Subgroups — C₂×#22586455 #31912387

Order 18176.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556064	C₂	1	1	yes	maximal, characteristic
2	C₂×#17986037	C₂	1	1	yes	maximal, characteristic
3	#22586455	C₂	1	4	yes	maximal, direct product factor
4	C₂²×M₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11765849	—	2	1	no	—
6	C₂×#14556087	—	2	1	no	—
7	C₂×#14556064	—	2	1	no	—
8	C₂×#14556064	—	2	1	no	—
9	C₂×#14556064	—	2	1	no	—
10	C₂×#14556064	C₄	1	2	yes	complemented
11	C₂×#14556064	C₄	1	2	yes	complemented
12	C₂×#14556064	C₂²	1	2	yes	—
13	#17986037	—	2	1	no	—
14	#17986037	—	2	1	no	—
15	#17986037	C₄	1	2	yes	—
16	#17986037	C₂²	1	2	yes	—
17	C₂×#14556062	—	2	1	no	—
18	C₂×#14556060	C₄	1	2	yes	—
19	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×M₃₂×C₇₁	—	2	1	no	—
21	C₂×M₃₂×C₇₁	—	2	1	no	—
22	C₂×M₃₂×C₇₁	—	2	1	no	—
23	C₂×M₃₂×C₇₁	C₄	1	2	yes	complemented
24	C₂×M₃₂×C₇₁	C₄	1	2	yes	complemented
25	C₂×M₃₂×C₇₁	C₂²	1	2	yes	—
26	C₂²×C₁₆×C₇₁	—	2	1	no	—
27	C₂×#11765849	—	2	2	no	—
28	C₂×#11765849	—	2	2	no	—
29	C₂×#11765849	—	2	2	no	—
30	C₂×#11765849	—	4	1	no	—
31	C₂×#11765849	—	4	1	no	—
32	C₂×#11765849	—	4	1	no	—
33	C₂²×C₇₁⋊C₈	—	4	1	no	—
34	#14556087	—	2	2	no	—
35	#14556087	—	2	2	no	—
36	#14556087	—	4	1	no	—
37	#14556087	—	4	1	no	—
38	C₂×C₄⋊Dic₇₁	—	2	2	no	—
39	C₂×C₂²⋊Dic₇₁	—	4	1	no	—
40	C₂×C₄×Dic₇₁	—	4	1	no	—
41	#14556064	—	2	2	no	—
42	#14556064	—	2	2	no	—
43	#14556064	—	2	2	no	—
44	#14556064	C₂×C₄	1	4	yes	complemented
45	#14556062	—	2	2	no	—
46	#14556062	—	2	2	no	—
47	#14556060	—	2	2	no	—
48	#14556060	C₂×C₄	1	4	yes	—
49	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₇₁	Q₈	1	1	yes	characteristic
62	C₂²×C₈×C₇₁	Q₈	1	1	yes	characteristic
63	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
64	M₃₂×C₇₁	—	2	2	no	—
65	M₃₂×C₇₁	—	2	2	no	—
66	M₃₂×C₇₁	—	2	2	no	—
67	M₃₂×C₇₁	C₂×C₄	1	4	yes	complemented
68	C₂×C₁₆×C₇₁	—	2	2	no	—
69	C₂×C₁₆×C₇₁	—	2	2	no	—
70	C₂×C₁₆×C₇₁	—	2	2	no	—
71	C₂²×Dic₇₁	—	4	2	no	—
72	#11765849	—	2	4	no	—
73	#11765849	—	4	2	no	—
74	#11765849	—	4	2	no	—
75	#11765849	—	4	2	no	—
76	C₂×C₇₁⋊C₈	—	4	2	no	—
77	C₂×C₇₁⋊C₈	—	4	2	no	—
78	C₂×C₇₁⋊C₈	—	4	2	no	—
79	C₄⋊Dic₇₁	—	2	4	no	—
80	C₄⋊Dic₇₁	—	4	2	no	—
81	C₂²⋊Dic₇₁	—	4	2	no	—
82	C₂²⋊Dic₇₁	—	4	2	no	—
83	C₄×Dic₇₁	—	4	2	no	—
84	C₄×Dic₇₁	—	4	2	no	—
85	C₂⁴×C₇₁	SD₁₆	1	1	yes	characteristic
86	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₇₁	C₂²⋊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	1	yes	characteristic
93	C₂²×C₄×C₇₁	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
95	C₂²×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
96	C₂²×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
97	C₂²×C₄×C₇₁	Q₁₆	1	1	yes	characteristic
98	C₂²×C₄×C₇₁	Q₁₆	1	1	yes	characteristic
99	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₇₁	C₄²	1	1	yes	characteristic
101	C₂×C₈×C₇₁	C₄²	1	1	yes	characteristic
102	C₂×C₈×C₇₁	C₄²	1	1	yes	characteristic
103	C₂×C₈×C₇₁	C₄²	1	1	yes	characteristic
104	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
128	C₁₆×C₇₁	—	2	4	no	—
129	C₂³×C₇₁	—	4	2	no	—
130	C₂³×C₇₁	#102	1	1	yes	characteristic
131	C₂³×C₇₁	#102	1	1	yes	characteristic
132	C₂³×C₇₁	#103	1	1	yes	characteristic
133	C₂³×C₇₁	#103	1	1	yes	characteristic
134	C₂³×C₇₁	#106	1	1	yes	characteristic
135	C₂³×C₇₁	#106	1	1	yes	characteristic
136	C₂³×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
137	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
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	#102	1	1	yes	characteristic
142	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
143	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
144	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
145	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
146	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
147	C₂×C₄×C₇₁	#103	1	1	yes	characteristic
148	C₂×C₄×C₇₁	#103	1	1	yes	characteristic
149	C₂×C₄×C₇₁	#103	1	1	yes	characteristic
150	C₂×C₄×C₇₁	#103	1	1	yes	characteristic
151	C₂×C₄×C₇₁	#103	1	1	yes	characteristic
152	C₂×C₄×C₇₁	#103	1	1	yes	characteristic
153	C₂×C₄×C₇₁	#106	1	1	yes	characteristic
154	C₂×C₄×C₇₁	#106	1	1	yes	characteristic
155	C₂×C₄×C₇₁	#107	1	1	yes	characteristic
156	C₂×C₄×C₇₁	#107	1	1	yes	characteristic
157	C₂×C₄×C₇₁	#107	1	1	yes	characteristic
158	C₂×C₄×C₇₁	#107	1	1	yes	characteristic
159	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₇₁	C₂×D₈	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	C₂×Dic₇₁	—	4	4	no	—
166	C₂×Dic₇₁	—	8	4	no	—
167	C₈×C₇₁	#95	1	1	yes	characteristic
168	C₈×C₇₁	#95	1	1	yes	characteristic
169	C₈×C₇₁	#95	1	1	yes	characteristic
170	C₈×C₇₁	#95	1	1	yes	characteristic
171	C₈×C₇₁	C₂×C₄²	1	1	yes	characteristic
172	C₈×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₈×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₈×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₇₁⋊C₈	—	4	4	no	—
176	C₂²×C₇₁	—	2	2	no	—
177	C₂²×C₇₁	—	2	2	no	—
178	C₂²×C₇₁	—	2	2	no	—
179	C₂²×C₇₁	—	4	1	no	—
180	C₂²×C₇₁	—	4	1	no	—
181	C₂²×C₇₁	—	4	1	no	—
182	C₂²×C₇₁	—	4	1	no	—
183	C₂²×C₇₁	#340	1	1	yes	characteristic
184	C₂²×C₇₁	#340	1	1	yes	characteristic
185	C₂²×C₇₁	#340	1	1	yes	characteristic
186	C₂²×C₇₁	#340	1	1	yes	characteristic
187	C₂²×C₇₁	C₂×#102	1	1	yes	characteristic
188	C₂²×C₇₁	C₂×#103	1	1	yes	characteristic
189	C₂²×C₇₁	C₂×#106	1	1	yes	characteristic
190	C₄×C₇₁	#340	1	1	yes	characteristic
191	C₄×C₇₁	#340	1	1	yes	characteristic
192	C₄×C₇₁	#340	1	1	yes	characteristic
193	C₄×C₇₁	#340	1	1	yes	characteristic
194	C₄×C₇₁	C₂×#95	1	1	yes	characteristic
195	C₄×C₇₁	C₂×#102	1	1	yes	characteristic
196	C₄×C₇₁	C₂×#103	1	1	yes	characteristic
197	C₄×C₇₁	C₂×#107	1	1	yes	characteristic
198	Dic₇₁	—	8	4	no	—
199	C₂×#1389	—	71	1	no	maximal, Sylow
200	C₂×C₇₁	—	2	1	no	—
201	C₂×C₇₁	—	2	1	no	—
202	C₂×C₇₁	—	2	1	no	—
203	C₂×C₇₁	—	2	1	no	—
204	C₂×C₇₁	—	2	1	no	—
205	C₂×C₇₁	—	2	1	no	—
206	C₂×C₇₁	#1389	1	2	yes	complemented
207	C₂×C₇₁	C₂×#340	1	1	yes	characteristic
208	C₂²×M₃₂	D₇₁	1	1	yes	characteristic
209	C₂²×#108	—	71	1	no	—
210	C₂×#427	—	71	1	no	—
211	#1389	—	71	4	no	—
212	C₇₁	C₂×#1389	1	1	yes	characteristic, complemented, Sylow
213	C₂²×M₁₆	—	142	1	no	—
214	C₂³×C₈	C₂×D₇₁	1	1	yes	characteristic
215	C₂×#117	—	142	1	no	—
216	C₂×M₃₂	—	2	1	no	—
217	C₂×M₃₂	—	2	1	no	—
218	C₂×M₃₂	—	2	1	no	—
219	C₂×M₃₂	Dic₇₁	1	2	yes	complemented
220	C₂×M₃₂	Dic₇₁	1	2	yes	complemented
221	C₂×M₃₂	C₂×D₇₁	1	2	yes	—
222	C₂²×C₁₆	—	2	1	no	—
223	C₂×#108	—	71	2	no	—
224	C₂×#108	—	71	2	no	—
225	C₂×#108	—	71	2	no	—
226	C₂×#108	—	142	1	no	—
227	C₂×#108	—	142	1	no	—
228	C₂×#108	—	142	1	no	—
229	#427	—	71	2	no	—
230	#427	—	71	2	no	—
231	#427	—	142	1	no	—
232	#427	—	142	1	no	—
233	C₂×#107	—	142	1	no	—
234	C₂×#106	—	71	2	no	—
235	C₂³×C₄	D₂₈₄	1	1	yes	characteristic
236	C₂×M₁₆	—	284	1	no	—
237	C₂×M₁₆	—	284	1	no	—
238	C₂×M₁₆	—	284	1	no	—
239	C₂×M₁₆	—	142	2	no	—
240	C₂×M₁₆	—	142	2	no	—
241	C₂×M₁₆	—	142	2	no	—
242	C₂²×C₈	—	284	1	no	—
243	C₂²×C₈	Dic₁₄₂	1	1	yes	characteristic
244	C₂²×C₈	Dic₁₄₂	1	1	yes	characteristic
245	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
246	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
247	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
248	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
249	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
250	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
251	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
252	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
253	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
254	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
255	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
257	#117	—	284	1	no	—
258	#117	—	284	1	no	—
259	#117	—	142	2	no	—
260	#117	—	142	2	no	—
261	C₂×C₄⋊C₄	—	142	2	no	—
262	C₂×C₂²⋊C₄	—	284	1	no	—
263	C₂×C₄²	—	284	1	no	—
264	M₃₂	—	2	2	no	—
265	M₃₂	—	2	2	no	—
266	M₃₂	—	2	2	no	—
267	M₃₂	C₂×Dic₇₁	1	4	yes	complemented
268	C₂×C₁₆	—	2	2	no	—
269	C₂×C₁₆	—	2	2	no	—
270	C₂×C₁₆	—	2	2	no	—
271	#108	—	71	4	no	—
272	#108	—	142	2	no	—
273	#108	—	142	2	no	—
274	#108	—	142	2	no	—
275	#107	—	142	2	no	—
276	#107	—	142	2	no	—
277	#106	—	71	4	no	—
278	#106	—	142	2	no	—
279	C₂⁴	#11765854	1	1	yes	characteristic
280	C₂²×C₄	—	284	2	no	—
281	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
286	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
287	C₂²×C₄	D₅₆₈	1	1	yes	characteristic
288	C₂²×C₄	D₅₆₈	1	1	yes	characteristic
289	C₂²×C₄	#11765854	1	1	yes	characteristic
290	C₂²×C₄	#11765854	1	1	yes	characteristic
291	C₂²×C₄	#11765854	1	1	yes	characteristic
292	C₂²×C₄	Dic₂₈₄	1	1	yes	characteristic
293	C₂²×C₄	Dic₂₈₄	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
295	M₁₆	—	284	2	no	—
296	M₁₆	—	284	2	no	—
297	M₁₆	—	284	2	no	—
298	M₁₆	—	142	4	no	—
299	C₂×C₈	—	284	2	no	—
300	C₂×C₈	—	284	2	no	—
301	C₂×C₈	—	284	2	no	—
302	C₂×C₈	C₄×Dic₇₁	1	1	yes	characteristic
303	C₂×C₈	C₄×Dic₇₁	1	1	yes	characteristic
304	C₂×C₈	C₄×Dic₇₁	1	1	yes	characteristic
305	C₂×C₈	C₄×Dic₇₁	1	1	yes	characteristic
306	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
307	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
308	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
309	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
310	C₂×C₈	C₂²⋊Dic₇₁	1	1	yes	characteristic
311	C₂×C₈	C₂²⋊Dic₇₁	1	1	yes	characteristic
312	C₂×C₈	C₂²⋊Dic₇₁	1	1	yes	characteristic
313	C₂×C₈	C₂²⋊Dic₇₁	1	1	yes	characteristic
314	C₂×C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
315	C₂×C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
316	C₂×C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
317	C₂×C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
318	C₂×C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
319	C₂×C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
320	C₂×C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
321	C₂×C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
322	C₂×C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
323	C₂×C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
324	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
325	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
326	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
327	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
328	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
329	C₂×C₈	C₂×Dic₁₄₂	1	1	yes	characteristic
330	C₄⋊C₄	—	284	2	no	—
331	C₄⋊C₄	—	142	4	no	—
332	C₂²⋊C₄	—	284	2	no	—
333	C₂²⋊C₄	—	284	2	no	—
334	C₄²	—	284	2	no	—
335	C₄²	—	284	2	no	—
336	C₁₆	—	2	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	#14556050	1	1	yes	characteristic
339	C₂³	#14556050	1	1	yes	characteristic
340	C₂³	#14556053	1	1	yes	characteristic
341	C₂³	#14556053	1	1	yes	characteristic
342	C₂³	#14556060	1	1	yes	characteristic
343	C₂³	#14556060	1	1	yes	characteristic
344	C₂³	C₂×#11765854	1	1	yes	characteristic
345	C₂×C₄	—	284	4	no	—
346	C₂×C₄	—	568	4	no	—
347	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
348	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
349	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
350	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
351	C₂×C₄	#14556050	1	1	yes	characteristic
352	C₂×C₄	#14556050	1	1	yes	characteristic
353	C₂×C₄	#14556050	1	1	yes	characteristic
354	C₂×C₄	#14556050	1	1	yes	characteristic
355	C₂×C₄	#14556050	1	1	yes	characteristic
356	C₂×C₄	#14556050	1	1	yes	characteristic
357	C₂×C₄	#14556053	1	1	yes	characteristic
358	C₂×C₄	#14556053	1	1	yes	characteristic
359	C₂×C₄	#14556053	1	1	yes	characteristic
360	C₂×C₄	#14556053	1	1	yes	characteristic
361	C₂×C₄	#14556053	1	1	yes	characteristic
362	C₂×C₄	#14556053	1	1	yes	characteristic
363	C₂×C₄	#14556060	1	1	yes	characteristic
364	C₂×C₄	#14556060	1	1	yes	characteristic
365	C₂×C₄	#14556062	1	1	yes	characteristic
366	C₂×C₄	#14556062	1	1	yes	characteristic
367	C₂×C₄	#14556062	1	1	yes	characteristic
368	C₂×C₄	#14556062	1	1	yes	characteristic
369	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
370	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
372	C₂×C₄	C₂×D₅₆₈	1	1	yes	characteristic
373	C₂×C₄	C₂×#11765854	1	1	yes	characteristic
374	C₂×C₄	C₂×Dic₂₈₄	1	1	yes	characteristic
375	C₈	—	284	4	no	—
376	C₈	C₇₁⋊#95	1	1	yes	characteristic
377	C₈	C₇₁⋊#95	1	1	yes	characteristic
378	C₈	C₇₁⋊#95	1	1	yes	characteristic
379	C₈	C₇₁⋊#95	1	1	yes	characteristic
380	C₈	C₂×C₄×Dic₇₁	1	1	yes	characteristic
381	C₈	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
382	C₈	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
383	C₈	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	#17985762	1	1	yes	characteristic
392	C₂²	#17985762	1	1	yes	characteristic
393	C₂²	#17985762	1	1	yes	characteristic
394	C₂²	#17985762	1	1	yes	characteristic
395	C₂²	C₂×#14556050	1	1	yes	characteristic
396	C₂²	C₂×#14556053	1	1	yes	characteristic
397	C₂²	C₂×#14556060	1	1	yes	characteristic
398	C₄	—	568	4	no	—
399	C₄	#17985762	1	1	yes	characteristic
400	C₄	#17985762	1	1	yes	characteristic
401	C₄	#17985762	1	1	yes	characteristic
402	C₄	#17985762	1	1	yes	characteristic
403	C₄	C₂×C₇₁⋊#95	1	1	yes	characteristic
404	C₄	C₂×#14556050	1	1	yes	characteristic
405	C₄	C₂×#14556053	1	1	yes	characteristic
406	C₄	C₂×#14556062	1	1	yes	characteristic
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	#22586455	1	2	yes	direct product factor
414	C₂	C₂×#17985762	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14556050
commutator	C₈×C₇₁	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₂²×M₃₂×C₇₁	C₂
socle	C₂²×C₇₁	#340
prime radical	C₂⁴×C₇₁	SD₁₆
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	C₂²×M₃₂	D₇₁
hypocenter	C₇₁	C₂×#1389
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
3. #22586455	C₂	direct (N × H)
10. C₂×#14556064	C₄	semidirect
11. C₂×#14556064	C₄	semidirect
23. C₂×M₃₂×C₇₁	C₄	semidirect
24. C₂×M₃₂×C₇₁	C₄	semidirect
44. #14556064	C₂×C₄	semidirect
67. M₃₂×C₇₁	C₂×C₄	semidirect
206. C₂×C₇₁	#1389	semidirect
212. C₇₁	C₂×#1389	semidirect
219. C₂×M₃₂	Dic₇₁	semidirect
220. C₂×M₃₂	Dic₇₁	semidirect
267. M₃₂	C₂×Dic₇₁	semidirect
413. C₂	#22586455	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×#14556064	2
C₂×#17986037	2
#22586455	2
C₂²×M₃₂×C₇₁	2
C₂×#1389	71

Subgroups — C2×#22586455 #31912387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22586455 #31912387