Subgroups — #31966701

Order 18176.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597307	C₂	1	1	yes	maximal, characteristic
2	#22597006	C₂	1	1	yes	maximal, characteristic
3	#22587131	C₂	1	2	yes	maximal, complemented
4	#22587123	C₂	1	2	yes	maximal, complemented
5	#22587114	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587112	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587105	C₂	1	2	yes	maximal, complemented
8	#22587098	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587090	C₂	1	2	yes	maximal, complemented
10	C₂×#17985749	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#2906	C₂	1	1	yes	maximal, characteristic
12	#17986130	C₄	1	1	yes	characteristic
13	#17986130	C₄	1	1	yes	characteristic
14	#17986077	C₄	1	1	yes	characteristic
15	#17986077	C₄	1	1	yes	characteristic
16	#17986071	C₄	1	2	yes	—
17	#17986071	C₄	1	2	yes	—
18	#17986060	—	2	2	no	—
19	#17986056	C₂²	1	2	yes	—
20	#17986052	C₂²	1	2	yes	—
21	#17986052	C₂²	1	1	yes	characteristic
22	#17986052	C₂²	1	2	yes	—
23	#17986023	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
25	#17985966	—	2	1	no	—
26	#17985955	—	2	1	no	—
27	C₄×#11765849	C₂²	1	2	yes	—
28	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
29	#17985751	C₂²	1	2	yes	—
30	#17985751	C₂²	1	2	yes	—
31	#17985751	C₂²	1	2	yes	—
32	#17985751	C₂²	1	2	yes	—
33	#17985749	C₂²	1	1	yes	characteristic
34	#17985749	C₂²	1	1	yes	characteristic
35	#17985749	C₂²	1	1	yes	characteristic
36	#17985749	C₂²	1	1	yes	characteristic
37	#17985749	C₂²	1	2	yes	—
38	#17985749	C₂²	1	2	yes	—
39	C₂×#131×C₇₁	—	2	1	no	—
40	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
41	#424×C₇₁	—	2	2	no	—
42	#424×C₇₁	—	2	1	no	—
43	#423×C₇₁	C₂²	1	1	yes	characteristic
44	#423×C₇₁	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
47	C₂×#11765849	—	2	1	no	—
48	C₂×#11765849	C₂×C₄	1	2	yes	—
49	C₂×#11765849	C₂×C₄	1	2	yes	—
50	C₂²×C₇₁⋊C₈	—	2	1	no	—
51	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
54	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
55	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
56	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
57	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
58	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
59	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
60	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
61	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
62	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
65	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
66	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
67	#14556039	—	2	2	no	—
68	#14556039	C₂×C₄	1	2	yes	—
69	#14556039	C₂×C₄	1	2	yes	—
70	C₄×C₇₁⋊C₈	—	2	2	no	—
71	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
74	C₄×C₇₁⋊C₈	C₂³	1	2	yes	—
75	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
76	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
77	#131×C₇₁	—	4	4	no	—
78	C₂×M₁₆×C₇₁	—	2	2	no	—
79	C₂×M₁₆×C₇₁	—	2	1	no	—
80	C₂²×C₈×C₇₁	—	2	2	no	—
81	C₂²×C₈×C₇₁	—	2	1	no	—
82	C₄×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₇₁	Q₈	1	1	yes	characteristic
84	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
85	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
86	C₄×D₄×C₇₁	Q₈	1	2	yes	—
87	C₄×D₄×C₇₁	Q₈	1	1	yes	characteristic
88	#117×C₇₁	D₄	1	2	yes	—
89	#117×C₇₁	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
91	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₇₁	—	2	2	no	—
93	C₄⋊C₈×C₇₁	—	2	1	no	—
94	C₄⋊C₈×C₇₁	—	2	2	no	—
95	C₄⋊C₈×C₇₁	—	2	1	no	—
96	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
99	#11765849	—	2	4	no	—
100	#11765849	—	4	2	no	—
101	#11765849	—	4	2	no	—
102	C₂×C₇₁⋊C₈	—	2	2	no	—
103	C₂×C₇₁⋊C₈	—	2	1	no	—
104	C₂×C₇₁⋊C₈	—	2	2	no	—
105	C₂×C₇₁⋊C₈	—	2	1	no	—
106	C₂×C₇₁⋊C₈	—	4	1	no	—
107	C₂×C₇₁⋊C₈	—	4	2	no	—
108	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
112	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
113	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
114	#41×C₇₁	—	2	2	no	—
115	#41×C₇₁	—	2	2	no	—
116	C₂×Q₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
117	C₂×D₄×C₇₁	C₄⋊C₄	1	2	yes	—
118	C₂×D₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₁	C₂×Q₈	1	2	yes	—
124	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
125	M₁₆×C₇₁	—	4	4	no	—
126	M₁₆×C₇₁	—	4	2	no	—
127	C₂×C₈×C₇₁	—	2	1	no	—
128	C₂×C₈×C₇₁	—	2	2	no	—
129	C₂×C₈×C₇₁	—	2	1	no	—
130	C₂×C₈×C₇₁	—	4	4	no	—
131	C₂×C₈×C₇₁	—	4	2	no	—
132	C₄⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
133	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
134	C₄⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
135	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
136	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
137	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
138	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
139	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
141	C₄²×C₇₁	C₂×D₄	1	2	yes	—
142	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₇₁	C₂×Q₈	1	2	yes	—
144	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
145	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
146	C₂³×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
147	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
148	Q₈×C₇₁	—	2	2	no	—
149	D₄×C₇₁	—	2	4	no	—
150	D₄×C₇₁	—	2	2	no	—
151	C₂×C₄×C₇₁	—	2	1	no	—
152	C₂×C₄×C₇₁	—	2	2	no	—
153	C₂×C₄×C₇₁	—	2	1	no	—
154	C₂×C₄×C₇₁	—	2	2	no	—
155	C₂×C₄×C₇₁	—	2	2	no	—
156	C₂×C₄×C₇₁	—	2	2	no	—
157	C₂×C₄×C₇₁	—	4	1	no	—
158	C₂×C₄×C₇₁	—	4	2	no	—
159	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₇₁	#137	1	2	yes	—
167	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
170	C₈×C₇₁	—	4	1	no	—
171	C₈×C₇₁	—	4	2	no	—
172	C₈×C₇₁	—	4	1	no	—
173	C₇₁⋊C₈	—	2	1	no	—
174	C₇₁⋊C₈	—	2	2	no	—
175	C₇₁⋊C₈	—	2	1	no	—
176	C₇₁⋊C₈	—	2	1	no	—
177	C₇₁⋊C₈	—	2	2	no	—
178	C₇₁⋊C₈	—	4	2	no	—
179	C₇₁⋊C₈	—	4	1	no	—
180	C₇₁⋊C₈	—	4	1	no	—
181	C₇₁⋊C₈	#131	1	2	yes	complemented
182	C₂²×C₇₁	—	2	1	no	—
183	C₂²×C₇₁	—	2	1	no	—
184	C₂²×C₇₁	—	2	2	no	—
185	C₂²×C₇₁	—	2	2	no	—
186	C₂²×C₇₁	—	2	2	no	—
187	C₂²×C₇₁	#428	1	2	yes	—
188	C₂²×C₇₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
189	C₄×C₇₁	—	2	1	no	—
190	C₄×C₇₁	—	2	2	no	—
191	C₄×C₇₁	—	2	2	no	—
192	C₄×C₇₁	—	2	1	no	—
193	C₄×C₇₁	—	2	1	no	—
194	C₄×C₇₁	—	2	2	no	—
195	C₄×C₇₁	#428	1	2	yes	—
196	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
197	C₄×C₇₁	#568	1	1	yes	characteristic
198	C₄×C₇₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₄×C₇₁	C₂×#137	1	1	yes	characteristic
200	#17830	—	71	1	no	maximal, Sylow
201	C₂×C₇₁	—	2	2	no	—
202	C₂×C₇₁	—	4	2	no	—
203	C₂×C₇₁	#2906	1	1	yes	characteristic
204	C₂×C₇₁	C₂×#428	1	1	yes	characteristic
205	C₂×C₇₁	#2916	1	1	yes	characteristic
206	#2965	—	71	1	no	—
207	#2925	—	71	1	no	—
208	#2906	D₇₁	1	1	yes	characteristic
209	#1574	—	71	2	no	—
210	#1573	—	71	2	no	—
211	#1571	—	71	1	no	—
212	#1570	—	71	1	no	—
213	#1569	—	71	2	no	—
214	#1567	—	71	1	no	—
215	#1565	—	71	2	no	—
216	C₂×#334	—	71	1	no	—
217	C₇₁	#17830	1	1	yes	characteristic, complemented, Sylow
218	C₂×#131	—	2	1	no	—
219	C₄×#41	C₂×D₇₁	1	1	yes	characteristic
220	#446	—	71	1	no	—
221	#446	—	71	1	no	—
222	#436	—	71	1	no	—
223	#436	—	71	1	no	—
224	#435	—	71	2	no	—
225	#435	—	71	2	no	—
226	#433	—	142	2	no	—
227	#432	—	71	2	no	—
228	#431	—	71	1	no	—
229	#431	—	71	2	no	—
230	#431	—	71	2	no	—
231	#424	—	2	1	no	—
232	#424	—	2	2	no	—
233	#423	—	71	1	no	—
234	#423	C₂×D₇₁	1	1	yes	characteristic
235	#423	C₂×D₇₁	1	2	yes	—
236	C₂×C₄⋊C₈	—	71	1	no	—
237	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂×D₇₁	1	2	yes	—
239	#408	—	142	1	no	—
240	#405	—	142	1	no	—
241	C₄×M₁₆	—	71	2	no	—
242	C₂×C₄×C₈	—	71	1	no	—
243	#335	—	71	2	no	—
244	#335	—	71	2	no	—
245	#335	—	71	2	no	—
246	#335	—	71	2	no	—
247	#334	—	71	1	no	—
248	#334	—	71	1	no	—
249	#334	—	71	1	no	—
250	#334	—	71	1	no	—
251	#334	—	71	2	no	—
252	#334	—	71	2	no	—
253	C₂×#41	C₂²⋊D₇₁	1	1	yes	characteristic
254	#131	—	4	4	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	71	2	no	—
258	C₂×M₁₆	—	71	2	no	—
259	C₂×M₁₆	—	142	1	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	71	1	no	—
263	C₂²×C₈	—	71	1	no	—
264	C₂²×C₈	—	142	1	no	—
265	C₄×Q₈	Dic₁₄₂	1	1	yes	characteristic
266	C₄×Q₈	C₄×D₇₁	1	1	yes	characteristic
267	C₄×D₄	Dic₁₄₂	1	2	yes	—
268	C₄×D₄	Dic₁₄₂	1	1	yes	characteristic
269	C₄×D₄	C₄×D₇₁	1	2	yes	—
270	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
271	#117	C₂²⋊D₇₁	1	1	yes	characteristic
272	#117	C₂²⋊D₇₁	1	2	yes	—
273	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₇₁	1	2	yes	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	71	2	no	—
280	C₄⋊C₈	—	71	2	no	—
281	C₄⋊C₈	—	71	1	no	—
282	C₄⋊C₈	—	71	1	no	—
283	C₄⋊C₈	—	71	1	no	—
284	C₄⋊C₈	—	71	1	no	—
285	C₄⋊C₈	—	71	2	no	—
286	C₄⋊C₈	—	142	1	no	—
287	C₄⋊C₈	—	142	1	no	—
288	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₇₁	1	2	yes	—
291	C₂²⋊C₈	—	71	2	no	—
292	C₂²⋊C₈	—	71	2	no	—
293	C₂²⋊C₈	—	71	2	no	—
294	C₂²⋊C₈	—	142	2	no	—
295	C₂²⋊C₈	—	142	2	no	—
296	#97	—	71	2	no	—
297	#97	—	71	2	no	—
298	#97	—	142	2	no	—
299	C₄×C₈	—	71	1	no	—
300	C₄×C₈	—	71	1	no	—
301	C₄×C₈	—	71	1	no	—
302	C₄×C₈	—	71	1	no	—
303	C₄×C₈	—	71	2	no	—
304	C₄×C₈	—	142	2	no	—
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	C₂×Q₈	Dic₇₁⋊C₄	1	1	yes	characteristic
308	C₂×D₄	Dic₇₁⋊C₄	1	2	yes	—
309	C₂×D₄	Dic₇₁⋊C₄	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₇₁	1	2	yes	—
312	C₂²×C₄	C₂×C₂²⋊D₇₁	1	2	yes	—
313	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×Dic₁₄₂	1	2	yes	—
315	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
316	M₁₆	—	4	4	no	—
317	M₁₆	—	4	2	no	—
318	M₁₆	—	284	2	no	—
319	M₁₆	—	284	2	no	—
320	M₁₆	—	142	4	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	4	4	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	—	284	2	no	—
327	C₂×C₈	—	284	1	no	—
328	C₂×C₈	—	71	1	no	—
329	C₂×C₈	—	71	1	no	—
330	C₂×C₈	—	71	1	no	—
331	C₂×C₈	—	71	1	no	—
332	C₂×C₈	—	71	2	no	—
333	C₂×C₈	—	71	2	no	—
334	C₂×C₈	—	142	1	no	—
335	C₂×C₈	—	142	2	no	—
336	C₂×C₈	—	142	1	no	—
337	C₂×C₈	—	142	2	no	—
338	C₄⋊C₄	Dic₇₁⋊C₄	1	2	yes	—
339	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
340	C₄⋊C₄	Dic₇₁⋊C₄	1	2	yes	—
341	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
342	C₂²⋊C₄	Dic₇₁⋊C₄	1	2	yes	—
343	C₂²⋊C₄	Dic₇₁⋊C₄	1	2	yes	—
344	C₂²⋊C₄	Dic₇₁⋊C₄	1	2	yes	—
345	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
346	C₄²	C₂×C₄×D₇₁	1	2	yes	—
347	C₄²	C₂×C₂²⋊D₇₁	1	2	yes	—
348	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
349	C₄²	C₂×Dic₁₄₂	1	2	yes	—
350	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
351	C₄²	C₂³×D₇₁	1	1	yes	characteristic
352	C₂³	C₂×Dic₇₁⋊C₄	1	2	yes	—
353	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
366	C₂×C₄	C₂×Dic₇₁⋊C₄	1	2	yes	—
367	C₂×C₄	C₂×Dic₇₁⋊C₄	1	2	yes	—
368	C₂×C₄	C₂×Dic₇₁⋊C₄	1	2	yes	—
369	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
370	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
371	C₂×C₄	#14556154	1	2	yes	—
372	C₂×C₄	#14556159	1	2	yes	—
373	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₇₁	1	1	yes	characteristic
375	C₂×C₄	C₂²×Dic₁₄₂	1	1	yes	characteristic
376	C₈	—	4	1	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	1	no	—
379	C₈	—	284	2	no	—
380	C₈	—	284	1	no	—
381	C₈	—	284	1	no	—
382	C₈	—	71	2	no	—
383	C₈	—	142	1	no	—
384	C₈	—	142	2	no	—
385	C₈	—	142	1	no	—
386	C₈	—	142	1	no	—
387	C₈	—	142	2	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	#17986039	1	2	yes	—
394	C₂²	C₂²×Dic₇₁⋊C₄	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	#17986039	1	2	yes	—
402	C₄	#131×D₇₁	1	1	yes	characteristic
403	C₄	#17986764	1	1	yes	characteristic
404	C₄	C₂×#14556154	1	1	yes	characteristic
405	C₄	C₂×#14556159	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	4	2	no	—
408	C₂	#22596906	1	1	yes	characteristic
409	C₂	C₂×#17986039	1	1	yes	characteristic
410	C₂	#22596949	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₇₁×#2906	C₂
socle	C₂²×C₇₁	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₇₁	D₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#2906	D₇₁
hypocenter	C₇₁	#17830
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2906

Complements

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

N	H ≅ G/N	type
3. #22587131	C₂	semidirect
4. #22587123	C₂	semidirect
5. #22587114	C₂	semidirect
6. #22587112	C₂	semidirect
7. #22587105	C₂	semidirect
8. #22587098	C₂	semidirect
9. #22587090	C₂	semidirect
10. C₂×#17985749	C₂	semidirect
181. C₇₁⋊C₈	#131	semidirect
217. C₇₁	#17830	semidirect

Maximal subgroups

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

subgroup	index
#22597307	2
#22597006	2
#22587131	2
#22587123	2
#22587114	2
#22587112	2
#22587105	2
#22587098	2
#22587090	2
C₂×#17985749	2
C₇₁×#2906	2
#17830	71