Subgroups — C₂×C₁₇×#2949 #16917907

Order 4352.

2870 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×#518	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2949	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₇×#440	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×SD₁₆×C₁₇	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₇×#419	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₇×#418	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₇	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₇	C₄	1	16	yes	complemented
14	C₂²×SD₁₆×C₁₇	C₂²	1	8	yes	—
15	C₂²×SD₁₆×C₁₇	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₁₇	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
19	C₁₇×#519	—	2	4	no	—
20	C₁₇×#519	C₂²	1	8	yes	complemented
21	C₁₇×#518	—	2	4	no	—
22	C₁₇×#518	C₂²	1	8	yes	—
23	C₂×C₄×Q₈×C₁₇	—	2	2	no	—
24	C₂×C₄×Q₈×C₁₇	C₂²	1	4	yes	complemented
25	C₂×C₄×D₄×C₁₇	—	2	2	no	—
26	C₂×C₄×D₄×C₁₇	C₂²	1	4	yes	—
27	C₂×C₁₇×#117	—	2	2	no	—
28	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
29	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₁₇	—	2	2	no	—
32	C₁₇×#440	C₂²	1	32	yes	complemented
33	C₄×SD₁₆×C₁₇	C₂²	1	32	yes	complemented
34	C₁₇×#427	C₂²	1	8	yes	complemented
35	C₂×C₁₇×#107	C₂²	1	2	yes	complemented
36	C₂×C₁₇×#106	C₂²	1	2	yes	complemented
37	C₁₇×#419	C₂²	1	8	yes	complemented
38	C₁₇×#418	C₂²	1	8	yes	—
39	C₂×C₁₇×#103	C₂²	1	4	yes	complemented
40	C₂×C₁₇×#102	C₂²	1	4	yes	—
41	C₁₇×#405	C₂²	1	8	yes	complemented
42	C₂×C₁₇×#97	C₂²	1	2	yes	complemented
43	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	complemented
44	C₂⁵×C₁₇	—	2	1	no	—
45	C₂²×Q₈×C₁₇	—	2	1	no	—
46	C₂²×Q₈×C₁₇	—	2	2	no	—
47	C₂²×Q₈×C₁₇	—	2	4	no	—
48	C₂²×Q₈×C₁₇	C₂×C₄	1	8	yes	complemented
49	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₇	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₇	—	2	1	no	—
52	C₂²×D₄×C₁₇	—	2	2	no	—
53	C₂²×D₄×C₁₇	—	2	4	no	—
54	C₂²×D₄×C₁₇	C₂×C₄	1	8	yes	—
55	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₇	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₇	—	2	1	no	—
58	C₂³×C₄×C₁₇	—	2	4	no	—
59	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
60	C₂×SD₁₆×C₁₇	C₂×C₄	1	16	yes	complemented
61	C₂×SD₁₆×C₁₇	C₂×C₄	1	16	yes	complemented
62	C₂×SD₁₆×C₁₇	C₂×C₄	1	64	yes	complemented
63	C₂×SD₁₆×C₁₇	C₂³	1	8	yes	—
64	C₂×SD₁₆×C₁₇	C₂³	1	8	yes	—
65	C₂×M₁₆×C₁₇	—	2	4	no	—
66	C₂×M₁₆×C₁₇	C₂³	1	4	yes	—
67	C₂²×C₈×C₁₇	C₂×C₄	1	8	yes	complemented
68	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
72	C₄×Q₈×C₁₇	—	2	16	no	—
73	C₄×Q₈×C₁₇	—	2	8	no	—
74	C₄×Q₈×C₁₇	C₂³	1	16	yes	complemented
75	C₄×D₄×C₁₇	—	2	16	no	—
76	C₄×D₄×C₁₇	—	2	8	no	—
77	C₄×D₄×C₁₇	C₂³	1	16	yes	—
78	C₁₇×#117	—	2	2	no	—
79	C₁₇×#117	—	2	2	no	—
80	C₁₇×#117	—	2	16	no	—
81	C₁₇×#117	D₄	1	4	yes	—
82	C₁₇×#117	C₂³	1	4	yes	—
83	C₁₇×#117	C₂³	1	4	yes	—
84	C₁₇×#117	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
92	C₂×C₂²⋊C₄×C₁₇	—	2	16	no	—
93	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
94	C₂×C₄²×C₁₇	—	2	4	no	—
95	C₂×C₄²×C₁₇	—	2	1	no	—
96	C₂×C₄²×C₁₇	—	2	1	no	—
97	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
98	C₁₇×#107	C₂³	1	8	yes	complemented
99	C₁₇×#106	C₂³	1	8	yes	complemented
100	C₁₇×#103	C₂³	1	16	yes	complemented
101	C₁₇×#102	C₂³	1	16	yes	—
102	C₁₇×#97	C₂³	1	8	yes	complemented
103	C₄×C₈×C₁₇	C₂³	1	8	yes	complemented
104	C₂⁴×C₁₇	—	2	2	no	—
105	C₂⁴×C₁₇	—	2	8	no	—
106	C₂⁴×C₁₇	—	2	4	no	—
107	C₂⁴×C₁₇	—	8	4	no	—
108	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
109	C₂×Q₈×C₁₇	—	2	8	no	—
110	C₂×Q₈×C₁₇	—	2	16	no	—
111	C₂×Q₈×C₁₇	—	2	4	no	—
112	C₂×Q₈×C₁₇	—	2	2	no	—
113	C₂×Q₈×C₁₇	—	2	4	no	—
114	C₂×Q₈×C₁₇	—	2	8	no	—
115	C₂×Q₈×C₁₇	C₂²×C₄	1	8	yes	—
116	C₂×Q₈×C₁₇	C₂²×C₄	1	16	yes	complemented
117	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
118	C₂×D₄×C₁₇	—	2	8	no	—
119	C₂×D₄×C₁₇	—	2	16	no	—
120	C₂×D₄×C₁₇	—	2	4	no	—
121	C₂×D₄×C₁₇	—	2	2	no	—
122	C₂×D₄×C₁₇	—	2	4	no	—
123	C₂×D₄×C₁₇	—	2	8	no	—
124	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
125	C₂×D₄×C₁₇	C₂²×C₄	1	16	yes	—
126	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₇	—	2	8	no	—
128	C₂²×C₄×C₁₇	—	2	4	no	—
129	C₂²×C₄×C₁₇	—	2	2	no	—
130	C₂²×C₄×C₁₇	—	2	2	no	—
131	C₂²×C₄×C₁₇	—	2	2	no	—
132	C₂²×C₄×C₁₇	—	2	16	no	—
133	C₂²×C₄×C₁₇	—	8	8	no	—
134	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₇	#41	1	4	yes	—
139	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
141	SD₁₆×C₁₇	C₂²×C₄	1	32	yes	complemented
142	SD₁₆×C₁₇	C₂²×C₄	1	32	yes	complemented
143	M₁₆×C₁₇	—	2	8	no	—
144	C₂×C₈×C₁₇	—	2	4	no	—
145	C₂×C₈×C₁₇	C₂²×C₄	1	4	yes	—
146	C₂×C₈×C₁₇	C₂²×C₄	1	4	yes	—
147	C₂×C₈×C₁₇	C₂²×C₄	1	16	yes	complemented
148	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
149	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
150	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
151	C₄⋊C₄×C₁₇	—	2	16	no	—
152	C₄⋊C₄×C₁₇	—	2	2	no	—
153	C₄⋊C₄×C₁₇	—	2	2	no	—
154	C₄⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
155	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
156	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
157	C₂²⋊C₄×C₁₇	—	2	4	no	—
158	C₂²⋊C₄×C₁₇	—	2	4	no	—
159	C₂²⋊C₄×C₁₇	—	2	16	no	—
160	C₂²⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
161	C₄²×C₁₇	—	2	16	no	—
162	C₄²×C₁₇	—	2	4	no	—
163	C₄²×C₁₇	—	2	4	no	—
164	C₄²×C₁₇	C₂×D₄	1	4	yes	—
165	C₄²×C₁₇	C₂⁴	1	4	yes	—
166	C₂×#2949	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₁₇	—	2	4	no	—
168	C₂³×C₁₇	—	2	8	no	—
169	C₂³×C₁₇	—	2	4	no	—
170	C₂³×C₁₇	—	2	16	no	—
171	C₂³×C₁₇	—	4	8	no	—
172	C₂³×C₁₇	—	8	16	no	—
173	C₂³×C₁₇	—	8	8	no	—
174	C₂³×C₁₇	C₄×D₄	1	4	yes	—
175	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
176	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₁₇	—	2	8	no	—
178	Q₈×C₁₇	—	2	16	no	—
179	Q₈×C₁₇	—	2	4	no	—
180	Q₈×C₁₇	C₂³×C₄	1	8	yes	—
181	D₄×C₁₇	—	2	8	no	—
182	D₄×C₁₇	—	2	16	no	—
183	D₄×C₁₇	—	2	4	no	—
184	D₄×C₁₇	C₂³×C₄	1	8	yes	—
185	C₂×C₄×C₁₇	—	2	8	no	—
186	C₂×C₄×C₁₇	—	2	16	no	—
187	C₂×C₄×C₁₇	—	2	8	no	—
188	C₂×C₄×C₁₇	—	2	4	no	—
189	C₂×C₄×C₁₇	—	2	4	no	—
190	C₂×C₄×C₁₇	—	2	4	no	—
191	C₂×C₄×C₁₇	—	4	4	no	—
192	C₂×C₄×C₁₇	—	4	4	no	—
193	C₂×C₄×C₁₇	—	8	16	no	—
194	C₂×C₄×C₁₇	C₄×D₄	1	8	yes	—
195	C₂×C₄×C₁₇	C₄×D₄	1	4	yes	—
196	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
197	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
198	C₂×C₄×C₁₇	C₂²×D₄	1	8	yes	—
199	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
202	C₂×C₄×C₁₇	C₂×#41	1	4	yes	—
203	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
204	C₈×C₁₇	—	2	4	no	—
205	C₈×C₁₇	C₂³×C₄	1	4	yes	—
206	C₈×C₁₇	C₂³×C₄	1	4	yes	—
207	C₂³×SD₁₆	C₂×C₁₇	1	1	yes	characteristic
208	C₂×#519	C₂×C₁₇	1	1	yes	characteristic, complemented
209	C₂×#518	C₂×C₁₇	1	1	yes	characteristic
210	#2949	C₂×C₁₇	1	16	yes	direct product factor
211	C₂×#440	C₂×C₁₇	1	4	yes	complemented
212	C₂×C₄×SD₁₆	C₂×C₁₇	1	4	yes	complemented
213	C₂×#427	C₂×C₁₇	1	1	yes	characteristic, complemented
214	C₂×#419	C₂×C₁₇	1	1	yes	characteristic, complemented
215	C₂×#418	C₂×C₁₇	1	1	yes	characteristic
216	C₂×#405	C₂×C₁₇	1	1	yes	characteristic, complemented
217	C₂²×C₁₇	—	2	8	no	—
218	C₂²×C₁₇	—	2	4	no	—
219	C₂²×C₁₇	—	2	8	no	—
220	C₂²×C₁₇	—	4	16	no	—
221	C₂²×C₁₇	—	4	8	no	—
222	C₂²×C₁₇	—	8	16	no	—
223	C₂²×C₁₇	C₂×C₄×D₄	1	4	yes	—
224	C₂²×C₁₇	C₂×C₄×D₄	1	2	yes	—
225	C₂²×C₁₇	#577	1	4	yes	—
226	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
227	C₄×C₁₇	—	2	8	no	—
228	C₄×C₁₇	—	2	8	no	—
229	C₄×C₁₇	—	4	4	no	—
230	C₄×C₁₇	—	4	4	no	—
231	C₄×C₁₇	C₂×C₄×D₄	1	2	yes	—
232	C₄×C₁₇	C₂×C₄×D₄	1	4	yes	—
233	C₄×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
234	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
235	C₂³×Q₈	C₂²×C₁₇	1	1	yes	characteristic
236	C₂³×D₄	C₂²×C₁₇	1	1	yes	characteristic
237	C₂²×SD₁₆	C₄×C₁₇	1	16	yes	complemented
238	C₂²×SD₁₆	C₂²×C₁₇	1	2	yes	—
239	C₂²×SD₁₆	C₂²×C₁₇	1	2	yes	—
240	C₂²×SD₁₆	C₂²×C₁₇	1	8	yes	—
241	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
242	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
243	#519	—	2	4	no	—
244	#519	C₂²×C₁₇	1	8	yes	complemented
245	#518	—	2	4	no	—
246	#518	C₂²×C₁₇	1	8	yes	—
247	C₂×C₄×Q₈	—	2	2	no	—
248	C₂×C₄×Q₈	C₂²×C₁₇	1	4	yes	complemented
249	C₂×C₄×D₄	—	2	2	no	—
250	C₂×C₄×D₄	C₂²×C₁₇	1	4	yes	—
251	C₂×#117	—	2	2	no	—
252	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
253	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
254	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	—	2	2	no	—
256	#440	C₂²×C₁₇	1	32	yes	complemented
257	C₄×SD₁₆	C₂²×C₁₇	1	32	yes	complemented
258	#427	C₂²×C₁₇	1	8	yes	complemented
259	C₂×#107	C₂²×C₁₇	1	2	yes	complemented
260	C₂×#106	C₂²×C₁₇	1	2	yes	complemented
261	#419	C₂²×C₁₇	1	8	yes	complemented
262	#418	C₂²×C₁₇	1	8	yes	—
263	C₂×#103	C₂²×C₁₇	1	4	yes	complemented
264	C₂×#102	C₂²×C₁₇	1	4	yes	—
265	#405	C₂²×C₁₇	1	8	yes	complemented
266	C₂×#97	C₂²×C₁₇	1	2	yes	complemented
267	C₂×C₄×C₈	C₂²×C₁₇	1	2	yes	complemented
268	C₂×C₁₇	—	2	4	no	—
269	C₂×C₁₇	—	4	8	no	—
270	C₂×C₁₇	#2949	1	4	yes	direct product factor
271	C₂×C₁₇	C₂²×C₄×D₄	1	1	yes	characteristic
272	C₂×C₁₇	C₂×#577	1	2	yes	—
273	C₂⁵	—	2	1	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	—	2	2	no	—
276	C₂²×Q₈	—	2	4	no	—
277	C₂²×Q₈	C₂×C₄×C₁₇	1	8	yes	complemented
278	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
279	C₂²×Q₈	C₂³×C₁₇	1	4	yes	—
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	—	2	4	no	—
283	C₂²×D₄	C₂×C₄×C₁₇	1	8	yes	—
284	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
285	C₂²×D₄	C₂³×C₁₇	1	4	yes	—
286	C₂³×C₄	—	2	1	no	—
287	C₂³×C₄	—	2	4	no	—
288	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
289	C₂×SD₁₆	C₂×C₄×C₁₇	1	16	yes	complemented
290	C₂×SD₁₆	C₂×C₄×C₁₇	1	16	yes	complemented
291	C₂×SD₁₆	C₂×C₄×C₁₇	1	64	yes	complemented
292	C₂×SD₁₆	C₂³×C₁₇	1	8	yes	—
293	C₂×SD₁₆	C₂³×C₁₇	1	8	yes	—
294	C₂×M₁₆	—	2	4	no	—
295	C₂×M₁₆	C₂³×C₁₇	1	4	yes	—
296	C₂²×C₈	C₂×C₄×C₁₇	1	8	yes	complemented
297	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
298	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
301	C₄×Q₈	—	2	16	no	—
302	C₄×Q₈	—	2	8	no	—
303	C₄×Q₈	C₂³×C₁₇	1	16	yes	complemented
304	C₄×D₄	—	2	16	no	—
305	C₄×D₄	—	2	8	no	—
306	C₄×D₄	C₂³×C₁₇	1	16	yes	—
307	#117	—	2	2	no	—
308	#117	—	2	2	no	—
309	#117	—	2	16	no	—
310	#117	D₄×C₁₇	1	4	yes	—
311	#117	C₂³×C₁₇	1	4	yes	—
312	#117	C₂³×C₁₇	1	4	yes	—
313	#117	C₂³×C₁₇	1	4	yes	—
314	C₂×C₄⋊C₄	—	2	4	no	—
315	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	4	no	—
321	C₂×C₂²⋊C₄	—	2	16	no	—
322	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
323	C₂×C₄²	—	2	4	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
327	#107	C₂³×C₁₇	1	8	yes	complemented
328	#106	C₂³×C₁₇	1	8	yes	complemented
329	#103	C₂³×C₁₇	1	16	yes	complemented
330	#102	C₂³×C₁₇	1	16	yes	—
331	#97	C₂³×C₁₇	1	8	yes	complemented
332	C₄×C₈	C₂³×C₁₇	1	8	yes	complemented
333	C₁₇	C₂×#2949	1	1	yes	characteristic, direct product factor, Sylow
334	C₂⁴	—	2	2	no	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	—	2	8	no	—
337	C₂⁴	—	8	4	no	—
338	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	8	no	—
343	C₂×Q₈	—	2	8	no	—
344	C₂×Q₈	—	2	16	no	—
345	C₂×Q₈	C₂²×C₄×C₁₇	1	8	yes	—
346	C₂×Q₈	C₂²×C₄×C₁₇	1	16	yes	complemented
347	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	16	no	—
354	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
355	C₂×D₄	C₂²×C₄×C₁₇	1	16	yes	—
356	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	16	no	—
363	C₂²×C₄	—	8	8	no	—
364	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
365	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
366	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
368	C₂²×C₄	#41×C₁₇	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
371	SD₁₆	C₂²×C₄×C₁₇	1	32	yes	complemented
372	SD₁₆	C₂²×C₄×C₁₇	1	32	yes	complemented
373	M₁₆	—	2	8	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	C₂²×C₄×C₁₇	1	4	yes	—
376	C₂×C₈	C₂²×C₄×C₁₇	1	4	yes	—
377	C₂×C₈	C₂²×C₄×C₁₇	1	16	yes	complemented
378	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
379	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
380	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
381	C₄⋊C₄	—	2	16	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
385	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
386	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	16	no	—
390	C₂²⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
391	C₄²	—	2	16	no	—
392	C₄²	—	2	4	no	—
393	C₄²	—	2	4	no	—
394	C₄²	C₂×D₄×C₁₇	1	4	yes	—
395	C₄²	C₂⁴×C₁₇	1	4	yes	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	8	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	2	16	no	—
400	C₂³	—	4	8	no	—
401	C₂³	—	8	16	no	—
402	C₂³	—	8	8	no	—
403	C₂³	C₄×D₄×C₁₇	1	4	yes	—
404	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
405	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
406	Q₈	—	2	8	no	—
407	Q₈	—	2	16	no	—
408	Q₈	—	2	4	no	—
409	Q₈	C₂³×C₄×C₁₇	1	8	yes	—
410	D₄	—	2	8	no	—
411	D₄	—	2	16	no	—
412	D₄	—	2	4	no	—
413	D₄	C₂³×C₄×C₁₇	1	8	yes	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	16	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	8	16	no	—
423	C₂×C₄	C₄×D₄×C₁₇	1	8	yes	—
424	C₂×C₄	C₄×D₄×C₁₇	1	4	yes	—
425	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
426	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₁₇	1	8	yes	—
428	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
431	C₂×C₄	C₂×#41×C₁₇	1	4	yes	—
432	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
433	C₈	—	2	4	no	—
434	C₈	C₂³×C₄×C₁₇	1	4	yes	—
435	C₈	C₂³×C₄×C₁₇	1	4	yes	—
436	C₂²	—	2	8	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	4	16	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	8	16	no	—
442	C₂²	C₂×C₄×D₄×C₁₇	1	4	yes	—
443	C₂²	C₂×C₄×D₄×C₁₇	1	2	yes	—
444	C₂²	C₁₇×#577	1	4	yes	—
445	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
446	C₄	—	2	8	no	—
447	C₄	—	2	8	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	4	no	—
450	C₄	C₂×C₄×D₄×C₁₇	1	2	yes	—
451	C₄	C₂×C₄×D₄×C₁₇	1	4	yes	—
452	C₄	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
453	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
454	C₂	—	2	4	no	—
455	C₂	—	4	8	no	—
456	C₂	C₁₇×#2949	1	4	yes	direct product factor
457	C₂	C₂²×C₄×D₄×C₁₇	1	1	yes	characteristic
458	C₂	C₂×C₁₇×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₂³×D₄×C₁₇	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₁₇×#117 ◁ 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×#2949	C₂	direct (N × H)
5. C₂×C₁₇×#440	C₂	semidirect
6. C₂×C₄×SD₁₆×C₁₇	C₂	semidirect
7. C₂×C₁₇×#427	C₂	semidirect
8. C₂×C₁₇×#419	C₂	semidirect
10. C₂×C₁₇×#405	C₂	semidirect
13. C₂²×SD₁₆×C₁₇	C₄	semidirect
20. C₁₇×#519	C₂²	semidirect
24. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
32. C₁₇×#440	C₂²	semidirect
33. C₄×SD₁₆×C₁₇	C₂²	semidirect
34. C₁₇×#427	C₂²	semidirect
35. C₂×C₁₇×#107	C₂²	semidirect
36. C₂×C₁₇×#106	C₂²	semidirect
37. C₁₇×#419	C₂²	semidirect
39. C₂×C₁₇×#103	C₂²	semidirect
41. C₁₇×#405	C₂²	semidirect
42. C₂×C₁₇×#97	C₂²	semidirect
43. C₂×C₄×C₈×C₁₇	C₂²	semidirect
48. C₂²×Q₈×C₁₇	C₂×C₄	semidirect
60. C₂×SD₁₆×C₁₇	C₂×C₄	semidirect
61. C₂×SD₁₆×C₁₇	C₂×C₄	semidirect
62. C₂×SD₁₆×C₁₇	C₂×C₄	semidirect
67. C₂²×C₈×C₁₇	C₂×C₄	semidirect
74. C₄×Q₈×C₁₇	C₂³	semidirect
98. C₁₇×#107	C₂³	semidirect
99. C₁₇×#106	C₂³	semidirect
100. C₁₇×#103	C₂³	semidirect
102. C₁₇×#97	C₂³	semidirect
103. C₄×C₈×C₁₇	C₂³	semidirect
116. C₂×Q₈×C₁₇	C₂²×C₄	semidirect
141. SD₁₆×C₁₇	C₂²×C₄	semidirect
142. SD₁₆×C₁₇	C₂²×C₄	semidirect
147. C₂×C₈×C₁₇	C₂²×C₄	semidirect
166. C₂×#2949	C₁₇	direct (N × H)
208. C₂×#519	C₂×C₁₇	semidirect
210. #2949	C₂×C₁₇	direct (N × H)
211. C₂×#440	C₂×C₁₇	semidirect
212. C₂×C₄×SD₁₆	C₂×C₁₇	semidirect
213. C₂×#427	C₂×C₁₇	semidirect
214. C₂×#419	C₂×C₁₇	semidirect
216. C₂×#405	C₂×C₁₇	semidirect
237. C₂²×SD₁₆	C₄×C₁₇	semidirect
244. #519	C₂²×C₁₇	semidirect
248. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
256. #440	C₂²×C₁₇	semidirect
257. C₄×SD₁₆	C₂²×C₁₇	semidirect
258. #427	C₂²×C₁₇	semidirect
259. C₂×#107	C₂²×C₁₇	semidirect
260. C₂×#106	C₂²×C₁₇	semidirect
261. #419	C₂²×C₁₇	semidirect
263. C₂×#103	C₂²×C₁₇	semidirect
265. #405	C₂²×C₁₇	semidirect
266. C₂×#97	C₂²×C₁₇	semidirect
267. C₂×C₄×C₈	C₂²×C₁₇	semidirect
270. C₂×C₁₇	#2949	direct (N × H)
277. C₂²×Q₈	C₂×C₄×C₁₇	semidirect
289. C₂×SD₁₆	C₂×C₄×C₁₇	semidirect
290. C₂×SD₁₆	C₂×C₄×C₁₇	semidirect
291. C₂×SD₁₆	C₂×C₄×C₁₇	semidirect
296. C₂²×C₈	C₂×C₄×C₁₇	semidirect
303. C₄×Q₈	C₂³×C₁₇	semidirect
327. #107	C₂³×C₁₇	semidirect
328. #106	C₂³×C₁₇	semidirect
329. #103	C₂³×C₁₇	semidirect
331. #97	C₂³×C₁₇	semidirect
332. C₄×C₈	C₂³×C₁₇	semidirect
333. C₁₇	C₂×#2949	direct (N × H)
346. C₂×Q₈	C₂²×C₄×C₁₇	semidirect
371. SD₁₆	C₂²×C₄×C₁₇	semidirect
372. SD₁₆	C₂²×C₄×C₁₇	semidirect
377. C₂×C₈	C₂²×C₄×C₁₇	semidirect
456. C₂	C₁₇×#2949	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₁₇	2
C₂×C₁₇×#519	2
C₂×C₁₇×#518	2
C₁₇×#2949	2
C₂×C₁₇×#440	2
C₂×C₄×SD₁₆×C₁₇	2
C₂×C₁₇×#427	2
C₂×C₁₇×#419	2
C₂×C₁₇×#418	2
C₂×C₁₇×#405	2
C₂×#2949	17

Subgroups — C2×C17×#2949 #16917907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#2949 #16917907