Subgroups — C₁₇×#21598 #16879342

Order 4352.

886 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×M₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1917	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1851	C₂	1	2	yes	maximal
8	C₁₇×#1797	C₂	1	1	yes	maximal, characteristic
9	C₁₇×#1770	C₂	1	2	yes	maximal, complemented
10	C₈×C₄⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1753	C₂	1	2	yes	maximal
12	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
14	C₂×C₁₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
17	C₁₇×#446	—	2	4	no	—
18	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₄×M₁₆×C₁₇	—	2	4	no	—
24	C₂×C₁₇×#97	C₂²	1	2	yes	—
25	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
30	C₁₇×#391	C₄	1	1	yes	characteristic
31	C₁₇×#389	C₄	1	1	yes	characteristic
32	C₁₇×#387	C₄	1	2	yes	—
33	C₁₇×#385	C₄	1	2	yes	—
34	C₁₇×#380	C₄	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
38	C₁₇×#336	C₂²	1	2	yes	—
39	C₁₇×#336	C₂²	1	2	yes	—
40	C₁₇×#336	C₂²	1	2	yes	—
41	C₁₇×#336	C₂²	1	2	yes	—
42	C₁₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₁₇	—	2	2	no	—
48	C₂×M₁₆×C₁₇	—	2	2	no	—
49	C₂×M₁₆×C₁₇	—	2	2	no	—
50	C₂×M₁₆×C₁₇	—	2	2	no	—
51	C₂×M₁₆×C₁₇	—	2	2	no	—
52	C₂×M₁₆×C₁₇	Q₈	1	4	yes	complemented
53	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
59	C₁₇×C₂²⋊Q₈	—	2	4	no	—
60	C₄×Q₈×C₁₇	—	2	2	no	—
61	C₄×Q₈×C₁₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₁₇	—	2	2	no	—
71	C₂×C₄²×C₁₇	—	2	2	no	—
72	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
78	C₁₇×C₄⋊C₈	—	2	4	no	—
79	C₁₇×C₄⋊C₈	—	2	4	no	—
80	C₁₇×C₄⋊C₈	—	2	2	no	—
81	C₁₇×C₄⋊C₈	—	2	2	no	—
82	C₁₇×C₂²⋊C₈	—	2	4	no	—
83	C₁₇×#97	—	2	2	no	—
84	C₁₇×#97	—	2	2	no	—
85	C₁₇×#97	—	2	4	no	—
86	C₄×C₈×C₁₇	—	2	4	no	—
87	C₄×C₈×C₁₇	—	2	2	no	—
88	C₄×C₈×C₁₇	D₄	1	4	yes	—
89	C₁₇×#95	C₂×C₄	1	2	yes	—
90	C₁₇×#95	C₂×C₄	1	2	yes	—
91	C₁₇×#95	C₂×C₄	1	2	yes	—
92	C₁₇×#95	C₂×C₄	1	2	yes	—
93	C₁₇×#95	C₂×C₄	1	2	yes	—
94	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₇	—	2	2	no	—
96	C₂×Q₈×C₁₇	—	2	2	no	—
97	C₂×Q₈×C₁₇	—	2	2	no	—
98	C₂²×C₄×C₁₇	—	2	1	no	—
99	C₂²×C₄×C₁₇	—	2	1	no	—
100	C₂²×C₄×C₁₇	—	2	1	no	—
101	C₂²×C₄×C₁₇	—	2	1	no	—
102	C₂²×C₄×C₁₇	—	2	2	no	—
103	C₂²×C₄×C₁₇	—	2	2	no	—
104	C₂²×C₄×C₁₇	—	2	2	no	—
105	C₂²×C₄×C₁₇	—	2	2	no	—
106	C₂²×C₄×C₁₇	—	4	1	no	—
107	C₂²×C₄×C₁₇	—	4	1	no	—
108	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₇	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₇	#41	1	2	yes	—
119	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
120	M₁₆×C₁₇	—	2	8	no	—
121	M₁₆×C₁₇	—	2	8	no	—
122	C₂×C₈×C₁₇	—	2	1	no	—
123	C₂×C₈×C₁₇	—	2	1	no	—
124	C₂×C₈×C₁₇	—	2	1	no	—
125	C₂×C₈×C₁₇	—	2	1	no	—
126	C₂×C₈×C₁₇	—	2	1	no	—
127	C₂×C₈×C₁₇	—	2	1	no	—
128	C₂×C₈×C₁₇	—	2	2	no	—
129	C₂×C₈×C₁₇	—	2	2	no	—
130	C₂×C₈×C₁₇	—	2	2	no	—
131	C₂×C₈×C₁₇	—	2	2	no	—
132	C₂×C₈×C₁₇	—	2	2	no	—
133	C₂×C₈×C₁₇	—	2	2	no	—
134	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
137	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
138	C₂×C₈×C₁₇	#41	1	2	yes	—
139	C₂×C₈×C₁₇	#41	1	2	yes	—
140	C₄⋊C₄×C₁₇	—	2	2	no	—
141	C₄⋊C₄×C₁₇	—	2	4	no	—
142	C₄⋊C₄×C₁₇	—	2	4	no	—
143	C₄⋊C₄×C₁₇	—	2	2	no	—
144	C₄⋊C₄×C₁₇	—	4	2	no	—
145	C₄⋊C₄×C₁₇	M₁₆	1	4	yes	complemented
146	C₂²⋊C₄×C₁₇	—	2	4	no	—
147	C₂²⋊C₄×C₁₇	—	4	2	no	—
148	C₄²×C₁₇	—	2	2	no	—
149	C₄²×C₁₇	—	2	2	no	—
150	C₄²×C₁₇	—	2	1	no	—
151	C₄²×C₁₇	—	2	2	no	—
152	C₄²×C₁₇	—	2	2	no	—
153	C₄²×C₁₇	—	2	2	no	—
154	C₄²×C₁₇	—	2	1	no	—
155	C₄²×C₁₇	—	2	2	no	—
156	C₄²×C₁₇	C₂×D₄	1	2	yes	—
157	C₄²×C₁₇	#41	1	2	yes	—
158	#21598	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₇	—	2	1	no	—
160	C₂³×C₁₇	—	2	1	no	—
161	C₂³×C₁₇	—	2	1	no	—
162	C₂³×C₁₇	—	2	1	no	—
163	C₂³×C₁₇	—	2	1	no	—
164	C₂³×C₁₇	—	2	1	no	—
165	C₂³×C₁₇	C₄×Q₈	1	2	yes	—
166	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
167	Q₈×C₁₇	—	4	4	no	—
168	C₂×C₄×C₁₇	—	2	1	no	—
169	C₂×C₄×C₁₇	—	2	2	no	—
170	C₂×C₄×C₁₇	—	2	1	no	—
171	C₂×C₄×C₁₇	—	2	2	no	—
172	C₂×C₄×C₁₇	—	2	1	no	—
173	C₂×C₄×C₁₇	—	2	1	no	—
174	C₂×C₄×C₁₇	—	2	2	no	—
175	C₂×C₄×C₁₇	—	2	2	no	—
176	C₂×C₄×C₁₇	—	2	2	no	—
177	C₂×C₄×C₁₇	—	2	2	no	—
178	C₂×C₄×C₁₇	—	2	1	no	—
179	C₂×C₄×C₁₇	—	2	1	no	—
180	C₂×C₄×C₁₇	—	2	2	no	—
181	C₂×C₄×C₁₇	—	2	2	no	—
182	C₂×C₄×C₁₇	—	2	2	no	—
183	C₂×C₄×C₁₇	—	2	2	no	—
184	C₂×C₄×C₁₇	—	2	1	no	—
185	C₂×C₄×C₁₇	—	2	2	no	—
186	C₂×C₄×C₁₇	—	2	1	no	—
187	C₂×C₄×C₁₇	—	2	2	no	—
188	C₂×C₄×C₁₇	—	2	2	no	—
189	C₂×C₄×C₁₇	—	2	2	no	—
190	C₂×C₄×C₁₇	—	2	1	no	—
191	C₂×C₄×C₁₇	—	2	2	no	—
192	C₂×C₄×C₁₇	—	2	1	no	—
193	C₂×C₄×C₁₇	—	4	4	no	—
194	C₂×C₄×C₁₇	—	4	4	no	—
195	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₁₇	C₄×Q₈	1	2	yes	—
198	C₂×C₄×C₁₇	C₂×M₁₆	1	4	yes	—
199	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
200	C₂×C₄×C₁₇	#131	1	2	yes	—
201	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
203	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
207	C₈×C₁₇	—	2	2	no	—
208	C₈×C₁₇	—	2	2	no	—
209	C₈×C₁₇	—	2	2	no	—
210	C₈×C₁₇	—	4	2	no	—
211	C₈×C₁₇	—	4	2	no	—
212	C₈×C₁₇	C₂²⋊Q₈	1	4	yes	complemented
213	C₂×#446	C₂×C₁₇	1	1	yes	characteristic, complemented
214	C₂×C₄×M₁₆	C₂×C₁₇	1	1	yes	characteristic
215	C₄×C₂²⋊Q₈	C₂×C₁₇	1	1	yes	characteristic
216	#1984	C₂×C₁₇	1	1	yes	characteristic, complemented
217	#1939	C₂×C₁₇	1	1	yes	characteristic, complemented
218	#1917	C₂×C₁₇	1	2	yes	complemented
219	#1851	C₂×C₁₇	1	2	yes	—
220	#1797	C₂×C₁₇	1	1	yes	characteristic
221	#1770	C₂×C₁₇	1	2	yes	complemented
222	C₈×C₄⋊C₄	C₂×C₁₇	1	1	yes	characteristic, complemented
223	#1753	C₂×C₁₇	1	2	yes	—
224	C₂²×C₁₇	—	2	2	no	—
225	C₂²×C₁₇	—	2	2	no	—
226	C₂²×C₁₇	—	2	2	no	—
227	C₂²×C₁₇	—	4	1	no	—
228	C₂²×C₁₇	—	4	1	no	—
229	C₂²×C₁₇	—	4	1	no	—
230	C₂²×C₁₇	—	4	1	no	—
231	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
232	C₂²×C₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
233	C₂²×C₁₇	C₄×#41	1	1	yes	characteristic
234	C₂²×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
235	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
236	C₂²×C₁₇	#568	1	1	yes	characteristic
237	C₂²×C₁₇	#568	1	1	yes	characteristic
238	C₄×C₁₇	—	2	2	no	—
239	C₄×C₁₇	—	2	4	no	—
240	C₄×C₁₇	—	2	2	no	—
241	C₄×C₁₇	—	4	1	no	—
242	C₄×C₁₇	—	4	2	no	—
243	C₄×C₁₇	—	4	2	no	—
244	C₄×C₁₇	—	4	1	no	—
245	C₄×C₁₇	—	4	2	no	—
246	C₄×C₁₇	#436	1	4	yes	—
247	C₄×C₁₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
248	C₄×C₁₇	#525	1	1	yes	characteristic
249	C₄×C₁₇	#529	1	1	yes	characteristic
250	C₄×C₁₇	#533	1	1	yes	characteristic
251	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
252	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	C₄×C₁₇	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
255	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
256	#446	—	2	4	no	—
257	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
260	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
261	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	—
262	C₄×M₁₆	—	2	4	no	—
263	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
264	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
265	C₂×#97	C₂²×C₁₇	1	2	yes	—
266	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₁₇	1	2	yes	—
268	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
269	#391	C₄×C₁₇	1	1	yes	characteristic
270	#389	C₄×C₁₇	1	1	yes	characteristic
271	#387	C₄×C₁₇	1	2	yes	—
272	#385	C₄×C₁₇	1	2	yes	—
273	#380	C₄×C₁₇	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
275	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
276	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
277	#336	C₂²×C₁₇	1	2	yes	—
278	#336	C₂²×C₁₇	1	2	yes	—
279	#336	C₂²×C₁₇	1	2	yes	—
280	#336	C₂²×C₁₇	1	2	yes	—
281	#336	C₂²×C₁₇	1	2	yes	—
282	C₂×C₁₇	—	4	2	no	—
283	C₂×C₁₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
284	C₂×C₁₇	C₂×#436	1	1	yes	characteristic
285	C₂×C₁₇	#2930	1	1	yes	characteristic
286	C₂×C₁₇	#2962	1	1	yes	characteristic
287	C₂×C₁₇	Q₈×M₁₆	1	1	yes	characteristic
288	C₂×C₁₇	#2969	1	1	yes	characteristic
289	C₂×C₁₇	#2970	1	1	yes	characteristic
290	C₂²×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
291	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
292	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	Q₈×C₁₇	1	4	yes	complemented
300	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
301	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
302	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
306	C₂²⋊Q₈	—	2	4	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
311	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
312	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
314	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
320	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
322	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
323	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
325	C₄⋊C₈	—	2	4	no	—
326	C₄⋊C₈	—	2	4	no	—
327	C₄⋊C₈	—	2	2	no	—
328	C₄⋊C₈	—	2	2	no	—
329	C₂²⋊C₈	—	2	4	no	—
330	#97	—	2	2	no	—
331	#97	—	2	2	no	—
332	#97	—	2	4	no	—
333	C₄×C₈	—	2	4	no	—
334	C₄×C₈	—	2	2	no	—
335	C₄×C₈	D₄×C₁₇	1	4	yes	—
336	#95	C₂×C₄×C₁₇	1	2	yes	—
337	#95	C₂×C₄×C₁₇	1	2	yes	—
338	#95	C₂×C₄×C₁₇	1	2	yes	—
339	#95	C₂×C₄×C₁₇	1	2	yes	—
340	#95	C₂×C₄×C₁₇	1	2	yes	—
341	C₁₇	#21598	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁴	C₂²×C₄×C₁₇	1	1	yes	characteristic
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
360	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
361	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
362	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
364	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×Q₈×C₁₇	1	2	yes	—
366	C₂²×C₄	#41×C₁₇	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
368	M₁₆	—	2	8	no	—
369	M₁₆	—	2	8	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
383	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
384	C₂×C₈	C₂×Q₈×C₁₇	1	2	yes	—
385	C₂×C₈	C₂×Q₈×C₁₇	1	2	yes	—
386	C₂×C₈	#41×C₁₇	1	2	yes	—
387	C₂×C₈	#41×C₁₇	1	2	yes	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	M₁₆×C₁₇	1	4	yes	complemented
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	C₂×D₄×C₁₇	1	2	yes	—
405	C₄²	#41×C₁₇	1	2	yes	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	C₄×Q₈×C₁₇	1	2	yes	—
413	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
414	Q₈	—	4	4	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
443	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
444	C₂×C₄	C₄×Q₈×C₁₇	1	2	yes	—
445	C₂×C₄	C₂×M₁₆×C₁₇	1	4	yes	—
446	C₂×C₄	C₂×M₁₆×C₁₇	1	2	yes	—
447	C₂×C₄	C₁₇×#131	1	2	yes	—
448	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
449	C₂×C₄	C₂²×Q₈×C₁₇	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	4	2	no	—
458	C₈	—	4	2	no	—
459	C₈	C₁₇×C₂²⋊Q₈	1	4	yes	complemented
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
468	C₂²	C₂×C₄×Q₈×C₁₇	1	1	yes	characteristic
469	C₂²	C₄×#41×C₁₇	1	1	yes	characteristic
470	C₂²	C₂²×M₁₆×C₁₇	1	1	yes	characteristic
471	C₂²	C₂×C₁₇×#131	1	1	yes	characteristic
472	C₂²	C₁₇×#568	1	1	yes	characteristic
473	C₂²	C₁₇×#568	1	1	yes	characteristic
474	C₄	—	2	4	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	2	no	—
482	C₄	C₁₇×#436	1	4	yes	—
483	C₄	C₂×C₁₇×C₂²⋊Q₈	1	1	yes	characteristic
484	C₄	C₁₇×#525	1	1	yes	characteristic
485	C₄	C₁₇×#529	1	1	yes	characteristic
486	C₄	C₁₇×#533	1	1	yes	characteristic
487	C₂	—	4	2	no	—
488	C₂	C₄×C₁₇×C₂²⋊Q₈	1	1	yes	characteristic
489	C₂	C₂×C₁₇×#436	1	1	yes	characteristic
490	C₂	C₁₇×#2930	1	1	yes	characteristic
491	C₂	C₁₇×#2962	1	1	yes	characteristic
492	C₂	Q₈×M₁₆×C₁₇	1	1	yes	characteristic
493	C₂	C₁₇×#2969	1	1	yes	characteristic
494	C₂	C₁₇×#2970	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#446	C₂	semidirect
4. C₁₇×#1984	C₂	semidirect
5. C₁₇×#1939	C₂	semidirect
6. C₁₇×#1917	C₂	semidirect
9. C₁₇×#1770	C₂	semidirect
10. C₈×C₄⋊C₄×C₁₇	C₂	semidirect
52. C₂×M₁₆×C₁₇	Q₈	semidirect
145. C₄⋊C₄×C₁₇	M₁₆	semidirect
158. #21598	C₁₇	direct (N × H)
212. C₈×C₁₇	C₂²⋊Q₈	semidirect
213. C₂×#446	C₂×C₁₇	semidirect
216. #1984	C₂×C₁₇	semidirect
217. #1939	C₂×C₁₇	semidirect
218. #1917	C₂×C₁₇	semidirect
221. #1770	C₂×C₁₇	semidirect
222. C₈×C₄⋊C₄	C₂×C₁₇	semidirect
299. C₂×M₁₆	Q₈×C₁₇	semidirect
341. C₁₇	#21598	direct (N × H)
393. C₄⋊C₄	M₁₆×C₁₇	semidirect
459. C₈	C₁₇×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#446	2
C₂×C₄×M₁₆×C₁₇	2
C₄×C₁₇×C₂²⋊Q₈	2
C₁₇×#1984	2
C₁₇×#1939	2
C₁₇×#1917	2
C₁₇×#1851	2
C₁₇×#1797	2
C₁₇×#1770	2
C₈×C₄⋊C₄×C₁₇	2
C₁₇×#1753	2
#21598	17

Subgroups — C17×#21598 #16879342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#21598 #16879342