Subgroups — #31903346

Order 18176.

982 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556060	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₇₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#17985761	C₂	1	2	yes	maximal
4	#22586569	C₂	1	2	yes	maximal
5	C₂²×#106×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₇₁	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₇₁	C₂²	1	1	yes	characteristic
9	C₂×#14556060	—	2	2	no	—
10	C₂×#14556060	—	2	2	no	—
11	C₂×#14556060	C₄	1	4	yes	complemented
12	C₂×C₈×Dic₇₁	—	2	2	no	—
13	C₂×C₈×Dic₇₁	—	2	2	no	—
14	C₂×C₈×Dic₇₁	C₄	1	4	yes	complemented
15	C₂×C₇₁⋊#95	—	2	4	no	—
16	#17985761	—	2	4	no	—
17	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
19	C₂×#106×C₇₁	—	2	2	no	—
20	C₂×#106×C₇₁	—	2	2	no	—
21	C₂×#106×C₇₁	C₄	1	4	yes	complemented
22	C₂³×Dic₇₁	—	2	2	no	—
23	C₂³×Dic₇₁	D₄	1	2	yes	—
24	C₂²×C₇₁⋊C₈	—	2	1	no	—
25	C₂²×C₇₁⋊C₈	—	2	1	no	—
26	C₂²×C₇₁⋊C₈	—	2	1	no	—
27	C₂²×C₇₁⋊C₈	—	2	1	no	—
28	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
29	C₂²×C₇₁⋊C₈	D₄	1	2	yes	—
30	C₂²×C₇₁⋊C₈	Q₈	1	2	yes	—
31	C₂×C₄⋊Dic₇₁	—	2	2	no	—
32	C₂×C₄⋊Dic₇₁	—	2	2	no	—
33	C₂×C₄⋊Dic₇₁	—	2	2	no	—
34	C₂×C₄⋊Dic₇₁	—	2	2	no	—
35	C₂×C₄⋊Dic₇₁	—	2	2	no	—
36	C₂×C₄⋊Dic₇₁	C₂×C₄	1	4	yes	—
37	C₂×C₄×Dic₇₁	—	2	1	no	—
38	C₂×C₄×Dic₇₁	—	2	1	no	—
39	C₂×C₄×Dic₇₁	—	2	1	no	—
40	C₂×C₄×Dic₇₁	—	2	1	no	—
41	C₂×C₄×Dic₇₁	C₂×C₄	1	2	yes	—
42	C₂×C₄×Dic₇₁	Q₈	1	2	yes	—
43	#14556060	—	2	8	no	—
44	C₈×Dic₇₁	—	2	8	no	—
45	C₇₁⋊#95	—	4	8	no	—
46	C₂³×C₄×C₇₁	—	2	2	no	—
47	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₇₁	D₄	1	2	yes	—
52	C₂²×C₈×C₇₁	D₄	1	2	yes	—
53	C₂²×C₈×C₇₁	D₄	1	2	yes	—
54	C₂²×C₈×C₇₁	Q₈	1	2	yes	—
55	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	4	yes	—
61	#106×C₇₁	—	2	8	no	—
62	C₂²×Dic₇₁	—	2	2	no	—
63	C₂²×Dic₇₁	—	2	2	no	—
64	C₂²×Dic₇₁	—	2	4	no	—
65	C₂²×Dic₇₁	—	2	4	no	—
66	C₂²×Dic₇₁	—	4	2	no	—
67	C₂²×Dic₇₁	—	4	2	no	—
68	C₂²×Dic₇₁	—	4	4	no	—
69	C₂²×Dic₇₁	—	4	4	no	—
70	C₂²×Dic₇₁	C₄⋊C₄	1	4	yes	—
71	C₂²×Dic₇₁	SD₁₆	1	8	yes	—
72	C₂×C₇₁⋊C₈	—	2	2	no	—
73	C₂×C₇₁⋊C₈	—	2	2	no	—
74	C₂×C₇₁⋊C₈	—	2	2	no	—
75	C₂×C₇₁⋊C₈	—	2	2	no	—
76	C₂×C₇₁⋊C₈	—	2	2	no	—
77	C₂×C₇₁⋊C₈	—	2	2	no	—
78	C₂×C₇₁⋊C₈	C₄⋊C₄	1	4	yes	—
79	C₄⋊Dic₇₁	—	2	4	no	—
80	C₄⋊Dic₇₁	—	2	4	no	—
81	C₄⋊Dic₇₁	—	4	2	no	—
82	C₄⋊Dic₇₁	—	4	2	no	—
83	C₄×Dic₇₁	—	2	2	no	—
84	C₄×Dic₇₁	—	2	2	no	—
85	C₄×Dic₇₁	—	2	2	no	—
86	C₄×Dic₇₁	—	2	2	no	—
87	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₇₁	—	2	4	no	—
89	C₂²×C₄×C₇₁	—	4	2	no	—
90	C₂²×C₄×C₇₁	—	4	2	no	—
91	C₂²×C₄×C₇₁	—	4	4	no	—
92	C₂²×C₄×C₇₁	—	4	4	no	—
93	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
104	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
105	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
106	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
107	C₂×C₈×C₇₁	C₄²	1	4	yes	—
108	C₂×C₈×C₇₁	C₂²⋊C₄	1	4	yes	—
109	C₂×C₈×C₇₁	C₂²⋊C₄	1	4	yes	—
110	C₂×C₈×C₇₁	C₂²⋊C₄	1	4	yes	—
111	C₂×C₈×C₇₁	C₄⋊C₄	1	4	yes	—
112	C₂×C₈×C₇₁	C₄⋊C₄	1	4	yes	—
113	C₂×C₈×C₇₁	C₄⋊C₄	1	4	yes	—
114	C₄⋊C₄×C₇₁	—	2	4	no	—
115	C₄⋊C₄×C₇₁	—	2	4	no	—
116	C₄⋊C₄×C₇₁	—	4	2	no	—
117	C₄⋊C₄×C₇₁	—	4	2	no	—
118	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
120	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
121	C₂³×C₇₁	#121	1	1	yes	characteristic
122	C₂³×C₇₁	#121	1	1	yes	characteristic
123	C₂³×C₇₁	#127	1	1	yes	characteristic
124	C₂³×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
125	C₂³×C₇₁	C₂×SD₁₆	1	4	yes	—
126	C₂³×C₇₁	#135	1	4	yes	—
127	C₂×C₄×C₇₁	—	4	4	no	—
128	C₂×C₄×C₇₁	—	4	8	no	—
129	C₂×C₄×C₇₁	—	8	4	no	—
130	C₂×C₄×C₇₁	—	8	2	no	—
131	C₂×C₄×C₇₁	—	8	2	no	—
132	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
133	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
141	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
142	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
149	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
150	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
155	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
156	C₂×C₄×C₇₁	#125	1	1	yes	characteristic
157	C₂×C₄×C₇₁	#125	1	1	yes	characteristic
158	C₂×C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
160	C₂×Dic₇₁	—	2	4	no	—
161	C₂×Dic₇₁	—	2	4	no	—
162	C₂×Dic₇₁	—	2	8	no	—
163	C₂×Dic₇₁	—	2	8	no	—
164	C₂×Dic₇₁	—	4	4	no	—
165	C₂×Dic₇₁	—	4	8	no	—
166	C₂×Dic₇₁	—	8	4	no	—
167	C₂×Dic₇₁	—	8	2	no	—
168	C₂×Dic₇₁	—	8	2	no	—
169	C₂×Dic₇₁	#106	1	8	yes	complemented
170	C₈×C₇₁	#95	1	8	yes	complemented
171	C₇₁⋊C₈	—	2	4	no	—
172	C₂²×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×C₇₁	#380	1	1	yes	characteristic
174	C₂²×C₇₁	#384	1	1	yes	characteristic
175	C₂²×C₇₁	#389	1	1	yes	characteristic
176	C₂²×C₇₁	#389	1	1	yes	characteristic
177	C₂²×C₇₁	#390	1	1	yes	characteristic
178	C₂²×C₇₁	#390	1	1	yes	characteristic
179	C₂²×C₇₁	C₂×#106	1	2	yes	—
180	C₂²×C₇₁	#427	1	2	yes	—
181	C₂²×C₇₁	C₄×SD₁₆	1	4	yes	—
182	C₂²×C₇₁	C₄×SD₁₆	1	4	yes	—
183	C₂²×C₇₁	#465	1	4	yes	—
184	C₂²×C₇₁	#465	1	4	yes	—
185	C₂²×C₇₁	#492	1	2	yes	—
186	C₂²×C₇₁	#495	1	2	yes	—
187	C₂²×C₇₁	#498	1	2	yes	—
188	C₂²×C₇₁	#499	1	2	yes	—
189	C₄×C₇₁	—	8	4	no	—
190	C₄×C₇₁	C₂×#95	1	1	yes	characteristic
191	C₄×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
192	C₄×C₇₁	#380	1	1	yes	characteristic
193	C₄×C₇₁	#382	1	1	yes	characteristic
194	C₄×C₇₁	#389	1	1	yes	characteristic
195	C₄×C₇₁	#389	1	1	yes	characteristic
196	C₄×C₇₁	#391	1	1	yes	characteristic
197	C₄×C₇₁	#391	1	1	yes	characteristic
198	Dic₇₁	—	2	8	no	—
199	Dic₇₁	—	8	4	no	—
200	#10861	—	71	1	no	maximal, Sylow
201	C₂×C₇₁	C₄⋊#95	1	1	yes	characteristic
202	C₂×C₇₁	C₄×#106	1	2	yes	—
203	C₂×C₇₁	#1807	1	2	yes	—
204	C₂×C₇₁	#1844	1	1	yes	characteristic
205	C₂×C₇₁	#1846	1	1	yes	characteristic
206	C₂×C₇₁	#1941	1	2	yes	—
207	C₂×C₇₁	#1941	1	2	yes	—
208	C₂×C₇₁	#1968	1	2	yes	—
209	C₂×C₇₁	#1968	1	2	yes	—
210	C₂²×#106	—	71	1	no	—
211	C₂²×#106	D₇₁	1	1	yes	characteristic
212	C₂²×C₄×C₈	—	71	1	no	—
213	C₂×#340	—	71	2	no	—
214	C₄⋊#95	—	71	2	no	—
215	C₇₁	#10861	1	1	yes	characteristic, complemented, Sylow
216	C₂³×C₈	—	71	1	no	—
217	C₂³×C₈	C₂×D₇₁	1	1	yes	characteristic
218	C₂²×C₄⋊C₄	—	71	2	no	—
219	C₂²×C₄⋊C₄	C₂×D₇₁	1	2	yes	—
220	C₂²×C₄²	—	71	1	no	—
221	C₂×#106	—	2	2	no	—
222	C₂×#106	—	2	2	no	—
223	C₂×#106	—	71	4	no	—
224	C₂×#106	—	142	2	no	—
225	C₂×#106	—	142	2	no	—
226	C₂×#106	Dic₇₁	1	4	yes	complemented
227	C₂×C₄×C₈	—	71	4	no	—
228	C₂×C₄×C₈	—	142	2	no	—
229	C₂×C₄×C₈	—	142	2	no	—
230	C₂×#95	—	142	4	no	—
231	#340	—	142	4	no	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	—	71	2	no	—
234	C₂³×C₄	—	142	2	no	—
235	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
236	C₂²×C₈	—	71	2	no	—
237	C₂²×C₈	—	71	2	no	—
238	C₂²×C₈	—	71	2	no	—
239	C₂²×C₈	—	142	1	no	—
240	C₂²×C₈	—	142	1	no	—
241	C₂²×C₈	—	142	1	no	—
242	C₂²×C₈	—	142	1	no	—
243	C₂²×C₈	Dic₁₄₂	1	2	yes	—
244	C₂²×C₈	C₄×D₇₁	1	2	yes	—
245	C₂²×C₈	C₄×D₇₁	1	2	yes	—
246	C₂²×C₈	D₂₈₄	1	2	yes	—
247	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
248	C₂²×C₈	C₂²⋊D₇₁	1	2	yes	—
249	C₂²×C₈	C₂²⋊D₇₁	1	2	yes	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	71	4	no	—
256	C₂×C₄⋊C₄	—	142	2	no	—
257	C₂×C₄⋊C₄	—	142	2	no	—
258	C₂×C₄⋊C₄	—	142	2	no	—
259	C₂×C₄⋊C₄	—	142	2	no	—
260	C₂×C₄⋊C₄	—	142	2	no	—
261	C₂×C₄⋊C₄	C₂×Dic₇₁	1	4	yes	—
262	C₂×C₄²	—	71	2	no	—
263	C₂×C₄²	—	71	2	no	—
264	C₂×C₄²	—	142	1	no	—
265	C₂×C₄²	—	142	1	no	—
266	C₂×C₄²	—	142	1	no	—
267	C₂×C₄²	—	142	1	no	—
268	#106	—	2	8	no	—
269	#106	—	142	8	no	—
270	C₄×C₈	—	142	8	no	—
271	#95	—	284	8	no	—
272	C₂⁴	D₄×D₇₁	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	284	2	no	—
279	C₂²×C₄	—	284	2	no	—
280	C₂²×C₄	—	284	4	no	—
281	C₂²×C₄	—	284	4	no	—
282	C₂²×C₄	—	71	4	no	—
283	C₂²×C₄	—	71	8	no	—
284	C₂²×C₄	—	142	4	no	—
285	C₂²×C₄	—	142	2	no	—
286	C₂²×C₄	—	142	2	no	—
287	C₂²×C₄	—	142	4	no	—
288	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
290	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
291	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
295	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
296	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
297	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
298	C₂²×C₄	#11765864	1	1	yes	characteristic
299	C₂²×C₄	#11765864	1	1	yes	characteristic
300	C₂²×C₄	#11765866	1	1	yes	characteristic
301	C₂²×C₄	#11765866	1	1	yes	characteristic
302	C₂×C₈	—	71	4	no	—
303	C₂×C₈	—	142	2	no	—
304	C₂×C₈	—	142	2	no	—
305	C₂×C₈	—	142	2	no	—
306	C₂×C₈	—	142	2	no	—
307	C₂×C₈	—	142	2	no	—
308	C₂×C₈	—	142	2	no	—
309	C₂×C₈	C₄×Dic₇₁	1	4	yes	—
310	C₂×C₈	(C₂×D₇₁)⋊C₄	1	4	yes	—
311	C₂×C₈	(C₂×D₇₁)⋊C₄	1	4	yes	—
312	C₂×C₈	C₂²⋊Dic₇₁	1	4	yes	—
313	C₂×C₈	Dic₇₁⋊C₄	1	4	yes	—
314	C₂×C₈	Dic₇₁⋊C₄	1	4	yes	—
315	C₂×C₈	C₄⋊Dic₇₁	1	4	yes	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	284	2	no	—
321	C₄⋊C₄	—	284	2	no	—
322	C₄⋊C₄	—	142	4	no	—
323	C₄⋊C₄	—	142	4	no	—
324	C₄²	—	142	2	no	—
325	C₄²	—	142	2	no	—
326	C₄²	—	142	2	no	—
327	C₄²	—	142	2	no	—
328	C₂³	C₄⋊C₄×D₇₁	1	1	yes	characteristic
329	C₂³	#14556090	1	1	yes	characteristic
330	C₂³	D₄×Dic₇₁	1	1	yes	characteristic
331	C₂³	#14556099	1	1	yes	characteristic
332	C₂³	#14556103	1	1	yes	characteristic
333	C₂³	#14556124	1	1	yes	characteristic
334	C₂³	#14556127	1	1	yes	characteristic
335	C₂³	SD₁₆×D₇₁	1	4	yes	—
336	C₂³	#14556149	1	4	yes	—
337	C₂×C₄	—	4	8	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	—	8	4	no	—
342	C₂×C₄	—	284	8	no	—
343	C₂×C₄	—	284	4	no	—
344	C₂×C₄	—	568	2	no	—
345	C₂×C₄	—	568	2	no	—
346	C₂×C₄	—	568	4	no	—
347	C₂×C₄	—	71	8	no	—
348	C₂×C₄	—	142	4	no	—
349	C₂×C₄	—	142	8	no	—
350	C₂×C₄	—	142	8	no	—
351	C₂×C₄	—	142	4	no	—
352	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
353	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
356	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
357	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
358	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
360	C₂×C₄	#14556086	1	1	yes	characteristic
361	C₂×C₄	#14556086	1	1	yes	characteristic
362	C₂×C₄	#14556090	1	1	yes	characteristic
363	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
364	C₂×C₄	#14556093	1	1	yes	characteristic
365	C₂×C₄	#14556093	1	1	yes	characteristic
366	C₂×C₄	Q₈×Dic₇₁	1	1	yes	characteristic
367	C₂×C₄	Q₈×Dic₇₁	1	1	yes	characteristic
368	C₂×C₄	#14556099	1	1	yes	characteristic
369	C₂×C₄	#14556103	1	1	yes	characteristic
370	C₂×C₄	#14556104	1	1	yes	characteristic
371	C₂×C₄	#14556104	1	1	yes	characteristic
372	C₂×C₄	#14556108	1	1	yes	characteristic
373	C₂×C₄	#14556108	1	1	yes	characteristic
374	C₂×C₄	#14556115	1	1	yes	characteristic
375	C₂×C₄	#14556117	1	1	yes	characteristic
376	C₂×C₄	#14556119	1	1	yes	characteristic
377	C₂×C₄	#14556119	1	1	yes	characteristic
378	C₂×C₄	#14556126	1	1	yes	characteristic
379	C₂×C₄	#14556127	1	1	yes	characteristic
380	C₈	—	142	4	no	—
381	C₈	C₇₁⋊#95	1	8	yes	complemented
382	C₂²	C₄⋊C₄×Dic₇₁	1	1	yes	characteristic
383	C₂²	#17985856	1	1	yes	characteristic
384	C₂²	#17985868	1	1	yes	characteristic
385	C₂²	#17985895	1	1	yes	characteristic
386	C₂²	#17985898	1	1	yes	characteristic
387	C₂²	#17985900	1	1	yes	characteristic
388	C₂²	#17985902	1	1	yes	characteristic
389	C₂²	#106×D₇₁	1	2	yes	—
390	C₂²	#17986034	1	2	yes	—
391	C₂²	#17986086	1	4	yes	—
392	C₂²	SD₁₆×Dic₇₁	1	4	yes	—
393	C₂²	#17986225	1	4	yes	—
394	C₂²	#17986229	1	4	yes	—
395	C₂²	#17986370	1	2	yes	—
396	C₂²	#17986380	1	2	yes	—
397	C₂²	#17986396	1	2	yes	—
398	C₂²	#17986399	1	2	yes	—
399	C₄	—	8	4	no	—
400	C₄	—	568	4	no	—
401	C₄	—	142	8	no	—
402	C₄	C₂×C₇₁⋊#95	1	1	yes	characteristic
403	C₄	C₄⋊C₄×Dic₇₁	1	1	yes	characteristic
404	C₄	#17985856	1	1	yes	characteristic
405	C₄	#17985864	1	1	yes	characteristic
406	C₄	#17985895	1	1	yes	characteristic
407	C₄	#17985898	1	1	yes	characteristic
408	C₄	#17985904	1	1	yes	characteristic
409	C₄	#17985906	1	1	yes	characteristic
410	C₂	#22586569	1	1	yes	characteristic
411	C₂	#106×Dic₇₁	1	2	yes	—
412	C₂	#22588362	1	2	yes	—
413	C₂	#22588495	1	1	yes	characteristic
414	C₂	#22588501	1	1	yes	characteristic
415	C₂	#22589066	1	2	yes	—
416	C₂	#22589069	1	2	yes	—
417	C₂	#22589192	1	2	yes	—
418	C₂	#22589196	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₄×D₇₁
commutator	C₂×C₄×C₇₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₁
Fitting	C₂²×#106×C₇₁	C₂
socle, prime radical	C₂⁴×C₇₁	C₂×D₄
cosocle	C₂³×C₄×C₇₁	C₂³
hypercenter	C₂²×#106	D₇₁
hypocenter	C₇₁	#10861
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×#106

Complements

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

N	H ≅ G/N	type
11. C₂×#14556060	C₄	semidirect
14. C₂×C₈×Dic₇₁	C₄	semidirect
21. C₂×#106×C₇₁	C₄	semidirect
169. C₂×Dic₇₁	#106	semidirect
170. C₈×C₇₁	#95	semidirect
215. C₇₁	#10861	semidirect
226. C₂×#106	Dic₇₁	semidirect
381. C₈	C₇₁⋊#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14556060	2
C₂²×C₈×Dic₇₁	2
C₂×#17985761	2
#22586569	2
C₂²×#106×C₇₁	2
#10861	71