Subgroups — #32911309

Order 18176.

10894 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22603150	C₂	1	2	yes	maximal, complemented
2	#22603120	C₂	1	2	yes	maximal, complemented
3	#22603116	C₂	1	12	yes	maximal, complemented
4	#22603115	C₂	1	16	yes	maximal, complemented
5	#22603114	C₂	1	1	yes	maximal, characteristic, complemented
6	#22603109	C₂	1	6	yes	maximal, complemented
7	#22603108	C₂	1	8	yes	maximal, complemented
8	C₂×#17986800	C₂	1	6	yes	maximal, complemented
9	#576×D₇₁	C₂	1	8	yes	maximal, complemented
10	#22603051	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#576×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#17986835	—	2	4	no	—
13	#17986835	C₂²	1	1	yes	characteristic
14	#17986835	C₂²	1	2	yes	complemented
15	#17986835	C₂²	1	12	yes	complemented
16	#17986834	—	2	8	no	—
17	#17986834	C₂²	1	16	yes	complemented
18	C₂×#14556173	—	2	12	no	—
19	C₂×#14556173	C₂²	1	12	yes	complemented
20	H(5,𝔽₂)×D₇₁	—	2	8	no	—
21	H(5,𝔽₂)×D₇₁	C₂²	1	16	yes	complemented
22	#17986816	C₂²	1	4	yes	complemented
23	#17986813	C₂²	1	12	yes	complemented
24	#17986812	C₂²	1	4	yes	complemented
25	#17986811	C₂²	1	8	yes	complemented
26	#17986810	C₂²	1	16	yes	complemented
27	#17986809	C₂²	1	48	yes	complemented
28	#17986806	C₂²	1	24	yes	complemented
29	#17986805	C₂²	1	24	yes	complemented
30	#17986804	C₂²	1	4	yes	complemented
31	#17986803	C₂²	1	48	yes	complemented
32	#17986802	C₂²	1	16	yes	complemented
33	#17986801	C₂²	1	12	yes	complemented
34	#17986800	C₂²	1	24	yes	complemented
35	#17986800	C₂²	1	12	yes	complemented
36	#17986800	C₂²	1	24	yes	complemented
37	#17986800	C₂²	1	24	yes	complemented
38	#17986799	C₂²	1	6	yes	complemented
39	#17986797	C₂²	1	12	yes	complemented
40	#17986796	C₂²	1	24	yes	complemented
41	#17986795	C₂²	1	48	yes	complemented
42	C₂×#14556154	C₂²	1	12	yes	complemented
43	C₂×#14556152	C₂²	1	24	yes	complemented
44	AGL(1,ℤ/8)×D₇₁	C₂²	1	48	yes	complemented
45	C₂×#14556150	C₂²	1	6	yes	complemented
46	C₂×#14556147	C₂²	1	12	yes	complemented
47	#135×D₇₁	C₂²	1	24	yes	complemented
48	C₂×D₈×D₇₁	C₂²	1	12	yes	complemented
49	#17986766	C₂²	1	1	yes	characteristic, complemented
50	#17986765	C₂²	1	6	yes	complemented
51	#17986764	C₂²	1	8	yes	complemented
52	C₂×#14556134	C₂²	1	6	yes	complemented
53	#131×D₇₁	C₂²	1	8	yes	complemented
54	C₂×H(5,𝔽₂)×C₇₁	C₂²	1	2	yes	complemented
55	#576×C₇₁	C₂²	1	8	yes	complemented
56	#576×C₇₁	C₂²	1	8	yes	complemented
57	C₂×AGL(1,ℤ/8)×C₇₁	C₂²	1	6	yes	complemented
58	C₂×#135×C₇₁	C₂²	1	3	yes	complemented
59	C₂²×D₈×C₇₁	C₂²	1	3	yes	complemented
60	C₂×#131×C₇₁	C₂²	1	1	yes	characteristic, complemented
61	#14556176	—	2	2	no	—
62	#14556176	D₄	1	2	yes	—
63	#14556176	C₂³	1	8	yes	complemented
64	#14556175	—	2	12	no	—
65	#14556175	—	2	16	no	—
66	#14556175	D₄	1	4	yes	—
67	#14556175	C₂³	1	8	yes	complemented
68	#14556175	C₂³	1	24	yes	complemented
69	#14556174	—	2	16	no	—
70	#14556174	—	2	12	no	—
71	#14556174	D₄	1	4	yes	—
72	#14556174	C₂³	1	8	yes	complemented
73	#14556174	C₂³	1	24	yes	complemented
74	#14556173	—	2	24	no	—
75	#14556173	—	2	24	no	—
76	#14556173	—	2	48	no	—
77	#14556173	—	2	24	no	—
78	#14556173	—	2	48	no	—
79	#14556173	—	2	6	no	—
80	#14556173	D₄	1	6	yes	—
81	#14556173	C₂³	1	48	yes	complemented
82	#14556173	C₂³	1	24	yes	complemented
83	C₂×#11765865	—	2	24	no	—
84	C₂×#11765865	C₂³	1	6	yes	—
85	C₂×#11765865	C₂³	1	12	yes	complemented
86	C₂×#11765864	—	2	48	no	—
87	C₂×#11765864	—	2	12	no	—
88	C₂×#11765864	C₂³	1	24	yes	complemented
89	#41×D₇₁	—	2	16	no	—
90	#41×D₇₁	—	2	24	no	—
91	#41×D₇₁	—	2	16	no	—
92	#41×D₇₁	—	2	8	no	—
93	#41×D₇₁	C₂³	1	8	yes	—
94	#41×D₇₁	C₂³	1	48	yes	complemented
95	C₂²×C₂²⋊D₇₁	—	2	24	no	—
96	C₂×D₄×D₇₁	—	2	12	no	—
97	C₂×D₄×D₇₁	—	2	48	no	—
98	C₂×D₄×D₇₁	C₂³	1	24	yes	complemented
99	#14556161	C₂³	1	24	yes	complemented
100	#14556160	C₂³	1	16	yes	complemented
101	#14556159	C₂³	1	8	yes	complemented
102	#14556158	C₂³	1	24	yes	complemented
103	#14556157	C₂³	1	48	yes	complemented
104	#14556156	C₂³	1	24	yes	complemented
105	#14556155	C₂³	1	48	yes	complemented
106	#14556154	C₂³	1	48	yes	complemented
107	#14556154	C₂³	1	24	yes	complemented
108	#14556153	C₂³	1	24	yes	complemented
109	#14556152	C₂³	1	96	yes	complemented
110	#14556152	C₂³	1	48	yes	complemented
111	#14556151	C₂³	1	8	yes	complemented
112	#14556150	C₂³	1	12	yes	complemented
113	#14556150	C₂³	1	4	yes	complemented
114	#14556150	C₂³	1	12	yes	complemented
115	#14556150	C₂³	1	12	yes	complemented
116	#14556149	C₂³	1	48	yes	complemented
117	#14556148	C₂³	1	48	yes	complemented
118	#14556147	C₂³	1	24	yes	complemented
119	#14556147	C₂³	1	48	yes	complemented
120	C₂×Dic₂₈₄	C₂³	1	6	yes	complemented
121	Q₁₆×D₇₁	C₂³	1	8	yes	complemented
122	C₂×#11765854	C₂³	1	12	yes	complemented
123	C₂×#11765853	C₂³	1	24	yes	complemented
124	SD₁₆×D₇₁	C₂³	1	48	yes	complemented
125	C₂×D₅₆₈	C₂³	1	6	yes	complemented
126	C₂×#11765850	C₂³	1	24	yes	complemented
127	D₈×D₇₁	C₂³	1	24	yes	complemented
128	D₈×D₇₁	C₂³	1	48	yes	complemented
129	#14556136	C₂³	1	24	yes	complemented
130	#14556135	C₂³	1	8	yes	complemented
131	#14556134	C₂³	1	12	yes	complemented
132	#14556134	C₂³	1	4	yes	complemented
133	#14556134	C₂³	1	12	yes	complemented
134	#14556134	C₂³	1	12	yes	complemented
135	C₂×#11765849	C₂³	1	6	yes	complemented
136	C₂×#11765848	C₂³	1	12	yes	complemented
137	M₁₆×D₇₁	C₂³	1	24	yes	complemented
138	C₂×C₈×D₇₁	C₂³	1	12	yes	complemented
139	H(5,𝔽₂)×C₇₁	—	2	8	no	—
140	H(5,𝔽₂)×C₇₁	C₂³	1	16	yes	complemented
141	C₂×#41×C₇₁	—	2	2	no	—
142	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
143	C₂×#41×C₇₁	C₂³	1	6	yes	complemented
144	C₂²×D₄×C₇₁	—	2	6	no	—
145	C₂²×D₄×C₇₁	C₂³	1	6	yes	complemented
146	AGL(1,ℤ/8)×C₇₁	C₂³	1	48	yes	complemented
147	#135×C₇₁	C₂³	1	12	yes	complemented
148	#135×C₇₁	C₂³	1	12	yes	complemented
149	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic, complemented
150	C₂×SD₁₆×C₇₁	C₂³	1	6	yes	complemented
151	C₂×D₈×C₇₁	C₂³	1	3	yes	complemented
152	C₂×D₈×C₇₁	C₂³	1	6	yes	complemented
153	C₂×D₈×C₇₁	C₂³	1	12	yes	complemented
154	C₂×D₈×C₇₁	C₂³	1	12	yes	complemented
155	#131×C₇₁	C₂³	1	4	yes	complemented
156	#131×C₇₁	C₂³	1	4	yes	complemented
157	C₂×M₁₆×C₇₁	C₂³	1	3	yes	complemented
158	C₂²×C₈×C₇₁	C₂³	1	3	yes	complemented
159	C₂³×D₇₁	—	2	24	no	—
160	#11765866	—	2	8	no	—
161	#11765866	—	2	8	no	—
162	#11765866	C₂×D₄	1	8	yes	—
163	#11765866	C₂⁴	1	16	yes	—
164	#11765865	—	2	12	no	—
165	#11765865	—	2	12	no	—
166	#11765865	—	2	16	no	—
167	#11765865	—	2	24	no	—
168	#11765865	—	2	48	no	—
169	#11765865	—	2	24	no	—
170	#11765865	C₂×D₄	1	12	yes	—
171	#11765865	C₂×D₄	1	12	yes	—
172	#11765865	C₂⁴	1	12	yes	—
173	#11765865	C₂⁴	1	4	yes	—
174	#11765865	C₂⁴	1	24	yes	—
175	#11765865	C₂⁴	1	8	yes	—
176	#11765864	—	2	24	no	—
177	#11765864	—	2	48	no	—
178	#11765864	—	2	48	no	—
179	#11765864	—	2	48	no	—
180	#11765864	—	2	24	no	—
181	#11765864	—	2	48	no	—
182	#11765864	C₂×D₄	1	24	yes	—
183	#11765864	C₂⁴	1	48	yes	—
184	C₂×Dic₁₄₂	—	2	24	no	—
185	C₂×Dic₁₄₂	C₂×D₄	1	6	yes	—
186	C₂×Dic₁₄₂	C₂⁴	1	12	yes	—
187	Q₈×D₇₁	—	2	8	no	—
188	Q₈×D₇₁	—	2	8	no	—
189	Q₈×D₇₁	C₂×D₄	1	8	yes	—
190	Q₈×D₇₁	C₂⁴	1	16	yes	—
191	C₂×D₂₈₄	—	2	24	no	—
192	C₂×D₂₈₄	C₂×D₄	1	6	yes	—
193	C₂×D₂₈₄	C₂⁴	1	12	yes	—
194	C₂×C₂²⋊D₇₁	—	2	12	no	—
195	C₂×C₂²⋊D₇₁	—	2	24	no	—
196	C₂×C₂²⋊D₇₁	—	2	96	no	—
197	C₂×C₂²⋊D₇₁	—	2	48	no	—
198	C₂×C₂²⋊D₇₁	—	2	24	no	—
199	C₂×C₂²⋊D₇₁	C₂×D₄	1	12	yes	—
200	D₄×D₇₁	—	2	48	no	—
201	D₄×D₇₁	—	2	24	no	—
202	D₄×D₇₁	—	2	48	no	—
203	D₄×D₇₁	—	2	24	no	—
204	D₄×D₇₁	—	2	48	no	—
205	D₄×D₇₁	—	2	48	no	—
206	D₄×D₇₁	C₂×D₄	1	24	yes	—
207	D₄×D₇₁	C₂⁴	1	48	yes	—
208	C₂²×Dic₇₁	—	2	24	no	—
209	C₂×C₄×D₇₁	—	2	12	no	—
210	C₂×C₄×D₇₁	—	2	48	no	—
211	C₂×C₄×D₇₁	C₂⁴	1	12	yes	—
212	Dic₂₈₄	C₂⁴	1	12	yes	—
213	Dic₂₈₄	C₂⁴	1	4	yes	—
214	#11765855	C₂⁴	1	16	yes	—
215	#11765854	C₂⁴	1	8	yes	—
216	#11765854	C₂⁴	1	24	yes	—
217	#11765853	C₂⁴	1	48	yes	—
218	#11765852	C₂⁴	1	16	yes	—
219	D₅₆₈	C₂⁴	1	4	yes	—
220	D₅₆₈	C₂⁴	1	12	yes	—
221	#11765850	C₂⁴	1	48	yes	—
222	#11765849	C₂⁴	1	12	yes	—
223	#11765849	C₂⁴	1	4	yes	—
224	#11765848	C₂⁴	1	8	yes	—
225	#11765848	C₂⁴	1	24	yes	—
226	C₂×C₇₁⋊C₈	C₂⁴	1	12	yes	—
227	C₈×D₇₁	C₂⁴	1	8	yes	—
228	C₈×D₇₁	C₂⁴	1	24	yes	—
229	C₂⁴×C₇₁	—	2	6	no	—
230	#41×C₇₁	—	2	16	no	—
231	#41×C₇₁	—	2	12	no	—
232	#41×C₇₁	C₂×D₄	1	4	yes	—
233	#41×C₇₁	C₂⁴	1	24	yes	—
234	#41×C₇₁	C₂⁴	1	4	yes	—
235	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
236	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
237	C₂×D₄×C₇₁	—	2	6	no	—
238	C₂×D₄×C₇₁	—	2	48	no	—
239	C₂×D₄×C₇₁	—	2	12	no	—
240	C₂×D₄×C₇₁	—	2	6	no	—
241	C₂×D₄×C₇₁	C₂×D₄	1	3	yes	—
242	C₂×D₄×C₇₁	C₂⁴	1	24	yes	—
243	C₂×D₄×C₇₁	C₂⁴	1	6	yes	—
244	C₂²×C₄×C₇₁	—	2	6	no	—
245	C₂²×C₄×C₇₁	C₂⁴	1	3	yes	—
246	Q₁₆×C₇₁	C₂⁴	1	2	yes	—
247	Q₁₆×C₇₁	C₂⁴	1	2	yes	—
248	SD₁₆×C₇₁	C₂⁴	1	24	yes	—
249	D₈×C₇₁	C₂⁴	1	6	yes	—
250	D₈×C₇₁	C₂⁴	1	6	yes	—
251	D₈×C₇₁	C₂⁴	1	24	yes	—
252	M₁₆×C₇₁	C₂⁴	1	12	yes	—
253	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₇₁	C₂⁴	1	3	yes	—
255	C₂×C₈×C₇₁	C₂⁴	1	6	yes	—
256	C₂×C₈×C₇₁	C₂⁴	1	6	yes	—
257	C₂³×C₇₁	—	2	6	no	—
258	C₂³×C₇₁	—	2	24	no	—
259	C₂³×C₇₁	—	16	6	no	—
260	C₂³×C₇₁	C₂²×D₄	1	3	yes	—
261	C₂²×D₇₁	—	2	12	no	—
262	C₂²×D₇₁	—	2	48	no	—
263	C₂²×D₇₁	—	16	24	no	—
264	C₂²×D₇₁	C₂²×D₄	1	12	yes	—
265	Q₈×C₇₁	—	2	2	no	—
266	Q₈×C₇₁	C₂²×D₄	1	4	yes	—
267	Q₈×C₇₁	C₂⁵	1	4	yes	—
268	D₄×C₇₁	—	2	24	no	—
269	D₄×C₇₁	—	2	24	no	—
270	D₄×C₇₁	—	2	6	no	—
271	D₄×C₇₁	C₂²×D₄	1	12	yes	—
272	D₄×C₇₁	C₂⁵	1	12	yes	—
273	C₂×C₄×C₇₁	—	2	2	no	—
274	C₂×C₄×C₇₁	—	2	24	no	—
275	C₂×C₄×C₇₁	C₂²×D₄	1	3	yes	—
276	C₂×C₄×C₇₁	C₂²×D₄	1	6	yes	—
277	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
278	C₂×C₄×C₇₁	C₂⁵	1	6	yes	—
279	C₂²⋊D₇₁	—	2	24	no	—
280	C₂²⋊D₇₁	—	2	8	no	—
281	C₂²⋊D₇₁	—	2	48	no	—
282	C₂²⋊D₇₁	—	2	48	no	—
283	C₂²⋊D₇₁	C₂²×D₄	1	24	yes	—
284	C₂²⋊D₇₁	C₂²×D₄	1	8	yes	—
285	C₂×Dic₇₁	—	2	12	no	—
286	C₂×Dic₇₁	—	2	48	no	—
287	C₂×Dic₇₁	C₂²×D₄	1	12	yes	—
288	D₂₈₄	—	2	16	no	—
289	D₂₈₄	—	2	12	no	—
290	D₂₈₄	C₂²×D₄	1	4	yes	—
291	D₂₈₄	C₂²×D₄	1	12	yes	—
292	D₂₈₄	C₂⁵	1	8	yes	—
293	C₄×D₇₁	—	2	16	no	—
294	C₄×D₇₁	—	2	24	no	—
295	C₄×D₇₁	—	2	8	no	—
296	C₄×D₇₁	—	2	16	no	—
297	C₄×D₇₁	C₂²×D₄	1	24	yes	—
298	C₄×D₇₁	C₂⁵	1	8	yes	—
299	Dic₁₄₂	—	2	12	no	—
300	Dic₁₄₂	—	2	16	no	—
301	Dic₁₄₂	C₂²×D₄	1	4	yes	—
302	Dic₁₄₂	C₂²×D₄	1	12	yes	—
303	Dic₁₄₂	C₂⁵	1	8	yes	—
304	C₈×C₇₁	C₂⁵	1	1	yes	characteristic
305	C₈×C₇₁	C₂⁵	1	1	yes	characteristic
306	C₈×C₇₁	C₂⁵	1	6	yes	—
307	C₇₁⋊C₈	C₂⁵	1	8	yes	—
308	C₂²×C₇₁	—	2	12	no	—
309	C₂²×C₇₁	—	4	3	no	—
310	C₂²×C₇₁	—	8	24	no	—
311	C₂²×C₇₁	—	8	6	no	—
312	C₂²×C₇₁	C₂³×D₄	1	6	yes	—
313	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
314	C₂×D₇₁	—	2	8	no	—
315	C₂×D₇₁	—	4	12	no	—
316	C₂×D₇₁	—	8	48	no	—
317	C₂×D₇₁	—	8	12	no	—
318	C₂×D₇₁	C₂³×D₄	1	8	yes	—
319	C₄×C₇₁	—	2	4	no	—
320	C₄×C₇₁	C₂³×D₄	1	6	yes	—
321	C₄×C₇₁	C₂³×D₄	1	1	yes	characteristic
322	C₄×C₇₁	C₂⁶	1	1	yes	characteristic
323	Dic₇₁	—	2	8	no	—
324	Dic₇₁	C₂³×D₄	1	8	yes	—
325	#63091	—	71	1	no	maximal, Sylow
326	C₂×C₇₁	—	2	6	no	—
327	C₂×C₇₁	—	2	1	no	—
328	C₂×C₇₁	—	4	12	no	—
329	C₂×C₇₁	C₂⁴×D₄	1	1	yes	characteristic
330	D₇₁	—	2	8	no	—
331	D₇₁	—	4	8	no	—
332	H(7,𝔽₂)	—	71	2	no	—
333	#3585	—	71	2	no	—
334	#3585	—	71	16	no	—
335	#3585	—	71	12	no	—
336	#3584	—	71	8	no	—
337	#3584	—	71	6	no	—
338	#3584	—	71	1	no	—
339	C₂×#576	—	71	8	no	—
340	C₂×#576	—	71	6	no	—
341	C₂×#576	D₇₁	1	1	yes	characteristic, complemented
342	#3573	—	71	1	no	—
343	C₇₁	#63091	1	1	yes	characteristic, complemented, Sylow
344	#585	—	71	1	no	—
345	#585	—	71	16	no	—
346	#585	—	71	2	no	—
347	#585	—	71	12	no	—
348	#585	—	142	4	no	—
349	#585	—	142	8	no	—
350	C₂×H(5,𝔽₂)	—	71	16	no	—
351	C₂×H(5,𝔽₂)	—	71	12	no	—
352	C₂×H(5,𝔽₂)	—	142	12	no	—
353	C₂×H(5,𝔽₂)	—	142	8	no	—
354	C₂×H(5,𝔽₂)	C₂×D₇₁	1	2	yes	complemented
355	#578	—	71	12	no	—
356	#578	—	71	4	no	—
357	#578	—	71	4	no	—
358	#577	—	71	16	no	—
359	#577	—	71	48	no	—
360	#577	—	71	24	no	—
361	#577	—	71	24	no	—
362	#577	—	71	8	no	—
363	#576	—	71	16	no	—
364	#576	—	71	48	no	—
365	#576	—	71	12	no	—
366	#576	—	71	24	no	—
367	#576	—	71	12	no	—
368	#576	—	71	24	no	—
369	#576	—	71	24	no	—
370	#576	—	71	4	no	—
371	#576	C₂×D₇₁	1	8	yes	complemented
372	#576	C₂×D₇₁	1	8	yes	complemented
373	#575	—	71	12	no	—
374	#575	—	71	48	no	—
375	#575	—	71	24	no	—
376	#575	—	71	6	no	—
377	C₂×AGL(1,ℤ/8)	—	71	12	no	—
378	C₂×AGL(1,ℤ/8)	—	71	48	no	—
379	C₂×AGL(1,ℤ/8)	—	71	24	no	—
380	C₂×AGL(1,ℤ/8)	C₂×D₇₁	1	6	yes	complemented
381	C₂×#135	—	71	24	no	—
382	C₂×#135	—	71	12	no	—
383	C₂×#135	—	71	6	no	—
384	C₂×#135	C₂×D₇₁	1	3	yes	complemented
385	C₂²×D₈	—	71	12	no	—
386	C₂²×D₈	C₂×D₇₁	1	3	yes	complemented
387	#568	—	71	1	no	—
388	#568	—	71	8	no	—
389	#568	—	71	6	no	—
390	C₂×#131	—	71	8	no	—
391	C₂×#131	—	71	6	no	—
392	C₂×#131	C₂×D₇₁	1	1	yes	characteristic, complemented
393	2₋¹⁺⁴	—	71	4	no	—
394	2₋¹⁺⁴	—	71	2	no	—
395	2₋¹⁺⁴	—	71	24	no	—
396	2₋¹⁺⁴	—	71	8	no	—
397	2₋¹⁺⁴	—	71	8	no	—
398	2₋¹⁺⁴	—	142	16	no	—
399	2₋¹⁺⁴	—	142	12	no	—
400	2₋¹⁺⁴	—	142	2	no	—
401	H(5,𝔽₂)	—	2	8	no	—
402	H(5,𝔽₂)	—	71	4	no	—
403	H(5,𝔽₂)	—	71	6	no	—
404	H(5,𝔽₂)	—	71	24	no	—
405	H(5,𝔽₂)	—	71	8	no	—
406	H(5,𝔽₂)	—	71	48	no	—
407	H(5,𝔽₂)	—	71	24	no	—
408	H(5,𝔽₂)	—	142	24	no	—
409	H(5,𝔽₂)	—	142	48	no	—
410	H(5,𝔽₂)	—	142	48	no	—
411	H(5,𝔽₂)	—	142	24	no	—
412	H(5,𝔽₂)	—	142	24	no	—
413	H(5,𝔽₂)	—	142	12	no	—
414	H(5,𝔽₂)	—	142	16	no	—
415	H(5,𝔽₂)	—	142	6	no	—
416	H(5,𝔽₂)	C₂²×D₇₁	1	16	yes	complemented
417	C₂×#41	—	2	2	no	—
418	C₂×#41	—	71	8	no	—
419	C₂×#41	—	71	6	no	—
420	C₂×#41	—	71	48	no	—
421	C₂×#41	—	71	24	no	—
422	C₂×#41	—	71	12	no	—
423	C₂×#41	—	142	24	no	—
424	C₂×#41	—	142	12	no	—
425	C₂×#41	—	142	48	no	—
426	C₂×#41	—	142	16	no	—
427	C₂×#41	—	142	16	no	—
428	C₂×#41	—	142	24	no	—
429	C₂×#41	—	142	8	no	—
430	C₂×#41	C₂²×D₇₁	1	1	yes	characteristic
431	C₂×#41	C₂²×D₇₁	1	6	yes	complemented
432	C₂²×D₄	—	2	6	no	—
433	C₂²×D₄	—	71	24	no	—
434	C₂²×D₄	—	142	48	no	—
435	C₂²×D₄	—	142	12	no	—
436	C₂²×D₄	—	142	24	no	—
437	C₂²×D₄	C₂²×D₇₁	1	6	yes	complemented
438	#137	—	71	24	no	—
439	#137	—	71	8	no	—
440	#137	—	71	16	no	—
441	#137	—	71	48	no	—
442	#137	—	71	24	no	—
443	AGL(1,ℤ/8)	—	71	24	no	—
444	AGL(1,ℤ/8)	—	71	48	no	—
445	AGL(1,ℤ/8)	—	71	24	no	—
446	AGL(1,ℤ/8)	—	71	48	no	—
447	AGL(1,ℤ/8)	—	71	96	no	—
448	AGL(1,ℤ/8)	—	71	48	no	—
449	AGL(1,ℤ/8)	—	71	24	no	—
450	AGL(1,ℤ/8)	C₂²×D₇₁	1	48	yes	complemented
451	#135	—	71	48	no	—
452	#135	—	71	8	no	—
453	#135	—	71	48	no	—
454	#135	—	71	24	no	—
455	#135	—	71	48	no	—
456	#135	—	71	12	no	—
457	#135	—	71	4	no	—
458	#135	—	71	12	no	—
459	#135	—	71	12	no	—
460	#135	C₂²×D₇₁	1	12	yes	complemented
461	#135	C₂²×D₇₁	1	12	yes	complemented
462	C₂×Q₁₆	—	71	8	no	—
463	C₂×Q₁₆	—	71	6	no	—
464	C₂×Q₁₆	C₂²×D₇₁	1	1	yes	characteristic, complemented
465	C₂×SD₁₆	—	71	24	no	—
466	C₂×SD₁₆	—	71	48	no	—
467	C₂×SD₁₆	—	71	12	no	—
468	C₂×SD₁₆	C₂²×D₇₁	1	6	yes	complemented
469	C₂×D₈	—	71	24	no	—
470	C₂×D₈	—	71	24	no	—
471	C₂×D₈	—	71	48	no	—
472	C₂×D₈	—	71	6	no	—
473	C₂×D₈	C₂²×D₇₁	1	12	yes	complemented
474	C₂×D₈	C₂²×D₇₁	1	3	yes	complemented
475	C₂×D₈	C₂²×D₇₁	1	12	yes	complemented
476	C₂×D₈	C₂²×D₇₁	1	6	yes	complemented
477	#131	—	71	8	no	—
478	#131	—	71	24	no	—
479	#131	—	71	12	no	—
480	#131	—	71	4	no	—
481	#131	—	71	12	no	—
482	#131	—	71	12	no	—
483	#131	C₂²×D₇₁	1	4	yes	complemented
484	#131	C₂²×D₇₁	1	4	yes	complemented
485	C₂×M₁₆	—	71	6	no	—
486	C₂×M₁₆	—	71	24	no	—
487	C₂×M₁₆	—	71	12	no	—
488	C₂×M₁₆	C₂²×D₇₁	1	3	yes	complemented
489	C₂²×C₈	—	71	12	no	—
490	C₂²×C₈	C₂²×D₇₁	1	3	yes	complemented
491	C₂⁴	—	2	6	no	—
492	C₂⁴	—	142	24	no	—
493	#41	—	2	16	no	—
494	#41	—	2	12	no	—
495	#41	—	71	8	no	—
496	#41	—	71	24	no	—
497	#41	—	71	12	no	—
498	#41	—	71	12	no	—
499	#41	—	71	12	no	—
500	#41	—	71	4	no	—
501	#41	—	71	16	no	—
502	#41	—	71	48	no	—
503	#41	—	71	24	no	—
504	#41	—	71	8	no	—
505	#41	—	142	48	no	—
506	#41	—	142	16	no	—
507	#41	—	142	24	no	—
508	#41	—	142	24	no	—
509	#41	—	142	48	no	—
510	#41	—	142	48	no	—
511	#41	—	142	48	no	—
512	#41	—	142	24	no	—
513	#41	—	142	48	no	—
514	#41	—	142	8	no	—
515	#41	—	142	8	no	—
516	#41	—	142	24	no	—
517	#41	—	142	12	no	—
518	#41	—	142	12	no	—
519	#41	D₄×D₇₁	1	4	yes	—
520	#41	C₂³×D₇₁	1	24	yes	—
521	#41	C₂³×D₇₁	1	4	yes	—
522	C₂×Q₈	—	71	8	no	—
523	C₂×Q₈	—	71	6	no	—
524	C₂×Q₈	—	71	16	no	—
525	C₂×Q₈	—	71	12	no	—
526	C₂×Q₈	—	142	24	no	—
527	C₂×Q₈	—	142	8	no	—
528	C₂×Q₈	—	142	8	no	—
529	C₂×Q₈	D₄×D₇₁	1	1	yes	characteristic
530	C₂×Q₈	C₂³×D₇₁	1	2	yes	—
531	C₂×D₄	—	2	6	no	—
532	C₂×D₄	—	2	48	no	—
533	C₂×D₄	—	2	6	no	—
534	C₂×D₄	—	2	12	no	—
535	C₂×D₄	—	71	12	no	—
536	C₂×D₄	—	71	24	no	—
537	C₂×D₄	—	71	48	no	—
538	C₂×D₄	—	71	6	no	—
539	C₂×D₄	—	71	12	no	—
540	C₂×D₄	—	142	24	no	—
541	C₂×D₄	—	142	48	no	—
542	C₂×D₄	—	142	24	no	—
543	C₂×D₄	—	142	48	no	—
544	C₂×D₄	—	142	48	no	—
545	C₂×D₄	—	142	24	no	—
546	C₂×D₄	—	142	48	no	—
547	C₂×D₄	—	142	48	no	—
548	C₂×D₄	—	142	96	no	—
549	C₂×D₄	—	142	24	no	—
550	C₂×D₄	—	142	12	no	—
551	C₂×D₄	—	142	24	no	—
552	C₂×D₄	D₄×D₇₁	1	3	yes	—
553	C₂×D₄	C₂³×D₇₁	1	24	yes	—
554	C₂×D₄	C₂³×D₇₁	1	6	yes	—
555	C₂²×C₄	—	2	6	no	—
556	C₂²×C₄	—	71	12	no	—
557	C₂²×C₄	—	142	48	no	—
558	C₂²×C₄	—	142	24	no	—
559	C₂²×C₄	—	142	12	no	—
560	C₂²×C₄	C₂³×D₇₁	1	3	yes	—
561	Q₁₆	—	71	16	no	—
562	Q₁₆	—	71	4	no	—
563	Q₁₆	—	71	12	no	—
564	Q₁₆	C₂³×D₇₁	1	2	yes	—
565	Q₁₆	C₂³×D₇₁	1	2	yes	—
566	SD₁₆	—	71	16	no	—
567	SD₁₆	—	71	48	no	—
568	SD₁₆	—	71	24	no	—
569	SD₁₆	—	71	8	no	—
570	SD₁₆	C₂³×D₇₁	1	24	yes	—
571	D₈	—	71	48	no	—
572	D₈	—	71	4	no	—
573	D₈	—	71	12	no	—
574	D₈	C₂³×D₇₁	1	6	yes	—
575	D₈	C₂³×D₇₁	1	24	yes	—
576	D₈	C₂³×D₇₁	1	6	yes	—
577	M₁₆	—	71	12	no	—
578	M₁₆	—	71	4	no	—
579	M₁₆	—	71	24	no	—
580	M₁₆	—	71	8	no	—
581	M₁₆	C₂³×D₇₁	1	12	yes	—
582	C₂×C₈	—	71	12	no	—
583	C₂×C₈	—	71	8	no	—
584	C₂×C₈	—	71	24	no	—
585	C₂×C₈	C₂³×D₇₁	1	6	yes	—
586	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
587	C₂×C₈	C₂³×D₇₁	1	6	yes	—
588	C₂×C₈	C₂³×D₇₁	1	3	yes	—
589	C₂³	—	2	6	no	—
590	C₂³	—	2	24	no	—
591	C₂³	—	16	6	no	—
592	C₂³	—	71	12	no	—
593	C₂³	—	1136	24	no	—
594	C₂³	—	142	48	no	—
595	C₂³	—	142	12	no	—
596	C₂³	C₂×D₄×D₇₁	1	3	yes	—
597	Q₈	—	2	2	no	—
598	Q₈	—	71	12	no	—
599	Q₈	—	71	4	no	—
600	Q₈	—	71	8	no	—
601	Q₈	—	142	16	no	—
602	Q₈	—	142	12	no	—
603	Q₈	C₂×D₄×D₇₁	1	4	yes	—
604	Q₈	C₂⁴×D₇₁	1	4	yes	—
605	D₄	—	2	24	no	—
606	D₄	—	2	24	no	—
607	D₄	—	2	6	no	—
608	D₄	—	71	8	no	—
609	D₄	—	71	24	no	—
610	D₄	—	71	12	no	—
611	D₄	—	71	4	no	—
612	D₄	—	71	8	no	—
613	D₄	—	142	16	no	—
614	D₄	—	142	48	no	—
615	D₄	—	142	48	no	—
616	D₄	—	142	8	no	—
617	D₄	—	142	24	no	—
618	D₄	—	142	12	no	—
619	D₄	C₂×D₄×D₇₁	1	12	yes	—
620	D₄	C₂⁴×D₇₁	1	12	yes	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	24	no	—
623	C₂×C₄	—	71	12	no	—
624	C₂×C₄	—	71	24	no	—
625	C₂×C₄	—	71	8	no	—
626	C₂×C₄	—	142	16	no	—
627	C₂×C₄	—	142	16	no	—
628	C₂×C₄	—	142	48	no	—
629	C₂×C₄	—	142	12	no	—
630	C₂×C₄	—	142	24	no	—
631	C₂×C₄	—	142	8	no	—
632	C₂×C₄	C₂×D₄×D₇₁	1	3	yes	—
633	C₂×C₄	C₂×D₄×D₇₁	1	6	yes	—
634	C₂×C₄	C₂⁴×D₇₁	1	6	yes	—
635	C₂×C₄	C₂⁴×D₇₁	1	1	yes	characteristic
636	C₈	—	71	8	no	—
637	C₈	C₂⁴×D₇₁	1	1	yes	characteristic
638	C₈	C₂⁴×D₇₁	1	6	yes	—
639	C₈	C₂⁴×D₇₁	1	1	yes	characteristic
640	C₂²	—	2	12	no	—
641	C₂²	—	4	3	no	—
642	C₂²	—	8	6	no	—
643	C₂²	—	8	24	no	—
644	C₂²	—	284	12	no	—
645	C₂²	—	568	12	no	—
646	C₂²	—	568	48	no	—
647	C₂²	—	71	8	no	—
648	C₂²	—	142	8	no	—
649	C₂²	C₂²×D₄×D₇₁	1	1	yes	characteristic
650	C₂²	C₂²×D₄×D₇₁	1	6	yes	—
651	C₄	—	2	4	no	—
652	C₄	—	71	8	no	—
653	C₄	—	142	8	no	—
654	C₄	C₂²×D₄×D₇₁	1	6	yes	—
655	C₄	C₂²×D₄×D₇₁	1	1	yes	characteristic
656	C₄	C₂⁵×D₇₁	1	1	yes	characteristic
657	C₂	—	2	1	no	—
658	C₂	—	2	6	no	—
659	C₂	—	4	12	no	—
660	C₂	—	284	8	no	—
661	C₂	—	142	8	no	—
662	C₂	C₂³×D₄×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂³×D₄×D₇₁
commutator, cosocle	C₄×C₇₁	C₂⁶
Frattini	C₄	C₂⁵×D₇₁
Fitting	C₂×#576×C₇₁	C₂
socle	C₂×C₇₁	C₂⁴×D₄
hypercenter	C₂×#576	D₇₁
hypocenter	C₇₁	#63091
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. #22603150	C₂	semidirect
2. #22603120	C₂	semidirect
3. #22603116	C₂	semidirect
4. #22603115	C₂	semidirect
5. #22603114	C₂	semidirect
6. #22603109	C₂	semidirect
7. #22603108	C₂	semidirect
8. C₂×#17986800	C₂	semidirect
9. #576×D₇₁	C₂	semidirect
10. #22603051	C₂	semidirect
11. C₂×#576×C₇₁	C₂	semidirect
14. #17986835	C₂²	semidirect
15. #17986835	C₂²	semidirect
17. #17986834	C₂²	semidirect
19. C₂×#14556173	C₂²	semidirect
21. H(5,𝔽₂)×D₇₁	C₂²	semidirect
22. #17986816	C₂²	semidirect
23. #17986813	C₂²	semidirect
24. #17986812	C₂²	semidirect
25. #17986811	C₂²	semidirect
26. #17986810	C₂²	semidirect
27. #17986809	C₂²	semidirect
28. #17986806	C₂²	semidirect
29. #17986805	C₂²	semidirect
30. #17986804	C₂²	semidirect
31. #17986803	C₂²	semidirect
32. #17986802	C₂²	semidirect
33. #17986801	C₂²	semidirect
34. #17986800	C₂²	semidirect
35. #17986800	C₂²	semidirect
36. #17986800	C₂²	semidirect
37. #17986800	C₂²	semidirect
38. #17986799	C₂²	semidirect
39. #17986797	C₂²	semidirect
40. #17986796	C₂²	semidirect
41. #17986795	C₂²	semidirect
42. C₂×#14556154	C₂²	semidirect
43. C₂×#14556152	C₂²	semidirect
44. AGL(1,ℤ/8)×D₇₁	C₂²	semidirect
45. C₂×#14556150	C₂²	semidirect
46. C₂×#14556147	C₂²	semidirect
47. #135×D₇₁	C₂²	semidirect
48. C₂×D₈×D₇₁	C₂²	semidirect
49. #17986766	C₂²	semidirect
50. #17986765	C₂²	semidirect
51. #17986764	C₂²	semidirect
52. C₂×#14556134	C₂²	semidirect
53. #131×D₇₁	C₂²	semidirect
54. C₂×H(5,𝔽₂)×C₇₁	C₂²	semidirect
55. #576×C₇₁	C₂²	semidirect
56. #576×C₇₁	C₂²	semidirect
57. C₂×AGL(1,ℤ/8)×C₇₁	C₂²	semidirect
58. C₂×#135×C₇₁	C₂²	semidirect
59. C₂²×D₈×C₇₁	C₂²	semidirect
60. C₂×#131×C₇₁	C₂²	semidirect
63. #14556176	C₂³	semidirect
67. #14556175	C₂³	semidirect
68. #14556175	C₂³	semidirect
72. #14556174	C₂³	semidirect
73. #14556174	C₂³	semidirect
81. #14556173	C₂³	semidirect
82. #14556173	C₂³	semidirect
85. C₂×#11765865	C₂³	semidirect
88. C₂×#11765864	C₂³	semidirect
94. #41×D₇₁	C₂³	semidirect
98. C₂×D₄×D₇₁	C₂³	semidirect
99. #14556161	C₂³	semidirect
100. #14556160	C₂³	semidirect
101. #14556159	C₂³	semidirect
102. #14556158	C₂³	semidirect
103. #14556157	C₂³	semidirect
104. #14556156	C₂³	semidirect
105. #14556155	C₂³	semidirect
106. #14556154	C₂³	semidirect
107. #14556154	C₂³	semidirect
108. #14556153	C₂³	semidirect
109. #14556152	C₂³	semidirect
110. #14556152	C₂³	semidirect
111. #14556151	C₂³	semidirect
112. #14556150	C₂³	semidirect
113. #14556150	C₂³	semidirect
114. #14556150	C₂³	semidirect
115. #14556150	C₂³	semidirect
116. #14556149	C₂³	semidirect
117. #14556148	C₂³	semidirect
118. #14556147	C₂³	semidirect
119. #14556147	C₂³	semidirect
120. C₂×Dic₂₈₄	C₂³	semidirect
121. Q₁₆×D₇₁	C₂³	semidirect
122. C₂×#11765854	C₂³	semidirect
123. C₂×#11765853	C₂³	semidirect
124. SD₁₆×D₇₁	C₂³	semidirect
125. C₂×D₅₆₈	C₂³	semidirect
126. C₂×#11765850	C₂³	semidirect
127. D₈×D₇₁	C₂³	semidirect
128. D₈×D₇₁	C₂³	semidirect
129. #14556136	C₂³	semidirect
130. #14556135	C₂³	semidirect
131. #14556134	C₂³	semidirect
132. #14556134	C₂³	semidirect
133. #14556134	C₂³	semidirect
134. #14556134	C₂³	semidirect
135. C₂×#11765849	C₂³	semidirect
136. C₂×#11765848	C₂³	semidirect
137. M₁₆×D₇₁	C₂³	semidirect
138. C₂×C₈×D₇₁	C₂³	semidirect
140. H(5,𝔽₂)×C₇₁	C₂³	semidirect
143. C₂×#41×C₇₁	C₂³	semidirect
145. C₂²×D₄×C₇₁	C₂³	semidirect
146. AGL(1,ℤ/8)×C₇₁	C₂³	semidirect
147. #135×C₇₁	C₂³	semidirect
148. #135×C₇₁	C₂³	semidirect
149. C₂×Q₁₆×C₇₁	C₂³	semidirect
150. C₂×SD₁₆×C₇₁	C₂³	semidirect
151. C₂×D₈×C₇₁	C₂³	semidirect
152. C₂×D₈×C₇₁	C₂³	semidirect
153. C₂×D₈×C₇₁	C₂³	semidirect
154. C₂×D₈×C₇₁	C₂³	semidirect
155. #131×C₇₁	C₂³	semidirect
156. #131×C₇₁	C₂³	semidirect
157. C₂×M₁₆×C₇₁	C₂³	semidirect
158. C₂²×C₈×C₇₁	C₂³	semidirect
341. C₂×#576	D₇₁	semidirect
343. C₇₁	#63091	semidirect
354. C₂×H(5,𝔽₂)	C₂×D₇₁	semidirect
371. #576	C₂×D₇₁	semidirect
372. #576	C₂×D₇₁	semidirect
380. C₂×AGL(1,ℤ/8)	C₂×D₇₁	semidirect
384. C₂×#135	C₂×D₇₁	semidirect
386. C₂²×D₈	C₂×D₇₁	semidirect
392. C₂×#131	C₂×D₇₁	semidirect
416. H(5,𝔽₂)	C₂²×D₇₁	semidirect
431. C₂×#41	C₂²×D₇₁	semidirect
437. C₂²×D₄	C₂²×D₇₁	semidirect
450. AGL(1,ℤ/8)	C₂²×D₇₁	semidirect
460. #135	C₂²×D₇₁	semidirect
461. #135	C₂²×D₇₁	semidirect
464. C₂×Q₁₆	C₂²×D₇₁	semidirect
468. C₂×SD₁₆	C₂²×D₇₁	semidirect
473. C₂×D₈	C₂²×D₇₁	semidirect
474. C₂×D₈	C₂²×D₇₁	semidirect
475. C₂×D₈	C₂²×D₇₁	semidirect
476. C₂×D₈	C₂²×D₇₁	semidirect
483. #131	C₂²×D₇₁	semidirect
484. #131	C₂²×D₇₁	semidirect
488. C₂×M₁₆	C₂²×D₇₁	semidirect
490. C₂²×C₈	C₂²×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22603150	2
#22603120	2
#22603116	2
#22603115	2
#22603114	2
#22603109	2
#22603108	2
C₂×#17986800	2
#576×D₇₁	2
#22603051	2
C₂×#576×C₇₁	2
#63091	71