Subgroups — C₂²×C₁₇×#413 #16917817

Order 4352.

5118 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂²⋊C₄
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
socle	C₂³×C₁₇	C₂×C₂²⋊C₄
prime radical	C₂³×#41×C₁₇	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ C₂⁴×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×M₁₆×C₁₇	C₂	semidirect
3. C₂×C₁₇×#413	C₂	direct (N × H)
4. C₂²×C₁₇×#101	C₂	semidirect
5. C₂²×C₁₇×#100	C₂	semidirect
19. C₂²×M₁₆×C₁₇	C₂²	semidirect
21. C₁₇×#413	C₂²	direct (N × H)
22. C₂×C₁₇×#101	C₂²	semidirect
23. C₂×C₁₇×#100	C₂²	semidirect
61. C₂×M₁₆×C₁₇	C₂³	semidirect
64. C₁₇×#101	C₂³	semidirect
65. C₁₇×#100	C₂³	semidirect
122. C₂²×#413	C₁₇	direct (N × H)
165. C₂³×M₁₆	C₂×C₁₇	semidirect
166. C₂×#413	C₂×C₁₇	direct (N × H)
167. C₂²×#101	C₂×C₁₇	semidirect
168. C₂²×#100	C₂×C₁₇	semidirect
178. C₂²×C₁₇	#413	direct (N × H)
201. C₂²×M₁₆	C₂²×C₁₇	semidirect
203. #413	C₂²×C₁₇	direct (N × H)
204. C₂×#101	C₂²×C₁₇	semidirect
205. C₂×#100	C₂²×C₁₇	semidirect
210. C₂×C₁₇	C₂×#413	direct (N × H)
249. C₂×M₁₆	C₂³×C₁₇	semidirect
252. #101	C₂³×C₁₇	semidirect
253. #100	C₂³×C₁₇	semidirect
254. C₁₇	C₂²×#413	direct (N × H)
361. C₂²	C₁₇×#413	direct (N × H)
375. C₂	C₂×C₁₇×#413	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×#41×C₁₇	2
C₂³×M₁₆×C₁₇	2
C₂×C₁₇×#413	2
C₂²×C₁₇×#101	2
C₂²×C₁₇×#100	2
C₂²×#413	17

Subgroups — C22×C17×#413 #16917817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₇×#413 #16917817