Subgroups — #17000041

Order 4352.

806 conjugacy classes of subgroups.

The subgroup lattice has 386 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	#14527079	C₂	1	4	yes	maximal, complemented
5	#14527077	C₂	1	2	yes	maximal, complemented
6	#14527068	C₂	1	2	yes	maximal, complemented
7	C₁₇×#2920	C₂	1	1	yes	maximal, characteristic
8	C₂²×#63223	C₄	1	2	yes	—
9	#11762866	C₄	1	2	yes	—
10	#11762866	C₄	1	2	yes	—
11	#11762862	C₂²	1	2	yes	—
12	#11762862	C₂²	1	2	yes	—
13	#11762833	C₄	1	2	yes	—
14	#11762773	C₄	1	2	yes	—
15	C₄×#63223	C₄	1	2	yes	—
16	C₄×#63223	C₄	1	2	yes	—
17	C₄×#63223	C₂²	1	2	yes	—
18	C₄×#63223	C₂²	1	2	yes	—
19	C₄×#63223	C₂²	1	2	yes	—
20	C₂×#10587474	C₄	1	2	yes	—
21	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
22	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
23	#11762531	C₂²	1	4	yes	complemented
24	#11762531	C₂²	1	4	yes	complemented
25	#11762530	C₂²	1	4	yes	complemented
26	C₈×#3622	C₂²	1	4	yes	complemented
27	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
28	C₁₇×#432	C₄	1	2	yes	—
29	C₁₇×#432	C₄	1	2	yes	—
30	C₁₇×#431	C₂²	1	2	yes	—
31	C₁₇×#431	C₂²	1	2	yes	—
32	C₁₇×#423	C₄	1	2	yes	—
33	C₁₇×#407	C₄	1	2	yes	—
34	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
35	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×M₁₆×C₁₇	C₂×C₄	1	4	yes	—
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	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	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
51	C₂×#63223	—	2	8	no	—
52	C₂×#63223	C₂×C₄	1	4	yes	—
53	C₂×#63223	C₂×C₄	1	4	yes	—
54	C₂×#63223	C₂×C₄	1	4	yes	—
55	C₂²×#3622	C₂×C₄	1	2	yes	—
56	C₂²×#3622	C₂×C₄	1	2	yes	—
57	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
59	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
60	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
61	C₁₇×#97	C₂×C₄	1	4	yes	—
62	C₄×C₈×C₁₇	C₂³	1	4	yes	—
63	C₂²⋊#3622	C₂×C₄	1	4	yes	—
64	C₂²⋊#3622	C₂×C₄	1	4	yes	—
65	C₄⋊#3622	C₂×C₄	1	4	yes	—
66	C₄⋊#3622	C₂×C₄	1	4	yes	—
67	#10587474	C₂×C₄	1	4	yes	—
68	#10587474	C₂×C₄	1	4	yes	—
69	#10587474	C₂×C₄	1	4	yes	—
70	C₄×#3622	C₂×C₄	1	2	yes	—
71	C₄×#3622	C₂×C₄	1	2	yes	—
72	C₄×#3622	C₂³	1	2	yes	—
73	C₄×#3622	C₂³	1	2	yes	—
74	C₄×#3622	C₂³	1	4	yes	—
75	C₂⁴×C₁₇	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	—	2	4	no	—
77	C₂²×C₄×C₁₇	—	4	2	no	—
78	C₂²×C₄×C₁₇	—	4	2	no	—
79	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₇	C₂²×C₄	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	M₁₆×C₁₇	—	4	4	no	—
98	C₂×C₈×C₁₇	C₂²×C₄	1	8	yes	—
99	C₄²×C₁₇	C₄²	1	1	yes	characteristic
100	C₄²×C₁₇	C₄²	1	1	yes	characteristic
101	C₄²×C₁₇	C₄²	1	1	yes	characteristic
102	C₄²×C₁₇	C₄²	1	1	yes	characteristic
103	C₄²×C₁₇	C₄²	1	1	yes	characteristic
104	C₄²×C₁₇	C₄²	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	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
115	#63223	—	2	8	no	—
116	#63223	—	2	8	no	—
117	#63223	—	4	4	no	—
118	C₂×#3622	—	2	4	no	—
119	C₂×#3622	M₁₆	1	8	yes	complemented
120	C₂×#3622	C₂²×C₄	1	4	yes	—
121	C₂×#3622	C₂²×C₄	1	8	yes	—
122	C₂×#3622	C₂²×C₄	1	4	yes	—
123	#17334	—	17	1	no	maximal, Sylow
124	C₂³×C₁₇	—	2	2	no	—
125	C₂³×C₁₇	—	4	1	no	—
126	C₂³×C₁₇	—	4	1	no	—
127	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
128	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
129	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
130	C₂×C₄×C₁₇	—	2	2	no	—
131	C₂×C₄×C₁₇	—	2	2	no	—
132	C₂×C₄×C₁₇	—	2	2	no	—
133	C₂×C₄×C₁₇	—	2	2	no	—
134	C₂×C₄×C₁₇	—	2	2	no	—
135	C₂×C₄×C₁₇	—	2	2	no	—
136	C₂×C₄×C₁₇	—	2	2	no	—
137	C₂×C₄×C₁₇	—	2	2	no	—
138	C₂×C₄×C₁₇	—	2	2	no	—
139	C₂×C₄×C₁₇	—	2	2	no	—
140	C₂×C₄×C₁₇	—	2	2	no	—
141	C₂×C₄×C₁₇	—	4	1	no	—
142	C₂×C₄×C₁₇	—	4	1	no	—
143	C₂×C₄×C₁₇	—	4	1	no	—
144	C₂×C₄×C₁₇	—	4	1	no	—
145	C₂×C₄×C₁₇	—	4	1	no	—
146	C₂×C₄×C₁₇	—	4	1	no	—
147	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₁₇	C₂×M₁₆	1	4	yes	—
157	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
160	C₈×C₁₇	—	2	8	no	—
161	#3622	—	2	4	no	—
162	#3622	—	2	8	no	—
163	#3622	C₂×M₁₆	1	8	yes	—
164	#2920	—	17	1	no	—
165	#2920	D₁₇	1	1	yes	characteristic
166	C₂×C₄×M₁₆	—	17	1	no	—
167	#1455	—	17	4	no	—
168	#1453	—	17	4	no	—
169	#1452	—	17	2	no	—
170	#1450	—	17	2	no	—
171	C₂²×C₁₇	—	2	1	no	—
172	C₂²×C₁₇	—	2	1	no	—
173	C₂²×C₁₇	—	2	1	no	—
174	C₂²×C₁₇	—	2	1	no	—
175	C₂²×C₁₇	—	2	1	no	—
176	C₂²×C₁₇	—	2	1	no	—
177	C₂²×C₁₇	—	2	1	no	—
178	C₂²×C₁₇	—	2	1	no	—
179	C₂²×C₁₇	—	4	4	no	—
180	C₂²×C₁₇	C₄×M₁₆	1	2	yes	—
181	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
182	C₄×C₁₇	—	2	1	no	—
183	C₄×C₁₇	—	2	1	no	—
184	C₄×C₁₇	—	2	1	no	—
185	C₄×C₁₇	—	2	1	no	—
186	C₄×C₁₇	—	2	1	no	—
187	C₄×C₁₇	—	2	1	no	—
188	C₄×C₁₇	—	2	1	no	—
189	C₄×C₁₇	—	2	1	no	—
190	C₄×C₁₇	C₄×M₁₆	1	2	yes	—
191	C₄×C₁₇	C₂²×M₁₆	1	2	yes	—
192	C₄×C₁₇	#568	1	2	yes	—
193	C₄×C₁₇	#568	1	2	yes	—
194	C₂²×M₁₆	—	17	2	no	—
195	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
196	#432	—	17	2	no	—
197	#432	—	17	2	no	—
198	#432	Dic₁₇	1	2	yes	—
199	#432	Dic₁₇	1	2	yes	—
200	#431	—	17	2	no	—
201	#431	—	17	2	no	—
202	#431	C₂×D₁₇	1	2	yes	—
203	#431	C₂×D₁₇	1	2	yes	—
204	#423	—	17	2	no	—
205	#423	Dic₁₇	1	2	yes	—
206	#407	—	17	2	no	—
207	#407	Dic₁₇	1	2	yes	—
208	C₄×M₁₆	—	17	2	no	—
209	C₄×M₁₆	—	17	2	no	—
210	C₄×M₁₆	—	17	2	no	—
211	C₄×M₁₆	—	17	2	no	—
212	C₄×M₁₆	—	17	2	no	—
213	C₄×M₁₆	C₂×D₁₇	1	2	yes	—
214	C₂×#97	—	17	2	no	—
215	C₂×C₄×C₈	—	17	1	no	—
216	C₂×C₄×C₈	—	17	1	no	—
217	#322	—	17	4	no	—
218	#322	—	17	4	no	—
219	#322	—	17	4	no	—
220	C₈²	—	17	4	no	—
221	C₂×C₁₇	—	2	2	no	—
222	C₂×C₁₇	—	4	1	no	—
223	C₂×C₁₇	—	4	1	no	—
224	C₂×C₁₇	C₂×C₄×M₁₆	1	1	yes	characteristic
225	C₂×C₁₇	#2873	1	1	yes	characteristic
226	C₂×C₁₇	#2873	1	1	yes	characteristic
227	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
228	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
229	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
230	C₂×M₁₆	—	17	4	no	—
231	C₂×M₁₆	—	17	4	no	—
232	C₂×M₁₆	—	17	4	no	—
233	C₂×M₁₆	—	34	8	no	—
234	C₂×M₁₆	C₂×Dic₁₇	1	4	yes	—
235	C₂²×C₈	—	17	2	no	—
236	C₂²×C₈	—	17	2	no	—
237	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
238	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
239	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
240	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
241	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
242	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
243	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
244	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
245	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
246	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
247	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
248	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
249	C₄⋊C₈	—	17	4	no	—
250	C₄⋊C₈	—	17	4	no	—
251	C₄⋊C₈	C₂×Dic₁₇	1	4	yes	—
252	C₄⋊C₈	C₂×Dic₁₇	1	4	yes	—
253	C₂²⋊C₈	—	17	4	no	—
254	C₂²⋊C₈	—	17	4	no	—
255	C₂²⋊C₈	C₂×Dic₁₇	1	4	yes	—
256	C₂²⋊C₈	C₂×Dic₁₇	1	4	yes	—
257	#97	—	17	4	no	—
258	#97	—	17	4	no	—
259	#97	—	17	4	no	—
260	#97	C₂×Dic₁₇	1	4	yes	—
261	C₄×C₈	—	17	2	no	—
262	C₄×C₈	—	17	2	no	—
263	C₄×C₈	—	17	2	no	—
264	C₄×C₈	—	17	4	no	—
265	C₄×C₈	—	17	2	no	—
266	C₄×C₈	C₂²×D₁₇	1	4	yes	—
267	C₁₇	#17334	1	1	yes	characteristic, complemented, Sylow
268	C₂⁴	C₄×Dic₁₇	1	1	yes	characteristic
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
273	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
274	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
275	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
276	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
277	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
278	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
279	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
280	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
288	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
289	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
290	M₁₆	—	4	4	no	—
291	M₁₆	—	34	8	no	—
292	M₁₆	—	34	8	no	—
293	M₁₆	—	68	4	no	—
294	C₂×C₈	—	17	4	no	—
295	C₂×C₈	—	17	8	no	—
296	C₂×C₈	—	17	4	no	—
297	C₂×C₈	—	17	8	no	—
298	C₂×C₈	—	34	4	no	—
299	C₂×C₈	C₂²×Dic₁₇	1	8	yes	—
300	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
301	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
302	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
303	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
304	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
305	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
306	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
307	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
308	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
309	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
310	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
311	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
312	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
313	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
314	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
315	C₄²	C₂³×D₁₇	1	1	yes	characteristic
316	C₂³	—	2	2	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	1	no	—
319	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
320	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
321	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	M₁₆×D₁₇	1	4	yes	—
340	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
342	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
349	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
350	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
351	C₂×C₄	C₂³×Dic₁₇	1	1	yes	characteristic
352	C₈	—	2	8	no	—
353	C₈	—	17	8	no	—
354	C₈	—	34	4	no	—
355	C₈	—	34	8	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	4	4	no	—
365	C₂²	M₁₆×Dic₁₇	1	2	yes	—
366	C₂²	C₂²×C₄×Dic₁₇	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	M₁₆×Dic₁₇	1	2	yes	—
376	C₄	C₂×M₁₆×D₁₇	1	2	yes	—
377	C₄	#11763575	1	2	yes	—
378	C₄	#11763576	1	2	yes	—
379	C₂	—	2	2	no	—
380	C₂	—	4	1	no	—
381	C₂	—	4	1	no	—
382	C₂	C₂×M₁₆×Dic₁₇	1	1	yes	characteristic
383	C₂	#14537202	1	1	yes	characteristic
384	C₂	#14537203	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	#17334
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. #14527087	C₂	semidirect
4. #14527079	C₂	semidirect
5. #14527077	C₂	semidirect
6. #14527068	C₂	semidirect
23. #11762531	C₂²	semidirect
24. #11762531	C₂²	semidirect
25. #11762530	C₂²	semidirect
26. C₈×#3622	C₂²	semidirect
119. C₂×#3622	M₁₆	semidirect
267. C₁₇	#17334	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
#14527079	2
#14527077	2
#14527068	2
C₁₇×#2920	2
#17334	17