Subgroups — #26199420

Order 12032.

714 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254303	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689471	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252100	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242923	C₂	1	4	yes	maximal, complemented
5	#20242799	C₂	1	4	yes	maximal, complemented
6	#20242134	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242069	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13094031	—	2	1	no	—
11	C₂×#13094021	C₂²	1	1	yes	characteristic
12	#15689499	—	2	1	no	—
13	#15689471	—	2	1	no	—
14	#15689471	—	2	1	no	—
15	#15689471	—	2	1	no	—
16	#15689471	C₂²	1	2	yes	—
17	#15689471	C₂²	1	2	yes	—
18	#15689318	C₂²	1	4	yes	—
19	#15689256	—	2	2	no	—
20	#15689201	—	2	1	no	—
21	#15689201	C₂²	1	2	yes	complemented
22	D₄×C₄₇⋊C₈	—	2	1	no	—
23	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
24	#15689176	C₂²	1	1	yes	characteristic
25	#15689147	C₂²	1	1	yes	characteristic
26	C₂×#13093944	—	2	1	no	—
27	C₂×#13093944	—	2	1	no	—
28	#15689090	—	2	1	no	—
29	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	#15688875	C₂²	1	2	yes	complemented
31	#15688873	C₂²	1	2	yes	complemented
32	#15688872	C₂²	1	4	yes	complemented
33	#15688866	C₂²	1	4	yes	—
34	C₄₇×#532	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#498	—	2	1	no	—
37	C₄₇×#486	—	2	1	no	—
38	C₄₇×#481	—	2	2	no	—
39	C₄₇×#476	C₂²	1	4	yes	complemented
40	C₄₇×#431	C₂²	1	1	yes	characteristic
41	C₂²×D₁₈₈	—	2	1	no	—
42	C₂²×D₁₈₈	—	2	1	no	—
43	C₂²×D₁₈₈	—	2	1	no	—
44	C₂×#10625334	—	2	4	no	—
45	#13094031	—	4	4	no	—
46	C₂×#10625329	—	2	1	no	—
47	C₂×#10625329	—	2	2	no	—
48	C₂²×C₄₇⋊C₈	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
51	#13094021	—	2	1	no	—
52	#13094021	—	2	1	no	—
53	#13094021	—	2	1	no	—
54	#13094021	C₂³	1	2	yes	—
55	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
58	#13093944	—	2	4	no	—
59	#13093944	—	2	2	no	—
60	#13093944	—	2	2	no	—
61	#13093944	—	2	2	no	—
62	#13093944	—	2	2	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
66	C₄×C₄₇⋊C₈	—	2	1	no	—
67	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
68	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
69	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
70	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₂×#41×C₄₇	—	2	1	no	—
72	C₂²×Q₈×C₄₇	—	2	1	no	—
73	C₄⋊Q₈×C₄₇	—	2	1	no	—
74	C₄⋊Q₈×C₄₇	—	2	1	no	—
75	C₄⋊Q₈×C₄₇	—	2	1	no	—
76	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
77	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
78	#127×C₄₇	D₄	1	1	yes	characteristic
79	#124×C₄₇	—	2	1	no	—
80	#121×C₄₇	—	2	1	no	—
81	#121×C₄₇	D₄	1	2	yes	—
82	C₄×D₄×C₄₇	—	2	1	no	—
83	C₄×D₄×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	#106×C₄₇	—	2	4	no	—
88	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
89	#102×C₄₇	—	2	4	no	—
90	C₂²⋊C₈×C₄₇	—	2	1	no	—
91	C₄×C₈×C₄₇	—	2	1	no	—
92	C₂³×D₄₇	—	4	1	no	—
93	#41×C₄₇	—	4	2	no	—
94	#41×C₄₇	—	4	2	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	4	1	no	—
98	C₂×Q₈×C₄₇	—	8	2	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	1	no	—
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	4	1	no	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
108	C₂×D₁₈₈	—	2	2	no	—
109	C₂×D₁₈₈	—	2	2	no	—
110	C₂×D₁₈₈	—	2	2	no	—
111	C₂×D₁₈₈	—	4	2	no	—
112	C₂×D₁₈₈	—	4	2	no	—
113	C₂×D₁₈₈	—	4	1	no	—
114	C₂×D₁₈₈	—	4	1	no	—
115	C₂×D₁₈₈	—	4	1	no	—
116	C₂×D₁₈₈	—	8	2	no	—
117	C₂×D₁₈₈	—	8	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	4	1	no	—
123	C₄⋊C₄×C₄₇	—	4	1	no	—
124	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
125	C₂²⋊C₄×C₄₇	—	2	2	no	—
126	C₂²⋊C₄×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₇	#41	1	1	yes	characteristic
130	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
131	#10625334	—	8	4	no	—
132	#10625329	—	4	4	no	—
133	#10625329	—	4	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	4	4	no	—
139	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	#121	1	1	yes	characteristic
145	C₂²×D₄₇	—	4	2	no	—
146	C₂²×D₄₇	—	8	2	no	—
147	C₂²×D₄₇	—	8	2	no	—
148	C₂²×D₄₇	—	8	2	no	—
149	Q₈×C₄₇	—	4	2	no	—
150	Q₈×C₄₇	—	8	2	no	—
151	Q₈×C₄₇	—	8	2	no	—
152	D₄×C₄₇	—	2	4	no	—
153	D₄×C₄₇	—	4	4	no	—
154	D₄×C₄₇	—	4	2	no	—
155	D₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	8	2	no	—
163	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#135	1	2	yes	—
167	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	D₁₈₈	—	4	2	no	—
172	D₁₈₈	—	4	2	no	—
173	D₁₈₈	—	4	4	no	—
174	D₁₈₈	—	8	2	no	—
175	D₁₈₈	—	8	2	no	—
176	D₁₈₈	—	8	2	no	—
177	D₁₈₈	—	8	2	no	—
178	C₈×C₄₇	—	4	2	no	—
179	C₄₇⋊C₈	—	2	1	no	—
180	C₄₇⋊C₈	—	2	1	no	—
181	C₄₇⋊C₈	—	2	1	no	—
182	C₄₇⋊C₈	—	2	1	no	—
183	C₄₇⋊C₈	—	4	2	no	—
184	C₄₇⋊C₈	—	4	2	no	—
185	#19196	—	47	1	no	maximal, Sylow
186	C₂²×C₄₇	—	2	1	no	—
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	#463	1	2	yes	—
192	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
193	C₂×D₄₇	—	8	2	no	—
194	C₂×D₄₇	—	8	2	no	—
195	C₂×D₄₇	—	8	2	no	—
196	C₂×D₄₇	—	16	4	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	4	2	no	—
200	C₄×C₄₇	—	8	2	no	—
201	C₄×C₄₇	#463	1	2	yes	—
202	C₄×C₄₇	#472	1	2	yes	—
203	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
204	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₄×C₄₇	#577	1	2	yes	—
206	#3227	D₄₇	1	1	yes	characteristic, complemented
207	#3205	—	47	1	no	—
208	C₂×#486	—	47	1	no	—
209	#2931	—	47	1	no	—
210	#1697	—	47	4	no	—
211	#1677	—	47	4	no	—
212	#1564	—	47	1	no	—
213	#1548	—	47	1	no	—
214	#1545	—	47	1	no	—
215	C₂×C₄₇	—	2	2	no	—
216	C₂×C₄₇	—	8	2	no	—
217	C₂×C₄₇	C₂×#463	1	1	yes	characteristic
218	C₂×C₄₇	#3057	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
220	D₄₇	—	16	2	no	—
221	C₂×#131	—	94	1	no	—
222	#532	C₂×D₄₇	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×#127	—	47	1	no	—
225	#498	—	2	1	no	—
226	#493	—	94	1	no	—
227	#486	—	2	1	no	—
228	#486	—	47	2	no	—
229	#486	—	47	2	no	—
230	#486	—	94	1	no	—
231	#486	—	94	1	no	—
232	#486	—	94	1	no	—
233	#481	—	2	2	no	—
234	#476	C₂×D₄₇	1	4	yes	complemented
235	#459	—	47	4	no	—
236	#447	—	94	2	no	—
237	#436	—	47	2	no	—
238	#436	—	94	1	no	—
239	C₈×D₄	—	47	2	no	—
240	C₈×D₄	—	94	1	no	—
241	#431	—	47	1	no	—
242	#431	C₂×D₄₇	1	1	yes	characteristic
243	#423	—	47	1	no	—
244	C₂×#102	—	94	1	no	—
245	C₂×#102	—	94	1	no	—
246	#408	—	94	1	no	—
247	C₂×C₄×C₈	—	47	1	no	—
248	#335	—	47	2	no	—
249	#334	—	47	2	no	—
250	#333	—	47	4	no	—
251	#331	—	47	4	no	—
252	C₄₇	#19196	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	—	2	1	no	—
254	C₂²×Q₈	—	2	1	no	—
255	C₂²×D₄	—	94	1	no	—
256	C₂²×D₄	—	94	1	no	—
257	C₂²×D₄	—	94	1	no	—
258	C₂×D₈	—	94	4	no	—
259	#131	—	188	4	no	—
260	C₂×M₁₆	—	94	2	no	—
261	C₂×M₁₆	—	94	1	no	—
262	C₂²×C₈	—	47	1	no	—
263	C₂²×C₈	—	47	1	no	—
264	C₂²×C₈	—	94	2	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
269	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
270	#127	—	47	2	no	—
271	#127	—	94	1	no	—
272	#127	—	94	1	no	—
273	#127	—	94	1	no	—
274	#127	C₂²⋊D₄₇	1	1	yes	characteristic
275	#124	—	2	1	no	—
276	#121	—	2	1	no	—
277	#121	C₂²⋊D₄₇	1	2	yes	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	C₂²×D₄₇	1	2	yes	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
283	#106	—	2	4	no	—
284	C₄⋊C₈	—	47	2	no	—
285	C₄⋊C₈	—	47	2	no	—
286	C₄⋊C₈	—	94	1	no	—
287	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
288	#102	—	2	4	no	—
289	#102	—	94	2	no	—
290	#102	—	94	2	no	—
291	#102	—	94	2	no	—
292	#102	—	94	2	no	—
293	#102	—	94	4	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	—	94	2	no	—
296	C₂²⋊C₈	—	94	2	no	—
297	C₂²⋊C₈	—	94	1	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	—	47	1	no	—
300	C₄×C₈	—	47	1	no	—
301	C₄×C₈	—	47	1	no	—
302	C₄×C₈	—	47	1	no	—
303	C₄×C₈	—	94	1	no	—
304	C₂⁴	—	188	1	no	—
305	#41	—	4	2	no	—
306	#41	—	4	2	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	4	1	no	—
310	C₂×Q₈	—	8	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	94	2	no	—
315	C₂×D₄	—	94	2	no	—
316	C₂×D₄	—	94	2	no	—
317	C₂×D₄	—	376	2	no	—
318	C₂×D₄	—	376	2	no	—
319	C₂×D₄	—	188	1	no	—
320	C₂×D₄	—	188	1	no	—
321	C₂×D₄	—	188	1	no	—
322	C₂×D₄	—	188	2	no	—
323	C₂×D₄	—	188	2	no	—
324	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
328	C₂²×C₄	#10625352	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
330	D₈	—	376	4	no	—
331	M₁₆	—	188	4	no	—
332	M₁₆	—	188	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	47	1	no	—
335	C₂×C₈	—	47	1	no	—
336	C₂×C₈	—	47	1	no	—
337	C₂×C₈	—	47	1	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	—	188	4	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₄²	D₄×D₄₇	1	1	yes	characteristic
352	C₄²	#10625352	1	1	yes	characteristic
353	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₄²	C₂³×D₄₇	1	1	yes	characteristic
355	C₂³	—	2	2	no	—
356	C₂³	—	376	2	no	—
357	C₂³	—	376	2	no	—
358	C₂³	—	376	2	no	—
359	C₂³	—	188	2	no	—
360	C₂³	#13093996	1	1	yes	characteristic
361	Q₈	—	4	2	no	—
362	Q₈	—	8	2	no	—
363	Q₈	—	8	2	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	376	2	no	—
369	D₄	—	376	2	no	—
370	D₄	—	376	2	no	—
371	D₄	—	376	2	no	—
372	D₄	—	188	2	no	—
373	D₄	—	188	2	no	—
374	D₄	—	188	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	#13093996	1	1	yes	characteristic
383	C₂×C₄	#13093996	1	1	yes	characteristic
384	C₂×C₄	#13093996	1	1	yes	characteristic
385	C₂×C₄	#13094045	1	2	yes	—
386	C₂×C₄	#13094051	1	2	yes	—
387	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
388	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	94	1	no	—
392	C₈	—	94	1	no	—
393	C₈	—	94	1	no	—
394	C₈	—	94	1	no	—
395	C₈	—	188	2	no	—
396	C₈	—	188	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	376	2	no	—
403	C₂²	—	376	2	no	—
404	C₂²	—	376	2	no	—
405	C₂²	—	752	4	no	—
406	C₂²	#15689340	1	2	yes	—
407	C₂²	C₂×#13093996	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	8	2	no	—
412	C₄	#15689340	1	2	yes	—
413	C₄	#15689391	1	2	yes	—
414	C₄	C₂×#13094045	1	1	yes	characteristic
415	C₄	C₂×#13094051	1	1	yes	characteristic
416	C₄	#15689931	1	2	yes	—
417	C₂	—	2	2	no	—
418	C₂	—	8	2	no	—
419	C₂	—	752	2	no	—
420	C₂	C₂×#15689340	1	1	yes	characteristic
421	C₂	#20253029	1	1	yes	characteristic
422	C₂	C₂×#15689391	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3227	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	#20254303	C₂
hypercenter	#3227	D₄₇
hypocenter	C₄₇	#19196
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3227

Complements

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

N	H ≅ G/N	type
2. C₂×#15689471	C₂	semidirect
3. #20252100	C₂	semidirect
4. #20242923	C₂	semidirect
5. #20242799	C₂	semidirect
6. #20242134	C₂	semidirect
7. #20242069	C₂	semidirect
8. #20242055	C₂	semidirect
9. C₄₇×#3227	C₂	semidirect
21. #15689201	C₂²	semidirect
23. D₄×C₄₇⋊C₈	C₂²	semidirect
30. #15688875	C₂²	semidirect
31. #15688873	C₂²	semidirect
32. #15688872	C₂²	semidirect
39. C₄₇×#476	C₂²	semidirect
206. #3227	D₄₇	semidirect
234. #476	C₂×D₄₇	semidirect
252. C₄₇	#19196	semidirect

Maximal subgroups

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

subgroup	index
#20254303	2
C₂×#15689471	2
#20252100	2
#20242923	2
#20242799	2
#20242134	2
#20242069	2
#20242055	2
C₄₇×#3227	2
#19196	47