Subgroups — #26373055

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	#20256531	C₂	1	2	yes	maximal, complemented
2	#20255193	C₂	1	1	yes	maximal, characteristic, complemented
3	#20255188	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245644	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245519	C₂	1	2	yes	maximal, complemented
6	#20245469	C₂	1	1	yes	maximal, characteristic, complemented
7	#20245464	C₂	1	1	yes	maximal, characteristic, complemented
8	#20245360	C₂	1	2	yes	maximal, complemented
9	#20245353	C₂	1	2	yes	maximal, complemented
10	#20245226	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2178	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689940	—	2	1	no	—
13	#15689937	C₂²	1	2	yes	complemented
14	#15689928	—	2	1	no	—
15	#15689925	C₂²	1	2	yes	—
16	#15689565	—	2	2	no	—
17	#15689563	C₂²	1	2	yes	—
18	#15689558	C₂²	1	2	yes	complemented
19	#15689557	—	2	2	no	—
20	#15689554	—	2	2	no	—
21	C₂×#13093969	C₂²	1	2	yes	complemented
22	C₂×#13093969	C₂²	1	2	yes	complemented
23	SD₃₂×D₄₇	—	2	2	no	—
24	#15689539	C₂²	1	2	yes	complemented
25	#15689503	C₂²	1	1	yes	characteristic, complemented
26	#15689500	C₂²	1	1	yes	characteristic
27	#15689399	C₂²	1	2	yes	complemented
28	#15689398	—	2	1	no	—
29	#15689394	C₂²	1	2	yes	—
30	#15689393	—	2	1	no	—
31	#15689307	—	2	2	no	—
32	#15689292	—	2	2	no	—
33	#15689241	C₂²	1	1	yes	characteristic
34	#15688944	C₂²	1	1	yes	characteristic, complemented
35	#15688938	C₂²	1	2	yes	complemented
36	#15688935	C₂²	1	2	yes	complemented
37	#15688906	C₂²	1	2	yes	complemented
38	C₄₇×#508	C₂²	1	1	yes	characteristic
39	C₄₇×#443	C₂²	1	1	yes	characteristic
40	C₄₇×#443	C₂²	1	1	yes	characteristic, complemented
41	C₄₇×#368	C₂²	1	1	yes	characteristic, complemented
42	C₄₇×#359	C₂²	1	1	yes	characteristic
43	C₄₇×#359	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
45	#13094071	—	2	2	no	—
46	#13094070	—	2	2	no	—
47	#13094057	—	2	2	no	—
48	#13094057	—	4	2	no	—
49	#13094054	—	2	2	no	—
50	#13094053	—	4	2	no	—
51	#13094052	—	2	2	no	—
52	#13094052	—	4	2	no	—
53	#13094051	—	4	2	no	—
54	#13094049	—	2	2	no	—
55	#13094047	—	2	2	no	—
56	#13094046	—	4	1	no	—
57	#13094046	—	4	1	no	—
58	#13094046	D₄	1	1	yes	characteristic
59	#13094043	—	2	2	no	—
60	C₂×Dic₁₈₈	—	2	1	no	—
61	C₂×Dic₁₈₈	—	4	1	no	—
62	C₂×Dic₁₈₈	C₂³	1	2	yes	—
63	Q₁₆×D₄₇	—	2	2	no	—
64	C₂×D₃₇₆	—	2	1	no	—
65	C₂×D₃₇₆	—	4	1	no	—
66	C₂×D₃₇₆	C₂³	1	2	yes	—
67	D₈×D₄₇	—	2	2	no	—
68	#13094030	C₂³	1	2	yes	—
69	#13094024	—	2	1	no	—
70	#13094021	—	2	1	no	—
71	#13093970	—	2	2	no	—
72	#13093969	—	2	2	no	—
73	#13093969	—	2	2	no	—
74	#13093969	—	4	2	no	—
75	#13093968	—	2	2	no	—
76	#13093967	—	2	2	no	—
77	#13093965	—	2	2	no	—
78	#13093964	C₂³	1	2	yes	—
79	#13093963	—	2	2	no	—
80	C₁₆×D₄₇	—	2	2	no	—
81	#13093960	D₄	1	1	yes	characteristic
82	#13093952	D₄	1	2	yes	—
83	#13093942	—	2	2	no	—
84	#13093940	—	2	2	no	—
85	#135×C₄₇	C₂³	1	1	yes	characteristic
86	#135×C₄₇	C₂³	1	1	yes	characteristic
87	#131×C₄₇	—	2	1	no	—
88	#131×C₄₇	—	2	1	no	—
89	Q₃₂×C₄₇	D₄	1	1	yes	characteristic, complemented
90	SD₃₂×C₄₇	D₄	1	1	yes	characteristic, complemented
91	SD₃₂×C₄₇	D₄	1	1	yes	characteristic, complemented
92	D₁₆×C₄₇	D₄	1	1	yes	characteristic, complemented
93	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
95	#108×C₄₇	C₂³	1	1	yes	characteristic
96	#108×C₄₇	C₂³	1	1	yes	characteristic
97	#104×C₄₇	—	2	1	no	—
98	#104×C₄₇	—	2	1	no	—
99	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	#41×C₄₇	—	2	1	no	—
101	#41×C₄₇	—	2	1	no	—
102	#10625354	—	4	2	no	—
103	Q₈×D₄₇	—	4	2	no	—
104	#10625352	—	4	2	no	—
105	#10625352	—	8	2	no	—
106	D₄×D₄₇	—	4	2	no	—
107	D₄×D₄₇	—	8	2	no	—
108	#10625350	—	4	2	no	—
109	#10625350	—	4	2	no	—
110	#10625350	C₂×D₄	1	2	yes	—
111	C₂×D₁₈₈	—	2	2	no	—
112	C₂×D₁₈₈	—	4	2	no	—
113	C₂×D₁₈₈	—	8	1	no	—
114	C₂×Dic₉₄	—	2	2	no	—
115	C₂×Dic₉₄	—	4	2	no	—
116	Q₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
117	Q₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
118	SD₁₆×C₄₇	—	2	1	no	—
119	SD₁₆×C₄₇	—	2	1	no	—
120	D₈×C₄₇	C₂×D₄	1	1	yes	characteristic
121	D₈×C₄₇	C₂×D₄	1	1	yes	characteristic
122	M₁₆×C₄₇	—	2	1	no	—
123	M₁₆×C₄₇	—	2	1	no	—
124	M₁₆×C₄₇	—	4	1	no	—
125	M₁₆×C₄₇	—	4	1	no	—
126	C₂×C₈×C₄₇	—	4	1	no	—
127	C₂×C₈×C₄₇	—	4	1	no	—
128	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
130	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
131	#10625337	—	4	2	no	—
132	#10625336	—	4	2	no	—
133	#10625335	—	4	2	no	—
134	#10625334	—	4	2	no	—
135	C₄⋊Dic₄₇	—	8	1	no	—
136	#10625329	C₂×D₄	1	2	yes	—
137	Dic₁₈₈	—	2	2	no	—
138	Dic₁₈₈	—	2	2	no	—
139	Dic₁₈₈	—	4	2	no	—
140	Dic₁₈₈	—	4	1	no	—
141	Dic₁₈₈	—	4	1	no	—
142	Dic₁₈₈	D₈	1	1	yes	characteristic
143	D₃₇₆	—	2	2	no	—
144	D₃₇₆	—	2	2	no	—
145	D₃₇₆	—	4	2	no	—
146	D₃₇₆	—	4	1	no	—
147	D₃₇₆	—	4	1	no	—
148	D₃₇₆	D₈	1	1	yes	characteristic
149	#10625325	—	4	2	no	—
150	#10625325	—	4	2	no	—
151	#10625325	D₈	1	2	yes	—
152	#10625324	—	2	2	no	—
153	C₈×D₄₇	—	2	2	no	—
154	C₁₆×C₄₇	—	2	1	no	—
155	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
156	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₄₇⋊C₁₆	—	2	2	no	—
158	C₂²×D₄₇	—	4	2	no	—
159	C₂²×D₄₇	—	8	2	no	—
160	Q₈×C₄₇	—	2	1	no	—
161	Q₈×C₄₇	—	2	1	no	—
162	D₄×C₄₇	—	2	1	no	—
163	D₄×C₄₇	—	2	1	no	—
164	D₄×C₄₇	—	4	1	no	—
165	D₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂²⋊D₄₇	—	2	2	no	—
171	C₂²⋊D₄₇	—	8	2	no	—
172	C₂²⋊D₄₇	—	8	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	8	2	no	—
175	D₁₈₈	—	4	2	no	—
176	D₁₈₈	—	4	2	no	—
177	D₁₈₈	—	8	2	no	—
178	D₁₈₈	—	16	2	no	—
179	D₁₈₈	C₂×D₈	1	2	yes	—
180	C₄×D₄₇	—	2	2	no	—
181	C₄×D₄₇	—	8	2	no	—
182	C₄×D₄₇	—	8	2	no	—
183	Dic₉₄	—	4	2	no	—
184	Dic₉₄	—	4	2	no	—
185	Dic₉₄	—	8	2	no	—
186	Dic₉₄	C₂×D₈	1	2	yes	—
187	C₈×C₄₇	—	4	1	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	—	2	2	no	—
194	#33856	—	47	1	no	maximal, Sylow
195	C₂²×C₄₇	—	4	1	no	—
196	C₂²×C₄₇	—	4	1	no	—
197	C₂²×C₄₇	#576	1	1	yes	characteristic
198	C₂×D₄₇	—	2	2	no	—
199	C₂×D₄₇	—	8	2	no	—
200	C₂×D₄₇	—	16	2	no	—
201	C₂×D₄₇	—	32	2	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	4	1	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	—	2	2	no	—
208	Dic₄₇	—	8	2	no	—
209	#3416	—	47	2	no	—
210	#3293	—	47	1	no	—
211	#3292	—	47	1	no	—
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	D₄₇	1	1	yes	characteristic, complemented
219	#2170	—	47	1	no	—
220	C₂×C₄₇	—	2	1	no	—
221	C₂×C₄₇	—	8	1	no	—
222	C₂×C₄₇	—	8	1	no	—
223	C₂×C₄₇	D₄×D₈	1	1	yes	characteristic
224	D₄₇	—	4	2	no	—
225	D₄₇	—	16	2	no	—
226	#578	—	47	2	no	—
227	#578	—	94	1	no	—
228	#576	—	47	2	no	—
229	#576	—	94	1	no	—
230	#510	—	47	2	no	—
231	#510	—	94	2	no	—
232	#509	—	47	2	no	—
233	#509	—	94	2	no	—
234	#508	—	94	2	no	—
235	#508	C₂×D₄₇	1	1	yes	characteristic
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	—	47	1	no	—
242	#473	—	47	2	no	—
243	#473	—	94	1	no	—
244	#472	—	47	2	no	—
245	#472	—	94	1	no	—
246	#456	—	94	2	no	—
247	#453	—	94	2	no	—
248	#443	—	47	1	no	—
249	#443	C₂×D₄₇	1	1	yes	characteristic
250	#443	C₂×D₄₇	1	1	yes	characteristic, complemented
251	#368	C₂×D₄₇	1	1	yes	characteristic, complemented
252	#364	—	47	1	no	—
253	#362	—	47	2	no	—
254	#361	—	47	2	no	—
255	#359	C₂×D₄₇	1	1	yes	characteristic
256	#359	C₂×D₄₇	1	1	yes	characteristic, complemented
257	#350	—	47	2	no	—
258	C₄×C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
259	C₄₇	#33856	1	1	yes	characteristic, complemented, Sylow
260	2₋¹⁺⁴	—	94	2	no	—
261	H(5,𝔽₂)	—	94	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)	—	94	2	no	—
267	AGL(1,ℤ/8)	—	94	2	no	—
268	AGL(1,ℤ/8)	—	188	2	no	—
269	AGL(1,ℤ/8)	—	188	2	no	—
270	#135	—	47	1	no	—
271	#135	—	94	2	no	—
272	#135	—	94	2	no	—
273	#135	—	188	1	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	—	47	2	no	—
282	C₂×D₈	—	94	2	no	—
283	C₂×D₈	—	94	1	no	—
284	C₂×D₈	—	188	1	no	—
285	#131	—	2	1	no	—
286	#131	—	2	1	no	—
287	#131	—	47	2	no	—
288	C₄⋊Q₈	—	94	1	no	—
289	#127	—	94	1	no	—
290	Q₃₂	—	94	2	no	—
291	Q₃₂	D₁₈₈	1	1	yes	characteristic, complemented
292	SD₃₂	—	94	2	no	—
293	SD₃₂	—	94	2	no	—
294	SD₃₂	—	94	2	no	—
295	SD₃₂	—	94	2	no	—
296	SD₃₂	—	188	2	no	—
297	SD₃₂	D₁₈₈	1	1	yes	characteristic, complemented
298	SD₃₂	D₁₈₈	1	1	yes	characteristic, complemented
299	D₁₆	—	94	2	no	—
300	D₁₆	D₁₈₈	1	1	yes	characteristic, complemented
301	M₃₂	—	47	2	no	—
302	M₃₂	—	94	2	no	—
303	C₂×C₁₆	—	94	2	no	—
304	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
305	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
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	—	2	1	no	—
311	#104	—	47	2	no	—
312	#101	—	94	2	no	—
313	#100	—	94	2	no	—
314	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
315	#41	—	2	1	no	—
316	#41	—	2	1	no	—
317	#41	—	47	2	no	—
318	#41	—	376	2	no	—
319	#41	—	188	2	no	—
320	#41	—	188	2	no	—
321	#41	—	188	2	no	—
322	#41	—	188	2	no	—
323	C₂×Q₈	—	94	2	no	—
324	C₂×Q₈	—	188	2	no	—
325	C₂×Q₈	—	188	2	no	—
326	C₂×D₄	—	94	2	no	—
327	C₂×D₄	—	376	1	no	—
328	C₂×D₄	—	376	2	no	—
329	C₂×D₄	—	188	2	no	—
330	C₂×D₄	—	188	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	C₂×D₁₈₈	1	1	yes	characteristic
339	Q₁₆	C₂×D₁₈₈	1	1	yes	characteristic
340	SD₁₆	—	2	1	no	—
341	SD₁₆	—	2	1	no	—
342	SD₁₆	—	47	2	no	—
343	SD₁₆	—	188	2	no	—
344	SD₁₆	—	188	2	no	—
345	SD₁₆	—	188	2	no	—
346	SD₁₆	—	188	2	no	—
347	D₈	—	47	1	no	—
348	D₈	—	94	2	no	—
349	D₈	—	94	2	no	—
350	D₈	—	188	2	no	—
351	D₈	—	188	2	no	—
352	D₈	—	188	1	no	—
353	D₈	—	188	1	no	—
354	D₈	C₂×D₁₈₈	1	1	yes	characteristic
355	D₈	C₂×D₁₈₈	1	1	yes	characteristic
356	M₁₆	—	2	1	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	4	1	no	—
359	M₁₆	—	4	1	no	—
360	M₁₆	—	47	2	no	—
361	M₁₆	—	94	2	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	94	2	no	—
365	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
366	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
367	C₄⋊C₄	—	376	1	no	—
368	C₄²	D₄×D₄₇	1	1	yes	characteristic
369	C₁₆	—	2	1	no	—
370	C₁₆	—	94	2	no	—
371	C₁₆	C₂×D₁₈₈	1	1	yes	characteristic
372	C₁₆	C₂×D₁₈₈	1	1	yes	characteristic
373	C₂³	—	376	2	no	—
374	C₂³	—	188	2	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	—	47	2	no	—
378	Q₈	—	376	2	no	—
379	Q₈	—	188	2	no	—
380	Q₈	—	188	2	no	—
381	D₄	—	2	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	47	2	no	—
386	D₄	—	94	2	no	—
387	D₄	—	376	2	no	—
388	D₄	—	376	2	no	—
389	D₄	—	376	2	no	—
390	D₄	—	188	2	no	—
391	D₄	—	188	2	no	—
392	D₄	—	752	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	—	376	2	no	—
398	C₂×C₄	—	376	2	no	—
399	C₂×C₄	—	376	2	no	—
400	C₂×C₄	—	188	2	no	—
401	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
402	C₈	—	4	1	no	—
403	C₈	—	4	1	no	—
404	C₈	—	94	2	no	—
405	C₈	D₈×D₄₇	1	1	yes	characteristic
406	C₈	D₈×D₄₇	1	1	yes	characteristic
407	C₈	C₂²×D₁₈₈	1	1	yes	characteristic
408	C₈	#13094070	1	1	yes	characteristic
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	94	2	no	—
412	C₂²	—	376	2	no	—
413	C₂²	—	1504	2	no	—
414	C₂²	—	752	2	no	—
415	C₂²	#15689925	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	94	2	no	—
420	C₄	—	376	2	no	—
421	C₄	D₄×D₁₈₈	1	1	yes	characteristic
422	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	8	1	no	—
425	C₂	—	8	1	no	—
426	C₂	—	188	2	no	—
427	C₂	—	752	2	no	—
428	C₂	D₈×D₁₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₈₈
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#2178	C₂
socle	C₂×C₄₇	D₄×D₈
hypercenter	#2178	D₄₇
hypocenter	C₄₇	#33856
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2178

Complements

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

N	H ≅ G/N	type
1. #20256531	C₂	semidirect
2. #20255193	C₂	semidirect
3. #20255188	C₂	semidirect
4. #20245644	C₂	semidirect
5. #20245519	C₂	semidirect
6. #20245469	C₂	semidirect
7. #20245464	C₂	semidirect
8. #20245360	C₂	semidirect
9. #20245353	C₂	semidirect
10. #20245226	C₂	semidirect
11. C₄₇×#2178	C₂	semidirect
13. #15689937	C₂²	semidirect
18. #15689558	C₂²	semidirect
21. C₂×#13093969	C₂²	semidirect
22. C₂×#13093969	C₂²	semidirect
24. #15689539	C₂²	semidirect
25. #15689503	C₂²	semidirect
27. #15689399	C₂²	semidirect
34. #15688944	C₂²	semidirect
35. #15688938	C₂²	semidirect
36. #15688935	C₂²	semidirect
37. #15688906	C₂²	semidirect
40. C₄₇×#443	C₂²	semidirect
41. C₄₇×#368	C₂²	semidirect
43. C₄₇×#359	C₂²	semidirect
44. C₄×C₁₆×C₄₇	C₂²	semidirect
89. Q₃₂×C₄₇	D₄	semidirect
90. SD₃₂×C₄₇	D₄	semidirect
91. SD₃₂×C₄₇	D₄	semidirect
92. D₁₆×C₄₇	D₄	semidirect
218. #2178	D₄₇	semidirect
250. #443	C₂×D₄₇	semidirect
251. #368	C₂×D₄₇	semidirect
256. #359	C₂×D₄₇	semidirect
258. C₄×C₁₆	C₂×D₄₇	semidirect
259. C₄₇	#33856	semidirect
291. Q₃₂	D₁₈₈	semidirect
297. SD₃₂	D₁₈₈	semidirect
298. SD₃₂	D₁₈₈	semidirect
300. D₁₆	D₁₈₈	semidirect

Maximal subgroups

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

subgroup	index
#20256531	2
#20255193	2
#20255188	2
#20245644	2
#20245519	2
#20245469	2
#20245464	2
#20245360	2
#20245353	2
#20245226	2
C₄₇×#2178	2
#33856	47