Subgroups — C₄₇×#62992 #26102690

Order 12032.

7278 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3521	C₂	1	8	yes	maximal, complemented
2	C₄₇×#3519	C₂	1	4	yes	maximal, complemented
3	C₄₇×#3515	C₂	1	4	yes	maximal, complemented
4	C₄₇×#3513	C₂	1	8	yes	maximal, complemented
5	C₄₇×#3512	C₂	1	4	yes	maximal, complemented
6	C₄₇×#3511	C₂	1	2	yes	maximal, complemented
7	C₄₇×#3505	C₂	1	4	yes	maximal, complemented
8	C₄₇×#3505	C₂	1	8	yes	maximal, complemented
9	C₄₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#3496	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3481	C₂	1	4	yes	maximal, complemented
12	C₄₇×#3480	C₂	1	2	yes	maximal, complemented
13	C₄₇×#3475	C₂	1	4	yes	maximal, complemented
14	C₂×C₄₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₇×#553	C₂	1	4	yes	maximal, complemented
16	C₄×H(5,𝔽₂)×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×H(5,𝔽₂)×C₄₇	C₂	1	2	yes	maximal, complemented
18	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	2	yes	—
20	C₄₇×#559	C₂²	1	2	yes	complemented
21	C₄₇×#559	C₂²	1	4	yes	complemented
22	C₄₇×#557	C₂²	1	2	yes	complemented
23	C₄₇×#556	C₂²	1	2	yes	complemented
24	C₄₇×#556	C₂²	1	4	yes	complemented
25	C₄₇×#556	C₂²	1	4	yes	complemented
26	C₄₇×#555	C₂²	1	4	yes	complemented
27	C₄₇×#554	C₂²	1	4	yes	complemented
28	C₄₇×#554	C₂²	1	8	yes	complemented
29	C₄₇×#554	C₂²	1	4	yes	complemented
30	C₄₇×#554	C₂²	1	4	yes	complemented
31	C₄₇×#553	C₂²	1	4	yes	complemented
32	C₄₇×#553	C₂²	1	8	yes	complemented
33	C₄₇×#553	C₂²	1	8	yes	complemented
34	C₄₇×#553	C₂²	1	16	yes	complemented
35	C₄₇×#553	C₂²	1	16	yes	complemented
36	C₄₇×#553	C₂²	1	8	yes	complemented
37	C₄₇×#553	C₂²	1	8	yes	complemented
38	C₄₇×#553	C₂²	1	8	yes	complemented
39	C₄₇×#553	C₂²	1	16	yes	complemented
40	C₄₇×#553	C₂²	1	8	yes	complemented
41	C₄₇×#552	C₂²	1	8	yes	complemented
42	C₄₇×#552	C₂²	1	8	yes	complemented
43	C₄₇×#552	C₂²	1	16	yes	complemented
44	C₄₇×#552	C₂²	1	8	yes	complemented
45	C₄₇×#551	C₂²	1	16	yes	complemented
46	C₄₇×#551	C₂²	1	16	yes	complemented
47	C₄₇×#551	C₂²	1	16	yes	complemented
48	C₄₇×#550	C₂²	1	2	yes	complemented
49	C₄₇×#548	C₂²	1	4	yes	complemented
50	C₄₇×#548	C₂²	1	8	yes	complemented
51	C₄₇×#547	C₂²	1	4	yes	complemented
52	C₄₇×#547	C₂²	1	8	yes	complemented
53	C₄₇×#547	C₂²	1	4	yes	complemented
54	C₄₇×#546	C₂²	1	8	yes	complemented
55	C₄₇×#546	C₂²	1	8	yes	complemented
56	C₄₇×#546	C₂²	1	8	yes	complemented
57	C₄₇×#546	C₂²	1	8	yes	complemented
58	C₄₇×#546	C₂²	1	16	yes	complemented
59	D₄²×C₄₇	C₂²	1	4	yes	complemented
60	D₄²×C₄₇	C₂²	1	8	yes	complemented
61	C₄₇×#542	C₂²	1	8	yes	complemented
62	C₄₇×#541	C₂²	1	8	yes	complemented
63	C₄₇×#540	C₂²	1	8	yes	complemented
64	C₄₇×#539	C₂²	1	16	yes	complemented
65	C₄₇×#539	C₂²	1	8	yes	complemented
66	C₄₇×#538	C₂²	1	8	yes	complemented
67	C₄₇×#538	C₂²	1	16	yes	complemented
68	C₄₇×#537	C₂²	1	4	yes	complemented
69	C₄₇×#537	C₂²	1	2	yes	complemented
70	C₄₇×#534	C₂²	1	8	yes	complemented
71	C₄₇×#534	C₂²	1	4	yes	complemented
72	C₄₇×#533	C₂²	1	4	yes	complemented
73	C₄₇×#532	C₂²	1	2	yes	complemented
74	C₄₇×#532	C₂²	1	4	yes	complemented
75	C₄₇×#532	C₂²	1	4	yes	complemented
76	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
77	C₄₇×#529	C₂²	1	16	yes	complemented
78	C₄₇×#529	C₂²	1	8	yes	complemented
79	C₄₇×#529	C₂²	1	8	yes	complemented
80	C₄₇×#529	C₂²	1	4	yes	complemented
81	C₄₇×#529	C₂²	1	8	yes	complemented
82	C₄₇×#529	C₂²	1	8	yes	complemented
83	C₂×#126×C₄₇	C₂²	1	8	yes	complemented
84	C₂×#125×C₄₇	C₂²	1	4	yes	complemented
85	C₂×#125×C₄₇	C₂²	1	2	yes	complemented
86	C₄₇×#525	C₂²	1	8	yes	complemented
87	C₄₇×#525	C₂²	1	16	yes	complemented
88	C₂×#123×C₄₇	C₂²	1	8	yes	complemented
89	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	complemented
90	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
91	C₂×#121×C₄₇	C₂²	1	8	yes	complemented
92	C₂×#121×C₄₇	C₂²	1	4	yes	complemented
93	C₂×#121×C₄₇	C₂²	1	4	yes	complemented
94	C₄₇×#520	C₂²	1	4	yes	complemented
95	C₄₇×#520	C₂²	1	2	yes	complemented
96	C₄₇×#520	C₂²	1	8	yes	complemented
97	C₄₇×#520	C₂²	1	4	yes	complemented
98	C₄₇×#518	C₂²	1	1	yes	characteristic
99	C₄₇×#518	C₂²	1	8	yes	complemented
100	C₄₇×#518	C₂²	1	4	yes	complemented
101	C₄₇×#518	C₂²	1	4	yes	complemented
102	C₄₇×#518	C₂²	1	8	yes	complemented
103	C₄×#41×C₄₇	C₂²	1	8	yes	complemented
104	C₄×#41×C₄₇	C₂²	1	2	yes	complemented
105	C₄×#41×C₄₇	C₂²	1	4	yes	complemented
106	C₄×#41×C₄₇	C₂²	1	4	yes	complemented
107	C₄×#41×C₄₇	C₂²	1	4	yes	complemented
108	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
110	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
111	C₂×C₄×D₄×C₄₇	C₂²	1	8	yes	complemented
112	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	complemented
113	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	complemented
114	C₂×C₄×D₄×C₄₇	C₂²	1	8	yes	complemented
115	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	complemented
116	C₂×#117×C₄₇	C₂²	1	4	yes	complemented
117	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
118	H(5,𝔽₂)×C₄₇	—	2	8	no	—
119	H(5,𝔽₂)×C₄₇	—	2	16	no	—
120	C₂×#41×C₄₇	C₂³	1	2	yes	—
121	C₂×#41×C₄₇	C₂³	1	4	yes	—
122	C₂×#41×C₄₇	C₂³	1	8	yes	—
123	C₂×#41×C₄₇	C₂³	1	4	yes	—
124	C₂×#41×C₄₇	C₂³	1	4	yes	—
125	C₂×#41×C₄₇	C₂³	1	8	yes	—
126	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
128	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
129	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
130	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
131	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
132	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
133	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
134	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
137	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
138	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
139	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
140	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
141	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
142	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
143	#127×C₄₇	C₂³	1	2	yes	—
144	#127×C₄₇	C₂³	1	4	yes	—
145	#126×C₄₇	C₂³	1	8	yes	—
146	#126×C₄₇	C₂³	1	16	yes	—
147	#126×C₄₇	C₂³	1	16	yes	—
148	#126×C₄₇	C₂³	1	16	yes	—
149	#126×C₄₇	C₂³	1	8	yes	—
150	#126×C₄₇	C₂³	1	8	yes	—
151	#126×C₄₇	C₂³	1	16	yes	—
152	#126×C₄₇	C₂³	1	16	yes	—
153	#125×C₄₇	C₂³	1	4	yes	—
154	#125×C₄₇	C₂³	1	8	yes	—
155	#125×C₄₇	C₂³	1	8	yes	—
156	#125×C₄₇	C₂³	1	16	yes	—
157	#125×C₄₇	C₂³	1	8	yes	—
158	#125×C₄₇	C₂³	1	8	yes	—
159	#125×C₄₇	C₂³	1	16	yes	—
160	#124×C₄₇	C₂³	1	4	yes	—
161	#124×C₄₇	C₂³	1	4	yes	—
162	#124×C₄₇	C₂³	1	4	yes	—
163	#124×C₄₇	C₂³	1	8	yes	—
164	#124×C₄₇	C₂³	1	16	yes	—
165	#124×C₄₇	C₂³	1	8	yes	—
166	#124×C₄₇	C₂³	1	4	yes	—
167	#123×C₄₇	C₂³	1	8	yes	—
168	#123×C₄₇	C₂³	1	16	yes	—
169	#123×C₄₇	C₂³	1	16	yes	—
170	#123×C₄₇	C₂³	1	16	yes	—
171	#123×C₄₇	C₂³	1	8	yes	—
172	#123×C₄₇	C₂³	1	16	yes	—
173	#123×C₄₇	C₂³	1	16	yes	—
174	#123×C₄₇	C₂³	1	16	yes	—
175	#123×C₄₇	C₂³	1	16	yes	—
176	#123×C₄₇	C₂³	1	16	yes	—
177	#123×C₄₇	C₂³	1	8	yes	—
178	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
179	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	—
180	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	—
181	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
182	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
183	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	—
184	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
185	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
186	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
187	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
188	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
189	#121×C₄₇	C₂³	1	4	yes	—
190	#121×C₄₇	C₂³	1	4	yes	—
191	#121×C₄₇	C₂³	1	8	yes	—
192	#121×C₄₇	C₂³	1	8	yes	—
193	#121×C₄₇	C₂³	1	16	yes	—
194	#121×C₄₇	C₂³	1	8	yes	—
195	#121×C₄₇	C₂³	1	16	yes	—
196	#121×C₄₇	C₂³	1	8	yes	—
197	#121×C₄₇	C₂³	1	16	yes	—
198	#121×C₄₇	C₂³	1	8	yes	—
199	#121×C₄₇	C₂³	1	16	yes	—
200	#121×C₄₇	C₂³	1	16	yes	—
201	#121×C₄₇	C₂³	1	8	yes	—
202	#121×C₄₇	C₂³	1	8	yes	—
203	#121×C₄₇	C₂³	1	8	yes	—
204	#121×C₄₇	C₂³	1	4	yes	—
205	#121×C₄₇	C₂³	1	8	yes	—
206	#121×C₄₇	C₂³	1	8	yes	—
207	#120×C₄₇	C₂³	1	16	yes	—
208	#120×C₄₇	C₂³	1	16	yes	—
209	#120×C₄₇	C₂³	1	16	yes	—
210	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
211	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
212	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
213	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
214	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
215	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
216	C₄×Q₈×C₄₇	C₂³	1	8	yes	—
217	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
218	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
219	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
220	C₄×Q₈×C₄₇	C₂³	1	8	yes	—
221	C₄×D₄×C₄₇	C₂³	1	4	yes	—
222	C₄×D₄×C₄₇	C₂³	1	8	yes	—
223	C₄×D₄×C₄₇	C₂³	1	8	yes	—
224	C₄×D₄×C₄₇	C₂³	1	4	yes	—
225	C₄×D₄×C₄₇	C₂³	1	4	yes	—
226	C₄×D₄×C₄₇	C₂³	1	8	yes	—
227	C₄×D₄×C₄₇	C₂³	1	4	yes	—
228	C₄×D₄×C₄₇	C₂³	1	2	yes	—
229	C₄×D₄×C₄₇	C₂³	1	16	yes	—
230	C₄×D₄×C₄₇	C₂³	1	8	yes	—
231	C₄×D₄×C₄₇	C₂³	1	4	yes	—
232	C₄×D₄×C₄₇	C₂³	1	4	yes	—
233	C₄×D₄×C₄₇	C₂³	1	4	yes	—
234	C₄×D₄×C₄₇	C₂³	1	16	yes	—
235	C₄×D₄×C₄₇	C₂³	1	8	yes	—
236	C₄×D₄×C₄₇	C₂³	1	4	yes	—
237	C₄×D₄×C₄₇	C₂³	1	8	yes	—
238	C₄×D₄×C₄₇	C₂³	1	16	yes	—
239	C₄×D₄×C₄₇	C₂³	1	16	yes	—
240	C₄×D₄×C₄₇	C₂³	1	8	yes	—
241	C₄×D₄×C₄₇	C₂³	1	8	yes	—
242	C₄×D₄×C₄₇	C₂³	1	16	yes	—
243	C₄×D₄×C₄₇	C₂³	1	8	yes	—
244	C₄×D₄×C₄₇	C₂³	1	8	yes	—
245	C₄×D₄×C₄₇	C₂³	1	16	yes	—
246	C₄×D₄×C₄₇	C₂³	1	2	yes	—
247	C₄×D₄×C₄₇	C₂³	1	4	yes	—
248	C₄×D₄×C₄₇	C₂³	1	8	yes	—
249	C₄×D₄×C₄₇	C₂³	1	4	yes	—
250	C₄×D₄×C₄₇	C₂³	1	8	yes	—
251	C₄×D₄×C₄₇	C₂³	1	4	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	#117×C₄₇	C₂³	1	4	yes	—
257	#117×C₄₇	C₂³	1	8	yes	—
258	#117×C₄₇	C₂³	1	16	yes	—
259	#117×C₄₇	C₂³	1	2	yes	—
260	#117×C₄₇	C₂³	1	8	yes	—
261	#117×C₄₇	C₂³	1	4	yes	—
262	#117×C₄₇	C₂³	1	8	yes	—
263	#117×C₄₇	C₂³	1	16	yes	—
264	#117×C₄₇	C₂³	1	4	yes	—
265	#117×C₄₇	C₂³	1	8	yes	—
266	#117×C₄₇	C₂³	1	8	yes	—
267	#117×C₄₇	C₂³	1	16	yes	—
268	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
270	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
271	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
272	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
273	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
274	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
275	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
277	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
278	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
279	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
280	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
281	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
282	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
283	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
284	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
285	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
286	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
287	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
288	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
289	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
290	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	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×C₄²×C₄₇	C₂³	1	8	yes	—
295	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
296	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
298	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
299	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
300	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
301	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
302	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
303	#41×C₄₇	—	2	32	no	—
304	#41×C₄₇	—	2	16	no	—
305	#41×C₄₇	—	2	8	no	—
306	#41×C₄₇	—	2	16	no	—
307	#41×C₄₇	—	4	8	no	—
308	#41×C₄₇	—	8	8	no	—
309	C₂×Q₈×C₄₇	—	4	2	no	—
310	C₂×Q₈×C₄₇	—	8	2	no	—
311	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
312	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
313	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
314	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
315	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
316	C₂×D₄×C₄₇	—	2	32	no	—
317	C₂×D₄×C₄₇	—	2	16	no	—
318	C₂×D₄×C₄₇	—	2	16	no	—
319	C₂×D₄×C₄₇	—	2	32	no	—
320	C₂×D₄×C₄₇	—	4	8	no	—
321	C₂×D₄×C₄₇	—	8	8	no	—
322	C₂×D₄×C₄₇	#41	1	8	yes	complemented
323	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
324	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
325	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
326	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
327	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
328	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
329	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
330	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
331	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
332	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
333	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
334	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
335	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
336	C₂²×C₄×C₄₇	—	4	4	no	—
337	C₂²×C₄×C₄₇	—	4	8	no	—
338	C₂²×C₄×C₄₇	—	8	8	no	—
339	C₂²×C₄×C₄₇	—	8	4	no	—
340	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
341	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
342	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
344	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
345	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
346	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
347	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
348	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
350	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
352	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
353	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
354	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
356	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
357	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
360	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
361	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
362	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
363	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
368	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
369	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
370	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
371	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
373	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
374	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
375	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
376	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
377	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
378	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
379	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
380	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
381	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
382	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
383	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
384	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
385	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
386	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
387	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
388	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
389	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
390	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
391	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
392	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
393	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
394	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
395	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
396	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
397	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
398	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
399	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
400	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
401	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
402	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
403	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
404	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
405	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
407	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
408	C₄²×C₄₇	C₂⁴	1	4	yes	—
409	C₄²×C₄₇	C₂⁴	1	8	yes	—
410	C₄²×C₄₇	C₂⁴	1	4	yes	—
411	C₄²×C₄₇	C₂⁴	1	4	yes	—
412	C₄²×C₄₇	C₂⁴	1	2	yes	—
413	C₄²×C₄₇	C₂⁴	1	8	yes	—
414	C₄²×C₄₇	C₂⁴	1	16	yes	—
415	C₄²×C₄₇	C₂⁴	1	8	yes	—
416	C₄²×C₄₇	C₂⁴	1	4	yes	—
417	C₄²×C₄₇	C₂⁴	1	2	yes	—
418	C₄²×C₄₇	C₂⁴	1	4	yes	—
419	C₂³×C₄₇	—	2	8	no	—
420	C₂³×C₄₇	—	2	16	no	—
421	C₂³×C₄₇	—	4	2	no	—
422	C₂³×C₄₇	—	4	2	no	—
423	C₂³×C₄₇	—	4	4	no	—
424	C₂³×C₄₇	—	4	8	no	—
425	C₂³×C₄₇	—	4	8	no	—
426	C₂³×C₄₇	—	4	4	no	—
427	C₂³×C₄₇	C₂×#41	1	8	yes	—
428	C₂³×C₄₇	C₂⁵	1	4	yes	—
429	C₂³×C₄₇	C₂⁵	1	8	yes	—
430	C₂³×C₄₇	C₂⁵	1	4	yes	—
431	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
432	Q₈×C₄₇	—	2	8	no	—
433	Q₈×C₄₇	—	2	4	no	—
434	Q₈×C₄₇	—	2	4	no	—
435	Q₈×C₄₇	—	4	2	no	—
436	Q₈×C₄₇	—	4	8	no	—
437	D₄×C₄₇	—	2	16	no	—
438	D₄×C₄₇	—	2	32	no	—
439	D₄×C₄₇	—	2	8	no	—
440	D₄×C₄₇	—	2	16	no	—
441	D₄×C₄₇	—	2	4	no	—
442	D₄×C₄₇	—	2	8	no	—
443	D₄×C₄₇	—	2	8	no	—
444	D₄×C₄₇	—	4	8	no	—
445	D₄×C₄₇	—	4	8	no	—
446	D₄×C₄₇	—	4	16	no	—
447	D₄×C₄₇	—	4	8	no	—
448	D₄×C₄₇	—	4	4	no	—
449	D₄×C₄₇	C₂×#41	1	16	yes	—
450	C₂×C₄×C₄₇	—	2	16	no	—
451	C₂×C₄×C₄₇	—	2	8	no	—
452	C₂×C₄×C₄₇	—	2	16	no	—
453	C₂×C₄×C₄₇	—	2	8	no	—
454	C₂×C₄×C₄₇	—	2	8	no	—
455	C₂×C₄×C₄₇	—	2	2	no	—
456	C₂×C₄×C₄₇	—	2	8	no	—
457	C₂×C₄×C₄₇	—	4	4	no	—
458	C₂×C₄×C₄₇	—	4	8	no	—
459	C₂×C₄×C₄₇	—	4	2	no	—
460	C₂×C₄×C₄₇	—	4	4	no	—
461	C₂×C₄×C₄₇	—	4	4	no	—
462	C₂×C₄×C₄₇	—	4	8	no	—
463	C₂×C₄×C₄₇	—	4	2	no	—
464	C₂×C₄×C₄₇	—	4	8	no	—
465	C₂×C₄×C₄₇	—	4	8	no	—
466	C₂×C₄×C₄₇	—	4	4	no	—
467	C₂×C₄×C₄₇	—	4	16	no	—
468	C₂×C₄×C₄₇	—	4	2	no	—
469	C₂×C₄×C₄₇	—	4	1	no	—
470	C₂×C₄×C₄₇	—	4	8	no	—
471	C₂×C₄×C₄₇	—	4	4	no	—
472	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
473	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
474	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
475	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
476	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
477	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
478	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
479	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
480	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
481	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
482	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
483	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
484	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
485	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
486	#62992	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
487	C₂²×C₄₇	—	2	1	no	—
488	C₂²×C₄₇	—	2	4	no	—
489	C₂²×C₄₇	—	2	1	no	—
490	C₂²×C₄₇	—	2	4	no	—
491	C₂²×C₄₇	—	2	4	no	—
492	C₂²×C₄₇	—	2	8	no	—
493	C₂²×C₄₇	—	2	4	no	—
494	C₂²×C₄₇	—	2	8	no	—
495	C₂²×C₄₇	—	2	8	no	—
496	C₂²×C₄₇	—	2	4	no	—
497	C₂²×C₄₇	—	4	8	no	—
498	C₂²×C₄₇	—	8	8	no	—
499	C₂²×C₄₇	—	8	16	no	—
500	C₂²×C₄₇	C₂²×#41	1	8	yes	—
501	C₂²×C₄₇	C₂²×#41	1	2	yes	—
502	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
503	C₄×C₄₇	—	2	8	no	—
504	C₄×C₄₇	—	2	4	no	—
505	C₄×C₄₇	—	2	4	no	—
506	C₄×C₄₇	—	2	4	no	—
507	C₄×C₄₇	—	2	1	no	—
508	C₄×C₄₇	—	2	4	no	—
509	C₄×C₄₇	—	2	2	no	—
510	C₄×C₄₇	—	2	4	no	—
511	C₄×C₄₇	—	2	2	no	—
512	C₄×C₄₇	—	2	8	no	—
513	C₄×C₄₇	—	2	2	no	—
514	C₄×C₄₇	C₂²×#41	1	4	yes	—
515	C₄×C₄₇	#585	1	2	yes	—
516	#3521	C₂×C₄₇	1	8	yes	complemented
517	#3519	C₂×C₄₇	1	4	yes	complemented
518	#3515	C₂×C₄₇	1	4	yes	complemented
519	#3513	C₂×C₄₇	1	8	yes	complemented
520	#3512	C₂×C₄₇	1	4	yes	complemented
521	#3511	C₂×C₄₇	1	2	yes	complemented
522	#3505	C₂×C₄₇	1	4	yes	complemented
523	#3505	C₂×C₄₇	1	8	yes	complemented
524	#3496	C₂×C₄₇	1	1	yes	characteristic, complemented
525	#3496	C₂×C₄₇	1	2	yes	complemented
526	#3481	C₂×C₄₇	1	4	yes	complemented
527	#3480	C₂×C₄₇	1	2	yes	complemented
528	#3475	C₂×C₄₇	1	4	yes	complemented
529	C₂×#554	C₂×C₄₇	1	1	yes	characteristic, complemented
530	C₂×#553	C₂×C₄₇	1	4	yes	complemented
531	C₄×H(5,𝔽₂)	C₂×C₄₇	1	1	yes	characteristic, complemented
532	C₄×H(5,𝔽₂)	C₂×C₄₇	1	2	yes	complemented
533	C₂×C₄₇	—	2	2	no	—
534	C₂×C₄₇	—	2	8	no	—
535	C₂×C₄₇	—	4	4	no	—
536	C₂×C₄₇	—	4	8	no	—
537	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
538	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
539	C₂×C₄₇	H(7,𝔽₂)	1	1	yes	characteristic
540	C₂×H(5,𝔽₂)	C₂²×C₄₇	1	1	yes	characteristic
541	C₂×H(5,𝔽₂)	C₂²×C₄₇	1	2	yes	—
542	#559	C₂²×C₄₇	1	2	yes	complemented
543	#559	C₂²×C₄₇	1	4	yes	complemented
544	#557	C₂²×C₄₇	1	2	yes	complemented
545	#556	C₂²×C₄₇	1	2	yes	complemented
546	#556	C₂²×C₄₇	1	4	yes	complemented
547	#556	C₂²×C₄₇	1	4	yes	complemented
548	#555	C₂²×C₄₇	1	4	yes	complemented
549	#554	C₂²×C₄₇	1	4	yes	complemented
550	#554	C₂²×C₄₇	1	8	yes	complemented
551	#554	C₂²×C₄₇	1	4	yes	complemented
552	#554	C₂²×C₄₇	1	4	yes	complemented
553	#553	C₂²×C₄₇	1	4	yes	complemented
554	#553	C₂²×C₄₇	1	8	yes	complemented
555	#553	C₂²×C₄₇	1	8	yes	complemented
556	#553	C₂²×C₄₇	1	16	yes	complemented
557	#553	C₂²×C₄₇	1	16	yes	complemented
558	#553	C₂²×C₄₇	1	8	yes	complemented
559	#553	C₂²×C₄₇	1	8	yes	complemented
560	#553	C₂²×C₄₇	1	8	yes	complemented
561	#553	C₂²×C₄₇	1	16	yes	complemented
562	#553	C₂²×C₄₇	1	8	yes	complemented
563	#552	C₂²×C₄₇	1	8	yes	complemented
564	#552	C₂²×C₄₇	1	8	yes	complemented
565	#552	C₂²×C₄₇	1	16	yes	complemented
566	#552	C₂²×C₄₇	1	8	yes	complemented
567	#551	C₂²×C₄₇	1	16	yes	complemented
568	#551	C₂²×C₄₇	1	16	yes	complemented
569	#551	C₂²×C₄₇	1	16	yes	complemented
570	#550	C₂²×C₄₇	1	2	yes	complemented
571	#548	C₂²×C₄₇	1	4	yes	complemented
572	#548	C₂²×C₄₇	1	8	yes	complemented
573	#547	C₂²×C₄₇	1	4	yes	complemented
574	#547	C₂²×C₄₇	1	8	yes	complemented
575	#547	C₂²×C₄₇	1	4	yes	complemented
576	#546	C₂²×C₄₇	1	8	yes	complemented
577	#546	C₂²×C₄₇	1	8	yes	complemented
578	#546	C₂²×C₄₇	1	8	yes	complemented
579	#546	C₂²×C₄₇	1	8	yes	complemented
580	#546	C₂²×C₄₇	1	16	yes	complemented
581	D₄²	C₂²×C₄₇	1	4	yes	complemented
582	D₄²	C₂²×C₄₇	1	8	yes	complemented
583	#542	C₂²×C₄₇	1	8	yes	complemented
584	#541	C₂²×C₄₇	1	8	yes	complemented
585	#540	C₂²×C₄₇	1	8	yes	complemented
586	#539	C₂²×C₄₇	1	16	yes	complemented
587	#539	C₂²×C₄₇	1	8	yes	complemented
588	#538	C₂²×C₄₇	1	8	yes	complemented
589	#538	C₂²×C₄₇	1	16	yes	complemented
590	#537	C₂²×C₄₇	1	4	yes	complemented
591	#537	C₂²×C₄₇	1	2	yes	complemented
592	#534	C₂²×C₄₇	1	8	yes	complemented
593	#534	C₂²×C₄₇	1	4	yes	complemented
594	#533	C₂²×C₄₇	1	4	yes	complemented
595	#532	C₂²×C₄₇	1	2	yes	complemented
596	#532	C₂²×C₄₇	1	4	yes	complemented
597	#532	C₂²×C₄₇	1	4	yes	complemented
598	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
599	#529	C₂²×C₄₇	1	16	yes	complemented
600	#529	C₂²×C₄₇	1	8	yes	complemented
601	#529	C₂²×C₄₇	1	8	yes	complemented
602	#529	C₂²×C₄₇	1	4	yes	complemented
603	#529	C₂²×C₄₇	1	8	yes	complemented
604	#529	C₂²×C₄₇	1	8	yes	complemented
605	C₂×#126	C₂²×C₄₇	1	8	yes	complemented
606	C₂×#125	C₂²×C₄₇	1	4	yes	complemented
607	C₂×#125	C₂²×C₄₇	1	2	yes	complemented
608	#525	C₂²×C₄₇	1	8	yes	complemented
609	#525	C₂²×C₄₇	1	16	yes	complemented
610	C₂×#123	C₂²×C₄₇	1	8	yes	complemented
611	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	4	yes	complemented
612	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	complemented
613	C₂×#121	C₂²×C₄₇	1	8	yes	complemented
614	C₂×#121	C₂²×C₄₇	1	4	yes	complemented
615	C₂×#121	C₂²×C₄₇	1	4	yes	complemented
616	#520	C₂²×C₄₇	1	4	yes	complemented
617	#520	C₂²×C₄₇	1	2	yes	complemented
618	#520	C₂²×C₄₇	1	8	yes	complemented
619	#520	C₂²×C₄₇	1	4	yes	complemented
620	#518	C₂²×C₄₇	1	1	yes	characteristic
621	#518	C₂²×C₄₇	1	8	yes	complemented
622	#518	C₂²×C₄₇	1	4	yes	complemented
623	#518	C₂²×C₄₇	1	4	yes	complemented
624	#518	C₂²×C₄₇	1	8	yes	complemented
625	C₄×#41	C₂²×C₄₇	1	8	yes	complemented
626	C₄×#41	C₂²×C₄₇	1	2	yes	complemented
627	C₄×#41	C₂²×C₄₇	1	4	yes	complemented
628	C₄×#41	C₂²×C₄₇	1	4	yes	complemented
629	C₄×#41	C₂²×C₄₇	1	4	yes	complemented
630	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
631	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
632	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
633	C₂×C₄×D₄	C₂²×C₄₇	1	8	yes	complemented
634	C₂×C₄×D₄	C₂²×C₄₇	1	4	yes	complemented
635	C₂×C₄×D₄	C₂²×C₄₇	1	4	yes	complemented
636	C₂×C₄×D₄	C₂²×C₄₇	1	8	yes	complemented
637	C₂×C₄×D₄	C₂²×C₄₇	1	4	yes	complemented
638	C₂×#117	C₂²×C₄₇	1	4	yes	complemented
639	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
640	C₄₇	#62992	1	1	yes	characteristic, direct product factor, Sylow
641	H(5,𝔽₂)	—	2	8	no	—
642	H(5,𝔽₂)	—	2	16	no	—
643	C₂×#41	C₂³×C₄₇	1	2	yes	—
644	C₂×#41	C₂³×C₄₇	1	4	yes	—
645	C₂×#41	C₂³×C₄₇	1	8	yes	—
646	C₂×#41	C₂³×C₄₇	1	4	yes	—
647	C₂×#41	C₂³×C₄₇	1	4	yes	—
648	C₂×#41	C₂³×C₄₇	1	8	yes	—
649	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
650	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
651	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
652	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
653	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
654	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
655	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
656	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
657	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
658	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
659	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
660	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
661	C₂³×C₄	C₂³×C₄₇	1	8	yes	—
662	C₄⋊Q₈	C₂³×C₄₇	1	4	yes	—
663	C₄⋊Q₈	C₂³×C₄₇	1	4	yes	—
664	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
665	C₄⋊Q₈	C₂³×C₄₇	1	4	yes	—
666	#127	C₂³×C₄₇	1	2	yes	—
667	#127	C₂³×C₄₇	1	4	yes	—
668	#126	C₂³×C₄₇	1	8	yes	—
669	#126	C₂³×C₄₇	1	16	yes	—
670	#126	C₂³×C₄₇	1	16	yes	—
671	#126	C₂³×C₄₇	1	16	yes	—
672	#126	C₂³×C₄₇	1	8	yes	—
673	#126	C₂³×C₄₇	1	8	yes	—
674	#126	C₂³×C₄₇	1	16	yes	—
675	#126	C₂³×C₄₇	1	16	yes	—
676	#125	C₂³×C₄₇	1	4	yes	—
677	#125	C₂³×C₄₇	1	8	yes	—
678	#125	C₂³×C₄₇	1	8	yes	—
679	#125	C₂³×C₄₇	1	16	yes	—
680	#125	C₂³×C₄₇	1	8	yes	—
681	#125	C₂³×C₄₇	1	8	yes	—
682	#125	C₂³×C₄₇	1	16	yes	—
683	#124	C₂³×C₄₇	1	4	yes	—
684	#124	C₂³×C₄₇	1	4	yes	—
685	#124	C₂³×C₄₇	1	4	yes	—
686	#124	C₂³×C₄₇	1	8	yes	—
687	#124	C₂³×C₄₇	1	16	yes	—
688	#124	C₂³×C₄₇	1	8	yes	—
689	#124	C₂³×C₄₇	1	4	yes	—
690	#123	C₂³×C₄₇	1	8	yes	—
691	#123	C₂³×C₄₇	1	16	yes	—
692	#123	C₂³×C₄₇	1	16	yes	—
693	#123	C₂³×C₄₇	1	16	yes	—
694	#123	C₂³×C₄₇	1	8	yes	—
695	#123	C₂³×C₄₇	1	16	yes	—
696	#123	C₂³×C₄₇	1	16	yes	—
697	#123	C₂³×C₄₇	1	16	yes	—
698	#123	C₂³×C₄₇	1	16	yes	—
699	#123	C₂³×C₄₇	1	16	yes	—
700	#123	C₂³×C₄₇	1	8	yes	—
701	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
702	C₂²⋊Q₈	C₂³×C₄₇	1	16	yes	—
703	C₂²⋊Q₈	C₂³×C₄₇	1	16	yes	—
704	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
705	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
706	C₂²⋊Q₈	C₂³×C₄₇	1	16	yes	—
707	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
708	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
709	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
710	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
711	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
712	#121	C₂³×C₄₇	1	4	yes	—
713	#121	C₂³×C₄₇	1	4	yes	—
714	#121	C₂³×C₄₇	1	8	yes	—
715	#121	C₂³×C₄₇	1	8	yes	—
716	#121	C₂³×C₄₇	1	16	yes	—
717	#121	C₂³×C₄₇	1	8	yes	—
718	#121	C₂³×C₄₇	1	16	yes	—
719	#121	C₂³×C₄₇	1	8	yes	—
720	#121	C₂³×C₄₇	1	16	yes	—
721	#121	C₂³×C₄₇	1	8	yes	—
722	#121	C₂³×C₄₇	1	16	yes	—
723	#121	C₂³×C₄₇	1	16	yes	—
724	#121	C₂³×C₄₇	1	8	yes	—
725	#121	C₂³×C₄₇	1	8	yes	—
726	#121	C₂³×C₄₇	1	8	yes	—
727	#121	C₂³×C₄₇	1	4	yes	—
728	#121	C₂³×C₄₇	1	8	yes	—
729	#121	C₂³×C₄₇	1	8	yes	—
730	#120	C₂³×C₄₇	1	16	yes	—
731	#120	C₂³×C₄₇	1	16	yes	—
732	#120	C₂³×C₄₇	1	16	yes	—
733	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
734	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
735	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
736	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
737	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
738	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
739	C₄×Q₈	C₂³×C₄₇	1	8	yes	—
740	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
741	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
742	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
743	C₄×Q₈	C₂³×C₄₇	1	8	yes	—
744	C₄×D₄	C₂³×C₄₇	1	4	yes	—
745	C₄×D₄	C₂³×C₄₇	1	8	yes	—
746	C₄×D₄	C₂³×C₄₇	1	8	yes	—
747	C₄×D₄	C₂³×C₄₇	1	4	yes	—
748	C₄×D₄	C₂³×C₄₇	1	4	yes	—
749	C₄×D₄	C₂³×C₄₇	1	8	yes	—
750	C₄×D₄	C₂³×C₄₇	1	4	yes	—
751	C₄×D₄	C₂³×C₄₇	1	2	yes	—
752	C₄×D₄	C₂³×C₄₇	1	16	yes	—
753	C₄×D₄	C₂³×C₄₇	1	8	yes	—
754	C₄×D₄	C₂³×C₄₇	1	4	yes	—
755	C₄×D₄	C₂³×C₄₇	1	4	yes	—
756	C₄×D₄	C₂³×C₄₇	1	4	yes	—
757	C₄×D₄	C₂³×C₄₇	1	16	yes	—
758	C₄×D₄	C₂³×C₄₇	1	8	yes	—
759	C₄×D₄	C₂³×C₄₇	1	4	yes	—
760	C₄×D₄	C₂³×C₄₇	1	8	yes	—
761	C₄×D₄	C₂³×C₄₇	1	16	yes	—
762	C₄×D₄	C₂³×C₄₇	1	16	yes	—
763	C₄×D₄	C₂³×C₄₇	1	8	yes	—
764	C₄×D₄	C₂³×C₄₇	1	8	yes	—
765	C₄×D₄	C₂³×C₄₇	1	16	yes	—
766	C₄×D₄	C₂³×C₄₇	1	8	yes	—
767	C₄×D₄	C₂³×C₄₇	1	8	yes	—
768	C₄×D₄	C₂³×C₄₇	1	16	yes	—
769	C₄×D₄	C₂³×C₄₇	1	2	yes	—
770	C₄×D₄	C₂³×C₄₇	1	4	yes	—
771	C₄×D₄	C₂³×C₄₇	1	8	yes	—
772	C₄×D₄	C₂³×C₄₇	1	4	yes	—
773	C₄×D₄	C₂³×C₄₇	1	8	yes	—
774	C₄×D₄	C₂³×C₄₇	1	4	yes	—
775	C₄×D₄	C₂³×C₄₇	1	8	yes	—
776	C₄×D₄	C₂³×C₄₇	1	16	yes	—
777	C₄×D₄	C₂³×C₄₇	1	8	yes	—
778	C₄×D₄	C₂³×C₄₇	1	4	yes	—
779	#117	C₂³×C₄₇	1	4	yes	—
780	#117	C₂³×C₄₇	1	8	yes	—
781	#117	C₂³×C₄₇	1	16	yes	—
782	#117	C₂³×C₄₇	1	2	yes	—
783	#117	C₂³×C₄₇	1	8	yes	—
784	#117	C₂³×C₄₇	1	4	yes	—
785	#117	C₂³×C₄₇	1	8	yes	—
786	#117	C₂³×C₄₇	1	16	yes	—
787	#117	C₂³×C₄₇	1	4	yes	—
788	#117	C₂³×C₄₇	1	8	yes	—
789	#117	C₂³×C₄₇	1	8	yes	—
790	#117	C₂³×C₄₇	1	16	yes	—
791	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
793	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
794	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
795	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
796	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
797	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
798	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
800	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
801	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
802	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
803	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
804	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
805	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
806	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₄₇	1	16	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
817	C₂×C₄²	C₂³×C₄₇	1	8	yes	—
818	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
819	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
821	C₂×C₄²	C₂³×C₄₇	1	8	yes	—
822	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
823	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
824	C₂⁴	C₂⁴×C₄₇	1	8	yes	—
825	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
826	#41	—	2	32	no	—
827	#41	—	2	16	no	—
828	#41	—	2	8	no	—
829	#41	—	2	16	no	—
830	#41	—	4	8	no	—
831	#41	—	8	8	no	—
832	C₂×Q₈	—	4	2	no	—
833	C₂×Q₈	—	8	2	no	—
834	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
835	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
836	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
837	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
838	C₂×Q₈	C₂⁴×C₄₇	1	8	yes	—
839	C₂×D₄	—	2	32	no	—
840	C₂×D₄	—	2	16	no	—
841	C₂×D₄	—	2	16	no	—
842	C₂×D₄	—	2	32	no	—
843	C₂×D₄	—	4	8	no	—
844	C₂×D₄	—	8	8	no	—
845	C₂×D₄	#41×C₄₇	1	8	yes	complemented
846	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
847	C₂×D₄	C₂⁴×C₄₇	1	16	yes	—
848	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
849	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
850	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
851	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
852	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
853	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
854	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
855	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
856	C₂×D₄	C₂⁴×C₄₇	1	16	yes	—
857	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
858	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
859	C₂²×C₄	—	4	4	no	—
860	C₂²×C₄	—	4	8	no	—
861	C₂²×C₄	—	8	8	no	—
862	C₂²×C₄	—	8	4	no	—
863	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
864	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
865	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
867	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
868	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
869	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
870	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
871	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
873	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
875	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
876	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
877	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
879	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
880	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
882	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
883	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
884	C₂²×C₄	C₂⁴×C₄₇	1	16	yes	—
885	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
886	C₄⋊C₄	C₂⁴×C₄₇	1	1	yes	characteristic
887	C₄⋊C₄	C₂⁴×C₄₇	1	1	yes	characteristic
888	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
889	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
890	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
891	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
892	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
893	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
894	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
895	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
896	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
897	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
898	C₄⋊C₄	C₂⁴×C₄₇	1	16	yes	—
899	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
900	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
901	C₄⋊C₄	C₂⁴×C₄₇	1	8	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	16	yes	—
906	C₄⋊C₄	C₂⁴×C₄₇	1	16	yes	—
907	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
908	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
909	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
910	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
911	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
912	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
913	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
914	C₂²⋊C₄	C₂⁴×C₄₇	1	4	yes	—
915	C₂²⋊C₄	C₂⁴×C₄₇	1	16	yes	—
916	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
917	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
918	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
919	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
920	C₂²⋊C₄	C₂⁴×C₄₇	1	16	yes	—
921	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
922	C₂²⋊C₄	C₂⁴×C₄₇	1	4	yes	—
923	C₂²⋊C₄	C₂⁴×C₄₇	1	4	yes	—
924	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
925	C₂²⋊C₄	C₂⁴×C₄₇	1	16	yes	—
926	C₂²⋊C₄	C₂⁴×C₄₇	1	16	yes	—
927	C₂²⋊C₄	C₂⁴×C₄₇	1	16	yes	—
928	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
929	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
930	C₂²⋊C₄	C₂⁴×C₄₇	1	8	yes	—
931	C₄²	C₂⁴×C₄₇	1	4	yes	—
932	C₄²	C₂⁴×C₄₇	1	8	yes	—
933	C₄²	C₂⁴×C₄₇	1	4	yes	—
934	C₄²	C₂⁴×C₄₇	1	4	yes	—
935	C₄²	C₂⁴×C₄₇	1	2	yes	—
936	C₄²	C₂⁴×C₄₇	1	8	yes	—
937	C₄²	C₂⁴×C₄₇	1	16	yes	—
938	C₄²	C₂⁴×C₄₇	1	8	yes	—
939	C₄²	C₂⁴×C₄₇	1	4	yes	—
940	C₄²	C₂⁴×C₄₇	1	2	yes	—
941	C₄²	C₂⁴×C₄₇	1	4	yes	—
942	C₂³	—	2	8	no	—
943	C₂³	—	2	16	no	—
944	C₂³	—	4	2	no	—
945	C₂³	—	4	2	no	—
946	C₂³	—	4	4	no	—
947	C₂³	—	4	8	no	—
948	C₂³	—	4	8	no	—
949	C₂³	—	4	4	no	—
950	C₂³	C₂×#41×C₄₇	1	8	yes	—
951	C₂³	C₂⁵×C₄₇	1	4	yes	—
952	C₂³	C₂⁵×C₄₇	1	8	yes	—
953	C₂³	C₂⁵×C₄₇	1	4	yes	—
954	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
955	Q₈	—	2	8	no	—
956	Q₈	—	2	4	no	—
957	Q₈	—	2	4	no	—
958	Q₈	—	4	2	no	—
959	Q₈	—	4	8	no	—
960	D₄	—	2	16	no	—
961	D₄	—	2	32	no	—
962	D₄	—	2	8	no	—
963	D₄	—	2	16	no	—
964	D₄	—	2	4	no	—
965	D₄	—	2	8	no	—
966	D₄	—	2	8	no	—
967	D₄	—	4	8	no	—
968	D₄	—	4	8	no	—
969	D₄	—	4	16	no	—
970	D₄	—	4	8	no	—
971	D₄	—	4	4	no	—
972	D₄	C₂×#41×C₄₇	1	16	yes	—
973	C₂×C₄	—	2	16	no	—
974	C₂×C₄	—	2	8	no	—
975	C₂×C₄	—	2	16	no	—
976	C₂×C₄	—	2	8	no	—
977	C₂×C₄	—	2	8	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	8	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	8	no	—
982	C₂×C₄	—	4	2	no	—
983	C₂×C₄	—	4	4	no	—
984	C₂×C₄	—	4	4	no	—
985	C₂×C₄	—	4	8	no	—
986	C₂×C₄	—	4	2	no	—
987	C₂×C₄	—	4	8	no	—
988	C₂×C₄	—	4	8	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	4	16	no	—
991	C₂×C₄	—	4	2	no	—
992	C₂×C₄	—	4	1	no	—
993	C₂×C₄	—	4	8	no	—
994	C₂×C₄	—	4	4	no	—
995	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
996	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
997	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
998	C₂×C₄	C₂⁵×C₄₇	1	2	yes	—
999	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
1000	C₂×C₄	C₂⁵×C₄₇	1	2	yes	—
1001	C₂×C₄	C₂⁵×C₄₇	1	8	yes	—
1002	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
1003	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
1004	C₂×C₄	C₂⁵×C₄₇	1	4	yes	—
1005	C₂×C₄	C₂⁵×C₄₇	1	8	yes	—
1006	C₂×C₄	C₂⁵×C₄₇	1	2	yes	—
1007	C₂×C₄	C₂⁵×C₄₇	1	2	yes	—
1008	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	8	no	—
1015	C₂²	—	2	4	no	—
1016	C₂²	—	2	8	no	—
1017	C₂²	—	2	8	no	—
1018	C₂²	—	2	4	no	—
1019	C₂²	—	4	8	no	—
1020	C₂²	—	8	8	no	—
1021	C₂²	—	8	16	no	—
1022	C₂²	C₂²×#41×C₄₇	1	8	yes	—
1023	C₂²	C₂²×#41×C₄₇	1	2	yes	—
1024	C₂²	C₂⁶×C₄₇	1	1	yes	characteristic
1025	C₄	—	2	8	no	—
1026	C₄	—	2	4	no	—
1027	C₄	—	2	4	no	—
1028	C₄	—	2	4	no	—
1029	C₄	—	2	1	no	—
1030	C₄	—	2	4	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	4	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	8	no	—
1035	C₄	—	2	2	no	—
1036	C₄	C₂²×#41×C₄₇	1	4	yes	—
1037	C₄	C₄₇×#585	1	2	yes	—
1038	C₂	—	2	2	no	—
1039	C₂	—	2	8	no	—
1040	C₂	—	4	4	no	—
1041	C₂	—	4	8	no	—
1042	C₂	C₂³×#41×C₄₇	1	1	yes	characteristic
1043	C₂	C₂×C₄₇×#585	1	1	yes	characteristic
1044	C₂	C₄₇×H(7,𝔽₂)	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×#3521	C₂	semidirect
2. C₄₇×#3519	C₂	semidirect
3. C₄₇×#3515	C₂	semidirect
4. C₄₇×#3513	C₂	semidirect
5. C₄₇×#3512	C₂	semidirect
6. C₄₇×#3511	C₂	semidirect
7. C₄₇×#3505	C₂	semidirect
8. C₄₇×#3505	C₂	semidirect
9. C₄₇×#3496	C₂	semidirect
10. C₄₇×#3496	C₂	semidirect
11. C₄₇×#3481	C₂	semidirect
12. C₄₇×#3480	C₂	semidirect
13. C₄₇×#3475	C₂	semidirect
14. C₂×C₄₇×#554	C₂	semidirect
15. C₂×C₄₇×#553	C₂	semidirect
16. C₄×H(5,𝔽₂)×C₄₇	C₂	semidirect
17. C₄×H(5,𝔽₂)×C₄₇	C₂	semidirect
20. C₄₇×#559	C₂²	semidirect
21. C₄₇×#559	C₂²	semidirect
22. C₄₇×#557	C₂²	semidirect
23. C₄₇×#556	C₂²	semidirect
24. C₄₇×#556	C₂²	semidirect
25. C₄₇×#556	C₂²	semidirect
26. C₄₇×#555	C₂²	semidirect
27. C₄₇×#554	C₂²	semidirect
28. C₄₇×#554	C₂²	semidirect
29. C₄₇×#554	C₂²	semidirect
30. C₄₇×#554	C₂²	semidirect
31. C₄₇×#553	C₂²	semidirect
32. C₄₇×#553	C₂²	semidirect
33. C₄₇×#553	C₂²	semidirect
34. C₄₇×#553	C₂²	semidirect
35. C₄₇×#553	C₂²	semidirect
36. C₄₇×#553	C₂²	semidirect
37. C₄₇×#553	C₂²	semidirect
38. C₄₇×#553	C₂²	semidirect
39. C₄₇×#553	C₂²	semidirect
40. C₄₇×#553	C₂²	semidirect
41. C₄₇×#552	C₂²	semidirect
42. C₄₇×#552	C₂²	semidirect
43. C₄₇×#552	C₂²	semidirect
44. C₄₇×#552	C₂²	semidirect
45. C₄₇×#551	C₂²	semidirect
46. C₄₇×#551	C₂²	semidirect
47. C₄₇×#551	C₂²	semidirect
48. C₄₇×#550	C₂²	semidirect
49. C₄₇×#548	C₂²	semidirect
50. C₄₇×#548	C₂²	semidirect
51. C₄₇×#547	C₂²	semidirect
52. C₄₇×#547	C₂²	semidirect
53. C₄₇×#547	C₂²	semidirect
54. C₄₇×#546	C₂²	semidirect
55. C₄₇×#546	C₂²	semidirect
56. C₄₇×#546	C₂²	semidirect
57. C₄₇×#546	C₂²	semidirect
58. C₄₇×#546	C₂²	semidirect
59. D₄²×C₄₇	C₂²	semidirect
60. D₄²×C₄₇	C₂²	semidirect
61. C₄₇×#542	C₂²	semidirect
62. C₄₇×#541	C₂²	semidirect
63. C₄₇×#540	C₂²	semidirect
64. C₄₇×#539	C₂²	semidirect
65. C₄₇×#539	C₂²	semidirect
66. C₄₇×#538	C₂²	semidirect
67. C₄₇×#538	C₂²	semidirect
68. C₄₇×#537	C₂²	semidirect
69. C₄₇×#537	C₂²	semidirect
70. C₄₇×#534	C₂²	semidirect
71. C₄₇×#534	C₂²	semidirect
72. C₄₇×#533	C₂²	semidirect
73. C₄₇×#532	C₂²	semidirect
74. C₄₇×#532	C₂²	semidirect
75. C₄₇×#532	C₂²	semidirect
76. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
77. C₄₇×#529	C₂²	semidirect
78. C₄₇×#529	C₂²	semidirect
79. C₄₇×#529	C₂²	semidirect
80. C₄₇×#529	C₂²	semidirect
81. C₄₇×#529	C₂²	semidirect
82. C₄₇×#529	C₂²	semidirect
83. C₂×#126×C₄₇	C₂²	semidirect
84. C₂×#125×C₄₇	C₂²	semidirect
85. C₂×#125×C₄₇	C₂²	semidirect
86. C₄₇×#525	C₂²	semidirect
87. C₄₇×#525	C₂²	semidirect
88. C₂×#123×C₄₇	C₂²	semidirect
89. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
90. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
91. C₂×#121×C₄₇	C₂²	semidirect
92. C₂×#121×C₄₇	C₂²	semidirect
93. C₂×#121×C₄₇	C₂²	semidirect
94. C₄₇×#520	C₂²	semidirect
95. C₄₇×#520	C₂²	semidirect
96. C₄₇×#520	C₂²	semidirect
97. C₄₇×#520	C₂²	semidirect
99. C₄₇×#518	C₂²	semidirect
100. C₄₇×#518	C₂²	semidirect
101. C₄₇×#518	C₂²	semidirect
102. C₄₇×#518	C₂²	semidirect
103. C₄×#41×C₄₇	C₂²	semidirect
104. C₄×#41×C₄₇	C₂²	semidirect
105. C₄×#41×C₄₇	C₂²	semidirect
106. C₄×#41×C₄₇	C₂²	semidirect
107. C₄×#41×C₄₇	C₂²	semidirect
108. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
111. C₂×C₄×D₄×C₄₇	C₂²	semidirect
112. C₂×C₄×D₄×C₄₇	C₂²	semidirect
113. C₂×C₄×D₄×C₄₇	C₂²	semidirect
114. C₂×C₄×D₄×C₄₇	C₂²	semidirect
115. C₂×C₄×D₄×C₄₇	C₂²	semidirect
116. C₂×#117×C₄₇	C₂²	semidirect
117. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
322. C₂×D₄×C₄₇	#41	semidirect
486. #62992	C₄₇	direct (N × H)
516. #3521	C₂×C₄₇	semidirect
517. #3519	C₂×C₄₇	semidirect
518. #3515	C₂×C₄₇	semidirect
519. #3513	C₂×C₄₇	semidirect
520. #3512	C₂×C₄₇	semidirect
521. #3511	C₂×C₄₇	semidirect
522. #3505	C₂×C₄₇	semidirect
523. #3505	C₂×C₄₇	semidirect
524. #3496	C₂×C₄₇	semidirect
525. #3496	C₂×C₄₇	semidirect
526. #3481	C₂×C₄₇	semidirect
527. #3480	C₂×C₄₇	semidirect
528. #3475	C₂×C₄₇	semidirect
529. C₂×#554	C₂×C₄₇	semidirect
530. C₂×#553	C₂×C₄₇	semidirect
531. C₄×H(5,𝔽₂)	C₂×C₄₇	semidirect
532. C₄×H(5,𝔽₂)	C₂×C₄₇	semidirect
542. #559	C₂²×C₄₇	semidirect
543. #559	C₂²×C₄₇	semidirect
544. #557	C₂²×C₄₇	semidirect
545. #556	C₂²×C₄₇	semidirect
546. #556	C₂²×C₄₇	semidirect
547. #556	C₂²×C₄₇	semidirect
548. #555	C₂²×C₄₇	semidirect
549. #554	C₂²×C₄₇	semidirect
550. #554	C₂²×C₄₇	semidirect
551. #554	C₂²×C₄₇	semidirect
552. #554	C₂²×C₄₇	semidirect
553. #553	C₂²×C₄₇	semidirect
554. #553	C₂²×C₄₇	semidirect
555. #553	C₂²×C₄₇	semidirect
556. #553	C₂²×C₄₇	semidirect
557. #553	C₂²×C₄₇	semidirect
558. #553	C₂²×C₄₇	semidirect
559. #553	C₂²×C₄₇	semidirect
560. #553	C₂²×C₄₇	semidirect
561. #553	C₂²×C₄₇	semidirect
562. #553	C₂²×C₄₇	semidirect
563. #552	C₂²×C₄₇	semidirect
564. #552	C₂²×C₄₇	semidirect
565. #552	C₂²×C₄₇	semidirect
566. #552	C₂²×C₄₇	semidirect
567. #551	C₂²×C₄₇	semidirect
568. #551	C₂²×C₄₇	semidirect
569. #551	C₂²×C₄₇	semidirect
570. #550	C₂²×C₄₇	semidirect
571. #548	C₂²×C₄₇	semidirect
572. #548	C₂²×C₄₇	semidirect
573. #547	C₂²×C₄₇	semidirect
574. #547	C₂²×C₄₇	semidirect
575. #547	C₂²×C₄₇	semidirect
576. #546	C₂²×C₄₇	semidirect
577. #546	C₂²×C₄₇	semidirect
578. #546	C₂²×C₄₇	semidirect
579. #546	C₂²×C₄₇	semidirect
580. #546	C₂²×C₄₇	semidirect
581. D₄²	C₂²×C₄₇	semidirect
582. D₄²	C₂²×C₄₇	semidirect
583. #542	C₂²×C₄₇	semidirect
584. #541	C₂²×C₄₇	semidirect
585. #540	C₂²×C₄₇	semidirect
586. #539	C₂²×C₄₇	semidirect
587. #539	C₂²×C₄₇	semidirect
588. #538	C₂²×C₄₇	semidirect
589. #538	C₂²×C₄₇	semidirect
590. #537	C₂²×C₄₇	semidirect
591. #537	C₂²×C₄₇	semidirect
592. #534	C₂²×C₄₇	semidirect
593. #534	C₂²×C₄₇	semidirect
594. #533	C₂²×C₄₇	semidirect
595. #532	C₂²×C₄₇	semidirect
596. #532	C₂²×C₄₇	semidirect
597. #532	C₂²×C₄₇	semidirect
598. C₂×C₄⋊Q₈	C₂²×C₄₇	semidirect
599. #529	C₂²×C₄₇	semidirect
600. #529	C₂²×C₄₇	semidirect
601. #529	C₂²×C₄₇	semidirect
602. #529	C₂²×C₄₇	semidirect
603. #529	C₂²×C₄₇	semidirect
604. #529	C₂²×C₄₇	semidirect
605. C₂×#126	C₂²×C₄₇	semidirect
606. C₂×#125	C₂²×C₄₇	semidirect
607. C₂×#125	C₂²×C₄₇	semidirect
608. #525	C₂²×C₄₇	semidirect
609. #525	C₂²×C₄₇	semidirect
610. C₂×#123	C₂²×C₄₇	semidirect
611. C₂×C₂²⋊Q₈	C₂²×C₄₇	semidirect
612. C₂×C₂²⋊Q₈	C₂²×C₄₇	semidirect
613. C₂×#121	C₂²×C₄₇	semidirect
614. C₂×#121	C₂²×C₄₇	semidirect
615. C₂×#121	C₂²×C₄₇	semidirect
616. #520	C₂²×C₄₇	semidirect
617. #520	C₂²×C₄₇	semidirect
618. #520	C₂²×C₄₇	semidirect
619. #520	C₂²×C₄₇	semidirect
621. #518	C₂²×C₄₇	semidirect
622. #518	C₂²×C₄₇	semidirect
623. #518	C₂²×C₄₇	semidirect
624. #518	C₂²×C₄₇	semidirect
625. C₄×#41	C₂²×C₄₇	semidirect
626. C₄×#41	C₂²×C₄₇	semidirect
627. C₄×#41	C₂²×C₄₇	semidirect
628. C₄×#41	C₂²×C₄₇	semidirect
629. C₄×#41	C₂²×C₄₇	semidirect
630. C₂×C₄×Q₈	C₂²×C₄₇	semidirect
633. C₂×C₄×D₄	C₂²×C₄₇	semidirect
634. C₂×C₄×D₄	C₂²×C₄₇	semidirect
635. C₂×C₄×D₄	C₂²×C₄₇	semidirect
636. C₂×C₄×D₄	C₂²×C₄₇	semidirect
637. C₂×C₄×D₄	C₂²×C₄₇	semidirect
638. C₂×#117	C₂²×C₄₇	semidirect
639. C₂²×C₄⋊C₄	C₂²×C₄₇	semidirect
640. C₄₇	#62992	direct (N × H)
845. C₂×D₄	#41×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3521	2
C₄₇×#3519	2
C₄₇×#3515	2
C₄₇×#3513	2
C₄₇×#3512	2
C₄₇×#3511	2
C₄₇×#3505	2
C₄₇×#3496	2
C₄₇×#3481	2
C₄₇×#3480	2
C₄₇×#3475	2
C₂×C₄₇×#554	2
C₂×C₄₇×#553	2
C₄×H(5,𝔽₂)×C₄₇	2
#62992	47

Subgroups — C47×#62992 #26102690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#62992 #26102690