Subgroups — #26373050

Order 12032.

652 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256535	C₂	1	2	yes	maximal, complemented
2	#20255193	C₂	1	1	yes	maximal, characteristic, complemented
3	#20245643	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245516	C₂	1	2	yes	maximal, complemented
5	#20245469	C₂	1	1	yes	maximal, characteristic, complemented
6	#20245461	C₂	1	1	yes	maximal, characteristic, complemented
7	#20245359	C₂	1	2	yes	maximal, complemented
8	#20245350	C₂	1	2	yes	maximal, complemented
9	#20245267	C₂	1	1	yes	maximal, characteristic, complemented
10	#20245225	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3292	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689940	C₂²	1	2	yes	complemented
13	#15689937	—	2	1	no	—
14	#15689563	—	2	2	no	—
15	#15689563	C₂²	1	2	yes	—
16	#15689559	—	2	2	no	—
17	#15689559	C₂²	1	2	yes	complemented
18	#15689553	—	2	2	no	—
19	#15689553	C₂²	1	1	yes	characteristic
20	C₂×#13093968	—	2	2	no	—
21	C₂×#13093968	C₂²	1	2	yes	complemented
22	C₂×#13093968	C₂²	1	2	yes	complemented
23	#15689540	C₂²	1	2	yes	complemented
24	#15689503	C₂²	1	1	yes	characteristic, complemented
25	#15689399	—	2	1	no	—
26	#15689398	C₂²	1	2	yes	complemented
27	#15689307	—	2	2	no	—
28	#15689241	C₂²	1	1	yes	characteristic, complemented
29	#15688952	C₂²	1	1	yes	characteristic, complemented
30	#15688944	C₂²	1	1	yes	characteristic, complemented
31	#15688938	C₂²	1	2	yes	complemented
32	#15688936	C₂²	1	2	yes	complemented
33	#15688930	C₂²	1	1	yes	characteristic
34	#15688929	C₂²	1	1	yes	characteristic, complemented
35	#15688907	C₂²	1	2	yes	complemented
36	C₄×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
37	C₄₇×#576	—	2	1	no	—
38	C₄₇×#576	C₂²	1	2	yes	—
39	C₄₇×#493	C₂²	1	1	yes	characteristic
40	C₄₇×#472	—	2	1	no	—
41	C₄₇×#472	C₂²	1	2	yes	—
42	C₄₇×#453	—	2	2	no	—
43	C₄₇×#443	C₂²	1	1	yes	characteristic
44	C₄₇×#443	C₂²	1	1	yes	characteristic
45	#13094071	—	2	2	no	—
46	#13094057	—	2	2	no	—
47	#13094057	—	4	2	no	—
48	#13094054	—	2	2	no	—
49	#13094053	—	4	2	no	—
50	#13094046	—	2	2	no	—
51	#13094046	C₂³	1	1	yes	characteristic
52	#13094043	—	4	1	no	—
53	C₂×Dic₁₈₈	—	2	2	no	—
54	C₂×Dic₁₈₈	—	2	1	no	—
55	C₂×Dic₁₈₈	C₂³	1	2	yes	—
56	Q₁₆×D₄₇	—	4	1	no	—
57	#13094030	—	2	1	no	—
58	#13094024	—	2	1	no	—
59	#13093970	—	2	2	no	—
60	#13093970	D₄	1	1	yes	characteristic, complemented
61	#13093968	—	2	2	no	—
62	#13093968	—	2	2	no	—
63	#13093968	—	2	2	no	—
64	#13093968	—	2	2	no	—
65	#13093968	—	4	2	no	—
66	#13093968	D₄	1	1	yes	characteristic, complemented
67	#13093967	D₄	1	1	yes	characteristic, complemented
68	#13093965	—	2	2	no	—
69	#13093965	D₄	1	1	yes	characteristic, complemented
70	#13093964	—	2	2	no	—
71	#13093964	C₂³	1	2	yes	—
72	C₂×C₄₇⋊C₁₆	—	2	2	no	—
73	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
75	#13093960	C₂³	1	1	yes	characteristic
76	#13093952	—	2	1	no	—
77	#13093942	—	2	2	no	—
78	H(5,𝔽₂)×C₄₇	—	2	2	no	—
79	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
80	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
81	AGL(1,ℤ/8)×C₄₇	—	4	2	no	—
82	AGL(1,ℤ/8)×C₄₇	—	4	2	no	—
83	#135×C₄₇	—	2	2	no	—
84	#135×C₄₇	—	4	1	no	—
85	#135×C₄₇	D₄	1	1	yes	characteristic
86	#135×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×D₈×C₄₇	—	2	2	no	—
88	C₂×D₈×C₄₇	—	2	1	no	—
89	C₂×D₈×C₄₇	—	4	1	no	—
90	C₂×D₈×C₄₇	C₂³	1	2	yes	—
91	#131×C₄₇	—	2	1	no	—
92	#131×C₄₇	C₂³	1	2	yes	—
93	#127×C₄₇	—	2	1	no	—
94	#108×C₄₇	D₄	1	1	yes	characteristic
95	#108×C₄₇	C₂³	1	1	yes	characteristic
96	#104×C₄₇	—	2	1	no	—
97	#104×C₄₇	D₄	1	2	yes	—
98	#100×C₄₇	—	2	2	no	—
99	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	#41×C₄₇	—	2	1	no	—
101	#41×C₄₇	—	4	2	no	—
102	#41×C₄₇	—	4	2	no	—
103	#41×C₄₇	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₄₇	—	2	2	no	—
105	C₂×D₄×C₄₇	—	4	2	no	—
106	C₂×D₄×C₄₇	—	4	2	no	—
107	C₂×D₄×C₄₇	—	8	1	no	—
108	C₂×D₄×C₄₇	—	8	2	no	—
109	Q₈×D₄₇	—	4	2	no	—
110	#10625352	—	4	2	no	—
111	#10625352	—	8	2	no	—
112	#10625350	—	2	1	no	—
113	#10625350	—	4	2	no	—
114	C₂×Dic₉₄	—	2	2	no	—
115	C₂×Dic₉₄	—	4	2	no	—
116	Q₁₆×C₄₇	D₈	1	1	yes	characteristic
117	Q₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
118	SD₁₆×C₄₇	—	2	1	no	—
119	SD₁₆×C₄₇	—	4	2	no	—
120	SD₁₆×C₄₇	—	4	2	no	—
121	SD₁₆×C₄₇	D₈	1	2	yes	—
122	D₈×C₄₇	—	2	2	no	—
123	D₈×C₄₇	—	2	2	no	—
124	D₈×C₄₇	—	4	2	no	—
125	D₈×C₄₇	—	4	2	no	—
126	D₈×C₄₇	—	4	1	no	—
127	D₈×C₄₇	—	4	1	no	—
128	D₈×C₄₇	D₈	1	1	yes	characteristic
129	D₈×C₄₇	C₂×D₄	1	1	yes	characteristic
130	M₁₆×C₄₇	—	2	2	no	—
131	M₁₆×C₄₇	—	2	1	no	—
132	M₁₆×C₄₇	—	4	1	no	—
133	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	4	1	no	—
136	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
139	#10625337	—	4	2	no	—
140	#10625335	—	4	2	no	—
141	C₄⋊Dic₄₇	—	8	1	no	—
142	#10625329	—	2	1	no	—
143	Dic₁₈₈	—	2	2	no	—
144	Dic₁₈₈	—	2	2	no	—
145	Dic₁₈₈	—	4	2	no	—
146	Dic₁₈₈	—	4	1	no	—
147	Dic₁₈₈	—	4	1	no	—
148	Dic₁₈₈	C₂×D₄	1	1	yes	characteristic
149	D₃₇₆	C₂×D₄	1	1	yes	characteristic
150	#10625325	—	2	1	no	—
151	#10625325	—	4	2	no	—
152	#10625324	—	4	1	no	—
153	C₈×D₄₇	—	4	1	no	—
154	C₄₇⋊C₁₆	—	2	2	no	—
155	C₄₇⋊C₁₆	—	2	1	no	—
156	C₄₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
157	C₄₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
158	C₂³×C₄₇	—	4	2	no	—
159	C₂³×C₄₇	—	8	2	no	—
160	Q₈×C₄₇	—	2	1	no	—
161	Q₈×C₄₇	C₂×D₈	1	2	yes	—
162	D₄×C₄₇	—	2	2	no	—
163	D₄×C₄₇	—	2	1	no	—
164	D₄×C₄₇	—	4	1	no	—
165	D₄×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	4	2	no	—
167	D₄×C₄₇	—	8	2	no	—
168	D₄×C₄₇	—	8	2	no	—
169	D₄×C₄₇	—	16	2	no	—
170	D₄×C₄₇	C₂×D₈	1	2	yes	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	8	2	no	—
175	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₂²⋊D₄₇	—	4	1	no	—
177	C₂²⋊D₄₇	—	8	2	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	C₂×Dic₄₇	—	8	2	no	—
180	D₁₈₈	—	2	1	no	—
181	C₄×D₄₇	—	4	1	no	—
182	C₄×D₄₇	—	8	2	no	—
183	Dic₉₄	—	2	1	no	—
184	Dic₉₄	—	4	2	no	—
185	Dic₉₄	—	4	2	no	—
186	Dic₉₄	—	8	2	no	—
187	C₈×C₄₇	—	2	2	no	—
188	C₈×C₄₇	—	4	1	no	—
189	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
190	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
191	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
192	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
193	C₄₇⋊C₈	—	4	1	no	—
194	#33856	—	47	1	no	maximal, Sylow
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	4	1	no	—
197	C₂²×C₄₇	—	8	2	no	—
198	C₂²×C₄₇	—	16	2	no	—
199	C₂²×C₄₇	—	32	2	no	—
200	C₂²×C₄₇	#576	1	1	yes	characteristic
201	C₂×D₄₇	—	4	1	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	—	4	1	no	—
205	C₄×C₄₇	D₄²	1	1	yes	characteristic
206	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
207	Dic₄₇	—	4	1	no	—
208	Dic₄₇	—	8	2	no	—
209	#3416	—	47	2	no	—
210	#3293	—	47	1	no	—
211	#3292	D₄₇	1	1	yes	characteristic, complemented
212	#2248	—	47	1	no	—
213	#2223	—	47	2	no	—
214	#2214	—	47	1	no	—
215	#2213	—	47	1	no	—
216	#2194	—	47	2	no	—
217	#2193	—	47	2	no	—
218	#2178	—	47	1	no	—
219	#2170	—	47	1	no	—
220	C₂×C₄₇	—	2	1	no	—
221	C₂×C₄₇	—	4	2	no	—
222	C₂×C₄₇	—	8	1	no	—
223	C₂×C₄₇	—	16	2	no	—
224	C₂×C₄₇	D₄×D₈	1	1	yes	characteristic
225	D₄₇	—	8	1	no	—
226	#578	—	47	2	no	—
227	#578	—	94	1	no	—
228	#576	—	2	1	no	—
229	#576	C₂×D₄₇	1	2	yes	—
230	#510	—	47	2	no	—
231	#510	—	94	2	no	—
232	#509	—	47	2	no	—
233	#509	—	94	2	no	—
234	#508	—	47	1	no	—
235	#508	—	94	2	no	—
236	C₂×SD₃₂	—	47	2	no	—
237	C₂×SD₃₂	—	47	2	no	—
238	C₂×SD₃₂	—	94	2	no	—
239	#504	—	47	2	no	—
240	#494	—	47	1	no	—
241	#493	C₂×D₄₇	1	1	yes	characteristic
242	#473	—	47	2	no	—
243	#473	—	94	1	no	—
244	#472	—	2	1	no	—
245	#472	C₂×D₄₇	1	2	yes	—
246	#456	—	94	2	no	—
247	#453	—	2	2	no	—
248	#443	—	47	1	no	—
249	#443	C₂×D₄₇	1	1	yes	characteristic
250	#443	C₂×D₄₇	1	1	yes	characteristic
251	#368	—	47	1	no	—
252	#364	—	47	1	no	—
253	#362	—	47	2	no	—
254	#361	—	47	2	no	—
255	#359	—	47	1	no	—
256	#359	—	47	1	no	—
257	#350	—	47	2	no	—
258	C₄×C₁₆	—	47	1	no	—
259	C₄₇	#33856	1	1	yes	characteristic, complemented, Sylow
260	2₋¹⁺⁴	—	94	2	no	—
261	H(5,𝔽₂)	—	2	2	no	—
262	#137	—	94	2	no	—
263	#137	—	94	2	no	—
264	#137	—	188	2	no	—
265	#137	—	188	2	no	—
266	AGL(1,ℤ/8)	—	2	2	no	—
267	AGL(1,ℤ/8)	—	2	2	no	—
268	AGL(1,ℤ/8)	—	4	2	no	—
269	AGL(1,ℤ/8)	—	4	2	no	—
270	#135	—	2	2	no	—
271	#135	—	4	1	no	—
272	#135	—	47	1	no	—
273	#135	—	94	2	no	—
274	#135	—	188	1	no	—
275	#135	C₂²⋊D₄₇	1	1	yes	characteristic
276	#135	C₂²×D₄₇	1	1	yes	characteristic
277	C₂×Q₁₆	—	47	2	no	—
278	C₂×Q₁₆	—	94	2	no	—
279	C₂×Q₁₆	—	94	1	no	—
280	C₂×Q₁₆	—	188	1	no	—
281	C₂×D₈	—	2	2	no	—
282	C₂×D₈	—	2	1	no	—
283	C₂×D₈	—	4	1	no	—
284	C₂×D₈	C₂²×D₄₇	1	2	yes	—
285	#131	—	2	1	no	—
286	#131	—	94	1	no	—
287	#131	C₂²×D₄₇	1	2	yes	—
288	C₄⋊Q₈	—	94	1	no	—
289	#127	—	2	1	no	—
290	Q₃₂	—	47	1	no	—
291	Q₃₂	—	94	2	no	—
292	SD₃₂	—	47	1	no	—
293	SD₃₂	—	47	1	no	—
294	SD₃₂	—	94	2	no	—
295	SD₃₂	—	94	2	no	—
296	SD₃₂	—	94	2	no	—
297	SD₃₂	—	94	2	no	—
298	SD₃₂	—	188	2	no	—
299	D₁₆	—	47	1	no	—
300	D₁₆	—	94	2	no	—
301	M₃₂	—	47	2	no	—
302	M₃₂	—	94	2	no	—
303	C₂×C₁₆	—	47	1	no	—
304	C₂×C₁₆	—	47	1	no	—
305	C₂×C₁₆	—	94	2	no	—
306	#108	—	47	1	no	—
307	#108	C₂²⋊D₄₇	1	1	yes	characteristic
308	#108	C₂²×D₄₇	1	1	yes	characteristic
309	#104	—	2	1	no	—
310	#104	—	94	1	no	—
311	#104	C₂²⋊D₄₇	1	2	yes	—
312	#101	—	94	2	no	—
313	#100	—	2	2	no	—
314	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
315	#41	—	2	1	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	94	1	no	—
319	#41	—	376	2	no	—
320	#41	—	188	2	no	—
321	#41	—	188	2	no	—
322	#41	C₂×C₂²⋊D₄₇	1	2	yes	—
323	C₂×Q₈	—	94	2	no	—
324	C₂×Q₈	—	188	2	no	—
325	C₂×Q₈	—	188	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	8	1	no	—
330	C₂×D₄	—	8	2	no	—
331	Q₁₆	—	47	1	no	—
332	Q₁₆	—	94	2	no	—
333	Q₁₆	—	94	2	no	—
334	Q₁₆	—	188	2	no	—
335	Q₁₆	—	188	2	no	—
336	Q₁₆	—	188	1	no	—
337	Q₁₆	—	188	1	no	—
338	Q₁₆	#10625334	1	1	yes	characteristic
339	Q₁₆	D₄×D₄₇	1	1	yes	characteristic
340	SD₁₆	—	2	1	no	—
341	SD₁₆	—	4	2	no	—
342	SD₁₆	—	4	2	no	—
343	SD₁₆	—	94	1	no	—
344	SD₁₆	—	188	2	no	—
345	SD₁₆	—	188	2	no	—
346	SD₁₆	#10625334	1	2	yes	—
347	D₈	—	2	2	no	—
348	D₈	—	2	2	no	—
349	D₈	—	4	2	no	—
350	D₈	—	4	2	no	—
351	D₈	—	4	1	no	—
352	D₈	—	4	1	no	—
353	D₈	—	47	1	no	—
354	D₈	#10625334	1	1	yes	characteristic
355	D₈	D₄×D₄₇	1	1	yes	characteristic
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	4	1	no	—
359	M₁₆	—	94	1	no	—
360	M₁₆	—	188	1	no	—
361	M₁₆	C₂×C₂²⋊D₄₇	1	2	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	188	1	no	—
365	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
366	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
367	C₄⋊C₄	—	376	1	no	—
368	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
369	C₁₆	—	47	1	no	—
370	C₁₆	—	47	1	no	—
371	C₁₆	—	94	2	no	—
372	C₁₆	—	94	1	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	8	2	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	94	1	no	—
377	Q₈	—	376	2	no	—
378	Q₈	—	188	2	no	—
379	Q₈	—	188	2	no	—
380	Q₈	C₂×#10625334	1	2	yes	—
381	D₄	—	2	2	no	—
382	D₄	—	2	1	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	8	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	16	2	no	—
389	D₄	—	94	1	no	—
390	D₄	—	376	2	no	—
391	D₄	—	188	1	no	—
392	D₄	C₂×#10625334	1	2	yes	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	—	376	2	no	—
398	C₂×C₄	—	376	2	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	—	188	1	no	—
401	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	4	1	no	—
404	C₈	—	188	1	no	—
405	C₈	C₂×#10625334	1	1	yes	characteristic
406	C₈	C₂×#10625334	1	1	yes	characteristic
407	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
408	C₈	#13094069	1	1	yes	characteristic
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	16	2	no	—
413	C₂²	—	32	2	no	—
414	C₂²	—	188	1	no	—
415	C₂²	#15689926	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	376	2	no	—
420	C₄	—	188	1	no	—
421	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
422	C₄	C₂²×#10625334	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	8	1	no	—
426	C₂	—	16	2	no	—
427	C₂	—	376	1	no	—
428	C₂	D₄×#10625334	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#10625334
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#3292	C₂
socle	C₂×C₄₇	D₄×D₈
hypercenter	#3292	D₄₇
hypocenter	C₄₇	#33856
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #443 ◁ #3292

Complements

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

N	H ≅ G/N	type
1. #20256535	C₂	semidirect
2. #20255193	C₂	semidirect
3. #20245643	C₂	semidirect
4. #20245516	C₂	semidirect
5. #20245469	C₂	semidirect
6. #20245461	C₂	semidirect
7. #20245359	C₂	semidirect
8. #20245350	C₂	semidirect
9. #20245267	C₂	semidirect
10. #20245225	C₂	semidirect
11. C₄₇×#3292	C₂	semidirect
12. #15689940	C₂²	semidirect
17. #15689559	C₂²	semidirect
21. C₂×#13093968	C₂²	semidirect
22. C₂×#13093968	C₂²	semidirect
23. #15689540	C₂²	semidirect
24. #15689503	C₂²	semidirect
26. #15689398	C₂²	semidirect
28. #15689241	C₂²	semidirect
29. #15688952	C₂²	semidirect
30. #15688944	C₂²	semidirect
31. #15688938	C₂²	semidirect
32. #15688936	C₂²	semidirect
34. #15688929	C₂²	semidirect
35. #15688907	C₂²	semidirect
36. C₄×C₄₇⋊C₁₆	C₂²	semidirect
60. #13093970	D₄	semidirect
66. #13093968	D₄	semidirect
67. #13093967	D₄	semidirect
69. #13093965	D₄	semidirect
211. #3292	D₄₇	semidirect
259. C₄₇	#33856	semidirect

Maximal subgroups

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

subgroup	index
#20256535	2
#20255193	2
#20245643	2
#20245516	2
#20245469	2
#20245461	2
#20245359	2
#20245350	2
#20245267	2
#20245225	2
C₄₇×#3292	2
#33856	47