Subgroups — C₄₇×#34396 #26074094

Order 12032.

2486 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#525	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2378	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2377	C₂	1	2	yes	maximal, complemented
4	C₄₇×#2359	C₂	1	4	yes	maximal, complemented
5	C₄₇×#2357	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2353	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2343	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2339	C₂	1	2	yes	maximal, complemented
9	C₄₇×#2333	C₂	1	2	yes	maximal, complemented
10	C₄₇×#2332	C₂	1	2	yes	maximal, complemented
11	C₄₇×#2321	C₂	1	4	yes	maximal, complemented
12	C₄₇×#2319	C₂	1	2	yes	maximal, complemented
13	C₄₇×#2318	C₂	1	2	yes	maximal, complemented
14	C₄₇×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₇×#381	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#525	C₄	1	16	yes	complemented
19	C₂×#123×C₄₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#120×C₄₇	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
28	C₂×#117×C₄₇	C₂²	1	2	yes	—
29	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
31	C₄₇×#391	C₂²	1	4	yes	complemented
32	C₄₇×#390	C₂²	1	4	yes	—
33	C₄₇×#390	C₂²	1	4	yes	—
34	C₄₇×#389	C₂²	1	4	yes	complemented
35	C₄₇×#388	C₂²	1	4	yes	—
36	C₄₇×#388	C₂²	1	4	yes	—
37	C₄₇×#388	C₂²	1	4	yes	—
38	C₄₇×#388	C₂²	1	4	yes	—
39	C₄₇×#388	C₂²	1	4	yes	complemented
40	C₄₇×#388	C₂²	1	4	yes	complemented
41	C₄₇×#387	C₂²	1	4	yes	complemented
42	C₄₇×#387	C₂²	1	4	yes	complemented
43	C₄₇×#387	C₂²	1	4	yes	complemented
44	C₄₇×#387	C₂²	1	4	yes	complemented
45	C₄₇×#386	C₂²	1	4	yes	—
46	C₄₇×#386	C₂²	1	4	yes	—
47	C₄₇×#386	C₂²	1	4	yes	—
48	C₄₇×#386	C₂²	1	4	yes	complemented
49	C₄₇×#385	C₂²	1	4	yes	—
50	C₄₇×#385	C₂²	1	4	yes	complemented
51	C₄₇×#383	C₂²	1	2	yes	complemented
52	C₄₇×#382	C₂²	1	2	yes	complemented
53	C₄₇×#381	C₂²	1	1	yes	characteristic
54	C₄₇×#381	C₂²	1	1	yes	characteristic
55	C₄₇×#381	C₂²	1	2	yes	—
56	C₄₇×#381	C₂²	1	2	yes	—
57	C₄₇×#381	C₂²	1	2	yes	—
58	C₄₇×#381	C₂²	1	2	yes	—
59	C₄₇×#381	C₂²	1	2	yes	complemented
60	C₄₇×#380	C₂²	1	2	yes	—
61	C₄₇×#380	C₂²	1	2	yes	—
62	C₄₇×#380	C₂²	1	2	yes	complemented
63	C₄₇×#379	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
65	C₄×C₄⋊C₄×C₄₇	C₂²	1	4	yes	complemented
66	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
67	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
70	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	complemented
72	C₄₇×#376	C₂²	1	2	yes	complemented
73	C₂×#95×C₄₇	C₂²	1	2	yes	—
74	C₂×#95×C₄₇	C₂²	1	2	yes	—
75	C₂×#95×C₄₇	C₂²	1	2	yes	complemented
76	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×#41×C₄₇	—	4	4	no	—
78	C₂×#41×C₄₇	C₂×C₄	1	8	yes	—
79	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
81	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
82	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
83	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₄₇	—	4	4	no	—
85	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
86	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
89	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
93	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
95	#123×C₄₇	C₂×C₄	1	16	yes	complemented
96	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
97	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
98	#121×C₄₇	C₂×C₄	1	8	yes	complemented
99	#121×C₄₇	C₂×C₄	1	8	yes	complemented
100	#120×C₄₇	C₂×C₄	1	16	yes	complemented
101	C₄×D₄×C₄₇	—	4	8	no	—
102	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
103	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
104	#117×C₄₇	—	4	4	no	—
105	#117×C₄₇	C₂×C₄	1	8	yes	complemented
106	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
115	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
130	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
131	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
132	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
133	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
134	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
135	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
136	#95×C₄₇	C₂³	1	2	yes	—
137	#95×C₄₇	C₂³	1	2	yes	—
138	#95×C₄₇	C₂³	1	4	yes	—
139	#95×C₄₇	C₂³	1	2	yes	—
140	#95×C₄₇	C₂³	1	4	yes	—
141	#95×C₄₇	C₂³	1	2	yes	—
142	#95×C₄₇	C₂³	1	2	yes	—
143	#95×C₄₇	C₂³	1	4	yes	—
144	#95×C₄₇	C₂³	1	4	yes	—
145	#95×C₄₇	C₂³	1	2	yes	—
146	#95×C₄₇	C₂³	1	4	yes	—
147	#95×C₄₇	C₂³	1	4	yes	—
148	#95×C₄₇	C₂³	1	4	yes	—
149	#95×C₄₇	C₂³	1	4	yes	—
150	#95×C₄₇	C₂³	1	4	yes	—
151	C₂⁴×C₄₇	—	2	4	no	—
152	C₂⁴×C₄₇	—	4	2	no	—
153	C₂⁴×C₄₇	—	4	2	no	—
154	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
155	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
156	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
157	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
158	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
159	#41×C₄₇	—	4	16	no	—
160	C₂×Q₈×C₄₇	—	4	2	no	—
161	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
162	C₂×D₄×C₄₇	—	2	8	no	—
163	C₂×D₄×C₄₇	—	4	2	no	—
164	C₂×D₄×C₄₇	—	4	4	no	—
165	C₂×D₄×C₄₇	—	4	2	no	—
166	C₂×D₄×C₄₇	—	4	2	no	—
167	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
168	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
169	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
170	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₄₇	—	2	4	no	—
172	C₂²×C₄×C₄₇	—	2	4	no	—
173	C₂²×C₄×C₄₇	—	2	8	no	—
174	C₂²×C₄×C₄₇	—	4	16	no	—
175	C₂²×C₄×C₄₇	—	4	2	no	—
176	C₂²×C₄×C₄₇	—	4	2	no	—
177	C₂²×C₄×C₄₇	—	4	2	no	—
178	C₂²×C₄×C₄₇	—	4	2	no	—
179	C₂²×C₄×C₄₇	—	4	4	no	—
180	C₂²×C₄×C₄₇	—	4	4	no	—
181	C₂²×C₄×C₄₇	—	4	4	no	—
182	C₂²×C₄×C₄₇	—	4	4	no	—
183	C₂²×C₄×C₄₇	—	4	4	no	—
184	C₂²×C₄×C₄₇	—	4	4	no	—
185	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
186	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
187	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
188	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
189	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
190	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
203	C₄⋊C₄×C₄₇	—	4	4	no	—
204	C₄⋊C₄×C₄₇	—	4	4	no	—
205	C₄⋊C₄×C₄₇	—	4	4	no	—
206	C₄⋊C₄×C₄₇	—	4	4	no	—
207	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
208	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
209	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
210	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
211	C₂²⋊C₄×C₄₇	—	2	8	no	—
212	C₂²⋊C₄×C₄₇	—	4	2	no	—
213	C₂²⋊C₄×C₄₇	—	4	4	no	—
214	C₂²⋊C₄×C₄₇	—	4	2	no	—
215	C₂²⋊C₄×C₄₇	—	4	4	no	—
216	C₂²⋊C₄×C₄₇	—	4	2	no	—
217	C₂²⋊C₄×C₄₇	—	4	4	no	—
218	C₂²⋊C₄×C₄₇	—	4	2	no	—
219	C₂²⋊C₄×C₄₇	—	4	4	no	—
220	C₂²⋊C₄×C₄₇	—	4	4	no	—
221	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
223	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
226	C₄²×C₄₇	—	4	4	no	—
227	C₄²×C₄₇	—	4	4	no	—
228	C₄²×C₄₇	—	4	2	no	—
229	C₄²×C₄₇	—	4	2	no	—
230	C₄²×C₄₇	—	4	4	no	—
231	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
232	C₂³×C₄₇	—	2	2	no	—
233	C₂³×C₄₇	—	2	2	no	—
234	C₂³×C₄₇	—	2	8	no	—
235	C₂³×C₄₇	—	2	2	no	—
236	C₂³×C₄₇	—	2	2	no	—
237	C₂³×C₄₇	—	2	4	no	—
238	C₂³×C₄₇	—	2	2	no	—
239	C₂³×C₄₇	—	2	2	no	—
240	C₂³×C₄₇	—	2	2	no	—
241	C₂³×C₄₇	—	2	4	no	—
242	C₂³×C₄₇	—	2	2	no	—
243	C₂³×C₄₇	—	2	2	no	—
244	C₂³×C₄₇	—	2	2	no	—
245	C₂³×C₄₇	—	4	4	no	—
246	C₂³×C₄₇	—	4	4	no	—
247	C₂³×C₄₇	—	4	16	no	—
248	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
249	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
250	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
251	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
252	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
253	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
254	Q₈×C₄₇	—	4	4	no	—
255	D₄×C₄₇	—	2	16	no	—
256	D₄×C₄₇	—	4	8	no	—
257	D₄×C₄₇	—	4	8	no	—
258	D₄×C₄₇	—	4	4	no	—
259	C₂×C₄×C₄₇	—	2	8	no	—
260	C₂×C₄×C₄₇	—	2	8	no	—
261	C₂×C₄×C₄₇	—	2	2	no	—
262	C₂×C₄×C₄₇	—	2	4	no	—
263	C₂×C₄×C₄₇	—	2	2	no	—
264	C₂×C₄×C₄₇	—	2	2	no	—
265	C₂×C₄×C₄₇	—	2	2	no	—
266	C₂×C₄×C₄₇	—	2	2	no	—
267	C₂×C₄×C₄₇	—	2	4	no	—
268	C₂×C₄×C₄₇	—	2	2	no	—
269	C₂×C₄×C₄₇	—	2	4	no	—
270	C₂×C₄×C₄₇	—	2	4	no	—
271	C₂×C₄×C₄₇	—	2	4	no	—
272	C₂×C₄×C₄₇	—	2	4	no	—
273	C₂×C₄×C₄₇	—	2	4	no	—
274	C₂×C₄×C₄₇	—	2	4	no	—
275	C₂×C₄×C₄₇	—	2	4	no	—
276	C₂×C₄×C₄₇	—	2	4	no	—
277	C₂×C₄×C₄₇	—	2	4	no	—
278	C₂×C₄×C₄₇	—	2	4	no	—
279	C₂×C₄×C₄₇	—	2	4	no	—
280	C₂×C₄×C₄₇	—	2	4	no	—
281	C₂×C₄×C₄₇	—	4	4	no	—
282	C₂×C₄×C₄₇	—	4	4	no	—
283	C₂×C₄×C₄₇	—	4	4	no	—
284	C₂×C₄×C₄₇	—	4	4	no	—
285	C₂×C₄×C₄₇	—	4	8	no	—
286	C₂×C₄×C₄₇	—	8	8	no	—
287	C₂×C₄×C₄₇	—	8	8	no	—
288	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
290	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
291	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
293	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
295	#34396	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂²×C₄₇	—	2	2	no	—
297	C₂²×C₄₇	—	2	2	no	—
298	C₂²×C₄₇	—	2	8	no	—
299	C₂²×C₄₇	—	2	2	no	—
300	C₂²×C₄₇	—	2	2	no	—
301	C₂²×C₄₇	—	2	4	no	—
302	C₂²×C₄₇	—	2	2	no	—
303	C₂²×C₄₇	—	2	2	no	—
304	C₂²×C₄₇	—	2	4	no	—
305	C₂²×C₄₇	—	2	4	no	—
306	C₂²×C₄₇	—	2	2	no	—
307	C₂²×C₄₇	—	2	2	no	—
308	C₂²×C₄₇	—	4	16	no	—
309	C₂²×C₄₇	—	4	4	no	—
310	C₂²×C₄₇	—	4	4	no	—
311	C₂²×C₄₇	—	4	4	no	—
312	C₂²×C₄₇	—	4	4	no	—
313	C₂²×C₄₇	#518	1	4	yes	—
314	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
315	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
316	C₂²×C₄₇	#585	1	2	yes	—
317	C₂²×C₄₇	#585	1	2	yes	—
318	C₄×C₄₇	—	2	2	no	—
319	C₄×C₄₇	—	2	2	no	—
320	C₄×C₄₇	—	2	2	no	—
321	C₄×C₄₇	—	2	2	no	—
322	C₄×C₄₇	—	2	4	no	—
323	C₄×C₄₇	—	2	4	no	—
324	C₄×C₄₇	—	2	4	no	—
325	C₄×C₄₇	—	4	4	no	—
326	C₄×C₄₇	—	4	4	no	—
327	C₄×C₄₇	—	4	4	no	—
328	C₄×C₄₇	—	4	4	no	—
329	C₂×#525	C₂×C₄₇	1	1	yes	characteristic
330	#2378	C₂×C₄₇	1	2	yes	complemented
331	#2377	C₂×C₄₇	1	2	yes	complemented
332	#2359	C₂×C₄₇	1	4	yes	complemented
333	#2357	C₂×C₄₇	1	2	yes	complemented
334	#2353	C₂×C₄₇	1	2	yes	complemented
335	#2343	C₂×C₄₇	1	2	yes	complemented
336	#2339	C₂×C₄₇	1	2	yes	complemented
337	#2333	C₂×C₄₇	1	2	yes	complemented
338	#2332	C₂×C₄₇	1	2	yes	complemented
339	#2321	C₂×C₄₇	1	4	yes	complemented
340	#2319	C₂×C₄₇	1	2	yes	complemented
341	#2318	C₂×C₄₇	1	2	yes	complemented
342	#2280	C₂×C₄₇	1	1	yes	characteristic, complemented
343	C₂×#381	C₂×C₄₇	1	1	yes	characteristic, complemented
344	C₂×C₄₇	—	2	4	no	—
345	C₂×C₄₇	—	4	4	no	—
346	C₂×C₄₇	—	4	2	no	—
347	C₂×C₄₇	—	4	2	no	—
348	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
349	C₂×C₄₇	#3428	1	1	yes	characteristic
350	C₂×C₄₇	#3428	1	1	yes	characteristic
351	C₂×C₄₇	#3533	1	4	yes	—
352	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
353	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
354	#525	C₄×C₄₇	1	16	yes	complemented
355	C₂×#123	C₂²×C₄₇	1	2	yes	—
356	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
357	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
358	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
359	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
360	C₂×#120	C₂²×C₄₇	1	2	yes	—
361	C₂×C₄×D₄	C₂²×C₄₇	1	4	yes	—
362	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
363	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
364	C₂×#117	C₂²×C₄₇	1	2	yes	—
365	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
366	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
367	#391	C₂²×C₄₇	1	4	yes	complemented
368	#390	C₂²×C₄₇	1	4	yes	—
369	#390	C₂²×C₄₇	1	4	yes	—
370	#389	C₂²×C₄₇	1	4	yes	complemented
371	#388	C₂²×C₄₇	1	4	yes	—
372	#388	C₂²×C₄₇	1	4	yes	—
373	#388	C₂²×C₄₇	1	4	yes	—
374	#388	C₂²×C₄₇	1	4	yes	—
375	#388	C₂²×C₄₇	1	4	yes	complemented
376	#388	C₂²×C₄₇	1	4	yes	complemented
377	#387	C₂²×C₄₇	1	4	yes	complemented
378	#387	C₂²×C₄₇	1	4	yes	complemented
379	#387	C₂²×C₄₇	1	4	yes	complemented
380	#387	C₂²×C₄₇	1	4	yes	complemented
381	#386	C₂²×C₄₇	1	4	yes	—
382	#386	C₂²×C₄₇	1	4	yes	—
383	#386	C₂²×C₄₇	1	4	yes	—
384	#386	C₂²×C₄₇	1	4	yes	complemented
385	#385	C₂²×C₄₇	1	4	yes	—
386	#385	C₂²×C₄₇	1	4	yes	complemented
387	#383	C₂²×C₄₇	1	2	yes	complemented
388	#382	C₂²×C₄₇	1	2	yes	complemented
389	#381	C₂²×C₄₇	1	1	yes	characteristic
390	#381	C₂²×C₄₇	1	1	yes	characteristic
391	#381	C₂²×C₄₇	1	2	yes	—
392	#381	C₂²×C₄₇	1	2	yes	—
393	#381	C₂²×C₄₇	1	2	yes	—
394	#381	C₂²×C₄₇	1	2	yes	—
395	#381	C₂²×C₄₇	1	2	yes	complemented
396	#380	C₂²×C₄₇	1	2	yes	—
397	#380	C₂²×C₄₇	1	2	yes	—
398	#380	C₂²×C₄₇	1	2	yes	complemented
399	#379	C₂²×C₄₇	1	2	yes	—
400	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
401	C₄×C₄⋊C₄	C₂²×C₄₇	1	4	yes	complemented
402	C₄×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
403	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
404	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
405	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
406	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	complemented
407	C₄×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	complemented
408	#376	C₂²×C₄₇	1	2	yes	complemented
409	C₂×#95	C₂²×C₄₇	1	2	yes	—
410	C₂×#95	C₂²×C₄₇	1	2	yes	—
411	C₂×#95	C₂²×C₄₇	1	2	yes	complemented
412	C₄₇	#34396	1	1	yes	characteristic, direct product factor, Sylow
413	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
414	C₂×#41	—	4	4	no	—
415	C₂×#41	C₂×C₄×C₄₇	1	8	yes	—
416	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
417	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
418	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
419	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
420	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
421	C₂³×C₄	—	4	4	no	—
422	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	complemented
423	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
426	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
427	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
430	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
432	#123	C₂×C₄×C₄₇	1	16	yes	complemented
433	C₂²⋊Q₈	C₂×C₄×C₄₇	1	8	yes	complemented
434	C₂²⋊Q₈	C₂×C₄×C₄₇	1	8	yes	complemented
435	#121	C₂×C₄×C₄₇	1	8	yes	complemented
436	#121	C₂×C₄×C₄₇	1	8	yes	complemented
437	#120	C₂×C₄×C₄₇	1	16	yes	complemented
438	C₄×D₄	—	4	8	no	—
439	C₄×D₄	C₂×C₄×C₄₇	1	16	yes	complemented
440	C₄×D₄	C₂×C₄×C₄₇	1	16	yes	complemented
441	#117	—	4	4	no	—
442	#117	C₂×C₄×C₄₇	1	8	yes	complemented
443	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
447	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
451	C₂×C₂²⋊C₄	—	4	4	no	—
452	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
467	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
468	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
469	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
470	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
471	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
472	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
473	#95	C₂³×C₄₇	1	2	yes	—
474	#95	C₂³×C₄₇	1	2	yes	—
475	#95	C₂³×C₄₇	1	4	yes	—
476	#95	C₂³×C₄₇	1	2	yes	—
477	#95	C₂³×C₄₇	1	4	yes	—
478	#95	C₂³×C₄₇	1	2	yes	—
479	#95	C₂³×C₄₇	1	2	yes	—
480	#95	C₂³×C₄₇	1	4	yes	—
481	#95	C₂³×C₄₇	1	4	yes	—
482	#95	C₂³×C₄₇	1	2	yes	—
483	#95	C₂³×C₄₇	1	4	yes	—
484	#95	C₂³×C₄₇	1	4	yes	—
485	#95	C₂³×C₄₇	1	4	yes	—
486	#95	C₂³×C₄₇	1	4	yes	—
487	#95	C₂³×C₄₇	1	4	yes	—
488	C₂⁴	—	2	4	no	—
489	C₂⁴	—	4	2	no	—
490	C₂⁴	—	4	2	no	—
491	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
492	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
493	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
494	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
495	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
496	#41	—	4	16	no	—
497	C₂×Q₈	—	4	2	no	—
498	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
499	C₂×D₄	—	2	8	no	—
500	C₂×D₄	—	4	2	no	—
501	C₂×D₄	—	4	4	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	C₂²×C₄×C₄₇	1	8	yes	—
505	C₂×D₄	C₂²×C₄×C₄₇	1	8	yes	—
506	C₂×D₄	C₂²×C₄×C₄₇	1	8	yes	—
507	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	8	no	—
511	C₂²×C₄	—	4	16	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	4	no	—
517	C₂²×C₄	—	4	4	no	—
518	C₂²×C₄	—	4	4	no	—
519	C₂²×C₄	—	4	4	no	—
520	C₂²×C₄	—	4	4	no	—
521	C₂²×C₄	—	4	4	no	—
522	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
523	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
524	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
525	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
526	C₂²×C₄	C₂²×C₄×C₄₇	1	8	yes	—
527	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
528	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
533	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
540	C₄⋊C₄	—	4	4	no	—
541	C₄⋊C₄	—	4	4	no	—
542	C₄⋊C₄	—	4	4	no	—
543	C₄⋊C₄	—	4	4	no	—
544	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
545	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
546	C₄⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
547	C₄⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	4	2	no	—
550	C₂²⋊C₄	—	4	4	no	—
551	C₂²⋊C₄	—	4	2	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	—	4	4	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	4	no	—
557	C₂²⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
559	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
560	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
561	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
563	C₄²	—	4	4	no	—
564	C₄²	—	4	4	no	—
565	C₄²	—	4	2	no	—
566	C₄²	—	4	2	no	—
567	C₄²	—	4	4	no	—
568	C₄²	C₂²×C₄×C₄₇	1	8	yes	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	8	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	4	4	no	—
583	C₂³	—	4	4	no	—
584	C₂³	—	4	16	no	—
585	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
586	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
587	C₂³	C₂³×C₄×C₄₇	1	4	yes	—
588	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
589	C₂³	H(5,𝔽₂)×C₄₇	1	4	yes	—
590	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
591	Q₈	—	4	4	no	—
592	D₄	—	2	16	no	—
593	D₄	—	4	8	no	—
594	D₄	—	4	8	no	—
595	D₄	—	4	4	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	2	8	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	—	4	4	no	—
621	C₂×C₄	—	4	4	no	—
622	C₂×C₄	—	4	8	no	—
623	C₂×C₄	—	8	8	no	—
624	C₂×C₄	—	8	8	no	—
625	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
626	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
627	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
628	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
629	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
630	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
631	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	8	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	2	4	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	4	16	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	—	4	4	no	—
649	C₂²	C₄₇×#518	1	4	yes	—
650	C₂²	C₂⁴×C₄×C₄₇	1	1	yes	characteristic
651	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	2	yes	—
652	C₂²	C₄₇×#585	1	2	yes	—
653	C₂²	C₄₇×#585	1	2	yes	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	4	no	—
661	C₄	—	4	4	no	—
662	C₄	—	4	4	no	—
663	C₄	—	4	4	no	—
664	C₄	—	4	4	no	—
665	C₂	—	2	4	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	2	no	—
668	C₂	—	4	4	no	—
669	C₂	C₂×C₄₇×#518	1	1	yes	characteristic
670	C₂	C₄₇×#3428	1	1	yes	characteristic
671	C₂	C₄₇×#3428	1	1	yes	characteristic
672	C₂	C₄₇×#3533	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₇
Frattini, cosocle	C₂³	C₂⁵×C₄₇
prime radical	C₂×C₄₇×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2378	C₂	semidirect
3. C₄₇×#2377	C₂	semidirect
4. C₄₇×#2359	C₂	semidirect
5. C₄₇×#2357	C₂	semidirect
6. C₄₇×#2353	C₂	semidirect
7. C₄₇×#2343	C₂	semidirect
8. C₄₇×#2339	C₂	semidirect
9. C₄₇×#2333	C₂	semidirect
10. C₄₇×#2332	C₂	semidirect
11. C₄₇×#2321	C₂	semidirect
12. C₄₇×#2319	C₂	semidirect
13. C₄₇×#2318	C₂	semidirect
14. C₄₇×#2280	C₂	semidirect
15. C₂×C₄₇×#381	C₂	semidirect
18. C₄₇×#525	C₄	semidirect
31. C₄₇×#391	C₂²	semidirect
34. C₄₇×#389	C₂²	semidirect
39. C₄₇×#388	C₂²	semidirect
40. C₄₇×#388	C₂²	semidirect
41. C₄₇×#387	C₂²	semidirect
42. C₄₇×#387	C₂²	semidirect
43. C₄₇×#387	C₂²	semidirect
44. C₄₇×#387	C₂²	semidirect
48. C₄₇×#386	C₂²	semidirect
50. C₄₇×#385	C₂²	semidirect
51. C₄₇×#383	C₂²	semidirect
52. C₄₇×#382	C₂²	semidirect
59. C₄₇×#381	C₂²	semidirect
62. C₄₇×#380	C₂²	semidirect
64. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
65. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
70. C₄×C₂²⋊C₄×C₄₇	C₂²	semidirect
71. C₄×C₂²⋊C₄×C₄₇	C₂²	semidirect
72. C₄₇×#376	C₂²	semidirect
75. C₂×#95×C₄₇	C₂²	semidirect
85. C₂³×C₄×C₄₇	C₂×C₄	semidirect
95. #123×C₄₇	C₂×C₄	semidirect
96. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
97. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
98. #121×C₄₇	C₂×C₄	semidirect
99. #121×C₄₇	C₂×C₄	semidirect
100. #120×C₄₇	C₂×C₄	semidirect
102. C₄×D₄×C₄₇	C₂×C₄	semidirect
103. C₄×D₄×C₄₇	C₂×C₄	semidirect
105. #117×C₄₇	C₂×C₄	semidirect
295. #34396	C₄₇	direct (N × H)
330. #2378	C₂×C₄₇	semidirect
331. #2377	C₂×C₄₇	semidirect
332. #2359	C₂×C₄₇	semidirect
333. #2357	C₂×C₄₇	semidirect
334. #2353	C₂×C₄₇	semidirect
335. #2343	C₂×C₄₇	semidirect
336. #2339	C₂×C₄₇	semidirect
337. #2333	C₂×C₄₇	semidirect
338. #2332	C₂×C₄₇	semidirect
339. #2321	C₂×C₄₇	semidirect
340. #2319	C₂×C₄₇	semidirect
341. #2318	C₂×C₄₇	semidirect
342. #2280	C₂×C₄₇	semidirect
343. C₂×#381	C₂×C₄₇	semidirect
354. #525	C₄×C₄₇	semidirect
367. #391	C₂²×C₄₇	semidirect
370. #389	C₂²×C₄₇	semidirect
375. #388	C₂²×C₄₇	semidirect
376. #388	C₂²×C₄₇	semidirect
377. #387	C₂²×C₄₇	semidirect
378. #387	C₂²×C₄₇	semidirect
379. #387	C₂²×C₄₇	semidirect
380. #387	C₂²×C₄₇	semidirect
384. #386	C₂²×C₄₇	semidirect
386. #385	C₂²×C₄₇	semidirect
387. #383	C₂²×C₄₇	semidirect
388. #382	C₂²×C₄₇	semidirect
395. #381	C₂²×C₄₇	semidirect
398. #380	C₂²×C₄₇	semidirect
400. C₄×C₄⋊C₄	C₂²×C₄₇	semidirect
401. C₄×C₄⋊C₄	C₂²×C₄₇	semidirect
406. C₄×C₂²⋊C₄	C₂²×C₄₇	semidirect
407. C₄×C₂²⋊C₄	C₂²×C₄₇	semidirect
408. #376	C₂²×C₄₇	semidirect
411. C₂×#95	C₂²×C₄₇	semidirect
412. C₄₇	#34396	direct (N × H)
422. C₂³×C₄	C₂×C₄×C₄₇	semidirect
432. #123	C₂×C₄×C₄₇	semidirect
433. C₂²⋊Q₈	C₂×C₄×C₄₇	semidirect
434. C₂²⋊Q₈	C₂×C₄×C₄₇	semidirect
435. #121	C₂×C₄×C₄₇	semidirect
436. #121	C₂×C₄×C₄₇	semidirect
437. #120	C₂×C₄×C₄₇	semidirect
439. C₄×D₄	C₂×C₄×C₄₇	semidirect
440. C₄×D₄	C₂×C₄×C₄₇	semidirect
442. #117	C₂×C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#525	2
C₄₇×#2378	2
C₄₇×#2377	2
C₄₇×#2359	2
C₄₇×#2357	2
C₄₇×#2353	2
C₄₇×#2343	2
C₄₇×#2339	2
C₄₇×#2333	2
C₄₇×#2332	2
C₄₇×#2321	2
C₄₇×#2319	2
C₄₇×#2318	2
C₄₇×#2280	2
C₂×C₄₇×#381	2
#34396	47

Subgroups — C47×#34396 #26074094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#34396 #26074094