Subgroups — #16940274

Order 4352.

714 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10587490	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10587490	C₂	1	1	yes	maximal, characteristic
3	C₂×#11762579	C₂	1	2	yes	maximal
4	#14528510	C₂	1	2	yes	maximal
5	C₂×C₁₇×#405	C₂	1	1	yes	maximal, characteristic
6	C₂²×#63223	C₂²	1	2	yes	—
7	C₂²×#63223	C₂²	1	2	yes	—
8	C₂×#10587490	—	2	2	no	—
9	C₂×#10587490	—	2	2	no	—
10	C₂×#10587490	—	2	1	no	—
11	C₂×#10587490	—	2	1	no	—
12	C₂×#10587490	—	2	2	no	—
13	C₂×#10587490	C₄	1	4	yes	complemented
14	C₂×#10587490	C₄	1	4	yes	complemented
15	#11762579	—	2	4	no	—
16	#11762573	—	2	4	no	—
17	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
19	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
20	C₁₇×#405	—	2	2	no	—
21	C₁₇×#405	C₄	1	4	yes	—
22	C₂×C₁₇×#97	—	2	1	no	—
23	C₂×C₄×C₈×C₁₇	—	2	1	no	—
24	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
25	C₂×M₁₆×C₁₇	—	2	1	no	—
26	C₂×M₁₆×C₁₇	—	2	1	no	—
27	C₂×M₁₆×C₁₇	—	2	1	no	—
28	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
29	C₂×M₁₆×C₁₇	D₄	1	2	yes	—
30	C₂×M₁₆×C₁₇	Q₈	1	2	yes	—
31	C₂²×C₈×C₁₇	—	2	1	no	—
32	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₁₇	D₄	1	2	yes	—
36	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₇	D₄	1	2	yes	—
39	C₂²×C₈×C₁₇	Q₈	1	2	yes	—
40	C₁₇×#117	—	2	1	no	—
41	C₁₇×#117	—	2	1	no	—
42	C₁₇×#117	C₂×C₄	1	2	yes	—
43	C₁₇×#117	D₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₇	Q₈	1	2	yes	—
46	C₂×C₄²×C₁₇	—	2	1	no	—
47	C₂×#63223	—	2	2	no	—
48	C₂×#63223	—	2	2	no	—
49	C₂×#63223	—	2	2	no	—
50	C₂×#63223	—	2	2	no	—
51	C₂×#63223	—	2	2	no	—
52	C₂×#63223	—	2	2	no	—
53	C₂×#63223	—	2	2	no	—
54	C₂×#63223	—	2	2	no	—
55	C₂×#63223	—	2	2	no	—
56	C₂×#63223	—	2	2	no	—
57	C₂×#63223	C₂×C₄	1	4	yes	—
58	C₂×#63223	C₂×C₄	1	4	yes	—
59	C₂²×#3622	—	2	2	no	—
60	C₂²×#3622	—	2	2	no	—
61	C₁₇×#97	—	2	4	no	—
62	C₄×C₈×C₁₇	—	2	4	no	—
63	#10587490	—	2	4	no	—
64	#10587490	—	2	4	no	—
65	#10587490	—	2	8	no	—
66	C₂⁴×C₁₇	C₂×Q₈	1	1	yes	characteristic
67	C₂²×C₄×C₁₇	—	2	2	no	—
68	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
82	M₁₆×C₁₇	—	2	2	no	—
83	M₁₆×C₁₇	—	2	2	no	—
84	M₁₆×C₁₇	—	2	2	no	—
85	M₁₆×C₁₇	C₄⋊C₄	1	4	yes	—
86	C₂×C₈×C₁₇	—	2	2	no	—
87	C₂×C₈×C₁₇	—	2	2	no	—
88	C₂×C₈×C₁₇	—	2	2	no	—
89	C₂×C₈×C₁₇	C₄²	1	4	yes	—
90	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
91	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
92	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
93	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
94	C₂×C₈×C₁₇	C₂²⋊C₄	1	4	yes	—
95	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
96	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
97	C₂×C₈×C₁₇	C₄⋊C₄	1	4	yes	—
98	C₂×C₈×C₁₇	C₄⋊C₄	1	4	yes	—
99	C₄⋊C₄×C₁₇	—	2	2	no	—
100	C₄⋊C₄×C₁₇	—	2	2	no	—
101	C₂²⋊C₄×C₁₇	—	2	2	no	—
102	C₂²⋊C₄×C₁₇	C₄⋊C₄	1	4	yes	—
103	C₄²×C₁₇	—	2	2	no	—
104	C₄²×C₁₇	—	2	2	no	—
105	#63223	—	2	4	no	—
106	#63223	—	2	4	no	—
107	#63223	—	2	4	no	—
108	#63223	—	2	4	no	—
109	#63223	—	4	2	no	—
110	#63223	—	4	2	no	—
111	#63223	—	4	2	no	—
112	#63223	—	4	2	no	—
113	C₂×#3622	—	2	4	no	—
114	C₂×#3622	—	2	4	no	—
115	C₂×#3622	—	4	2	no	—
116	C₂×#3622	—	4	2	no	—
117	C₂×#3622	—	4	2	no	—
118	C₂×#3622	—	4	2	no	—
119	#10873	—	17	1	no	maximal, Sylow
120	C₂³×C₁₇	—	4	2	no	—
121	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₇	C₄×Q₈	1	1	yes	characteristic
123	C₂³×C₁₇	C₄×Q₈	1	1	yes	characteristic
124	C₂³×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
125	C₂³×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
126	C₂³×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
127	C₂³×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
128	C₂×C₄×C₁₇	—	2	4	no	—
129	C₂×C₄×C₁₇	—	4	4	no	—
130	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
131	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
139	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
140	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
147	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
153	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
154	C₂×C₄×C₁₇	#125	1	1	yes	characteristic
155	C₂×C₄×C₁₇	#125	1	1	yes	characteristic
156	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
158	C₈×C₁₇	—	2	4	no	—
159	C₈×C₁₇	#95	1	4	yes	—
160	C₈×C₁₇	#95	1	4	yes	—
161	#3622	—	4	4	no	—
162	#3622	—	4	4	no	—
163	C₂²×#108	—	17	1	no	—
164	C₂²×#108	—	17	1	no	—
165	C₂×#405	D₁₇	1	1	yes	characteristic
166	C₂×#344	—	17	2	no	—
167	#1738	—	17	2	no	—
168	C₂²×C₁₇	—	2	2	no	—
169	C₂²×C₁₇	—	2	2	no	—
170	C₂²×C₁₇	—	2	2	no	—
171	C₂²×C₁₇	—	4	1	no	—
172	C₂²×C₁₇	—	4	1	no	—
173	C₂²×C₁₇	—	4	1	no	—
174	C₂²×C₁₇	—	4	1	no	—
175	C₂²×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₁₇	#380	1	1	yes	characteristic
177	C₂²×C₁₇	#384	1	1	yes	characteristic
178	C₂²×C₁₇	#389	1	1	yes	characteristic
179	C₂²×C₁₇	#389	1	1	yes	characteristic
180	C₂²×C₁₇	#391	1	1	yes	characteristic
181	C₂²×C₁₇	#391	1	1	yes	characteristic
182	C₄×C₁₇	—	4	4	no	—
183	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
184	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
185	C₄×C₁₇	#380	1	1	yes	characteristic
186	C₄×C₁₇	#382	1	1	yes	characteristic
187	C₄×C₁₇	#389	1	1	yes	characteristic
188	C₄×C₁₇	#389	1	1	yes	characteristic
189	C₄×C₁₇	#390	1	1	yes	characteristic
190	C₄×C₁₇	#390	1	1	yes	characteristic
191	C₂²×M₁₆	—	17	2	no	—
192	C₂²×M₁₆	—	17	2	no	—
193	C₂²×M₁₆	C₂×D₁₇	1	1	yes	characteristic
194	C₂³×C₈	C₂×D₁₇	1	1	yes	characteristic
195	C₂×#117	C₂×D₁₇	1	1	yes	characteristic
196	C₂×#108	—	17	4	no	—
197	C₂×#108	—	17	4	no	—
198	C₂×#108	—	34	2	no	—
199	C₂×#108	—	34	2	no	—
200	C₂×#108	—	34	1	no	—
201	C₂×#108	—	34	1	no	—
202	C₂×#108	—	34	2	no	—
203	#405	—	2	2	no	—
204	#405	Dic₁₇	1	4	yes	—
205	C₂×#97	—	2	1	no	—
206	C₂×C₄×C₈	—	2	1	no	—
207	#344	—	34	4	no	—
208	#341	—	34	4	no	—
209	C₂×C₁₇	—	2	1	no	—
210	C₂×C₁₇	—	2	1	no	—
211	C₂×C₁₇	—	2	1	no	—
212	C₂×C₁₇	—	2	1	no	—
213	C₂×C₁₇	—	2	1	no	—
214	C₂×C₁₇	—	2	1	no	—
215	C₂×C₁₇	C₄⋊#95	1	1	yes	characteristic
216	C₂×C₁₇	#1953	1	2	yes	—
217	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
218	C₂×M₁₆	—	2	1	no	—
219	C₂×M₁₆	—	2	1	no	—
220	C₂×M₁₆	—	2	1	no	—
221	C₂×M₁₆	—	17	4	no	—
222	C₂×M₁₆	—	17	4	no	—
223	C₂×M₁₆	—	34	2	no	—
224	C₂×M₁₆	—	34	2	no	—
225	C₂×M₁₆	—	34	2	no	—
226	C₂×M₁₆	—	34	2	no	—
227	C₂×M₁₆	—	34	2	no	—
228	C₂×M₁₆	—	34	2	no	—
229	C₂×M₁₆	—	34	2	no	—
230	C₂×M₁₆	—	34	2	no	—
231	C₂×M₁₆	—	34	2	no	—
232	C₂×M₁₆	—	34	2	no	—
233	C₂×M₁₆	Dic₃₄	1	2	yes	—
234	C₂×M₁₆	D₆₈	1	2	yes	—
235	C₂×M₁₆	C₂×Dic₁₇	1	2	yes	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	34	2	no	—
238	C₂²×C₈	—	34	2	no	—
239	C₂²×C₈	Dic₃₄	1	2	yes	—
240	C₂²×C₈	C₄×D₁₇	1	2	yes	—
241	C₂²×C₈	C₄×D₁₇	1	2	yes	—
242	C₂²×C₈	D₆₈	1	2	yes	—
243	C₂²×C₈	C₂×Dic₁₇	1	2	yes	—
244	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
245	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
246	C₂²×C₈	C₂²⋊D₁₇	1	2	yes	—
247	#117	—	2	1	no	—
248	#117	—	2	1	no	—
249	#117	D₆₈	1	2	yes	—
250	#117	C₂×Dic₁₇	1	2	yes	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	Dic₃₄	1	2	yes	—
253	C₂×C₄²	—	2	1	no	—
254	#108	—	34	4	no	—
255	#108	—	34	4	no	—
256	#108	—	34	8	no	—
257	#97	—	2	4	no	—
258	C₄×C₈	—	2	4	no	—
259	C₁₇	#10873	1	1	yes	characteristic, complemented, Sylow
260	C₂⁴	C₂×Dic₃₄	1	1	yes	characteristic
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
269	C₂²×C₄	#63252	1	1	yes	characteristic
270	C₂²×C₄	#63252	1	1	yes	characteristic
271	C₂²×C₄	#63252	1	1	yes	characteristic
272	C₂²×C₄	#63252	1	1	yes	characteristic
273	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
276	M₁₆	—	2	2	no	—
277	M₁₆	—	2	2	no	—
278	M₁₆	—	2	2	no	—
279	M₁₆	—	34	4	no	—
280	M₁₆	—	34	4	no	—
281	M₁₆	—	34	4	no	—
282	M₁₆	—	34	4	no	—
283	M₁₆	—	68	2	no	—
284	M₁₆	—	68	2	no	—
285	M₁₆	—	68	2	no	—
286	M₁₆	—	68	2	no	—
287	M₁₆	C₄⋊Dic₁₇	1	4	yes	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	34	4	no	—
292	C₂×C₈	—	34	4	no	—
293	C₂×C₈	—	68	2	no	—
294	C₂×C₈	—	68	2	no	—
295	C₂×C₈	—	68	2	no	—
296	C₂×C₈	—	68	2	no	—
297	C₂×C₈	C₄×Dic₁₇	1	4	yes	—
298	C₂×C₈	#63225	1	2	yes	—
299	C₂×C₈	#63225	1	2	yes	—
300	C₂×C₈	#63225	1	4	yes	—
301	C₂×C₈	C₄⋊Dic₁₇	1	4	yes	—
302	C₂×C₈	#63227	1	2	yes	—
303	C₂×C₈	#63227	1	2	yes	—
304	C₂×C₈	#63227	1	4	yes	—
305	C₂×C₈	C₂²⋊Dic₁₇	1	2	yes	—
306	C₂×C₈	C₂²⋊Dic₁₇	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	C₄⋊Dic₁₇	1	4	yes	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	C₄×Dic₃₄	1	1	yes	characteristic
315	C₂³	C₄×Dic₃₄	1	1	yes	characteristic
316	C₂³	#10587555	1	1	yes	characteristic
317	C₂³	#10587555	1	1	yes	characteristic
318	C₂³	#10587610	1	1	yes	characteristic
319	C₂³	#10587610	1	1	yes	characteristic
320	C₂³	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	C₄×Dic₃₄	1	1	yes	characteristic
324	C₂×C₄	C₄×Dic₃₄	1	1	yes	characteristic
325	C₂×C₄	#10587555	1	1	yes	characteristic
326	C₂×C₄	#10587556	1	1	yes	characteristic
327	C₂×C₄	#10587556	1	1	yes	characteristic
328	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
329	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
330	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
331	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
332	C₂×C₄	#10587560	1	1	yes	characteristic
333	C₂×C₄	#10587561	1	1	yes	characteristic
334	C₂×C₄	#10587561	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
336	C₂×C₄	C₂×#63225	1	1	yes	characteristic
337	C₂×C₄	C₂×#63225	1	1	yes	characteristic
338	C₂×C₄	#10587610	1	1	yes	characteristic
339	C₂×C₄	#10587610	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
342	C₂×C₄	#10587612	1	1	yes	characteristic
343	C₂×C₄	#10587612	1	1	yes	characteristic
344	C₂×C₄	C₂×#63227	1	1	yes	characteristic
345	C₂×C₄	C₂×#63227	1	1	yes	characteristic
346	C₂×C₄	#10587616	1	1	yes	characteristic
347	C₂×C₄	#10587616	1	1	yes	characteristic
348	C₂×C₄	#10587616	1	1	yes	characteristic
349	C₂×C₄	#10587616	1	1	yes	characteristic
350	C₂×C₄	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
351	C₈	—	2	4	no	—
352	C₈	—	68	4	no	—
353	C₈	—	68	4	no	—
354	C₈	#10587502	1	4	yes	—
355	C₈	#10587502	1	4	yes	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	C₄×C₄⋊Dic₁₇	1	1	yes	characteristic
364	C₂²	#11762669	1	1	yes	characteristic
365	C₂²	#11762679	1	1	yes	characteristic
366	C₂²	#11762707	1	1	yes	characteristic
367	C₂²	#11762707	1	1	yes	characteristic
368	C₂²	#11762715	1	1	yes	characteristic
369	C₂²	#11762715	1	1	yes	characteristic
370	C₄	—	4	4	no	—
371	C₄	C₂×#10587502	1	1	yes	characteristic
372	C₄	C₄×C₄⋊Dic₁₇	1	1	yes	characteristic
373	C₄	#11762669	1	1	yes	characteristic
374	C₄	#11762675	1	1	yes	characteristic
375	C₄	#11762707	1	1	yes	characteristic
376	C₄	#11762707	1	1	yes	characteristic
377	C₄	#11762711	1	1	yes	characteristic
378	C₄	#11762711	1	1	yes	characteristic
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	#14527014	1	1	yes	characteristic
386	C₂	#14529574	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10587616
commutator	C₂×C₄×C₁₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₇
Fitting	C₂×C₁₇×#405	C₂
socle	C₂²×C₁₇	#389
prime radical	C₂⁴×C₁₇	C₂×Q₈
cosocle	C₂³×C₄×C₁₇	C₂³
hypercenter	C₂×#405	D₁₇
hypocenter	C₁₇	#10873
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
13. C₂×#10587490	C₄	semidirect
14. C₂×#10587490	C₄	semidirect
259. C₁₇	#10873	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10587490	2
C₂×#11762579	2
#14528510	2
C₂×C₁₇×#405	2
#10873	17