Subgroups — C₄₇×#62998 #26102696

Order 12032.

6930 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3523	C₂	1	8	yes	maximal, complemented
2	C₄₇×#3523	C₂	1	4	yes	maximal, complemented
3	C₄₇×#3518	C₂	1	4	yes	maximal, complemented
4	C₄₇×#3516	C₂	1	8	yes	maximal, complemented
5	C₄₇×#3509	C₂	1	6	yes	maximal, complemented
6	C₄₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#3495	C₂	1	12	yes	maximal, complemented
8	C₄₇×#3486	C₂	1	2	yes	maximal, complemented
9	C₄₇×#3482	C₂	1	4	yes	maximal, complemented
10	Q₈×#41×C₄₇	C₂	1	4	yes	maximal, complemented
11	C₄₇×#3475	C₂	1	6	yes	maximal, complemented
12	C₂×D₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×2₋¹⁺⁴×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₇×#519	C₂	1	2	yes	maximal, complemented
15	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
17	Q₈²×C₄₇	C₂²	1	4	yes	complemented
18	C₄₇×#557	C₂²	1	12	yes	complemented
19	C₄₇×#557	C₂²	1	4	yes	complemented
20	C₄₇×#557	C₂²	1	8	yes	complemented
21	C₄₇×#557	C₂²	1	12	yes	complemented
22	C₄₇×#556	C₂²	1	6	yes	—
23	C₄₇×#556	C₂²	1	12	yes	complemented
24	C₄₇×#556	C₂²	1	24	yes	complemented
25	C₄₇×#556	C₂²	1	12	yes	complemented
26	C₄₇×#555	C₂²	1	6	yes	—
27	C₄₇×#554	C₂²	1	6	yes	—
28	C₄₇×#554	C₂²	1	24	yes	complemented
29	C₄₇×#553	C₂²	1	12	yes	—
30	C₄₇×#552	C₂²	1	12	yes	—
31	C₄₇×#552	C₂²	1	12	yes	—
32	C₄₇×#552	C₂²	1	24	yes	—
33	C₄₇×#552	C₂²	1	24	yes	complemented
34	C₄₇×#552	C₂²	1	24	yes	complemented
35	C₄₇×#551	C₂²	1	24	yes	—
36	D₄×Q₈×C₄₇	C₂²	1	4	yes	—
37	D₄×Q₈×C₄₇	C₂²	1	8	yes	—
38	D₄×Q₈×C₄₇	C₂²	1	4	yes	—
39	D₄×Q₈×C₄₇	C₂²	1	8	yes	complemented
40	D₄×Q₈×C₄₇	C₂²	1	8	yes	complemented
41	C₄₇×#548	C₂²	1	8	yes	complemented
42	C₄₇×#548	C₂²	1	8	yes	complemented
43	C₄₇×#547	C₂²	1	6	yes	—
44	C₄₇×#546	C₂²	1	4	yes	—
45	C₄₇×#544	C₂²	1	6	yes	—
46	C₄₇×#542	C₂²	1	24	yes	complemented
47	C₄₇×#541	C₂²	1	24	yes	complemented
48	C₄₇×#541	C₂²	1	24	yes	complemented
49	C₄₇×#536	C₂²	1	12	yes	—
50	C₄₇×#533	C₂²	1	6	yes	—
51	C₄₇×#533	C₂²	1	24	yes	complemented
52	C₄₇×#533	C₂²	1	12	yes	complemented
53	C₄₇×#533	C₂²	1	12	yes	complemented
54	C₂×C₄⋊Q₈×C₄₇	C₂²	1	3	yes	—
55	C₄₇×#529	C₂²	1	24	yes	—
56	C₄₇×#529	C₂²	1	12	yes	—
57	C₄₇×#529	C₂²	1	24	yes	complemented
58	C₄₇×#525	C₂²	1	12	yes	—
59	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	6	yes	—
60	C₄₇×#520	C₂²	1	6	yes	—
61	C₄₇×#520	C₂²	1	4	yes	complemented
62	C₄₇×#519	C₂²	1	1	yes	characteristic
63	C₄₇×#519	C₂²	1	2	yes	—
64	C₄₇×#519	C₂²	1	12	yes	—
65	C₄₇×#519	C₂²	1	8	yes	complemented
66	C₄₇×#519	C₂²	1	8	yes	complemented
67	C₄₇×#519	C₂²	1	4	yes	complemented
68	C₄×#41×C₄₇	C₂²	1	6	yes	—
69	C₄×#41×C₄₇	C₂²	1	12	yes	—
70	C₄×#41×C₄₇	C₂²	1	4	yes	complemented
71	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
72	C₂×C₄×Q₈×C₄₇	C₂²	1	8	yes	complemented
73	C₂×C₄×Q₈×C₄₇	C₂²	1	8	yes	complemented
74	C₂×C₄×Q₈×C₄₇	C₂²	1	4	yes	complemented
75	C₂×C₄×D₄×C₄₇	C₂²	1	3	yes	—
76	C₂×#117×C₄₇	C₂²	1	12	yes	—
77	2₋¹⁺⁴×C₄₇	—	2	8	no	—
78	C₂×#41×C₄₇	C₂³	1	4	yes	—
79	C₂×#41×C₄₇	C₂³	1	6	yes	—
80	C₂×#41×C₄₇	C₂³	1	4	yes	—
81	C₂²×Q₈×C₄₇	—	2	16	no	—
82	C₂²×Q₈×C₄₇	C₂³	1	8	yes	—
83	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
84	C₂²×Q₈×C₄₇	C₂³	1	6	yes	—
85	C₂²×Q₈×C₄₇	C₂³	1	8	yes	—
86	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
89	C₄⋊Q₈×C₄₇	C₂³	1	12	yes	—
90	C₄⋊Q₈×C₄₇	C₂³	1	12	yes	—
91	C₄⋊Q₈×C₄₇	C₂³	1	6	yes	—
92	C₄⋊Q₈×C₄₇	C₂³	1	6	yes	—
93	C₄⋊Q₈×C₄₇	C₂³	1	24	yes	—
94	C₄⋊Q₈×C₄₇	C₂³	1	24	yes	—
95	#126×C₄₇	C₂³	1	24	yes	—
96	#126×C₄₇	C₂³	1	24	yes	—
97	#126×C₄₇	C₂³	1	24	yes	—
98	#126×C₄₇	C₂³	1	48	yes	—
99	#125×C₄₇	C₂³	1	12	yes	—
100	#125×C₄₇	C₂³	1	24	yes	—
101	#125×C₄₇	C₂³	1	24	yes	—
102	#125×C₄₇	C₂³	1	12	yes	—
103	#125×C₄₇	C₂³	1	24	yes	—
104	#125×C₄₇	C₂³	1	48	yes	—
105	#124×C₄₇	C₂³	1	4	yes	—
106	#124×C₄₇	C₂³	1	24	yes	—
107	#124×C₄₇	C₂³	1	24	yes	—
108	#123×C₄₇	C₂³	1	24	yes	—
109	#123×C₄₇	C₂³	1	8	yes	—
110	#123×C₄₇	C₂³	1	24	yes	—
111	#123×C₄₇	C₂³	1	24	yes	—
112	C₂²⋊Q₈×C₄₇	C₂³	1	24	yes	—
113	C₂²⋊Q₈×C₄₇	C₂³	1	24	yes	—
114	C₂²⋊Q₈×C₄₇	C₂³	1	12	yes	—
115	C₂²⋊Q₈×C₄₇	C₂³	1	12	yes	—
116	C₂²⋊Q₈×C₄₇	C₂³	1	12	yes	—
117	C₂²⋊Q₈×C₄₇	C₂³	1	24	yes	—
118	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
119	C₂²⋊Q₈×C₄₇	C₂³	1	12	yes	—
120	C₂²⋊Q₈×C₄₇	C₂³	1	24	yes	—
121	C₂²⋊Q₈×C₄₇	C₂³	1	24	yes	—
122	C₂²⋊Q₈×C₄₇	C₂³	1	24	yes	—
123	#121×C₄₇	C₂³	1	12	yes	—
124	#121×C₄₇	C₂³	1	12	yes	—
125	#121×C₄₇	C₂³	1	8	yes	—
126	#121×C₄₇	C₂³	1	4	yes	—
127	#120×C₄₇	C₂³	1	8	yes	—
128	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
129	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
130	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
131	C₄×Q₈×C₄₇	C₂³	1	6	yes	—
132	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
133	C₄×Q₈×C₄₇	C₂³	1	24	yes	—
134	C₄×Q₈×C₄₇	C₂³	1	24	yes	—
135	C₄×Q₈×C₄₇	C₂³	1	8	yes	—
136	C₄×Q₈×C₄₇	C₂³	1	8	yes	—
137	C₄×Q₈×C₄₇	C₂³	1	24	yes	—
138	C₄×Q₈×C₄₇	C₂³	1	24	yes	—
139	C₄×Q₈×C₄₇	C₂³	1	12	yes	—
140	C₄×Q₈×C₄₇	C₂³	1	6	yes	—
141	C₄×Q₈×C₄₇	C₂³	1	12	yes	—
142	C₄×Q₈×C₄₇	C₂³	1	12	yes	—
143	C₄×Q₈×C₄₇	C₂³	1	12	yes	—
144	C₄×Q₈×C₄₇	C₂³	1	24	yes	—
145	C₄×D₄×C₄₇	C₂³	1	6	yes	—
146	C₄×D₄×C₄₇	C₂³	1	12	yes	—
147	C₄×D₄×C₄₇	C₂³	1	6	yes	—
148	C₄×D₄×C₄₇	C₂³	1	4	yes	—
149	C₄×D₄×C₄₇	C₂³	1	4	yes	—
150	C₄×D₄×C₄₇	C₂³	1	6	yes	—
151	C₄×D₄×C₄₇	C₂³	1	12	yes	—
152	C₄×D₄×C₄₇	C₂³	1	6	yes	—
153	C₄×D₄×C₄₇	C₂³	1	24	yes	—
154	C₄×D₄×C₄₇	C₂³	1	24	yes	—
155	C₄×D₄×C₄₇	C₂³	1	12	yes	—
156	C₄×D₄×C₄₇	C₂³	1	24	yes	—
157	#117×C₄₇	C₂³	1	6	yes	—
158	#117×C₄₇	C₂³	1	12	yes	—
159	#117×C₄₇	C₂³	1	24	yes	—
160	#117×C₄₇	C₂³	1	24	yes	—
161	#117×C₄₇	C₂³	1	12	yes	—
162	#117×C₄₇	C₂³	1	12	yes	—
163	#117×C₄₇	C₂³	1	12	yes	—
164	#117×C₄₇	C₂³	1	24	yes	—
165	#117×C₄₇	C₂³	1	12	yes	—
166	#117×C₄₇	C₂³	1	12	yes	—
167	#117×C₄₇	C₂³	1	24	yes	—
168	C₂×C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
169	C₂×C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
170	C₂×C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
171	C₂×C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
172	C₂×C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
173	C₂×C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
174	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
175	C₂×C₂²⋊C₄×C₄₇	C₂³	1	6	yes	—
176	C₂×C₄²×C₄₇	C₂³	1	24	yes	—
177	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
178	C₂×C₄²×C₄₇	C₂³	1	12	yes	—
179	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
180	#41×C₄₇	—	2	16	no	—
181	#41×C₄₇	—	2	16	no	—
182	#41×C₄₇	—	2	24	no	—
183	C₂×Q₈×C₄₇	—	2	32	no	—
184	C₂×Q₈×C₄₇	—	2	32	no	—
185	C₂×Q₈×C₄₇	—	2	16	no	—
186	C₂×Q₈×C₄₇	—	2	24	no	—
187	C₂×Q₈×C₄₇	#41	1	8	yes	complemented
188	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
189	C₂×Q₈×C₄₇	C₂⁴	1	24	yes	—
190	C₂×Q₈×C₄₇	C₂⁴	1	6	yes	—
191	C₂×Q₈×C₄₇	C₂⁴	1	12	yes	—
192	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
193	C₂×D₄×C₄₇	—	2	4	no	—
194	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
195	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
196	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
197	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
198	C₂×D₄×C₄₇	C₂⁴	1	6	yes	—
199	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
200	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₄₇	—	2	24	no	—
202	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
203	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
206	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
207	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
208	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
209	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
210	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
211	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
212	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
213	C₄⋊C₄×C₄₇	C₂⁴	1	6	yes	—
214	C₄⋊C₄×C₄₇	C₂⁴	1	6	yes	—
215	C₄⋊C₄×C₄₇	C₂⁴	1	12	yes	—
216	C₄⋊C₄×C₄₇	C₂⁴	1	12	yes	—
217	C₄⋊C₄×C₄₇	C₂⁴	1	6	yes	—
218	C₄⋊C₄×C₄₇	C₂⁴	1	12	yes	—
219	C₄⋊C₄×C₄₇	C₂⁴	1	12	yes	—
220	C₄⋊C₄×C₄₇	C₂⁴	1	24	yes	—
221	C₄⋊C₄×C₄₇	C₂⁴	1	24	yes	—
222	C₄⋊C₄×C₄₇	C₂⁴	1	24	yes	—
223	C₄⋊C₄×C₄₇	C₂⁴	1	6	yes	—
224	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
225	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
226	C₄⋊C₄×C₄₇	C₂⁴	1	12	yes	—
227	C₄⋊C₄×C₄₇	C₂⁴	1	24	yes	—
228	C₄⋊C₄×C₄₇	C₂⁴	1	24	yes	—
229	C₄⋊C₄×C₄₇	C₂⁴	1	24	yes	—
230	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
231	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
232	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
233	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
234	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
235	C₂²⋊C₄×C₄₇	C₂⁴	1	12	yes	—
236	C₂²⋊C₄×C₄₇	C₂⁴	1	12	yes	—
237	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
238	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
239	C₂²⋊C₄×C₄₇	C₂⁴	1	12	yes	—
240	C₂²⋊C₄×C₄₇	C₂⁴	1	24	yes	—
241	C₂²⋊C₄×C₄₇	C₂⁴	1	24	yes	—
242	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
243	C₄²×C₄₇	C₂⁴	1	12	yes	—
244	C₄²×C₄₇	C₂⁴	1	6	yes	—
245	C₄²×C₄₇	C₂⁴	1	4	yes	—
246	C₄²×C₄₇	C₂⁴	1	12	yes	—
247	C₄²×C₄₇	C₂⁴	1	24	yes	—
248	C₄²×C₄₇	C₂⁴	1	24	yes	—
249	C₄²×C₄₇	C₂⁴	1	6	yes	—
250	C₄²×C₄₇	C₂⁴	1	24	yes	—
251	C₂³×C₄₇	—	2	4	no	—
252	C₂³×C₄₇	—	2	4	no	—
253	C₂³×C₄₇	—	4	2	no	—
254	C₂³×C₄₇	C₂⁵	1	2	yes	—
255	C₂³×C₄₇	C₂⁵	1	4	yes	—
256	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
257	C₂³×C₄₇	C₂⁵	1	2	yes	—
258	Q₈×C₄₇	—	2	48	no	—
259	Q₈×C₄₇	—	2	12	no	—
260	Q₈×C₄₇	—	2	8	no	—
261	Q₈×C₄₇	—	4	12	no	—
262	Q₈×C₄₇	C₂×#41	1	16	yes	—
263	D₄×C₄₇	—	2	8	no	—
264	D₄×C₄₇	—	2	4	no	—
265	D₄×C₄₇	—	2	16	no	—
266	D₄×C₄₇	—	2	12	no	—
267	D₄×C₄₇	—	2	2	no	—
268	D₄×C₄₇	—	4	8	no	—
269	D₄×C₄₇	2₋¹⁺⁴	1	4	yes	complemented
270	C₂×C₄×C₄₇	—	2	12	no	—
271	C₂×C₄×C₄₇	—	2	16	no	—
272	C₂×C₄×C₄₇	—	2	24	no	—
273	C₂×C₄×C₄₇	—	2	24	no	—
274	C₂×C₄×C₄₇	—	2	24	no	—
275	C₂×C₄×C₄₇	—	2	2	no	—
276	C₂×C₄×C₄₇	—	2	8	no	—
277	C₂×C₄×C₄₇	—	4	12	no	—
278	C₂×C₄×C₄₇	—	4	8	no	—
279	C₂×C₄×C₄₇	—	4	3	no	—
280	C₂×C₄×C₄₇	C₂×#41	1	12	yes	—
281	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
282	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
283	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
284	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
285	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
286	C₂×C₄×C₄₇	C₂⁵	1	6	yes	—
287	C₂×C₄×C₄₇	C₂⁵	1	12	yes	—
288	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
289	C₂×C₄×C₄₇	C₂⁵	1	6	yes	—
290	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
291	#62998	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂²×C₄₇	—	2	2	no	—
293	C₂²×C₄₇	—	2	1	no	—
294	C₂²×C₄₇	—	2	2	no	—
295	C₂²×C₄₇	—	2	1	no	—
296	C₂²×C₄₇	—	2	2	no	—
297	C₂²×C₄₇	—	2	4	no	—
298	C₂²×C₄₇	—	2	4	no	—
299	C₂²×C₄₇	—	2	2	no	—
300	C₂²×C₄₇	—	2	4	no	—
301	C₂²×C₄₇	—	2	2	no	—
302	C₂²×C₄₇	—	4	8	no	—
303	C₂²×C₄₇	C₂²×#41	1	2	yes	—
304	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	4	yes	—
305	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
306	C₄×C₄₇	—	2	4	no	—
307	C₄×C₄₇	—	2	12	no	—
308	C₄×C₄₇	—	2	4	no	—
309	C₄×C₄₇	—	2	1	no	—
310	C₄×C₄₇	—	2	8	no	—
311	C₄×C₄₇	—	2	4	no	—
312	C₄×C₄₇	—	2	6	no	—
313	C₄×C₄₇	—	2	8	no	—
314	C₄×C₄₇	C₂²×#41	1	12	yes	—
315	C₄×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
316	#3523	C₂×C₄₇	1	8	yes	complemented
317	#3523	C₂×C₄₇	1	4	yes	complemented
318	#3518	C₂×C₄₇	1	4	yes	complemented
319	#3516	C₂×C₄₇	1	8	yes	complemented
320	#3509	C₂×C₄₇	1	6	yes	complemented
321	#3502	C₂×C₄₇	1	1	yes	characteristic, complemented
322	#3495	C₂×C₄₇	1	12	yes	complemented
323	#3486	C₂×C₄₇	1	2	yes	complemented
324	#3482	C₂×C₄₇	1	4	yes	complemented
325	Q₈×#41	C₂×C₄₇	1	4	yes	complemented
326	#3475	C₂×C₄₇	1	6	yes	complemented
327	C₂×D₄×Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
328	C₄×2₋¹⁺⁴	C₂×C₄₇	1	1	yes	characteristic, complemented
329	C₂×#519	C₂×C₄₇	1	2	yes	complemented
330	C₂×C₄₇	—	2	2	no	—
331	C₂×C₄₇	—	2	4	no	—
332	C₂×C₄₇	—	4	4	no	—
333	C₂×C₄₇	—	4	2	no	—
334	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
335	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
336	C₂×C₄₇	2₋¹⁺⁶	1	1	yes	characteristic
337	C₂×2₋¹⁺⁴	C₂²×C₄₇	1	1	yes	characteristic
338	C₂³×Q₈	C₂²×C₄₇	1	2	yes	—
339	Q₈²	C₂²×C₄₇	1	4	yes	complemented
340	#557	C₂²×C₄₇	1	12	yes	complemented
341	#557	C₂²×C₄₇	1	4	yes	complemented
342	#557	C₂²×C₄₇	1	8	yes	complemented
343	#557	C₂²×C₄₇	1	12	yes	complemented
344	#556	C₂²×C₄₇	1	6	yes	—
345	#556	C₂²×C₄₇	1	12	yes	complemented
346	#556	C₂²×C₄₇	1	24	yes	complemented
347	#556	C₂²×C₄₇	1	12	yes	complemented
348	#555	C₂²×C₄₇	1	6	yes	—
349	#554	C₂²×C₄₇	1	6	yes	—
350	#554	C₂²×C₄₇	1	24	yes	complemented
351	#553	C₂²×C₄₇	1	12	yes	—
352	#552	C₂²×C₄₇	1	12	yes	—
353	#552	C₂²×C₄₇	1	12	yes	—
354	#552	C₂²×C₄₇	1	24	yes	—
355	#552	C₂²×C₄₇	1	24	yes	complemented
356	#552	C₂²×C₄₇	1	24	yes	complemented
357	#551	C₂²×C₄₇	1	24	yes	—
358	D₄×Q₈	C₂²×C₄₇	1	4	yes	—
359	D₄×Q₈	C₂²×C₄₇	1	8	yes	—
360	D₄×Q₈	C₂²×C₄₇	1	4	yes	—
361	D₄×Q₈	C₂²×C₄₇	1	8	yes	complemented
362	D₄×Q₈	C₂²×C₄₇	1	8	yes	complemented
363	#548	C₂²×C₄₇	1	8	yes	complemented
364	#548	C₂²×C₄₇	1	8	yes	complemented
365	#547	C₂²×C₄₇	1	6	yes	—
366	#546	C₂²×C₄₇	1	4	yes	—
367	#544	C₂²×C₄₇	1	6	yes	—
368	#542	C₂²×C₄₇	1	24	yes	complemented
369	#541	C₂²×C₄₇	1	24	yes	complemented
370	#541	C₂²×C₄₇	1	24	yes	complemented
371	#536	C₂²×C₄₇	1	12	yes	—
372	#533	C₂²×C₄₇	1	6	yes	—
373	#533	C₂²×C₄₇	1	24	yes	complemented
374	#533	C₂²×C₄₇	1	12	yes	complemented
375	#533	C₂²×C₄₇	1	12	yes	complemented
376	C₂×C₄⋊Q₈	C₂²×C₄₇	1	3	yes	—
377	#529	C₂²×C₄₇	1	24	yes	—
378	#529	C₂²×C₄₇	1	12	yes	—
379	#529	C₂²×C₄₇	1	24	yes	complemented
380	#525	C₂²×C₄₇	1	12	yes	—
381	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	6	yes	—
382	#520	C₂²×C₄₇	1	6	yes	—
383	#520	C₂²×C₄₇	1	4	yes	complemented
384	#519	C₂²×C₄₇	1	1	yes	characteristic
385	#519	C₂²×C₄₇	1	2	yes	—
386	#519	C₂²×C₄₇	1	12	yes	—
387	#519	C₂²×C₄₇	1	8	yes	complemented
388	#519	C₂²×C₄₇	1	8	yes	complemented
389	#519	C₂²×C₄₇	1	4	yes	complemented
390	C₄×#41	C₂²×C₄₇	1	6	yes	—
391	C₄×#41	C₂²×C₄₇	1	12	yes	—
392	C₄×#41	C₂²×C₄₇	1	4	yes	complemented
393	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
394	C₂×C₄×Q₈	C₂²×C₄₇	1	8	yes	complemented
395	C₂×C₄×Q₈	C₂²×C₄₇	1	8	yes	complemented
396	C₂×C₄×Q₈	C₂²×C₄₇	1	4	yes	complemented
397	C₂×C₄×D₄	C₂²×C₄₇	1	3	yes	—
398	C₂×#117	C₂²×C₄₇	1	12	yes	—
399	C₄₇	#62998	1	1	yes	characteristic, direct product factor, Sylow
400	2₋¹⁺⁴	—	2	8	no	—
401	C₂×#41	C₂³×C₄₇	1	4	yes	—
402	C₂×#41	C₂³×C₄₇	1	6	yes	—
403	C₂×#41	C₂³×C₄₇	1	4	yes	—
404	C₂²×Q₈	—	2	16	no	—
405	C₂²×Q₈	C₂³×C₄₇	1	8	yes	—
406	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
407	C₂²×Q₈	C₂³×C₄₇	1	6	yes	—
408	C₂²×Q₈	C₂³×C₄₇	1	8	yes	—
409	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
410	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₄₇	1	6	yes	—
412	C₄⋊Q₈	C₂³×C₄₇	1	12	yes	—
413	C₄⋊Q₈	C₂³×C₄₇	1	12	yes	—
414	C₄⋊Q₈	C₂³×C₄₇	1	6	yes	—
415	C₄⋊Q₈	C₂³×C₄₇	1	6	yes	—
416	C₄⋊Q₈	C₂³×C₄₇	1	24	yes	—
417	C₄⋊Q₈	C₂³×C₄₇	1	24	yes	—
418	#126	C₂³×C₄₇	1	24	yes	—
419	#126	C₂³×C₄₇	1	24	yes	—
420	#126	C₂³×C₄₇	1	24	yes	—
421	#126	C₂³×C₄₇	1	48	yes	—
422	#125	C₂³×C₄₇	1	12	yes	—
423	#125	C₂³×C₄₇	1	24	yes	—
424	#125	C₂³×C₄₇	1	24	yes	—
425	#125	C₂³×C₄₇	1	12	yes	—
426	#125	C₂³×C₄₇	1	24	yes	—
427	#125	C₂³×C₄₇	1	48	yes	—
428	#124	C₂³×C₄₇	1	4	yes	—
429	#124	C₂³×C₄₇	1	24	yes	—
430	#124	C₂³×C₄₇	1	24	yes	—
431	#123	C₂³×C₄₇	1	24	yes	—
432	#123	C₂³×C₄₇	1	8	yes	—
433	#123	C₂³×C₄₇	1	24	yes	—
434	#123	C₂³×C₄₇	1	24	yes	—
435	C₂²⋊Q₈	C₂³×C₄₇	1	24	yes	—
436	C₂²⋊Q₈	C₂³×C₄₇	1	24	yes	—
437	C₂²⋊Q₈	C₂³×C₄₇	1	12	yes	—
438	C₂²⋊Q₈	C₂³×C₄₇	1	12	yes	—
439	C₂²⋊Q₈	C₂³×C₄₇	1	12	yes	—
440	C₂²⋊Q₈	C₂³×C₄₇	1	24	yes	—
441	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
442	C₂²⋊Q₈	C₂³×C₄₇	1	12	yes	—
443	C₂²⋊Q₈	C₂³×C₄₇	1	24	yes	—
444	C₂²⋊Q₈	C₂³×C₄₇	1	24	yes	—
445	C₂²⋊Q₈	C₂³×C₄₇	1	24	yes	—
446	#121	C₂³×C₄₇	1	12	yes	—
447	#121	C₂³×C₄₇	1	12	yes	—
448	#121	C₂³×C₄₇	1	8	yes	—
449	#121	C₂³×C₄₇	1	4	yes	—
450	#120	C₂³×C₄₇	1	8	yes	—
451	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
452	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
453	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
454	C₄×Q₈	C₂³×C₄₇	1	6	yes	—
455	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
456	C₄×Q₈	C₂³×C₄₇	1	24	yes	—
457	C₄×Q₈	C₂³×C₄₇	1	24	yes	—
458	C₄×Q₈	C₂³×C₄₇	1	8	yes	—
459	C₄×Q₈	C₂³×C₄₇	1	8	yes	—
460	C₄×Q₈	C₂³×C₄₇	1	24	yes	—
461	C₄×Q₈	C₂³×C₄₇	1	24	yes	—
462	C₄×Q₈	C₂³×C₄₇	1	12	yes	—
463	C₄×Q₈	C₂³×C₄₇	1	6	yes	—
464	C₄×Q₈	C₂³×C₄₇	1	12	yes	—
465	C₄×Q₈	C₂³×C₄₇	1	12	yes	—
466	C₄×Q₈	C₂³×C₄₇	1	12	yes	—
467	C₄×Q₈	C₂³×C₄₇	1	24	yes	—
468	C₄×D₄	C₂³×C₄₇	1	6	yes	—
469	C₄×D₄	C₂³×C₄₇	1	12	yes	—
470	C₄×D₄	C₂³×C₄₇	1	6	yes	—
471	C₄×D₄	C₂³×C₄₇	1	4	yes	—
472	C₄×D₄	C₂³×C₄₇	1	4	yes	—
473	C₄×D₄	C₂³×C₄₇	1	6	yes	—
474	C₄×D₄	C₂³×C₄₇	1	12	yes	—
475	C₄×D₄	C₂³×C₄₇	1	6	yes	—
476	C₄×D₄	C₂³×C₄₇	1	24	yes	—
477	C₄×D₄	C₂³×C₄₇	1	24	yes	—
478	C₄×D₄	C₂³×C₄₇	1	12	yes	—
479	C₄×D₄	C₂³×C₄₇	1	24	yes	—
480	#117	C₂³×C₄₇	1	6	yes	—
481	#117	C₂³×C₄₇	1	12	yes	—
482	#117	C₂³×C₄₇	1	24	yes	—
483	#117	C₂³×C₄₇	1	24	yes	—
484	#117	C₂³×C₄₇	1	12	yes	—
485	#117	C₂³×C₄₇	1	12	yes	—
486	#117	C₂³×C₄₇	1	12	yes	—
487	#117	C₂³×C₄₇	1	24	yes	—
488	#117	C₂³×C₄₇	1	12	yes	—
489	#117	C₂³×C₄₇	1	12	yes	—
490	#117	C₂³×C₄₇	1	24	yes	—
491	C₂×C₄⋊C₄	C₂³×C₄₇	1	12	yes	—
492	C₂×C₄⋊C₄	C₂³×C₄₇	1	12	yes	—
493	C₂×C₄⋊C₄	C₂³×C₄₇	1	3	yes	—
494	C₂×C₄⋊C₄	C₂³×C₄₇	1	3	yes	—
495	C₂×C₄⋊C₄	C₂³×C₄₇	1	12	yes	—
496	C₂×C₄⋊C₄	C₂³×C₄₇	1	6	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₄₇	1	6	yes	—
499	C₂×C₄²	C₂³×C₄₇	1	24	yes	—
500	C₂×C₄²	C₂³×C₄₇	1	3	yes	—
501	C₂×C₄²	C₂³×C₄₇	1	12	yes	—
502	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
503	#41	—	2	16	no	—
504	#41	—	2	16	no	—
505	#41	—	2	24	no	—
506	C₂×Q₈	—	2	32	no	—
507	C₂×Q₈	—	2	32	no	—
508	C₂×Q₈	—	2	16	no	—
509	C₂×Q₈	—	2	24	no	—
510	C₂×Q₈	#41×C₄₇	1	8	yes	complemented
511	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
512	C₂×Q₈	C₂⁴×C₄₇	1	24	yes	—
513	C₂×Q₈	C₂⁴×C₄₇	1	6	yes	—
514	C₂×Q₈	C₂⁴×C₄₇	1	12	yes	—
515	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
518	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
519	C₂×D₄	C₂⁴×C₄₇	1	1	yes	characteristic
520	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
521	C₂×D₄	C₂⁴×C₄₇	1	6	yes	—
522	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
523	C₂×D₄	C₂⁴×C₄₇	1	1	yes	characteristic
524	C₂²×C₄	—	2	24	no	—
525	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
526	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₄₇	1	12	yes	—
529	C₂²×C₄	C₂⁴×C₄₇	1	12	yes	—
530	C₂²×C₄	C₂⁴×C₄₇	1	6	yes	—
531	C₂²×C₄	C₂⁴×C₄₇	1	12	yes	—
532	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
533	C₂²×C₄	C₂⁴×C₄₇	1	3	yes	—
534	C₂²×C₄	C₂⁴×C₄₇	1	12	yes	—
535	C₂²×C₄	C₂⁴×C₄₇	1	3	yes	—
536	C₄⋊C₄	C₂⁴×C₄₇	1	6	yes	—
537	C₄⋊C₄	C₂⁴×C₄₇	1	6	yes	—
538	C₄⋊C₄	C₂⁴×C₄₇	1	12	yes	—
539	C₄⋊C₄	C₂⁴×C₄₇	1	12	yes	—
540	C₄⋊C₄	C₂⁴×C₄₇	1	6	yes	—
541	C₄⋊C₄	C₂⁴×C₄₇	1	12	yes	—
542	C₄⋊C₄	C₂⁴×C₄₇	1	12	yes	—
543	C₄⋊C₄	C₂⁴×C₄₇	1	24	yes	—
544	C₄⋊C₄	C₂⁴×C₄₇	1	24	yes	—
545	C₄⋊C₄	C₂⁴×C₄₇	1	24	yes	—
546	C₄⋊C₄	C₂⁴×C₄₇	1	6	yes	—
547	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
548	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
549	C₄⋊C₄	C₂⁴×C₄₇	1	12	yes	—
550	C₄⋊C₄	C₂⁴×C₄₇	1	24	yes	—
551	C₄⋊C₄	C₂⁴×C₄₇	1	24	yes	—
552	C₄⋊C₄	C₂⁴×C₄₇	1	24	yes	—
553	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
554	C₂²⋊C₄	C₂⁴×C₄₇	1	4	yes	—
555	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
556	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
557	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
558	C₂²⋊C₄	C₂⁴×C₄₇	1	12	yes	—
559	C₂²⋊C₄	C₂⁴×C₄₇	1	12	yes	—
560	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
561	C₂²⋊C₄	C₂⁴×C₄₇	1	4	yes	—
562	C₂²⋊C₄	C₂⁴×C₄₇	1	12	yes	—
563	C₂²⋊C₄	C₂⁴×C₄₇	1	24	yes	—
564	C₂²⋊C₄	C₂⁴×C₄₇	1	24	yes	—
565	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
566	C₄²	C₂⁴×C₄₇	1	12	yes	—
567	C₄²	C₂⁴×C₄₇	1	6	yes	—
568	C₄²	C₂⁴×C₄₇	1	4	yes	—
569	C₄²	C₂⁴×C₄₇	1	12	yes	—
570	C₄²	C₂⁴×C₄₇	1	24	yes	—
571	C₄²	C₂⁴×C₄₇	1	24	yes	—
572	C₄²	C₂⁴×C₄₇	1	6	yes	—
573	C₄²	C₂⁴×C₄₇	1	24	yes	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	4	no	—
576	C₂³	—	4	2	no	—
577	C₂³	C₂⁵×C₄₇	1	2	yes	—
578	C₂³	C₂⁵×C₄₇	1	4	yes	—
579	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
580	C₂³	C₂⁵×C₄₇	1	2	yes	—
581	Q₈	—	2	48	no	—
582	Q₈	—	2	12	no	—
583	Q₈	—	2	8	no	—
584	Q₈	—	4	12	no	—
585	Q₈	C₂×#41×C₄₇	1	16	yes	—
586	D₄	—	2	8	no	—
587	D₄	—	2	4	no	—
588	D₄	—	2	16	no	—
589	D₄	—	2	12	no	—
590	D₄	—	2	2	no	—
591	D₄	—	4	8	no	—
592	D₄	2₋¹⁺⁴×C₄₇	1	4	yes	complemented
593	C₂×C₄	—	2	12	no	—
594	C₂×C₄	—	2	16	no	—
595	C₂×C₄	—	2	24	no	—
596	C₂×C₄	—	2	24	no	—
597	C₂×C₄	—	2	24	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	8	no	—
600	C₂×C₄	—	4	12	no	—
601	C₂×C₄	—	4	8	no	—
602	C₂×C₄	—	4	3	no	—
603	C₂×C₄	C₂×#41×C₄₇	1	12	yes	—
604	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
605	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
606	C₂×C₄	C₂⁵×C₄₇	1	8	yes	—
607	C₂×C₄	C₂⁵×C₄₇	1	8	yes	—
608	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
609	C₂×C₄	C₂⁵×C₄₇	1	6	yes	—
610	C₂×C₄	C₂⁵×C₄₇	1	12	yes	—
611	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
612	C₂×C₄	C₂⁵×C₄₇	1	6	yes	—
613	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	4	no	—
620	C₂²	—	2	4	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	4	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	4	8	no	—
625	C₂²	C₂²×#41×C₄₇	1	2	yes	—
626	C₂²	C₂×2₋¹⁺⁴×C₄₇	1	4	yes	—
627	C₂²	C₂⁶×C₄₇	1	1	yes	characteristic
628	C₄	—	2	4	no	—
629	C₄	—	2	12	no	—
630	C₄	—	2	4	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	8	no	—
633	C₄	—	2	4	no	—
634	C₄	—	2	6	no	—
635	C₄	—	2	8	no	—
636	C₄	C₂²×#41×C₄₇	1	12	yes	—
637	C₄	C₂×2₋¹⁺⁴×C₄₇	1	2	yes	—
638	C₂	—	2	2	no	—
639	C₂	—	2	4	no	—
640	C₂	—	4	2	no	—
641	C₂	—	4	4	no	—
642	C₂	C₂³×#41×C₄₇	1	1	yes	characteristic
643	C₂	C₂²×2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
644	C₂	C₄₇×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₄₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#3523	C₂	semidirect
2. C₄₇×#3523	C₂	semidirect
3. C₄₇×#3518	C₂	semidirect
4. C₄₇×#3516	C₂	semidirect
5. C₄₇×#3509	C₂	semidirect
6. C₄₇×#3502	C₂	semidirect
7. C₄₇×#3495	C₂	semidirect
8. C₄₇×#3486	C₂	semidirect
9. C₄₇×#3482	C₂	semidirect
10. Q₈×#41×C₄₇	C₂	semidirect
11. C₄₇×#3475	C₂	semidirect
12. C₂×D₄×Q₈×C₄₇	C₂	semidirect
13. C₄×2₋¹⁺⁴×C₄₇	C₂	semidirect
14. C₂×C₄₇×#519	C₂	semidirect
17. Q₈²×C₄₇	C₂²	semidirect
18. C₄₇×#557	C₂²	semidirect
19. C₄₇×#557	C₂²	semidirect
20. C₄₇×#557	C₂²	semidirect
21. C₄₇×#557	C₂²	semidirect
23. C₄₇×#556	C₂²	semidirect
24. C₄₇×#556	C₂²	semidirect
25. C₄₇×#556	C₂²	semidirect
28. C₄₇×#554	C₂²	semidirect
33. C₄₇×#552	C₂²	semidirect
34. C₄₇×#552	C₂²	semidirect
39. D₄×Q₈×C₄₇	C₂²	semidirect
40. D₄×Q₈×C₄₇	C₂²	semidirect
41. C₄₇×#548	C₂²	semidirect
42. C₄₇×#548	C₂²	semidirect
46. C₄₇×#542	C₂²	semidirect
47. C₄₇×#541	C₂²	semidirect
48. C₄₇×#541	C₂²	semidirect
51. C₄₇×#533	C₂²	semidirect
52. C₄₇×#533	C₂²	semidirect
53. C₄₇×#533	C₂²	semidirect
57. C₄₇×#529	C₂²	semidirect
61. C₄₇×#520	C₂²	semidirect
65. C₄₇×#519	C₂²	semidirect
66. C₄₇×#519	C₂²	semidirect
67. C₄₇×#519	C₂²	semidirect
70. C₄×#41×C₄₇	C₂²	semidirect
72. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
73. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
74. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
187. C₂×Q₈×C₄₇	#41	semidirect
269. D₄×C₄₇	2₋¹⁺⁴	semidirect
291. #62998	C₄₇	direct (N × H)
316. #3523	C₂×C₄₇	semidirect
317. #3523	C₂×C₄₇	semidirect
318. #3518	C₂×C₄₇	semidirect
319. #3516	C₂×C₄₇	semidirect
320. #3509	C₂×C₄₇	semidirect
321. #3502	C₂×C₄₇	semidirect
322. #3495	C₂×C₄₇	semidirect
323. #3486	C₂×C₄₇	semidirect
324. #3482	C₂×C₄₇	semidirect
325. Q₈×#41	C₂×C₄₇	semidirect
326. #3475	C₂×C₄₇	semidirect
327. C₂×D₄×Q₈	C₂×C₄₇	semidirect
328. C₄×2₋¹⁺⁴	C₂×C₄₇	semidirect
329. C₂×#519	C₂×C₄₇	semidirect
339. Q₈²	C₂²×C₄₇	semidirect
340. #557	C₂²×C₄₇	semidirect
341. #557	C₂²×C₄₇	semidirect
342. #557	C₂²×C₄₇	semidirect
343. #557	C₂²×C₄₇	semidirect
345. #556	C₂²×C₄₇	semidirect
346. #556	C₂²×C₄₇	semidirect
347. #556	C₂²×C₄₇	semidirect
350. #554	C₂²×C₄₇	semidirect
355. #552	C₂²×C₄₇	semidirect
356. #552	C₂²×C₄₇	semidirect
361. D₄×Q₈	C₂²×C₄₇	semidirect
362. D₄×Q₈	C₂²×C₄₇	semidirect
363. #548	C₂²×C₄₇	semidirect
364. #548	C₂²×C₄₇	semidirect
368. #542	C₂²×C₄₇	semidirect
369. #541	C₂²×C₄₇	semidirect
370. #541	C₂²×C₄₇	semidirect
373. #533	C₂²×C₄₇	semidirect
374. #533	C₂²×C₄₇	semidirect
375. #533	C₂²×C₄₇	semidirect
379. #529	C₂²×C₄₇	semidirect
383. #520	C₂²×C₄₇	semidirect
387. #519	C₂²×C₄₇	semidirect
388. #519	C₂²×C₄₇	semidirect
389. #519	C₂²×C₄₇	semidirect
392. C₄×#41	C₂²×C₄₇	semidirect
394. C₂×C₄×Q₈	C₂²×C₄₇	semidirect
395. C₂×C₄×Q₈	C₂²×C₄₇	semidirect
396. C₂×C₄×Q₈	C₂²×C₄₇	semidirect
399. C₄₇	#62998	direct (N × H)
510. C₂×Q₈	#41×C₄₇	semidirect
592. D₄	2₋¹⁺⁴×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3523	2
C₄₇×#3518	2
C₄₇×#3516	2
C₄₇×#3509	2
C₄₇×#3502	2
C₄₇×#3495	2
C₄₇×#3486	2
C₄₇×#3482	2
Q₈×#41×C₄₇	2
C₄₇×#3475	2
C₂×D₄×Q₈×C₄₇	2
C₄×2₋¹⁺⁴×C₄₇	2
C₂×C₄₇×#519	2
#62998	47

Subgroups — C47×#62998 #26102696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#62998 #26102696