Subgroups — #26216845

Order 12032.

810 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689081	C₂	1	1	yes	maximal, characteristic
2	#20245995	C₂	1	2	yes	maximal
3	#20243549	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243546	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243520	C₂	1	2	yes	maximal, complemented
6	#20243421	C₂	1	1	yes	maximal, characteristic
7	#20243415	C₂	1	2	yes	maximal
8	#20243288	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243287	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243280	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1809	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×#13093983	C₂²	1	1	yes	characteristic
14	C₂×#13093958	C₂²	1	1	yes	characteristic
15	C₂×#13093957	C₂²	1	2	yes	—
16	C₂×#13093957	C₂²	1	2	yes	—
17	C₂×#13093956	C₂²	1	1	yes	characteristic
18	#15689081	C₄	1	8	yes	complemented
19	C₂×#13093934	C₂²	1	1	yes	characteristic
20	C₂×#13093934	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
23	#15689017	—	2	2	no	—
24	#15689011	—	2	2	no	—
25	#15689008	—	2	2	no	—
26	#15689006	—	2	2	no	—
27	#15688992	C₂²	1	2	yes	—
28	#15688988	C₂²	1	2	yes	—
29	#15688983	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
32	#15688886	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#380	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₂²×C₄₇⋊C₈	—	2	2	no	—
41	C₂²×C₄₇⋊C₈	—	2	2	no	—
42	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	#13093983	C₂×C₄	1	4	yes	—
46	#13093983	Q₈	1	4	yes	—
47	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×Dic₄₇⋊C₄	—	2	2	no	—
51	C₂×Dic₄₇⋊C₄	—	2	2	no	—
52	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
53	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	C₂×C₄×Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
58	#13093958	—	2	2	no	—
59	#13093957	—	2	4	no	—
60	#13093957	—	2	4	no	—
61	#13093956	—	2	2	no	—
62	#13093934	C₂×C₄	1	4	yes	—
63	#13093934	C₂×C₄	1	4	yes	—
64	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
65	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₄₇	—	2	2	no	—
73	C₂×M₁₆×C₄₇	—	2	2	no	—
74	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
80	#107×C₄₇	—	2	2	no	—
81	#106×C₄₇	—	2	2	no	—
82	#95×C₄₇	—	2	2	no	—
83	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	—	2	1	no	—
85	C₂²×C₄×C₄₇	—	2	1	no	—
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
97	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
98	M₁₆×C₄₇	—	2	8	no	—
99	C₂×C₈×C₄₇	—	2	1	no	—
100	C₂×C₈×C₄₇	—	2	1	no	—
101	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₄₇	#41	1	2	yes	—
104	C₂×C₈×C₄₇	#41	1	2	yes	—
105	C₄⋊C₄×C₄₇	—	2	2	no	—
106	C₄⋊C₄×C₄₇	—	2	2	no	—
107	C₄⋊C₄×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₂²⋊C₄×C₄₇	—	8	2	no	—
110	C₂²⋊Dic₄₇	—	8	2	no	—
111	C₂²⋊Dic₄₇	C₄⋊C₄	1	8	yes	—
112	C₄⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	—	2	2	no	—
114	C₄⋊Dic₄₇	—	2	2	no	—
115	C₄⋊Dic₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	C₄⋊C₄	1	8	yes	—
117	Dic₄₇⋊C₄	—	8	2	no	—
118	Dic₄₇⋊C₄	—	8	2	no	—
119	C₄×Dic₄₇	—	8	2	no	—
120	C₄×Dic₄₇	—	8	2	no	—
121	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
122	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
123	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
124	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
125	C₂×C₄₇⋊C₈	—	2	1	no	—
126	C₂×C₄₇⋊C₈	—	2	1	no	—
127	C₂×C₄₇⋊C₈	—	2	8	no	—
128	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
130	C₂×C₄₇⋊C₈	#41	1	2	yes	—
131	C₂×C₄₇⋊C₈	#41	1	2	yes	—
132	C₂³×C₄₇	—	2	1	no	—
133	C₂³×C₄₇	—	2	1	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
137	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×Dic₄₇	—	2	2	no	—
158	C₂×Dic₄₇	—	2	2	no	—
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
168	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
169	C₈×C₄₇	—	2	2	no	—
170	C₈×C₄₇	#117	1	4	yes	—
171	C₄₇⋊C₈	—	2	2	no	—
172	C₄₇⋊C₈	#117	1	4	yes	—
173	#20821	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	—	2	4	no	—
175	C₂²×C₄₇	—	2	2	no	—
176	C₂²×C₄₇	—	4	2	no	—
177	C₂²×C₄₇	—	4	1	no	—
178	C₂²×C₄₇	—	4	1	no	—
179	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×C₄₇	#532	1	1	yes	characteristic
181	C₂²×C₄₇	#532	1	1	yes	characteristic
182	C₂²×C₄₇	#576	1	2	yes	—
183	C₂²×C₄₇	#578	1	2	yes	—
184	C₄×C₄₇	—	2	2	no	—
185	C₄×C₄₇	—	8	2	no	—
186	C₄×C₄₇	—	8	2	no	—
187	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
188	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
189	C₄×C₄₇	#533	1	1	yes	characteristic
190	C₄×C₄₇	#533	1	1	yes	characteristic
191	Dic₄₇	—	2	4	no	—
192	Dic₄₇	—	2	4	no	—
193	Dic₄₇	—	8	2	no	—
194	Dic₄₇	—	8	2	no	—
195	C₂×#405	—	47	1	no	—
196	#2314	—	47	2	no	—
197	#1846	—	47	1	no	—
198	#1845	—	47	1	no	—
199	#1836	—	47	2	no	—
200	#1809	—	47	1	no	—
201	#1809	D₄₇	1	1	yes	characteristic
202	#1808	—	47	2	no	—
203	#1776	—	47	1	no	—
204	#1776	—	47	1	no	—
205	C₄×#107	—	47	2	no	—
206	C₂×C₄₇	—	4	2	no	—
207	C₂×C₄₇	#2285	1	1	yes	characteristic
208	C₂×C₄₇	#2913	1	2	yes	—
209	C₂×C₄₇	#3175	1	2	yes	—
210	C₂×C₄₇	#3176	1	1	yes	characteristic
211	C₂×C₄₇	#3177	1	1	yes	characteristic
212	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
213	C₂³×C₈	—	47	1	no	—
214	C₂×#117	—	47	1	no	—
215	C₂×#107	—	47	1	no	—
216	C₂×#107	—	47	2	no	—
217	C₂×#107	—	47	2	no	—
218	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
219	C₂×#106	—	47	1	no	—
220	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
221	#405	—	47	8	no	—
222	C₂×#97	—	47	1	no	—
223	C₂×#97	—	47	1	no	—
224	C₂×C₄×C₈	—	47	1	no	—
225	C₂×C₄×C₈	—	47	1	no	—
226	#388	—	94	2	no	—
227	#388	—	94	2	no	—
228	#387	—	94	2	no	—
229	#387	—	94	2	no	—
230	#384	—	47	2	no	—
231	#382	—	47	2	no	—
232	#380	—	47	2	no	—
233	#380	C₂×D₄₇	1	2	yes	—
234	C₄×C₄⋊C₄	—	47	2	no	—
235	C₄×C₄⋊C₄	—	47	2	no	—
236	#340	—	47	2	no	—
237	#340	—	47	2	no	—
238	#340	—	47	2	no	—
239	#340	C₂×D₄₇	1	2	yes	—
240	C₄₇	#20821	1	1	yes	characteristic, complemented, Sylow
241	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
245	C₂²×C₈	—	47	1	no	—
246	C₂²×C₈	—	47	4	no	—
247	C₂²×C₈	—	47	1	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₂²×C₈	—	94	2	no	—
250	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
251	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
252	#117	—	47	4	no	—
253	#117	—	47	4	no	—
254	C₂×C₄⋊C₄	—	47	2	no	—
255	C₂×C₄⋊C₄	—	47	2	no	—
256	C₂×C₄⋊C₄	—	47	2	no	—
257	C₂×C₄⋊C₄	—	94	2	no	—
258	C₂×C₄⋊C₄	—	94	2	no	—
259	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
260	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	47	2	no	—
263	C₂×C₂²⋊C₄	—	94	2	no	—
264	C₂×C₄²	—	47	1	no	—
265	C₂×C₄²	—	47	1	no	—
266	C₂×C₄²	—	94	2	no	—
267	C₂×C₄²	—	94	2	no	—
268	#107	—	2	2	no	—
269	#107	—	94	4	no	—
270	#107	—	94	4	no	—
271	#107	—	94	2	no	—
272	#106	—	2	2	no	—
273	#106	—	94	2	no	—
274	#97	—	47	4	no	—
275	#97	—	47	4	no	—
276	C₄×C₈	—	47	4	no	—
277	C₄×C₈	—	47	4	no	—
278	#95	—	2	2	no	—
279	#95	—	94	2	no	—
280	#95	—	94	2	no	—
281	#95	—	94	2	no	—
282	#95	—	94	2	no	—
283	#95	—	94	2	no	—
284	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	47	2	no	—
292	C₂²×C₄	—	47	2	no	—
293	C₂²×C₄	—	94	2	no	—
294	C₂²×C₄	—	94	2	no	—
295	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
296	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
297	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
298	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
299	M₁₆	—	2	8	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	47	2	no	—
303	C₂×C₈	—	47	2	no	—
304	C₂×C₈	—	47	2	no	—
305	C₂×C₈	—	47	2	no	—
306	C₂×C₈	—	94	8	no	—
307	C₂×C₈	—	94	1	no	—
308	C₂×C₈	—	94	1	no	—
309	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
310	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
311	C₂×C₈	#10625352	1	2	yes	—
312	C₂×C₈	#10625352	1	2	yes	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	47	8	no	—
318	C₄⋊C₄	—	94	2	no	—
319	C₄⋊C₄	—	94	2	no	—
320	C₄⋊C₄	—	94	2	no	—
321	C₄⋊C₄	—	94	2	no	—
322	C₄⋊C₄	—	376	2	no	—
323	C₄⋊C₄	—	376	2	no	—
324	C₂²⋊C₄	—	8	2	no	—
325	C₂²⋊C₄	—	47	8	no	—
326	C₂²⋊C₄	—	376	2	no	—
327	C₄²	—	47	2	no	—
328	C₄²	—	47	2	no	—
329	C₄²	—	47	2	no	—
330	C₄²	—	47	2	no	—
331	C₄²	—	376	2	no	—
332	C₄²	—	376	2	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
338	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	47	4	no	—
352	C₂×C₄	—	47	4	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	188	2	no	—
358	C₂×C₄	—	188	2	no	—
359	C₂×C₄	—	188	2	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
364	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
366	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
367	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
369	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	47	4	no	—
372	C₈	—	94	2	no	—
373	C₈	#13093980	1	4	yes	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
380	C₂²	#15689668	1	1	yes	characteristic
381	C₂²	#15689668	1	1	yes	characteristic
382	C₂²	#15689927	1	2	yes	—
383	C₂²	#15689939	1	2	yes	—
384	C₄	—	2	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	—	94	4	no	—
388	C₄	—	94	4	no	—
389	C₄	—	376	2	no	—
390	C₄	—	376	2	no	—
391	C₄	#117×D₄₇	1	1	yes	characteristic
392	C₄	C₂×#13093980	1	1	yes	characteristic
393	C₄	#15689675	1	1	yes	characteristic
394	C₄	#15689675	1	1	yes	characteristic
395	C₂	—	4	2	no	—
396	C₂	#20245790	1	1	yes	characteristic
397	C₂	#20251987	1	2	yes	—
398	C₂	#20254022	1	2	yes	—
399	C₂	#20254033	1	1	yes	characteristic
400	C₂	#20254042	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1809	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1809	D₄₇
hypocenter	C₄₇	#20821
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #1809

Complements

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

N	H ≅ G/N	type
3. #20243549	C₂	semidirect
4. #20243546	C₂	semidirect
5. #20243520	C₂	semidirect
8. #20243288	C₂	semidirect
9. #20243287	C₂	semidirect
10. #20243280	C₂	semidirect
18. #15689081	C₄	semidirect
240. C₄₇	#20821	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689081	2
#20245995	2
#20243549	2
#20243546	2
#20243520	2
#20243421	2
#20243415	2
#20243288	2
#20243287	2
#20243280	2
C₄₇×#1809	2
#20821	47