Subgroups — C₁₇×#19863 #16877607

Order 4352.

594 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3393	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3353	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3340	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3303	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1723	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1684	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1673	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1669	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1650	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1647	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1646	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1638	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#556	C₂²	1	1	yes	characteristic
17	C₁₇×#556	C₂²	1	1	yes	characteristic
18	C₁₇×#555	C₂²	1	1	yes	characteristic
19	C₁₇×#547	C₂²	1	1	yes	characteristic
20	C₁₇×#500	C₂²	1	1	yes	characteristic
21	C₁₇×#500	C₂²	1	1	yes	characteristic
22	C₁₇×#498	C₂²	1	1	yes	characteristic
23	C₁₇×#495	—	2	1	no	—
24	C₁₇×#494	C₂²	1	1	yes	characteristic
25	C₁₇×#487	C₂²	1	1	yes	characteristic
26	C₁₇×#487	C₂²	1	1	yes	characteristic
27	C₁₇×#485	—	2	1	no	—
28	C₁₇×#485	—	2	1	no	—
29	C₁₇×#484	—	2	1	no	—
30	C₁₇×#482	—	2	1	no	—
31	C₁₇×#482	—	2	1	no	—
32	C₁₇×#477	C₂²	1	1	yes	characteristic
33	C₁₇×#476	C₂²	1	1	yes	characteristic
34	C₁₇×#475	C₂²	1	1	yes	characteristic
35	C₁₇×#474	C₂²	1	1	yes	characteristic
36	C₁₇×#474	C₂²	1	1	yes	characteristic
37	C₁₇×#468	—	2	1	no	—
38	C₁₇×#465	—	2	1	no	—
39	C₁₇×#465	—	2	1	no	—
40	C₁₇×#464	—	2	1	no	—
41	C₁₇×#464	—	2	1	no	—
42	C₁₇×#461	C₂²	1	1	yes	characteristic
43	C₁₇×#461	C₂²	1	1	yes	characteristic
44	C₁₇×#461	C₂²	1	1	yes	characteristic
45	C₁₇×#449	—	2	1	no	—
46	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
47	C₄×Q₁₆×C₁₇	—	2	1	no	—
48	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
49	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
50	C₁₇×#436	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
53	C₁₇×#428	—	2	1	no	—
54	C₁₇×#427	—	2	1	no	—
55	C₁₇×#416	—	2	1	no	—
56	C₁₇×#335	C₂²	1	1	yes	characteristic
57	C₁₇×#335	C₂²	1	1	yes	characteristic
58	C₁₇×#333	C₂²	1	1	yes	characteristic
59	C₁₇×#332	C₂²	1	1	yes	characteristic
60	C₁₇×#332	C₂²	1	1	yes	characteristic
61	C₁₇×#332	C₂²	1	1	yes	characteristic
62	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₇×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₇	—	2	1	no	—
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	C₂×SD₁₆×C₁₇	—	2	1	no	—
73	C₂×SD₁₆×C₁₇	D₄	1	1	yes	characteristic
74	C₂×D₈×C₁₇	D₄	1	1	yes	characteristic
75	C₂×M₁₆×C₁₇	—	2	1	no	—
76	C₂²×C₈×C₁₇	—	2	1	no	—
77	C₂²×C₈×C₁₇	—	2	1	no	—
78	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₇×#126	—	4	1	no	—
83	C₁₇×#126	—	4	1	no	—
84	C₁₇×#124	—	2	1	no	—
85	C₁₇×#124	—	2	1	no	—
86	C₁₇×#124	—	4	1	no	—
87	C₁₇×#123	—	4	1	no	—
88	C₁₇×C₂²⋊Q₈	—	2	1	no	—
89	C₁₇×C₂²⋊Q₈	—	2	1	no	—
90	C₁₇×C₂²⋊Q₈	—	2	1	no	—
91	C₁₇×#121	—	2	1	no	—
92	C₁₇×#121	—	2	1	no	—
93	C₁₇×#121	—	2	1	no	—
94	C₄×Q₈×C₁₇	—	2	1	no	—
95	C₄×Q₈×C₁₇	—	2	1	no	—
96	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
100	C₁₇×#117	—	2	1	no	—
101	C₁₇×#117	—	2	1	no	—
102	C₁₇×#117	—	2	1	no	—
103	C₁₇×#117	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
105	C₁₇×#107	—	2	1	no	—
106	C₁₇×#107	—	2	1	no	—
107	C₁₇×#107	—	2	1	no	—
108	C₁₇×#107	—	2	1	no	—
109	C₁₇×#107	—	2	1	no	—
110	C₁₇×#107	—	4	1	no	—
111	C₁₇×#107	D₄	1	1	yes	characteristic
112	C₁₇×#106	—	2	1	no	—
113	C₁₇×#106	—	2	1	no	—
114	C₁₇×#106	—	2	1	no	—
115	C₁₇×#106	—	2	1	no	—
116	C₁₇×#106	D₄	1	1	yes	characteristic
117	C₁₇×C₄⋊C₈	—	2	1	no	—
118	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	—	4	1	no	—
130	C₁₇×#103	D₄	1	1	yes	characteristic
131	C₁₇×#102	—	2	1	no	—
132	C₁₇×#102	—	2	1	no	—
133	C₁₇×#102	—	2	1	no	—
134	C₁₇×#102	D₄	1	1	yes	characteristic
135	C₁₇×#102	D₄	1	1	yes	characteristic
136	C₁₇×#102	D₄	1	1	yes	characteristic
137	C₁₇×C₂²⋊C₈	—	2	1	no	—
138	C₁₇×C₂²⋊C₈	—	2	1	no	—
139	C₁₇×C₂²⋊C₈	—	2	1	no	—
140	C₄×C₈×C₁₇	—	2	1	no	—
141	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
144	#41×C₁₇	—	4	2	no	—
145	#41×C₁₇	—	8	1	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	—	4	1	no	—
152	C₂×D₄×C₁₇	—	4	1	no	—
153	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₇	—	2	1	no	—
157	C₂²×C₄×C₁₇	—	2	1	no	—
158	C₂²×C₄×C₁₇	—	2	1	no	—
159	C₂²×C₄×C₁₇	—	4	1	no	—
160	Q₁₆×C₁₇	—	4	2	no	—
161	Q₁₆×C₁₇	—	8	1	no	—
162	SD₁₆×C₁₇	—	2	2	no	—
163	SD₁₆×C₁₇	—	8	1	no	—
164	SD₁₆×C₁₇	—	8	1	no	—
165	SD₁₆×C₁₇	—	8	1	no	—
166	D₈×C₁₇	—	4	1	no	—
167	M₁₆×C₁₇	—	4	2	no	—
168	C₂×C₈×C₁₇	—	2	1	no	—
169	C₂×C₈×C₁₇	—	2	1	no	—
170	C₂×C₈×C₁₇	—	2	1	no	—
171	C₂×C₈×C₁₇	—	2	1	no	—
172	C₂×C₈×C₁₇	—	2	1	no	—
173	C₂×C₈×C₁₇	—	4	2	no	—
174	C₂×C₈×C₁₇	—	8	1	no	—
175	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
187	C₄⋊C₄×C₁₇	—	2	1	no	—
188	C₄⋊C₄×C₁₇	—	4	1	no	—
189	C₄⋊C₄×C₁₇	—	4	1	no	—
190	C₄⋊C₄×C₁₇	—	4	1	no	—
191	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
195	C₂²⋊C₄×C₁₇	—	2	1	no	—
196	C₂²⋊C₄×C₁₇	—	2	1	no	—
197	C₂²⋊C₄×C₁₇	—	2	1	no	—
198	C₂²⋊C₄×C₁₇	—	4	1	no	—
199	C₂²⋊C₄×C₁₇	—	4	1	no	—
200	C₂²⋊C₄×C₁₇	—	4	1	no	—
201	C₂²⋊C₄×C₁₇	—	4	1	no	—
202	C₂²⋊C₄×C₁₇	—	4	1	no	—
203	C₂²⋊C₄×C₁₇	—	4	1	no	—
204	C₂²⋊C₄×C₁₇	—	4	1	no	—
205	C₄²×C₁₇	—	2	1	no	—
206	C₄²×C₁₇	—	4	1	no	—
207	C₄²×C₁₇	—	4	1	no	—
208	C₄²×C₁₇	—	4	1	no	—
209	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
210	#19863	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₁₇	—	2	1	no	—
212	C₂³×C₁₇	—	2	1	no	—
213	C₂³×C₁₇	—	2	1	no	—
214	Q₈×C₁₇	—	2	1	no	—
215	Q₈×C₁₇	—	2	1	no	—
216	Q₈×C₁₇	—	4	1	no	—
217	Q₈×C₁₇	—	4	1	no	—
218	Q₈×C₁₇	—	4	1	no	—
219	Q₈×C₁₇	—	4	1	no	—
220	Q₈×C₁₇	—	4	1	no	—
221	Q₈×C₁₇	—	4	1	no	—
222	Q₈×C₁₇	—	8	1	no	—
223	D₄×C₁₇	—	2	1	no	—
224	D₄×C₁₇	—	2	1	no	—
225	D₄×C₁₇	—	2	1	no	—
226	D₄×C₁₇	—	2	1	no	—
227	D₄×C₁₇	—	2	1	no	—
228	D₄×C₁₇	—	2	1	no	—
229	D₄×C₁₇	—	8	2	no	—
230	D₄×C₁₇	—	16	1	no	—
231	C₂×C₄×C₁₇	—	2	1	no	—
232	C₂×C₄×C₁₇	—	2	1	no	—
233	C₂×C₄×C₁₇	—	2	1	no	—
234	C₂×C₄×C₁₇	—	2	1	no	—
235	C₂×C₄×C₁₇	—	2	1	no	—
236	C₂×C₄×C₁₇	—	4	1	no	—
237	C₂×C₄×C₁₇	—	4	1	no	—
238	C₂×C₄×C₁₇	—	4	1	no	—
239	C₂×C₄×C₁₇	—	4	1	no	—
240	C₂×C₄×C₁₇	—	4	1	no	—
241	C₂×C₄×C₁₇	—	4	1	no	—
242	C₂×C₄×C₁₇	—	4	1	no	—
243	C₂×C₄×C₁₇	—	4	1	no	—
244	C₂×C₄×C₁₇	—	4	1	no	—
245	C₂×C₄×C₁₇	—	4	1	no	—
246	C₂×C₄×C₁₇	—	8	2	no	—
247	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
250	C₈×C₁₇	—	2	1	no	—
251	C₈×C₁₇	—	2	1	no	—
252	C₈×C₁₇	—	2	1	no	—
253	C₈×C₁₇	—	4	1	no	—
254	C₈×C₁₇	—	4	1	no	—
255	C₈×C₁₇	—	4	1	no	—
256	C₈×C₁₇	—	4	1	no	—
257	C₈×C₁₇	—	4	1	no	—
258	C₈×C₁₇	#135	1	2	yes	—
259	#3393	C₂×C₁₇	1	1	yes	characteristic, complemented
260	#3353	C₂×C₁₇	1	1	yes	characteristic, complemented
261	#3340	C₂×C₁₇	1	1	yes	characteristic, complemented
262	#3303	C₂×C₁₇	1	1	yes	characteristic
263	#1723	C₂×C₁₇	1	1	yes	characteristic, complemented
264	#1691	C₂×C₁₇	1	1	yes	characteristic, complemented
265	#1684	C₂×C₁₇	1	1	yes	characteristic, complemented
266	#1673	C₂×C₁₇	1	1	yes	characteristic, complemented
267	#1669	C₂×C₁₇	1	1	yes	characteristic, complemented
268	#1650	C₂×C₁₇	1	1	yes	characteristic, complemented
269	#1647	C₂×C₁₇	1	1	yes	characteristic, complemented
270	#1646	C₂×C₁₇	1	1	yes	characteristic, complemented
271	#1638	C₂×C₁₇	1	1	yes	characteristic, complemented
272	#1581	C₂×C₁₇	1	1	yes	characteristic, complemented
273	SD₁₆⋊C₈	C₂×C₁₇	1	1	yes	characteristic, complemented
274	C₂²×C₁₇	—	4	1	no	—
275	C₂²×C₁₇	—	4	1	no	—
276	C₂²×C₁₇	—	4	1	no	—
277	C₂²×C₁₇	—	4	1	no	—
278	C₂²×C₁₇	—	4	1	no	—
279	C₂²×C₁₇	—	4	1	no	—
280	C₂²×C₁₇	—	4	1	no	—
281	C₂²×C₁₇	—	4	1	no	—
282	C₂²×C₁₇	—	4	1	no	—
283	C₂²×C₁₇	D₄²	1	1	yes	characteristic
284	C₄×C₁₇	—	2	1	no	—
285	C₄×C₁₇	—	4	1	no	—
286	C₄×C₁₇	—	4	1	no	—
287	C₄×C₁₇	—	4	1	no	—
288	C₄×C₁₇	—	4	1	no	—
289	C₄×C₁₇	—	4	1	no	—
290	C₄×C₁₇	—	8	1	no	—
291	C₄×C₁₇	—	8	1	no	—
292	C₄×C₁₇	—	8	1	no	—
293	C₄×C₁₇	—	8	1	no	—
294	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
295	C₄×C₁₇	#575	1	1	yes	characteristic
296	C₄×C₁₇	#576	1	1	yes	characteristic
297	C₄×C₁₇	#578	1	1	yes	characteristic
298	#556	C₂²×C₁₇	1	1	yes	characteristic
299	#556	C₂²×C₁₇	1	1	yes	characteristic
300	#555	C₂²×C₁₇	1	1	yes	characteristic
301	#547	C₂²×C₁₇	1	1	yes	characteristic
302	#500	C₂²×C₁₇	1	1	yes	characteristic
303	#500	C₂²×C₁₇	1	1	yes	characteristic
304	#498	C₂²×C₁₇	1	1	yes	characteristic
305	#495	—	2	1	no	—
306	#494	C₂²×C₁₇	1	1	yes	characteristic
307	#487	C₂²×C₁₇	1	1	yes	characteristic
308	#487	C₂²×C₁₇	1	1	yes	characteristic
309	#485	—	2	1	no	—
310	#485	—	2	1	no	—
311	#484	—	2	1	no	—
312	#482	—	2	1	no	—
313	#482	—	2	1	no	—
314	#477	C₂²×C₁₇	1	1	yes	characteristic
315	#476	C₂²×C₁₇	1	1	yes	characteristic
316	#475	C₂²×C₁₇	1	1	yes	characteristic
317	#474	C₂²×C₁₇	1	1	yes	characteristic
318	#474	C₂²×C₁₇	1	1	yes	characteristic
319	#468	—	2	1	no	—
320	#465	—	2	1	no	—
321	#465	—	2	1	no	—
322	#464	—	2	1	no	—
323	#464	—	2	1	no	—
324	#461	C₂²×C₁₇	1	1	yes	characteristic
325	#461	C₂²×C₁₇	1	1	yes	characteristic
326	#461	C₂²×C₁₇	1	1	yes	characteristic
327	#449	—	2	1	no	—
328	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
329	C₄×Q₁₆	—	2	1	no	—
330	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
331	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
332	#436	C₂²×C₁₇	1	1	yes	characteristic
333	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
334	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
335	#428	—	2	1	no	—
336	#427	—	2	1	no	—
337	#416	—	2	1	no	—
338	#335	C₂²×C₁₇	1	1	yes	characteristic
339	#335	C₂²×C₁₇	1	1	yes	characteristic
340	#333	C₂²×C₁₇	1	1	yes	characteristic
341	#332	C₂²×C₁₇	1	1	yes	characteristic
342	#332	C₂²×C₁₇	1	1	yes	characteristic
343	#332	C₂²×C₁₇	1	1	yes	characteristic
344	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
345	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
346	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
347	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
348	#322	C₂²×C₁₇	1	1	yes	characteristic
349	C₂×C₁₇	—	8	1	no	—
350	C₂×C₁₇	—	8	1	no	—
351	C₂×C₁₇	—	8	1	no	—
352	C₂×C₁₇	#3268	1	1	yes	characteristic
353	C₂×C₁₇	#3283	1	1	yes	characteristic
354	C₂×C₁₇	#3289	1	1	yes	characteristic
355	C₂×#41	—	2	1	no	—
356	C₂×Q₁₆	—	2	1	no	—
357	C₂×Q₁₆	—	2	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×SD₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×SD₁₆	D₄×C₁₇	1	1	yes	characteristic
362	C₂×D₈	D₄×C₁₇	1	1	yes	characteristic
363	C₂×M₁₆	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
367	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
368	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
370	#126	—	4	1	no	—
371	#126	—	4	1	no	—
372	#124	—	2	1	no	—
373	#124	—	2	1	no	—
374	#124	—	4	1	no	—
375	#123	—	4	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	#121	—	2	1	no	—
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
385	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
386	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
387	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
388	#117	—	2	1	no	—
389	#117	—	2	1	no	—
390	#117	—	2	1	no	—
391	#117	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	#107	—	2	1	no	—
394	#107	—	2	1	no	—
395	#107	—	2	1	no	—
396	#107	—	2	1	no	—
397	#107	—	2	1	no	—
398	#107	—	4	1	no	—
399	#107	D₄×C₁₇	1	1	yes	characteristic
400	#106	—	2	1	no	—
401	#106	—	2	1	no	—
402	#106	—	2	1	no	—
403	#106	—	2	1	no	—
404	#106	D₄×C₁₇	1	1	yes	characteristic
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	4	1	no	—
418	#103	D₄×C₁₇	1	1	yes	characteristic
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	D₄×C₁₇	1	1	yes	characteristic
423	#102	D₄×C₁₇	1	1	yes	characteristic
424	#102	D₄×C₁₇	1	1	yes	characteristic
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₄×C₈	—	2	1	no	—
429	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
431	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
432	C₁₇	#19863	1	1	yes	characteristic, direct product factor, Sylow
433	#41	—	4	2	no	—
434	#41	—	8	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
443	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
444	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	4	1	no	—
449	Q₁₆	—	4	2	no	—
450	Q₁₆	—	8	1	no	—
451	SD₁₆	—	2	2	no	—
452	SD₁₆	—	8	1	no	—
453	SD₁₆	—	8	1	no	—
454	SD₁₆	—	8	1	no	—
455	D₈	—	4	1	no	—
456	M₁₆	—	4	2	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	4	2	no	—
463	C₂×C₈	—	8	1	no	—
464	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
465	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
466	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
467	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
481	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
482	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
483	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	4	1	no	—
496	C₄²	—	4	1	no	—
497	C₄²	—	4	1	no	—
498	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	8	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	2	1	no	—
513	D₄	—	2	1	no	—
514	D₄	—	2	1	no	—
515	D₄	—	2	1	no	—
516	D₄	—	2	1	no	—
517	D₄	—	8	2	no	—
518	D₄	—	16	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
537	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	C₁₇×#135	1	2	yes	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	D₄²×C₁₇	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	—	8	1	no	—
567	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
568	C₄	C₁₇×#575	1	1	yes	characteristic
569	C₄	C₁₇×#576	1	1	yes	characteristic
570	C₄	C₁₇×#578	1	1	yes	characteristic
571	C₂	—	8	1	no	—
572	C₂	—	8	1	no	—
573	C₂	—	8	1	no	—
574	C₂	C₁₇×#3268	1	1	yes	characteristic
575	C₂	C₁₇×#3283	1	1	yes	characteristic
576	C₂	C₁₇×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#3303	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3393	C₂	semidirect
2. C₁₇×#3353	C₂	semidirect
3. C₁₇×#3340	C₂	semidirect
5. C₁₇×#1723	C₂	semidirect
6. C₁₇×#1691	C₂	semidirect
7. C₁₇×#1684	C₂	semidirect
8. C₁₇×#1673	C₂	semidirect
9. C₁₇×#1669	C₂	semidirect
10. C₁₇×#1650	C₂	semidirect
11. C₁₇×#1647	C₂	semidirect
12. C₁₇×#1646	C₂	semidirect
13. C₁₇×#1638	C₂	semidirect
14. C₁₇×#1581	C₂	semidirect
15. C₁₇×SD₁₆⋊C₈	C₂	semidirect
210. #19863	C₁₇	direct (N × H)
259. #3393	C₂×C₁₇	semidirect
260. #3353	C₂×C₁₇	semidirect
261. #3340	C₂×C₁₇	semidirect
263. #1723	C₂×C₁₇	semidirect
264. #1691	C₂×C₁₇	semidirect
265. #1684	C₂×C₁₇	semidirect
266. #1673	C₂×C₁₇	semidirect
267. #1669	C₂×C₁₇	semidirect
268. #1650	C₂×C₁₇	semidirect
269. #1647	C₂×C₁₇	semidirect
270. #1646	C₂×C₁₇	semidirect
271. #1638	C₂×C₁₇	semidirect
272. #1581	C₂×C₁₇	semidirect
273. SD₁₆⋊C₈	C₂×C₁₇	semidirect
432. C₁₇	#19863	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×#3393	2
C₁₇×#3353	2
C₁₇×#3340	2
C₁₇×#3303	2
C₁₇×#1723	2
C₁₇×#1691	2
C₁₇×#1684	2
C₁₇×#1673	2
C₁₇×#1669	2
C₁₇×#1650	2
C₁₇×#1647	2
C₁₇×#1646	2
C₁₇×#1638	2
C₁₇×#1581	2
C₁₇×SD₁₆⋊C₈	2
#19863	17

Subgroups — C17×#19863 #16877607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#19863 #16877607