Subgroups — C₂×C₄₇×#2407 #26074407

Order 12032.

5998 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#121×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2407	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄₇×#394	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₇×#392	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₇×#390	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₇×#386	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#385	C₂	1	2	yes	maximal, complemented
12	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₄₇	—	2	8	no	—
14	C₂²×#41×C₄₇	—	2	8	no	—
15	C₂²×#41×C₄₇	—	2	8	no	—
16	C₂²×#41×C₄₇	C₂²	1	8	yes	complemented
17	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
19	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
21	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
23	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₄₇	—	2	8	no	—
26	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	8	yes	complemented
27	C₂×#121×C₄₇	—	2	8	no	—
28	C₂×#121×C₄₇	C₂²	1	8	yes	complemented
29	C₂×C₄×D₄×C₄₇	—	2	8	no	—
30	C₂×C₄×D₄×C₄₇	C₂²	1	8	yes	complemented
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	2	yes	—
35	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
37	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
39	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
41	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
42	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#394	C₂²	1	16	yes	complemented
44	C₄₇×#392	C₂²	1	16	yes	complemented
45	C₄₇×#391	C₂²	1	8	yes	complemented
46	C₄₇×#390	C₂²	1	8	yes	complemented
47	C₄₇×#386	C₂²	1	16	yes	complemented
48	C₄₇×#385	C₂²	1	16	yes	complemented
49	C₄₇×#380	C₂²	1	8	yes	complemented
50	C₂×#95×C₄₇	C₂²	1	2	yes	—
51	C₂×#95×C₄₇	C₂²	1	2	yes	—
52	C₂×#95×C₄₇	C₂²	1	2	yes	—
53	C₂⁵×C₄₇	C₂³	1	2	yes	—
54	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
55	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
56	C₂×#41×C₄₇	—	2	128	no	—
57	C₂×#41×C₄₇	—	2	32	no	—
58	C₂×#41×C₄₇	—	2	32	no	—
59	C₂×#41×C₄₇	—	2	32	no	—
60	C₂²×Q₈×C₄₇	—	2	4	no	—
61	C₂²×Q₈×C₄₇	—	2	4	no	—
62	C₂²×Q₈×C₄₇	D₄	1	8	yes	complemented
63	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
64	C₂²×D₄×C₄₇	—	2	4	no	—
65	C₂²×D₄×C₄₇	—	2	8	no	—
66	C₂²×D₄×C₄₇	—	2	8	no	—
67	C₂²×D₄×C₄₇	—	2	4	no	—
68	C₂²×D₄×C₄₇	—	2	8	no	—
69	C₂²×D₄×C₄₇	—	2	8	no	—
70	C₂²×D₄×C₄₇	—	2	8	no	—
71	C₂²×D₄×C₄₇	—	2	4	no	—
72	C₂²×D₄×C₄₇	—	2	4	no	—
73	C₂²×D₄×C₄₇	—	2	4	no	—
74	C₂²×D₄×C₄₇	—	4	4	no	—
75	C₂²×D₄×C₄₇	D₄	1	8	yes	complemented
76	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
77	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
78	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
79	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
80	C₂³×C₄×C₄₇	—	2	8	no	—
81	C₂³×C₄×C₄₇	—	2	8	no	—
82	C₂³×C₄×C₄₇	—	2	8	no	—
83	C₂³×C₄×C₄₇	—	2	4	no	—
84	C₂³×C₄×C₄₇	—	2	4	no	—
85	C₂³×C₄×C₄₇	—	2	4	no	—
86	C₂³×C₄×C₄₇	—	2	4	no	—
87	C₂³×C₄×C₄₇	—	2	4	no	—
88	C₂³×C₄×C₄₇	D₄	1	8	yes	complemented
89	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
90	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
91	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
93	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
95	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
97	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
98	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
100	C₂²⋊Q₈×C₄₇	—	2	32	no	—
101	#121×C₄₇	—	2	32	no	—
102	C₄×D₄×C₄₇	—	2	32	no	—
103	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
104	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
105	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
106	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
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	8	yes	—
111	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
112	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
113	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
114	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
115	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
116	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
117	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
118	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
122	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
123	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
124	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
125	C₂×C₄²×C₄₇	—	2	4	no	—
126	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
127	#95×C₄₇	C₂³	1	8	yes	—
128	#95×C₄₇	C₂³	1	8	yes	—
129	#95×C₄₇	C₂³	1	8	yes	—
130	C₂⁴×C₄₇	—	2	2	no	—
131	C₂⁴×C₄₇	—	2	2	no	—
132	C₂⁴×C₄₇	—	2	4	no	—
133	C₂⁴×C₄₇	—	2	2	no	—
134	C₂⁴×C₄₇	—	2	4	no	—
135	C₂⁴×C₄₇	—	2	2	no	—
136	C₂⁴×C₄₇	—	2	2	no	—
137	C₂⁴×C₄₇	—	2	4	no	—
138	C₂⁴×C₄₇	—	2	2	no	—
139	C₂⁴×C₄₇	—	2	2	no	—
140	C₂⁴×C₄₇	—	2	2	no	—
141	C₂⁴×C₄₇	—	2	4	no	—
142	C₂⁴×C₄₇	—	2	2	no	—
143	C₂⁴×C₄₇	—	2	4	no	—
144	C₂⁴×C₄₇	—	2	2	no	—
145	C₂⁴×C₄₇	—	2	2	no	—
146	C₂⁴×C₄₇	—	2	4	no	—
147	C₂⁴×C₄₇	—	2	2	no	—
148	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
149	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
150	C₂⁴×C₄₇	#41	1	4	yes	complemented
151	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
152	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
153	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
154	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
155	#41×C₄₇	—	2	256	no	—
156	C₂×Q₈×C₄₇	—	2	32	no	—
157	C₂×Q₈×C₄₇	—	2	8	no	—
158	C₂×Q₈×C₄₇	—	2	8	no	—
159	C₂×Q₈×C₄₇	C₂×D₄	1	16	yes	complemented
160	C₂×D₄×C₄₇	—	2	32	no	—
161	C₂×D₄×C₄₇	—	2	64	no	—
162	C₂×D₄×C₄₇	—	2	8	no	—
163	C₂×D₄×C₄₇	—	2	16	no	—
164	C₂×D₄×C₄₇	—	2	16	no	—
165	C₂×D₄×C₄₇	—	2	8	no	—
166	C₂×D₄×C₄₇	—	2	16	no	—
167	C₂×D₄×C₄₇	—	2	16	no	—
168	C₂×D₄×C₄₇	—	2	32	no	—
169	C₂×D₄×C₄₇	—	2	16	no	—
170	C₂×D₄×C₄₇	—	2	8	no	—
171	C₂×D₄×C₄₇	—	2	8	no	—
172	C₂×D₄×C₄₇	—	2	8	no	—
173	C₂×D₄×C₄₇	—	4	8	no	—
174	C₂×D₄×C₄₇	—	4	32	no	—
175	C₂×D₄×C₄₇	C₂×D₄	1	16	yes	complemented
176	C₂²×C₄×C₄₇	—	2	64	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	4	no	—
181	C₂²×C₄×C₄₇	—	2	4	no	—
182	C₂²×C₄×C₄₇	—	2	16	no	—
183	C₂²×C₄×C₄₇	—	2	2	no	—
184	C₂²×C₄×C₄₇	—	2	32	no	—
185	C₂²×C₄×C₄₇	—	2	16	no	—
186	C₂²×C₄×C₄₇	—	2	16	no	—
187	C₂²×C₄×C₄₇	—	2	8	no	—
188	C₂²×C₄×C₄₇	—	2	8	no	—
189	C₂²×C₄×C₄₇	—	2	2	no	—
190	C₂²×C₄×C₄₇	—	2	2	no	—
191	C₂²×C₄×C₄₇	—	2	4	no	—
192	C₂²×C₄×C₄₇	—	2	2	no	—
193	C₂²×C₄×C₄₇	—	2	4	no	—
194	C₂²×C₄×C₄₇	—	2	2	no	—
195	C₂²×C₄×C₄₇	—	2	4	no	—
196	C₂²×C₄×C₄₇	—	2	4	no	—
197	C₂²×C₄×C₄₇	—	2	2	no	—
198	C₂²×C₄×C₄₇	—	2	4	no	—
199	C₂²×C₄×C₄₇	—	2	4	no	—
200	C₂²×C₄×C₄₇	—	2	2	no	—
201	C₂²×C₄×C₄₇	—	2	8	no	—
202	C₂²×C₄×C₄₇	—	2	8	no	—
203	C₂²×C₄×C₄₇	—	2	8	no	—
204	C₂²×C₄×C₄₇	—	4	16	no	—
205	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
207	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
208	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₄₇	C₂×D₄	1	16	yes	complemented
211	C₂²×C₄×C₄₇	#41	1	4	yes	complemented
212	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
220	C₄⋊C₄×C₄₇	—	2	8	no	—
221	C₄⋊C₄×C₄₇	—	2	8	no	—
222	C₄⋊C₄×C₄₇	—	2	8	no	—
223	C₄⋊C₄×C₄₇	—	2	16	no	—
224	C₂²⋊C₄×C₄₇	—	2	8	no	—
225	C₂²⋊C₄×C₄₇	—	2	16	no	—
226	C₂²⋊C₄×C₄₇	—	2	8	no	—
227	C₂²⋊C₄×C₄₇	—	2	16	no	—
228	C₂²⋊C₄×C₄₇	—	2	16	no	—
229	C₂²⋊C₄×C₄₇	—	4	8	no	—
230	C₂²⋊C₄×C₄₇	—	4	8	no	—
231	C₄²×C₄₇	—	2	8	no	—
232	C₂³×C₄₇	—	2	16	no	—
233	C₂³×C₄₇	—	2	8	no	—
234	C₂³×C₄₇	—	2	8	no	—
235	C₂³×C₄₇	—	2	8	no	—
236	C₂³×C₄₇	—	2	8	no	—
237	C₂³×C₄₇	—	2	8	no	—
238	C₂³×C₄₇	—	2	16	no	—
239	C₂³×C₄₇	—	2	16	no	—
240	C₂³×C₄₇	—	2	8	no	—
241	C₂³×C₄₇	—	2	2	no	—
242	C₂³×C₄₇	—	2	2	no	—
243	C₂³×C₄₇	—	2	4	no	—
244	C₂³×C₄₇	—	2	2	no	—
245	C₂³×C₄₇	—	2	4	no	—
246	C₂³×C₄₇	—	2	2	no	—
247	C₂³×C₄₇	—	2	2	no	—
248	C₂³×C₄₇	—	2	4	no	—
249	C₂³×C₄₇	—	2	2	no	—
250	C₂³×C₄₇	—	2	2	no	—
251	C₂³×C₄₇	—	2	2	no	—
252	C₂³×C₄₇	—	2	4	no	—
253	C₂³×C₄₇	—	2	2	no	—
254	C₂³×C₄₇	—	2	4	no	—
255	C₂³×C₄₇	—	2	2	no	—
256	C₂³×C₄₇	—	2	2	no	—
257	C₂³×C₄₇	—	2	4	no	—
258	C₂³×C₄₇	—	2	2	no	—
259	C₂³×C₄₇	—	4	4	no	—
260	C₂³×C₄₇	—	4	8	no	—
261	C₂³×C₄₇	—	4	4	no	—
262	C₂³×C₄₇	—	4	8	no	—
263	C₂³×C₄₇	—	4	4	no	—
264	C₂³×C₄₇	—	4	4	no	—
265	C₂³×C₄₇	—	4	4	no	—
266	C₂³×C₄₇	—	4	4	no	—
267	C₂³×C₄₇	—	4	8	no	—
268	C₂³×C₄₇	—	4	4	no	—
269	C₂³×C₄₇	—	4	8	no	—
270	C₂³×C₄₇	—	4	4	no	—
271	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
272	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
273	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
274	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
275	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
276	C₂³×C₄₇	C₂×#41	1	2	yes	—
277	C₂³×C₄₇	C₂×#41	1	2	yes	—
278	C₂³×C₄₇	C₂×#41	1	4	yes	complemented
279	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
280	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
281	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
282	Q₈×C₄₇	—	2	32	no	—
283	D₄×C₄₇	—	2	32	no	—
284	D₄×C₄₇	—	2	64	no	—
285	D₄×C₄₇	—	2	32	no	—
286	D₄×C₄₇	—	4	32	no	—
287	C₂×C₄×C₄₇	—	2	64	no	—
288	C₂×C₄×C₄₇	—	2	8	no	—
289	C₂×C₄×C₄₇	—	2	16	no	—
290	C₂×C₄×C₄₇	—	2	8	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	4	no	—
295	C₂×C₄×C₄₇	—	2	4	no	—
296	C₂×C₄×C₄₇	—	2	2	no	—
297	C₂×C₄×C₄₇	—	2	32	no	—
298	C₂×C₄×C₄₇	—	2	2	no	—
299	C₂×C₄×C₄₇	—	2	2	no	—
300	C₂×C₄×C₄₇	—	2	4	no	—
301	C₂×C₄×C₄₇	—	2	2	no	—
302	C₂×C₄×C₄₇	—	2	4	no	—
303	C₂×C₄×C₄₇	—	2	2	no	—
304	C₂×C₄×C₄₇	—	2	4	no	—
305	C₂×C₄×C₄₇	—	2	4	no	—
306	C₂×C₄×C₄₇	—	2	2	no	—
307	C₂×C₄×C₄₇	—	2	4	no	—
308	C₂×C₄×C₄₇	—	2	4	no	—
309	C₂×C₄×C₄₇	—	2	2	no	—
310	C₂×C₄×C₄₇	—	4	4	no	—
311	C₂×C₄×C₄₇	—	4	4	no	—
312	C₂×C₄×C₄₇	—	4	8	no	—
313	C₂×C₄×C₄₇	—	4	8	no	—
314	C₂×C₄×C₄₇	—	4	16	no	—
315	C₂×C₄×C₄₇	#120	1	16	yes	—
316	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
317	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
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	C₂×#41	1	4	yes	complemented
322	C₂×#2407	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
323	C₂²×C₄₇	—	2	8	no	—
324	C₂²×C₄₇	—	2	4	no	—
325	C₂²×C₄₇	—	2	4	no	—
326	C₂²×C₄₇	—	2	4	no	—
327	C₂²×C₄₇	—	2	4	no	—
328	C₂²×C₄₇	—	2	4	no	—
329	C₂²×C₄₇	—	2	8	no	—
330	C₂²×C₄₇	—	2	8	no	—
331	C₂²×C₄₇	—	2	4	no	—
332	C₂²×C₄₇	—	4	16	no	—
333	C₂²×C₄₇	—	4	32	no	—
334	C₂²×C₄₇	—	4	16	no	—
335	C₂²×C₄₇	—	4	2	no	—
336	C₂²×C₄₇	—	4	4	no	—
337	C₂²×C₄₇	—	4	2	no	—
338	C₂²×C₄₇	—	4	4	no	—
339	C₂²×C₄₇	—	4	2	no	—
340	C₂²×C₄₇	—	4	2	no	—
341	C₂²×C₄₇	—	4	2	no	—
342	C₂²×C₄₇	—	4	2	no	—
343	C₂²×C₄₇	—	4	4	no	—
344	C₂²×C₄₇	—	4	2	no	—
345	C₂²×C₄₇	—	4	4	no	—
346	C₂²×C₄₇	—	4	2	no	—
347	C₂²×C₄₇	C₂×#120	1	4	yes	—
348	C₂²×C₄₇	#525	1	4	yes	—
349	C₂²×C₄₇	#537	1	4	yes	—
350	C₂²×C₄₇	#546	1	4	yes	—
351	C₂²×C₄₇	#547	1	4	yes	—
352	C₂²×C₄₇	#548	1	4	yes	—
353	C₂²×C₄₇	#550	1	4	yes	—
354	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
355	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
356	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
357	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
358	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
359	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
361	C₄×C₄₇	—	2	4	no	—
362	C₄×C₄₇	—	2	8	no	—
363	C₄×C₄₇	—	2	4	no	—
364	C₄×C₄₇	—	4	2	no	—
365	C₄×C₄₇	—	4	2	no	—
366	C₄×C₄₇	—	4	4	no	—
367	C₄×C₄₇	—	4	4	no	—
368	C₄×C₄₇	C₂×#120	1	8	yes	—
369	C₂³×#41	C₂×C₄₇	1	1	yes	characteristic, complemented
370	C₂²×C₂²⋊Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
371	C₂²×#121	C₂×C₄₇	1	1	yes	characteristic, complemented
372	C₂²×C₄×D₄	C₂×C₄₇	1	1	yes	characteristic, complemented
373	#2407	C₂×C₄₇	1	16	yes	direct product factor
374	C₂×#394	C₂×C₄₇	1	2	yes	complemented
375	C₂×#392	C₂×C₄₇	1	2	yes	complemented
376	C₂×#391	C₂×C₄₇	1	1	yes	characteristic, complemented
377	C₂×#390	C₂×C₄₇	1	1	yes	characteristic, complemented
378	C₂×#386	C₂×C₄₇	1	2	yes	complemented
379	C₂×#385	C₂×C₄₇	1	2	yes	complemented
380	C₂×#380	C₂×C₄₇	1	1	yes	characteristic, complemented
381	C₂×C₄₇	—	4	4	no	—
382	C₂×C₄₇	—	4	8	no	—
383	C₂×C₄₇	—	4	4	no	—
384	C₂×C₄₇	#2407	1	8	yes	direct product factor
385	C₂×C₄₇	C₂²×#120	1	1	yes	characteristic
386	C₂×C₄₇	C₂×#525	1	1	yes	characteristic
387	C₂×C₄₇	C₂×#537	1	1	yes	characteristic
388	C₂×C₄₇	C₂×#546	1	1	yes	characteristic
389	C₂×C₄₇	C₂×#547	1	1	yes	characteristic
390	C₂×C₄₇	C₂×#548	1	1	yes	characteristic
391	C₂×C₄₇	C₂×#550	1	1	yes	characteristic
392	C₂²×#41	—	2	8	no	—
393	C₂²×#41	—	2	8	no	—
394	C₂²×#41	—	2	8	no	—
395	C₂²×#41	C₂²×C₄₇	1	8	yes	complemented
396	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
397	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
398	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
399	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
400	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
401	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
402	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
403	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
404	C₂×C₂²⋊Q₈	—	2	8	no	—
405	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	8	yes	complemented
406	C₂×#121	—	2	8	no	—
407	C₂×#121	C₂²×C₄₇	1	8	yes	complemented
408	C₂×C₄×D₄	—	2	8	no	—
409	C₂×C₄×D₄	C₂²×C₄₇	1	8	yes	complemented
410	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
411	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
412	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
413	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
414	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
415	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
416	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
417	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
418	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
419	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
420	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
421	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
422	#394	C₂²×C₄₇	1	16	yes	complemented
423	#392	C₂²×C₄₇	1	16	yes	complemented
424	#391	C₂²×C₄₇	1	8	yes	complemented
425	#390	C₂²×C₄₇	1	8	yes	complemented
426	#386	C₂²×C₄₇	1	16	yes	complemented
427	#385	C₂²×C₄₇	1	16	yes	complemented
428	#380	C₂²×C₄₇	1	8	yes	complemented
429	C₂×#95	C₂²×C₄₇	1	2	yes	—
430	C₂×#95	C₂²×C₄₇	1	2	yes	—
431	C₂×#95	C₂²×C₄₇	1	2	yes	—
432	C₄₇	C₂×#2407	1	1	yes	characteristic, direct product factor, Sylow
433	C₂⁵	C₂³×C₄₇	1	2	yes	—
434	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
435	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
436	C₂×#41	—	2	128	no	—
437	C₂×#41	—	2	32	no	—
438	C₂×#41	—	2	32	no	—
439	C₂×#41	—	2	32	no	—
440	C₂²×Q₈	—	2	4	no	—
441	C₂²×Q₈	—	2	4	no	—
442	C₂²×Q₈	D₄×C₄₇	1	8	yes	complemented
443	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
444	C₂²×D₄	—	2	4	no	—
445	C₂²×D₄	—	2	8	no	—
446	C₂²×D₄	—	2	8	no	—
447	C₂²×D₄	—	2	4	no	—
448	C₂²×D₄	—	2	8	no	—
449	C₂²×D₄	—	2	8	no	—
450	C₂²×D₄	—	2	8	no	—
451	C₂²×D₄	—	2	4	no	—
452	C₂²×D₄	—	2	4	no	—
453	C₂²×D₄	—	2	4	no	—
454	C₂²×D₄	—	4	4	no	—
455	C₂²×D₄	D₄×C₄₇	1	8	yes	complemented
456	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
457	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
458	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
459	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
460	C₂³×C₄	—	2	8	no	—
461	C₂³×C₄	—	2	8	no	—
462	C₂³×C₄	—	2	8	no	—
463	C₂³×C₄	—	2	4	no	—
464	C₂³×C₄	—	2	4	no	—
465	C₂³×C₄	—	2	4	no	—
466	C₂³×C₄	—	2	4	no	—
467	C₂³×C₄	—	2	4	no	—
468	C₂³×C₄	D₄×C₄₇	1	8	yes	complemented
469	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
470	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
473	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
474	C₂³×C₄	C₂³×C₄₇	1	8	yes	—
475	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
477	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
478	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
480	C₂²⋊Q₈	—	2	32	no	—
481	#121	—	2	32	no	—
482	C₄×D₄	—	2	32	no	—
483	C₂×C₄⋊C₄	—	2	4	no	—
484	C₂×C₄⋊C₄	—	2	4	no	—
485	C₂×C₄⋊C₄	—	2	4	no	—
486	C₂×C₄⋊C₄	—	2	8	no	—
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	8	yes	—
491	C₂×C₂²⋊C₄	—	2	4	no	—
492	C₂×C₂²⋊C₄	—	2	8	no	—
493	C₂×C₂²⋊C₄	—	2	4	no	—
494	C₂×C₂²⋊C₄	—	2	8	no	—
495	C₂×C₂²⋊C₄	—	2	8	no	—
496	C₂×C₂²⋊C₄	—	4	4	no	—
497	C₂×C₂²⋊C₄	—	4	4	no	—
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	8	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
505	C₂×C₄²	—	2	4	no	—
506	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
507	#95	C₂³×C₄₇	1	8	yes	—
508	#95	C₂³×C₄₇	1	8	yes	—
509	#95	C₂³×C₄₇	1	8	yes	—
510	C₂⁴	—	2	2	no	—
511	C₂⁴	—	2	2	no	—
512	C₂⁴	—	2	4	no	—
513	C₂⁴	—	2	2	no	—
514	C₂⁴	—	2	4	no	—
515	C₂⁴	—	2	2	no	—
516	C₂⁴	—	2	2	no	—
517	C₂⁴	—	2	4	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	2	no	—
520	C₂⁴	—	2	2	no	—
521	C₂⁴	—	2	4	no	—
522	C₂⁴	—	2	2	no	—
523	C₂⁴	—	2	4	no	—
524	C₂⁴	—	2	2	no	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
529	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
530	C₂⁴	#41×C₄₇	1	4	yes	complemented
531	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
532	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
533	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
534	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
535	#41	—	2	256	no	—
536	C₂×Q₈	—	2	32	no	—
537	C₂×Q₈	—	2	8	no	—
538	C₂×Q₈	—	2	8	no	—
539	C₂×Q₈	C₂×D₄×C₄₇	1	16	yes	complemented
540	C₂×D₄	—	2	32	no	—
541	C₂×D₄	—	2	64	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	16	no	—
544	C₂×D₄	—	2	16	no	—
545	C₂×D₄	—	2	8	no	—
546	C₂×D₄	—	2	16	no	—
547	C₂×D₄	—	2	16	no	—
548	C₂×D₄	—	2	32	no	—
549	C₂×D₄	—	2	16	no	—
550	C₂×D₄	—	2	8	no	—
551	C₂×D₄	—	2	8	no	—
552	C₂×D₄	—	2	8	no	—
553	C₂×D₄	—	4	8	no	—
554	C₂×D₄	—	4	32	no	—
555	C₂×D₄	C₂×D₄×C₄₇	1	16	yes	complemented
556	C₂²×C₄	—	2	64	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	16	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	32	no	—
565	C₂²×C₄	—	2	16	no	—
566	C₂²×C₄	—	2	16	no	—
567	C₂²×C₄	—	2	8	no	—
568	C₂²×C₄	—	2	8	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	—	2	8	no	—
583	C₂²×C₄	—	2	8	no	—
584	C₂²×C₄	—	4	16	no	—
585	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
586	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
587	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
588	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
589	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
590	C₂²×C₄	C₂×D₄×C₄₇	1	16	yes	complemented
591	C₂²×C₄	#41×C₄₇	1	4	yes	complemented
592	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
595	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
598	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	8	no	—
603	C₄⋊C₄	—	2	16	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	16	no	—
606	C₂²⋊C₄	—	2	8	no	—
607	C₂²⋊C₄	—	2	16	no	—
608	C₂²⋊C₄	—	2	16	no	—
609	C₂²⋊C₄	—	4	8	no	—
610	C₂²⋊C₄	—	4	8	no	—
611	C₄²	—	2	8	no	—
612	C₂³	—	2	16	no	—
613	C₂³	—	2	8	no	—
614	C₂³	—	2	8	no	—
615	C₂³	—	2	8	no	—
616	C₂³	—	2	8	no	—
617	C₂³	—	2	8	no	—
618	C₂³	—	2	16	no	—
619	C₂³	—	2	16	no	—
620	C₂³	—	2	8	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	4	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	4	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	4	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	4	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	4	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	4	4	no	—
640	C₂³	—	4	8	no	—
641	C₂³	—	4	4	no	—
642	C₂³	—	4	8	no	—
643	C₂³	—	4	4	no	—
644	C₂³	—	4	4	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	8	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	4	8	no	—
650	C₂³	—	4	4	no	—
651	C₂³	C₂²×D₄×C₄₇	1	8	yes	—
652	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
653	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
654	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
655	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
656	C₂³	C₂×#41×C₄₇	1	2	yes	—
657	C₂³	C₂×#41×C₄₇	1	2	yes	—
658	C₂³	C₂×#41×C₄₇	1	4	yes	complemented
659	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
660	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
661	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
662	Q₈	—	2	32	no	—
663	D₄	—	2	32	no	—
664	D₄	—	2	64	no	—
665	D₄	—	2	32	no	—
666	D₄	—	4	32	no	—
667	C₂×C₄	—	2	64	no	—
668	C₂×C₄	—	2	8	no	—
669	C₂×C₄	—	2	16	no	—
670	C₂×C₄	—	2	8	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	32	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	4	4	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	—	4	8	no	—
694	C₂×C₄	—	4	16	no	—
695	C₂×C₄	#120×C₄₇	1	16	yes	—
696	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
697	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
698	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
699	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
700	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
701	C₂×C₄	C₂×#41×C₄₇	1	4	yes	complemented
702	C₂²	—	2	8	no	—
703	C₂²	—	2	4	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	8	no	—
709	C₂²	—	2	8	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	4	16	no	—
712	C₂²	—	4	32	no	—
713	C₂²	—	4	16	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	4	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	4	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	2	no	—
726	C₂²	C₂×#120×C₄₇	1	4	yes	—
727	C₂²	C₄₇×#525	1	4	yes	—
728	C₂²	C₄₇×#537	1	4	yes	—
729	C₂²	C₄₇×#546	1	4	yes	—
730	C₂²	C₄₇×#547	1	4	yes	—
731	C₂²	C₄₇×#548	1	4	yes	—
732	C₂²	C₄₇×#550	1	4	yes	—
733	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
734	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
735	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
736	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
737	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
738	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
739	C₂²	C₂×2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
740	C₄	—	2	4	no	—
741	C₄	—	2	8	no	—
742	C₄	—	2	4	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	4	no	—
746	C₄	—	4	4	no	—
747	C₄	C₂×#120×C₄₇	1	8	yes	—
748	C₂	—	4	4	no	—
749	C₂	—	4	8	no	—
750	C₂	—	4	4	no	—
751	C₂	C₄₇×#2407	1	8	yes	direct product factor
752	C₂	C₂²×#120×C₄₇	1	1	yes	characteristic
753	C₂	C₂×C₄₇×#525	1	1	yes	characteristic
754	C₂	C₂×C₄₇×#537	1	1	yes	characteristic
755	C₂	C₂×C₄₇×#546	1	1	yes	characteristic
756	C₂	C₂×C₄₇×#547	1	1	yes	characteristic
757	C₂	C₂×C₄₇×#548	1	1	yes	characteristic
758	C₂	C₂×C₄₇×#550	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
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. C₂³×#41×C₄₇	C₂	semidirect
2. C₂²×C₂²⋊Q₈×C₄₇	C₂	semidirect
3. C₂²×#121×C₄₇	C₂	semidirect
4. C₂²×C₄×D₄×C₄₇	C₂	semidirect
5. C₄₇×#2407	C₂	direct (N × H)
6. C₂×C₄₇×#394	C₂	semidirect
7. C₂×C₄₇×#392	C₂	semidirect
8. C₂×C₄₇×#391	C₂	semidirect
9. C₂×C₄₇×#390	C₂	semidirect
10. C₂×C₄₇×#386	C₂	semidirect
11. C₂×C₄₇×#385	C₂	semidirect
12. C₂×C₄₇×#380	C₂	semidirect
16. C₂²×#41×C₄₇	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
28. C₂×#121×C₄₇	C₂²	semidirect
30. C₂×C₄×D₄×C₄₇	C₂²	semidirect
43. C₄₇×#394	C₂²	semidirect
44. C₄₇×#392	C₂²	semidirect
45. C₄₇×#391	C₂²	semidirect
46. C₄₇×#390	C₂²	semidirect
47. C₄₇×#386	C₂²	semidirect
48. C₄₇×#385	C₂²	semidirect
49. C₄₇×#380	C₂²	semidirect
62. C₂²×Q₈×C₄₇	D₄	semidirect
75. C₂²×D₄×C₄₇	D₄	semidirect
88. C₂³×C₄×C₄₇	D₄	semidirect
150. C₂⁴×C₄₇	#41	semidirect
159. C₂×Q₈×C₄₇	C₂×D₄	semidirect
175. C₂×D₄×C₄₇	C₂×D₄	semidirect
210. C₂²×C₄×C₄₇	C₂×D₄	semidirect
211. C₂²×C₄×C₄₇	#41	semidirect
278. C₂³×C₄₇	C₂×#41	semidirect
321. C₂×C₄×C₄₇	C₂×#41	semidirect
322. C₂×#2407	C₄₇	direct (N × H)
369. C₂³×#41	C₂×C₄₇	semidirect
370. C₂²×C₂²⋊Q₈	C₂×C₄₇	semidirect
371. C₂²×#121	C₂×C₄₇	semidirect
372. C₂²×C₄×D₄	C₂×C₄₇	semidirect
373. #2407	C₂×C₄₇	direct (N × H)
374. C₂×#394	C₂×C₄₇	semidirect
375. C₂×#392	C₂×C₄₇	semidirect
376. C₂×#391	C₂×C₄₇	semidirect
377. C₂×#390	C₂×C₄₇	semidirect
378. C₂×#386	C₂×C₄₇	semidirect
379. C₂×#385	C₂×C₄₇	semidirect
380. C₂×#380	C₂×C₄₇	semidirect
384. C₂×C₄₇	#2407	direct (N × H)
395. C₂²×#41	C₂²×C₄₇	semidirect
405. C₂×C₂²⋊Q₈	C₂²×C₄₇	semidirect
407. C₂×#121	C₂²×C₄₇	semidirect
409. C₂×C₄×D₄	C₂²×C₄₇	semidirect
422. #394	C₂²×C₄₇	semidirect
423. #392	C₂²×C₄₇	semidirect
424. #391	C₂²×C₄₇	semidirect
425. #390	C₂²×C₄₇	semidirect
426. #386	C₂²×C₄₇	semidirect
427. #385	C₂²×C₄₇	semidirect
428. #380	C₂²×C₄₇	semidirect
432. C₄₇	C₂×#2407	direct (N × H)
442. C₂²×Q₈	D₄×C₄₇	semidirect
455. C₂²×D₄	D₄×C₄₇	semidirect
468. C₂³×C₄	D₄×C₄₇	semidirect
530. C₂⁴	#41×C₄₇	semidirect
539. C₂×Q₈	C₂×D₄×C₄₇	semidirect
555. C₂×D₄	C₂×D₄×C₄₇	semidirect
590. C₂²×C₄	C₂×D₄×C₄₇	semidirect
591. C₂²×C₄	#41×C₄₇	semidirect
658. C₂³	C₂×#41×C₄₇	semidirect
701. C₂×C₄	C₂×#41×C₄₇	semidirect
751. C₂	C₄₇×#2407	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₄₇	2
C₂²×C₂²⋊Q₈×C₄₇	2
C₂²×#121×C₄₇	2
C₂²×C₄×D₄×C₄₇	2
C₄₇×#2407	2
C₂×C₄₇×#394	2
C₂×C₄₇×#392	2
C₂×C₄₇×#391	2
C₂×C₄₇×#390	2
C₂×C₄₇×#386	2
C₂×C₄₇×#385	2
C₂×C₄₇×#380	2
C₂×#2407	47

Subgroups — C2×C47×#2407 #26074407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2407 #26074407