Subgroups — #26232202

Order 12032.

1294 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252256	C₂	1	2	yes	maximal, complemented
2	#20251852	C₂	1	2	yes	maximal, complemented
3	#20244287	C₂	1	2	yes	maximal, complemented
4	#20243884	C₂	1	4	yes	maximal, complemented
5	#20243434	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243363	C₂	1	2	yes	maximal, complemented
7	#20243188	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#578	C₂	1	1	yes	maximal, characteristic
9	#15689601	C₂²	1	4	yes	—
10	#15689230	—	2	4	no	—
11	Q₁₆×Dic₄₇	—	2	4	no	—
12	#15689161	C₂²	1	2	yes	—
13	#15689140	C₂²	1	4	yes	—
14	#15689132	C₂²	1	4	yes	—
15	#15689107	C₂²	1	1	yes	characteristic
16	#15689097	—	2	8	no	—
17	#15689097	C₂²	1	4	yes	—
18	#15689097	C₂²	1	2	yes	—
19	#15689097	C₂²	1	1	yes	characteristic
20	#15689078	C₂²	1	2	yes	—
21	#15688894	C₂²	1	2	yes	—
22	#15688880	C₂²	1	2	yes	—
23	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	2	yes	—
24	C₄₇×#578	—	2	4	no	—
25	C₄₇×#578	—	2	4	no	—
26	C₂×#137×C₄₇	C₄	1	4	yes	complemented
27	C₂×#137×C₄₇	C₂²	1	2	yes	—
28	C₂×#135×C₄₇	C₄	1	2	yes	complemented
29	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×Q₁₆×C₄₇	C₄	1	2	yes	complemented
31	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#10625329	C₂³	1	2	yes	—
34	Q₈×Dic₄₇	—	2	8	no	—
35	Q₈×Dic₄₇	—	4	4	no	—
36	#13093983	—	2	8	no	—
37	#13093983	C₂³	1	4	yes	—
38	#13093983	C₂³	1	2	yes	—
39	#13093958	—	2	2	no	—
40	#13093956	—	2	2	no	—
41	#13093951	—	4	4	no	—
42	#13093948	—	2	8	no	—
43	#13093943	—	2	1	no	—
44	#13093941	—	2	1	no	—
45	#13093939	—	2	4	no	—
46	#13093939	—	2	8	no	—
47	#13093939	D₄	1	4	yes	—
48	#13093934	—	2	2	no	—
49	C₈×Dic₄₇	—	2	2	no	—
50	2₋¹⁺⁴×C₄₇	—	2	8	no	—
51	2₋¹⁺⁴×C₄₇	—	4	4	no	—
52	C₂×#41×C₄₇	—	2	4	no	—
53	C₂×#41×C₄₇	—	2	2	no	—
54	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
55	C₂×#41×C₄₇	C₂³	1	2	yes	—
56	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₄₇	—	2	2	no	—
58	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
59	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
60	#137×C₄₇	—	2	8	no	—
61	#137×C₄₇	—	2	16	no	—
62	#135×C₄₇	—	2	4	no	—
63	#135×C₄₇	—	2	4	no	—
64	#135×C₄₇	—	2	2	no	—
65	#135×C₄₇	—	2	2	no	—
66	C₂×Q₁₆×C₄₇	—	2	4	no	—
67	C₂×Q₁₆×C₄₇	—	2	4	no	—
68	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×Q₁₆×C₄₇	D₄	1	4	yes	—
73	C₂×Q₁₆×C₄₇	D₄	1	4	yes	—
74	C₂×SD₁₆×C₄₇	C₂×C₄	1	4	yes	—
75	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
77	#131×C₄₇	—	2	2	no	—
78	#131×C₄₇	—	2	2	no	—
79	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
80	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	#41×C₄₇	—	2	2	no	—
84	#41×C₄₇	—	2	2	no	—
85	#41×C₄₇	—	2	8	no	—
86	#41×C₄₇	—	2	4	no	—
87	#41×C₄₇	—	2	4	no	—
88	#41×C₄₇	—	4	4	no	—
89	#41×C₄₇	—	4	16	no	—
90	#41×C₄₇	—	4	8	no	—
91	C₂×Q₈×C₄₇	—	2	4	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	2	4	no	—
94	C₂×Q₈×C₄₇	—	2	8	no	—
95	C₂×Q₈×C₄₇	—	4	4	no	—
96	C₂×Q₈×C₄₇	—	4	8	no	—
97	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
99	C₂×Q₈×C₄₇	C₂×D₄	1	8	yes	—
100	C₂×Q₈×C₄₇	#41	1	1	yes	characteristic
101	C₂×D₄×C₄₇	—	2	4	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂×D₄×C₄₇	#41	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	4	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
112	Q₁₆×C₄₇	—	2	8	no	—
113	Q₁₆×C₄₇	—	2	1	no	—
114	Q₁₆×C₄₇	—	2	1	no	—
115	Q₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
116	Q₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
117	Q₁₆×C₄₇	C₂²⋊C₄	1	8	yes	—
118	SD₁₆×C₄₇	—	2	8	no	—
119	SD₁₆×C₄₇	—	2	4	no	—
120	D₈×C₄₇	—	2	1	no	—
121	D₈×C₄₇	—	2	1	no	—
122	M₁₆×C₄₇	—	2	2	no	—
123	M₁₆×C₄₇	—	2	4	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
131	C₂²⋊Dic₄₇	—	2	4	no	—
132	C₂²⋊Dic₄₇	C₂×D₄	1	4	yes	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	—	2	4	no	—
135	C₄⋊Dic₄₇	—	4	8	no	—
136	C₄×Dic₄₇	—	2	2	no	—
137	C₄×Dic₄₇	—	2	4	no	—
138	C₄×Dic₄₇	—	4	8	no	—
139	#10625329	—	2	2	no	—
140	#10625329	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	C₄×D₄	1	2	yes	—
144	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₄₇	—	2	4	no	—
146	Q₈×C₄₇	—	2	8	no	—
147	Q₈×C₄₇	—	2	2	no	—
148	Q₈×C₄₇	—	2	2	no	—
149	Q₈×C₄₇	—	2	2	no	—
150	Q₈×C₄₇	—	4	8	no	—
151	Q₈×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
152	D₄×C₄₇	—	2	4	no	—
153	D₄×C₄₇	—	2	2	no	—
154	D₄×C₄₇	—	2	2	no	—
155	D₄×C₄₇	—	2	2	no	—
156	D₄×C₄₇	—	4	8	no	—
157	D₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	8	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	4	8	no	—
164	C₂×C₄×C₄₇	—	4	8	no	—
165	C₂×C₄×C₄₇	—	4	4	no	—
166	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
171	C₂×Dic₄₇	—	2	4	no	—
172	C₂×Dic₄₇	—	4	4	no	—
173	C₈×C₄₇	—	2	2	no	—
174	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
177	C₄₇⋊C₈	—	4	2	no	—
178	#22457	—	47	1	no	maximal, Sylow
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	4	1	no	—
181	C₂²×C₄₇	—	4	2	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	8	2	no	—
184	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂²×C₄₇	D₄²	1	2	yes	—
186	C₄×C₄₇	—	2	8	no	—
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	4	2	no	—
189	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
190	C₄×C₄₇	#518	1	1	yes	characteristic
191	C₄×C₄₇	#546	1	2	yes	—
192	Dic₄₇	—	4	4	no	—
193	Dic₄₇	—	8	4	no	—
194	C₂×#578	D₄₇	1	1	yes	characteristic
195	#2950	—	47	2	no	—
196	#2884	—	47	2	no	—
197	#1976	—	47	2	no	—
198	#1905	—	47	4	no	—
199	#1812	—	47	1	no	—
200	#1796	—	47	2	no	—
201	#1757	—	47	1	no	—
202	C₂×C₄₇	—	2	2	no	—
203	C₂×C₄₇	—	2	1	no	—
204	C₂×C₄₇	—	4	2	no	—
205	C₂×C₄₇	—	8	2	no	—
206	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×2₋¹⁺⁴	C₂×D₄₇	1	2	yes	—
208	#578	—	2	4	no	—
209	#578	—	2	4	no	—
210	C₂×#137	Dic₄₇	1	4	yes	complemented
211	C₂×#137	C₂×D₄₇	1	2	yes	—
212	C₂×#135	Dic₄₇	1	2	yes	complemented
213	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
214	C₂²×Q₁₆	Dic₄₇	1	2	yes	complemented
215	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
216	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
217	#519	—	47	4	no	—
218	#441	—	94	4	no	—
219	C₄×Q₁₆	—	94	4	no	—
220	#427	—	47	2	no	—
221	#421	—	47	4	no	—
222	#419	—	47	4	no	—
223	#413	—	47	1	no	—
224	#410	—	47	1	no	—
225	#410	—	47	2	no	—
226	#410	—	47	4	no	—
227	#410	—	94	8	no	—
228	#405	—	47	2	no	—
229	#344	—	47	2	no	—
230	H(3,ℤ/4)	—	47	2	no	—
231	C₄₇	#22457	1	1	yes	characteristic, complemented, Sylow
232	2₋¹⁺⁴	—	2	8	no	—
233	2₋¹⁺⁴	—	4	4	no	—
234	C₂×#41	—	2	4	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	C₂×Dic₄₇	1	4	yes	—
237	C₂×#41	C₂²×D₄₇	1	2	yes	—
238	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
239	C₂²×Q₈	—	2	2	no	—
240	C₂²×Q₈	C₂×Dic₄₇	1	4	yes	—
241	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
242	#137	—	2	8	no	—
243	#137	—	2	16	no	—
244	#135	—	2	4	no	—
245	#135	—	2	4	no	—
246	#135	—	2	2	no	—
247	#135	—	2	2	no	—
248	C₂×Q₁₆	—	2	4	no	—
249	C₂×Q₁₆	—	2	4	no	—
250	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic
251	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	—
252	C₂×Q₁₆	C₂×Dic₄₇	1	2	yes	—
253	C₂×Q₁₆	C₂×Dic₄₇	1	2	yes	—
254	C₂×Q₁₆	C₂²⋊D₄₇	1	4	yes	—
255	C₂×Q₁₆	C₂²⋊D₄₇	1	4	yes	—
256	C₂×SD₁₆	C₂×Dic₄₇	1	4	yes	—
257	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
258	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic
259	#131	—	2	2	no	—
260	#131	—	2	2	no	—
261	C₂×M₁₆	—	47	2	no	—
262	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
263	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
264	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
265	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
266	C₄×Q₈	—	94	8	no	—
267	C₄×Q₈	—	188	4	no	—
268	#117	—	47	2	no	—
269	#117	—	47	4	no	—
270	#117	—	94	8	no	—
271	#107	—	94	2	no	—
272	#106	—	94	2	no	—
273	#104	—	188	4	no	—
274	#103	—	94	8	no	—
275	#101	—	94	1	no	—
276	#100	—	94	1	no	—
277	#99	—	47	4	no	—
278	#99	—	94	8	no	—
279	#99	—	94	4	no	—
280	#97	—	94	2	no	—
281	C₄×C₈	—	94	2	no	—
282	#41	—	2	2	no	—
283	#41	—	2	2	no	—
284	#41	—	2	8	no	—
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	4	4	no	—
288	#41	—	4	16	no	—
289	#41	—	4	8	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	8	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	8	no	—
296	C₂×Q₈	#10625352	1	1	yes	characteristic
297	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
298	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
299	C₂×Q₈	C₂×C₂²⋊D₄₇	1	8	yes	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	D₄×D₄₇	1	2	yes	—
303	C₂×D₄	#10625352	1	1	yes	characteristic
304	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
310	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
311	Q₁₆	—	2	8	no	—
312	Q₁₆	—	2	1	no	—
313	Q₁₆	—	2	1	no	—
314	Q₁₆	C₂²⋊Dic₄₇	1	4	yes	—
315	Q₁₆	C₂²⋊Dic₄₇	1	4	yes	—
316	Q₁₆	C₂²⋊Dic₄₇	1	8	yes	—
317	SD₁₆	—	2	8	no	—
318	SD₁₆	—	2	4	no	—
319	D₈	—	2	1	no	—
320	D₈	—	2	1	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	2	4	no	—
323	M₁₆	—	94	2	no	—
324	M₁₆	—	94	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
329	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
330	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
331	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
332	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
333	C₄⋊C₄	—	94	2	no	—
334	C₄⋊C₄	—	94	4	no	—
335	C₄⋊C₄	—	188	8	no	—
336	C₂²⋊C₄	—	47	4	no	—
337	C₂²⋊C₄	—	94	4	no	—
338	C₄²	—	94	2	no	—
339	C₄²	—	94	4	no	—
340	C₄²	—	188	8	no	—
341	C₂³	—	2	2	no	—
342	C₂³	D₄×Dic₄₇	1	2	yes	—
343	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	Q₈	—	2	2	no	—
346	Q₈	—	2	4	no	—
347	Q₈	—	2	2	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	4	8	no	—
350	Q₈	C₂×C₂²⋊Dic₄₇	1	8	yes	—
351	D₄	—	2	4	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	2	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	8	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	94	4	no	—
366	C₂×C₄	—	188	4	no	—
367	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
368	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
369	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
370	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
371	C₂×C₄	#13094069	1	2	yes	—
372	C₈	—	2	2	no	—
373	C₈	—	188	2	no	—
374	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
375	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
376	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
383	C₂²	D₄×C₂²⋊D₄₇	1	2	yes	—
384	C₄	—	2	8	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	376	4	no	—
388	C₄	—	188	4	no	—
389	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
390	C₄	#15689598	1	1	yes	characteristic
391	C₄	#15689767	1	2	yes	—
392	C₂	—	2	2	no	—
393	C₂	—	2	1	no	—
394	C₂	—	4	2	no	—
395	C₂	—	8	2	no	—
396	C₂	D₄×C₂²⋊Dic₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#578	C₂
socle	C₂×C₄₇	D₄×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#578	D₄₇
hypocenter	C₄₇	#22457
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#578

Complements

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

N	H ≅ G/N	type
1. #20252256	C₂	semidirect
2. #20251852	C₂	semidirect
3. #20244287	C₂	semidirect
4. #20243884	C₂	semidirect
5. #20243434	C₂	semidirect
6. #20243363	C₂	semidirect
7. #20243188	C₂	semidirect
26. C₂×#137×C₄₇	C₄	semidirect
28. C₂×#135×C₄₇	C₄	semidirect
30. C₂²×Q₁₆×C₄₇	C₄	semidirect
210. C₂×#137	Dic₄₇	semidirect
212. C₂×#135	Dic₄₇	semidirect
214. C₂²×Q₁₆	Dic₄₇	semidirect
231. C₄₇	#22457	semidirect

Maximal subgroups

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

subgroup	index
#20252256	2
#20251852	2
#20244287	2
#20243884	2
#20243434	2
#20243363	2
#20243188	2
C₂×C₄₇×#578	2
#22457	47