Subgroups — #31903374

Order 18176.

730 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556063	C₂	1	1	yes	maximal, characteristic
2	C₂×#17986035	C₂	1	1	yes	maximal, characteristic
3	C₂×#17985957	C₂	1	1	yes	maximal, characteristic
4	C₂×#17985770	C₂	1	1	yes	maximal, characteristic
5	C₂×#17985756	C₂	1	1	yes	maximal, characteristic
6	C₂×#17985755	C₂	1	1	yes	maximal, characteristic
7	C₂×#344×C₇₁	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11765849	C₂²	1	1	yes	characteristic
9	C₂³×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×#14556087	C₂²	1	1	yes	characteristic
11	C₂×#14556087	C₂²	1	1	yes	characteristic
12	C₂×#14556063	—	2	2	no	—
13	C₂×#14556063	—	2	1	no	—
14	C₂×#14556063	—	2	1	no	—
15	C₂×#14556063	C₄	1	4	yes	complemented
16	#17986035	—	2	2	no	—
17	#17986035	C₄	1	4	yes	complemented
18	C₂×#14556061	—	2	1	no	—
19	C₂×#14556059	—	2	1	no	—
20	#17985957	—	2	2	no	—
21	#17985957	—	2	2	no	—
22	C₂×#14556038	C₄	1	2	yes	complemented
23	C₂×C₈×Dic₇₁	C₄	1	2	yes	complemented
24	#17985770	—	2	2	no	—
25	#17985756	—	2	2	no	—
26	#17985755	—	2	2	no	—
27	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
29	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
30	#344×C₇₁	—	2	2	no	—
31	C₂×#11765849	—	2	1	no	—
32	C₂×#11765849	—	2	1	no	—
33	C₂×#11765849	—	2	1	no	—
34	C₂×#11765849	—	2	1	no	—
35	C₂×#11765849	—	2	1	no	—
36	C₂×#11765849	C₂×C₄	1	2	yes	—
37	C₂²×C₇₁⋊C₈	—	2	1	no	—
38	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
41	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₇₁⋊C₈	D₄	1	2	yes	—
43	C₂²×C₇₁⋊C₈	D₄	1	2	yes	—
44	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
45	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
46	C₂²×C₇₁⋊C₈	Q₈	1	1	yes	characteristic
47	C₂²×C₇₁⋊C₈	Q₈	1	1	yes	characteristic
48	#14556087	—	2	1	no	—
49	#14556087	—	2	1	no	—
50	#14556087	—	2	1	no	—
51	#14556087	—	2	1	no	—
52	#14556087	—	2	1	no	—
53	#14556087	C₂×C₄	1	2	yes	—
54	#14556087	D₄	1	2	yes	—
55	#14556087	Q₈	1	2	yes	—
56	C₂×C₄⋊Dic₇₁	—	2	1	no	—
57	C₂×C₄⋊Dic₇₁	—	2	1	no	—
58	C₂×C₂²⋊Dic₇₁	—	2	1	no	—
59	C₂×C₂²⋊Dic₇₁	—	2	1	no	—
60	C₂×C₄×Dic₇₁	—	2	1	no	—
61	C₂×C₄×Dic₇₁	C₂×C₄	1	2	yes	—
62	#14556063	—	2	4	no	—
63	#14556063	—	2	4	no	—
64	#14556061	—	2	4	no	—
65	#14556059	—	2	4	no	—
66	#14556038	—	2	4	no	—
67	C₈×Dic₇₁	—	2	4	no	—
68	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
69	C₂×M₁₆×C₇₁	—	2	1	no	—
70	C₂×M₁₆×C₇₁	—	2	1	no	—
71	C₂×M₁₆×C₇₁	—	2	1	no	—
72	C₂×M₁₆×C₇₁	—	2	1	no	—
73	C₂×M₁₆×C₇₁	—	2	1	no	—
74	C₂×M₁₆×C₇₁	—	2	1	no	—
75	C₂×M₁₆×C₇₁	—	2	1	no	—
76	C₂×M₁₆×C₇₁	—	2	1	no	—
77	C₂×M₁₆×C₇₁	—	2	1	no	—
78	C₂×M₁₆×C₇₁	C₂×C₄	1	2	yes	—
79	C₂×M₁₆×C₇₁	D₄	1	2	yes	—
80	C₂×M₁₆×C₇₁	Q₈	1	2	yes	—
81	C₂²×C₈×C₇₁	—	2	1	no	—
82	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
83	#117×C₇₁	—	2	1	no	—
84	#117×C₇₁	—	2	1	no	—
85	#117×C₇₁	—	2	1	no	—
86	#117×C₇₁	C₂×C₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
89	C₂×C₄²×C₇₁	—	2	1	no	—
90	C₂²×Dic₇₁	—	2	2	no	—
91	C₂²×Dic₇₁	—	4	1	no	—
92	#11765849	—	2	2	no	—
93	#11765849	—	2	2	no	—
94	#11765849	—	4	1	no	—
95	#11765849	—	4	1	no	—
96	C₂×C₇₁⋊C₈	—	2	2	no	—
97	C₂×C₇₁⋊C₈	—	4	1	no	—
98	C₂×C₇₁⋊C₈	—	4	1	no	—
99	C₂×C₇₁⋊C₈	C₄²	1	2	yes	—
100	C₂×C₇₁⋊C₈	C₄²	1	2	yes	—
101	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	2	yes	—
102	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	2	yes	—
103	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	2	yes	—
104	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	2	yes	—
105	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	2	yes	—
106	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	2	yes	—
107	C₂×C₇₁⋊C₈	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₇₁⋊C₈	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₇₁⋊C₈	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₇₁⋊C₈	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₇₁⋊C₈	C₄⋊C₄	1	2	yes	—
112	C₂×C₇₁⋊C₈	C₄⋊C₄	1	2	yes	—
113	C₂×C₇₁⋊C₈	C₄⋊C₄	1	2	yes	—
114	C₂×C₇₁⋊C₈	C₄⋊C₄	1	2	yes	—
115	C₄⋊Dic₇₁	—	2	2	no	—
116	C₄⋊Dic₇₁	—	2	2	no	—
117	C₄⋊Dic₇₁	—	2	2	no	—
118	C₄⋊Dic₇₁	—	4	1	no	—
119	C₂²⋊Dic₇₁	—	2	2	no	—
120	C₂²⋊Dic₇₁	—	2	2	no	—
121	C₂²⋊Dic₇₁	—	2	2	no	—
122	C₂²⋊Dic₇₁	—	4	1	no	—
123	C₄×Dic₇₁	—	2	2	no	—
124	C₄×Dic₇₁	—	2	2	no	—
125	C₄×Dic₇₁	—	4	1	no	—
126	C₄×Dic₇₁	C₄⋊C₄	1	4	yes	—
127	C₂⁴×C₇₁	#41	1	1	yes	characteristic
128	C₂²×C₄×C₇₁	—	4	1	no	—
129	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
138	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
139	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
140	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
141	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
142	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
143	M₁₆×C₇₁	—	2	2	no	—
144	M₁₆×C₇₁	—	2	2	no	—
145	M₁₆×C₇₁	—	2	2	no	—
146	M₁₆×C₇₁	—	2	2	no	—
147	M₁₆×C₇₁	—	2	2	no	—
148	M₁₆×C₇₁	—	2	2	no	—
149	M₁₆×C₇₁	—	4	1	no	—
150	M₁₆×C₇₁	—	4	1	no	—
151	C₂×C₈×C₇₁	—	2	2	no	—
152	C₂×C₈×C₇₁	—	2	2	no	—
153	C₂×C₈×C₇₁	—	2	2	no	—
154	C₂×C₈×C₇₁	—	4	1	no	—
155	C₂×C₈×C₇₁	—	4	1	no	—
156	C₂×C₈×C₇₁	C₄⋊C₄	1	4	yes	—
157	C₄⋊C₄×C₇₁	—	2	2	no	—
158	C₄⋊C₄×C₇₁	—	4	1	no	—
159	C₂²⋊C₄×C₇₁	—	2	2	no	—
160	C₂²⋊C₄×C₇₁	—	4	1	no	—
161	C₄²×C₇₁	—	2	2	no	—
162	C₄²×C₇₁	—	4	1	no	—
163	C₂³×C₇₁	—	4	2	no	—
164	C₂³×C₇₁	#117	1	1	yes	characteristic
165	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
166	C₂³×C₇₁	C₄×Q₈	1	1	yes	characteristic
167	C₂³×C₇₁	#121	1	1	yes	characteristic
168	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂³×C₇₁	#124	1	1	yes	characteristic
170	C₂³×C₇₁	#125	1	1	yes	characteristic
171	C₂×C₄×C₇₁	—	4	2	no	—
172	C₂×C₄×C₇₁	—	8	2	no	—
173	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
183	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
189	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
190	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
191	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
192	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
193	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
194	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
195	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
196	C₂×C₄×C₇₁	#125	1	1	yes	characteristic
197	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
198	C₂×C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
199	C₂×C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
201	C₂×Dic₇₁	—	2	4	no	—
202	C₂×Dic₇₁	—	4	4	no	—
203	C₂×Dic₇₁	—	4	2	no	—
204	C₂×Dic₇₁	—	8	2	no	—
205	C₈×C₇₁	—	2	4	no	—
206	C₈×C₇₁	—	4	2	no	—
207	C₇₁⋊C₈	—	4	2	no	—
208	C₇₁⋊C₈	#95	1	2	yes	—
209	C₇₁⋊C₈	#95	1	2	yes	—
210	C₇₁⋊C₈	#95	1	2	yes	—
211	C₇₁⋊C₈	#95	1	2	yes	—
212	C₂²×C₇₁	—	2	2	no	—
213	C₂²×C₇₁	—	2	2	no	—
214	C₂²×C₇₁	—	2	2	no	—
215	C₂²×C₇₁	—	4	1	no	—
216	C₂²×C₇₁	—	4	1	no	—
217	C₂²×C₇₁	—	4	1	no	—
218	C₂²×C₇₁	—	4	1	no	—
219	C₂²×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
220	C₂²×C₇₁	#380	1	1	yes	characteristic
221	C₂²×C₇₁	#382	1	1	yes	characteristic
222	C₂²×C₇₁	#389	1	1	yes	characteristic
223	C₂²×C₇₁	#389	1	1	yes	characteristic
224	C₂²×C₇₁	#390	1	1	yes	characteristic
225	C₂²×C₇₁	#391	1	1	yes	characteristic
226	C₄×C₇₁	—	8	2	no	—
227	C₄×C₇₁	C₂×#95	1	1	yes	characteristic
228	C₄×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
229	C₄×C₇₁	#380	1	1	yes	characteristic
230	C₄×C₇₁	#384	1	1	yes	characteristic
231	C₄×C₇₁	#389	1	1	yes	characteristic
232	C₄×C₇₁	#389	1	1	yes	characteristic
233	C₄×C₇₁	#390	1	1	yes	characteristic
234	C₄×C₇₁	#391	1	1	yes	characteristic
235	Dic₇₁	—	4	4	no	—
236	Dic₇₁	—	8	2	no	—
237	#10868	—	71	1	no	maximal, Sylow
238	C₂×C₇₁	—	2	1	no	—
239	C₂×C₇₁	—	2	1	no	—
240	C₂×C₇₁	—	2	1	no	—
241	C₂×C₇₁	—	2	1	no	—
242	C₂×C₇₁	—	2	1	no	—
243	C₂×C₇₁	—	2	1	no	—
244	C₂×C₇₁	C₄⋊#95	1	1	yes	characteristic
245	C₂×C₇₁	#1833	1	2	yes	—
246	C₂²×#108	—	71	1	no	—
247	C₂×#427	—	71	1	no	—
248	C₂×#405	—	71	1	no	—
249	C₂×#344	—	71	1	no	—
250	C₂×#344	D₇₁	1	1	yes	characteristic
251	C₂×H(3,ℤ/4)	—	71	1	no	—
252	C₂×H(3,ℤ/4)	—	71	1	no	—
253	C₇₁	#10868	1	1	yes	characteristic, complemented, Sylow
254	C₂²×M₁₆	—	71	1	no	—
255	C₂²×M₁₆	C₂×D₇₁	1	1	yes	characteristic
256	C₂²×M₁₆	C₂×D₇₁	1	1	yes	characteristic
257	C₂³×C₈	—	71	1	no	—
258	C₂×#117	—	71	1	no	—
259	C₂×#117	—	71	1	no	—
260	C₂×#117	C₂×D₇₁	1	1	yes	characteristic
261	C₂×#108	—	71	4	no	—
262	C₂×#108	—	142	2	no	—
263	C₂×#108	—	142	1	no	—
264	C₂×#108	—	142	1	no	—
265	#427	—	71	4	no	—
266	#427	—	142	2	no	—
267	C₂×#107	—	142	1	no	—
268	C₂×#106	—	142	1	no	—
269	#405	—	142	2	no	—
270	#405	—	142	2	no	—
271	C₂×#97	—	71	2	no	—
272	C₂×C₄×C₈	—	71	2	no	—
273	#344	—	2	2	no	—
274	#344	—	142	2	no	—
275	H(3,ℤ/4)	—	142	2	no	—
276	H(3,ℤ/4)	—	142	2	no	—
277	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	71	2	no	—
288	C₂×M₁₆	—	142	1	no	—
289	C₂×M₁₆	—	142	1	no	—
290	C₂×M₁₆	—	142	1	no	—
291	C₂×M₁₆	—	142	1	no	—
292	C₂×M₁₆	—	142	1	no	—
293	C₂×M₁₆	Dic₁₄₂	1	2	yes	—
294	C₂×M₁₆	C₄×D₇₁	1	2	yes	—
295	C₂×M₁₆	C₂²⋊D₇₁	1	2	yes	—
296	C₂²×C₈	—	2	1	no	—
297	C₂²×C₈	—	71	1	no	—
298	C₂²×C₈	—	71	1	no	—
299	C₂²×C₈	—	71	2	no	—
300	C₂²×C₈	—	71	2	no	—
301	C₂²×C₈	—	71	2	no	—
302	C₂²×C₈	—	71	2	no	—
303	C₂²×C₈	—	71	1	no	—
304	C₂²×C₈	—	71	1	no	—
305	C₂²×C₈	—	71	1	no	—
306	C₂²×C₈	—	71	1	no	—
307	C₂²×C₈	—	142	1	no	—
308	C₂²×C₈	C₄×D₇₁	1	2	yes	—
309	#117	—	2	1	no	—
310	#117	—	2	1	no	—
311	#117	—	2	1	no	—
312	#117	—	71	2	no	—
313	#117	—	71	2	no	—
314	#117	—	71	2	no	—
315	#117	—	142	1	no	—
316	#117	—	142	1	no	—
317	#117	—	142	1	no	—
318	#117	—	142	1	no	—
319	#117	—	142	1	no	—
320	#117	C₄×D₇₁	1	2	yes	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	142	1	no	—
323	C₂×C₄⋊C₄	—	142	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	142	1	no	—
326	C₂×C₂²⋊C₄	—	142	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	71	2	no	—
329	C₂×C₄²	—	142	1	no	—
330	#108	—	142	4	no	—
331	#108	—	142	4	no	—
332	#107	—	142	4	no	—
333	#106	—	142	4	no	—
334	#97	—	142	4	no	—
335	C₄×C₈	—	142	4	no	—
336	C₂⁴	#11765865	1	1	yes	characteristic
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	284	1	no	—
339	C₂²×C₄	—	142	2	no	—
340	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
344	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
348	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
349	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
351	C₂²×C₄	#11765864	1	1	yes	characteristic
352	C₂²×C₄	#11765864	1	1	yes	characteristic
353	C₂²×C₄	#11765865	1	1	yes	characteristic
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	2	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	4	1	no	—
361	M₁₆	—	4	1	no	—
362	M₁₆	—	284	1	no	—
363	M₁₆	—	284	1	no	—
364	M₁₆	—	142	2	no	—
365	M₁₆	—	142	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	284	1	no	—
372	C₂×C₈	—	284	1	no	—
373	C₂×C₈	—	71	2	no	—
374	C₂×C₈	—	71	2	no	—
375	C₂×C₈	—	71	2	no	—
376	C₂×C₈	—	71	2	no	—
377	C₂×C₈	—	71	2	no	—
378	C₂×C₈	—	71	2	no	—
379	C₂×C₈	—	71	2	no	—
380	C₂×C₈	—	71	2	no	—
381	C₂×C₈	—	71	1	no	—
382	C₂×C₈	—	71	1	no	—
383	C₂×C₈	—	71	1	no	—
384	C₂×C₈	—	71	1	no	—
385	C₂×C₈	—	71	2	no	—
386	C₂×C₈	—	71	2	no	—
387	C₂×C₈	—	71	2	no	—
388	C₂×C₈	—	71	2	no	—
389	C₂×C₈	—	142	2	no	—
390	C₂×C₈	Dic₇₁⋊C₄	1	4	yes	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	1	no	—
393	C₄⋊C₄	—	284	1	no	—
394	C₄⋊C₄	—	142	2	no	—
395	C₄⋊C₄	—	142	2	no	—
396	C₄⋊C₄	—	142	2	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	4	1	no	—
399	C₂²⋊C₄	—	284	1	no	—
400	C₂²⋊C₄	—	142	2	no	—
401	C₂²⋊C₄	—	142	2	no	—
402	C₂²⋊C₄	—	142	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	4	1	no	—
405	C₄²	—	284	1	no	—
406	C₄²	—	71	4	no	—
407	C₄²	—	142	2	no	—
408	C₄²	—	142	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	#14556085	1	1	yes	characteristic
411	C₂³	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
412	C₂³	C₄×Dic₁₄₂	1	1	yes	characteristic
413	C₂³	#14556101	1	1	yes	characteristic
414	C₂³	#14556106	1	1	yes	characteristic
415	C₂³	#14556114	1	1	yes	characteristic
416	C₂³	#14556118	1	1	yes	characteristic
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	284	4	no	—
420	C₂×C₄	—	284	2	no	—
421	C₂×C₄	—	568	2	no	—
422	C₂×C₄	—	142	4	no	—
423	C₂×C₄	C₄²×D₇₁	1	1	yes	characteristic
424	C₂×C₄	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
425	C₂×C₄	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
426	C₂×C₄	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
427	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
428	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
429	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
430	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
431	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
432	C₂×C₄	#14556084	1	1	yes	characteristic
433	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
434	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
435	C₂×C₄	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
436	C₂×C₄	#14556093	1	1	yes	characteristic
437	C₂×C₄	#14556093	1	1	yes	characteristic
438	C₂×C₄	C₄×Dic₁₄₂	1	1	yes	characteristic
439	C₂×C₄	#14556100	1	1	yes	characteristic
440	C₂×C₄	#14556100	1	1	yes	characteristic
441	C₂×C₄	#14556101	1	1	yes	characteristic
442	C₂×C₄	#14556105	1	1	yes	characteristic
443	C₂×C₄	#14556105	1	1	yes	characteristic
444	C₂×C₄	#14556106	1	1	yes	characteristic
445	C₂×C₄	#14556114	1	1	yes	characteristic
446	C₂×C₄	#14556118	1	1	yes	characteristic
447	C₂×C₄	#14556124	1	1	yes	characteristic
448	C₂×C₄	#14556126	1	1	yes	characteristic
449	C₂×C₄	#14556127	1	1	yes	characteristic
450	C₂×C₄	#14556127	1	1	yes	characteristic
451	C₈	—	2	4	no	—
452	C₈	—	4	2	no	—
453	C₈	—	284	2	no	—
454	C₈	—	71	2	no	—
455	C₈	—	71	2	no	—
456	C₈	—	71	2	no	—
457	C₈	—	71	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	C₄×Dic₇₁⋊C₄	1	1	yes	characteristic
466	C₂²	#17985858	1	1	yes	characteristic
467	C₂²	#17985863	1	1	yes	characteristic
468	C₂²	#17985894	1	1	yes	characteristic
469	C₂²	#17985896	1	1	yes	characteristic
470	C₂²	#17985899	1	1	yes	characteristic
471	C₂²	#17985903	1	1	yes	characteristic
472	C₄	—	8	2	no	—
473	C₄	—	284	4	no	—
474	C₄	—	568	2	no	—
475	C₄	#95×D₇₁	1	1	yes	characteristic
476	C₄	#17985850	1	1	yes	characteristic
477	C₄	#17985857	1	1	yes	characteristic
478	C₄	#17985868	1	1	yes	characteristic
479	C₄	#17985894	1	1	yes	characteristic
480	C₄	#17985896	1	1	yes	characteristic
481	C₄	#17985899	1	1	yes	characteristic
482	C₄	#17985903	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	2	1	no	—
488	C₂	—	2	1	no	—
489	C₂	Dic₇₁⋊#95	1	1	yes	characteristic
490	C₂	#22588461	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#14556084
commutator	C₂×C₄×C₇₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₁
Fitting	C₂×#344×C₇₁	C₂
socle	C₂²×C₇₁	#382
prime radical	C₂⁴×C₇₁	#41
cosocle	C₂³×C₄×C₇₁	C₂³
hypercenter	C₂×#344	D₇₁
hypocenter	C₇₁	#10868
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
15. C₂×#14556063	C₄	semidirect
17. #17986035	C₄	semidirect
22. C₂×#14556038	C₄	semidirect
23. C₂×C₈×Dic₇₁	C₄	semidirect
253. C₇₁	#10868	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14556063	2
C₂×#17986035	2
C₂×#17985957	2
C₂×#17985770	2
C₂×#17985756	2
C₂×#17985755	2
C₂×#344×C₇₁	2
#10868	71