Subgroups — C₂×C₇₁×#3189 #31881603

Order 18176.

2354 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₇₁	C₂	1	2	yes	maximal
2	C₇₁×#3189	C₂	1	16	yes	maximal, direct product factor
3	C₂×#484×C₇₁	C₂	1	4	yes	maximal, complemented
4	C₂×#467×C₇₁	C₂	1	4	yes	maximal, complemented
5	C₂×#451×C₇₁	C₂	1	4	yes	maximal, complemented
6	C₂²×C₂²⋊C₈×C₇₁	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₇₁	C₂²	1	2	yes	—
8	C₂⁴×C₄×C₇₁	C₂²	1	1	yes	characteristic
9	C₂²×Q₁₆×C₇₁	C₂²	1	4	yes	complemented
10	C₂³×C₈×C₇₁	C₂²	1	2	yes	—
11	C₂×C₂²⋊Q₈×C₇₁	—	2	2	no	—
12	C₂×C₂²⋊Q₈×C₇₁	—	2	8	no	—
13	C₂×C₂²⋊Q₈×C₇₁	—	2	2	no	—
14	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	4	yes	—
15	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	4	yes	—
16	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	16	yes	—
17	C₂²×C₄⋊C₄×C₇₁	—	2	2	no	—
18	C₂²×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₇₁	—	2	2	no	—
20	#484×C₇₁	C₂²	1	32	yes	complemented
21	#467×C₇₁	C₂²	1	32	yes	complemented
22	#451×C₇₁	C₂²	1	32	yes	complemented
23	C₂×#107×C₇₁	C₂²	1	4	yes	complemented
24	C₂×#103×C₇₁	C₂²	1	8	yes	complemented
25	C₂×C₂²⋊C₈×C₇₁	C₂²	1	4	yes	—
26	C₂×C₂²⋊C₈×C₇₁	C₂²	1	8	yes	—
27	C₂⁵×C₇₁	D₄	1	1	yes	characteristic
28	C₂²×Q₈×C₇₁	—	2	4	no	—
29	C₂²×Q₈×C₇₁	—	2	2	no	—
30	C₂²×Q₈×C₇₁	—	4	8	no	—
31	C₂²×Q₈×C₇₁	C₂³	1	4	yes	—
32	C₂²×Q₈×C₇₁	C₂³	1	8	yes	—
33	C₂³×C₄×C₇₁	—	2	2	no	—
34	C₂³×C₄×C₇₁	—	2	2	no	—
35	C₂³×C₄×C₇₁	—	4	4	no	—
36	C₂³×C₄×C₇₁	D₄	1	2	yes	—
37	C₂³×C₄×C₇₁	D₄	1	4	yes	—
38	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₇₁	C₂³	1	4	yes	—
42	C₂×Q₁₆×C₇₁	—	4	8	no	—
43	C₂×Q₁₆×C₇₁	C₂³	1	16	yes	complemented
44	C₂²×C₈×C₇₁	—	4	4	no	—
45	C₂²×C₈×C₇₁	C₂³	1	4	yes	—
46	C₂²×C₈×C₇₁	C₂³	1	8	yes	—
47	C₂²⋊Q₈×C₇₁	—	2	8	no	—
48	C₂²⋊Q₈×C₇₁	—	2	8	no	—
49	C₂²⋊Q₈×C₇₁	—	2	16	no	—
50	C₂²⋊Q₈×C₇₁	—	2	16	no	—
51	C₂²⋊Q₈×C₇₁	C₂³	1	16	yes	—
52	C₂²⋊Q₈×C₇₁	C₂³	1	16	yes	—
53	C₂×C₄⋊C₄×C₇₁	—	2	16	no	—
54	C₂×C₄⋊C₄×C₇₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₇₁	—	2	4	no	—
56	C₂×C₄⋊C₄×C₇₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₇₁	C₂³	1	8	yes	—
60	C₂×C₂²⋊C₄×C₇₁	—	2	16	no	—
61	C₂×C₂²⋊C₄×C₇₁	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₇₁	—	2	4	no	—
63	#107×C₇₁	C₂³	1	16	yes	complemented
64	#103×C₇₁	C₂³	1	32	yes	complemented
65	C₂²⋊C₈×C₇₁	C₂³	1	16	yes	—
66	C₂⁴×C₇₁	—	4	2	no	—
67	C₂⁴×C₇₁	—	4	2	no	—
68	C₂⁴×C₇₁	Q₁₆	1	8	yes	complemented
69	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
70	C₂⁴×C₇₁	C₂×D₄	1	2	yes	—
71	C₂⁴×C₇₁	C₂×D₄	1	4	yes	—
72	C₂×Q₈×C₇₁	—	2	8	no	—
73	C₂×Q₈×C₇₁	—	2	4	no	—
74	C₂×Q₈×C₇₁	—	2	16	no	—
75	C₂×Q₈×C₇₁	—	4	16	no	—
76	C₂×Q₈×C₇₁	—	4	8	no	—
77	C₂×Q₈×C₇₁	—	4	16	no	—
78	C₂×Q₈×C₇₁	C₂⁴	1	8	yes	—
79	C₂²×C₄×C₇₁	—	2	4	no	—
80	C₂²×C₄×C₇₁	—	2	8	no	—
81	C₂²×C₄×C₇₁	—	2	8	no	—
82	C₂²×C₄×C₇₁	—	2	8	no	—
83	C₂²×C₄×C₇₁	—	2	4	no	—
84	C₂²×C₄×C₇₁	—	2	4	no	—
85	C₂²×C₄×C₇₁	—	4	8	no	—
86	C₂²×C₄×C₇₁	—	4	8	no	—
87	C₂²×C₄×C₇₁	—	4	4	no	—
88	C₂²×C₄×C₇₁	—	4	2	no	—
89	C₂²×C₄×C₇₁	—	4	8	no	—
90	C₂²×C₄×C₇₁	—	4	8	no	—
91	C₂²×C₄×C₇₁	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₇₁	C₂×D₄	1	8	yes	—
96	C₂²×C₄×C₇₁	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₇₁	C₂⁴	1	4	yes	—
98	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
100	Q₁₆×C₇₁	—	4	16	no	—
101	C₂×C₈×C₇₁	—	2	8	no	—
102	C₂×C₈×C₇₁	—	4	8	no	—
103	C₂×C₈×C₇₁	C₂⁴	1	8	yes	—
104	C₄⋊C₄×C₇₁	—	2	16	no	—
105	C₄⋊C₄×C₇₁	—	2	16	no	—
106	C₄⋊C₄×C₇₁	—	2	8	no	—
107	C₄⋊C₄×C₇₁	—	2	4	no	—
108	C₄⋊C₄×C₇₁	C₂⁴	1	8	yes	—
109	C₂²⋊C₄×C₇₁	—	2	16	no	—
110	C₂²⋊C₄×C₇₁	—	2	16	no	—
111	C₂³×C₇₁	—	2	4	no	—
112	C₂³×C₇₁	—	2	2	no	—
113	C₂³×C₇₁	—	2	4	no	—
114	C₂³×C₇₁	—	2	2	no	—
115	C₂³×C₇₁	—	4	4	no	—
116	C₂³×C₇₁	—	4	16	no	—
117	C₂³×C₇₁	—	4	4	no	—
118	C₂³×C₇₁	C₂×Q₁₆	1	4	yes	—
119	C₂³×C₇₁	C₂×Q₁₆	1	8	yes	—
120	C₂³×C₇₁	C₂×Q₁₆	1	16	yes	complemented
121	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
122	C₂³×C₇₁	C₂²×D₄	1	4	yes	—
123	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
124	Q₈×C₇₁	—	2	16	no	—
125	Q₈×C₇₁	—	4	16	no	—
126	Q₈×C₇₁	—	4	8	no	—
127	C₂×C₄×C₇₁	—	2	2	no	—
128	C₂×C₄×C₇₁	—	2	4	no	—
129	C₂×C₄×C₇₁	—	2	4	no	—
130	C₂×C₄×C₇₁	—	2	8	no	—
131	C₂×C₄×C₇₁	—	2	4	no	—
132	C₂×C₄×C₇₁	—	2	8	no	—
133	C₂×C₄×C₇₁	—	2	8	no	—
134	C₂×C₄×C₇₁	—	2	8	no	—
135	C₂×C₄×C₇₁	—	4	8	no	—
136	C₂×C₄×C₇₁	—	4	4	no	—
137	C₂×C₄×C₇₁	—	4	16	no	—
138	C₂×C₄×C₇₁	—	4	16	no	—
139	C₂×C₄×C₇₁	—	4	8	no	—
140	C₂×C₄×C₇₁	—	4	8	no	—
141	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
142	C₂×C₄×C₇₁	C₂²×D₄	1	4	yes	—
143	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₇₁	H(5,𝔽₂)	1	4	yes	—
145	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
146	C₈×C₇₁	—	2	8	no	—
147	C₂²×C₇₁	—	2	16	no	—
148	C₂²×C₇₁	—	2	8	no	—
149	C₂²×C₇₁	—	2	4	no	—
150	C₂²×C₇₁	—	2	2	no	—
151	C₂²×C₇₁	—	2	4	no	—
152	C₂²×C₇₁	—	2	2	no	—
153	C₂²×C₇₁	—	4	16	no	—
154	C₂²×C₇₁	#534	1	2	yes	—
155	C₂²×C₇₁	C₂²×Q₁₆	1	4	yes	—
156	C₂²×C₇₁	C₂²×Q₁₆	1	8	yes	—
157	C₂²×C₇₁	C₂²×Q₁₆	1	2	yes	—
158	C₂²×C₇₁	#575	1	2	yes	—
159	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
160	C₄×C₇₁	—	2	2	no	—
161	C₄×C₇₁	—	2	4	no	—
162	C₄×C₇₁	—	4	8	no	—
163	C₄×C₇₁	—	4	8	no	—
164	C₄×C₇₁	#534	1	2	yes	—
165	C₄×C₇₁	C₂×H(5,𝔽₂)	1	2	yes	—
166	C₂×#3189	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂×C₇₁	—	2	8	no	—
168	C₂×C₇₁	—	2	4	no	—
169	C₂×C₇₁	#3189	1	4	yes	direct product factor
170	C₂×C₇₁	C₂×#534	1	1	yes	characteristic
171	C₂×C₇₁	C₂³×Q₁₆	1	1	yes	characteristic
172	C₂×C₇₁	C₂×#575	1	1	yes	characteristic
173	C₂²×C₂²⋊Q₈	C₂×C₇₁	1	2	yes	—
174	#3189	C₂×C₇₁	1	16	yes	direct product factor
175	C₂×#484	C₂×C₇₁	1	4	yes	complemented
176	C₂×#467	C₂×C₇₁	1	4	yes	complemented
177	C₂×#451	C₂×C₇₁	1	4	yes	complemented
178	C₂²×C₂²⋊C₈	C₂×C₇₁	1	1	yes	characteristic
179	C₇₁	C₂×#3189	1	1	yes	characteristic, direct product factor, Sylow
180	C₂³×Q₈	C₂²×C₇₁	1	2	yes	—
181	C₂⁴×C₄	C₂²×C₇₁	1	1	yes	characteristic
182	C₂²×Q₁₆	C₂²×C₇₁	1	4	yes	complemented
183	C₂³×C₈	C₂²×C₇₁	1	2	yes	—
184	C₂×C₂²⋊Q₈	—	2	2	no	—
185	C₂×C₂²⋊Q₈	—	2	2	no	—
186	C₂×C₂²⋊Q₈	—	2	8	no	—
187	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	4	yes	—
188	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	16	yes	—
189	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	4	yes	—
190	C₂²×C₄⋊C₄	—	2	2	no	—
191	C₂²×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
192	C₂²×C₂²⋊C₄	—	2	2	no	—
193	#484	C₂²×C₇₁	1	32	yes	complemented
194	#467	C₂²×C₇₁	1	32	yes	complemented
195	#451	C₂²×C₇₁	1	32	yes	complemented
196	C₂×#107	C₂²×C₇₁	1	4	yes	complemented
197	C₂×#103	C₂²×C₇₁	1	8	yes	complemented
198	C₂×C₂²⋊C₈	C₂²×C₇₁	1	4	yes	—
199	C₂×C₂²⋊C₈	C₂²×C₇₁	1	8	yes	—
200	C₂⁵	D₄×C₇₁	1	1	yes	characteristic
201	C₂²×Q₈	—	2	2	no	—
202	C₂²×Q₈	—	2	4	no	—
203	C₂²×Q₈	—	4	8	no	—
204	C₂²×Q₈	C₂³×C₇₁	1	4	yes	—
205	C₂²×Q₈	C₂³×C₇₁	1	8	yes	—
206	C₂³×C₄	—	2	2	no	—
207	C₂³×C₄	—	2	2	no	—
208	C₂³×C₄	—	4	4	no	—
209	C₂³×C₄	D₄×C₇₁	1	2	yes	—
210	C₂³×C₄	D₄×C₇₁	1	4	yes	—
211	C₂³×C₄	D₄×C₇₁	1	1	yes	characteristic
212	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
213	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
214	C₂³×C₄	C₂³×C₇₁	1	4	yes	—
215	C₂×Q₁₆	—	4	8	no	—
216	C₂×Q₁₆	C₂³×C₇₁	1	16	yes	complemented
217	C₂²×C₈	—	4	4	no	—
218	C₂²×C₈	C₂³×C₇₁	1	4	yes	—
219	C₂²×C₈	C₂³×C₇₁	1	8	yes	—
220	C₂²⋊Q₈	—	2	8	no	—
221	C₂²⋊Q₈	—	2	8	no	—
222	C₂²⋊Q₈	—	2	16	no	—
223	C₂²⋊Q₈	—	2	16	no	—
224	C₂²⋊Q₈	C₂³×C₇₁	1	16	yes	—
225	C₂²⋊Q₈	C₂³×C₇₁	1	16	yes	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	4	no	—
228	C₂×C₄⋊C₄	—	2	16	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
232	C₂×C₄⋊C₄	C₂³×C₇₁	1	8	yes	—
233	C₂×C₂²⋊C₄	—	2	4	no	—
234	C₂×C₂²⋊C₄	—	2	4	no	—
235	C₂×C₂²⋊C₄	—	2	16	no	—
236	#107	C₂³×C₇₁	1	16	yes	complemented
237	#103	C₂³×C₇₁	1	32	yes	complemented
238	C₂²⋊C₈	C₂³×C₇₁	1	16	yes	—
239	C₂⁴	—	4	2	no	—
240	C₂⁴	—	4	2	no	—
241	C₂⁴	Q₁₆×C₇₁	1	8	yes	complemented
242	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
243	C₂⁴	C₂×D₄×C₇₁	1	2	yes	—
244	C₂⁴	C₂×D₄×C₇₁	1	4	yes	—
245	C₂×Q₈	—	2	8	no	—
246	C₂×Q₈	—	2	4	no	—
247	C₂×Q₈	—	2	16	no	—
248	C₂×Q₈	—	4	16	no	—
249	C₂×Q₈	—	4	8	no	—
250	C₂×Q₈	—	4	16	no	—
251	C₂×Q₈	C₂⁴×C₇₁	1	8	yes	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	4	8	no	—
259	C₂²×C₄	—	4	8	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	4	no	—
262	C₂²×C₄	—	4	8	no	—
263	C₂²×C₄	—	4	8	no	—
264	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
266	C₂²×C₄	C₂×D₄×C₇₁	1	4	yes	—
267	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
268	C₂²×C₄	C₂×D₄×C₇₁	1	8	yes	—
269	C₂²×C₄	C₂×D₄×C₇₁	1	4	yes	—
270	C₂²×C₄	C₂⁴×C₇₁	1	4	yes	—
271	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
272	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
273	Q₁₆	—	4	16	no	—
274	C₂×C₈	—	2	8	no	—
275	C₂×C₈	—	4	8	no	—
276	C₂×C₈	C₂⁴×C₇₁	1	8	yes	—
277	C₄⋊C₄	—	2	16	no	—
278	C₄⋊C₄	—	2	16	no	—
279	C₄⋊C₄	—	2	8	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	C₂⁴×C₇₁	1	8	yes	—
282	C₂²⋊C₄	—	2	16	no	—
283	C₂²⋊C₄	—	2	16	no	—
284	C₂³	—	2	4	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	2	no	—
288	C₂³	—	4	4	no	—
289	C₂³	—	4	16	no	—
290	C₂³	—	4	4	no	—
291	C₂³	C₂×Q₁₆×C₇₁	1	4	yes	—
292	C₂³	C₂×Q₁₆×C₇₁	1	8	yes	—
293	C₂³	C₂×Q₁₆×C₇₁	1	16	yes	complemented
294	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
295	C₂³	C₂²×D₄×C₇₁	1	4	yes	—
296	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
297	Q₈	—	2	16	no	—
298	Q₈	—	4	16	no	—
299	Q₈	—	4	8	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	8	no	—
310	C₂×C₄	—	4	16	no	—
311	C₂×C₄	—	4	16	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	—	4	8	no	—
314	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
315	C₂×C₄	C₂²×D₄×C₇₁	1	4	yes	—
316	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
317	C₂×C₄	H(5,𝔽₂)×C₇₁	1	4	yes	—
318	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
319	C₈	—	2	8	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	16	no	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	4	16	no	—
327	C₂²	#534×C₇₁	1	2	yes	—
328	C₂²	C₂²×Q₁₆×C₇₁	1	4	yes	—
329	C₂²	C₂²×Q₁₆×C₇₁	1	8	yes	—
330	C₂²	C₂²×Q₁₆×C₇₁	1	2	yes	—
331	C₂²	#575×C₇₁	1	2	yes	—
332	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
333	C₄	—	2	4	no	—
334	C₄	—	2	2	no	—
335	C₄	—	4	8	no	—
336	C₄	—	4	8	no	—
337	C₄	#534×C₇₁	1	2	yes	—
338	C₄	C₂×H(5,𝔽₂)×C₇₁	1	2	yes	—
339	C₂	—	2	8	no	—
340	C₂	—	2	4	no	—
341	C₂	C₇₁×#3189	1	4	yes	direct product factor
342	C₂	C₂×#534×C₇₁	1	1	yes	characteristic
343	C₂	C₂³×Q₁₆×C₇₁	1	1	yes	characteristic
344	C₂	C₂×#575×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
prime radical	C₂⁵×C₇₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₂⁴×C₄×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₁×#3189	C₂	direct (N × H)
3. C₂×#484×C₇₁	C₂	semidirect
4. C₂×#467×C₇₁	C₂	semidirect
5. C₂×#451×C₇₁	C₂	semidirect
9. C₂²×Q₁₆×C₇₁	C₂²	semidirect
20. #484×C₇₁	C₂²	semidirect
21. #467×C₇₁	C₂²	semidirect
22. #451×C₇₁	C₂²	semidirect
23. C₂×#107×C₇₁	C₂²	semidirect
24. C₂×#103×C₇₁	C₂²	semidirect
43. C₂×Q₁₆×C₇₁	C₂³	semidirect
63. #107×C₇₁	C₂³	semidirect
64. #103×C₇₁	C₂³	semidirect
68. C₂⁴×C₇₁	Q₁₆	semidirect
120. C₂³×C₇₁	C₂×Q₁₆	semidirect
166. C₂×#3189	C₇₁	direct (N × H)
169. C₂×C₇₁	#3189	direct (N × H)
174. #3189	C₂×C₇₁	direct (N × H)
175. C₂×#484	C₂×C₇₁	semidirect
176. C₂×#467	C₂×C₇₁	semidirect
177. C₂×#451	C₂×C₇₁	semidirect
179. C₇₁	C₂×#3189	direct (N × H)
182. C₂²×Q₁₆	C₂²×C₇₁	semidirect
193. #484	C₂²×C₇₁	semidirect
194. #467	C₂²×C₇₁	semidirect
195. #451	C₂²×C₇₁	semidirect
196. C₂×#107	C₂²×C₇₁	semidirect
197. C₂×#103	C₂²×C₇₁	semidirect
216. C₂×Q₁₆	C₂³×C₇₁	semidirect
236. #107	C₂³×C₇₁	semidirect
237. #103	C₂³×C₇₁	semidirect
241. C₂⁴	Q₁₆×C₇₁	semidirect
293. C₂³	C₂×Q₁₆×C₇₁	semidirect
341. C₂	C₇₁×#3189	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₇₁	2
C₇₁×#3189	2
C₂×#484×C₇₁	2
C₂×#467×C₇₁	2
C₂×#451×C₇₁	2
C₂²×C₂²⋊C₈×C₇₁	2
C₂×#3189	71

Subgroups — C2×C71×#3189 #31881603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₁×#3189 #31881603