Subgroups — #25068370

Order 11008.

586 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	#19145177	C₂	1	1	yes	maximal, characteristic
2	#19143544	C₂	1	1	yes	maximal, characteristic
3	#19143538	C₂	1	1	yes	maximal, characteristic
4	#19133489	C₂	1	2	yes	maximal, complemented
5	#19133448	C₂	1	2	yes	maximal, complemented
6	#19133442	C₂	1	2	yes	maximal, complemented
7	#19133399	C₂	1	2	yes	maximal, complemented
8	C₂×#14582651	C₂	1	1	yes	maximal, characteristic
9	#19132999	C₂	1	1	yes	maximal, characteristic
10	#19132876	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1481	C₂	1	1	yes	maximal, characteristic
12	#14583456	C₂²	1	1	yes	characteristic
13	#14583302	C₄	1	1	yes	characteristic
14	#14583278	C₄	1	1	yes	characteristic
15	#14583251	C₄	1	1	yes	characteristic
16	#14583249	C₄	1	1	yes	characteristic
17	#14583138	C₄	1	2	yes	—
18	#14583138	C₄	1	2	yes	—
19	#14583030	—	2	2	no	—
20	#14583030	C₂²	1	2	yes	—
21	#14583028	—	2	2	no	—
22	#14583026	C₂²	1	2	yes	—
23	Q₈×C₄₃⋊C₈	C₂²	1	2	yes	—
24	#14583023	C₂²	1	2	yes	—
25	C₄×#10621885	C₂²	1	2	yes	—
26	C₄×#10621885	C₂²	1	2	yes	—
27	#14582926	—	2	1	no	—
28	#14582925	—	2	1	no	—
29	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
30	#14582855	—	2	1	no	—
31	#14582854	—	2	1	no	—
32	C₄×#10621877	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
34	#14582651	C₂²	1	1	yes	characteristic
35	#14582651	C₂²	1	1	yes	characteristic
36	#14582651	C₂²	1	1	yes	characteristic
37	#14582651	C₂²	1	1	yes	characteristic
38	#14582631	C₂²	1	2	yes	—
39	#14582631	C₂²	1	2	yes	—
40	#14582621	C₂²	1	2	yes	—
41	C₈×C₄₃⋊C₈	C₂²	1	2	yes	—
42	C₄₃×#533	C₂²	1	1	yes	characteristic
43	C₄₃×#431	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	—
47	C₂×#10621885	C₂×C₄	1	2	yes	—
48	C₂×#10621885	C₂×C₄	1	2	yes	—
49	C₂×#10621877	D₄	1	1	yes	characteristic
50	C₂×#10621877	D₄	1	1	yes	characteristic
51	C₂²×C₄₃⋊C₈	—	2	1	no	—
52	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
54	#13063325	C₂×C₄	1	1	yes	characteristic
55	#13063325	C₂×C₄	1	1	yes	characteristic
56	#13063317	—	2	1	no	—
57	#13063304	—	2	1	no	—
58	#13063304	C₂×C₄	1	2	yes	—
59	C₄×Dic₈₆	—	2	1	no	—
60	C₄×Dic₈₆	C₂³	1	2	yes	—
61	#13063284	—	2	1	no	—
62	#13063258	C₂×C₄	1	2	yes	—
63	#13063258	C₂×C₄	1	2	yes	—
64	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
66	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
69	Dic₄₃⋊C₈	—	2	2	no	—
70	Dic₄₃⋊C₈	—	2	2	no	—
71	#13063249	C₂×C₄	1	2	yes	—
72	#13063249	C₂×C₄	1	2	yes	—
73	#13063248	C₂×C₄	1	2	yes	—
74	#13063248	C₂×C₄	1	2	yes	—
75	#13063236	—	2	2	no	—
76	#13063236	D₄	1	2	yes	—
77	#13063235	—	2	2	no	—
78	C₄×C₄₃⋊C₈	—	2	2	no	—
79	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
84	C₈×Dic₄₃	—	2	2	no	—
85	C₂²×C₈×C₄₃	—	2	1	no	—
86	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
87	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
88	#125×C₄₃	—	2	1	no	—
89	C₂²⋊Q₈×C₄₃	—	2	1	no	—
90	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
91	C₄×Q₈×C₄₃	—	2	1	no	—
92	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
93	#117×C₄₃	—	2	1	no	—
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₃	—	2	1	no	—
96	C₄⋊C₈×C₄₃	—	2	1	no	—
97	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₄₃	—	2	1	no	—
100	C₄×C₈×C₄₃	C₂³	1	2	yes	—
101	C₂×Q₈×C₄₃	—	2	1	no	—
102	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
106	C₂×Dic₈₆	—	2	1	no	—
107	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₄₃	—	2	1	no	—
109	C₂×C₈×C₄₃	—	2	1	no	—
110	C₂×C₈×C₄₃	—	2	2	no	—
111	C₂×C₈×C₄₃	—	4	2	no	—
112	C₄⋊C₄×C₄₃	—	2	1	no	—
113	C₄⋊C₄×C₄₃	—	2	1	no	—
114	C₄⋊C₄×C₄₃	—	2	1	no	—
115	C₄⋊C₄×C₄₃	—	2	2	no	—
116	C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
118	C₂²⋊C₄×C₄₃	—	2	2	no	—
119	C₄²×C₄₃	—	2	2	no	—
120	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₃	#41	1	1	yes	characteristic
123	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₂²⋊Dic₄₃	—	2	2	no	—
125	#10621885	—	2	4	no	—
126	#10621885	—	4	2	no	—
127	C₄⋊Dic₄₃	—	2	1	no	—
128	C₄⋊Dic₄₃	—	2	1	no	—
129	C₄⋊Dic₄₃	—	2	1	no	—
130	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
131	Dic₄₃⋊C₄	—	2	2	no	—
132	Dic₄₃⋊C₄	—	2	2	no	—
133	C₄×Dic₄₃	—	2	2	no	—
134	#10621877	—	2	2	no	—
135	#10621877	Q₁₆	1	4	yes	complemented
136	C₂×C₄₃⋊C₈	—	2	2	no	—
137	C₂×C₄₃⋊C₈	—	2	1	no	—
138	C₂×C₄₃⋊C₈	—	2	1	no	—
139	C₂×C₄₃⋊C₈	—	4	1	no	—
140	C₂×C₄₃⋊C₈	—	4	2	no	—
141	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
146	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
147	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
148	Q₈×C₄₃	—	2	2	no	—
149	Q₈×C₄₃	—	2	2	no	—
150	Q₈×C₄₃	—	8	1	no	—
151	C₂×C₄×C₄₃	—	2	1	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	4	1	no	—
156	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
160	C₂×C₄×C₄₃	#135	1	2	yes	—
161	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₄₃	—	2	2	no	—
165	C₂×Dic₄₃	—	2	2	no	—
166	Dic₈₆	—	2	2	no	—
167	Dic₈₆	—	2	2	no	—
168	Dic₈₆	—	8	1	no	—
169	C₈×C₄₃	—	4	2	no	—
170	C₈×C₄₃	—	4	1	no	—
171	C₈×C₄₃	—	4	1	no	—
172	C₄₃⋊C₈	—	2	1	no	—
173	C₄₃⋊C₈	—	2	1	no	—
174	C₄₃⋊C₈	—	2	1	no	—
175	C₄₃⋊C₈	—	2	2	no	—
176	C₄₃⋊C₈	—	4	1	no	—
177	C₄₃⋊C₈	—	4	1	no	—
178	C₄₃⋊C₈	#131	1	2	yes	—
179	C₄₃⋊C₈	C₂×Q₁₆	1	4	yes	—
180	#18068	—	43	1	no	maximal, Sylow
181	C₂²×C₄₃	—	2	1	no	—
182	C₂²×C₄₃	—	2	1	no	—
183	C₂²×C₄₃	C₄×Q₁₆	1	2	yes	—
184	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
185	C₄×C₄₃	—	2	1	no	—
186	C₄×C₄₃	—	2	1	no	—
187	C₄×C₄₃	—	2	1	no	—
188	C₄×C₄₃	—	4	2	no	—
189	C₄×C₄₃	—	4	2	no	—
190	C₄×C₄₃	C₄×Q₁₆	1	2	yes	—
191	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
192	C₄×C₄₃	#568	1	1	yes	characteristic
193	C₄×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
194	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
195	Dic₄₃	—	4	2	no	—
196	Dic₄₃	—	4	2	no	—
197	#3170	—	43	1	no	—
198	#2962	—	43	1	no	—
199	#2962	—	43	1	no	—
200	#1591	—	43	2	no	—
201	#1584	—	43	2	no	—
202	#1584	—	43	2	no	—
203	C₈×Q₁₆	—	43	2	no	—
204	C₂×#335	—	43	1	no	—
205	#1481	—	43	1	no	—
206	#1481	D₄₃	1	1	yes	characteristic
207	C₈×M₁₆	—	43	1	no	—
208	C₂×C₄₃	—	2	2	no	—
209	C₂×C₄₃	#2935	1	1	yes	characteristic
210	C₂×C₄₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
211	C₂×C₄₃	#2957	1	1	yes	characteristic
212	#533	—	43	1	no	—
213	#533	C₂×D₄₃	1	1	yes	characteristic
214	#500	—	43	1	no	—
215	#494	—	43	1	no	—
216	#487	—	43	1	no	—
217	#487	—	43	1	no	—
218	#467	—	43	2	no	—
219	#467	—	43	2	no	—
220	#446	—	43	2	no	—
221	#446	—	43	2	no	—
222	#446	—	86	2	no	—
223	#446	—	86	2	no	—
224	C₈×Q₈	—	43	2	no	—
225	C₈×Q₈	—	43	2	no	—
226	C₄×Q₁₆	—	43	2	no	—
227	C₄×Q₁₆	—	43	2	no	—
228	#431	C₂×D₄₃	1	1	yes	characteristic
229	#424	—	86	1	no	—
230	#424	—	86	1	no	—
231	C₂×C₄⋊C₈	—	43	1	no	—
232	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
233	#405	—	86	1	no	—
234	#405	—	86	1	no	—
235	C₄×M₁₆	—	43	1	no	—
236	C₂×C₄×C₈	—	43	1	no	—
237	#335	—	43	1	no	—
238	#335	—	43	1	no	—
239	#335	—	43	1	no	—
240	#335	—	43	1	no	—
241	Q₈⋊C₈	—	43	2	no	—
242	Q₈⋊C₈	—	43	2	no	—
243	Q₈⋊C₈	C₂×D₄₃	1	2	yes	—
244	Q₈⋊C₈	C₂×D₄₃	1	2	yes	—
245	#322	—	43	2	no	—
246	C₈²	—	43	2	no	—
247	C₄₃	#18068	1	1	yes	characteristic, complemented, Sylow
248	C₂×Q₁₆	—	43	2	no	—
249	C₂×Q₁₆	—	43	2	no	—
250	C₂×M₁₆	—	43	1	no	—
251	C₂×M₁₆	—	43	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	43	1	no	—
254	C₂²×C₈	—	43	1	no	—
255	C₂²×C₈	—	86	1	no	—
256	C₄⋊Q₈	—	43	1	no	—
257	C₄⋊Q₈	—	43	1	no	—
258	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
259	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
260	#125	—	2	1	no	—
261	#125	—	86	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	—	43	2	no	—
264	C₂²⋊Q₈	—	86	1	no	—
265	C₂²⋊Q₈	C₄×D₄₃	1	2	yes	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	43	2	no	—
268	C₄×Q₈	—	86	1	no	—
269	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
270	#117	—	2	1	no	—
271	#117	—	86	1	no	—
272	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
273	#107	—	43	2	no	—
274	#107	—	43	2	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	43	1	no	—
278	C₄⋊C₈	—	43	1	no	—
279	C₄⋊C₈	—	86	2	no	—
280	C₄⋊C₈	—	86	2	no	—
281	C₄⋊C₈	—	86	2	no	—
282	C₄⋊C₈	—	86	2	no	—
283	C₄⋊C₈	—	86	1	no	—
284	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
285	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
286	#103	—	43	2	no	—
287	#103	—	43	2	no	—
288	#103	—	43	2	no	—
289	#103	—	43	2	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	#97	—	43	2	no	—
292	#97	—	86	2	no	—
293	#97	—	86	2	no	—
294	C₄×C₈	—	43	1	no	—
295	C₄×C₈	—	43	1	no	—
296	C₄×C₈	—	43	1	no	—
297	C₄×C₈	—	43	2	no	—
298	C₄×C₈	—	43	1	no	—
299	C₄×C₈	—	86	2	no	—
300	C₄×C₈	—	86	2	no	—
301	C₄×C₈	C₂²×D₄₃	1	2	yes	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	43	2	no	—
304	C₂×Q₈	—	86	1	no	—
305	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
306	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
307	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
308	C₂²×C₄	#10621900	1	1	yes	characteristic
309	Q₁₆	—	86	4	no	—
310	Q₁₆	—	172	2	no	—
311	M₁₆	—	43	4	no	—
312	M₁₆	—	86	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	43	1	no	—
318	C₂×C₈	—	43	2	no	—
319	C₂×C₈	—	43	1	no	—
320	C₂×C₈	—	43	1	no	—
321	C₂×C₈	—	43	1	no	—
322	C₂×C₈	—	43	2	no	—
323	C₂×C₈	—	86	2	no	—
324	C₂×C₈	—	86	1	no	—
325	C₂×C₈	—	86	1	no	—
326	C₂×C₈	—	172	1	no	—
327	C₂×C₈	—	172	2	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	43	2	no	—
334	C₄⋊C₄	—	86	1	no	—
335	C₄⋊C₄	—	86	1	no	—
336	C₄⋊C₄	—	86	2	no	—
337	C₄⋊C₄	—	86	1	no	—
338	C₄⋊C₄	—	86	2	no	—
339	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	86	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	86	2	no	—
344	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
345	C₄²	D₄×D₄₃	1	1	yes	characteristic
346	C₄²	#10621900	1	1	yes	characteristic
347	C₄²	C₂³×D₄₃	1	1	yes	characteristic
348	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
349	Q₈	—	2	2	no	—
350	Q₈	—	2	2	no	—
351	Q₈	—	8	1	no	—
352	Q₈	—	86	2	no	—
353	Q₈	—	86	2	no	—
354	Q₈	—	344	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	86	2	no	—
361	C₂×C₄	—	86	2	no	—
362	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
363	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
364	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
365	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
366	C₂×C₄	#13063346	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
369	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
370	C₈	—	4	2	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	1	no	—
373	C₈	—	43	2	no	—
374	C₈	—	43	4	no	—
375	C₈	—	86	1	no	—
376	C₈	—	86	1	no	—
377	C₈	—	86	1	no	—
378	C₈	—	86	2	no	—
379	C₈	—	172	1	no	—
380	C₈	—	172	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	#14582991	1	2	yes	—
384	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	172	2	no	—
391	C₄	—	172	2	no	—
392	C₄	#14582991	1	2	yes	—
393	C₄	#131×D₄₃	1	1	yes	characteristic
394	C₄	#14583664	1	1	yes	characteristic
395	C₄	C₂×Q₁₆×D₄₃	1	1	yes	characteristic
396	C₄	C₂×#13063346	1	1	yes	characteristic
397	C₂	—	2	2	no	—
398	C₂	#19143335	1	1	yes	characteristic
399	C₂	C₂×#14582991	1	1	yes	characteristic
400	C₂	#19143508	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1481	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂³×C₄₃	C₄×D₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1481	D₄₃
hypocenter	C₄₃	#18068
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1481

Complements

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

N	H ≅ G/N	type
4. #19133489	C₂	semidirect
5. #19133448	C₂	semidirect
6. #19133442	C₂	semidirect
7. #19133399	C₂	semidirect
135. #10621877	Q₁₆	semidirect
247. C₄₃	#18068	semidirect

Maximal subgroups

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

subgroup	index
#19145177	2
#19143544	2
#19143538	2
#19133489	2
#19133448	2
#19133442	2
#19133399	2
C₂×#14582651	2
#19132999	2
#19132876	2
C₄₃×#1481	2
#18068	43