Subgroups — #26372852

Order 12032.

738 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689559	C₂	1	2	yes	maximal, complemented
2	#20255110	C₂	1	1	yes	maximal, characteristic, complemented
3	#20245643	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245499	C₂	1	2	yes	maximal, complemented
5	#20245433	C₂	1	1	yes	maximal, characteristic, complemented
6	#20245420	C₂	1	1	yes	maximal, characteristic, complemented
7	#20245317	C₂	1	2	yes	maximal, complemented
8	#20245309	C₂	1	2	yes	maximal, complemented
9	C₄×#13093965	C₂	1	1	yes	maximal, characteristic, complemented
10	#20245220	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	2	yes	complemented
13	#15689778	—	2	1	no	—
14	#15689559	—	2	8	no	—
15	C₂×#13093968	C₂²	1	2	yes	—
16	C₂×#13093968	C₂²	1	2	yes	complemented
17	C₂×#13093968	C₂²	1	2	yes	complemented
18	C₂×#13093965	C₂²	1	1	yes	characteristic
19	C₂×#13093965	C₂²	1	2	yes	complemented
20	C₂×#13093964	C₂²	1	2	yes	complemented
21	#15689503	C₂²	1	1	yes	characteristic, complemented
22	#15689364	C₂²	1	2	yes	complemented
23	#15689329	—	2	1	no	—
24	#15689287	—	2	2	no	—
25	C₄×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
26	#15688948	C₂²	1	1	yes	characteristic, complemented
27	C₄⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
28	#15688926	C₂²	1	2	yes	complemented
29	#15688924	C₂²	1	1	yes	characteristic
30	#15688924	C₂²	1	2	yes	complemented
31	#15688923	C₂²	1	1	yes	characteristic, complemented
32	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	complemented
33	C₄×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂²×D₈×C₄₇	C₂²	1	2	yes	—
35	D₄²×C₄₇	—	2	1	no	—
36	C₄₇×#493	C₂²	1	1	yes	characteristic
37	C₄₇×#466	C₂²	1	2	yes	—
38	C₄₇×#459	—	2	1	no	—
39	C₄₇×#447	—	2	2	no	—
40	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#10625350	—	2	2	no	—
43	#13094046	—	2	4	no	—
44	#13094046	—	4	2	no	—
45	C₂×Dic₁₈₈	—	2	1	no	—
46	C₂×Dic₁₈₈	C₂³	1	2	yes	—
47	C₂×#10625325	—	2	2	no	—
48	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
49	#13094024	—	2	1	no	—
50	#13094006	—	4	2	no	—
51	#13094003	—	2	2	no	—
52	#13093995	—	4	1	no	—
53	C₄×D₁₈₈	—	2	1	no	—
54	C₄⋊C₄×D₄₇	—	4	1	no	—
55	#13093968	—	2	4	no	—
56	#13093968	—	2	4	no	—
57	#13093968	—	4	2	no	—
58	#13093965	—	2	4	no	—
59	#13093965	D₄	1	4	yes	complemented
60	#13093964	—	2	4	no	—
61	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
62	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
64	#13093958	C₂³	1	1	yes	characteristic
65	#13093949	—	2	2	no	—
66	#13093946	—	2	1	no	—
67	C₂²×D₄×C₄₇	—	2	2	no	—
68	C₂²×D₄×C₄₇	—	4	1	no	—
69	C₂×D₈×C₄₇	—	2	4	no	—
70	C₂×D₈×C₄₇	—	2	2	no	—
71	C₂×D₈×C₄₇	—	2	1	no	—
72	C₂×D₈×C₄₇	—	4	2	no	—
73	C₂×D₈×C₄₇	C₂³	1	2	yes	—
74	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
76	#127×C₄₇	—	2	1	no	—
77	#121×C₄₇	—	2	2	no	—
78	#121×C₄₇	—	4	1	no	—
79	#120×C₄₇	—	4	2	no	—
80	C₄×D₄×C₄₇	—	2	1	no	—
81	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
82	#107×C₄₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
84	#102×C₄₇	—	2	2	no	—
85	#102×C₄₇	—	2	1	no	—
86	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
87	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₂⁴×C₄₇	—	4	2	no	—
89	C₂×D₄×C₄₇	—	2	1	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	4	4	no	—
92	C₂×D₄×C₄₇	—	4	2	no	—
93	C₂×D₄×C₄₇	—	4	2	no	—
94	C₂×D₄×C₄₇	—	4	1	no	—
95	C₂×D₄×C₄₇	—	4	1	no	—
96	C₂×D₄×C₄₇	—	8	2	no	—
97	C₂×D₄×C₄₇	—	8	4	no	—
98	C₂×D₄×C₄₇	D₈	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	—	4	1	no	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
101	C₂×C₂²⋊D₄₇	—	4	2	no	—
102	#10625350	—	4	4	no	—
103	#10625350	—	8	2	no	—
104	C₂×D₁₈₈	—	2	1	no	—
105	C₂×C₄×D₄₇	—	4	1	no	—
106	C₂×C₄×D₄₇	—	4	2	no	—
107	C₂×Dic₉₄	—	2	2	no	—
108	D₈×C₄₇	—	2	2	no	—
109	D₈×C₄₇	—	2	1	no	—
110	D₈×C₄₇	—	2	2	no	—
111	D₈×C₄₇	—	4	4	no	—
112	D₈×C₄₇	—	8	1	no	—
113	D₈×C₄₇	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	D₈	1	1	yes	characteristic
121	C₂²⋊C₄×C₄₇	—	4	1	no	—
122	C₂²⋊C₄×C₄₇	—	4	2	no	—
123	C₂²⋊C₄×C₄₇	D₈	1	2	yes	—
124	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂²⋊Dic₄₇	—	4	2	no	—
126	(C₂×D₄₇)⋊C₄	—	4	1	no	—
127	C₄⋊Dic₄₇	—	2	1	no	—
128	C₄⋊Dic₄₇	—	4	1	no	—
129	C₄⋊Dic₄₇	—	4	1	no	—
130	Dic₄₇⋊C₄	—	4	2	no	—
131	Dic₁₈₈	—	2	2	no	—
132	Dic₁₈₈	—	2	2	no	—
133	Dic₁₈₈	—	8	1	no	—
134	D₃₇₆	—	2	1	no	—
135	D₃₇₆	C₂×D₄	1	2	yes	complemented
136	#10625325	—	4	4	no	—
137	C₄₇⋊C₁₆	—	2	2	no	—
138	C₄₇⋊C₁₆	—	2	1	no	—
139	C₄₇⋊C₁₆	C₂×D₄	1	2	yes	complemented
140	C₂³×C₄₇	—	4	1	no	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	—	8	4	no	—
143	C₂³×C₄₇	—	8	4	no	—
144	C₂³×C₄₇	—	16	2	no	—
145	C₂³×C₄₇	C₂×D₈	1	2	yes	—
146	C₂²×D₄₇	—	4	1	no	—
147	D₄×C₄₇	—	2	2	no	—
148	D₄×C₄₇	—	2	2	no	—
149	D₄×C₄₇	—	4	2	no	—
150	D₄×C₄₇	—	4	1	no	—
151	D₄×C₄₇	—	4	2	no	—
152	D₄×C₄₇	—	8	4	no	—
153	D₄×C₄₇	—	8	4	no	—
154	D₄×C₄₇	—	8	2	no	—
155	D₄×C₄₇	—	16	1	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	8	2	no	—
160	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂²⋊D₄₇	—	8	4	no	—
165	C₂×Dic₄₇	—	4	1	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	D₁₈₈	—	2	2	no	—
168	D₁₈₈	—	4	1	no	—
169	C₄×D₄₇	—	8	4	no	—
170	C₄×D₄₇	—	8	2	no	—
171	Dic₉₄	—	4	2	no	—
172	Dic₉₄	—	4	2	no	—
173	C₈×C₄₇	—	2	2	no	—
174	C₈×C₄₇	—	2	1	no	—
175	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
177	#33838	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	—	4	2	no	—
182	C₂²×C₄₇	—	8	1	no	—
183	C₂²×C₄₇	—	8	1	no	—
184	C₂²×C₄₇	—	8	2	no	—
185	C₂²×C₄₇	—	8	2	no	—
186	C₂²×C₄₇	—	8	2	no	—
187	C₂²×C₄₇	—	16	8	no	—
188	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
189	C₂×D₄₇	—	4	2	no	—
190	C₂×D₄₇	—	8	1	no	—
191	C₂×D₄₇	—	8	1	no	—
192	C₄×C₄₇	—	2	1	no	—
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	8	1	no	—
195	C₄×C₄₇	#509	1	2	yes	complemented
196	C₄×C₄₇	D₄²	1	1	yes	characteristic
197	C₄×C₄₇	#576	1	1	yes	characteristic
198	Dic₄₇	—	8	1	no	—
199	Dic₄₇	—	8	2	no	—
200	C₂×#509	—	47	2	no	—
201	#3283	—	47	1	no	—
202	D₄×D₈	D₄₇	1	1	yes	characteristic, complemented
203	#2248	—	47	1	no	—
204	#2220	—	47	2	no	—
205	#2208	—	47	1	no	—
206	#2206	—	47	1	no	—
207	#2187	—	47	2	no	—
208	#2186	—	47	2	no	—
209	C₄×D₁₆	—	47	1	no	—
210	#2169	—	47	1	no	—
211	C₂×C₄₇	—	4	2	no	—
212	C₂×C₄₇	—	8	2	no	—
213	C₂×C₄₇	—	16	2	no	—
214	C₂×C₄₇	D₄×D₈	1	1	yes	characteristic
215	C₂×C₄₇	C₂×#509	1	1	yes	characteristic
216	C₂×C₄₇	#3416	1	1	yes	characteristic
217	D₄₇	—	8	2	no	—
218	C₂×#135	—	47	2	no	—
219	C₂²×D₈	C₂×D₄₇	1	2	yes	—
220	#547	—	94	1	no	—
221	D₄²	—	2	1	no	—
222	#509	—	94	8	no	—
223	C₂×SD₃₂	—	47	2	no	—
224	C₂×SD₃₂	—	47	2	no	—
225	C₂×SD₃₂	—	47	2	no	—
226	C₂×D₁₆	—	47	1	no	—
227	C₂×D₁₆	—	47	2	no	—
228	C₂×M₃₂	—	47	2	no	—
229	#494	—	47	1	no	—
230	#493	C₂×D₄₇	1	1	yes	characteristic
231	#467	—	47	2	no	—
232	#466	C₂×D₄₇	1	2	yes	—
233	#461	—	94	1	no	—
234	#459	—	2	1	no	—
235	#452	—	94	2	no	—
236	#447	—	2	2	no	—
237	C₄×D₈	—	47	1	no	—
238	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
239	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
240	#366	—	47	1	no	—
241	C₄⋊C₁₆	—	47	1	no	—
242	#358	—	47	2	no	—
243	#357	—	47	1	no	—
244	#357	—	47	2	no	—
245	#357	—	47	1	no	—
246	C₂²⋊C₁₆	—	47	2	no	—
247	C₄×C₁₆	—	47	1	no	—
248	C₄₇	#33838	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	—	94	2	no	—
250	C₂²×D₄	—	2	2	no	—
251	C₂²×D₄	—	4	1	no	—
252	#135	—	94	4	no	—
253	#135	—	188	2	no	—
254	C₂×Q₁₆	—	47	2	no	—
255	C₂×Q₁₆	—	94	1	no	—
256	C₂×SD₁₆	—	94	2	no	—
257	C₂×D₈	—	2	4	no	—
258	C₂×D₈	—	2	2	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×D₈	—	4	2	no	—
261	C₂×D₈	—	47	1	no	—
262	C₂×D₈	C₂²×D₄₇	1	2	yes	—
263	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
264	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
265	C₄⋊Q₈	—	94	1	no	—
266	#127	—	2	1	no	—
267	#123	—	188	2	no	—
268	C₂²⋊Q₈	—	94	2	no	—
269	#121	—	2	2	no	—
270	#121	—	4	1	no	—
271	#121	—	188	1	no	—
272	#120	—	4	2	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	94	1	no	—
275	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
276	C₂×C₄⋊C₄	—	188	1	no	—
277	SD₃₂	—	94	4	no	—
278	SD₃₂	—	94	4	no	—
279	SD₃₂	—	188	2	no	—
280	D₁₆	—	47	4	no	—
281	D₁₆	—	94	4	no	—
282	M₃₂	—	94	4	no	—
283	C₂×C₁₆	—	47	1	no	—
284	C₂×C₁₆	—	47	1	no	—
285	C₂×C₁₆	—	47	2	no	—
286	#107	—	47	1	no	—
287	#107	C₂²×D₄₇	1	1	yes	characteristic
288	C₄⋊C₈	C₂²⋊D₄₇	1	1	yes	characteristic
289	#103	—	94	2	no	—
290	#102	—	2	1	no	—
291	#102	—	2	2	no	—
292	#102	—	94	1	no	—
293	C₂²⋊C₈	C₂²⋊D₄₇	1	2	yes	—
294	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
295	C₂⁴	—	4	2	no	—
296	#41	—	376	2	no	—
297	#41	—	188	4	no	—
298	C₂×Q₈	—	94	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	8	2	no	—
307	C₂×D₄	—	8	4	no	—
308	C₂×D₄	—	94	1	no	—
309	C₂×D₄	—	188	2	no	—
310	C₂×D₄	#10625334	1	1	yes	characteristic
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	188	1	no	—
313	C₂²×C₄	—	188	2	no	—
314	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
315	Q₁₆	—	94	2	no	—
316	Q₁₆	—	94	2	no	—
317	Q₁₆	—	376	1	no	—
318	SD₁₆	—	188	4	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	1	no	—
321	D₈	—	2	2	no	—
322	D₈	—	4	4	no	—
323	D₈	—	8	1	no	—
324	D₈	—	47	2	no	—
325	D₈	—	94	1	no	—
326	D₈	D₄×D₄₇	1	2	yes	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
330	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
331	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	94	1	no	—
334	C₄⋊C₄	—	188	2	no	—
335	C₄⋊C₄	—	188	1	no	—
336	C₄⋊C₄	—	188	1	no	—
337	C₄⋊C₄	#10625334	1	1	yes	characteristic
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	188	2	no	—
341	C₂²⋊C₄	—	188	1	no	—
342	C₂²⋊C₄	#10625334	1	2	yes	—
343	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
344	C₁₆	—	47	2	no	—
345	C₁₆	—	94	2	no	—
346	C₁₆	—	94	1	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	8	4	no	—
350	C₂³	—	8	4	no	—
351	C₂³	—	16	2	no	—
352	C₂³	—	188	1	no	—
353	C₂³	C₂×#10625334	1	2	yes	—
354	Q₈	—	188	2	no	—
355	Q₈	—	188	2	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	2	no	—
361	D₄	—	8	4	no	—
362	D₄	—	8	4	no	—
363	D₄	—	8	2	no	—
364	D₄	—	16	1	no	—
365	D₄	—	94	2	no	—
366	D₄	—	376	4	no	—
367	D₄	—	188	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	8	2	no	—
372	C₂×C₄	—	376	4	no	—
373	C₂×C₄	—	376	2	no	—
374	C₂×C₄	—	188	1	no	—
375	C₂×C₄	—	188	2	no	—
376	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
377	C₂×C₄	C₂×#10625334	1	2	yes	—
378	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
380	C₈	—	2	2	no	—
381	C₈	—	2	1	no	—
382	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
383	C₈	#13094069	1	1	yes	characteristic
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	16	8	no	—
394	C₂²	—	376	1	no	—
395	C₂²	—	376	1	no	—
396	C₂²	—	188	2	no	—
397	C₂²	C₂²×#10625334	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	8	1	no	—
401	C₄	—	376	2	no	—
402	C₄	—	376	1	no	—
403	C₄	#15689559	1	2	yes	complemented
404	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
405	C₄	#15689926	1	1	yes	characteristic
406	C₂	—	4	2	no	—
407	C₂	—	8	2	no	—
408	C₂	—	16	2	no	—
409	C₂	—	376	2	no	—
410	C₂	D₄×#10625334	1	1	yes	characteristic
411	C₂	C₂×#15689559	1	1	yes	characteristic
412	C₂	#20256535	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#10625334
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	D₄×D₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×D₈
hypercenter	D₄×D₈	D₄₇
hypocenter	C₄₇	#33838
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄ ◁ D₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×#15689559	C₂	semidirect
2. #20255110	C₂	semidirect
3. #20245643	C₂	semidirect
4. #20245499	C₂	semidirect
5. #20245433	C₂	semidirect
6. #20245420	C₂	semidirect
7. #20245317	C₂	semidirect
8. #20245309	C₂	semidirect
9. C₄×#13093965	C₂	semidirect
10. #20245220	C₂	semidirect
11. D₄×D₈×C₄₇	C₂	semidirect
12. C₂×#13094046	C₂²	semidirect
16. C₂×#13093968	C₂²	semidirect
17. C₂×#13093968	C₂²	semidirect
19. C₂×#13093965	C₂²	semidirect
20. C₂×#13093964	C₂²	semidirect
21. #15689503	C₂²	semidirect
22. #15689364	C₂²	semidirect
25. C₄×D₃₇₆	C₂²	semidirect
26. #15688948	C₂²	semidirect
27. C₄⋊(C₄₇⋊C₁₆)	C₂²	semidirect
28. #15688926	C₂²	semidirect
30. #15688924	C₂²	semidirect
31. #15688923	C₂²	semidirect
32. C₂²⋊(C₄₇⋊C₁₆)	C₂²	semidirect
33. C₄×C₄₇⋊C₁₆	C₂²	semidirect
59. #13093965	D₄	semidirect
135. D₃₇₆	C₂×D₄	semidirect
139. C₄₇⋊C₁₆	C₂×D₄	semidirect
195. C₄×C₄₇	#509	semidirect
202. D₄×D₈	D₄₇	semidirect
248. C₄₇	#33838	semidirect
403. C₄	#15689559	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689559	2
#20255110	2
#20245643	2
#20245499	2
#20245433	2
#20245420	2
#20245317	2
#20245309	2
C₄×#13093965	2
#20245220	2
D₄×D₈×C₄₇	2
#33838	47