Subgroups — #31968643

Order 18176.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598422	C₂	1	1	yes	maximal, characteristic
2	#22597496	C₂	1	1	yes	maximal, characteristic
3	#22597430	C₂	1	1	yes	maximal, characteristic, complemented
4	#22587236	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587229	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587217	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587210	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587210	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587196	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587146	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587139	C₂	1	1	yes	maximal, characteristic, complemented
12	#22586798	C₂	1	1	yes	maximal, characteristic
13	C₂×#17985729	C₂	1	1	yes	maximal, characteristic, complemented
14	#22586624	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#1573	C₂	1	1	yes	maximal, characteristic, complemented
16	#17986533	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₁₄₂	C₂²	1	1	yes	characteristic
18	#17986330	C₄	1	1	yes	characteristic
19	#17986313	C₄	1	1	yes	characteristic
20	#17986307	C₄	1	1	yes	characteristic
21	#17986307	C₄	1	1	yes	characteristic
22	#17986222	C₄	1	1	yes	characteristic
23	#17986222	C₄	1	1	yes	characteristic
24	#17986157	C₄	1	1	yes	characteristic
25	#17986140	C₄	1	1	yes	characteristic
26	#17986127	—	2	1	no	—
27	#17986127	—	2	1	no	—
28	#17986126	C₂²	1	1	yes	characteristic
29	#17986126	C₂²	1	1	yes	characteristic
30	#17986126	C₂²	1	1	yes	characteristic
31	#17986123	C₂²	1	1	yes	characteristic
32	#17986123	C₂²	1	1	yes	characteristic
33	#17986123	C₂²	1	1	yes	characteristic
34	C₄×Dic₂₈₄	C₂²	1	1	yes	characteristic
35	C₄×Dic₂₈₄	C₂²	1	1	yes	characteristic
36	C₄×#11765854	C₂²	1	1	yes	characteristic
37	C₄×#11765854	C₂²	1	1	yes	characteristic
38	#17986076	C₂²	1	1	yes	characteristic
39	#17986070	—	2	1	no	—
40	#17986064	C₂²	1	1	yes	characteristic
41	C₈×C₂²⋊D₇₁	—	2	1	no	—
42	#17986059	—	2	1	no	—
43	#17986053	—	2	1	no	—
44	#17986052	C₂²	1	1	yes	characteristic
45	#17986049	—	2	1	no	—
46	#17986024	—	2	1	no	—
47	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
48	#17985729	C₂²	1	1	yes	characteristic
49	#17985729	C₂²	1	1	yes	characteristic
50	#17985729	C₂²	1	1	yes	characteristic
51	#17985729	C₂²	1	1	yes	characteristic
52	#17985729	C₂²	1	1	yes	characteristic
53	#17985729	C₂²	1	1	yes	characteristic
54	#17985726	C₂²	1	1	yes	characteristic
55	#17985726	C₂²	1	1	yes	characteristic
56	#17985721	C₂²	1	1	yes	characteristic
57	#17985721	C₂²	1	1	yes	characteristic
58	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
59	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
60	#432×C₇₁	C₂²	1	1	yes	characteristic
61	#431×C₇₁	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
63	#335×C₇₁	C₂²	1	1	yes	characteristic
64	#335×C₇₁	C₂²	1	1	yes	characteristic
65	#334×C₇₁	C₂²	1	1	yes	characteristic
66	#334×C₇₁	C₂²	1	1	yes	characteristic
67	C₂²×Dic₁₄₂	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₂₈₄	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₂₈₄	C₂×C₄	1	1	yes	characteristic
70	C₂×#11765854	C₂×C₄	1	1	yes	characteristic
71	C₂×#11765854	C₂×C₄	1	1	yes	characteristic
72	C₂×#11765848	—	2	1	no	—
73	C₂²×C₇₁⋊C₈	—	2	1	no	—
74	C₂×C₈×D₇₁	—	2	1	no	—
75	#14556122	—	2	1	no	—
76	#14556120	C₂×C₄	1	1	yes	characteristic
77	#14556116	C₂×C₄	1	1	yes	characteristic
78	#14556111	—	2	1	no	—
79	#14556107	C₂×C₄	1	1	yes	characteristic
80	#14556102	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₄₂	—	2	1	no	—
82	C₄×Dic₁₄₂	—	2	1	no	—
83	C₄×Dic₁₄₂	C₂×C₄	1	1	yes	characteristic
84	C₄×Dic₁₄₂	C₂×C₄	1	1	yes	characteristic
85	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
86	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
87	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
88	C₄×D₂₈₄	C₂³	1	1	yes	characteristic
89	C₄×C₂²⋊D₇₁	—	2	1	no	—
90	#14556085	—	2	1	no	—
91	C₂×C₄⋊Dic₇₁	C₂×C₄	1	1	yes	characteristic
92	C₂×Dic₇₁⋊C₄	—	2	1	no	—
93	C₂×C₄×Dic₇₁	—	2	1	no	—
94	#14556062	C₂×C₄	1	1	yes	characteristic
95	#14556062	C₂×C₄	1	1	yes	characteristic
96	#14556060	C₂×C₄	1	1	yes	characteristic
97	#14556060	C₂×C₄	1	1	yes	characteristic
98	C₄⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
99	C₄⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
100	Dic₇₁⋊C₈	—	2	1	no	—
101	Dic₇₁⋊C₈	—	2	1	no	—
102	Dic₇₁⋊C₈	—	2	1	no	—
103	Dic₇₁⋊C₈	—	2	1	no	—
104	Dic₇₁⋊C₈	—	2	1	no	—
105	Dic₇₁⋊C₈	—	2	1	no	—
106	#14556053	C₂×C₄	1	1	yes	characteristic
107	#14556053	C₂×C₄	1	1	yes	characteristic
108	#14556053	C₂×C₄	1	1	yes	characteristic
109	#14556053	C₂×C₄	1	1	yes	characteristic
110	#14556053	C₂×C₄	1	1	yes	characteristic
111	#14556053	C₂×C₄	1	1	yes	characteristic
112	#14556050	C₂×C₄	1	1	yes	characteristic
113	#14556050	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
115	C₂²⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
116	(C₂×D₇₁)⋊C₈	—	2	1	no	—
117	(C₂×D₇₁)⋊C₈	—	2	1	no	—
118	#14556038	—	2	1	no	—
119	#14556038	—	2	1	no	—
120	#14556038	—	2	1	no	—
121	C₄×C₇₁⋊C₈	—	2	1	no	—
122	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
126	C₈×Dic₇₁	—	2	1	no	—
127	C₈×Dic₇₁	—	2	1	no	—
128	C₈×Dic₇₁	—	2	1	no	—
129	C₂²×C₈×C₇₁	—	2	1	no	—
130	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
131	C₄⋊C₈×C₇₁	—	2	1	no	—
132	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
138	C₂²⋊C₈×C₇₁	—	2	1	no	—
139	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
141	#97×C₇₁	—	2	1	no	—
142	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₄₂	—	2	2	no	—
145	C₂×Dic₁₄₂	—	2	1	no	—
146	C₂×Dic₁₄₂	—	4	1	no	—
147	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₂₈₄	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₂²⋊D₇₁	—	2	1	no	—
152	C₂²×Dic₇₁	—	2	1	no	—
153	C₂²×Dic₇₁	—	2	1	no	—
154	C₂×C₄×D₇₁	—	2	1	no	—
155	Dic₂₈₄	—	2	2	no	—
156	Dic₂₈₄	—	4	1	no	—
157	#11765854	—	2	2	no	—
158	#11765854	—	4	1	no	—
159	#11765848	—	8	1	no	—
160	C₂×C₇₁⋊C₈	—	2	4	no	—
161	C₂×C₇₁⋊C₈	—	2	1	no	—
162	C₂×C₇₁⋊C₈	—	2	1	no	—
163	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₈×D₇₁	—	8	1	no	—
168	C₄⋊Dic₇₁	—	2	1	no	—
169	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
170	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
171	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
173	Dic₇₁⋊C₄	—	2	1	no	—
174	Dic₇₁⋊C₄	—	2	1	no	—
175	Dic₇₁⋊C₄	—	2	1	no	—
176	Dic₇₁⋊C₄	—	2	1	no	—
177	Dic₇₁⋊C₄	—	2	1	no	—
178	Dic₇₁⋊C₄	—	2	1	no	—
179	Dic₇₁⋊C₄	—	2	1	no	—
180	Dic₇₁⋊C₄	—	2	1	no	—
181	C₂²⋊Dic₇₁	—	2	1	no	—
182	(C₂×D₇₁)⋊C₄	—	2	1	no	—
183	(C₂×D₇₁)⋊C₄	—	2	1	no	—
184	(C₂×D₇₁)⋊C₄	—	2	1	no	—
185	(C₂×D₇₁)⋊C₄	—	2	1	no	—
186	C₄×Dic₇₁	—	2	1	no	—
187	C₄×Dic₇₁	—	2	1	no	—
188	C₄×Dic₇₁	—	2	1	no	—
189	C₄×Dic₇₁	—	2	1	no	—
190	C₄×Dic₇₁	—	2	1	no	—
191	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
194	C₂×C₈×C₇₁	—	2	1	no	—
195	C₂×C₈×C₇₁	—	2	1	no	—
196	C₂×C₈×C₇₁	—	2	1	no	—
197	C₂×C₈×C₇₁	—	2	1	no	—
198	C₂×C₈×C₇₁	—	8	1	no	—
199	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
204	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₇₁	#41	1	1	yes	characteristic
206	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
207	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
208	C₂²×D₇₁	—	2	1	no	—
209	C₂×C₄×C₇₁	—	2	2	no	—
210	C₂×C₄×C₇₁	—	2	1	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	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
220	C₂²⋊D₇₁	—	4	2	no	—
221	C₂×Dic₇₁	—	2	1	no	—
222	C₂×Dic₇₁	—	2	1	no	—
223	C₂×Dic₇₁	—	2	1	no	—
224	C₂×Dic₇₁	—	2	1	no	—
225	C₂×Dic₇₁	—	2	1	no	—
226	C₂×Dic₇₁	—	2	1	no	—
227	C₂×Dic₇₁	—	2	1	no	—
228	C₂×Dic₇₁	—	4	2	no	—
229	C₂×Dic₇₁	—	4	2	no	—
230	D₂₈₄	—	2	1	no	—
231	D₂₈₄	—	2	1	no	—
232	C₄×D₇₁	—	4	1	no	—
233	C₄×D₇₁	—	4	1	no	—
234	Dic₁₄₂	—	2	1	no	—
235	Dic₁₄₂	—	2	1	no	—
236	Dic₁₄₂	—	2	1	no	—
237	Dic₁₄₂	—	2	1	no	—
238	Dic₁₄₂	—	2	1	no	—
239	Dic₁₄₂	—	4	2	no	—
240	Dic₁₄₂	#131	1	2	yes	—
241	C₈×C₇₁	—	2	1	no	—
242	C₈×C₇₁	—	2	1	no	—
243	C₈×C₇₁	—	2	1	no	—
244	C₈×C₇₁	—	2	1	no	—
245	C₈×C₇₁	—	4	1	no	—
246	C₈×C₇₁	—	4	1	no	—
247	C₈×C₇₁	—	4	1	no	—
248	C₈×C₇₁	—	4	1	no	—
249	C₇₁⋊C₈	—	2	2	no	—
250	C₇₁⋊C₈	—	2	2	no	—
251	C₇₁⋊C₈	—	2	1	no	—
252	C₇₁⋊C₈	—	2	1	no	—
253	C₇₁⋊C₈	—	2	1	no	—
254	C₇₁⋊C₈	—	2	1	no	—
255	C₂²×C₇₁	—	2	1	no	—
256	C₂²×C₇₁	—	2	1	no	—
257	C₂²×C₇₁	#443	1	2	yes	—
258	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂×D₇₁	—	4	1	no	—
260	C₂×D₇₁	—	4	1	no	—
261	C₂×D₇₁	—	4	1	no	—
262	C₄×C₇₁	—	2	1	no	—
263	C₄×C₇₁	—	2	1	no	—
264	C₄×C₇₁	—	2	1	no	—
265	C₄×C₇₁	—	2	1	no	—
266	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
267	C₄×C₇₁	#568	1	1	yes	characteristic
268	C₄×C₇₁	#577	1	1	yes	characteristic
269	C₄×C₇₁	#578	1	1	yes	characteristic
270	Dic₇₁	—	2	2	no	—
271	Dic₇₁	—	4	1	no	—
272	Dic₇₁	—	4	1	no	—
273	Dic₇₁	—	4	1	no	—
274	Dic₇₁	—	4	1	no	—
275	Dic₇₁	—	4	1	no	—
276	Dic₇₁	—	4	1	no	—
277	#18017	—	71	1	no	maximal, Sylow
278	C₂×C₇₁	—	2	2	no	—
279	C₂×C₇₁	#2933	1	1	yes	characteristic
280	C₂×C₇₁	#2947	1	1	yes	characteristic
281	C₂×C₇₁	C₂×#443	1	1	yes	characteristic
282	D₇₁	—	8	1	no	—
283	#3108	—	71	1	no	—
284	#2994	—	71	1	no	—
285	#2984	—	71	1	no	—
286	#1591	—	71	1	no	—
287	#1590	—	71	1	no	—
288	#1588	—	71	1	no	—
289	#1587	—	71	1	no	—
290	#1587	—	71	1	no	—
291	#1585	—	71	1	no	—
292	C₈×Q₁₆	—	71	1	no	—
293	C₈×SD₁₆	—	71	1	no	—
294	#1573	D₇₁	1	1	yes	characteristic, complemented
295	#1494	—	71	1	no	—
296	C₂×Q₈⋊C₈	—	71	1	no	—
297	#1450	—	71	1	no	—
298	C₇₁	#18017	1	1	yes	characteristic, complemented, Sylow
299	#529	—	71	1	no	—
300	C₂×C₄×Q₈	—	71	1	no	—
301	#483	—	71	1	no	—
302	#480	—	71	1	no	—
303	#479	—	71	1	no	—
304	#479	—	71	1	no	—
305	#464	—	71	1	no	—
306	#464	—	71	1	no	—
307	#451	—	71	1	no	—
308	#448	—	71	1	no	—
309	#446	—	71	1	no	—
310	#446	—	71	1	no	—
311	#446	—	71	1	no	—
312	#446	—	142	1	no	—
313	#446	—	142	1	no	—
314	C₈×Q₈	—	71	1	no	—
315	C₈×Q₈	—	71	1	no	—
316	C₈×Q₈	—	71	1	no	—
317	C₄×Q₁₆	—	71	1	no	—
318	C₄×Q₁₆	—	71	1	no	—
319	C₄×SD₁₆	—	71	1	no	—
320	C₄×SD₁₆	—	71	1	no	—
321	#436	—	71	1	no	—
322	#435	—	142	1	no	—
323	C₈×D₄	—	71	1	no	—
324	C₈×D₄	—	142	1	no	—
325	#433	—	142	1	no	—
326	#432	—	142	1	no	—
327	#432	C₂×D₇₁	1	1	yes	characteristic
328	#431	—	71	1	no	—
329	#431	—	142	1	no	—
330	#431	C₂×D₇₁	1	1	yes	characteristic
331	#424	—	142	1	no	—
332	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
333	C₂×C₄×C₈	—	71	1	no	—
334	#335	C₂×D₇₁	1	1	yes	characteristic
335	#335	C₂×D₇₁	1	1	yes	characteristic
336	#334	C₂×D₇₁	1	1	yes	characteristic
337	#334	C₂×D₇₁	1	1	yes	characteristic
338	Q₈⋊C₈	—	71	1	no	—
339	Q₈⋊C₈	—	71	1	no	—
340	Q₈⋊C₈	—	71	1	no	—
341	Q₈⋊C₈	—	71	1	no	—
342	Q₈⋊C₈	—	71	1	no	—
343	Q₈⋊C₈	—	71	1	no	—
344	D₄⋊C₈	—	71	1	no	—
345	D₄⋊C₈	—	71	1	no	—
346	#322	—	71	1	no	—
347	#322	—	71	1	no	—
348	C₈²	—	71	1	no	—
349	C₈²	—	71	1	no	—
350	C₂²×Q₈	—	71	1	no	—
351	C₂×Q₁₆	—	71	1	no	—
352	C₂×Q₁₆	—	71	1	no	—
353	C₂×SD₁₆	—	71	1	no	—
354	C₂×SD₁₆	—	71	1	no	—
355	C₂×M₁₆	—	142	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	—	142	1	no	—
358	C₂²×C₈	—	142	1	no	—
359	#126	—	142	1	no	—
360	#125	—	71	1	no	—
361	#124	—	71	1	no	—
362	#123	—	142	1	no	—
363	C₂²⋊Q₈	—	71	1	no	—
364	#121	—	71	1	no	—
365	C₄×Q₈	—	71	1	no	—
366	C₄×Q₈	—	71	1	no	—
367	C₄×Q₈	—	71	1	no	—
368	C₄×Q₈	—	71	1	no	—
369	C₄×Q₈	—	71	1	no	—
370	C₄×Q₈	—	142	1	no	—
371	C₄×Q₈	—	142	1	no	—
372	C₄×D₄	—	71	1	no	—
373	C₄×D₄	—	142	1	no	—
374	#117	—	142	1	no	—
375	C₂×C₄⋊C₄	—	71	1	no	—
376	C₂×C₄⋊C₄	—	142	1	no	—
377	C₂×C₄²	—	142	1	no	—
378	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
379	#107	—	71	1	no	—
380	#107	—	71	1	no	—
381	#106	—	71	1	no	—
382	#106	—	71	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	71	1	no	—
385	C₄⋊C₈	—	71	1	no	—
386	C₄⋊C₈	—	142	1	no	—
387	C₄⋊C₈	—	142	1	no	—
388	C₄⋊C₈	—	142	1	no	—
389	C₄⋊C₈	—	142	1	no	—
390	C₄⋊C₈	—	142	1	no	—
391	C₄⋊C₈	—	142	1	no	—
392	C₄⋊C₈	C₄×D₇₁	1	1	yes	characteristic
393	C₄⋊C₈	C₄×D₇₁	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
396	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
397	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
398	#103	—	71	1	no	—
399	#103	—	71	1	no	—
400	#103	—	71	1	no	—
401	#103	—	71	1	no	—
402	#103	—	71	1	no	—
403	#103	—	71	1	no	—
404	#102	—	71	1	no	—
405	#102	—	71	1	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	71	1	no	—
408	C₂²⋊C₈	—	71	1	no	—
409	C₂²⋊C₈	—	142	1	no	—
410	C₂²⋊C₈	—	142	1	no	—
411	C₂²⋊C₈	C₄×D₇₁	1	1	yes	characteristic
412	C₂²⋊C₈	C₄×D₇₁	1	1	yes	characteristic
413	#97	—	2	1	no	—
414	#97	—	142	1	no	—
415	#97	—	142	1	no	—
416	#97	—	142	1	no	—
417	C₄×C₈	—	71	1	no	—
418	C₄×C₈	—	71	1	no	—
419	C₄×C₈	—	71	1	no	—
420	C₄×C₈	—	71	1	no	—
421	C₄×C₈	—	142	1	no	—
422	C₄×C₈	—	142	1	no	—
423	C₄×C₈	—	142	1	no	—
424	C₄×C₈	—	142	1	no	—
425	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
426	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
427	C₂×Q₈	—	284	1	no	—
428	C₂×Q₈	—	71	1	no	—
429	C₂×Q₈	—	71	1	no	—
430	C₂×Q₈	—	71	1	no	—
431	C₂×Q₈	—	142	2	no	—
432	C₂×Q₈	—	142	1	no	—
433	C₂×D₄	—	71	1	no	—
434	C₂×D₄	—	142	1	no	—
435	C₂²×C₄	—	142	1	no	—
436	C₂²×C₄	—	142	1	no	—
437	C₂²×C₄	—	142	1	no	—
438	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
439	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
440	C₂²×C₄	#11765866	1	1	yes	characteristic
441	Q₁₆	—	284	1	no	—
442	Q₁₆	—	142	2	no	—
443	SD₁₆	—	284	1	no	—
444	SD₁₆	—	142	2	no	—
445	M₁₆	—	568	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	8	1	no	—
451	C₂×C₈	—	568	1	no	—
452	C₂×C₈	—	71	1	no	—
453	C₂×C₈	—	71	1	no	—
454	C₂×C₈	—	71	1	no	—
455	C₂×C₈	—	71	1	no	—
456	C₂×C₈	—	142	4	no	—
457	C₂×C₈	—	142	1	no	—
458	C₂×C₈	—	142	1	no	—
459	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
460	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
461	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
462	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
463	C₄⋊C₄	—	71	1	no	—
464	C₄⋊C₄	—	71	1	no	—
465	C₄⋊C₄	—	71	1	no	—
466	C₄⋊C₄	—	71	1	no	—
467	C₄⋊C₄	—	142	1	no	—
468	C₄⋊C₄	—	142	1	no	—
469	C₄⋊C₄	—	142	1	no	—
470	C₄⋊C₄	—	142	1	no	—
471	C₄⋊C₄	—	142	1	no	—
472	C₄⋊C₄	—	142	1	no	—
473	C₄⋊C₄	—	142	1	no	—
474	C₄⋊C₄	—	142	1	no	—
475	C₄⋊C₄	—	142	1	no	—
476	C₂²⋊C₄	—	142	1	no	—
477	C₂²⋊C₄	—	142	1	no	—
478	C₂²⋊C₄	—	142	1	no	—
479	C₂²⋊C₄	—	142	1	no	—
480	C₂²⋊C₄	—	142	1	no	—
481	C₄²	—	142	1	no	—
482	C₄²	—	142	1	no	—
483	C₄²	—	142	1	no	—
484	C₄²	—	142	1	no	—
485	C₄²	—	142	1	no	—
486	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
487	C₄²	D₄×D₇₁	1	1	yes	characteristic
488	C₄²	#11765866	1	1	yes	characteristic
489	C₄²	C₂³×D₇₁	1	1	yes	characteristic
490	C₂³	—	142	1	no	—
491	C₂³	#14556090	1	1	yes	characteristic
492	Q₈	—	284	2	no	—
493	Q₈	—	71	2	no	—
494	Q₈	—	142	1	no	—
495	Q₈	—	142	1	no	—
496	Q₈	—	142	1	no	—
497	Q₈	—	142	1	no	—
498	Q₈	—	142	1	no	—
499	D₄	—	284	2	no	—
500	D₄	—	142	1	no	—
501	D₄	—	142	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	284	2	no	—
508	C₂×C₄	—	284	2	no	—
509	C₂×C₄	—	284	1	no	—
510	C₂×C₄	—	284	1	no	—
511	C₂×C₄	—	142	1	no	—
512	C₂×C₄	—	142	1	no	—
513	C₂×C₄	—	142	1	no	—
514	C₂×C₄	—	142	1	no	—
515	C₂×C₄	—	142	1	no	—
516	C₂×C₄	—	142	1	no	—
517	C₂×C₄	—	142	1	no	—
518	C₂×C₄	#14556090	1	1	yes	characteristic
519	C₂×C₄	#14556090	1	1	yes	characteristic
520	C₂×C₄	#14556090	1	1	yes	characteristic
521	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
522	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
523	C₂×C₄	C₂×#11765866	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	142	2	no	—
533	C₈	—	142	2	no	—
534	C₈	—	142	1	no	—
535	C₈	—	142	1	no	—
536	C₈	—	142	1	no	—
537	C₈	—	142	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	284	1	no	—
541	C₂²	—	284	1	no	—
542	C₂²	—	284	1	no	—
543	C₂²	#17986115	1	2	yes	—
544	C₂²	C₂×#14556090	1	1	yes	characteristic
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	284	1	no	—
550	C₄	—	284	1	no	—
551	C₄	—	284	1	no	—
552	C₄	—	284	1	no	—
553	C₄	—	284	1	no	—
554	C₄	—	284	1	no	—
555	C₄	—	142	2	no	—
556	C₄	#131×D₇₁	1	1	yes	characteristic
557	C₄	#17986764	1	1	yes	characteristic
558	C₄	#17986809	1	1	yes	characteristic
559	C₄	#17986815	1	1	yes	characteristic
560	C₂	—	2	2	no	—
561	C₂	—	568	1	no	—
562	C₂	#22597064	1	1	yes	characteristic
563	C₂	#22597181	1	1	yes	characteristic
564	C₂	C₂×#17986115	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₇₁×#1573	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	#14556102	C₂×C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#1573	D₇₁
hypocenter	C₇₁	#18017
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
3. #22597430	C₂	semidirect
4. #22587236	C₂	semidirect
5. #22587229	C₂	semidirect
6. #22587217	C₂	semidirect
7. #22587210	C₂	semidirect
8. #22587210	C₂	semidirect
9. #22587196	C₂	semidirect
10. #22587146	C₂	semidirect
11. #22587139	C₂	semidirect
13. C₂×#17985729	C₂	semidirect
14. #22586624	C₂	semidirect
15. C₇₁×#1573	C₂	semidirect
294. #1573	D₇₁	semidirect
298. C₇₁	#18017	semidirect

Maximal subgroups

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

subgroup	index
#22598422	2
#22597496	2
#22597430	2
#22587236	2
#22587229	2
#22587217	2
#22587210	2
#22587196	2
#22587146	2
#22587139	2
#22586798	2
C₂×#17985729	2
#22586624	2
C₇₁×#1573	2
#18017	71