Subgroups — D₄²×D₂₇₁ #46849799

Order 34688.

2536 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₂₇₁	C₂	1	4	yes	maximal, complemented
2	D₄×D₁₀₈₄	C₂	1	2	yes	maximal, complemented
3	#31774532	C₂	1	1	yes	maximal, characteristic, complemented
4	#31774531	C₂	1	4	yes	maximal, complemented
5	D₄×C₂²⋊D₂₇₁	C₂	1	4	yes	maximal, complemented
6	#31774529	C₂	1	4	yes	maximal, complemented
7	#127×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#121×D₂₇₁	C₂	1	4	yes	maximal, complemented
9	#120×D₂₇₁	C₂	1	4	yes	maximal, complemented
10	C₄×D₄×D₂₇₁	C₂	1	2	yes	maximal, complemented
11	D₄²×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×D₂₇₁	C₂²	1	4	yes	complemented
13	C₂²×D₁₀₈₄	C₂²	1	4	yes	complemented
14	C₂²×C₂²⋊D₂₇₁	C₂²	1	8	yes	complemented
15	C₂×D₄×D₂₇₁	—	2	32	no	—
16	C₂×D₄×D₂₇₁	C₂²	1	2	yes	—
17	C₂×D₄×D₂₇₁	C₂²	1	4	yes	complemented
18	C₂×D₄×D₂₇₁	C₂²	1	8	yes	complemented
19	C₂×D₄×D₂₇₁	C₂²	1	4	yes	complemented
20	C₂×D₄×D₂₇₁	C₂²	1	2	yes	complemented
21	C₂×D₄×D₂₇₁	C₂²	1	8	yes	complemented
22	C₂×D₄×D₂₇₁	C₂²	1	4	yes	complemented
23	C₂²×C₄×D₂₇₁	C₂²	1	4	yes	complemented
24	#22576157	C₂²	1	1	yes	characteristic, complemented
25	#22576156	C₂²	1	2	yes	complemented
26	#22576156	C₂²	1	4	yes	complemented
27	#22576135	C₂²	1	4	yes	complemented
28	#22576134	C₂²	1	4	yes	complemented
29	#22576133	C₂²	1	8	yes	complemented
30	#22576132	C₂²	1	8	yes	complemented
31	#22576131	C₂²	1	4	yes	complemented
32	#22576130	C₂²	1	8	yes	complemented
33	#22576130	C₂²	1	4	yes	complemented
34	#22576129	C₂²	1	4	yes	complemented
35	#22576128	C₂²	1	4	yes	complemented
36	#22576128	C₂²	1	8	yes	complemented
37	C₄×D₁₀₈₄	C₂²	1	2	yes	complemented
38	D₄×Dic₂₇₁	C₂²	1	2	yes	complemented
39	#22576122	C₂²	1	2	yes	complemented
40	C₄×C₂²⋊D₂₇₁	C₂²	1	4	yes	complemented
41	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	4	yes	complemented
42	C₄⋊C₄×D₂₇₁	C₂²	1	2	yes	complemented
43	C₂²⋊C₄×D₂₇₁	C₂²	1	4	yes	complemented
44	C₂²⋊C₄×D₂₇₁	C₂²	1	4	yes	complemented
45	C₄²×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
46	C₂²×D₄×C₂₇₁	C₂²	1	4	yes	complemented
47	#127×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
48	#121×C₂₇₁	C₂²	1	4	yes	complemented
49	#120×C₂₇₁	C₂²	1	4	yes	complemented
50	C₄×D₄×C₂₇₁	C₂²	1	2	yes	complemented
51	C₂³×D₂₇₁	—	2	32	no	—
52	C₂³×D₂₇₁	—	4	8	no	—
53	C₂³×D₂₇₁	C₂³	1	4	yes	—
54	C₂³×D₂₇₁	C₂³	1	4	yes	—
55	C₂³×D₂₇₁	C₂³	1	4	yes	complemented
56	C₂³×D₂₇₁	C₂³	1	8	yes	complemented
57	C₂×D₁₀₈₄	—	2	16	no	—
58	C₂×D₁₀₈₄	C₂³	1	2	yes	—
59	C₂×D₁₀₈₄	C₂³	1	8	yes	complemented
60	C₂×D₁₀₈₄	C₂³	1	4	yes	complemented
61	C₂×D₁₀₈₄	C₂³	1	2	yes	complemented
62	C₂×C₂²⋊D₂₇₁	—	2	32	no	—
63	C₂×C₂²⋊D₂₇₁	C₂³	1	4	yes	—
64	C₂×C₂²⋊D₂₇₁	C₂³	1	8	yes	complemented
65	C₂×C₂²⋊D₂₇₁	C₂³	1	8	yes	complemented
66	C₂×C₂²⋊D₂₇₁	C₂³	1	8	yes	complemented
67	C₂×C₂²⋊D₂₇₁	C₂³	1	4	yes	complemented
68	D₄×D₂₇₁	—	2	32	no	—
69	D₄×D₂₇₁	—	2	16	no	—
70	D₄×D₂₇₁	—	2	32	no	—
71	D₄×D₂₇₁	—	2	16	no	—
72	D₄×D₂₇₁	—	2	16	no	—
73	D₄×D₂₇₁	—	4	4	no	—
74	D₄×D₂₇₁	D₄	1	16	yes	direct product factor
75	C₂²×Dic₂₇₁	C₂³	1	4	yes	complemented
76	C₂×C₄×D₂₇₁	—	2	16	no	—
77	C₂×C₄×D₂₇₁	C₂³	1	4	yes	—
78	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₂₇₁	C₂³	1	2	yes	—
80	C₂×C₄×D₂₇₁	C₂³	1	4	yes	complemented
81	C₂×C₄×D₂₇₁	C₂³	1	4	yes	complemented
82	C₄⋊Dic₂₇₁	C₂³	1	2	yes	complemented
83	Dic₂₇₁⋊C₄	C₂³	1	4	yes	complemented
84	C₂²⋊Dic₂₇₁	C₂³	1	4	yes	complemented
85	C₂²⋊Dic₂₇₁	C₂³	1	4	yes	complemented
86	(C₂×D₂₇₁)⋊C₄	C₂³	1	4	yes	complemented
87	(C₂×D₂₇₁)⋊C₄	C₂³	1	4	yes	complemented
88	(C₂×D₂₇₁)⋊C₄	C₂³	1	8	yes	complemented
89	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic, complemented
90	C₄×Dic₂₇₁	C₂³	1	2	yes	complemented
91	C₂⁴×C₂₇₁	C₂³	1	4	yes	complemented
92	C₂×D₄×C₂₇₁	—	2	16	no	—
93	C₂×D₄×C₂₇₁	C₂³	1	2	yes	—
94	C₂×D₄×C₂₇₁	C₂³	1	8	yes	complemented
95	C₂×D₄×C₂₇₁	C₂³	1	4	yes	complemented
96	C₂×D₄×C₂₇₁	C₂³	1	2	yes	complemented
97	C₂²×C₄×C₂₇₁	C₂³	1	4	yes	complemented
98	C₄⋊C₄×C₂₇₁	C₂³	1	2	yes	complemented
99	C₂²⋊C₄×C₂₇₁	C₂³	1	4	yes	complemented
100	C₂²⋊C₄×C₂₇₁	C₂³	1	4	yes	complemented
101	C₄²×C₂₇₁	C₂³	1	1	yes	characteristic, complemented
102	C₂²×D₂₇₁	—	2	8	no	—
103	C₂²×D₂₇₁	—	2	8	no	—
104	C₂²×D₂₇₁	—	2	16	no	—
105	C₂²×D₂₇₁	—	2	16	no	—
106	C₂²×D₂₇₁	—	2	16	no	—
107	C₂²×D₂₇₁	—	2	16	no	—
108	C₂²×D₂₇₁	—	2	8	no	—
109	C₂²×D₂₇₁	—	4	4	no	—
110	C₂²×D₂₇₁	—	4	8	no	—
111	C₂²×D₂₇₁	—	4	64	no	—
112	C₂²×D₂₇₁	C₂×D₄	1	16	yes	complemented
113	C₂²×D₂₇₁	C₂⁴	1	4	yes	—
114	C₂²×D₂₇₁	C₂⁴	1	4	yes	—
115	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
116	D₁₀₈₄	—	2	16	no	—
117	D₁₀₈₄	—	2	8	no	—
118	D₁₀₈₄	—	4	2	no	—
119	D₁₀₈₄	C₂×D₄	1	8	yes	complemented
120	C₂²⋊D₂₇₁	—	2	16	no	—
121	C₂²⋊D₂₇₁	—	2	16	no	—
122	C₂²⋊D₂₇₁	—	2	16	no	—
123	C₂²⋊D₂₇₁	—	4	4	no	—
124	C₂²⋊D₂₇₁	C₂×D₄	1	16	yes	complemented
125	C₂×Dic₂₇₁	—	2	8	no	—
126	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
127	C₂×Dic₂₇₁	C₂⁴	1	4	yes	—
128	C₂×Dic₂₇₁	C₂⁴	1	2	yes	—
129	C₄×D₂₇₁	—	2	8	no	—
130	C₄×D₂₇₁	—	2	2	no	—
131	C₄×D₂₇₁	—	2	8	no	—
132	C₄×D₂₇₁	—	2	8	no	—
133	C₄×D₂₇₁	C₂×D₄	1	8	yes	complemented
134	C₂³×C₂₇₁	—	2	16	no	—
135	C₂³×C₂₇₁	—	4	4	no	—
136	C₂³×C₂₇₁	C₂⁴	1	4	yes	—
137	C₂³×C₂₇₁	C₂⁴	1	4	yes	—
138	D₄×C₂₇₁	—	2	16	no	—
139	D₄×C₂₇₁	—	2	8	no	—
140	D₄×C₂₇₁	—	4	2	no	—
141	D₄×C₂₇₁	C₂×D₄	1	8	yes	complemented
142	C₂×C₄×C₂₇₁	—	2	8	no	—
143	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
144	C₂×C₄×C₂₇₁	C₂⁴	1	4	yes	—
145	C₂×C₄×C₂₇₁	C₂⁴	1	2	yes	—
146	C₂²×C₂₇₁	—	2	4	no	—
147	C₂²×C₂₇₁	—	2	4	no	—
148	C₂²×C₂₇₁	—	2	8	no	—
149	C₂²×C₂₇₁	—	2	4	no	—
150	C₂²×C₂₇₁	—	4	16	no	—
151	C₂²×C₂₇₁	C₂²×D₄	1	8	yes	complemented
152	C₂²×C₂₇₁	C₂⁵	1	1	yes	characteristic
153	C₂×D₂₇₁	—	2	4	no	—
154	C₂×D₂₇₁	—	2	4	no	—
155	C₂×D₂₇₁	—	2	32	no	—
156	C₂×D₂₇₁	—	2	8	no	—
157	C₂×D₂₇₁	—	2	4	no	—
158	C₂×D₂₇₁	—	4	16	no	—
159	C₂×D₂₇₁	—	4	32	no	—
160	C₂×D₂₇₁	—	4	16	no	—
161	C₂×D₂₇₁	C₂²×D₄	1	4	yes	—
162	C₂×D₂₇₁	C₂²×D₄	1	8	yes	complemented
163	C₂×D₂₇₁	H(5,𝔽₂)	1	2	yes	—
164	C₄×C₂₇₁	—	2	4	no	—
165	C₄×C₂₇₁	—	2	1	no	—
166	C₄×C₂₇₁	C₂²×D₄	1	4	yes	complemented
167	Dic₂₇₁	—	2	4	no	—
168	Dic₂₇₁	—	2	1	no	—
169	Dic₂₇₁	C₂²×D₄	1	4	yes	complemented
170	C₂×C₂₇₁	—	2	8	no	—
171	C₂×C₂₇₁	—	4	4	no	—
172	C₂×C₂₇₁	C₂³×D₄	1	2	yes	—
173	C₂×C₂₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
174	D₂₇₁	—	2	8	no	—
175	D₂₇₁	—	4	4	no	—
176	D₂₇₁	D₄²	1	4	yes	direct product factor
177	C₂₇₁	C₂×D₄²	1	1	yes	characteristic, complemented, Sylow
178	C₂×D₄²	—	271	1	no	maximal, Sylow
179	C₂³×D₄	—	271	4	no	—
180	D₄²	—	271	4	no	—
181	D₄²	—	271	1	no	—
182	D₄²	—	271	4	no	—
183	D₄²	—	271	4	no	—
184	D₄²	—	271	2	no	—
185	D₄²	D₂₇₁	1	1	yes	characteristic, direct product factor
186	C₂×#127	—	271	1	no	—
187	C₂×#121	—	271	4	no	—
188	C₂×#120	—	271	4	no	—
189	C₂×C₄×D₄	—	271	2	no	—
190	C₂⁵	—	271	4	no	—
191	C₂²×D₄	—	271	2	no	—
192	C₂²×D₄	—	271	8	no	—
193	C₂²×D₄	—	271	4	no	—
194	C₂²×D₄	—	271	8	no	—
195	C₂²×D₄	—	271	4	no	—
196	C₂²×D₄	—	271	8	no	—
197	C₂²×D₄	—	271	4	no	—
198	C₂²×D₄	—	271	2	no	—
199	C₂²×D₄	—	271	4	no	—
200	C₂²×D₄	—	542	32	no	—
201	C₂²×D₄	C₂×D₂₇₁	1	4	yes	complemented
202	C₂³×C₄	—	271	4	no	—
203	#127	—	271	2	no	—
204	#127	—	271	4	no	—
205	#127	—	271	1	no	—
206	#127	C₂×D₂₇₁	1	1	yes	characteristic, complemented
207	#121	—	271	4	no	—
208	#121	—	271	8	no	—
209	#121	—	271	4	no	—
210	#121	—	271	4	no	—
211	#121	—	271	8	no	—
212	#121	C₂×D₂₇₁	1	4	yes	complemented
213	#120	—	271	4	no	—
214	#120	—	271	8	no	—
215	#120	—	271	4	no	—
216	#120	—	271	4	no	—
217	#120	—	271	8	no	—
218	#120	C₂×D₂₇₁	1	4	yes	complemented
219	C₄×D₄	—	271	2	no	—
220	C₄×D₄	—	271	4	no	—
221	C₄×D₄	—	271	2	no	—
222	C₄×D₄	—	271	4	no	—
223	C₄×D₄	—	271	2	no	—
224	C₄×D₄	C₂×D₂₇₁	1	2	yes	complemented
225	C₂×C₄⋊C₄	—	271	2	no	—
226	C₂×C₂²⋊C₄	—	271	4	no	—
227	C₂×C₂²⋊C₄	—	271	4	no	—
228	C₂×C₄²	—	271	1	no	—
229	C₂⁴	—	271	4	no	—
230	C₂⁴	—	271	4	no	—
231	C₂⁴	—	271	4	no	—
232	C₂⁴	—	271	8	no	—
233	C₂⁴	—	542	32	no	—
234	C₂⁴	—	1084	8	no	—
235	C₂⁴	C₂²×D₂₇₁	1	4	yes	complemented
236	C₂×D₄	—	2	16	no	—
237	C₂×D₄	—	271	4	no	—
238	C₂×D₄	—	271	16	no	—
239	C₂×D₄	—	271	8	no	—
240	C₂×D₄	—	271	8	no	—
241	C₂×D₄	—	271	8	no	—
242	C₂×D₄	—	271	4	no	—
243	C₂×D₄	—	271	2	no	—
244	C₂×D₄	—	271	8	no	—
245	C₂×D₄	—	271	4	no	—
246	C₂×D₄	—	271	2	no	—
247	C₂×D₄	—	542	16	no	—
248	C₂×D₄	—	542	16	no	—
249	C₂×D₄	—	542	32	no	—
250	C₂×D₄	—	542	16	no	—
251	C₂×D₄	—	542	32	no	—
252	C₂×D₄	—	542	32	no	—
253	C₂×D₄	—	542	16	no	—
254	C₂×D₄	—	1084	4	no	—
255	C₂×D₄	C₂²×D₂₇₁	1	2	yes	—
256	C₂×D₄	C₂²×D₂₇₁	1	8	yes	complemented
257	C₂×D₄	C₂²×D₂₇₁	1	4	yes	complemented
258	C₂×D₄	C₂²×D₂₇₁	1	2	yes	complemented
259	C₂²×C₄	—	271	2	no	—
260	C₂²×C₄	—	271	4	no	—
261	C₂²×C₄	—	271	1	no	—
262	C₂²×C₄	—	271	4	no	—
263	C₂²×C₄	—	271	4	no	—
264	C₂²×C₄	—	271	4	no	—
265	C₂²×C₄	—	542	16	no	—
266	C₂²×C₄	C₂²×D₂₇₁	1	4	yes	complemented
267	C₄⋊C₄	—	271	4	no	—
268	C₄⋊C₄	—	271	2	no	—
269	C₄⋊C₄	C₂²×D₂₇₁	1	2	yes	complemented
270	C₂²⋊C₄	—	271	4	no	—
271	C₂²⋊C₄	—	271	4	no	—
272	C₂²⋊C₄	—	271	4	no	—
273	C₂²⋊C₄	—	271	4	no	—
274	C₂²⋊C₄	—	271	8	no	—
275	C₂²⋊C₄	C₂²×D₂₇₁	1	4	yes	complemented
276	C₂²⋊C₄	C₂²×D₂₇₁	1	4	yes	complemented
277	C₄²	—	271	1	no	—
278	C₄²	—	271	2	no	—
279	C₄²	C₂²×D₂₇₁	1	1	yes	characteristic, complemented
280	C₂³	—	2	16	no	—
281	C₂³	—	4	4	no	—
282	C₂³	—	271	1	no	—
283	C₂³	—	271	16	no	—
284	C₂³	—	271	4	no	—
285	C₂³	—	271	4	no	—
286	C₂³	—	542	8	no	—
287	C₂³	—	542	8	no	—
288	C₂³	—	542	16	no	—
289	C₂³	—	542	16	no	—
290	C₂³	—	542	16	no	—
291	C₂³	—	542	8	no	—
292	C₂³	—	542	16	no	—
293	C₂³	—	1084	8	no	—
294	C₂³	—	1084	4	no	—
295	C₂³	—	1084	64	no	—
296	C₂³	C₂³×D₂₇₁	1	4	yes	—
297	C₂³	C₂³×D₂₇₁	1	4	yes	—
298	D₄	—	2	16	no	—
299	D₄	—	2	8	no	—
300	D₄	—	4	2	no	—
301	D₄	—	271	16	no	—
302	D₄	—	271	8	no	—
303	D₄	—	542	16	no	—
304	D₄	—	542	16	no	—
305	D₄	—	542	16	no	—
306	D₄	—	542	16	no	—
307	D₄	—	542	8	no	—
308	D₄	—	1084	2	no	—
309	D₄	—	1084	4	no	—
310	D₄	D₄×D₂₇₁	1	8	yes	direct product factor
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	271	2	no	—
313	C₂×C₄	—	271	8	no	—
314	C₂×C₄	—	271	1	no	—
315	C₂×C₄	—	271	4	no	—
316	C₂×C₄	—	542	8	no	—
317	C₂×C₄	—	542	8	no	—
318	C₂×C₄	—	542	2	no	—
319	C₂×C₄	—	542	8	no	—
320	C₂×C₄	—	542	8	no	—
321	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
322	C₂×C₄	C₂³×D₂₇₁	1	4	yes	—
323	C₂×C₄	C₂³×D₂₇₁	1	2	yes	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	2	4	no	—
327	C₂²	—	2	8	no	—
328	C₂²	—	4	16	no	—
329	C₂²	—	271	2	no	—
330	C₂²	—	271	4	no	—
331	C₂²	—	271	8	no	—
332	C₂²	—	542	32	no	—
333	C₂²	—	542	4	no	—
334	C₂²	—	542	4	no	—
335	C₂²	—	542	4	no	—
336	C₂²	—	542	8	no	—
337	C₂²	—	1084	32	no	—
338	C₂²	—	1084	16	no	—
339	C₂²	—	1084	16	no	—
340	C₂²	C₂×D₄×D₂₇₁	1	8	yes	complemented
341	C₂²	C₂⁴×D₂₇₁	1	1	yes	characteristic
342	C₄	—	2	1	no	—
343	C₄	—	2	4	no	—
344	C₄	—	271	4	no	—
345	C₄	—	542	1	no	—
346	C₄	—	542	4	no	—
347	C₄	C₂×D₄×D₂₇₁	1	4	yes	complemented
348	C₂	—	2	8	no	—
349	C₂	—	4	4	no	—
350	C₂	—	271	4	no	—
351	C₂	—	542	8	no	—
352	C₂	—	1084	4	no	—
353	C₂	C₂²×D₄×D₂₇₁	1	2	yes	—
354	C₂	H(5,𝔽₂)×D₂₇₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₇₁
commutator, socle, cosocle	C₂²×C₂₇₁	C₂⁵
Fitting	D₄²×C₂₇₁	C₂
hypercenter	D₄²	D₂₇₁
hypocenter	C₂₇₁	C₂×D₄²
LCS	G ▷ C₂²×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₂₇₁	C₂	semidirect
2. D₄×D₁₀₈₄	C₂	semidirect
3. #31774532	C₂	semidirect
4. #31774531	C₂	semidirect
5. D₄×C₂²⋊D₂₇₁	C₂	semidirect
6. #31774529	C₂	semidirect
7. #127×D₂₇₁	C₂	semidirect
8. #121×D₂₇₁	C₂	semidirect
9. #120×D₂₇₁	C₂	semidirect
10. C₄×D₄×D₂₇₁	C₂	semidirect
11. D₄²×C₂₇₁	C₂	semidirect
12. C₂⁴×D₂₇₁	C₂²	semidirect
13. C₂²×D₁₀₈₄	C₂²	semidirect
14. C₂²×C₂²⋊D₂₇₁	C₂²	semidirect
17. C₂×D₄×D₂₇₁	C₂²	semidirect
18. C₂×D₄×D₂₇₁	C₂²	semidirect
19. C₂×D₄×D₂₇₁	C₂²	semidirect
20. C₂×D₄×D₂₇₁	C₂²	semidirect
21. C₂×D₄×D₂₇₁	C₂²	semidirect
22. C₂×D₄×D₂₇₁	C₂²	semidirect
23. C₂²×C₄×D₂₇₁	C₂²	semidirect
24. #22576157	C₂²	semidirect
25. #22576156	C₂²	semidirect
26. #22576156	C₂²	semidirect
27. #22576135	C₂²	semidirect
28. #22576134	C₂²	semidirect
29. #22576133	C₂²	semidirect
30. #22576132	C₂²	semidirect
31. #22576131	C₂²	semidirect
32. #22576130	C₂²	semidirect
33. #22576130	C₂²	semidirect
34. #22576129	C₂²	semidirect
35. #22576128	C₂²	semidirect
36. #22576128	C₂²	semidirect
37. C₄×D₁₀₈₄	C₂²	semidirect
38. D₄×Dic₂₇₁	C₂²	semidirect
39. #22576122	C₂²	semidirect
40. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
41. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
42. C₄⋊C₄×D₂₇₁	C₂²	semidirect
43. C₂²⋊C₄×D₂₇₁	C₂²	semidirect
44. C₂²⋊C₄×D₂₇₁	C₂²	semidirect
45. C₄²×D₂₇₁	C₂²	semidirect
46. C₂²×D₄×C₂₇₁	C₂²	semidirect
47. #127×C₂₇₁	C₂²	semidirect
48. #121×C₂₇₁	C₂²	semidirect
49. #120×C₂₇₁	C₂²	semidirect
50. C₄×D₄×C₂₇₁	C₂²	semidirect
55. C₂³×D₂₇₁	C₂³	semidirect
56. C₂³×D₂₇₁	C₂³	semidirect
59. C₂×D₁₀₈₄	C₂³	semidirect
60. C₂×D₁₀₈₄	C₂³	semidirect
61. C₂×D₁₀₈₄	C₂³	semidirect
64. C₂×C₂²⋊D₂₇₁	C₂³	semidirect
65. C₂×C₂²⋊D₂₇₁	C₂³	semidirect
66. C₂×C₂²⋊D₂₇₁	C₂³	semidirect
67. C₂×C₂²⋊D₂₇₁	C₂³	semidirect
74. D₄×D₂₇₁	D₄	direct (N × H)
75. C₂²×Dic₂₇₁	C₂³	semidirect
80. C₂×C₄×D₂₇₁	C₂³	semidirect
81. C₂×C₄×D₂₇₁	C₂³	semidirect
82. C₄⋊Dic₂₇₁	C₂³	semidirect
83. Dic₂₇₁⋊C₄	C₂³	semidirect
84. C₂²⋊Dic₂₇₁	C₂³	semidirect
85. C₂²⋊Dic₂₇₁	C₂³	semidirect
86. (C₂×D₂₇₁)⋊C₄	C₂³	semidirect
87. (C₂×D₂₇₁)⋊C₄	C₂³	semidirect
88. (C₂×D₂₇₁)⋊C₄	C₂³	semidirect
89. C₄×Dic₂₇₁	C₂³	semidirect
90. C₄×Dic₂₇₁	C₂³	semidirect
91. C₂⁴×C₂₇₁	C₂³	semidirect
94. C₂×D₄×C₂₇₁	C₂³	semidirect
95. C₂×D₄×C₂₇₁	C₂³	semidirect
96. C₂×D₄×C₂₇₁	C₂³	semidirect
97. C₂²×C₄×C₂₇₁	C₂³	semidirect
98. C₄⋊C₄×C₂₇₁	C₂³	semidirect
99. C₂²⋊C₄×C₂₇₁	C₂³	semidirect
100. C₂²⋊C₄×C₂₇₁	C₂³	semidirect
101. C₄²×C₂₇₁	C₂³	semidirect
112. C₂²×D₂₇₁	C₂×D₄	semidirect
119. D₁₀₈₄	C₂×D₄	semidirect
124. C₂²⋊D₂₇₁	C₂×D₄	semidirect
133. C₄×D₂₇₁	C₂×D₄	semidirect
141. D₄×C₂₇₁	C₂×D₄	semidirect
151. C₂²×C₂₇₁	C₂²×D₄	semidirect
162. C₂×D₂₇₁	C₂²×D₄	semidirect
166. C₄×C₂₇₁	C₂²×D₄	semidirect
169. Dic₂₇₁	C₂²×D₄	semidirect
176. D₂₇₁	D₄²	direct (N × H)
177. C₂₇₁	C₂×D₄²	semidirect
185. D₄²	D₂₇₁	direct (N × H)
201. C₂²×D₄	C₂×D₂₇₁	semidirect
206. #127	C₂×D₂₇₁	semidirect
212. #121	C₂×D₂₇₁	semidirect
218. #120	C₂×D₂₇₁	semidirect
224. C₄×D₄	C₂×D₂₇₁	semidirect
235. C₂⁴	C₂²×D₂₇₁	semidirect
256. C₂×D₄	C₂²×D₂₇₁	semidirect
257. C₂×D₄	C₂²×D₂₇₁	semidirect
258. C₂×D₄	C₂²×D₂₇₁	semidirect
266. C₂²×C₄	C₂²×D₂₇₁	semidirect
269. C₄⋊C₄	C₂²×D₂₇₁	semidirect
275. C₂²⋊C₄	C₂²×D₂₇₁	semidirect
276. C₂²⋊C₄	C₂²×D₂₇₁	semidirect
279. C₄²	C₂²×D₂₇₁	semidirect
310. D₄	D₄×D₂₇₁	direct (N × H)
340. C₂²	C₂×D₄×D₂₇₁	semidirect
347. C₄	C₂×D₄×D₂₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₄×D₂₇₁	2
D₄×D₁₀₈₄	2
#31774532	2
#31774531	2
D₄×C₂²⋊D₂₇₁	2
#31774529	2
#127×D₂₇₁	2
#121×D₂₇₁	2
#120×D₂₇₁	2
C₄×D₄×D₂₇₁	2
D₄²×C₂₇₁	2
C₂×D₄²	271

Subgroups — D42×D271 #46849799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄²×D₂₇₁ #46849799