Subgroups — C₁₇×#61376 #16919120

Order 4352.

1706 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3504	C₂	1	2	yes	maximal, complemented
2	C₁₇×#3388	C₂	1	8	yes	maximal, complemented
3	C₁₇×#3383	C₂	1	4	yes	maximal, complemented
4	C₁₇×#3380	C₂	1	4	yes	maximal, complemented
5	C₁₇×#3164	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#3084	C₂	1	4	yes	maximal, complemented
8	C₁₇×#3080	C₂	1	2	yes	maximal, complemented
9	C₁₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2951	C₂	1	2	yes	maximal
11	C₄×C₁₇×#135	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
13	C₁₇×#557	C₂²	1	8	yes	—
14	C₁₇×#554	—	2	8	no	—
15	C₁₇×#554	C₂²	1	8	yes	—
16	C₁₇×#544	—	2	4	no	—
17	C₁₇×#544	C₂²	1	4	yes	—
18	C₁₇×#533	—	2	2	no	—
19	C₁₇×#533	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×#125	—	2	2	no	—
21	C₂×C₁₇×#125	C₂²	1	2	yes	—
22	C₁₇×#520	C₂²	1	4	yes	—
23	C₄×#41×C₁₇	C₂²	1	2	yes	—
24	C₁₇×#501	C₂²	1	8	yes	—
25	C₁₇×#500	C₂²	1	4	yes	—
26	C₁₇×#499	C₂²	1	4	yes	—
27	C₁₇×#499	C₂²	1	4	yes	—
28	C₁₇×#499	C₂²	1	4	yes	—
29	C₁₇×#479	C₂²	1	8	yes	—
30	C₁₇×#479	C₂²	1	8	yes	—
31	C₁₇×#478	C₂²	1	8	yes	—
32	C₁₇×#478	C₂²	1	8	yes	—
33	C₁₇×#476	C₂²	1	8	yes	—
34	C₁₇×#475	C₂²	1	8	yes	—
35	C₁₇×#446	C₂²	1	4	yes	—
36	C₈×Q₈×C₁₇	C₂²	1	4	yes	—
37	C₁₇×#440	C₂²	1	8	yes	—
38	C₄×Q₁₆×C₁₇	C₂²	1	4	yes	—
39	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
40	C₄×SD₁₆×C₁₇	C₂²	1	4	yes	—
41	C₄×D₈×C₁₇	C₂²	1	4	yes	—
42	C₄×D₈×C₁₇	C₂²	1	2	yes	—
43	C₁₇×#428	C₂²	1	4	yes	—
44	C₁₇×#427	C₂²	1	1	yes	characteristic
45	C₂×C₁₇×#107	C₂²	1	2	yes	—
46	C₂×C₁₇×#106	C₂²	1	2	yes	—
47	C₁₇×#424	C₂²	1	2	yes	—
48	C₁₇×#423	C₂²	1	1	yes	characteristic
49	C₁₇×#417	C₂²	1	4	yes	—
50	C₁₇×#416	C₂²	1	2	yes	—
51	C₁₇×#405	C₂²	1	2	yes	—
52	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
53	C₂×#41×C₁₇	C₂³	1	2	yes	—
54	C₁₇×#135	Q₈	1	8	yes	complemented
55	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
57	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
61	C₁₇×C₄⋊Q₈	—	2	8	no	—
62	C₁₇×C₄⋊Q₈	—	2	4	no	—
63	C₁₇×C₄⋊Q₈	D₄	1	2	yes	—
64	C₁₇×C₄⋊Q₈	C₂³	1	8	yes	—
65	C₁₇×#125	—	2	4	no	—
66	C₁₇×#125	—	2	8	no	—
67	C₁₇×#125	—	2	8	no	—
68	C₁₇×#125	—	2	2	no	—
69	C₁₇×#125	—	2	2	no	—
70	C₁₇×#125	D₄	1	1	yes	characteristic
71	C₁₇×#125	D₄	1	1	yes	characteristic
72	C₁₇×#125	C₂³	1	8	yes	—
73	C₁₇×#125	C₂³	1	8	yes	—
74	C₁₇×C₂²⋊Q₈	—	2	8	no	—
75	C₁₇×C₂²⋊Q₈	—	2	8	no	—
76	C₁₇×C₂²⋊Q₈	—	2	8	no	—
77	C₁₇×C₂²⋊Q₈	—	2	8	no	—
78	C₁₇×C₂²⋊Q₈	D₄	1	4	yes	—
79	C₄×Q₈×C₁₇	—	2	8	no	—
80	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
81	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
82	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
83	C₄×D₄×C₁₇	—	2	4	no	—
84	C₄×D₄×C₁₇	—	2	8	no	—
85	C₄×D₄×C₁₇	C₂³	1	4	yes	—
86	C₄×D₄×C₁₇	C₂³	1	8	yes	—
87	C₁₇×#117	—	2	4	no	—
88	C₁₇×#117	—	2	2	no	—
89	C₁₇×#117	C₂³	1	2	yes	—
90	C₁₇×#117	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
92	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
93	C₂×C₄⋊C₄×C₁₇	—	2	8	no	—
94	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
95	C₂×C₄²×C₁₇	—	2	2	no	—
96	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
97	C₁₇×#107	C₂³	1	4	yes	—
98	C₁₇×#107	C₂³	1	2	yes	—
99	C₁₇×#107	C₂³	1	4	yes	—
100	C₁₇×#107	C₂³	1	8	yes	—
101	C₁₇×#106	C₂³	1	8	yes	—
102	C₁₇×#106	C₂³	1	8	yes	—
103	C₁₇×#106	C₂³	1	2	yes	—
104	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
105	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
106	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
107	C₁₇×#103	C₂³	1	4	yes	—
108	C₁₇×#103	C₂³	1	8	yes	—
109	C₁₇×#102	C₂³	1	4	yes	—
110	C₁₇×#102	C₂³	1	8	yes	—
111	C₁₇×#97	C₂³	1	4	yes	—
112	C₄×C₈×C₁₇	C₂³	1	2	yes	—
113	C₄×C₈×C₁₇	C₂³	1	2	yes	—
114	C₄×C₈×C₁₇	C₂³	1	4	yes	—
115	#41×C₁₇	—	2	4	no	—
116	#41×C₁₇	C₂×Q₈	1	8	yes	—
117	C₂×Q₈×C₁₇	—	2	8	no	—
118	C₂×Q₈×C₁₇	C₂×D₄	1	4	yes	—
119	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
120	C₂×D₄×C₁₇	—	2	2	no	—
121	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₁₇	—	2	2	no	—
123	C₂²×C₄×C₁₇	—	2	4	no	—
124	C₂²×C₄×C₁₇	—	2	4	no	—
125	C₂²×C₄×C₁₇	—	2	8	no	—
126	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
128	Q₁₆×C₁₇	C₂×Q₈	1	4	yes	—
129	SD₁₆×C₁₇	C₂×Q₈	1	8	yes	—
130	D₈×C₁₇	C₂×Q₈	1	4	yes	—
131	M₁₆×C₁₇	—	2	4	no	—
132	C₂×C₈×C₁₇	—	2	2	no	—
133	C₂×C₈×C₁₇	C₂×Q₈	1	4	yes	—
134	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
135	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
136	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
137	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
138	C₄⋊C₄×C₁₇	—	2	8	no	—
139	C₄⋊C₄×C₁₇	—	2	8	no	—
140	C₄⋊C₄×C₁₇	—	2	8	no	—
141	C₄⋊C₄×C₁₇	—	2	8	no	—
142	C₄⋊C₄×C₁₇	—	2	8	no	—
143	C₄⋊C₄×C₁₇	—	2	4	no	—
144	C₄⋊C₄×C₁₇	—	2	8	no	—
145	C₄⋊C₄×C₁₇	—	2	4	no	—
146	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
147	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
148	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
149	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
151	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
152	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
153	C₂²⋊C₄×C₁₇	—	2	2	no	—
154	C₂²⋊C₄×C₁₇	—	2	4	no	—
155	C₂²⋊C₄×C₁₇	—	2	8	no	—
156	C₂²⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
157	C₄²×C₁₇	—	2	2	no	—
158	C₄²×C₁₇	—	2	4	no	—
159	C₄²×C₁₇	—	2	8	no	—
160	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₇	C₂⁴	1	2	yes	—
163	C₄²×C₁₇	C₂⁴	1	4	yes	—
164	#61376	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₁₇	—	2	2	no	—
166	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₇	—	2	2	no	—
168	Q₈×C₁₇	—	4	4	no	—
169	Q₈×C₁₇	—	8	8	no	—
170	Q₈×C₁₇	C₂²×Q₈	1	4	yes	—
171	D₄×C₁₇	—	2	8	no	—
172	D₄×C₁₇	—	2	2	no	—
173	D₄×C₁₇	C₂²×Q₈	1	4	yes	—
174	C₂×C₄×C₁₇	—	2	2	no	—
175	C₂×C₄×C₁₇	—	2	8	no	—
176	C₂×C₄×C₁₇	—	2	4	no	—
177	C₂×C₄×C₁₇	—	2	8	no	—
178	C₂×C₄×C₁₇	—	4	2	no	—
179	C₂×C₄×C₁₇	—	8	4	no	—
180	C₂×C₄×C₁₇	—	8	8	no	—
181	C₂×C₄×C₁₇	—	8	4	no	—
182	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
184	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
186	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₇	C₂²×Q₈	1	2	yes	—
188	C₂×C₄×C₁₇	2₋¹⁺⁴	1	2	yes	—
189	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
190	C₈×C₁₇	—	2	2	no	—
191	C₈×C₁₇	—	2	4	no	—
192	C₈×C₁₇	C₂²×Q₈	1	2	yes	—
193	C₈×C₁₇	C₂²×Q₈	1	2	yes	—
194	#3504	C₂×C₁₇	1	2	yes	complemented
195	#3388	C₂×C₁₇	1	8	yes	complemented
196	#3383	C₂×C₁₇	1	4	yes	complemented
197	#3380	C₂×C₁₇	1	4	yes	complemented
198	#3164	C₂×C₁₇	1	2	yes	complemented
199	C₂×#499	C₂×C₁₇	1	1	yes	characteristic, complemented
200	#3084	C₂×C₁₇	1	4	yes	complemented
201	#3080	C₂×C₁₇	1	2	yes	complemented
202	#2960	C₂×C₁₇	1	1	yes	characteristic, complemented
203	#2951	C₂×C₁₇	1	2	yes	—
204	C₄×#135	C₂×C₁₇	1	1	yes	characteristic
205	C₂²×C₁₇	—	2	2	no	—
206	C₂²×C₁₇	—	2	4	no	—
207	C₂²×C₁₇	—	4	4	no	—
208	C₂²×C₁₇	D₄×Q₈	1	2	yes	—
209	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
210	C₄×C₁₇	—	2	2	no	—
211	C₄×C₁₇	—	2	2	no	—
212	C₄×C₁₇	—	2	4	no	—
213	C₄×C₁₇	—	2	4	no	—
214	C₄×C₁₇	—	2	4	no	—
215	C₄×C₁₇	—	4	8	no	—
216	C₄×C₁₇	—	4	4	no	—
217	C₄×C₁₇	D₄×Q₈	1	2	yes	—
218	C₄×C₁₇	C₂³×Q₈	1	1	yes	characteristic
219	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
220	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
221	#557	C₂²×C₁₇	1	8	yes	—
222	#554	—	2	8	no	—
223	#554	C₂²×C₁₇	1	8	yes	—
224	#544	—	2	4	no	—
225	#544	C₂²×C₁₇	1	4	yes	—
226	#533	—	2	2	no	—
227	#533	C₂²×C₁₇	1	1	yes	characteristic
228	C₂×#125	—	2	2	no	—
229	C₂×#125	C₂²×C₁₇	1	2	yes	—
230	#520	C₂²×C₁₇	1	4	yes	—
231	C₄×#41	C₂²×C₁₇	1	2	yes	—
232	#501	C₂²×C₁₇	1	8	yes	—
233	#500	C₂²×C₁₇	1	4	yes	—
234	#499	C₂²×C₁₇	1	4	yes	—
235	#499	C₂²×C₁₇	1	4	yes	—
236	#499	C₂²×C₁₇	1	4	yes	—
237	#479	C₂²×C₁₇	1	8	yes	—
238	#479	C₂²×C₁₇	1	8	yes	—
239	#478	C₂²×C₁₇	1	8	yes	—
240	#478	C₂²×C₁₇	1	8	yes	—
241	#476	C₂²×C₁₇	1	8	yes	—
242	#475	C₂²×C₁₇	1	8	yes	—
243	#446	C₂²×C₁₇	1	4	yes	—
244	C₈×Q₈	C₂²×C₁₇	1	4	yes	—
245	#440	C₂²×C₁₇	1	8	yes	—
246	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
247	C₄×Q₁₆	C₂²×C₁₇	1	4	yes	—
248	C₄×SD₁₆	C₂²×C₁₇	1	4	yes	—
249	C₄×D₈	C₂²×C₁₇	1	2	yes	—
250	C₄×D₈	C₂²×C₁₇	1	4	yes	—
251	#428	C₂²×C₁₇	1	4	yes	—
252	#427	C₂²×C₁₇	1	1	yes	characteristic
253	C₂×#107	C₂²×C₁₇	1	2	yes	—
254	C₂×#106	C₂²×C₁₇	1	2	yes	—
255	#424	C₂²×C₁₇	1	2	yes	—
256	#423	C₂²×C₁₇	1	1	yes	characteristic
257	#417	C₂²×C₁₇	1	4	yes	—
258	#416	C₂²×C₁₇	1	2	yes	—
259	#405	C₂²×C₁₇	1	2	yes	—
260	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
261	C₂×C₁₇	—	2	2	no	—
262	C₂×C₁₇	—	4	4	no	—
263	C₂×C₁₇	C₂×D₄×Q₈	1	1	yes	characteristic
264	C₂×C₁₇	#3584	1	2	yes	—
265	C₂×#41	C₂³×C₁₇	1	2	yes	—
266	#135	Q₈×C₁₇	1	8	yes	complemented
267	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
268	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
269	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
270	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
271	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
273	C₄⋊Q₈	—	2	8	no	—
274	C₄⋊Q₈	—	2	4	no	—
275	C₄⋊Q₈	D₄×C₁₇	1	2	yes	—
276	C₄⋊Q₈	C₂³×C₁₇	1	8	yes	—
277	#125	—	2	4	no	—
278	#125	—	2	8	no	—
279	#125	—	2	8	no	—
280	#125	—	2	2	no	—
281	#125	—	2	2	no	—
282	#125	D₄×C₁₇	1	1	yes	characteristic
283	#125	D₄×C₁₇	1	1	yes	characteristic
284	#125	C₂³×C₁₇	1	8	yes	—
285	#125	C₂³×C₁₇	1	8	yes	—
286	C₂²⋊Q₈	—	2	8	no	—
287	C₂²⋊Q₈	—	2	8	no	—
288	C₂²⋊Q₈	—	2	8	no	—
289	C₂²⋊Q₈	—	2	8	no	—
290	C₂²⋊Q₈	D₄×C₁₇	1	4	yes	—
291	C₄×Q₈	—	2	8	no	—
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	4	no	—
296	C₄×D₄	—	2	8	no	—
297	C₄×D₄	C₂³×C₁₇	1	4	yes	—
298	C₄×D₄	C₂³×C₁₇	1	8	yes	—
299	#117	—	2	4	no	—
300	#117	—	2	2	no	—
301	#117	C₂³×C₁₇	1	2	yes	—
302	#117	C₂³×C₁₇	1	2	yes	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	4	no	—
305	C₂×C₄⋊C₄	—	2	8	no	—
306	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
309	#107	C₂³×C₁₇	1	4	yes	—
310	#107	C₂³×C₁₇	1	4	yes	—
311	#107	C₂³×C₁₇	1	2	yes	—
312	#107	C₂³×C₁₇	1	8	yes	—
313	#106	C₂³×C₁₇	1	8	yes	—
314	#106	C₂³×C₁₇	1	2	yes	—
315	#106	C₂³×C₁₇	1	8	yes	—
316	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
317	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
318	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
319	#103	C₂³×C₁₇	1	4	yes	—
320	#103	C₂³×C₁₇	1	8	yes	—
321	#102	C₂³×C₁₇	1	4	yes	—
322	#102	C₂³×C₁₇	1	8	yes	—
323	#97	C₂³×C₁₇	1	4	yes	—
324	C₄×C₈	C₂³×C₁₇	1	2	yes	—
325	C₄×C₈	C₂³×C₁₇	1	2	yes	—
326	C₄×C₈	C₂³×C₁₇	1	4	yes	—
327	C₁₇	#61376	1	1	yes	characteristic, direct product factor, Sylow
328	#41	—	2	4	no	—
329	#41	C₂×Q₈×C₁₇	1	8	yes	—
330	C₂×Q₈	—	2	8	no	—
331	C₂×Q₈	C₂×D₄×C₁₇	1	4	yes	—
332	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
341	Q₁₆	C₂×Q₈×C₁₇	1	4	yes	—
342	SD₁₆	C₂×Q₈×C₁₇	1	8	yes	—
343	D₈	C₂×Q₈×C₁₇	1	4	yes	—
344	M₁₆	—	2	4	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	C₂×Q₈×C₁₇	1	4	yes	—
347	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
348	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
349	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
350	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	8	no	—
355	C₄⋊C₄	—	2	8	no	—
356	C₄⋊C₄	—	2	8	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
360	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
361	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
362	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
363	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
364	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
365	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	8	no	—
369	C₂²⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	8	no	—
373	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
374	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
375	C₄²	C₂⁴×C₁₇	1	2	yes	—
376	C₄²	C₂⁴×C₁₇	1	4	yes	—
377	C₂³	—	2	2	no	—
378	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	4	4	no	—
381	Q₈	—	8	8	no	—
382	Q₈	C₂²×Q₈×C₁₇	1	4	yes	—
383	D₄	—	2	8	no	—
384	D₄	—	2	2	no	—
385	D₄	C₂²×Q₈×C₁₇	1	4	yes	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	8	4	no	—
392	C₂×C₄	—	8	8	no	—
393	C₂×C₄	—	8	4	no	—
394	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
395	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
396	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
398	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
399	C₂×C₄	C₂²×Q₈×C₁₇	1	2	yes	—
400	C₂×C₄	C₁₇×2₋¹⁺⁴	1	2	yes	—
401	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	2	4	no	—
404	C₈	C₂²×Q₈×C₁₇	1	2	yes	—
405	C₈	C₂²×Q₈×C₁₇	1	2	yes	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	D₄×Q₈×C₁₇	1	2	yes	—
410	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
411	C₄	—	2	4	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	4	no	—
416	C₄	—	4	8	no	—
417	C₄	—	4	4	no	—
418	C₄	D₄×Q₈×C₁₇	1	2	yes	—
419	C₄	C₂³×Q₈×C₁₇	1	1	yes	characteristic
420	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
421	C₂	—	2	2	no	—
422	C₂	—	4	4	no	—
423	C₂	C₂×D₄×Q₈×C₁₇	1	1	yes	characteristic
424	C₂	C₁₇×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₂×C₁₇×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₁₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3504	C₂	semidirect
2. C₁₇×#3388	C₂	semidirect
3. C₁₇×#3383	C₂	semidirect
4. C₁₇×#3380	C₂	semidirect
5. C₁₇×#3164	C₂	semidirect
6. C₂×C₁₇×#499	C₂	semidirect
7. C₁₇×#3084	C₂	semidirect
8. C₁₇×#3080	C₂	semidirect
9. C₁₇×#2960	C₂	semidirect
54. C₁₇×#135	Q₈	semidirect
164. #61376	C₁₇	direct (N × H)
194. #3504	C₂×C₁₇	semidirect
195. #3388	C₂×C₁₇	semidirect
196. #3383	C₂×C₁₇	semidirect
197. #3380	C₂×C₁₇	semidirect
198. #3164	C₂×C₁₇	semidirect
199. C₂×#499	C₂×C₁₇	semidirect
200. #3084	C₂×C₁₇	semidirect
201. #3080	C₂×C₁₇	semidirect
202. #2960	C₂×C₁₇	semidirect
266. #135	Q₈×C₁₇	semidirect
327. C₁₇	#61376	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×#3504	2
C₁₇×#3388	2
C₁₇×#3383	2
C₁₇×#3380	2
C₁₇×#3164	2
C₂×C₁₇×#499	2
C₁₇×#3084	2
C₁₇×#3080	2
C₁₇×#2960	2
C₁₇×#2951	2
C₄×C₁₇×#135	2
#61376	17

Subgroups — C17×#61376 #16919120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61376 #16919120