Subgroups — #31903460

Order 18176.

742 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17986025	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14556038	C₂	1	1	yes	maximal, characteristic
3	C₂×#17985763	C₂	1	1	yes	maximal, characteristic
4	#22588056	C₂	1	1	yes	maximal, characteristic
5	C₂×#17985760	C₂	1	1	yes	maximal, characteristic
6	C₂×#17985758	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	#17986025	—	2	2	no	—
13	#17986025	C₄	1	4	yes	complemented
14	C₂×Dic₇₁⋊C₈	—	2	2	no	—
15	C₂×#14556038	—	2	2	no	—
16	C₂×#14556038	—	2	2	no	—
17	C₂×#14556038	—	2	2	no	—
18	#17985763	—	2	2	no	—
19	#17985761	C₄	1	4	yes	complemented
20	#17985760	C₄	1	4	yes	complemented
21	#17985758	—	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	C₂³×Dic₇₁	—	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	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
37	C₂²×C₇₁⋊C₈	—	2	1	no	—
38	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
39	C₂²×C₇₁⋊C₈	D₄	1	2	yes	—
40	C₂²×C₇₁⋊C₈	Q₈	1	2	yes	—
41	#14556087	—	2	1	no	—
42	#14556087	—	2	1	no	—
43	#14556087	C₂×C₄	1	2	yes	—
44	#14556087	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊Dic₇₁	C₂×C₄	1	2	yes	—
46	C₂×C₂²⋊Dic₇₁	—	2	1	no	—
47	C₂×C₄×Dic₇₁	—	2	1	no	—
48	C₂×C₄×Dic₇₁	—	2	1	no	—
49	C₂×C₄×Dic₇₁	—	2	1	no	—
50	C₂×C₄×Dic₇₁	—	2	1	no	—
51	C₂×C₄×Dic₇₁	C₂×C₄	1	2	yes	—
52	C₂×C₄×Dic₇₁	D₄	1	2	yes	—
53	C₂×C₄×Dic₇₁	Q₈	1	2	yes	—
54	Dic₇₁⋊C₈	—	2	8	no	—
55	#14556038	—	2	8	no	—
56	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₇₁	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
63	C₂²×C₈×C₇₁	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₇₁	D₄	1	2	yes	—
70	C₂²×C₈×C₇₁	D₄	1	2	yes	—
71	#117×C₇₁	—	2	1	no	—
72	#117×C₇₁	—	2	1	no	—
73	#117×C₇₁	—	2	1	no	—
74	#117×C₇₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
77	C₂×C₄²×C₇₁	—	2	1	no	—
78	C₂²×Dic₇₁	—	2	2	no	—
79	C₂²×Dic₇₁	—	2	2	no	—
80	C₂²×Dic₇₁	—	2	2	no	—
81	C₂²×Dic₇₁	—	2	2	no	—
82	C₂²×Dic₇₁	—	4	4	no	—
83	#11765849	—	2	2	no	—
84	#11765849	—	2	2	no	—
85	#11765849	—	4	1	no	—
86	#11765849	—	4	1	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	—	2	2	no	—
92	C₂×C₇₁⋊C₈	—	2	2	no	—
93	C₂×C₇₁⋊C₈	—	2	2	no	—
94	C₂×C₇₁⋊C₈	—	4	1	no	—
95	C₂×C₇₁⋊C₈	—	4	1	no	—
96	C₂×C₇₁⋊C₈	C₄⋊C₄	1	4	yes	—
97	C₄⋊Dic₇₁	—	2	2	no	—
98	C₄⋊Dic₇₁	C₄²	1	4	yes	—
99	C₂²⋊Dic₇₁	—	2	2	no	—
100	C₂²⋊Dic₇₁	—	2	2	no	—
101	C₄×Dic₇₁	—	2	2	no	—
102	C₄×Dic₇₁	—	2	2	no	—
103	C₄×Dic₇₁	—	2	2	no	—
104	C₄×Dic₇₁	—	2	2	no	—
105	C₄×Dic₇₁	—	2	2	no	—
106	C₄×Dic₇₁	C₄⋊C₄	1	4	yes	—
107	C₂⁴×C₇₁	#41	1	1	yes	characteristic
108	C₂²×C₄×C₇₁	—	2	2	no	—
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	C₂×Q₈	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	—	2	2	no	—
132	C₂×C₈×C₇₁	—	2	2	no	—
133	C₂×C₈×C₇₁	—	2	2	no	—
134	C₂×C₈×C₇₁	—	4	1	no	—
135	C₂×C₈×C₇₁	—	4	1	no	—
136	C₂×C₈×C₇₁	C₂²⋊C₄	1	4	yes	—
137	C₄⋊C₄×C₇₁	—	2	2	no	—
138	C₄⋊C₄×C₇₁	—	2	2	no	—
139	C₂²⋊C₄×C₇₁	—	4	1	no	—
140	C₂²⋊C₄×C₇₁	—	4	1	no	—
141	C₄²×C₇₁	—	4	1	no	—
142	C₄²×C₇₁	—	4	1	no	—
143	C₂³×C₇₁	—	2	4	no	—
144	C₂³×C₇₁	#117	1	1	yes	characteristic
145	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
146	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
147	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂³×C₇₁	#123	1	1	yes	characteristic
149	C₂³×C₇₁	#125	1	1	yes	characteristic
150	C₂³×C₇₁	#126	1	1	yes	characteristic
151	C₂×C₄×C₇₁	—	4	2	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	C₂×C₄⋊C₄	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×Q₈	1	1	yes	characteristic
166	C₂×C₄×C₇₁	C₄×Q₈	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	C₂²⋊Q₈	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	C₄⋊Q₈	1	1	yes	characteristic
181	C₂×Dic₇₁	—	2	4	no	—
182	C₂×Dic₇₁	—	2	4	no	—
183	C₂×Dic₇₁	—	4	4	no	—
184	C₂×Dic₇₁	—	4	4	no	—
185	C₂×Dic₇₁	—	4	4	no	—
186	C₂×Dic₇₁	—	4	4	no	—
187	C₈×C₇₁	—	2	4	no	—
188	C₈×C₇₁	—	4	2	no	—
189	C₇₁⋊C₈	—	2	4	no	—
190	C₇₁⋊C₈	—	4	2	no	—
191	C₂²×C₇₁	—	2	2	no	—
192	C₂²×C₇₁	—	2	2	no	—
193	C₂²×C₇₁	—	2	2	no	—
194	C₂²×C₇₁	—	2	2	no	—
195	C₂²×C₇₁	—	2	2	no	—
196	C₂²×C₇₁	—	2	2	no	—
197	C₂²×C₇₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₇₁	#385	1	1	yes	characteristic
199	C₂²×C₇₁	#387	1	1	yes	characteristic
200	C₂²×C₇₁	#387	1	1	yes	characteristic
201	C₂²×C₇₁	#387	1	1	yes	characteristic
202	C₂²×C₇₁	#388	1	1	yes	characteristic
203	C₂²×C₇₁	#389	1	1	yes	characteristic
204	C₂²×C₇₁	#444	1	4	yes	—
205	C₄×C₇₁	—	8	2	no	—
206	C₄×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
207	C₄×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
208	C₄×C₇₁	#385	1	1	yes	characteristic
209	C₄×C₇₁	#386	1	1	yes	characteristic
210	C₄×C₇₁	#387	1	1	yes	characteristic
211	C₄×C₇₁	#388	1	1	yes	characteristic
212	C₄×C₇₁	#389	1	1	yes	characteristic
213	C₄×C₇₁	#391	1	1	yes	characteristic
214	Dic₇₁	—	4	4	no	—
215	Dic₇₁	—	4	4	no	—
216	#10883	—	71	1	no	maximal, Sylow
217	C₂×C₇₁	—	2	1	no	—
218	C₂×C₇₁	—	2	1	no	—
219	C₂×C₇₁	—	2	1	no	—
220	C₂×C₇₁	—	2	1	no	—
221	C₂×C₇₁	#1436	1	1	yes	characteristic
222	C₂×C₇₁	#1765	1	2	yes	—
223	C₂×C₇₁	#1938	1	2	yes	—
224	C₂×C₇₁	#1946	1	2	yes	—
225	C₂×#424	—	71	1	no	—
226	C₂²×#97	—	71	1	no	—
227	C₂×#341	—	71	1	no	—
228	#1735	—	71	1	no	—
229	C₂×#339	—	71	1	no	—
230	C₂×#339	—	71	1	no	—
231	#1729	D₇₁	1	1	yes	characteristic
232	C₇₁	#10883	1	1	yes	characteristic, complemented, Sylow
233	C₂²×M₁₆	—	71	1	no	—
234	C₂²×M₁₆	C₂×D₇₁	1	1	yes	characteristic
235	C₂³×C₈	—	71	1	no	—
236	C₂³×C₈	C₂×D₇₁	1	1	yes	characteristic
237	C₂×#117	—	71	1	no	—
238	C₂×#117	C₂×D₇₁	1	1	yes	characteristic
239	C₂²×C₄²	—	71	1	no	—
240	#424	—	71	4	no	—
241	#424	—	142	2	no	—
242	C₂×C₄⋊C₈	—	142	2	no	—
243	C₂×#97	—	142	2	no	—
244	C₂×#97	—	142	2	no	—
245	C₂×#97	—	142	2	no	—
246	#341	—	142	2	no	—
247	#340	—	71	4	no	—
248	#339	—	71	4	no	—
249	#339	—	142	2	no	—
250	#336	—	2	2	no	—
251	C₂³×C₄	—	142	1	no	—
252	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	71	2	no	—
259	C₂×M₁₆	—	142	1	no	—
260	C₂×M₁₆	—	142	1	no	—
261	C₂×M₁₆	—	142	1	no	—
262	C₂×M₁₆	—	142	1	no	—
263	C₂×M₁₆	—	142	1	no	—
264	C₂×M₁₆	C₄×D₇₁	1	2	yes	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	71	2	no	—
271	C₂²×C₈	—	71	2	no	—
272	C₂²×C₈	—	71	2	no	—
273	C₂²×C₈	—	142	1	no	—
274	C₂²×C₈	—	142	1	no	—
275	C₂²×C₈	—	142	1	no	—
276	C₂²×C₈	—	142	1	no	—
277	C₂²×C₈	—	142	1	no	—
278	C₂²×C₈	C₄×D₇₁	1	2	yes	—
279	C₂²×C₈	D₂₈₄	1	2	yes	—
280	C₂²×C₈	C₂²⋊D₇₁	1	2	yes	—
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	—	2	1	no	—
285	#117	—	71	2	no	—
286	#117	—	71	2	no	—
287	#117	—	142	1	no	—
288	#117	—	142	1	no	—
289	C₂×C₄⋊C₄	—	71	2	no	—
290	C₂×C₄⋊C₄	C₄×D₇₁	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	142	1	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	71	2	no	—
295	C₂×C₄²	—	71	2	no	—
296	C₂×C₄²	—	71	2	no	—
297	C₂×C₄²	—	142	1	no	—
298	C₂×C₄²	—	142	1	no	—
299	C₂×C₄²	—	142	1	no	—
300	C₂×C₄²	—	142	1	no	—
301	C₄⋊C₈	—	142	8	no	—
302	#97	—	142	8	no	—
303	C₂⁴	#11765865	1	1	yes	characteristic
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	284	4	no	—
306	C₂²×C₄	—	142	2	no	—
307	C₂²×C₄	—	142	2	no	—
308	C₂²×C₄	—	142	2	no	—
309	C₂²×C₄	—	142	2	no	—
310	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
313	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
317	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
318	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
319	C₂²×C₄	#11765864	1	1	yes	characteristic
320	C₂²×C₄	#11765864	1	1	yes	characteristic
321	C₂²×C₄	#11765864	1	1	yes	characteristic
322	C₂²×C₄	#11765864	1	1	yes	characteristic
323	C₂²×C₄	#11765865	1	1	yes	characteristic
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	4	1	no	—
327	M₁₆	—	4	1	no	—
328	M₁₆	—	284	1	no	—
329	M₁₆	—	284	1	no	—
330	M₁₆	—	142	2	no	—
331	M₁₆	—	142	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	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	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	284	1	no	—
342	C₂×C₈	—	284	1	no	—
343	C₂×C₈	—	71	4	no	—
344	C₂×C₈	—	142	2	no	—
345	C₂×C₈	—	142	2	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	(C₂×D₇₁)⋊C₄	1	4	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	71	4	no	—
355	C₄⋊C₄	—	142	2	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	142	2	no	—
359	C₂²⋊C₄	—	142	2	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	71	4	no	—
363	C₄²	—	142	2	no	—
364	C₄²	—	142	2	no	—
365	C₄²	—	142	2	no	—
366	C₄²	—	142	2	no	—
367	C₄²	—	142	2	no	—
368	C₂³	—	2	4	no	—
369	C₂³	#14556085	1	1	yes	characteristic
370	C₂³	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
371	C₂³	C₄×D₂₈₄	1	1	yes	characteristic
372	C₂³	#14556106	1	1	yes	characteristic
373	C₂³	#14556110	1	1	yes	characteristic
374	C₂³	#14556118	1	1	yes	characteristic
375	C₂³	#14556121	1	1	yes	characteristic
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	284	4	no	—
379	C₂×C₄	—	284	4	no	—
380	C₂×C₄	—	284	4	no	—
381	C₂×C₄	—	284	4	no	—
382	C₂×C₄	—	142	4	no	—
383	C₂×C₄	—	142	4	no	—
384	C₂×C₄	C₄²×D₇₁	1	1	yes	characteristic
385	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
386	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
387	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
388	C₂×C₄	#14556084	1	1	yes	characteristic
389	C₂×C₄	#14556084	1	1	yes	characteristic
390	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
391	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
392	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
393	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
394	C₂×C₄	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
395	C₂×C₄	C₄×D₂₈₄	1	1	yes	characteristic
396	C₂×C₄	#14556093	1	1	yes	characteristic
397	C₂×C₄	#14556093	1	1	yes	characteristic
398	C₂×C₄	#14556093	1	1	yes	characteristic
399	C₂×C₄	#14556093	1	1	yes	characteristic
400	C₂×C₄	#14556098	1	1	yes	characteristic
401	C₂×C₄	#14556100	1	1	yes	characteristic
402	C₂×C₄	#14556100	1	1	yes	characteristic
403	C₂×C₄	#14556106	1	1	yes	characteristic
404	C₂×C₄	#14556108	1	1	yes	characteristic
405	C₂×C₄	#14556108	1	1	yes	characteristic
406	C₂×C₄	#14556110	1	1	yes	characteristic
407	C₂×C₄	#14556112	1	1	yes	characteristic
408	C₂×C₄	#14556115	1	1	yes	characteristic
409	C₂×C₄	#14556118	1	1	yes	characteristic
410	C₂×C₄	#14556121	1	1	yes	characteristic
411	C₂×C₄	#14556126	1	1	yes	characteristic
412	C₈	—	2	4	no	—
413	C₈	—	4	2	no	—
414	C₈	—	284	2	no	—
415	C₈	—	142	4	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	C₄×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
423	C₂²	#17985873	1	1	yes	characteristic
424	C₂²	#17985881	1	1	yes	characteristic
425	C₂²	#17985881	1	1	yes	characteristic
426	C₂²	#17985884	1	1	yes	characteristic
427	C₂²	#17985893	1	1	yes	characteristic
428	C₂²	#17985894	1	1	yes	characteristic
429	C₂²	#17986119	1	4	yes	—
430	C₄	—	8	2	no	—
431	C₄	—	284	4	no	—
432	C₄	—	284	4	no	—
433	C₄	#17985850	1	1	yes	characteristic
434	C₄	#17985850	1	1	yes	characteristic
435	C₄	#17985873	1	1	yes	characteristic
436	C₄	#17985876	1	1	yes	characteristic
437	C₄	#17985884	1	1	yes	characteristic
438	C₄	#17985893	1	1	yes	characteristic
439	C₄	#17985894	1	1	yes	characteristic
440	C₄	#17985904	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	#22586575	1	1	yes	characteristic
446	C₂	#22588186	1	2	yes	—
447	C₂	#22589054	1	2	yes	—
448	C₂	#22589090	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	#10883
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
13. #17986025	C₄	semidirect
19. #17985761	C₄	semidirect
20. #17985760	C₄	semidirect
232. C₇₁	#10883	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17986025	2
C₂²×#14556038	2
C₂×#17985763	2
#22588056	2
C₂×#17985760	2
C₂×#17985758	2
C₇₁×#1729	2
#10883	71