Subgroups — C₁₇×#61378 #16919122

Order 4352.

1810 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3501	C₂	1	2	yes	maximal, complemented
2	C₁₇×#3389	C₂	1	8	yes	maximal, complemented
3	C₁₇×#3384	C₂	1	8	yes	maximal, complemented
4	C₁₇×#3163	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#3081	C₂	1	4	yes	maximal, complemented
7	C₁₇×#3077	C₂	1	2	yes	maximal, complemented
8	C₁₇×#2961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#2948	C₂	1	2	yes	maximal
10	C₂×C₁₇×#442	C₂	1	1	yes	maximal, characteristic
11	C₂²×D₈×C₁₇	C₂²	1	1	yes	characteristic
12	C₁₇×#554	—	2	2	no	—
13	C₁₇×#554	—	2	4	no	—
14	C₁₇×#554	C₂²	1	8	yes	complemented
15	C₁₇×#554	C₂²	1	4	yes	complemented
16	D₄×Q₈×C₁₇	—	2	2	no	—
17	D₄×Q₈×C₁₇	C₂²	1	4	yes	complemented
18	C₁₇×#544	C₂²	1	4	yes	—
19	C₁₇×#543	—	2	4	no	—
20	C₁₇×#533	C₂²	1	2	yes	—
21	C₁₇×#533	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×C₂²⋊Q₈	—	2	4	no	—
23	C₁₇×#518	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
25	C₁₇×#501	C₂²	1	4	yes	complemented
26	C₁₇×#501	C₂²	1	8	yes	complemented
27	C₁₇×#501	C₂²	1	4	yes	complemented
28	C₁₇×#499	C₂²	1	4	yes	complemented
29	C₁₇×#498	C₂²	1	4	yes	complemented
30	C₁₇×#478	C₂²	1	8	yes	complemented
31	C₁₇×#478	C₂²	1	8	yes	complemented
32	C₁₇×#478	C₂²	1	8	yes	complemented
33	C₁₇×#476	C₂²	1	4	yes	complemented
34	C₁₇×#476	C₂²	1	8	yes	complemented
35	C₁₇×#474	C₂²	1	4	yes	complemented
36	C₁₇×#474	C₂²	1	8	yes	complemented
37	C₁₇×#446	C₂²	1	8	yes	complemented
38	C₁₇×#442	C₂²	1	4	yes	—
39	C₁₇×#442	C₂²	1	4	yes	—
40	C₁₇×#442	C₂²	1	8	yes	—
41	C₄×D₈×C₁₇	C₂²	1	8	yes	—
42	C₁₇×#428	C₂²	1	4	yes	—
43	C₁₇×#427	C₂²	1	2	yes	—
44	C₁₇×#427	C₂²	1	2	yes	—
45	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
46	C₁₇×#424	C₂²	1	2	yes	—
47	C₁₇×#423	C₂²	1	1	yes	characteristic
48	C₁₇×#418	C₂²	1	4	yes	—
49	C₂×C₁₇×#102	C₂²	1	2	yes	—
50	C₁₇×#405	C₂²	1	2	yes	—
51	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₁₇	—	2	4	no	—
53	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₇	—	2	2	no	—
55	C₂×D₈×C₁₇	Q₈	1	8	yes	complemented
56	C₂×D₈×C₁₇	C₂³	1	4	yes	—
57	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
60	C₁₇×C₄⋊Q₈	—	2	4	no	—
61	C₁₇×C₄⋊Q₈	D₄	1	2	yes	—
62	C₁₇×C₄⋊Q₈	C₂³	1	8	yes	—
63	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₇×#125	—	2	4	no	—
66	C₁₇×#125	D₄	1	2	yes	—
67	C₁₇×#125	C₂³	1	8	yes	—
68	C₁₇×#125	C₂³	1	4	yes	—
69	C₁₇×C₂²⋊Q₈	—	2	4	no	—
70	C₁₇×C₂²⋊Q₈	—	2	8	no	—
71	C₁₇×C₂²⋊Q₈	—	2	2	no	—
72	C₁₇×C₂²⋊Q₈	—	2	2	no	—
73	C₁₇×C₂²⋊Q₈	—	2	4	no	—
74	C₁₇×C₂²⋊Q₈	—	2	8	no	—
75	C₁₇×C₂²⋊Q₈	—	2	8	no	—
76	C₁₇×C₂²⋊Q₈	—	2	8	no	—
77	C₁₇×C₂²⋊Q₈	—	2	8	no	—
78	C₁₇×C₂²⋊Q₈	—	2	8	no	—
79	C₁₇×C₂²⋊Q₈	D₄	1	4	yes	—
80	C₄×Q₈×C₁₇	—	2	2	no	—
81	C₄×Q₈×C₁₇	—	2	2	no	—
82	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
83	C₄×D₄×C₁₇	—	2	4	no	—
84	C₄×D₄×C₁₇	—	2	4	no	—
85	C₄×D₄×C₁₇	—	2	2	no	—
86	C₄×D₄×C₁₇	—	2	2	no	—
87	C₄×D₄×C₁₇	C₂³	1	4	yes	—
88	C₄×D₄×C₁₇	C₂³	1	4	yes	—
89	C₄×D₄×C₁₇	C₂³	1	8	yes	—
90	C₄×D₄×C₁₇	C₂³	1	8	yes	—
91	C₁₇×#117	C₂³	1	4	yes	—
92	C₁₇×#117	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
94	C₂×C₄⋊C₄×C₁₇	—	2	8	no	—
95	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
96	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₁₇	—	2	8	no	—
98	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
99	C₁₇×#107	C₂³	1	8	yes	—
100	C₁₇×#107	C₂³	1	4	yes	—
101	C₁₇×#107	C₂³	1	4	yes	—
102	C₁₇×#106	C₂³	1	2	yes	—
103	C₁₇×#106	C₂³	1	4	yes	—
104	C₁₇×#106	C₂³	1	8	yes	—
105	C₁₇×#106	C₂³	1	2	yes	—
106	C₁₇×#106	C₂³	1	2	yes	—
107	C₁₇×#106	C₂³	1	2	yes	—
108	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
109	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
110	C₁₇×#102	C₂³	1	8	yes	—
111	C₁₇×#102	C₂³	1	8	yes	—
112	C₁₇×#102	C₂³	1	8	yes	—
113	C₁₇×#97	C₂³	1	4	yes	—
114	C₁₇×#97	C₂³	1	4	yes	—
115	C₄×C₈×C₁₇	C₂³	1	4	yes	—
116	C₂⁴×C₁₇	—	2	2	no	—
117	C₂×Q₈×C₁₇	—	2	2	no	—
118	C₂×Q₈×C₁₇	—	2	2	no	—
119	C₂×Q₈×C₁₇	—	2	8	no	—
120	C₂×Q₈×C₁₇	—	8	8	no	—
121	C₂×Q₈×C₁₇	C₂×D₄	1	4	yes	—
122	C₂×D₄×C₁₇	—	2	2	no	—
123	C₂×D₄×C₁₇	—	2	4	no	—
124	C₂×D₄×C₁₇	C₂×Q₈	1	8	yes	complemented
125	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₁₇	—	2	2	no	—
127	C₂²×C₄×C₁₇	—	2	4	no	—
128	C₂²×C₄×C₁₇	—	2	4	no	—
129	C₂²×C₄×C₁₇	—	2	8	no	—
130	C₂²×C₄×C₁₇	—	2	8	no	—
131	C₂²×C₄×C₁₇	—	8	4	no	—
132	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
134	D₈×C₁₇	C₂×Q₈	1	16	yes	complemented
135	M₁₆×C₁₇	—	2	4	no	—
136	C₂×C₈×C₁₇	—	2	2	no	—
137	C₂×C₈×C₁₇	C₂×Q₈	1	4	yes	complemented
138	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
139	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
140	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
141	C₄⋊C₄×C₁₇	—	2	4	no	—
142	C₄⋊C₄×C₁₇	—	2	2	no	—
143	C₄⋊C₄×C₁₇	—	2	8	no	—
144	C₄⋊C₄×C₁₇	—	2	8	no	—
145	C₄⋊C₄×C₁₇	—	2	8	no	—
146	C₄⋊C₄×C₁₇	—	2	4	no	—
147	C₄⋊C₄×C₁₇	—	2	2	no	—
148	C₄⋊C₄×C₁₇	—	2	2	no	—
149	C₄⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
150	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
151	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
152	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
153	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
154	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
155	C₂²⋊C₄×C₁₇	—	2	4	no	—
156	C₂²⋊C₄×C₁₇	—	2	8	no	—
157	C₂²⋊C₄×C₁₇	—	2	8	no	—
158	C₂²⋊C₄×C₁₇	—	2	4	no	—
159	C₂²⋊C₄×C₁₇	—	2	4	no	—
160	C₂²⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
161	C₄²×C₁₇	—	2	4	no	—
162	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₇	C₂⁴	1	4	yes	—
165	C₄²×C₁₇	C₂⁴	1	2	yes	—
166	#61378	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₁₇	—	2	4	no	—
168	C₂³×C₁₇	—	2	8	no	—
169	C₂³×C₁₇	—	8	2	no	—
170	C₂³×C₁₇	—	8	2	no	—
171	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₁₇	—	4	4	no	—
173	Q₈×C₁₇	—	4	4	no	—
174	Q₈×C₁₇	—	8	2	no	—
175	Q₈×C₁₇	—	8	8	no	—
176	D₄×C₁₇	—	2	8	no	—
177	D₄×C₁₇	—	2	4	no	—
178	D₄×C₁₇	C₂²×Q₈	1	8	yes	—
179	C₂×C₄×C₁₇	—	2	4	no	—
180	C₂×C₄×C₁₇	—	2	4	no	—
181	C₂×C₄×C₁₇	—	2	4	no	—
182	C₂×C₄×C₁₇	—	4	2	no	—
183	C₂×C₄×C₁₇	—	4	8	no	—
184	C₂×C₄×C₁₇	—	8	8	no	—
185	C₂×C₄×C₁₇	—	8	4	no	—
186	C₂×C₄×C₁₇	—	8	8	no	—
187	C₂×C₄×C₁₇	—	8	2	no	—
188	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₁₇	C₂²×D₄	1	8	yes	—
191	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₇	C₂²×Q₈	1	2	yes	—
193	C₂×C₄×C₁₇	2₋¹⁺⁴	1	2	yes	—
194	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
195	C₈×C₁₇	—	2	2	no	—
196	C₈×C₁₇	—	2	4	no	—
197	C₈×C₁₇	C₂²×Q₈	1	4	yes	—
198	#3501	C₂×C₁₇	1	2	yes	complemented
199	#3389	C₂×C₁₇	1	8	yes	complemented
200	#3384	C₂×C₁₇	1	8	yes	complemented
201	#3163	C₂×C₁₇	1	2	yes	complemented
202	#3162	C₂×C₁₇	1	1	yes	characteristic, complemented
203	#3081	C₂×C₁₇	1	4	yes	complemented
204	#3077	C₂×C₁₇	1	2	yes	complemented
205	#2961	C₂×C₁₇	1	1	yes	characteristic, complemented
206	#2948	C₂×C₁₇	1	2	yes	—
207	C₂×#442	C₂×C₁₇	1	1	yes	characteristic
208	C₂²×C₁₇	—	2	2	no	—
209	C₂²×C₁₇	—	2	8	no	—
210	C₂²×C₁₇	—	4	4	no	—
211	C₂²×C₁₇	—	4	4	no	—
212	C₂²×C₁₇	—	8	8	no	—
213	C₂²×C₁₇	D₄×Q₈	1	2	yes	—
214	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
215	C₄×C₁₇	—	2	2	no	—
216	C₄×C₁₇	—	2	2	no	—
217	C₄×C₁₇	—	2	8	no	—
218	C₄×C₁₇	—	4	4	no	—
219	C₄×C₁₇	—	4	4	no	—
220	C₄×C₁₇	—	4	4	no	—
221	C₄×C₁₇	D₄×Q₈	1	2	yes	—
222	C₄×C₁₇	C₂³×Q₈	1	1	yes	characteristic
223	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
224	C₂²×D₈	C₂²×C₁₇	1	1	yes	characteristic
225	#554	—	2	2	no	—
226	#554	—	2	4	no	—
227	#554	C₂²×C₁₇	1	8	yes	complemented
228	#554	C₂²×C₁₇	1	4	yes	complemented
229	D₄×Q₈	—	2	2	no	—
230	D₄×Q₈	C₂²×C₁₇	1	4	yes	complemented
231	#544	C₂²×C₁₇	1	4	yes	—
232	#543	—	2	4	no	—
233	#533	C₂²×C₁₇	1	2	yes	—
234	#533	C₂²×C₁₇	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	—	2	4	no	—
236	#518	C₂²×C₁₇	1	4	yes	—
237	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
238	#501	C₂²×C₁₇	1	4	yes	complemented
239	#501	C₂²×C₁₇	1	8	yes	complemented
240	#501	C₂²×C₁₇	1	4	yes	complemented
241	#499	C₂²×C₁₇	1	4	yes	complemented
242	#498	C₂²×C₁₇	1	4	yes	complemented
243	#478	C₂²×C₁₇	1	8	yes	complemented
244	#478	C₂²×C₁₇	1	8	yes	complemented
245	#478	C₂²×C₁₇	1	8	yes	complemented
246	#476	C₂²×C₁₇	1	4	yes	complemented
247	#476	C₂²×C₁₇	1	8	yes	complemented
248	#474	C₂²×C₁₇	1	4	yes	complemented
249	#474	C₂²×C₁₇	1	8	yes	complemented
250	#446	C₂²×C₁₇	1	8	yes	complemented
251	#442	C₂²×C₁₇	1	4	yes	—
252	#442	C₂²×C₁₇	1	8	yes	—
253	#442	C₂²×C₁₇	1	4	yes	—
254	C₄×D₈	C₂²×C₁₇	1	8	yes	—
255	#428	C₂²×C₁₇	1	4	yes	—
256	#427	C₂²×C₁₇	1	2	yes	—
257	#427	C₂²×C₁₇	1	2	yes	—
258	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
259	#424	C₂²×C₁₇	1	2	yes	—
260	#423	C₂²×C₁₇	1	1	yes	characteristic
261	#418	C₂²×C₁₇	1	4	yes	—
262	C₂×#102	C₂²×C₁₇	1	2	yes	—
263	#405	C₂²×C₁₇	1	2	yes	—
264	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
265	C₂×C₁₇	—	2	2	no	—
266	C₂×C₁₇	—	4	8	no	—
267	C₂×C₁₇	C₂×D₄×Q₈	1	1	yes	characteristic
268	C₂×C₁₇	#3585	1	2	yes	—
269	C₂²×Q₈	—	2	4	no	—
270	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
271	C₂³×C₄	—	2	2	no	—
272	C₂×D₈	Q₈×C₁₇	1	8	yes	complemented
273	C₂×D₈	C₂³×C₁₇	1	4	yes	—
274	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
277	C₄⋊Q₈	—	2	4	no	—
278	C₄⋊Q₈	D₄×C₁₇	1	2	yes	—
279	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
280	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
281	C₄⋊Q₈	C₂³×C₁₇	1	8	yes	—
282	#125	—	2	4	no	—
283	#125	D₄×C₁₇	1	2	yes	—
284	#125	C₂³×C₁₇	1	4	yes	—
285	#125	C₂³×C₁₇	1	8	yes	—
286	C₂²⋊Q₈	—	2	4	no	—
287	C₂²⋊Q₈	—	2	8	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	2	8	no	—
292	C₂²⋊Q₈	—	2	8	no	—
293	C₂²⋊Q₈	—	2	8	no	—
294	C₂²⋊Q₈	—	2	8	no	—
295	C₂²⋊Q₈	—	2	8	no	—
296	C₂²⋊Q₈	D₄×C₁₇	1	4	yes	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	C₂³×C₁₇	1	4	yes	—
305	C₄×D₄	C₂³×C₁₇	1	4	yes	—
306	C₄×D₄	C₂³×C₁₇	1	8	yes	—
307	C₄×D₄	C₂³×C₁₇	1	8	yes	—
308	#117	C₂³×C₁₇	1	4	yes	—
309	#117	C₂³×C₁₇	1	2	yes	—
310	C₂×C₄⋊C₄	—	2	8	no	—
311	C₂×C₄⋊C₄	—	2	4	no	—
312	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	8	no	—
315	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
316	#107	C₂³×C₁₇	1	4	yes	—
317	#107	C₂³×C₁₇	1	4	yes	—
318	#107	C₂³×C₁₇	1	8	yes	—
319	#106	C₂³×C₁₇	1	4	yes	—
320	#106	C₂³×C₁₇	1	2	yes	—
321	#106	C₂³×C₁₇	1	2	yes	—
322	#106	C₂³×C₁₇	1	2	yes	—
323	#106	C₂³×C₁₇	1	2	yes	—
324	#106	C₂³×C₁₇	1	8	yes	—
325	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
326	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
327	#102	C₂³×C₁₇	1	8	yes	—
328	#102	C₂³×C₁₇	1	8	yes	—
329	#102	C₂³×C₁₇	1	8	yes	—
330	#97	C₂³×C₁₇	1	4	yes	—
331	#97	C₂³×C₁₇	1	4	yes	—
332	C₄×C₈	C₂³×C₁₇	1	4	yes	—
333	C₁₇	#61378	1	1	yes	characteristic, direct product factor, Sylow
334	C₂⁴	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	8	no	—
338	C₂×Q₈	—	8	8	no	—
339	C₂×Q₈	C₂×D₄×C₁₇	1	4	yes	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	C₂×Q₈×C₁₇	1	8	yes	complemented
343	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	8	4	no	—
350	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
352	D₈	C₂×Q₈×C₁₇	1	16	yes	complemented
353	M₁₆	—	2	4	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	C₂×Q₈×C₁₇	1	4	yes	complemented
356	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
357	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
358	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
368	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
369	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
370	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
371	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
372	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
379	C₄²	—	2	4	no	—
380	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
381	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
382	C₄²	C₂⁴×C₁₇	1	4	yes	—
383	C₄²	C₂⁴×C₁₇	1	2	yes	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	8	no	—
386	C₂³	—	8	2	no	—
387	C₂³	—	8	2	no	—
388	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
389	Q₈	—	4	4	no	—
390	Q₈	—	4	4	no	—
391	Q₈	—	8	8	no	—
392	Q₈	—	8	2	no	—
393	D₄	—	2	8	no	—
394	D₄	—	2	4	no	—
395	D₄	C₂²×Q₈×C₁₇	1	8	yes	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	—	8	8	no	—
403	C₂×C₄	—	8	8	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
406	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₁₇	1	8	yes	—
408	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
409	C₂×C₄	C₂²×Q₈×C₁₇	1	2	yes	—
410	C₂×C₄	C₁₇×2₋¹⁺⁴	1	2	yes	—
411	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	4	no	—
414	C₈	C₂²×Q₈×C₁₇	1	4	yes	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	8	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	8	8	no	—
420	C₂²	D₄×Q₈×C₁₇	1	2	yes	—
421	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	8	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	D₄×Q₈×C₁₇	1	2	yes	—
429	C₄	C₂³×Q₈×C₁₇	1	1	yes	characteristic
430	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
431	C₂	—	2	2	no	—
432	C₂	—	4	8	no	—
433	C₂	C₂×D₄×Q₈×C₁₇	1	1	yes	characteristic
434	C₂	C₁₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₂²×D₈×C₁₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₁₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3501	C₂	semidirect
2. C₁₇×#3389	C₂	semidirect
3. C₁₇×#3384	C₂	semidirect
4. C₁₇×#3163	C₂	semidirect
5. C₁₇×#3162	C₂	semidirect
6. C₁₇×#3081	C₂	semidirect
7. C₁₇×#3077	C₂	semidirect
8. C₁₇×#2961	C₂	semidirect
14. C₁₇×#554	C₂²	semidirect
15. C₁₇×#554	C₂²	semidirect
17. D₄×Q₈×C₁₇	C₂²	semidirect
25. C₁₇×#501	C₂²	semidirect
26. C₁₇×#501	C₂²	semidirect
27. C₁₇×#501	C₂²	semidirect
28. C₁₇×#499	C₂²	semidirect
29. C₁₇×#498	C₂²	semidirect
30. C₁₇×#478	C₂²	semidirect
31. C₁₇×#478	C₂²	semidirect
32. C₁₇×#478	C₂²	semidirect
33. C₁₇×#476	C₂²	semidirect
34. C₁₇×#476	C₂²	semidirect
35. C₁₇×#474	C₂²	semidirect
36. C₁₇×#474	C₂²	semidirect
37. C₁₇×#446	C₂²	semidirect
55. C₂×D₈×C₁₇	Q₈	semidirect
124. C₂×D₄×C₁₇	C₂×Q₈	semidirect
134. D₈×C₁₇	C₂×Q₈	semidirect
137. C₂×C₈×C₁₇	C₂×Q₈	semidirect
166. #61378	C₁₇	direct (N × H)
198. #3501	C₂×C₁₇	semidirect
199. #3389	C₂×C₁₇	semidirect
200. #3384	C₂×C₁₇	semidirect
201. #3163	C₂×C₁₇	semidirect
202. #3162	C₂×C₁₇	semidirect
203. #3081	C₂×C₁₇	semidirect
204. #3077	C₂×C₁₇	semidirect
205. #2961	C₂×C₁₇	semidirect
227. #554	C₂²×C₁₇	semidirect
228. #554	C₂²×C₁₇	semidirect
230. D₄×Q₈	C₂²×C₁₇	semidirect
238. #501	C₂²×C₁₇	semidirect
239. #501	C₂²×C₁₇	semidirect
240. #501	C₂²×C₁₇	semidirect
241. #499	C₂²×C₁₇	semidirect
242. #498	C₂²×C₁₇	semidirect
243. #478	C₂²×C₁₇	semidirect
244. #478	C₂²×C₁₇	semidirect
245. #478	C₂²×C₁₇	semidirect
246. #476	C₂²×C₁₇	semidirect
247. #476	C₂²×C₁₇	semidirect
248. #474	C₂²×C₁₇	semidirect
249. #474	C₂²×C₁₇	semidirect
250. #446	C₂²×C₁₇	semidirect
272. C₂×D₈	Q₈×C₁₇	semidirect
333. C₁₇	#61378	direct (N × H)
342. C₂×D₄	C₂×Q₈×C₁₇	semidirect
352. D₈	C₂×Q₈×C₁₇	semidirect
355. C₂×C₈	C₂×Q₈×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3501	2
C₁₇×#3389	2
C₁₇×#3384	2
C₁₇×#3163	2
C₁₇×#3162	2
C₁₇×#3081	2
C₁₇×#3077	2
C₁₇×#2961	2
C₁₇×#2948	2
C₂×C₁₇×#442	2
#61378	17

Subgroups — C17×#61378 #16919122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61378 #16919122