Subgroups — C₂×#20257524 #27123167

Order 12032.

7418 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257524	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689873	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689872	C₂	1	2	yes	maximal, complemented
4	C₂×#15689868	C₂	1	4	yes	maximal, complemented
5	C₂×#15689867	C₂	1	2	yes	maximal, complemented
6	C₂×#15689865	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689861	C₂	1	4	yes	maximal, complemented
8	C₂×#15689860	C₂	1	2	yes	maximal, complemented
9	C₂×#15689669	C₂	1	2	yes	maximal, complemented
10	C₂×#15689657	C₂	1	2	yes	maximal, complemented
11	C₂×#15689653	C₂	1	4	yes	maximal, complemented
12	C₂×#15689632	C₂	1	4	yes	maximal, complemented
13	C₂×#15689630	C₂	1	2	yes	maximal, complemented
14	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#10625350	C₂²	1	2	yes	—
16	C₂³×C₄×D₄₇	C₂²	1	2	yes	complemented
17	#15689873	C₂²	1	16	yes	complemented
18	#15689872	C₂²	1	32	yes	complemented
19	#15689868	C₂²	1	64	yes	complemented
20	#15689867	C₂²	1	32	yes	complemented
21	#15689865	C₂²	1	16	yes	complemented
22	#15689861	C₂²	1	64	yes	complemented
23	#15689860	C₂²	1	32	yes	complemented
24	#15689669	C₂²	1	32	yes	complemented
25	C₂×#13094022	C₂²	1	2	yes	complemented
26	C₂×#13094020	C₂²	1	2	yes	—
27	#15689657	C₂²	1	32	yes	complemented
28	#15689653	C₂²	1	64	yes	complemented
29	C₂×#13094019	C₂²	1	4	yes	complemented
30	C₂×#13094018	C₂²	1	4	yes	complemented
31	C₂×#13094017	C₂²	1	4	yes	complemented
32	C₂×#13094016	C₂²	1	2	yes	complemented
33	C₂×#13094014	C₂²	1	4	yes	complemented
34	C₂×#13094013	C₂²	1	2	yes	—
35	C₂×#13094012	C₂²	1	2	yes	—
36	C₂×#13094011	C₂²	1	2	yes	complemented
37	C₂×#13094010	C₂²	1	4	yes	—
38	#15689632	C₂²	1	64	yes	complemented
39	#15689630	C₂²	1	32	yes	complemented
40	C₂×#13094009	C₂²	1	4	yes	—
41	C₂×#13094008	C₂²	1	4	yes	complemented
42	C₂×#13094007	C₂²	1	4	yes	complemented
43	C₂×#13094006	C₂²	1	4	yes	complemented
44	C₂×#13094005	C₂²	1	2	yes	—
45	C₂×#13094005	C₂²	1	2	yes	complemented
46	C₂×#13094005	C₂²	1	4	yes	complemented
47	C₂×#13094003	C₂²	1	2	yes	complemented
48	C₂×#13094002	C₂²	1	4	yes	complemented
49	C₂×#13094001	C₂²	1	4	yes	complemented
50	C₂×#13094001	C₂²	1	4	yes	complemented
51	C₂×#13094000	C₂²	1	4	yes	complemented
52	C₂×#13093998	C₂²	1	2	yes	—
53	C₂×#13093997	C₂²	1	4	yes	—
54	C₂×#13093996	C₂²	1	4	yes	—
55	C₂×#13093996	C₂²	1	4	yes	—
56	C₂×#13093996	C₂²	1	4	yes	complemented
57	C₂×#13093996	C₂²	1	4	yes	complemented
58	C₂×#13093995	C₂²	1	4	yes	—
59	C₂×#13093994	C₂²	1	4	yes	—
60	C₂×#13093992	C₂²	1	2	yes	—
61	C₂×#13093992	C₂²	1	2	yes	complemented
62	C₂×#13093992	C₂²	1	4	yes	complemented
63	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
64	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
65	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
66	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
67	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
68	C₂×#13093983	C₂²	1	2	yes	complemented
69	C₂×#13093981	C₂²	1	4	yes	complemented
70	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	complemented
71	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
72	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
73	C₄₇×#532	C₂²	1	16	yes	complemented
74	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
75	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
76	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
77	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic, complemented
78	C₂×#121×C₄₇	C₂²	1	4	yes	complemented
79	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	complemented
80	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic, complemented
81	C₂⁴×D₄₇	C₂³	1	2	yes	—
82	C₂×#10625350	—	4	8	no	—
83	C₂×#10625350	C₂³	1	16	yes	—
84	C₂²×Dic₉₄	C₂³	1	2	yes	—
85	C₂²×Dic₉₄	C₂³	1	2	yes	—
86	C₂²×D₁₈₈	C₂³	1	2	yes	—
87	C₂²×D₁₈₈	C₂³	1	2	yes	—
88	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
89	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
90	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
91	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
92	C₂³×Dic₄₇	C₂³	1	4	yes	—
93	C₂³×Dic₄₇	C₂³	1	2	yes	—
94	C₂²×C₄×D₄₇	—	4	8	no	—
95	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
96	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
97	C₂²×C₄×D₄₇	C₂³	1	16	yes	complemented
98	#13094022	C₂³	1	16	yes	complemented
99	#13094020	C₂³	1	16	yes	—
100	#13094019	C₂³	1	32	yes	complemented
101	#13094018	C₂³	1	32	yes	complemented
102	#13094017	C₂³	1	32	yes	complemented
103	#13094016	C₂³	1	16	yes	complemented
104	#13094014	C₂³	1	32	yes	complemented
105	#13094013	C₂³	1	16	yes	—
106	#13094012	C₂³	1	16	yes	—
107	#13094011	C₂³	1	16	yes	complemented
108	#13094010	C₂³	1	32	yes	—
109	#13094009	C₂³	1	32	yes	—
110	#13094008	C₂³	1	32	yes	complemented
111	#13094007	C₂³	1	32	yes	complemented
112	#13094006	C₂³	1	32	yes	complemented
113	#13094005	C₂³	1	16	yes	—
114	#13094005	C₂³	1	32	yes	complemented
115	#13094005	C₂³	1	16	yes	complemented
116	#13094003	C₂³	1	16	yes	complemented
117	#13094002	C₂³	1	32	yes	complemented
118	#13094001	C₂³	1	32	yes	complemented
119	#13094001	C₂³	1	32	yes	complemented
120	#13094000	C₂³	1	32	yes	complemented
121	#13093998	C₂³	1	16	yes	—
122	#13093997	C₂³	1	32	yes	—
123	#13093996	C₂³	1	32	yes	—
124	#13093996	C₂³	1	32	yes	—
125	#13093996	C₂³	1	32	yes	complemented
126	#13093996	C₂³	1	32	yes	complemented
127	#13093995	C₂³	1	32	yes	—
128	#13093994	C₂³	1	32	yes	—
129	#13093992	C₂³	1	16	yes	—
130	#13093992	C₂³	1	32	yes	complemented
131	#13093992	C₂³	1	16	yes	complemented
132	C₄×Dic₉₄	C₂³	1	16	yes	complemented
133	C₄×D₁₈₈	C₂³	1	16	yes	—
134	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	—
135	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
136	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
137	#13093983	C₂³	1	16	yes	complemented
138	#13093981	C₂³	1	32	yes	complemented
139	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
140	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
141	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
142	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
143	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
144	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
145	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
146	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
147	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
148	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
151	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
152	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
153	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
154	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
155	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
156	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
157	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
158	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
159	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
160	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
161	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
162	C₂×C₄×Dic₄₇	C₂³	1	16	yes	complemented
163	C₂×#41×C₄₇	—	4	4	no	—
164	C₂×#41×C₄₇	—	4	4	no	—
165	C₂×#41×C₄₇	C₂³	1	8	yes	—
166	C₂×#41×C₄₇	C₂³	1	8	yes	complemented
167	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
168	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
169	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
170	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
171	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
172	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
173	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
174	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
175	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
176	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
177	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
178	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
179	#127×C₄₇	C₂³	1	8	yes	—
180	#124×C₄₇	C₂³	1	8	yes	—
181	#124×C₄₇	C₂³	1	8	yes	complemented
182	#121×C₄₇	C₂³	1	32	yes	complemented
183	C₄×D₄×C₄₇	C₂³	1	32	yes	complemented
184	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
185	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
186	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
187	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₄₇	C₂³	1	8	yes	complemented
191	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
192	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
193	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
194	C₂³×D₄₇	—	4	4	no	—
195	C₂³×D₄₇	—	4	8	no	—
196	C₂³×D₄₇	C₂⁴	1	4	yes	—
197	C₂³×D₄₇	C₂⁴	1	8	yes	—
198	#41×C₄₇	—	4	16	no	—
199	#41×C₄₇	—	4	16	no	—
200	C₂×Q₈×C₄₇	—	4	2	no	—
201	C₂×Q₈×C₄₇	—	4	2	no	—
202	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
203	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
204	C₂×D₄×C₄₇	—	4	8	no	—
205	C₂×D₄×C₄₇	—	4	4	no	—
206	C₂×D₄×C₄₇	—	4	4	no	—
207	C₂×D₄×C₄₇	—	4	2	no	—
208	C₂×D₄×C₄₇	—	4	2	no	—
209	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
210	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
211	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
212	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
213	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₄₇	—	2	4	no	—
215	C₂²×C₄×C₄₇	—	2	8	no	—
216	C₂²×C₄×C₄₇	—	2	8	no	—
217	C₂²×C₄×C₄₇	—	4	4	no	—
218	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
225	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
226	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
227	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
228	C₂×C₂²⋊D₄₇	—	4	8	no	—
229	C₂×C₂²⋊D₄₇	—	4	8	no	—
230	C₂×C₂²⋊D₄₇	—	4	8	no	—
231	C₂×C₂²⋊D₄₇	—	4	8	no	—
232	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
233	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
234	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
235	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
236	C₂²×Dic₄₇	—	4	4	no	—
237	C₂²×Dic₄₇	—	4	8	no	—
238	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
239	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
240	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
241	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
242	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
243	#10625350	—	4	32	no	—
244	C₂×D₁₈₈	—	4	4	no	—
245	C₂×D₁₈₈	—	4	4	no	—
246	C₂×D₁₈₈	C₂⁴	1	8	yes	—
247	C₂×D₁₈₈	C₂⁴	1	8	yes	—
248	C₂×C₄×D₄₇	—	2	16	no	—
249	C₂×C₄×D₄₇	—	4	32	no	—
250	C₂×C₄×D₄₇	—	4	8	no	—
251	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
252	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
253	C₂×Dic₉₄	—	4	4	no	—
254	C₂×Dic₉₄	—	4	4	no	—
255	C₂×Dic₉₄	C₂⁴	1	8	yes	—
256	C₂×Dic₉₄	C₂⁴	1	8	yes	—
257	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
258	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
259	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
260	C₄²×C₄₇	C₂⁴	1	8	yes	—
261	C₄²×C₄₇	C₂⁴	1	4	yes	—
262	C₄²×C₄₇	C₂⁴	1	4	yes	—
263	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
264	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
265	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
266	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
267	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
268	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
269	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
270	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
271	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
272	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
273	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
274	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
275	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
276	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
277	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
278	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
279	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
280	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
281	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
282	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
283	C₄×Dic₄₇	C₂⁴	1	16	yes	—
284	C₄×Dic₄₇	C₂⁴	1	8	yes	—
285	C₄×Dic₄₇	C₂⁴	1	8	yes	—
286	C₂³×C₄₇	—	2	4	no	—
287	C₂³×C₄₇	—	2	4	no	—
288	C₂³×C₄₇	—	2	2	no	—
289	C₂³×C₄₇	—	2	8	no	—
290	C₂³×C₄₇	—	2	4	no	—
291	C₂³×C₄₇	—	2	8	no	—
292	C₂³×C₄₇	C₂⁵	1	4	yes	—
293	C₂³×C₄₇	C₂⁵	1	2	yes	—
294	C₂³×C₄₇	C₂⁵	1	4	yes	—
295	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
296	C₂²×D₄₇	—	2	8	no	—
297	C₂²×D₄₇	—	2	8	no	—
298	C₂²×D₄₇	—	2	8	no	—
299	C₂²×D₄₇	—	4	8	no	—
300	C₂²×D₄₇	—	4	16	no	—
301	C₂²×D₄₇	—	4	32	no	—
302	C₂²×D₄₇	C₂⁵	1	8	yes	—
303	Q₈×C₄₇	—	4	4	no	—
304	Q₈×C₄₇	—	4	4	no	—
305	D₄×C₄₇	—	4	16	no	—
306	D₄×C₄₇	—	4	8	no	—
307	D₄×C₄₇	—	4	8	no	—
308	D₄×C₄₇	—	4	4	no	—
309	D₄×C₄₇	—	4	4	no	—
310	C₂×C₄×C₄₇	—	2	4	no	—
311	C₂×C₄×C₄₇	—	2	4	no	—
312	C₂×C₄×C₄₇	—	2	2	no	—
313	C₂×C₄×C₄₇	—	2	4	no	—
314	C₂×C₄×C₄₇	—	2	4	no	—
315	C₂×C₄×C₄₇	—	2	16	no	—
316	C₂×C₄×C₄₇	—	2	16	no	—
317	C₂×C₄×C₄₇	—	2	8	no	—
318	C₂×C₄×C₄₇	—	4	8	no	—
319	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
320	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
321	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
322	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
323	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
324	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
325	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
326	C₂²⋊D₄₇	—	4	16	no	—
327	C₂²⋊D₄₇	—	4	16	no	—
328	C₂²⋊D₄₇	—	4	16	no	—
329	C₂²⋊D₄₇	—	4	16	no	—
330	C₂×Dic₄₇	—	2	8	no	—
331	C₂×Dic₄₇	—	2	8	no	—
332	C₂×Dic₄₇	—	2	8	no	—
333	C₂×Dic₄₇	—	4	8	no	—
334	C₂×Dic₄₇	—	4	16	no	—
335	C₂×Dic₄₇	C₂⁵	1	8	yes	—
336	C₂×Dic₄₇	C₂⁵	1	8	yes	—
337	C₂×Dic₄₇	C₂⁵	1	8	yes	—
338	D₁₈₈	—	4	8	no	—
339	D₁₈₈	—	4	8	no	—
340	C₄×D₄₇	—	2	32	no	—
341	C₄×D₄₇	—	4	16	no	—
342	Dic₉₄	—	4	8	no	—
343	Dic₉₄	—	4	8	no	—
344	C₂×#3529	—	47	1	no	maximal, Sylow
345	C₂²×C₄₇	—	2	4	no	—
346	C₂²×C₄₇	—	2	4	no	—
347	C₂²×C₄₇	—	2	2	no	—
348	C₂²×C₄₇	—	2	8	no	—
349	C₂²×C₄₇	—	2	4	no	—
350	C₂²×C₄₇	—	2	8	no	—
351	C₂²×C₄₇	—	4	8	no	—
352	C₂²×C₄₇	—	4	8	no	—
353	C₂²×C₄₇	—	4	4	no	—
354	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
355	C₂²×C₄₇	#585	1	4	yes	—
356	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
357	C₂×D₄₇	—	2	8	no	—
358	C₂×D₄₇	—	2	8	no	—
359	C₂×D₄₇	—	2	8	no	—
360	C₂×D₄₇	—	4	32	no	—
361	C₂×D₄₇	—	4	16	no	—
362	C₄×C₄₇	—	2	4	no	—
363	C₄×C₄₇	—	2	4	no	—
364	C₄×C₄₇	—	2	2	no	—
365	C₄×C₄₇	—	2	4	no	—
366	C₄×C₄₇	—	2	4	no	—
367	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
368	Dic₄₇	—	2	8	no	—
369	Dic₄₇	—	2	8	no	—
370	Dic₄₇	—	2	8	no	—
371	#3529	—	47	32	no	—
372	C₂×#563	—	47	2	no	—
373	C₂×#563	—	47	1	no	—
374	C₂×#562	—	47	2	no	—
375	C₂×#562	—	47	4	no	—
376	C₂×H(3,𝔽₄)	—	47	1	no	—
377	C₂×#560	—	47	2	no	—
378	C₂×#560	—	47	4	no	—
379	C₂×#532	—	47	2	no	—
380	C₂×#532	D₄₇	1	1	yes	characteristic, complemented
381	C₂×#529	—	47	2	no	—
382	C₂×#529	—	47	4	no	—
383	C₂×#525	—	47	2	no	—
384	C₂×#525	—	47	4	no	—
385	C₂×C₄₇	—	4	4	no	—
386	C₂×C₄₇	—	4	4	no	—
387	C₂×C₄₇	—	4	2	no	—
388	C₂×C₄₇	#3529	1	4	yes	complemented
389	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂×C₄₇	C₂×#585	1	2	yes	—
391	D₄₇	—	4	8	no	—
392	C₂²×#41	—	47	2	no	—
393	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
394	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
395	C₂⁴×C₄	—	47	2	no	—
396	#563	—	47	32	no	—
397	#563	—	47	16	no	—
398	#562	—	47	32	no	—
399	#562	—	47	64	no	—
400	H(3,𝔽₄)	—	47	16	no	—
401	#560	—	47	32	no	—
402	#560	—	47	64	no	—
403	#532	—	47	32	no	—
404	#532	C₂×D₄₇	1	16	yes	complemented
405	C₂×C₄⋊Q₈	—	47	2	no	—
406	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
407	C₂×#127	—	47	2	no	—
408	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
409	#529	—	47	64	no	—
410	#529	—	47	32	no	—
411	C₂×#126	—	47	4	no	—
412	C₂×#126	—	47	4	no	—
413	C₂×#126	—	47	4	no	—
414	C₂×#125	—	47	4	no	—
415	C₂×#125	—	47	2	no	—
416	C₂×#124	—	47	2	no	—
417	C₂×#124	—	47	2	no	—
418	C₂×#124	—	47	4	no	—
419	C₂×#124	—	47	2	no	—
420	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
421	C₂×#124	C₂×D₄₇	1	1	yes	characteristic, complemented
422	#525	—	47	32	no	—
423	#525	—	47	64	no	—
424	C₂×#123	—	47	2	no	—
425	C₂×#123	—	47	2	no	—
426	C₂×#123	—	47	4	no	—
427	C₂×#123	—	47	4	no	—
428	C₂×#123	—	47	4	no	—
429	C₂×#123	—	47	4	no	—
430	C₂×#123	—	47	4	no	—
431	C₂×C₂²⋊Q₈	—	47	4	no	—
432	C₂×C₂²⋊Q₈	—	47	2	no	—
433	C₂×C₂²⋊Q₈	—	47	4	no	—
434	C₂×C₂²⋊Q₈	—	47	4	no	—
435	C₂×C₂²⋊Q₈	—	47	4	no	—
436	C₂×#121	—	47	4	no	—
437	C₂×#121	—	47	4	no	—
438	C₂×#121	—	47	4	no	—
439	C₂×#121	—	47	4	no	—
440	C₂×#121	—	47	4	no	—
441	C₂×#121	—	47	2	no	—
442	C₂×#121	—	47	4	no	—
443	C₂×#121	C₂×D₄₇	1	4	yes	complemented
444	C₂×#120	—	47	2	no	—
445	C₂×#120	—	47	2	no	—
446	C₂×#120	—	47	4	no	—
447	C₂×#120	—	47	4	no	—
448	C₂×C₄×Q₈	—	47	2	no	—
449	C₂×C₄×D₄	—	47	4	no	—
450	C₂×C₄×D₄	—	47	4	no	—
451	C₂×C₄×D₄	—	47	4	no	—
452	C₂×C₄×D₄	—	47	2	no	—
453	C₂×C₄×D₄	C₂×D₄₇	1	4	yes	complemented
454	C₂×#117	—	47	2	no	—
455	C₂×#117	—	47	4	no	—
456	C₂²×C₄²	—	47	2	no	—
457	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic, complemented
458	C₄₇	C₂×#3529	1	1	yes	characteristic, complemented, Sylow
459	C₂⁵	—	47	2	no	—
460	C₂×#41	—	4	4	no	—
461	C₂×#41	—	4	4	no	—
462	C₂×#41	—	47	16	no	—
463	C₂×#41	—	188	8	no	—
464	C₂×#41	C₂²×D₄₇	1	8	yes	—
465	C₂×#41	C₂²×D₄₇	1	8	yes	complemented
466	C₂²×Q₈	—	47	2	no	—
467	C₂²×Q₈	—	47	2	no	—
468	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
469	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
470	C₂²×D₄	—	47	4	no	—
471	C₂²×D₄	—	47	4	no	—
472	C₂²×D₄	—	47	4	no	—
473	C₂²×D₄	—	47	4	no	—
474	C₂²×D₄	—	47	2	no	—
475	C₂²×D₄	—	47	2	no	—
476	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
477	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
478	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
479	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
480	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
481	C₂³×C₄	—	47	4	no	—
482	C₂³×C₄	—	47	2	no	—
483	C₂³×C₄	—	47	4	no	—
484	C₂³×C₄	—	47	4	no	—
485	C₂³×C₄	—	47	16	no	—
486	C₂³×C₄	—	188	8	no	—
487	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
488	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
489	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
490	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
491	C₄⋊Q₈	—	47	16	no	—
492	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
493	#127	—	47	16	no	—
494	#127	C₂²×D₄₇	1	8	yes	—
495	#126	—	47	32	no	—
496	#126	—	47	32	no	—
497	#126	—	47	32	no	—
498	#125	—	47	32	no	—
499	#125	—	47	16	no	—
500	#124	—	47	16	no	—
501	#124	—	47	16	no	—
502	#124	—	47	32	no	—
503	#124	—	47	16	no	—
504	#124	C₂²×D₄₇	1	8	yes	—
505	#124	C₂²×D₄₇	1	8	yes	complemented
506	#123	—	47	16	no	—
507	#123	—	47	16	no	—
508	#123	—	47	32	no	—
509	#123	—	47	32	no	—
510	#123	—	47	32	no	—
511	#123	—	47	32	no	—
512	#123	—	47	32	no	—
513	C₂²⋊Q₈	—	47	32	no	—
514	C₂²⋊Q₈	—	47	16	no	—
515	C₂²⋊Q₈	—	47	32	no	—
516	C₂²⋊Q₈	—	47	32	no	—
517	C₂²⋊Q₈	—	47	32	no	—
518	#121	—	47	32	no	—
519	#121	—	47	32	no	—
520	#121	—	47	32	no	—
521	#121	—	47	32	no	—
522	#121	—	47	32	no	—
523	#121	—	47	16	no	—
524	#121	—	47	32	no	—
525	#121	C₂²×D₄₇	1	32	yes	complemented
526	#120	—	47	16	no	—
527	#120	—	47	32	no	—
528	#120	—	47	16	no	—
529	#120	—	47	32	no	—
530	C₄×Q₈	—	47	16	no	—
531	C₄×D₄	—	47	32	no	—
532	C₄×D₄	—	47	32	no	—
533	C₄×D₄	—	47	32	no	—
534	C₄×D₄	—	47	16	no	—
535	C₄×D₄	C₂²×D₄₇	1	32	yes	complemented
536	#117	—	47	16	no	—
537	#117	—	47	32	no	—
538	C₂×C₄⋊C₄	—	47	4	no	—
539	C₂×C₄⋊C₄	—	47	4	no	—
540	C₂×C₄⋊C₄	—	47	4	no	—
541	C₂×C₄⋊C₄	—	47	4	no	—
542	C₂×C₄⋊C₄	—	47	4	no	—
543	C₂×C₄⋊C₄	—	47	4	no	—
544	C₂×C₄⋊C₄	—	47	2	no	—
545	C₂×C₄⋊C₄	—	47	4	no	—
546	C₂×C₄⋊C₄	—	47	2	no	—
547	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
548	C₂×C₂²⋊C₄	—	47	2	no	—
549	C₂×C₂²⋊C₄	—	47	2	no	—
550	C₂×C₂²⋊C₄	—	47	4	no	—
551	C₂×C₂²⋊C₄	—	47	4	no	—
552	C₂×C₂²⋊C₄	—	47	4	no	—
553	C₂×C₂²⋊C₄	—	47	4	no	—
554	C₂×C₂²⋊C₄	—	47	4	no	—
555	C₂×C₂²⋊C₄	—	47	4	no	—
556	C₂×C₂²⋊C₄	—	47	4	no	—
557	C₂×C₂²⋊C₄	—	47	4	no	—
558	C₂×C₂²⋊C₄	—	47	4	no	—
559	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
561	C₂×C₄²	—	47	2	no	—
562	C₂×C₄²	—	47	2	no	—
563	C₂×C₄²	—	47	16	no	—
564	C₂×C₄²	—	47	4	no	—
565	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
566	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
567	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
568	C₂×C₄²	C₂²×D₄₇	1	8	yes	complemented
569	C₂⁴	—	47	4	no	—
570	C₂⁴	—	47	8	no	—
571	C₂⁴	—	188	4	no	—
572	C₂⁴	—	188	8	no	—
573	C₂⁴	C₂³×D₄₇	1	2	yes	—
574	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
575	C₂⁴	C₂³×D₄₇	1	2	yes	—
576	#41	—	4	16	no	—
577	#41	—	4	16	no	—
578	#41	—	188	32	no	—
579	C₂×Q₈	—	4	2	no	—
580	C₂×Q₈	—	4	2	no	—
581	C₂×Q₈	—	47	8	no	—
582	C₂×Q₈	—	47	8	no	—
583	C₂×Q₈	—	188	4	no	—
584	C₂×Q₈	—	188	4	no	—
585	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
586	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
587	C₂×D₄	—	4	8	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	4	2	no	—
591	C₂×D₄	—	4	4	no	—
592	C₂×D₄	—	47	16	no	—
593	C₂×D₄	—	47	16	no	—
594	C₂×D₄	—	47	16	no	—
595	C₂×D₄	—	47	16	no	—
596	C₂×D₄	—	47	8	no	—
597	C₂×D₄	—	47	8	no	—
598	C₂×D₄	—	188	4	no	—
599	C₂×D₄	—	188	4	no	—
600	C₂×D₄	—	188	8	no	—
601	C₂×D₄	—	188	8	no	—
602	C₂×D₄	—	188	8	no	—
603	C₂×D₄	—	188	8	no	—
604	C₂×D₄	C₂³×D₄₇	1	16	yes	—
605	C₂×D₄	C₂³×D₄₇	1	4	yes	—
606	C₂×D₄	C₂³×D₄₇	1	8	yes	—
607	C₂×D₄	C₂³×D₄₇	1	4	yes	—
608	C₂×D₄	C₂³×D₄₇	1	8	yes	—
609	C₂²×C₄	—	2	8	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	8	no	—
612	C₂²×C₄	—	4	4	no	—
613	C₂²×C₄	—	47	4	no	—
614	C₂²×C₄	—	47	4	no	—
615	C₂²×C₄	—	47	4	no	—
616	C₂²×C₄	—	47	16	no	—
617	C₂²×C₄	—	47	8	no	—
618	C₂²×C₄	—	47	16	no	—
619	C₂²×C₄	—	47	16	no	—
620	C₂²×C₄	—	94	16	no	—
621	C₂²×C₄	—	188	32	no	—
622	C₂²×C₄	—	188	8	no	—
623	C₂²×C₄	—	188	8	no	—
624	C₂²×C₄	—	188	4	no	—
625	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
626	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
627	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
628	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
629	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
630	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
631	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
632	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
633	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
634	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
635	C₄⋊C₄	—	47	16	no	—
636	C₄⋊C₄	—	47	16	no	—
637	C₄⋊C₄	—	47	16	no	—
638	C₄⋊C₄	—	47	16	no	—
639	C₄⋊C₄	—	47	16	no	—
640	C₄⋊C₄	—	47	16	no	—
641	C₄⋊C₄	—	47	16	no	—
642	C₄⋊C₄	—	47	8	no	—
643	C₄⋊C₄	—	47	8	no	—
644	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
645	C₂²⋊C₄	—	47	8	no	—
646	C₂²⋊C₄	—	47	8	no	—
647	C₂²⋊C₄	—	47	16	no	—
648	C₂²⋊C₄	—	47	16	no	—
649	C₂²⋊C₄	—	47	16	no	—
650	C₂²⋊C₄	—	47	16	no	—
651	C₂²⋊C₄	—	47	16	no	—
652	C₂²⋊C₄	—	47	16	no	—
653	C₂²⋊C₄	—	47	16	no	—
654	C₂²⋊C₄	—	47	16	no	—
655	C₂²⋊C₄	—	47	16	no	—
656	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
657	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
658	C₄²	—	47	16	no	—
659	C₄²	—	47	8	no	—
660	C₄²	—	47	8	no	—
661	C₄²	C₂³×D₄₇	1	8	yes	—
662	C₄²	C₂³×D₄₇	1	4	yes	—
663	C₄²	C₂³×D₄₇	1	4	yes	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	8	no	—
669	C₂³	—	2	8	no	—
670	C₂³	—	47	8	no	—
671	C₂³	—	94	8	no	—
672	C₂³	—	94	8	no	—
673	C₂³	—	94	8	no	—
674	C₂³	—	188	8	no	—
675	C₂³	—	188	16	no	—
676	C₂³	—	188	32	no	—
677	C₂³	C₂⁴×D₄₇	1	4	yes	—
678	C₂³	C₂⁴×D₄₇	1	2	yes	—
679	C₂³	C₂⁴×D₄₇	1	4	yes	—
680	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
681	Q₈	—	4	4	no	—
682	Q₈	—	4	4	no	—
683	Q₈	—	188	8	no	—
684	Q₈	—	188	8	no	—
685	D₄	—	4	16	no	—
686	D₄	—	4	8	no	—
687	D₄	—	4	4	no	—
688	D₄	—	4	4	no	—
689	D₄	—	4	8	no	—
690	D₄	—	188	8	no	—
691	D₄	—	188	8	no	—
692	D₄	—	188	16	no	—
693	D₄	—	188	16	no	—
694	D₄	—	188	16	no	—
695	D₄	—	188	16	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	16	no	—
702	C₂×C₄	—	2	8	no	—
703	C₂×C₄	—	2	16	no	—
704	C₂×C₄	—	4	8	no	—
705	C₂×C₄	—	47	8	no	—
706	C₂×C₄	—	47	8	no	—
707	C₂×C₄	—	47	8	no	—
708	C₂×C₄	—	94	8	no	—
709	C₂×C₄	—	94	8	no	—
710	C₂×C₄	—	94	8	no	—
711	C₂×C₄	—	94	32	no	—
712	C₂×C₄	—	188	16	no	—
713	C₂×C₄	—	188	16	no	—
714	C₂×C₄	—	188	8	no	—
715	C₂×C₄	#13094069	1	4	yes	—
716	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
717	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
718	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
719	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
720	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
721	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	8	no	—
727	C₂²	—	2	8	no	—
728	C₂²	—	4	8	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	8	no	—
731	C₂²	—	94	8	no	—
732	C₂²	—	94	8	no	—
733	C₂²	—	94	8	no	—
734	C₂²	—	188	32	no	—
735	C₂²	—	188	16	no	—
736	C₂²	C₂×#13094069	1	2	yes	—
737	C₂²	#15689959	1	4	yes	—
738	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
739	C₄	—	2	4	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	4	no	—
742	C₄	—	2	4	no	—
743	C₄	—	2	4	no	—
744	C₄	—	94	8	no	—
745	C₄	—	94	8	no	—
746	C₄	—	94	8	no	—
747	C₄	C₂×#13094069	1	4	yes	—
748	C₂	—	4	4	no	—
749	C₂	—	4	2	no	—
750	C₂	—	4	4	no	—
751	C₂	—	188	8	no	—
752	C₂	#20257524	1	4	yes	direct product factor
753	C₂	C₂²×#13094069	1	1	yes	characteristic
754	C₂	C₂×#15689959	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#532	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	C₂×#3529
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #20257524	C₂	direct (N × H)
2. C₂×#15689873	C₂	semidirect
3. C₂×#15689872	C₂	semidirect
4. C₂×#15689868	C₂	semidirect
5. C₂×#15689867	C₂	semidirect
6. C₂×#15689865	C₂	semidirect
7. C₂×#15689861	C₂	semidirect
8. C₂×#15689860	C₂	semidirect
9. C₂×#15689669	C₂	semidirect
10. C₂×#15689657	C₂	semidirect
11. C₂×#15689653	C₂	semidirect
12. C₂×#15689632	C₂	semidirect
13. C₂×#15689630	C₂	semidirect
14. C₂×C₄₇×#532	C₂	semidirect
16. C₂³×C₄×D₄₇	C₂²	semidirect
17. #15689873	C₂²	semidirect
18. #15689872	C₂²	semidirect
19. #15689868	C₂²	semidirect
20. #15689867	C₂²	semidirect
21. #15689865	C₂²	semidirect
22. #15689861	C₂²	semidirect
23. #15689860	C₂²	semidirect
24. #15689669	C₂²	semidirect
25. C₂×#13094022	C₂²	semidirect
27. #15689657	C₂²	semidirect
28. #15689653	C₂²	semidirect
29. C₂×#13094019	C₂²	semidirect
30. C₂×#13094018	C₂²	semidirect
31. C₂×#13094017	C₂²	semidirect
32. C₂×#13094016	C₂²	semidirect
33. C₂×#13094014	C₂²	semidirect
36. C₂×#13094011	C₂²	semidirect
38. #15689632	C₂²	semidirect
39. #15689630	C₂²	semidirect
41. C₂×#13094008	C₂²	semidirect
42. C₂×#13094007	C₂²	semidirect
43. C₂×#13094006	C₂²	semidirect
45. C₂×#13094005	C₂²	semidirect
46. C₂×#13094005	C₂²	semidirect
47. C₂×#13094003	C₂²	semidirect
48. C₂×#13094002	C₂²	semidirect
49. C₂×#13094001	C₂²	semidirect
50. C₂×#13094001	C₂²	semidirect
51. C₂×#13094000	C₂²	semidirect
56. C₂×#13093996	C₂²	semidirect
57. C₂×#13093996	C₂²	semidirect
61. C₂×#13093992	C₂²	semidirect
62. C₂×#13093992	C₂²	semidirect
63. C₂×C₄×Dic₉₄	C₂²	semidirect
66. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
67. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
68. C₂×#13093983	C₂²	semidirect
69. C₂×#13093981	C₂²	semidirect
70. C₂²×C₄×Dic₄₇	C₂²	semidirect
72. C₂²×#41×C₄₇	C₂²	semidirect
73. C₄₇×#532	C₂²	semidirect
74. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
77. C₂×#124×C₄₇	C₂²	semidirect
78. C₂×#121×C₄₇	C₂²	semidirect
79. C₂×C₄×D₄×C₄₇	C₂²	semidirect
80. C₂²×C₄²×C₄₇	C₂²	semidirect
97. C₂²×C₄×D₄₇	C₂³	semidirect
98. #13094022	C₂³	semidirect
100. #13094019	C₂³	semidirect
101. #13094018	C₂³	semidirect
102. #13094017	C₂³	semidirect
103. #13094016	C₂³	semidirect
104. #13094014	C₂³	semidirect
107. #13094011	C₂³	semidirect
110. #13094008	C₂³	semidirect
111. #13094007	C₂³	semidirect
112. #13094006	C₂³	semidirect
114. #13094005	C₂³	semidirect
115. #13094005	C₂³	semidirect
116. #13094003	C₂³	semidirect
117. #13094002	C₂³	semidirect
118. #13094001	C₂³	semidirect
119. #13094001	C₂³	semidirect
120. #13094000	C₂³	semidirect
125. #13093996	C₂³	semidirect
126. #13093996	C₂³	semidirect
130. #13093992	C₂³	semidirect
131. #13093992	C₂³	semidirect
132. C₄×Dic₉₄	C₂³	semidirect
135. C₄×C₂²⋊D₄₇	C₂³	semidirect
136. C₄×C₂²⋊D₄₇	C₂³	semidirect
137. #13093983	C₂³	semidirect
138. #13093981	C₂³	semidirect
162. C₂×C₄×Dic₄₇	C₂³	semidirect
166. C₂×#41×C₄₇	C₂³	semidirect
178. C₄⋊Q₈×C₄₇	C₂³	semidirect
181. #124×C₄₇	C₂³	semidirect
182. #121×C₄₇	C₂³	semidirect
183. C₄×D₄×C₄₇	C₂³	semidirect
190. C₂×C₄²×C₄₇	C₂³	semidirect
380. C₂×#532	D₄₇	semidirect
388. C₂×C₄₇	#3529	semidirect
394. C₂²×#41	C₂×D₄₇	semidirect
404. #532	C₂×D₄₇	semidirect
406. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
421. C₂×#124	C₂×D₄₇	semidirect
443. C₂×#121	C₂×D₄₇	semidirect
453. C₂×C₄×D₄	C₂×D₄₇	semidirect
457. C₂²×C₄²	C₂×D₄₇	semidirect
458. C₄₇	C₂×#3529	semidirect
465. C₂×#41	C₂²×D₄₇	semidirect
492. C₄⋊Q₈	C₂²×D₄₇	semidirect
505. #124	C₂²×D₄₇	semidirect
525. #121	C₂²×D₄₇	semidirect
535. C₄×D₄	C₂²×D₄₇	semidirect
568. C₂×C₄²	C₂²×D₄₇	semidirect
752. C₂	#20257524	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257524	2
C₂×#15689873	2
C₂×#15689872	2
C₂×#15689868	2
C₂×#15689867	2
C₂×#15689865	2
C₂×#15689861	2
C₂×#15689860	2
C₂×#15689669	2
C₂×#15689657	2
C₂×#15689653	2
C₂×#15689632	2
C₂×#15689630	2
C₂×C₄₇×#532	2
C₂×#3529	47

Subgroups — C2×#20257524 #27123167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257524 #27123167