Subgroups — C₄₇×#63021 #26102719

Order 12032.

7272 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3558	C₂	1	8	yes	maximal, complemented
2	C₄₇×#3554	C₂	1	4	yes	maximal, complemented
3	C₄₇×#3550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3543	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3540	C₂	1	4	yes	maximal, complemented
6	C₄₇×#3533	C₂	1	8	yes	maximal, complemented
7	C₄₇×#3522	C₂	1	4	yes	maximal, complemented
8	C₄₇×#3514	C₂	1	4	yes	maximal, complemented
9	C₄₇×#3513	C₂	1	8	yes	maximal, complemented
10	C₄₇×#3508	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3506	C₂	1	4	yes	maximal, complemented
12	C₄₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₇×#3485	C₂	1	4	yes	maximal, complemented
14	C₄₇×#3482	C₂	1	2	yes	maximal, complemented
15	C₄₇×#3481	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄₇×#559	C₂	1	2	yes	maximal, complemented
17	D₄×#41×C₄₇	C₂	1	4	yes	maximal, complemented
18	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	2	yes	complemented
19	C₂²×#41×C₄₇	C₂²	1	4	yes	complemented
20	C₄₇×#563	C₂²	1	4	yes	complemented
21	C₄₇×#562	C₂²	1	16	yes	complemented
22	C₄₇×H(3,𝔽₄)	C₂²	1	8	yes	complemented
23	C₄₇×#560	C₂²	1	8	yes	complemented
24	C₄₇×#559	C₂²	1	2	yes	complemented
25	C₄₇×#559	C₂²	1	8	yes	complemented
26	C₄₇×#559	C₂²	1	4	yes	complemented
27	C₄₇×#559	C₂²	1	8	yes	complemented
28	C₄₇×#559	C₂²	1	1	yes	characteristic, complemented
29	C₄₇×#559	C₂²	1	8	yes	complemented
30	C₄₇×#559	C₂²	1	4	yes	complemented
31	C₄₇×#559	C₂²	1	8	yes	complemented
32	Q₈²×C₄₇	C₂²	1	2	yes	complemented
33	C₄₇×#557	C₂²	1	2	yes	complemented
34	C₄₇×#556	C₂²	1	4	yes	complemented
35	C₄₇×#556	C₂²	1	2	yes	complemented
36	C₄₇×#556	C₂²	1	4	yes	complemented
37	C₄₇×#555	C₂²	1	8	yes	complemented
38	C₄₇×#554	C₂²	1	8	yes	complemented
39	C₄₇×#554	C₂²	1	2	yes	complemented
40	C₄₇×#553	C₂²	1	4	yes	complemented
41	C₄₇×#553	C₂²	1	16	yes	complemented
42	C₄₇×#552	C₂²	1	4	yes	complemented
43	C₄₇×#552	C₂²	1	8	yes	complemented
44	C₄₇×#551	C₂²	1	4	yes	complemented
45	C₄₇×#551	C₂²	1	8	yes	complemented
46	C₄₇×#551	C₂²	1	16	yes	complemented
47	C₄₇×#550	C₂²	1	4	yes	complemented
48	C₄₇×#550	C₂²	1	4	yes	complemented
49	C₄₇×#550	C₂²	1	4	yes	complemented
50	D₄×Q₈×C₄₇	C₂²	1	4	yes	complemented
51	D₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
52	C₄₇×#548	C₂²	1	8	yes	complemented
53	C₄₇×#548	C₂²	1	4	yes	complemented
54	C₄₇×#548	C₂²	1	8	yes	complemented
55	C₄₇×#547	C₂²	1	8	yes	complemented
56	C₄₇×#547	C₂²	1	2	yes	complemented
57	C₄₇×#547	C₂²	1	8	yes	complemented
58	C₄₇×#547	C₂²	1	4	yes	complemented
59	C₄₇×#547	C₂²	1	16	yes	complemented
60	C₄₇×#546	C₂²	1	8	yes	complemented
61	C₄₇×#546	C₂²	1	4	yes	complemented
62	C₄₇×#546	C₂²	1	16	yes	complemented
63	C₄₇×#546	C₂²	1	16	yes	complemented
64	C₄₇×#546	C₂²	1	8	yes	complemented
65	C₄₇×#546	C₂²	1	8	yes	complemented
66	C₄₇×#546	C₂²	1	8	yes	complemented
67	D₄²×C₄₇	C₂²	1	1	yes	characteristic, complemented
68	D₄²×C₄₇	C₂²	1	8	yes	complemented
69	D₄²×C₄₇	C₂²	1	8	yes	complemented
70	D₄²×C₄₇	C₂²	1	4	yes	complemented
71	C₄₇×#542	C₂²	1	8	yes	complemented
72	C₄₇×#542	C₂²	1	8	yes	complemented
73	C₄₇×#542	C₂²	1	8	yes	complemented
74	C₄₇×#542	C₂²	1	16	yes	complemented
75	C₄₇×#540	C₂²	1	8	yes	complemented
76	C₄₇×#540	C₂²	1	8	yes	complemented
77	C₄₇×#539	C₂²	1	16	yes	complemented
78	C₄₇×#538	C₂²	1	16	yes	complemented
79	C₄₇×#538	C₂²	1	16	yes	complemented
80	C₄₇×#538	C₂²	1	16	yes	complemented
81	C₄₇×#536	C₂²	1	4	yes	complemented
82	C₄₇×#536	C₂²	1	4	yes	complemented
83	C₄₇×#535	C₂²	1	8	yes	complemented
84	C₄₇×#535	C₂²	1	4	yes	complemented
85	C₄₇×#535	C₂²	1	4	yes	complemented
86	C₄₇×#535	C₂²	1	2	yes	complemented
87	C₄₇×#534	C₂²	1	8	yes	complemented
88	C₄₇×#534	C₂²	1	8	yes	complemented
89	C₄₇×#533	C₂²	1	2	yes	complemented
90	C₄₇×#533	C₂²	1	4	yes	complemented
91	C₄₇×#532	C₂²	1	1	yes	characteristic
92	C₄₇×#532	C₂²	1	4	yes	complemented
93	C₄₇×#532	C₂²	1	8	yes	complemented
94	C₄₇×#532	C₂²	1	2	yes	complemented
95	C₄₇×#532	C₂²	1	4	yes	complemented
96	C₂×#127×C₄₇	C₂²	1	2	yes	—
97	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic, complemented
98	C₄₇×#529	C₂²	1	4	yes	complemented
99	C₄₇×#529	C₂²	1	4	yes	complemented
100	C₄₇×#529	C₂²	1	8	yes	complemented
101	C₄₇×#529	C₂²	1	8	yes	complemented
102	C₂×#124×C₄₇	C₂²	1	8	yes	complemented
103	C₄₇×#525	C₂²	1	8	yes	complemented
104	C₄₇×#525	C₂²	1	16	yes	complemented
105	C₄₇×#525	C₂²	1	4	yes	complemented
106	C₄₇×#525	C₂²	1	4	yes	complemented
107	C₂×#123×C₄₇	C₂²	1	8	yes	complemented
108	C₂×#123×C₄₇	C₂²	1	8	yes	complemented
109	C₄₇×#520	C₂²	1	8	yes	complemented
110	C₄₇×#518	C₂²	1	4	yes	complemented
111	C₄₇×#518	C₂²	1	4	yes	complemented
112	C₄×#41×C₄₇	C₂²	1	4	yes	complemented
113	C₄×#41×C₄₇	C₂²	1	2	yes	complemented
114	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₄×Q₈×C₄₇	C₂²	1	4	yes	complemented
116	C₂×C₄×D₄×C₄₇	C₂²	1	8	yes	complemented
117	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	complemented
118	H(5,𝔽₂)×C₄₇	—	4	8	no	—
119	C₂×#41×C₄₇	—	4	16	no	—
120	C₂×#41×C₄₇	C₂³	1	4	yes	—
121	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
122	C₂×#41×C₄₇	C₂³	1	2	yes	—
123	C₂×#41×C₄₇	C₂³	1	8	yes	—
124	C₂×#41×C₄₇	C₂³	1	2	yes	—
125	C₂×#41×C₄₇	C₂³	1	16	yes	—
126	C₂×#41×C₄₇	C₂³	1	8	yes	—
127	C₂×#41×C₄₇	C₂³	1	4	yes	—
128	C₂×#41×C₄₇	C₂³	1	4	yes	—
129	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
130	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
131	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
132	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
133	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
134	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
135	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
136	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
137	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
138	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
139	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
140	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
141	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
143	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
144	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	—
145	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
146	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
147	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	—
148	#127×C₄₇	C₂³	1	1	yes	characteristic
149	#127×C₄₇	C₂³	1	2	yes	—
150	#127×C₄₇	C₂³	1	4	yes	—
151	#127×C₄₇	C₂³	1	8	yes	—
152	#127×C₄₇	C₂³	1	4	yes	—
153	#127×C₄₇	C₂³	1	2	yes	—
154	#127×C₄₇	C₂³	1	8	yes	—
155	#126×C₄₇	C₂³	1	16	yes	—
156	#126×C₄₇	C₂³	1	8	yes	—
157	#126×C₄₇	C₂³	1	8	yes	—
158	#126×C₄₇	C₂³	1	8	yes	—
159	#126×C₄₇	C₂³	1	8	yes	—
160	#126×C₄₇	C₂³	1	16	yes	—
161	#125×C₄₇	C₂³	1	4	yes	—
162	#125×C₄₇	C₂³	1	8	yes	—
163	#125×C₄₇	C₂³	1	4	yes	—
164	#125×C₄₇	C₂³	1	8	yes	—
165	#125×C₄₇	C₂³	1	4	yes	—
166	#124×C₄₇	C₂³	1	4	yes	—
167	#124×C₄₇	C₂³	1	8	yes	—
168	#124×C₄₇	C₂³	1	8	yes	—
169	#124×C₄₇	C₂³	1	8	yes	—
170	#124×C₄₇	C₂³	1	16	yes	—
171	#124×C₄₇	C₂³	1	16	yes	—
172	#124×C₄₇	C₂³	1	4	yes	—
173	#124×C₄₇	C₂³	1	8	yes	—
174	#124×C₄₇	C₂³	1	2	yes	—
175	#124×C₄₇	C₂³	1	4	yes	—
176	#124×C₄₇	C₂³	1	8	yes	—
177	#124×C₄₇	C₂³	1	16	yes	—
178	#124×C₄₇	C₂³	1	8	yes	—
179	#124×C₄₇	C₂³	1	16	yes	—
180	#123×C₄₇	C₂³	1	4	yes	—
181	#123×C₄₇	C₂³	1	4	yes	—
182	#123×C₄₇	C₂³	1	8	yes	—
183	#123×C₄₇	C₂³	1	8	yes	—
184	#123×C₄₇	C₂³	1	16	yes	—
185	#123×C₄₇	C₂³	1	8	yes	—
186	#123×C₄₇	C₂³	1	8	yes	—
187	#123×C₄₇	C₂³	1	8	yes	—
188	#123×C₄₇	C₂³	1	8	yes	—
189	#123×C₄₇	C₂³	1	16	yes	—
190	#123×C₄₇	C₂³	1	16	yes	—
191	#123×C₄₇	C₂³	1	8	yes	—
192	#123×C₄₇	C₂³	1	16	yes	—
193	#123×C₄₇	C₂³	1	8	yes	—
194	#123×C₄₇	C₂³	1	8	yes	—
195	#123×C₄₇	C₂³	1	16	yes	—
196	#123×C₄₇	C₂³	1	16	yes	—
197	#123×C₄₇	C₂³	1	16	yes	—
198	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
199	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
200	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
201	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	—
202	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	—
203	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
204	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
205	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
206	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
207	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
208	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
209	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
210	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	—
211	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	—
212	#121×C₄₇	C₂³	1	8	yes	—
213	#121×C₄₇	C₂³	1	8	yes	—
214	#121×C₄₇	C₂³	1	8	yes	—
215	#121×C₄₇	C₂³	1	16	yes	—
216	#121×C₄₇	C₂³	1	16	yes	—
217	#121×C₄₇	C₂³	1	4	yes	—
218	#121×C₄₇	C₂³	1	8	yes	—
219	#121×C₄₇	C₂³	1	8	yes	—
220	#121×C₄₇	C₂³	1	4	yes	—
221	#121×C₄₇	C₂³	1	4	yes	—
222	#121×C₄₇	C₂³	1	16	yes	—
223	#121×C₄₇	C₂³	1	8	yes	—
224	#121×C₄₇	C₂³	1	8	yes	—
225	#121×C₄₇	C₂³	1	8	yes	—
226	#121×C₄₇	C₂³	1	16	yes	—
227	#121×C₄₇	C₂³	1	16	yes	—
228	#121×C₄₇	C₂³	1	16	yes	—
229	#121×C₄₇	C₂³	1	16	yes	—
230	#120×C₄₇	C₂³	1	8	yes	—
231	#120×C₄₇	C₂³	1	4	yes	—
232	#120×C₄₇	C₂³	1	4	yes	—
233	#120×C₄₇	C₂³	1	16	yes	—
234	#120×C₄₇	C₂³	1	16	yes	—
235	#120×C₄₇	C₂³	1	16	yes	—
236	#120×C₄₇	C₂³	1	16	yes	—
237	#120×C₄₇	C₂³	1	8	yes	—
238	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
239	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
240	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
241	C₄×Q₈×C₄₇	C₂³	1	8	yes	—
242	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
243	C₄×Q₈×C₄₇	C₂³	1	8	yes	—
244	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
245	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
246	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
247	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
248	C₄×Q₈×C₄₇	C₂³	1	8	yes	—
249	C₄×D₄×C₄₇	C₂³	1	4	yes	—
250	C₄×D₄×C₄₇	C₂³	1	2	yes	—
251	C₄×D₄×C₄₇	C₂³	1	8	yes	—
252	C₄×D₄×C₄₇	C₂³	1	8	yes	—
253	C₄×D₄×C₄₇	C₂³	1	16	yes	—
254	C₄×D₄×C₄₇	C₂³	1	8	yes	—
255	C₄×D₄×C₄₇	C₂³	1	4	yes	—
256	C₄×D₄×C₄₇	C₂³	1	8	yes	—
257	C₄×D₄×C₄₇	C₂³	1	4	yes	—
258	C₄×D₄×C₄₇	C₂³	1	16	yes	—
259	C₄×D₄×C₄₇	C₂³	1	8	yes	—
260	C₄×D₄×C₄₇	C₂³	1	2	yes	—
261	C₄×D₄×C₄₇	C₂³	1	4	yes	—
262	C₄×D₄×C₄₇	C₂³	1	4	yes	—
263	C₄×D₄×C₄₇	C₂³	1	4	yes	—
264	C₄×D₄×C₄₇	C₂³	1	8	yes	—
265	C₄×D₄×C₄₇	C₂³	1	2	yes	—
266	C₄×D₄×C₄₇	C₂³	1	4	yes	—
267	C₄×D₄×C₄₇	C₂³	1	8	yes	—
268	C₄×D₄×C₄₇	C₂³	1	8	yes	—
269	C₄×D₄×C₄₇	C₂³	1	16	yes	—
270	C₄×D₄×C₄₇	C₂³	1	8	yes	—
271	C₄×D₄×C₄₇	C₂³	1	8	yes	—
272	C₄×D₄×C₄₇	C₂³	1	8	yes	—
273	C₄×D₄×C₄₇	C₂³	1	16	yes	—
274	C₄×D₄×C₄₇	C₂³	1	16	yes	—
275	C₄×D₄×C₄₇	C₂³	1	8	yes	—
276	#117×C₄₇	C₂³	1	2	yes	—
277	#117×C₄₇	C₂³	1	8	yes	—
278	#117×C₄₇	C₂³	1	4	yes	—
279	#117×C₄₇	C₂³	1	2	yes	—
280	#117×C₄₇	C₂³	1	1	yes	characteristic
281	#117×C₄₇	C₂³	1	4	yes	—
282	#117×C₄₇	C₂³	1	4	yes	—
283	#117×C₄₇	C₂³	1	4	yes	—
284	#117×C₄₇	C₂³	1	4	yes	—
285	#117×C₄₇	C₂³	1	8	yes	—
286	#117×C₄₇	C₂³	1	16	yes	—
287	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
288	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
289	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
290	C₂×C₄⋊C₄×C₄₇	C₂³	1	16	yes	—
291	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
292	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
293	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
294	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
295	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
296	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
297	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
298	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
299	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
300	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
301	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
302	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
303	#41×C₄₇	—	2	16	no	—
304	#41×C₄₇	—	2	4	no	—
305	#41×C₄₇	—	4	4	no	—
306	#41×C₄₇	—	4	32	no	—
307	#41×C₄₇	—	4	8	no	—
308	#41×C₄₇	—	4	16	no	—
309	#41×C₄₇	—	4	4	no	—
310	#41×C₄₇	—	4	16	no	—
311	#41×C₄₇	—	4	8	no	—
312	C₂×Q₈×C₄₇	—	4	8	no	—
313	C₂×Q₈×C₄₇	—	4	8	no	—
314	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
315	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
316	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
317	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
318	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
319	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
320	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
321	C₂×D₄×C₄₇	—	2	16	no	—
322	C₂×D₄×C₄₇	—	4	16	no	—
323	C₂×D₄×C₄₇	—	4	8	no	—
324	C₂×D₄×C₄₇	—	4	8	no	—
325	C₂×D₄×C₄₇	—	4	4	no	—
326	C₂×D₄×C₄₇	—	4	8	no	—
327	C₂×D₄×C₄₇	—	4	16	no	—
328	C₂×D₄×C₄₇	—	4	16	no	—
329	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
330	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
331	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
332	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
333	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
334	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
335	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
336	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
337	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
338	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
339	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
340	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
341	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
342	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
343	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
344	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
345	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
346	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₄₇	—	4	8	no	—
348	C₂²×C₄×C₄₇	—	4	16	no	—
349	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
350	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
351	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
353	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
355	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
357	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
358	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
360	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
361	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
362	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
363	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
364	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
365	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
367	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
368	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
369	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
370	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
371	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
372	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
373	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
374	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
375	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
376	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
377	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
379	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
381	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
382	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
383	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
384	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
385	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
386	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
387	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
388	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
389	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
390	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
391	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
392	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
393	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
394	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
395	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
396	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
397	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
398	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
399	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
400	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
401	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
402	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
403	C₂²⋊C₄×C₄₇	C₂⁴	1	2	yes	—
404	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
405	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
407	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
408	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
409	C₄²×C₄₇	C₂⁴	1	4	yes	—
410	C₄²×C₄₇	C₂⁴	1	2	yes	—
411	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
412	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
413	C₄²×C₄₇	C₂⁴	1	4	yes	—
414	C₄²×C₄₇	C₂⁴	1	8	yes	—
415	C₄²×C₄₇	C₂⁴	1	4	yes	—
416	C₄²×C₄₇	C₂⁴	1	8	yes	—
417	C₄²×C₄₇	C₂⁴	1	4	yes	—
418	C₄²×C₄₇	C₂⁴	1	2	yes	—
419	C₄²×C₄₇	C₂⁴	1	8	yes	—
420	C₄²×C₄₇	C₂⁴	1	8	yes	—
421	C₂³×C₄₇	—	2	16	no	—
422	C₂³×C₄₇	—	4	4	no	—
423	C₂³×C₄₇	—	4	16	no	—
424	C₂³×C₄₇	—	4	8	no	—
425	C₂³×C₄₇	—	4	4	no	—
426	C₂³×C₄₇	—	4	8	no	—
427	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
428	C₂³×C₄₇	C₂⁵	1	4	yes	—
429	C₂³×C₄₇	C₂⁵	1	4	yes	—
430	C₂³×C₄₇	C₂⁵	1	8	yes	—
431	C₂³×C₄₇	C₂⁵	1	2	yes	—
432	Q₈×C₄₇	—	2	8	no	—
433	Q₈×C₄₇	—	2	2	no	—
434	Q₈×C₄₇	—	2	4	no	—
435	Q₈×C₄₇	—	2	8	no	—
436	Q₈×C₄₇	—	4	8	no	—
437	Q₈×C₄₇	—	4	8	no	—
438	Q₈×C₄₇	—	4	2	no	—
439	D₄×C₄₇	—	2	16	no	—
440	D₄×C₄₇	—	2	4	no	—
441	D₄×C₄₇	—	2	16	no	—
442	D₄×C₄₇	—	2	8	no	—
443	D₄×C₄₇	—	2	8	no	—
444	D₄×C₄₇	—	2	4	no	—
445	D₄×C₄₇	—	2	16	no	—
446	D₄×C₄₇	—	4	2	no	—
447	D₄×C₄₇	—	4	4	no	—
448	D₄×C₄₇	—	4	4	no	—
449	D₄×C₄₇	—	4	8	no	—
450	D₄×C₄₇	—	4	8	no	—
451	D₄×C₄₇	—	4	8	no	—
452	D₄×C₄₇	—	4	16	no	—
453	D₄×C₄₇	—	4	16	no	—
454	D₄×C₄₇	—	4	16	no	—
455	D₄×C₄₇	—	4	4	no	—
456	D₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
457	C₂×C₄×C₄₇	—	2	16	no	—
458	C₂×C₄×C₄₇	—	2	4	no	—
459	C₂×C₄×C₄₇	—	2	8	no	—
460	C₂×C₄×C₄₇	—	2	8	no	—
461	C₂×C₄×C₄₇	—	2	2	no	—
462	C₂×C₄×C₄₇	—	2	8	no	—
463	C₂×C₄×C₄₇	—	2	4	no	—
464	C₂×C₄×C₄₇	—	2	8	no	—
465	C₂×C₄×C₄₇	—	4	4	no	—
466	C₂×C₄×C₄₇	—	4	8	no	—
467	C₂×C₄×C₄₇	—	4	8	no	—
468	C₂×C₄×C₄₇	—	4	16	no	—
469	C₂×C₄×C₄₇	—	4	8	no	—
470	C₂×C₄×C₄₇	—	4	8	no	—
471	C₂×C₄×C₄₇	—	4	16	no	—
472	C₂×C₄×C₄₇	—	4	4	no	—
473	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
474	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
475	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
476	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
477	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
478	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
479	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
480	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
481	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
482	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
483	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
484	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
485	#63021	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
486	C₂²×C₄₇	—	2	4	no	—
487	C₂²×C₄₇	—	2	4	no	—
488	C₂²×C₄₇	—	2	4	no	—
489	C₂²×C₄₇	—	2	1	no	—
490	C₂²×C₄₇	—	2	8	no	—
491	C₂²×C₄₇	—	2	4	no	—
492	C₂²×C₄₇	—	2	2	no	—
493	C₂²×C₄₇	—	2	4	no	—
494	C₂²×C₄₇	—	2	16	no	—
495	C₂²×C₄₇	—	2	8	no	—
496	C₂²×C₄₇	—	8	16	no	—
497	C₂²×C₄₇	—	8	8	no	—
498	C₂²×C₄₇	—	16	4	no	—
499	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
500	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
501	C₄×C₄₇	—	2	4	no	—
502	C₄×C₄₇	—	2	1	no	—
503	C₄×C₄₇	—	2	4	no	—
504	C₄×C₄₇	—	2	2	no	—
505	C₄×C₄₇	—	2	8	no	—
506	C₄×C₄₇	—	2	4	no	—
507	C₄×C₄₇	—	2	2	no	—
508	C₄×C₄₇	—	2	4	no	—
509	C₄×C₄₇	—	2	8	no	—
510	C₄×C₄₇	—	2	4	no	—
511	C₄×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
512	C₄×C₄₇	#585	1	4	yes	—
513	#3558	C₂×C₄₇	1	8	yes	complemented
514	#3554	C₂×C₄₇	1	4	yes	complemented
515	#3550	C₂×C₄₇	1	1	yes	characteristic, complemented
516	#3543	C₂×C₄₇	1	2	yes	complemented
517	#3540	C₂×C₄₇	1	4	yes	complemented
518	#3533	C₂×C₄₇	1	8	yes	complemented
519	#3522	C₂×C₄₇	1	4	yes	complemented
520	#3514	C₂×C₄₇	1	4	yes	complemented
521	#3513	C₂×C₄₇	1	8	yes	complemented
522	#3508	C₂×C₄₇	1	2	yes	complemented
523	#3506	C₂×C₄₇	1	4	yes	complemented
524	#3498	C₂×C₄₇	1	1	yes	characteristic, complemented
525	#3485	C₂×C₄₇	1	4	yes	complemented
526	#3482	C₂×C₄₇	1	2	yes	complemented
527	#3481	C₂×C₄₇	1	1	yes	characteristic, complemented
528	C₂×#559	C₂×C₄₇	1	2	yes	complemented
529	D₄×#41	C₂×C₄₇	1	4	yes	complemented
530	C₂×C₄₇	—	2	4	no	—
531	C₂×C₄₇	—	4	4	no	—
532	C₂×C₄₇	—	4	4	no	—
533	C₂×C₄₇	—	4	8	no	—
534	C₂×C₄₇	—	4	1	no	—
535	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
536	C₂×C₄₇	C₂×#585	1	2	yes	—
537	C₂×H(5,𝔽₂)	C₂²×C₄₇	1	2	yes	complemented
538	C₂²×#41	C₂²×C₄₇	1	4	yes	complemented
539	#563	C₂²×C₄₇	1	4	yes	complemented
540	#562	C₂²×C₄₇	1	16	yes	complemented
541	H(3,𝔽₄)	C₂²×C₄₇	1	8	yes	complemented
542	#560	C₂²×C₄₇	1	8	yes	complemented
543	#559	C₂²×C₄₇	1	1	yes	characteristic, complemented
544	#559	C₂²×C₄₇	1	8	yes	complemented
545	#559	C₂²×C₄₇	1	4	yes	complemented
546	#559	C₂²×C₄₇	1	8	yes	complemented
547	#559	C₂²×C₄₇	1	2	yes	complemented
548	#559	C₂²×C₄₇	1	8	yes	complemented
549	#559	C₂²×C₄₇	1	8	yes	complemented
550	#559	C₂²×C₄₇	1	4	yes	complemented
551	Q₈²	C₂²×C₄₇	1	2	yes	complemented
552	#557	C₂²×C₄₇	1	2	yes	complemented
553	#556	C₂²×C₄₇	1	2	yes	complemented
554	#556	C₂²×C₄₇	1	4	yes	complemented
555	#556	C₂²×C₄₇	1	4	yes	complemented
556	#555	C₂²×C₄₇	1	8	yes	complemented
557	#554	C₂²×C₄₇	1	2	yes	complemented
558	#554	C₂²×C₄₇	1	8	yes	complemented
559	#553	C₂²×C₄₇	1	4	yes	complemented
560	#553	C₂²×C₄₇	1	16	yes	complemented
561	#552	C₂²×C₄₇	1	4	yes	complemented
562	#552	C₂²×C₄₇	1	8	yes	complemented
563	#551	C₂²×C₄₇	1	4	yes	complemented
564	#551	C₂²×C₄₇	1	8	yes	complemented
565	#551	C₂²×C₄₇	1	16	yes	complemented
566	#550	C₂²×C₄₇	1	4	yes	complemented
567	#550	C₂²×C₄₇	1	4	yes	complemented
568	#550	C₂²×C₄₇	1	4	yes	complemented
569	D₄×Q₈	C₂²×C₄₇	1	4	yes	complemented
570	D₄×Q₈	C₂²×C₄₇	1	2	yes	complemented
571	#548	C₂²×C₄₇	1	8	yes	complemented
572	#548	C₂²×C₄₇	1	4	yes	complemented
573	#548	C₂²×C₄₇	1	8	yes	complemented
574	#547	C₂²×C₄₇	1	2	yes	complemented
575	#547	C₂²×C₄₇	1	8	yes	complemented
576	#547	C₂²×C₄₇	1	4	yes	complemented
577	#547	C₂²×C₄₇	1	8	yes	complemented
578	#547	C₂²×C₄₇	1	16	yes	complemented
579	#546	C₂²×C₄₇	1	8	yes	complemented
580	#546	C₂²×C₄₇	1	16	yes	complemented
581	#546	C₂²×C₄₇	1	4	yes	complemented
582	#546	C₂²×C₄₇	1	8	yes	complemented
583	#546	C₂²×C₄₇	1	16	yes	complemented
584	#546	C₂²×C₄₇	1	8	yes	complemented
585	#546	C₂²×C₄₇	1	8	yes	complemented
586	D₄²	C₂²×C₄₇	1	4	yes	complemented
587	D₄²	C₂²×C₄₇	1	8	yes	complemented
588	D₄²	C₂²×C₄₇	1	1	yes	characteristic, complemented
589	D₄²	C₂²×C₄₇	1	8	yes	complemented
590	#542	C₂²×C₄₇	1	8	yes	complemented
591	#542	C₂²×C₄₇	1	8	yes	complemented
592	#542	C₂²×C₄₇	1	16	yes	complemented
593	#542	C₂²×C₄₇	1	8	yes	complemented
594	#540	C₂²×C₄₇	1	8	yes	complemented
595	#540	C₂²×C₄₇	1	8	yes	complemented
596	#539	C₂²×C₄₇	1	16	yes	complemented
597	#538	C₂²×C₄₇	1	16	yes	complemented
598	#538	C₂²×C₄₇	1	16	yes	complemented
599	#538	C₂²×C₄₇	1	16	yes	complemented
600	#536	C₂²×C₄₇	1	4	yes	complemented
601	#536	C₂²×C₄₇	1	4	yes	complemented
602	#535	C₂²×C₄₇	1	4	yes	complemented
603	#535	C₂²×C₄₇	1	2	yes	complemented
604	#535	C₂²×C₄₇	1	8	yes	complemented
605	#535	C₂²×C₄₇	1	4	yes	complemented
606	#534	C₂²×C₄₇	1	8	yes	complemented
607	#534	C₂²×C₄₇	1	8	yes	complemented
608	#533	C₂²×C₄₇	1	4	yes	complemented
609	#533	C₂²×C₄₇	1	2	yes	complemented
610	#532	C₂²×C₄₇	1	1	yes	characteristic
611	#532	C₂²×C₄₇	1	4	yes	complemented
612	#532	C₂²×C₄₇	1	8	yes	complemented
613	#532	C₂²×C₄₇	1	2	yes	complemented
614	#532	C₂²×C₄₇	1	4	yes	complemented
615	C₂×#127	C₂²×C₄₇	1	2	yes	—
616	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic, complemented
617	#529	C₂²×C₄₇	1	4	yes	complemented
618	#529	C₂²×C₄₇	1	8	yes	complemented
619	#529	C₂²×C₄₇	1	4	yes	complemented
620	#529	C₂²×C₄₇	1	8	yes	complemented
621	C₂×#124	C₂²×C₄₇	1	8	yes	complemented
622	#525	C₂²×C₄₇	1	8	yes	complemented
623	#525	C₂²×C₄₇	1	16	yes	complemented
624	#525	C₂²×C₄₇	1	4	yes	complemented
625	#525	C₂²×C₄₇	1	4	yes	complemented
626	C₂×#123	C₂²×C₄₇	1	8	yes	complemented
627	C₂×#123	C₂²×C₄₇	1	8	yes	complemented
628	#520	C₂²×C₄₇	1	8	yes	complemented
629	#518	C₂²×C₄₇	1	4	yes	complemented
630	#518	C₂²×C₄₇	1	4	yes	complemented
631	C₄×#41	C₂²×C₄₇	1	4	yes	complemented
632	C₄×#41	C₂²×C₄₇	1	2	yes	complemented
633	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic, complemented
634	C₂×C₄×Q₈	C₂²×C₄₇	1	4	yes	complemented
635	C₂×C₄×D₄	C₂²×C₄₇	1	8	yes	complemented
636	C₂×C₄×D₄	C₂²×C₄₇	1	4	yes	complemented
637	C₄₇	#63021	1	1	yes	characteristic, direct product factor, Sylow
638	H(5,𝔽₂)	—	4	8	no	—
639	C₂×#41	—	4	16	no	—
640	C₂×#41	C₂³×C₄₇	1	4	yes	—
641	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
642	C₂×#41	C₂³×C₄₇	1	2	yes	—
643	C₂×#41	C₂³×C₄₇	1	8	yes	—
644	C₂×#41	C₂³×C₄₇	1	2	yes	—
645	C₂×#41	C₂³×C₄₇	1	16	yes	—
646	C₂×#41	C₂³×C₄₇	1	8	yes	—
647	C₂×#41	C₂³×C₄₇	1	4	yes	—
648	C₂×#41	C₂³×C₄₇	1	4	yes	—
649	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
650	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
651	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
652	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
653	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
654	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
655	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
656	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
657	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
658	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
659	C₂³×C₄	C₂³×C₄₇	1	8	yes	—
660	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
661	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
662	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
663	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
664	C₄⋊Q₈	C₂³×C₄₇	1	8	yes	—
665	C₄⋊Q₈	C₂³×C₄₇	1	4	yes	—
666	C₄⋊Q₈	C₂³×C₄₇	1	4	yes	—
667	C₄⋊Q₈	C₂³×C₄₇	1	8	yes	—
668	#127	C₂³×C₄₇	1	1	yes	characteristic
669	#127	C₂³×C₄₇	1	2	yes	—
670	#127	C₂³×C₄₇	1	4	yes	—
671	#127	C₂³×C₄₇	1	8	yes	—
672	#127	C₂³×C₄₇	1	4	yes	—
673	#127	C₂³×C₄₇	1	2	yes	—
674	#127	C₂³×C₄₇	1	8	yes	—
675	#126	C₂³×C₄₇	1	16	yes	—
676	#126	C₂³×C₄₇	1	8	yes	—
677	#126	C₂³×C₄₇	1	8	yes	—
678	#126	C₂³×C₄₇	1	8	yes	—
679	#126	C₂³×C₄₇	1	8	yes	—
680	#126	C₂³×C₄₇	1	16	yes	—
681	#125	C₂³×C₄₇	1	4	yes	—
682	#125	C₂³×C₄₇	1	8	yes	—
683	#125	C₂³×C₄₇	1	4	yes	—
684	#125	C₂³×C₄₇	1	8	yes	—
685	#125	C₂³×C₄₇	1	4	yes	—
686	#124	C₂³×C₄₇	1	4	yes	—
687	#124	C₂³×C₄₇	1	8	yes	—
688	#124	C₂³×C₄₇	1	8	yes	—
689	#124	C₂³×C₄₇	1	8	yes	—
690	#124	C₂³×C₄₇	1	16	yes	—
691	#124	C₂³×C₄₇	1	16	yes	—
692	#124	C₂³×C₄₇	1	4	yes	—
693	#124	C₂³×C₄₇	1	8	yes	—
694	#124	C₂³×C₄₇	1	2	yes	—
695	#124	C₂³×C₄₇	1	4	yes	—
696	#124	C₂³×C₄₇	1	8	yes	—
697	#124	C₂³×C₄₇	1	16	yes	—
698	#124	C₂³×C₄₇	1	8	yes	—
699	#124	C₂³×C₄₇	1	16	yes	—
700	#123	C₂³×C₄₇	1	4	yes	—
701	#123	C₂³×C₄₇	1	4	yes	—
702	#123	C₂³×C₄₇	1	8	yes	—
703	#123	C₂³×C₄₇	1	8	yes	—
704	#123	C₂³×C₄₇	1	16	yes	—
705	#123	C₂³×C₄₇	1	8	yes	—
706	#123	C₂³×C₄₇	1	8	yes	—
707	#123	C₂³×C₄₇	1	8	yes	—
708	#123	C₂³×C₄₇	1	8	yes	—
709	#123	C₂³×C₄₇	1	16	yes	—
710	#123	C₂³×C₄₇	1	16	yes	—
711	#123	C₂³×C₄₇	1	8	yes	—
712	#123	C₂³×C₄₇	1	16	yes	—
713	#123	C₂³×C₄₇	1	8	yes	—
714	#123	C₂³×C₄₇	1	8	yes	—
715	#123	C₂³×C₄₇	1	16	yes	—
716	#123	C₂³×C₄₇	1	16	yes	—
717	#123	C₂³×C₄₇	1	16	yes	—
718	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
719	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
720	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
721	C₂²⋊Q₈	C₂³×C₄₇	1	16	yes	—
722	C₂²⋊Q₈	C₂³×C₄₇	1	16	yes	—
723	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
724	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
725	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
726	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
727	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
728	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
729	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
730	C₂²⋊Q₈	C₂³×C₄₇	1	16	yes	—
731	C₂²⋊Q₈	C₂³×C₄₇	1	16	yes	—
732	#121	C₂³×C₄₇	1	8	yes	—
733	#121	C₂³×C₄₇	1	8	yes	—
734	#121	C₂³×C₄₇	1	8	yes	—
735	#121	C₂³×C₄₇	1	16	yes	—
736	#121	C₂³×C₄₇	1	16	yes	—
737	#121	C₂³×C₄₇	1	4	yes	—
738	#121	C₂³×C₄₇	1	8	yes	—
739	#121	C₂³×C₄₇	1	8	yes	—
740	#121	C₂³×C₄₇	1	4	yes	—
741	#121	C₂³×C₄₇	1	4	yes	—
742	#121	C₂³×C₄₇	1	16	yes	—
743	#121	C₂³×C₄₇	1	8	yes	—
744	#121	C₂³×C₄₇	1	8	yes	—
745	#121	C₂³×C₄₇	1	8	yes	—
746	#121	C₂³×C₄₇	1	16	yes	—
747	#121	C₂³×C₄₇	1	16	yes	—
748	#121	C₂³×C₄₇	1	16	yes	—
749	#121	C₂³×C₄₇	1	16	yes	—
750	#120	C₂³×C₄₇	1	8	yes	—
751	#120	C₂³×C₄₇	1	4	yes	—
752	#120	C₂³×C₄₇	1	4	yes	—
753	#120	C₂³×C₄₇	1	16	yes	—
754	#120	C₂³×C₄₇	1	16	yes	—
755	#120	C₂³×C₄₇	1	16	yes	—
756	#120	C₂³×C₄₇	1	16	yes	—
757	#120	C₂³×C₄₇	1	8	yes	—
758	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
759	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
760	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
761	C₄×Q₈	C₂³×C₄₇	1	8	yes	—
762	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
763	C₄×Q₈	C₂³×C₄₇	1	8	yes	—
764	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
765	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
766	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
767	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
768	C₄×Q₈	C₂³×C₄₇	1	8	yes	—
769	C₄×D₄	C₂³×C₄₇	1	4	yes	—
770	C₄×D₄	C₂³×C₄₇	1	2	yes	—
771	C₄×D₄	C₂³×C₄₇	1	8	yes	—
772	C₄×D₄	C₂³×C₄₇	1	8	yes	—
773	C₄×D₄	C₂³×C₄₇	1	16	yes	—
774	C₄×D₄	C₂³×C₄₇	1	8	yes	—
775	C₄×D₄	C₂³×C₄₇	1	4	yes	—
776	C₄×D₄	C₂³×C₄₇	1	8	yes	—
777	C₄×D₄	C₂³×C₄₇	1	4	yes	—
778	C₄×D₄	C₂³×C₄₇	1	16	yes	—
779	C₄×D₄	C₂³×C₄₇	1	8	yes	—
780	C₄×D₄	C₂³×C₄₇	1	2	yes	—
781	C₄×D₄	C₂³×C₄₇	1	4	yes	—
782	C₄×D₄	C₂³×C₄₇	1	4	yes	—
783	C₄×D₄	C₂³×C₄₇	1	4	yes	—
784	C₄×D₄	C₂³×C₄₇	1	8	yes	—
785	C₄×D₄	C₂³×C₄₇	1	2	yes	—
786	C₄×D₄	C₂³×C₄₇	1	4	yes	—
787	C₄×D₄	C₂³×C₄₇	1	8	yes	—
788	C₄×D₄	C₂³×C₄₇	1	8	yes	—
789	C₄×D₄	C₂³×C₄₇	1	16	yes	—
790	C₄×D₄	C₂³×C₄₇	1	8	yes	—
791	C₄×D₄	C₂³×C₄₇	1	8	yes	—
792	C₄×D₄	C₂³×C₄₇	1	8	yes	—
793	C₄×D₄	C₂³×C₄₇	1	16	yes	—
794	C₄×D₄	C₂³×C₄₇	1	16	yes	—
795	C₄×D₄	C₂³×C₄₇	1	8	yes	—
796	#117	C₂³×C₄₇	1	2	yes	—
797	#117	C₂³×C₄₇	1	8	yes	—
798	#117	C₂³×C₄₇	1	4	yes	—
799	#117	C₂³×C₄₇	1	2	yes	—
800	#117	C₂³×C₄₇	1	1	yes	characteristic
801	#117	C₂³×C₄₇	1	4	yes	—
802	#117	C₂³×C₄₇	1	4	yes	—
803	#117	C₂³×C₄₇	1	4	yes	—
804	#117	C₂³×C₄₇	1	4	yes	—
805	#117	C₂³×C₄₇	1	8	yes	—
806	#117	C₂³×C₄₇	1	16	yes	—
807	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
808	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
809	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
810	C₂×C₄⋊C₄	C₂³×C₄₇	1	16	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₄₇	1	16	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₄₇	1	16	yes	—
816	C₂×C₄²	C₂³×C₄₇	1	8	yes	—
817	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
818	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
819	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
820	C₂⁴	C₂⁴×C₄₇	1	8	yes	—
821	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
822	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
823	#41	—	2	16	no	—
824	#41	—	2	4	no	—
825	#41	—	4	4	no	—
826	#41	—	4	32	no	—
827	#41	—	4	8	no	—
828	#41	—	4	16	no	—
829	#41	—	4	4	no	—
830	#41	—	4	16	no	—
831	#41	—	4	8	no	—
832	C₂×Q₈	—	4	8	no	—
833	C₂×Q₈	—	4	8	no	—
834	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
835	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
836	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
837	C₂×Q₈	C₂⁴×C₄₇	1	1	yes	characteristic
838	C₂×Q₈	C₂⁴×C₄₇	1	8	yes	—
839	C₂×Q₈	C₂⁴×C₄₇	1	8	yes	—
840	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
841	C₂×D₄	—	2	16	no	—
842	C₂×D₄	—	4	16	no	—
843	C₂×D₄	—	4	8	no	—
844	C₂×D₄	—	4	8	no	—
845	C₂×D₄	—	4	4	no	—
846	C₂×D₄	—	4	8	no	—
847	C₂×D₄	—	4	16	no	—
848	C₂×D₄	—	4	16	no	—
849	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
850	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
851	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
852	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
853	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
854	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
855	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
856	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
857	C₂×D₄	C₂⁴×C₄₇	1	16	yes	—
858	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
859	C₂×D₄	C₂⁴×C₄₇	1	16	yes	—
860	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
861	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
862	C₂×D₄	C₂⁴×C₄₇	1	16	yes	—
863	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
864	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
865	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
866	C₂×D₄	C₂⁴×C₄₇	1	1	yes	characteristic
867	C₂²×C₄	—	4	8	no	—
868	C₂²×C₄	—	4	16	no	—
869	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
870	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
871	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
873	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
875	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
877	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
878	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
879	C₂²×C₄	C₂⁴×C₄₇	1	16	yes	—
880	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
881	C₂²×C₄	C₂⁴×C₄₇	1	16	yes	—
882	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
883	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
884	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
885	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
886	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
887	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
888	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
889	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
890	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
891	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
892	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
893	C₄⋊C₄	C₂⁴×C₄₇	1	16	yes	—
894	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
895	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
896	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
897	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
898	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
899	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
900	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
901	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
902	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
903	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
904	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
905	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
906	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
907	C₂²⋊C₄	C₂⁴×C₄₇	1	4	yes	—
908	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
909	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
910	C₂²⋊C₄	C₂⁴×C₄₇	1	4	yes	—
911	C₂²⋊C₄	C₂⁴×C₄₇	1	16	yes	—
912	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
913	C₂²⋊C₄	C₂⁴×C₄₇	1	4	yes	—
914	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
915	C₂²⋊C₄	C₂⁴×C₄₇	1	4	yes	—
916	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
917	C₂²⋊C₄	C₂⁴×C₄₇	1	16	yes	—
918	C₂²⋊C₄	C₂⁴×C₄₇	1	16	yes	—
919	C₂²⋊C₄	C₂⁴×C₄₇	1	16	yes	—
920	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
921	C₂²⋊C₄	C₂⁴×C₄₇	1	16	yes	—
922	C₂²⋊C₄	C₂⁴×C₄₇	1	4	yes	—
923	C₂²⋊C₄	C₂⁴×C₄₇	1	2	yes	—
924	C₂²⋊C₄	C₂⁴×C₄₇	1	4	yes	—
925	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
926	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
927	C₂²⋊C₄	C₂⁴×C₄₇	1	16	yes	—
928	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
929	C₄²	C₂⁴×C₄₇	1	4	yes	—
930	C₄²	C₂⁴×C₄₇	1	2	yes	—
931	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
932	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
933	C₄²	C₂⁴×C₄₇	1	4	yes	—
934	C₄²	C₂⁴×C₄₇	1	8	yes	—
935	C₄²	C₂⁴×C₄₇	1	4	yes	—
936	C₄²	C₂⁴×C₄₇	1	8	yes	—
937	C₄²	C₂⁴×C₄₇	1	4	yes	—
938	C₄²	C₂⁴×C₄₇	1	2	yes	—
939	C₄²	C₂⁴×C₄₇	1	8	yes	—
940	C₄²	C₂⁴×C₄₇	1	8	yes	—
941	C₂³	—	2	16	no	—
942	C₂³	—	4	4	no	—
943	C₂³	—	4	16	no	—
944	C₂³	—	4	8	no	—
945	C₂³	—	4	4	no	—
946	C₂³	—	4	8	no	—
947	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
948	C₂³	C₂⁵×C₄₇	1	4	yes	—
949	C₂³	C₂⁵×C₄₇	1	4	yes	—
950	C₂³	C₂⁵×C₄₇	1	8	yes	—
951	C₂³	C₂⁵×C₄₇	1	2	yes	—
952	Q₈	—	2	8	no	—
953	Q₈	—	2	2	no	—
954	Q₈	—	2	4	no	—
955	Q₈	—	2	8	no	—
956	Q₈	—	4	8	no	—
957	Q₈	—	4	8	no	—
958	Q₈	—	4	2	no	—
959	D₄	—	2	16	no	—
960	D₄	—	2	4	no	—
961	D₄	—	2	16	no	—
962	D₄	—	2	8	no	—
963	D₄	—	2	8	no	—
964	D₄	—	2	4	no	—
965	D₄	—	2	16	no	—
966	D₄	—	4	2	no	—
967	D₄	—	4	4	no	—
968	D₄	—	4	4	no	—
969	D₄	—	4	8	no	—
970	D₄	—	4	8	no	—
971	D₄	—	4	8	no	—
972	D₄	—	4	16	no	—
973	D₄	—	4	16	no	—
974	D₄	—	4	16	no	—
975	D₄	—	4	4	no	—
976	D₄	H(5,𝔽₂)×C₄₇	1	4	yes	—
977	C₂×C₄	—	2	16	no	—
978	C₂×C₄	—	2	4	no	—
979	C₂×C₄	—	2	8	no	—
980	C₂×C₄	—	2	8	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	8	no	—
983	C₂×C₄	—	2	4	no	—
984	C₂×C₄	—	2	8	no	—
985	C₂×C₄	—	4	4	no	—
986	C₂×C₄	—	4	8	no	—
987	C₂×C₄	—	4	8	no	—
988	C₂×C₄	—	4	16	no	—
989	C₂×C₄	—	4	8	no	—
990	C₂×C₄	—	4	8	no	—
991	C₂×C₄	—	4	16	no	—
992	C₂×C₄	—	4	4	no	—
993	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
994	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
995	C₂×C₄	C₂⁵×C₄₇	1	8	yes	—
996	C₂×C₄	C₂⁵×C₄₇	1	2	yes	—
997	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
998	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
999	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
1000	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
1001	C₂×C₄	C₂⁵×C₄₇	1	8	yes	—
1002	C₂×C₄	C₂⁵×C₄₇	1	2	yes	—
1003	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
1004	C₂×C₄	C₂⁵×C₄₇	1	2	yes	—
1005	C₂²	—	2	4	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	2	4	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	8	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	16	no	—
1014	C₂²	—	2	8	no	—
1015	C₂²	—	8	16	no	—
1016	C₂²	—	8	8	no	—
1017	C₂²	—	16	4	no	—
1018	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	4	yes	—
1019	C₂²	C₂⁶×C₄₇	1	1	yes	characteristic
1020	C₄	—	2	4	no	—
1021	C₄	—	2	1	no	—
1022	C₄	—	2	4	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	8	no	—
1025	C₄	—	2	4	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	4	no	—
1028	C₄	—	2	8	no	—
1029	C₄	—	2	4	no	—
1030	C₄	C₂×H(5,𝔽₂)×C₄₇	1	2	yes	—
1031	C₄	C₄₇×#585	1	4	yes	—
1032	C₂	—	2	4	no	—
1033	C₂	—	4	4	no	—
1034	C₂	—	4	4	no	—
1035	C₂	—	4	8	no	—
1036	C₂	—	4	1	no	—
1037	C₂	C₂²×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
1038	C₂	C₂×C₄₇×#585	1	2	yes	—

	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×#3558	C₂	semidirect
2. C₄₇×#3554	C₂	semidirect
3. C₄₇×#3550	C₂	semidirect
4. C₄₇×#3543	C₂	semidirect
5. C₄₇×#3540	C₂	semidirect
6. C₄₇×#3533	C₂	semidirect
7. C₄₇×#3522	C₂	semidirect
8. C₄₇×#3514	C₂	semidirect
9. C₄₇×#3513	C₂	semidirect
10. C₄₇×#3508	C₂	semidirect
11. C₄₇×#3506	C₂	semidirect
12. C₄₇×#3498	C₂	semidirect
13. C₄₇×#3485	C₂	semidirect
14. C₄₇×#3482	C₂	semidirect
15. C₄₇×#3481	C₂	semidirect
16. C₂×C₄₇×#559	C₂	semidirect
17. D₄×#41×C₄₇	C₂	semidirect
18. C₂×H(5,𝔽₂)×C₄₇	C₂²	semidirect
19. C₂²×#41×C₄₇	C₂²	semidirect
20. C₄₇×#563	C₂²	semidirect
21. C₄₇×#562	C₂²	semidirect
22. C₄₇×H(3,𝔽₄)	C₂²	semidirect
23. C₄₇×#560	C₂²	semidirect
24. C₄₇×#559	C₂²	semidirect
25. C₄₇×#559	C₂²	semidirect
26. C₄₇×#559	C₂²	semidirect
27. C₄₇×#559	C₂²	semidirect
28. C₄₇×#559	C₂²	semidirect
29. C₄₇×#559	C₂²	semidirect
30. C₄₇×#559	C₂²	semidirect
31. C₄₇×#559	C₂²	semidirect
32. Q₈²×C₄₇	C₂²	semidirect
33. C₄₇×#557	C₂²	semidirect
34. C₄₇×#556	C₂²	semidirect
35. C₄₇×#556	C₂²	semidirect
36. C₄₇×#556	C₂²	semidirect
37. C₄₇×#555	C₂²	semidirect
38. C₄₇×#554	C₂²	semidirect
39. C₄₇×#554	C₂²	semidirect
40. C₄₇×#553	C₂²	semidirect
41. C₄₇×#553	C₂²	semidirect
42. C₄₇×#552	C₂²	semidirect
43. C₄₇×#552	C₂²	semidirect
44. C₄₇×#551	C₂²	semidirect
45. C₄₇×#551	C₂²	semidirect
46. C₄₇×#551	C₂²	semidirect
47. C₄₇×#550	C₂²	semidirect
48. C₄₇×#550	C₂²	semidirect
49. C₄₇×#550	C₂²	semidirect
50. D₄×Q₈×C₄₇	C₂²	semidirect
51. D₄×Q₈×C₄₇	C₂²	semidirect
52. C₄₇×#548	C₂²	semidirect
53. C₄₇×#548	C₂²	semidirect
54. C₄₇×#548	C₂²	semidirect
55. C₄₇×#547	C₂²	semidirect
56. C₄₇×#547	C₂²	semidirect
57. C₄₇×#547	C₂²	semidirect
58. C₄₇×#547	C₂²	semidirect
59. C₄₇×#547	C₂²	semidirect
60. C₄₇×#546	C₂²	semidirect
61. C₄₇×#546	C₂²	semidirect
62. C₄₇×#546	C₂²	semidirect
63. C₄₇×#546	C₂²	semidirect
64. C₄₇×#546	C₂²	semidirect
65. C₄₇×#546	C₂²	semidirect
66. C₄₇×#546	C₂²	semidirect
67. D₄²×C₄₇	C₂²	semidirect
68. D₄²×C₄₇	C₂²	semidirect
69. D₄²×C₄₇	C₂²	semidirect
70. D₄²×C₄₇	C₂²	semidirect
71. C₄₇×#542	C₂²	semidirect
72. C₄₇×#542	C₂²	semidirect
73. C₄₇×#542	C₂²	semidirect
74. C₄₇×#542	C₂²	semidirect
75. C₄₇×#540	C₂²	semidirect
76. C₄₇×#540	C₂²	semidirect
77. C₄₇×#539	C₂²	semidirect
78. C₄₇×#538	C₂²	semidirect
79. C₄₇×#538	C₂²	semidirect
80. C₄₇×#538	C₂²	semidirect
81. C₄₇×#536	C₂²	semidirect
82. C₄₇×#536	C₂²	semidirect
83. C₄₇×#535	C₂²	semidirect
84. C₄₇×#535	C₂²	semidirect
85. C₄₇×#535	C₂²	semidirect
86. C₄₇×#535	C₂²	semidirect
87. C₄₇×#534	C₂²	semidirect
88. C₄₇×#534	C₂²	semidirect
89. C₄₇×#533	C₂²	semidirect
90. C₄₇×#533	C₂²	semidirect
92. C₄₇×#532	C₂²	semidirect
93. C₄₇×#532	C₂²	semidirect
94. C₄₇×#532	C₂²	semidirect
95. C₄₇×#532	C₂²	semidirect
97. C₂×#127×C₄₇	C₂²	semidirect
98. C₄₇×#529	C₂²	semidirect
99. C₄₇×#529	C₂²	semidirect
100. C₄₇×#529	C₂²	semidirect
101. C₄₇×#529	C₂²	semidirect
102. C₂×#124×C₄₇	C₂²	semidirect
103. C₄₇×#525	C₂²	semidirect
104. C₄₇×#525	C₂²	semidirect
105. C₄₇×#525	C₂²	semidirect
106. C₄₇×#525	C₂²	semidirect
107. C₂×#123×C₄₇	C₂²	semidirect
108. C₂×#123×C₄₇	C₂²	semidirect
109. C₄₇×#520	C₂²	semidirect
110. C₄₇×#518	C₂²	semidirect
111. C₄₇×#518	C₂²	semidirect
112. C₄×#41×C₄₇	C₂²	semidirect
113. C₄×#41×C₄₇	C₂²	semidirect
114. C₄×#41×C₄₇	C₂²	semidirect
115. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
116. C₂×C₄×D₄×C₄₇	C₂²	semidirect
117. C₂×C₄×D₄×C₄₇	C₂²	semidirect
485. #63021	C₄₇	direct (N × H)
513. #3558	C₂×C₄₇	semidirect
514. #3554	C₂×C₄₇	semidirect
515. #3550	C₂×C₄₇	semidirect
516. #3543	C₂×C₄₇	semidirect
517. #3540	C₂×C₄₇	semidirect
518. #3533	C₂×C₄₇	semidirect
519. #3522	C₂×C₄₇	semidirect
520. #3514	C₂×C₄₇	semidirect
521. #3513	C₂×C₄₇	semidirect
522. #3508	C₂×C₄₇	semidirect
523. #3506	C₂×C₄₇	semidirect
524. #3498	C₂×C₄₇	semidirect
525. #3485	C₂×C₄₇	semidirect
526. #3482	C₂×C₄₇	semidirect
527. #3481	C₂×C₄₇	semidirect
528. C₂×#559	C₂×C₄₇	semidirect
529. D₄×#41	C₂×C₄₇	semidirect
537. C₂×H(5,𝔽₂)	C₂²×C₄₇	semidirect
538. C₂²×#41	C₂²×C₄₇	semidirect
539. #563	C₂²×C₄₇	semidirect
540. #562	C₂²×C₄₇	semidirect
541. H(3,𝔽₄)	C₂²×C₄₇	semidirect
542. #560	C₂²×C₄₇	semidirect
543. #559	C₂²×C₄₇	semidirect
544. #559	C₂²×C₄₇	semidirect
545. #559	C₂²×C₄₇	semidirect
546. #559	C₂²×C₄₇	semidirect
547. #559	C₂²×C₄₇	semidirect
548. #559	C₂²×C₄₇	semidirect
549. #559	C₂²×C₄₇	semidirect
550. #559	C₂²×C₄₇	semidirect
551. Q₈²	C₂²×C₄₇	semidirect
552. #557	C₂²×C₄₇	semidirect
553. #556	C₂²×C₄₇	semidirect
554. #556	C₂²×C₄₇	semidirect
555. #556	C₂²×C₄₇	semidirect
556. #555	C₂²×C₄₇	semidirect
557. #554	C₂²×C₄₇	semidirect
558. #554	C₂²×C₄₇	semidirect
559. #553	C₂²×C₄₇	semidirect
560. #553	C₂²×C₄₇	semidirect
561. #552	C₂²×C₄₇	semidirect
562. #552	C₂²×C₄₇	semidirect
563. #551	C₂²×C₄₇	semidirect
564. #551	C₂²×C₄₇	semidirect
565. #551	C₂²×C₄₇	semidirect
566. #550	C₂²×C₄₇	semidirect
567. #550	C₂²×C₄₇	semidirect
568. #550	C₂²×C₄₇	semidirect
569. D₄×Q₈	C₂²×C₄₇	semidirect
570. D₄×Q₈	C₂²×C₄₇	semidirect
571. #548	C₂²×C₄₇	semidirect
572. #548	C₂²×C₄₇	semidirect
573. #548	C₂²×C₄₇	semidirect
574. #547	C₂²×C₄₇	semidirect
575. #547	C₂²×C₄₇	semidirect
576. #547	C₂²×C₄₇	semidirect
577. #547	C₂²×C₄₇	semidirect
578. #547	C₂²×C₄₇	semidirect
579. #546	C₂²×C₄₇	semidirect
580. #546	C₂²×C₄₇	semidirect
581. #546	C₂²×C₄₇	semidirect
582. #546	C₂²×C₄₇	semidirect
583. #546	C₂²×C₄₇	semidirect
584. #546	C₂²×C₄₇	semidirect
585. #546	C₂²×C₄₇	semidirect
586. D₄²	C₂²×C₄₇	semidirect
587. D₄²	C₂²×C₄₇	semidirect
588. D₄²	C₂²×C₄₇	semidirect
589. D₄²	C₂²×C₄₇	semidirect
590. #542	C₂²×C₄₇	semidirect
591. #542	C₂²×C₄₇	semidirect
592. #542	C₂²×C₄₇	semidirect
593. #542	C₂²×C₄₇	semidirect
594. #540	C₂²×C₄₇	semidirect
595. #540	C₂²×C₄₇	semidirect
596. #539	C₂²×C₄₇	semidirect
597. #538	C₂²×C₄₇	semidirect
598. #538	C₂²×C₄₇	semidirect
599. #538	C₂²×C₄₇	semidirect
600. #536	C₂²×C₄₇	semidirect
601. #536	C₂²×C₄₇	semidirect
602. #535	C₂²×C₄₇	semidirect
603. #535	C₂²×C₄₇	semidirect
604. #535	C₂²×C₄₇	semidirect
605. #535	C₂²×C₄₇	semidirect
606. #534	C₂²×C₄₇	semidirect
607. #534	C₂²×C₄₇	semidirect
608. #533	C₂²×C₄₇	semidirect
609. #533	C₂²×C₄₇	semidirect
611. #532	C₂²×C₄₇	semidirect
612. #532	C₂²×C₄₇	semidirect
613. #532	C₂²×C₄₇	semidirect
614. #532	C₂²×C₄₇	semidirect
616. C₂×#127	C₂²×C₄₇	semidirect
617. #529	C₂²×C₄₇	semidirect
618. #529	C₂²×C₄₇	semidirect
619. #529	C₂²×C₄₇	semidirect
620. #529	C₂²×C₄₇	semidirect
621. C₂×#124	C₂²×C₄₇	semidirect
622. #525	C₂²×C₄₇	semidirect
623. #525	C₂²×C₄₇	semidirect
624. #525	C₂²×C₄₇	semidirect
625. #525	C₂²×C₄₇	semidirect
626. C₂×#123	C₂²×C₄₇	semidirect
627. C₂×#123	C₂²×C₄₇	semidirect
628. #520	C₂²×C₄₇	semidirect
629. #518	C₂²×C₄₇	semidirect
630. #518	C₂²×C₄₇	semidirect
631. C₄×#41	C₂²×C₄₇	semidirect
632. C₄×#41	C₂²×C₄₇	semidirect
633. C₄×#41	C₂²×C₄₇	semidirect
634. C₂×C₄×Q₈	C₂²×C₄₇	semidirect
635. C₂×C₄×D₄	C₂²×C₄₇	semidirect
636. C₂×C₄×D₄	C₂²×C₄₇	semidirect
637. C₄₇	#63021	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#3558	2
C₄₇×#3554	2
C₄₇×#3550	2
C₄₇×#3543	2
C₄₇×#3540	2
C₄₇×#3533	2
C₄₇×#3522	2
C₄₇×#3514	2
C₄₇×#3513	2
C₄₇×#3508	2
C₄₇×#3506	2
C₄₇×#3498	2
C₄₇×#3485	2
C₄₇×#3482	2
C₄₇×#3481	2
C₂×C₄₇×#559	2
D₄×#41×C₄₇	2
#63021	47

Subgroups — C47×#63021 #26102719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#63021 #26102719