Subgroups — #26232229

Order 12032.

1286 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252305	C₂	1	2	yes	maximal, complemented
2	#20251871	C₂	1	2	yes	maximal, complemented
3	#20244304	C₂	1	2	yes	maximal, complemented
4	#20243863	C₂	1	4	yes	maximal, complemented
5	#20243438	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	#15689890	C₂²	1	4	yes	—
10	#15689245	—	2	4	no	—
11	#15689240	—	2	4	no	—
12	C₂×#13093960	C₂²	1	2	yes	—
13	#15689140	C₂²	1	4	yes	—
14	#15689132	C₂²	1	4	yes	—
15	#15689107	—	2	4	no	—
16	#15689107	C₂²	1	2	yes	—
17	#15689107	C₂²	1	1	yes	characteristic
18	C₂×#13093943	—	2	4	no	—
19	C₂×#13093943	C₂²	1	4	yes	—
20	#15689097	C₂²	1	1	yes	characteristic
21	#15689078	C₂²	1	2	yes	—
22	#15688894	C₂²	1	2	yes	—
23	C₄₇⋊#338	C₂²	1	2	yes	—
24	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	2	yes	—
25	C₄₇×#578	—	2	4	no	—
26	C₄₇×#578	—	2	4	no	—
27	C₂×#137×C₄₇	C₄	1	4	yes	complemented
28	C₂×#137×C₄₇	C₂²	1	2	yes	—
29	C₂×#135×C₄₇	C₄	1	2	yes	complemented
30	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×Q₁₆×C₄₇	C₄	1	2	yes	complemented
32	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
34	#13094031	—	2	8	no	—
35	#13094031	—	4	4	no	—
36	C₂×#10625329	—	2	8	no	—
37	C₂×#10625329	C₂³	1	4	yes	—
38	C₂×#10625329	C₂³	1	2	yes	—
39	#13093983	C₂³	1	2	yes	—
40	#13093960	—	2	2	no	—
41	#13093960	—	2	2	no	—
42	#13093951	—	2	8	no	—
43	#13093948	—	4	4	no	—
44	#13093943	—	2	2	no	—
45	#13093943	—	2	8	no	—
46	#13093943	D₄	1	2	yes	—
47	#13093941	—	2	2	no	—
48	#13093941	D₄	1	2	yes	—
49	#13093939	—	2	2	no	—
50	#13093934	—	2	2	no	—
51	C₈×Dic₄₇	—	2	2	no	—
52	2₋¹⁺⁴×C₄₇	—	2	8	no	—
53	2₋¹⁺⁴×C₄₇	—	4	4	no	—
54	C₂×#41×C₄₇	—	2	2	no	—
55	C₂×#41×C₄₇	—	2	4	no	—
56	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
57	C₂×#41×C₄₇	C₂³	1	2	yes	—
58	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₄₇	—	2	2	no	—
60	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
61	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
62	#137×C₄₇	—	2	8	no	—
63	#137×C₄₇	—	2	16	no	—
64	#135×C₄₇	—	2	4	no	—
65	#135×C₄₇	—	2	4	no	—
66	#135×C₄₇	D₄	1	4	yes	—
67	#135×C₄₇	D₄	1	4	yes	—
68	C₂×Q₁₆×C₄₇	—	2	4	no	—
69	C₂×Q₁₆×C₄₇	—	2	4	no	—
70	C₂×Q₁₆×C₄₇	—	2	2	no	—
71	C₂×Q₁₆×C₄₇	—	2	2	no	—
72	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
74	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×SD₁₆×C₄₇	C₂×C₄	1	4	yes	—
77	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	#131×C₄₇	—	2	2	no	—
80	#131×C₄₇	—	2	2	no	—
81	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	#41×C₄₇	—	2	2	no	—
86	#41×C₄₇	—	2	2	no	—
87	#41×C₄₇	—	2	4	no	—
88	#41×C₄₇	—	2	8	no	—
89	#41×C₄₇	—	4	4	no	—
90	#41×C₄₇	—	4	8	no	—
91	#41×C₄₇	—	4	16	no	—
92	#41×C₄₇	C₂×D₄	1	8	yes	—
93	C₂×Q₈×C₄₇	—	2	4	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	8	no	—
96	C₂×Q₈×C₄₇	—	2	4	no	—
97	C₂×Q₈×C₄₇	—	2	4	no	—
98	C₂×Q₈×C₄₇	—	4	4	no	—
99	C₂×Q₈×C₄₇	—	4	8	no	—
100	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
101	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	2	4	no	—
105	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₄₇	#41	1	2	yes	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₄₇	—	2	8	no	—
115	Q₁₆×C₄₇	—	2	2	no	—
116	Q₁₆×C₄₇	—	2	2	no	—
117	Q₁₆×C₄₇	—	2	4	no	—
118	Q₁₆×C₄₇	C₂²⋊C₄	1	2	yes	—
119	Q₁₆×C₄₇	C₂²⋊C₄	1	2	yes	—
120	SD₁₆×C₄₇	—	2	8	no	—
121	SD₁₆×C₄₇	C₂²⋊C₄	1	8	yes	—
122	D₈×C₄₇	C₂²⋊C₄	1	2	yes	—
123	D₈×C₄₇	C₂²⋊C₄	1	2	yes	—
124	M₁₆×C₄₇	—	2	2	no	—
125	M₁₆×C₄₇	—	2	4	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
133	C₂²⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄×Dic₄₇	—	2	2	no	—
136	#10625329	—	2	2	no	—
137	#10625329	—	2	4	no	—
138	#10625329	—	2	4	no	—
139	#10625329	—	4	8	no	—
140	#10625329	C₂×D₄	1	4	yes	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	4	no	—
143	C₂×C₄₇⋊C₈	—	4	8	no	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	C₄×D₄	1	2	yes	—
146	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
147	Q₈×C₄₇	—	2	2	no	—
148	Q₈×C₄₇	—	2	2	no	—
149	Q₈×C₄₇	—	2	4	no	—
150	Q₈×C₄₇	—	2	4	no	—
151	Q₈×C₄₇	—	4	8	no	—
152	Q₈×C₄₇	—	4	4	no	—
153	Q₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
154	D₄×C₄₇	—	2	8	no	—
155	D₄×C₄₇	—	2	4	no	—
156	D₄×C₄₇	—	2	2	no	—
157	D₄×C₄₇	—	2	2	no	—
158	D₄×C₄₇	—	4	8	no	—
159	D₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
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	—	2	8	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	4	8	no	—
166	C₂×C₄×C₄₇	—	4	8	no	—
167	C₂×C₄×C₄₇	—	4	4	no	—
168	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₈×C₄₇	—	2	2	no	—
175	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
178	C₄₇⋊C₈	—	2	4	no	—
179	C₄₇⋊C₈	—	4	4	no	—
180	#22460	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	4	no	—
183	C₂²×C₄₇	—	4	1	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	8	2	no	—
186	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₄₇	#546	1	2	yes	—
188	C₄×C₄₇	—	2	4	no	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	4	4	no	—
191	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
192	C₄×C₄₇	#518	1	1	yes	characteristic
193	C₄×C₄₇	D₄²	1	2	yes	—
194	Dic₄₇	—	8	2	no	—
195	C₂×#578	D₄₇	1	1	yes	characteristic
196	#2957	—	47	2	no	—
197	#2889	—	47	2	no	—
198	#1979	—	47	2	no	—
199	#1902	—	47	4	no	—
200	#1813	—	47	1	no	—
201	#1796	—	47	2	no	—
202	#1757	—	47	1	no	—
203	C₂×C₄₇	—	2	2	no	—
204	C₂×C₄₇	—	2	1	no	—
205	C₂×C₄₇	—	4	2	no	—
206	C₂×C₄₇	—	4	4	no	—
207	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×2₋¹⁺⁴	C₂×D₄₇	1	2	yes	—
209	#578	—	2	4	no	—
210	#578	—	2	4	no	—
211	C₂×#137	Dic₄₇	1	4	yes	complemented
212	C₂×#137	C₂×D₄₇	1	2	yes	—
213	C₂×#135	Dic₄₇	1	2	yes	complemented
214	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
215	C₂²×Q₁₆	Dic₄₇	1	2	yes	complemented
216	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
217	#568	—	47	4	no	—
218	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
219	#444	—	94	4	no	—
220	#443	—	94	4	no	—
221	C₂×#108	—	47	2	no	—
222	#421	—	47	4	no	—
223	#419	—	47	4	no	—
224	#413	—	47	1	no	—
225	#413	—	47	2	no	—
226	#413	—	94	4	no	—
227	C₂×#101	—	47	4	no	—
228	C₂×#101	—	94	4	no	—
229	#410	—	47	1	no	—
230	#405	—	47	2	no	—
231	#344	—	47	2	no	—
232	#338	—	47	2	no	—
233	C₄₇	#22460	1	1	yes	characteristic, complemented, Sylow
234	2₋¹⁺⁴	—	2	8	no	—
235	2₋¹⁺⁴	—	4	4	no	—
236	C₂×#41	—	2	2	no	—
237	C₂×#41	—	2	4	no	—
238	C₂×#41	C₂×Dic₄₇	1	4	yes	—
239	C₂×#41	C₂²×D₄₇	1	2	yes	—
240	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
241	C₂²×Q₈	—	2	2	no	—
242	C₂²×Q₈	C₂×Dic₄₇	1	4	yes	—
243	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
244	#137	—	2	8	no	—
245	#137	—	2	16	no	—
246	#135	—	2	4	no	—
247	#135	—	2	4	no	—
248	#135	C₂²⋊D₄₇	1	4	yes	—
249	#135	C₂²⋊D₄₇	1	4	yes	—
250	C₂×Q₁₆	—	2	4	no	—
251	C₂×Q₁₆	—	2	4	no	—
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×Q₁₆	—	2	2	no	—
254	C₂×Q₁₆	C₂×Dic₄₇	1	2	yes	—
255	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	—
256	C₂×Q₁₆	C₂×Dic₄₇	1	2	yes	—
257	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic
258	C₂×SD₁₆	C₂×Dic₄₇	1	4	yes	—
259	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
260	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic
261	#131	—	2	2	no	—
262	#131	—	2	2	no	—
263	#131	—	94	8	no	—
264	#131	—	188	4	no	—
265	C₂×M₁₆	—	47	2	no	—
266	C₂×M₁₆	—	47	4	no	—
267	C₂×M₁₆	—	94	8	no	—
268	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
269	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
270	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
271	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
272	#117	—	47	2	no	—
273	#108	—	94	2	no	—
274	#108	—	94	2	no	—
275	#104	—	94	8	no	—
276	#103	—	188	4	no	—
277	#101	—	47	2	no	—
278	#101	—	94	8	no	—
279	#101	—	94	2	no	—
280	#100	—	47	2	no	—
281	#100	—	94	2	no	—
282	#99	—	94	2	no	—
283	#97	—	94	2	no	—
284	C₄×C₈	—	94	2	no	—
285	#41	—	2	2	no	—
286	#41	—	2	4	no	—
287	#41	—	2	2	no	—
288	#41	—	2	8	no	—
289	#41	—	4	4	no	—
290	#41	—	4	8	no	—
291	#41	—	4	16	no	—
292	#41	C₂×C₂²⋊D₄₇	1	8	yes	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	8	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	4	4	no	—
299	C₂×Q₈	—	4	8	no	—
300	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
301	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
302	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
306	C₂×D₄	#10625352	1	2	yes	—
307	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
313	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
314	Q₁₆	—	2	8	no	—
315	Q₁₆	—	2	2	no	—
316	Q₁₆	—	2	2	no	—
317	Q₁₆	—	2	4	no	—
318	Q₁₆	C₂²⋊Dic₄₇	1	2	yes	—
319	Q₁₆	C₂²⋊Dic₄₇	1	2	yes	—
320	SD₁₆	—	2	8	no	—
321	SD₁₆	C₂²⋊Dic₄₇	1	8	yes	—
322	D₈	C₂²⋊Dic₄₇	1	2	yes	—
323	D₈	C₂²⋊Dic₄₇	1	2	yes	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	—	47	4	no	—
327	M₁₆	—	94	2	no	—
328	M₁₆	—	94	4	no	—
329	M₁₆	—	94	4	no	—
330	M₁₆	—	188	8	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	94	2	no	—
334	C₂×C₈	—	94	4	no	—
335	C₂×C₈	—	188	8	no	—
336	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
337	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
338	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
339	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
340	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
341	C₄⋊C₄	—	94	2	no	—
342	C₂²⋊C₄	—	94	2	no	—
343	C₄²	—	94	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	D₄×Dic₄₇	1	2	yes	—
346	C₂³	C₂×#10625352	1	1	yes	characteristic
347	Q₈	—	2	2	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	2	4	no	—
350	Q₈	—	2	4	no	—
351	Q₈	—	4	8	no	—
352	Q₈	—	4	4	no	—
353	Q₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
354	D₄	—	2	8	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	8	no	—
359	D₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	8	no	—
366	C₂×C₄	—	4	8	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	188	2	no	—
369	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
370	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
373	C₂×C₄	#13094069	1	2	yes	—
374	C₈	—	2	2	no	—
375	C₈	—	94	4	no	—
376	C₈	—	188	4	no	—
377	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
378	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
379	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
386	C₂²	#15689767	1	2	yes	—
387	C₄	—	2	4	no	—
388	C₄	—	2	2	no	—
389	C₄	—	4	4	no	—
390	C₄	—	376	2	no	—
391	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
392	C₄	#15689598	1	1	yes	characteristic
393	C₄	D₄×C₂²⋊D₄₇	1	2	yes	—
394	C₂	—	2	2	no	—
395	C₂	—	2	1	no	—
396	C₂	—	4	2	no	—
397	C₂	—	4	4	no	—
398	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	#22460
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. #20252305	C₂	semidirect
2. #20251871	C₂	semidirect
3. #20244304	C₂	semidirect
4. #20243863	C₂	semidirect
5. #20243438	C₂	semidirect
6. #20243363	C₂	semidirect
7. #20243188	C₂	semidirect
27. C₂×#137×C₄₇	C₄	semidirect
29. C₂×#135×C₄₇	C₄	semidirect
31. C₂²×Q₁₆×C₄₇	C₄	semidirect
211. C₂×#137	Dic₄₇	semidirect
213. C₂×#135	Dic₄₇	semidirect
215. C₂²×Q₁₆	Dic₄₇	semidirect
233. C₄₇	#22460	semidirect

Maximal subgroups

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

subgroup	index
#20252305	2
#20251871	2
#20244304	2
#20243863	2
#20243438	2
#20243363	2
#20243188	2
C₂×C₄₇×#578	2
#22460	47