Subgroups — C₁₇×#10944 #16868688

Order 4352.

930 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#421	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#416	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₇×#410	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1740	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1735	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
11	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
12	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
15	C₁₇×#421	—	2	2	no	—
16	C₁₇×#421	C₄	1	4	yes	complemented
17	C₂×C₁₇×#104	—	2	2	no	—
18	C₁₇×#416	—	2	2	no	—
19	C₁₇×#416	—	2	1	no	—
20	C₁₇×#416	—	2	1	no	—
21	C₂×C₁₇×#103	C₄	1	2	yes	complemented
22	C₂×C₁₇×#102	C₄	1	2	yes	complemented
23	C₁₇×#410	—	2	2	no	—
24	C₁₇×#410	C₄	1	4	yes	complemented
25	C₂×C₁₇×#99	—	2	2	no	—
26	C₁₇×#405	—	2	2	no	—
27	C₁₇×#405	—	2	2	no	—
28	C₂×C₁₇×#97	—	2	1	no	—
29	C₂×C₄×C₈×C₁₇	—	2	1	no	—
30	C₁₇×#342	—	2	2	no	—
31	C₁₇×#340	—	2	2	no	—
32	C₁₇×#339	—	2	2	no	—
33	C₂×#41×C₁₇	—	2	1	no	—
34	C₂×#41×C₁₇	—	2	1	no	—
35	C₂×#41×C₁₇	—	2	1	no	—
36	C₂×#41×C₁₇	—	2	1	no	—
37	C₂×#41×C₁₇	—	2	1	no	—
38	C₂×#41×C₁₇	—	2	1	no	—
39	C₂×#41×C₁₇	—	2	1	no	—
40	C₂×#41×C₁₇	—	2	1	no	—
41	C₂×#41×C₁₇	—	2	1	no	—
42	C₂×#41×C₁₇	—	2	1	no	—
43	C₂×#41×C₁₇	C₂×C₄	1	2	yes	—
44	C₂×#41×C₁₇	C₂×C₄	1	2	yes	—
45	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₇	—	2	1	no	—
47	C₂²×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₇	—	2	1	no	—
49	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₁₇	—	2	1	no	—
51	C₂×M₁₆×C₁₇	—	2	1	no	—
52	C₂×M₁₆×C₁₇	—	2	1	no	—
53	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
54	C₂×M₁₆×C₁₇	D₄	1	2	yes	—
55	C₂×M₁₆×C₁₇	D₄	1	2	yes	—
56	C₂²×C₈×C₁₇	—	2	1	no	—
57	C₂²×C₈×C₁₇	—	2	1	no	—
58	C₂²×C₈×C₁₇	—	2	1	no	—
59	C₂²×C₈×C₁₇	—	2	1	no	—
60	C₂²×C₈×C₁₇	—	2	1	no	—
61	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
62	C₂²×C₈×C₁₇	D₄	1	2	yes	—
63	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
65	C₁₇×#117	—	2	1	no	—
66	C₁₇×#117	—	2	1	no	—
67	C₁₇×#117	—	2	1	no	—
68	C₁₇×#117	—	2	1	no	—
69	C₁₇×#117	—	2	1	no	—
70	C₁₇×#117	—	2	1	no	—
71	C₁₇×#117	—	2	1	no	—
72	C₁₇×#117	—	2	1	no	—
73	C₁₇×#117	—	2	1	no	—
74	C₁₇×#117	—	2	1	no	—
75	C₁₇×#117	—	2	1	no	—
76	C₁₇×#117	—	2	1	no	—
77	C₁₇×#117	C₂×C₄	1	2	yes	—
78	C₁₇×#117	C₂×C₄	1	2	yes	—
79	C₁₇×#117	C₂×C₄	1	2	yes	—
80	C₁₇×#117	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
89	C₂×C₄²×C₁₇	—	2	1	no	—
90	C₂×C₄²×C₁₇	—	2	1	no	—
91	C₂×C₄²×C₁₇	—	2	1	no	—
92	C₂×C₄²×C₁₇	—	2	1	no	—
93	C₁₇×#104	—	2	8	no	—
94	C₁₇×#103	—	2	2	no	—
95	C₁₇×#103	—	2	2	no	—
96	C₁₇×#102	—	2	2	no	—
97	C₁₇×#102	—	2	2	no	—
98	C₁₇×#99	—	2	8	no	—
99	C₁₇×#97	—	2	4	no	—
100	C₄×C₈×C₁₇	—	2	4	no	—
101	C₂⁴×C₁₇	—	2	1	no	—
102	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
103	#41×C₁₇	—	2	2	no	—
104	#41×C₁₇	—	2	2	no	—
105	#41×C₁₇	—	2	2	no	—
106	#41×C₁₇	—	2	2	no	—
107	#41×C₁₇	—	2	2	no	—
108	#41×C₁₇	—	2	2	no	—
109	#41×C₁₇	—	2	2	no	—
110	#41×C₁₇	—	2	2	no	—
111	#41×C₁₇	—	4	1	no	—
112	#41×C₁₇	—	4	1	no	—
113	#41×C₁₇	—	4	1	no	—
114	#41×C₁₇	—	4	1	no	—
115	#41×C₁₇	—	4	1	no	—
116	#41×C₁₇	—	4	1	no	—
117	#41×C₁₇	—	4	1	no	—
118	#41×C₁₇	—	4	1	no	—
119	C₂×Q₈×C₁₇	—	2	1	no	—
120	C₂×Q₈×C₁₇	—	2	1	no	—
121	C₂×Q₈×C₁₇	—	2	1	no	—
122	C₂×Q₈×C₁₇	—	2	1	no	—
123	C₂×Q₈×C₁₇	—	2	1	no	—
124	C₂×Q₈×C₁₇	C₄²	1	2	yes	—
125	C₂×D₄×C₁₇	—	2	2	no	—
126	C₂×D₄×C₁₇	—	2	2	no	—
127	C₂×D₄×C₁₇	—	2	1	no	—
128	C₂×D₄×C₁₇	—	2	1	no	—
129	C₂×D₄×C₁₇	—	2	1	no	—
130	C₂×D₄×C₁₇	—	2	1	no	—
131	C₂×D₄×C₁₇	—	2	1	no	—
132	C₂×D₄×C₁₇	—	4	1	no	—
133	C₂×D₄×C₁₇	—	4	1	no	—
134	C₂×D₄×C₁₇	—	4	1	no	—
135	C₂×D₄×C₁₇	—	4	1	no	—
136	C₂×D₄×C₁₇	C₄²	1	2	yes	—
137	C₂²×C₄×C₁₇	—	2	1	no	—
138	C₂²×C₄×C₁₇	—	2	2	no	—
139	C₂²×C₄×C₁₇	—	2	2	no	—
140	C₂²×C₄×C₁₇	—	2	2	no	—
141	C₂²×C₄×C₁₇	—	2	2	no	—
142	C₂²×C₄×C₁₇	—	4	1	no	—
143	C₂²×C₄×C₁₇	—	4	1	no	—
144	C₂²×C₄×C₁₇	—	4	1	no	—
145	C₂²×C₄×C₁₇	—	4	1	no	—
146	C₂²×C₄×C₁₇	—	4	1	no	—
147	C₂²×C₄×C₁₇	—	4	1	no	—
148	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
157	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
158	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
159	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
160	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
161	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
162	M₁₆×C₁₇	—	2	2	no	—
163	M₁₆×C₁₇	—	2	2	no	—
164	M₁₆×C₁₇	—	2	2	no	—
165	M₁₆×C₁₇	C₂²⋊C₄	1	4	yes	—
166	C₂×C₈×C₁₇	—	2	2	no	—
167	C₂×C₈×C₁₇	—	2	2	no	—
168	C₂×C₈×C₁₇	—	2	2	no	—
169	C₂×C₈×C₁₇	—	2	1	no	—
170	C₂×C₈×C₁₇	—	2	1	no	—
171	C₂×C₈×C₁₇	—	2	2	no	—
172	C₂×C₈×C₁₇	—	2	2	no	—
173	C₂×C₈×C₁₇	—	2	2	no	—
174	C₂×C₈×C₁₇	—	2	2	no	—
175	C₂×C₈×C₁₇	—	2	1	no	—
176	C₂×C₈×C₁₇	—	2	1	no	—
177	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
178	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
179	C₄⋊C₄×C₁₇	—	2	2	no	—
180	C₄⋊C₄×C₁₇	—	2	2	no	—
181	C₄⋊C₄×C₁₇	—	2	2	no	—
182	C₄⋊C₄×C₁₇	—	2	2	no	—
183	C₄⋊C₄×C₁₇	—	2	2	no	—
184	C₄⋊C₄×C₁₇	—	2	2	no	—
185	C₄⋊C₄×C₁₇	—	4	1	no	—
186	C₄⋊C₄×C₁₇	—	4	1	no	—
187	C₂²⋊C₄×C₁₇	—	2	2	no	—
188	C₂²⋊C₄×C₁₇	—	2	2	no	—
189	C₂²⋊C₄×C₁₇	—	2	2	no	—
190	C₂²⋊C₄×C₁₇	—	4	1	no	—
191	C₂²⋊C₄×C₁₇	—	4	1	no	—
192	C₂²⋊C₄×C₁₇	—	4	1	no	—
193	C₂²⋊C₄×C₁₇	—	4	1	no	—
194	C₂²⋊C₄×C₁₇	C₂²⋊C₄	1	4	yes	—
195	C₄²×C₁₇	—	2	2	no	—
196	C₄²×C₁₇	—	2	2	no	—
197	C₄²×C₁₇	—	2	2	no	—
198	C₄²×C₁₇	—	2	2	no	—
199	C₄²×C₁₇	—	4	1	no	—
200	C₄²×C₁₇	—	4	1	no	—
201	C₄²×C₁₇	—	4	1	no	—
202	C₄²×C₁₇	—	4	1	no	—
203	#10944	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂³×C₁₇	—	2	2	no	—
205	C₂³×C₁₇	—	4	2	no	—
206	C₂³×C₁₇	—	4	1	no	—
207	C₂³×C₁₇	—	4	1	no	—
208	C₂³×C₁₇	—	8	2	no	—
209	C₂³×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
211	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
212	C₂³×C₁₇	#121	1	1	yes	characteristic
213	C₂³×C₁₇	#121	1	1	yes	characteristic
214	C₂³×C₁₇	#124	1	1	yes	characteristic
215	C₂³×C₁₇	#127	1	1	yes	characteristic
216	Q₈×C₁₇	—	2	2	no	—
217	Q₈×C₁₇	—	2	2	no	—
218	Q₈×C₁₇	—	4	1	no	—
219	Q₈×C₁₇	—	4	1	no	—
220	D₄×C₁₇	—	2	2	no	—
221	D₄×C₁₇	—	2	2	no	—
222	D₄×C₁₇	—	4	2	no	—
223	D₄×C₁₇	—	4	2	no	—
224	D₄×C₁₇	—	4	2	no	—
225	D₄×C₁₇	—	4	2	no	—
226	D₄×C₁₇	—	4	1	no	—
227	D₄×C₁₇	—	4	1	no	—
228	C₂×C₄×C₁₇	—	2	2	no	—
229	C₂×C₄×C₁₇	—	2	4	no	—
230	C₂×C₄×C₁₇	—	4	4	no	—
231	C₂×C₄×C₁₇	—	4	1	no	—
232	C₂×C₄×C₁₇	—	4	1	no	—
233	C₂×C₄×C₁₇	—	4	2	no	—
234	C₂×C₄×C₁₇	—	4	2	no	—
235	C₂×C₄×C₁₇	—	4	2	no	—
236	C₂×C₄×C₁₇	—	4	2	no	—
237	C₂×C₄×C₁₇	—	4	2	no	—
238	C₂×C₄×C₁₇	—	4	2	no	—
239	C₂×C₄×C₁₇	—	4	2	no	—
240	C₂×C₄×C₁₇	—	8	2	no	—
241	C₂×C₄×C₁₇	—	8	2	no	—
242	C₂×C₄×C₁₇	—	8	2	no	—
243	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
244	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
247	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
248	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
249	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
260	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
261	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
262	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
263	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
264	C₂×C₄×C₁₇	#123	1	1	yes	characteristic
265	C₂×C₄×C₁₇	#123	1	1	yes	characteristic
266	C₂×C₄×C₁₇	#123	1	1	yes	characteristic
267	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
268	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
269	C₂×C₄×C₁₇	#126	1	1	yes	characteristic
270	C₂×C₄×C₁₇	#126	1	1	yes	characteristic
271	C₈×C₁₇	—	2	2	no	—
272	C₈×C₁₇	—	2	2	no	—
273	C₈×C₁₇	—	2	4	no	—
274	C₂×#421	C₂×C₁₇	1	1	yes	characteristic
275	C₂×#416	C₂×C₁₇	1	1	yes	characteristic
276	C₂×#410	C₂×C₁₇	1	1	yes	characteristic
277	C₂×#405	C₂×C₁₇	1	1	yes	characteristic, complemented
278	#1740	C₂×C₁₇	1	1	yes	characteristic, complemented
279	#1735	C₂×C₁₇	1	1	yes	characteristic, complemented
280	#1733	C₂×C₁₇	1	1	yes	characteristic, complemented
281	C₂²×C₁₇	—	2	2	no	—
282	C₂²×C₁₇	—	2	2	no	—
283	C₂²×C₁₇	—	2	2	no	—
284	C₂²×C₁₇	—	4	1	no	—
285	C₂²×C₁₇	—	4	1	no	—
286	C₂²×C₁₇	—	4	1	no	—
287	C₂²×C₁₇	—	4	1	no	—
288	C₂²×C₁₇	—	4	2	no	—
289	C₂²×C₁₇	—	8	2	no	—
290	C₂²×C₁₇	—	8	2	no	—
291	C₂²×C₁₇	—	8	2	no	—
292	C₂²×C₁₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
293	C₂²×C₁₇	#386	1	1	yes	characteristic
294	C₂²×C₁₇	#388	1	1	yes	characteristic
295	C₂²×C₁₇	#388	1	1	yes	characteristic
296	C₂²×C₁₇	#390	1	1	yes	characteristic
297	C₂²×C₁₇	#390	1	1	yes	characteristic
298	C₂²×C₁₇	#390	1	1	yes	characteristic
299	C₄×C₁₇	—	4	4	no	—
300	C₄×C₁₇	—	4	2	no	—
301	C₄×C₁₇	—	8	2	no	—
302	C₄×C₁₇	—	8	2	no	—
303	C₄×C₁₇	—	8	2	no	—
304	C₄×C₁₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
305	C₄×C₁₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
306	C₄×C₁₇	#386	1	1	yes	characteristic
307	C₄×C₁₇	#386	1	1	yes	characteristic
308	C₄×C₁₇	#388	1	1	yes	characteristic
309	C₄×C₁₇	#388	1	1	yes	characteristic
310	C₄×C₁₇	#388	1	1	yes	characteristic
311	C₄×C₁₇	#388	1	1	yes	characteristic
312	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
313	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
314	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
315	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
316	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
317	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
318	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
319	#421	—	2	2	no	—
320	#421	C₄×C₁₇	1	4	yes	complemented
321	C₂×#104	—	2	2	no	—
322	#416	—	2	2	no	—
323	#416	—	2	1	no	—
324	#416	—	2	1	no	—
325	C₂×#103	C₄×C₁₇	1	2	yes	complemented
326	C₂×#102	C₄×C₁₇	1	2	yes	complemented
327	#410	—	2	2	no	—
328	#410	C₄×C₁₇	1	4	yes	complemented
329	C₂×#99	—	2	2	no	—
330	#405	—	2	2	no	—
331	#405	—	2	2	no	—
332	C₂×#97	—	2	1	no	—
333	C₂×C₄×C₈	—	2	1	no	—
334	#342	—	2	2	no	—
335	#340	—	2	2	no	—
336	#339	—	2	2	no	—
337	C₂×C₁₇	—	2	1	no	—
338	C₂×C₁₇	—	2	1	no	—
339	C₂×C₁₇	—	2	1	no	—
340	C₂×C₁₇	—	2	1	no	—
341	C₂×C₁₇	—	2	1	no	—
342	C₂×C₁₇	—	2	1	no	—
343	C₂×C₁₇	—	8	2	no	—
344	C₂×C₁₇	#1437	1	1	yes	characteristic
345	C₂×C₁₇	#1976	1	2	yes	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	1	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	C₂×C₄×C₁₇	1	2	yes	—
357	C₂×#41	C₂×C₄×C₁₇	1	2	yes	—
358	C₂²×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	C₂×C₄×C₁₇	1	2	yes	—
367	C₂×M₁₆	D₄×C₁₇	1	2	yes	—
368	C₂×M₁₆	D₄×C₁₇	1	2	yes	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	C₂×C₄×C₁₇	1	2	yes	—
375	C₂²×C₈	D₄×C₁₇	1	2	yes	—
376	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
377	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
378	#117	—	2	1	no	—
379	#117	—	2	1	no	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	—	2	1	no	—
388	#117	—	2	1	no	—
389	#117	—	2	1	no	—
390	#117	C₂×C₄×C₁₇	1	2	yes	—
391	#117	C₂×C₄×C₁₇	1	2	yes	—
392	#117	C₂×C₄×C₁₇	1	2	yes	—
393	#117	D₄×C₁₇	1	2	yes	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	#104	—	2	8	no	—
407	#103	—	2	2	no	—
408	#103	—	2	2	no	—
409	#102	—	2	2	no	—
410	#102	—	2	2	no	—
411	#99	—	2	8	no	—
412	#97	—	2	4	no	—
413	C₄×C₈	—	2	4	no	—
414	C₁₇	#10944	1	1	yes	characteristic, direct product factor, Sylow
415	C₂⁴	—	2	1	no	—
416	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	4	1	no	—
426	#41	—	4	1	no	—
427	#41	—	4	1	no	—
428	#41	—	4	1	no	—
429	#41	—	4	1	no	—
430	#41	—	4	1	no	—
431	#41	—	4	1	no	—
432	#41	—	4	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	C₄²×C₁₇	1	2	yes	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	—	4	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	C₄²×C₁₇	1	2	yes	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
463	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
464	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
470	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
471	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
472	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
473	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
474	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
475	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	C₂²⋊C₄×C₁₇	1	4	yes	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	C₂²⋊C₄×C₁₇	1	2	yes	—
492	C₂×C₈	C₂²⋊C₄×C₁₇	1	2	yes	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	C₂²⋊C₄×C₁₇	1	4	yes	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	4	1	no	—
514	C₄²	—	4	1	no	—
515	C₄²	—	4	1	no	—
516	C₄²	—	4	1	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	8	2	no	—
522	C₂³	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
523	C₂³	C₄×D₄×C₁₇	1	1	yes	characteristic
524	C₂³	C₄×D₄×C₁₇	1	1	yes	characteristic
525	C₂³	C₁₇×#121	1	1	yes	characteristic
526	C₂³	C₁₇×#121	1	1	yes	characteristic
527	C₂³	C₁₇×#124	1	1	yes	characteristic
528	C₂³	C₁₇×#127	1	1	yes	characteristic
529	Q₈	—	2	2	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	4	1	no	—
532	Q₈	—	4	1	no	—
533	D₄	—	2	2	no	—
534	D₄	—	2	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	8	2	no	—
554	C₂×C₄	—	8	2	no	—
555	C₂×C₄	—	8	2	no	—
556	C₂×C₄	C₂×C₄²×C₁₇	1	1	yes	characteristic
557	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
558	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
559	C₂×C₄	C₁₇×#117	1	1	yes	characteristic
560	C₂×C₄	C₁₇×#117	1	1	yes	characteristic
561	C₂×C₄	C₁₇×#117	1	1	yes	characteristic
562	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
563	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
564	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
565	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
566	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
567	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
568	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
569	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
570	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
571	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
572	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
573	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
574	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
575	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
576	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
577	C₂×C₄	C₁₇×#123	1	1	yes	characteristic
578	C₂×C₄	C₁₇×#123	1	1	yes	characteristic
579	C₂×C₄	C₁₇×#123	1	1	yes	characteristic
580	C₂×C₄	C₁₇×#124	1	1	yes	characteristic
581	C₂×C₄	C₁₇×#124	1	1	yes	characteristic
582	C₂×C₄	C₁₇×#126	1	1	yes	characteristic
583	C₂×C₄	C₁₇×#126	1	1	yes	characteristic
584	C₈	—	2	2	no	—
585	C₈	—	2	2	no	—
586	C₈	—	2	4	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	8	2	no	—
596	C₂²	—	8	2	no	—
597	C₂²	—	8	2	no	—
598	C₂²	C₄×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
599	C₂²	C₁₇×#386	1	1	yes	characteristic
600	C₂²	C₁₇×#388	1	1	yes	characteristic
601	C₂²	C₁₇×#388	1	1	yes	characteristic
602	C₂²	C₁₇×#390	1	1	yes	characteristic
603	C₂²	C₁₇×#390	1	1	yes	characteristic
604	C₂²	C₁₇×#390	1	1	yes	characteristic
605	C₄	—	4	4	no	—
606	C₄	—	4	2	no	—
607	C₄	—	8	2	no	—
608	C₄	—	8	2	no	—
609	C₄	—	8	2	no	—
610	C₄	C₄×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
611	C₄	C₄×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
612	C₄	C₁₇×#386	1	1	yes	characteristic
613	C₄	C₁₇×#386	1	1	yes	characteristic
614	C₄	C₁₇×#388	1	1	yes	characteristic
615	C₄	C₁₇×#388	1	1	yes	characteristic
616	C₄	C₁₇×#388	1	1	yes	characteristic
617	C₄	C₁₇×#388	1	1	yes	characteristic
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	1	no	—
623	C₂	—	2	1	no	—
624	C₂	—	8	2	no	—
625	C₂	C₁₇×#1437	1	1	yes	characteristic
626	C₂	C₁₇×#1976	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₇	#121
commutator	C₂×C₄	C₂×C₄²×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
socle	C₂²×C₁₇	#390
prime radical	C₂²×#41×C₁₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₇×#405	C₂	semidirect
5. C₁₇×#1740	C₂	semidirect
6. C₁₇×#1735	C₂	semidirect
7. C₁₇×#1733	C₂	semidirect
16. C₁₇×#421	C₄	semidirect
21. C₂×C₁₇×#103	C₄	semidirect
22. C₂×C₁₇×#102	C₄	semidirect
24. C₁₇×#410	C₄	semidirect
203. #10944	C₁₇	direct (N × H)
277. C₂×#405	C₂×C₁₇	semidirect
278. #1740	C₂×C₁₇	semidirect
279. #1735	C₂×C₁₇	semidirect
280. #1733	C₂×C₁₇	semidirect
320. #421	C₄×C₁₇	semidirect
325. C₂×#103	C₄×C₁₇	semidirect
326. C₂×#102	C₄×C₁₇	semidirect
328. #410	C₄×C₁₇	semidirect
414. C₁₇	#10944	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#421	2
C₂×C₁₇×#416	2
C₂×C₁₇×#410	2
C₂×C₁₇×#405	2
C₁₇×#1740	2
C₁₇×#1735	2
C₁₇×#1733	2
#10944	17

Subgroups — C17×#10944 #16868688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#10944 #16868688