Subgroups — C₂×C₁₇×#3325 #16918889

Order 4352.

2630 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3325	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₇×#482	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₇×#469	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₇×#447	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₇×#418	C₂	1	2	yes	maximal, complemented
13	C₂³×D₄×C₁₇	—	2	1	no	—
14	C₂³×D₄×C₁₇	C₂²	1	2	yes	—
15	C₂²×D₈×C₁₇	C₂²	1	1	yes	characteristic
16	C₂²×D₈×C₁₇	C₂²	1	2	yes	complemented
17	C₂²×M₁₆×C₁₇	C₂²	1	2	yes	complemented
18	C₁₇×#555	—	2	4	no	—
19	C₁₇×#555	C₂²	1	8	yes	complemented
20	D₄²×C₁₇	—	2	4	no	—
21	D₄²×C₁₇	C₂²	1	8	yes	complemented
22	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₇×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#124	—	2	2	no	—
25	C₂×C₁₇×#121	—	2	1	no	—
26	C₂×C₁₇×#121	—	2	1	no	—
27	C₂×C₁₇×#121	C₂²	1	2	yes	—
28	C₂×C₁₇×#121	C₂²	1	2	yes	complemented
29	C₂×C₁₇×#120	—	2	2	no	—
30	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₇×#117	—	2	1	no	—
34	C₂×C₁₇×#117	C₂²	1	2	yes	complemented
35	C₁₇×#486	C₂²	1	8	yes	complemented
36	C₁₇×#482	C₂²	1	16	yes	complemented
37	C₁₇×#476	C₂²	1	8	yes	complemented
38	C₁₇×#469	C₂²	1	16	yes	complemented
39	C₁₇×#459	C₂²	1	8	yes	complemented
40	C₁₇×#447	C₂²	1	16	yes	complemented
41	C₄×D₈×C₁₇	C₂²	1	8	yes	complemented
42	C₁₇×#436	C₂²	1	8	yes	complemented
43	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₇×#106	C₂²	1	2	yes	complemented
45	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₁₇×#418	C₂²	1	16	yes	complemented
47	C₂×C₁₇×#102	C₂²	1	2	yes	—
48	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
49	C₂×C₁₇×#102	C₂²	1	2	yes	complemented
50	C₂×C₁₇×#102	C₂²	1	2	yes	complemented
51	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₇×#102	C₂²	1	2	yes	complemented
53	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
54	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
55	C₂⁵×C₁₇	—	2	2	no	—
56	C₂²×Q₈×C₁₇	—	2	1	no	—
57	C₂²×D₄×C₁₇	—	2	8	no	—
58	C₂²×D₄×C₁₇	—	2	2	no	—
59	C₂²×D₄×C₁₇	—	2	2	no	—
60	C₂²×D₄×C₁₇	—	2	8	no	—
61	C₂²×D₄×C₁₇	—	2	2	no	—
62	C₂²×D₄×C₁₇	—	2	1	no	—
63	C₂²×D₄×C₁₇	—	2	4	no	—
64	C₂²×D₄×C₁₇	—	2	1	no	—
65	C₂²×D₄×C₁₇	—	4	4	no	—
66	C₂²×D₄×C₁₇	—	4	8	no	—
67	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₇	C₂³	1	8	yes	—
71	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₇	—	2	1	no	—
73	C₂³×C₄×C₁₇	—	2	1	no	—
74	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
75	C₂×D₈×C₁₇	—	2	4	no	—
76	C₂×D₈×C₁₇	—	4	4	no	—
77	C₂×D₈×C₁₇	C₂³	1	4	yes	—
78	C₂×D₈×C₁₇	C₂³	1	8	yes	complemented
79	C₂×M₁₆×C₁₇	—	4	4	no	—
80	C₂×M₁₆×C₁₇	C₂³	1	8	yes	complemented
81	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
84	C₁₇×C₄⋊Q₈	—	2	2	no	—
85	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
86	C₁₇×#127	—	2	2	no	—
87	C₁₇×#127	C₂³	1	4	yes	—
88	C₁₇×#124	—	2	16	no	—
89	C₁₇×#121	—	2	8	no	—
90	C₁₇×#121	—	2	4	no	—
91	C₁₇×#121	—	2	4	no	—
92	C₁₇×#121	—	2	8	no	—
93	C₁₇×#121	C₂³	1	8	yes	—
94	C₁₇×#121	C₂³	1	8	yes	complemented
95	C₁₇×#120	—	2	16	no	—
96	C₄×D₄×C₁₇	—	2	2	no	—
97	C₄×D₄×C₁₇	—	2	2	no	—
98	C₄×D₄×C₁₇	D₄	1	4	yes	—
99	C₄×D₄×C₁₇	C₂³	1	4	yes	—
100	C₄×D₄×C₁₇	C₂³	1	4	yes	—
101	C₄×D₄×C₁₇	C₂³	1	4	yes	complemented
102	C₁₇×#117	—	2	4	no	—
103	C₁₇×#117	—	2	8	no	—
104	C₁₇×#117	C₂³	1	8	yes	complemented
105	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
115	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
116	C₂×C₄²×C₁₇	—	2	2	no	—
117	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
118	C₁₇×#107	C₂³	1	4	yes	complemented
119	C₁₇×#106	C₂³	1	8	yes	complemented
120	C₁₇×C₄⋊C₈	C₂³	1	4	yes	complemented
121	C₁₇×#102	C₂³	1	4	yes	—
122	C₁₇×#102	C₂³	1	8	yes	—
123	C₁₇×#102	C₂³	1	8	yes	complemented
124	C₁₇×#102	C₂³	1	8	yes	complemented
125	C₁₇×#102	C₂³	1	4	yes	complemented
126	C₁₇×#102	C₂³	1	8	yes	complemented
127	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	complemented
128	C₄×C₈×C₁₇	C₂³	1	4	yes	complemented
129	C₂⁴×C₁₇	—	2	1	no	—
130	C₂⁴×C₁₇	—	2	1	no	—
131	C₂⁴×C₁₇	—	2	2	no	—
132	C₂⁴×C₁₇	—	2	8	no	—
133	C₂⁴×C₁₇	—	4	8	no	—
134	C₂⁴×C₁₇	—	4	8	no	—
135	C₂⁴×C₁₇	—	8	4	no	—
136	C₂⁴×C₁₇	C₂×D₄	1	2	yes	—
137	C₂×Q₈×C₁₇	—	2	4	no	—
138	C₂×Q₈×C₁₇	—	8	2	no	—
139	C₂×D₄×C₁₇	—	2	16	no	—
140	C₂×D₄×C₁₇	—	2	8	no	—
141	C₂×D₄×C₁₇	—	2	8	no	—
142	C₂×D₄×C₁₇	—	2	4	no	—
143	C₂×D₄×C₁₇	—	2	1	no	—
144	C₂×D₄×C₁₇	—	2	2	no	—
145	C₂×D₄×C₁₇	—	2	4	no	—
146	C₂×D₄×C₁₇	—	2	8	no	—
147	C₂×D₄×C₁₇	—	2	1	no	—
148	C₂×D₄×C₁₇	—	2	4	no	—
149	C₂×D₄×C₁₇	—	2	2	no	—
150	C₂×D₄×C₁₇	—	2	4	no	—
151	C₂×D₄×C₁₇	—	2	2	no	—
152	C₂×D₄×C₁₇	—	2	2	no	—
153	C₂×D₄×C₁₇	—	2	4	no	—
154	C₂×D₄×C₁₇	—	4	8	no	—
155	C₂×D₄×C₁₇	—	4	16	no	—
156	C₂×D₄×C₁₇	—	4	8	no	—
157	C₂×D₄×C₁₇	—	4	32	no	—
158	C₂×D₄×C₁₇	—	4	8	no	—
159	C₂×D₄×C₁₇	—	4	4	no	—
160	C₂×D₄×C₁₇	—	8	2	no	—
161	C₂×D₄×C₁₇	—	8	4	no	—
162	C₂×D₄×C₁₇	C₂×D₄	1	4	yes	—
163	C₂×D₄×C₁₇	#41	1	4	yes	—
164	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
165	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
166	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₇	—	2	4	no	—
168	C₂²×C₄×C₁₇	—	2	4	no	—
169	C₂²×C₄×C₁₇	—	2	1	no	—
170	C₂²×C₄×C₁₇	—	2	1	no	—
171	C₂²×C₄×C₁₇	—	2	2	no	—
172	C₂²×C₄×C₁₇	—	2	4	no	—
173	C₂²×C₄×C₁₇	—	2	4	no	—
174	C₂²×C₄×C₁₇	—	4	4	no	—
175	C₂²×C₄×C₁₇	—	4	4	no	—
176	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
182	D₈×C₁₇	—	2	8	no	—
183	D₈×C₁₇	—	4	8	no	—
184	M₁₆×C₁₇	—	4	8	no	—
185	C₂×C₈×C₁₇	—	2	2	no	—
186	C₂×C₈×C₁₇	—	2	2	no	—
187	C₂×C₈×C₁₇	—	2	4	no	—
188	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
189	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
190	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
191	C₄⋊C₄×C₁₇	—	2	2	no	—
192	C₄⋊C₄×C₁₇	—	2	4	no	—
193	C₄⋊C₄×C₁₇	—	2	1	no	—
194	C₄⋊C₄×C₁₇	—	2	1	no	—
195	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
196	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
197	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
198	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
199	C₂²⋊C₄×C₁₇	—	2	8	no	—
200	C₂²⋊C₄×C₁₇	—	2	4	no	—
201	C₂²⋊C₄×C₁₇	—	2	8	no	—
202	C₂²⋊C₄×C₁₇	—	2	4	no	—
203	C₂²⋊C₄×C₁₇	—	2	8	no	—
204	C₂²⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
205	C₄²×C₁₇	—	2	8	no	—
206	C₄²×C₁₇	C₂×D₄	1	2	yes	—
207	C₄²×C₁₇	C₂⁴	1	2	yes	—
208	C₂×#3325	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₁₇	—	2	4	no	—
210	C₂³×C₁₇	—	2	4	no	—
211	C₂³×C₁₇	—	2	4	no	—
212	C₂³×C₁₇	—	2	4	no	—
213	C₂³×C₁₇	—	2	2	no	—
214	C₂³×C₁₇	—	2	2	no	—
215	C₂³×C₁₇	—	2	4	no	—
216	C₂³×C₁₇	—	4	16	no	—
217	C₂³×C₁₇	—	4	16	no	—
218	C₂³×C₁₇	—	4	2	no	—
219	C₂³×C₁₇	—	4	2	no	—
220	C₂³×C₁₇	—	4	4	no	—
221	C₂³×C₁₇	—	4	2	no	—
222	C₂³×C₁₇	—	4	2	no	—
223	C₂³×C₁₇	—	4	4	no	—
224	C₂³×C₁₇	—	4	2	no	—
225	C₂³×C₁₇	—	4	4	no	—
226	C₂³×C₁₇	—	8	8	no	—
227	C₂³×C₁₇	—	8	32	no	—
228	C₂³×C₁₇	C₂²×D₄	1	4	yes	—
229	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
230	Q₈×C₁₇	—	8	4	no	—
231	D₄×C₁₇	—	2	4	no	—
232	D₄×C₁₇	—	2	8	no	—
233	D₄×C₁₇	—	2	2	no	—
234	D₄×C₁₇	—	2	4	no	—
235	D₄×C₁₇	—	2	2	no	—
236	D₄×C₁₇	—	2	2	no	—
237	D₄×C₁₇	—	2	4	no	—
238	D₄×C₁₇	—	4	16	no	—
239	D₄×C₁₇	—	4	16	no	—
240	D₄×C₁₇	—	4	2	no	—
241	D₄×C₁₇	—	4	4	no	—
242	D₄×C₁₇	—	4	8	no	—
243	D₄×C₁₇	—	8	4	no	—
244	D₄×C₁₇	—	8	8	no	—
245	D₄×C₁₇	C₂×#41	1	4	yes	—
246	C₂×C₄×C₁₇	—	2	4	no	—
247	C₂×C₄×C₁₇	—	2	2	no	—
248	C₂×C₄×C₁₇	—	2	8	no	—
249	C₂×C₄×C₁₇	—	2	4	no	—
250	C₂×C₄×C₁₇	—	2	4	no	—
251	C₂×C₄×C₁₇	—	2	2	no	—
252	C₂×C₄×C₁₇	—	2	4	no	—
253	C₂×C₄×C₁₇	—	2	2	no	—
254	C₂×C₄×C₁₇	—	4	2	no	—
255	C₂×C₄×C₁₇	—	4	2	no	—
256	C₂×C₄×C₁₇	—	4	4	no	—
257	C₂×C₄×C₁₇	—	4	8	no	—
258	C₂×C₄×C₁₇	—	4	8	no	—
259	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	4	yes	—
260	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
261	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
265	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
266	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
267	C₈×C₁₇	—	2	2	no	—
268	C₈×C₁₇	—	2	2	no	—
269	C₈×C₁₇	—	2	4	no	—
270	C₂×#555	C₂×C₁₇	1	1	yes	characteristic, complemented
271	C₂×D₄²	C₂×C₁₇	1	1	yes	characteristic, complemented
272	#3325	C₂×C₁₇	1	16	yes	direct product factor
273	C₂×#486	C₂×C₁₇	1	1	yes	characteristic, complemented
274	C₂×#482	C₂×C₁₇	1	2	yes	complemented
275	C₂×#476	C₂×C₁₇	1	1	yes	characteristic, complemented
276	C₂×#469	C₂×C₁₇	1	2	yes	complemented
277	C₂×#459	C₂×C₁₇	1	1	yes	characteristic, complemented
278	C₂×#447	C₂×C₁₇	1	2	yes	complemented
279	C₂×C₄×D₈	C₂×C₁₇	1	1	yes	characteristic, complemented
280	C₂×#436	C₂×C₁₇	1	1	yes	characteristic, complemented
281	C₂×#418	C₂×C₁₇	1	2	yes	complemented
282	C₂²×C₁₇	—	2	4	no	—
283	C₂²×C₁₇	—	2	4	no	—
284	C₂²×C₁₇	—	2	4	no	—
285	C₂²×C₁₇	—	2	4	no	—
286	C₂²×C₁₇	—	4	2	no	—
287	C₂²×C₁₇	—	4	8	no	—
288	C₂²×C₁₇	—	4	8	no	—
289	C₂²×C₁₇	—	4	2	no	—
290	C₂²×C₁₇	—	4	4	no	—
291	C₂²×C₁₇	—	4	2	no	—
292	C₂²×C₁₇	—	4	2	no	—
293	C₂²×C₁₇	—	4	4	no	—
294	C₂²×C₁₇	—	4	2	no	—
295	C₂²×C₁₇	—	4	4	no	—
296	C₂²×C₁₇	—	8	32	no	—
297	C₂²×C₁₇	—	8	4	no	—
298	C₂²×C₁₇	—	8	8	no	—
299	C₂²×C₁₇	#546	1	2	yes	—
300	C₂²×C₁₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
301	C₂²×C₁₇	#576	1	2	yes	—
302	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
303	C₄×C₁₇	—	2	4	no	—
304	C₄×C₁₇	—	2	2	no	—
305	C₄×C₁₇	—	4	2	no	—
306	C₄×C₁₇	—	4	2	no	—
307	C₄×C₁₇	—	4	4	no	—
308	C₄×C₁₇	#546	1	2	yes	—
309	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
310	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
311	C₄×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
312	C₂³×D₄	—	2	1	no	—
313	C₂³×D₄	C₂²×C₁₇	1	2	yes	—
314	C₂²×D₈	C₂²×C₁₇	1	1	yes	characteristic
315	C₂²×D₈	C₂²×C₁₇	1	2	yes	complemented
316	C₂²×M₁₆	C₂²×C₁₇	1	2	yes	complemented
317	#555	—	2	4	no	—
318	#555	C₂²×C₁₇	1	8	yes	complemented
319	D₄²	—	2	4	no	—
320	D₄²	C₂²×C₁₇	1	8	yes	complemented
321	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
322	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic
323	C₂×#124	—	2	2	no	—
324	C₂×#121	—	2	1	no	—
325	C₂×#121	—	2	1	no	—
326	C₂×#121	C₂²×C₁₇	1	2	yes	—
327	C₂×#121	C₂²×C₁₇	1	2	yes	complemented
328	C₂×#120	—	2	2	no	—
329	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
330	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
331	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
332	C₂×#117	—	2	1	no	—
333	C₂×#117	C₂²×C₁₇	1	2	yes	complemented
334	#486	C₂²×C₁₇	1	8	yes	complemented
335	#482	C₂²×C₁₇	1	16	yes	complemented
336	#476	C₂²×C₁₇	1	8	yes	complemented
337	#469	C₂²×C₁₇	1	16	yes	complemented
338	#459	C₂²×C₁₇	1	8	yes	complemented
339	#447	C₂²×C₁₇	1	16	yes	complemented
340	C₄×D₈	C₂²×C₁₇	1	8	yes	complemented
341	#436	C₂²×C₁₇	1	8	yes	complemented
342	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic, complemented
343	C₂×#106	C₂²×C₁₇	1	2	yes	complemented
344	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
345	#418	C₂²×C₁₇	1	16	yes	complemented
346	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
347	C₂×#102	C₂²×C₁₇	1	2	yes	—
348	C₂×#102	C₂²×C₁₇	1	2	yes	complemented
349	C₂×#102	C₂²×C₁₇	1	2	yes	complemented
350	C₂×#102	C₂²×C₁₇	1	2	yes	complemented
351	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic, complemented
352	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	complemented
353	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
354	C₂×C₁₇	—	4	4	no	—
355	C₂×C₁₇	—	4	4	no	—
356	C₂×C₁₇	—	8	2	no	—
357	C₂×C₁₇	—	8	4	no	—
358	C₂×C₁₇	#3325	1	4	yes	direct product factor
359	C₂×C₁₇	C₂×#546	1	1	yes	characteristic
360	C₂×C₁₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
361	C₂×C₁₇	C₂×#576	1	1	yes	characteristic
362	C₂⁵	—	2	2	no	—
363	C₂²×Q₈	—	2	1	no	—
364	C₂²×D₄	—	2	8	no	—
365	C₂²×D₄	—	2	2	no	—
366	C₂²×D₄	—	2	2	no	—
367	C₂²×D₄	—	2	8	no	—
368	C₂²×D₄	—	2	2	no	—
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	—	2	4	no	—
371	C₂²×D₄	—	2	1	no	—
372	C₂²×D₄	—	4	4	no	—
373	C₂²×D₄	—	4	8	no	—
374	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
376	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
377	C₂²×D₄	C₂³×C₁₇	1	8	yes	—
378	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
379	C₂³×C₄	—	2	1	no	—
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
382	C₂×D₈	—	2	4	no	—
383	C₂×D₈	—	4	4	no	—
384	C₂×D₈	C₂³×C₁₇	1	4	yes	—
385	C₂×D₈	C₂³×C₁₇	1	8	yes	complemented
386	C₂×M₁₆	—	4	4	no	—
387	C₂×M₁₆	C₂³×C₁₇	1	8	yes	complemented
388	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
390	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
391	C₄⋊Q₈	—	2	2	no	—
392	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	complemented
393	#127	—	2	2	no	—
394	#127	C₂³×C₁₇	1	4	yes	—
395	#124	—	2	16	no	—
396	#121	—	2	8	no	—
397	#121	—	2	4	no	—
398	#121	—	2	4	no	—
399	#121	—	2	8	no	—
400	#121	C₂³×C₁₇	1	8	yes	—
401	#121	C₂³×C₁₇	1	8	yes	complemented
402	#120	—	2	16	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	D₄×C₁₇	1	4	yes	—
406	C₄×D₄	C₂³×C₁₇	1	4	yes	—
407	C₄×D₄	C₂³×C₁₇	1	4	yes	—
408	C₄×D₄	C₂³×C₁₇	1	4	yes	complemented
409	#117	—	2	4	no	—
410	#117	—	2	8	no	—
411	#117	C₂³×C₁₇	1	8	yes	complemented
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	—	2	2	no	—
418	C₂×C₂²⋊C₄	—	2	2	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	2	no	—
422	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
423	C₂×C₄²	—	2	2	no	—
424	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
425	#107	C₂³×C₁₇	1	4	yes	complemented
426	#106	C₂³×C₁₇	1	8	yes	complemented
427	C₄⋊C₈	C₂³×C₁₇	1	4	yes	complemented
428	#102	C₂³×C₁₇	1	4	yes	—
429	#102	C₂³×C₁₇	1	8	yes	—
430	#102	C₂³×C₁₇	1	8	yes	complemented
431	#102	C₂³×C₁₇	1	8	yes	complemented
432	#102	C₂³×C₁₇	1	4	yes	complemented
433	#102	C₂³×C₁₇	1	8	yes	complemented
434	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	complemented
435	C₄×C₈	C₂³×C₁₇	1	4	yes	complemented
436	C₁₇	C₂×#3325	1	1	yes	characteristic, direct product factor, Sylow
437	C₂⁴	—	2	1	no	—
438	C₂⁴	—	2	1	no	—
439	C₂⁴	—	2	2	no	—
440	C₂⁴	—	2	8	no	—
441	C₂⁴	—	4	8	no	—
442	C₂⁴	—	4	8	no	—
443	C₂⁴	—	8	4	no	—
444	C₂⁴	C₂×D₄×C₁₇	1	2	yes	—
445	C₂×Q₈	—	2	4	no	—
446	C₂×Q₈	—	8	2	no	—
447	C₂×D₄	—	2	16	no	—
448	C₂×D₄	—	2	8	no	—
449	C₂×D₄	—	2	8	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	4	8	no	—
463	C₂×D₄	—	4	16	no	—
464	C₂×D₄	—	4	8	no	—
465	C₂×D₄	—	4	32	no	—
466	C₂×D₄	—	4	8	no	—
467	C₂×D₄	—	4	4	no	—
468	C₂×D₄	—	8	2	no	—
469	C₂×D₄	—	8	4	no	—
470	C₂×D₄	C₂×D₄×C₁₇	1	4	yes	—
471	C₂×D₄	#41×C₁₇	1	4	yes	—
472	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
473	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
474	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	4	4	no	—
483	C₂²×C₄	—	4	4	no	—
484	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
485	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
487	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
490	D₈	—	2	8	no	—
491	D₈	—	4	8	no	—
492	M₁₆	—	4	8	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	4	no	—
496	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
497	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
498	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
504	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
505	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
506	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
513	C₄²	—	2	8	no	—
514	C₄²	C₂×D₄×C₁₇	1	2	yes	—
515	C₄²	C₂⁴×C₁₇	1	2	yes	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	4	16	no	—
524	C₂³	—	4	16	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	4	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	4	4	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	4	no	—
533	C₂³	—	8	8	no	—
534	C₂³	—	8	32	no	—
535	C₂³	C₂²×D₄×C₁₇	1	4	yes	—
536	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
537	Q₈	—	8	4	no	—
538	D₄	—	2	4	no	—
539	D₄	—	2	8	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	2	no	—
544	D₄	—	2	4	no	—
545	D₄	—	4	16	no	—
546	D₄	—	4	16	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	8	no	—
550	D₄	—	8	4	no	—
551	D₄	—	8	8	no	—
552	D₄	C₂×#41×C₁₇	1	4	yes	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	8	no	—
565	C₂×C₄	—	4	8	no	—
566	C₂×C₄	C₁₇×AGL(1,ℤ/8)	1	4	yes	—
567	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
568	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
571	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
572	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
573	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
574	C₈	—	2	2	no	—
575	C₈	—	2	2	no	—
576	C₈	—	2	4	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	8	no	—
583	C₂²	—	4	8	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	8	32	no	—
592	C₂²	—	8	8	no	—
593	C₂²	—	8	4	no	—
594	C₂²	C₁₇×#546	1	2	yes	—
595	C₂²	C₂×C₁₇×AGL(1,ℤ/8)	1	2	yes	—
596	C₂²	C₁₇×#576	1	2	yes	—
597	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
598	C₄	—	2	4	no	—
599	C₄	—	2	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	4	no	—
603	C₄	C₁₇×#546	1	2	yes	—
604	C₄	C₂×C₁₇×AGL(1,ℤ/8)	1	4	yes	—
605	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
606	C₄	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
607	C₂	—	4	4	no	—
608	C₂	—	4	4	no	—
609	C₂	—	8	4	no	—
610	C₂	—	8	2	no	—
611	C₂	C₁₇×#3325	1	4	yes	direct product factor
612	C₂	C₂×C₁₇×#546	1	1	yes	characteristic
613	C₂	C₂²×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
614	C₂	C₂×C₁₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#555	C₂	semidirect
2. C₂×D₄²×C₁₇	C₂	semidirect
3. C₁₇×#3325	C₂	direct (N × H)
4. C₂×C₁₇×#486	C₂	semidirect
5. C₂×C₁₇×#482	C₂	semidirect
6. C₂×C₁₇×#476	C₂	semidirect
7. C₂×C₁₇×#469	C₂	semidirect
8. C₂×C₁₇×#459	C₂	semidirect
9. C₂×C₁₇×#447	C₂	semidirect
10. C₂×C₄×D₈×C₁₇	C₂	semidirect
11. C₂×C₁₇×#436	C₂	semidirect
12. C₂×C₁₇×#418	C₂	semidirect
16. C₂²×D₈×C₁₇	C₂²	semidirect
17. C₂²×M₁₆×C₁₇	C₂²	semidirect
19. C₁₇×#555	C₂²	semidirect
21. D₄²×C₁₇	C₂²	semidirect
22. C₂×C₁₇×C₄⋊Q₈	C₂²	semidirect
28. C₂×C₁₇×#121	C₂²	semidirect
32. C₂×C₄×D₄×C₁₇	C₂²	semidirect
34. C₂×C₁₇×#117	C₂²	semidirect
35. C₁₇×#486	C₂²	semidirect
36. C₁₇×#482	C₂²	semidirect
37. C₁₇×#476	C₂²	semidirect
38. C₁₇×#469	C₂²	semidirect
39. C₁₇×#459	C₂²	semidirect
40. C₁₇×#447	C₂²	semidirect
41. C₄×D₈×C₁₇	C₂²	semidirect
42. C₁₇×#436	C₂²	semidirect
43. C₂×C₁₇×#107	C₂²	semidirect
44. C₂×C₁₇×#106	C₂²	semidirect
45. C₂×C₁₇×C₄⋊C₈	C₂²	semidirect
46. C₁₇×#418	C₂²	semidirect
49. C₂×C₁₇×#102	C₂²	semidirect
50. C₂×C₁₇×#102	C₂²	semidirect
51. C₂×C₁₇×#102	C₂²	semidirect
52. C₂×C₁₇×#102	C₂²	semidirect
53. C₂×C₁₇×C₂²⋊C₈	C₂²	semidirect
54. C₂×C₄×C₈×C₁₇	C₂²	semidirect
78. C₂×D₈×C₁₇	C₂³	semidirect
80. C₂×M₁₆×C₁₇	C₂³	semidirect
85. C₁₇×C₄⋊Q₈	C₂³	semidirect
94. C₁₇×#121	C₂³	semidirect
101. C₄×D₄×C₁₇	C₂³	semidirect
104. C₁₇×#117	C₂³	semidirect
118. C₁₇×#107	C₂³	semidirect
119. C₁₇×#106	C₂³	semidirect
120. C₁₇×C₄⋊C₈	C₂³	semidirect
123. C₁₇×#102	C₂³	semidirect
124. C₁₇×#102	C₂³	semidirect
125. C₁₇×#102	C₂³	semidirect
126. C₁₇×#102	C₂³	semidirect
127. C₁₇×C₂²⋊C₈	C₂³	semidirect
128. C₄×C₈×C₁₇	C₂³	semidirect
208. C₂×#3325	C₁₇	direct (N × H)
270. C₂×#555	C₂×C₁₇	semidirect
271. C₂×D₄²	C₂×C₁₇	semidirect
272. #3325	C₂×C₁₇	direct (N × H)
273. C₂×#486	C₂×C₁₇	semidirect
274. C₂×#482	C₂×C₁₇	semidirect
275. C₂×#476	C₂×C₁₇	semidirect
276. C₂×#469	C₂×C₁₇	semidirect
277. C₂×#459	C₂×C₁₇	semidirect
278. C₂×#447	C₂×C₁₇	semidirect
279. C₂×C₄×D₈	C₂×C₁₇	semidirect
280. C₂×#436	C₂×C₁₇	semidirect
281. C₂×#418	C₂×C₁₇	semidirect
315. C₂²×D₈	C₂²×C₁₇	semidirect
316. C₂²×M₁₆	C₂²×C₁₇	semidirect
318. #555	C₂²×C₁₇	semidirect
320. D₄²	C₂²×C₁₇	semidirect
321. C₂×C₄⋊Q₈	C₂²×C₁₇	semidirect
327. C₂×#121	C₂²×C₁₇	semidirect
331. C₂×C₄×D₄	C₂²×C₁₇	semidirect
333. C₂×#117	C₂²×C₁₇	semidirect
334. #486	C₂²×C₁₇	semidirect
335. #482	C₂²×C₁₇	semidirect
336. #476	C₂²×C₁₇	semidirect
337. #469	C₂²×C₁₇	semidirect
338. #459	C₂²×C₁₇	semidirect
339. #447	C₂²×C₁₇	semidirect
340. C₄×D₈	C₂²×C₁₇	semidirect
341. #436	C₂²×C₁₇	semidirect
342. C₂×#107	C₂²×C₁₇	semidirect
343. C₂×#106	C₂²×C₁₇	semidirect
344. C₂×C₄⋊C₈	C₂²×C₁₇	semidirect
345. #418	C₂²×C₁₇	semidirect
348. C₂×#102	C₂²×C₁₇	semidirect
349. C₂×#102	C₂²×C₁₇	semidirect
350. C₂×#102	C₂²×C₁₇	semidirect
351. C₂×#102	C₂²×C₁₇	semidirect
352. C₂×C₂²⋊C₈	C₂²×C₁₇	semidirect
353. C₂×C₄×C₈	C₂²×C₁₇	semidirect
358. C₂×C₁₇	#3325	direct (N × H)
385. C₂×D₈	C₂³×C₁₇	semidirect
387. C₂×M₁₆	C₂³×C₁₇	semidirect
392. C₄⋊Q₈	C₂³×C₁₇	semidirect
401. #121	C₂³×C₁₇	semidirect
408. C₄×D₄	C₂³×C₁₇	semidirect
411. #117	C₂³×C₁₇	semidirect
425. #107	C₂³×C₁₇	semidirect
426. #106	C₂³×C₁₇	semidirect
427. C₄⋊C₈	C₂³×C₁₇	semidirect
430. #102	C₂³×C₁₇	semidirect
431. #102	C₂³×C₁₇	semidirect
432. #102	C₂³×C₁₇	semidirect
433. #102	C₂³×C₁₇	semidirect
434. C₂²⋊C₈	C₂³×C₁₇	semidirect
435. C₄×C₈	C₂³×C₁₇	semidirect
436. C₁₇	C₂×#3325	direct (N × H)
611. C₂	C₁₇×#3325	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×#555	2
C₂×D₄²×C₁₇	2
C₁₇×#3325	2
C₂×C₁₇×#486	2
C₂×C₁₇×#482	2
C₂×C₁₇×#476	2
C₂×C₁₇×#469	2
C₂×C₁₇×#459	2
C₂×C₁₇×#447	2
C₂×C₄×D₈×C₁₇	2
C₂×C₁₇×#436	2
C₂×C₁₇×#418	2
C₂×#3325	17

Subgroups — C2×C17×#3325 #16918889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#3325 #16918889