Subgroups — #26186103

Order 12032.

710 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252429	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#10625334	C₂	1	1	yes	maximal, characteristic
4	#20242299	C₂	1	4	yes	maximal, complemented
5	#20242270	C₂	1	4	yes	maximal, complemented
6	#20242134	C₂	1	1	yes	maximal, characteristic, complemented
7	#20241780	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241672	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#10625334	C₄	1	1	yes	characteristic
11	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
12	C₄×#10625334	C₄	1	2	yes	—
13	C₄×#10625334	C₄	1	2	yes	—
14	C₄×#10625334	C₂²	1	2	yes	—
15	C₄×#10625334	C₂²	1	2	yes	—
16	#15689202	—	2	2	no	—
17	#15689201	—	2	2	no	—
18	#15689201	C₂²	1	4	yes	complemented
19	#15689200	C₂²	1	4	yes	complemented
20	#15689176	C₂²	1	1	yes	characteristic
21	#15689176	C₂²	1	1	yes	characteristic
22	C₂×#13093957	C₄	1	1	yes	characteristic
23	C₂×#13093945	C₄	1	1	yes	characteristic
24	C₂×#13093944	C₄	1	1	yes	characteristic
25	#15689087	—	2	2	no	—
26	#15689085	—	2	2	no	—
27	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	#15688875	C₂²	1	2	yes	complemented
29	#15688873	C₂²	1	2	yes	complemented
30	#15688852	C₂²	1	4	yes	complemented
31	#15688845	C₂²	1	2	yes	complemented
32	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
33	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#431	C₂²	1	1	yes	characteristic
35	C₄₇×#431	C₂²	1	1	yes	characteristic
36	C₄₇×D₄⋊C₈	C₂²	1	4	yes	complemented
37	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₄×D₄₇	—	2	1	no	—
39	C₂×#10625334	—	2	4	no	—
40	C₂×#10625334	C₂×C₄	1	2	yes	—
41	C₂×#10625334	C₂×C₄	1	2	yes	—
42	C₂×#10625329	—	2	4	no	—
43	C₂×#10625324	—	2	4	no	—
44	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
46	C₄×D₁₈₈	—	2	1	no	—
47	C₄×D₁₈₈	—	2	1	no	—
48	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
49	C₄×D₁₈₈	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
52	#13093957	C₂×C₄	1	2	yes	—
53	#13093957	C₂×C₄	1	2	yes	—
54	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	#13093945	C₂×C₄	1	2	yes	—
57	#13093945	C₂×C₄	1	2	yes	—
58	#13093944	C₂×C₄	1	2	yes	—
59	#13093944	C₂×C₄	1	2	yes	—
60	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
61	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
62	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
63	(C₂×D₄₇)⋊C₈	—	2	4	no	—
64	C₄×C₄₇⋊C₈	—	2	1	no	—
65	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
67	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
70	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₄₇	—	2	1	no	—
72	C₄×D₄×C₄₇	—	2	1	no	—
73	C₄×D₄×C₄₇	—	2	1	no	—
74	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
75	C₄×D₄×C₄₇	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₇	—	2	1	no	—
80	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
81	C₂²⋊C₈×C₄₇	—	2	1	no	—
82	C₂²⋊C₈×C₄₇	—	2	1	no	—
83	C₄×C₈×C₄₇	—	2	1	no	—
84	C₄×C₈×C₄₇	C₂³	1	2	yes	—
85	C₂⁴×C₄₇	—	2	1	no	—
86	C₂³×D₄₇	—	2	1	no	—
87	C₂×D₄×C₄₇	—	2	1	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	—	2	1	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	8	2	no	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
98	C₂²×Dic₄₇	—	2	1	no	—
99	C₂×D₁₈₈	—	2	2	no	—
100	C₂×D₁₈₈	—	2	2	no	—
101	C₂×D₁₈₈	—	2	1	no	—
102	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
103	C₂×C₄×D₄₇	—	2	2	no	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	—	8	2	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	2	1	no	—
109	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²⋊C₄×C₄₇	—	2	2	no	—
111	C₂²⋊C₄×C₄₇	—	2	2	no	—
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	C₂⁴	1	1	yes	characteristic
116	#10625334	—	2	4	no	—
117	#10625334	—	2	4	no	—
118	(C₂×D₄₇)⋊C₄	—	2	2	no	—
119	(C₂×D₄₇)⋊C₄	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	1	no	—
121	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
122	#10625329	—	8	4	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	M₁₆	1	4	yes	complemented
126	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
131	#10625324	—	8	4	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	4	2	no	—
134	C₂³×C₄₇	—	8	1	no	—
135	C₂³×C₄₇	—	8	1	no	—
136	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
137	C₂²×D₄₇	—	2	2	no	—
138	C₂²×D₄₇	—	4	2	no	—
139	C₂²×D₄₇	—	8	1	no	—
140	C₂²×D₄₇	—	8	1	no	—
141	D₄×C₄₇	—	2	2	no	—
142	D₄×C₄₇	—	2	2	no	—
143	D₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	4	1	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	8	2	no	—
149	C₂×C₄×C₄₇	—	8	1	no	—
150	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
154	C₂×C₄×C₄₇	#131	1	2	yes	—
155	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×Dic₄₇	—	2	2	no	—
159	C₂×Dic₄₇	—	8	1	no	—
160	D₁₈₈	—	2	2	no	—
161	D₁₈₈	—	2	2	no	—
162	D₁₈₈	—	4	2	no	—
163	C₄×D₄₇	—	4	4	no	—
164	C₄×D₄₇	—	8	2	no	—
165	C₈×C₄₇	—	4	2	no	—
166	C₈×C₄₇	—	4	2	no	—
167	C₄₇⋊C₈	—	2	1	no	—
168	C₄₇⋊C₈	—	2	1	no	—
169	C₄₇⋊C₈	—	2	4	no	—
170	C₄₇⋊C₈	—	4	2	no	—
171	C₄₇⋊C₈	C₂×M₁₆	1	2	yes	—
172	C₄₇⋊C₈	C₂×M₁₆	1	2	yes	—
173	#17895	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	4	2	no	—
177	C₂²×C₄₇	—	4	2	no	—
178	C₂²×C₄₇	—	4	2	no	—
179	C₂²×C₄₇	—	8	4	no	—
180	C₂²×C₄₇	#436	1	2	yes	—
181	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
182	C₂×D₄₇	—	4	2	no	—
183	C₂×D₄₇	—	4	2	no	—
184	C₂×D₄₇	—	4	2	no	—
185	C₂×D₄₇	—	8	4	no	—
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	4	2	no	—
190	C₄×C₄₇	#436	1	2	yes	—
191	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
192	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
193	C₄×C₄₇	#576	1	2	yes	—
194	Dic₄₇	—	4	2	no	—
195	#2975	—	47	1	no	—
196	#2975	—	47	1	no	—
197	C₂×C₄×D₈	—	47	1	no	—
198	#1594	—	47	4	no	—
199	#1589	—	47	4	no	—
200	#1564	—	47	1	no	—
201	#1478	—	47	1	no	—
202	#1478	D₄₇	1	1	yes	characteristic, complemented
203	#1450	—	47	1	no	—
204	C₂×C₄₇	—	2	2	no	—
205	C₂×C₄₇	—	8	2	no	—
206	C₂×C₄₇	C₂×#436	1	1	yes	characteristic
207	C₂×C₄₇	#2948	1	1	yes	characteristic
208	C₂×C₄₇	#2957	1	1	yes	characteristic
209	D₄₇	—	8	2	no	—
210	C₂²×D₈	—	47	1	no	—
211	C₂×C₄×D₄	—	47	1	no	—
212	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
213	C₄×D₈	—	47	2	no	—
214	C₄×D₈	—	47	2	no	—
215	C₄×D₈	—	47	2	no	—
216	C₄×D₈	—	47	2	no	—
217	#436	—	47	4	no	—
218	#436	—	47	4	no	—
219	#436	—	94	2	no	—
220	#436	—	94	2	no	—
221	#431	—	47	1	no	—
222	#431	—	47	1	no	—
223	#431	C₂×D₄₇	1	1	yes	characteristic
224	#431	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#107	—	47	1	no	—
226	C₂×#102	—	47	1	no	—
227	C₂×#102	—	47	1	no	—
228	#407	—	94	2	no	—
229	#407	—	94	2	no	—
230	C₂×C₄×C₈	—	47	1	no	—
231	#335	—	47	2	no	—
232	#334	—	47	2	no	—
233	D₄⋊C₈	—	47	4	no	—
234	D₄⋊C₈	C₂×D₄₇	1	4	yes	complemented
235	#322	—	47	2	no	—
236	C₈²	—	47	2	no	—
237	C₄₇	#17895	1	1	yes	characteristic, complemented, Sylow
238	C₂²×D₄	—	47	1	no	—
239	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	—	94	1	no	—
242	C₂×D₈	—	47	2	no	—
243	C₂×D₈	—	47	2	no	—
244	C₂×D₈	—	94	4	no	—
245	C₂×M₁₆	—	94	4	no	—
246	C₂×M₁₆	—	94	4	no	—
247	C₂²×C₈	—	47	1	no	—
248	C₂²×C₈	—	47	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	47	2	no	—
252	C₄×D₄	—	47	2	no	—
253	C₄×D₄	—	94	1	no	—
254	C₄×D₄	—	94	1	no	—
255	C₄×D₄	C₄×D₄₇	1	2	yes	—
256	C₄×D₄	C₂²×D₄₇	1	2	yes	—
257	C₂×C₄⋊C₄	—	47	1	no	—
258	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	94	1	no	—
261	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
262	#107	—	47	2	no	—
263	#107	—	47	2	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	47	2	no	—
266	C₄⋊C₈	—	47	2	no	—
267	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
268	#102	—	47	2	no	—
269	#102	—	47	2	no	—
270	#102	—	47	2	no	—
271	#102	—	47	2	no	—
272	C₂²⋊C₈	—	2	1	no	—
273	C₂²⋊C₈	—	2	1	no	—
274	C₂²⋊C₈	—	47	2	no	—
275	C₂²⋊C₈	—	94	4	no	—
276	C₂²⋊C₈	—	94	4	no	—
277	C₂²⋊C₈	—	94	1	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	—	47	1	no	—
280	C₄×C₈	—	47	1	no	—
281	C₄×C₈	—	47	1	no	—
282	C₄×C₈	—	47	2	no	—
283	C₄×C₈	—	47	1	no	—
284	C₄×C₈	—	94	1	no	—
285	C₄×C₈	C₂²×D₄₇	1	2	yes	—
286	C₂⁴	—	2	1	no	—
287	C₂⁴	—	94	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	47	2	no	—
292	C₂×D₄	—	94	1	no	—
293	C₂×D₄	—	94	2	no	—
294	C₂×D₄	—	94	2	no	—
295	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	8	2	no	—
300	C₂²×C₄	—	94	1	no	—
301	C₂²×C₄	—	94	2	no	—
302	C₂²×C₄	—	94	2	no	—
303	C₂²×C₄	—	376	2	no	—
304	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
305	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
306	C₂²×C₄	#10625352	1	1	yes	characteristic
307	D₈	—	94	4	no	—
308	D₈	—	94	4	no	—
309	M₁₆	—	376	4	no	—
310	M₁₆	—	376	4	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	47	4	no	—
314	C₂×C₈	—	47	1	no	—
315	C₂×C₈	—	47	1	no	—
316	C₂×C₈	—	47	1	no	—
317	C₂×C₈	—	47	1	no	—
318	C₂×C₈	—	47	4	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	94	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	47	2	no	—
323	C₄⋊C₄	—	94	1	no	—
324	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	94	2	no	—
328	C₂²⋊C₄	—	94	2	no	—
329	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
330	C₄²	D₄×D₄₇	1	1	yes	characteristic
331	C₄²	#10625352	1	1	yes	characteristic
332	C₄²	C₂³×D₄₇	1	1	yes	characteristic
333	C₂³	—	2	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	8	1	no	—
336	C₂³	—	8	1	no	—
337	C₂³	—	94	2	no	—
338	C₂³	—	376	1	no	—
339	C₂³	—	376	1	no	—
340	C₂³	—	188	2	no	—
341	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
342	D₄	—	2	2	no	—
343	D₄	—	2	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	94	2	no	—
346	D₄	—	94	2	no	—
347	D₄	—	188	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	—	8	1	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	376	2	no	—
356	C₂×C₄	—	376	1	no	—
357	C₂×C₄	—	188	4	no	—
358	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
359	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
360	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
361	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
362	C₂×C₄	#13094030	1	2	yes	—
363	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
366	C₈	—	4	2	no	—
367	C₈	—	4	2	no	—
368	C₈	—	47	2	no	—
369	C₈	—	47	2	no	—
370	C₈	—	94	1	no	—
371	C₈	—	94	1	no	—
372	C₈	—	94	4	no	—
373	C₈	—	188	2	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	4	no	—
380	C₂²	—	376	4	no	—
381	C₂²	—	188	2	no	—
382	C₂²	—	188	2	no	—
383	C₂²	—	188	2	no	—
384	C₂²	#15689198	1	2	yes	—
385	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	188	2	no	—
391	C₄	#15689198	1	2	yes	—
392	C₄	C₂×M₁₆×D₄₇	1	1	yes	characteristic
393	C₄	C₂×#13094030	1	1	yes	characteristic
394	C₄	#15689927	1	2	yes	—
395	C₂	—	2	2	no	—
396	C₂	—	8	2	no	—
397	C₂	—	376	2	no	—
398	C₂	C₂×#15689198	1	1	yes	characteristic
399	C₂	#20252236	1	1	yes	characteristic
400	C₂	#20252301	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1478	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂²×#10625334	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1478	D₄₇
hypocenter	C₄₇	#17895
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1478

Complements

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

N	H ≅ G/N	type
1. #20252429	C₂	semidirect
2. #20252428	C₂	semidirect
4. #20242299	C₂	semidirect
5. #20242270	C₂	semidirect
6. #20242134	C₂	semidirect
7. #20241780	C₂	semidirect
8. #20241672	C₂	semidirect
9. C₄₇×#1478	C₂	semidirect
18. #15689201	C₂²	semidirect
19. #15689200	C₂²	semidirect
28. #15688875	C₂²	semidirect
29. #15688873	C₂²	semidirect
30. #15688852	C₂²	semidirect
31. #15688845	C₂²	semidirect
32. C₈×C₄₇⋊C₈	C₂²	semidirect
36. C₄₇×D₄⋊C₈	C₂²	semidirect
125. C₂×C₄₇⋊C₈	M₁₆	semidirect
202. #1478	D₄₇	semidirect
234. D₄⋊C₈	C₂×D₄₇	semidirect
237. C₄₇	#17895	semidirect

Maximal subgroups

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

subgroup	index
#20252429	2
#20252428	2
C₂×C₄×#10625334	2
#20242299	2
#20242270	2
#20242134	2
#20241780	2
#20241672	2
C₄₇×#1478	2
#17895	47