Subgroups — #16999908

Order 4352.

914 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11762862	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#63223	C₂	1	1	yes	maximal, characteristic
3	#14527068	C₂	1	4	yes	maximal, complemented
4	#14527065	C₂	1	4	yes	maximal, complemented
5	C₈×#63223	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₇×#431	C₂	1	1	yes	maximal, characteristic
7	C₂²×#63223	C₄	1	2	yes	—
8	#11762862	C₄	1	2	yes	—
9	#11762862	C₄	1	2	yes	—
10	#11762862	C₂²	1	2	yes	—
11	#11762862	C₂²	1	2	yes	—
12	C₂×C₄⋊#3622	C₄	1	2	yes	—
13	C₂×C₂²⋊#3622	C₄	1	2	yes	—
14	C₄×#63223	C₄	1	2	yes	—
15	C₄×#63223	C₄	1	2	yes	—
16	C₄×#63223	C₂²	1	2	yes	—
17	C₄×#63223	C₂²	1	2	yes	—
18	C₂×#10587474	C₄	1	2	yes	—
19	C₂×C₄×#3622	C₂²	1	2	yes	—
20	C₂×C₄×#3622	C₂²	1	2	yes	—
21	#11762531	C₂²	1	8	yes	complemented
22	C₈×#3622	C₂²	1	8	yes	complemented
23	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
24	C₁₇×#431	C₄	1	2	yes	—
25	C₁₇×#431	C₄	1	2	yes	—
26	C₁₇×#431	C₂²	1	2	yes	—
27	C₁₇×#431	C₂²	1	2	yes	—
28	C₂×C₁₇×C₄⋊C₈	C₄	1	2	yes	—
29	C₂×C₁₇×C₂²⋊C₈	C₄	1	2	yes	—
30	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
31	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₇	C₂×C₄	1	4	yes	—
35	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
45	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
47	C₂×#63223	C₈	1	16	yes	complemented
48	C₂×#63223	C₂×C₄	1	4	yes	—
49	C₂×#63223	C₂×C₄	1	4	yes	—
50	C₂²×#3622	C₂×C₄	1	4	yes	—
51	C₂²×#3622	C₂×C₄	1	4	yes	—
52	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
53	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
54	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
55	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
56	C₄×C₈×C₁₇	C₂×C₄	1	4	yes	—
57	C₄×C₈×C₁₇	C₂³	1	4	yes	—
58	C₂²⋊#3622	C₂×C₄	1	4	yes	—
59	C₂²⋊#3622	C₂×C₄	1	4	yes	—
60	C₄⋊#3622	C₂×C₄	1	4	yes	—
61	C₄⋊#3622	C₂×C₄	1	4	yes	—
62	#10587474	C₂×C₄	1	4	yes	—
63	#10587474	C₂×C₄	1	4	yes	—
64	C₄×#3622	C₂×C₄	1	4	yes	—
65	C₄×#3622	C₂×C₄	1	4	yes	—
66	C₄×#3622	C₂³	1	4	yes	—
67	C₄×#3622	C₂³	1	4	yes	—
68	C₂⁴×C₁₇	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₁₇	—	4	2	no	—
70	C₂²×C₄×C₁₇	—	4	2	no	—
71	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₂×C₈	1	8	yes	—
81	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₈×C₁₇	—	4	4	no	—
91	C₂×C₈×C₁₇	C₂²×C₄	1	8	yes	—
92	C₄²×C₁₇	C₄²	1	1	yes	characteristic
93	C₄²×C₁₇	C₄²	1	1	yes	characteristic
94	C₄²×C₁₇	C₄²	1	1	yes	characteristic
95	C₄²×C₁₇	C₄²	1	1	yes	characteristic
96	C₄²×C₁₇	C₄²	1	1	yes	characteristic
97	C₄²×C₁₇	C₄²	1	1	yes	characteristic
98	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
99	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
100	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
108	#63223	C₂×C₈	1	16	yes	complemented
109	#63223	C₂×C₈	1	16	yes	complemented
110	C₂×#3622	—	4	4	no	—
111	C₂×#3622	C₂×C₈	1	16	yes	complemented
112	C₂×#3622	C₂²×C₄	1	8	yes	—
113	C₂×#3622	C₂²×C₄	1	8	yes	—
114	#17314	—	17	1	no	maximal, Sylow
115	C₂³×C₁₇	—	4	1	no	—
116	C₂³×C₁₇	—	4	1	no	—
117	C₂³×C₁₇	C₄×C₈	1	4	yes	—
118	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
119	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
120	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
121	C₂×C₄×C₁₇	—	2	2	no	—
122	C₂×C₄×C₁₇	—	2	2	no	—
123	C₂×C₄×C₁₇	—	2	2	no	—
124	C₂×C₄×C₁₇	—	2	2	no	—
125	C₂×C₄×C₁₇	—	2	2	no	—
126	C₂×C₄×C₁₇	—	2	2	no	—
127	C₂×C₄×C₁₇	—	4	1	no	—
128	C₂×C₄×C₁₇	—	4	1	no	—
129	C₂×C₄×C₁₇	—	4	1	no	—
130	C₂×C₄×C₁₇	—	4	1	no	—
131	C₂×C₄×C₁₇	—	4	1	no	—
132	C₂×C₄×C₁₇	—	4	1	no	—
133	C₂×C₄×C₁₇	C₄×C₈	1	4	yes	—
134	C₂×C₄×C₁₇	C₄×C₈	1	4	yes	—
135	C₂×C₄×C₁₇	C₄×C₈	1	4	yes	—
136	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
137	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
138	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
141	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
142	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₁₇	C₂²×C₈	1	4	yes	—
146	C₂×C₄×C₁₇	C₂²×C₈	1	4	yes	—
147	C₂×C₄×C₁₇	C₂²×C₈	1	4	yes	—
148	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
151	C₈×C₁₇	—	2	8	no	—
152	#3622	—	2	8	no	—
153	#3622	C₂²×C₈	1	16	yes	—
154	C₂×#431	—	17	1	no	—
155	C₂×#431	D₁₇	1	1	yes	characteristic
156	C₂×C₄×M₁₆	—	17	1	no	—
157	#1450	—	17	4	no	—
158	C₈×M₁₆	—	17	4	no	—
159	C₈×M₁₆	—	17	4	no	—
160	C₂²×C₁₇	—	2	1	no	—
161	C₂²×C₁₇	—	2	1	no	—
162	C₂²×C₁₇	—	2	1	no	—
163	C₂²×C₁₇	—	2	1	no	—
164	C₂²×C₁₇	—	2	1	no	—
165	C₂²×C₁₇	—	2	1	no	—
166	C₂²×C₁₇	—	4	4	no	—
167	C₂²×C₁₇	C₂×C₄×C₈	1	2	yes	—
168	C₂²×C₁₇	C₂×C₄×C₈	1	2	yes	—
169	C₂²×C₁₇	C₂×C₄×C₈	1	2	yes	—
170	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
171	C₄×C₁₇	—	2	1	no	—
172	C₄×C₁₇	—	2	1	no	—
173	C₄×C₁₇	—	2	1	no	—
174	C₄×C₁₇	—	2	1	no	—
175	C₄×C₁₇	—	2	1	no	—
176	C₄×C₁₇	—	2	1	no	—
177	C₄×C₁₇	C₂×C₄×C₈	1	2	yes	—
178	C₄×C₁₇	C₂×C₄×C₈	1	2	yes	—
179	C₄×C₁₇	C₂×C₄×C₈	1	2	yes	—
180	C₄×C₁₇	C₂³×C₈	1	2	yes	—
181	C₄×C₁₇	#568	1	2	yes	—
182	C₄×C₁₇	#568	1	2	yes	—
183	C₂²×M₁₆	—	17	2	no	—
184	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
185	#431	—	17	2	no	—
186	#431	—	17	2	no	—
187	#431	—	17	2	no	—
188	#431	—	17	2	no	—
189	#431	Dic₁₇	1	2	yes	—
190	#431	Dic₁₇	1	2	yes	—
191	#431	C₂×D₁₇	1	2	yes	—
192	#431	C₂×D₁₇	1	2	yes	—
193	C₂×C₄⋊C₈	—	17	2	no	—
194	C₂×C₄⋊C₈	Dic₁₇	1	2	yes	—
195	C₂×C₂²⋊C₈	—	17	2	no	—
196	C₂×C₂²⋊C₈	Dic₁₇	1	2	yes	—
197	C₄×M₁₆	—	17	2	no	—
198	C₄×M₁₆	—	17	2	no	—
199	C₄×M₁₆	—	17	2	no	—
200	C₄×M₁₆	—	17	2	no	—
201	C₂×#97	—	17	2	no	—
202	C₂×C₄×C₈	—	17	2	no	—
203	C₂×C₄×C₈	—	17	2	no	—
204	C₂×C₄×C₈	C₂×D₁₇	1	2	yes	—
205	#322	—	17	8	no	—
206	C₈²	—	17	8	no	—
207	C₂×C₁₇	—	2	2	no	—
208	C₂×C₁₇	—	2	2	no	—
209	C₂×C₁₇	—	2	2	no	—
210	C₂×C₁₇	C₂²×C₄×C₈	1	1	yes	characteristic
211	C₂×C₁₇	#2873	1	1	yes	characteristic
212	C₂×C₁₇	#2873	1	1	yes	characteristic
213	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
214	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
215	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
216	C₂×M₁₆	—	17	4	no	—
217	C₂×M₁₆	—	17	4	no	—
218	C₂×M₁₆	—	17	16	no	—
219	C₂²×C₈	—	17	4	no	—
220	C₂²×C₈	—	17	4	no	—
221	C₂²×C₈	C₂×Dic₁₇	1	4	yes	—
222	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
223	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
228	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
229	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
230	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
231	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
232	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
233	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
234	C₄⋊C₈	—	17	4	no	—
235	C₄⋊C₈	—	17	4	no	—
236	C₄⋊C₈	C₂×Dic₁₇	1	4	yes	—
237	C₄⋊C₈	C₂×Dic₁₇	1	4	yes	—
238	C₂²⋊C₈	—	17	4	no	—
239	C₂²⋊C₈	—	17	4	no	—
240	C₂²⋊C₈	C₂×Dic₁₇	1	4	yes	—
241	C₂²⋊C₈	C₂×Dic₁₇	1	4	yes	—
242	#97	—	17	4	no	—
243	#97	—	17	4	no	—
244	C₄×C₈	—	17	4	no	—
245	C₄×C₈	—	17	4	no	—
246	C₄×C₈	—	17	4	no	—
247	C₄×C₈	—	17	4	no	—
248	C₄×C₈	C₂×Dic₁₇	1	4	yes	—
249	C₄×C₈	C₂²×D₁₇	1	4	yes	—
250	C₁₇	#17314	1	1	yes	characteristic, complemented, Sylow
251	C₂⁴	C₄×Dic₁₇	1	1	yes	characteristic
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₈×D₁₇	1	8	yes	—
255	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
256	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
257	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
258	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
259	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
260	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
261	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
262	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
263	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
270	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
271	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
272	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
273	M₁₆	—	17	16	no	—
274	M₁₆	—	17	16	no	—
275	C₂×C₈	—	4	4	no	—
276	C₂×C₈	—	17	8	no	—
277	C₂×C₈	—	17	16	no	—
278	C₂×C₈	—	17	8	no	—
279	C₂×C₈	—	68	4	no	—
280	C₂×C₈	C₂²×Dic₁₇	1	8	yes	—
281	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
282	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
283	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
284	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
285	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
286	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
287	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
288	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
289	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
290	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
291	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
292	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
293	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
294	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
295	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
296	C₄²	C₂³×D₁₇	1	1	yes	characteristic
297	C₂³	—	4	1	no	—
298	C₂³	—	4	1	no	—
299	C₂³	C₈×Dic₁₇	1	4	yes	—
300	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
301	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
302	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	C₈×Dic₁₇	1	4	yes	—
316	C₂×C₄	C₈×Dic₁₇	1	4	yes	—
317	C₂×C₄	C₈×Dic₁₇	1	4	yes	—
318	C₂×C₄	C₂×C₈×D₁₇	1	4	yes	—
319	C₂×C₄	C₂×C₈×D₁₇	1	4	yes	—
320	C₂×C₄	C₂×C₈×D₁₇	1	4	yes	—
321	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
322	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
323	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
324	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
325	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
327	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
330	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
331	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
332	C₂×C₄	C₂³×Dic₁₇	1	1	yes	characteristic
333	C₈	—	2	8	no	—
334	C₈	—	17	16	no	—
335	C₈	—	34	8	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	4	4	no	—
343	C₂²	C₂×C₈×Dic₁₇	1	2	yes	—
344	C₂²	C₂×C₈×Dic₁₇	1	2	yes	—
345	C₂²	C₂×C₈×Dic₁₇	1	2	yes	—
346	C₂²	C₂²×C₄×Dic₁₇	1	1	yes	characteristic
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	C₂×C₈×Dic₁₇	1	2	yes	—
354	C₄	C₂×C₈×Dic₁₇	1	2	yes	—
355	C₄	C₂×C₈×Dic₁₇	1	2	yes	—
356	C₄	C₂²×C₈×D₁₇	1	2	yes	—
357	C₄	#11763575	1	2	yes	—
358	C₄	#11763576	1	2	yes	—
359	C₂	—	2	2	no	—
360	C₂	—	2	2	no	—
361	C₂	—	2	2	no	—
362	C₂	C₂²×C₈×Dic₁₇	1	1	yes	characteristic
363	C₂	#14537202	1	1	yes	characteristic
364	C₂	#14537203	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₇
commutator	C₂×C₁₇	C₂²×C₄×C₈
Fitting	C₂×C₁₇×#431	C₂
socle	C₂²×C₁₇	C₂²×C₄²
prime radical	C₂⁴×C₁₇	C₄²
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	C₂×#431	D₁₇
hypocenter	C₁₇	#17314
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #14527068	C₂	semidirect
4. #14527065	C₂	semidirect
5. C₈×#63223	C₂	semidirect
21. #11762531	C₂²	semidirect
22. C₈×#3622	C₂²	semidirect
47. C₂×#63223	C₈	semidirect
108. #63223	C₂×C₈	semidirect
109. #63223	C₂×C₈	semidirect
111. C₂×#3622	C₂×C₈	semidirect
250. C₁₇	#17314	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11762862	2
C₂×C₄×#63223	2
#14527068	2
#14527065	2
C₈×#63223	2
C₂×C₁₇×#431	2
#17314	17