂×#41×C₁₇	C₂×C₄	1	16	yes	complemented
51	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₇	C₂³	1	3	yes	—
53	C₂²×D₄×C₁₇	C₂³	1	6	yes	—
54	C₂²×D₄×C₁₇	C₂³	1	6	yes	—
55	C₂³×C₄×C₁₇	C₂³	1	6	yes	—
56	C₂³×C₄×C₁₇	C₂³	1	12	yes	—
57	C₁₇×#127	C₂×C₄	1	24	yes	complemented
58	C₁₇×#121	C₂×C₄	1	48	yes	complemented
59	C₄×Q₈×C₁₇	—	2	8	no	—
60	C₄×Q₈×C₁₇	—	2	4	no	—
61	C₄×Q₈×C₁₇	C₂×C₄	1	8	yes	complemented
62	C₄×Q₈×C₁₇	D₄	1	8	yes	complemented
63	C₄×D₄×C₁₇	—	2	24	no	—
64	C₄×D₄×C₁₇	—	2	24	no	—
65	C₄×D₄×C₁₇	—	4	12	no	—
66	C₄×D₄×C₁₇	—	4	12	no	—
67	C₄×D₄×C₁₇	C₂×C₄	1	24	yes	complemented
68	C₁₇×#117	—	2	24	no	—
69	C₂×C₄⋊C₄×C₁₇	—	2	24	no	—
70	C₂×C₄⋊C₄×C₁₇	C₂³	1	6	yes	—
71	C₂×C₄⋊C₄×C₁₇	C₂³	1	6	yes	—
72	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
74	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
75	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₇	C₂³	1	6	yes	—
77	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
79	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
80	C₂×C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
81	C₂×C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
82	C₂×C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
83	C₂×C₂²⋊C₄×C₁₇	C₂³	1	12	yes	—
84	C₂×C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
85	C₂×C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
86	C₂×C₄²×C₁₇	C₂³	1	6	yes	—
87	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
88	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
89	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
90	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
92	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
93	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
94	C₁₇×#95	C₂³	1	2	yes	—
95	C₁₇×#95	C₂³	1	6	yes	—
96	C₁₇×#95	C₂³	1	6	yes	—
97	C₁₇×#95	C₂³	1	6	yes	—
98	C₂⁴×C₁₇	C₂⁴	1	6	yes	—
99	#41×C₁₇	—	2	64	no	—
100	C₂×Q₈×C₁₇	C₂²×C₄	1	4	yes	—
101	C₂×Q₈×C₁₇	C₂×D₄	1	4	yes	—
102	C₂×Q₈×C₁₇	#41	1	4	yes	—
103	C₂×D₄×C₁₇	—	2	12	no	—
104	C₂×D₄×C₁₇	—	2	12	no	—
105	C₂×D₄×C₁₇	—	2	6	no	—
106	C₂×D₄×C₁₇	—	2	6	no	—
107	C₂×D₄×C₁₇	—	4	6	no	—
108	C₂×D₄×C₁₇	—	4	6	no	—
109	C₂×D₄×C₁₇	C₂²×C₄	1	12	yes	—
110	C₂×D₄×C₁₇	C₂²×C₄	1	24	yes	—
111	C₂×D₄×C₁₇	C₂²×C₄	1	24	yes	—
112	C₂²×C₄×C₁₇	—	2	12	no	—
113	C₂²×C₄×C₁₇	—	2	12	no	—
114	C₂²×C₄×C₁₇	—	2	24	no	—
115	C₂²×C₄×C₁₇	—	4	12	no	—
116	C₂²×C₄×C₁₇	—	4	12	no	—
117	C₂²×C₄×C₁₇	C₂²×C₄	1	24	yes	—
118	C₂²×C₄×C₁₇	C₂⁴	1	6	yes	—
119	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
121	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
123	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
124	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
125	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
126	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
127	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
128	C₄⋊C₄×C₁₇	—	2	12	no	—
129	C₄⋊C₄×C₁₇	—	2	12	no	—
130	C₄⋊C₄×C₁₇	—	2	4	no	—
131	C₄⋊C₄×C₁₇	—	2	6	no	—
132	C₄⋊C₄×C₁₇	—	2	6	no	—
133	C₄⋊C₄×C₁₇	—	2	2	no	—
134	C₄⋊C₄×C₁₇	—	4	6	no	—
135	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
136	C₄⋊C₄×C₁₇	C₂²×C₄	1	12	yes	—
137	C₄⋊C₄×C₁₇	C₂×D₄	1	12	yes	—
138	C₂²⋊C₄×C₁₇	—	2	12	no	—
139	C₂²⋊C₄×C₁₇	—	2	12	no	—
140	C₂²⋊C₄×C₁₇	—	2	12	no	—
141	C₂²⋊C₄×C₁₇	—	4	6	no	—
142	C₂²⋊C₄×C₁₇	—	4	12	no	—
143	C₂²⋊C₄×C₁₇	C₂²×C₄	1	24	yes	—
144	C₄²×C₁₇	—	2	12	no	—
145	C₄²×C₁₇	—	2	6	no	—
146	C₄²×C₁₇	—	2	6	no	—
147	C₄²×C₁₇	—	2	6	no	—
148	C₄²×C₁₇	—	2	2	no	—
149	C₄²×C₁₇	—	4	3	no	—
150	C₄²×C₁₇	C₂²×C₄	1	12	yes	—
151	C₄²×C₁₇	C₂×D₄	1	12	yes	—
152	#34313	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₁₇	—	2	6	no	—
154	C₂³×C₁₇	—	2	6	no	—
155	C₂³×C₁₇	—	2	6	no	—
156	C₂³×C₁₇	—	2	6	no	—
157	C₂³×C₁₇	—	2	6	no	—
158	C₂³×C₁₇	—	2	6	no	—
159	C₂³×C₁₇	C₂³×C₄	1	12	yes	—
160	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
161	Q₈×C₁₇	C₄×D₄	1	16	yes	complemented
162	D₄×C₁₇	—	2	48	no	—
163	D₄×C₁₇	—	2	24	no	—
164	D₄×C₁₇	—	4	24	no	—
165	C₂×C₄×C₁₇	—	2	2	no	—
166	C₂×C₄×C₁₇	—	2	1	no	—
167	C₂×C₄×C₁₇	—	2	2	no	—
168	C₂×C₄×C₁₇	—	2	3	no	—
169	C₂×C₄×C₁₇	—	2	3	no	—
170	C₂×C₄×C₁₇	—	2	3	no	—
171	C₂×C₄×C₁₇	—	2	1	no	—
172	C₂×C₄×C₁₇	—	2	1	no	—
173	C₂×C₄×C₁₇	—	2	1	no	—
174	C₂×C₄×C₁₇	—	2	3	no	—
175	C₂×C₄×C₁₇	—	2	48	no	—
176	C₂×C₄×C₁₇	—	2	2	no	—
177	C₂×C₄×C₁₇	—	2	6	no	—
178	C₂×C₄×C₁₇	—	2	3	no	—
179	C₂×C₄×C₁₇	—	2	3	no	—
180	C₂×C₄×C₁₇	—	2	6	no	—
181	C₂×C₄×C₁₇	—	2	6	no	—
182	C₂×C₄×C₁₇	—	2	2	no	—
183	C₂×C₄×C₁₇	—	2	3	no	—
184	C₂×C₄×C₁₇	—	2	2	no	—
185	C₂×C₄×C₁₇	—	8	24	no	—
186	C₂×C₄×C₁₇	C₂³×C₄	1	6	yes	—
187	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
188	C₂×C₄×C₁₇	C₂³×C₄	1	6	yes	—
189	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
190	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₁₇	C₂²×D₄	1	6	yes	—
192	C₂×C₄×C₁₇	C₂²×D₄	1	6	yes	—
193	C₂×C₄×C₁₇	C₂×#41	1	6	yes	—
194	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
195	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
196	C₂×C₄×C₁₇	2₋¹⁺⁴	1	2	yes	—
197	C₂×#550	C₂×C₁₇	1	1	yes	characteristic
198	C₂×#520	C₂×C₁₇	1	2	yes	complemented
199	#2366	C₂×C₁₇	1	3	yes	complemented
200	#2361	C₂×C₁₇	1	6	yes	complemented
201	Q₈×C₄⋊C₄	C₂×C₁₇	1	1	yes	characteristic, complemented
202	D₄×C₄⋊C₄	C₂×C₁₇	1	3	yes	complemented
203	#2341	C₂×C₁₇	1	2	yes	complemented
204	#2324	C₂×C₁₇	1	6	yes	complemented
205	C₄×#127	C₂×C₁₇	1	3	yes	complemented
206	#2293	C₂×C₁₇	1	3	yes	complemented
207	C₄²×Q₈	C₂×C₁₇	1	1	yes	characteristic, complemented
208	C₂²×C₁₇	—	2	12	no	—
209	C₂²×C₁₇	—	2	12	no	—
210	C₂²×C₁₇	—	2	12	no	—
211	C₂²×C₁₇	—	4	6	no	—
212	C₂²×C₁₇	—	4	6	no	—
213	C₂²×C₁₇	—	4	6	no	—
214	C₂²×C₁₇	—	4	6	no	—
215	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
216	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
217	C₂²×C₁₇	C₂²×#41	1	1	yes	characteristic
218	C₂²×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
219	C₂²×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
220	C₂²×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
221	C₂²×C₁₇	#585	1	1	yes	characteristic
222	C₄×C₁₇	—	2	4	no	—
223	C₄×C₁₇	—	2	6	no	—
224	C₄×C₁₇	—	2	2	no	—
225	C₄×C₁₇	—	2	6	no	—
226	C₄×C₁₇	—	2	2	no	—
227	C₄×C₁₇	—	4	2	no	—
228	C₄×C₁₇	—	4	6	no	—
229	C₄×C₁₇	—	4	3	no	—
230	C₄×C₁₇	C₂×C₄×D₄	1	12	yes	—
231	C₄×C₁₇	#520	1	4	yes	complemented
232	C₂²×#41	C₂²×C₁₇	1	2	yes	—
233	#550	C₄×C₁₇	1	16	yes	complemented
234	C₂×#127	C₂²×C₁₇	1	3	yes	—
235	C₂×#121	C₂²×C₁₇	1	6	yes	—
236	#520	—	2	16	no	—
237	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	—
239	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂²×C₁₇	1	6	yes	—
242	C₂×C₄×D₄	C₂²×C₁₇	1	6	yes	—
243	C₂×C₄×D₄	C₂²×C₁₇	1	6	yes	—
244	C₂×C₄×D₄	C₂²×C₁₇	1	6	yes	—
245	C₂×C₄×D₄	C₂²×C₁₇	1	3	yes	—
246	C₂×#117	C₂²×C₁₇	1	6	yes	—
247	C₂²×C₄⋊C₄	C₂²×C₁₇	1	6	yes	—
248	#390	C₂²×C₁₇	1	3	yes	—
249	#390	C₂²×C₁₇	1	6	yes	—
250	#390	C₂²×C₁₇	1	6	yes	—
251	#390	C₂²×C₁₇	1	6	yes	—
252	#390	C₂²×C₁₇	1	3	yes	—
253	#389	C₂²×C₁₇	1	6	yes	—
254	#389	C₂²×C₁₇	1	3	yes	—
255	#389	C₂²×C₁₇	1	1	yes	characteristic
256	#388	C₂²×C₁₇	1	6	yes	—
257	#388	C₂²×C₁₇	1	6	yes	—
258	#386	C₂²×C₁₇	1	12	yes	—
259	#385	C₂²×C₁₇	1	12	yes	—
260	#384	C₂²×C₁₇	1	3	yes	—
261	#380	C₂²×C₁₇	1	6	yes	—
262	C₄×C₄⋊C₄	C₂²×C₁₇	1	3	yes	—
263	C₄×C₄⋊C₄	C₂²×C₁₇	1	3	yes	—
264	C₄×C₄⋊C₄	C₂²×C₁₇	1	3	yes	—
265	C₄×C₄⋊C₄	C₂²×C₁₇	1	3	yes	—
266	C₄×C₂²⋊C₄	C₂²×C₁₇	1	6	yes	—
267	C₄³	C₂²×C₁₇	1	3	yes	—
268	C₂×C₁₇	—	4	12	no	—
269	C₂×C₁₇	C₂²×C₄×D₄	1	1	yes	characteristic
270	C₂×C₁₇	C₂×#520	1	1	yes	characteristic
271	C₂×C₁₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₁₇	#3497	1	1	yes	characteristic
273	C₂×C₁₇	#3498	1	1	yes	characteristic
274	C₂×C₁₇	#3517	1	1	yes	characteristic
275	C₂×C₁₇	#3522	1	1	yes	characteristic
276	C₂×#41	—	2	8	no	—
277	C₂×#41	—	2	8	no	—
278	C₂×#41	C₂×C₄×C₁₇	1	16	yes	complemented
279	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
280	C₂²×D₄	C₂³×C₁₇	1	3	yes	—
281	C₂²×D₄	C₂³×C₁₇	1	6	yes	—
282	C₂²×D₄	C₂³×C₁₇	1	6	yes	—
283	C₂³×C₄	C₂³×C₁₇	1	6	yes	—
284	C₂³×C₄	C₂³×C₁₇	1	12	yes	—
285	#127	C₂×C₄×C₁₇	1	24	yes	complemented
286	#121	C₂×C₄×C₁₇	1	48	yes	complemented
287	C₄×Q₈	—	2	8	no	—
288	C₄×Q₈	—	2	4	no	—
289	C₄×Q₈	C₂×C₄×C₁₇	1	8	yes	complemented
290	C₄×Q₈	D₄×C₁₇	1	8	yes	complemented
291	C₄×D₄	—	2	24	no	—
292	C₄×D₄	—	2	24	no	—
293	C₄×D₄	—	4	12	no	—
294	C₄×D₄	—	4	12	no	—
295	C₄×D₄	C₂×C₄×C₁₇	1	24	yes	complemented
296	#117	—	2	24	no	—
297	C₂×C₄⋊C₄	—	2	24	no	—
298	C₂×C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₁₇	1	6	yes	—
309	C₂×C₂²⋊C₄	C₂³×C₁₇	1	6	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₁₇	1	6	yes	—
311	C₂×C₂²⋊C₄	C₂³×C₁₇	1	12	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₁₇	1	6	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₁₇	1	6	yes	—
314	C₂×C₄²	C₂³×C₁₇	1	6	yes	—
315	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
316	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
317	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
318	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
320	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
321	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
322	#95	C₂³×C₁₇	1	2	yes	—
323	#95	C₂³×C₁₇	1	6	yes	—
324	#95	C₂³×C₁₇	1	6	yes	—
325	#95	C₂³×C₁₇	1	6	yes	—
326	C₁₇	#34313	1	1	yes	characteristic, direct product factor, Sylow
327	C₂⁴	C₂⁴×C₁₇	1	6	yes	—
328	#41	—	2	64	no	—
329	C₂×Q₈	C₂²×C₄×C₁₇	1	4	yes	—
330	C₂×Q₈	C₂×D₄×C₁₇	1	4	yes	—
331	C₂×Q₈	#41×C₁₇	1	4	yes	—
332	C₂×D₄	—	2	12	no	—
333	C₂×D₄	—	2	12	no	—
334	C₂×D₄	—	2	6	no	—
335	C₂×D₄	—	2	6	no	—
336	C₂×D₄	—	4	6	no	—
337	C₂×D₄	—	4	6	no	—
338	C₂×D₄	C₂²×C₄×C₁₇	1	12	yes	—
339	C₂×D₄	C₂²×C₄×C₁₇	1	24	yes	—
340	C₂×D₄	C₂²×C₄×C₁₇	1	24	yes	—
341	C₂²×C₄	—	2	12	no	—
342	C₂²×C₄	—	2	12	no	—
343	C₂²×C₄	—	2	24	no	—
344	C₂²×C₄	—	4	12	no	—
345	C₂²×C₄	—	4	12	no	—
346	C₂²×C₄	C₂²×C₄×C₁₇	1	24	yes	—
347	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
348	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
349	C₂²×C₄	C₂⁴×C₁₇	1	6	yes	—
350	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
351	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
353	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
356	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
357	C₄⋊C₄	—	2	12	no	—
358	C₄⋊C₄	—	2	12	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	6	no	—
361	C₄⋊C₄	—	2	6	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	4	6	no	—
364	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
365	C₄⋊C₄	C₂²×C₄×C₁₇	1	12	yes	—
366	C₄⋊C₄	C₂×D₄×C₁₇	1	12	yes	—
367	C₂²⋊C₄	—	2	12	no	—
368	C₂²⋊C₄	—	2	12	no	—
369	C₂²⋊C₄	—	2	12	no	—
370	C₂²⋊C₄	—	4	6	no	—
371	C₂²⋊C₄	—	4	12	no	—
372	C₂²⋊C₄	C₂²×C₄×C₁₇	1	24	yes	—
373	C₄²	—	2	12	no	—
374	C₄²	—	2	6	no	—
375	C₄²	—	2	6	no	—
376	C₄²	—	2	6	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	4	3	no	—
379	C₄²	C₂²×C₄×C₁₇	1	12	yes	—
380	C₄²	C₂×D₄×C₁₇	1	12	yes	—
381	C₂³	—	2	6	no	—
382	C₂³	—	2	6	no	—
383	C₂³	—	2	6	no	—
384	C₂³	—	2	6	no	—
385	C₂³	—	2	6	no	—
386	C₂³	—	2	6	no	—
387	C₂³	C₂³×C₄×C₁₇	1	12	yes	—
388	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
389	Q₈	C₄×D₄×C₁₇	1	16	yes	complemented
390	D₄	—	2	48	no	—
391	D₄	—	2	24	no	—
392	D₄	—	4	24	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	3	no	—
397	C₂×C₄	—	2	3	no	—
398	C₂×C₄	—	2	3	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	3	no	—
403	C₂×C₄	—	2	48	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	6	no	—
406	C₂×C₄	—	2	3	no	—
407	C₂×C₄	—	2	3	no	—
408	C₂×C₄	—	2	6	no	—
409	C₂×C₄	—	2	6	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	3	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	8	24	no	—
414	C₂×C₄	C₂³×C₄×C₁₇	1	6	yes	—
415	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
416	C₂×C₄	C₂³×C₄×C₁₇	1	6	yes	—
417	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
419	C₂×C₄	C₂²×D₄×C₁₇	1	6	yes	—
420	C₂×C₄	C₂²×D₄×C₁₇	1	6	yes	—
421	C₂×C₄	C₂×#41×C₁₇	1	6	yes	—
422	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
423	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
424	C₂×C₄	C₁₇×2₋¹⁺⁴	1	2	yes	—
425	C₂²	—	2	12	no	—
426	C₂²	—	2	12	no	—
427	C₂²	—	2	12	no	—
428	C₂²	—	4	6	no	—
429	C₂²	—	4	6	no	—
430	C₂²	—	4	6	no	—
431	C₂²	—	4	6	no	—
432	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
433	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
434	C₂²	C₂²×#41×C₁₇	1	1	yes	characteristic
435	C₂²	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂²	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂²	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
438	C₂²	C₁₇×#585	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	6	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	6	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	6	no	—
446	C₄	—	4	3	no	—
447	C₄	C₂×C₄×D₄×C₁₇	1	12	yes	—
448	C₄	C₁₇×#520	1	4	yes	complemented
449	C₂	—	4	12	no	—
450	C₂	C₂²×C₄×D₄×C₁₇	1	1	yes	characteristic
451	C₂	C₂×C₁₇×#520	1	1	yes	characteristic
452	C₂	C₄×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂	C₁₇×#3497	1	1	yes	characteristic
454	C₂	C₁₇×#3498	1	1	yes	characteristic
455	C₂	C₁₇×#3517	1	1	yes	characteristic
456	C₂	C₁₇×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁵×C₁₇
prime radical	C₂×C₁₇×#550	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₇×#520	C₂	semidirect
3. C₁₇×#2366	C₂	semidirect
4. C₁₇×#2361	C₂	semidirect
5. Q₈×C₄⋊C₄×C₁₇	C₂	semidirect
6. D₄×C₄⋊C₄×C₁₇	C₂	semidirect
7. C₁₇×#2341	C₂	semidirect
8. C₁₇×#2324	C₂	semidirect
9. C₄×C₁₇×#127	C₂	semidirect
10. C₁₇×#2293	C₂	semidirect
11. C₄²×Q₈×C₁₇	C₂	semidirect
13. C₁₇×#550	C₄	semidirect
50. C₂×#41×C₁₇	C₂×C₄	semidirect
57. C₁₇×#127	C₂×C₄	semidirect
58. C₁₇×#121	C₂×C₄	semidirect
61. C₄×Q₈×C₁₇	C₂×C₄	semidirect
62. C₄×Q₈×C₁₇	D₄	semidirect
67. C₄×D₄×C₁₇	C₂×C₄	semidirect
152. #34313	C₁₇	direct (N × H)
161. Q₈×C₁₇	C₄×D₄	semidirect
198. C₂×#520	C₂×C₁₇	semidirect
199. #2366	C₂×C₁₇	semidirect
200. #2361	C₂×C₁₇	semidirect
201. Q₈×C₄⋊C₄	C₂×C₁₇	semidirect
202. D₄×C₄⋊C₄	C₂×C₁₇	semidirect
203. #2341	C₂×C₁₇	semidirect
204. #2324	C₂×C₁₇	semidirect
205. C₄×#127	C₂×C₁₇	semidirect
206. #2293	C₂×C₁₇	semidirect
207. C₄²×Q₈	C₂×C₁₇	semidirect
231. C₄×C₁₇	#520	semidirect
233. #550	C₄×C₁₇	semidirect
278. C₂×#41	C₂×C₄×C₁₇	semidirect
285. #127	C₂×C₄×C₁₇	semidirect
286. #121	C₂×C₄×C₁₇	semidirect
289. C₄×Q₈	C₂×C₄×C₁₇	semidirect
290. C₄×Q₈	D₄×C₁₇	semidirect
295. C₄×D₄	C₂×C₄×C₁₇	semidirect
326. C₁₇	#34313	direct (N × H)
389. Q₈	C₄×D₄×C₁₇	semidirect
448. C₄	C₁₇×#520	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#550	2
C₂×C₁₇×#520	2
C₁₇×#2366	2
C₁₇×#2361	2
Q₈×C₄⋊C₄×C₁₇	2
D₄×C₄⋊C₄×C₁₇	2
C₁₇×#2341	2
C₁₇×#2324	2
C₄×C₁₇×#127	2
C₁₇×#2293	2
C₄²×Q₈×C₁₇	2
#34313	17

Subgroups — C17×#34313 #16892057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#34313 #16892057