Subgroups — #31966465

Order 18176.

762 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22596973	C₂	1	2	yes	maximal
2	#22587103	C₂	1	4	yes	maximal, complemented
3	#22587099	C₂	1	2	yes	maximal, complemented
4	#22587096	C₂	1	2	yes	maximal, complemented
5	#22587088	C₂	1	4	yes	maximal, complemented
6	C₂²×C₄×C₈×C₇₁	C₂	1	1	yes	maximal, characteristic
7	#17986056	—	2	2	no	—
8	#17986056	C₂²	1	4	yes	—
9	#17986052	—	2	2	no	—
10	#17986052	C₂²	1	4	yes	—
11	#17986023	C₂²	1	4	yes	—
12	#17985963	—	2	2	no	—
13	C₄×#11765849	—	2	2	no	—
14	#17985752	C₂²	1	8	yes	complemented
15	#17985750	C₂²	1	8	yes	complemented
16	C₂³×C₈×C₇₁	C₄	1	2	yes	—
17	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₇₁	C₄	1	1	yes	characteristic
19	C₂×C₄×C₈×C₇₁	C₄	1	1	yes	characteristic
20	C₂×C₄×C₈×C₇₁	C₄	1	1	yes	characteristic
21	C₂×C₄×C₈×C₇₁	C₄	1	2	yes	—
22	C₂×C₄×C₈×C₇₁	C₄	1	1	yes	characteristic
23	C₂×C₄×C₈×C₇₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₇₁	C₂²	1	2	yes	—
27	C₂×#11765849	—	2	4	no	—
28	C₄⋊(C₇₁⋊C₈)	—	2	4	no	—
29	C₄⋊(C₇₁⋊C₈)	C₂³	1	8	yes	—
30	C₂²⋊(C₇₁⋊C₈)	—	2	4	no	—
31	C₂²⋊(C₇₁⋊C₈)	—	2	4	no	—
32	#14556039	—	2	4	no	—
33	C₄×C₇₁⋊C₈	—	2	4	no	—
34	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₇₁	Q₈	1	1	yes	characteristic
37	C₂²×C₈×C₇₁	—	2	8	no	—
38	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₇₁	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₇₁	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₇₁	Q₈	1	1	yes	characteristic
53	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
56	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
57	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
58	C₄×C₈×C₇₁	C₂×C₄	1	2	yes	—
59	C₄×C₈×C₇₁	C₂×C₄	1	2	yes	—
60	C₄×C₈×C₇₁	C₂×C₄	1	2	yes	—
61	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
62	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
63	C₄×C₈×C₇₁	C₂×C₄	1	2	yes	—
64	C₄×C₈×C₇₁	C₂³	1	2	yes	—
65	C₄×C₈×C₇₁	C₂³	1	2	yes	—
66	#11765849	—	4	8	no	—
67	C₂×C₇₁⋊C₈	—	2	8	no	—
68	C₂⁴×C₇₁	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₇₁	—	2	4	no	—
70	C₂²×C₄×C₇₁	—	2	4	no	—
71	C₂²×C₄×C₇₁	—	2	4	no	—
72	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
90	C₂×C₈×C₇₁	—	2	4	no	—
91	C₂×C₈×C₇₁	—	2	4	no	—
92	C₂×C₈×C₇₁	—	2	4	no	—
93	C₂×C₈×C₇₁	—	2	4	no	—
94	C₂×C₈×C₇₁	—	2	4	no	—
95	C₂×C₈×C₇₁	M₁₆	1	8	yes	complemented
96	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
100	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
113	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
114	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
115	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
116	C₂³×C₇₁	—	2	2	no	—
117	C₂³×C₇₁	—	2	2	no	—
118	C₂³×C₇₁	—	2	2	no	—
119	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
120	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₇₁	—	2	2	no	—
123	C₂×C₄×C₇₁	—	2	2	no	—
124	C₂×C₄×C₇₁	—	2	2	no	—
125	C₂×C₄×C₇₁	—	2	2	no	—
126	C₂×C₄×C₇₁	—	2	2	no	—
127	C₂×C₄×C₇₁	—	2	2	no	—
128	C₂×C₄×C₇₁	—	2	2	no	—
129	C₂×C₄×C₇₁	—	2	2	no	—
130	C₂×C₄×C₇₁	—	2	2	no	—
131	C₂×C₄×C₇₁	—	2	2	no	—
132	C₂×C₄×C₇₁	—	2	2	no	—
133	C₂×C₄×C₇₁	—	2	2	no	—
134	C₂×C₄×C₇₁	—	2	2	no	—
135	C₂×C₄×C₇₁	—	2	2	no	—
136	C₂×C₄×C₇₁	—	2	2	no	—
137	C₂×C₄×C₇₁	#108	1	4	yes	—
138	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₁	C₂×M₁₆	1	4	yes	—
148	C₂×C₄×C₇₁	#135	1	4	yes	—
149	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
152	C₈×C₇₁	—	2	2	no	—
153	C₈×C₇₁	—	2	2	no	—
154	C₈×C₇₁	C₂×M₁₆	1	4	yes	—
155	C₈×C₇₁	C₂×M₁₆	1	4	yes	—
156	C₇₁⋊C₈	—	4	8	no	—
157	C₂²×C₇₁	—	2	8	no	—
158	C₂²×C₇₁	—	2	1	no	—
159	C₂²×C₇₁	—	2	1	no	—
160	C₂²×C₇₁	—	2	1	no	—
161	C₂²×C₇₁	—	2	1	no	—
162	C₂²×C₇₁	—	2	1	no	—
163	C₂²×C₇₁	—	2	1	no	—
164	C₂²×C₇₁	#423	1	2	yes	—
165	C₂²×C₇₁	#427	1	2	yes	—
166	C₂²×C₇₁	C₂×#108	1	2	yes	—
167	C₂²×C₇₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
168	C₄×C₇₁	—	2	1	no	—
169	C₄×C₇₁	—	2	1	no	—
170	C₄×C₇₁	—	2	1	no	—
171	C₄×C₇₁	—	2	1	no	—
172	C₄×C₇₁	—	2	1	no	—
173	C₄×C₇₁	—	2	1	no	—
174	C₄×C₇₁	#423	1	2	yes	—
175	C₄×C₇₁	#427	1	2	yes	—
176	C₄×C₇₁	C₂×#108	1	2	yes	—
177	C₄×C₇₁	C₂×#108	1	2	yes	—
178	C₄×C₇₁	C₂²×M₁₆	1	2	yes	—
179	C₄×C₇₁	C₂×#135	1	2	yes	—
180	#17793	—	71	1	no	maximal, Sylow
181	C₂×C₇₁	—	2	2	no	—
182	C₂×C₇₁	—	2	2	no	—
183	C₂×C₇₁	—	2	2	no	—
184	C₂×C₇₁	C₂×#423	1	1	yes	characteristic
185	C₂×C₇₁	C₂×#427	1	1	yes	characteristic
186	C₂×C₇₁	C₂²×#108	1	1	yes	characteristic
187	#2920	—	71	2	no	—
188	C₂²×C₄×C₈	D₇₁	1	1	yes	characteristic
189	#1568	—	71	4	no	—
190	#1567	—	71	2	no	—
191	#1566	—	71	2	no	—
192	#1564	—	71	4	no	—
193	C₇₁	#17793	1	1	yes	characteristic, complemented, Sylow
194	C₂³×C₈	Dic₇₁	1	2	yes	—
195	C₂²×C₄²	C₂×D₇₁	1	1	yes	characteristic
196	#432	—	71	4	no	—
197	#432	—	142	2	no	—
198	#431	—	71	4	no	—
199	#431	—	142	2	no	—
200	#423	—	71	4	no	—
201	#407	—	142	2	no	—
202	C₄×M₁₆	—	142	2	no	—
203	C₂×C₄×C₈	Dic₇₁	1	1	yes	characteristic
204	C₂×C₄×C₈	Dic₇₁	1	1	yes	characteristic
205	C₂×C₄×C₈	Dic₇₁	1	1	yes	characteristic
206	C₂×C₄×C₈	Dic₇₁	1	2	yes	—
207	C₂×C₄×C₈	Dic₇₁	1	1	yes	characteristic
208	C₂×C₄×C₈	C₂×D₇₁	1	2	yes	—
209	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
211	C₂×C₄×C₈	C₂×D₇₁	1	2	yes	—
212	#335	—	71	8	no	—
213	#334	—	71	8	no	—
214	C₂³×C₄	Dic₁₄₂	1	1	yes	characteristic
215	C₂³×C₄	D₂₈₄	1	1	yes	characteristic
216	C₂³×C₄	C₂×Dic₇₁	1	1	yes	characteristic
217	C₂×M₁₆	—	142	4	no	—
218	C₂²×C₈	—	2	8	no	—
219	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
220	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
221	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
222	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
223	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
224	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
225	C₂×C₄²	Dic₁₄₂	1	1	yes	characteristic
226	C₂×C₄²	Dic₁₄₂	1	1	yes	characteristic
227	C₂×C₄²	Dic₁₄₂	1	1	yes	characteristic
228	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
229	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
230	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
231	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
232	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
237	C₄⋊C₈	—	71	8	no	—
238	C₄⋊C₈	—	142	4	no	—
239	C₂²⋊C₈	—	142	4	no	—
240	C₂²⋊C₈	—	142	4	no	—
241	#97	—	142	4	no	—
242	C₄×C₈	—	142	4	no	—
243	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
244	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
245	C₄×C₈	C₂×Dic₇₁	1	2	yes	—
246	C₄×C₈	C₂×Dic₇₁	1	2	yes	—
247	C₄×C₈	C₂×Dic₇₁	1	2	yes	—
248	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
249	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
250	C₄×C₈	C₂×Dic₇₁	1	2	yes	—
251	C₄×C₈	C₂²×D₇₁	1	2	yes	—
252	C₄×C₈	C₂²×D₇₁	1	2	yes	—
253	C₂⁴	C₄⋊Dic₇₁	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
258	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
259	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
260	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
261	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
266	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
267	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
272	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
274	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
275	M₁₆	—	284	8	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	142	8	no	—
282	C₂×C₈	#11765849	1	8	yes	complemented
283	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
284	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
285	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
286	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
287	C₄²	C₄⋊Dic₇₁	1	1	yes	characteristic
288	C₄²	C₄⋊Dic₇₁	1	1	yes	characteristic
289	C₄²	C₄⋊Dic₇₁	1	1	yes	characteristic
290	C₄²	C₄⋊Dic₇₁	1	1	yes	characteristic
291	C₄²	C₄⋊Dic₇₁	1	1	yes	characteristic
292	C₄²	C₄⋊Dic₇₁	1	1	yes	characteristic
293	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
294	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
295	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
296	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
297	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
298	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
299	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
300	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
301	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
302	C₄²	C₂³×D₇₁	1	1	yes	characteristic
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
307	C₂³	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	#14556064	1	4	yes	—
325	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
327	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
334	C₂×C₄	C₂×#11765849	1	4	yes	—
335	C₂×C₄	#14556150	1	4	yes	—
336	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
338	C₂×C₄	C₂²×Dic₁₄₂	1	1	yes	characteristic
339	C₈	—	2	2	no	—
340	C₈	—	2	2	no	—
341	C₈	—	284	8	no	—
342	C₈	C₂×#11765849	1	4	yes	—
343	C₈	C₂×#11765849	1	4	yes	—
344	C₂²	—	2	8	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	#17986023	1	2	yes	—
352	C₂²	#17986037	1	2	yes	—
353	C₂²	C₂×#14556064	1	2	yes	—
354	C₂²	C₂²×C₄⋊Dic₇₁	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	#17986023	1	2	yes	—
362	C₄	#17986037	1	2	yes	—
363	C₄	C₂×#14556064	1	2	yes	—
364	C₄	C₂×#14556064	1	2	yes	—
365	C₄	C₂²×#11765849	1	2	yes	—
366	C₄	C₂×#14556150	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	2	2	no	—
370	C₂	C₂×#17986023	1	1	yes	characteristic
371	C₂	C₂×#17986037	1	1	yes	characteristic
372	C₂	C₂²×#14556064	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₂₈₄
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₂²×C₄×C₈×C₇₁	C₂
socle	C₂²×C₇₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₇₁	C₄⋊C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	C₂²×C₄×C₈	D₇₁
hypocenter	C₇₁	#17793
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #22587103	C₂	semidirect
3. #22587099	C₂	semidirect
4. #22587096	C₂	semidirect
5. #22587088	C₂	semidirect
14. #17985752	C₂²	semidirect
15. #17985750	C₂²	semidirect
95. C₂×C₈×C₇₁	M₁₆	semidirect
193. C₇₁	#17793	semidirect
282. C₂×C₈	#11765849	semidirect

Maximal subgroups

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

subgroup	index
#22596973	2
#22587103	2
#22587099	2
#22587096	2
#22587088	2
C₂²×C₄×C₈×C₇₁	2
#17793	71