Subgroups — #16999952

Order 4352.

874 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14537417	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×#3622	C₂	1	1	yes	maximal, characteristic
3	#14527077	C₂	1	2	yes	maximal, complemented
4	#14527074	C₂	1	2	yes	maximal, complemented
5	#14527071	C₂	1	2	yes	maximal, complemented
6	#14527068	C₂	1	2	yes	maximal, complemented
7	#14527065	C₂	1	2	yes	maximal, complemented
8	M₁₆×#3622	C₂	1	2	yes	maximal, complemented
9	C₁₇×#2920	C₂	1	1	yes	maximal, characteristic
10	C₂³×#3622	C₄	1	2	yes	—
11	#11762866	C₄	1	2	yes	—
12	#11762866	C₄	1	2	yes	—
13	#11762862	C₂²	1	2	yes	—
14	#11762862	C₂²	1	2	yes	—
15	#11762833	C₄	1	2	yes	—
16	#11762773	C₄	1	2	yes	—
17	C₄×#63223	C₂²	1	2	yes	—
18	C₂×C₄×#3622	C₄	1	2	yes	—
19	C₂×C₄×#3622	C₄	1	2	yes	—
20	C₂×C₄×#3622	C₄	1	2	yes	—
21	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
22	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
23	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
24	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
25	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
26	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
27	#11762531	C₂²	1	4	yes	complemented
28	#11762531	C₂²	1	4	yes	complemented
29	#11762530	C₂²	1	4	yes	complemented
30	C₈×#3622	C₂²	1	4	yes	complemented
31	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
32	C₁₇×#432	C₄	1	2	yes	—
33	C₁₇×#432	C₄	1	2	yes	—
34	C₁₇×#431	C₂²	1	2	yes	—
35	C₁₇×#431	C₂²	1	2	yes	—
36	C₁₇×#423	C₄	1	2	yes	—
37	C₁₇×#407	C₄	1	2	yes	—
38	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
39	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
42	C₂×M₁₆×C₁₇	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
55	C₂×#63223	C₂×C₄	1	4	yes	—
56	C₂²×#3622	—	2	8	no	—
57	C₂²×#3622	C₂×C₄	1	2	yes	—
58	C₂²×#3622	C₂×C₄	1	2	yes	—
59	C₂²×#3622	C₂×C₄	1	2	yes	—
60	C₂²×#3622	C₂×C₄	1	2	yes	—
61	C₂²×#3622	C₂×C₄	1	2	yes	—
62	C₂²×#3622	C₂×C₄	1	2	yes	—
63	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
64	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
65	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
66	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
67	C₁₇×#97	C₂×C₄	1	4	yes	—
68	C₄×C₈×C₁₇	C₂³	1	4	yes	—
69	C₂²⋊#3622	C₂×C₄	1	4	yes	—
70	C₂²⋊#3622	C₂×C₄	1	4	yes	—
71	C₄⋊#3622	C₂×C₄	1	4	yes	—
72	C₄⋊#3622	C₂×C₄	1	4	yes	—
73	#10587474	C₂×C₄	1	4	yes	—
74	C₄×#3622	C₂×C₄	1	2	yes	—
75	C₄×#3622	C₂×C₄	1	2	yes	—
76	C₄×#3622	C₂×C₄	1	2	yes	—
77	C₄×#3622	C₂×C₄	1	2	yes	—
78	C₄×#3622	C₂×C₄	1	2	yes	—
79	C₄×#3622	C₂×C₄	1	2	yes	—
80	C₄×#3622	C₂³	1	1	yes	characteristic
81	C₄×#3622	C₂³	1	1	yes	characteristic
82	C₄×#3622	C₂³	1	1	yes	characteristic
83	C₄×#3622	C₂³	1	1	yes	characteristic
84	C₄×#3622	C₂³	1	4	yes	—
85	C₂⁴×C₁₇	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	—	2	4	no	—
87	C₂²×C₄×C₁₇	—	2	4	no	—
88	C₂²×C₄×C₁₇	—	2	4	no	—
89	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
90	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
97	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
98	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
107	M₁₆×C₁₇	—	2	8	no	—
108	C₂×C₈×C₁₇	C₂²×C₄	1	8	yes	—
109	C₄²×C₁₇	C₄²	1	1	yes	characteristic
110	C₄²×C₁₇	C₄²	1	1	yes	characteristic
111	C₄²×C₁₇	C₄²	1	1	yes	characteristic
112	C₄²×C₁₇	C₄²	1	1	yes	characteristic
113	C₄²×C₁₇	C₄²	1	1	yes	characteristic
114	C₄²×C₁₇	C₄²	1	1	yes	characteristic
115	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
125	#63223	—	2	8	no	—
126	C₂×#3622	—	2	4	no	—
127	C₂×#3622	—	2	4	no	—
128	C₂×#3622	—	2	4	no	—
129	C₂×#3622	—	2	4	no	—
130	C₂×#3622	—	2	4	no	—
131	C₂×#3622	M₁₆	1	8	yes	complemented
132	C₂×#3622	C₂²×C₄	1	2	yes	—
133	C₂×#3622	C₂²×C₄	1	2	yes	—
134	C₂×#3622	C₂²×C₄	1	8	yes	—
135	C₂×#3622	C₂²×C₄	1	2	yes	—
136	C₂×#3622	C₂²×C₄	1	2	yes	—
137	#17323	—	17	1	no	maximal, Sylow
138	C₂³×C₁₇	—	2	2	no	—
139	C₂³×C₁₇	—	2	2	no	—
140	C₂³×C₁₇	—	2	2	no	—
141	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
142	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
143	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₁₇	—	2	2	no	—
145	C₂×C₄×C₁₇	—	2	2	no	—
146	C₂×C₄×C₁₇	—	2	2	no	—
147	C₂×C₄×C₁₇	—	2	2	no	—
148	C₂×C₄×C₁₇	—	2	2	no	—
149	C₂×C₄×C₁₇	—	2	2	no	—
150	C₂×C₄×C₁₇	—	2	2	no	—
151	C₂×C₄×C₁₇	—	2	2	no	—
152	C₂×C₄×C₁₇	—	2	2	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	2	no	—
158	C₂×C₄×C₁₇	—	2	2	no	—
159	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₁₇	C₂×M₁₆	1	4	yes	—
169	C₂×C₄×C₁₇	#131	1	4	yes	—
170	C₂×C₄×C₁₇	#131	1	4	yes	—
171	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
174	C₈×C₁₇	—	2	8	no	—
175	#3622	—	2	2	no	—
176	#3622	—	2	2	no	—
177	#3622	—	2	8	no	—
178	#3622	C₂×M₁₆	1	4	yes	—
179	#3622	C₂×M₁₆	1	4	yes	—
180	#2920	—	17	1	no	—
181	#2920	D₁₇	1	1	yes	characteristic
182	C₂²×C₄×C₈	—	17	1	no	—
183	#1452	—	17	2	no	—
184	#1451	—	17	2	no	—
185	#1451	—	17	2	no	—
186	#1450	—	17	2	no	—
187	C₈×M₁₆	—	17	2	no	—
188	C₈×M₁₆	—	17	2	no	—
189	C₂²×C₁₇	—	2	8	no	—
190	C₂²×C₁₇	—	2	1	no	—
191	C₂²×C₁₇	—	2	1	no	—
192	C₂²×C₁₇	—	2	1	no	—
193	C₂²×C₁₇	—	2	1	no	—
194	C₂²×C₁₇	—	2	1	no	—
195	C₂²×C₁₇	—	2	1	no	—
196	C₂²×C₁₇	C₄×M₁₆	1	2	yes	—
197	C₂²×C₁₇	#405	1	2	yes	—
198	C₂²×C₁₇	#405	1	2	yes	—
199	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
200	C₄×C₁₇	—	2	1	no	—
201	C₄×C₁₇	—	2	1	no	—
202	C₄×C₁₇	—	2	1	no	—
203	C₄×C₁₇	—	2	1	no	—
204	C₄×C₁₇	—	2	1	no	—
205	C₄×C₁₇	—	2	1	no	—
206	C₄×C₁₇	C₄×M₁₆	1	2	yes	—
207	C₄×C₁₇	#405	1	2	yes	—
208	C₄×C₁₇	#405	1	2	yes	—
209	C₄×C₁₇	C₂²×M₁₆	1	2	yes	—
210	C₄×C₁₇	C₂×#131	1	2	yes	—
211	C₄×C₁₇	C₂×#131	1	2	yes	—
212	C₂³×C₈	—	17	2	no	—
213	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
214	#432	—	17	2	no	—
215	#432	—	17	2	no	—
216	#432	Dic₁₇	1	2	yes	—
217	#432	Dic₁₇	1	2	yes	—
218	#431	—	17	2	no	—
219	#431	—	17	2	no	—
220	#431	C₂×D₁₇	1	2	yes	—
221	#431	C₂×D₁₇	1	2	yes	—
222	#423	—	17	2	no	—
223	#423	Dic₁₇	1	2	yes	—
224	#407	—	17	2	no	—
225	#407	Dic₁₇	1	2	yes	—
226	C₄×M₁₆	—	17	2	no	—
227	C₄×M₁₆	C₂×D₁₇	1	2	yes	—
228	C₂×C₄×C₈	—	17	2	no	—
229	C₂×C₄×C₈	—	17	2	no	—
230	C₂×C₄×C₈	—	17	2	no	—
231	C₂×C₄×C₈	—	17	1	no	—
232	C₂×C₄×C₈	—	17	1	no	—
233	C₂×C₄×C₈	—	17	1	no	—
234	C₂×C₄×C₈	—	17	1	no	—
235	C₂×C₄×C₈	—	17	1	no	—
236	C₂×C₄×C₈	—	17	1	no	—
237	#322	—	17	4	no	—
238	#322	—	17	4	no	—
239	#322	—	17	4	no	—
240	C₈²	—	17	4	no	—
241	C₂×C₁₇	—	2	2	no	—
242	C₂×C₁₇	—	2	2	no	—
243	C₂×C₁₇	—	2	2	no	—
244	C₂×C₁₇	C₂×C₄×M₁₆	1	1	yes	characteristic
245	C₂×C₁₇	C₂×#405	1	1	yes	characteristic
246	C₂×C₁₇	C₂×#405	1	1	yes	characteristic
247	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
248	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
249	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
250	C₂×M₁₆	—	17	4	no	—
251	C₂×M₁₆	C₂×Dic₁₇	1	4	yes	—
252	C₂²×C₈	—	17	2	no	—
253	C₂²×C₈	—	17	2	no	—
254	C₂²×C₈	—	17	2	no	—
255	C₂²×C₈	—	17	2	no	—
256	C₂²×C₈	—	17	2	no	—
257	C₂²×C₈	—	17	2	no	—
258	C₂²×C₈	—	34	8	no	—
259	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
260	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
261	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
262	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
263	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
264	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
265	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
266	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
267	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
269	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
270	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
271	C₄⋊C₈	—	17	4	no	—
272	C₄⋊C₈	—	17	4	no	—
273	C₄⋊C₈	C₂×Dic₁₇	1	4	yes	—
274	C₄⋊C₈	C₂×Dic₁₇	1	4	yes	—
275	C₂²⋊C₈	—	17	4	no	—
276	C₂²⋊C₈	—	17	4	no	—
277	C₂²⋊C₈	C₂×Dic₁₇	1	4	yes	—
278	C₂²⋊C₈	C₂×Dic₁₇	1	4	yes	—
279	#97	—	17	4	no	—
280	#97	C₂×Dic₁₇	1	4	yes	—
281	C₄×C₈	—	17	2	no	—
282	C₄×C₈	—	17	2	no	—
283	C₄×C₈	—	17	2	no	—
284	C₄×C₈	—	17	2	no	—
285	C₄×C₈	—	17	2	no	—
286	C₄×C₈	—	17	2	no	—
287	C₄×C₈	—	17	1	no	—
288	C₄×C₈	—	17	4	no	—
289	C₄×C₈	—	17	1	no	—
290	C₄×C₈	—	17	1	no	—
291	C₄×C₈	—	17	1	no	—
292	C₄×C₈	C₂²×D₁₇	1	4	yes	—
293	C₁₇	#17323	1	1	yes	characteristic, complemented, Sylow
294	C₂⁴	C₄×Dic₁₇	1	1	yes	characteristic
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
299	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
300	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
301	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
302	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
303	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
304	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
305	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
306	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
313	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
315	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
316	M₁₆	—	2	8	no	—
317	M₁₆	—	34	8	no	—
318	C₂×C₈	—	17	2	no	—
319	C₂×C₈	—	17	2	no	—
320	C₂×C₈	—	17	8	no	—
321	C₂×C₈	—	17	2	no	—
322	C₂×C₈	—	17	2	no	—
323	C₂×C₈	—	17	8	no	—
324	C₂×C₈	—	34	4	no	—
325	C₂×C₈	—	34	4	no	—
326	C₂×C₈	—	34	4	no	—
327	C₂×C₈	—	34	4	no	—
328	C₂×C₈	—	34	4	no	—
329	C₂×C₈	C₂²×Dic₁₇	1	8	yes	—
330	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
331	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
332	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
333	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
334	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
335	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
336	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
337	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
338	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
339	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
340	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
341	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
342	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
343	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
344	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
345	C₄²	C₂³×D₁₇	1	1	yes	characteristic
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
350	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
351	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	M₁₆×D₁₇	1	4	yes	—
368	C₂×C₄	#10587593	1	4	yes	—
369	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
376	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
377	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
378	C₂×C₄	#10587634	1	4	yes	—
379	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
381	C₂×C₄	C₂³×Dic₁₇	1	1	yes	characteristic
382	C₈	—	2	8	no	—
383	C₈	—	17	4	no	—
384	C₈	—	17	4	no	—
385	C₈	—	34	2	no	—
386	C₈	—	34	2	no	—
387	C₈	—	34	8	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	M₁₆×Dic₁₇	1	2	yes	—
396	C₂²	#11762765	1	2	yes	—
397	C₂²	#11762767	1	2	yes	—
398	C₂²	C₂²×C₄×Dic₁₇	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	M₁₆×Dic₁₇	1	2	yes	—
406	C₄	#11762765	1	2	yes	—
407	C₄	#11762767	1	2	yes	—
408	C₄	C₂×M₁₆×D₁₇	1	2	yes	—
409	C₄	C₂×#10587634	1	2	yes	—
410	C₄	C₂×#10587593	1	2	yes	—
411	C₂	—	2	2	no	—
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	C₂×M₁₆×Dic₁₇	1	1	yes	characteristic
415	C₂	C₂×#11762765	1	1	yes	characteristic
416	C₂	C₂×#11762767	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₇
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₁₇×#2920	C₂
prime radical	C₂⁴×C₁₇	C₄²
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#2920	D₁₇
hypocenter	C₁₇	#17323
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #14527077	C₂	semidirect
4. #14527074	C₂	semidirect
5. #14527071	C₂	semidirect
6. #14527068	C₂	semidirect
7. #14527065	C₂	semidirect
8. M₁₆×#3622	C₂	semidirect
27. #11762531	C₂²	semidirect
28. #11762531	C₂²	semidirect
29. #11762530	C₂²	semidirect
30. C₈×#3622	C₂²	semidirect
131. C₂×#3622	M₁₆	semidirect
293. C₁₇	#17323	semidirect

Maximal subgroups

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

subgroup	index
#14537417	2
C₂²×C₄×#3622	2
#14527077	2
#14527074	2
#14527071	2
#14527068	2
#14527065	2
M₁₆×#3622	2
C₁₇×#2920	2
#17323	17