Subgroups — C₁₇×#22103 #16879847

Order 4352.

728 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#433	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2396	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1939	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1924	C₂	1	2	yes	maximal
8	C₁₇×#1923	C₂	1	2	yes	maximal
9	C₁₇×#1917	C₂	1	2	yes	maximal, complemented
10	C₁₇×#1798	C₂	1	1	yes	maximal, characteristic
11	C₈×C₄⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
13	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
14	C₁₇×#446	—	2	4	no	—
15	C₁₇×#433	—	2	4	no	—
16	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₇×#97	C₂²	1	2	yes	—
26	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
29	C₁₇×#400	C₄	1	1	yes	characteristic
30	C₁₇×#399	C₄	1	1	yes	characteristic
31	C₁₇×#398	C₄	1	2	yes	—
32	C₁₇×#396	C₄	1	2	yes	—
33	C₁₇×#395	C₄	1	1	yes	characteristic
34	C₁₇×#393	C₄	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
38	C₁₇×#336	C₂²	1	2	yes	—
39	C₁₇×#336	C₂²	1	2	yes	—
40	C₁₇×#336	C₂²	1	2	yes	—
41	C₁₇×#336	C₂²	1	2	yes	—
42	C₁₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
51	C₄×Q₈×C₁₇	—	2	2	no	—
52	C₄×Q₈×C₁₇	—	2	2	no	—
53	C₁₇×#117	—	2	2	no	—
54	C₁₇×#117	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
70	C₁₇×C₄⋊C₈	—	2	2	no	—
71	C₁₇×C₄⋊C₈	—	2	2	no	—
72	C₁₇×C₄⋊C₈	—	2	4	no	—
73	C₁₇×C₄⋊C₈	—	2	2	no	—
74	C₁₇×C₄⋊C₈	—	2	2	no	—
75	C₁₇×C₄⋊C₈	—	4	2	no	—
76	C₁₇×C₂²⋊C₈	—	2	2	no	—
77	C₁₇×C₂²⋊C₈	—	2	2	no	—
78	C₁₇×C₂²⋊C₈	—	4	2	no	—
79	C₁₇×#97	—	2	4	no	—
80	C₁₇×#97	—	2	2	no	—
81	C₄×C₈×C₁₇	—	4	2	no	—
82	C₄×C₈×C₁₇	D₄	1	4	yes	—
83	C₁₇×#95	C₂×C₄	1	2	yes	—
84	C₁₇×#95	C₂×C₄	1	2	yes	—
85	C₁₇×#95	C₂×C₄	1	2	yes	—
86	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
87	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
88	C₁₇×#95	C₂×C₄	1	2	yes	—
89	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
90	C₂×Q₈×C₁₇	—	2	2	no	—
91	C₂×Q₈×C₁₇	—	4	2	no	—
92	C₂²×C₄×C₁₇	—	2	1	no	—
93	C₂²×C₄×C₁₇	—	2	1	no	—
94	C₂²×C₄×C₁₇	—	2	1	no	—
95	C₂²×C₄×C₁₇	—	2	1	no	—
96	C₂²×C₄×C₁₇	—	2	1	no	—
97	C₂²×C₄×C₁₇	—	2	1	no	—
98	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₁₇	—	2	1	no	—
109	C₂×C₈×C₁₇	—	2	1	no	—
110	C₂×C₈×C₁₇	—	2	1	no	—
111	C₂×C₈×C₁₇	—	2	1	no	—
112	C₂×C₈×C₁₇	—	2	1	no	—
113	C₂×C₈×C₁₇	—	2	1	no	—
114	C₂×C₈×C₁₇	—	2	2	no	—
115	C₂×C₈×C₁₇	—	2	2	no	—
116	C₂×C₈×C₁₇	—	2	2	no	—
117	C₂×C₈×C₁₇	—	2	2	no	—
118	C₂×C₈×C₁₇	—	2	1	no	—
119	C₂×C₈×C₁₇	—	2	1	no	—
120	C₂×C₈×C₁₇	—	2	1	no	—
121	C₂×C₈×C₁₇	—	2	1	no	—
122	C₂×C₈×C₁₇	—	2	2	no	—
123	C₂×C₈×C₁₇	—	2	2	no	—
124	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₁₇	—	2	2	no	—
127	C₄⋊C₄×C₁₇	—	2	2	no	—
128	C₄⋊C₄×C₁₇	—	2	2	no	—
129	C₄⋊C₄×C₁₇	—	2	4	no	—
130	C₄⋊C₄×C₁₇	—	2	4	no	—
131	C₄⋊C₄×C₁₇	—	2	4	no	—
132	C₄⋊C₄×C₁₇	—	4	2	no	—
133	C₂²⋊C₄×C₁₇	—	2	2	no	—
134	C₂²⋊C₄×C₁₇	—	2	2	no	—
135	C₂²⋊C₄×C₁₇	—	2	4	no	—
136	C₂²⋊C₄×C₁₇	—	4	2	no	—
137	C₄²×C₁₇	—	2	2	no	—
138	C₄²×C₁₇	—	2	1	no	—
139	C₄²×C₁₇	—	2	1	no	—
140	C₄²×C₁₇	—	2	2	no	—
141	C₄²×C₁₇	—	2	2	no	—
142	C₄²×C₁₇	—	2	2	no	—
143	C₄²×C₁₇	C₂×D₄	1	2	yes	—
144	C₄²×C₁₇	#41	1	2	yes	—
145	#22103	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂³×C₁₇	—	2	1	no	—
147	C₂³×C₁₇	—	2	1	no	—
148	C₂³×C₁₇	—	2	1	no	—
149	C₂³×C₁₇	—	2	2	no	—
150	C₂³×C₁₇	—	2	2	no	—
151	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
152	Q₈×C₁₇	—	4	4	no	—
153	C₂×C₄×C₁₇	—	2	2	no	—
154	C₂×C₄×C₁₇	—	2	2	no	—
155	C₂×C₄×C₁₇	—	2	2	no	—
156	C₂×C₄×C₁₇	—	2	2	no	—
157	C₂×C₄×C₁₇	—	2	1	no	—
158	C₂×C₄×C₁₇	—	2	1	no	—
159	C₂×C₄×C₁₇	—	2	2	no	—
160	C₂×C₄×C₁₇	—	2	2	no	—
161	C₂×C₄×C₁₇	—	2	1	no	—
162	C₂×C₄×C₁₇	—	2	1	no	—
163	C₂×C₄×C₁₇	—	2	2	no	—
164	C₂×C₄×C₁₇	—	2	1	no	—
165	C₂×C₄×C₁₇	—	2	2	no	—
166	C₂×C₄×C₁₇	—	2	2	no	—
167	C₂×C₄×C₁₇	—	2	2	no	—
168	C₂×C₄×C₁₇	—	2	2	no	—
169	C₂×C₄×C₁₇	—	2	2	no	—
170	C₂×C₄×C₁₇	—	2	2	no	—
171	C₂×C₄×C₁₇	—	2	2	no	—
172	C₂×C₄×C₁₇	—	2	2	no	—
173	C₂×C₄×C₁₇	—	4	1	no	—
174	C₂×C₄×C₁₇	—	4	1	no	—
175	C₂×C₄×C₁₇	—	4	1	no	—
176	C₂×C₄×C₁₇	—	4	1	no	—
177	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₁₇	#131	1	4	yes	—
180	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
186	C₈×C₁₇	—	2	2	no	—
187	C₈×C₁₇	—	2	2	no	—
188	C₈×C₁₇	—	4	1	no	—
189	C₈×C₁₇	—	4	1	no	—
190	C₈×C₁₇	—	4	2	no	—
191	C₈×C₁₇	—	4	2	no	—
192	C₂×#446	C₂×C₁₇	1	1	yes	characteristic, complemented
193	C₂×#433	C₂×C₁₇	1	1	yes	characteristic
194	#2396	C₂×C₁₇	1	1	yes	characteristic
195	#1985	C₂×C₁₇	1	1	yes	characteristic, complemented
196	#1940	C₂×C₁₇	1	1	yes	characteristic, complemented
197	#1939	C₂×C₁₇	1	2	yes	complemented
198	#1924	C₂×C₁₇	1	2	yes	—
199	#1923	C₂×C₁₇	1	2	yes	—
200	#1917	C₂×C₁₇	1	2	yes	complemented
201	#1798	C₂×C₁₇	1	1	yes	characteristic
202	C₈×C₄⋊C₄	C₂×C₁₇	1	1	yes	characteristic, complemented
203	C₂²×C₁₇	—	4	1	no	—
204	C₂²×C₁₇	—	4	1	no	—
205	C₂²×C₁₇	—	4	1	no	—
206	C₂²×C₁₇	—	4	2	no	—
207	C₂²×C₁₇	—	4	2	no	—
208	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
209	C₂²×C₁₇	#519	1	1	yes	characteristic
210	C₂²×C₁₇	#520	1	1	yes	characteristic
211	C₂²×C₁₇	C₂×#131	1	2	yes	—
212	C₂²×C₁₇	#568	1	2	yes	—
213	C₄×C₁₇	—	2	2	no	—
214	C₄×C₁₇	—	2	2	no	—
215	C₄×C₁₇	—	2	4	no	—
216	C₄×C₁₇	—	4	1	no	—
217	C₄×C₁₇	—	4	1	no	—
218	C₄×C₁₇	—	4	2	no	—
219	C₄×C₁₇	—	4	1	no	—
220	C₄×C₁₇	—	4	2	no	—
221	C₄×C₁₇	—	4	2	no	—
222	C₄×C₁₇	#536	1	1	yes	characteristic
223	C₄×C₁₇	#537	1	1	yes	characteristic
224	C₄×C₁₇	#541	1	1	yes	characteristic
225	C₄×C₁₇	#542	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
227	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
228	#446	—	2	4	no	—
229	#433	—	2	4	no	—
230	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
235	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
236	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
237	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
238	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	—
239	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
240	C₂×#97	C₂²×C₁₇	1	2	yes	—
241	C₂×C₄×C₈	C₂²×C₁₇	1	2	yes	—
242	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
243	#400	C₄×C₁₇	1	1	yes	characteristic
244	#399	C₄×C₁₇	1	1	yes	characteristic
245	#398	C₄×C₁₇	1	2	yes	—
246	#396	C₄×C₁₇	1	2	yes	—
247	#395	C₄×C₁₇	1	1	yes	characteristic
248	#393	C₄×C₁₇	1	1	yes	characteristic
249	C₄×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
250	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
251	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
252	#336	C₂²×C₁₇	1	2	yes	—
253	#336	C₂²×C₁₇	1	2	yes	—
254	#336	C₂²×C₁₇	1	2	yes	—
255	#336	C₂²×C₁₇	1	2	yes	—
256	#336	C₂²×C₁₇	1	2	yes	—
257	C₂×C₁₇	—	8	1	no	—
258	C₂×C₁₇	#2323	1	1	yes	characteristic
259	C₂×C₁₇	#2930	1	1	yes	characteristic
260	C₂×C₁₇	#2931	1	1	yes	characteristic
261	C₂×C₁₇	#2985	1	2	yes	—
262	C₂×C₁₇	#2992	1	2	yes	—
263	C₂²×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
266	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
269	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
278	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
280	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
281	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
285	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
286	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
288	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
289	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	4	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	4	2	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	C₂²⋊C₈	—	2	2	no	—
298	C₂²⋊C₈	—	4	2	no	—
299	#97	—	2	4	no	—
300	#97	—	2	2	no	—
301	C₄×C₈	—	4	2	no	—
302	C₄×C₈	D₄×C₁₇	1	4	yes	—
303	#95	C₂×C₄×C₁₇	1	2	yes	—
304	#95	C₂×C₄×C₁₇	1	2	yes	—
305	#95	C₂×C₄×C₁₇	1	2	yes	—
306	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
307	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
308	#95	C₂×C₄×C₁₇	1	2	yes	—
309	C₁₇	#22103	1	1	yes	characteristic, direct product factor, Sylow
310	C₂⁴	C₂²×C₄×C₁₇	1	1	yes	characteristic
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
320	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
321	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
322	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
324	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
325	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
326	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
327	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
328	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
346	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	C₂×D₄×C₁₇	1	2	yes	—
365	C₄²	#41×C₁₇	1	2	yes	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
372	Q₈	—	4	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
398	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
399	C₂×C₄	C₁₇×#131	1	4	yes	—
400	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
402	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
404	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
405	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	2	no	—
411	C₈	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
418	C₂²	C₁₇×#519	1	1	yes	characteristic
419	C₂²	C₁₇×#520	1	1	yes	characteristic
420	C₂²	C₂×C₁₇×#131	1	2	yes	—
421	C₂²	C₁₇×#568	1	2	yes	—
422	C₄	—	2	4	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	2	no	—
431	C₄	C₁₇×#536	1	1	yes	characteristic
432	C₄	C₁₇×#537	1	1	yes	characteristic
433	C₄	C₁₇×#541	1	1	yes	characteristic
434	C₄	C₁₇×#542	1	1	yes	characteristic
435	C₂	—	8	1	no	—
436	C₂	C₁₇×#2323	1	1	yes	characteristic
437	C₂	C₁₇×#2930	1	1	yes	characteristic
438	C₂	C₁₇×#2931	1	1	yes	characteristic
439	C₂	C₁₇×#2985	1	2	yes	—
440	C₂	C₁₇×#2992	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
socle	C₂³×C₁₇	C₂³×C₄
prime radical	C₂⁴×C₁₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#446	C₂	semidirect
4. C₁₇×#1985	C₂	semidirect
5. C₁₇×#1940	C₂	semidirect
6. C₁₇×#1939	C₂	semidirect
9. C₁₇×#1917	C₂	semidirect
11. C₈×C₄⋊C₄×C₁₇	C₂	semidirect
145. #22103	C₁₇	direct (N × H)
192. C₂×#446	C₂×C₁₇	semidirect
195. #1985	C₂×C₁₇	semidirect
196. #1940	C₂×C₁₇	semidirect
197. #1939	C₂×C₁₇	semidirect
200. #1917	C₂×C₁₇	semidirect
202. C₈×C₄⋊C₄	C₂×C₁₇	semidirect
309. C₁₇	#22103	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×#446	2
C₂×C₁₇×#433	2
C₁₇×#2396	2
C₁₇×#1985	2
C₁₇×#1940	2
C₁₇×#1939	2
C₁₇×#1924	2
C₁₇×#1923	2
C₁₇×#1917	2
C₁₇×#1798	2
C₈×C₄⋊C₄×C₁₇	2
#22103	17

Subgroups — C17×#22103 #16879847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22103 #16879847