Subgroups — #16999971

Order 4352.

772 conjugacy classes of subgroups.

The subgroup lattice has 392 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×#11762862	C₂	1	1	yes	maximal, characteristic
3	#14527084	C₂	1	4	yes	maximal, complemented
4	#14527076	C₂	1	2	yes	maximal, complemented
5	#14527074	C₂	1	2	yes	maximal, complemented
6	#14527067	C₂	1	2	yes	maximal, complemented
7	#14527065	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₇×#431	C₂	1	1	yes	maximal, characteristic
9	#11762866	C₄	1	2	yes	—
10	#11762866	C₄	1	2	yes	—
11	#11762862	C₄	1	2	yes	—
12	#11762862	C₄	1	2	yes	—
13	#11762862	C₂²	1	1	yes	characteristic
14	#11762862	C₂²	1	2	yes	—
15	#11762862	C₂²	1	1	yes	characteristic
16	#11762862	C₂²	1	2	yes	—
17	#11762862	C₂²	1	2	yes	—
18	#11762833	C₄	1	2	yes	—
19	C₂×C₄⋊#3622	C₄	1	2	yes	—
20	#11762773	C₄	1	2	yes	—
21	C₂×C₂²⋊#3622	C₄	1	2	yes	—
22	C₄×#63223	C₂²	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×C₄²×C₁₇	C₂²	1	1	yes	characteristic
29	C₁₇×#431	C₄	1	2	yes	—
30	C₁₇×#431	C₄	1	2	yes	—
31	C₁₇×#431	C₂²	1	1	yes	characteristic
32	C₁₇×#431	C₂²	1	1	yes	characteristic
33	C₁₇×#431	C₂²	1	2	yes	—
34	C₂×C₁₇×C₄⋊C₈	C₄	1	2	yes	—
35	C₂×C₁₇×C₂²⋊C₈	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	C₂²×C₈×C₁₇	C₂×C₄	1	4	yes	—
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	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
53	C₂×#63223	C₂×C₄	1	4	yes	—
54	C₂²×#3622	C₂×C₄	1	4	yes	—
55	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
56	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
57	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₁₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
59	C₁₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
60	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
61	C₄×C₈×C₁₇	C₂×C₄	1	4	yes	—
62	C₄×C₈×C₁₇	C₂³	1	2	yes	—
63	C₄×C₈×C₁₇	C₂³	1	2	yes	—
64	C₂²⋊#3622	C₂×C₄	1	2	yes	—
65	C₂²⋊#3622	C₂×C₄	1	2	yes	—
66	C₂²⋊#3622	C₂×C₄	1	4	yes	—
67	C₂²⋊#3622	C₂×C₄	1	4	yes	—
68	C₂²⋊#3622	C₂×C₄	1	4	yes	—
69	C₄⋊#3622	C₂×C₄	1	2	yes	—
70	C₄⋊#3622	C₂×C₄	1	2	yes	—
71	C₄⋊#3622	C₂×C₄	1	4	yes	—
72	C₄⋊#3622	C₂×C₄	1	4	yes	—
73	C₄⋊#3622	C₂×C₄	1	4	yes	—
74	#10587474	C₂×C₄	1	4	yes	—
75	C₄×#3622	C₂×C₄	1	4	yes	—
76	C₄×#3622	C₂³	1	2	yes	—
77	C₄×#3622	C₂³	1	2	yes	—
78	C₄×#3622	C₂³	1	4	yes	—
79	C₂⁴×C₁₇	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	—	2	4	no	—
81	C₂²×C₄×C₁₇	—	2	4	no	—
82	C₂²×C₄×C₁₇	—	4	2	no	—
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	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	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	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	C₂×C₈×C₁₇	—	2	8	no	—
102	C₂×C₈×C₁₇	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₁₇	C₂²×C₄	1	4	yes	—
104	C₄²×C₁₇	C₄²	1	1	yes	characteristic
105	C₄²×C₁₇	C₄²	1	1	yes	characteristic
106	C₄²×C₁₇	C₄²	1	1	yes	characteristic
107	C₄²×C₁₇	C₄²	1	1	yes	characteristic
108	C₄²×C₁₇	C₄²	1	1	yes	characteristic
109	C₄²×C₁₇	C₄²	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	C₂²×C₄	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	C₂⁴	1	1	yes	characteristic
120	#63223	—	2	8	no	—
121	C₂×#3622	—	4	4	no	—
122	C₂×#3622	C₂²×C₄	1	4	yes	—
123	C₂×#3622	C₂²×C₄	1	4	yes	—
124	C₂×#3622	C₂²×C₄	1	8	yes	—
125	#17326	—	17	1	no	maximal, Sylow
126	C₂³×C₁₇	—	2	2	no	—
127	C₂³×C₁₇	—	2	2	no	—
128	C₂³×C₁₇	—	4	1	no	—
129	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
130	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
131	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
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	—	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	—	4	1	no	—
146	C₂×C₄×C₁₇	—	4	1	no	—
147	C₂×C₄×C₁₇	—	4	1	no	—
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×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₇	#131	1	4	yes	—
158	C₂×C₄×C₁₇	#131	1	4	yes	—
159	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
162	C₈×C₁₇	—	2	4	no	—
163	C₈×C₁₇	—	2	4	no	—
164	#3622	—	2	8	no	—
165	#3622	—	2	4	no	—
166	#3622	—	2	4	no	—
167	#2920	—	17	1	no	—
168	C₂×#431	—	17	1	no	—
169	C₂×#431	D₁₇	1	1	yes	characteristic
170	#1454	—	17	4	no	—
171	#1452	—	17	2	no	—
172	#1451	—	17	2	no	—
173	#1450	—	17	2	no	—
174	C₈×M₁₆	—	17	2	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	—	2	1	no	—
180	C₂²×C₁₇	—	2	1	no	—
181	C₂²×C₁₇	—	2	1	no	—
182	C₂²×C₁₇	—	4	4	no	—
183	C₂²×C₁₇	#405	1	2	yes	—
184	C₂²×C₁₇	#405	1	2	yes	—
185	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
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	—	2	1	no	—
191	C₄×C₁₇	—	2	1	no	—
192	C₄×C₁₇	—	2	1	no	—
193	C₄×C₁₇	#405	1	2	yes	—
194	C₄×C₁₇	#405	1	2	yes	—
195	C₄×C₁₇	C₂×#131	1	2	yes	—
196	C₄×C₁₇	C₂×#131	1	2	yes	—
197	C₄×C₁₇	#568	1	2	yes	—
198	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
199	#432	—	17	2	no	—
200	#432	—	17	2	no	—
201	#431	—	17	2	no	—
202	#431	—	17	2	no	—
203	#431	—	17	1	no	—
204	#431	—	17	1	no	—
205	#431	—	17	2	no	—
206	#431	—	17	2	no	—
207	#431	—	17	2	no	—
208	#431	Dic₁₇	1	2	yes	—
209	#431	Dic₁₇	1	2	yes	—
210	#431	C₂×D₁₇	1	1	yes	characteristic
211	#431	C₂×D₁₇	1	1	yes	characteristic
212	#431	C₂×D₁₇	1	2	yes	—
213	#423	—	17	2	no	—
214	C₂×C₄⋊C₈	—	17	2	no	—
215	C₂×C₄⋊C₈	Dic₁₇	1	2	yes	—
216	#407	—	17	2	no	—
217	C₂×C₂²⋊C₈	—	17	2	no	—
218	C₂×C₂²⋊C₈	Dic₁₇	1	2	yes	—
219	C₄×M₁₆	—	17	2	no	—
220	C₂×C₄×C₈	—	17	2	no	—
221	C₂×C₄×C₈	C₂×D₁₇	1	2	yes	—
222	#322	—	17	4	no	—
223	#322	—	17	4	no	—
224	#322	—	17	4	no	—
225	C₈²	—	17	4	no	—
226	C₂×C₁₇	—	2	2	no	—
227	C₂×C₁₇	—	2	2	no	—
228	C₂×C₁₇	—	4	1	no	—
229	C₂×C₁₇	C₂×#405	1	1	yes	characteristic
230	C₂×C₁₇	C₂×#405	1	1	yes	characteristic
231	C₂×C₁₇	#2873	1	1	yes	characteristic
232	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
233	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
234	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
235	C₂×M₁₆	—	17	4	no	—
236	C₂²×C₈	—	17	4	no	—
237	C₂²×C₈	C₂×Dic₁₇	1	4	yes	—
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	C₄×D₁₇	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	C₂×Dic₁₇	1	1	yes	characteristic
247	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
248	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
249	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
250	C₄⋊C₈	—	17	2	no	—
251	C₄⋊C₈	—	17	2	no	—
252	C₄⋊C₈	—	17	4	no	—
253	C₄⋊C₈	—	17	4	no	—
254	C₄⋊C₈	—	17	4	no	—
255	C₄⋊C₈	C₂×Dic₁₇	1	2	yes	—
256	C₄⋊C₈	C₂×Dic₁₇	1	2	yes	—
257	C₄⋊C₈	C₂×Dic₁₇	1	4	yes	—
258	C₂²⋊C₈	—	17	2	no	—
259	C₂²⋊C₈	—	17	2	no	—
260	C₂²⋊C₈	—	17	4	no	—
261	C₂²⋊C₈	—	17	4	no	—
262	C₂²⋊C₈	—	17	4	no	—
263	C₂²⋊C₈	C₂×Dic₁₇	1	2	yes	—
264	C₂²⋊C₈	C₂×Dic₁₇	1	2	yes	—
265	C₂²⋊C₈	C₂×Dic₁₇	1	4	yes	—
266	#97	—	17	4	no	—
267	C₄×C₈	—	17	4	no	—
268	C₄×C₈	—	17	2	no	—
269	C₄×C₈	—	17	4	no	—
270	C₄×C₈	—	17	2	no	—
271	C₄×C₈	C₂×Dic₁₇	1	4	yes	—
272	C₄×C₈	C₂²×D₁₇	1	2	yes	—
273	C₄×C₈	C₂²×D₁₇	1	2	yes	—
274	C₁₇	#17326	1	1	yes	characteristic, complemented, Sylow
275	C₂⁴	C₄×Dic₁₇	1	1	yes	characteristic
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
280	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
281	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
282	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
283	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
284	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
285	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
286	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
287	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
295	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
296	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
297	M₁₆	—	34	8	no	—
298	C₂×C₈	—	2	8	no	—
299	C₂×C₈	—	17	4	no	—
300	C₂×C₈	—	17	4	no	—
301	C₂×C₈	—	17	8	no	—
302	C₂×C₈	—	68	4	no	—
303	C₂×C₈	C₂²×Dic₁₇	1	4	yes	—
304	C₂×C₈	C₂²×Dic₁₇	1	4	yes	—
305	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
306	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
307	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
308	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
309	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
310	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
311	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
312	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
313	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
314	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
315	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
316	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
317	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
318	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
319	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
320	C₄²	C₂³×D₁₇	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	4	1	no	—
324	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
325	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
326	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
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	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	#10587587	1	4	yes	—
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	C₂×C₄×Dic₁₇	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
353	C₂×C₄	#10587634	1	4	yes	—
354	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
356	C₂×C₄	C₂³×Dic₁₇	1	1	yes	characteristic
357	C₈	—	2	4	no	—
358	C₈	—	2	4	no	—
359	C₈	—	34	8	no	—
360	C₈	—	34	4	no	—
361	C₈	—	34	4	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	4	no	—
370	C₂²	#11762764	1	2	yes	—
371	C₂²	#11762765	1	2	yes	—
372	C₂²	C₂²×C₄×Dic₁₇	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	#11762764	1	2	yes	—
381	C₄	#11762765	1	2	yes	—
382	C₄	C₂×#10587587	1	2	yes	—
383	C₄	C₂×#10587634	1	2	yes	—
384	C₄	#11763575	1	2	yes	—
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	C₂×#11762764	1	1	yes	characteristic
389	C₂	C₂×#11762765	1	1	yes	characteristic
390	C₂	#14537202	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₇
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₂×C₁₇×#431	C₂
prime radical	C₂⁴×C₁₇	C₄²
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	C₂×#431	D₁₇
hypocenter	C₁₇	#17326
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #14527084	C₂	semidirect
4. #14527076	C₂	semidirect
5. #14527074	C₂	semidirect
6. #14527067	C₂	semidirect
7. #14527065	C₂	semidirect
24. #11762531	C₂²	semidirect
25. #11762531	C₂²	semidirect
26. #11762530	C₂²	semidirect
27. C₈×#3622	C₂²	semidirect
274. C₁₇	#17326	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×#11762862	2
#14527084	2
#14527076	2
#14527074	2
#14527067	2
#14527065	2
C₂×C₁₇×#431	2
#17326	17