Subgroups — C₁₇×#10872 #16868616

Order 4352.

730 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₇×#108	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#427	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₇×#405	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₇×#344	C₂	1	2	yes	maximal
5	C₁₇×#1733	C₂	1	2	yes	maximal
6	C₂²×M₁₆×C₁₇	C₂²	1	2	yes	—
7	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
9	C₂×C₁₇×#117	C₂²	1	2	yes	—
10	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
11	C₂×C₁₇×#108	—	2	1	no	—
12	C₂×C₁₇×#108	—	2	1	no	—
13	C₂×C₁₇×#108	—	2	2	no	—
14	C₂×C₁₇×#108	C₄	1	4	yes	complemented
15	C₁₇×#427	—	2	2	no	—
16	C₁₇×#427	C₄	1	4	yes	complemented
17	C₂×C₁₇×#107	—	2	1	no	—
18	C₂×C₁₇×#106	—	2	1	no	—
19	C₁₇×#405	—	2	1	no	—
20	C₁₇×#405	—	2	1	no	—
21	C₁₇×#405	C₄	1	2	yes	complemented
22	C₁₇×#405	C₄	1	2	yes	complemented
23	C₂×C₁₇×#97	—	2	1	no	—
24	C₂×C₄×C₈×C₁₇	—	2	1	no	—
25	C₁₇×#344	—	2	4	no	—
26	C₁₇×#339	—	2	4	no	—
27	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
28	C₂×M₁₆×C₁₇	—	2	1	no	—
29	C₂×M₁₆×C₁₇	—	2	1	no	—
30	C₂×M₁₆×C₁₇	—	2	1	no	—
31	C₂×M₁₆×C₁₇	—	2	2	no	—
32	C₂×M₁₆×C₁₇	—	2	2	no	—
33	C₂×M₁₆×C₁₇	—	2	2	no	—
34	C₂×M₁₆×C₁₇	—	2	2	no	—
35	C₂×M₁₆×C₁₇	—	2	2	no	—
36	C₂×M₁₆×C₁₇	C₂×C₄	1	4	yes	—
37	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₁₇	D₄	1	2	yes	—
39	C₂×M₁₆×C₁₇	Q₈	1	2	yes	—
40	C₂²×C₈×C₁₇	—	2	1	no	—
41	C₂²×C₈×C₁₇	—	2	2	no	—
42	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
46	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₇	D₄	1	2	yes	—
51	C₂²×C₈×C₁₇	Q₈	1	2	yes	—
52	C₁₇×#117	—	2	1	no	—
53	C₁₇×#117	—	2	1	no	—
54	C₁₇×#117	—	2	2	no	—
55	C₁₇×#117	—	2	2	no	—
56	C₁₇×#117	—	2	2	no	—
57	C₁₇×#117	C₂×C₄	1	4	yes	—
58	C₁₇×#117	C₂×C₄	1	2	yes	—
59	C₁₇×#117	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₇	Q₈	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
64	C₂×C₄²×C₁₇	—	2	1	no	—
65	C₂×C₄²×C₁₇	—	2	2	no	—
66	C₁₇×#108	—	2	4	no	—
67	C₁₇×#108	—	2	4	no	—
68	C₁₇×#107	—	2	4	no	—
69	C₁₇×#106	—	2	4	no	—
70	C₁₇×#97	—	2	2	no	—
71	C₁₇×#97	—	2	2	no	—
72	C₄×C₈×C₁₇	—	2	2	no	—
73	C₄×C₈×C₁₇	—	2	2	no	—
74	C₂⁴×C₁₇	#41	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	—	2	2	no	—
76	C₂²×C₄×C₁₇	—	4	2	no	—
77	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
91	M₁₆×C₁₇	—	2	2	no	—
92	M₁₆×C₁₇	—	2	2	no	—
93	M₁₆×C₁₇	—	2	2	no	—
94	M₁₆×C₁₇	—	2	4	no	—
95	M₁₆×C₁₇	—	2	4	no	—
96	M₁₆×C₁₇	—	4	2	no	—
97	M₁₆×C₁₇	—	4	2	no	—
98	M₁₆×C₁₇	C₄⋊C₄	1	4	yes	—
99	C₂×C₈×C₁₇	—	2	2	no	—
100	C₂×C₈×C₁₇	—	2	2	no	—
101	C₂×C₈×C₁₇	—	2	2	no	—
102	C₂×C₈×C₁₇	—	2	4	no	—
103	C₂×C₈×C₁₇	—	4	2	no	—
104	C₂×C₈×C₁₇	—	4	2	no	—
105	C₂×C₈×C₁₇	C₄²	1	2	yes	—
106	C₂×C₈×C₁₇	C₄²	1	2	yes	—
107	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
112	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
113	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
114	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
115	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
116	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
117	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
118	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
119	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
120	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
121	C₄⋊C₄×C₁₇	—	2	2	no	—
122	C₄⋊C₄×C₁₇	—	2	4	no	—
123	C₄⋊C₄×C₁₇	—	4	2	no	—
124	C₄⋊C₄×C₁₇	C₄⋊C₄	1	4	yes	—
125	C₂²⋊C₄×C₁₇	—	2	2	no	—
126	C₂²⋊C₄×C₁₇	—	2	2	no	—
127	C₂²⋊C₄×C₁₇	—	2	4	no	—
128	C₂²⋊C₄×C₁₇	—	4	2	no	—
129	C₄²×C₁₇	—	2	2	no	—
130	C₄²×C₁₇	—	2	2	no	—
131	C₄²×C₁₇	—	2	4	no	—
132	C₄²×C₁₇	—	4	2	no	—
133	#10872	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₇	—	4	2	no	—
135	C₂³×C₁₇	#117	1	1	yes	characteristic
136	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
137	C₂³×C₁₇	C₄×Q₈	1	1	yes	characteristic
138	C₂³×C₁₇	#121	1	1	yes	characteristic
139	C₂³×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂³×C₁₇	#124	1	1	yes	characteristic
141	C₂³×C₁₇	#125	1	1	yes	characteristic
142	C₂×C₄×C₁₇	—	2	4	no	—
143	C₂×C₄×C₁₇	—	4	4	no	—
144	C₂×C₄×C₁₇	—	4	4	no	—
145	C₂×C₄×C₁₇	—	8	4	no	—
146	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
156	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
168	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
169	C₂×C₄×C₁₇	#125	1	1	yes	characteristic
170	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
171	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
172	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
174	C₈×C₁₇	—	2	4	no	—
175	C₈×C₁₇	—	4	4	no	—
176	C₈×C₁₇	#95	1	2	yes	—
177	C₈×C₁₇	#95	1	2	yes	—
178	C₈×C₁₇	#95	1	2	yes	—
179	C₈×C₁₇	#95	1	2	yes	—
180	C₂²×#108	C₂×C₁₇	1	1	yes	characteristic
181	C₂×#427	C₂×C₁₇	1	1	yes	characteristic
182	C₂×#405	C₂×C₁₇	1	1	yes	characteristic
183	C₂×#344	C₂×C₁₇	1	2	yes	—
184	#1733	C₂×C₁₇	1	2	yes	—
185	C₂²×C₁₇	—	2	2	no	—
186	C₂²×C₁₇	—	2	2	no	—
187	C₂²×C₁₇	—	2	2	no	—
188	C₂²×C₁₇	—	4	1	no	—
189	C₂²×C₁₇	—	4	1	no	—
190	C₂²×C₁₇	—	4	1	no	—
191	C₂²×C₁₇	—	4	1	no	—
192	C₂²×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×C₁₇	#380	1	1	yes	characteristic
194	C₂²×C₁₇	#382	1	1	yes	characteristic
195	C₂²×C₁₇	#389	1	1	yes	characteristic
196	C₂²×C₁₇	#389	1	1	yes	characteristic
197	C₂²×C₁₇	#390	1	1	yes	characteristic
198	C₂²×C₁₇	#391	1	1	yes	characteristic
199	C₄×C₁₇	—	4	4	no	—
200	C₄×C₁₇	—	8	4	no	—
201	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
202	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
203	C₄×C₁₇	#380	1	1	yes	characteristic
204	C₄×C₁₇	#384	1	1	yes	characteristic
205	C₄×C₁₇	#389	1	1	yes	characteristic
206	C₄×C₁₇	#389	1	1	yes	characteristic
207	C₄×C₁₇	#390	1	1	yes	characteristic
208	C₄×C₁₇	#391	1	1	yes	characteristic
209	C₂²×M₁₆	C₂²×C₁₇	1	2	yes	—
210	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
211	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
212	C₂×#117	C₂²×C₁₇	1	2	yes	—
213	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
214	C₂×#108	—	2	1	no	—
215	C₂×#108	—	2	1	no	—
216	C₂×#108	—	2	2	no	—
217	C₂×#108	C₄×C₁₇	1	4	yes	complemented
218	#427	—	2	2	no	—
219	#427	C₄×C₁₇	1	4	yes	complemented
220	C₂×#107	—	2	1	no	—
221	C₂×#106	—	2	1	no	—
222	#405	—	2	1	no	—
223	#405	—	2	1	no	—
224	#405	C₄×C₁₇	1	2	yes	complemented
225	#405	C₄×C₁₇	1	2	yes	complemented
226	C₂×#97	—	2	1	no	—
227	C₂×C₄×C₈	—	2	1	no	—
228	#344	—	2	4	no	—
229	#339	—	2	4	no	—
230	C₂×C₁₇	—	2	1	no	—
231	C₂×C₁₇	—	2	1	no	—
232	C₂×C₁₇	—	2	1	no	—
233	C₂×C₁₇	—	2	1	no	—
234	C₂×C₁₇	—	2	1	no	—
235	C₂×C₁₇	—	2	1	no	—
236	C₂×C₁₇	C₄⋊#95	1	1	yes	characteristic
237	C₂×C₁₇	#1814	1	2	yes	—
238	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
239	C₂×M₁₆	—	2	1	no	—
240	C₂×M₁₆	—	2	1	no	—
241	C₂×M₁₆	—	2	1	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	C₂×C₄×C₁₇	1	4	yes	—
248	C₂×M₁₆	C₂×C₄×C₁₇	1	2	yes	—
249	C₂×M₁₆	D₄×C₁₇	1	2	yes	—
250	C₂×M₁₆	Q₈×C₁₇	1	2	yes	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
254	C₂²×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
255	C₂²×C₈	C₂×C₄×C₁₇	1	2	yes	—
256	C₂²×C₈	C₂×C₄×C₁₇	1	2	yes	—
257	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
258	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
259	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
260	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
261	C₂²×C₈	D₄×C₁₇	1	2	yes	—
262	C₂²×C₈	Q₈×C₁₇	1	2	yes	—
263	#117	—	2	1	no	—
264	#117	—	2	1	no	—
265	#117	—	2	2	no	—
266	#117	—	2	2	no	—
267	#117	—	2	2	no	—
268	#117	C₂×C₄×C₁₇	1	4	yes	—
269	#117	C₂×C₄×C₁₇	1	2	yes	—
270	#117	D₄×C₁₇	1	2	yes	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	Q₈×C₁₇	1	2	yes	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	—	2	2	no	—
277	#108	—	2	4	no	—
278	#108	—	2	4	no	—
279	#107	—	2	4	no	—
280	#106	—	2	4	no	—
281	#97	—	2	2	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	—	2	2	no	—
285	C₁₇	#10872	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	#41×C₁₇	1	1	yes	characteristic
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×Q₈×C₁₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×Q₈×C₁₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×Q₈×C₁₇	1	1	yes	characteristic
300	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
301	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
302	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
303	M₁₆	—	2	2	no	—
304	M₁₆	—	2	2	no	—
305	M₁₆	—	2	2	no	—
306	M₁₆	—	2	4	no	—
307	M₁₆	—	2	4	no	—
308	M₁₆	—	4	2	no	—
309	M₁₆	—	4	2	no	—
310	M₁₆	C₄⋊C₄×C₁₇	1	4	yes	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	C₄²×C₁₇	1	2	yes	—
318	C₂×C₈	C₄²×C₁₇	1	2	yes	—
319	C₂×C₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
320	C₂×C₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
321	C₂×C₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
322	C₂×C₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
323	C₂×C₈	C₂²⋊C₄×C₁₇	1	2	yes	—
324	C₂×C₈	C₂²⋊C₄×C₁₇	1	2	yes	—
325	C₂×C₈	C₂²⋊C₄×C₁₇	1	2	yes	—
326	C₂×C₈	C₂²⋊C₄×C₁₇	1	2	yes	—
327	C₂×C₈	C₄⋊C₄×C₁₇	1	2	yes	—
328	C₂×C₈	C₄⋊C₄×C₁₇	1	2	yes	—
329	C₂×C₈	C₄⋊C₄×C₁₇	1	2	yes	—
330	C₂×C₈	C₄⋊C₄×C₁₇	1	2	yes	—
331	C₂×C₈	C₄⋊C₄×C₁₇	1	2	yes	—
332	C₂×C₈	C₄⋊C₄×C₁₇	1	2	yes	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	C₄⋊C₄×C₁₇	1	4	yes	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	C₁₇×#117	1	1	yes	characteristic
347	C₂³	C₄×D₄×C₁₇	1	1	yes	characteristic
348	C₂³	C₄×Q₈×C₁₇	1	1	yes	characteristic
349	C₂³	C₁₇×#121	1	1	yes	characteristic
350	C₂³	C₁₇×C₂²⋊Q₈	1	1	yes	characteristic
351	C₂³	C₁₇×#124	1	1	yes	characteristic
352	C₂³	C₁₇×#125	1	1	yes	characteristic
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	8	4	no	—
357	C₂×C₄	C₂×C₄²×C₁₇	1	1	yes	characteristic
358	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
359	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
365	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
366	C₂×C₄	C₁₇×#117	1	1	yes	characteristic
367	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
368	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
369	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
370	C₂×C₄	C₄×Q₈×C₁₇	1	1	yes	characteristic
371	C₂×C₄	C₄×Q₈×C₁₇	1	1	yes	characteristic
372	C₂×C₄	C₄×Q₈×C₁₇	1	1	yes	characteristic
373	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
374	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
375	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
376	C₂×C₄	C₁₇×C₂²⋊Q₈	1	1	yes	characteristic
377	C₂×C₄	C₁₇×C₂²⋊Q₈	1	1	yes	characteristic
378	C₂×C₄	C₁₇×C₂²⋊Q₈	1	1	yes	characteristic
379	C₂×C₄	C₁₇×#124	1	1	yes	characteristic
380	C₂×C₄	C₁₇×#125	1	1	yes	characteristic
381	C₂×C₄	C₁₇×#127	1	1	yes	characteristic
382	C₂×C₄	C₁₇×C₄⋊Q₈	1	1	yes	characteristic
383	C₂×C₄	C₁₇×C₄⋊Q₈	1	1	yes	characteristic
384	C₂×C₄	C₁₇×C₄⋊Q₈	1	1	yes	characteristic
385	C₈	—	2	4	no	—
386	C₈	—	4	4	no	—
387	C₈	C₁₇×#95	1	2	yes	—
388	C₈	C₁₇×#95	1	2	yes	—
389	C₈	C₁₇×#95	1	2	yes	—
390	C₈	C₁₇×#95	1	2	yes	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	C₄×C₄⋊C₄×C₁₇	1	1	yes	characteristic
399	C₂²	C₁₇×#380	1	1	yes	characteristic
400	C₂²	C₁₇×#382	1	1	yes	characteristic
401	C₂²	C₁₇×#389	1	1	yes	characteristic
402	C₂²	C₁₇×#389	1	1	yes	characteristic
403	C₂²	C₁₇×#390	1	1	yes	characteristic
404	C₂²	C₁₇×#391	1	1	yes	characteristic
405	C₄	—	4	4	no	—
406	C₄	—	8	4	no	—
407	C₄	C₂×C₁₇×#95	1	1	yes	characteristic
408	C₄	C₄×C₄⋊C₄×C₁₇	1	1	yes	characteristic
409	C₄	C₁₇×#380	1	1	yes	characteristic
410	C₄	C₁₇×#384	1	1	yes	characteristic
411	C₄	C₁₇×#389	1	1	yes	characteristic
412	C₄	C₁₇×#389	1	1	yes	characteristic
413	C₄	C₁₇×#390	1	1	yes	characteristic
414	C₄	C₁₇×#391	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	C₁₇×C₄⋊#95	1	1	yes	characteristic
422	C₂	C₁₇×#1814	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₇	#121
commutator	C₂×C₄	C₂×C₄²×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
socle	C₂²×C₁₇	#380
prime radical	C₂⁴×C₁₇	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₂×C₁₇×#108	C₄	semidirect
16. C₁₇×#427	C₄	semidirect
21. C₁₇×#405	C₄	semidirect
22. C₁₇×#405	C₄	semidirect
133. #10872	C₁₇	direct (N × H)
217. C₂×#108	C₄×C₁₇	semidirect
219. #427	C₄×C₁₇	semidirect
224. #405	C₄×C₁₇	semidirect
225. #405	C₄×C₁₇	semidirect
285. C₁₇	#10872	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₇×#108	2
C₂×C₁₇×#427	2
C₂×C₁₇×#405	2
C₂×C₁₇×#344	2
C₁₇×#1733	2
#10872	17

Subgroups — C17×#10872 #16868616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#10872 #16868616