Subgroups — C₂×C₄₇×#1819 #26060384

Order 12032.

3118 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#379	C₂	1	2	yes	maximal
3	C₄₇×#1819	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄₇×#342	C₂	1	4	yes	maximal, complemented
5	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
6	C₂⁴×C₄×C₄₇	C₄	1	2	yes	complemented
7	C₂²×C₂²⋊C₄×C₄₇	—	2	4	no	—
8	C₂²×C₂²⋊C₄×C₄₇	—	2	4	no	—
9	C₂²×C₂²⋊C₄×C₄₇	—	2	4	no	—
10	C₂²×C₂²⋊C₄×C₄₇	C₄	1	4	yes	complemented
11	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	complemented
12	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
13	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
15	C₄₇×#379	—	2	4	no	—
16	C₄₇×#379	C₂²	1	8	yes	—
17	C₄₇×#342	C₂²	1	16	yes	complemented
18	C₂⁵×C₄₇	—	2	8	no	—
19	C₂⁵×C₄₇	—	4	8	no	—
20	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂⁵×C₄₇	C₂×C₄	1	2	yes	—
23	C₂⁵×C₄₇	D₄	1	4	yes	—
24	C₂⁵×C₄₇	D₄	1	4	yes	—
25	C₂⁵×C₄₇	C₂³	1	2	yes	—
26	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
27	C₂³×C₄×C₄₇	—	2	4	no	—
28	C₂³×C₄×C₄₇	—	2	2	no	—
29	C₂³×C₄×C₄₇	—	2	2	no	—
30	C₂³×C₄×C₄₇	—	2	4	no	—
31	C₂³×C₄×C₄₇	—	4	8	no	—
32	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
33	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
34	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
35	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
36	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
37	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
38	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
39	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
40	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
41	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
42	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
43	C₂×C₂²⋊C₄×C₄₇	—	4	16	no	—
44	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
45	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
46	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
47	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
48	C₂⁴×C₄₇	—	2	8	no	—
49	C₂⁴×C₄₇	—	2	4	no	—
50	C₂⁴×C₄₇	—	2	16	no	—
51	C₂⁴×C₄₇	—	2	8	no	—
52	C₂⁴×C₄₇	—	2	4	no	—
53	C₂⁴×C₄₇	—	2	16	no	—
54	C₂⁴×C₄₇	—	2	16	no	—
55	C₂⁴×C₄₇	—	2	8	no	—
56	C₂⁴×C₄₇	—	4	8	no	—
57	C₂⁴×C₄₇	—	4	4	no	—
58	C₂⁴×C₄₇	—	4	8	no	—
59	C₂⁴×C₄₇	—	4	16	no	—
60	C₂⁴×C₄₇	—	4	4	no	—
61	C₂⁴×C₄₇	—	4	8	no	—
62	C₂⁴×C₄₇	—	4	64	no	—
63	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
64	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
65	C₂⁴×C₄₇	C₂²⋊C₄	1	8	yes	—
66	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
67	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
68	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
69	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
70	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
71	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
72	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
73	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
74	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
75	C₂⁴×C₄₇	#41	1	8	yes	—
76	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	8	no	—
79	C₂²×C₄×C₄₇	—	2	8	no	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	8	no	—
82	C₂²×C₄×C₄₇	—	4	16	no	—
83	C₂²×C₄×C₄₇	—	4	8	no	—
84	C₂²×C₄×C₄₇	—	4	8	no	—
85	C₂²×C₄×C₄₇	—	4	8	no	—
86	C₂²×C₄×C₄₇	—	4	16	no	—
87	C₂²×C₄×C₄₇	—	4	16	no	—
88	C₂²×C₄×C₄₇	—	4	8	no	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
90	C₂²⋊C₄×C₄₇	—	2	8	no	—
91	C₂²⋊C₄×C₄₇	—	2	16	no	—
92	C₂²⋊C₄×C₄₇	—	2	8	no	—
93	C₂²⋊C₄×C₄₇	—	2	16	no	—
94	C₂²⋊C₄×C₄₇	—	4	32	no	—
95	C₂²⋊C₄×C₄₇	—	4	8	no	—
96	C₂³×C₄₇	—	2	32	no	—
97	C₂³×C₄₇	—	2	4	no	—
98	C₂³×C₄₇	—	2	4	no	—
99	C₂³×C₄₇	—	2	4	no	—
100	C₂³×C₄₇	—	2	8	no	—
101	C₂³×C₄₇	—	2	4	no	—
102	C₂³×C₄₇	—	2	8	no	—
103	C₂³×C₄₇	—	2	4	no	—
104	C₂³×C₄₇	—	2	8	no	—
105	C₂³×C₄₇	—	2	4	no	—
106	C₂³×C₄₇	—	2	16	no	—
107	C₂³×C₄₇	—	2	16	no	—
108	C₂³×C₄₇	—	2	4	no	—
109	C₂³×C₄₇	—	2	4	no	—
110	C₂³×C₄₇	—	2	16	no	—
111	C₂³×C₄₇	—	2	16	no	—
112	C₂³×C₄₇	—	2	8	no	—
113	C₂³×C₄₇	—	4	8	no	—
114	C₂³×C₄₇	—	4	4	no	—
115	C₂³×C₄₇	—	4	2	no	—
116	C₂³×C₄₇	—	4	4	no	—
117	C₂³×C₄₇	—	4	4	no	—
118	C₂³×C₄₇	—	4	8	no	—
119	C₂³×C₄₇	—	4	16	no	—
120	C₂³×C₄₇	—	4	2	no	—
121	C₂³×C₄₇	—	4	64	no	—
122	C₂³×C₄₇	—	4	32	no	—
123	C₂³×C₄₇	—	4	64	no	—
124	C₂³×C₄₇	—	4	32	no	—
125	C₂³×C₄₇	—	4	16	no	—
126	C₂³×C₄₇	#99	1	8	yes	—
127	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
128	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
131	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₄₇	#117	1	4	yes	—
133	C₂³×C₄₇	#117	1	4	yes	—
134	C₂³×C₄₇	#123	1	8	yes	—
135	C₂³×C₄₇	#123	1	8	yes	—
136	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
137	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
138	C₂³×C₄₇	C₂×#41	1	4	yes	—
139	C₂×C₄×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	—	4	8	no	—
141	C₂×C₄×C₄₇	—	4	16	no	—
142	C₂×C₄×C₄₇	—	4	16	no	—
143	C₂×C₄×C₄₇	—	4	8	no	—
144	C₂×C₄×C₄₇	—	4	8	no	—
145	C₂×C₄×C₄₇	—	4	16	no	—
146	C₂×C₄×C₄₇	—	4	8	no	—
147	C₂×C₄×C₄₇	—	8	16	no	—
148	C₂×#1819	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂²×C₄₇	—	2	16	no	—
150	C₂²×C₄₇	—	2	16	no	—
151	C₂²×C₄₇	—	2	16	no	—
152	C₂²×C₄₇	—	2	16	no	—
153	C₂²×C₄₇	—	2	8	no	—
154	C₂²×C₄₇	—	2	2	no	—
155	C₂²×C₄₇	—	2	4	no	—
156	C₂²×C₄₇	—	2	2	no	—
157	C₂²×C₄₇	—	2	4	no	—
158	C₂²×C₄₇	—	2	4	no	—
159	C₂²×C₄₇	—	2	4	no	—
160	C₂²×C₄₇	—	2	8	no	—
161	C₂²×C₄₇	—	2	4	no	—
162	C₂²×C₄₇	—	4	4	no	—
163	C₂²×C₄₇	—	4	8	no	—
164	C₂²×C₄₇	—	4	4	no	—
165	C₂²×C₄₇	—	4	32	no	—
166	C₂²×C₄₇	—	4	32	no	—
167	C₂²×C₄₇	—	4	8	no	—
168	C₂²×C₄₇	—	4	8	no	—
169	C₂²×C₄₇	—	4	8	no	—
170	C₂²×C₄₇	#381	1	2	yes	—
171	C₂²×C₄₇	#381	1	4	yes	—
172	C₂²×C₄₇	#381	1	2	yes	—
173	C₂²×C₄₇	C₂×#99	1	8	yes	—
174	C₂²×C₄₇	C₂×#99	1	4	yes	—
175	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₄₇	C₂×#117	1	2	yes	—
177	C₂²×C₄₇	C₂×#123	1	4	yes	—
178	C₄×C₄₇	—	4	8	no	—
179	C₄×C₄₇	—	8	8	no	—
180	C₂³×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic
181	C₂×#379	C₂×C₄₇	1	2	yes	—
182	#1819	C₂×C₄₇	1	8	yes	direct product factor
183	C₂×#342	C₂×C₄₇	1	4	yes	complemented
184	C₂×C₄₇	—	2	4	no	—
185	C₂×C₄₇	—	2	2	no	—
186	C₂×C₄₇	—	2	2	no	—
187	C₂×C₄₇	—	2	8	no	—
188	C₂×C₄₇	—	2	4	no	—
189	C₂×C₄₇	—	4	4	no	—
190	C₂×C₄₇	#1819	1	4	yes	direct product factor
191	C₂×C₄₇	C₂×#381	1	1	yes	characteristic
192	C₂×C₄₇	C₂²×#99	1	2	yes	—
193	C₂⁶	C₂²×C₄₇	1	1	yes	characteristic
194	C₂⁴×C₄	C₄×C₄₇	1	2	yes	complemented
195	C₂²×C₂²⋊C₄	—	2	4	no	—
196	C₂²×C₂²⋊C₄	—	2	4	no	—
197	C₂²×C₂²⋊C₄	—	2	4	no	—
198	C₂²×C₂²⋊C₄	C₄×C₄₇	1	4	yes	complemented
199	C₂²×C₂²⋊C₄	C₄×C₄₇	1	2	yes	complemented
200	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
201	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
202	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
203	#379	—	2	4	no	—
204	#379	C₂²×C₄₇	1	8	yes	—
205	#342	C₂²×C₄₇	1	16	yes	complemented
206	C₄₇	C₂×#1819	1	1	yes	characteristic, direct product factor, Sylow
207	C₂⁵	—	2	8	no	—
208	C₂⁵	—	4	8	no	—
209	C₂⁵	C₂×C₄×C₄₇	1	1	yes	characteristic
210	C₂⁵	C₂×C₄×C₄₇	1	1	yes	characteristic
211	C₂⁵	C₂×C₄×C₄₇	1	2	yes	—
212	C₂⁵	D₄×C₄₇	1	4	yes	—
213	C₂⁵	D₄×C₄₇	1	4	yes	—
214	C₂⁵	C₂³×C₄₇	1	2	yes	—
215	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
216	C₂³×C₄	—	2	4	no	—
217	C₂³×C₄	—	2	2	no	—
218	C₂³×C₄	—	2	2	no	—
219	C₂³×C₄	—	2	4	no	—
220	C₂³×C₄	—	4	8	no	—
221	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
222	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	complemented
223	C₂×C₂²⋊C₄	—	2	16	no	—
224	C₂×C₂²⋊C₄	—	2	4	no	—
225	C₂×C₂²⋊C₄	—	2	4	no	—
226	C₂×C₂²⋊C₄	—	2	4	no	—
227	C₂×C₂²⋊C₄	—	2	4	no	—
228	C₂×C₂²⋊C₄	—	2	16	no	—
229	C₂×C₂²⋊C₄	—	2	16	no	—
230	C₂×C₂²⋊C₄	—	2	16	no	—
231	C₂×C₂²⋊C₄	—	2	4	no	—
232	C₂×C₂²⋊C₄	—	4	16	no	—
233	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
234	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	complemented
235	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
236	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
237	C₂⁴	—	2	4	no	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	2	8	no	—
240	C₂⁴	—	2	4	no	—
241	C₂⁴	—	2	16	no	—
242	C₂⁴	—	2	16	no	—
243	C₂⁴	—	2	8	no	—
244	C₂⁴	—	2	16	no	—
245	C₂⁴	—	4	8	no	—
246	C₂⁴	—	4	4	no	—
247	C₂⁴	—	4	8	no	—
248	C₂⁴	—	4	16	no	—
249	C₂⁴	—	4	4	no	—
250	C₂⁴	—	4	8	no	—
251	C₂⁴	—	4	64	no	—
252	C₂⁴	C₂²⋊C₄×C₄₇	1	2	yes	—
253	C₂⁴	C₂²⋊C₄×C₄₇	1	2	yes	—
254	C₂⁴	C₂²⋊C₄×C₄₇	1	8	yes	—
255	C₂⁴	C₂²⋊C₄×C₄₇	1	2	yes	—
256	C₂⁴	C₂²⋊C₄×C₄₇	1	2	yes	—
257	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
258	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
259	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
260	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
261	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
262	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
263	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
264	C₂⁴	#41×C₄₇	1	8	yes	—
265	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	4	16	no	—
272	C₂²×C₄	—	4	8	no	—
273	C₂²×C₄	—	4	8	no	—
274	C₂²×C₄	—	4	8	no	—
275	C₂²×C₄	—	4	16	no	—
276	C₂²×C₄	—	4	16	no	—
277	C₂²×C₄	—	4	8	no	—
278	C₂²×C₄	C₂²×C₄×C₄₇	1	8	yes	—
279	C₂²⋊C₄	—	2	8	no	—
280	C₂²⋊C₄	—	2	16	no	—
281	C₂²⋊C₄	—	2	8	no	—
282	C₂²⋊C₄	—	2	16	no	—
283	C₂²⋊C₄	—	4	32	no	—
284	C₂²⋊C₄	—	4	8	no	—
285	C₂³	—	2	32	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	2	4	no	—
291	C₂³	—	2	8	no	—
292	C₂³	—	2	4	no	—
293	C₂³	—	2	8	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	16	no	—
296	C₂³	—	2	16	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	4	no	—
299	C₂³	—	2	16	no	—
300	C₂³	—	2	16	no	—
301	C₂³	—	2	8	no	—
302	C₂³	—	4	8	no	—
303	C₂³	—	4	4	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	4	4	no	—
306	C₂³	—	4	4	no	—
307	C₂³	—	4	8	no	—
308	C₂³	—	4	16	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	64	no	—
311	C₂³	—	4	32	no	—
312	C₂³	—	4	64	no	—
313	C₂³	—	4	32	no	—
314	C₂³	—	4	16	no	—
315	C₂³	#99×C₄₇	1	8	yes	—
316	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
317	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
318	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
319	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
320	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
321	C₂³	#117×C₄₇	1	4	yes	—
322	C₂³	#117×C₄₇	1	4	yes	—
323	C₂³	#123×C₄₇	1	8	yes	—
324	C₂³	#123×C₄₇	1	8	yes	—
325	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
326	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
327	C₂³	C₂×#41×C₄₇	1	4	yes	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	4	8	no	—
330	C₂×C₄	—	4	16	no	—
331	C₂×C₄	—	4	16	no	—
332	C₂×C₄	—	4	8	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	16	no	—
335	C₂×C₄	—	4	8	no	—
336	C₂×C₄	—	8	16	no	—
337	C₂²	—	2	16	no	—
338	C₂²	—	2	16	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	16	no	—
341	C₂²	—	2	8	no	—
342	C₂²	—	2	16	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	8	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	4	32	no	—
354	C₂²	—	4	32	no	—
355	C₂²	—	4	8	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	4	8	no	—
358	C₂²	C₄₇×#381	1	2	yes	—
359	C₂²	C₄₇×#381	1	4	yes	—
360	C₂²	C₄₇×#381	1	2	yes	—
361	C₂²	C₂×#99×C₄₇	1	8	yes	—
362	C₂²	C₂×#99×C₄₇	1	4	yes	—
363	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
364	C₂²	C₂×#117×C₄₇	1	2	yes	—
365	C₂²	C₂×#123×C₄₇	1	4	yes	—
366	C₄	—	4	8	no	—
367	C₄	—	8	8	no	—
368	C₂	—	2	4	no	—
369	C₂	—	2	2	no	—
370	C₂	—	2	2	no	—
371	C₂	—	2	8	no	—
372	C₂	—	2	4	no	—
373	C₂	—	4	4	no	—
374	C₂	C₄₇×#1819	1	4	yes	direct product factor
375	C₂	C₂×C₄₇×#381	1	1	yes	characteristic
376	C₂	C₂²×#99×C₄₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂⁶×C₄₇	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂⁶×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₇×#1819	C₂	direct (N × H)
4. C₂×C₄₇×#342	C₂	semidirect
6. C₂⁴×C₄×C₄₇	C₄	semidirect
10. C₂²×C₂²⋊C₄×C₄₇	C₄	semidirect
11. C₂²×C₂²⋊C₄×C₄₇	C₄	semidirect
17. C₄₇×#342	C₂²	semidirect
33. C₂³×C₄×C₄₇	C₂×C₄	semidirect
45. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
148. C₂×#1819	C₄₇	direct (N × H)
182. #1819	C₂×C₄₇	direct (N × H)
183. C₂×#342	C₂×C₄₇	semidirect
190. C₂×C₄₇	#1819	direct (N × H)
194. C₂⁴×C₄	C₄×C₄₇	semidirect
198. C₂²×C₂²⋊C₄	C₄×C₄₇	semidirect
199. C₂²×C₂²⋊C₄	C₄×C₄₇	semidirect
205. #342	C₂²×C₄₇	semidirect
206. C₄₇	C₂×#1819	direct (N × H)
222. C₂³×C₄	C₂×C₄×C₄₇	semidirect
234. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
374. C₂	C₄₇×#1819	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₂²⋊C₄×C₄₇	2
C₂×C₄₇×#379	2
C₄₇×#1819	2
C₂×C₄₇×#342	2
C₂×#1819	47

Subgroups — C2×C47×#1819 #26060384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1819 #26060384