Subgroups — #32023865

Order 18176.

700 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22589281	C₂	1	1	yes	maximal, characteristic, complemented
2	#22589277	C₂	1	1	yes	maximal, characteristic, complemented
3	#22589064	C₂	1	1	yes	maximal, characteristic, complemented
4	#22589059	C₂	1	1	yes	maximal, characteristic, complemented
5	#22588955	C₂	1	1	yes	maximal, characteristic
6	#22588955	C₂	1	1	yes	maximal, characteristic
7	#22588948	C₂	1	1	yes	maximal, characteristic
8	#22588948	C₂	1	1	yes	maximal, characteristic
9	#22588906	C₂	1	1	yes	maximal, characteristic, complemented
10	#22588906	C₂	1	1	yes	maximal, characteristic, complemented
11	#22588899	C₂	1	1	yes	maximal, characteristic, complemented
12	#22588899	C₂	1	1	yes	maximal, characteristic, complemented
13	#22588408	C₂	1	1	yes	maximal, characteristic
14	#22588320	C₂	1	1	yes	maximal, characteristic
15	C₄×C₂²⋊Q₈×C₇₁	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×#14556039	C₂²	1	1	yes	characteristic
27	C₂×#14556039	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
30	#17985754	C₂²	1	1	yes	characteristic
31	#17985754	C₂²	1	1	yes	characteristic
32	#17985754	C₂²	1	1	yes	characteristic
33	#17985754	C₂²	1	1	yes	characteristic
34	#17985754	C₂²	1	1	yes	characteristic
35	#17985754	C₂²	1	1	yes	characteristic
36	#17985754	C₂²	1	1	yes	characteristic
37	#17985754	C₂²	1	1	yes	characteristic
38	#17985754	C₂²	1	1	yes	characteristic
39	#17985754	C₂²	1	1	yes	characteristic
40	#17985754	C₂²	1	1	yes	characteristic
41	#17985754	C₂²	1	1	yes	characteristic
42	#17985754	C₂²	1	1	yes	characteristic
43	#17985754	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊Q₈×C₇₁	C₄	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
47	#391×C₇₁	C₄	1	1	yes	characteristic
48	#389×C₇₁	C₄	1	1	yes	characteristic
49	#387×C₇₁	C₄	1	1	yes	characteristic
50	#387×C₇₁	C₄	1	1	yes	characteristic
51	#385×C₇₁	C₄	1	1	yes	characteristic
52	#385×C₇₁	C₄	1	1	yes	characteristic
53	#380×C₇₁	C₄	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
59	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
67	C₄⋊(C₇₁⋊C₈)	—	4	1	no	—
68	C₄⋊(C₇₁⋊C₈)	—	4	1	no	—
69	C₄⋊(C₇₁⋊C₈)	—	4	1	no	—
70	C₄⋊(C₇₁⋊C₈)	—	4	1	no	—
71	C₄⋊(C₇₁⋊C₈)	—	4	1	no	—
72	C₄⋊(C₇₁⋊C₈)	—	4	1	no	—
73	C₂²⋊(C₇₁⋊C₈)	—	4	1	no	—
74	C₂²⋊(C₇₁⋊C₈)	—	4	1	no	—
75	C₂²⋊(C₇₁⋊C₈)	—	4	1	no	—
76	C₂²⋊(C₇₁⋊C₈)	—	4	1	no	—
77	#14556039	—	4	1	no	—
78	#14556039	—	4	1	no	—
79	C₄×C₇₁⋊C₈	—	4	1	no	—
80	C₄×C₇₁⋊C₈	—	4	1	no	—
81	C₂²×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
85	C₂²⋊Q₈×C₇₁	—	2	4	no	—
86	C₄×Q₈×C₇₁	—	4	1	no	—
87	C₄×Q₈×C₇₁	—	4	1	no	—
88	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₇₁	—	4	1	no	—
102	C₂×C₄²×C₇₁	—	4	1	no	—
103	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
111	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
112	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
113	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
114	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
115	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
116	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
117	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
118	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
119	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
120	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
121	C₂×C₇₁⋊C₈	—	2	1	no	—
122	C₂×C₇₁⋊C₈	—	2	1	no	—
123	C₂×C₇₁⋊C₈	—	2	1	no	—
124	C₂×C₇₁⋊C₈	—	2	1	no	—
125	C₂×C₇₁⋊C₈	—	2	1	no	—
126	C₂×C₇₁⋊C₈	—	2	1	no	—
127	C₂×C₇₁⋊C₈	—	2	1	no	—
128	C₂×C₇₁⋊C₈	—	2	1	no	—
129	C₂×C₇₁⋊C₈	—	2	1	no	—
130	C₂×C₇₁⋊C₈	—	2	1	no	—
131	C₂×C₇₁⋊C₈	—	2	1	no	—
132	C₂×C₇₁⋊C₈	—	2	1	no	—
133	C₂×C₇₁⋊C₈	—	2	1	no	—
134	C₂×C₇₁⋊C₈	—	2	1	no	—
135	C₂×C₇₁⋊C₈	—	2	1	no	—
136	C₂×C₇₁⋊C₈	—	2	1	no	—
137	C₂×C₇₁⋊C₈	—	2	1	no	—
138	C₂×C₇₁⋊C₈	—	2	1	no	—
139	C₂×C₇₁⋊C₈	—	2	1	no	—
140	C₂×C₇₁⋊C₈	—	2	1	no	—
141	C₂×C₇₁⋊C₈	—	2	1	no	—
142	C₂×C₇₁⋊C₈	—	2	1	no	—
143	C₂×C₇₁⋊C₈	—	2	1	no	—
144	C₂×C₇₁⋊C₈	—	2	1	no	—
145	C₂⁴×C₇₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₇₁	—	2	2	no	—
147	C₂×Q₈×C₇₁	—	2	2	no	—
148	C₂×Q₈×C₇₁	—	4	1	no	—
149	C₂²×C₄×C₇₁	—	2	2	no	—
150	C₂²×C₄×C₇₁	—	2	2	no	—
151	C₂²×C₄×C₇₁	—	2	2	no	—
152	C₂²×C₄×C₇₁	—	2	1	no	—
153	C₂²×C₄×C₇₁	—	2	1	no	—
154	C₂²×C₄×C₇₁	—	2	1	no	—
155	C₂²×C₄×C₇₁	—	2	1	no	—
156	C₂²×C₄×C₇₁	—	2	1	no	—
157	C₂²×C₄×C₇₁	—	2	1	no	—
158	C₂²×C₄×C₇₁	—	4	1	no	—
159	C₂²×C₄×C₇₁	—	4	1	no	—
160	C₂²×C₄×C₇₁	—	4	1	no	—
161	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
175	C₄⋊C₄×C₇₁	—	2	2	no	—
176	C₄⋊C₄×C₇₁	—	2	2	no	—
177	C₄⋊C₄×C₇₁	—	2	2	no	—
178	C₄⋊C₄×C₇₁	—	2	2	no	—
179	C₄⋊C₄×C₇₁	—	2	2	no	—
180	C₄⋊C₄×C₇₁	—	2	2	no	—
181	C₄⋊C₄×C₇₁	—	4	1	no	—
182	C₄⋊C₄×C₇₁	—	4	1	no	—
183	C₄⋊C₄×C₇₁	—	4	1	no	—
184	C₂²⋊C₄×C₇₁	—	2	2	no	—
185	C₂²⋊C₄×C₇₁	—	4	1	no	—
186	C₂²⋊C₄×C₇₁	—	4	1	no	—
187	C₂²⋊C₄×C₇₁	M₁₆	1	4	yes	—
188	C₄²×C₇₁	—	2	1	no	—
189	C₄²×C₇₁	—	2	1	no	—
190	C₄²×C₇₁	—	2	1	no	—
191	C₄²×C₇₁	—	2	1	no	—
192	C₄²×C₇₁	—	2	1	no	—
193	C₄²×C₇₁	—	2	1	no	—
194	C₄²×C₇₁	—	2	1	no	—
195	C₄²×C₇₁	—	2	1	no	—
196	C₄²×C₇₁	—	2	1	no	—
197	C₄²×C₇₁	—	2	1	no	—
198	C₄²×C₇₁	—	2	1	no	—
199	C₄²×C₇₁	—	2	1	no	—
200	C₄²×C₇₁	—	4	1	no	—
201	C₄²×C₇₁	—	4	1	no	—
202	C₂³×C₇₁	—	2	1	no	—
203	C₂³×C₇₁	—	2	1	no	—
204	C₂³×C₇₁	—	2	1	no	—
205	C₂³×C₇₁	—	2	1	no	—
206	C₂³×C₇₁	—	2	1	no	—
207	C₂³×C₇₁	—	2	1	no	—
208	C₂³×C₇₁	C₂×M₁₆	1	2	yes	—
209	C₂³×C₇₁	C₂³×C₄	1	1	yes	characteristic
210	Q₈×C₇₁	—	4	4	no	—
211	C₂×C₄×C₇₁	—	2	1	no	—
212	C₂×C₄×C₇₁	—	2	1	no	—
213	C₂×C₄×C₇₁	—	2	1	no	—
214	C₂×C₄×C₇₁	—	2	1	no	—
215	C₂×C₄×C₇₁	—	2	1	no	—
216	C₂×C₄×C₇₁	—	2	1	no	—
217	C₂×C₄×C₇₁	—	2	1	no	—
218	C₂×C₄×C₇₁	—	2	1	no	—
219	C₂×C₄×C₇₁	—	2	1	no	—
220	C₂×C₄×C₇₁	—	2	1	no	—
221	C₂×C₄×C₇₁	—	2	1	no	—
222	C₂×C₄×C₇₁	—	2	1	no	—
223	C₂×C₄×C₇₁	—	2	1	no	—
224	C₂×C₄×C₇₁	—	2	1	no	—
225	C₂×C₄×C₇₁	—	2	1	no	—
226	C₂×C₄×C₇₁	—	2	1	no	—
227	C₂×C₄×C₇₁	—	2	1	no	—
228	C₂×C₄×C₇₁	—	2	1	no	—
229	C₂×C₄×C₇₁	—	2	1	no	—
230	C₂×C₄×C₇₁	—	2	1	no	—
231	C₂×C₄×C₇₁	—	2	1	no	—
232	C₂×C₄×C₇₁	—	2	1	no	—
233	C₂×C₄×C₇₁	—	2	1	no	—
234	C₂×C₄×C₇₁	—	2	1	no	—
235	C₂×C₄×C₇₁	—	2	1	no	—
236	C₂×C₄×C₇₁	—	2	1	no	—
237	C₂×C₄×C₇₁	—	2	1	no	—
238	C₂×C₄×C₇₁	—	2	1	no	—
239	C₂×C₄×C₇₁	—	2	1	no	—
240	C₂×C₄×C₇₁	—	2	1	no	—
241	C₂×C₄×C₇₁	—	2	1	no	—
242	C₂×C₄×C₇₁	—	2	1	no	—
243	C₂×C₄×C₇₁	—	2	1	no	—
244	C₂×C₄×C₇₁	—	2	1	no	—
245	C₂×C₄×C₇₁	—	2	1	no	—
246	C₂×C₄×C₇₁	—	4	4	no	—
247	C₂×C₄×C₇₁	—	4	4	no	—
248	C₂×C₄×C₇₁	—	4	1	no	—
249	C₂×C₄×C₇₁	—	4	1	no	—
250	C₂×C₄×C₇₁	—	4	1	no	—
251	C₂×C₄×C₇₁	—	4	1	no	—
252	C₂×C₄×C₇₁	C₂×M₁₆	1	2	yes	—
253	C₂×C₄×C₇₁	C₂×M₁₆	1	2	yes	—
254	C₂×C₄×C₇₁	#131	1	2	yes	—
255	C₂×C₄×C₇₁	#131	1	2	yes	—
256	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
257	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×C₄×C₇₁	2₋¹⁺⁴	1	1	yes	characteristic
260	C₂×C₄×C₇₁	2₋¹⁺⁴	1	1	yes	characteristic
261	C₂×C₄×C₇₁	2₋¹⁺⁴	1	1	yes	characteristic
262	C₇₁⋊C₈	—	4	1	no	—
263	C₇₁⋊C₈	—	4	1	no	—
264	C₇₁⋊C₈	—	4	1	no	—
265	C₇₁⋊C₈	—	4	1	no	—
266	C₇₁⋊C₈	—	4	1	no	—
267	C₇₁⋊C₈	—	4	1	no	—
268	C₇₁⋊C₈	—	4	1	no	—
269	C₇₁⋊C₈	—	4	1	no	—
270	C₂²×C₇₁	—	2	2	no	—
271	C₂²×C₇₁	—	2	2	no	—
272	C₂²×C₇₁	—	2	2	no	—
273	C₂²×C₇₁	—	4	1	no	—
274	C₂²×C₇₁	—	4	1	no	—
275	C₂²×C₇₁	—	4	1	no	—
276	C₂²×C₇₁	—	4	1	no	—
277	C₂²×C₇₁	#518	1	1	yes	characteristic
278	C₂²×C₇₁	#519	1	1	yes	characteristic
279	C₂²×C₇₁	#520	1	1	yes	characteristic
280	C₂²×C₇₁	C₂²×M₁₆	1	1	yes	characteristic
281	C₂²×C₇₁	C₂×#131	1	1	yes	characteristic
282	C₂²×C₇₁	C₂×#131	1	1	yes	characteristic
283	C₂²×C₇₁	#568	1	1	yes	characteristic
284	C₄×C₇₁	—	2	2	no	—
285	C₄×C₇₁	—	2	2	no	—
286	C₄×C₇₁	—	2	2	no	—
287	C₄×C₇₁	—	2	2	no	—
288	C₄×C₇₁	—	4	1	no	—
289	C₄×C₇₁	—	4	1	no	—
290	C₄×C₇₁	—	4	1	no	—
291	C₄×C₇₁	—	4	1	no	—
292	C₄×C₇₁	—	4	1	no	—
293	C₄×C₇₁	—	4	1	no	—
294	C₄×C₇₁	—	4	1	no	—
295	C₄×C₇₁	—	4	1	no	—
296	C₄×C₇₁	—	4	1	no	—
297	C₄×C₇₁	#562	1	1	yes	characteristic
298	C₄×C₇₁	#562	1	1	yes	characteristic
299	C₄×C₇₁	#563	1	1	yes	characteristic
300	C₄×C₇₁	#563	1	1	yes	characteristic
301	#23341	—	71	1	no	maximal, Sylow
302	C₂×C₇₁	—	4	2	no	—
303	C₂×C₇₁	#2378	1	1	yes	characteristic
304	C₂×C₇₁	#2974	1	1	yes	characteristic
305	C₂×C₇₁	#2976	1	1	yes	characteristic
306	C₂×C₇₁	#2983	1	1	yes	characteristic
307	C₂×C₇₁	#2986	1	1	yes	characteristic
308	C₂×C₇₁	#2990	1	1	yes	characteristic
309	C₂×C₇₁	#2993	1	1	yes	characteristic
310	C₄×C₂²⋊Q₈	D₇₁	1	1	yes	characteristic
311	#1985	—	71	1	no	—
312	#1984	—	71	1	no	—
313	#1940	—	71	1	no	—
314	#1939	—	71	1	no	—
315	#1924	—	71	1	no	—
316	#1924	—	71	1	no	—
317	#1923	—	71	1	no	—
318	#1923	—	71	1	no	—
319	#1917	—	71	1	no	—
320	#1917	—	71	1	no	—
321	#1916	—	71	1	no	—
322	#1916	—	71	1	no	—
323	#1817	—	71	1	no	—
324	#1797	—	71	1	no	—
325	C₇₁	#23341	1	1	yes	characteristic, complemented, Sylow
326	C₂×C₂²⋊Q₈	Dic₇₁	1	1	yes	characteristic
327	C₂×C₄×Q₈	C₂×D₇₁	1	1	yes	characteristic
328	C₂²×C₄²	C₂×D₇₁	1	1	yes	characteristic
329	C₂×C₄⋊C₈	—	71	1	no	—
330	C₂×C₄⋊C₈	—	71	1	no	—
331	C₂×C₄⋊C₈	—	71	1	no	—
332	C₂×C₄⋊C₈	—	71	1	no	—
333	C₂×C₄⋊C₈	—	71	1	no	—
334	C₂×C₄⋊C₈	—	71	1	no	—
335	C₂×C₂²⋊C₈	—	71	1	no	—
336	C₂×C₂²⋊C₈	—	71	1	no	—
337	C₂×C₂²⋊C₈	—	71	1	no	—
338	C₂×C₂²⋊C₈	—	71	1	no	—
339	C₂×#97	—	71	1	no	—
340	C₂×#97	—	71	1	no	—
341	C₂×C₄×C₈	—	71	1	no	—
342	C₂×C₄×C₈	—	71	1	no	—
343	#391	Dic₇₁	1	1	yes	characteristic
344	#389	Dic₇₁	1	1	yes	characteristic
345	#387	Dic₇₁	1	1	yes	characteristic
346	#387	Dic₇₁	1	1	yes	characteristic
347	#385	Dic₇₁	1	1	yes	characteristic
348	#385	Dic₇₁	1	1	yes	characteristic
349	#380	Dic₇₁	1	1	yes	characteristic
350	C₄×C₄⋊C₄	C₂×D₇₁	1	1	yes	characteristic
351	C₄×C₄⋊C₄	C₂×D₇₁	1	1	yes	characteristic
352	C₄×C₄⋊C₄	C₂×D₇₁	1	1	yes	characteristic
353	C₄×C₂²⋊C₄	C₂×D₇₁	1	1	yes	characteristic
354	C₄×C₂²⋊C₄	C₂×D₇₁	1	1	yes	characteristic
355	#336	—	71	1	no	—
356	#336	—	71	1	no	—
357	#336	—	71	1	no	—
358	#336	—	71	1	no	—
359	#336	—	71	1	no	—
360	#336	—	71	1	no	—
361	#336	—	71	1	no	—
362	#336	—	71	1	no	—
363	#336	—	71	1	no	—
364	#336	—	71	1	no	—
365	#336	—	71	1	no	—
366	#336	—	71	1	no	—
367	#336	—	71	1	no	—
368	#336	—	71	1	no	—
369	C₂²×Q₈	C₂×Dic₇₁	1	1	yes	characteristic
370	C₂³×C₄	C₂×Dic₇₁	1	1	yes	characteristic
371	C₂³×C₄	C₂×Dic₇₁	1	1	yes	characteristic
372	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
373	C₂²×C₈	—	71	1	no	—
374	C₂²×C₈	—	71	1	no	—
375	C₂²×C₈	—	71	1	no	—
376	C₂²×C₈	—	71	1	no	—
377	C₂²×C₈	—	71	1	no	—
378	C₂²×C₈	—	71	1	no	—
379	C₂²×C₈	—	71	1	no	—
380	C₂²×C₈	—	71	1	no	—
381	C₂²⋊Q₈	—	2	4	no	—
382	C₄×Q₈	—	4	1	no	—
383	C₄×Q₈	—	4	1	no	—
384	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
397	C₂×C₄²	—	4	1	no	—
398	C₂×C₄²	—	4	1	no	—
399	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
400	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
401	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
402	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
403	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
404	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
405	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
406	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
407	C₄⋊C₈	—	284	1	no	—
408	C₄⋊C₈	—	284	1	no	—
409	C₄⋊C₈	—	284	1	no	—
410	C₄⋊C₈	—	284	1	no	—
411	C₄⋊C₈	—	284	1	no	—
412	C₄⋊C₈	—	284	1	no	—
413	C₂²⋊C₈	—	284	1	no	—
414	C₂²⋊C₈	—	284	1	no	—
415	C₂²⋊C₈	—	284	1	no	—
416	C₂²⋊C₈	—	284	1	no	—
417	#97	—	284	1	no	—
418	#97	—	284	1	no	—
419	C₄×C₈	—	284	1	no	—
420	C₄×C₈	—	284	1	no	—
421	#95	C₂×Dic₇₁	1	1	yes	characteristic
422	#95	C₂×Dic₇₁	1	1	yes	characteristic
423	#95	C₂×Dic₇₁	1	1	yes	characteristic
424	#95	C₂×Dic₇₁	1	1	yes	characteristic
425	#95	C₂×Dic₇₁	1	1	yes	characteristic
426	#95	C₂×Dic₇₁	1	1	yes	characteristic
427	#95	C₂×Dic₇₁	1	1	yes	characteristic
428	#95	C₂×Dic₇₁	1	1	yes	characteristic
429	#95	C₂×Dic₇₁	1	1	yes	characteristic
430	#95	C₂×Dic₇₁	1	1	yes	characteristic
431	C₂⁴	C₂²×Dic₇₁	1	1	yes	characteristic
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	4	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
448	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
449	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
450	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
451	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
452	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
453	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
454	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
455	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
456	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
457	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
458	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
459	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
460	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
461	C₂×C₈	—	142	1	no	—
462	C₂×C₈	—	142	1	no	—
463	C₂×C₈	—	142	1	no	—
464	C₂×C₈	—	142	1	no	—
465	C₂×C₈	—	142	1	no	—
466	C₂×C₈	—	142	1	no	—
467	C₂×C₈	—	142	1	no	—
468	C₂×C₈	—	142	1	no	—
469	C₂×C₈	—	142	1	no	—
470	C₂×C₈	—	142	1	no	—
471	C₂×C₈	—	142	1	no	—
472	C₂×C₈	—	142	1	no	—
473	C₂×C₈	—	142	1	no	—
474	C₂×C₈	—	142	1	no	—
475	C₂×C₈	—	142	1	no	—
476	C₂×C₈	—	142	1	no	—
477	C₂×C₈	—	142	1	no	—
478	C₂×C₈	—	142	1	no	—
479	C₂×C₈	—	142	1	no	—
480	C₂×C₈	—	142	1	no	—
481	C₂×C₈	—	142	1	no	—
482	C₂×C₈	—	142	1	no	—
483	C₂×C₈	—	142	1	no	—
484	C₂×C₈	—	142	1	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	#11765849	1	4	yes	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	4	1	no	—
511	C₄²	—	4	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	C₂×#11765849	1	2	yes	—
519	C₂³	C₂³×Dic₇₁	1	1	yes	characteristic
520	Q₈	—	4	4	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	C₂×#11765849	1	2	yes	—
563	C₂×C₄	C₂×#11765849	1	2	yes	—
564	C₂×C₄	#14556135	1	2	yes	—
565	C₂×C₄	#14556135	1	2	yes	—
566	C₂×C₄	#14556173	1	1	yes	characteristic
567	C₂×C₄	#14556173	1	1	yes	characteristic
568	C₂×C₄	#14556174	1	1	yes	characteristic
569	C₂×C₄	#14556175	1	1	yes	characteristic
570	C₂×C₄	#14556176	1	1	yes	characteristic
571	C₂×C₄	#14556176	1	1	yes	characteristic
572	C₈	—	284	1	no	—
573	C₈	—	284	1	no	—
574	C₈	—	284	1	no	—
575	C₈	—	284	1	no	—
576	C₈	—	284	1	no	—
577	C₈	—	284	1	no	—
578	C₈	—	284	1	no	—
579	C₈	—	284	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	#17986474	1	1	yes	characteristic
588	C₂²	#17986477	1	1	yes	characteristic
589	C₂²	#17986482	1	1	yes	characteristic
590	C₂²	C₂²×#11765849	1	1	yes	characteristic
591	C₂²	C₂×#14556135	1	1	yes	characteristic
592	C₂²	C₂×#14556135	1	1	yes	characteristic
593	C₂²	#17986766	1	1	yes	characteristic
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	#17986745	1	1	yes	characteristic
608	C₄	#17986745	1	1	yes	characteristic
609	C₄	#17986750	1	1	yes	characteristic
610	C₄	#17986750	1	1	yes	characteristic
611	C₂	—	4	2	no	—
612	C₂	#22591506	1	1	yes	characteristic
613	C₂	#22597375	1	1	yes	characteristic
614	C₂	#22597388	1	1	yes	characteristic
615	C₂	#22597425	1	1	yes	characteristic
616	C₂	#22597442	1	1	yes	characteristic
617	C₂	#22597465	1	1	yes	characteristic
618	C₂	#22597489	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₁
commutator, socle	C₂³×C₇₁	C₂³×C₄
Fitting	C₄×C₂²⋊Q₈×C₇₁	C₂
prime radical	C₂⁴×C₇₁	C₂²×C₄
cosocle	C₂²×C₄×C₇₁	C₂⁴
hypercenter	C₄×C₂²⋊Q₈	D₇₁
hypocenter	C₇₁	#23341
LCS	G ▷ C₂³×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #22589281	C₂	semidirect
2. #22589277	C₂	semidirect
3. #22589064	C₂	semidirect
4. #22589059	C₂	semidirect
9. #22588906	C₂	semidirect
10. #22588906	C₂	semidirect
11. #22588899	C₂	semidirect
12. #22588899	C₂	semidirect
325. C₇₁	#23341	semidirect

Maximal subgroups

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

subgroup	index
#22589281	2
#22589277	2
#22589064	2
#22589059	2
#22588955	2
#22588948	2
#22588906	2
#22588899	2
#22588408	2
#22588320	2
C₄×C₂²⋊Q₈×C₇₁	2
#23341	71