Subgroups — C₁₇×#34268 #16892012

Order 4352.

2946 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₁₇	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2367	C₂	1	4	yes	maximal, complemented
5	C₁₇×#2365	C₂	1	4	yes	maximal, complemented
6	C₁₇×#2359	C₂	1	8	yes	maximal, complemented
7	C₁₇×#2323	C₂	1	4	yes	maximal, complemented
8	C₁₇×#2311	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₇×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
10	C₁₇×#2296	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#2274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₇	C₂²	1	1	yes	characteristic
15	C₁₇×#536	C₄	1	16	yes	complemented
16	C₂×C₁₇×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₇×#124	C₂²	1	2	yes	—
18	C₂×C₁₇×#123	C₂²	1	4	yes	—
19	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	4	yes	—
20	C₁₇×#519	—	2	8	no	—
21	C₄×#41×C₁₇	—	2	8	no	—
22	C₂×C₄×Q₈×C₁₇	C₂²	1	4	yes	—
23	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₇	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₇	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
27	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#117	C₂²	1	2	yes	—
29	C₂×C₁₇×#117	C₂²	1	4	yes	—
30	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₇	C₂²	1	2	yes	—
35	C₁₇×#391	C₂²	1	2	yes	—
36	C₁₇×#391	C₂²	1	2	yes	—
37	C₁₇×#391	C₂²	1	4	yes	—
38	C₁₇×#391	C₂²	1	2	yes	—
39	C₁₇×#390	C₂²	1	2	yes	—
40	C₁₇×#389	C₂²	1	2	yes	—
41	C₁₇×#389	C₂²	1	2	yes	—
42	C₁₇×#389	C₂²	1	8	yes	—
43	C₁₇×#388	C₂²	1	8	yes	—
44	C₁₇×#388	C₂²	1	8	yes	—
45	C₁₇×#387	C₂²	1	8	yes	—
46	C₁₇×#387	C₂²	1	8	yes	—
47	C₁₇×#386	C₂²	1	4	yes	—
48	C₁₇×#385	C₂²	1	4	yes	—
49	C₁₇×#385	C₂²	1	8	yes	—
50	C₁₇×#380	C₂²	1	4	yes	—
51	C₄×C₄⋊C₄×C₁₇	C₂²	1	4	yes	—
52	C₄×C₄⋊C₄×C₁₇	C₂²	1	4	yes	—
53	C₄×C₄⋊C₄×C₁₇	C₂²	1	4	yes	—
54	C₄×C₄⋊C₄×C₁₇	C₂²	1	8	yes	—
55	C₄×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	—
56	C₄×C₂²⋊C₄×C₁₇	C₂²	1	8	yes	—
57	C₂×C₁₇×#95	C₂²	1	4	yes	—
58	C₂×#41×C₁₇	—	2	4	no	—
59	C₂×#41×C₁₇	—	2	4	no	—
60	C₂×#41×C₁₇	C₂×C₄	1	8	yes	—
61	C₂²×Q₈×C₁₇	—	2	4	no	—
62	C₂²×Q₈×C₁₇	—	2	4	no	—
63	C₂²×Q₈×C₁₇	C₂×C₄	1	8	yes	complemented
64	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
65	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
75	C₁₇×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
76	C₁₇×#124	C₂×C₄	1	16	yes	complemented
77	C₁₇×#123	C₂×C₄	1	32	yes	complemented
78	C₁₇×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
79	C₄×Q₈×C₁₇	—	2	8	no	—
80	C₄×Q₈×C₁₇	—	2	16	no	—
81	C₄×Q₈×C₁₇	—	2	16	no	—
82	C₄×D₄×C₁₇	—	2	8	no	—
83	C₄×D₄×C₁₇	—	2	16	no	—
84	C₁₇×#117	—	2	4	no	—
85	C₁₇×#117	—	2	16	no	—
86	C₁₇×#117	—	2	8	no	—
87	C₁₇×#117	C₂×C₄	1	8	yes	complemented
88	C₁₇×#117	D₄	1	8	yes	—
89	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
90	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
95	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
99	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
101	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
104	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
105	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₇	—	2	4	no	—
107	C₂×C₄²×C₁₇	—	2	8	no	—
108	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₇	C₂³	1	8	yes	—
113	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₇	C₂³	1	8	yes	—
115	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
117	C₁₇×#95	C₂³	1	8	yes	—
118	C₁₇×#95	C₂³	1	8	yes	—
119	C₁₇×#95	C₂³	1	4	yes	—
120	C₁₇×#95	C₂³	1	8	yes	—
121	C₁₇×#95	C₂³	1	8	yes	—
122	C₁₇×#95	C₂³	1	4	yes	—
123	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
124	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
125	#41×C₁₇	—	2	32	no	—
126	C₂×Q₈×C₁₇	—	2	32	no	—
127	C₂×Q₈×C₁₇	—	2	4	no	—
128	C₂×Q₈×C₁₇	—	2	4	no	—
129	C₂×Q₈×C₁₇	—	2	2	no	—
130	C₂×Q₈×C₁₇	—	2	4	no	—
131	C₂×Q₈×C₁₇	—	2	4	no	—
132	C₂×Q₈×C₁₇	—	2	2	no	—
133	C₂×Q₈×C₁₇	C₂²×C₄	1	8	yes	—
134	C₂×Q₈×C₁₇	C₂²×C₄	1	8	yes	—
135	C₂×Q₈×C₁₇	C₂²×C₄	1	4	yes	—
136	C₂×D₄×C₁₇	—	2	4	no	—
137	C₂×D₄×C₁₇	—	2	4	no	—
138	C₂×D₄×C₁₇	—	2	2	no	—
139	C₂×D₄×C₁₇	—	2	2	no	—
140	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
141	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₁₇	—	2	4	no	—
143	C₂²×C₄×C₁₇	—	2	4	no	—
144	C₂²×C₄×C₁₇	—	2	4	no	—
145	C₂²×C₄×C₁₇	—	2	4	no	—
146	C₂²×C₄×C₁₇	—	2	4	no	—
147	C₂²×C₄×C₁₇	—	2	4	no	—
148	C₂²×C₄×C₁₇	—	2	8	no	—
149	C₂²×C₄×C₁₇	—	2	8	no	—
150	C₂²×C₄×C₁₇	—	2	4	no	—
151	C₂²×C₄×C₁₇	—	4	4	no	—
152	C₂²×C₄×C₁₇	—	4	2	no	—
153	C₂²×C₄×C₁₇	—	4	4	no	—
154	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
155	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
156	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
157	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₇	#41	1	4	yes	—
159	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
169	C₄⋊C₄×C₁₇	—	2	8	no	—
170	C₄⋊C₄×C₁₇	—	2	16	no	—
171	C₄⋊C₄×C₁₇	—	2	4	no	—
172	C₄⋊C₄×C₁₇	—	2	4	no	—
173	C₄⋊C₄×C₁₇	—	2	4	no	—
174	C₄⋊C₄×C₁₇	—	2	8	no	—
175	C₄⋊C₄×C₁₇	—	4	4	no	—
176	C₄⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
177	C₄⋊C₄×C₁₇	C₂²×C₄	1	32	yes	—
178	C₄⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
179	C₂²⋊C₄×C₁₇	—	2	4	no	—
180	C₂²⋊C₄×C₁₇	—	2	8	no	—
181	C₂²⋊C₄×C₁₇	—	4	8	no	—
182	C₂²⋊C₄×C₁₇	C₂²×C₄	1	32	yes	—
183	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
184	C₂²⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
185	C₄²×C₁₇	—	2	2	no	—
186	C₄²×C₁₇	—	2	2	no	—
187	C₄²×C₁₇	—	2	8	no	—
188	C₄²×C₁₇	—	2	4	no	—
189	C₄²×C₁₇	—	2	16	no	—
190	C₄²×C₁₇	—	2	4	no	—
191	C₄²×C₁₇	—	4	8	no	—
192	C₄²×C₁₇	C₂²×C₄	1	8	yes	—
193	C₄²×C₁₇	C₂×D₄	1	8	yes	—
194	#34268	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₁₇	—	2	2	no	—
196	C₂³×C₁₇	—	2	2	no	—
197	C₂³×C₁₇	—	2	2	no	—
198	C₂³×C₁₇	—	2	2	no	—
199	C₂³×C₁₇	—	2	4	no	—
200	C₂³×C₁₇	—	2	4	no	—
201	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
202	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
203	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
204	C₂³×C₁₇	C₂×#41	1	2	yes	—
205	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
206	Q₈×C₁₇	—	2	16	no	—
207	Q₈×C₁₇	—	2	16	no	—
208	Q₈×C₁₇	—	2	8	no	—
209	D₄×C₁₇	—	2	16	no	—
210	D₄×C₁₇	—	2	8	no	—
211	C₂×C₄×C₁₇	—	2	16	no	—
212	C₂×C₄×C₁₇	—	2	2	no	—
213	C₂×C₄×C₁₇	—	2	2	no	—
214	C₂×C₄×C₁₇	—	2	4	no	—
215	C₂×C₄×C₁₇	—	2	2	no	—
216	C₂×C₄×C₁₇	—	2	4	no	—
217	C₂×C₄×C₁₇	—	2	4	no	—
218	C₂×C₄×C₁₇	—	2	4	no	—
219	C₂×C₄×C₁₇	—	2	4	no	—
220	C₂×C₄×C₁₇	—	2	4	no	—
221	C₂×C₄×C₁₇	—	2	2	no	—
222	C₂×C₄×C₁₇	—	2	16	no	—
223	C₂×C₄×C₁₇	—	2	4	no	—
224	C₂×C₄×C₁₇	—	2	2	no	—
225	C₂×C₄×C₁₇	—	2	4	no	—
226	C₂×C₄×C₁₇	—	2	4	no	—
227	C₂×C₄×C₁₇	—	2	2	no	—
228	C₂×C₄×C₁₇	—	2	8	no	—
229	C₂×C₄×C₁₇	—	2	4	no	—
230	C₂×C₄×C₁₇	—	2	2	no	—
231	C₂×C₄×C₁₇	—	4	16	no	—
232	C₂×C₄×C₁₇	—	4	8	no	—
233	C₂×C₄×C₁₇	—	8	4	no	—
234	C₂×C₄×C₁₇	C₄×D₄	1	16	yes	—
235	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
236	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
237	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
238	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
239	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
240	C₂×C₄×C₁₇	C₂²×D₄	1	8	yes	—
241	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
245	C₂×C₄×C₁₇	2₋¹⁺⁴	1	4	yes	—
246	C₂×#536	C₂×C₁₇	1	1	yes	characteristic
247	C₂×#519	C₂×C₁₇	1	1	yes	characteristic, complemented
248	C₂×C₄×#41	C₂×C₁₇	1	1	yes	characteristic
249	#2367	C₂×C₁₇	1	4	yes	complemented
250	#2365	C₂×C₁₇	1	4	yes	complemented
251	#2359	C₂×C₁₇	1	8	yes	complemented
252	#2323	C₂×C₁₇	1	4	yes	complemented
253	#2311	C₂×C₁₇	1	1	yes	characteristic
254	C₄×C₂²⋊Q₈	C₂×C₁₇	1	4	yes	complemented
255	#2296	C₂×C₁₇	1	1	yes	characteristic, complemented
256	C₂×#391	C₂×C₁₇	1	1	yes	characteristic, complemented
257	#2274	C₂×C₁₇	1	1	yes	characteristic, complemented
258	C₂²×C₁₇	—	2	4	no	—
259	C₂²×C₁₇	—	2	4	no	—
260	C₂²×C₁₇	—	2	2	no	—
261	C₂²×C₁₇	—	2	2	no	—
262	C₂²×C₁₇	—	2	4	no	—
263	C₂²×C₁₇	—	2	8	no	—
264	C₂²×C₁₇	—	4	4	no	—
265	C₂²×C₁₇	—	4	2	no	—
266	C₂²×C₁₇	—	4	2	no	—
267	C₂²×C₁₇	C₂×C₄×D₄	1	4	yes	—
268	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
269	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
270	C₂²×C₁₇	C₂²×#41	1	1	yes	characteristic
271	C₂²×C₁₇	C₂×2₋¹⁺⁴	1	2	yes	—
272	C₂²×C₁₇	#585	1	2	yes	—
273	C₄×C₁₇	—	2	4	no	—
274	C₄×C₁₇	—	2	8	no	—
275	C₄×C₁₇	—	2	8	no	—
276	C₄×C₁₇	—	2	4	no	—
277	C₄×C₁₇	—	2	8	no	—
278	C₄×C₁₇	—	4	4	no	—
279	C₄×C₁₇	—	4	2	no	—
280	C₄×C₁₇	—	4	4	no	—
281	C₄×C₁₇	C₂×C₄×D₄	1	4	yes	—
282	C₄×C₁₇	C₂×C₄×D₄	1	4	yes	—
283	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
284	C₂³×Q₈	C₂²×C₁₇	1	1	yes	characteristic
285	#536	C₄×C₁₇	1	16	yes	complemented
286	C₂×C₄⋊Q₈	C₂²×C₁₇	1	2	yes	—
287	C₂×#124	C₂²×C₁₇	1	2	yes	—
288	C₂×#123	C₂²×C₁₇	1	4	yes	—
289	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	4	yes	—
290	#519	—	2	8	no	—
291	C₄×#41	—	2	8	no	—
292	C₂×C₄×Q₈	C₂²×C₁₇	1	4	yes	—
293	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	—
294	C₂×C₄×Q₈	C₂²×C₁₇	1	4	yes	—
295	C₂×C₄×D₄	C₂²×C₁₇	1	4	yes	—
296	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
297	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
298	C₂×#117	C₂²×C₁₇	1	2	yes	—
299	C₂×#117	C₂²×C₁₇	1	4	yes	—
300	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
301	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
302	C₂²×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
303	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
304	C₂²×C₄²	C₂²×C₁₇	1	2	yes	—
305	#391	C₂²×C₁₇	1	2	yes	—
306	#391	C₂²×C₁₇	1	2	yes	—
307	#391	C₂²×C₁₇	1	4	yes	—
308	#391	C₂²×C₁₇	1	2	yes	—
309	#390	C₂²×C₁₇	1	2	yes	—
310	#389	C₂²×C₁₇	1	2	yes	—
311	#389	C₂²×C₁₇	1	8	yes	—
312	#389	C₂²×C₁₇	1	2	yes	—
313	#388	C₂²×C₁₇	1	8	yes	—
314	#388	C₂²×C₁₇	1	8	yes	—
315	#387	C₂²×C₁₇	1	8	yes	—
316	#387	C₂²×C₁₇	1	8	yes	—
317	#386	C₂²×C₁₇	1	4	yes	—
318	#385	C₂²×C₁₇	1	4	yes	—
319	#385	C₂²×C₁₇	1	8	yes	—
320	#380	C₂²×C₁₇	1	4	yes	—
321	C₄×C₄⋊C₄	C₂²×C₁₇	1	4	yes	—
322	C₄×C₄⋊C₄	C₂²×C₁₇	1	8	yes	—
323	C₄×C₄⋊C₄	C₂²×C₁₇	1	4	yes	—
324	C₄×C₄⋊C₄	C₂²×C₁₇	1	4	yes	—
325	C₄×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	—
326	C₄×C₂²⋊C₄	C₂²×C₁₇	1	8	yes	—
327	C₂×#95	C₂²×C₁₇	1	4	yes	—
328	C₂×C₁₇	—	2	4	no	—
329	C₂×C₁₇	—	4	4	no	—
330	C₂×C₁₇	C₂²×C₄×D₄	1	1	yes	characteristic
331	C₂×C₁₇	C₄×2₋¹⁺⁴	1	2	yes	—
332	C₂×C₁₇	#3489	1	2	yes	—
333	C₂×C₁₇	#3509	1	1	yes	characteristic
334	C₂×C₁₇	#3510	1	1	yes	characteristic
335	C₂×#41	—	2	4	no	—
336	C₂×#41	—	2	4	no	—
337	C₂×#41	C₂×C₄×C₁₇	1	8	yes	—
338	C₂²×Q₈	—	2	4	no	—
339	C₂²×Q₈	—	2	4	no	—
340	C₂²×Q₈	C₂×C₄×C₁₇	1	8	yes	complemented
341	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
342	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
343	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
344	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
345	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
347	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
348	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
349	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
350	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
351	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
352	C₄⋊Q₈	C₂×C₄×C₁₇	1	16	yes	complemented
353	#124	C₂×C₄×C₁₇	1	16	yes	complemented
354	#123	C₂×C₄×C₁₇	1	32	yes	complemented
355	C₂²⋊Q₈	C₂×C₄×C₁₇	1	32	yes	complemented
356	C₄×Q₈	—	2	8	no	—
357	C₄×Q₈	—	2	16	no	—
358	C₄×Q₈	—	2	16	no	—
359	C₄×D₄	—	2	8	no	—
360	C₄×D₄	—	2	16	no	—
361	#117	—	2	4	no	—
362	#117	—	2	16	no	—
363	#117	—	2	8	no	—
364	#117	C₂×C₄×C₁₇	1	8	yes	complemented
365	#117	D₄×C₁₇	1	8	yes	—
366	C₂×C₄⋊C₄	—	2	4	no	—
367	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
383	C₂×C₄²	—	2	4	no	—
384	C₂×C₄²	—	2	8	no	—
385	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₁₇	1	8	yes	—
387	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
388	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
389	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
390	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₁₇	1	8	yes	—
392	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
393	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
394	#95	C₂³×C₁₇	1	8	yes	—
395	#95	C₂³×C₁₇	1	8	yes	—
396	#95	C₂³×C₁₇	1	4	yes	—
397	#95	C₂³×C₁₇	1	8	yes	—
398	#95	C₂³×C₁₇	1	8	yes	—
399	#95	C₂³×C₁₇	1	4	yes	—
400	C₁₇	#34268	1	1	yes	characteristic, direct product factor, Sylow
401	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
402	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
403	#41	—	2	32	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	32	no	—
411	C₂×Q₈	C₂²×C₄×C₁₇	1	8	yes	—
412	C₂×Q₈	C₂²×C₄×C₁₇	1	8	yes	—
413	C₂×Q₈	C₂²×C₄×C₁₇	1	4	yes	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
419	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	8	no	—
427	C₂²×C₄	—	2	8	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	4	4	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	4	no	—
432	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
433	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
434	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
435	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
436	C₂²×C₄	#41×C₁₇	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	2	16	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	4	4	no	—
454	C₄⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
455	C₄⋊C₄	C₂²×C₄×C₁₇	1	32	yes	—
456	C₄⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	8	no	—
459	C₂²⋊C₄	—	4	8	no	—
460	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
461	C₂²⋊C₄	C₂²×C₄×C₁₇	1	32	yes	—
462	C₂²⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	8	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	16	no	—
468	C₄²	—	2	4	no	—
469	C₄²	—	4	8	no	—
470	C₄²	C₂²×C₄×C₁₇	1	8	yes	—
471	C₄²	C₂×D₄×C₁₇	1	8	yes	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	4	no	—
478	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
479	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
480	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
481	C₂³	C₂×#41×C₁₇	1	2	yes	—
482	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
483	Q₈	—	2	16	no	—
484	Q₈	—	2	16	no	—
485	Q₈	—	2	8	no	—
486	D₄	—	2	16	no	—
487	D₄	—	2	8	no	—
488	C₂×C₄	—	2	16	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	16	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	8	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	4	16	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	8	4	no	—
511	C₂×C₄	C₄×D₄×C₁₇	1	16	yes	—
512	C₂×C₄	C₂³×C₄×C₁₇	1	8	yes	—
513	C₂×C₄	C₂³×C₄×C₁₇	1	8	yes	—
514	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
515	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
516	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
517	C₂×C₄	C₂²×D₄×C₁₇	1	8	yes	—
518	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
520	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
521	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
522	C₂×C₄	C₁₇×2₋¹⁺⁴	1	4	yes	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	8	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	C₂×C₄×D₄×C₁₇	1	4	yes	—
533	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
534	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
535	C₂²	C₂²×#41×C₁₇	1	1	yes	characteristic
536	C₂²	C₂×C₁₇×2₋¹⁺⁴	1	2	yes	—
537	C₂²	C₁₇×#585	1	2	yes	—
538	C₄	—	2	4	no	—
539	C₄	—	2	8	no	—
540	C₄	—	2	4	no	—
541	C₄	—	2	8	no	—
542	C₄	—	2	8	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	4	no	—
546	C₄	C₂×C₄×D₄×C₁₇	1	4	yes	—
547	C₄	C₂×C₄×D₄×C₁₇	1	4	yes	—
548	C₂	—	2	4	no	—
549	C₂	—	4	4	no	—
550	C₂	C₂²×C₄×D₄×C₁₇	1	1	yes	characteristic
551	C₂	C₄×C₁₇×2₋¹⁺⁴	1	2	yes	—
552	C₂	C₁₇×#3489	1	2	yes	—
553	C₂	C₁₇×#3509	1	1	yes	characteristic
554	C₂	C₁₇×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁵×C₁₇
prime radical	C₂²×#41×C₁₇	C₂²
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×#519	C₂	semidirect
4. C₁₇×#2367	C₂	semidirect
5. C₁₇×#2365	C₂	semidirect
6. C₁₇×#2359	C₂	semidirect
7. C₁₇×#2323	C₂	semidirect
9. C₄×C₁₇×C₂²⋊Q₈	C₂	semidirect
10. C₁₇×#2296	C₂	semidirect
11. C₂×C₁₇×#391	C₂	semidirect
12. C₁₇×#2274	C₂	semidirect
15. C₁₇×#536	C₄	semidirect
63. C₂²×Q₈×C₁₇	C₂×C₄	semidirect
75. C₁₇×C₄⋊Q₈	C₂×C₄	semidirect
76. C₁₇×#124	C₂×C₄	semidirect
77. C₁₇×#123	C₂×C₄	semidirect
78. C₁₇×C₂²⋊Q₈	C₂×C₄	semidirect
87. C₁₇×#117	C₂×C₄	semidirect
194. #34268	C₁₇	direct (N × H)
247. C₂×#519	C₂×C₁₇	semidirect
249. #2367	C₂×C₁₇	semidirect
250. #2365	C₂×C₁₇	semidirect
251. #2359	C₂×C₁₇	semidirect
252. #2323	C₂×C₁₇	semidirect
254. C₄×C₂²⋊Q₈	C₂×C₁₇	semidirect
255. #2296	C₂×C₁₇	semidirect
256. C₂×#391	C₂×C₁₇	semidirect
257. #2274	C₂×C₁₇	semidirect
285. #536	C₄×C₁₇	semidirect
340. C₂²×Q₈	C₂×C₄×C₁₇	semidirect
352. C₄⋊Q₈	C₂×C₄×C₁₇	semidirect
353. #124	C₂×C₄×C₁₇	semidirect
354. #123	C₂×C₄×C₁₇	semidirect
355. C₂²⋊Q₈	C₂×C₄×C₁₇	semidirect
364. #117	C₂×C₄×C₁₇	semidirect
400. C₁₇	#34268	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×#536	2
C₂×C₁₇×#519	2
C₂×C₄×#41×C₁₇	2
C₁₇×#2367	2
C₁₇×#2365	2
C₁₇×#2359	2
C₁₇×#2323	2
C₁₇×#2311	2
C₄×C₁₇×C₂²⋊Q₈	2
C₁₇×#2296	2
C₂×C₁₇×#391	2
C₁₇×#2274	2
#34268	17

Subgroups — C17×#34268 #16892012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#34268 #16892012