Subgroups — #26112532

Order 12032.

686 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253392	C₂	1	1	yes	maximal, characteristic
2	C₄²×D₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#20241887	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241812	C₂	1	1	yes	maximal, characteristic
5	#20241289	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241221	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1994	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₈₈	—	2	1	no	—
9	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
10	C₂×C₄²×D₄₇	—	2	1	no	—
11	#15689451	—	2	1	no	—
12	#15689410	C₄	1	2	yes	complemented
13	#15689325	C₄	1	2	yes	complemented
14	#15689273	—	2	1	no	—
15	C₄×#10625336	—	2	2	no	—
16	#15689176	C₂²	1	1	yes	characteristic
17	#15689176	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊Dic₄₇	—	2	1	no	—
19	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
20	C₄×(C₂×D₄₇)⋊C₄	—	2	2	no	—
21	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
22	#15688860	—	2	2	no	—
23	#15688850	—	2	2	no	—
24	C₄₇×#533	C₂²	1	1	yes	characteristic
25	C₄₇×#423	C₂²	1	1	yes	characteristic
26	C₄³×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#339	—	2	1	no	—
28	C₄₇×#339	—	2	1	no	—
29	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₇	—	2	2	no	—
31	C₂²×C₄×D₄₇	—	2	1	no	—
32	C₂×#10625336	—	2	2	no	—
33	C₄×D₁₈₈	—	2	8	no	—
34	C₄×D₁₈₈	—	2	1	no	—
35	C₄×D₁₈₈	—	2	1	no	—
36	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
37	C₄×D₁₈₈	D₄	1	2	yes	—
38	C₂×C₄⋊Dic₄₇	—	2	1	no	—
39	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
40	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
41	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
42	C₂×C₄×Dic₄₇	—	2	2	no	—
43	C₂×C₄×Dic₄₇	—	2	1	no	—
44	C₄²×D₄₇	—	4	2	no	—
45	C₄²×D₄₇	—	4	2	no	—
46	#13093955	—	2	2	no	—
47	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
48	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	complemented
49	#13093948	—	2	2	no	—
50	#13093944	—	2	2	no	—
51	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
52	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄×C₄₇⋊C₈	—	2	1	no	—
54	C₄×C₄₇⋊C₈	—	2	1	no	—
55	C₄₇⋊#95	—	2	2	no	—
56	C₄₇⋊#95	D₄	1	2	yes	—
57	C₂×M₁₆×C₄₇	—	2	1	no	—
58	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
59	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
60	#125×C₄₇	—	2	1	no	—
61	C₂²⋊Q₈×C₄₇	—	2	1	no	—
62	C₂²⋊Q₈×C₄₇	—	2	1	no	—
63	C₄×Q₈×C₄₇	—	2	1	no	—
64	C₄×Q₈×C₄₇	—	2	1	no	—
65	#117×C₄₇	—	2	1	no	—
66	C₂×C₄²×C₄₇	—	2	1	no	—
67	C₂×C₄²×C₄₇	—	2	1	no	—
68	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₄₇	—	2	1	no	—
72	C₄⋊C₈×C₄₇	—	2	1	no	—
73	C₂³×D₄₇	—	2	1	no	—
74	C₂×Q₈×C₄₇	—	2	1	no	—
75	C₂×Q₈×C₄₇	—	2	1	no	—
76	C₂²×C₄×C₄₇	—	2	1	no	—
77	C₂²×C₄×C₄₇	—	2	1	no	—
78	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×Dic₄₇	—	2	1	no	—
82	C₂²×Dic₄₇	—	2	2	no	—
83	C₂×D₁₈₈	—	2	1	no	—
84	C₂×D₁₈₈	—	2	4	no	—
85	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
86	C₂×C₄×D₄₇	—	2	8	no	—
87	C₂×C₄×D₄₇	—	2	2	no	—
88	C₂×C₄×D₄₇	—	2	2	no	—
89	C₂×C₄×D₄₇	—	4	4	no	—
90	C₂×C₄×D₄₇	—	4	4	no	—
91	C₂×C₄×D₄₇	—	4	1	no	—
92	C₂×C₄×D₄₇	—	4	1	no	—
93	C₂×C₄×D₄₇	—	4	1	no	—
94	C₂×C₄×D₄₇	—	4	1	no	—
95	M₁₆×C₄₇	—	4	1	no	—
96	M₁₆×C₄₇	—	4	1	no	—
97	C₂×C₈×C₄₇	—	4	1	no	—
98	C₄⋊C₄×C₄₇	—	2	1	no	—
99	C₄⋊C₄×C₄₇	—	2	1	no	—
100	C₄⋊C₄×C₄₇	—	2	1	no	—
101	C₄⋊C₄×C₄₇	—	2	1	no	—
102	C₄⋊C₄×C₄₇	—	4	1	no	—
103	C₄⋊C₄×C₄₇	—	4	1	no	—
104	C₂²⋊C₄×C₄₇	—	4	1	no	—
105	C₄²×C₄₇	—	2	4	no	—
106	C₄²×C₄₇	—	2	1	no	—
107	C₄²×C₄₇	—	2	1	no	—
108	C₄²×C₄₇	—	2	1	no	—
109	C₄²×C₄₇	—	4	2	no	—
110	C₄²×C₄₇	—	4	1	no	—
111	C₄²×C₄₇	SD₁₆	1	2	yes	complemented
112	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₄₇	#41	1	1	yes	characteristic
115	C₄²×C₄₇	#41	1	1	yes	characteristic
116	#10625336	—	4	4	no	—
117	(C₂×D₄₇)⋊C₄	—	2	8	no	—
118	(C₂×D₄₇)⋊C₄	—	2	2	no	—
119	(C₂×D₄₇)⋊C₄	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	4	no	—
121	C₄⋊Dic₄₇	—	2	1	no	—
122	C₄⋊Dic₄₇	C₂²⋊C₄	1	2	yes	—
123	C₄×Dic₄₇	—	4	4	no	—
124	C₄×Dic₄₇	—	4	1	no	—
125	C₄×Dic₄₇	—	4	1	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	4	1	no	—
128	C₂³×C₄₇	#120	1	1	yes	characteristic
129	C₂²×D₄₇	—	2	4	no	—
130	C₂²×D₄₇	—	2	2	no	—
131	C₂²×D₄₇	—	4	2	no	—
132	C₂²×D₄₇	—	4	1	no	—
133	C₂²×D₄₇	—	4	1	no	—
134	Q₈×C₄₇	—	4	2	no	—
135	Q₈×C₄₇	—	8	1	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	4	1	no	—
142	C₂×C₄×C₄₇	—	4	1	no	—
143	C₂×C₄×C₄₇	—	4	1	no	—
144	C₂×C₄×C₄₇	—	4	1	no	—
145	C₂×C₄×C₄₇	—	4	1	no	—
146	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
154	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
156	C₂×Dic₄₇	—	2	4	no	—
157	C₂×Dic₄₇	—	2	2	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	1	no	—
161	C₂×Dic₄₇	—	4	1	no	—
162	D₁₈₈	—	2	4	no	—
163	D₁₈₈	—	2	2	no	—
164	D₁₈₈	#104	1	4	yes	—
165	C₄×D₄₇	—	4	16	no	—
166	C₄×D₄₇	—	4	2	no	—
167	C₄×D₄₇	—	4	2	no	—
168	C₄×D₄₇	—	4	2	no	—
169	C₄×D₄₇	—	4	2	no	—
170	C₈×C₄₇	—	8	1	no	—
171	C₄₇⋊C₈	—	4	2	no	—
172	C₄₇⋊C₈	—	8	1	no	—
173	#9231	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	#386	1	1	yes	characteristic
177	C₂²×C₄₇	#450	1	1	yes	characteristic
178	C₂²×C₄₇	#452	1	1	yes	characteristic
179	C₂×D₄₇	—	2	4	no	—
180	C₂×D₄₇	—	4	4	no	—
181	C₂×D₄₇	—	4	4	no	—
182	C₂×D₄₇	—	4	2	no	—
183	C₂×D₄₇	—	4	2	no	—
184	C₄×C₄₇	—	2	4	no	—
185	C₄×C₄₇	—	2	1	no	—
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	4	2	no	—
189	C₄×C₄₇	—	8	1	no	—
190	C₄×C₄₇	—	8	1	no	—
191	C₄×C₄₇	C₂×#104	1	2	yes	—
192	C₄×C₄₇	C₄×SD₁₆	1	1	yes	characteristic
193	C₄×C₄₇	#440	1	1	yes	characteristic
194	C₄×C₄₇	#461	1	1	yes	characteristic
195	C₄×C₄₇	#463	1	1	yes	characteristic
196	Dic₄₇	—	4	4	no	—
197	Dic₄₇	—	4	2	no	—
198	#3101	—	47	1	no	—
199	C₄²×D₄	—	47	1	no	—
200	#1994	D₄₇	1	1	yes	characteristic, complemented
201	#1503	—	47	1	no	—
202	#1486	—	47	1	no	—
203	#1303	—	47	1	no	—
204	#1276	—	47	1	no	—
205	C₂×C₄₇	—	2	1	no	—
206	C₂×C₄₇	—	2	1	no	—
207	C₂×C₄₇	#1877	1	1	yes	characteristic
208	C₂×C₄₇	#1896	1	1	yes	characteristic
209	C₂×C₄₇	#1906	1	1	yes	characteristic
210	D₄₇	—	4	4	no	—
211	#533	C₂×D₄₇	1	1	yes	characteristic
212	C₂×C₄×D₄	—	47	1	no	—
213	C₂×C₄×D₄	—	94	1	no	—
214	C₂²×C₄²	—	94	1	no	—
215	#483	—	94	1	no	—
216	#476	—	47	2	no	—
217	#461	—	47	2	no	—
218	#450	—	94	1	no	—
219	C₄×SD₁₆	—	94	2	no	—
220	#431	—	47	1	no	—
221	#431	—	47	1	no	—
222	#423	C₂×D₄₇	1	1	yes	characteristic
223	C₄×C₄⋊C₄	—	47	1	no	—
224	C₄×C₄⋊C₄	—	94	1	no	—
225	C₄×C₂²⋊C₄	—	94	2	no	—
226	C₄×C₂²⋊C₄	—	94	1	no	—
227	C₄³	C₂×D₄₇	1	1	yes	characteristic
228	#339	—	2	1	no	—
229	#339	—	2	1	no	—
230	#328	—	94	2	no	—
231	D₄⋊C₈	—	94	2	no	—
232	C₄₇	#9231	1	1	yes	characteristic, complemented, Sylow
233	C₂²×D₄	—	47	1	no	—
234	C₂³×C₄	—	94	2	no	—
235	C₂³×C₄	—	94	1	no	—
236	C₂×SD₁₆	—	94	2	no	—
237	C₂×M₁₆	—	2	1	no	—
238	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic, complemented
239	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic, complemented
240	#125	—	2	1	no	—
241	C₂²⋊Q₈	—	2	1	no	—
242	C₂²⋊Q₈	—	2	1	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×Q₈	—	2	1	no	—
245	C₄×D₄	—	47	2	no	—
246	C₄×D₄	—	47	2	no	—
247	C₄×D₄	—	94	8	no	—
248	C₄×D₄	—	94	1	no	—
249	C₄×D₄	—	94	1	no	—
250	#117	—	2	1	no	—
251	C₂×C₄⋊C₄	—	47	1	no	—
252	C₂×C₄⋊C₄	—	94	1	no	—
253	C₂×C₂²⋊C₄	—	94	2	no	—
254	C₂×C₂²⋊C₄	—	94	1	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	—	94	2	no	—
258	C₂×C₄²	—	94	1	no	—
259	C₂×C₄²	—	188	2	no	—
260	C₂×C₄²	—	188	2	no	—
261	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
262	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
263	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
264	#106	—	94	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	47	2	no	—
268	C₄⋊C₈	—	94	1	no	—
269	#103	—	94	2	no	—
270	#102	—	94	2	no	—
271	C₂²⋊C₈	—	94	1	no	—
272	C₂²⋊C₈	—	94	1	no	—
273	C₄×C₈	—	94	1	no	—
274	C₄×C₈	—	94	1	no	—
275	#95	—	47	2	no	—
276	#95	—	94	2	no	—
277	C₂⁴	—	94	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	1	no	—
280	C₂×D₄	—	47	2	no	—
281	C₂×D₄	—	94	4	no	—
282	C₂×D₄	—	94	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	94	8	no	—
286	C₂²×C₄	—	94	2	no	—
287	C₂²×C₄	—	94	1	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	—	188	4	no	—
291	C₂²×C₄	—	188	4	no	—
292	C₂²×C₄	—	188	1	no	—
293	C₂²×C₄	—	188	1	no	—
294	C₂²×C₄	—	188	1	no	—
295	C₂²×C₄	—	188	1	no	—
296	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
297	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
299	SD₁₆	—	188	4	no	—
300	M₁₆	—	4	1	no	—
301	M₁₆	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	94	2	no	—
304	C₂×C₈	—	188	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	47	2	no	—
312	C₄⋊C₄	—	94	4	no	—
313	C₄⋊C₄	—	94	1	no	—
314	C₂²⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	94	8	no	—
316	C₂²⋊C₄	—	94	2	no	—
317	C₂²⋊C₄	—	94	2	no	—
318	C₄²	—	2	4	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	4	2	no	—
323	C₄²	—	4	1	no	—
324	C₄²	—	188	4	no	—
325	C₄²	—	188	1	no	—
326	C₄²	—	188	1	no	—
327	C₄²	#10625336	1	2	yes	complemented
328	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
329	C₄²	#10625350	1	1	yes	characteristic
330	C₄²	D₄×D₄₇	1	1	yes	characteristic
331	C₄²	#10625352	1	1	yes	characteristic
332	C₂³	—	94	4	no	—
333	C₂³	—	94	2	no	—
334	C₂³	—	188	2	no	—
335	C₂³	—	188	1	no	—
336	C₂³	—	188	1	no	—
337	C₂³	#13093992	1	1	yes	characteristic
338	Q₈	—	4	2	no	—
339	Q₈	—	8	1	no	—
340	D₄	—	47	4	no	—
341	D₄	—	94	4	no	—
342	D₄	—	94	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	94	4	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	188	16	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	—	188	2	no	—
358	C₂×C₄	—	188	1	no	—
359	C₂×C₄	—	188	1	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	—	188	2	no	—
364	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
365	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
366	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
367	C₂×C₄	#13093995	1	1	yes	characteristic
368	C₂×C₄	#13093997	1	1	yes	characteristic
369	C₂×C₄	#13094006	1	1	yes	characteristic
370	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
371	C₂×C₄	#13094044	1	1	yes	characteristic
372	C₂×C₄	#13094049	1	1	yes	characteristic
373	C₂×C₄	#13094055	1	1	yes	characteristic
374	C₈	—	8	1	no	—
375	C₈	—	376	1	no	—
376	C₈	—	188	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	94	4	no	—
380	C₂²	—	188	4	no	—
381	C₂²	—	188	4	no	—
382	C₂²	—	188	2	no	—
383	C₂²	—	188	2	no	—
384	C₂²	#15688999	1	1	yes	characteristic
385	C₂²	#15689273	1	1	yes	characteristic
386	C₂²	#15689283	1	1	yes	characteristic
387	C₄	—	2	4	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	8	1	no	—
393	C₄	—	8	1	no	—
394	C₄	—	188	4	no	—
395	C₄	—	188	2	no	—
396	C₄	#104×D₄₇	1	2	yes	—
397	C₄	C₄×#10625336	1	1	yes	characteristic
398	C₄	#15689221	1	1	yes	characteristic
399	C₄	#15689325	1	1	yes	characteristic
400	C₄	#15689335	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	188	4	no	—
404	C₂	#20243725	1	1	yes	characteristic
405	C₂	#20243828	1	1	yes	characteristic
406	C₂	#20243892	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093995
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1994	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂²×D₁₈₈	D₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1994	D₄₇
hypocenter	C₄₇	#9231
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1994

Complements

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

N	H ≅ G/N	type
3. #20241887	C₂	semidirect
5. #20241289	C₂	semidirect
6. #20241221	C₂	semidirect
7. C₄₇×#1994	C₂	semidirect
12. #15689410	C₄	semidirect
13. #15689325	C₄	semidirect
48. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
58. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
59. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
111. C₄²×C₄₇	SD₁₆	semidirect
200. #1994	D₄₇	semidirect
232. C₄₇	#9231	semidirect
238. C₄⋊Q₈	C₄×D₄₇	semidirect
239. C₄⋊Q₈	C₄×D₄₇	semidirect
327. C₄²	#10625336	semidirect

Maximal subgroups

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

subgroup	index
#20253392	2
C₄²×D₁₈₈	2
#20241887	2
#20241812	2
#20241289	2
#20241221	2
C₄₇×#1994	2
#9231	47