Subgroups — C₁₇×#18642 #16876386

Order 4352.

1002 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3038	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1627	C₂	1	4	yes	maximal, complemented
6	C₁₇×#1626	C₂	1	4	yes	maximal, complemented
7	C₁₇×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₇×AGL(1,ℤ/8)	—	2	1	no	—
11	Q₈²×C₁₇	—	2	1	no	—
12	C₁₇×#557	C₂²	1	2	yes	complemented
13	C₁₇×#554	—	2	1	no	—
14	C₁₇×#554	—	2	2	no	—
15	D₄×Q₈×C₁₇	—	2	2	no	—
16	D₄×Q₈×C₁₇	C₂²	1	2	yes	complemented
17	C₁₇×#544	—	2	1	no	—
18	C₁₇×#544	—	2	2	no	—
19	C₁₇×#533	—	2	1	no	—
20	C₁₇×#533	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×#127	C₂²	1	1	yes	characteristic
24	C₁₇×#520	—	2	1	no	—
25	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
26	C₁₇×#492	—	2	1	no	—
27	C₁₇×#486	—	2	1	no	—
28	C₁₇×#486	—	2	2	no	—
29	C₁₇×#486	C₂²	1	4	yes	—
30	C₁₇×#460	—	2	1	no	—
31	C₁₇×#460	C₂²	1	4	yes	—
32	C₁₇×#460	C₂²	1	2	yes	—
33	C₁₇×#459	—	2	1	no	—
34	C₁₇×#459	C₂²	1	2	yes	—
35	C₁₇×#450	—	2	2	no	—
36	C₁₇×#431	C₂²	1	1	yes	characteristic
37	C₁₇×#423	C₂²	1	1	yes	characteristic
38	C₁₇×#418	—	2	1	no	—
39	C₂×C₁₇×#102	—	2	2	no	—
40	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
41	C₁₇×#332	C₂²	1	4	yes	complemented
42	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
43	C₁₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
44	C₁₇×D₄⋊C₈	C₂²	1	2	yes	complemented
45	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₇	—	2	2	no	—
47	C₂²×Q₈×C₁₇	—	2	1	no	—
48	C₂²×D₄×C₁₇	—	2	1	no	—
49	C₂²×D₄×C₁₇	—	2	1	no	—
50	C₂²×D₄×C₁₇	—	2	1	no	—
51	C₁₇×AGL(1,ℤ/8)	—	4	4	no	—
52	C₂×SD₁₆×C₁₇	—	2	2	no	—
53	C₂×SD₁₆×C₁₇	—	2	4	no	—
54	C₂×D₈×C₁₇	—	2	2	no	—
55	C₂×M₁₆×C₁₇	—	2	1	no	—
56	C₂²×C₈×C₁₇	—	2	1	no	—
57	C₁₇×C₄⋊Q₈	—	2	2	no	—
58	C₁₇×C₄⋊Q₈	—	2	2	no	—
59	C₁₇×C₄⋊Q₈	—	2	4	no	—
60	C₁₇×C₄⋊Q₈	—	2	2	no	—
61	C₁₇×C₄⋊Q₈	—	2	2	no	—
62	C₁₇×C₄⋊Q₈	—	2	1	no	—
63	C₁₇×C₄⋊Q₈	—	2	1	no	—
64	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₇×C₄⋊Q₈	D₄	1	2	yes	—
66	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
67	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₁₇×#127	—	2	1	no	—
69	C₁₇×#127	—	2	1	no	—
70	C₁₇×#127	—	2	1	no	—
71	C₁₇×#127	C₂³	1	2	yes	—
72	C₁₇×#125	—	2	2	no	—
73	C₁₇×#125	—	2	4	no	—
74	C₁₇×#125	—	2	2	no	—
75	C₁₇×#125	—	2	1	no	—
76	C₁₇×C₂²⋊Q₈	—	2	2	no	—
77	C₁₇×C₂²⋊Q₈	—	2	4	no	—
78	C₁₇×C₂²⋊Q₈	—	2	4	no	—
79	C₁₇×C₂²⋊Q₈	—	2	1	no	—
80	C₁₇×C₂²⋊Q₈	—	2	2	no	—
81	C₁₇×C₂²⋊Q₈	—	2	4	no	—
82	C₁₇×C₂²⋊Q₈	D₄	1	2	yes	—
83	C₄×Q₈×C₁₇	—	2	2	no	—
84	C₄×Q₈×C₁₇	—	2	2	no	—
85	C₄×Q₈×C₁₇	—	2	2	no	—
86	C₄×Q₈×C₁₇	—	2	1	no	—
87	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
88	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
89	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
90	C₄×D₄×C₁₇	—	2	4	no	—
91	C₄×D₄×C₁₇	—	2	2	no	—
92	C₄×D₄×C₁₇	—	2	1	no	—
93	C₄×D₄×C₁₇	—	2	1	no	—
94	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
95	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
96	C₁₇×#117	—	2	2	no	—
97	C₁₇×#117	—	2	1	no	—
98	C₁₇×#117	—	2	1	no	—
99	C₁₇×#117	D₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
101	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
102	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
104	C₂×C₄²×C₁₇	—	2	1	no	—
105	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
106	C₁₇×C₄⋊C₈	—	2	1	no	—
107	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
108	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
109	C₁₇×#102	—	2	8	no	—
110	C₁₇×#102	—	2	2	no	—
111	C₁₇×#102	—	2	2	no	—
112	C₁₇×#102	—	2	4	no	—
113	C₁₇×C₂²⋊C₈	—	2	1	no	—
114	C₄×C₈×C₁₇	—	2	1	no	—
115	C₄×C₈×C₁₇	—	2	1	no	—
116	C₄×C₈×C₁₇	C₂³	1	2	yes	—
117	C₂⁴×C₁₇	—	4	1	no	—
118	#41×C₁₇	—	2	2	no	—
119	#41×C₁₇	SD₁₆	1	4	yes	complemented
120	C₂×Q₈×C₁₇	—	2	4	no	—
121	C₂×Q₈×C₁₇	—	2	1	no	—
122	C₂×Q₈×C₁₇	—	2	2	no	—
123	C₂×Q₈×C₁₇	—	2	2	no	—
124	C₂×Q₈×C₁₇	—	8	2	no	—
125	C₂×Q₈×C₁₇	—	8	4	no	—
126	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
127	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
128	C₂×D₄×C₁₇	—	2	1	no	—
129	C₂×D₄×C₁₇	—	2	2	no	—
130	C₂×D₄×C₁₇	—	2	2	no	—
131	C₂×D₄×C₁₇	—	2	2	no	—
132	C₂×D₄×C₁₇	—	4	4	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	—	4	2	no	—
137	C₂×D₄×C₁₇	—	4	2	no	—
138	C₂×D₄×C₁₇	—	8	2	no	—
139	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₇	—	2	1	no	—
141	C₂²×C₄×C₁₇	—	2	4	no	—
142	C₂²×C₄×C₁₇	—	2	2	no	—
143	C₂²×C₄×C₁₇	—	2	1	no	—
144	C₂²×C₄×C₁₇	—	2	1	no	—
145	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
148	SD₁₆×C₁₇	—	4	4	no	—
149	SD₁₆×C₁₇	—	8	4	no	—
150	D₈×C₁₇	—	4	4	no	—
151	M₁₆×C₁₇	—	4	2	no	—
152	C₂×C₈×C₁₇	—	2	2	no	—
153	C₂×C₈×C₁₇	—	2	2	no	—
154	C₂×C₈×C₁₇	—	2	2	no	—
155	C₂×C₈×C₁₇	—	4	2	no	—
156	C₄⋊C₄×C₁₇	—	2	4	no	—
157	C₄⋊C₄×C₁₇	—	2	4	no	—
158	C₄⋊C₄×C₁₇	—	2	4	no	—
159	C₄⋊C₄×C₁₇	—	2	4	no	—
160	C₄⋊C₄×C₁₇	—	2	2	no	—
161	C₄⋊C₄×C₁₇	—	2	2	no	—
162	C₄⋊C₄×C₁₇	—	2	1	no	—
163	C₄⋊C₄×C₁₇	—	2	1	no	—
164	C₄⋊C₄×C₁₇	—	2	1	no	—
165	C₄⋊C₄×C₁₇	—	2	2	no	—
166	C₄⋊C₄×C₁₇	—	2	1	no	—
167	C₄⋊C₄×C₁₇	—	2	2	no	—
168	C₄⋊C₄×C₁₇	—	2	1	no	—
169	C₄⋊C₄×C₁₇	—	2	2	no	—
170	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
171	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
172	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
173	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
174	C₂²⋊C₄×C₁₇	—	2	4	no	—
175	C₂²⋊C₄×C₁₇	—	2	1	no	—
176	C₂²⋊C₄×C₁₇	—	2	2	no	—
177	C₂²⋊C₄×C₁₇	—	2	1	no	—
178	C₂²⋊C₄×C₁₇	—	2	1	no	—
179	C₄²×C₁₇	—	2	4	no	—
180	C₄²×C₁₇	—	2	1	no	—
181	C₄²×C₁₇	—	2	1	no	—
182	C₄²×C₁₇	—	2	2	no	—
183	C₄²×C₁₇	—	2	1	no	—
184	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
188	#18642	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂³×C₁₇	—	2	1	no	—
190	C₂³×C₁₇	—	4	2	no	—
191	C₂³×C₁₇	—	8	2	no	—
192	C₂³×C₁₇	—	8	2	no	—
193	C₂³×C₁₇	—	8	2	no	—
194	C₂³×C₁₇	#120	1	1	yes	characteristic
195	Q₈×C₁₇	—	2	1	no	—
196	Q₈×C₁₇	—	2	4	no	—
197	Q₈×C₁₇	—	4	4	no	—
198	Q₈×C₁₇	—	4	2	no	—
199	Q₈×C₁₇	—	8	2	no	—
200	Q₈×C₁₇	—	8	4	no	—
201	Q₈×C₁₇	C₂×SD₁₆	1	2	yes	—
202	D₄×C₁₇	—	2	4	no	—
203	D₄×C₁₇	—	2	1	no	—
204	D₄×C₁₇	—	4	4	no	—
205	D₄×C₁₇	—	4	2	no	—
206	D₄×C₁₇	—	4	2	no	—
207	D₄×C₁₇	—	4	4	no	—
208	D₄×C₁₇	—	8	2	no	—
209	D₄×C₁₇	—	8	2	no	—
210	D₄×C₁₇	—	8	2	no	—
211	D₄×C₁₇	C₂×SD₁₆	1	2	yes	—
212	C₂×C₄×C₁₇	—	2	1	no	—
213	C₂×C₄×C₁₇	—	2	2	no	—
214	C₂×C₄×C₁₇	—	2	4	no	—
215	C₂×C₄×C₁₇	—	2	2	no	—
216	C₂×C₄×C₁₇	—	2	2	no	—
217	C₂×C₄×C₁₇	—	2	1	no	—
218	C₂×C₄×C₁₇	—	2	1	no	—
219	C₂×C₄×C₁₇	—	2	2	no	—
220	C₂×C₄×C₁₇	—	2	4	no	—
221	C₂×C₄×C₁₇	—	4	2	no	—
222	C₂×C₄×C₁₇	—	4	2	no	—
223	C₂×C₄×C₁₇	—	8	2	no	—
224	C₂×C₄×C₁₇	—	8	4	no	—
225	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
226	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
227	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
228	C₂×C₄×C₁₇	C₂×SD₁₆	1	2	yes	—
229	C₂×C₄×C₁₇	#137	1	2	yes	—
230	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
233	C₈×C₁₇	—	4	2	no	—
234	C₈×C₁₇	—	4	2	no	—
235	C₈×C₁₇	—	4	2	no	—
236	#3503	C₂×C₁₇	1	1	yes	characteristic, complemented
237	#3208	C₂×C₁₇	1	1	yes	characteristic, complemented
238	C₂×#486	C₂×C₁₇	1	1	yes	characteristic, complemented
239	#3038	C₂×C₁₇	1	1	yes	characteristic
240	#1627	C₂×C₁₇	1	4	yes	complemented
241	#1626	C₂×C₁₇	1	4	yes	complemented
242	#1549	C₂×C₁₇	1	1	yes	characteristic, complemented
243	#1493	C₂×C₁₇	1	1	yes	characteristic, complemented
244	#1476	C₂×C₁₇	1	1	yes	characteristic, complemented
245	C₂²×C₁₇	—	2	1	no	—
246	C₂²×C₁₇	—	2	1	no	—
247	C₂²×C₁₇	—	2	2	no	—
248	C₂²×C₁₇	—	4	1	no	—
249	C₂²×C₁₇	—	4	1	no	—
250	C₂²×C₁₇	—	8	2	no	—
251	C₂²×C₁₇	—	8	2	no	—
252	C₂²×C₁₇	—	8	2	no	—
253	C₂²×C₁₇	—	16	4	no	—
254	C₂²×C₁₇	#448	1	2	yes	—
255	C₂²×C₁₇	C₂×#120	1	1	yes	characteristic
256	C₄×C₁₇	—	2	2	no	—
257	C₄×C₁₇	—	2	1	no	—
258	C₄×C₁₇	—	2	1	no	—
259	C₄×C₁₇	—	4	1	no	—
260	C₄×C₁₇	—	4	2	no	—
261	C₄×C₁₇	—	4	4	no	—
262	C₄×C₁₇	—	4	1	no	—
263	C₄×C₁₇	—	4	2	no	—
264	C₄×C₁₇	#448	1	2	yes	—
265	C₄×C₁₇	#454	1	2	yes	—
266	C₄×C₁₇	C₂²×SD₁₆	1	1	yes	characteristic
267	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
268	C₄×C₁₇	#576	1	2	yes	—
269	C₂×AGL(1,ℤ/8)	—	2	1	no	—
270	Q₈²	—	2	1	no	—
271	#557	C₂²×C₁₇	1	2	yes	complemented
272	#554	—	2	1	no	—
273	#554	—	2	2	no	—
274	D₄×Q₈	—	2	2	no	—
275	D₄×Q₈	C₂²×C₁₇	1	2	yes	complemented
276	#544	—	2	2	no	—
277	#544	—	2	1	no	—
278	#533	—	2	1	no	—
279	#533	C₂²×C₁₇	1	1	yes	characteristic
280	C₂×C₄⋊Q₈	—	2	1	no	—
281	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
282	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic
283	#520	—	2	1	no	—
284	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
285	#492	—	2	1	no	—
286	#486	—	2	2	no	—
287	#486	—	2	1	no	—
288	#486	C₂²×C₁₇	1	4	yes	—
289	#460	—	2	1	no	—
290	#460	C₂²×C₁₇	1	2	yes	—
291	#460	C₂²×C₁₇	1	4	yes	—
292	#459	—	2	1	no	—
293	#459	C₂²×C₁₇	1	2	yes	—
294	#450	—	2	2	no	—
295	#431	C₂²×C₁₇	1	1	yes	characteristic
296	#423	C₂²×C₁₇	1	1	yes	characteristic
297	#418	—	2	1	no	—
298	C₂×#102	—	2	2	no	—
299	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
300	#332	C₂²×C₁₇	1	4	yes	complemented
301	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	complemented
302	Q₈⋊C₈	C₂²×C₁₇	1	4	yes	complemented
303	D₄⋊C₈	C₂²×C₁₇	1	2	yes	complemented
304	C₂×C₁₇	—	2	2	no	—
305	C₂×C₁₇	—	4	2	no	—
306	C₂×C₁₇	—	16	2	no	—
307	C₂×C₁₇	C₂×#448	1	1	yes	characteristic
308	C₂×C₁₇	#3008	1	1	yes	characteristic
309	C₂×C₁₇	C₂×#454	1	1	yes	characteristic
310	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
311	C₂²×Q₈	—	2	2	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	1	no	—
316	AGL(1,ℤ/8)	—	4	4	no	—
317	C₂×SD₁₆	—	2	2	no	—
318	C₂×SD₁₆	—	2	4	no	—
319	C₂×D₈	—	2	2	no	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂²×C₈	—	2	1	no	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	4	no	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	—	2	2	no	—
327	C₄⋊Q₈	—	2	1	no	—
328	C₄⋊Q₈	—	2	1	no	—
329	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
330	C₄⋊Q₈	D₄×C₁₇	1	2	yes	—
331	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
332	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
333	#127	—	2	1	no	—
334	#127	—	2	1	no	—
335	#127	—	2	1	no	—
336	#127	C₂³×C₁₇	1	2	yes	—
337	#125	—	2	2	no	—
338	#125	—	2	4	no	—
339	#125	—	2	2	no	—
340	#125	—	2	1	no	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	—	2	4	no	—
343	C₂²⋊Q₈	—	2	4	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	—	2	2	no	—
346	C₂²⋊Q₈	—	2	4	no	—
347	C₂²⋊Q₈	D₄×C₁₇	1	2	yes	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
353	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
354	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
355	C₄×D₄	—	2	4	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
360	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
361	#117	—	2	2	no	—
362	#117	—	2	1	no	—
363	#117	—	2	1	no	—
364	#117	D₄×C₁₇	1	1	yes	characteristic
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
373	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
374	#102	—	2	8	no	—
375	#102	—	2	2	no	—
376	#102	—	2	2	no	—
377	#102	—	2	4	no	—
378	C₂²⋊C₈	—	2	1	no	—
379	C₄×C₈	—	2	1	no	—
380	C₄×C₈	—	2	1	no	—
381	C₄×C₈	C₂³×C₁₇	1	2	yes	—
382	C₁₇	#18642	1	1	yes	characteristic, direct product factor, Sylow
383	C₂⁴	—	4	1	no	—
384	#41	—	2	2	no	—
385	#41	SD₁₆×C₁₇	1	4	yes	complemented
386	C₂×Q₈	—	2	4	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	8	2	no	—
391	C₂×Q₈	—	8	4	no	—
392	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
393	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	1	no	—
402	C₂×D₄	—	4	1	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	—	8	2	no	—
405	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
414	SD₁₆	—	4	4	no	—
415	SD₁₆	—	8	4	no	—
416	D₈	—	4	4	no	—
417	M₁₆	—	4	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	4	2	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
437	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
438	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
439	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₄²	—	2	4	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
452	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
453	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
454	C₂³	—	2	1	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	8	2	no	—
458	C₂³	—	8	2	no	—
459	C₂³	C₁₇×#120	1	1	yes	characteristic
460	Q₈	—	2	1	no	—
461	Q₈	—	2	4	no	—
462	Q₈	—	4	4	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	8	2	no	—
465	Q₈	—	8	4	no	—
466	Q₈	C₂×SD₁₆×C₁₇	1	2	yes	—
467	D₄	—	2	4	no	—
468	D₄	—	2	1	no	—
469	D₄	—	4	4	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	4	no	—
473	D₄	—	8	2	no	—
474	D₄	—	8	2	no	—
475	D₄	—	8	2	no	—
476	D₄	C₂×SD₁₆×C₁₇	1	2	yes	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	8	2	no	—
489	C₂×C₄	—	8	4	no	—
490	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
491	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
492	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
493	C₂×C₄	C₂×SD₁₆×C₁₇	1	2	yes	—
494	C₂×C₄	C₁₇×#137	1	2	yes	—
495	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
498	C₈	—	4	2	no	—
499	C₈	—	4	2	no	—
500	C₈	—	4	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	16	4	no	—
510	C₂²	C₁₇×#448	1	2	yes	—
511	C₂²	C₂×C₁₇×#120	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	4	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	C₁₇×#448	1	2	yes	—
521	C₄	C₁₇×#454	1	2	yes	—
522	C₄	C₂²×SD₁₆×C₁₇	1	1	yes	characteristic
523	C₄	C₂×C₁₇×#137	1	1	yes	characteristic
524	C₄	C₁₇×#576	1	2	yes	—
525	C₂	—	2	2	no	—
526	C₂	—	4	2	no	—
527	C₂	—	16	2	no	—
528	C₂	C₂×C₁₇×#448	1	1	yes	characteristic
529	C₂	C₁₇×#3008	1	1	yes	characteristic
530	C₂	C₂×C₁₇×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#3038	C₂
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×#3503	C₂	semidirect
2. C₁₇×#3208	C₂	semidirect
3. C₂×C₁₇×#486	C₂	semidirect
5. C₁₇×#1627	C₂	semidirect
6. C₁₇×#1626	C₂	semidirect
7. C₁₇×#1549	C₂	semidirect
8. C₁₇×#1493	C₂	semidirect
9. C₁₇×#1476	C₂	semidirect
12. C₁₇×#557	C₂²	semidirect
16. D₄×Q₈×C₁₇	C₂²	semidirect
41. C₁₇×#332	C₂²	semidirect
42. C₁₇×Q₈⋊C₈	C₂²	semidirect
43. C₁₇×Q₈⋊C₈	C₂²	semidirect
44. C₁₇×D₄⋊C₈	C₂²	semidirect
119. #41×C₁₇	SD₁₆	semidirect
188. #18642	C₁₇	direct (N × H)
236. #3503	C₂×C₁₇	semidirect
237. #3208	C₂×C₁₇	semidirect
238. C₂×#486	C₂×C₁₇	semidirect
240. #1627	C₂×C₁₇	semidirect
241. #1626	C₂×C₁₇	semidirect
242. #1549	C₂×C₁₇	semidirect
243. #1493	C₂×C₁₇	semidirect
244. #1476	C₂×C₁₇	semidirect
271. #557	C₂²×C₁₇	semidirect
275. D₄×Q₈	C₂²×C₁₇	semidirect
300. #332	C₂²×C₁₇	semidirect
301. Q₈⋊C₈	C₂²×C₁₇	semidirect
302. Q₈⋊C₈	C₂²×C₁₇	semidirect
303. D₄⋊C₈	C₂²×C₁₇	semidirect
382. C₁₇	#18642	direct (N × H)
385. #41	SD₁₆×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3503	2
C₁₇×#3208	2
C₂×C₁₇×#486	2
C₁₇×#3038	2
C₁₇×#1627	2
C₁₇×#1626	2
C₁₇×#1549	2
C₁₇×#1493	2
C₁₇×#1476	2
#18642	17

Subgroups — C17×#18642 #16876386

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#18642 #16876386