Subgroups — C₁₇×#61889 #16919633

Order 4352.

1706 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#556	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3398	C₂	1	8	yes	maximal, complemented
4	C₁₇×#3369	C₂	1	8	yes	maximal, complemented
5	C₁₇×#3215	C₂	1	4	yes	maximal
6	C₁₇×#3209	C₂	1	2	yes	maximal, complemented
7	C₁₇×#3113	C₂	1	4	yes	maximal, complemented
8	C₁₇×#3101	C₂	1	2	yes	maximal
9	C₁₇×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₈²×C₁₇	C₂²	1	4	yes	complemented
11	C₁₇×#557	—	2	4	no	—
12	C₁₇×#557	C₂²	1	4	yes	complemented
13	C₁₇×#556	—	2	4	no	—
14	C₁₇×#556	C₂²	1	8	yes	—
15	C₁₇×#544	—	2	1	no	—
16	C₁₇×#544	—	2	2	no	—
17	C₁₇×#533	C₂²	1	2	yes	—
18	C₁₇×#533	C₂²	1	4	yes	—
19	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×#126	—	2	2	no	—
21	C₂×C₁₇×#124	C₂²	1	2	yes	—
22	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
23	C₁₇×#519	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×#117	—	2	1	no	—
28	C₁₇×#497	C₂²	1	8	yes	—
29	C₁₇×#494	C₂²	1	4	yes	complemented
30	C₁₇×#489	C₂²	1	8	yes	—
31	C₁₇×#487	C₂²	1	4	yes	complemented
32	C₁₇×#483	C₂²	1	4	yes	—
33	C₁₇×#476	C₂²	1	4	yes	—
34	C₁₇×#475	C₂²	1	8	yes	complemented
35	C₁₇×#464	C₂²	1	16	yes	—
36	C₁₇×#462	C₂²	1	8	yes	complemented
37	C₁₇×#462	C₂²	1	8	yes	complemented
38	C₁₇×#461	C₂²	1	4	yes	—
39	C₁₇×#451	C₂²	1	8	yes	—
40	C₁₇×#450	C₂²	1	4	yes	—
41	C₁₇×#446	C₂²	1	8	yes	complemented
42	C₁₇×#441	C₂²	1	16	yes	complemented
43	C₄×SD₁₆×C₁₇	C₂²	1	8	yes	—
44	C₁₇×#432	C₂²	1	4	yes	—
45	C₁₇×#431	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₇	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₇	—	2	1	no	—
50	C₂×Q₁₆×C₁₇	C₂³	1	16	yes	—
51	C₂×SD₁₆×C₁₇	C₂³	1	8	yes	—
52	C₁₇×C₄⋊Q₈	—	2	8	no	—
53	C₁₇×C₄⋊Q₈	—	2	4	no	—
54	C₁₇×C₄⋊Q₈	—	2	2	no	—
55	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
57	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
58	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
59	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₇×#126	—	2	16	no	—
61	C₁₇×#125	—	2	8	no	—
62	C₁₇×#125	—	2	4	no	—
63	C₁₇×#125	—	2	4	no	—
64	C₁₇×#125	—	2	2	no	—
65	C₁₇×#124	—	2	4	no	—
66	C₁₇×#124	C₂³	1	8	yes	—
67	C₁₇×C₂²⋊Q₈	—	2	8	no	—
68	C₁₇×C₂²⋊Q₈	—	2	4	no	—
69	C₁₇×C₂²⋊Q₈	—	2	2	no	—
70	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
71	C₄×Q₈×C₁₇	—	2	4	no	—
72	C₄×Q₈×C₁₇	—	2	4	no	—
73	C₄×Q₈×C₁₇	—	2	4	no	—
74	C₄×Q₈×C₁₇	—	2	4	no	—
75	C₄×Q₈×C₁₇	—	2	2	no	—
76	C₄×Q₈×C₁₇	D₄	1	4	yes	—
77	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
78	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
79	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
80	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
81	C₄×D₄×C₁₇	—	2	2	no	—
82	C₄×D₄×C₁₇	C₂³	1	4	yes	—
83	C₁₇×#117	—	2	4	no	—
84	C₁₇×#117	—	2	2	no	—
85	C₁₇×#117	—	2	8	no	—
86	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
95	C₂×C₄²×C₁₇	—	2	2	no	—
96	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
98	C₁₇×#106	C₂³	1	8	yes	—
99	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
100	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
101	C₁₇×#103	C₂³	1	8	yes	—
102	C₁₇×#103	C₂³	1	16	yes	—
103	C₁₇×#102	C₂³	1	8	yes	—
104	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
105	C₁₇×#97	C₂³	1	8	yes	—
106	C₄×C₈×C₁₇	C₂³	1	4	yes	—
107	C₂⁴×C₁₇	—	2	1	no	—
108	C₂×Q₈×C₁₇	—	2	4	no	—
109	C₂×Q₈×C₁₇	—	2	2	no	—
110	C₂×Q₈×C₁₇	—	2	4	no	—
111	C₂×Q₈×C₁₇	—	2	2	no	—
112	C₂×Q₈×C₁₇	—	4	4	no	—
113	C₂×Q₈×C₁₇	C₂×D₄	1	4	yes	—
114	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
115	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
116	C₂×D₄×C₁₇	—	2	1	no	—
117	C₂×D₄×C₁₇	—	4	2	no	—
118	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₁₇	—	2	1	no	—
120	C₂²×C₄×C₁₇	—	2	2	no	—
121	C₂²×C₄×C₁₇	—	2	4	no	—
122	C₂²×C₄×C₁₇	—	4	4	no	—
123	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
128	Q₁₆×C₁₇	—	4	16	no	—
129	SD₁₆×C₁₇	—	4	8	no	—
130	C₂×C₈×C₁₇	C₂⁴	1	8	yes	—
131	C₄⋊C₄×C₁₇	—	2	8	no	—
132	C₄⋊C₄×C₁₇	—	2	4	no	—
133	C₄⋊C₄×C₁₇	—	2	4	no	—
134	C₄⋊C₄×C₁₇	—	2	2	no	—
135	C₄⋊C₄×C₁₇	—	2	8	no	—
136	C₄⋊C₄×C₁₇	—	2	4	no	—
137	C₄⋊C₄×C₁₇	—	2	4	no	—
138	C₄⋊C₄×C₁₇	—	2	4	no	—
139	C₄⋊C₄×C₁₇	—	2	2	no	—
140	C₄⋊C₄×C₁₇	—	2	4	no	—
141	C₄⋊C₄×C₁₇	—	2	2	no	—
142	C₄⋊C₄×C₁₇	—	2	4	no	—
143	C₄⋊C₄×C₁₇	—	2	1	no	—
144	C₄⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
145	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
146	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
147	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
148	C₂²⋊C₄×C₁₇	—	2	4	no	—
149	C₂²⋊C₄×C₁₇	—	2	8	no	—
150	C₂²⋊C₄×C₁₇	—	2	8	no	—
151	C₂²⋊C₄×C₁₇	—	2	4	no	—
152	C₄²×C₁₇	—	2	8	no	—
153	C₄²×C₁₇	—	2	4	no	—
154	C₄²×C₁₇	—	2	8	no	—
155	C₄²×C₁₇	C₂×D₄	1	4	yes	—
156	C₄²×C₁₇	C₂×D₄	1	2	yes	—
157	C₄²×C₁₇	C₂⁴	1	4	yes	—
158	C₄²×C₁₇	C₂⁴	1	2	yes	—
159	#61889	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₁₇	—	2	2	no	—
161	C₂³×C₁₇	—	4	2	no	—
162	C₂³×C₁₇	—	4	2	no	—
163	C₂³×C₁₇	—	4	2	no	—
164	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₇	—	2	8	no	—
166	Q₈×C₁₇	—	2	8	no	—
167	Q₈×C₁₇	—	2	8	no	—
168	Q₈×C₁₇	—	4	4	no	—
169	Q₈×C₁₇	—	8	4	no	—
170	Q₈×C₁₇	—	8	2	no	—
171	D₄×C₁₇	—	2	4	no	—
172	D₄×C₁₇	—	4	2	no	—
173	C₂×C₄×C₁₇	—	2	4	no	—
174	C₂×C₄×C₁₇	—	2	2	no	—
175	C₂×C₄×C₁₇	—	2	2	no	—
176	C₂×C₄×C₁₇	—	2	4	no	—
177	C₂×C₄×C₁₇	—	2	4	no	—
178	C₂×C₄×C₁₇	—	2	4	no	—
179	C₂×C₄×C₁₇	—	4	2	no	—
180	C₂×C₄×C₁₇	—	4	1	no	—
181	C₂×C₄×C₁₇	—	4	4	no	—
182	C₂×C₄×C₁₇	—	4	2	no	—
183	C₂×C₄×C₁₇	—	4	8	no	—
184	C₂×C₄×C₁₇	#137	1	4	yes	—
185	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
186	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
187	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
191	C₈×C₁₇	—	2	8	no	—
192	#3502	C₂×C₁₇	1	1	yes	characteristic, complemented
193	C₂×#556	C₂×C₁₇	1	1	yes	characteristic
194	#3398	C₂×C₁₇	1	8	yes	complemented
195	#3369	C₂×C₁₇	1	8	yes	complemented
196	#3215	C₂×C₁₇	1	4	yes	—
197	#3209	C₂×C₁₇	1	2	yes	complemented
198	#3113	C₂×C₁₇	1	4	yes	complemented
199	#3101	C₂×C₁₇	1	2	yes	—
200	#2983	C₂×C₁₇	1	1	yes	characteristic, complemented
201	C₂²×C₁₇	—	2	1	no	—
202	C₂²×C₁₇	—	2	1	no	—
203	C₂²×C₁₇	—	4	2	no	—
204	C₂²×C₁₇	—	4	2	no	—
205	C₂²×C₁₇	—	4	2	no	—
206	C₂²×C₁₇	—	8	4	no	—
207	C₂²×C₁₇	C₂×#137	1	2	yes	—
208	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
209	C₄×C₁₇	—	2	4	no	—
210	C₄×C₁₇	—	2	2	no	—
211	C₄×C₁₇	—	2	1	no	—
212	C₄×C₁₇	—	2	4	no	—
213	C₄×C₁₇	—	4	4	no	—
214	C₄×C₁₇	—	4	4	no	—
215	C₄×C₁₇	—	4	4	no	—
216	C₄×C₁₇	—	4	2	no	—
217	C₄×C₁₇	C₂×#137	1	4	yes	—
218	C₄×C₁₇	#585	1	2	yes	—
219	Q₈²	C₂²×C₁₇	1	4	yes	complemented
220	#557	—	2	4	no	—
221	#557	C₂²×C₁₇	1	4	yes	complemented
222	#556	—	2	4	no	—
223	#556	C₂²×C₁₇	1	8	yes	—
224	#544	—	2	1	no	—
225	#544	—	2	2	no	—
226	#533	C₂²×C₁₇	1	2	yes	—
227	#533	C₂²×C₁₇	1	4	yes	—
228	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
229	C₂×#126	—	2	2	no	—
230	C₂×#124	C₂²×C₁₇	1	2	yes	—
231	C₂×C₂²⋊Q₈	—	2	1	no	—
232	#519	—	2	1	no	—
233	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	—
234	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
236	C₂×#117	—	2	1	no	—
237	#497	C₂²×C₁₇	1	8	yes	—
238	#494	C₂²×C₁₇	1	4	yes	complemented
239	#489	C₂²×C₁₇	1	8	yes	—
240	#487	C₂²×C₁₇	1	4	yes	complemented
241	#483	C₂²×C₁₇	1	4	yes	—
242	#476	C₂²×C₁₇	1	4	yes	—
243	#475	C₂²×C₁₇	1	8	yes	complemented
244	#464	C₂²×C₁₇	1	16	yes	—
245	#462	C₂²×C₁₇	1	8	yes	complemented
246	#462	C₂²×C₁₇	1	8	yes	complemented
247	#461	C₂²×C₁₇	1	4	yes	—
248	#451	C₂²×C₁₇	1	8	yes	—
249	#450	C₂²×C₁₇	1	4	yes	—
250	#446	C₂²×C₁₇	1	8	yes	complemented
251	#441	C₂²×C₁₇	1	16	yes	complemented
252	C₄×SD₁₆	C₂²×C₁₇	1	8	yes	—
253	#432	C₂²×C₁₇	1	4	yes	—
254	#431	C₂²×C₁₇	1	2	yes	—
255	C₂×C₁₇	—	2	2	no	—
256	C₂×C₁₇	—	8	2	no	—
257	C₂×C₁₇	#3487	1	1	yes	characteristic
258	C₂×C₁₇	C₂²×#137	1	1	yes	characteristic
259	C₂×C₁₇	#3586	1	1	yes	characteristic
260	C₂²×Q₈	D₄×C₁₇	1	1	yes	characteristic
261	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
262	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
263	C₂³×C₄	—	2	1	no	—
264	C₂×Q₁₆	C₂³×C₁₇	1	16	yes	—
265	C₂×SD₁₆	C₂³×C₁₇	1	8	yes	—
266	C₄⋊Q₈	—	2	4	no	—
267	C₄⋊Q₈	—	2	8	no	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
270	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
271	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
272	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
273	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
274	#126	—	2	16	no	—
275	#125	—	2	4	no	—
276	#125	—	2	8	no	—
277	#125	—	2	2	no	—
278	#125	—	2	4	no	—
279	#124	—	2	4	no	—
280	#124	C₂³×C₁₇	1	8	yes	—
281	C₂²⋊Q₈	—	2	8	no	—
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	—	2	2	no	—
284	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
285	C₄×Q₈	—	2	4	no	—
286	C₄×Q₈	—	2	4	no	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	—	2	4	no	—
290	C₄×Q₈	D₄×C₁₇	1	4	yes	—
291	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
292	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
293	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
294	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	C₂³×C₁₇	1	4	yes	—
297	#117	—	2	4	no	—
298	#117	—	2	2	no	—
299	#117	—	2	8	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
304	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
312	#106	C₂³×C₁₇	1	8	yes	—
313	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
314	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
315	#103	C₂³×C₁₇	1	8	yes	—
316	#103	C₂³×C₁₇	1	16	yes	—
317	#102	C₂³×C₁₇	1	8	yes	—
318	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
319	#97	C₂³×C₁₇	1	8	yes	—
320	C₄×C₈	C₂³×C₁₇	1	4	yes	—
321	C₁₇	#61889	1	1	yes	characteristic, direct product factor, Sylow
322	C₂⁴	—	2	1	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	4	4	no	—
328	C₂×Q₈	C₂×D₄×C₁₇	1	4	yes	—
329	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
330	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
343	Q₁₆	—	4	16	no	—
344	SD₁₆	—	4	8	no	—
345	C₂×C₈	C₂⁴×C₁₇	1	8	yes	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
360	C₄⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
361	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
362	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₂²⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	2	8	no	—
367	C₄²	—	2	8	no	—
368	C₄²	—	2	8	no	—
369	C₄²	—	2	4	no	—
370	C₄²	C₂×D₄×C₁₇	1	2	yes	—
371	C₄²	C₂×D₄×C₁₇	1	4	yes	—
372	C₄²	C₂⁴×C₁₇	1	2	yes	—
373	C₄²	C₂⁴×C₁₇	1	4	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
379	Q₈	—	2	8	no	—
380	Q₈	—	2	8	no	—
381	Q₈	—	2	8	no	—
382	Q₈	—	4	4	no	—
383	Q₈	—	8	4	no	—
384	Q₈	—	8	2	no	—
385	D₄	—	2	4	no	—
386	D₄	—	4	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	C₁₇×#137	1	4	yes	—
399	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
400	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
401	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
402	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
403	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
404	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
405	C₈	—	2	8	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	8	4	no	—
412	C₂²	C₂×C₁₇×#137	1	2	yes	—
413	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	4	no	—
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	4	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	4	no	—
422	C₄	C₂×C₁₇×#137	1	4	yes	—
423	C₄	C₁₇×#585	1	2	yes	—
424	C₂	—	2	2	no	—
425	C₂	—	8	2	no	—
426	C₂	C₁₇×#3487	1	1	yes	characteristic
427	C₂	C₂²×C₁₇×#137	1	1	yes	characteristic
428	C₂	C₁₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄×Q₈×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3502	C₂	semidirect
3. C₁₇×#3398	C₂	semidirect
4. C₁₇×#3369	C₂	semidirect
6. C₁₇×#3209	C₂	semidirect
7. C₁₇×#3113	C₂	semidirect
9. C₁₇×#2983	C₂	semidirect
10. Q₈²×C₁₇	C₂²	semidirect
12. C₁₇×#557	C₂²	semidirect
29. C₁₇×#494	C₂²	semidirect
31. C₁₇×#487	C₂²	semidirect
34. C₁₇×#475	C₂²	semidirect
36. C₁₇×#462	C₂²	semidirect
37. C₁₇×#462	C₂²	semidirect
41. C₁₇×#446	C₂²	semidirect
42. C₁₇×#441	C₂²	semidirect
159. #61889	C₁₇	direct (N × H)
192. #3502	C₂×C₁₇	semidirect
194. #3398	C₂×C₁₇	semidirect
195. #3369	C₂×C₁₇	semidirect
197. #3209	C₂×C₁₇	semidirect
198. #3113	C₂×C₁₇	semidirect
200. #2983	C₂×C₁₇	semidirect
219. Q₈²	C₂²×C₁₇	semidirect
221. #557	C₂²×C₁₇	semidirect
238. #494	C₂²×C₁₇	semidirect
240. #487	C₂²×C₁₇	semidirect
243. #475	C₂²×C₁₇	semidirect
245. #462	C₂²×C₁₇	semidirect
246. #462	C₂²×C₁₇	semidirect
250. #446	C₂²×C₁₇	semidirect
251. #441	C₂²×C₁₇	semidirect
321. C₁₇	#61889	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#3502	2
C₂×C₁₇×#556	2
C₁₇×#3398	2
C₁₇×#3369	2
C₁₇×#3215	2
C₁₇×#3209	2
C₁₇×#3113	2
C₁₇×#3101	2
C₁₇×#2983	2
#61889	17

Subgroups — C17×#61889 #16919633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61889 #16919633