Subgroups — C₁₇×#19400 #16877144

Order 4352.

610 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3210	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3103	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1682	C₂	1	2	yes	maximal, complemented
6	C₁₇×#1680	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1670	C₂	1	2	yes	maximal, complemented
8	C₁₇×#1666	C₂	1	2	yes	maximal, complemented
9	C₁₇×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1553	C₂	1	1	yes	maximal, characteristic
11	C₁₇×#1544	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#533	C₂²	1	1	yes	characteristic
13	C₁₇×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
15	C₁₇×#494	C₂²	1	1	yes	characteristic
16	C₁₇×#492	C₂²	1	1	yes	characteristic
17	C₁₇×#487	C₂²	1	1	yes	characteristic
18	C₁₇×#486	C₂²	1	1	yes	characteristic
19	C₁₇×#483	—	2	1	no	—
20	C₁₇×#481	—	2	1	no	—
21	C₁₇×#475	C₂²	1	2	yes	—
22	C₁₇×#475	C₂²	1	2	yes	—
23	C₁₇×#464	—	2	2	no	—
24	C₁₇×#462	C₂²	1	2	yes	—
25	C₁₇×#460	C₂²	1	2	yes	—
26	C₁₇×#452	—	2	2	no	—
27	C₁₇×#451	—	2	1	no	—
28	C₁₇×#448	—	2	1	no	—
29	C₈×Q₈×C₁₇	—	2	2	no	—
30	C₈×Q₈×C₁₇	C₂²	1	2	yes	—
31	C₈×Q₈×C₁₇	C₂²	1	2	yes	—
32	C₁₇×#441	—	2	2	no	—
33	C₄×SD₁₆×C₁₇	—	2	2	no	—
34	C₁₇×#432	C₂²	1	1	yes	characteristic
35	C₁₇×#431	—	2	2	no	—
36	C₁₇×#431	C₂²	1	1	yes	characteristic
37	C₁₇×#431	C₂²	1	1	yes	characteristic
38	C₁₇×#431	C₂²	1	1	yes	characteristic
39	C₁₇×#335	C₂²	1	2	yes	—
40	C₁₇×#334	C₂²	1	2	yes	—
41	C₁₇×#332	C₂²	1	2	yes	—
42	C₁₇×#332	C₂²	1	2	yes	—
43	C₁₇×#332	C₂²	1	2	yes	—
44	C₁₇×#331	C₂²	1	2	yes	—
45	C₂×#41×C₁₇	—	2	1	no	—
46	C₂²×Q₈×C₁₇	D₄	1	1	yes	characteristic
47	C₂×Q₁₆×C₁₇	—	2	2	no	—
48	C₂×Q₁₆×C₁₇	—	2	2	no	—
49	C₂×SD₁₆×C₁₇	—	2	2	no	—
50	C₂×SD₁₆×C₁₇	—	2	2	no	—
51	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
52	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
53	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
54	C₁₇×#127	C₂³	1	1	yes	characteristic
55	C₁₇×#125	—	2	1	no	—
56	C₁₇×#124	—	2	1	no	—
57	C₁₇×C₂²⋊Q₈	—	2	1	no	—
58	C₁₇×C₂²⋊Q₈	—	2	1	no	—
59	C₁₇×#121	—	2	1	no	—
60	C₁₇×#121	—	2	1	no	—
61	C₄×Q₈×C₁₇	—	2	1	no	—
62	C₄×Q₈×C₁₇	—	2	1	no	—
63	C₄×Q₈×C₁₇	—	2	1	no	—
64	C₄×Q₈×C₁₇	—	2	1	no	—
65	C₄×Q₈×C₁₇	D₄	1	2	yes	—
66	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
67	C₄×D₄×C₁₇	—	2	1	no	—
68	C₄×D₄×C₁₇	—	2	1	no	—
69	C₁₇×#117	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₇	—	2	1	no	—
73	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
74	C₁₇×#106	—	2	2	no	—
75	C₁₇×#106	—	2	2	no	—
76	C₁₇×C₄⋊C₈	—	2	2	no	—
77	C₁₇×C₄⋊C₈	—	2	2	no	—
78	C₁₇×C₄⋊C₈	D₄	1	2	yes	—
79	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
81	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
82	C₁₇×#103	—	2	2	no	—
83	C₁₇×#103	—	2	2	no	—
84	C₁₇×#103	—	2	2	no	—
85	C₁₇×#103	—	2	2	no	—
86	C₁₇×#102	—	2	2	no	—
87	C₁₇×#102	—	2	2	no	—
88	C₁₇×C₂²⋊C₈	—	2	1	no	—
89	C₁₇×C₂²⋊C₈	—	2	1	no	—
90	C₁₇×C₂²⋊C₈	—	2	1	no	—
91	C₁₇×C₂²⋊C₈	D₄	1	2	yes	—
92	C₁₇×#97	—	2	1	no	—
93	C₄×C₈×C₁₇	—	2	2	no	—
94	C₄×C₈×C₁₇	—	2	2	no	—
95	C₄×C₈×C₁₇	—	2	1	no	—
96	C₄×C₈×C₁₇	—	2	1	no	—
97	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
99	#41×C₁₇	—	8	2	no	—
100	C₂×Q₈×C₁₇	—	2	4	no	—
101	C₂×Q₈×C₁₇	—	2	1	no	—
102	C₂×Q₈×C₁₇	—	2	1	no	—
103	C₂×Q₈×C₁₇	—	2	1	no	—
104	C₂×Q₈×C₁₇	—	2	1	no	—
105	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₁₇	—	2	1	no	—
107	C₂×D₄×C₁₇	—	2	1	no	—
108	C₂×D₄×C₁₇	—	2	1	no	—
109	C₂×D₄×C₁₇	—	4	1	no	—
110	C₂²×C₄×C₁₇	—	2	1	no	—
111	C₂²×C₄×C₁₇	—	2	1	no	—
112	C₂²×C₄×C₁₇	—	4	1	no	—
113	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
116	Q₁₆×C₁₇	—	4	4	no	—
117	Q₁₆×C₁₇	—	8	2	no	—
118	SD₁₆×C₁₇	—	4	4	no	—
119	SD₁₆×C₁₇	—	8	2	no	—
120	C₂×C₈×C₁₇	—	2	2	no	—
121	C₂×C₈×C₁₇	—	2	2	no	—
122	C₂×C₈×C₁₇	—	2	2	no	—
123	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₁₇	—	2	2	no	—
126	C₄⋊C₄×C₁₇	—	2	1	no	—
127	C₄⋊C₄×C₁₇	—	2	2	no	—
128	C₄⋊C₄×C₁₇	—	2	1	no	—
129	C₄⋊C₄×C₁₇	—	2	1	no	—
130	C₄⋊C₄×C₁₇	—	2	1	no	—
131	C₄⋊C₄×C₁₇	—	2	1	no	—
132	C₄⋊C₄×C₁₇	—	2	1	no	—
133	C₄⋊C₄×C₁₇	—	2	1	no	—
134	C₄⋊C₄×C₁₇	—	4	1	no	—
135	C₄⋊C₄×C₁₇	—	4	1	no	—
136	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₁₇	—	4	1	no	—
138	C₂²⋊C₄×C₁₇	—	4	1	no	—
139	C₂²⋊C₄×C₁₇	—	4	1	no	—
140	C₄²×C₁₇	—	2	2	no	—
141	C₄²×C₁₇	—	2	2	no	—
142	C₄²×C₁₇	—	4	1	no	—
143	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₇	#41	1	1	yes	characteristic
146	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
147	#19400	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₇	—	4	1	no	—
149	C₂³×C₁₇	#121	1	1	yes	characteristic
150	Q₈×C₁₇	—	2	4	no	—
151	Q₈×C₁₇	—	2	2	no	—
152	Q₈×C₁₇	—	4	2	no	—
153	Q₈×C₁₇	—	4	2	no	—
154	Q₈×C₁₇	—	4	2	no	—
155	Q₈×C₁₇	#135	1	4	yes	—
156	D₄×C₁₇	—	4	2	no	—
157	D₄×C₁₇	—	4	2	no	—
158	D₄×C₁₇	—	8	1	no	—
159	D₄×C₁₇	—	8	2	no	—
160	C₂×C₄×C₁₇	—	2	4	no	—
161	C₂×C₄×C₁₇	—	2	2	no	—
162	C₂×C₄×C₁₇	—	2	2	no	—
163	C₂×C₄×C₁₇	—	2	2	no	—
164	C₂×C₄×C₁₇	—	2	2	no	—
165	C₂×C₄×C₁₇	—	4	1	no	—
166	C₂×C₄×C₁₇	—	4	1	no	—
167	C₂×C₄×C₁₇	—	4	1	no	—
168	C₂×C₄×C₁₇	—	4	1	no	—
169	C₂×C₄×C₁₇	—	8	2	no	—
170	C₂×C₄×C₁₇	—	8	1	no	—
171	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
177	C₈×C₁₇	—	2	2	no	—
178	C₈×C₁₇	—	2	2	no	—
179	C₈×C₁₇	—	4	2	no	—
180	C₈×C₁₇	—	4	2	no	—
181	C₈×C₁₇	—	4	2	no	—
182	#3210	C₂×C₁₇	1	1	yes	characteristic
183	#3113	C₂×C₁₇	1	1	yes	characteristic, complemented
184	#3103	C₂×C₁₇	1	1	yes	characteristic
185	#2982	C₂×C₁₇	1	1	yes	characteristic, complemented
186	#1682	C₂×C₁₇	1	2	yes	complemented
187	#1680	C₂×C₁₇	1	2	yes	complemented
188	#1670	C₂×C₁₇	1	2	yes	complemented
189	#1666	C₂×C₁₇	1	2	yes	complemented
190	#1572	C₂×C₁₇	1	1	yes	characteristic, complemented
191	#1553	C₂×C₁₇	1	1	yes	characteristic
192	#1544	C₂×C₁₇	1	1	yes	characteristic, complemented
193	C₂²×C₁₇	—	2	1	no	—
194	C₂²×C₁₇	—	2	1	no	—
195	C₂²×C₁₇	—	2	1	no	—
196	C₂²×C₁₇	—	8	1	no	—
197	C₂²×C₁₇	—	8	1	no	—
198	C₂²×C₁₇	—	8	1	no	—
199	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
200	C₄×C₁₇	—	2	1	no	—
201	C₄×C₁₇	—	2	4	no	—
202	C₄×C₁₇	—	2	1	no	—
203	C₄×C₁₇	—	2	1	no	—
204	C₄×C₁₇	—	2	1	no	—
205	C₄×C₁₇	—	4	2	no	—
206	C₄×C₁₇	—	8	1	no	—
207	C₄×C₁₇	—	8	1	no	—
208	C₄×C₁₇	—	8	1	no	—
209	C₄×C₁₇	C₂×#135	1	2	yes	—
210	C₄×C₁₇	#577	1	2	yes	—
211	#533	C₂²×C₁₇	1	1	yes	characteristic
212	#532	C₂²×C₁₇	1	1	yes	characteristic
213	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
214	#494	C₂²×C₁₇	1	1	yes	characteristic
215	#492	C₂²×C₁₇	1	1	yes	characteristic
216	#487	C₂²×C₁₇	1	1	yes	characteristic
217	#486	C₂²×C₁₇	1	1	yes	characteristic
218	#483	—	2	1	no	—
219	#481	—	2	1	no	—
220	#475	C₂²×C₁₇	1	2	yes	—
221	#475	C₂²×C₁₇	1	2	yes	—
222	#464	—	2	2	no	—
223	#462	C₂²×C₁₇	1	2	yes	—
224	#460	C₂²×C₁₇	1	2	yes	—
225	#452	—	2	2	no	—
226	#451	—	2	1	no	—
227	#448	—	2	1	no	—
228	C₈×Q₈	—	2	2	no	—
229	C₈×Q₈	C₂²×C₁₇	1	2	yes	—
230	C₈×Q₈	C₂²×C₁₇	1	2	yes	—
231	#441	—	2	2	no	—
232	C₄×SD₁₆	—	2	2	no	—
233	#432	C₂²×C₁₇	1	1	yes	characteristic
234	#431	—	2	2	no	—
235	#431	C₂²×C₁₇	1	1	yes	characteristic
236	#431	C₂²×C₁₇	1	1	yes	characteristic
237	#431	C₂²×C₁₇	1	1	yes	characteristic
238	#335	C₂²×C₁₇	1	2	yes	—
239	#334	C₂²×C₁₇	1	2	yes	—
240	#332	C₂²×C₁₇	1	2	yes	—
241	#332	C₂²×C₁₇	1	2	yes	—
242	#332	C₂²×C₁₇	1	2	yes	—
243	#331	C₂²×C₁₇	1	2	yes	—
244	C₂×C₁₇	—	4	1	no	—
245	C₂×C₁₇	—	16	1	no	—
246	C₂×C₁₇	#3043	1	1	yes	characteristic
247	C₂×C₁₇	#3050	1	1	yes	characteristic
248	C₂×C₁₇	#3069	1	1	yes	characteristic
249	C₂×#41	—	2	1	no	—
250	C₂²×Q₈	D₄×C₁₇	1	1	yes	characteristic
251	C₂×Q₁₆	—	2	2	no	—
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×SD₁₆	—	2	2	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
256	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
257	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
258	#127	C₂³×C₁₇	1	1	yes	characteristic
259	#125	—	2	1	no	—
260	#124	—	2	1	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	#121	—	2	1	no	—
264	#121	—	2	1	no	—
265	C₄×Q₈	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	C₄×Q₈	D₄×C₁₇	1	2	yes	—
270	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	#117	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
278	#106	—	2	2	no	—
279	#106	—	2	2	no	—
280	C₄⋊C₈	—	2	2	no	—
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	D₄×C₁₇	1	2	yes	—
283	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
284	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
285	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
286	#103	—	2	2	no	—
287	#103	—	2	2	no	—
288	#103	—	2	2	no	—
289	#103	—	2	2	no	—
290	#102	—	2	2	no	—
291	#102	—	2	2	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	D₄×C₁₇	1	2	yes	—
296	#97	—	2	1	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	—	2	1	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
302	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
303	C₁₇	#19400	1	1	yes	characteristic, direct product factor, Sylow
304	#41	—	8	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
320	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
321	Q₁₆	—	4	4	no	—
322	Q₁₆	—	8	2	no	—
323	SD₁₆	—	4	4	no	—
324	SD₁₆	—	8	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
329	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	4	1	no	—
348	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
350	C₄²	#41×C₁₇	1	1	yes	characteristic
351	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
352	C₂³	—	4	1	no	—
353	C₂³	C₁₇×#121	1	1	yes	characteristic
354	Q₈	—	2	4	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	2	no	—
359	Q₈	C₁₇×#135	1	4	yes	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	8	1	no	—
363	D₄	—	8	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
376	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
377	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	1	no	—
391	C₂²	—	8	1	no	—
392	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	4	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	1	no	—
402	C₄	C₂×C₁₇×#135	1	2	yes	—
403	C₄	C₁₇×#577	1	2	yes	—
404	C₂	—	4	1	no	—
405	C₂	—	16	1	no	—
406	C₂	C₁₇×#3043	1	1	yes	characteristic
407	C₂	C₁₇×#3050	1	1	yes	characteristic
408	C₂	C₁₇×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#532	C₂²
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
2. C₁₇×#3113	C₂	semidirect
4. C₁₇×#2982	C₂	semidirect
5. C₁₇×#1682	C₂	semidirect
6. C₁₇×#1680	C₂	semidirect
7. C₁₇×#1670	C₂	semidirect
8. C₁₇×#1666	C₂	semidirect
9. C₁₇×#1572	C₂	semidirect
11. C₁₇×#1544	C₂	semidirect
147. #19400	C₁₇	direct (N × H)
183. #3113	C₂×C₁₇	semidirect
185. #2982	C₂×C₁₇	semidirect
186. #1682	C₂×C₁₇	semidirect
187. #1680	C₂×C₁₇	semidirect
188. #1670	C₂×C₁₇	semidirect
189. #1666	C₂×C₁₇	semidirect
190. #1572	C₂×C₁₇	semidirect
192. #1544	C₂×C₁₇	semidirect
303. C₁₇	#19400	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×#3210	2
C₁₇×#3113	2
C₁₇×#3103	2
C₁₇×#2982	2
C₁₇×#1682	2
C₁₇×#1680	2
C₁₇×#1670	2
C₁₇×#1666	2
C₁₇×#1572	2
C₁₇×#1553	2
C₁₇×#1544	2
#19400	17

Subgroups — C17×#19400 #16877144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#19400 #16877144