Subgroups — #31903574

Order 18176.

670 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17986047	C₂	1	1	yes	maximal, characteristic
2	#22596759	C₂	1	1	yes	maximal, characteristic
3	#22588079	C₂	1	1	yes	maximal, characteristic
4	#22588066	C₂	1	1	yes	maximal, characteristic
5	C₂×#17985764	C₂	1	1	yes	maximal, characteristic
6	C₂×#17985764	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1729	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11765849	C₂²	1	1	yes	characteristic
9	C₂²×#11765849	C₂²	1	1	yes	characteristic
10	C₂²×#11765849	C₂²	1	1	yes	characteristic
11	C₂²×#11765849	C₂²	1	1	yes	characteristic
12	#17986047	—	2	2	no	—
13	#17986047	C₄	1	4	yes	complemented
14	C₂×#14556063	—	2	2	no	—
15	#17985955	—	2	2	no	—
16	#17985955	—	2	2	no	—
17	C₄×#11765849	—	2	2	no	—
18	#17985768	C₄	1	4	yes	—
19	#17985764	—	2	2	no	—
20	#17985764	C₄	1	4	yes	complemented
21	#17985763	—	2	2	no	—
22	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic
24	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
25	#336×C₇₁	—	2	2	no	—
26	C₂×#11765849	—	2	1	no	—
27	C₂×#11765849	—	2	1	no	—
28	C₂×#11765849	—	2	1	no	—
29	C₂×#11765849	—	2	1	no	—
30	C₂×#11765849	—	2	1	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	—	2	1	no	—
37	C₂×#11765849	—	2	1	no	—
38	C₂×#11765849	—	2	1	no	—
39	C₂×#11765849	—	2	1	no	—
40	C₂×#11765849	C₂×C₄	1	2	yes	—
41	C₂×#11765849	C₂×C₄	1	2	yes	—
42	C₂×#11765849	C₂×C₄	1	2	yes	—
43	C₂×#11765849	C₂×C₄	1	2	yes	—
44	C₂×#11765849	C₂×C₄	1	2	yes	—
45	C₂×#11765849	C₂×C₄	1	2	yes	—
46	C₂×#11765849	D₄	1	2	yes	—
47	C₂×#11765849	D₄	1	2	yes	—
48	C₂×#11765849	D₄	1	2	yes	—
49	C₂×#11765849	Q₈	1	2	yes	—
50	C₂²×C₇₁⋊C₈	—	2	1	no	—
51	C₂²×C₇₁⋊C₈	—	2	1	no	—
52	C₂²×C₇₁⋊C₈	—	2	1	no	—
53	C₂²×C₇₁⋊C₈	—	2	1	no	—
54	#14556063	—	2	8	no	—
55	#14556039	—	2	4	no	—
56	C₄×C₇₁⋊C₈	—	2	4	no	—
57	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₇₁	—	2	1	no	—
59	C₂×M₁₆×C₇₁	—	2	1	no	—
60	C₂×M₁₆×C₇₁	—	2	1	no	—
61	C₂×M₁₆×C₇₁	—	2	1	no	—
62	C₂×M₁₆×C₇₁	—	2	1	no	—
63	C₂×M₁₆×C₇₁	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₇₁	—	2	1	no	—
65	C₂²×C₈×C₇₁	—	2	1	no	—
66	C₂²×C₈×C₇₁	—	2	1	no	—
67	C₂²×C₈×C₇₁	—	2	1	no	—
68	C₂²×C₈×C₇₁	—	2	1	no	—
69	C₂²×C₈×C₇₁	—	2	1	no	—
70	C₂²×C₈×C₇₁	—	2	1	no	—
71	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
72	#117×C₇₁	—	2	1	no	—
73	#117×C₇₁	—	2	1	no	—
74	#117×C₇₁	—	2	1	no	—
75	#117×C₇₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊C₄×C₇₁	Q₈	1	2	yes	—
78	C₂×C₄²×C₇₁	D₄	1	2	yes	—
79	#11765849	—	2	2	no	—
80	#11765849	—	2	2	no	—
81	#11765849	—	2	2	no	—
82	#11765849	—	2	2	no	—
83	#11765849	—	2	2	no	—
84	#11765849	—	2	2	no	—
85	#11765849	—	2	2	no	—
86	#11765849	—	2	2	no	—
87	#11765849	—	2	2	no	—
88	#11765849	—	2	2	no	—
89	#11765849	—	2	2	no	—
90	#11765849	—	4	1	no	—
91	#11765849	—	4	1	no	—
92	#11765849	C₄²	1	4	yes	—
93	#11765849	C₂²⋊C₄	1	4	yes	—
94	#11765849	C₄⋊C₄	1	4	yes	—
95	C₂×C₇₁⋊C₈	—	2	2	no	—
96	C₂×C₇₁⋊C₈	—	2	2	no	—
97	C₂×C₇₁⋊C₈	—	2	2	no	—
98	C₂×C₇₁⋊C₈	—	2	2	no	—
99	C₂×C₇₁⋊C₈	—	2	2	no	—
100	C₂×C₇₁⋊C₈	—	2	2	no	—
101	C₂×C₇₁⋊C₈	—	2	2	no	—
102	C₂×C₇₁⋊C₈	—	2	2	no	—
103	C₂×C₇₁⋊C₈	—	2	2	no	—
104	C₂×C₇₁⋊C₈	—	2	2	no	—
105	C₂×C₇₁⋊C₈	—	4	1	no	—
106	C₂×C₇₁⋊C₈	—	4	1	no	—
107	C₂⁴×C₇₁	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₄×C₇₁	C₄⋊C₄	1	4	yes	—
109	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
118	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
119	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
120	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
121	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
122	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
123	M₁₆×C₇₁	—	2	2	no	—
124	M₁₆×C₇₁	—	2	2	no	—
125	M₁₆×C₇₁	—	4	1	no	—
126	M₁₆×C₇₁	—	4	1	no	—
127	C₂×C₈×C₇₁	—	2	2	no	—
128	C₂×C₈×C₇₁	—	2	2	no	—
129	C₂×C₈×C₇₁	—	2	2	no	—
130	C₂×C₈×C₇₁	—	2	2	no	—
131	C₂×C₈×C₇₁	—	4	1	no	—
132	C₂×C₈×C₇₁	—	4	1	no	—
133	C₂×C₈×C₇₁	—	4	1	no	—
134	C₂×C₈×C₇₁	—	4	1	no	—
135	C₂×C₈×C₇₁	—	4	1	no	—
136	C₂×C₈×C₇₁	—	4	1	no	—
137	C₄⋊C₄×C₇₁	—	2	2	no	—
138	C₄⋊C₄×C₇₁	—	2	2	no	—
139	C₂²⋊C₄×C₇₁	—	2	2	no	—
140	C₂²⋊C₄×C₇₁	—	2	2	no	—
141	C₄²×C₇₁	—	2	2	no	—
142	C₄²×C₇₁	—	2	2	no	—
143	C₂³×C₇₁	—	4	2	no	—
144	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂³×C₇₁	C₄×Q₈	1	1	yes	characteristic
146	C₂³×C₇₁	C₄×Q₈	1	1	yes	characteristic
147	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂³×C₇₁	#125	1	1	yes	characteristic
150	C₂³×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₇₁	—	2	4	no	—
152	C₂×C₄×C₇₁	—	4	4	no	—
153	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
157	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
158	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
159	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
170	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
171	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
172	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
173	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
174	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
175	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
176	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
177	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
178	C₂×C₄×C₇₁	#125	1	1	yes	characteristic
179	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
180	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
181	C₈×C₇₁	—	4	2	no	—
182	C₈×C₇₁	—	4	2	no	—
183	C₇₁⋊C₈	—	2	4	no	—
184	C₇₁⋊C₈	—	2	4	no	—
185	C₇₁⋊C₈	—	2	4	no	—
186	C₇₁⋊C₈	—	4	2	no	—
187	C₂²×C₇₁	—	2	2	no	—
188	C₂²×C₇₁	—	2	2	no	—
189	C₂²×C₇₁	—	2	2	no	—
190	C₂²×C₇₁	—	4	1	no	—
191	C₂²×C₇₁	—	4	1	no	—
192	C₂²×C₇₁	—	4	1	no	—
193	C₂²×C₇₁	—	4	1	no	—
194	C₂²×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
195	C₂²×C₇₁	#385	1	1	yes	characteristic
196	C₂²×C₇₁	#387	1	1	yes	characteristic
197	C₂²×C₇₁	#387	1	1	yes	characteristic
198	C₂²×C₇₁	#389	1	1	yes	characteristic
199	C₂²×C₇₁	#389	1	1	yes	characteristic
200	C₂²×C₇₁	#391	1	1	yes	characteristic
201	C₄×C₇₁	—	4	4	no	—
202	C₄×C₇₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
203	C₄×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
204	C₄×C₇₁	#385	1	1	yes	characteristic
205	C₄×C₇₁	#386	1	1	yes	characteristic
206	C₄×C₇₁	#387	1	1	yes	characteristic
207	C₄×C₇₁	#387	1	1	yes	characteristic
208	C₄×C₇₁	#388	1	1	yes	characteristic
209	C₄×C₇₁	#388	1	1	yes	characteristic
210	#10902	—	71	1	no	maximal, Sylow
211	C₂×C₇₁	—	2	1	no	—
212	C₂×C₇₁	—	2	1	no	—
213	C₂×C₇₁	—	2	1	no	—
214	C₂×C₇₁	—	2	1	no	—
215	C₂×C₇₁	—	2	1	no	—
216	C₂×C₇₁	—	2	1	no	—
217	C₂×C₇₁	#1436	1	1	yes	characteristic
218	C₂×C₇₁	#1858	1	2	yes	—
219	C₂×#430	—	71	1	no	—
220	#2873	—	71	1	no	—
221	#1742	—	71	1	no	—
222	#1738	—	71	1	no	—
223	C₂×#341	—	71	1	no	—
224	C₂×#341	—	71	1	no	—
225	#1729	D₇₁	1	1	yes	characteristic
226	C₇₁	#10902	1	1	yes	characteristic, complemented, Sylow
227	C₂²×M₁₆	—	71	1	no	—
228	C₂²×M₁₆	—	71	1	no	—
229	C₂²×M₁₆	—	71	1	no	—
230	C₂²×M₁₆	—	71	1	no	—
231	C₂²×M₁₆	C₂×D₇₁	1	1	yes	characteristic
232	C₂³×C₈	C₂×D₇₁	1	1	yes	characteristic
233	C₂×#117	C₂×D₇₁	1	1	yes	characteristic
234	#430	—	71	4	no	—
235	#430	—	142	2	no	—
236	C₂×#108	—	142	2	no	—
237	#405	—	142	2	no	—
238	#405	—	142	2	no	—
239	C₄×M₁₆	—	142	2	no	—
240	#343	—	71	4	no	—
241	#341	—	71	4	no	—
242	#341	—	142	2	no	—
243	#341	—	142	2	no	—
244	#336	—	2	2	no	—
245	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
246	C₂×M₁₆	—	2	1	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	71	2	no	—
252	C₂×M₁₆	—	71	2	no	—
253	C₂×M₁₆	—	71	2	no	—
254	C₂×M₁₆	—	71	2	no	—
255	C₂×M₁₆	—	71	2	no	—
256	C₂×M₁₆	—	71	2	no	—
257	C₂×M₁₆	—	71	2	no	—
258	C₂×M₁₆	—	71	2	no	—
259	C₂×M₁₆	—	71	2	no	—
260	C₂×M₁₆	—	71	2	no	—
261	C₂×M₁₆	—	142	1	no	—
262	C₂×M₁₆	—	142	1	no	—
263	C₂×M₁₆	—	142	1	no	—
264	C₂×M₁₆	—	142	1	no	—
265	C₂×M₁₆	—	142	1	no	—
266	C₂×M₁₆	—	142	1	no	—
267	C₂×M₁₆	—	142	1	no	—
268	C₂×M₁₆	—	142	1	no	—
269	C₂×M₁₆	—	142	1	no	—
270	C₂×M₁₆	—	142	1	no	—
271	C₂×M₁₆	—	142	1	no	—
272	C₂×M₁₆	—	142	1	no	—
273	C₂×M₁₆	—	142	1	no	—
274	C₂×M₁₆	—	142	1	no	—
275	C₂×M₁₆	C₄×D₇₁	1	2	yes	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	142	1	no	—
284	C₂²×C₈	—	142	1	no	—
285	C₂²×C₈	—	142	1	no	—
286	C₂²×C₈	—	142	1	no	—
287	C₂²×C₈	C₄×D₇₁	1	2	yes	—
288	#117	—	2	1	no	—
289	#117	—	2	1	no	—
290	#117	—	2	1	no	—
291	#117	—	2	1	no	—
292	C₂×C₄⋊C₄	C₄×D₇₁	1	2	yes	—
293	C₂×C₂²⋊C₄	Dic₁₄₂	1	2	yes	—
294	C₂×C₄²	C₂²⋊D₇₁	1	2	yes	—
295	#108	—	142	8	no	—
296	#97	—	142	4	no	—
297	C₄×C₈	—	142	4	no	—
298	C₂⁴	C₂×Dic₁₄₂	1	1	yes	characteristic
299	C₂²×C₄	Dic₇₁⋊C₄	1	4	yes	—
300	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
303	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
304	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
305	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
307	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
308	C₂²×C₄	#11765864	1	1	yes	characteristic
309	C₂²×C₄	#11765864	1	1	yes	characteristic
310	C₂²×C₄	#11765864	1	1	yes	characteristic
311	C₂²×C₄	#11765865	1	1	yes	characteristic
312	C₂²×C₄	#11765865	1	1	yes	characteristic
313	C₂²×C₄	#11765866	1	1	yes	characteristic
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	4	1	no	—
317	M₁₆	—	4	1	no	—
318	M₁₆	—	284	1	no	—
319	M₁₆	—	284	1	no	—
320	M₁₆	—	71	4	no	—
321	M₁₆	—	71	4	no	—
322	M₁₆	—	71	4	no	—
323	M₁₆	—	142	2	no	—
324	M₁₆	—	142	2	no	—
325	M₁₆	—	142	2	no	—
326	M₁₆	—	142	2	no	—
327	M₁₆	—	142	2	no	—
328	M₁₆	—	142	2	no	—
329	M₁₆	—	142	2	no	—
330	M₁₆	—	142	2	no	—
331	M₁₆	—	142	2	no	—
332	M₁₆	—	142	2	no	—
333	M₁₆	—	142	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	284	1	no	—
345	C₂×C₈	—	284	1	no	—
346	C₂×C₈	—	142	2	no	—
347	C₂×C₈	—	142	2	no	—
348	C₂×C₈	—	142	2	no	—
349	C₂×C₈	—	142	2	no	—
350	C₂×C₈	—	142	2	no	—
351	C₂×C₈	—	142	2	no	—
352	C₂×C₈	—	142	2	no	—
353	C₂×C₈	—	142	2	no	—
354	C₂×C₈	—	142	2	no	—
355	C₂×C₈	—	142	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
364	C₂³	C₄×Dic₁₄₂	1	1	yes	characteristic
365	C₂³	C₄×Dic₁₄₂	1	1	yes	characteristic
366	C₂³	#14556105	1	1	yes	characteristic
367	C₂³	#14556105	1	1	yes	characteristic
368	C₂³	#14556119	1	1	yes	characteristic
369	C₂³	#14556127	1	1	yes	characteristic
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	C₄²×D₇₁	1	1	yes	characteristic
373	C₂×C₄	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
374	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
375	C₂×C₄	#14556084	1	1	yes	characteristic
376	C₂×C₄	#14556085	1	1	yes	characteristic
377	C₂×C₄	#14556086	1	1	yes	characteristic
378	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
379	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
380	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
381	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
382	C₂×C₄	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
383	C₂×C₄	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
384	C₂×C₄	#14556090	1	1	yes	characteristic
385	C₂×C₄	#14556090	1	1	yes	characteristic
386	C₂×C₄	#14556093	1	1	yes	characteristic
387	C₂×C₄	#14556093	1	1	yes	characteristic
388	C₂×C₄	#14556096	1	1	yes	characteristic
389	C₂×C₄	#14556099	1	1	yes	characteristic
390	C₂×C₄	#14556101	1	1	yes	characteristic
391	C₂×C₄	#14556104	1	1	yes	characteristic
392	C₂×C₄	#14556106	1	1	yes	characteristic
393	C₂×C₄	#14556109	1	1	yes	characteristic
394	C₂×C₄	#14556110	1	1	yes	characteristic
395	C₂×C₄	#14556113	1	1	yes	characteristic
396	C₂×C₄	#14556114	1	1	yes	characteristic
397	C₂×C₄	#14556118	1	1	yes	characteristic
398	C₂×C₄	#14556121	1	1	yes	characteristic
399	C₂×C₄	#14556123	1	1	yes	characteristic
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₈	—	284	2	no	—
403	C₈	—	142	4	no	—
404	C₈	—	142	4	no	—
405	C₈	—	142	4	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	C₄×Dic₇₁⋊C₄	1	1	yes	characteristic
414	C₂²	#17985871	1	1	yes	characteristic
415	C₂²	#17985882	1	1	yes	characteristic
416	C₂²	#17985886	1	1	yes	characteristic
417	C₂²	#17985895	1	1	yes	characteristic
418	C₂²	#17985896	1	1	yes	characteristic
419	C₂²	#17985903	1	1	yes	characteristic
420	C₄	—	4	4	no	—
421	C₄	#17985846	1	1	yes	characteristic
422	C₄	#17985850	1	1	yes	characteristic
423	C₄	#17985870	1	1	yes	characteristic
424	C₄	#17985875	1	1	yes	characteristic
425	C₄	#17985880	1	1	yes	characteristic
426	C₄	#17985881	1	1	yes	characteristic
427	C₄	#17985887	1	1	yes	characteristic
428	C₄	#17985888	1	1	yes	characteristic
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	#22586571	1	1	yes	characteristic
436	C₂	#22588559	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#14556096
commutator	C₂×C₄×C₇₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₁
Fitting	C₇₁×#1729	C₂
socle	C₂²×C₇₁	#385
prime radical	C₂⁴×C₇₁	C₂×Q₈
cosocle	C₂³×C₄×C₇₁	C₂³
hypercenter	#1729	D₇₁
hypocenter	C₇₁	#10902
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1729

Complements

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

N	H ≅ G/N	type
13. #17986047	C₄	semidirect
20. #17985764	C₄	semidirect
226. C₇₁	#10902	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17986047	2
#22596759	2
#22588079	2
#22588066	2
C₂×#17985764	2
C₇₁×#1729	2
#10902	71