Subgroups — C₂×#22586237 #31887677

Order 18176.

666 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17986052	C₂	1	1	yes	maximal, characteristic
2	C₂×#17986023	C₂	1	1	yes	maximal, characteristic
3	#22586237	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄⋊C₈×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11765849	—	2	1	no	—
6	#17986052	—	2	1	no	—
7	#17986052	—	2	1	no	—
8	#17986052	C₄	1	2	yes	—
9	#17986052	C₂²	1	2	yes	—
10	#17986023	—	2	1	no	—
11	#17986023	—	2	1	no	—
12	#17986023	C₄	1	2	yes	—
13	#17986023	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
16	C₂×C₄⋊(C₇₁⋊C₈)	C₄	1	2	yes	—
17	C₂×C₂²⋊(C₇₁⋊C₈)	C₄	1	2	yes	—
18	C₂×C₄×C₇₁⋊C₈	—	2	1	no	—
19	C₂³×C₈×C₇₁	—	2	1	no	—
20	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₇₁	—	2	1	no	—
22	C₂×C₄⋊C₈×C₇₁	—	2	1	no	—
23	C₂×C₄⋊C₈×C₇₁	—	2	1	no	—
24	C₂×C₄⋊C₈×C₇₁	C₄	1	2	yes	—
25	C₂×C₄⋊C₈×C₇₁	C₄	1	2	yes	—
26	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
27	C₂×#11765849	—	2	2	no	—
28	C₂×#11765849	—	2	2	no	—
29	C₂×#11765849	—	4	2	no	—
30	C₂×#11765849	—	4	2	no	—
31	C₂²×C₇₁⋊C₈	—	2	2	no	—
32	C₂²×C₇₁⋊C₈	—	2	2	no	—
33	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
34	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
35	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
36	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
37	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
38	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
39	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
41	C₄×C₇₁⋊C₈	—	2	2	no	—
42	C₄×C₇₁⋊C₈	—	2	2	no	—
43	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₇₁	Q₈	1	1	yes	characteristic
46	C₂²×C₈×C₇₁	—	2	2	no	—
47	C₂²×C₈×C₇₁	—	2	2	no	—
48	C₂²×C₈×C₇₁	—	2	2	no	—
49	C₂²×C₈×C₇₁	—	4	2	no	—
50	C₂²×C₈×C₇₁	—	4	2	no	—
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	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₇₁	Q₈	1	1	yes	characteristic
62	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₇₁	—	2	2	no	—
64	C₄⋊C₈×C₇₁	—	2	2	no	—
65	C₄⋊C₈×C₇₁	—	2	2	no	—
66	C₄⋊C₈×C₇₁	C₂×C₄	1	4	yes	—
67	#11765849	—	4	4	no	—
68	#11765849	—	4	2	no	—
69	#11765849	—	4	2	no	—
70	C₂×C₇₁⋊C₈	—	2	4	no	—
71	C₂×C₇₁⋊C₈	—	2	4	no	—
72	C₂×C₇₁⋊C₈	—	4	4	no	—
73	C₂×C₇₁⋊C₈	—	4	4	no	—
74	C₂⁴×C₇₁	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₇₁	—	2	4	no	—
76	C₂²×C₄×C₇₁	—	4	2	no	—
77	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
84	C₂²×C₄×C₇₁	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₁	D₈	1	2	yes	—
93	C₂²×C₄×C₇₁	SD₁₆	1	2	yes	—
94	C₂²×C₄×C₇₁	SD₁₆	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×Q₈	1	1	yes	characteristic
99	C₂×C₈×C₇₁	—	2	4	no	—
100	C₂×C₈×C₇₁	—	4	4	no	—
101	C₂×C₈×C₇₁	—	4	4	no	—
102	C₂×C₈×C₇₁	—	4	2	no	—
103	C₂×C₈×C₇₁	—	4	2	no	—
104	C₄²×C₇₁	C₄²	1	1	yes	characteristic
105	C₄²×C₇₁	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
120	C₂³×C₇₁	—	2	2	no	—
121	C₂³×C₇₁	—	2	2	no	—
122	C₂³×C₇₁	#95	1	1	yes	characteristic
123	C₂³×C₇₁	#95	1	1	yes	characteristic
124	C₂³×C₇₁	#106	1	2	yes	—
125	C₂³×C₇₁	#107	1	2	yes	—
126	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	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	#95	1	1	yes	characteristic
139	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
140	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
141	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
142	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
143	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
144	C₂×C₄×C₇₁	#102	1	2	yes	—
145	C₂×C₄×C₇₁	#102	1	2	yes	—
146	C₂×C₄×C₇₁	#102	1	2	yes	—
147	C₂×C₄×C₇₁	#102	1	2	yes	—
148	C₂×C₄×C₇₁	#103	1	2	yes	—
149	C₂×C₄×C₇₁	#103	1	2	yes	—
150	C₂×C₄×C₇₁	#103	1	2	yes	—
151	C₂×C₄×C₇₁	#103	1	2	yes	—
152	C₂×C₄×C₇₁	#106	1	2	yes	—
153	C₂×C₄×C₇₁	#107	1	2	yes	—
154	C₂×C₄×C₇₁	#108	1	4	yes	—
155	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
163	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₇₁	C₂×Q₁₆	1	1	yes	characteristic
165	C₈×C₇₁	—	4	4	no	—
166	C₇₁⋊C₈	—	4	4	no	—
167	C₇₁⋊C₈	—	4	4	no	—
168	C₂²×C₇₁	—	2	4	no	—
169	C₂²×C₇₁	—	2	4	no	—
170	C₂²×C₇₁	—	2	1	no	—
171	C₂²×C₇₁	—	2	1	no	—
172	C₂²×C₇₁	—	2	1	no	—
173	C₂²×C₇₁	—	2	1	no	—
174	C₂²×C₇₁	#340	1	2	yes	—
175	C₂²×C₇₁	#340	1	2	yes	—
176	C₂²×C₇₁	#341	1	2	yes	—
177	C₂²×C₇₁	#344	1	2	yes	—
178	C₂²×C₇₁	C₂×#95	1	1	yes	characteristic
179	C₂²×C₇₁	C₂×#106	1	1	yes	characteristic
180	C₂²×C₇₁	C₂×#107	1	1	yes	characteristic
181	C₄×C₇₁	—	2	1	no	—
182	C₄×C₇₁	—	2	1	no	—
183	C₄×C₇₁	—	2	1	no	—
184	C₄×C₇₁	—	2	1	no	—
185	C₄×C₇₁	—	2	1	no	—
186	C₄×C₇₁	—	2	1	no	—
187	C₄×C₇₁	#340	1	2	yes	—
188	C₄×C₇₁	#340	1	2	yes	—
189	C₄×C₇₁	#341	1	2	yes	—
190	C₄×C₇₁	C₂×#102	1	1	yes	characteristic
191	C₄×C₇₁	C₂×#102	1	1	yes	characteristic
192	C₄×C₇₁	C₂×#103	1	1	yes	characteristic
193	C₄×C₇₁	C₂×#103	1	1	yes	characteristic
194	C₄×C₇₁	C₂×#108	1	2	yes	—
195	C₂×#1301	—	71	1	no	maximal, Sylow
196	C₂×C₇₁	—	2	2	no	—
197	C₂×C₇₁	—	2	1	no	—
198	C₂×C₇₁	—	2	1	no	—
199	C₂×C₇₁	#1301	1	4	yes	complemented
200	C₂×C₇₁	C₂×#340	1	1	yes	characteristic
201	C₂×C₇₁	C₂×#341	1	1	yes	characteristic
202	C₂×C₇₁	C₂×#344	1	1	yes	characteristic
203	C₂×#431	—	71	1	no	—
204	C₂×#423	—	71	1	no	—
205	C₂²×C₄⋊C₈	D₇₁	1	1	yes	characteristic
206	#1301	—	71	4	no	—
207	C₇₁	C₂×#1301	1	1	yes	characteristic, complemented, Sylow
208	C₂²×M₁₆	—	142	1	no	—
209	C₂³×C₈	—	2	1	no	—
210	C₂²×C₄²	C₂×D₇₁	1	1	yes	characteristic
211	#431	—	71	2	no	—
212	#431	—	71	2	no	—
213	#431	—	142	1	no	—
214	#431	—	142	1	no	—
215	#423	—	71	2	no	—
216	#423	—	71	2	no	—
217	#423	—	142	1	no	—
218	#423	—	142	1	no	—
219	C₂×C₄⋊C₈	—	2	1	no	—
220	C₂×C₄⋊C₈	—	2	1	no	—
221	C₂×C₄⋊C₈	—	2	1	no	—
222	C₂×C₄⋊C₈	—	71	2	no	—
223	C₂×C₄⋊C₈	—	142	1	no	—
224	C₂×C₄⋊C₈	—	142	1	no	—
225	C₂×C₄⋊C₈	Dic₇₁	1	2	yes	—
226	C₂×C₄⋊C₈	Dic₇₁	1	2	yes	—
227	C₂×C₄⋊C₈	C₂×D₇₁	1	2	yes	—
228	C₂×C₂²⋊C₈	—	71	2	no	—
229	C₂×C₄×C₈	—	142	1	no	—
230	C₂³×C₄	Dic₁₄₂	1	1	yes	characteristic
231	C₂³×C₄	C₄×D₇₁	1	1	yes	characteristic
232	C₂³×C₄	C₂²⋊D₇₁	1	1	yes	characteristic
233	C₂×M₁₆	—	284	2	no	—
234	C₂×M₁₆	—	284	2	no	—
235	C₂×M₁₆	—	142	2	no	—
236	C₂×M₁₆	—	142	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	4	2	no	—
241	C₂²×C₈	—	4	2	no	—
242	C₂²×C₈	—	142	2	no	—
243	C₂²×C₈	—	142	2	no	—
244	C₂×C₄²	Dic₁₄₂	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
247	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
248	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
249	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
250	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
251	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
254	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	—	71	4	no	—
260	C₄⋊C₈	—	142	2	no	—
261	C₄⋊C₈	—	142	2	no	—
262	C₄⋊C₈	—	142	2	no	—
263	C₄⋊C₈	—	142	2	no	—
264	C₄⋊C₈	—	142	2	no	—
265	C₄⋊C₈	C₂×Dic₇₁	1	4	yes	—
266	C₂²⋊C₈	—	71	4	no	—
267	C₂²⋊C₈	—	142	2	no	—
268	C₄×C₈	—	142	2	no	—
269	C₄×C₈	—	142	2	no	—
270	C₂⁴	Dic₇₁⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
274	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
275	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊Dic₇₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊Dic₇₁	1	1	yes	characteristic
281	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
286	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
287	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
288	C₂²×C₄	#11765850	1	2	yes	—
289	C₂²×C₄	#11765852	1	2	yes	—
290	C₂²×C₄	#11765853	1	2	yes	—
291	C₂²×C₄	#11765855	1	2	yes	—
292	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
294	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
295	M₁₆	—	284	4	no	—
296	M₁₆	—	284	2	no	—
297	M₁₆	—	284	2	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	4	4	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	—	284	4	no	—
304	C₂×C₈	—	284	4	no	—
305	C₂×C₈	—	142	4	no	—
306	C₂×C₈	—	142	4	no	—
307	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
308	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
309	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
310	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
311	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
312	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
313	C₄²	C₂²⋊Dic₇₁	1	1	yes	characteristic
314	C₄²	C₂²⋊Dic₇₁	1	1	yes	characteristic
315	C₄²	Dic₇₁⋊C₄	1	1	yes	characteristic
316	C₄²	Dic₇₁⋊C₄	1	1	yes	characteristic
317	C₄²	C₄⋊Dic₇₁	1	1	yes	characteristic
318	C₄²	C₄⋊Dic₇₁	1	1	yes	characteristic
319	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
320	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
321	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
322	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	C₇₁⋊#95	1	1	yes	characteristic
326	C₂³	C₇₁⋊#95	1	1	yes	characteristic
327	C₂³	#14556059	1	2	yes	—
328	C₂³	#14556061	1	2	yes	—
329	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
342	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
343	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
344	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
345	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
346	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
347	C₂×C₄	#14556048	1	2	yes	—
348	C₂×C₄	#14556048	1	2	yes	—
349	C₂×C₄	#14556049	1	2	yes	—
350	C₂×C₄	#14556049	1	2	yes	—
351	C₂×C₄	#14556051	1	2	yes	—
352	C₂×C₄	#14556051	1	2	yes	—
353	C₂×C₄	#14556052	1	2	yes	—
354	C₂×C₄	#14556052	1	2	yes	—
355	C₂×C₄	#14556059	1	2	yes	—
356	C₂×C₄	#14556061	1	2	yes	—
357	C₂×C₄	#14556064	1	4	yes	—
358	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
359	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
360	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
362	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
364	C₂×C₄	C₂×#11765850	1	1	yes	characteristic
365	C₂×C₄	C₂×#11765852	1	1	yes	characteristic
366	C₂×C₄	C₂×#11765853	1	1	yes	characteristic
367	C₂×C₄	C₂×#11765855	1	1	yes	characteristic
368	C₈	—	4	4	no	—
369	C₈	—	284	4	no	—
370	C₈	—	284	4	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	#17985761	1	2	yes	—
378	C₂²	#17985761	1	2	yes	—
379	C₂²	#17985764	1	2	yes	—
380	C₂²	#17985771	1	2	yes	—
381	C₂²	C₂×C₇₁⋊#95	1	1	yes	characteristic
382	C₂²	C₂×#14556059	1	1	yes	characteristic
383	C₂²	C₂×#14556061	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	#17985761	1	2	yes	—
391	C₄	#17985761	1	2	yes	—
392	C₄	#17985764	1	2	yes	—
393	C₄	C₂×#14556048	1	1	yes	characteristic
394	C₄	C₂×#14556049	1	1	yes	characteristic
395	C₄	C₂×#14556051	1	1	yes	characteristic
396	C₄	C₂×#14556052	1	1	yes	characteristic
397	C₄	C₂×#14556064	1	2	yes	—
398	C₂	—	2	2	no	—
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	#22586237	1	4	yes	direct product factor
402	C₂	C₂×#17985761	1	1	yes	characteristic
403	C₂	C₂×#17985764	1	1	yes	characteristic
404	C₂	C₂×#17985771	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	(C₂×D₇₁)⋊C₄
commutator	C₂×C₄×C₇₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₂²×C₄⋊C₈×C₇₁	C₂
socle	C₂³×C₇₁	#95
prime radical	C₂⁴×C₇₁	C₄⋊C₄
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	C₂²×C₄⋊C₈	D₇₁
hypocenter	C₇₁	C₂×#1301
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #22586237	C₂	direct (N × H)
199. C₂×C₇₁	#1301	semidirect
207. C₇₁	C₂×#1301	semidirect
401. C₂	#22586237	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#17986052	2
C₂×#17986023	2
#22586237	2
C₂²×C₄⋊C₈×C₇₁	2
C₂×#1301	71

Subgroups — C2×#22586237 #31887677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22586237 #31887677