Subgroups — #30674792

Order 16768.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16862273	C₂	1	1	yes	maximal, characteristic
2	#22553794	C₂	1	1	yes	maximal, characteristic, complemented
3	#22553784	C₂	1	1	yes	maximal, characteristic, complemented
4	#22553425	C₂	1	1	yes	maximal, characteristic, complemented
5	#22553421	C₂	1	1	yes	maximal, characteristic, complemented
6	#22553415	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×Dic₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#14523500	C₂	1	1	yes	maximal, characteristic, complemented
9	#22553394	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14523498	C₂	1	1	yes	maximal, characteristic, complemented
11	#22553353	C₂	1	1	yes	maximal, characteristic, complemented
12	#22553307	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#22553269	C₂	1	1	yes	maximal, characteristic, complemented
15	#440×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14523514	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₃₁	C₂²	1	1	yes	characteristic
18	#16862273	C₄	1	8	yes	complemented
19	C₂×#14523500	C₂²	1	1	yes	characteristic
20	C₂×D₁₀₄₈	C₂²	1	1	yes	characteristic
21	C₂×#14523498	C₂²	1	1	yes	characteristic
22	C₂×#14523496	C₂²	1	1	yes	characteristic
23	C₂×C₈×D₁₃₁	C₂²	1	1	yes	characteristic
24	Q₈×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₄×D₅₂₄	—	2	1	no	—
26	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
27	C₄×D₅₂₄	C₂²	1	1	yes	characteristic, complemented
28	D₄×Dic₁₃₁	C₂²	1	1	yes	characteristic
29	#16862208	—	2	1	no	—
30	#16862208	C₂²	1	1	yes	characteristic
31	#16862208	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₂²⋊D₁₃₁	—	2	1	no	—
33	(C₂²⋊D₁₃₁)⋊C₄	—	2	1	no	—
34	#16862204	C₂²	1	1	yes	characteristic
35	#16862203	—	2	1	no	—
36	#16862203	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×D₁₃₁	—	2	1	no	—
38	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic
39	C₂×(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
40	C₂²⋊C₄×D₁₃₁	—	2	1	no	—
41	#16862179	C₂²	1	1	yes	characteristic, complemented
42	#16862178	C₂²	1	1	yes	characteristic, complemented
43	#16862177	C₂²	1	1	yes	characteristic, complemented
44	#16862170	C₂²	1	1	yes	characteristic, complemented
45	#16862168	C₂²	1	1	yes	characteristic
46	#16862168	C₂²	1	1	yes	characteristic, complemented
47	#16862167	C₂²	1	1	yes	characteristic
48	#16862166	C₂²	1	1	yes	characteristic
49	#16862166	C₂²	1	1	yes	characteristic, complemented
50	#16862156	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₁₃₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
54	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
55	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
56	#107×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
57	#103×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
58	#102×C₁₃₁	C₂²	1	1	yes	characteristic
59	#97×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₁₃₁	—	2	1	no	—
61	#14523514	—	2	2	no	—
62	#14523514	C₂×C₄	1	4	yes	complemented
63	C₂×D₅₂₄	—	2	1	no	—
64	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
65	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₃₁	—	2	1	no	—
67	D₄×D₁₃₁	—	2	2	no	—
68	D₄×D₁₃₁	C₂×C₄	1	4	yes	complemented
69	C₂²×Dic₁₃₁	—	2	1	no	—
70	C₂×C₄×D₁₃₁	—	2	1	no	—
71	C₂×C₄×D₁₃₁	—	2	1	no	—
72	C₂×C₄×D₁₃₁	—	2	1	no	—
73	C₂×C₄×D₁₃₁	—	2	1	no	—
74	C₂×C₄×D₁₃₁	—	2	1	no	—
75	C₂×C₄×D₁₃₁	—	2	1	no	—
76	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
77	#14523500	C₂×C₄	1	4	yes	complemented
78	D₁₀₄₈	C₂×C₄	1	4	yes	complemented
79	#14523498	C₂×C₄	1	4	yes	complemented
80	#14523496	C₂×C₄	1	4	yes	complemented
81	C₂×C₁₃₁⋊C₈	C₂³	1	1	yes	characteristic
82	C₂×C₁₃₁⋊C₈	C₂³	1	1	yes	characteristic
83	C₈×D₁₃₁	—	2	2	no	—
84	C₄⋊Dic₁₃₁	—	2	1	no	—
85	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
86	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
87	Dic₁₃₁⋊C₄	—	2	1	no	—
88	Dic₁₃₁⋊C₄	D₄	1	1	yes	characteristic
89	Dic₁₃₁⋊C₄	D₄	1	1	yes	characteristic
90	C₂²⋊Dic₁₃₁	—	2	1	no	—
91	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
92	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
93	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
94	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
95	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
96	(C₂×D₁₃₁)⋊C₄	D₄	1	1	yes	characteristic
97	(C₂×D₁₃₁)⋊C₄	D₄	1	1	yes	characteristic
98	C₄×Dic₁₃₁	—	2	1	no	—
99	C₄×Dic₁₃₁	—	2	1	no	—
100	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
101	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
102	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₁	—	2	1	no	—
104	SD₁₆×C₁₃₁	C₂×C₄	1	4	yes	complemented
105	C₂×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
106	C₂×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
107	C₄⋊C₄×C₁₃₁	—	2	1	no	—
108	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
109	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
110	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
111	C₄²×C₁₃₁	—	2	1	no	—
112	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
113	C₂²×D₁₃₁	—	2	1	no	—
114	C₂²×D₁₃₁	—	2	1	no	—
115	C₂²×D₁₃₁	—	2	4	no	—
116	C₂²×D₁₃₁	—	8	1	no	—
117	C₂²×D₁₃₁	—	8	1	no	—
118	C₂²×D₁₃₁	C₂×D₄	1	1	yes	characteristic
119	D₅₂₄	—	2	4	no	—
120	D₅₂₄	—	2	1	no	—
121	D₅₂₄	—	2	1	no	—
122	D₅₂₄	C₂²×C₄	1	2	yes	—
123	D₅₂₄	C₂²×C₄	1	2	yes	—
124	C₂²⋊D₁₃₁	—	2	4	no	—
125	C₂×Dic₁₃₁	—	2	1	no	—
126	C₂×Dic₁₃₁	—	2	1	no	—
127	C₂×Dic₁₃₁	—	8	1	no	—
128	C₂×Dic₁₃₁	C₂×D₄	1	1	yes	characteristic
129	C₂×Dic₁₃₁	C₂×D₄	1	1	yes	characteristic
130	C₂×Dic₁₃₁	C₂×D₄	1	1	yes	characteristic
131	C₄×D₁₃₁	—	2	4	no	—
132	C₄×D₁₃₁	—	8	1	no	—
133	C₄×D₁₃₁	—	8	1	no	—
134	C₄×D₁₃₁	—	8	1	no	—
135	C₄×D₁₃₁	—	8	1	no	—
136	C₄×D₁₃₁	—	8	1	no	—
137	C₄×D₁₃₁	C₂²×C₄	1	2	yes	—
138	C₄×D₁₃₁	#41	1	2	yes	—
139	C₁₃₁⋊C₈	—	2	1	no	—
140	C₁₃₁⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂³×C₁₃₁	—	2	1	no	—
142	Q₈×C₁₃₁	—	2	1	no	—
143	Q₈×C₁₃₁	C₂²×C₄	1	2	yes	—
144	D₄×C₁₃₁	—	2	1	no	—
145	D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
146	C₂×C₄×C₁₃₁	—	2	1	no	—
147	C₂×C₄×C₁₃₁	—	2	1	no	—
148	C₂×C₄×C₁₃₁	—	2	1	no	—
149	C₂×C₄×C₁₃₁	—	8	1	no	—
150	C₂×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
153	C₈×C₁₃₁	—	2	1	no	—
154	C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
155	C₂²×C₁₃₁	—	2	2	no	—
156	C₂²×C₁₃₁	—	4	1	no	—
157	C₂²×C₁₃₁	—	4	1	no	—
158	C₂²×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×D₁₃₁	—	2	1	no	—
160	C₂×D₁₃₁	—	2	1	no	—
161	C₂×D₁₃₁	—	2	2	no	—
162	C₂×D₁₃₁	—	2	2	no	—
163	C₂×D₁₃₁	—	4	1	no	—
164	C₂×D₁₃₁	—	4	1	no	—
165	C₂×D₁₃₁	—	4	1	no	—
166	C₂×D₁₃₁	—	4	1	no	—
167	C₂×D₁₃₁	—	8	4	no	—
168	C₂×D₁₃₁	C₄×D₄	1	2	yes	—
169	C₄×C₁₃₁	—	2	2	no	—
170	C₄×C₁₃₁	—	2	1	no	—
171	C₄×C₁₃₁	—	2	1	no	—
172	C₄×C₁₃₁	—	4	1	no	—
173	C₄×C₁₃₁	—	4	1	no	—
174	C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
175	C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
176	Dic₁₃₁	—	2	1	no	—
177	Dic₁₃₁	—	2	1	no	—
178	Dic₁₃₁	—	4	1	no	—
179	Dic₁₃₁	—	4	1	no	—
180	Dic₁₃₁	C₄×D₄	1	2	yes	—
181	C₂×C₁₃₁	—	4	2	no	—
182	C₂×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂×C₁₃₁	#576	1	1	yes	characteristic
184	C₂×C₁₃₁	#577	1	1	yes	characteristic
185	D₁₃₁	—	2	2	no	—
186	D₁₃₁	—	4	2	no	—
187	D₁₃₁	—	4	2	no	—
188	C₁₃₁	#2946	1	1	yes	characteristic, complemented, Sylow
189	#2946	—	131	1	no	maximal, Sylow
190	C₂×AGL(1,ℤ/8)	—	131	1	no	—
191	#520	—	131	1	no	—
192	#518	—	131	1	no	—
193	#442	—	131	1	no	—
194	#442	—	131	1	no	—
195	#440	—	131	1	no	—
196	#440	D₁₃₁	1	1	yes	characteristic, complemented
197	C₄×SD₁₆	—	131	1	no	—
198	C₄×SD₁₆	—	131	1	no	—
199	C₄×D₈	—	131	1	no	—
200	C₄×D₈	—	131	1	no	—
201	#428	—	131	1	no	—
202	#416	—	131	1	no	—
203	C₂×#102	—	131	1	no	—
204	#405	—	131	1	no	—
205	C₂×#41	—	131	1	no	—
206	C₂²×D₄	—	131	1	no	—
207	AGL(1,ℤ/8)	—	131	8	no	—
208	C₂×SD₁₆	—	131	1	no	—
209	C₂×SD₁₆	C₂×D₁₃₁	1	1	yes	characteristic
210	C₂×D₈	—	131	1	no	—
211	C₂×D₈	—	131	1	no	—
212	C₂×M₁₆	—	131	1	no	—
213	C₂²×C₈	—	131	1	no	—
214	C₄×Q₈	—	131	1	no	—
215	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
216	C₄×D₄	—	262	1	no	—
217	C₄×D₄	—	262	1	no	—
218	C₄×D₄	—	262	1	no	—
219	C₄×D₄	—	262	1	no	—
220	C₄×D₄	—	131	1	no	—
221	C₄×D₄	—	131	1	no	—
222	C₄×D₄	—	131	1	no	—
223	C₄×D₄	—	131	1	no	—
224	C₄×D₄	—	131	1	no	—
225	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic
226	#117	—	262	1	no	—
227	#117	—	131	1	no	—
228	#117	—	131	1	no	—
229	C₂×C₄⋊C₄	—	262	1	no	—
230	C₂×C₄⋊C₄	—	131	1	no	—
231	C₂×C₂²⋊C₄	—	262	1	no	—
232	C₂×C₂²⋊C₄	—	262	1	no	—
233	#107	—	131	1	no	—
234	#107	C₂×D₁₃₁	1	1	yes	characteristic, complemented
235	#106	—	131	1	no	—
236	#106	—	131	1	no	—
237	#103	—	131	1	no	—
238	#103	C₂×D₁₃₁	1	1	yes	characteristic, complemented
239	#102	—	131	1	no	—
240	#102	—	131	1	no	—
241	#102	—	131	1	no	—
242	#102	—	131	1	no	—
243	#102	—	131	1	no	—
244	#102	C₂×D₁₃₁	1	1	yes	characteristic
245	#97	—	131	1	no	—
246	#97	C₂×D₁₃₁	1	1	yes	characteristic, complemented
247	C₄×C₈	—	131	1	no	—
248	C₄×C₈	—	131	1	no	—
249	C₂⁴	—	262	1	no	—
250	#41	—	262	2	no	—
251	#41	—	131	4	no	—
252	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
253	C₂×D₄	—	262	1	no	—
254	C₂×D₄	—	262	2	no	—
255	C₂×D₄	—	262	1	no	—
256	C₂×D₄	—	131	4	no	—
257	C₂×D₄	—	131	1	no	—
258	C₂×D₄	—	131	1	no	—
259	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	262	1	no	—
262	C₂²×C₄	—	262	1	no	—
263	C₂²×C₄	—	262	1	no	—
264	C₂²×C₄	—	262	1	no	—
265	C₂²×C₄	—	262	1	no	—
266	C₂²×C₄	—	262	1	no	—
267	C₂²×C₄	—	262	1	no	—
268	C₂²×C₄	—	131	1	no	—
269	SD₁₆	—	131	4	no	—
270	SD₁₆	C₄×D₁₃₁	1	4	yes	complemented
271	D₈	—	131	4	no	—
272	D₈	—	131	4	no	—
273	M₁₆	—	131	4	no	—
274	C₂×C₈	—	262	2	no	—
275	C₂×C₈	—	131	1	no	—
276	C₂×C₈	—	131	1	no	—
277	C₂×C₈	C₂²×D₁₃₁	1	1	yes	characteristic
278	C₂×C₈	C₂²×D₁₃₁	1	1	yes	characteristic
279	C₄⋊C₄	—	2	1	no	—
280	C₄⋊C₄	—	262	1	no	—
281	C₄⋊C₄	—	262	1	no	—
282	C₄⋊C₄	—	131	1	no	—
283	C₄⋊C₄	—	131	1	no	—
284	C₄⋊C₄	—	131	1	no	—
285	C₄⋊C₄	—	131	1	no	—
286	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
287	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
288	C₂²⋊C₄	—	2	1	no	—
289	C₂²⋊C₄	—	262	1	no	—
290	C₂²⋊C₄	—	262	1	no	—
291	C₂²⋊C₄	—	262	1	no	—
292	C₂²⋊C₄	—	262	1	no	—
293	C₂²⋊C₄	—	262	1	no	—
294	C₂²⋊C₄	—	262	1	no	—
295	C₂²⋊C₄	—	131	1	no	—
296	C₂²⋊C₄	—	131	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	262	1	no	—
299	C₄²	—	262	1	no	—
300	C₄²	—	131	1	no	—
301	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
302	C₂³	—	2	1	no	—
303	C₂³	—	262	4	no	—
304	C₂³	—	262	1	no	—
305	C₂³	—	262	1	no	—
306	C₂³	—	1048	1	no	—
307	C₂³	—	1048	1	no	—
308	C₂³	—	131	1	no	—
309	Q₈	—	2	1	no	—
310	Q₈	C₂×C₄×D₁₃₁	1	2	yes	—
311	D₄	—	2	1	no	—
312	D₄	—	262	4	no	—
313	D₄	—	262	4	no	—
314	D₄	—	262	1	no	—
315	D₄	—	262	1	no	—
316	D₄	—	131	2	no	—
317	D₄	—	131	2	no	—
318	D₄	C₂×C₄×D₁₃₁	1	2	yes	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	262	4	no	—
323	C₂×C₄	—	262	1	no	—
324	C₂×C₄	—	262	1	no	—
325	C₂×C₄	—	8	1	no	—
326	C₂×C₄	—	1048	1	no	—
327	C₂×C₄	—	1048	1	no	—
328	C₂×C₄	—	1048	1	no	—
329	C₂×C₄	—	1048	1	no	—
330	C₂×C₄	—	1048	1	no	—
331	C₂×C₄	—	1048	1	no	—
332	C₂×C₄	—	131	1	no	—
333	C₂×C₄	—	131	1	no	—
334	C₂×C₄	—	131	1	no	—
335	C₂×C₄	—	131	2	no	—
336	C₂×C₄	—	131	2	no	—
337	C₂×C₄	D₄×D₁₃₁	1	1	yes	characteristic
338	C₂×C₄	D₄×D₁₃₁	1	1	yes	characteristic
339	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
340	C₈	—	2	1	no	—
341	C₈	—	262	1	no	—
342	C₈	—	131	2	no	—
343	C₈	C₂×C₄×D₁₃₁	1	2	yes	—
344	C₂²	—	2	2	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	262	1	no	—
348	C₂²	—	262	1	no	—
349	C₂²	—	262	2	no	—
350	C₂²	—	262	2	no	—
351	C₂²	—	524	1	no	—
352	C₂²	—	524	1	no	—
353	C₂²	—	524	1	no	—
354	C₂²	—	524	1	no	—
355	C₂²	—	1048	4	no	—
356	C₂²	—	131	2	no	—
357	C₂²	C₂×D₄×D₁₃₁	1	1	yes	characteristic
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	2	no	—
361	C₄	—	4	1	no	—
362	C₄	—	4	1	no	—
363	C₄	—	262	1	no	—
364	C₄	—	262	1	no	—
365	C₄	—	524	1	no	—
366	C₄	—	524	1	no	—
367	C₄	—	131	2	no	—
368	C₄	C₂²×C₄×D₁₃₁	1	1	yes	characteristic
369	C₄	#41×D₁₃₁	1	1	yes	characteristic
370	C₂	—	4	2	no	—
371	C₂	—	262	2	no	—
372	C₂	—	524	2	no	—
373	C₂	—	524	2	no	—
374	C₂	C₄×D₄×D₁₃₁	1	1	yes	characteristic
375	C₂	#22554116	1	1	yes	characteristic
376	C₂	#22554121	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₁
commutator	C₄×C₁₃₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₃₁
Fitting	#440×C₁₃₁	C₂
socle	C₂²×C₁₃₁	C₂²×D₄
prime radical	C₂×#16862273	C₂
cosocle	C₂×C₄×C₁₃₁	C₂⁴
hypercenter	#440	D₁₃₁
hypocenter	C₁₃₁	#2946
LCS	G ▷ C₄×C₁₃₁ ▷ C₂×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #440

Complements

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

N	H ≅ G/N	type
2. #22553794	C₂	semidirect
3. #22553784	C₂	semidirect
4. #22553425	C₂	semidirect
5. #22553421	C₂	semidirect
6. #22553415	C₂	semidirect
7. SD₁₆×Dic₁₃₁	C₂	semidirect
8. C₄×#14523500	C₂	semidirect
9. #22553394	C₂	semidirect
10. C₄×#14523498	C₂	semidirect
11. #22553353	C₂	semidirect
12. #22553307	C₂	semidirect
13. #102×D₁₃₁	C₂	semidirect
14. #22553269	C₂	semidirect
15. #440×C₁₃₁	C₂	semidirect
18. #16862273	C₄	semidirect
24. Q₈×Dic₁₃₁	C₂²	semidirect
27. C₄×D₅₂₄	C₂²	semidirect
31. #16862208	C₂²	semidirect
41. #16862179	C₂²	semidirect
42. #16862178	C₂²	semidirect
43. #16862177	C₂²	semidirect
44. #16862170	C₂²	semidirect
46. #16862168	C₂²	semidirect
49. #16862166	C₂²	semidirect
50. #16862156	C₂²	semidirect
51. C₄×C₁₃₁⋊C₈	C₂²	semidirect
52. C₈×Dic₁₃₁	C₂²	semidirect
54. C₄×Q₈×C₁₃₁	C₂²	semidirect
56. #107×C₁₃₁	C₂²	semidirect
57. #103×C₁₃₁	C₂²	semidirect
59. #97×C₁₃₁	C₂²	semidirect
62. #14523514	C₂×C₄	semidirect
68. D₄×D₁₃₁	C₂×C₄	semidirect
77. #14523500	C₂×C₄	semidirect
78. D₁₀₄₈	C₂×C₄	semidirect
79. #14523498	C₂×C₄	semidirect
80. #14523496	C₂×C₄	semidirect
104. SD₁₆×C₁₃₁	C₂×C₄	semidirect
188. C₁₃₁	#2946	semidirect
196. #440	D₁₃₁	semidirect
215. C₄×Q₈	C₂×D₁₃₁	semidirect
234. #107	C₂×D₁₃₁	semidirect
238. #103	C₂×D₁₃₁	semidirect
246. #97	C₂×D₁₃₁	semidirect
270. SD₁₆	C₄×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16862273	2
#22553794	2
#22553784	2
#22553425	2
#22553421	2
#22553415	2
SD₁₆×Dic₁₃₁	2
C₄×#14523500	2
#22553394	2
C₄×#14523498	2
#22553353	2
#22553307	2
#102×D₁₃₁	2
#22553269	2
#440×C₁₃₁	2
#2946	131