Subgroups — C₄×M₃₂×D₁₇ #17186951

Order 4352.

918 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₁₇	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
3	C₄×#10587483	C₂	1	1	yes	maximal, characteristic, complemented
4	#14530377	C₂	1	2	yes	maximal, complemented
5	M₃₂×Dic₁₇	C₂	1	2	yes	maximal, complemented
6	C₄×#10587469	C₂	1	2	yes	maximal, complemented
7	D₁₇×#346	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₆×D₁₇	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₇×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₁₇	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₁₇	C₄	1	1	yes	characteristic
13	C₂×#10587483	C₂²	1	2	yes	—
14	C₂×#10587469	C₂²	1	4	yes	—
15	M₃₂×D₁₇	C₄	1	16	yes	direct product factor
16	C₂×C₁₆×D₁₇	C₂²	1	4	yes	—
17	C₂×C₄×#3622	C₄	1	1	yes	characteristic
18	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
19	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
20	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
21	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
22	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
23	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
24	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
25	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
28	#11762585	C₂²	1	2	yes	complemented
29	#11762584	C₂²	1	4	yes	complemented
30	C₄×#63214	C₂²	1	2	yes	complemented
31	C₁₆×Dic₁₇	C₂²	1	4	yes	complemented
32	C₂×C₁₇×M₃₂	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
34	C₁₇×#346	C₂²	1	2	yes	complemented
35	C₄×C₁₆×C₁₇	C₂²	1	2	yes	complemented
36	C₂²×C₄×D₁₇	C₈	1	2	yes	—
37	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×Dic₁₇	C₈	1	2	yes	—
42	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
44	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₁₇	C₈	1	8	yes	—
46	C₂×C₈×D₁₇	C₂×C₄	1	8	yes	—
47	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
55	C₄²×D₁₇	C₈	1	2	yes	—
56	C₄²×D₁₇	C₈	1	2	yes	—
57	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
61	C₁₇×M₃₂	C₂×C₄	1	8	yes	complemented
62	C₂×C₁₆×C₁₇	C₂³	1	4	yes	—
63	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
64	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
65	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
66	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
67	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
68	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
69	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
70	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
74	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
75	#10587483	C₂×C₄	1	8	yes	complemented
76	C₂×#63214	C₂³	1	4	yes	—
77	C₄×#3622	C₂×C₄	1	1	yes	characteristic
78	C₄×#3622	C₂×C₄	1	1	yes	characteristic
79	C₄×#3622	C₂×C₄	1	1	yes	characteristic
80	C₄×#3622	C₂×C₄	1	1	yes	characteristic
81	#10587469	C₂×C₄	1	16	yes	complemented
82	C₁₆×D₁₇	C₂×C₄	1	16	yes	complemented
83	C₂³×D₁₇	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂×C₈	1	2	yes	—
85	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×Dic₁₇	C₂×C₈	1	2	yes	—
87	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
88	C₂×C₄×D₁₇	—	2	8	no	—
89	C₂×C₄×D₁₇	C₄²	1	4	yes	—
90	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
91	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
92	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
93	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₁₇	C₂×C₈	1	4	yes	—
96	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
97	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₇	C₂×C₈	1	4	yes	—
100	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₇	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
105	C₄²×C₁₇	C₂×C₈	1	2	yes	—
106	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
108	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
109	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
110	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
111	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
112	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
113	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×#3622	C₄²	1	4	yes	—
116	C₂×#3622	C₂×C₈	1	4	yes	—
117	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
118	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
119	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
120	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
121	C₈×D₁₇	C₄²	1	4	yes	—
122	C₈×D₁₇	C₄²	1	4	yes	—
123	C₈×D₁₇	C₂×C₈	1	4	yes	—
124	C₈×D₁₇	C₂×C₈	1	4	yes	—
125	C₈×D₁₇	C₂×C₈	1	4	yes	—
126	C₈×D₁₇	C₂×C₈	1	4	yes	—
127	C₈×D₁₇	C₂²×C₄	1	4	yes	—
128	C₈×D₁₇	C₂²×C₄	1	4	yes	—
129	C₁₆×C₁₇	C₂²×C₄	1	8	yes	complemented
130	#63214	C₂²×C₄	1	8	yes	complemented
131	C₂×C₄×M₃₂	—	17	1	no	maximal, Sylow
132	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
133	C₂²×D₁₇	—	2	4	no	—
134	C₂²×D₁₇	C₄×C₈	1	4	yes	—
135	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
136	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
137	C₂×C₄×C₁₇	—	2	4	no	—
138	C₂×C₄×C₁₇	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
140	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
143	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
144	C₂×Dic₁₇	—	2	4	no	—
145	C₂×Dic₁₇	C₄×C₈	1	4	yes	—
146	C₂×Dic₁₇	C₂²×C₈	1	2	yes	—
147	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
148	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
149	C₂×Dic₁₇	C₂²×C₈	1	2	yes	—
150	C₄×D₁₇	—	2	4	no	—
151	C₄×D₁₇	—	2	4	no	—
152	C₄×D₁₇	—	2	4	no	—
153	C₄×D₁₇	C₄×C₈	1	4	yes	—
154	C₄×D₁₇	C₄×C₈	1	4	yes	—
155	C₄×D₁₇	M₃₂	1	8	yes	direct product factor
156	C₄×D₁₇	C₂×C₄²	1	2	yes	—
157	C₄×D₁₇	C₂×C₄²	1	2	yes	—
158	C₄×D₁₇	C₂²×C₈	1	2	yes	—
159	C₄×D₁₇	C₂²×C₈	1	2	yes	—
160	C₈×C₁₇	C₂×C₄²	1	2	yes	—
161	C₈×C₁₇	C₂²×C₈	1	2	yes	—
162	C₈×C₁₇	C₂²×C₈	1	2	yes	—
163	C₈×C₁₇	C₂³×C₄	1	2	yes	—
164	#3622	C₂×C₄²	1	2	yes	—
165	#3622	C₂×C₄²	1	2	yes	—
166	#3622	C₂²×C₈	1	2	yes	—
167	#3622	C₂²×C₈	1	2	yes	—
168	C₂²×M₃₂	—	17	2	no	—
169	C₂²×C₄×C₈	—	17	1	no	—
170	C₄×M₃₂	—	17	2	no	—
171	C₄×M₃₂	—	17	1	no	—
172	C₄×M₃₂	—	17	2	no	—
173	C₄×M₃₂	—	17	2	no	—
174	C₄×M₃₂	D₁₇	1	1	yes	characteristic, direct product factor
175	C₂×#346	—	17	2	no	—
176	C₂×C₄×C₁₆	—	17	2	no	—
177	C₂²×C₁₇	—	2	2	no	—
178	C₂²×C₁₇	C₂×C₄×C₈	1	2	yes	—
179	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
180	C₂×D₁₇	—	2	2	no	—
181	C₂×D₁₇	—	2	8	no	—
182	C₂×D₁₇	C₂×C₄×C₈	1	2	yes	—
183	C₂×D₁₇	C₂×C₄×C₈	1	2	yes	—
184	C₂×D₁₇	C₂×M₃₂	1	4	yes	—
185	C₄×C₁₇	—	2	2	no	—
186	C₄×C₁₇	C₂×C₄×C₈	1	2	yes	—
187	C₄×C₁₇	C₂×M₃₂	1	4	yes	complemented
188	C₄×C₁₇	C₂²×C₄²	1	1	yes	characteristic
189	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
190	Dic₁₇	—	2	2	no	—
191	Dic₁₇	C₂×C₄×C₈	1	2	yes	—
192	Dic₁₇	C₂×C₄×C₈	1	2	yes	—
193	Dic₁₇	C₂×M₃₂	1	4	yes	complemented
194	C₂³×C₈	—	17	1	no	—
195	C₂³×C₈	—	17	1	no	—
196	C₂²×C₄²	—	17	1	no	—
197	C₂×M₃₂	—	17	2	no	—
198	C₂×M₃₂	—	17	16	no	—
199	C₂×M₃₂	—	17	4	no	—
200	C₂×M₃₂	C₂×D₁₇	1	2	yes	—
201	C₂²×C₁₆	—	17	4	no	—
202	C₂×C₄×C₈	—	17	1	no	—
203	C₂×C₄×C₈	—	17	1	no	—
204	C₂×C₄×C₈	—	17	1	no	—
205	C₂×C₄×C₈	—	17	1	no	—
206	C₂×C₄×C₈	—	17	1	no	—
207	C₂×C₄×C₈	—	17	1	no	—
208	C₂×C₄×C₈	—	17	1	no	—
209	C₂×C₄×C₈	—	17	1	no	—
210	C₂×C₄×C₈	—	17	1	no	—
211	C₂×C₄×C₈	—	17	1	no	—
212	C₂×C₄×C₈	—	17	1	no	—
213	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
214	#346	—	17	4	no	—
215	#346	—	17	2	no	—
216	#346	C₂×D₁₇	1	2	yes	complemented
217	C₄×C₁₆	—	17	4	no	—
218	C₄×C₁₆	—	17	2	no	—
219	C₄×C₁₆	C₂×D₁₇	1	2	yes	complemented
220	C₂×C₁₇	—	2	2	no	—
221	C₂×C₁₇	C₂²×C₄×C₈	1	1	yes	characteristic
222	C₂×C₁₇	C₂²×M₃₂	1	2	yes	—
223	D₁₇	—	2	2	no	—
224	D₁₇	C₄×M₃₂	1	4	yes	direct product factor
225	C₂³×C₄	—	17	1	no	—
226	C₂³×C₄	—	17	2	no	—
227	C₂²×C₈	—	17	1	no	—
228	C₂²×C₈	—	17	1	no	—
229	C₂²×C₈	—	17	1	no	—
230	C₂²×C₈	—	17	1	no	—
231	C₂²×C₈	—	17	1	no	—
232	C₂²×C₈	—	17	1	no	—
233	C₂²×C₈	—	17	1	no	—
234	C₂²×C₈	—	17	1	no	—
235	C₂²×C₈	—	17	8	no	—
236	C₂²×C₈	—	17	1	no	—
237	C₂²×C₈	—	17	1	no	—
238	C₂²×C₈	—	17	8	no	—
239	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
240	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
241	C₂×C₄²	—	17	1	no	—
242	C₂×C₄²	—	17	2	no	—
243	C₂×C₄²	—	17	1	no	—
244	C₂×C₄²	—	17	1	no	—
245	C₂×C₄²	—	17	1	no	—
246	C₂×C₄²	—	17	1	no	—
247	C₂×C₄²	—	17	2	no	—
248	C₂×C₄²	—	17	2	no	—
249	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
250	M₃₂	—	17	8	no	—
251	M₃₂	—	17	16	no	—
252	M₃₂	C₄×D₁₇	1	8	yes	direct product factor
253	C₂×C₁₆	—	17	4	no	—
254	C₂×C₁₆	—	17	16	no	—
255	C₂×C₁₆	C₂²×D₁₇	1	4	yes	—
256	C₄×C₈	—	17	1	no	—
257	C₄×C₈	—	17	1	no	—
258	C₄×C₈	—	17	1	no	—
259	C₄×C₈	—	17	1	no	—
260	C₄×C₈	—	17	1	no	—
261	C₄×C₈	—	17	1	no	—
262	C₄×C₈	—	17	1	no	—
263	C₄×C₈	—	17	1	no	—
264	C₄×C₈	—	17	1	no	—
265	C₄×C₈	—	17	1	no	—
266	C₄×C₈	—	17	1	no	—
267	C₄×C₈	—	17	1	no	—
268	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
269	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
270	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
271	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
272	C₁₇	C₂×C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
273	C₂⁴	—	17	1	no	—
274	C₂²×C₄	—	17	1	no	—
275	C₂²×C₄	—	17	1	no	—
276	C₂²×C₄	—	17	1	no	—
277	C₂²×C₄	—	17	4	no	—
278	C₂²×C₄	—	17	2	no	—
279	C₂²×C₄	—	17	1	no	—
280	C₂²×C₄	—	17	1	no	—
281	C₂²×C₄	—	17	4	no	—
282	C₂²×C₄	—	17	2	no	—
283	C₂²×C₄	—	17	2	no	—
284	C₂²×C₄	—	17	2	no	—
285	C₂²×C₄	—	17	2	no	—
286	C₂²×C₄	—	34	8	no	—
287	C₂²×C₄	C₈×D₁₇	1	2	yes	—
288	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
289	C₂×C₈	—	17	1	no	—
290	C₂×C₈	—	17	1	no	—
291	C₂×C₈	—	17	1	no	—
292	C₂×C₈	—	17	1	no	—
293	C₂×C₈	—	17	4	no	—
294	C₂×C₈	—	17	4	no	—
295	C₂×C₈	—	17	4	no	—
296	C₂×C₈	—	17	4	no	—
297	C₂×C₈	—	17	4	no	—
298	C₂×C₈	—	17	4	no	—
299	C₂×C₈	—	17	4	no	—
300	C₂×C₈	—	17	4	no	—
301	C₂×C₈	—	17	4	no	—
302	C₂×C₈	—	17	4	no	—
303	C₂×C₈	C₈×D₁₇	1	4	yes	—
304	C₂×C₈	C₂×C₄×D₁₇	1	4	yes	—
305	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
306	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
307	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
308	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
309	C₄²	—	17	1	no	—
310	C₄²	—	17	1	no	—
311	C₄²	—	17	2	no	—
312	C₄²	—	17	2	no	—
313	C₄²	—	17	2	no	—
314	C₄²	—	17	2	no	—
315	C₄²	—	17	2	no	—
316	C₄²	C₈×D₁₇	1	2	yes	—
317	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
318	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
319	C₁₆	—	17	8	no	—
320	C₁₆	C₂×C₄×D₁₇	1	8	yes	complemented
321	C₂³	—	17	1	no	—
322	C₂³	—	17	4	no	—
323	C₂³	—	17	1	no	—
324	C₂³	—	34	4	no	—
325	C₂³	C₂×C₈×D₁₇	1	1	yes	characteristic
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	17	4	no	—
328	C₂×C₄	—	17	2	no	—
329	C₂×C₄	—	17	1	no	—
330	C₂×C₄	—	17	1	no	—
331	C₂×C₄	—	17	8	no	—
332	C₂×C₄	—	17	2	no	—
333	C₂×C₄	—	17	2	no	—
334	C₂×C₄	—	17	4	no	—
335	C₂×C₄	—	17	4	no	—
336	C₂×C₄	—	17	2	no	—
337	C₂×C₄	—	17	2	no	—
338	C₂×C₄	—	17	2	no	—
339	C₂×C₄	—	34	4	no	—
340	C₂×C₄	—	34	4	no	—
341	C₂×C₄	—	34	4	no	—
342	C₂×C₄	—	34	4	no	—
343	C₂×C₄	C₄²×D₁₇	1	2	yes	—
344	C₂×C₄	C₂×C₈×D₁₇	1	2	yes	—
345	C₂×C₄	C₂×C₈×D₁₇	1	2	yes	—
346	C₂×C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₁₇	1	2	yes	—
348	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
349	C₈	—	17	2	no	—
350	C₈	—	17	2	no	—
351	C₈	—	17	2	no	—
352	C₈	—	17	2	no	—
353	C₈	C₄²×D₁₇	1	2	yes	—
354	C₈	C₂×C₈×D₁₇	1	2	yes	—
355	C₈	C₂×C₈×D₁₇	1	2	yes	—
356	C₈	C₂²×C₄×D₁₇	1	2	yes	—
357	C₂²	—	2	2	no	—
358	C₂²	—	17	4	no	—
359	C₂²	—	17	2	no	—
360	C₂²	—	17	2	no	—
361	C₂²	—	34	8	no	—
362	C₂²	—	34	2	no	—
363	C₂²	C₄×C₈×D₁₇	1	2	yes	—
364	C₂²	C₂²×C₈×D₁₇	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	17	4	no	—
367	C₄	—	17	2	no	—
368	C₄	—	17	2	no	—
369	C₄	—	34	2	no	—
370	C₄	C₄×C₈×D₁₇	1	2	yes	—
371	C₄	M₃₂×D₁₇	1	4	yes	direct product factor
372	C₄	C₂×C₄²×D₁₇	1	1	yes	characteristic
373	C₄	C₂²×C₈×D₁₇	1	1	yes	characteristic
374	C₂	—	2	2	no	—
375	C₂	—	17	4	no	—
376	C₂	—	34	2	no	—
377	C₂	C₂×C₄×C₈×D₁₇	1	1	yes	characteristic
378	C₂	C₂×M₃₂×D₁₇	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂²×D₁₇
commutator	C₂×C₁₇	C₂²×C₄×C₈
Frattini	C₂×C₈	C₂³×D₁₇
Fitting	C₄×C₁₇×M₃₂	C₂
socle	C₂²×C₁₇	C₂³×C₈
prime radical	C₂³×D₁₇	C₂×C₈
cosocle	C₂×C₈×C₁₇	C₂⁴
hypercenter	C₄×M₃₂	D₁₇
hypocenter	C₁₇	C₂×C₄×M₃₂
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
3. C₄×#10587483	C₂	semidirect
4. #14530377	C₂	semidirect
5. M₃₂×Dic₁₇	C₂	semidirect
6. C₄×#10587469	C₂	semidirect
7. D₁₇×#346	C₂	semidirect
8. C₄×C₁₆×D₁₇	C₂	semidirect
9. C₄×C₁₇×M₃₂	C₂	semidirect
15. M₃₂×D₁₇	C₄	direct (N × H)
28. #11762585	C₂²	semidirect
29. #11762584	C₂²	semidirect
30. C₄×#63214	C₂²	semidirect
31. C₁₆×Dic₁₇	C₂²	semidirect
34. C₁₇×#346	C₂²	semidirect
35. C₄×C₁₆×C₁₇	C₂²	semidirect
61. C₁₇×M₃₂	C₂×C₄	semidirect
75. #10587483	C₂×C₄	semidirect
81. #10587469	C₂×C₄	semidirect
82. C₁₆×D₁₇	C₂×C₄	semidirect
129. C₁₆×C₁₇	C₂²×C₄	semidirect
130. #63214	C₂²×C₄	semidirect
155. C₄×D₁₇	M₃₂	direct (N × H)
174. C₄×M₃₂	D₁₇	direct (N × H)
187. C₄×C₁₇	C₂×M₃₂	semidirect
193. Dic₁₇	C₂×M₃₂	semidirect
216. #346	C₂×D₁₇	semidirect
219. C₄×C₁₆	C₂×D₁₇	semidirect
224. D₁₇	C₄×M₃₂	direct (N × H)
252. M₃₂	C₄×D₁₇	direct (N × H)
272. C₁₇	C₂×C₄×M₃₂	semidirect
320. C₁₆	C₂×C₄×D₁₇	semidirect
371. C₄	M₃₂×D₁₇	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×M₃₂×D₁₇	2
C₂×C₄×C₈×D₁₇	2
C₄×#10587483	2
#14530377	2
M₃₂×Dic₁₇	2
C₄×#10587469	2
D₁₇×#346	2
C₄×C₁₆×D₁₇	2
C₄×C₁₇×M₃₂	2
C₂×C₄×M₃₂	17

Subgroups — C4×M32×D17 #17186951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×M₃₂×D₁₇ #17186951