Subgroups — #32002139

Order 18176.

814 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22589277	C₂	1	2	yes	maximal
2	#22589059	C₂	1	2	yes	maximal
3	#22588899	C₂	1	4	yes	maximal
4	C₄×C₄⋊(C₇₁⋊C₈)	C₂	1	2	yes	maximal
5	C₄×C₄⋊(C₇₁⋊C₈)	C₂	1	1	yes	maximal, characteristic
6	#22588086	C₂	1	2	yes	maximal
7	C₄²×C₇₁⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₄²×Q₈×C₇₁	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	4	yes	—
11	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₇₁⋊C₈	C₂²	1	2	yes	—
13	C₂×C₄×C₇₁⋊C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₇₁⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
16	#17985754	C₂²	1	4	yes	—
17	#17985754	C₂²	1	2	yes	—
18	#17985754	C₂²	1	4	yes	—
19	#17985754	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₇₁	C₄	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₇₁	C₄	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₇₁	C₄	1	2	yes	—
24	C₄×C₄⋊C₄×C₇₁	C₄	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₇₁	C₄	1	2	yes	—
26	C₄×C₄⋊C₄×C₇₁	C₄	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
29	C₄³×C₇₁	C₂²	1	1	yes	characteristic
30	C₄³×C₇₁	C₂²	1	2	yes	—
31	C₂²×C₇₁⋊C₈	C₂³	1	4	yes	—
32	C₂²×C₇₁⋊C₈	C₂³	1	2	yes	—
33	C₂²×C₇₁⋊C₈	C₂³	1	2	yes	—
34	C₄⋊(C₇₁⋊C₈)	—	2	8	no	—
35	C₄⋊(C₇₁⋊C₈)	—	2	4	no	—
36	C₄×C₇₁⋊C₈	—	2	4	no	—
37	C₄×C₇₁⋊C₈	—	2	4	no	—
38	C₄×C₇₁⋊C₈	—	2	2	no	—
39	C₄×C₇₁⋊C₈	—	2	4	no	—
40	C₄×C₇₁⋊C₈	Q₈	1	4	yes	complemented
41	C₂²×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
42	C₄×Q₈×C₇₁	—	2	4	no	—
43	C₄×Q₈×C₇₁	—	2	4	no	—
44	C₄×Q₈×C₇₁	C₈	1	8	yes	complemented
45	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₇₁	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₇₁	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₇₁	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₇₁	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
60	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
62	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
64	#95×C₇₁	C₂×C₄	1	2	yes	—
65	#95×C₇₁	C₂×C₄	1	2	yes	—
66	#95×C₇₁	C₂×C₄	1	2	yes	—
67	C₂×C₇₁⋊C₈	—	2	2	no	—
68	C₂×C₇₁⋊C₈	—	2	2	no	—
69	C₂×C₇₁⋊C₈	—	2	2	no	—
70	C₂×C₇₁⋊C₈	—	2	2	no	—
71	C₂×C₇₁⋊C₈	—	2	4	no	—
72	C₂×C₇₁⋊C₈	—	2	4	no	—
73	C₂×C₇₁⋊C₈	—	2	4	no	—
74	C₂×C₇₁⋊C₈	C₂×Q₈	1	4	yes	—
75	C₂×C₇₁⋊C₈	#41	1	4	yes	—
76	C₂×Q₈×C₇₁	—	2	2	no	—
77	C₂×Q₈×C₇₁	—	2	2	no	—
78	C₂×Q₈×C₇₁	C₂×C₈	1	4	yes	—
79	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
90	C₄⋊C₄×C₇₁	—	2	4	no	—
91	C₄⋊C₄×C₇₁	—	2	2	no	—
92	C₄⋊C₄×C₇₁	—	2	4	no	—
93	C₄⋊C₄×C₇₁	—	2	2	no	—
94	C₄⋊C₄×C₇₁	C₂×C₈	1	8	yes	—
95	C₄⋊C₄×C₇₁	C₂×C₈	1	4	yes	—
96	C₄²×C₇₁	—	2	4	no	—
97	C₄²×C₇₁	—	2	2	no	—
98	C₄²×C₇₁	—	2	2	no	—
99	C₄²×C₇₁	—	2	4	no	—
100	C₄²×C₇₁	—	2	4	no	—
101	C₄²×C₇₁	—	2	4	no	—
102	C₄²×C₇₁	—	2	2	no	—
103	C₄²×C₇₁	—	2	4	no	—
104	C₄²×C₇₁	C₂×C₈	1	8	yes	—
105	C₄²×C₇₁	C₂×C₈	1	4	yes	—
106	C₄²×C₇₁	M₁₆	1	4	yes	—
107	C₄²×C₇₁	C₂×Q₈	1	2	yes	—
108	C₄²×C₇₁	#41	1	4	yes	—
109	C₄²×C₇₁	#41	1	2	yes	—
110	C₂³×C₇₁	C₂³×C₄	1	1	yes	characteristic
111	Q₈×C₇₁	—	2	8	no	—
112	C₂×C₄×C₇₁	—	2	2	no	—
113	C₂×C₄×C₇₁	—	2	1	no	—
114	C₂×C₄×C₇₁	—	2	2	no	—
115	C₂×C₄×C₇₁	—	2	1	no	—
116	C₂×C₄×C₇₁	—	2	2	no	—
117	C₂×C₄×C₇₁	—	2	1	no	—
118	C₂×C₄×C₇₁	—	2	1	no	—
119	C₂×C₄×C₇₁	—	2	1	no	—
120	C₂×C₄×C₇₁	—	2	2	no	—
121	C₂×C₄×C₇₁	—	2	1	no	—
122	C₂×C₄×C₇₁	—	2	2	no	—
123	C₂×C₄×C₇₁	—	2	2	no	—
124	C₂×C₄×C₇₁	—	2	2	no	—
125	C₂×C₄×C₇₁	—	2	2	no	—
126	C₂×C₄×C₇₁	—	2	2	no	—
127	C₂×C₄×C₇₁	—	2	2	no	—
128	C₂×C₄×C₇₁	#117	1	2	yes	—
129	C₂×C₄×C₇₁	#117	1	2	yes	—
130	C₂×C₄×C₇₁	C₄×Q₈	1	2	yes	—
131	C₂×C₄×C₇₁	C₄×Q₈	1	2	yes	—
132	C₂×C₄×C₇₁	C₂²×C₈	1	4	yes	—
133	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
134	C₂×C₄×C₇₁	C₂²×C₈	1	4	yes	—
135	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
136	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
137	C₂×C₄×C₇₁	C₂×M₁₆	1	2	yes	—
138	C₂×C₄×C₇₁	C₂×M₁₆	1	2	yes	—
139	C₂×C₄×C₇₁	C₂×M₁₆	1	2	yes	—
140	C₂×C₄×C₇₁	#131	1	2	yes	—
141	C₂×C₄×C₇₁	#131	1	2	yes	—
142	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
144	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
145	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
146	C₇₁⋊C₈	—	2	4	no	—
147	C₇₁⋊C₈	—	2	4	no	—
148	C₇₁⋊C₈	—	4	4	no	—
149	C₂²×C₇₁	C₂×#117	1	1	yes	characteristic
150	C₂²×C₇₁	C₂×C₄×Q₈	1	1	yes	characteristic
151	C₂²×C₇₁	C₄×#41	1	1	yes	characteristic
152	C₂²×C₇₁	C₂³×C₈	1	1	yes	characteristic
153	C₂²×C₇₁	C₂²×M₁₆	1	1	yes	characteristic
154	C₂²×C₇₁	C₂×#131	1	1	yes	characteristic
155	C₂²×C₇₁	C₂×#131	1	1	yes	characteristic
156	C₄×C₇₁	—	2	4	no	—
157	C₄×C₇₁	—	2	2	no	—
158	C₄×C₇₁	—	2	2	no	—
159	C₄×C₇₁	—	2	4	no	—
160	C₄×C₇₁	—	2	2	no	—
161	C₄×C₇₁	—	4	2	no	—
162	C₄×C₇₁	—	4	2	no	—
163	C₄×C₇₁	#431	1	4	yes	—
164	C₄×C₇₁	C₈×Q₈	1	4	yes	—
165	C₄×C₇₁	#446	1	4	yes	—
166	C₄×C₇₁	#529	1	2	yes	—
167	C₄×C₇₁	#533	1	2	yes	—
168	#21339	—	71	1	no	maximal, Sylow
169	C₂×C₇₁	#2295	1	1	yes	characteristic
170	C₂×C₇₁	C₂×#431	1	1	yes	characteristic
171	C₂×C₇₁	#2922	1	1	yes	characteristic
172	C₂×C₇₁	C₂×C₈×Q₈	1	1	yes	characteristic
173	C₂×C₇₁	C₂×#446	1	1	yes	characteristic
174	C₂×C₇₁	C₈×#41	1	1	yes	characteristic
175	C₂×C₇₁	#2965	1	1	yes	characteristic
176	C₄²×Q₈	D₇₁	1	1	yes	characteristic
177	#1984	—	71	2	no	—
178	#1939	—	71	2	no	—
179	#1916	—	71	4	no	—
180	C₄×C₄⋊C₈	—	71	1	no	—
181	C₄×C₄⋊C₈	—	71	2	no	—
182	#1744	—	71	2	no	—
183	C₄²×C₈	—	71	1	no	—
184	C₇₁	#21339	1	1	yes	characteristic, complemented, Sylow
185	C₂×C₄×Q₈	Dic₇₁	1	1	yes	characteristic
186	C₂×C₄×Q₈	Dic₇₁	1	1	yes	characteristic
187	C₂×C₄×Q₈	C₂×D₇₁	1	1	yes	characteristic
188	C₂×C₄⋊C₈	—	71	4	no	—
189	C₂×C₄⋊C₈	—	71	2	no	—
190	C₂×C₄×C₈	—	71	1	no	—
191	C₂×C₄×C₈	—	71	2	no	—
192	C₂×C₄×C₈	—	71	2	no	—
193	C₂×C₄×C₈	—	71	1	no	—
194	C₂×C₄×C₈	—	71	2	no	—
195	C₄×C₄⋊C₄	Dic₇₁	1	2	yes	—
196	C₄×C₄⋊C₄	Dic₇₁	1	1	yes	characteristic
197	C₄×C₄⋊C₄	Dic₇₁	1	2	yes	—
198	C₄×C₄⋊C₄	Dic₇₁	1	1	yes	characteristic
199	C₄×C₄⋊C₄	C₂×D₇₁	1	2	yes	—
200	C₄×C₄⋊C₄	C₂×D₇₁	1	1	yes	characteristic
201	C₄³	C₂×D₇₁	1	1	yes	characteristic
202	C₄³	C₂×D₇₁	1	2	yes	—
203	#336	—	71	2	no	—
204	#336	—	71	4	no	—
205	#336	—	71	4	no	—
206	#336	—	71	4	no	—
207	C₂²×Q₈	C₂×Dic₇₁	1	1	yes	characteristic
208	C₂²×C₈	—	71	2	no	—
209	C₂²×C₈	—	71	2	no	—
210	C₂²×C₈	—	71	4	no	—
211	C₄×Q₈	—	2	4	no	—
212	C₄×Q₈	—	2	4	no	—
213	C₄×Q₈	C₇₁⋊C₈	1	8	yes	complemented
214	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂×Dic₇₁	1	2	yes	—
216	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×Dic₇₁	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×Dic₇₁	1	2	yes	—
219	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
220	C₂×C₄²	C₂×Dic₇₁	1	2	yes	—
221	C₂×C₄²	C₂×Dic₇₁	1	2	yes	—
222	C₂×C₄²	C₂×Dic₇₁	1	2	yes	—
223	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
224	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
225	C₂×C₄²	C₂×Dic₇₁	1	2	yes	—
226	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
227	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
228	C₂×C₄²	C₂²×D₇₁	1	2	yes	—
229	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
230	C₂×C₄²	C₂²×D₇₁	1	2	yes	—
231	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
232	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
233	C₄⋊C₈	—	142	8	no	—
234	C₄⋊C₈	—	142	4	no	—
235	C₄×C₈	—	71	4	no	—
236	C₄×C₈	—	142	4	no	—
237	C₄×C₈	—	142	4	no	—
238	C₄×C₈	—	142	4	no	—
239	C₄×C₈	—	142	2	no	—
240	#95	C₂×Dic₇₁	1	2	yes	—
241	#95	C₂×Dic₇₁	1	2	yes	—
242	#95	C₂×Dic₇₁	1	2	yes	—
243	C₂×Q₈	—	2	2	no	—
244	C₂×Q₈	—	2	2	no	—
245	C₂×Q₈	C₂×C₇₁⋊C₈	1	4	yes	—
246	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
247	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
248	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
249	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
250	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
251	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
252	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
253	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
254	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
255	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
256	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
257	C₂×C₈	—	71	4	no	—
258	C₂×C₈	—	71	4	no	—
259	C₂×C₈	—	142	4	no	—
260	C₂×C₈	—	142	4	no	—
261	C₂×C₈	—	142	4	no	—
262	C₂×C₈	—	142	2	no	—
263	C₂×C₈	—	142	2	no	—
264	C₂×C₈	—	142	2	no	—
265	C₂×C₈	—	142	2	no	—
266	C₄⋊C₄	—	2	4	no	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	C₂×C₇₁⋊C₈	1	8	yes	—
271	C₄⋊C₄	C₂×C₇₁⋊C₈	1	4	yes	—
272	C₄²	—	2	2	no	—
273	C₄²	—	2	4	no	—
274	C₄²	—	2	4	no	—
275	C₄²	—	2	4	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	2	no	—
278	C₄²	—	2	4	no	—
279	C₄²	—	2	4	no	—
280	C₄²	C₂×C₇₁⋊C₈	1	8	yes	—
281	C₄²	C₂×C₇₁⋊C₈	1	4	yes	—
282	C₄²	#11765849	1	4	yes	—
283	C₄²	Q₈×D₇₁	1	2	yes	—
284	C₄²	#11765865	1	4	yes	—
285	C₄²	#11765866	1	2	yes	—
286	C₂³	C₂³×Dic₇₁	1	1	yes	characteristic
287	Q₈	—	2	8	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	#14556087	1	2	yes	—
305	C₂×C₄	#14556087	1	2	yes	—
306	C₂×C₄	Q₈×Dic₇₁	1	2	yes	—
307	C₂×C₄	Q₈×Dic₇₁	1	2	yes	—
308	C₂×C₄	C₂²×C₇₁⋊C₈	1	4	yes	—
309	C₂×C₄	C₂²×C₇₁⋊C₈	1	2	yes	—
310	C₂×C₄	C₂²×C₇₁⋊C₈	1	4	yes	—
311	C₂×C₄	C₂²×C₇₁⋊C₈	1	2	yes	—
312	C₂×C₄	C₂²×C₇₁⋊C₈	1	2	yes	—
313	C₂×C₄	C₂×#11765849	1	2	yes	—
314	C₂×C₄	C₂×#11765849	1	2	yes	—
315	C₂×C₄	C₂×#11765849	1	2	yes	—
316	C₂×C₄	#14556135	1	2	yes	—
317	C₂×C₄	#14556135	1	2	yes	—
318	C₂×C₄	C₂×Q₈×D₇₁	1	1	yes	characteristic
319	C₂×C₄	#41×D₇₁	1	2	yes	—
320	C₂×C₄	C₂×#11765865	1	2	yes	—
321	C₂×C₄	C₂×#11765866	1	1	yes	characteristic
322	C₈	—	284	4	no	—
323	C₈	—	142	4	no	—
324	C₈	—	142	4	no	—
325	C₂²	C₂×#14556087	1	1	yes	characteristic
326	C₂²	C₂×Q₈×Dic₇₁	1	1	yes	characteristic
327	C₂²	#41×Dic₇₁	1	1	yes	characteristic
328	C₂²	C₂³×C₇₁⋊C₈	1	1	yes	characteristic
329	C₂²	C₂²×#11765849	1	1	yes	characteristic
330	C₂²	C₂×#14556135	1	1	yes	characteristic
331	C₂²	C₂×#14556135	1	1	yes	characteristic
332	C₄	—	2	4	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	4	no	—
336	C₄	—	2	2	no	—
337	C₄	—	4	2	no	—
338	C₄	—	4	2	no	—
339	C₄	#17986052	1	4	yes	—
340	C₄	Q₈×C₇₁⋊C₈	1	4	yes	—
341	C₄	#17986130	1	4	yes	—
342	C₄	#17986536	1	2	yes	—
343	C₄	#17986553	1	2	yes	—
344	C₂	#22590818	1	1	yes	characteristic
345	C₂	C₂×#17986052	1	1	yes	characteristic
346	C₂	#22596984	1	1	yes	characteristic
347	C₂	C₂×Q₈×C₇₁⋊C₈	1	1	yes	characteristic
348	C₂	C₂×#17986130	1	1	yes	characteristic
349	C₂	#41×C₇₁⋊C₈	1	1	yes	characteristic
350	C₂	#22597307	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²×D₇₁
commutator	C₂²×C₇₁	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₇₁
Fitting	C₄²×Q₈×C₇₁	C₂
socle, prime radical	C₂³×C₇₁	C₂³×C₄
cosocle	C₂²×C₄×C₇₁	C₂⁴
hypercenter	C₄²×Q₈	D₇₁
hypocenter	C₇₁	#21339
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄² ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
40. C₄×C₇₁⋊C₈	Q₈	semidirect
44. C₄×Q₈×C₇₁	C₈	semidirect
184. C₇₁	#21339	semidirect
213. C₄×Q₈	C₇₁⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#22589277	2
#22589059	2
#22588899	2
C₄×C₄⋊(C₇₁⋊C₈)	2
#22588086	2
C₄²×C₇₁⋊C₈	2
C₄²×Q₈×C₇₁	2
#21339	71