Subgroups — C₁₇×#61436 #16919180

Order 4352.

1960 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	C₁₇×#3483	C₂	1	2	yes	maximal, complemented
2	C₁₇×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Q₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3362	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3341	C₂	1	3	yes	maximal, complemented
6	C₁₇×#3305	C₂	1	6	yes	maximal, complemented
7	C₁₇×#3287	C₂	1	3	yes	maximal, complemented
8	C₁₇×#3169	C₂	1	3	yes	maximal, complemented
9	C₁₇×#3106	C₂	1	6	yes	maximal, complemented
10	C₈×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₇×#135	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₇×#135	C₂²	1	3	yes	—
13	Q₈²×C₁₇	C₂²	1	2	yes	—
14	C₁₇×#555	—	2	6	no	—
15	C₁₇×#555	C₂²	1	6	yes	—
16	C₁₇×#550	—	2	2	no	—
17	C₁₇×#550	C₂²	1	6	yes	—
18	C₁₇×#550	C₂²	1	2	yes	—
19	C₁₇×#532	—	2	6	no	—
20	C₁₇×#532	C₂²	1	6	yes	—
21	C₄×#41×C₁₇	—	2	2	no	—
22	C₄×#41×C₁₇	C₂²	1	6	yes	—
23	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
24	C₁₇×#500	C₂²	1	3	yes	—
25	C₁₇×#493	C₂²	1	3	yes	—
26	C₁₇×#486	C₂²	1	6	yes	—
27	C₁₇×#482	C₂²	1	12	yes	—
28	C₁₇×#477	C₂²	1	6	yes	—
29	C₁₇×#476	C₂²	1	6	yes	—
30	C₁₇×#466	C₂²	1	6	yes	—
31	C₁₇×#466	C₂²	1	6	yes	—
32	C₁₇×#460	C₂²	1	6	yes	—
33	C₁₇×#459	C₂²	1	6	yes	—
34	C₁₇×#449	C₂²	1	12	yes	—
35	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
36	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
38	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
39	C₄×SD₁₆×C₁₇	C₂²	1	6	yes	—
40	C₄×SD₁₆×C₁₇	C₂²	1	6	yes	—
41	C₄×D₈×C₁₇	C₂²	1	3	yes	—
42	C₄×D₈×C₁₇	C₂²	1	6	yes	—
43	C₄×D₈×C₁₇	C₂²	1	3	yes	—
44	C₈×D₄×C₁₇	C₂²	1	3	yes	—
45	C₈×D₄×C₁₇	C₂²	1	3	yes	—
46	C₁₇×#431	C₂²	1	3	yes	—
47	C₁₇×#427	C₂²	1	3	yes	—
48	C₁₇×#416	C₂²	1	6	yes	—
49	C₂×C₄×C₈×C₁₇	C₂²	1	3	yes	—
50	C₂×#41×C₁₇	—	2	2	no	—
51	C₂×#41×C₁₇	—	2	6	no	—
52	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
53	C₂×#41×C₁₇	C₂³	1	6	yes	—
54	C₁₇×#135	—	2	12	no	—
55	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₁₇	C₂³	1	6	yes	—
57	C₂×D₈×C₁₇	C₂³	1	3	yes	—
58	C₂×D₈×C₁₇	C₂³	1	6	yes	—
59	C₂²×C₈×C₁₇	C₂³	1	3	yes	—
60	C₂²×C₈×C₁₇	C₂³	1	3	yes	—
61	C₁₇×C₄⋊Q₈	—	2	6	no	—
62	C₁₇×C₄⋊Q₈	C₂³	1	6	yes	—
63	C₁₇×#127	—	2	6	no	—
64	C₁₇×#127	C₂³	1	6	yes	—
65	C₁₇×#124	—	2	12	no	—
66	C₁₇×#124	—	2	6	no	—
67	C₁₇×#121	—	2	6	no	—
68	C₁₇×#121	—	2	6	no	—
69	C₁₇×#121	—	2	6	no	—
70	C₁₇×#121	—	2	12	no	—
71	C₁₇×#121	C₂³	1	12	yes	—
72	C₄×Q₈×C₁₇	—	2	2	no	—
73	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
74	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
75	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
76	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
77	C₄×D₄×C₁₇	—	2	6	no	—
78	C₄×D₄×C₁₇	—	2	6	no	—
79	C₄×D₄×C₁₇	—	2	6	no	—
80	C₄×D₄×C₁₇	—	2	6	no	—
81	C₄×D₄×C₁₇	D₄	1	3	yes	—
82	C₄×D₄×C₁₇	C₂³	1	6	yes	—
83	C₄×D₄×C₁₇	C₂³	1	6	yes	—
84	C₄×D₄×C₁₇	C₂³	1	3	yes	—
85	C₁₇×#117	—	2	6	no	—
86	C₁₇×#117	—	2	6	no	—
87	C₁₇×#117	D₄	1	3	yes	—
88	C₁₇×#117	C₂³	1	6	yes	—
89	C₂×C₄²×C₁₇	—	2	6	no	—
90	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
91	C₁₇×#107	C₂³	1	3	yes	—
92	C₁₇×#107	C₂³	1	6	yes	—
93	C₁₇×#107	C₂³	1	1	yes	characteristic
94	C₁₇×#106	C₂³	1	6	yes	—
95	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
96	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
97	C₁₇×#103	C₂³	1	2	yes	—
98	C₁₇×#103	C₂³	1	6	yes	—
99	C₁₇×#102	C₂³	1	6	yes	—
100	C₁₇×#102	C₂³	1	6	yes	—
101	C₁₇×#102	C₂³	1	12	yes	—
102	C₁₇×C₂²⋊C₈	C₂³	1	6	yes	—
103	C₄×C₈×C₁₇	C₂³	1	3	yes	—
104	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
105	C₄×C₈×C₁₇	C₂³	1	3	yes	—
106	C₄×C₈×C₁₇	C₂³	1	3	yes	—
107	#41×C₁₇	—	2	4	no	—
108	#41×C₁₇	—	2	12	no	—
109	#41×C₁₇	—	4	6	no	—
110	#41×C₁₇	—	4	8	no	—
111	#41×C₁₇	—	8	12	no	—
112	C₂×Q₈×C₁₇	—	2	6	no	—
113	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
114	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
115	C₂×D₄×C₁₇	—	2	6	no	—
116	C₂×D₄×C₁₇	—	2	12	no	—
117	C₂×D₄×C₁₇	—	2	6	no	—
118	C₂×D₄×C₁₇	—	2	6	no	—
119	C₂×D₄×C₁₇	C₂×D₄	1	3	yes	—
120	C₂×D₄×C₁₇	C₂⁴	1	6	yes	—
121	C₂²×C₄×C₁₇	—	2	6	no	—
122	C₂²×C₄×C₁₇	—	2	6	no	—
123	C₂²×C₄×C₁₇	—	2	6	no	—
124	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
125	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
126	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
127	Q₁₆×C₁₇	#41	1	4	yes	complemented
128	SD₁₆×C₁₇	—	2	12	no	—
129	D₈×C₁₇	—	2	6	no	—
130	D₈×C₁₇	—	4	6	no	—
131	C₂×C₈×C₁₇	—	2	6	no	—
132	C₂×C₈×C₁₇	—	4	3	no	—
133	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
135	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
136	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
137	C₄⋊C₄×C₁₇	—	2	6	no	—
138	C₄⋊C₄×C₁₇	—	2	6	no	—
139	C₄⋊C₄×C₁₇	—	2	2	no	—
140	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
141	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
142	C₄⋊C₄×C₁₇	C₂⁴	1	6	yes	—
143	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
144	C₂²⋊C₄×C₁₇	—	2	6	no	—
145	C₂²⋊C₄×C₁₇	—	2	12	no	—
146	C₂²⋊C₄×C₁₇	—	2	6	no	—
147	C₂²⋊C₄×C₁₇	—	2	6	no	—
148	C₂²⋊C₄×C₁₇	C₂×D₄	1	6	yes	—
149	C₄²×C₁₇	—	2	6	no	—
150	C₄²×C₁₇	—	2	6	no	—
151	C₄²×C₁₇	—	2	2	no	—
152	C₄²×C₁₇	C₂×D₄	1	3	yes	—
153	C₄²×C₁₇	C₂×D₄	1	3	yes	—
154	C₄²×C₁₇	C₂⁴	1	3	yes	—
155	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
156	#61436	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₇	—	2	6	no	—
158	C₂³×C₁₇	C₂²×D₄	1	3	yes	—
159	Q₈×C₁₇	—	2	2	no	—
160	Q₈×C₁₇	—	8	6	no	—
161	Q₈×C₁₇	#135	1	4	yes	complemented
162	Q₈×C₁₇	C₂×#41	1	4	yes	—
163	D₄×C₁₇	—	2	6	no	—
164	D₄×C₁₇	—	2	6	no	—
165	D₄×C₁₇	—	2	6	no	—
166	D₄×C₁₇	—	4	12	no	—
167	D₄×C₁₇	—	4	12	no	—
168	D₄×C₁₇	—	8	6	no	—
169	D₄×C₁₇	—	8	12	no	—
170	C₂×C₄×C₁₇	—	2	2	no	—
171	C₂×C₄×C₁₇	—	2	6	no	—
172	C₂×C₄×C₁₇	—	2	6	no	—
173	C₂×C₄×C₁₇	—	2	3	no	—
174	C₂×C₄×C₁₇	—	2	3	no	—
175	C₂×C₄×C₁₇	—	2	2	no	—
176	C₂×C₄×C₁₇	—	2	6	no	—
177	C₂×C₄×C₁₇	—	4	12	no	—
178	C₂×C₄×C₁₇	—	4	12	no	—
179	C₂×C₄×C₁₇	—	4	12	no	—
180	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
181	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
183	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
184	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
186	C₈×C₁₇	—	2	3	no	—
187	C₈×C₁₇	—	2	1	no	—
188	C₈×C₁₇	—	2	3	no	—
189	C₈×C₁₇	C₂×#41	1	2	yes	—
190	#3483	C₂×C₁₇	1	2	yes	complemented
191	#3391	C₂×C₁₇	1	1	yes	characteristic, complemented
192	Q₈×Q₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
193	#3362	C₂×C₁₇	1	2	yes	complemented
194	#3341	C₂×C₁₇	1	3	yes	complemented
195	#3305	C₂×C₁₇	1	6	yes	complemented
196	#3287	C₂×C₁₇	1	3	yes	complemented
197	#3169	C₂×C₁₇	1	3	yes	complemented
198	#3106	C₂×C₁₇	1	6	yes	complemented
199	C₈×#41	C₂×C₁₇	1	1	yes	characteristic, complemented
200	C₄×#135	C₂×C₁₇	1	3	yes	complemented
201	C₂²×C₁₇	—	2	3	no	—
202	C₂²×C₁₇	—	2	3	no	—
203	C₂²×C₁₇	—	2	3	no	—
204	C₂²×C₁₇	—	4	6	no	—
205	C₂²×C₁₇	—	4	6	no	—
206	C₂²×C₁₇	—	4	6	no	—
207	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
208	C₄×C₁₇	—	2	3	no	—
209	C₄×C₁₇	—	2	4	no	—
210	C₄×C₁₇	—	2	1	no	—
211	C₄×C₁₇	—	2	3	no	—
212	C₄×C₁₇	—	4	2	no	—
213	C₄×C₁₇	—	4	6	no	—
214	C₄×C₁₇	C₂×#135	1	6	yes	—
215	C₄×C₁₇	#576	1	2	yes	—
216	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
217	C₄×C₁₇	#585	1	1	yes	characteristic
218	C₂×#135	C₂²×C₁₇	1	3	yes	—
219	Q₈²	C₂²×C₁₇	1	2	yes	—
220	#555	—	2	6	no	—
221	#555	C₂²×C₁₇	1	6	yes	—
222	#550	—	2	2	no	—
223	#550	C₂²×C₁₇	1	6	yes	—
224	#550	C₂²×C₁₇	1	2	yes	—
225	#532	—	2	6	no	—
226	#532	C₂²×C₁₇	1	6	yes	—
227	C₄×#41	—	2	2	no	—
228	C₄×#41	C₂²×C₁₇	1	6	yes	—
229	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
230	#500	C₂²×C₁₇	1	3	yes	—
231	#493	C₂²×C₁₇	1	3	yes	—
232	#486	C₂²×C₁₇	1	6	yes	—
233	#482	C₂²×C₁₇	1	12	yes	—
234	#477	C₂²×C₁₇	1	6	yes	—
235	#476	C₂²×C₁₇	1	6	yes	—
236	#466	C₂²×C₁₇	1	6	yes	—
237	#466	C₂²×C₁₇	1	6	yes	—
238	#460	C₂²×C₁₇	1	6	yes	—
239	#459	C₂²×C₁₇	1	6	yes	—
240	#449	C₂²×C₁₇	1	12	yes	—
241	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
242	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
243	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
244	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
245	C₄×SD₁₆	C₂²×C₁₇	1	6	yes	—
246	C₄×SD₁₆	C₂²×C₁₇	1	6	yes	—
247	C₄×D₈	C₂²×C₁₇	1	3	yes	—
248	C₄×D₈	C₂²×C₁₇	1	6	yes	—
249	C₄×D₈	C₂²×C₁₇	1	3	yes	—
250	C₈×D₄	C₂²×C₁₇	1	3	yes	—
251	C₈×D₄	C₂²×C₁₇	1	3	yes	—
252	#431	C₂²×C₁₇	1	3	yes	—
253	#427	C₂²×C₁₇	1	3	yes	—
254	#416	C₂²×C₁₇	1	6	yes	—
255	C₂×C₄×C₈	C₂²×C₁₇	1	3	yes	—
256	C₂×C₁₇	—	4	3	no	—
257	C₂×C₁₇	—	8	6	no	—
258	C₂×C₁₇	D₄×#41	1	1	yes	characteristic
259	C₂×C₁₇	C₂²×#135	1	1	yes	characteristic
260	C₂×C₁₇	C₂×#576	1	1	yes	characteristic
261	C₂×#41	—	2	2	no	—
262	C₂×#41	—	2	6	no	—
263	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
264	C₂×#41	C₂³×C₁₇	1	6	yes	—
265	#135	—	2	12	no	—
266	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
267	C₂×SD₁₆	C₂³×C₁₇	1	6	yes	—
268	C₂×D₈	C₂³×C₁₇	1	3	yes	—
269	C₂×D₈	C₂³×C₁₇	1	6	yes	—
270	C₂²×C₈	C₂³×C₁₇	1	3	yes	—
271	C₂²×C₈	C₂³×C₁₇	1	3	yes	—
272	C₄⋊Q₈	—	2	6	no	—
273	C₄⋊Q₈	C₂³×C₁₇	1	6	yes	—
274	#127	—	2	6	no	—
275	#127	C₂³×C₁₇	1	6	yes	—
276	#124	—	2	12	no	—
277	#124	—	2	6	no	—
278	#121	—	2	6	no	—
279	#121	—	2	6	no	—
280	#121	—	2	6	no	—
281	#121	—	2	12	no	—
282	#121	C₂³×C₁₇	1	12	yes	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
285	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
286	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
287	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
288	C₄×D₄	—	2	6	no	—
289	C₄×D₄	—	2	6	no	—
290	C₄×D₄	—	2	6	no	—
291	C₄×D₄	—	2	6	no	—
292	C₄×D₄	D₄×C₁₇	1	3	yes	—
293	C₄×D₄	C₂³×C₁₇	1	6	yes	—
294	C₄×D₄	C₂³×C₁₇	1	6	yes	—
295	C₄×D₄	C₂³×C₁₇	1	3	yes	—
296	#117	—	2	6	no	—
297	#117	—	2	6	no	—
298	#117	D₄×C₁₇	1	3	yes	—
299	#117	C₂³×C₁₇	1	6	yes	—
300	C₂×C₄²	—	2	6	no	—
301	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
302	#107	C₂³×C₁₇	1	1	yes	characteristic
303	#107	C₂³×C₁₇	1	3	yes	—
304	#107	C₂³×C₁₇	1	6	yes	—
305	#106	C₂³×C₁₇	1	6	yes	—
306	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
307	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
308	#103	C₂³×C₁₇	1	2	yes	—
309	#103	C₂³×C₁₇	1	6	yes	—
310	#102	C₂³×C₁₇	1	6	yes	—
311	#102	C₂³×C₁₇	1	6	yes	—
312	#102	C₂³×C₁₇	1	12	yes	—
313	C₂²⋊C₈	C₂³×C₁₇	1	6	yes	—
314	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
315	C₄×C₈	C₂³×C₁₇	1	3	yes	—
316	C₄×C₈	C₂³×C₁₇	1	3	yes	—
317	C₄×C₈	C₂³×C₁₇	1	3	yes	—
318	C₁₇	#61436	1	1	yes	characteristic, direct product factor, Sylow
319	#41	—	2	4	no	—
320	#41	—	2	12	no	—
321	#41	—	4	6	no	—
322	#41	—	4	8	no	—
323	#41	—	8	12	no	—
324	C₂×Q₈	—	2	6	no	—
325	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
326	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
327	C₂×D₄	—	2	6	no	—
328	C₂×D₄	—	2	12	no	—
329	C₂×D₄	—	2	6	no	—
330	C₂×D₄	—	2	6	no	—
331	C₂×D₄	C₂×D₄×C₁₇	1	3	yes	—
332	C₂×D₄	C₂⁴×C₁₇	1	6	yes	—
333	C₂²×C₄	—	2	6	no	—
334	C₂²×C₄	—	2	6	no	—
335	C₂²×C₄	—	2	6	no	—
336	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
337	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
338	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
339	Q₁₆	#41×C₁₇	1	4	yes	complemented
340	SD₁₆	—	2	12	no	—
341	D₈	—	2	6	no	—
342	D₈	—	4	6	no	—
343	C₂×C₈	—	2	6	no	—
344	C₂×C₈	—	4	3	no	—
345	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
346	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
347	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
348	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	6	no	—
351	C₄⋊C₄	—	2	6	no	—
352	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
353	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
354	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
355	C₄⋊C₄	C₂⁴×C₁₇	1	6	yes	—
356	C₂²⋊C₄	—	2	6	no	—
357	C₂²⋊C₄	—	2	12	no	—
358	C₂²⋊C₄	—	2	6	no	—
359	C₂²⋊C₄	—	2	6	no	—
360	C₂²⋊C₄	C₂×D₄×C₁₇	1	6	yes	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	6	no	—
363	C₄²	—	2	6	no	—
364	C₄²	C₂×D₄×C₁₇	1	3	yes	—
365	C₄²	C₂×D₄×C₁₇	1	3	yes	—
366	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
367	C₄²	C₂⁴×C₁₇	1	3	yes	—
368	C₂³	—	2	6	no	—
369	C₂³	C₂²×D₄×C₁₇	1	3	yes	—
370	Q₈	—	2	2	no	—
371	Q₈	—	8	6	no	—
372	Q₈	C₁₇×#135	1	4	yes	complemented
373	Q₈	C₂×#41×C₁₇	1	4	yes	—
374	D₄	—	2	6	no	—
375	D₄	—	2	6	no	—
376	D₄	—	2	6	no	—
377	D₄	—	4	12	no	—
378	D₄	—	4	12	no	—
379	D₄	—	8	6	no	—
380	D₄	—	8	12	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	6	no	—
383	C₂×C₄	—	2	6	no	—
384	C₂×C₄	—	2	3	no	—
385	C₂×C₄	—	2	3	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	6	no	—
388	C₂×C₄	—	4	12	no	—
389	C₂×C₄	—	4	12	no	—
390	C₂×C₄	—	4	12	no	—
391	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
392	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
394	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
395	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
396	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
397	C₈	—	2	3	no	—
398	C₈	—	2	1	no	—
399	C₈	—	2	3	no	—
400	C₈	C₂×#41×C₁₇	1	2	yes	—
401	C₂²	—	2	3	no	—
402	C₂²	—	2	3	no	—
403	C₂²	—	2	3	no	—
404	C₂²	—	4	6	no	—
405	C₂²	—	4	6	no	—
406	C₂²	—	4	6	no	—
407	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
408	C₄	—	2	3	no	—
409	C₄	—	2	4	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	3	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	6	no	—
414	C₄	C₂×C₁₇×#135	1	6	yes	—
415	C₄	C₁₇×#576	1	2	yes	—
416	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
417	C₄	C₁₇×#585	1	1	yes	characteristic
418	C₂	—	4	3	no	—
419	C₂	—	8	6	no	—
420	C₂	D₄×#41×C₁₇	1	1	yes	characteristic
421	C₂	C₂²×C₁₇×#135	1	1	yes	characteristic
422	C₂	C₂×C₁₇×#576	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
socle	C₂²×C₁₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₄×#41×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3483	C₂	semidirect
2. C₁₇×#3391	C₂	semidirect
3. Q₈×Q₁₆×C₁₇	C₂	semidirect
4. C₁₇×#3362	C₂	semidirect
5. C₁₇×#3341	C₂	semidirect
6. C₁₇×#3305	C₂	semidirect
7. C₁₇×#3287	C₂	semidirect
8. C₁₇×#3169	C₂	semidirect
9. C₁₇×#3106	C₂	semidirect
10. C₈×#41×C₁₇	C₂	semidirect
11. C₄×C₁₇×#135	C₂	semidirect
127. Q₁₆×C₁₇	#41	semidirect
156. #61436	C₁₇	direct (N × H)
161. Q₈×C₁₇	#135	semidirect
190. #3483	C₂×C₁₇	semidirect
191. #3391	C₂×C₁₇	semidirect
192. Q₈×Q₁₆	C₂×C₁₇	semidirect
193. #3362	C₂×C₁₇	semidirect
194. #3341	C₂×C₁₇	semidirect
195. #3305	C₂×C₁₇	semidirect
196. #3287	C₂×C₁₇	semidirect
197. #3169	C₂×C₁₇	semidirect
198. #3106	C₂×C₁₇	semidirect
199. C₈×#41	C₂×C₁₇	semidirect
200. C₄×#135	C₂×C₁₇	semidirect
318. C₁₇	#61436	direct (N × H)
339. Q₁₆	#41×C₁₇	semidirect
372. Q₈	C₁₇×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3483	2
C₁₇×#3391	2
Q₈×Q₁₆×C₁₇	2
C₁₇×#3362	2
C₁₇×#3341	2
C₁₇×#3305	2
C₁₇×#3287	2
C₁₇×#3169	2
C₁₇×#3106	2
C₈×#41×C₁₇	2
C₄×C₁₇×#135	2
#61436	17

Subgroups — C17×#61436 #16919180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61436 #16919180