Subgroups — C₁₇×#19418 #16877162

Order 4352.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3231	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3116	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3107	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2988	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1684	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1683	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1680	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1674	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1673	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1671	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1572	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1552	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1542	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#533	C₂²	1	1	yes	characteristic
17	C₁₇×#533	C₂²	1	1	yes	characteristic
18	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
19	C₁₇×#500	C₂²	1	1	yes	characteristic
20	C₁₇×#498	C₂²	1	1	yes	characteristic
21	C₁₇×#487	C₂²	1	1	yes	characteristic
22	C₁₇×#487	C₂²	1	1	yes	characteristic
23	C₁₇×#485	—	2	1	no	—
24	C₁₇×#485	—	2	1	no	—
25	C₁₇×#485	—	2	1	no	—
26	C₁₇×#485	—	2	1	no	—
27	C₁₇×#479	—	2	1	no	—
28	C₁₇×#479	—	2	1	no	—
29	C₁₇×#477	C₂²	1	1	yes	characteristic
30	C₁₇×#476	C₂²	1	1	yes	characteristic
31	C₁₇×#475	C₂²	1	1	yes	characteristic
32	C₁₇×#474	C₂²	1	1	yes	characteristic
33	C₁₇×#462	C₂²	1	1	yes	characteristic
34	C₁₇×#462	C₂²	1	1	yes	characteristic
35	C₁₇×#461	C₂²	1	1	yes	characteristic
36	C₁₇×#461	C₂²	1	1	yes	characteristic
37	C₁₇×#452	—	2	1	no	—
38	C₁₇×#452	—	2	1	no	—
39	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
41	C₁₇×#441	—	2	1	no	—
42	C₁₇×#440	—	2	1	no	—
43	C₄×Q₁₆×C₁₇	—	2	1	no	—
44	C₄×SD₁₆×C₁₇	—	2	1	no	—
45	C₈×D₄×C₁₇	—	2	1	no	—
46	C₈×D₄×C₁₇	—	2	1	no	—
47	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
48	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
49	C₁₇×#432	C₂²	1	1	yes	characteristic
50	C₁₇×#431	—	2	1	no	—
51	C₁₇×#431	C₂²	1	1	yes	characteristic
52	C₁₇×#431	C₂²	1	1	yes	characteristic
53	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
54	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₁₇×#335	C₂²	1	1	yes	characteristic
56	C₁₇×#335	C₂²	1	1	yes	characteristic
57	C₁₇×#334	C₂²	1	1	yes	characteristic
58	C₁₇×#334	C₂²	1	1	yes	characteristic
59	C₁₇×#333	C₂²	1	1	yes	characteristic
60	C₁₇×#333	C₂²	1	1	yes	characteristic
61	C₁₇×#332	C₂²	1	1	yes	characteristic
62	C₁₇×#332	C₂²	1	1	yes	characteristic
63	C₁₇×#332	C₂²	1	1	yes	characteristic
64	C₁₇×#332	C₂²	1	1	yes	characteristic
65	C₁₇×#332	C₂²	1	1	yes	characteristic
66	C₁₇×#332	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
68	C₂×Q₁₆×C₁₇	—	2	1	no	—
69	C₂×Q₁₆×C₁₇	—	2	1	no	—
70	C₂×SD₁₆×C₁₇	—	2	1	no	—
71	C₂×SD₁₆×C₁₇	—	2	1	no	—
72	C₂²×C₈×C₁₇	—	2	1	no	—
73	C₂²×C₈×C₁₇	—	2	1	no	—
74	C₂²×C₈×C₁₇	—	2	1	no	—
75	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₇×#125	—	2	1	no	—
80	C₁₇×#125	—	2	1	no	—
81	C₁₇×C₂²⋊Q₈	—	2	1	no	—
82	C₁₇×C₂²⋊Q₈	—	2	1	no	—
83	C₁₇×C₂²⋊Q₈	—	2	1	no	—
84	C₁₇×C₂²⋊Q₈	—	2	1	no	—
85	C₄×Q₈×C₁₇	—	2	1	no	—
86	C₄×Q₈×C₁₇	—	2	1	no	—
87	C₄×Q₈×C₁₇	—	2	1	no	—
88	C₄×Q₈×C₁₇	—	2	1	no	—
89	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
91	C₄×D₄×C₁₇	—	2	1	no	—
92	C₄×D₄×C₁₇	—	2	1	no	—
93	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
94	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
95	C₁₇×#117	—	2	1	no	—
96	C₁₇×#117	—	2	1	no	—
97	C₁₇×#117	—	2	1	no	—
98	C₁₇×#117	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₇	—	2	1	no	—
100	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
101	C₁₇×#107	—	2	1	no	—
102	C₁₇×#107	—	2	1	no	—
103	C₁₇×#107	—	2	1	no	—
104	C₁₇×#107	—	2	1	no	—
105	C₁₇×#106	—	2	1	no	—
106	C₁₇×#106	—	2	1	no	—
107	C₁₇×#106	—	2	1	no	—
108	C₁₇×#106	—	2	1	no	—
109	C₁₇×C₄⋊C₈	—	2	1	no	—
110	C₁₇×C₄⋊C₈	—	2	1	no	—
111	C₁₇×C₄⋊C₈	—	2	1	no	—
112	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
113	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
114	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₇×#103	—	2	1	no	—
121	C₁₇×#103	—	2	1	no	—
122	C₁₇×#103	—	2	1	no	—
123	C₁₇×#103	—	2	1	no	—
124	C₁₇×#103	—	2	1	no	—
125	C₁₇×#103	—	2	1	no	—
126	C₁₇×#103	—	2	1	no	—
127	C₁₇×#103	—	2	1	no	—
128	C₁₇×#103	—	2	1	no	—
129	C₁₇×#103	—	2	1	no	—
130	C₁₇×#102	—	2	1	no	—
131	C₁₇×#102	—	2	1	no	—
132	C₁₇×C₂²⋊C₈	—	2	1	no	—
133	C₁₇×C₂²⋊C₈	—	2	1	no	—
134	C₁₇×C₂²⋊C₈	—	2	1	no	—
135	C₁₇×C₂²⋊C₈	—	2	1	no	—
136	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
137	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₇×#97	—	2	1	no	—
139	C₄×C₈×C₁₇	—	2	1	no	—
140	C₄×C₈×C₁₇	—	2	1	no	—
141	C₄×C₈×C₁₇	—	2	1	no	—
142	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
144	#41×C₁₇	—	2	2	no	—
145	#41×C₁₇	—	2	2	no	—
146	C₂×Q₈×C₁₇	—	2	1	no	—
147	C₂×Q₈×C₁₇	—	2	1	no	—
148	C₂×Q₈×C₁₇	—	2	1	no	—
149	C₂×Q₈×C₁₇	—	2	1	no	—
150	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₁₇	—	2	1	no	—
152	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₇	—	2	1	no	—
154	C₂²×C₄×C₁₇	—	2	1	no	—
155	C₂²×C₄×C₁₇	—	2	1	no	—
156	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
159	Q₁₆×C₁₇	—	4	2	no	—
160	Q₁₆×C₁₇	—	4	2	no	—
161	SD₁₆×C₁₇	—	4	2	no	—
162	SD₁₆×C₁₇	—	4	2	no	—
163	C₂×C₈×C₁₇	—	2	1	no	—
164	C₂×C₈×C₁₇	—	2	1	no	—
165	C₂×C₈×C₁₇	—	2	1	no	—
166	C₂×C₈×C₁₇	—	2	1	no	—
167	C₂×C₈×C₁₇	—	2	1	no	—
168	C₂×C₈×C₁₇	—	2	1	no	—
169	C₂×C₈×C₁₇	—	8	1	no	—
170	C₂×C₈×C₁₇	—	8	1	no	—
171	C₂×C₈×C₁₇	—	8	1	no	—
172	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
176	C₄⋊C₄×C₁₇	—	2	1	no	—
177	C₄⋊C₄×C₁₇	—	2	1	no	—
178	C₄⋊C₄×C₁₇	—	2	1	no	—
179	C₄⋊C₄×C₁₇	—	2	1	no	—
180	C₄⋊C₄×C₁₇	—	2	1	no	—
181	C₄⋊C₄×C₁₇	—	2	1	no	—
182	C₄⋊C₄×C₁₇	—	2	1	no	—
183	C₄⋊C₄×C₁₇	—	2	1	no	—
184	C₄⋊C₄×C₁₇	—	2	1	no	—
185	C₄⋊C₄×C₁₇	—	2	1	no	—
186	C₄⋊C₄×C₁₇	—	4	1	no	—
187	C₄⋊C₄×C₁₇	—	4	1	no	—
188	C₄⋊C₄×C₁₇	—	4	1	no	—
189	C₄⋊C₄×C₁₇	—	4	1	no	—
190	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
191	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
192	C₂²⋊C₄×C₁₇	—	2	1	no	—
193	C₂²⋊C₄×C₁₇	—	2	1	no	—
194	C₂²⋊C₄×C₁₇	—	2	1	no	—
195	C₂²⋊C₄×C₁₇	—	4	1	no	—
196	C₂²⋊C₄×C₁₇	—	4	1	no	—
197	C₄²×C₁₇	—	2	1	no	—
198	C₄²×C₁₇	—	2	1	no	—
199	C₄²×C₁₇	—	2	1	no	—
200	C₄²×C₁₇	—	4	1	no	—
201	C₄²×C₁₇	—	4	1	no	—
202	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₇	#41	1	1	yes	characteristic
205	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
206	#19418	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₇	—	2	1	no	—
208	C₂³×C₁₇	#121	1	1	yes	characteristic
209	Q₈×C₁₇	—	2	1	no	—
210	Q₈×C₁₇	—	4	1	no	—
211	Q₈×C₁₇	—	4	1	no	—
212	Q₈×C₁₇	—	4	1	no	—
213	Q₈×C₁₇	—	4	1	no	—
214	Q₈×C₁₇	—	4	1	no	—
215	Q₈×C₁₇	—	4	1	no	—
216	Q₈×C₁₇	—	8	1	no	—
217	Q₈×C₁₇	#135	1	2	yes	—
218	D₄×C₁₇	—	2	4	no	—
219	D₄×C₁₇	—	2	1	no	—
220	D₄×C₁₇	#135	1	2	yes	—
221	C₂×C₄×C₁₇	—	2	4	no	—
222	C₂×C₄×C₁₇	—	2	1	no	—
223	C₂×C₄×C₁₇	—	2	1	no	—
224	C₂×C₄×C₁₇	—	2	1	no	—
225	C₂×C₄×C₁₇	—	2	1	no	—
226	C₂×C₄×C₁₇	—	2	1	no	—
227	C₂×C₄×C₁₇	—	2	1	no	—
228	C₂×C₄×C₁₇	—	2	1	no	—
229	C₂×C₄×C₁₇	—	4	1	no	—
230	C₂×C₄×C₁₇	—	4	1	no	—
231	C₂×C₄×C₁₇	—	4	1	no	—
232	C₂×C₄×C₁₇	—	4	1	no	—
233	C₂×C₄×C₁₇	—	4	1	no	—
234	C₂×C₄×C₁₇	—	4	1	no	—
235	C₂×C₄×C₁₇	—	4	1	no	—
236	C₂×C₄×C₁₇	—	8	1	no	—
237	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
238	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
239	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
240	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
243	C₈×C₁₇	—	2	1	no	—
244	C₈×C₁₇	—	2	1	no	—
245	C₈×C₁₇	—	2	1	no	—
246	C₈×C₁₇	—	2	1	no	—
247	C₈×C₁₇	—	4	1	no	—
248	C₈×C₁₇	—	4	1	no	—
249	C₈×C₁₇	—	4	1	no	—
250	C₈×C₁₇	—	4	1	no	—
251	C₈×C₁₇	—	4	1	no	—
252	C₈×C₁₇	—	4	1	no	—
253	#3231	C₂×C₁₇	1	1	yes	characteristic, complemented
254	#3116	C₂×C₁₇	1	1	yes	characteristic
255	#3107	C₂×C₁₇	1	1	yes	characteristic
256	#2988	C₂×C₁₇	1	1	yes	characteristic
257	#1684	C₂×C₁₇	1	1	yes	characteristic, complemented
258	#1683	C₂×C₁₇	1	1	yes	characteristic, complemented
259	#1680	C₂×C₁₇	1	1	yes	characteristic, complemented
260	#1679	C₂×C₁₇	1	1	yes	characteristic, complemented
261	#1674	C₂×C₁₇	1	1	yes	characteristic, complemented
262	#1673	C₂×C₁₇	1	1	yes	characteristic, complemented
263	#1672	C₂×C₁₇	1	1	yes	characteristic, complemented
264	#1671	C₂×C₁₇	1	1	yes	characteristic, complemented
265	#1572	C₂×C₁₇	1	1	yes	characteristic, complemented
266	#1552	C₂×C₁₇	1	1	yes	characteristic, complemented
267	#1542	C₂×C₁₇	1	1	yes	characteristic, complemented
268	C₂²×C₁₇	—	2	1	no	—
269	C₂²×C₁₇	—	2	1	no	—
270	C₂²×C₁₇	—	2	2	no	—
271	C₂²×C₁₇	—	2	1	no	—
272	C₂²×C₁₇	—	4	1	no	—
273	C₂²×C₁₇	—	4	1	no	—
274	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
275	C₄×C₁₇	—	2	1	no	—
276	C₄×C₁₇	—	2	1	no	—
277	C₄×C₁₇	—	2	2	no	—
278	C₄×C₁₇	—	2	1	no	—
279	C₄×C₁₇	—	2	1	no	—
280	C₄×C₁₇	—	4	1	no	—
281	C₄×C₁₇	—	4	1	no	—
282	C₄×C₁₇	—	8	1	no	—
283	C₄×C₁₇	—	8	1	no	—
284	C₄×C₁₇	—	8	1	no	—
285	C₄×C₁₇	—	8	1	no	—
286	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
287	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
288	C₄×C₁₇	#577	1	1	yes	characteristic
289	C₄×C₁₇	#578	1	1	yes	characteristic
290	#533	C₂²×C₁₇	1	1	yes	characteristic
291	#533	C₂²×C₁₇	1	1	yes	characteristic
292	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
293	#500	C₂²×C₁₇	1	1	yes	characteristic
294	#498	C₂²×C₁₇	1	1	yes	characteristic
295	#487	C₂²×C₁₇	1	1	yes	characteristic
296	#487	C₂²×C₁₇	1	1	yes	characteristic
297	#485	—	2	1	no	—
298	#485	—	2	1	no	—
299	#485	—	2	1	no	—
300	#485	—	2	1	no	—
301	#479	—	2	1	no	—
302	#479	—	2	1	no	—
303	#477	C₂²×C₁₇	1	1	yes	characteristic
304	#476	C₂²×C₁₇	1	1	yes	characteristic
305	#475	C₂²×C₁₇	1	1	yes	characteristic
306	#474	C₂²×C₁₇	1	1	yes	characteristic
307	#462	C₂²×C₁₇	1	1	yes	characteristic
308	#462	C₂²×C₁₇	1	1	yes	characteristic
309	#461	C₂²×C₁₇	1	1	yes	characteristic
310	#461	C₂²×C₁₇	1	1	yes	characteristic
311	#452	—	2	1	no	—
312	#452	—	2	1	no	—
313	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
314	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
315	#441	—	2	1	no	—
316	#440	—	2	1	no	—
317	C₄×Q₁₆	—	2	1	no	—
318	C₄×SD₁₆	—	2	1	no	—
319	C₈×D₄	—	2	1	no	—
320	C₈×D₄	—	2	1	no	—
321	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
322	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
323	#432	C₂²×C₁₇	1	1	yes	characteristic
324	#431	—	2	1	no	—
325	#431	C₂²×C₁₇	1	1	yes	characteristic
326	#431	C₂²×C₁₇	1	1	yes	characteristic
327	C₂×C₄⋊C₈	—	2	1	no	—
328	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
329	#335	C₂²×C₁₇	1	1	yes	characteristic
330	#335	C₂²×C₁₇	1	1	yes	characteristic
331	#334	C₂²×C₁₇	1	1	yes	characteristic
332	#334	C₂²×C₁₇	1	1	yes	characteristic
333	#333	C₂²×C₁₇	1	1	yes	characteristic
334	#333	C₂²×C₁₇	1	1	yes	characteristic
335	#332	C₂²×C₁₇	1	1	yes	characteristic
336	#332	C₂²×C₁₇	1	1	yes	characteristic
337	#332	C₂²×C₁₇	1	1	yes	characteristic
338	#332	C₂²×C₁₇	1	1	yes	characteristic
339	#332	C₂²×C₁₇	1	1	yes	characteristic
340	#332	C₂²×C₁₇	1	1	yes	characteristic
341	C₂×C₁₇	—	4	1	no	—
342	C₂×C₁₇	—	4	2	no	—
343	C₂×C₁₇	#3046	1	1	yes	characteristic
344	C₂×C₁₇	#3050	1	1	yes	characteristic
345	C₂×C₁₇	#3069	1	1	yes	characteristic
346	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
347	C₂×Q₁₆	—	2	1	no	—
348	C₂×Q₁₆	—	2	1	no	—
349	C₂×SD₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	2	1	no	—
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₂²×C₈	—	2	1	no	—
354	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
356	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
357	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
358	#125	—	2	1	no	—
359	#125	—	2	1	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₂²⋊Q₈	—	2	1	no	—
362	C₂²⋊Q₈	—	2	1	no	—
363	C₂²⋊Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
369	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
373	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	D₄×C₁₇	1	1	yes	characteristic
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
380	#107	—	2	1	no	—
381	#107	—	2	1	no	—
382	#107	—	2	1	no	—
383	#107	—	2	1	no	—
384	#106	—	2	1	no	—
385	#106	—	2	1	no	—
386	#106	—	2	1	no	—
387	#106	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
392	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
395	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
396	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
416	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
417	#97	—	2	1	no	—
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	—	2	1	no	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
422	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
423	C₁₇	#19418	1	1	yes	characteristic, direct product factor, Sylow
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
438	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
439	Q₁₆	—	4	2	no	—
440	Q₁₆	—	4	2	no	—
441	SD₁₆	—	4	2	no	—
442	SD₁₆	—	4	2	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	8	1	no	—
450	C₂×C₈	—	8	1	no	—
451	C₂×C₈	—	8	1	no	—
452	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
453	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
454	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
455	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
471	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	4	1	no	—
481	C₄²	—	4	1	no	—
482	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
483	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
484	C₄²	#41×C₁₇	1	1	yes	characteristic
485	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
486	C₂³	—	2	1	no	—
487	C₂³	C₁₇×#121	1	1	yes	characteristic
488	Q₈	—	2	1	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	4	1	no	—
495	Q₈	—	8	1	no	—
496	Q₈	C₁₇×#135	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	1	no	—
499	D₄	C₁₇×#135	1	2	yes	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	8	1	no	—
516	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
517	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
518	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
521	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
551	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
552	C₄	C₁₇×#577	1	1	yes	characteristic
553	C₄	C₁₇×#578	1	1	yes	characteristic
554	C₂	—	4	1	no	—
555	C₂	—	4	2	no	—
556	C₂	C₁₇×#3046	1	1	yes	characteristic
557	C₂	C₁₇×#3050	1	1	yes	characteristic
558	C₂	C₁₇×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₂×#41×C₁₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3231	C₂	semidirect
5. C₁₇×#1684	C₂	semidirect
6. C₁₇×#1683	C₂	semidirect
7. C₁₇×#1680	C₂	semidirect
8. C₁₇×#1679	C₂	semidirect
9. C₁₇×#1674	C₂	semidirect
10. C₁₇×#1673	C₂	semidirect
11. C₁₇×#1672	C₂	semidirect
12. C₁₇×#1671	C₂	semidirect
13. C₁₇×#1572	C₂	semidirect
14. C₁₇×#1552	C₂	semidirect
15. C₁₇×#1542	C₂	semidirect
206. #19418	C₁₇	direct (N × H)
253. #3231	C₂×C₁₇	semidirect
257. #1684	C₂×C₁₇	semidirect
258. #1683	C₂×C₁₇	semidirect
259. #1680	C₂×C₁₇	semidirect
260. #1679	C₂×C₁₇	semidirect
261. #1674	C₂×C₁₇	semidirect
262. #1673	C₂×C₁₇	semidirect
263. #1672	C₂×C₁₇	semidirect
264. #1671	C₂×C₁₇	semidirect
265. #1572	C₂×C₁₇	semidirect
266. #1552	C₂×C₁₇	semidirect
267. #1542	C₂×C₁₇	semidirect
423. C₁₇	#19418	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×#3231	2
C₁₇×#3116	2
C₁₇×#3107	2
C₁₇×#2988	2
C₁₇×#1684	2
C₁₇×#1683	2
C₁₇×#1680	2
C₁₇×#1679	2
C₁₇×#1674	2
C₁₇×#1673	2
C₁₇×#1672	2
C₁₇×#1671	2
C₁₇×#1572	2
C₁₇×#1552	2
C₁₇×#1542	2
#19418	17

Subgroups — C17×#19418 #16877162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#19418 #16877162