Subgroups — #31968904

Order 18176.

654 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597360	C₂	1	1	yes	maximal, characteristic, complemented
2	#22597354	C₂	1	1	yes	maximal, characteristic, complemented
3	#22587231	C₂	1	2	yes	maximal, complemented
4	#22587191	C₂	1	2	yes	maximal, complemented
5	#22587170	C₂	1	2	yes	maximal, complemented
6	SD₁₆×C₇₁⋊C₈	C₂	1	2	yes	maximal, complemented
7	#22587103	C₂	1	1	yes	maximal, characteristic, complemented
8	#22586774	C₂	1	1	yes	maximal, characteristic, complemented
9	#22586774	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11765849	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#135×C₇₁	C₂	1	1	yes	maximal, characteristic
12	#17986130	C₂²	1	2	yes	—
13	Q₈×C₇₁⋊C₈	C₂²	1	2	yes	—
14	#17986077	—	2	2	no	—
15	#17986077	C₂²	1	2	yes	—
16	#17986071	—	2	2	no	—
17	D₄×C₇₁⋊C₈	C₂²	1	2	yes	—
18	#17986056	—	2	1	no	—
19	#17986056	—	2	1	no	—
20	#17986056	C₂²	1	1	yes	characteristic
21	#17986056	C₂²	1	1	yes	characteristic
22	#17986052	C₂²	1	1	yes	characteristic
23	C₄×#11765849	—	2	1	no	—
24	C₄×#11765849	C₂²	1	1	yes	characteristic
25	C₂×#14556039	—	2	1	no	—
26	#17985752	C₂²	1	2	yes	—
27	#17985750	C₂²	1	2	yes	—
28	Q₈⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
29	Q₈⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
30	D₄⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
31	D₄⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
32	#17985721	C₂²	1	2	yes	—
33	C₈×C₇₁⋊C₈	C₂²	1	2	yes	—
34	C₂×#135×C₇₁	C₄	1	1	yes	characteristic
35	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
36	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₇₁	C₄	1	1	yes	characteristic
38	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
39	C₄×SD₁₆×C₇₁	C₄	1	1	yes	characteristic
40	C₄×SD₁₆×C₇₁	C₄	1	1	yes	characteristic
41	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
42	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
43	C₄×D₈×C₇₁	C₄	1	1	yes	characteristic
44	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic
45	#427×C₇₁	C₄	1	1	yes	characteristic
46	#416×C₇₁	C₄	1	1	yes	characteristic
47	#416×C₇₁	C₄	1	1	yes	characteristic
48	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
49	C₂×#11765849	—	2	2	no	—
50	C₂×#11765849	D₄	1	2	yes	—
51	C₂²×C₇₁⋊C₈	—	2	2	no	—
52	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
53	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
54	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
55	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
57	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
58	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
60	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
61	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
62	#14556039	—	2	2	no	—
63	#14556039	—	2	1	no	—
64	#14556039	—	2	1	no	—
65	#14556039	D₄	1	1	yes	characteristic
66	#14556039	D₄	1	1	yes	characteristic
67	C₄×C₇₁⋊C₈	—	2	2	no	—
68	C₄×C₇₁⋊C₈	C₂³	1	2	yes	—
69	C₄×C₇₁⋊C₈	C₂³	1	2	yes	—
70	C₂×#41×C₇₁	C₂×C₄	1	1	yes	characteristic
71	C₂×#41×C₇₁	C₂×C₄	1	1	yes	characteristic
72	#135×C₇₁	—	2	4	no	—
73	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
75	C₂×SD₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
76	C₂×D₈×C₇₁	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
79	C₄×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
81	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
82	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₇₁	—	2	1	no	—
84	C₄×D₄×C₇₁	—	2	1	no	—
85	C₄×D₄×C₇₁	—	2	1	no	—
86	C₄×D₄×C₇₁	—	2	1	no	—
87	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
88	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
89	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
90	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
91	#117×C₇₁	—	2	1	no	—
92	#117×C₇₁	—	2	1	no	—
93	#117×C₇₁	C₂×C₄	1	1	yes	characteristic
94	#117×C₇₁	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₇₁	—	2	1	no	—
96	C₂×C₄²×C₇₁	—	2	1	no	—
97	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
98	#107×C₇₁	C₂×C₄	1	1	yes	characteristic
99	#107×C₇₁	C₂×C₄	1	1	yes	characteristic
100	#106×C₇₁	C₂×C₄	1	1	yes	characteristic
101	#106×C₇₁	C₂×C₄	1	1	yes	characteristic
102	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
103	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
104	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
105	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
106	#102×C₇₁	C₂×C₄	1	1	yes	characteristic
107	#102×C₇₁	C₂×C₄	1	1	yes	characteristic
108	#102×C₇₁	C₂×C₄	1	1	yes	characteristic
109	#102×C₇₁	C₂×C₄	1	1	yes	characteristic
110	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
111	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
112	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
114	#11765849	—	2	4	no	—
115	#11765849	—	4	4	no	—
116	C₂×C₇₁⋊C₈	—	2	2	no	—
117	C₂×C₇₁⋊C₈	—	2	2	no	—
118	C₂×C₇₁⋊C₈	—	2	2	no	—
119	C₂×C₇₁⋊C₈	—	4	4	no	—
120	C₂×C₇₁⋊C₈	C₂×D₄	1	2	yes	—
121	C₂×C₇₁⋊C₈	C₂×D₄	1	2	yes	—
122	#41×C₇₁	—	2	2	no	—
123	#41×C₇₁	—	2	2	no	—
124	#41×C₇₁	—	4	1	no	—
125	#41×C₇₁	—	4	1	no	—
126	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
127	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₇₁	—	2	1	no	—
129	C₂×D₄×C₇₁	—	2	1	no	—
130	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₁	—	2	1	no	—
133	C₂²×C₄×C₇₁	—	2	1	no	—
134	C₂²×C₄×C₇₁	—	2	1	no	—
135	C₂²×C₄×C₇₁	—	2	1	no	—
136	C₂²×C₄×C₇₁	—	2	1	no	—
137	C₂²×C₄×C₇₁	—	2	1	no	—
138	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
141	Q₁₆×C₇₁	—	2	2	no	—
142	SD₁₆×C₇₁	—	2	2	no	—
143	SD₁₆×C₇₁	M₁₆	1	4	yes	complemented
144	D₈×C₇₁	—	2	2	no	—
145	C₂×C₈×C₇₁	—	2	2	no	—
146	C₂×C₈×C₇₁	—	4	1	no	—
147	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
151	C₄⋊C₄×C₇₁	—	2	1	no	—
152	C₄⋊C₄×C₇₁	—	2	1	no	—
153	C₄⋊C₄×C₇₁	—	2	1	no	—
154	C₄⋊C₄×C₇₁	—	2	1	no	—
155	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
156	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
157	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
158	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
159	C₂²⋊C₄×C₇₁	—	2	1	no	—
160	C₂²⋊C₄×C₇₁	—	2	1	no	—
161	C₂²⋊C₄×C₇₁	—	2	1	no	—
162	C₂²⋊C₄×C₇₁	—	2	1	no	—
163	C₂²⋊C₄×C₇₁	—	2	1	no	—
164	C₂²⋊C₄×C₇₁	—	2	1	no	—
165	C₄²×C₇₁	—	2	1	no	—
166	C₄²×C₇₁	—	2	1	no	—
167	C₄²×C₇₁	—	2	1	no	—
168	C₄²×C₇₁	—	2	1	no	—
169	C₄²×C₇₁	—	2	1	no	—
170	C₄²×C₇₁	—	2	1	no	—
171	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₇₁	#41	1	1	yes	characteristic
174	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
175	C₂³×C₇₁	—	2	1	no	—
176	C₂³×C₇₁	—	2	1	no	—
177	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
178	Q₈×C₇₁	—	2	1	no	—
179	Q₈×C₇₁	—	2	1	no	—
180	Q₈×C₇₁	—	2	1	no	—
181	Q₈×C₇₁	C₂×M₁₆	1	2	yes	—
182	D₄×C₇₁	—	2	1	no	—
183	D₄×C₇₁	—	2	1	no	—
184	D₄×C₇₁	—	2	1	no	—
185	D₄×C₇₁	—	4	2	no	—
186	D₄×C₇₁	—	4	2	no	—
187	D₄×C₇₁	C₂×M₁₆	1	2	yes	—
188	C₂×C₄×C₇₁	—	2	1	no	—
189	C₂×C₄×C₇₁	—	2	1	no	—
190	C₂×C₄×C₇₁	—	2	1	no	—
191	C₂×C₄×C₇₁	—	2	2	no	—
192	C₂×C₄×C₇₁	—	2	1	no	—
193	C₂×C₄×C₇₁	—	2	1	no	—
194	C₂×C₄×C₇₁	—	2	1	no	—
195	C₂×C₄×C₇₁	—	2	1	no	—
196	C₂×C₄×C₇₁	—	2	1	no	—
197	C₂×C₄×C₇₁	—	4	1	no	—
198	C₂×C₄×C₇₁	—	4	2	no	—
199	C₂×C₄×C₇₁	—	4	2	no	—
200	C₂×C₄×C₇₁	—	4	2	no	—
201	C₂×C₄×C₇₁	—	4	2	no	—
202	C₂×C₄×C₇₁	—	8	1	no	—
203	C₂×C₄×C₇₁	—	8	1	no	—
204	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
210	C₈×C₇₁	—	2	1	no	—
211	C₈×C₇₁	—	2	1	no	—
212	C₈×C₇₁	—	2	1	no	—
213	C₈×C₇₁	C₂×M₁₆	1	2	yes	—
214	C₇₁⋊C₈	—	2	2	no	—
215	C₇₁⋊C₈	—	4	2	no	—
216	C₇₁⋊C₈	—	4	2	no	—
217	C₇₁⋊C₈	—	4	2	no	—
218	C₇₁⋊C₈	#135	1	4	yes	complemented
219	C₂²×C₇₁	—	2	1	no	—
220	C₂²×C₇₁	—	2	2	no	—
221	C₂²×C₇₁	—	2	1	no	—
222	C₂²×C₇₁	—	2	1	no	—
223	C₂²×C₇₁	—	4	1	no	—
224	C₂²×C₇₁	—	4	1	no	—
225	C₂²×C₇₁	—	4	1	no	—
226	C₂²×C₇₁	—	4	1	no	—
227	C₂²×C₇₁	—	4	1	no	—
228	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
229	C₄×C₇₁	—	2	1	no	—
230	C₄×C₇₁	—	2	2	no	—
231	C₄×C₇₁	—	2	1	no	—
232	C₄×C₇₁	—	2	1	no	—
233	C₄×C₇₁	—	2	1	no	—
234	C₄×C₇₁	—	4	1	no	—
235	C₄×C₇₁	—	4	1	no	—
236	C₄×C₇₁	—	4	1	no	—
237	C₄×C₇₁	—	4	1	no	—
238	C₄×C₇₁	—	4	1	no	—
239	C₄×C₇₁	C₂²×M₁₆	1	1	yes	characteristic
240	C₄×C₇₁	#568	1	1	yes	characteristic
241	C₄×C₇₁	C₂×#135	1	2	yes	—
242	#18037	—	71	1	no	maximal, Sylow
243	C₂×C₇₁	—	4	1	no	—
244	C₂×C₇₁	—	4	2	no	—
245	C₂×C₇₁	—	8	1	no	—
246	C₂×C₇₁	D₄×M₁₆	1	1	yes	characteristic
247	C₂×C₇₁	C₄×#135	1	1	yes	characteristic
248	C₂×C₇₁	#2957	1	1	yes	characteristic
249	#2971	—	71	1	no	—
250	#2970	—	71	1	no	—
251	C₄×#135	D₇₁	1	1	yes	characteristic
252	#1590	—	71	2	no	—
253	#1584	—	71	2	no	—
254	#1581	—	71	2	no	—
255	C₈×SD₁₆	—	71	2	no	—
256	#1568	—	71	1	no	—
257	#1488	—	71	1	no	—
258	#1488	—	71	1	no	—
259	C₈×M₁₆	—	71	1	no	—
260	C₇₁	#18037	1	1	yes	characteristic, complemented, Sylow
261	C₂×#135	Dic₇₁	1	1	yes	characteristic
262	C₄×#41	C₂×D₇₁	1	1	yes	characteristic
263	C₄×#41	C₂×D₇₁	1	1	yes	characteristic
264	#446	—	71	2	no	—
265	C₈×Q₈	—	71	2	no	—
266	C₄×Q₁₆	Dic₇₁	1	1	yes	characteristic
267	C₄×Q₁₆	C₂×D₇₁	1	1	yes	characteristic
268	C₄×SD₁₆	Dic₇₁	1	1	yes	characteristic
269	C₄×SD₁₆	Dic₇₁	1	1	yes	characteristic
270	C₄×SD₁₆	C₂×D₇₁	1	1	yes	characteristic
271	C₄×SD₁₆	C₂×D₇₁	1	1	yes	characteristic
272	C₄×D₈	Dic₇₁	1	1	yes	characteristic
273	C₄×D₈	C₂×D₇₁	1	1	yes	characteristic
274	#436	—	71	2	no	—
275	#436	—	142	2	no	—
276	#435	—	142	2	no	—
277	C₈×D₄	—	71	2	no	—
278	#432	—	71	1	no	—
279	#432	—	71	1	no	—
280	#432	—	142	1	no	—
281	#432	—	142	1	no	—
282	#431	—	71	1	no	—
283	#427	Dic₇₁	1	1	yes	characteristic
284	#416	Dic₇₁	1	1	yes	characteristic
285	#416	Dic₇₁	1	1	yes	characteristic
286	C₄×M₁₆	—	71	1	no	—
287	C₄×M₁₆	—	142	1	no	—
288	C₂×#97	—	142	1	no	—
289	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
290	#335	—	71	2	no	—
291	#334	—	71	2	no	—
292	Q₈⋊C₈	—	71	2	no	—
293	Q₈⋊C₈	—	71	2	no	—
294	D₄⋊C₈	—	71	2	no	—
295	D₄⋊C₈	—	71	2	no	—
296	#322	—	71	2	no	—
297	C₈²	—	71	2	no	—
298	C₂×#41	C₂×Dic₇₁	1	1	yes	characteristic
299	C₂×#41	C₂×Dic₇₁	1	1	yes	characteristic
300	#135	—	2	4	no	—
301	C₂×Q₁₆	C₂×Dic₇₁	1	1	yes	characteristic
302	C₂×SD₁₆	C₂×Dic₇₁	1	1	yes	characteristic
303	C₂×SD₁₆	C₂×Dic₇₁	1	1	yes	characteristic
304	C₂×D₈	C₂×Dic₇₁	1	1	yes	characteristic
305	C₂×M₁₆	—	71	2	no	—
306	C₂×M₁₆	—	142	2	no	—
307	C₂²×C₈	—	142	2	no	—
308	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
309	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
310	C₄×Q₈	C₂×Dic₇₁	1	1	yes	characteristic
311	C₄×Q₈	C₂×Dic₇₁	1	1	yes	characteristic
312	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
313	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
319	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
320	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
321	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
322	#117	—	2	1	no	—
323	#117	—	2	1	no	—
324	#117	C₂×Dic₇₁	1	1	yes	characteristic
325	#117	C₂×Dic₇₁	1	1	yes	characteristic
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
329	#107	C₂×Dic₇₁	1	1	yes	characteristic
330	#107	C₂×Dic₇₁	1	1	yes	characteristic
331	#106	C₂×Dic₇₁	1	1	yes	characteristic
332	#106	C₂×Dic₇₁	1	1	yes	characteristic
333	C₄⋊C₈	—	71	2	no	—
334	C₄⋊C₈	—	71	2	no	—
335	C₄⋊C₈	—	142	2	no	—
336	C₄⋊C₈	—	142	2	no	—
337	C₄⋊C₈	—	142	1	no	—
338	#103	C₂×Dic₇₁	1	1	yes	characteristic
339	#103	C₂×Dic₇₁	1	1	yes	characteristic
340	#103	C₂×Dic₇₁	1	1	yes	characteristic
341	#103	C₂×Dic₇₁	1	1	yes	characteristic
342	#102	C₂×Dic₇₁	1	1	yes	characteristic
343	#102	C₂×Dic₇₁	1	1	yes	characteristic
344	#102	C₂×Dic₇₁	1	1	yes	characteristic
345	#102	C₂×Dic₇₁	1	1	yes	characteristic
346	C₂²⋊C₈	—	142	2	no	—
347	C₂²⋊C₈	—	142	2	no	—
348	C₂²⋊C₈	—	142	1	no	—
349	C₂²⋊C₈	—	142	1	no	—
350	C₂²⋊C₈	—	142	1	no	—
351	#97	—	71	1	no	—
352	#97	—	71	1	no	—
353	#97	—	142	2	no	—
354	#97	—	142	1	no	—
355	#97	—	142	1	no	—
356	C₄×C₈	—	71	2	no	—
357	C₄×C₈	—	71	2	no	—
358	C₄×C₈	—	142	2	no	—
359	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
360	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
361	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
362	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	#41	—	4	1	no	—
366	#41	—	4	1	no	—
367	C₂×Q₈	C₂²×Dic₇₁	1	1	yes	characteristic
368	C₂×Q₈	C₂²×Dic₇₁	1	1	yes	characteristic
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	C₂²×Dic₇₁	1	1	yes	characteristic
372	C₂×D₄	C₂²×Dic₇₁	1	1	yes	characteristic
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
380	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
381	C₂²×C₄	#11765864	1	1	yes	characteristic
382	Q₁₆	—	2	2	no	—
383	SD₁₆	—	2	2	no	—
384	SD₁₆	#11765849	1	4	yes	complemented
385	D₈	—	2	2	no	—
386	M₁₆	—	284	4	no	—
387	M₁₆	—	142	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	4	1	no	—
390	C₂×C₈	—	284	4	no	—
391	C₂×C₈	—	71	2	no	—
392	C₂×C₈	—	71	2	no	—
393	C₂×C₈	—	142	2	no	—
394	C₂×C₈	—	142	2	no	—
395	C₂×C₈	—	142	2	no	—
396	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
397	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
398	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
399	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
405	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
406	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
407	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
421	C₄²	D₄×D₇₁	1	1	yes	characteristic
422	C₄²	#11765864	1	1	yes	characteristic
423	C₄²	C₂³×D₇₁	1	1	yes	characteristic
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	D₄×Dic₇₁	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	—	2	1	no	—
429	Q₈	—	2	1	no	—
430	Q₈	C₂×#11765849	1	2	yes	—
431	D₄	—	2	1	no	—
432	D₄	—	2	1	no	—
433	D₄	—	2	1	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	C₂×#11765849	1	2	yes	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	8	1	no	—
452	C₂×C₄	—	8	1	no	—
453	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
454	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
455	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
456	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
457	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
458	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
459	C₈	—	2	1	no	—
460	C₈	—	2	1	no	—
461	C₈	—	2	1	no	—
462	C₈	—	284	2	no	—
463	C₈	—	284	2	no	—
464	C₈	—	284	2	no	—
465	C₈	—	71	4	no	—
466	C₈	—	142	2	no	—
467	C₈	C₂×#11765849	1	2	yes	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	C₂×D₄×Dic₇₁	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	C₂²×#11765849	1	1	yes	characteristic
489	C₄	#17986766	1	1	yes	characteristic
490	C₄	#135×D₇₁	1	2	yes	—
491	C₂	—	4	1	no	—
492	C₂	—	4	2	no	—
493	C₂	—	8	1	no	—
494	C₂	D₄×#11765849	1	1	yes	characteristic
495	C₂	#135×Dic₇₁	1	1	yes	characteristic
496	C₂	#22597257	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₄×#135×C₇₁	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	C₂×#135×C₇₁	C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	C₄×#135	D₇₁
hypocenter	C₇₁	#18037
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #22597360	C₂	semidirect
2. #22597354	C₂	semidirect
3. #22587231	C₂	semidirect
4. #22587191	C₂	semidirect
5. #22587170	C₂	semidirect
6. SD₁₆×C₇₁⋊C₈	C₂	semidirect
7. #22587103	C₂	semidirect
8. #22586774	C₂	semidirect
9. #22586774	C₂	semidirect
10. C₈×#11765849	C₂	semidirect
143. SD₁₆×C₇₁	M₁₆	semidirect
218. C₇₁⋊C₈	#135	semidirect
260. C₇₁	#18037	semidirect
384. SD₁₆	#11765849	semidirect

Maximal subgroups

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

subgroup	index
#22597360	2
#22597354	2
#22587231	2
#22587191	2
#22587170	2
SD₁₆×C₇₁⋊C₈	2
#22587103	2
#22586774	2
C₈×#11765849	2
C₄×#135×C₇₁	2
#18037	71