Subgroups — #30674815

Order 16768.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#22553788	C₂	1	1	yes	maximal, characteristic, complemented
3	#22553784	C₂	1	1	yes	maximal, characteristic
4	#22553415	C₂	1	1	yes	maximal, characteristic, complemented
5	#22553412	C₂	1	1	yes	maximal, characteristic, complemented
6	#22553410	C₂	1	1	yes	maximal, characteristic, complemented
7	#22553409	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#14523502	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆×Dic₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#22553399	C₂	1	1	yes	maximal, characteristic, complemented
11	#22553347	C₂	1	1	yes	maximal, characteristic, complemented
12	#22553319	C₂	1	1	yes	maximal, characteristic, complemented
13	#22553315	C₂	1	1	yes	maximal, characteristic
14	#22553266	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₃₁	C₂²	1	1	yes	characteristic
18	C₂×#14523502	C₂²	1	1	yes	characteristic
19	C₂×#14523501	C₂²	1	1	yes	characteristic
20	C₂×#14523500	C₂²	1	1	yes	characteristic
21	SD₁₆×D₁₃₁	C₄	1	8	yes	complemented
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×Dic₂₆₂	—	2	1	no	—
26	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
27	#16862211	—	2	1	no	—
28	#16862211	C₂²	1	1	yes	characteristic, complemented
29	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
30	D₄×Dic₁₃₁	C₂²	1	1	yes	characteristic
31	#16862208	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊D₁₃₁	—	2	1	no	—
33	(C₂²⋊D₁₃₁)⋊C₄	—	2	1	no	—
34	#16862204	—	2	1	no	—
35	#16862204	C₂²	1	1	yes	characteristic
36	#16862204	C₂²	1	1	yes	characteristic
37	#16862203	—	2	1	no	—
38	#16862203	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	#16862179	C₂²	1	1	yes	characteristic, complemented
43	#16862178	C₂²	1	1	yes	characteristic, complemented
44	#16862171	C₂²	1	1	yes	characteristic, complemented
45	#16862170	C₂²	1	1	yes	characteristic, complemented
46	#16862169	C₂²	1	1	yes	characteristic, complemented
47	#16862168	C₂²	1	1	yes	characteristic
48	#16862167	C₂²	1	1	yes	characteristic
49	#16862166	C₂²	1	1	yes	characteristic
50	#16862157	C₂²	1	1	yes	characteristic, complemented
51	#16862156	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	#106×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	C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₁₃₁	—	2	1	no	—
61	C₂×Dic₂₆₂	—	2	1	no	—
62	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
63	Q₈×D₁₃₁	—	2	2	no	—
64	Q₈×D₁₃₁	C₂×C₄	1	4	yes	complemented
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	—
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	C₂³	1	1	yes	characteristic
74	#14523502	C₂×C₄	1	4	yes	complemented
75	#14523501	C₂×C₄	1	4	yes	complemented
76	#14523500	C₂×C₄	1	4	yes	complemented
77	#14523496	—	2	2	no	—
78	C₂×C₁₃₁⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×C₁₃₁⋊C₈	C₂³	1	1	yes	characteristic
80	C₈×D₁₃₁	C₂×C₄	1	4	yes	complemented
81	C₄⋊Dic₁₃₁	—	2	1	no	—
82	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
83	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
84	Dic₁₃₁⋊C₄	—	2	1	no	—
85	Dic₁₃₁⋊C₄	—	2	1	no	—
86	Dic₁₃₁⋊C₄	D₄	1	1	yes	characteristic
87	Dic₁₃₁⋊C₄	D₄	1	1	yes	characteristic
88	C₂²⋊Dic₁₃₁	—	2	1	no	—
89	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
90	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
91	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
92	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
93	(C₂×D₁₃₁)⋊C₄	D₄	1	1	yes	characteristic
94	(C₂×D₁₃₁)⋊C₄	D₄	1	1	yes	characteristic
95	C₄×Dic₁₃₁	—	2	1	no	—
96	C₄×Dic₁₃₁	—	2	1	no	—
97	C₄×Dic₁₃₁	—	2	1	no	—
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	4	no	—
115	C₂²×D₁₃₁	—	8	1	no	—
116	C₂²×D₁₃₁	—	8	1	no	—
117	C₂²×D₁₃₁	C₂×D₄	1	1	yes	characteristic
118	Dic₂₆₂	—	2	1	no	—
119	Dic₂₆₂	—	2	4	no	—
120	Dic₂₆₂	C₂²×C₄	1	2	yes	—
121	D₅₂₄	—	2	1	no	—
122	D₅₂₄	C₂²×C₄	1	2	yes	—
123	C₂²⋊D₁₃₁	—	2	4	no	—
124	C₂×Dic₁₃₁	—	2	1	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	C₂²×C₄	1	2	yes	—
135	C₄×D₁₃₁	#41	1	2	yes	—
136	C₁₃₁⋊C₈	—	2	1	no	—
137	C₁₃₁⋊C₈	C₂²×C₄	1	2	yes	—
138	C₂³×C₁₃₁	—	2	1	no	—
139	Q₈×C₁₃₁	—	2	1	no	—
140	Q₈×C₁₃₁	C₂²×C₄	1	2	yes	—
141	D₄×C₁₃₁	—	2	1	no	—
142	D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
143	C₂×C₄×C₁₃₁	—	2	1	no	—
144	C₂×C₄×C₁₃₁	—	2	1	no	—
145	C₂×C₄×C₁₃₁	—	2	1	no	—
146	C₂×C₄×C₁₃₁	—	8	1	no	—
147	C₂×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
150	C₈×C₁₃₁	—	2	1	no	—
151	C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
152	C₂²×C₁₃₁	—	2	2	no	—
153	C₂²×C₁₃₁	—	4	1	no	—
154	C₂²×C₁₃₁	—	4	1	no	—
155	C₂²×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
156	C₂×D₁₃₁	—	2	1	no	—
157	C₂×D₁₃₁	—	2	1	no	—
158	C₂×D₁₃₁	—	2	2	no	—
159	C₂×D₁₃₁	—	4	1	no	—
160	C₂×D₁₃₁	—	4	1	no	—
161	C₂×D₁₃₁	—	8	4	no	—
162	C₂×D₁₃₁	C₄×D₄	1	2	yes	—
163	C₄×C₁₃₁	—	2	2	no	—
164	C₄×C₁₃₁	—	2	1	no	—
165	C₄×C₁₃₁	—	2	1	no	—
166	C₄×C₁₃₁	—	4	1	no	—
167	C₄×C₁₃₁	—	4	1	no	—
168	C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
169	C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
170	Dic₁₃₁	—	2	2	no	—
171	Dic₁₃₁	—	2	1	no	—
172	Dic₁₃₁	—	2	1	no	—
173	Dic₁₃₁	—	4	1	no	—
174	Dic₁₃₁	—	4	1	no	—
175	Dic₁₃₁	C₄×D₄	1	2	yes	—
176	C₂×C₁₃₁	—	4	2	no	—
177	C₂×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
178	C₂×C₁₃₁	#577	1	1	yes	characteristic
179	C₂×C₁₃₁	#577	1	1	yes	characteristic
180	D₁₃₁	—	2	2	no	—
181	D₁₃₁	—	4	2	no	—
182	C₁₃₁	#2949	1	1	yes	characteristic, complemented, Sylow
183	#2949	—	131	1	no	maximal, Sylow
184	C₂²×SD₁₆	—	131	1	no	—
185	#519	—	131	1	no	—
186	#518	—	131	1	no	—
187	#440	—	131	1	no	—
188	#440	—	131	1	no	—
189	#440	—	131	1	no	—
190	#440	—	131	1	no	—
191	C₄×SD₁₆	—	131	1	no	—
192	C₄×SD₁₆	—	131	1	no	—
193	C₄×SD₁₆	—	131	1	no	—
194	C₄×SD₁₆	D₁₃₁	1	1	yes	characteristic, complemented
195	#427	—	131	1	no	—
196	#419	—	131	1	no	—
197	#418	—	131	1	no	—
198	#405	—	131	1	no	—
199	C₂²×Q₈	—	131	1	no	—
200	C₂²×D₄	—	131	1	no	—
201	C₂×SD₁₆	—	131	1	no	—
202	C₂×SD₁₆	—	131	1	no	—
203	C₂×SD₁₆	—	131	8	no	—
204	C₂×SD₁₆	—	131	1	no	—
205	C₂×SD₁₆	C₂×D₁₃₁	1	1	yes	characteristic
206	C₂×M₁₆	—	131	1	no	—
207	C₂²×C₈	—	131	1	no	—
208	C₄×Q₈	—	262	1	no	—
209	C₄×Q₈	—	262	1	no	—
210	C₄×Q₈	—	131	1	no	—
211	C₄×Q₈	—	131	1	no	—
212	C₄×Q₈	—	131	1	no	—
213	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
214	C₄×D₄	—	262	1	no	—
215	C₄×D₄	—	262	1	no	—
216	C₄×D₄	—	131	1	no	—
217	C₄×D₄	—	131	1	no	—
218	C₄×D₄	—	131	1	no	—
219	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic
220	#117	—	262	1	no	—
221	#117	—	262	1	no	—
222	#117	—	131	1	no	—
223	#117	—	131	1	no	—
224	#117	—	131	1	no	—
225	C₂×C₂²⋊C₄	—	262	1	no	—
226	C₂×C₂²⋊C₄	—	262	1	no	—
227	#107	—	131	1	no	—
228	#107	—	131	1	no	—
229	#106	—	131	1	no	—
230	#106	C₂×D₁₃₁	1	1	yes	characteristic, complemented
231	#103	—	131	1	no	—
232	#103	—	131	1	no	—
233	#103	—	131	1	no	—
234	#103	C₂×D₁₃₁	1	1	yes	characteristic, complemented
235	#102	—	131	1	no	—
236	#102	—	131	1	no	—
237	#102	—	131	1	no	—
238	#102	C₂×D₁₃₁	1	1	yes	characteristic
239	#97	—	131	1	no	—
240	#97	—	131	1	no	—
241	C₄×C₈	—	131	1	no	—
242	C₄×C₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
243	C₂⁴	—	262	1	no	—
244	C₂×Q₈	—	262	1	no	—
245	C₂×Q₈	—	262	2	no	—
246	C₂×Q₈	—	131	4	no	—
247	C₂×Q₈	—	131	1	no	—
248	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
249	C₂×D₄	—	262	2	no	—
250	C₂×D₄	—	262	1	no	—
251	C₂×D₄	—	131	4	no	—
252	C₂×D₄	—	131	1	no	—
253	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	262	1	no	—
256	C₂²×C₄	—	262	1	no	—
257	C₂²×C₄	—	262	1	no	—
258	C₂²×C₄	—	262	1	no	—
259	C₂²×C₄	—	131	1	no	—
260	SD₁₆	—	131	4	no	—
261	SD₁₆	—	131	4	no	—
262	SD₁₆	—	131	4	no	—
263	SD₁₆	C₄×D₁₃₁	1	4	yes	complemented
264	M₁₆	—	262	2	no	—
265	C₂×C₈	—	131	1	no	—
266	C₂×C₈	—	131	1	no	—
267	C₂×C₈	—	131	4	no	—
268	C₂×C₈	C₂²×D₁₃₁	1	1	yes	characteristic
269	C₂×C₈	C₂²×D₁₃₁	1	1	yes	characteristic
270	C₄⋊C₄	—	2	1	no	—
271	C₄⋊C₄	—	262	1	no	—
272	C₄⋊C₄	—	262	1	no	—
273	C₄⋊C₄	—	262	1	no	—
274	C₄⋊C₄	—	131	1	no	—
275	C₄⋊C₄	—	131	1	no	—
276	C₄⋊C₄	—	131	1	no	—
277	C₄⋊C₄	—	131	1	no	—
278	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
279	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
280	C₂²⋊C₄	—	2	1	no	—
281	C₂²⋊C₄	—	262	1	no	—
282	C₂²⋊C₄	—	262	1	no	—
283	C₂²⋊C₄	—	262	1	no	—
284	C₂²⋊C₄	—	262	1	no	—
285	C₂²⋊C₄	—	262	1	no	—
286	C₂²⋊C₄	—	131	1	no	—
287	C₂²⋊C₄	—	131	1	no	—
288	C₄²	—	2	1	no	—
289	C₄²	—	262	1	no	—
290	C₄²	—	262	1	no	—
291	C₄²	—	262	1	no	—
292	C₄²	—	262	1	no	—
293	C₄²	—	262	1	no	—
294	C₄²	—	131	1	no	—
295	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
296	C₂³	—	2	1	no	—
297	C₂³	—	262	4	no	—
298	C₂³	—	262	1	no	—
299	C₂³	—	1048	1	no	—
300	C₂³	—	1048	1	no	—
301	C₂³	—	131	1	no	—
302	Q₈	—	2	1	no	—
303	Q₈	—	262	4	no	—
304	Q₈	—	262	1	no	—
305	Q₈	—	131	2	no	—
306	Q₈	C₂×C₄×D₁₃₁	1	2	yes	—
307	D₄	—	2	1	no	—
308	D₄	—	262	4	no	—
309	D₄	—	262	1	no	—
310	D₄	—	131	2	no	—
311	D₄	C₂×C₄×D₁₃₁	1	2	yes	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	262	4	no	—
316	C₂×C₄	—	262	1	no	—
317	C₂×C₄	—	262	1	no	—
318	C₂×C₄	—	262	1	no	—
319	C₂×C₄	—	8	1	no	—
320	C₂×C₄	—	1048	1	no	—
321	C₂×C₄	—	1048	1	no	—
322	C₂×C₄	—	1048	1	no	—
323	C₂×C₄	—	131	1	no	—
324	C₂×C₄	—	131	1	no	—
325	C₂×C₄	—	131	1	no	—
326	C₂×C₄	—	131	2	no	—
327	C₂×C₄	—	131	2	no	—
328	C₂×C₄	D₄×D₁₃₁	1	1	yes	characteristic
329	C₂×C₄	D₄×D₁₃₁	1	1	yes	characteristic
330	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
331	C₈	—	2	1	no	—
332	C₈	—	262	1	no	—
333	C₈	—	131	2	no	—
334	C₈	C₂×C₄×D₁₃₁	1	2	yes	—
335	C₂²	—	2	2	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	262	1	no	—
339	C₂²	—	262	1	no	—
340	C₂²	—	262	2	no	—
341	C₂²	—	524	1	no	—
342	C₂²	—	524	1	no	—
343	C₂²	—	1048	4	no	—
344	C₂²	—	131	2	no	—
345	C₂²	C₂×D₄×D₁₃₁	1	1	yes	characteristic
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	2	no	—
349	C₄	—	4	1	no	—
350	C₄	—	4	1	no	—
351	C₄	—	262	1	no	—
352	C₄	—	262	1	no	—
353	C₄	—	262	2	no	—
354	C₄	—	524	1	no	—
355	C₄	—	524	1	no	—
356	C₄	—	131	2	no	—
357	C₄	C₂²×C₄×D₁₃₁	1	1	yes	characteristic
358	C₄	#41×D₁₃₁	1	1	yes	characteristic
359	C₂	—	4	2	no	—
360	C₂	—	262	2	no	—
361	C₂	—	524	2	no	—
362	C₂	C₄×D₄×D₁₃₁	1	1	yes	characteristic
363	C₂	#22554118	1	1	yes	characteristic
364	C₂	#22554119	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₁
commutator	C₄×C₁₃₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₃₁
Fitting	C₄×SD₁₆×C₁₃₁	C₂
socle	C₂²×C₁₃₁	C₂²×D₄
prime radical	C₂×D₄×D₁₃₁	C₂²
cosocle	C₂×C₄×C₁₃₁	C₂⁴
hypercenter	C₄×SD₁₆	D₁₃₁
hypocenter	C₁₃₁	#2949
LCS	G ▷ C₄×C₁₃₁ ▷ C₂×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. #22553788	C₂	semidirect
4. #22553415	C₂	semidirect
5. #22553412	C₂	semidirect
6. #22553410	C₂	semidirect
7. #22553409	C₂	semidirect
8. C₄×#14523502	C₂	semidirect
9. SD₁₆×Dic₁₃₁	C₂	semidirect
10. #22553399	C₂	semidirect
11. #22553347	C₂	semidirect
12. #22553319	C₂	semidirect
14. #22553266	C₂	semidirect
15. C₄×SD₁₆×C₁₃₁	C₂	semidirect
21. SD₁₆×D₁₃₁	C₄	semidirect
24. Q₈×Dic₁₃₁	C₂²	semidirect
26. C₄×Dic₂₆₂	C₂²	semidirect
28. #16862211	C₂²	semidirect
41. #16862179	C₂²	semidirect
42. #16862179	C₂²	semidirect
43. #16862178	C₂²	semidirect
44. #16862171	C₂²	semidirect
45. #16862170	C₂²	semidirect
46. #16862169	C₂²	semidirect
50. #16862157	C₂²	semidirect
51. #16862156	C₂²	semidirect
52. C₈×Dic₁₃₁	C₂²	semidirect
54. C₄×Q₈×C₁₃₁	C₂²	semidirect
56. #106×C₁₃₁	C₂²	semidirect
57. #103×C₁₃₁	C₂²	semidirect
59. C₄×C₈×C₁₃₁	C₂²	semidirect
64. Q₈×D₁₃₁	C₂×C₄	semidirect
74. #14523502	C₂×C₄	semidirect
75. #14523501	C₂×C₄	semidirect
76. #14523500	C₂×C₄	semidirect
80. C₈×D₁₃₁	C₂×C₄	semidirect
104. SD₁₆×C₁₃₁	C₂×C₄	semidirect
182. C₁₃₁	#2949	semidirect
194. C₄×SD₁₆	D₁₃₁	semidirect
213. C₄×Q₈	C₂×D₁₃₁	semidirect
230. #106	C₂×D₁₃₁	semidirect
234. #103	C₂×D₁₃₁	semidirect
242. C₄×C₈	C₂×D₁₃₁	semidirect
263. 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×SD₁₆×D₁₃₁	2
#22553788	2
#22553784	2
#22553415	2
#22553412	2
#22553410	2
#22553409	2
C₄×#14523502	2
SD₁₆×Dic₁₃₁	2
#22553399	2
#22553347	2
#22553319	2
#22553315	2
#22553266	2
C₄×SD₁₆×C₁₃₁	2
#2949	131