Subgroups — #576×D₁₃₁ #30680709

Order 16768.

1512 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(5,𝔽₂)×D₁₃₁	C₂	1	2	yes	maximal, complemented
2	#22554117	C₂	1	1	yes	maximal, characteristic, complemented
3	#22554116	C₂	1	6	yes	maximal, complemented
4	#22554115	C₂	1	2	yes	maximal, complemented
5	#22554114	C₂	1	3	yes	maximal, complemented
6	#22554113	C₂	1	3	yes	maximal, complemented
7	AGL(1,ℤ/8)×D₁₃₁	C₂	1	6	yes	maximal, complemented
8	#135×D₁₃₁	C₂	1	3	yes	maximal, complemented
9	C₂×D₈×D₁₃₁	C₂	1	3	yes	maximal, complemented
10	#131×D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#576×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#16862292	—	2	2	no	—
13	#16862292	C₂²	1	2	yes	complemented
14	#16862292	C₂²	1	6	yes	complemented
15	#16862291	—	2	6	no	—
16	#16862291	C₂²	1	6	yes	complemented
17	#41×D₁₃₁	—	2	2	no	—
18	#41×D₁₃₁	C₂²	1	1	yes	characteristic
19	#41×D₁₃₁	C₂²	1	6	yes	complemented
20	C₂×D₄×D₁₃₁	—	2	6	no	—
21	C₂×D₄×D₁₃₁	C₂²	1	6	yes	complemented
22	#16862274	C₂²	1	6	yes	complemented
23	#16862273	C₂²	1	12	yes	complemented
24	#16862272	C₂²	1	6	yes	complemented
25	#16862271	C₂²	1	6	yes	complemented
26	#16862270	C₂²	1	12	yes	complemented
27	#16862269	C₂²	1	3	yes	complemented
28	#16862268	C₂²	1	3	yes	complemented
29	#16862267	C₂²	1	6	yes	complemented
30	#16862266	C₂²	1	6	yes	complemented
31	#16862265	C₂²	1	3	yes	complemented
32	Q₁₆×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
33	SD₁₆×D₁₃₁	C₂²	1	6	yes	complemented
34	C₂×D₁₀₄₈	C₂²	1	3	yes	complemented
35	C₂×#14523498	C₂²	1	6	yes	complemented
36	D₈×D₁₃₁	C₂²	1	3	yes	complemented
37	D₈×D₁₃₁	C₂²	1	6	yes	complemented
38	D₈×D₁₃₁	C₂²	1	6	yes	complemented
39	D₈×D₁₃₁	C₂²	1	6	yes	complemented
40	#16862254	C₂²	1	3	yes	complemented
41	#16862253	C₂²	1	1	yes	characteristic, complemented
42	#16862252	C₂²	1	3	yes	complemented
43	M₁₆×D₁₃₁	C₂²	1	3	yes	complemented
44	C₂×C₈×D₁₃₁	C₂²	1	3	yes	complemented
45	H(5,𝔽₂)×C₁₃₁	C₂²	1	2	yes	complemented
46	AGL(1,ℤ/8)×C₁₃₁	C₂²	1	6	yes	complemented
47	#135×C₁₃₁	C₂²	1	3	yes	complemented
48	C₂×D₈×C₁₃₁	C₂²	1	3	yes	complemented
49	#131×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
50	C₂³×D₁₃₁	—	2	6	no	—
51	#14523514	—	2	2	no	—
52	#14523514	D₄	1	1	yes	characteristic
53	#14523514	C₂³	1	6	yes	complemented
54	#14523513	—	2	6	no	—
55	#14523513	—	2	6	no	—
56	#14523513	C₂³	1	3	yes	—
57	#14523513	C₂³	1	6	yes	complemented
58	#14523512	—	2	6	no	—
59	#14523512	—	2	6	no	—
60	#14523512	D₄	1	3	yes	—
61	#14523512	C₂³	1	6	yes	complemented
62	Q₈×D₁₃₁	D₄	1	1	yes	characteristic
63	Q₈×D₁₃₁	C₂³	1	2	yes	—
64	C₂×D₅₂₄	—	2	6	no	—
65	C₂×D₅₂₄	C₂³	1	6	yes	complemented
66	C₂×C₂²⋊D₁₃₁	—	2	12	no	—
67	C₂×C₂²⋊D₁₃₁	—	2	6	no	—
68	D₄×D₁₃₁	—	2	6	no	—
69	D₄×D₁₃₁	—	2	6	no	—
70	D₄×D₁₃₁	—	2	12	no	—
71	D₄×D₁₃₁	—	2	6	no	—
72	D₄×D₁₃₁	—	2	6	no	—
73	D₄×D₁₃₁	—	2	6	no	—
74	D₄×D₁₃₁	D₄	1	3	yes	—
75	D₄×D₁₃₁	C₂³	1	6	yes	—
76	D₄×D₁₃₁	C₂³	1	12	yes	complemented
77	C₂×C₄×D₁₃₁	—	2	6	no	—
78	C₂×C₄×D₁₃₁	C₂³	1	3	yes	—
79	Dic₅₂₄	C₂³	1	1	yes	characteristic, complemented
80	#14523503	C₂³	1	2	yes	complemented
81	#14523502	C₂³	1	6	yes	complemented
82	#14523501	C₂³	1	6	yes	complemented
83	#14523500	C₂³	1	6	yes	complemented
84	D₁₀₄₈	C₂³	1	3	yes	complemented
85	D₁₀₄₈	C₂³	1	6	yes	complemented
86	#14523498	C₂³	1	6	yes	complemented
87	#14523498	C₂³	1	12	yes	complemented
88	#14523497	C₂³	1	3	yes	complemented
89	#14523496	C₂³	1	6	yes	complemented
90	C₂×C₁₃₁⋊C₈	C₂³	1	3	yes	complemented
91	C₈×D₁₃₁	C₂³	1	1	yes	characteristic
92	C₈×D₁₃₁	C₂³	1	3	yes	—
93	C₈×D₁₃₁	C₂³	1	3	yes	complemented
94	C₈×D₁₃₁	C₂³	1	3	yes	complemented
95	#41×C₁₃₁	—	2	2	no	—
96	#41×C₁₃₁	C₂³	1	1	yes	characteristic
97	#41×C₁₃₁	C₂³	1	6	yes	complemented
98	C₂×D₄×C₁₃₁	—	2	6	no	—
99	C₂×D₄×C₁₃₁	C₂³	1	6	yes	complemented
100	Q₁₆×C₁₃₁	C₂³	1	1	yes	characteristic, complemented
101	SD₁₆×C₁₃₁	C₂³	1	6	yes	complemented
102	D₈×C₁₃₁	C₂³	1	3	yes	complemented
103	D₈×C₁₃₁	C₂³	1	6	yes	complemented
104	M₁₆×C₁₃₁	C₂³	1	3	yes	complemented
105	C₂×C₈×C₁₃₁	C₂³	1	3	yes	complemented
106	C₂²×D₁₃₁	—	2	6	no	—
107	C₂²×D₁₃₁	—	2	6	no	—
108	C₂²×D₁₃₁	—	2	12	no	—
109	C₂²×D₁₃₁	—	8	12	no	—
110	C₂²×D₁₃₁	C₂×D₄	1	3	yes	—
111	Dic₂₆₂	—	2	2	no	—
112	Dic₂₆₂	C₂×D₄	1	3	yes	—
113	Dic₂₆₂	C₂⁴	1	2	yes	—
114	D₅₂₄	—	2	6	no	—
115	D₅₂₄	—	2	6	no	—
116	D₅₂₄	C₂×D₄	1	3	yes	—
117	D₅₂₄	C₂⁴	1	6	yes	—
118	C₂²⋊D₁₃₁	—	2	6	no	—
119	C₂²⋊D₁₃₁	—	2	6	no	—
120	C₂²⋊D₁₃₁	—	2	6	no	—
121	C₂²⋊D₁₃₁	—	2	12	no	—
122	C₂²⋊D₁₃₁	C₂×D₄	1	6	yes	—
123	C₂×Dic₁₃₁	—	2	6	no	—
124	C₂×Dic₁₃₁	C₂×D₄	1	3	yes	—
125	C₄×D₁₃₁	—	2	2	no	—
126	C₄×D₁₃₁	—	2	6	no	—
127	C₄×D₁₃₁	—	2	6	no	—
128	C₄×D₁₃₁	C₂×D₄	1	3	yes	—
129	C₄×D₁₃₁	C₂×D₄	1	3	yes	—
130	C₄×D₁₃₁	C₂⁴	1	1	yes	characteristic
131	C₄×D₁₃₁	C₂⁴	1	3	yes	—
132	C₁₃₁⋊C₈	C₂⁴	1	1	yes	characteristic
133	C₁₃₁⋊C₈	C₂⁴	1	3	yes	—
134	C₂³×C₁₃₁	—	2	6	no	—
135	Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₁₃₁	C₂⁴	1	2	yes	—
137	D₄×C₁₃₁	—	2	6	no	—
138	D₄×C₁₃₁	—	2	6	no	—
139	D₄×C₁₃₁	C₂×D₄	1	3	yes	—
140	D₄×C₁₃₁	C₂⁴	1	6	yes	—
141	C₂×C₄×C₁₃₁	—	2	6	no	—
142	C₂×C₄×C₁₃₁	C₂⁴	1	3	yes	—
143	C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
144	C₈×C₁₃₁	C₂⁴	1	3	yes	—
145	C₂²×C₁₃₁	—	2	6	no	—
146	C₂²×C₁₃₁	—	8	6	no	—
147	C₂²×C₁₃₁	C₂²×D₄	1	3	yes	—
148	C₂×D₁₃₁	—	2	6	no	—
149	C₂×D₁₃₁	—	2	6	no	—
150	C₂×D₁₃₁	—	4	12	no	—
151	C₂×D₁₃₁	—	8	12	no	—
152	C₂×D₁₃₁	—	8	6	no	—
153	C₂×D₁₃₁	C₂²×D₄	1	3	yes	—
154	C₂×D₁₃₁	C₂²×D₄	1	1	yes	characteristic
155	C₄×C₁₃₁	—	2	2	no	—
156	C₄×C₁₃₁	C₂²×D₄	1	3	yes	—
157	C₄×C₁₃₁	C₂⁵	1	1	yes	characteristic
158	Dic₁₃₁	—	2	2	no	—
159	Dic₁₃₁	C₂²×D₄	1	3	yes	—
160	Dic₁₃₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₁₃₁	—	2	3	no	—
162	C₂×C₁₃₁	—	4	6	no	—
163	C₂×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
164	D₁₃₁	—	2	3	no	—
165	D₁₃₁	—	4	6	no	—
166	D₁₃₁	#576	1	2	yes	direct product factor
167	C₁₃₁	C₂×#576	1	1	yes	characteristic, complemented, Sylow
168	C₂×#576	—	131	1	no	maximal, Sylow
169	C₂×H(5,𝔽₂)	—	131	2	no	—
170	#576	—	131	2	no	—
171	#576	—	131	6	no	—
172	#576	—	131	3	no	—
173	#576	—	131	3	no	—
174	#576	—	131	1	no	—
175	#576	D₁₃₁	1	1	yes	characteristic, direct product factor
176	C₂×AGL(1,ℤ/8)	—	131	6	no	—
177	C₂×#135	—	131	3	no	—
178	C₂²×D₈	—	131	3	no	—
179	C₂×#131	—	131	1	no	—
180	H(5,𝔽₂)	—	262	6	no	—
181	H(5,𝔽₂)	—	262	2	no	—
182	H(5,𝔽₂)	—	131	2	no	—
183	H(5,𝔽₂)	—	131	6	no	—
184	H(5,𝔽₂)	—	131	6	no	—
185	H(5,𝔽₂)	C₂×D₁₃₁	1	2	yes	complemented
186	C₂×#41	—	262	2	no	—
187	C₂×#41	—	131	6	no	—
188	C₂×#41	—	131	1	no	—
189	C₂²×D₄	—	262	6	no	—
190	C₂²×D₄	—	131	6	no	—
191	AGL(1,ℤ/8)	—	131	6	no	—
192	AGL(1,ℤ/8)	—	131	6	no	—
193	AGL(1,ℤ/8)	—	131	12	no	—
194	AGL(1,ℤ/8)	—	131	12	no	—
195	AGL(1,ℤ/8)	—	131	6	no	—
196	AGL(1,ℤ/8)	C₂×D₁₃₁	1	6	yes	complemented
197	#135	—	131	6	no	—
198	#135	—	131	3	no	—
199	#135	—	131	6	no	—
200	#135	—	131	3	no	—
201	#135	—	131	3	no	—
202	#135	C₂×D₁₃₁	1	3	yes	complemented
203	C₂×Q₁₆	—	131	1	no	—
204	C₂×SD₁₆	—	131	6	no	—
205	C₂×D₈	—	131	6	no	—
206	C₂×D₈	—	131	3	no	—
207	C₂×D₈	—	131	6	no	—
208	C₂×D₈	—	131	6	no	—
209	C₂×D₈	—	131	6	no	—
210	C₂×D₈	—	131	3	no	—
211	C₂×D₈	C₂×D₁₃₁	1	3	yes	complemented
212	#131	—	131	1	no	—
213	#131	—	131	3	no	—
214	#131	—	131	3	no	—
215	#131	C₂×D₁₃₁	1	1	yes	characteristic, complemented
216	C₂×M₁₆	—	131	3	no	—
217	C₂²×C₈	—	131	3	no	—
218	C₂⁴	—	262	6	no	—
219	#41	—	2	2	no	—
220	#41	—	262	6	no	—
221	#41	—	262	6	no	—
222	#41	—	262	6	no	—
223	#41	—	262	2	no	—
224	#41	—	262	6	no	—
225	#41	—	131	6	no	—
226	#41	—	131	6	no	—
227	#41	—	131	6	no	—
228	#41	—	131	1	no	—
229	#41	—	131	3	no	—
230	#41	—	131	3	no	—
231	#41	C₂²×D₁₃₁	1	1	yes	characteristic
232	#41	C₂²×D₁₃₁	1	6	yes	complemented
233	C₂×Q₈	—	131	2	no	—
234	C₂×Q₈	—	131	1	no	—
235	C₂×D₄	—	2	6	no	—
236	C₂×D₄	—	262	6	no	—
237	C₂×D₄	—	262	6	no	—
238	C₂×D₄	—	262	12	no	—
239	C₂×D₄	—	262	6	no	—
240	C₂×D₄	—	262	12	no	—
241	C₂×D₄	—	262	6	no	—
242	C₂×D₄	—	262	6	no	—
243	C₂×D₄	—	262	6	no	—
244	C₂×D₄	—	262	6	no	—
245	C₂×D₄	—	131	6	no	—
246	C₂×D₄	—	131	12	no	—
247	C₂×D₄	—	131	3	no	—
248	C₂×D₄	—	131	6	no	—
249	C₂×D₄	C₂²×D₁₃₁	1	6	yes	complemented
250	C₂²×C₄	—	262	6	no	—
251	C₂²×C₄	—	131	3	no	—
252	Q₁₆	—	131	2	no	—
253	Q₁₆	—	131	1	no	—
254	Q₁₆	C₂²×D₁₃₁	1	1	yes	characteristic, complemented
255	SD₁₆	—	131	6	no	—
256	SD₁₆	—	131	6	no	—
257	SD₁₆	—	131	6	no	—
258	SD₁₆	C₂²×D₁₃₁	1	6	yes	complemented
259	D₈	—	131	6	no	—
260	D₈	—	131	12	no	—
261	D₈	—	131	3	no	—
262	D₈	—	131	6	no	—
263	D₈	C₂²×D₁₃₁	1	3	yes	complemented
264	D₈	C₂²×D₁₃₁	1	6	yes	complemented
265	M₁₆	—	131	3	no	—
266	M₁₆	—	131	6	no	—
267	M₁₆	C₂²×D₁₃₁	1	3	yes	complemented
268	C₂×C₈	—	131	3	no	—
269	C₂×C₈	—	131	1	no	—
270	C₂×C₈	—	131	3	no	—
271	C₂×C₈	—	131	3	no	—
272	C₂×C₈	—	131	3	no	—
273	C₂×C₈	C₂²×D₁₃₁	1	3	yes	complemented
274	C₂³	—	2	6	no	—
275	C₂³	—	262	6	no	—
276	C₂³	—	262	12	no	—
277	C₂³	—	262	6	no	—
278	C₂³	—	1048	12	no	—
279	C₂³	—	131	3	no	—
280	Q₈	—	262	2	no	—
281	Q₈	—	131	2	no	—
282	Q₈	—	131	3	no	—
283	Q₈	D₄×D₁₃₁	1	1	yes	characteristic
284	Q₈	C₂³×D₁₃₁	1	2	yes	—
285	D₄	—	2	6	no	—
286	D₄	—	2	6	no	—
287	D₄	—	262	6	no	—
288	D₄	—	262	6	no	—
289	D₄	—	262	6	no	—
290	D₄	—	262	12	no	—
291	D₄	—	262	6	no	—
292	D₄	—	262	6	no	—
293	D₄	—	131	6	no	—
294	D₄	—	131	3	no	—
295	D₄	—	131	6	no	—
296	D₄	D₄×D₁₃₁	1	3	yes	—
297	D₄	C₂³×D₁₃₁	1	6	yes	—
298	C₂×C₄	—	2	6	no	—
299	C₂×C₄	—	262	2	no	—
300	C₂×C₄	—	262	6	no	—
301	C₂×C₄	—	262	6	no	—
302	C₂×C₄	—	262	6	no	—
303	C₂×C₄	—	131	3	no	—
304	C₂×C₄	—	131	3	no	—
305	C₂×C₄	—	131	3	no	—
306	C₂×C₄	—	131	1	no	—
307	C₂×C₄	—	131	3	no	—
308	C₂×C₄	C₂³×D₁₃₁	1	3	yes	—
309	C₈	—	131	1	no	—
310	C₈	—	131	3	no	—
311	C₈	C₂³×D₁₃₁	1	1	yes	characteristic
312	C₈	C₂³×D₁₃₁	1	3	yes	—
313	C₂²	—	2	6	no	—
314	C₂²	—	262	6	no	—
315	C₂²	—	262	6	no	—
316	C₂²	—	8	6	no	—
317	C₂²	—	524	12	no	—
318	C₂²	—	1048	6	no	—
319	C₂²	—	1048	12	no	—
320	C₂²	—	131	3	no	—
321	C₂²	—	131	1	no	—
322	C₂²	C₂×D₄×D₁₃₁	1	3	yes	—
323	C₄	—	2	2	no	—
324	C₄	—	262	2	no	—
325	C₄	—	131	3	no	—
326	C₄	—	131	1	no	—
327	C₄	C₂×D₄×D₁₃₁	1	3	yes	—
328	C₄	C₂⁴×D₁₃₁	1	1	yes	characteristic
329	C₂	—	2	3	no	—
330	C₂	—	4	6	no	—
331	C₂	—	262	3	no	—
332	C₂	—	524	6	no	—
333	C₂	—	131	2	no	—
334	C₂	C₂²×D₄×D₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₁₃₁
commutator, cosocle	C₄×C₁₃₁	C₂⁵
Frattini	C₄	C₂⁴×D₁₃₁
Fitting	#576×C₁₃₁	C₂
socle	C₂×C₁₃₁	C₂³×D₄
hypercenter	#576	D₁₃₁
hypocenter	C₁₃₁	C₂×#576
LCS	G ▷ C₄×C₁₃₁ ▷ C₂×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂ ◁ #41 ◁ #576

Complements

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

N	H ≅ G/N	type
1. H(5,𝔽₂)×D₁₃₁	C₂	semidirect
2. #22554117	C₂	semidirect
3. #22554116	C₂	semidirect
4. #22554115	C₂	semidirect
5. #22554114	C₂	semidirect
6. #22554113	C₂	semidirect
7. AGL(1,ℤ/8)×D₁₃₁	C₂	semidirect
8. #135×D₁₃₁	C₂	semidirect
9. C₂×D₈×D₁₃₁	C₂	semidirect
10. #131×D₁₃₁	C₂	semidirect
11. #576×C₁₃₁	C₂	semidirect
13. #16862292	C₂²	semidirect
14. #16862292	C₂²	semidirect
16. #16862291	C₂²	semidirect
19. #41×D₁₃₁	C₂²	semidirect
21. C₂×D₄×D₁₃₁	C₂²	semidirect
22. #16862274	C₂²	semidirect
23. #16862273	C₂²	semidirect
24. #16862272	C₂²	semidirect
25. #16862271	C₂²	semidirect
26. #16862270	C₂²	semidirect
27. #16862269	C₂²	semidirect
28. #16862268	C₂²	semidirect
29. #16862267	C₂²	semidirect
30. #16862266	C₂²	semidirect
31. #16862265	C₂²	semidirect
32. Q₁₆×D₁₃₁	C₂²	semidirect
33. SD₁₆×D₁₃₁	C₂²	semidirect
34. C₂×D₁₀₄₈	C₂²	semidirect
35. C₂×#14523498	C₂²	semidirect
36. D₈×D₁₃₁	C₂²	semidirect
37. D₈×D₁₃₁	C₂²	semidirect
38. D₈×D₁₃₁	C₂²	semidirect
39. D₈×D₁₃₁	C₂²	semidirect
40. #16862254	C₂²	semidirect
41. #16862253	C₂²	semidirect
42. #16862252	C₂²	semidirect
43. M₁₆×D₁₃₁	C₂²	semidirect
44. C₂×C₈×D₁₃₁	C₂²	semidirect
45. H(5,𝔽₂)×C₁₃₁	C₂²	semidirect
46. AGL(1,ℤ/8)×C₁₃₁	C₂²	semidirect
47. #135×C₁₃₁	C₂²	semidirect
48. C₂×D₈×C₁₃₁	C₂²	semidirect
49. #131×C₁₃₁	C₂²	semidirect
53. #14523514	C₂³	semidirect
57. #14523513	C₂³	semidirect
61. #14523512	C₂³	semidirect
65. C₂×D₅₂₄	C₂³	semidirect
76. D₄×D₁₃₁	C₂³	semidirect
79. Dic₅₂₄	C₂³	semidirect
80. #14523503	C₂³	semidirect
81. #14523502	C₂³	semidirect
82. #14523501	C₂³	semidirect
83. #14523500	C₂³	semidirect
84. D₁₀₄₈	C₂³	semidirect
85. D₁₀₄₈	C₂³	semidirect
86. #14523498	C₂³	semidirect
87. #14523498	C₂³	semidirect
88. #14523497	C₂³	semidirect
89. #14523496	C₂³	semidirect
90. C₂×C₁₃₁⋊C₈	C₂³	semidirect
93. C₈×D₁₃₁	C₂³	semidirect
94. C₈×D₁₃₁	C₂³	semidirect
97. #41×C₁₃₁	C₂³	semidirect
99. C₂×D₄×C₁₃₁	C₂³	semidirect
100. Q₁₆×C₁₃₁	C₂³	semidirect
101. SD₁₆×C₁₃₁	C₂³	semidirect
102. D₈×C₁₃₁	C₂³	semidirect
103. D₈×C₁₃₁	C₂³	semidirect
104. M₁₆×C₁₃₁	C₂³	semidirect
105. C₂×C₈×C₁₃₁	C₂³	semidirect
166. D₁₃₁	#576	direct (N × H)
167. C₁₃₁	C₂×#576	semidirect
175. #576	D₁₃₁	direct (N × H)
185. H(5,𝔽₂)	C₂×D₁₃₁	semidirect
196. AGL(1,ℤ/8)	C₂×D₁₃₁	semidirect
202. #135	C₂×D₁₃₁	semidirect
211. C₂×D₈	C₂×D₁₃₁	semidirect
215. #131	C₂×D₁₃₁	semidirect
232. #41	C₂²×D₁₃₁	semidirect
249. C₂×D₄	C₂²×D₁₃₁	semidirect
254. Q₁₆	C₂²×D₁₃₁	semidirect
258. SD₁₆	C₂²×D₁₃₁	semidirect
263. D₈	C₂²×D₁₃₁	semidirect
264. D₈	C₂²×D₁₃₁	semidirect
267. M₁₆	C₂²×D₁₃₁	semidirect
273. C₂×C₈	C₂²×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
H(5,𝔽₂)×D₁₃₁	2
#22554117	2
#22554116	2
#22554115	2
#22554114	2
#22554113	2
AGL(1,ℤ/8)×D₁₃₁	2
#135×D₁₃₁	2
C₂×D₈×D₁₃₁	2
#131×D₁₃₁	2
#576×C₁₃₁	2
C₂×#576	131

Subgroups — #576×D131 #30680709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #576×D₁₃₁ #30680709