Subgroups — C₁₇×#62851 #16920595

Order 4352.

7066 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3524	C₂	1	8	yes	maximal, complemented
2	C₁₇×#3522	C₂	1	8	yes	maximal, complemented
3	C₁₇×#3517	C₂	1	8	yes	maximal, complemented
4	C₁₇×#3516	C₂	1	8	yes	maximal, complemented
5	C₁₇×#3506	C₂	1	6	yes	maximal, complemented
6	C₁₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#3492	C₂	1	6	yes	maximal, complemented
9	C₁₇×#3487	C₂	1	2	yes	maximal, complemented
10	C₁₇×#3460	C₂	1	6	yes	maximal, complemented
11	C₁₇×#3455	C₂	1	6	yes	maximal, complemented
12	C₄×C₁₇×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₇×2₋¹⁺⁴	C₂²	1	2	yes	—
15	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
16	C₁₇×#559	C₂²	1	24	yes	complemented
17	Q₈²×C₁₇	C₂²	1	4	yes	complemented
18	C₁₇×#557	C₂²	1	8	yes	complemented
19	C₁₇×#557	C₂²	1	4	yes	complemented
20	C₁₇×#556	C₂²	1	12	yes	complemented
21	C₁₇×#555	C₂²	1	12	yes	complemented
22	C₁₇×#554	C₂²	1	24	yes	complemented
23	C₁₇×#553	C₂²	1	24	yes	complemented
24	C₁₇×#553	C₂²	1	24	yes	complemented
25	C₁₇×#552	C₂²	1	24	yes	complemented
26	C₁₇×#550	C₂²	1	8	yes	—
27	C₁₇×#550	C₂²	1	8	yes	—
28	C₁₇×#550	C₂²	1	4	yes	complemented
29	C₁₇×#550	C₂²	1	12	yes	complemented
30	D₄×Q₈×C₁₇	C₂²	1	4	yes	complemented
31	C₁₇×#548	C₂²	1	8	yes	—
32	C₁₇×#548	C₂²	1	8	yes	—
33	C₁₇×#548	C₂²	1	8	yes	complemented
34	C₁₇×#547	C₂²	1	24	yes	complemented
35	C₁₇×#547	C₂²	1	12	yes	complemented
36	C₁₇×#544	C₂²	1	6	yes	—
37	C₁₇×#542	C₂²	1	24	yes	complemented
38	C₁₇×#542	C₂²	1	12	yes	complemented
39	C₁₇×#542	C₂²	1	12	yes	complemented
40	C₁₇×#541	C₂²	1	12	yes	complemented
41	C₁₇×#540	C₂²	1	24	yes	complemented
42	C₁₇×#540	C₂²	1	12	yes	complemented
43	C₁₇×#539	C₂²	1	12	yes	—
44	C₁₇×#539	C₂²	1	4	yes	—
45	C₁₇×#538	C₂²	1	12	yes	—
46	C₁₇×#538	C₂²	1	12	yes	—
47	C₁₇×#537	C₂²	1	6	yes	—
48	C₁₇×#535	C₂²	1	12	yes	—
49	C₁₇×#533	C₂²	1	6	yes	—
50	C₁₇×#532	C₂²	1	6	yes	—
51	C₁₇×#532	C₂²	1	24	yes	complemented
52	C₁₇×#529	C₂²	1	24	yes	complemented
53	C₁₇×#529	C₂²	1	24	yes	complemented
54	C₁₇×#529	C₂²	1	24	yes	complemented
55	C₁₇×#525	C₂²	1	24	yes	—
56	C₁₇×#525	C₂²	1	12	yes	—
57	C₁₇×#520	C₂²	1	12	yes	—
58	C₁₇×#520	C₂²	1	8	yes	—
59	C₁₇×#520	C₂²	1	8	yes	—
60	C₁₇×#520	C₂²	1	8	yes	complemented
61	C₁₇×#519	C₂²	1	2	yes	—
62	C₁₇×#519	C₂²	1	8	yes	complemented
63	C₄×#41×C₁₇	C₂²	1	12	yes	—
64	C₄×#41×C₁₇	C₂²	1	8	yes	complemented
65	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
66	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
67	C₂×C₄×Q₈×C₁₇	C₂²	1	8	yes	complemented
68	C₂×C₄×D₄×C₁₇	C₂²	1	3	yes	—
69	C₂×C₄×D₄×C₁₇	C₂²	1	3	yes	—
70	C₂×C₁₇×#117	C₂²	1	3	yes	—
71	C₂²×C₄⋊C₄×C₁₇	C₂²	1	3	yes	—
72	C₁₇×2₋¹⁺⁴	—	2	16	no	—
73	C₂×#41×C₁₇	—	2	8	no	—
74	C₂×#41×C₁₇	C₂³	1	12	yes	—
75	C₂×#41×C₁₇	C₂³	1	8	yes	—
76	C₂×#41×C₁₇	C₂³	1	8	yes	—
77	C₂×#41×C₁₇	C₂³	1	24	yes	—
78	C₂²×Q₈×C₁₇	C₂³	1	8	yes	—
79	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₇	C₂³	1	3	yes	—
81	C₂³×C₄×C₁₇	C₂³	1	3	yes	—
82	C₂³×C₄×C₁₇	C₂³	1	6	yes	—
83	C₁₇×C₄⋊Q₈	C₂³	1	6	yes	—
84	C₁₇×C₄⋊Q₈	C₂³	1	24	yes	—
85	C₁₇×C₄⋊Q₈	C₂³	1	6	yes	—
86	C₁₇×C₄⋊Q₈	C₂³	1	6	yes	—
87	C₁₇×#127	C₂³	1	6	yes	—
88	C₁₇×#127	C₂³	1	24	yes	—
89	C₁₇×#126	C₂³	1	24	yes	—
90	C₁₇×#126	C₂³	1	8	yes	—
91	C₁₇×#126	C₂³	1	24	yes	—
92	C₁₇×#126	C₂³	1	24	yes	—
93	C₁₇×#125	C₂³	1	8	yes	—
94	C₁₇×#125	C₂³	1	24	yes	—
95	C₁₇×#125	C₂³	1	24	yes	—
96	C₁₇×#125	C₂³	1	12	yes	—
97	C₁₇×#124	C₂³	1	24	yes	—
98	C₁₇×#124	C₂³	1	24	yes	—
99	C₁₇×#124	C₂³	1	24	yes	—
100	C₁₇×#124	C₂³	1	12	yes	—
101	C₁₇×#123	C₂³	1	8	yes	—
102	C₁₇×#123	C₂³	1	48	yes	—
103	C₁₇×#123	C₂³	1	24	yes	—
104	C₁₇×#123	C₂³	1	8	yes	—
105	C₁₇×#123	C₂³	1	24	yes	—
106	C₁₇×#123	C₂³	1	24	yes	—
107	C₁₇×C₂²⋊Q₈	C₂³	1	12	yes	—
108	C₁₇×C₂²⋊Q₈	C₂³	1	12	yes	—
109	C₁₇×C₂²⋊Q₈	C₂³	1	12	yes	—
110	C₁₇×C₂²⋊Q₈	C₂³	1	24	yes	—
111	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
112	C₁₇×C₂²⋊Q₈	C₂³	1	24	yes	—
113	C₁₇×C₂²⋊Q₈	C₂³	1	24	yes	—
114	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₁₇×#121	C₂³	1	12	yes	—
116	C₁₇×#121	C₂³	1	24	yes	—
117	C₁₇×#121	C₂³	1	12	yes	—
118	C₁₇×#121	C₂³	1	12	yes	—
119	C₁₇×#121	C₂³	1	24	yes	—
120	C₁₇×#121	C₂³	1	24	yes	—
121	C₁₇×#121	C₂³	1	24	yes	—
122	C₁₇×#121	C₂³	1	4	yes	—
123	C₁₇×#121	C₂³	1	24	yes	—
124	C₁₇×#121	C₂³	1	24	yes	—
125	C₁₇×#120	C₂³	1	24	yes	—
126	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
127	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
128	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
129	C₄×Q₈×C₁₇	C₂³	1	12	yes	—
130	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
131	C₄×Q₈×C₁₇	C₂³	1	24	yes	—
132	C₄×Q₈×C₁₇	C₂³	1	12	yes	—
133	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
134	C₄×Q₈×C₁₇	C₂³	1	12	yes	—
135	C₄×Q₈×C₁₇	C₂³	1	12	yes	—
136	C₄×D₄×C₁₇	C₂³	1	24	yes	—
137	C₄×D₄×C₁₇	C₂³	1	12	yes	—
138	C₄×D₄×C₁₇	C₂³	1	12	yes	—
139	C₄×D₄×C₁₇	C₂³	1	8	yes	—
140	C₄×D₄×C₁₇	C₂³	1	12	yes	—
141	C₄×D₄×C₁₇	C₂³	1	24	yes	—
142	C₄×D₄×C₁₇	C₂³	1	12	yes	—
143	C₄×D₄×C₁₇	C₂³	1	24	yes	—
144	C₄×D₄×C₁₇	C₂³	1	24	yes	—
145	C₄×D₄×C₁₇	C₂³	1	24	yes	—
146	C₄×D₄×C₁₇	C₂³	1	48	yes	—
147	C₄×D₄×C₁₇	C₂³	1	12	yes	—
148	C₄×D₄×C₁₇	C₂³	1	12	yes	—
149	C₁₇×#117	C₂³	1	12	yes	—
150	C₁₇×#117	C₂³	1	12	yes	—
151	C₁₇×#117	C₂³	1	12	yes	—
152	C₁₇×#117	C₂³	1	24	yes	—
153	C₁₇×#117	C₂³	1	24	yes	—
154	C₁₇×#117	C₂³	1	24	yes	—
155	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
156	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
157	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
158	C₂×C₄⋊C₄×C₁₇	C₂³	1	24	yes	—
159	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₇	C₂³	1	24	yes	—
161	C₂×C₂²⋊C₄×C₁₇	C₂³	1	3	yes	—
162	C₂×C₂²⋊C₄×C₁₇	C₂³	1	3	yes	—
163	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
164	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
165	C₂×C₄²×C₁₇	C₂³	1	24	yes	—
166	C₂⁴×C₁₇	C₂⁴	1	3	yes	—
167	#41×C₁₇	—	2	32	no	—
168	#41×C₁₇	—	2	32	no	—
169	#41×C₁₇	—	2	48	no	—
170	#41×C₁₇	—	8	24	no	—
171	C₂×Q₈×C₁₇	—	2	32	no	—
172	C₂×Q₈×C₁₇	#41	1	8	yes	complemented
173	C₂×Q₈×C₁₇	C₂⁴	1	12	yes	—
174	C₂×Q₈×C₁₇	C₂⁴	1	12	yes	—
175	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
176	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
177	C₂×D₄×C₁₇	—	2	12	no	—
178	C₂×D₄×C₁₇	C₂⁴	1	8	yes	—
179	C₂×D₄×C₁₇	C₂⁴	1	12	yes	—
180	C₂×D₄×C₁₇	C₂⁴	1	12	yes	—
181	C₂×D₄×C₁₇	C₂⁴	1	24	yes	—
182	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
183	C₂×D₄×C₁₇	C₂⁴	1	12	yes	—
184	C₂×D₄×C₁₇	C₂⁴	1	24	yes	—
185	C₂²×C₄×C₁₇	—	2	12	no	—
186	C₂²×C₄×C₁₇	—	8	6	no	—
187	C₂²×C₄×C₁₇	C₂⁴	1	12	yes	—
188	C₂²×C₄×C₁₇	C₂⁴	1	24	yes	—
189	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
191	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
193	C₂²×C₄×C₁₇	C₂⁴	1	24	yes	—
194	C₂²×C₄×C₁₇	C₂⁴	1	24	yes	—
195	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
196	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
198	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
199	C₄⋊C₄×C₁₇	C₂⁴	1	12	yes	—
200	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
201	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
202	C₄⋊C₄×C₁₇	C₂⁴	1	24	yes	—
203	C₄⋊C₄×C₁₇	C₂⁴	1	12	yes	—
204	C₄⋊C₄×C₁₇	C₂⁴	1	12	yes	—
205	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
206	C₄⋊C₄×C₁₇	C₂⁴	1	24	yes	—
207	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
208	C₄⋊C₄×C₁₇	C₂⁴	1	12	yes	—
209	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
210	C₄⋊C₄×C₁₇	C₂⁴	1	12	yes	—
211	C₄⋊C₄×C₁₇	C₂⁴	1	12	yes	—
212	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
213	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
214	C₄⋊C₄×C₁₇	C₂⁴	1	12	yes	—
215	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
216	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
217	C₂²⋊C₄×C₁₇	C₂⁴	1	24	yes	—
218	C₂²⋊C₄×C₁₇	C₂⁴	1	24	yes	—
219	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
220	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
221	C₂²⋊C₄×C₁₇	C₂⁴	1	24	yes	—
222	C₂²⋊C₄×C₁₇	C₂⁴	1	6	yes	—
223	C₂²⋊C₄×C₁₇	C₂⁴	1	24	yes	—
224	C₂²⋊C₄×C₁₇	C₂⁴	1	12	yes	—
225	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
226	C₂²⋊C₄×C₁₇	C₂⁴	1	6	yes	—
227	C₄²×C₁₇	C₂⁴	1	8	yes	—
228	C₄²×C₁₇	C₂⁴	1	6	yes	—
229	C₄²×C₁₇	C₂⁴	1	24	yes	—
230	C₄²×C₁₇	C₂⁴	1	24	yes	—
231	C₄²×C₁₇	C₂⁴	1	6	yes	—
232	C₄²×C₁₇	C₂⁴	1	12	yes	—
233	#62851	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₁₇	—	2	6	no	—
235	C₂³×C₁₇	—	4	3	no	—
236	C₂³×C₁₇	—	4	3	no	—
237	C₂³×C₁₇	C₂⁵	1	6	yes	—
238	C₂³×C₁₇	C₂⁵	1	8	yes	—
239	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
240	Q₈×C₁₇	—	2	24	no	—
241	Q₈×C₁₇	—	4	4	no	—
242	Q₈×C₁₇	—	4	12	no	—
243	Q₈×C₁₇	C₂×#41	1	16	yes	—
244	D₄×C₁₇	—	2	16	no	—
245	D₄×C₁₇	—	2	24	no	—
246	D₄×C₁₇	—	2	24	no	—
247	D₄×C₁₇	—	4	4	no	—
248	D₄×C₁₇	—	4	24	no	—
249	D₄×C₁₇	—	4	12	no	—
250	D₄×C₁₇	—	4	24	no	—
251	C₂×C₄×C₁₇	—	2	2	no	—
252	C₂×C₄×C₁₇	—	2	24	no	—
253	C₂×C₄×C₁₇	—	2	48	no	—
254	C₂×C₄×C₁₇	—	4	3	no	—
255	C₂×C₄×C₁₇	—	4	3	no	—
256	C₂×C₄×C₁₇	—	4	24	no	—
257	C₂×C₄×C₁₇	—	4	1	no	—
258	C₂×C₄×C₁₇	—	4	8	no	—
259	C₂×C₄×C₁₇	—	4	1	no	—
260	C₂×C₄×C₁₇	—	4	24	no	—
261	C₂×C₄×C₁₇	C₂×#41	1	12	yes	—
262	C₂×C₄×C₁₇	C₂⁵	1	2	yes	—
263	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
264	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
265	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
266	C₂×C₄×C₁₇	C₂⁵	1	6	yes	—
267	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
268	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
269	C₂×C₄×C₁₇	C₂⁵	1	6	yes	—
270	C₂×C₄×C₁₇	C₂⁵	1	2	yes	—
271	C₂×C₄×C₁₇	C₂⁵	1	6	yes	—
272	#3524	C₂×C₁₇	1	8	yes	complemented
273	#3522	C₂×C₁₇	1	8	yes	complemented
274	#3517	C₂×C₁₇	1	8	yes	complemented
275	#3516	C₂×C₁₇	1	8	yes	complemented
276	#3506	C₂×C₁₇	1	6	yes	complemented
277	#3502	C₂×C₁₇	1	1	yes	characteristic, complemented
278	#3497	C₂×C₁₇	1	1	yes	characteristic, complemented
279	#3492	C₂×C₁₇	1	6	yes	complemented
280	#3487	C₂×C₁₇	1	2	yes	complemented
281	#3460	C₂×C₁₇	1	6	yes	complemented
282	#3455	C₂×C₁₇	1	6	yes	complemented
283	C₄×2₋¹⁺⁴	C₂×C₁₇	1	2	yes	complemented
284	C₂×#520	C₂×C₁₇	1	1	yes	characteristic, complemented
285	C₂²×C₁₇	—	2	1	no	—
286	C₂²×C₁₇	—	2	1	no	—
287	C₂²×C₁₇	—	2	8	no	—
288	C₂²×C₁₇	—	2	6	no	—
289	C₂²×C₁₇	—	2	6	no	—
290	C₂²×C₁₇	—	2	8	no	—
291	C₂²×C₁₇	—	2	8	no	—
292	C₂²×C₁₇	—	2	6	no	—
293	C₂²×C₁₇	—	4	12	no	—
294	C₂²×C₁₇	C₂²×#41	1	2	yes	—
295	C₂²×C₁₇	C₂⁶	1	1	yes	characteristic
296	C₄×C₁₇	—	2	2	no	—
297	C₄×C₁₇	—	2	8	no	—
298	C₄×C₁₇	—	2	6	no	—
299	C₄×C₁₇	—	2	6	no	—
300	C₄×C₁₇	—	2	8	no	—
301	C₄×C₁₇	—	2	2	no	—
302	C₄×C₁₇	—	2	1	no	—
303	C₄×C₁₇	—	2	8	no	—
304	C₄×C₁₇	—	2	1	no	—
305	C₄×C₁₇	C₂²×#41	1	12	yes	—
306	C₂×2₋¹⁺⁴	C₂²×C₁₇	1	2	yes	—
307	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
308	#559	C₂²×C₁₇	1	24	yes	complemented
309	Q₈²	C₂²×C₁₇	1	4	yes	complemented
310	#557	C₂²×C₁₇	1	8	yes	complemented
311	#557	C₂²×C₁₇	1	4	yes	complemented
312	#556	C₂²×C₁₇	1	12	yes	complemented
313	#555	C₂²×C₁₇	1	12	yes	complemented
314	#554	C₂²×C₁₇	1	24	yes	complemented
315	#553	C₂²×C₁₇	1	24	yes	complemented
316	#553	C₂²×C₁₇	1	24	yes	complemented
317	#552	C₂²×C₁₇	1	24	yes	complemented
318	#550	C₂²×C₁₇	1	8	yes	—
319	#550	C₂²×C₁₇	1	8	yes	—
320	#550	C₂²×C₁₇	1	4	yes	complemented
321	#550	C₂²×C₁₇	1	12	yes	complemented
322	D₄×Q₈	C₂²×C₁₇	1	4	yes	complemented
323	#548	C₂²×C₁₇	1	8	yes	—
324	#548	C₂²×C₁₇	1	8	yes	—
325	#548	C₂²×C₁₇	1	8	yes	complemented
326	#547	C₂²×C₁₇	1	24	yes	complemented
327	#547	C₂²×C₁₇	1	12	yes	complemented
328	#544	C₂²×C₁₇	1	6	yes	—
329	#542	C₂²×C₁₇	1	12	yes	complemented
330	#542	C₂²×C₁₇	1	12	yes	complemented
331	#542	C₂²×C₁₇	1	24	yes	complemented
332	#541	C₂²×C₁₇	1	12	yes	complemented
333	#540	C₂²×C₁₇	1	12	yes	complemented
334	#540	C₂²×C₁₇	1	24	yes	complemented
335	#539	C₂²×C₁₇	1	4	yes	—
336	#539	C₂²×C₁₇	1	12	yes	—
337	#538	C₂²×C₁₇	1	12	yes	—
338	#538	C₂²×C₁₇	1	12	yes	—
339	#537	C₂²×C₁₇	1	6	yes	—
340	#535	C₂²×C₁₇	1	12	yes	—
341	#533	C₂²×C₁₇	1	6	yes	—
342	#532	C₂²×C₁₇	1	6	yes	—
343	#532	C₂²×C₁₇	1	24	yes	complemented
344	#529	C₂²×C₁₇	1	24	yes	complemented
345	#529	C₂²×C₁₇	1	24	yes	complemented
346	#529	C₂²×C₁₇	1	24	yes	complemented
347	#525	C₂²×C₁₇	1	12	yes	—
348	#525	C₂²×C₁₇	1	24	yes	—
349	#520	C₂²×C₁₇	1	8	yes	—
350	#520	C₂²×C₁₇	1	8	yes	—
351	#520	C₂²×C₁₇	1	12	yes	—
352	#520	C₂²×C₁₇	1	8	yes	complemented
353	#519	C₂²×C₁₇	1	2	yes	—
354	#519	C₂²×C₁₇	1	8	yes	complemented
355	C₄×#41	C₂²×C₁₇	1	12	yes	—
356	C₄×#41	C₂²×C₁₇	1	8	yes	complemented
357	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
358	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
359	C₂×C₄×Q₈	C₂²×C₁₇	1	8	yes	complemented
360	C₂×C₄×D₄	C₂²×C₁₇	1	3	yes	—
361	C₂×C₄×D₄	C₂²×C₁₇	1	3	yes	—
362	C₂×#117	C₂²×C₁₇	1	3	yes	—
363	C₂²×C₄⋊C₄	C₂²×C₁₇	1	3	yes	—
364	C₂×C₁₇	—	2	2	no	—
365	C₂×C₁₇	—	4	8	no	—
366	C₂×C₁₇	—	4	6	no	—
367	C₂×C₁₇	C₂³×#41	1	1	yes	characteristic
368	C₂×C₁₇	H(7,𝔽₂)	1	1	yes	characteristic
369	C₂×C₁₇	2₋¹⁺⁶	1	1	yes	characteristic
370	2₋¹⁺⁴	—	2	16	no	—
371	C₂×#41	—	2	8	no	—
372	C₂×#41	C₂³×C₁₇	1	12	yes	—
373	C₂×#41	C₂³×C₁₇	1	8	yes	—
374	C₂×#41	C₂³×C₁₇	1	8	yes	—
375	C₂×#41	C₂³×C₁₇	1	24	yes	—
376	C₂²×Q₈	C₂³×C₁₇	1	8	yes	—
377	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
378	C₂²×D₄	C₂³×C₁₇	1	3	yes	—
379	C₂³×C₄	C₂³×C₁₇	1	3	yes	—
380	C₂³×C₄	C₂³×C₁₇	1	6	yes	—
381	C₄⋊Q₈	C₂³×C₁₇	1	6	yes	—
382	C₄⋊Q₈	C₂³×C₁₇	1	24	yes	—
383	C₄⋊Q₈	C₂³×C₁₇	1	6	yes	—
384	C₄⋊Q₈	C₂³×C₁₇	1	6	yes	—
385	#127	C₂³×C₁₇	1	6	yes	—
386	#127	C₂³×C₁₇	1	24	yes	—
387	#126	C₂³×C₁₇	1	24	yes	—
388	#126	C₂³×C₁₇	1	8	yes	—
389	#126	C₂³×C₁₇	1	24	yes	—
390	#126	C₂³×C₁₇	1	24	yes	—
391	#125	C₂³×C₁₇	1	8	yes	—
392	#125	C₂³×C₁₇	1	24	yes	—
393	#125	C₂³×C₁₇	1	24	yes	—
394	#125	C₂³×C₁₇	1	12	yes	—
395	#124	C₂³×C₁₇	1	24	yes	—
396	#124	C₂³×C₁₇	1	24	yes	—
397	#124	C₂³×C₁₇	1	24	yes	—
398	#124	C₂³×C₁₇	1	12	yes	—
399	#123	C₂³×C₁₇	1	8	yes	—
400	#123	C₂³×C₁₇	1	48	yes	—
401	#123	C₂³×C₁₇	1	24	yes	—
402	#123	C₂³×C₁₇	1	8	yes	—
403	#123	C₂³×C₁₇	1	24	yes	—
404	#123	C₂³×C₁₇	1	24	yes	—
405	C₂²⋊Q₈	C₂³×C₁₇	1	12	yes	—
406	C₂²⋊Q₈	C₂³×C₁₇	1	12	yes	—
407	C₂²⋊Q₈	C₂³×C₁₇	1	12	yes	—
408	C₂²⋊Q₈	C₂³×C₁₇	1	24	yes	—
409	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
410	C₂²⋊Q₈	C₂³×C₁₇	1	24	yes	—
411	C₂²⋊Q₈	C₂³×C₁₇	1	24	yes	—
412	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
413	#121	C₂³×C₁₇	1	12	yes	—
414	#121	C₂³×C₁₇	1	24	yes	—
415	#121	C₂³×C₁₇	1	12	yes	—
416	#121	C₂³×C₁₇	1	12	yes	—
417	#121	C₂³×C₁₇	1	24	yes	—
418	#121	C₂³×C₁₇	1	24	yes	—
419	#121	C₂³×C₁₇	1	24	yes	—
420	#121	C₂³×C₁₇	1	4	yes	—
421	#121	C₂³×C₁₇	1	24	yes	—
422	#121	C₂³×C₁₇	1	24	yes	—
423	#120	C₂³×C₁₇	1	24	yes	—
424	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
425	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
426	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
427	C₄×Q₈	C₂³×C₁₇	1	12	yes	—
428	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
429	C₄×Q₈	C₂³×C₁₇	1	24	yes	—
430	C₄×Q₈	C₂³×C₁₇	1	12	yes	—
431	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
432	C₄×Q₈	C₂³×C₁₇	1	12	yes	—
433	C₄×Q₈	C₂³×C₁₇	1	12	yes	—
434	C₄×D₄	C₂³×C₁₇	1	24	yes	—
435	C₄×D₄	C₂³×C₁₇	1	12	yes	—
436	C₄×D₄	C₂³×C₁₇	1	12	yes	—
437	C₄×D₄	C₂³×C₁₇	1	8	yes	—
438	C₄×D₄	C₂³×C₁₇	1	12	yes	—
439	C₄×D₄	C₂³×C₁₇	1	24	yes	—
440	C₄×D₄	C₂³×C₁₇	1	12	yes	—
441	C₄×D₄	C₂³×C₁₇	1	24	yes	—
442	C₄×D₄	C₂³×C₁₇	1	24	yes	—
443	C₄×D₄	C₂³×C₁₇	1	24	yes	—
444	C₄×D₄	C₂³×C₁₇	1	48	yes	—
445	C₄×D₄	C₂³×C₁₇	1	12	yes	—
446	C₄×D₄	C₂³×C₁₇	1	12	yes	—
447	#117	C₂³×C₁₇	1	12	yes	—
448	#117	C₂³×C₁₇	1	12	yes	—
449	#117	C₂³×C₁₇	1	12	yes	—
450	#117	C₂³×C₁₇	1	24	yes	—
451	#117	C₂³×C₁₇	1	24	yes	—
452	#117	C₂³×C₁₇	1	24	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₇	1	24	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₇	1	24	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₇	1	3	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₇	1	3	yes	—
461	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
462	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
463	C₂×C₄²	C₂³×C₁₇	1	24	yes	—
464	C₁₇	#62851	1	1	yes	characteristic, direct product factor, Sylow
465	C₂⁴	C₂⁴×C₁₇	1	3	yes	—
466	#41	—	2	32	no	—
467	#41	—	2	32	no	—
468	#41	—	2	48	no	—
469	#41	—	8	24	no	—
470	C₂×Q₈	—	2	32	no	—
471	C₂×Q₈	#41×C₁₇	1	8	yes	complemented
472	C₂×Q₈	C₂⁴×C₁₇	1	12	yes	—
473	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
474	C₂×Q₈	C₂⁴×C₁₇	1	12	yes	—
475	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
476	C₂×D₄	—	2	12	no	—
477	C₂×D₄	C₂⁴×C₁₇	1	8	yes	—
478	C₂×D₄	C₂⁴×C₁₇	1	12	yes	—
479	C₂×D₄	C₂⁴×C₁₇	1	12	yes	—
480	C₂×D₄	C₂⁴×C₁₇	1	24	yes	—
481	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
482	C₂×D₄	C₂⁴×C₁₇	1	24	yes	—
483	C₂×D₄	C₂⁴×C₁₇	1	12	yes	—
484	C₂²×C₄	—	2	12	no	—
485	C₂²×C₄	—	8	6	no	—
486	C₂²×C₄	C₂⁴×C₁₇	1	24	yes	—
487	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₁₇	1	12	yes	—
489	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
492	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
493	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
494	C₂²×C₄	C₂⁴×C₁₇	1	24	yes	—
495	C₂²×C₄	C₂⁴×C₁₇	1	24	yes	—
496	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
497	C₄⋊C₄	C₂⁴×C₁₇	1	12	yes	—
498	C₄⋊C₄	C₂⁴×C₁₇	1	12	yes	—
499	C₄⋊C₄	C₂⁴×C₁₇	1	12	yes	—
500	C₄⋊C₄	C₂⁴×C₁₇	1	12	yes	—
501	C₄⋊C₄	C₂⁴×C₁₇	1	24	yes	—
502	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
503	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
504	C₄⋊C₄	C₂⁴×C₁₇	1	12	yes	—
505	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
506	C₄⋊C₄	C₂⁴×C₁₇	1	12	yes	—
507	C₄⋊C₄	C₂⁴×C₁₇	1	12	yes	—
508	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
509	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
510	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
511	C₄⋊C₄	C₂⁴×C₁₇	1	24	yes	—
512	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
513	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
514	C₂²⋊C₄	C₂⁴×C₁₇	1	6	yes	—
515	C₂²⋊C₄	C₂⁴×C₁₇	1	12	yes	—
516	C₂²⋊C₄	C₂⁴×C₁₇	1	6	yes	—
517	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
518	C₂²⋊C₄	C₂⁴×C₁₇	1	24	yes	—
519	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
520	C₂²⋊C₄	C₂⁴×C₁₇	1	24	yes	—
521	C₂²⋊C₄	C₂⁴×C₁₇	1	24	yes	—
522	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
523	C₂²⋊C₄	C₂⁴×C₁₇	1	24	yes	—
524	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
525	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
526	C₄²	C₂⁴×C₁₇	1	12	yes	—
527	C₄²	C₂⁴×C₁₇	1	8	yes	—
528	C₄²	C₂⁴×C₁₇	1	24	yes	—
529	C₄²	C₂⁴×C₁₇	1	6	yes	—
530	C₄²	C₂⁴×C₁₇	1	6	yes	—
531	C₄²	C₂⁴×C₁₇	1	24	yes	—
532	C₂³	—	2	6	no	—
533	C₂³	—	4	3	no	—
534	C₂³	—	4	3	no	—
535	C₂³	C₂⁵×C₁₇	1	6	yes	—
536	C₂³	C₂⁵×C₁₇	1	8	yes	—
537	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
538	Q₈	—	2	24	no	—
539	Q₈	—	4	12	no	—
540	Q₈	—	4	4	no	—
541	Q₈	C₂×#41×C₁₇	1	16	yes	—
542	D₄	—	2	16	no	—
543	D₄	—	2	24	no	—
544	D₄	—	2	24	no	—
545	D₄	—	4	12	no	—
546	D₄	—	4	24	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	24	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	24	no	—
551	C₂×C₄	—	2	48	no	—
552	C₂×C₄	—	4	3	no	—
553	C₂×C₄	—	4	3	no	—
554	C₂×C₄	—	4	24	no	—
555	C₂×C₄	—	4	24	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	8	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	C₂×#41×C₁₇	1	12	yes	—
560	C₂×C₄	C₂⁵×C₁₇	1	2	yes	—
561	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
562	C₂×C₄	C₂⁵×C₁₇	1	8	yes	—
563	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
564	C₂×C₄	C₂⁵×C₁₇	1	6	yes	—
565	C₂×C₄	C₂⁵×C₁₇	1	8	yes	—
566	C₂×C₄	C₂⁵×C₁₇	1	8	yes	—
567	C₂×C₄	C₂⁵×C₁₇	1	6	yes	—
568	C₂×C₄	C₂⁵×C₁₇	1	2	yes	—
569	C₂×C₄	C₂⁵×C₁₇	1	6	yes	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	8	no	—
573	C₂²	—	2	6	no	—
574	C₂²	—	2	6	no	—
575	C₂²	—	2	8	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	6	no	—
578	C₂²	—	4	12	no	—
579	C₂²	C₂²×#41×C₁₇	1	2	yes	—
580	C₂²	C₂⁶×C₁₇	1	1	yes	characteristic
581	C₄	—	2	2	no	—
582	C₄	—	2	8	no	—
583	C₄	—	2	6	no	—
584	C₄	—	2	6	no	—
585	C₄	—	2	8	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	8	no	—
589	C₄	—	2	1	no	—
590	C₄	C₂²×#41×C₁₇	1	12	yes	—
591	C₂	—	2	2	no	—
592	C₂	—	4	6	no	—
593	C₂	—	4	8	no	—
594	C₂	C₂³×#41×C₁₇	1	1	yes	characteristic
595	C₂	C₁₇×H(7,𝔽₂)	1	1	yes	characteristic
596	C₂	C₁₇×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×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. C₁₇×#3524	C₂	semidirect
2. C₁₇×#3522	C₂	semidirect
3. C₁₇×#3517	C₂	semidirect
4. C₁₇×#3516	C₂	semidirect
5. C₁₇×#3506	C₂	semidirect
6. C₁₇×#3502	C₂	semidirect
7. C₁₇×#3497	C₂	semidirect
8. C₁₇×#3492	C₂	semidirect
9. C₁₇×#3487	C₂	semidirect
10. C₁₇×#3460	C₂	semidirect
11. C₁₇×#3455	C₂	semidirect
12. C₄×C₁₇×2₋¹⁺⁴	C₂	semidirect
13. C₂×C₁₇×#520	C₂	semidirect
16. C₁₇×#559	C₂²	semidirect
17. Q₈²×C₁₇	C₂²	semidirect
18. C₁₇×#557	C₂²	semidirect
19. C₁₇×#557	C₂²	semidirect
20. C₁₇×#556	C₂²	semidirect
21. C₁₇×#555	C₂²	semidirect
22. C₁₇×#554	C₂²	semidirect
23. C₁₇×#553	C₂²	semidirect
24. C₁₇×#553	C₂²	semidirect
25. C₁₇×#552	C₂²	semidirect
28. C₁₇×#550	C₂²	semidirect
29. C₁₇×#550	C₂²	semidirect
30. D₄×Q₈×C₁₇	C₂²	semidirect
33. C₁₇×#548	C₂²	semidirect
34. C₁₇×#547	C₂²	semidirect
35. C₁₇×#547	C₂²	semidirect
37. C₁₇×#542	C₂²	semidirect
38. C₁₇×#542	C₂²	semidirect
39. C₁₇×#542	C₂²	semidirect
40. C₁₇×#541	C₂²	semidirect
41. C₁₇×#540	C₂²	semidirect
42. C₁₇×#540	C₂²	semidirect
51. C₁₇×#532	C₂²	semidirect
52. C₁₇×#529	C₂²	semidirect
53. C₁₇×#529	C₂²	semidirect
54. C₁₇×#529	C₂²	semidirect
60. C₁₇×#520	C₂²	semidirect
62. C₁₇×#519	C₂²	semidirect
64. C₄×#41×C₁₇	C₂²	semidirect
67. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
172. C₂×Q₈×C₁₇	#41	semidirect
233. #62851	C₁₇	direct (N × H)
272. #3524	C₂×C₁₇	semidirect
273. #3522	C₂×C₁₇	semidirect
274. #3517	C₂×C₁₇	semidirect
275. #3516	C₂×C₁₇	semidirect
276. #3506	C₂×C₁₇	semidirect
277. #3502	C₂×C₁₇	semidirect
278. #3497	C₂×C₁₇	semidirect
279. #3492	C₂×C₁₇	semidirect
280. #3487	C₂×C₁₇	semidirect
281. #3460	C₂×C₁₇	semidirect
282. #3455	C₂×C₁₇	semidirect
283. C₄×2₋¹⁺⁴	C₂×C₁₇	semidirect
284. C₂×#520	C₂×C₁₇	semidirect
308. #559	C₂²×C₁₇	semidirect
309. Q₈²	C₂²×C₁₇	semidirect
310. #557	C₂²×C₁₇	semidirect
311. #557	C₂²×C₁₇	semidirect
312. #556	C₂²×C₁₇	semidirect
313. #555	C₂²×C₁₇	semidirect
314. #554	C₂²×C₁₇	semidirect
315. #553	C₂²×C₁₇	semidirect
316. #553	C₂²×C₁₇	semidirect
317. #552	C₂²×C₁₇	semidirect
320. #550	C₂²×C₁₇	semidirect
321. #550	C₂²×C₁₇	semidirect
322. D₄×Q₈	C₂²×C₁₇	semidirect
325. #548	C₂²×C₁₇	semidirect
326. #547	C₂²×C₁₇	semidirect
327. #547	C₂²×C₁₇	semidirect
329. #542	C₂²×C₁₇	semidirect
330. #542	C₂²×C₁₇	semidirect
331. #542	C₂²×C₁₇	semidirect
332. #541	C₂²×C₁₇	semidirect
333. #540	C₂²×C₁₇	semidirect
334. #540	C₂²×C₁₇	semidirect
343. #532	C₂²×C₁₇	semidirect
344. #529	C₂²×C₁₇	semidirect
345. #529	C₂²×C₁₇	semidirect
346. #529	C₂²×C₁₇	semidirect
352. #520	C₂²×C₁₇	semidirect
354. #519	C₂²×C₁₇	semidirect
356. C₄×#41	C₂²×C₁₇	semidirect
359. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
464. C₁₇	#62851	direct (N × H)
471. C₂×Q₈	#41×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3524	2
C₁₇×#3522	2
C₁₇×#3517	2
C₁₇×#3516	2
C₁₇×#3506	2
C₁₇×#3502	2
C₁₇×#3497	2
C₁₇×#3492	2
C₁₇×#3487	2
C₁₇×#3460	2
C₁₇×#3455	2
C₄×C₁₇×2₋¹⁺⁴	2
C₂×C₁₇×#520	2
#62851	17

Subgroups — C17×#62851 #16920595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#62851 #16920595