Subgroups — M₁₆×#63223 #17000034

Order 4352.

900 conjugacy classes of subgroups.

The subgroup lattice has 408 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	C₂×C₄×#63223	C₂	1	1	yes	maximal, characteristic
3	#14527087	C₂	1	4	yes	maximal, complemented
4	#14527073	C₂	1	2	yes	maximal, complemented
5	#14527071	C₂	1	2	yes	maximal, complemented
6	C₈×#63223	C₂	1	2	yes	maximal, complemented
7	M₁₆×#3622	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×M₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#63223	C₄	1	2	yes	—
10	#11762866	C₄	1	2	yes	—
11	#11762866	C₄	1	2	yes	—
12	#11762862	C₂²	1	2	yes	—
13	#11762862	C₂²	1	2	yes	—
14	#11762833	C₄	1	2	yes	—
15	#11762773	C₄	1	2	yes	—
16	C₄×#63223	C₄	1	2	yes	—
17	C₄×#63223	C₄	1	2	yes	—
18	C₄×#63223	C₂²	1	1	yes	characteristic
19	C₄×#63223	C₂²	1	1	yes	characteristic
20	C₄×#63223	C₂²	1	2	yes	—
21	C₄×#63223	C₂²	1	2	yes	—
22	C₂×#10587474	C₄	1	2	yes	—
23	C₂×C₄×#3622	C₂²	1	2	yes	—
24	#11762531	C₂²	1	4	yes	complemented
25	#11762531	C₂²	1	4	yes	complemented
26	#11762530	C₂²	1	4	yes	complemented
27	C₈×#3622	C₂²	1	4	yes	complemented
28	C₂²×M₁₆×C₁₇	C₄	1	2	yes	—
29	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
30	C₄×M₁₆×C₁₇	C₄	1	2	yes	—
31	C₄×M₁₆×C₁₇	C₄	1	2	yes	—
32	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
33	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
34	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
35	C₂×C₁₇×#97	C₄	1	2	yes	—
36	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
37	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₁₇	—	2	8	no	—
41	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
42	C₂×M₁₆×C₁₇	C₂×C₄	1	4	yes	—
43	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₇	C₂×C₄	1	4	yes	—
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	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
57	C₂×#63223	—	2	8	no	—
58	C₂×#63223	C₂×C₄	1	4	yes	—
59	C₂×#63223	C₂×C₄	1	2	yes	—
60	C₂×#63223	C₂×C₄	1	4	yes	—
61	C₂×#63223	C₂×C₄	1	2	yes	—
62	C₂²×#3622	C₂×C₄	1	4	yes	—
63	C₁₇×#97	C₂×C₄	1	2	yes	—
64	C₁₇×#97	C₂×C₄	1	4	yes	—
65	C₁₇×#97	C₂×C₄	1	2	yes	—
66	C₄×C₈×C₁₇	C₂×C₄	1	4	yes	—
67	C₄×C₈×C₁₇	C₂³	1	2	yes	—
68	C₄×C₈×C₁₇	C₂³	1	2	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	2	yes	—
74	#10587474	C₂×C₄	1	4	yes	—
75	#10587474	C₂×C₄	1	2	yes	—
76	#10587474	C₂×C₄	1	4	yes	—
77	C₄×#3622	C₂×C₄	1	4	yes	—
78	C₄×#3622	C₂³	1	2	yes	—
79	C₄×#3622	C₂³	1	2	yes	—
80	C₄×#3622	C₂³	1	4	yes	—
81	C₂⁴×C₁₇	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	—	2	4	no	—
83	C₂²×C₄×C₁₇	—	2	4	no	—
84	C₂²×C₄×C₁₇	—	4	2	no	—
85	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
87	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
88	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₇	C₂²×C₄	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	M₁₆×C₁₇	—	2	4	no	—
104	M₁₆×C₁₇	—	2	8	no	—
105	M₁₆×C₁₇	M₁₆	1	8	yes	complemented
106	C₂×C₈×C₁₇	—	2	8	no	—
107	C₂×C₈×C₁₇	C₂²×C₄	1	4	yes	—
108	C₂×C₈×C₁₇	C₂²×C₄	1	4	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	4	no	—
126	#63223	—	2	8	no	—
127	#63223	—	4	4	no	—
128	#63223	M₁₆	1	8	yes	direct product factor
129	C₂×#3622	—	2	8	no	—
130	C₂×#3622	C₂²×C₄	1	4	yes	—
131	C₂×#3622	C₂²×C₄	1	8	yes	—
132	C₂×#3622	C₂²×C₄	1	4	yes	—
133	M₁₆²	—	17	1	no	maximal, Sylow
134	C₂³×C₁₇	—	2	2	no	—
135	C₂³×C₁₇	—	2	2	no	—
136	C₂³×C₁₇	—	4	1	no	—
137	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
138	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
139	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₁₇	—	2	2	no	—
141	C₂×C₄×C₁₇	—	2	2	no	—
142	C₂×C₄×C₁₇	—	2	2	no	—
143	C₂×C₄×C₁₇	—	2	2	no	—
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	—	4	1	no	—
154	C₂×C₄×C₁₇	—	4	1	no	—
155	C₂×C₄×C₁₇	—	4	1	no	—
156	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
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×M₁₆	1	4	yes	—
166	C₂×C₄×C₁₇	C₂×M₁₆	1	4	yes	—
167	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
170	C₈×C₁₇	—	2	4	no	—
171	C₈×C₁₇	C₂×M₁₆	1	8	yes	complemented
172	#3622	—	2	4	no	—
173	#3622	—	2	8	no	—
174	#3622	C₂×M₁₆	1	8	yes	complemented
175	#2920	—	17	1	no	—
176	C₂×C₄×M₁₆	—	17	1	no	—
177	C₂×C₄×M₁₆	D₁₇	1	1	yes	characteristic
178	#1455	—	17	4	no	—
179	#1451	—	17	2	no	—
180	#1451	—	17	2	no	—
181	C₈×M₁₆	—	17	2	no	—
182	C₈×M₁₆	—	17	2	no	—
183	C₂²×C₁₇	—	2	1	no	—
184	C₂²×C₁₇	—	2	1	no	—
185	C₂²×C₁₇	—	2	1	no	—
186	C₂²×C₁₇	—	2	1	no	—
187	C₂²×C₁₇	—	2	1	no	—
188	C₂²×C₁₇	—	2	1	no	—
189	C₂²×C₁₇	—	2	1	no	—
190	C₂²×C₁₇	—	4	4	no	—
191	C₂²×C₁₇	C₄×M₁₆	1	2	yes	—
192	C₂²×C₁₇	C₄×M₁₆	1	2	yes	—
193	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
194	C₄×C₁₇	—	2	1	no	—
195	C₄×C₁₇	—	2	1	no	—
196	C₄×C₁₇	—	2	1	no	—
197	C₄×C₁₇	—	2	1	no	—
198	C₄×C₁₇	—	2	1	no	—
199	C₄×C₁₇	—	2	1	no	—
200	C₄×C₁₇	—	2	1	no	—
201	C₄×C₁₇	C₄×M₁₆	1	2	yes	—
202	C₄×C₁₇	C₄×M₁₆	1	2	yes	—
203	C₄×C₁₇	C₂²×M₁₆	1	2	yes	—
204	C₄×C₁₇	C₂²×M₁₆	1	2	yes	—
205	C₄×C₁₇	#568	1	2	yes	—
206	C₂²×M₁₆	—	17	2	no	—
207	C₂²×M₁₆	Dic₁₇	1	2	yes	—
208	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
209	#432	—	17	2	no	—
210	#432	—	17	2	no	—
211	#431	—	17	2	no	—
212	#431	—	17	2	no	—
213	#423	—	17	2	no	—
214	#407	—	17	2	no	—
215	C₄×M₁₆	—	17	2	no	—
216	C₄×M₁₆	—	17	2	no	—
217	C₄×M₁₆	—	17	1	no	—
218	C₄×M₁₆	—	17	1	no	—
219	C₄×M₁₆	—	17	2	no	—
220	C₄×M₁₆	—	17	2	no	—
221	C₄×M₁₆	Dic₁₇	1	2	yes	—
222	C₄×M₁₆	Dic₁₇	1	2	yes	—
223	C₄×M₁₆	C₂×D₁₇	1	1	yes	characteristic
224	C₄×M₁₆	C₂×D₁₇	1	1	yes	characteristic
225	C₄×M₁₆	C₂×D₁₇	1	2	yes	—
226	C₂×#97	—	17	2	no	—
227	C₂×#97	Dic₁₇	1	2	yes	—
228	C₂×C₄×C₈	—	17	2	no	—
229	C₂×C₄×C₈	C₂×D₁₇	1	2	yes	—
230	#322	—	17	4	no	—
231	#322	—	17	4	no	—
232	#322	—	17	4	no	—
233	C₈²	—	17	4	no	—
234	C₂×C₁₇	—	2	2	no	—
235	C₂×C₁₇	—	2	2	no	—
236	C₂×C₁₇	—	4	1	no	—
237	C₂×C₁₇	C₂×C₄×M₁₆	1	1	yes	characteristic
238	C₂×C₁₇	C₂×C₄×M₁₆	1	1	yes	characteristic
239	C₂×C₁₇	#2873	1	1	yes	characteristic
240	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
241	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
242	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
243	C₂×M₁₆	—	2	8	no	—
244	C₂×M₁₆	—	17	2	no	—
245	C₂×M₁₆	—	17	4	no	—
246	C₂×M₁₆	—	17	2	no	—
247	C₂×M₁₆	—	17	4	no	—
248	C₂×M₁₆	—	34	8	no	—
249	C₂×M₁₆	C₂×Dic₁₇	1	2	yes	—
250	C₂×M₁₆	C₂×Dic₁₇	1	4	yes	—
251	C₂×M₁₆	C₂×Dic₁₇	1	2	yes	—
252	C₂²×C₈	—	17	4	no	—
253	C₂²×C₈	C₂×Dic₁₇	1	4	yes	—
254	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
255	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
256	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
257	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
258	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
259	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
260	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
261	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
262	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
263	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
264	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
265	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
266	C₄⋊C₈	—	17	4	no	—
267	C₄⋊C₈	—	17	4	no	—
268	C₂²⋊C₈	—	17	4	no	—
269	C₂²⋊C₈	—	17	4	no	—
270	#97	—	17	2	no	—
271	#97	—	17	4	no	—
272	#97	—	17	2	no	—
273	#97	—	17	4	no	—
274	#97	C₂×Dic₁₇	1	2	yes	—
275	#97	C₂×Dic₁₇	1	4	yes	—
276	#97	C₂×Dic₁₇	1	2	yes	—
277	C₄×C₈	—	17	4	no	—
278	C₄×C₈	—	17	2	no	—
279	C₄×C₈	—	17	4	no	—
280	C₄×C₈	—	17	2	no	—
281	C₄×C₈	C₂×Dic₁₇	1	4	yes	—
282	C₄×C₈	C₂²×D₁₇	1	2	yes	—
283	C₄×C₈	C₂²×D₁₇	1	2	yes	—
284	C₁₇	M₁₆²	1	1	yes	characteristic, complemented, Sylow
285	C₂⁴	C₄×Dic₁₇	1	1	yes	characteristic
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
290	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
291	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
292	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
293	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
294	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
295	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
296	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
297	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
304	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
305	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
306	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
307	M₁₆	—	2	4	no	—
308	M₁₆	—	2	8	no	—
309	M₁₆	—	17	8	no	—
310	M₁₆	—	34	8	no	—
311	M₁₆	—	34	4	no	—
312	M₁₆	—	68	4	no	—
313	M₁₆	#63223	1	8	yes	direct product factor
314	C₂×C₈	—	2	8	no	—
315	C₂×C₈	—	17	4	no	—
316	C₂×C₈	—	17	4	no	—
317	C₂×C₈	—	17	8	no	—
318	C₂×C₈	—	34	8	no	—
319	C₂×C₈	C₂²×Dic₁₇	1	4	yes	—
320	C₂×C₈	C₂²×Dic₁₇	1	4	yes	—
321	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
322	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
323	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
324	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
325	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
326	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
327	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
328	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
329	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
330	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
331	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
332	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
333	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
334	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
335	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
336	C₄²	C₂³×D₁₇	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	4	1	no	—
340	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
341	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
342	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
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	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	M₁₆×D₁₇	1	4	yes	—
360	C₂×C₄	C₂×#63223	1	4	yes	—
361	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
365	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
367	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
369	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
372	C₂×C₄	C₂³×Dic₁₇	1	1	yes	characteristic
373	C₈	—	2	4	no	—
374	C₈	—	17	8	no	—
375	C₈	—	34	4	no	—
376	C₈	—	34	8	no	—
377	C₈	C₂×#63223	1	8	yes	complemented
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	4	4	no	—
386	C₂²	M₁₆×Dic₁₇	1	2	yes	—
387	C₂²	C₄×#63223	1	2	yes	—
388	C₂²	C₂²×C₄×Dic₁₇	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	M₁₆×Dic₁₇	1	2	yes	—
397	C₄	C₄×#63223	1	2	yes	—
398	C₄	C₂×M₁₆×D₁₇	1	2	yes	—
399	C₄	C₂²×#63223	1	2	yes	—
400	C₄	#11763575	1	2	yes	—
401	C₂	—	2	2	no	—
402	C₂	—	2	2	no	—
403	C₂	—	4	1	no	—
404	C₂	C₂×M₁₆×Dic₁₇	1	1	yes	characteristic
405	C₂	C₂×C₄×#63223	1	1	yes	characteristic
406	C₂	#14537202	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₇
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₂×C₄×M₁₆×C₁₇	C₂
prime radical	C₂⁴×C₁₇	C₄²
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₁₇
hypocenter	C₁₇	M₁₆²
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #14527087	C₂	semidirect
4. #14527073	C₂	semidirect
5. #14527071	C₂	semidirect
6. C₈×#63223	C₂	semidirect
7. M₁₆×#3622	C₂	semidirect
24. #11762531	C₂²	semidirect
25. #11762531	C₂²	semidirect
26. #11762530	C₂²	semidirect
27. C₈×#3622	C₂²	semidirect
105. M₁₆×C₁₇	M₁₆	semidirect
128. #63223	M₁₆	direct (N × H)
171. C₈×C₁₇	C₂×M₁₆	semidirect
174. #3622	C₂×M₁₆	semidirect
284. C₁₇	M₁₆²	semidirect
313. M₁₆	#63223	direct (N × H)
377. C₈	C₂×#63223	semidirect

Maximal subgroups

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

subgroup	index
#14537417	2
C₂×C₄×#63223	2
#14527087	2
#14527073	2
#14527071	2
C₈×#63223	2
M₁₆×#3622	2
C₂×C₄×M₁₆×C₁₇	2
M₁₆²	17

Subgroups — M16×#63223 #17000034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×#63223 #17000034