Subgroups — #31903169

Order 18176.

734 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₇₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#17985763	C₂	1	1	yes	maximal, characteristic
3	#22588056	C₂	1	1	yes	maximal, characteristic
4	C₂×#17985760	C₂	1	1	yes	maximal, characteristic
5	C₂×#17985758	C₂	1	1	yes	maximal, characteristic
6	#22588036	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1729	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	C₂²×C₄×Dic₇₁	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₇₁	—	2	2	no	—
13	C₂×C₈×Dic₇₁	—	2	2	no	—
14	C₂×C₈×Dic₇₁	C₄	1	4	yes	complemented
15	#17985763	C₄	1	4	yes	complemented
16	#17985761	C₄	1	4	yes	complemented
17	#17985760	—	2	2	no	—
18	#17985758	—	2	2	no	—
19	#17985753	—	2	2	no	—
20	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic
22	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
23	#336×C₇₁	—	2	2	no	—
24	C₂³×Dic₇₁	—	2	1	no	—
25	C₂×#11765849	—	2	1	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	C₂×C₄	1	2	yes	—
31	C₂²×C₇₁⋊C₈	—	2	1	no	—
32	C₂²×C₇₁⋊C₈	—	2	1	no	—
33	C₂²×C₇₁⋊C₈	—	2	1	no	—
34	C₂²×C₇₁⋊C₈	—	2	1	no	—
35	C₂²×C₇₁⋊C₈	—	2	1	no	—
36	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
37	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
38	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
39	#14556087	—	2	1	no	—
40	#14556087	—	2	1	no	—
41	#14556087	—	2	1	no	—
42	#14556087	—	2	1	no	—
43	C₂×C₄⋊Dic₇₁	C₂×C₄	1	2	yes	—
44	C₂×C₂²⋊Dic₇₁	—	2	1	no	—
45	C₂×C₄×Dic₇₁	—	2	1	no	—
46	C₂×C₄×Dic₇₁	—	2	1	no	—
47	C₂×C₄×Dic₇₁	—	2	1	no	—
48	C₂×C₄×Dic₇₁	—	2	1	no	—
49	C₂×C₄×Dic₇₁	C₂×C₄	1	2	yes	—
50	C₂×C₄×Dic₇₁	D₄	1	2	yes	—
51	C₂×C₄×Dic₇₁	D₄	1	2	yes	—
52	C₈×Dic₇₁	—	2	8	no	—
53	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₇₁	—	2	1	no	—
55	C₂×M₁₆×C₇₁	—	2	1	no	—
56	C₂×M₁₆×C₇₁	—	2	1	no	—
57	C₂×M₁₆×C₇₁	—	2	1	no	—
58	C₂×M₁₆×C₇₁	—	2	1	no	—
59	C₂×M₁₆×C₇₁	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₇₁	—	2	1	no	—
61	C₂²×C₈×C₇₁	—	2	1	no	—
62	C₂²×C₈×C₇₁	—	2	1	no	—
63	C₂²×C₈×C₇₁	—	2	1	no	—
64	C₂²×C₈×C₇₁	—	2	1	no	—
65	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₇₁	D₄	1	2	yes	—
67	C₂²×C₈×C₇₁	Q₈	1	2	yes	—
68	#117×C₇₁	—	2	1	no	—
69	#117×C₇₁	—	2	1	no	—
70	#117×C₇₁	—	2	1	no	—
71	#117×C₇₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
74	C₂×C₄²×C₇₁	—	2	1	no	—
75	C₂²×Dic₇₁	—	2	8	no	—
76	C₂²×Dic₇₁	—	2	2	no	—
77	C₂²×Dic₇₁	—	2	2	no	—
78	C₂²×Dic₇₁	—	2	2	no	—
79	C₂²×Dic₇₁	—	2	2	no	—
80	#11765849	—	2	2	no	—
81	#11765849	—	2	2	no	—
82	#11765849	—	4	1	no	—
83	#11765849	—	4	1	no	—
84	C₂×C₇₁⋊C₈	—	2	2	no	—
85	C₂×C₇₁⋊C₈	—	2	2	no	—
86	C₂×C₇₁⋊C₈	—	2	2	no	—
87	C₂×C₇₁⋊C₈	—	2	2	no	—
88	C₂×C₇₁⋊C₈	—	2	2	no	—
89	C₂×C₇₁⋊C₈	—	2	2	no	—
90	C₂×C₇₁⋊C₈	—	2	2	no	—
91	C₂×C₇₁⋊C₈	—	4	1	no	—
92	C₂×C₇₁⋊C₈	—	4	1	no	—
93	C₂×C₇₁⋊C₈	C₄²	1	4	yes	—
94	C₄⋊Dic₇₁	—	2	2	no	—
95	C₄⋊Dic₇₁	—	2	2	no	—
96	C₂²⋊Dic₇₁	—	4	1	no	—
97	C₂²⋊Dic₇₁	—	4	1	no	—
98	C₄×Dic₇₁	—	2	2	no	—
99	C₄×Dic₇₁	—	2	2	no	—
100	C₄×Dic₇₁	—	2	2	no	—
101	C₄×Dic₇₁	—	4	1	no	—
102	C₄×Dic₇₁	—	4	1	no	—
103	C₄×Dic₇₁	C₂²⋊C₄	1	4	yes	—
104	C₂⁴×C₇₁	#41	1	1	yes	characteristic
105	C₂²×C₄×C₇₁	—	2	2	no	—
106	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
114	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
115	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
116	C₂²×C₄×C₇₁	#41	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	M₁₆×C₇₁	—	2	2	no	—
121	M₁₆×C₇₁	—	2	2	no	—
122	M₁₆×C₇₁	—	4	1	no	—
123	M₁₆×C₇₁	—	4	1	no	—
124	C₂×C₈×C₇₁	—	2	2	no	—
125	C₂×C₈×C₇₁	—	2	2	no	—
126	C₂×C₈×C₇₁	—	2	2	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	C₄⋊C₄	1	4	yes	—
134	C₄⋊C₄×C₇₁	—	2	2	no	—
135	C₄⋊C₄×C₇₁	—	2	2	no	—
136	C₂²⋊C₄×C₇₁	—	4	1	no	—
137	C₂²⋊C₄×C₇₁	—	4	1	no	—
138	C₄²×C₇₁	—	4	1	no	—
139	C₄²×C₇₁	—	4	1	no	—
140	C₂³×C₇₁	—	2	4	no	—
141	C₂³×C₇₁	#117	1	1	yes	characteristic
142	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
143	C₂³×C₇₁	C₄×Q₈	1	1	yes	characteristic
144	C₂³×C₇₁	#123	1	1	yes	characteristic
145	C₂³×C₇₁	#123	1	1	yes	characteristic
146	C₂³×C₇₁	#126	1	1	yes	characteristic
147	C₂³×C₇₁	#126	1	1	yes	characteristic
148	C₂×C₄×C₇₁	—	4	2	no	—
149	C₂×C₄×C₇₁	—	4	4	no	—
150	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
154	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
155	C₂×C₄×C₇₁	#117	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	#117	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×Q₈	1	1	yes	characteristic
166	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
167	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
168	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
171	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
172	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
173	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
174	C₂×C₄×C₇₁	#125	1	1	yes	characteristic
175	C₂×C₄×C₇₁	#125	1	1	yes	characteristic
176	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
177	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
178	C₂×Dic₇₁	—	2	8	no	—
179	C₂×Dic₇₁	—	2	8	no	—
180	C₂×Dic₇₁	—	2	8	no	—
181	C₂×Dic₇₁	—	2	4	no	—
182	C₂×Dic₇₁	—	4	2	no	—
183	C₂×Dic₇₁	—	4	4	no	—
184	C₈×C₇₁	—	2	4	no	—
185	C₈×C₇₁	—	4	2	no	—
186	C₇₁⋊C₈	—	2	4	no	—
187	C₇₁⋊C₈	—	4	2	no	—
188	C₂²×C₇₁	—	2	2	no	—
189	C₂²×C₇₁	—	2	2	no	—
190	C₂²×C₇₁	—	2	2	no	—
191	C₂²×C₇₁	—	2	2	no	—
192	C₂²×C₇₁	—	2	2	no	—
193	C₂²×C₇₁	—	2	2	no	—
194	C₂²×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
195	C₂²×C₇₁	#381	1	1	yes	characteristic
196	C₂²×C₇₁	#383	1	1	yes	characteristic
197	C₂²×C₇₁	#387	1	1	yes	characteristic
198	C₂²×C₇₁	#387	1	1	yes	characteristic
199	C₂²×C₇₁	#388	1	1	yes	characteristic
200	C₂²×C₇₁	#388	1	1	yes	characteristic
201	C₂²×C₇₁	#443	1	4	yes	—
202	C₄×C₇₁	—	8	2	no	—
203	C₄×C₇₁	#376	1	1	yes	characteristic
204	C₄×C₇₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
205	C₄×C₇₁	#380	1	1	yes	characteristic
206	C₄×C₇₁	#382	1	1	yes	characteristic
207	C₄×C₇₁	#387	1	1	yes	characteristic
208	C₄×C₇₁	#387	1	1	yes	characteristic
209	C₄×C₇₁	#388	1	1	yes	characteristic
210	C₄×C₇₁	#388	1	1	yes	characteristic
211	Dic₇₁	—	2	8	no	—
212	Dic₇₁	—	8	2	no	—
213	#10818	—	71	1	no	maximal, Sylow
214	C₂×C₇₁	—	2	1	no	—
215	C₂×C₇₁	—	2	1	no	—
216	C₂×C₇₁	—	2	1	no	—
217	C₂×C₇₁	—	2	1	no	—
218	C₂×C₇₁	#1434	1	1	yes	characteristic
219	C₂×C₇₁	#1772	1	2	yes	—
220	C₂×C₇₁	#1937	1	2	yes	—
221	C₂×C₇₁	#1937	1	2	yes	—
222	C₂²×C₄×C₈	—	71	1	no	—
223	C₂×#341	—	71	1	no	—
224	#1735	—	71	1	no	—
225	C₂×#339	—	71	1	no	—
226	C₂×#339	—	71	1	no	—
227	#1729	—	71	1	no	—
228	#1729	D₇₁	1	1	yes	characteristic
229	C₇₁	#10818	1	1	yes	characteristic, complemented, Sylow
230	C₂²×M₁₆	—	71	1	no	—
231	C₂²×M₁₆	C₂×D₇₁	1	1	yes	characteristic
232	C₂³×C₈	—	71	1	no	—
233	C₂³×C₈	C₂×D₇₁	1	1	yes	characteristic
234	C₂×#117	—	71	1	no	—
235	C₂×#117	C₂×D₇₁	1	1	yes	characteristic
236	C₂²×C₄²	—	71	1	no	—
237	C₂×C₄×C₈	—	71	4	no	—
238	C₂×C₄×C₈	—	142	2	no	—
239	C₂×C₄×C₈	—	142	2	no	—
240	#341	—	71	4	no	—
241	#340	—	71	4	no	—
242	#339	—	142	2	no	—
243	#339	—	142	2	no	—
244	#336	—	2	2	no	—
245	#336	—	142	2	no	—
246	C₂³×C₄	—	142	1	no	—
247	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	71	2	no	—
254	C₂×M₁₆	—	142	1	no	—
255	C₂×M₁₆	—	142	1	no	—
256	C₂×M₁₆	—	142	1	no	—
257	C₂×M₁₆	—	142	1	no	—
258	C₂×M₁₆	—	142	1	no	—
259	C₂×M₁₆	C₄×D₇₁	1	2	yes	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	71	2	no	—
266	C₂²×C₈	—	71	2	no	—
267	C₂²×C₈	—	71	2	no	—
268	C₂²×C₈	—	142	1	no	—
269	C₂²×C₈	—	142	1	no	—
270	C₂²×C₈	—	142	1	no	—
271	C₂²×C₈	—	142	1	no	—
272	C₂²×C₈	—	142	1	no	—
273	C₂²×C₈	Dic₁₄₂	1	2	yes	—
274	C₂²×C₈	C₄×D₇₁	1	2	yes	—
275	C₂²×C₈	C₂²⋊D₇₁	1	2	yes	—
276	#117	—	2	1	no	—
277	#117	—	2	1	no	—
278	#117	—	2	1	no	—
279	#117	—	2	1	no	—
280	#117	—	142	1	no	—
281	#117	—	142	1	no	—
282	#117	—	142	1	no	—
283	#117	—	142	1	no	—
284	C₂×C₄⋊C₄	—	71	2	no	—
285	C₂×C₄⋊C₄	C₄×D₇₁	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	142	1	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	71	2	no	—
290	C₂×C₄²	—	71	2	no	—
291	C₂×C₄²	—	71	2	no	—
292	C₂×C₄²	—	142	1	no	—
293	C₂×C₄²	—	142	1	no	—
294	C₂×C₄²	—	142	1	no	—
295	C₂×C₄²	—	142	1	no	—
296	C₄×C₈	—	142	8	no	—
297	C₂⁴	#11765865	1	1	yes	characteristic
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	142	2	no	—
300	C₂²×C₄	—	142	8	no	—
301	C₂²×C₄	—	142	2	no	—
302	C₂²×C₄	—	142	2	no	—
303	C₂²×C₄	—	142	2	no	—
304	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
307	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
310	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
311	C₂²×C₄	#11765864	1	1	yes	characteristic
312	C₂²×C₄	#11765864	1	1	yes	characteristic
313	C₂²×C₄	#11765864	1	1	yes	characteristic
314	C₂²×C₄	#11765864	1	1	yes	characteristic
315	C₂²×C₄	#11765865	1	1	yes	characteristic
316	C₂²×C₄	#11765866	1	1	yes	characteristic
317	C₂²×C₄	#11765866	1	1	yes	characteristic
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	4	1	no	—
321	M₁₆	—	4	1	no	—
322	M₁₆	—	284	1	no	—
323	M₁₆	—	284	1	no	—
324	M₁₆	—	142	2	no	—
325	M₁₆	—	142	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	284	1	no	—
336	C₂×C₈	—	284	1	no	—
337	C₂×C₈	—	71	4	no	—
338	C₂×C₈	—	142	2	no	—
339	C₂×C₈	—	142	2	no	—
340	C₂×C₈	—	142	2	no	—
341	C₂×C₈	—	142	2	no	—
342	C₂×C₈	—	142	2	no	—
343	C₂×C₈	—	142	2	no	—
344	C₂×C₈	—	142	2	no	—
345	C₂×C₈	Dic₇₁⋊C₄	1	4	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	142	2	no	—
349	C₄⋊C₄	—	142	2	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	284	1	no	—
353	C₂²⋊C₄	—	284	1	no	—
354	C₄²	—	4	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	—	284	1	no	—
357	C₄²	—	284	1	no	—
358	C₄²	—	71	4	no	—
359	C₄²	—	142	2	no	—
360	C₄²	—	142	2	no	—
361	C₄²	—	142	2	no	—
362	C₂³	—	2	4	no	—
363	C₂³	#14556085	1	1	yes	characteristic
364	C₂³	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
365	C₂³	C₄×Dic₁₄₂	1	1	yes	characteristic
366	C₂³	#14556110	1	1	yes	characteristic
367	C₂³	#14556113	1	1	yes	characteristic
368	C₂³	#14556121	1	1	yes	characteristic
369	C₂³	#14556123	1	1	yes	characteristic
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	284	4	no	—
373	C₂×C₄	—	284	2	no	—
374	C₂×C₄	—	142	8	no	—
375	C₂×C₄	—	142	8	no	—
376	C₂×C₄	—	142	8	no	—
377	C₂×C₄	—	142	4	no	—
378	C₂×C₄	C₄²×D₇₁	1	1	yes	characteristic
379	C₂×C₄	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
380	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
381	C₂×C₄	#14556084	1	1	yes	characteristic
382	C₂×C₄	#14556084	1	1	yes	characteristic
383	C₂×C₄	#14556084	1	1	yes	characteristic
384	C₂×C₄	#14556086	1	1	yes	characteristic
385	C₂×C₄	#14556086	1	1	yes	characteristic
386	C₂×C₄	#14556086	1	1	yes	characteristic
387	C₂×C₄	#14556086	1	1	yes	characteristic
388	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
389	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
390	C₂×C₄	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
391	C₂×C₄	#14556090	1	1	yes	characteristic
392	C₂×C₄	#14556090	1	1	yes	characteristic
393	C₂×C₄	C₄×Dic₁₄₂	1	1	yes	characteristic
394	C₂×C₄	#14556100	1	1	yes	characteristic
395	C₂×C₄	#14556100	1	1	yes	characteristic
396	C₂×C₄	#14556105	1	1	yes	characteristic
397	C₂×C₄	#14556105	1	1	yes	characteristic
398	C₂×C₄	#14556110	1	1	yes	characteristic
399	C₂×C₄	#14556113	1	1	yes	characteristic
400	C₂×C₄	#14556115	1	1	yes	characteristic
401	C₂×C₄	#14556117	1	1	yes	characteristic
402	C₂×C₄	#14556119	1	1	yes	characteristic
403	C₂×C₄	#14556119	1	1	yes	characteristic
404	C₂×C₄	#14556121	1	1	yes	characteristic
405	C₂×C₄	#14556123	1	1	yes	characteristic
406	C₈	—	2	4	no	—
407	C₈	—	4	2	no	—
408	C₈	—	284	2	no	—
409	C₈	—	142	4	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	C₄×Dic₇₁⋊C₄	1	1	yes	characteristic
417	C₂²	#17985861	1	1	yes	characteristic
418	C₂²	#17985866	1	1	yes	characteristic
419	C₂²	#17985882	1	1	yes	characteristic
420	C₂²	#17985886	1	1	yes	characteristic
421	C₂²	#17985889	1	1	yes	characteristic
422	C₂²	#17985893	1	1	yes	characteristic
423	C₂²	#17986114	1	4	yes	—
424	C₄	—	8	2	no	—
425	C₄	—	568	2	no	—
426	C₄	—	142	8	no	—
427	C₄	#17985844	1	1	yes	characteristic
428	C₄	#17985846	1	1	yes	characteristic
429	C₄	#17985857	1	1	yes	characteristic
430	C₄	#17985864	1	1	yes	characteristic
431	C₄	#17985882	1	1	yes	characteristic
432	C₄	#17985886	1	1	yes	characteristic
433	C₄	#17985889	1	1	yes	characteristic
434	C₄	#17985893	1	1	yes	characteristic
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	2	1	no	—
439	C₂	#22586566	1	1	yes	characteristic
440	C₂	#22588220	1	2	yes	—
441	C₂	#22589043	1	2	yes	—
442	C₂	#22589047	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₇₁
commutator	C₂×C₄×C₇₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₁
Fitting	C₇₁×#1729	C₂
socle	C₂³×C₇₁	C₄×D₄
prime radical	C₂⁴×C₇₁	#41
cosocle	C₂³×C₄×C₇₁	C₂³
hypercenter	#1729	D₇₁
hypocenter	C₇₁	#10818
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ #1729

Complements

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

N	H ≅ G/N	type
14. C₂×C₈×Dic₇₁	C₄	semidirect
15. #17985763	C₄	semidirect
16. #17985761	C₄	semidirect
229. C₇₁	#10818	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₇₁	2
C₂×#17985763	2
#22588056	2
C₂×#17985760	2
C₂×#17985758	2
#22588036	2
C₇₁×#1729	2
#10818	71