Subgroups — C₂×C₄₇×#2556 #26074522

Order 12032.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2556	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₇×#399	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₇×#396	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₇×#395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#388	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄₇×#388	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄₇×#387	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₇×#385	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
17	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#125×C₄₇	—	2	8	no	—
20	C₂×#125×C₄₇	C₂²	1	8	yes	complemented
21	C₂×C₂²⋊Q₈×C₄₇	—	2	8	no	—
22	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	8	yes	—
23	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
46	C₄₇×#399	C₂²	1	8	yes	—
47	C₄₇×#398	C₂²	1	8	yes	complemented
48	C₄₇×#396	C₂²	1	8	yes	—
49	C₄₇×#395	C₂²	1	8	yes	complemented
50	C₄₇×#391	C₂²	1	8	yes	complemented
51	C₄₇×#389	C₂²	1	8	yes	complemented
52	C₄₇×#389	C₂²	1	8	yes	complemented
53	C₄₇×#388	C₂²	1	8	yes	—
54	C₄₇×#388	C₂²	1	8	yes	—
55	C₄₇×#387	C₂²	1	8	yes	complemented
56	C₄₇×#385	C₂²	1	8	yes	—
57	C₄×C₄⋊C₄×C₄₇	C₂²	1	8	yes	complemented
58	C₄×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	—
59	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
60	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
61	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
62	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
63	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
64	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
65	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
66	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
67	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
68	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
69	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₄₇	—	2	4	no	—
71	C₂²×Q₈×C₄₇	—	2	4	no	—
72	C₂²×Q₈×C₄₇	—	4	2	no	—
73	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
74	C₂³×C₄×C₄₇	—	2	4	no	—
75	C₂³×C₄×C₄₇	—	2	4	no	—
76	C₂³×C₄×C₄₇	—	4	2	no	—
77	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
84	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	#125×C₄₇	—	2	32	no	—
93	C₂²⋊Q₈×C₄₇	—	2	32	no	—
94	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
95	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
96	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
97	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
98	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
99	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
100	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
101	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
102	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
103	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
104	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
105	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
106	C₂×C₄⋊C₄×C₄₇	D₄	1	8	yes	—
107	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
121	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
123	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
124	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
125	C₂×C₂²⋊C₄×C₄₇	Q₈	1	8	yes	complemented
126	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
132	C₂×C₄²×C₄₇	—	2	4	no	—
133	C₂×C₄²×C₄₇	—	2	4	no	—
134	C₂×C₄²×C₄₇	—	4	2	no	—
135	C₂×C₄²×C₄₇	—	4	2	no	—
136	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
137	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
138	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
139	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
140	#95×C₄₇	C₂³	1	4	yes	—
141	#95×C₄₇	C₂³	1	4	yes	—
142	#95×C₄₇	C₂³	1	4	yes	—
143	#95×C₄₇	C₂³	1	4	yes	—
144	#95×C₄₇	C₂³	1	4	yes	—
145	#95×C₄₇	C₂³	1	4	yes	—
146	#95×C₄₇	C₂³	1	4	yes	—
147	#95×C₄₇	C₂³	1	4	yes	—
148	#95×C₄₇	C₂³	1	4	yes	—
149	#95×C₄₇	C₂³	1	4	yes	—
150	C₂⁴×C₄₇	—	2	2	no	—
151	C₂⁴×C₄₇	—	2	2	no	—
152	C₂⁴×C₄₇	—	2	2	no	—
153	C₂⁴×C₄₇	—	2	2	no	—
154	C₂⁴×C₄₇	—	2	2	no	—
155	C₂⁴×C₄₇	—	2	2	no	—
156	C₂⁴×C₄₇	C₂×Q₈	1	4	yes	—
157	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
158	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
159	C₂×Q₈×C₄₇	—	2	8	no	—
160	C₂×Q₈×C₄₇	—	2	8	no	—
161	C₂×Q₈×C₄₇	—	4	4	no	—
162	C₂×Q₈×C₄₇	—	4	16	no	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	2	2	no	—
165	C₂²×C₄×C₄₇	—	2	2	no	—
166	C₂²×C₄×C₄₇	—	2	2	no	—
167	C₂²×C₄×C₄₇	—	2	2	no	—
168	C₂²×C₄×C₄₇	—	2	2	no	—
169	C₂²×C₄×C₄₇	—	2	2	no	—
170	C₂²×C₄×C₄₇	—	2	2	no	—
171	C₂²×C₄×C₄₇	—	2	2	no	—
172	C₂²×C₄×C₄₇	—	2	2	no	—
173	C₂²×C₄×C₄₇	—	2	2	no	—
174	C₂²×C₄×C₄₇	—	2	2	no	—
175	C₂²×C₄×C₄₇	—	2	2	no	—
176	C₂²×C₄×C₄₇	—	2	2	no	—
177	C₂²×C₄×C₄₇	—	2	2	no	—
178	C₂²×C₄×C₄₇	—	2	2	no	—
179	C₂²×C₄×C₄₇	—	2	2	no	—
180	C₂²×C₄×C₄₇	—	2	2	no	—
181	C₂²×C₄×C₄₇	—	2	2	no	—
182	C₂²×C₄×C₄₇	—	2	2	no	—
183	C₂²×C₄×C₄₇	—	2	2	no	—
184	C₂²×C₄×C₄₇	—	2	2	no	—
185	C₂²×C₄×C₄₇	—	2	2	no	—
186	C₂²×C₄×C₄₇	—	2	2	no	—
187	C₂²×C₄×C₄₇	—	2	2	no	—
188	C₂²×C₄×C₄₇	—	2	2	no	—
189	C₂²×C₄×C₄₇	—	2	2	no	—
190	C₂²×C₄×C₄₇	—	2	2	no	—
191	C₂²×C₄×C₄₇	—	2	2	no	—
192	C₂²×C₄×C₄₇	—	2	2	no	—
193	C₂²×C₄×C₄₇	—	2	2	no	—
194	C₂²×C₄×C₄₇	—	2	2	no	—
195	C₂²×C₄×C₄₇	—	2	2	no	—
196	C₂²×C₄×C₄₇	—	2	2	no	—
197	C₂²×C₄×C₄₇	—	2	8	no	—
198	C₂²×C₄×C₄₇	—	2	8	no	—
199	C₂²×C₄×C₄₇	—	4	4	no	—
200	C₂²×C₄×C₄₇	—	4	16	no	—
201	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
205	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
206	C₂²×C₄×C₄₇	#41	1	4	yes	—
207	C₂²×C₄×C₄₇	#41	1	4	yes	—
208	C₂²×C₄×C₄₇	#41	1	4	yes	—
209	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
223	C₄⋊C₄×C₄₇	—	2	8	no	—
224	C₄⋊C₄×C₄₇	—	2	8	no	—
225	C₄⋊C₄×C₄₇	—	2	8	no	—
226	C₄⋊C₄×C₄₇	—	2	8	no	—
227	C₄⋊C₄×C₄₇	—	2	8	no	—
228	C₄⋊C₄×C₄₇	—	2	8	no	—
229	C₄⋊C₄×C₄₇	—	2	8	no	—
230	C₄⋊C₄×C₄₇	—	2	8	no	—
231	C₄⋊C₄×C₄₇	—	2	8	no	—
232	C₄⋊C₄×C₄₇	—	2	8	no	—
233	C₄⋊C₄×C₄₇	—	2	8	no	—
234	C₄⋊C₄×C₄₇	—	4	4	no	—
235	C₄⋊C₄×C₄₇	C₂×D₄	1	16	yes	—
236	C₂²⋊C₄×C₄₇	—	2	8	no	—
237	C₂²⋊C₄×C₄₇	—	2	8	no	—
238	C₂²⋊C₄×C₄₇	—	2	8	no	—
239	C₂²⋊C₄×C₄₇	—	2	8	no	—
240	C₂²⋊C₄×C₄₇	—	4	4	no	—
241	C₂²⋊C₄×C₄₇	C₂×Q₈	1	16	yes	complemented
242	C₄²×C₄₇	—	2	8	no	—
243	C₄²×C₄₇	—	2	8	no	—
244	C₄²×C₄₇	—	4	4	no	—
245	C₄²×C₄₇	—	4	4	no	—
246	C₂³×C₄₇	—	2	8	no	—
247	C₂³×C₄₇	—	2	8	no	—
248	C₂³×C₄₇	—	2	8	no	—
249	C₂³×C₄₇	—	2	2	no	—
250	C₂³×C₄₇	—	2	2	no	—
251	C₂³×C₄₇	—	2	2	no	—
252	C₂³×C₄₇	—	2	2	no	—
253	C₂³×C₄₇	—	2	2	no	—
254	C₂³×C₄₇	—	2	2	no	—
255	C₂³×C₄₇	—	4	4	no	—
256	C₂³×C₄₇	—	4	4	no	—
257	C₂³×C₄₇	—	4	4	no	—
258	C₂³×C₄₇	—	4	4	no	—
259	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
260	C₂³×C₄₇	C₂²×Q₈	1	4	yes	—
261	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
262	C₂³×C₄₇	C₂×#41	1	2	yes	—
263	C₂³×C₄₇	C₂×#41	1	2	yes	—
264	C₂³×C₄₇	C₂×#41	1	2	yes	—
265	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
266	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
267	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
268	Q₈×C₄₇	—	4	16	no	—
269	C₂×C₄×C₄₇	—	2	8	no	—
270	C₂×C₄×C₄₇	—	2	8	no	—
271	C₂×C₄×C₄₇	—	2	8	no	—
272	C₂×C₄×C₄₇	—	2	8	no	—
273	C₂×C₄×C₄₇	—	2	8	no	—
274	C₂×C₄×C₄₇	—	2	8	no	—
275	C₂×C₄×C₄₇	—	2	8	no	—
276	C₂×C₄×C₄₇	—	2	8	no	—
277	C₂×C₄×C₄₇	—	2	2	no	—
278	C₂×C₄×C₄₇	—	2	2	no	—
279	C₂×C₄×C₄₇	—	2	2	no	—
280	C₂×C₄×C₄₇	—	2	2	no	—
281	C₂×C₄×C₄₇	—	2	2	no	—
282	C₂×C₄×C₄₇	—	2	2	no	—
283	C₂×C₄×C₄₇	—	2	2	no	—
284	C₂×C₄×C₄₇	—	2	2	no	—
285	C₂×C₄×C₄₇	—	2	2	no	—
286	C₂×C₄×C₄₇	—	2	2	no	—
287	C₂×C₄×C₄₇	—	2	2	no	—
288	C₂×C₄×C₄₇	—	2	2	no	—
289	C₂×C₄×C₄₇	—	2	2	no	—
290	C₂×C₄×C₄₇	—	2	2	no	—
291	C₂×C₄×C₄₇	—	2	2	no	—
292	C₂×C₄×C₄₇	—	2	2	no	—
293	C₂×C₄×C₄₇	—	2	2	no	—
294	C₂×C₄×C₄₇	—	2	2	no	—
295	C₂×C₄×C₄₇	—	2	2	no	—
296	C₂×C₄×C₄₇	—	2	2	no	—
297	C₂×C₄×C₄₇	—	2	2	no	—
298	C₂×C₄×C₄₇	—	2	2	no	—
299	C₂×C₄×C₄₇	—	2	2	no	—
300	C₂×C₄×C₄₇	—	2	2	no	—
301	C₂×C₄×C₄₇	—	2	2	no	—
302	C₂×C₄×C₄₇	—	2	2	no	—
303	C₂×C₄×C₄₇	—	2	2	no	—
304	C₂×C₄×C₄₇	—	2	2	no	—
305	C₂×C₄×C₄₇	—	2	2	no	—
306	C₂×C₄×C₄₇	—	2	2	no	—
307	C₂×C₄×C₄₇	—	2	2	no	—
308	C₂×C₄×C₄₇	—	2	2	no	—
309	C₂×C₄×C₄₇	—	2	2	no	—
310	C₂×C₄×C₄₇	—	2	2	no	—
311	C₂×C₄×C₄₇	—	4	16	no	—
312	C₂×C₄×C₄₇	—	4	4	no	—
313	C₂×C₄×C₄₇	—	4	4	no	—
314	C₂×C₄×C₄₇	—	4	4	no	—
315	C₂×C₄×C₄₇	—	4	4	no	—
316	C₂×C₄×C₄₇	—	4	4	no	—
317	C₂×C₄×C₄₇	—	4	4	no	—
318	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
319	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
320	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
321	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
322	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
323	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
324	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
325	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
326	C₂×#2556	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
327	C₂²×C₄₇	—	2	4	no	—
328	C₂²×C₄₇	—	2	4	no	—
329	C₂²×C₄₇	—	2	4	no	—
330	C₂²×C₄₇	—	4	2	no	—
331	C₂²×C₄₇	—	4	2	no	—
332	C₂²×C₄₇	—	4	2	no	—
333	C₂²×C₄₇	—	4	2	no	—
334	C₂²×C₄₇	—	4	16	no	—
335	C₂²×C₄₇	#532	1	4	yes	—
336	C₂²×C₄₇	#533	1	4	yes	—
337	C₂²×C₄₇	#539	1	4	yes	—
338	C₂²×C₄₇	#546	1	4	yes	—
339	C₂²×C₄₇	D₄×Q₈	1	4	yes	—
340	C₂²×C₄₇	#552	1	4	yes	—
341	C₂²×C₄₇	#554	1	4	yes	—
342	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
343	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
344	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
345	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
346	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
347	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
349	C₄×C₄₇	—	2	4	no	—
350	C₄×C₄₇	—	2	4	no	—
351	C₄×C₄₇	—	2	4	no	—
352	C₄×C₄₇	—	2	4	no	—
353	C₄×C₄₇	—	2	4	no	—
354	C₄×C₄₇	—	2	4	no	—
355	C₄×C₄₇	—	2	4	no	—
356	C₄×C₄₇	—	2	4	no	—
357	C₄×C₄₇	—	4	2	no	—
358	C₄×C₄₇	—	4	2	no	—
359	C₄×C₄₇	—	4	2	no	—
360	C₄×C₄₇	—	4	2	no	—
361	C₄×C₄₇	—	4	2	no	—
362	C₄×C₄₇	—	4	2	no	—
363	C₂²×#125	C₂×C₄₇	1	1	yes	characteristic, complemented
364	C₂²×C₂²⋊Q₈	C₂×C₄₇	1	1	yes	characteristic
365	#2556	C₂×C₄₇	1	16	yes	direct product factor
366	C₂×#399	C₂×C₄₇	1	1	yes	characteristic
367	C₂×#398	C₂×C₄₇	1	1	yes	characteristic, complemented
368	C₂×#396	C₂×C₄₇	1	1	yes	characteristic
369	C₂×#395	C₂×C₄₇	1	1	yes	characteristic, complemented
370	C₂×#391	C₂×C₄₇	1	1	yes	characteristic, complemented
371	C₂×#389	C₂×C₄₇	1	1	yes	characteristic, complemented
372	C₂×#389	C₂×C₄₇	1	1	yes	characteristic, complemented
373	C₂×#388	C₂×C₄₇	1	1	yes	characteristic
374	C₂×#388	C₂×C₄₇	1	1	yes	characteristic
375	C₂×#387	C₂×C₄₇	1	1	yes	characteristic, complemented
376	C₂×#385	C₂×C₄₇	1	1	yes	characteristic
377	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
378	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic
379	C₂×C₄₇	—	4	4	no	—
380	C₂×C₄₇	#2556	1	8	yes	direct product factor
381	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
382	C₂×C₄₇	C₂×#533	1	1	yes	characteristic
383	C₂×C₄₇	C₂×#539	1	1	yes	characteristic
384	C₂×C₄₇	C₂×#546	1	1	yes	characteristic
385	C₂×C₄₇	C₂×D₄×Q₈	1	1	yes	characteristic
386	C₂×C₄₇	C₂×#552	1	1	yes	characteristic
387	C₂×C₄₇	C₂×#554	1	1	yes	characteristic
388	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
389	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
390	C₂×#125	—	2	8	no	—
391	C₂×#125	C₂²×C₄₇	1	8	yes	complemented
392	C₂×C₂²⋊Q₈	—	2	8	no	—
393	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	8	yes	—
394	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
395	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
396	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
397	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
398	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
399	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
400	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
401	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
402	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
404	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
405	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
406	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
412	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
413	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
414	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
415	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
416	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
417	#399	C₂²×C₄₇	1	8	yes	—
418	#398	C₂²×C₄₇	1	8	yes	complemented
419	#396	C₂²×C₄₇	1	8	yes	—
420	#395	C₂²×C₄₇	1	8	yes	complemented
421	#391	C₂²×C₄₇	1	8	yes	complemented
422	#389	C₂²×C₄₇	1	8	yes	complemented
423	#389	C₂²×C₄₇	1	8	yes	complemented
424	#388	C₂²×C₄₇	1	8	yes	—
425	#388	C₂²×C₄₇	1	8	yes	—
426	#387	C₂²×C₄₇	1	8	yes	complemented
427	#385	C₂²×C₄₇	1	8	yes	—
428	C₄×C₄⋊C₄	C₂²×C₄₇	1	8	yes	complemented
429	C₄×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	—
430	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
431	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
432	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
433	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
434	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
435	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
436	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
437	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
438	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
439	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
440	C₄₇	C₂×#2556	1	1	yes	characteristic, direct product factor, Sylow
441	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
442	C₂²×Q₈	—	2	4	no	—
443	C₂²×Q₈	—	2	4	no	—
444	C₂²×Q₈	—	4	2	no	—
445	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
446	C₂³×C₄	—	2	4	no	—
447	C₂³×C₄	—	2	4	no	—
448	C₂³×C₄	—	4	2	no	—
449	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
456	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
464	#125	—	2	32	no	—
465	C₂²⋊Q₈	—	2	32	no	—
466	C₂×C₄⋊C₄	—	2	4	no	—
467	C₂×C₄⋊C₄	—	2	4	no	—
468	C₂×C₄⋊C₄	—	2	4	no	—
469	C₂×C₄⋊C₄	—	2	4	no	—
470	C₂×C₄⋊C₄	—	2	4	no	—
471	C₂×C₄⋊C₄	—	2	4	no	—
472	C₂×C₄⋊C₄	—	2	4	no	—
473	C₂×C₄⋊C₄	—	2	4	no	—
474	C₂×C₄⋊C₄	—	2	4	no	—
475	C₂×C₄⋊C₄	—	2	4	no	—
476	C₂×C₄⋊C₄	—	2	4	no	—
477	C₂×C₄⋊C₄	—	4	2	no	—
478	C₂×C₄⋊C₄	D₄×C₄₇	1	8	yes	—
479	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
482	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
483	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
484	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
485	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
492	C₂×C₂²⋊C₄	—	2	4	no	—
493	C₂×C₂²⋊C₄	—	2	4	no	—
494	C₂×C₂²⋊C₄	—	2	4	no	—
495	C₂×C₂²⋊C₄	—	2	4	no	—
496	C₂×C₂²⋊C₄	—	4	2	no	—
497	C₂×C₂²⋊C₄	Q₈×C₄₇	1	8	yes	complemented
498	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
504	C₂×C₄²	—	2	4	no	—
505	C₂×C₄²	—	2	4	no	—
506	C₂×C₄²	—	4	2	no	—
507	C₂×C₄²	—	4	2	no	—
508	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
509	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
510	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
511	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
512	#95	C₂³×C₄₇	1	4	yes	—
513	#95	C₂³×C₄₇	1	4	yes	—
514	#95	C₂³×C₄₇	1	4	yes	—
515	#95	C₂³×C₄₇	1	4	yes	—
516	#95	C₂³×C₄₇	1	4	yes	—
517	#95	C₂³×C₄₇	1	4	yes	—
518	#95	C₂³×C₄₇	1	4	yes	—
519	#95	C₂³×C₄₇	1	4	yes	—
520	#95	C₂³×C₄₇	1	4	yes	—
521	#95	C₂³×C₄₇	1	4	yes	—
522	C₂⁴	—	2	2	no	—
523	C₂⁴	—	2	2	no	—
524	C₂⁴	—	2	2	no	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	C₂×Q₈×C₄₇	1	4	yes	—
529	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
530	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
531	C₂×Q₈	—	2	8	no	—
532	C₂×Q₈	—	2	8	no	—
533	C₂×Q₈	—	4	4	no	—
534	C₂×Q₈	—	4	16	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	8	no	—
570	C₂²×C₄	—	2	8	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	16	no	—
573	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
574	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
575	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
576	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
577	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
578	C₂²×C₄	#41×C₄₇	1	4	yes	—
579	C₂²×C₄	#41×C₄₇	1	4	yes	—
580	C₂²×C₄	#41×C₄₇	1	4	yes	—
581	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
595	C₄⋊C₄	—	2	8	no	—
596	C₄⋊C₄	—	2	8	no	—
597	C₄⋊C₄	—	2	8	no	—
598	C₄⋊C₄	—	2	8	no	—
599	C₄⋊C₄	—	2	8	no	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	8	no	—
603	C₄⋊C₄	—	2	8	no	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	2	8	no	—
606	C₄⋊C₄	—	4	4	no	—
607	C₄⋊C₄	C₂×D₄×C₄₇	1	16	yes	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	4	4	no	—
613	C₂²⋊C₄	C₂×Q₈×C₄₇	1	16	yes	complemented
614	C₄²	—	2	8	no	—
615	C₄²	—	2	8	no	—
616	C₄²	—	4	4	no	—
617	C₄²	—	4	4	no	—
618	C₂³	—	2	8	no	—
619	C₂³	—	2	8	no	—
620	C₂³	—	2	8	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	4	4	no	—
628	C₂³	—	4	4	no	—
629	C₂³	—	4	4	no	—
630	C₂³	—	4	4	no	—
631	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
632	C₂³	C₂²×Q₈×C₄₇	1	4	yes	—
633	C₂³	C₂²×Q₈×C₄₇	1	2	yes	—
634	C₂³	C₂×#41×C₄₇	1	2	yes	—
635	C₂³	C₂×#41×C₄₇	1	2	yes	—
636	C₂³	C₂×#41×C₄₇	1	2	yes	—
637	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
638	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
639	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
640	Q₈	—	4	16	no	—
641	C₂×C₄	—	2	8	no	—
642	C₂×C₄	—	2	8	no	—
643	C₂×C₄	—	2	8	no	—
644	C₂×C₄	—	2	8	no	—
645	C₂×C₄	—	2	8	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	8	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	4	16	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
691	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
692	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
693	C₂×C₄	C₂²×Q₈×C₄₇	1	4	yes	—
694	C₂×C₄	C₂²×Q₈×C₄₇	1	4	yes	—
695	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
696	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
697	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
698	C₂²	—	2	4	no	—
699	C₂²	—	2	4	no	—
700	C₂²	—	2	4	no	—
701	C₂²	—	4	16	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	C₄₇×#532	1	4	yes	—
707	C₂²	C₄₇×#533	1	4	yes	—
708	C₂²	C₄₇×#539	1	4	yes	—
709	C₂²	C₄₇×#546	1	4	yes	—
710	C₂²	D₄×Q₈×C₄₇	1	4	yes	—
711	C₂²	C₄₇×#552	1	4	yes	—
712	C₂²	C₄₇×#554	1	4	yes	—
713	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
714	C₂²	C₂³×Q₈×C₄₇	1	1	yes	characteristic
715	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
716	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
717	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
718	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
719	C₂²	C₂×2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
720	C₄	—	2	4	no	—
721	C₄	—	2	4	no	—
722	C₄	—	2	4	no	—
723	C₄	—	2	4	no	—
724	C₄	—	2	4	no	—
725	C₄	—	2	4	no	—
726	C₄	—	2	4	no	—
727	C₄	—	2	4	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₂	—	4	4	no	—
735	C₂	C₄₇×#2556	1	8	yes	direct product factor
736	C₂	C₂×C₄₇×#532	1	1	yes	characteristic
737	C₂	C₂×C₄₇×#533	1	1	yes	characteristic
738	C₂	C₂×C₄₇×#539	1	1	yes	characteristic
739	C₂	C₂×C₄₇×#546	1	1	yes	characteristic
740	C₂	C₂×D₄×Q₈×C₄₇	1	1	yes	characteristic
741	C₂	C₂×C₄₇×#552	1	1	yes	characteristic
742	C₂	C₂×C₄₇×#554	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#125×C₄₇	C₂	semidirect
3. C₄₇×#2556	C₂	direct (N × H)
5. C₂×C₄₇×#398	C₂	semidirect
7. C₂×C₄₇×#395	C₂	semidirect
8. C₂×C₄₇×#391	C₂	semidirect
9. C₂×C₄₇×#389	C₂	semidirect
10. C₂×C₄₇×#389	C₂	semidirect
13. C₂×C₄₇×#387	C₂	semidirect
15. C₂×C₄×C₄⋊C₄×C₄₇	C₂	semidirect
20. C₂×#125×C₄₇	C₂²	semidirect
47. C₄₇×#398	C₂²	semidirect
49. C₄₇×#395	C₂²	semidirect
50. C₄₇×#391	C₂²	semidirect
51. C₄₇×#389	C₂²	semidirect
52. C₄₇×#389	C₂²	semidirect
55. C₄₇×#387	C₂²	semidirect
57. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
125. C₂×C₂²⋊C₄×C₄₇	Q₈	semidirect
241. C₂²⋊C₄×C₄₇	C₂×Q₈	semidirect
326. C₂×#2556	C₄₇	direct (N × H)
363. C₂²×#125	C₂×C₄₇	semidirect
365. #2556	C₂×C₄₇	direct (N × H)
367. C₂×#398	C₂×C₄₇	semidirect
369. C₂×#395	C₂×C₄₇	semidirect
370. C₂×#391	C₂×C₄₇	semidirect
371. C₂×#389	C₂×C₄₇	semidirect
372. C₂×#389	C₂×C₄₇	semidirect
375. C₂×#387	C₂×C₄₇	semidirect
377. C₂×C₄×C₄⋊C₄	C₂×C₄₇	semidirect
380. C₂×C₄₇	#2556	direct (N × H)
391. C₂×#125	C₂²×C₄₇	semidirect
418. #398	C₂²×C₄₇	semidirect
420. #395	C₂²×C₄₇	semidirect
421. #391	C₂²×C₄₇	semidirect
422. #389	C₂²×C₄₇	semidirect
423. #389	C₂²×C₄₇	semidirect
426. #387	C₂²×C₄₇	semidirect
428. C₄×C₄⋊C₄	C₂²×C₄₇	semidirect
440. C₄₇	C₂×#2556	direct (N × H)
497. C₂×C₂²⋊C₄	Q₈×C₄₇	semidirect
613. C₂²⋊C₄	C₂×Q₈×C₄₇	semidirect
735. C₂	C₄₇×#2556	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#125×C₄₇	2
C₂²×C₂²⋊Q₈×C₄₇	2
C₄₇×#2556	2
C₂×C₄₇×#399	2
C₂×C₄₇×#398	2
C₂×C₄₇×#396	2
C₂×C₄₇×#395	2
C₂×C₄₇×#391	2
C₂×C₄₇×#389	2
C₂×C₄₇×#388	2
C₂×C₄₇×#387	2
C₂×C₄₇×#385	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₂×#2556	47

Subgroups — C2×C47×#2556 #26074522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2556 #26074522