Subgroups — C₂×#22586224 #31887536

Order 18176.

878 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₇₁⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#17985869	C₂	1	1	yes	maximal, characteristic
3	#22586224	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄⋊C₈×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₇₁⋊C₈	—	2	1	no	—
6	C₂²×C₄⋊Dic₇₁	—	2	1	no	—
7	C₂²×C₄⋊Dic₇₁	—	2	1	no	—
8	C₂²×C₄⋊Dic₇₁	C₄	1	2	yes	—
9	C₂×C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
10	C₂×C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
11	C₂×C₄⋊(C₇₁⋊C₈)	C₄	1	4	yes	complemented
12	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
13	#17985869	—	2	1	no	—
14	#17985869	—	2	1	no	—
15	#17985869	C₄	1	2	yes	—
16	#17985869	C₂²	1	2	yes	—
17	C₂³×C₈×C₇₁	—	2	1	no	—
18	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₇₁	—	2	1	no	—
20	C₂×C₄⋊C₈×C₇₁	—	2	2	no	—
21	C₂×C₄⋊C₈×C₇₁	C₄	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
23	C₂³×Dic₇₁	—	2	2	no	—
24	C₂²×C₇₁⋊C₈	—	2	4	no	—
25	C₂²×C₇₁⋊C₈	—	2	2	no	—
26	C₂²×C₇₁⋊C₈	—	4	2	no	—
27	C₂²×C₇₁⋊C₈	—	4	2	no	—
28	C₂×C₄⋊Dic₇₁	—	2	2	no	—
29	C₂×C₄⋊Dic₇₁	—	2	2	no	—
30	C₂×C₄⋊Dic₇₁	—	2	2	no	—
31	C₂×C₄⋊Dic₇₁	—	2	2	no	—
32	C₂×C₄⋊Dic₇₁	—	2	2	no	—
33	C₂×C₄⋊Dic₇₁	—	4	4	no	—
34	C₂×C₄⋊Dic₇₁	—	4	2	no	—
35	C₂×C₄⋊Dic₇₁	—	4	2	no	—
36	C₂×C₄⋊Dic₇₁	—	4	2	no	—
37	C₂×C₄⋊Dic₇₁	—	4	2	no	—
38	C₂×C₄⋊Dic₇₁	C₂×C₄	1	4	yes	—
39	C₄⋊(C₇₁⋊C₈)	—	2	4	no	—
40	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
41	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	complemented
42	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₇₁	—	2	4	no	—
46	C₂²×C₈×C₇₁	—	2	2	no	—
47	C₂²×C₈×C₇₁	—	4	2	no	—
48	C₂²×C₈×C₇₁	—	4	2	no	—
49	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₇₁	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₇₁	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₇₁	D₄	1	2	yes	—
55	C₂×C₄²×C₇₁	Q₈	1	2	yes	—
56	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
57	C₄⋊C₈×C₇₁	—	2	4	no	—
58	C₄⋊C₈×C₇₁	—	2	2	no	—
59	C₄⋊C₈×C₇₁	C₂×C₄	1	4	yes	complemented
60	C₂²×Dic₇₁	—	2	4	no	—
61	C₂²×Dic₇₁	—	4	4	no	—
62	C₂²×Dic₇₁	—	4	4	no	—
63	C₂²×Dic₇₁	—	4	4	no	—
64	C₂×C₇₁⋊C₈	—	2	4	no	—
65	C₂×C₇₁⋊C₈	—	4	8	no	—
66	C₂×C₇₁⋊C₈	—	4	2	no	—
67	C₂×C₇₁⋊C₈	—	4	2	no	—
68	C₄⋊Dic₇₁	—	4	4	no	—
69	C₄⋊Dic₇₁	—	4	4	no	—
70	C₄⋊Dic₇₁	—	4	4	no	—
71	C₄⋊Dic₇₁	—	4	2	no	—
72	C₄⋊Dic₇₁	—	4	2	no	—
73	C₄⋊Dic₇₁	—	4	2	no	—
74	C₄⋊Dic₇₁	—	4	2	no	—
75	C₄⋊Dic₇₁	—	4	4	no	—
76	C₂⁴×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₇₁	—	2	2	no	—
78	C₂²×C₄×C₇₁	—	2	2	no	—
79	C₂²×C₄×C₇₁	C₄²	1	2	yes	—
80	C₂²×C₄×C₇₁	C₂²⋊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	2	yes	—
84	C₂²×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₇₁	C₄⋊C₄	1	2	yes	—
86	C₂²×C₄×C₇₁	C₄⋊C₄	1	2	yes	—
87	C₂²×C₄×C₇₁	C₄⋊C₄	1	2	yes	—
88	C₂²×C₄×C₇₁	D₈	1	2	yes	—
89	C₂²×C₄×C₇₁	D₈	1	2	yes	—
90	C₂²×C₄×C₇₁	SD₁₆	1	2	yes	—
91	C₂²×C₄×C₇₁	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₇₁	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₇₁	SD₁₆	1	2	yes	—
94	C₂²×C₄×C₇₁	Q₁₆	1	2	yes	—
95	C₂²×C₄×C₇₁	Q₁₆	1	2	yes	—
96	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₇₁	—	2	4	no	—
100	C₂×C₈×C₇₁	—	4	8	no	—
101	C₂×C₈×C₇₁	—	4	2	no	—
102	C₂×C₈×C₇₁	—	4	2	no	—
103	C₄²×C₇₁	C₄²	1	2	yes	—
104	C₄²×C₇₁	C₂²⋊C₄	1	2	yes	—
105	C₄²×C₇₁	C₂²⋊C₄	1	2	yes	—
106	C₄²×C₇₁	C₄⋊C₄	1	2	yes	—
107	C₄²×C₇₁	C₄⋊C₄	1	2	yes	—
108	C₄²×C₇₁	C₄⋊C₄	1	2	yes	—
109	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
113	C₂³×C₇₁	#95	1	2	yes	—
114	C₂³×C₇₁	#100	1	2	yes	—
115	C₂³×C₇₁	#101	1	2	yes	—
116	C₂³×C₇₁	#102	1	2	yes	—
117	C₂³×C₇₁	#102	1	2	yes	—
118	C₂³×C₇₁	#103	1	2	yes	—
119	C₂³×C₇₁	#103	1	2	yes	—
120	C₂³×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₇₁	—	2	4	no	—
122	C₂×C₄×C₇₁	—	2	4	no	—
123	C₂×C₄×C₇₁	—	2	1	no	—
124	C₂×C₄×C₇₁	—	2	1	no	—
125	C₂×C₄×C₇₁	—	2	1	no	—
126	C₂×C₄×C₇₁	—	2	1	no	—
127	C₂×C₄×C₇₁	#95	1	2	yes	—
128	C₂×C₄×C₇₁	#95	1	2	yes	—
129	C₂×C₄×C₇₁	#95	1	2	yes	—
130	C₂×C₄×C₇₁	#102	1	2	yes	—
131	C₂×C₄×C₇₁	#102	1	4	yes	—
132	C₂×C₄×C₇₁	#102	1	2	yes	—
133	C₂×C₄×C₇₁	#102	1	4	yes	—
134	C₂×C₄×C₇₁	#103	1	2	yes	—
135	C₂×C₄×C₇₁	#103	1	4	yes	—
136	C₂×C₄×C₇₁	#103	1	2	yes	—
137	C₂×C₄×C₇₁	#103	1	4	yes	—
138	C₂×C₄×C₇₁	#106	1	4	yes	—
139	C₂×C₄×C₇₁	#106	1	4	yes	—
140	C₂×C₄×C₇₁	#107	1	4	yes	—
141	C₂×C₄×C₇₁	#107	1	4	yes	—
142	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₇₁	C₂×C₂²⋊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×D₈	1	1	yes	characteristic
149	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
150	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
151	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
152	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
154	C₂×C₄×C₇₁	C₂×Q₁₆	1	1	yes	characteristic
155	C₂×C₄×C₇₁	C₂×Q₁₆	1	1	yes	characteristic
156	C₂×Dic₇₁	—	4	4	no	—
157	C₂×Dic₇₁	—	4	4	no	—
158	C₂×Dic₇₁	—	4	4	no	—
159	C₂×Dic₇₁	—	8	8	no	—
160	C₈×C₇₁	—	4	4	no	—
161	C₇₁⋊C₈	—	4	4	no	—
162	C₂²×C₇₁	#331	1	4	yes	—
163	C₂²×C₇₁	#332	1	4	yes	—
164	C₂²×C₇₁	#332	1	4	yes	—
165	C₂²×C₇₁	#333	1	4	yes	—
166	C₂²×C₇₁	#340	1	4	yes	—
167	C₂²×C₇₁	#340	1	4	yes	—
168	C₂²×C₇₁	#343	1	4	yes	—
169	C₂²×C₇₁	C₂×#95	1	1	yes	characteristic
170	C₂²×C₇₁	C₂×#100	1	1	yes	characteristic
171	C₂²×C₇₁	C₂×#101	1	1	yes	characteristic
172	C₂²×C₇₁	C₂×#102	1	1	yes	characteristic
173	C₂²×C₇₁	C₂×#102	1	1	yes	characteristic
174	C₂²×C₇₁	C₂×#103	1	1	yes	characteristic
175	C₂²×C₇₁	C₂×#103	1	1	yes	characteristic
176	C₄×C₇₁	—	2	2	no	—
177	C₄×C₇₁	—	2	1	no	—
178	C₄×C₇₁	—	2	1	no	—
179	C₄×C₇₁	#340	1	4	yes	—
180	C₄×C₇₁	#340	1	4	yes	—
181	C₄×C₇₁	C₂×#102	1	1	yes	characteristic
182	C₄×C₇₁	C₂×#102	1	1	yes	characteristic
183	C₄×C₇₁	C₂×#103	1	1	yes	characteristic
184	C₄×C₇₁	C₂×#103	1	1	yes	characteristic
185	C₄×C₇₁	C₂×#106	1	1	yes	characteristic
186	C₄×C₇₁	C₂×#106	1	1	yes	characteristic
187	C₄×C₇₁	C₂×#107	1	1	yes	characteristic
188	C₄×C₇₁	C₂×#107	1	1	yes	characteristic
189	Dic₇₁	—	8	4	no	—
190	C₂×#1296	—	71	1	no	maximal, Sylow
191	C₂×C₇₁	#1296	1	8	yes	complemented
192	C₂×C₇₁	C₂×#331	1	1	yes	characteristic
193	C₂×C₇₁	C₂×#332	1	1	yes	characteristic
194	C₂×C₇₁	C₂×#332	1	1	yes	characteristic
195	C₂×C₇₁	C₂×#333	1	1	yes	characteristic
196	C₂×C₇₁	C₂×#340	1	1	yes	characteristic
197	C₂×C₇₁	C₂×#340	1	1	yes	characteristic
198	C₂×C₇₁	C₂×#343	1	1	yes	characteristic
199	C₂²×C₄⋊C₈	—	71	1	no	—
200	C₂²×C₄⋊C₈	D₇₁	1	1	yes	characteristic
201	C₂×#384	—	71	1	no	—
202	#1296	—	71	4	no	—
203	C₇₁	C₂×#1296	1	1	yes	characteristic, complemented, Sylow
204	C₂³×C₈	—	2	1	no	—
205	C₂³×C₈	—	142	1	no	—
206	C₂²×C₄⋊C₄	—	71	2	no	—
207	C₂²×C₄⋊C₄	—	142	1	no	—
208	C₂²×C₄⋊C₄	—	142	1	no	—
209	C₂²×C₄²	C₂×D₇₁	1	1	yes	characteristic
210	C₂×C₄⋊C₈	—	2	1	no	—
211	C₂×C₄⋊C₈	—	2	2	no	—
212	C₂×C₄⋊C₈	—	71	4	no	—
213	C₂×C₄⋊C₈	—	71	2	no	—
214	C₂×C₄⋊C₈	—	142	1	no	—
215	C₂×C₄⋊C₈	—	142	2	no	—
216	C₂×C₄⋊C₈	Dic₇₁	1	4	yes	complemented
217	C₂×C₄⋊C₈	C₂×D₇₁	1	2	yes	—
218	#384	—	71	2	no	—
219	#384	—	71	2	no	—
220	#384	—	142	1	no	—
221	#384	—	142	1	no	—
222	C₂³×C₄	—	142	2	no	—
223	C₂³×C₄	C₄×D₇₁	1	1	yes	characteristic
224	C₂³×C₄	D₂₈₄	1	1	yes	characteristic
225	C₂³×C₄	C₂²⋊D₇₁	1	1	yes	characteristic
226	C₂²×C₈	—	2	4	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	—	4	2	no	—
229	C₂²×C₈	—	4	2	no	—
230	C₂²×C₈	—	284	2	no	—
231	C₂²×C₈	—	284	2	no	—
232	C₂²×C₈	—	142	4	no	—
233	C₂²×C₈	—	142	2	no	—
234	C₂×C₄⋊C₄	—	284	4	no	—
235	C₂×C₄⋊C₄	—	284	2	no	—
236	C₂×C₄⋊C₄	—	284	2	no	—
237	C₂×C₄⋊C₄	—	284	2	no	—
238	C₂×C₄⋊C₄	—	284	2	no	—
239	C₂×C₄⋊C₄	—	71	4	no	—
240	C₂×C₄⋊C₄	—	142	2	no	—
241	C₂×C₄⋊C₄	—	142	2	no	—
242	C₂×C₄⋊C₄	—	142	2	no	—
243	C₂×C₄⋊C₄	—	142	2	no	—
244	C₂×C₄⋊C₄	—	142	2	no	—
245	C₂×C₄²	Dic₁₄₂	1	2	yes	—
246	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
247	C₂×C₄²	C₄×D₇₁	1	2	yes	—
248	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
249	C₂×C₄²	C₂×Dic₇₁	1	2	yes	—
250	C₂×C₄²	C₂²⋊D₇₁	1	2	yes	—
251	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
252	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
253	C₄⋊C₈	—	2	4	no	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	71	4	no	—
256	C₄⋊C₈	—	142	4	no	—
257	C₄⋊C₈	—	142	2	no	—
258	C₄⋊C₈	C₂×Dic₇₁	1	4	yes	complemented
259	C₂⁴	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	284	4	no	—
263	C₂²×C₄	—	284	4	no	—
264	C₂²×C₄	—	284	4	no	—
265	C₂²×C₄	—	142	4	no	—
266	C₂²×C₄	C₄×Dic₇₁	1	2	yes	—
267	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	2	yes	—
271	C₂²×C₄	C₂²⋊Dic₇₁	1	2	yes	—
272	C₂²×C₄	Dic₇₁⋊C₄	1	2	yes	—
273	C₂²×C₄	Dic₇₁⋊C₄	1	2	yes	—
274	C₂²×C₄	C₄⋊Dic₇₁	1	2	yes	—
275	C₂²×C₄	#11765850	1	2	yes	—
276	C₂²×C₄	D₅₆₈	1	2	yes	—
277	C₂²×C₄	#11765852	1	2	yes	—
278	C₂²×C₄	#11765853	1	2	yes	—
279	C₂²×C₄	#11765854	1	2	yes	—
280	C₂²×C₄	#11765854	1	2	yes	—
281	C₂²×C₄	#11765855	1	2	yes	—
282	C₂²×C₄	Dic₂₈₄	1	2	yes	—
283	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	4	8	no	—
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	—	284	8	no	—
291	C₂×C₈	—	284	2	no	—
292	C₂×C₈	—	284	2	no	—
293	C₂×C₈	—	142	4	no	—
294	C₄⋊C₄	—	284	4	no	—
295	C₄⋊C₄	—	284	4	no	—
296	C₄⋊C₄	—	284	4	no	—
297	C₄⋊C₄	—	284	4	no	—
298	C₄⋊C₄	—	284	2	no	—
299	C₄⋊C₄	—	284	2	no	—
300	C₄⋊C₄	—	284	2	no	—
301	C₄⋊C₄	—	284	2	no	—
302	C₄²	C₄×Dic₇₁	1	2	yes	—
303	C₄²	(C₂×D₇₁)⋊C₄	1	2	yes	—
304	C₄²	C₂²⋊Dic₇₁	1	2	yes	—
305	C₄²	Dic₇₁⋊C₄	1	2	yes	—
306	C₄²	Dic₇₁⋊C₄	1	2	yes	—
307	C₄²	C₄⋊Dic₇₁	1	2	yes	—
308	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
309	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
310	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
311	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
312	C₂³	C₇₁⋊#95	1	2	yes	—
313	C₂³	#14556044	1	2	yes	—
314	C₂³	#14556046	1	2	yes	—
315	C₂³	#14556048	1	2	yes	—
316	C₂³	#14556050	1	2	yes	—
317	C₂³	#14556051	1	2	yes	—
318	C₂³	#14556053	1	2	yes	—
319	C₂³	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	284	4	no	—
327	C₂×C₄	—	284	4	no	—
328	C₂×C₄	—	284	4	no	—
329	C₂×C₄	—	568	8	no	—
330	C₂×C₄	C₇₁⋊#95	1	2	yes	—
331	C₂×C₄	C₇₁⋊#95	1	2	yes	—
332	C₂×C₄	C₇₁⋊#95	1	2	yes	—
333	C₂×C₄	#14556048	1	2	yes	—
334	C₂×C₄	#14556049	1	4	yes	—
335	C₂×C₄	#14556050	1	4	yes	—
336	C₂×C₄	#14556050	1	2	yes	—
337	C₂×C₄	#14556051	1	2	yes	—
338	C₂×C₄	#14556052	1	4	yes	—
339	C₂×C₄	#14556053	1	4	yes	—
340	C₂×C₄	#14556053	1	2	yes	—
341	C₂×C₄	#14556059	1	4	yes	—
342	C₂×C₄	#14556060	1	4	yes	—
343	C₂×C₄	#14556061	1	4	yes	—
344	C₂×C₄	#14556062	1	4	yes	—
345	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
346	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
347	C₂×C₄	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
348	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
351	C₂×C₄	C₂×#11765850	1	1	yes	characteristic
352	C₂×C₄	C₂×D₅₆₈	1	1	yes	characteristic
353	C₂×C₄	C₂×#11765852	1	1	yes	characteristic
354	C₂×C₄	C₂×#11765853	1	1	yes	characteristic
355	C₂×C₄	C₂×#11765854	1	1	yes	characteristic
356	C₂×C₄	C₂×#11765854	1	1	yes	characteristic
357	C₂×C₄	C₂×#11765855	1	1	yes	characteristic
358	C₂×C₄	C₂×Dic₂₈₄	1	1	yes	characteristic
359	C₈	—	4	4	no	—
360	C₈	—	284	4	no	—
361	C₂²	#17985742	1	4	yes	—
362	C₂²	#17985744	1	4	yes	—
363	C₂²	#17985746	1	4	yes	—
364	C₂²	#17985747	1	4	yes	—
365	C₂²	#17985761	1	4	yes	—
366	C₂²	#17985762	1	4	yes	—
367	C₂²	#17985767	1	4	yes	—
368	C₂²	C₂×C₇₁⋊#95	1	1	yes	characteristic
369	C₂²	C₂×#14556044	1	1	yes	characteristic
370	C₂²	C₂×#14556046	1	1	yes	characteristic
371	C₂²	C₂×#14556048	1	1	yes	characteristic
372	C₂²	C₂×#14556050	1	1	yes	characteristic
373	C₂²	C₂×#14556051	1	1	yes	characteristic
374	C₂²	C₂×#14556053	1	1	yes	characteristic
375	C₄	—	2	2	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	568	4	no	—
379	C₄	#17985761	1	4	yes	—
380	C₄	#17985762	1	4	yes	—
381	C₄	C₂×#14556049	1	1	yes	characteristic
382	C₄	C₂×#14556050	1	1	yes	characteristic
383	C₄	C₂×#14556052	1	1	yes	characteristic
384	C₄	C₂×#14556053	1	1	yes	characteristic
385	C₄	C₂×#14556059	1	1	yes	characteristic
386	C₄	C₂×#14556060	1	1	yes	characteristic
387	C₄	C₂×#14556061	1	1	yes	characteristic
388	C₄	C₂×#14556062	1	1	yes	characteristic
389	C₂	#22586224	1	8	yes	direct product factor
390	C₂	C₂×#17985742	1	1	yes	characteristic
391	C₂	C₂×#17985744	1	1	yes	characteristic
392	C₂	C₂×#17985746	1	1	yes	characteristic
393	C₂	C₂×#17985747	1	1	yes	characteristic
394	C₂	C₂×#17985761	1	1	yes	characteristic
395	C₂	C₂×#17985762	1	1	yes	characteristic
396	C₂	C₂×#17985767	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	(C₂×D₇₁)⋊C₄
commutator	C₂×C₄×C₇₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₂²×C₄⋊C₈×C₇₁	C₂
socle, prime radical	C₂⁴×C₇₁	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	C₂²×C₄⋊C₈	D₇₁
hypocenter	C₇₁	C₂×#1296
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #22586224	C₂	direct (N × H)
11. C₂×C₄⋊(C₇₁⋊C₈)	C₄	semidirect
21. C₂×C₄⋊C₈×C₇₁	C₄	semidirect
41. C₄⋊(C₇₁⋊C₈)	C₂×C₄	semidirect
59. C₄⋊C₈×C₇₁	C₂×C₄	semidirect
191. C₂×C₇₁	#1296	semidirect
203. C₇₁	C₂×#1296	semidirect
216. C₂×C₄⋊C₈	Dic₇₁	semidirect
258. C₄⋊C₈	C₂×Dic₇₁	semidirect
389. C₂	#22586224	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₇₁⋊C₈)	2
C₂×#17985869	2
#22586224	2
C₂²×C₄⋊C₈×C₇₁	2
C₂×#1296	71

Subgroups — C2×#22586224 #31887536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22586224 #31887536