Subgroups — #31966612

Order 18176.

640 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	1	yes	maximal, characteristic
2	C₂×#17986056	C₂	1	1	yes	maximal, characteristic
3	#22587120	C₂	1	4	yes	maximal, complemented
4	#22587115	C₂	1	2	yes	maximal, complemented
5	#22587111	C₂	1	2	yes	maximal, complemented
6	#22587103	C₂	1	4	yes	maximal, complemented
7	C₂×#431×C₇₁	C₂	1	1	yes	maximal, characteristic
8	#17986056	—	2	1	no	—
9	#17986056	—	2	1	no	—
10	#17986056	—	2	1	no	—
11	#17986056	C₂²	1	2	yes	—
12	#17986056	C₂²	1	2	yes	—
13	#17986056	C₂²	1	2	yes	—
14	#17986052	—	2	1	no	—
15	#17986052	C₂²	1	2	yes	—
16	#17986023	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
18	#17985963	—	2	1	no	—
19	C₂×C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
20	C₄×#11765849	—	2	1	no	—
21	C₂×#14556039	—	2	1	no	—
22	#17985752	C₂²	1	8	yes	complemented
23	#17985750	C₂²	1	8	yes	complemented
24	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
25	#431×C₇₁	C₄	1	2	yes	—
26	#431×C₇₁	C₄	1	2	yes	—
27	#431×C₇₁	C₂²	1	1	yes	characteristic
28	#431×C₇₁	C₂²	1	1	yes	characteristic
29	#431×C₇₁	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₇₁	C₄	1	2	yes	—
31	C₂×C₂²⋊C₈×C₇₁	C₄	1	2	yes	—
32	C₂×C₄×C₈×C₇₁	C₂²	1	2	yes	—
33	C₂×#11765849	—	2	2	no	—
34	C₂²×C₇₁⋊C₈	—	2	2	no	—
35	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
36	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
37	C₄⋊(C₇₁⋊C₈)	C₂³	1	4	yes	—
38	C₄⋊(C₇₁⋊C₈)	C₂³	1	4	yes	—
39	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
43	#14556039	—	2	2	no	—
44	#14556039	—	2	2	no	—
45	#14556039	—	2	2	no	—
46	C₄×C₇₁⋊C₈	—	2	2	no	—
47	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₇₁	Q₈	1	1	yes	characteristic
50	C₂²×C₈×C₇₁	C₂×C₄	1	4	yes	—
51	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₇₁	Q₈	1	1	yes	characteristic
58	C₂×C₄²×C₇₁	Q₈	1	1	yes	characteristic
59	C₂×C₄²×C₇₁	Q₈	1	1	yes	characteristic
60	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
64	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
65	C₄⋊C₈×C₇₁	C₂×C₄	1	4	yes	—
66	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
67	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
68	C₂²⋊C₈×C₇₁	C₂×C₄	1	4	yes	—
69	C₄×C₈×C₇₁	C₂×C₄	1	4	yes	—
70	C₄×C₈×C₇₁	C₂³	1	2	yes	—
71	C₄×C₈×C₇₁	C₂³	1	2	yes	—
72	#11765849	—	4	4	no	—
73	C₂×C₇₁⋊C₈	—	2	4	no	—
74	C₂×C₇₁⋊C₈	—	2	4	no	—
75	C₂×C₇₁⋊C₈	—	4	4	no	—
76	C₂⁴×C₇₁	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₇₁	—	2	4	no	—
78	C₂²×C₄×C₇₁	—	4	2	no	—
79	C₂²×C₄×C₇₁	—	4	2	no	—
80	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
98	C₂×C₈×C₇₁	—	4	4	no	—
99	C₂×C₈×C₇₁	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₇₁	C₂²×C₄	1	4	yes	—
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	C₄⋊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	C₂²×C₄	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×D₄	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	C₂×Q₈	1	1	yes	characteristic
116	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
117	C₂³×C₇₁	—	2	2	no	—
118	C₂³×C₇₁	—	2	2	no	—
119	C₂³×C₇₁	—	4	1	no	—
120	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
134	C₂×C₄×C₇₁	—	4	1	no	—
135	C₂×C₄×C₇₁	—	4	1	no	—
136	C₂×C₄×C₇₁	—	4	1	no	—
137	C₂×C₄×C₇₁	—	4	1	no	—
138	C₂×C₄×C₇₁	—	4	1	no	—
139	C₂×C₄×C₇₁	—	4	1	no	—
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×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₇₁	#135	1	4	yes	—
150	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
153	C₈×C₇₁	—	2	4	no	—
154	C₈×C₇₁	—	2	4	no	—
155	C₇₁⋊C₈	—	4	4	no	—
156	C₇₁⋊C₈	—	4	4	no	—
157	C₂²×C₇₁	—	2	1	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	—	4	4	no	—
165	C₂²×C₇₁	#427	1	2	yes	—
166	C₂²×C₇₁	#430	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	—	2	1	no	—
175	C₄×C₇₁	—	2	1	no	—
176	C₄×C₇₁	—	2	1	no	—
177	C₄×C₇₁	#427	1	2	yes	—
178	C₄×C₇₁	#568	1	2	yes	—
179	C₄×C₇₁	C₂×#135	1	2	yes	—
180	#17816	—	71	1	no	maximal, Sylow
181	C₂×C₇₁	—	2	2	no	—
182	C₂×C₇₁	—	2	2	no	—
183	C₂×C₇₁	—	4	1	no	—
184	C₂×C₇₁	#2905	1	1	yes	characteristic
185	C₂×C₇₁	C₂×#427	1	1	yes	characteristic
186	C₂×C₇₁	C₂×#430	1	1	yes	characteristic
187	#2920	—	71	1	no	—
188	C₂×#432	—	71	1	no	—
189	C₂×#431	D₇₁	1	1	yes	characteristic
190	#1572	—	71	4	no	—
191	#1571	—	71	2	no	—
192	#1570	—	71	2	no	—
193	#1568	—	71	4	no	—
194	C₇₁	#17816	1	1	yes	characteristic, complemented, Sylow
195	C₂²×C₄²	C₂×D₇₁	1	1	yes	characteristic
196	#432	—	71	2	no	—
197	#432	—	71	2	no	—
198	#432	—	71	2	no	—
199	#432	—	142	1	no	—
200	#432	—	142	1	no	—
201	#432	—	142	1	no	—
202	#431	—	71	2	no	—
203	#431	—	142	1	no	—
204	#431	Dic₇₁	1	2	yes	—
205	#431	Dic₇₁	1	2	yes	—
206	#431	C₂×D₇₁	1	1	yes	characteristic
207	#431	C₂×D₇₁	1	1	yes	characteristic
208	#431	C₂×D₇₁	1	2	yes	—
209	#423	—	71	2	no	—
210	C₂×C₄⋊C₈	—	71	2	no	—
211	C₂×C₄⋊C₈	Dic₇₁	1	2	yes	—
212	#407	—	142	1	no	—
213	C₂×C₂²⋊C₈	—	142	1	no	—
214	C₂×C₂²⋊C₈	Dic₇₁	1	2	yes	—
215	C₄×M₁₆	—	142	1	no	—
216	C₂×#97	—	142	1	no	—
217	C₂×C₄×C₈	C₂×D₇₁	1	2	yes	—
218	#335	—	71	8	no	—
219	#334	—	71	8	no	—
220	C₂³×C₄	Dic₁₄₂	1	1	yes	characteristic
221	C₂³×C₄	D₂₈₄	1	1	yes	characteristic
222	C₂³×C₄	C₂×Dic₇₁	1	1	yes	characteristic
223	C₂×M₁₆	—	142	2	no	—
224	C₂²×C₈	—	142	2	no	—
225	C₂²×C₈	C₂×Dic₇₁	1	4	yes	—
226	C₂×C₄²	Dic₁₄₂	1	1	yes	characteristic
227	C₂×C₄²	Dic₁₄₂	1	1	yes	characteristic
228	C₂×C₄²	Dic₁₄₂	1	1	yes	characteristic
229	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
230	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
231	C₂×C₄²	D₂₈₄	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	C₂×Dic₇₁	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
238	C₄⋊C₈	—	71	4	no	—
239	C₄⋊C₈	—	71	4	no	—
240	C₄⋊C₈	—	142	2	no	—
241	C₄⋊C₈	—	142	2	no	—
242	C₄⋊C₈	C₂×Dic₇₁	1	2	yes	—
243	C₄⋊C₈	C₂×Dic₇₁	1	2	yes	—
244	C₄⋊C₈	C₂×Dic₇₁	1	4	yes	—
245	C₂²⋊C₈	—	142	2	no	—
246	C₂²⋊C₈	—	142	2	no	—
247	C₂²⋊C₈	—	142	2	no	—
248	C₂²⋊C₈	—	142	2	no	—
249	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
250	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
251	C₂²⋊C₈	C₂×Dic₇₁	1	4	yes	—
252	#97	—	142	2	no	—
253	#97	—	142	2	no	—
254	#97	—	142	2	no	—
255	C₄×C₈	—	142	2	no	—
256	C₄×C₈	C₂×Dic₇₁	1	4	yes	—
257	C₄×C₈	C₂²×D₇₁	1	2	yes	—
258	C₄×C₈	C₂²×D₇₁	1	2	yes	—
259	C₂⁴	C₄⋊Dic₇₁	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	2	no	—
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	C₄⋊Dic₇₁	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
272	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
278	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
279	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
280	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
281	M₁₆	—	284	4	no	—
282	C₂×C₈	—	4	4	no	—
283	C₂×C₈	—	284	4	no	—
284	C₂×C₈	—	142	4	no	—
285	C₂×C₈	—	142	4	no	—
286	C₂×C₈	C₂²×Dic₇₁	1	4	yes	—
287	C₂×C₈	C₂²×Dic₇₁	1	4	yes	—
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	C₄⋊Dic₇₁	1	1	yes	characteristic
294	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
295	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
296	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
297	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
298	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
299	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
300	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
301	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
302	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
303	C₄²	C₂³×D₇₁	1	1	yes	characteristic
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	4	1	no	—
307	C₂³	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
309	C₂³	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
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	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
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×C₄⋊Dic₇₁	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
336	C₂×C₄	#14556150	1	4	yes	—
337	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
339	C₂×C₄	C₂²×Dic₁₄₂	1	1	yes	characteristic
340	C₈	—	2	4	no	—
341	C₈	—	2	4	no	—
342	C₈	—	284	4	no	—
343	C₈	—	284	4	no	—
344	C₂²	—	2	1	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	—	4	4	no	—
352	C₂²	#17986037	1	2	yes	—
353	C₂²	#17986048	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	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	#17986037	1	2	yes	—
365	C₄	#17986766	1	2	yes	—
366	C₄	C₂×#14556150	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	#22596904	1	1	yes	characteristic
371	C₂	C₂×#17986037	1	1	yes	characteristic
372	C₂	C₂×#17986048	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₈₄
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₂×#431×C₇₁	C₂
socle	C₂²×C₇₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₇₁	C₄⋊C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	C₂×#431	D₇₁
hypocenter	C₇₁	#17816
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #22587120	C₂	semidirect
4. #22587115	C₂	semidirect
5. #22587111	C₂	semidirect
6. #22587103	C₂	semidirect
22. #17985752	C₂²	semidirect
23. #17985750	C₂²	semidirect
194. C₇₁	#17816	semidirect

Maximal subgroups

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

subgroup	index
#22596973	2
C₂×#17986056	2
#22587120	2
#22587115	2
#22587111	2
#22587103	2
C₂×#431×C₇₁	2
#17816	71