Subgroups — C₂×#20257150 #27124167

Order 12032.

12378 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	C₂²×#13094070	C₂	1	2	yes	maximal, complemented
2	#20257150	C₂	1	32	yes	maximal, direct product factor
3	C₂×#15689778	C₂	1	2	yes	maximal, complemented
4	C₂×#15689776	C₂	1	2	yes	maximal, complemented
5	C₂×#15689769	C₂	1	4	yes	maximal, complemented
6	C₂×#15689766	C₂	1	4	yes	maximal, complemented
7	C₂×D₄×D₁₈₈	C₂	1	2	yes	maximal, complemented
8	C₂×#15689758	C₂	1	2	yes	maximal, complemented
9	C₂×#15689701	C₂	1	2	yes	maximal, complemented
10	C₂×#15689681	C₂	1	4	yes	maximal, complemented
11	C₂×#15689673	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#121×D₄₇	C₂	1	4	yes	maximal, complemented
13	C₂²×C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#13094070	—	2	32	no	—
16	C₂×#13094070	C₂²	1	32	yes	complemented
17	C₂²×#10625354	C₂²	1	4	yes	complemented
18	C₂²×#10625350	C₂²	1	4	yes	complemented
19	C₂²×#10625350	C₂²	1	2	yes	complemented
20	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
21	C₂³×D₁₈₈	C₂²	1	4	yes	complemented
22	C₂²×D₄×D₄₇	C₂²	1	4	yes	complemented
23	C₂²×D₄×D₄₇	C₂²	1	8	yes	complemented
24	C₂²×D₄×D₄₇	C₂²	1	4	yes	complemented
25	C₂³×C₄×D₄₇	C₂²	1	2	yes	complemented
26	#15689778	C₂²	1	32	yes	complemented
27	#15689776	C₂²	1	32	yes	complemented
28	#15689769	C₂²	1	64	yes	complemented
29	#15689766	C₂²	1	64	yes	complemented
30	D₄×D₁₈₈	C₂²	1	32	yes	complemented
31	#15689758	C₂²	1	32	yes	complemented
32	#15689701	C₂²	1	32	yes	complemented
33	#15689681	C₂²	1	64	yes	complemented
34	#15689673	C₂²	1	16	yes	complemented
35	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13094021	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13094012	C₂²	1	2	yes	complemented
38	C₂×#13094009	C₂²	1	8	yes	complemented
39	C₂×#13094006	C₂²	1	8	yes	complemented
40	C₂×#13094003	C₂²	1	4	yes	complemented
41	C₂×#13094000	C₂²	1	4	yes	complemented
42	C₂×#13093999	C₂²	1	4	yes	complemented
43	C₂×#13093998	C₂²	1	4	yes	complemented
44	C₂×#13093998	C₂²	1	2	yes	complemented
45	C₂×#13093998	C₂²	1	2	yes	complemented
46	C₂×#13093997	C₂²	1	8	yes	complemented
47	C₂×#13093996	C₂²	1	8	yes	complemented
48	C₂×#13093995	C₂²	1	4	yes	complemented
49	C₂×#13093995	C₂²	1	4	yes	complemented
50	#121×D₄₇	C₂²	1	64	yes	complemented
51	C₂×#13093994	C₂²	1	8	yes	complemented
52	C₂×#13093992	C₂²	1	8	yes	complemented
53	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
54	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
55	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
56	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
57	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
58	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
59	C₂×C₄×D₁₈₈	C₂²	1	16	yes	complemented
60	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄⋊C₄×D₄₇	C₂²	1	4	yes	complemented
62	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
63	C₂×C₂²⋊C₄×D₄₇	C₂²	1	8	yes	complemented
64	C₂²×#41×C₄₇	C₂²	1	2	yes	complemented
65	C₄₇×#532	C₂²	1	16	yes	complemented
66	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
67	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic, complemented
68	C₂×#124×C₄₇	C₂²	1	2	yes	complemented
69	C₂×#121×C₄₇	C₂²	1	2	yes	complemented
70	C₂×#121×C₄₇	C₂²	1	2	yes	complemented
71	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
72	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
73	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic, complemented
74	C₂⁴×D₄₇	C₂³	1	8	yes	—
75	C₂⁴×D₄₇	C₂³	1	2	yes	—
76	#13094070	—	2	256	no	—
77	C₂×#10625354	—	2	32	no	—
78	C₂×#10625354	C₂³	1	32	yes	complemented
79	C₂×#10625350	—	2	16	no	—
80	C₂×#10625350	—	2	32	no	—
81	C₂×#10625350	C₂³	1	32	yes	complemented
82	C₂×#10625350	C₂³	1	16	yes	complemented
83	C₂²×Dic₉₄	C₂³	1	2	yes	—
84	C₂²×D₁₈₈	—	2	32	no	—
85	C₂²×D₁₈₈	D₄	1	16	yes	complemented
86	C₂²×D₁₈₈	C₂³	1	2	yes	—
87	C₂²×D₁₈₈	C₂³	1	8	yes	—
88	C₂²×D₁₈₈	C₂³	1	2	yes	—
89	C₂²×D₁₈₈	C₂³	1	2	yes	—
90	C₂²×D₁₈₈	C₂³	1	2	yes	—
91	C₂²×D₁₈₈	C₂³	1	2	yes	—
92	C₂²×D₁₈₈	C₂³	1	8	yes	—
93	C₂²×D₁₈₈	C₂³	1	32	yes	complemented
94	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
95	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
96	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
97	C₂×D₄×D₄₇	—	2	64	no	—
98	C₂×D₄×D₄₇	—	2	32	no	—
99	C₂×D₄×D₄₇	—	4	16	no	—
100	C₂×D₄×D₄₇	C₂³	1	32	yes	complemented
101	C₂×D₄×D₄₇	C₂³	1	64	yes	complemented
102	C₂×D₄×D₄₇	C₂³	1	32	yes	complemented
103	C₂³×Dic₄₇	C₂³	1	2	yes	—
104	C₂²×C₄×D₄₇	—	4	8	no	—
105	C₂²×C₄×D₄₇	C₂³	1	8	yes	—
106	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
107	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
108	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
109	C₂²×C₄×D₄₇	C₂³	1	16	yes	complemented
110	#13094024	C₂³	1	8	yes	complemented
111	#13094021	C₂³	1	8	yes	complemented
112	#13094012	C₂³	1	16	yes	complemented
113	#13094009	C₂³	1	64	yes	complemented
114	#13094006	C₂³	1	64	yes	complemented
115	#13094003	C₂³	1	32	yes	complemented
116	#13094000	C₂³	1	32	yes	complemented
117	#13093999	C₂³	1	32	yes	complemented
118	#13093998	C₂³	1	32	yes	complemented
119	#13093998	C₂³	1	16	yes	complemented
120	#13093998	C₂³	1	16	yes	complemented
121	#13093997	C₂³	1	64	yes	complemented
122	#13093996	C₂³	1	64	yes	complemented
123	#13093995	C₂³	1	32	yes	complemented
124	#13093995	C₂³	1	32	yes	complemented
125	#13093994	C₂³	1	64	yes	complemented
126	#13093992	C₂³	1	64	yes	complemented
127	C₄×D₁₈₈	C₂³	1	16	yes	complemented
128	C₄×D₁₈₈	C₂³	1	16	yes	complemented
129	C₄×D₁₈₈	C₂³	1	16	yes	complemented
130	C₄×D₁₈₈	C₂³	1	16	yes	complemented
131	C₄×D₁₈₈	C₂³	1	16	yes	complemented
132	C₄×D₁₈₈	C₂³	1	16	yes	complemented
133	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
134	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
135	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
136	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
137	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	complemented
138	C₂×Dic₄₇⋊C₄	C₂³	1	8	yes	—
139	C₄⋊C₄×D₄₇	C₂³	1	32	yes	complemented
140	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
141	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
142	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
143	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
144	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
145	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
146	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	complemented
147	C₂²⋊C₄×D₄₇	C₂³	1	64	yes	complemented
148	C₂×#41×C₄₇	—	2	16	no	—
149	C₂×#41×C₄₇	C₂³	1	16	yes	complemented
150	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
151	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
152	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
153	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
154	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
155	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
157	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
160	#127×C₄₇	C₂³	1	8	yes	complemented
161	#124×C₄₇	C₂³	1	16	yes	complemented
162	#121×C₄₇	C₂³	1	16	yes	complemented
163	#121×C₄₇	C₂³	1	16	yes	complemented
164	C₄×D₄×C₄₇	C₂³	1	16	yes	complemented
165	C₄×D₄×C₄₇	C₂³	1	16	yes	complemented
166	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
170	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₄₇	C₂³	1	8	yes	complemented
175	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
176	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
177	C₂³×D₄₇	—	2	32	no	—
178	C₂³×D₄₇	—	4	4	no	—
179	C₂³×D₄₇	—	4	4	no	—
180	C₂³×D₄₇	—	4	16	no	—
181	C₂³×D₄₇	—	4	16	no	—
182	C₂³×D₄₇	C₂×D₄	1	16	yes	complemented
183	C₂³×D₄₇	C₂⁴	1	4	yes	—
184	C₂³×D₄₇	C₂⁴	1	4	yes	—
185	C₂³×D₄₇	C₂⁴	1	32	yes	—
186	C₂³×D₄₇	C₂⁴	1	8	yes	—
187	#41×C₄₇	—	2	64	no	—
188	C₂×Q₈×C₄₇	—	2	8	no	—
189	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
190	C₂×D₄×C₄₇	—	2	16	no	—
191	C₂×D₄×C₄₇	—	2	8	no	—
192	C₂×D₄×C₄₇	—	2	8	no	—
193	C₂×D₄×C₄₇	—	4	4	no	—
194	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
195	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
196	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
197	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
198	C₂²×C₄×C₄₇	—	2	16	no	—
199	C₂²×C₄×C₄₇	—	2	4	no	—
200	C₂²×C₄×C₄₇	—	4	2	no	—
201	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	complemented
202	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
208	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
213	C₂×C₂²⋊D₄₇	—	2	16	no	—
214	C₂×C₂²⋊D₄₇	—	2	32	no	—
215	C₂×C₂²⋊D₄₇	—	4	16	no	—
216	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
217	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
218	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
219	C₂²×Dic₄₇	—	4	4	no	—
220	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
221	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
222	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
223	#10625354	—	2	128	no	—
224	D₄×D₄₇	—	2	256	no	—
225	D₄×D₄₇	—	2	128	no	—
226	D₄×D₄₇	—	4	64	no	—
227	#10625350	—	2	64	no	—
228	#10625350	—	2	128	no	—
229	C₂×D₁₈₈	—	2	32	no	—
230	C₂×D₁₈₈	—	2	8	no	—
231	C₂×D₁₈₈	—	2	8	no	—
232	C₂×D₁₈₈	—	2	128	no	—
233	C₂×D₁₈₈	—	4	4	no	—
234	C₂×D₁₈₈	C₂×D₄	1	16	yes	complemented
235	C₂×D₁₈₈	C₂×D₄	1	16	yes	complemented
236	C₂×D₁₈₈	C₂×D₄	1	64	yes	complemented
237	C₂×D₁₈₈	C₂⁴	1	8	yes	—
238	C₂×D₁₈₈	C₂⁴	1	32	yes	—
239	C₂×D₁₈₈	C₂⁴	1	8	yes	—
240	C₂×D₁₈₈	C₂⁴	1	8	yes	—
241	C₂×D₁₈₈	C₂⁴	1	8	yes	—
242	C₂×D₁₈₈	C₂⁴	1	8	yes	—
243	C₂×C₄×D₄₇	—	2	32	no	—
244	C₂×C₄×D₄₇	—	2	16	no	—
245	C₂×C₄×D₄₇	—	2	16	no	—
246	C₂×C₄×D₄₇	—	4	32	no	—
247	C₂×C₄×D₄₇	—	4	8	no	—
248	C₂×C₄×D₄₇	C₂⁴	1	32	yes	—
249	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
250	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
251	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
252	C₂×Dic₉₄	—	2	8	no	—
253	C₂×Dic₉₄	C₂⁴	1	8	yes	—
254	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
255	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
256	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
257	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
258	C₄²×C₄₇	C₂⁴	1	4	yes	—
259	C₄²×C₄₇	C₂⁴	1	4	yes	—
260	C₄²×C₄₇	C₂⁴	1	4	yes	—
261	C₄²×C₄₇	C₂⁴	1	4	yes	—
262	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
263	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
264	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
265	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
266	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
267	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
268	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
269	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
270	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
271	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
272	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
273	C₂³×C₄₇	—	2	2	no	—
274	C₂³×C₄₇	—	2	2	no	—
275	C₂³×C₄₇	—	2	8	no	—
276	C₂³×C₄₇	—	2	8	no	—
277	C₂³×C₄₇	—	2	8	no	—
278	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
279	C₂³×C₄₇	C₂⁵	1	8	yes	—
280	C₂³×C₄₇	C₂⁵	1	2	yes	—
281	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
282	C₂²×D₄₇	—	2	8	no	—
283	C₂²×D₄₇	—	2	8	no	—
284	C₂²×D₄₇	—	2	8	no	—
285	C₂²×D₄₇	—	2	8	no	—
286	C₂²×D₄₇	—	2	8	no	—
287	C₂²×D₄₇	—	2	64	no	—
288	C₂²×D₄₇	—	4	8	no	—
289	C₂²×D₄₇	—	4	32	no	—
290	C₂²×D₄₇	—	4	8	no	—
291	C₂²×D₄₇	—	4	32	no	—
292	C₂²×D₄₇	—	4	32	no	—
293	C₂²×D₄₇	—	8	64	no	—
294	C₂²×D₄₇	C₂²×D₄	1	16	yes	—
295	C₂²×D₄₇	C₂²×D₄	1	32	yes	complemented
296	C₂²×D₄₇	C₂⁵	1	8	yes	—
297	C₂²×D₄₇	C₂⁵	1	8	yes	—
298	Q₈×C₄₇	—	2	16	no	—
299	D₄×C₄₇	—	2	32	no	—
300	D₄×C₄₇	—	2	16	no	—
301	D₄×C₄₇	—	2	16	no	—
302	D₄×C₄₇	—	4	8	no	—
303	C₂×C₄×C₄₇	—	2	8	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	32	no	—
308	C₂×C₄×C₄₇	—	2	8	no	—
309	C₂×C₄×C₄₇	—	4	4	no	—
310	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
311	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
312	C₂×C₄×C₄₇	C₂²×D₄	1	16	yes	complemented
313	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	complemented
314	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
315	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
316	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
317	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
318	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
319	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
320	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
321	C₂²⋊D₄₇	—	2	32	no	—
322	C₂²⋊D₄₇	—	2	64	no	—
323	C₂²⋊D₄₇	—	4	32	no	—
324	C₂×Dic₄₇	—	2	8	no	—
325	C₂×Dic₄₇	—	2	8	no	—
326	C₂×Dic₄₇	—	4	8	no	—
327	C₂×Dic₄₇	C₂⁵	1	8	yes	—
328	C₂×Dic₄₇	C₂⁵	1	8	yes	—
329	D₁₈₈	—	2	64	no	—
330	D₁₈₈	—	2	16	no	—
331	D₁₈₈	—	2	16	no	—
332	D₁₈₈	—	4	8	no	—
333	D₁₈₈	C₂²×D₄	1	32	yes	complemented
334	D₁₈₈	C₂²×D₄	1	32	yes	complemented
335	C₄×D₄₇	—	2	64	no	—
336	C₄×D₄₇	—	2	32	no	—
337	C₄×D₄₇	—	2	32	no	—
338	C₄×D₄₇	—	4	16	no	—
339	Dic₉₄	—	2	16	no	—
340	C₂×#3496	—	47	1	no	maximal, Sylow
341	C₂²×C₄₇	—	2	2	no	—
342	C₂²×C₄₇	—	2	2	no	—
343	C₂²×C₄₇	—	2	8	no	—
344	C₂²×C₄₇	—	2	8	no	—
345	C₂²×C₄₇	—	2	8	no	—
346	C₂²×C₄₇	—	2	8	no	—
347	C₂²×C₄₇	—	4	16	no	—
348	C₂²×C₄₇	C₂³×D₄	1	4	yes	—
349	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
350	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
351	C₂²×C₄₇	#585	1	2	yes	—
352	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
353	C₂×D₄₇	—	2	8	no	—
354	C₂×D₄₇	—	2	8	no	—
355	C₂×D₄₇	—	2	32	no	—
356	C₂×D₄₇	—	2	8	no	—
357	C₂×D₄₇	—	2	8	no	—
358	C₂×D₄₇	—	2	8	no	—
359	C₂×D₄₇	—	4	32	no	—
360	C₂×D₄₇	—	4	16	no	—
361	C₂×D₄₇	—	8	64	no	—
362	C₂×D₄₇	C₂³×D₄	1	16	yes	—
363	C₄×C₄₇	—	2	8	no	—
364	C₄×C₄₇	—	2	2	no	—
365	C₄×C₄₇	—	2	2	no	—
366	C₄×C₄₇	—	2	2	no	—
367	C₄×C₄₇	C₂³×D₄	1	4	yes	—
368	C₄×C₄₇	C₂³×D₄	1	4	yes	—
369	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	complemented
370	Dic₄₇	—	2	8	no	—
371	Dic₄₇	—	2	8	no	—
372	C₂²×H(5,𝔽₂)	—	47	2	no	—
373	#3496	—	47	32	no	—
374	C₂×#547	—	47	2	no	—
375	C₂×#547	—	47	2	no	—
376	C₂×#546	—	47	4	no	—
377	C₂×#546	—	47	4	no	—
378	C₂×D₄²	—	47	2	no	—
379	C₂×D₄²	—	47	2	no	—
380	C₂×#537	—	47	2	no	—
381	C₂×#534	—	47	4	no	—
382	C₂×#532	—	47	1	no	—
383	C₂×#532	D₄₇	1	1	yes	characteristic, complemented
384	C₂²×#121	—	47	4	no	—
385	C₂²×C₄×D₄	—	47	1	no	—
386	C₂×C₄₇	—	2	4	no	—
387	C₂×C₄₇	—	4	8	no	—
388	C₂×C₄₇	#3496	1	4	yes	complemented
389	C₂×C₄₇	C₂⁴×D₄	1	1	yes	characteristic
390	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
392	D₄₇	—	2	16	no	—
393	D₄₇	—	4	8	no	—
394	C₂×H(5,𝔽₂)	—	47	32	no	—
395	C₂×H(5,𝔽₂)	—	94	32	no	—
396	C₂²×#41	—	47	4	no	—
397	C₂²×#41	—	47	2	no	—
398	C₂²×#41	—	47	4	no	—
399	C₂²×#41	C₂×D₄₇	1	2	yes	complemented
400	C₂³×D₄	—	47	8	no	—
401	C₂³×D₄	—	47	4	no	—
402	C₂³×D₄	—	47	4	no	—
403	C₂³×D₄	—	47	1	no	—
404	C₂³×D₄	—	47	4	no	—
405	C₂⁴×C₄	—	47	2	no	—
406	#547	—	47	32	no	—
407	#547	—	47	32	no	—
408	#546	—	47	64	no	—
409	#546	—	47	64	no	—
410	D₄²	—	47	32	no	—
411	D₄²	—	47	32	no	—
412	#537	—	47	32	no	—
413	#534	—	47	64	no	—
414	#532	—	47	16	no	—
415	#532	C₂×D₄₇	1	16	yes	complemented
416	C₂×C₄⋊Q₈	—	47	1	no	—
417	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
418	C₂×#127	—	47	1	no	—
419	C₂×#127	C₂×D₄₇	1	1	yes	characteristic, complemented
420	C₂×#124	—	47	2	no	—
421	C₂×#124	C₂×D₄₇	1	2	yes	complemented
422	C₂×#123	—	47	8	no	—
423	C₂×#123	—	47	8	no	—
424	C₂×C₂²⋊Q₈	—	47	4	no	—
425	C₂×C₂²⋊Q₈	—	47	4	no	—
426	C₂×#121	—	47	8	no	—
427	C₂×#121	—	47	4	no	—
428	C₂×#121	—	47	4	no	—
429	C₂×#121	—	47	2	no	—
430	C₂×#121	—	47	2	no	—
431	C₂×#121	—	47	4	no	—
432	C₂×#121	—	47	64	no	—
433	C₂×#121	—	47	4	no	—
434	C₂×#121	—	47	8	no	—
435	C₂×#121	C₂×D₄₇	1	2	yes	complemented
436	C₂×#121	C₂×D₄₇	1	2	yes	complemented
437	C₂×#120	—	47	8	no	—
438	C₂×#120	—	47	8	no	—
439	C₂×C₄×D₄	—	47	2	no	—
440	C₂×C₄×D₄	—	47	2	no	—
441	C₂×C₄×D₄	—	47	2	no	—
442	C₂×C₄×D₄	—	47	2	no	—
443	C₂×C₄×D₄	—	47	2	no	—
444	C₂×C₄×D₄	—	47	2	no	—
445	C₂×C₄×D₄	—	47	16	no	—
446	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	complemented
447	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	complemented
448	C₂²×C₄⋊C₄	—	47	1	no	—
449	C₂²×C₄⋊C₄	—	47	4	no	—
450	C₂²×C₂²⋊C₄	—	47	2	no	—
451	C₂²×C₂²⋊C₄	—	47	8	no	—
452	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic, complemented
453	C₄₇	C₂×#3496	1	1	yes	characteristic, complemented, Sylow
454	C₂⁵	—	47	2	no	—
455	C₂⁵	—	47	8	no	—
456	H(5,𝔽₂)	—	94	256	no	—
457	C₂×#41	—	2	16	no	—
458	C₂×#41	—	47	32	no	—
459	C₂×#41	—	47	16	no	—
460	C₂×#41	—	47	32	no	—
461	C₂×#41	—	94	32	no	—
462	C₂×#41	—	94	32	no	—
463	C₂×#41	—	94	16	no	—
464	C₂×#41	C₂²×D₄₇	1	16	yes	complemented
465	C₂²×Q₈	—	47	2	no	—
466	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
467	C₂²×D₄	—	47	8	no	—
468	C₂²×D₄	—	47	4	no	—
469	C₂²×D₄	—	47	8	no	—
470	C₂²×D₄	—	47	64	no	—
471	C₂²×D₄	—	47	32	no	—
472	C₂²×D₄	—	47	32	no	—
473	C₂²×D₄	—	47	16	no	—
474	C₂²×D₄	—	47	2	no	—
475	C₂²×D₄	—	47	2	no	—
476	C₂²×D₄	—	47	8	no	—
477	C₂²×D₄	—	47	2	no	—
478	C₂²×D₄	—	47	8	no	—
479	C₂²×D₄	—	47	2	no	—
480	C₂²×D₄	—	47	32	no	—
481	C₂²×D₄	—	47	2	no	—
482	C₂²×D₄	—	94	32	no	—
483	C₂²×D₄	—	94	32	no	—
484	C₂²×D₄	—	94	64	no	—
485	C₂²×D₄	—	188	16	no	—
486	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
487	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
488	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
489	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
490	C₂³×C₄	—	47	2	no	—
491	C₂³×C₄	—	47	8	no	—
492	C₂³×C₄	—	47	4	no	—
493	C₂³×C₄	—	47	4	no	—
494	C₂³×C₄	—	47	4	no	—
495	C₂³×C₄	—	47	16	no	—
496	C₂³×C₄	—	188	8	no	—
497	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
498	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
499	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
500	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
501	C₄⋊Q₈	—	47	8	no	—
502	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
503	#127	—	47	8	no	—
504	#127	C₂²×D₄₇	1	8	yes	complemented
505	#124	—	47	16	no	—
506	#124	C₂²×D₄₇	1	16	yes	complemented
507	#123	—	47	64	no	—
508	#123	—	47	64	no	—
509	C₂²⋊Q₈	—	47	32	no	—
510	C₂²⋊Q₈	—	47	32	no	—
511	#121	—	47	64	no	—
512	#121	—	47	32	no	—
513	#121	—	47	32	no	—
514	#121	—	47	16	no	—
515	#121	—	47	16	no	—
516	#121	—	47	32	no	—
517	#121	—	47	32	no	—
518	#121	—	47	64	no	—
519	#121	C₂²×D₄₇	1	16	yes	complemented
520	#121	C₂²×D₄₇	1	16	yes	complemented
521	#120	—	47	64	no	—
522	#120	—	47	64	no	—
523	C₄×D₄	—	47	16	no	—
524	C₄×D₄	—	47	16	no	—
525	C₄×D₄	—	47	16	no	—
526	C₄×D₄	—	47	16	no	—
527	C₄×D₄	—	47	16	no	—
528	C₄×D₄	—	47	16	no	—
529	C₄×D₄	C₂²×D₄₇	1	16	yes	complemented
530	C₄×D₄	C₂²×D₄₇	1	16	yes	complemented
531	C₂×C₄⋊C₄	—	47	2	no	—
532	C₂×C₄⋊C₄	—	47	2	no	—
533	C₂×C₄⋊C₄	—	47	2	no	—
534	C₂×C₄⋊C₄	—	47	8	no	—
535	C₂×C₄⋊C₄	—	47	8	no	—
536	C₂×C₄⋊C₄	—	47	2	no	—
537	C₂×C₄⋊C₄	—	47	32	no	—
538	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
539	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
540	C₂×C₂²⋊C₄	—	47	8	no	—
541	C₂×C₂²⋊C₄	—	47	4	no	—
542	C₂×C₂²⋊C₄	—	47	4	no	—
543	C₂×C₂²⋊C₄	—	47	4	no	—
544	C₂×C₂²⋊C₄	—	47	16	no	—
545	C₂×C₂²⋊C₄	—	47	8	no	—
546	C₂×C₂²⋊C₄	—	47	4	no	—
547	C₂×C₂²⋊C₄	—	47	64	no	—
548	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
550	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
551	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
552	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
553	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
554	C₂×C₄²	C₂²×D₄₇	1	8	yes	complemented
555	C₂⁴	—	47	4	no	—
556	C₂⁴	—	47	16	no	—
557	C₂⁴	—	47	8	no	—
558	C₂⁴	—	47	4	no	—
559	C₂⁴	—	47	32	no	—
560	C₂⁴	—	94	32	no	—
561	C₂⁴	—	188	16	no	—
562	C₂⁴	—	188	16	no	—
563	C₂⁴	—	188	4	no	—
564	C₂⁴	—	188	4	no	—
565	C₂⁴	C₂³×D₄₇	1	4	yes	—
566	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
567	#41	—	2	64	no	—
568	#41	—	94	128	no	—
569	#41	—	94	128	no	—
570	#41	—	94	64	no	—
571	C₂×Q₈	—	2	8	no	—
572	C₂×Q₈	—	47	8	no	—
573	C₂×Q₈	—	94	8	no	—
574	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
575	C₂×D₄	—	2	16	no	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	47	32	no	—
580	C₂×D₄	—	47	16	no	—
581	C₂×D₄	—	47	32	no	—
582	C₂×D₄	—	47	16	no	—
583	C₂×D₄	—	47	16	no	—
584	C₂×D₄	—	47	64	no	—
585	C₂×D₄	—	47	8	no	—
586	C₂×D₄	—	47	8	no	—
587	C₂×D₄	—	47	8	no	—
588	C₂×D₄	—	47	32	no	—
589	C₂×D₄	—	47	8	no	—
590	C₂×D₄	—	47	8	no	—
591	C₂×D₄	—	94	128	no	—
592	C₂×D₄	—	94	32	no	—
593	C₂×D₄	—	94	128	no	—
594	C₂×D₄	—	94	256	no	—
595	C₂×D₄	—	94	32	no	—
596	C₂×D₄	—	94	16	no	—
597	C₂×D₄	—	94	8	no	—
598	C₂×D₄	—	94	8	no	—
599	C₂×D₄	—	188	4	no	—
600	C₂×D₄	—	188	64	no	—
601	C₂×D₄	—	188	16	no	—
602	C₂×D₄	C₂³×D₄₇	1	8	yes	—
603	C₂×D₄	C₂³×D₄₇	1	16	yes	—
604	C₂×D₄	C₂³×D₄₇	1	8	yes	—
605	C₂×D₄	C₂³×D₄₇	1	8	yes	—
606	C₂²×C₄	—	2	16	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	—	47	4	no	—
610	C₂²×C₄	—	47	4	no	—
611	C₂²×C₄	—	47	8	no	—
612	C₂²×C₄	—	47	32	no	—
613	C₂²×C₄	—	47	16	no	—
614	C₂²×C₄	—	47	16	no	—
615	C₂²×C₄	—	47	16	no	—
616	C₂²×C₄	—	94	32	no	—
617	C₂²×C₄	—	94	16	no	—
618	C₂²×C₄	—	94	16	no	—
619	C₂²×C₄	—	188	32	no	—
620	C₂²×C₄	—	188	8	no	—
621	C₂²×C₄	—	188	4	no	—
622	C₂²×C₄	D₄×D₄₇	1	8	yes	complemented
623	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
624	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
625	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
626	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
627	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
628	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
629	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
630	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
631	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
632	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
633	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
634	C₄⋊C₄	—	47	32	no	—
635	C₄⋊C₄	—	47	8	no	—
636	C₄⋊C₄	—	47	8	no	—
637	C₄⋊C₄	—	47	8	no	—
638	C₄⋊C₄	—	47	8	no	—
639	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
640	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
641	C₂²⋊C₄	—	47	32	no	—
642	C₂²⋊C₄	—	47	16	no	—
643	C₂²⋊C₄	—	47	16	no	—
644	C₂²⋊C₄	—	47	16	no	—
645	C₂²⋊C₄	—	47	32	no	—
646	C₂²⋊C₄	—	47	16	no	—
647	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
648	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
649	C₄²	C₂³×D₄₇	1	4	yes	—
650	C₄²	C₂³×D₄₇	1	4	yes	—
651	C₄²	C₂³×D₄₇	1	4	yes	—
652	C₄²	C₂³×D₄₇	1	4	yes	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	8	no	—
656	C₂³	—	2	8	no	—
657	C₂³	—	2	8	no	—
658	C₂³	—	47	16	no	—
659	C₂³	—	47	8	no	—
660	C₂³	—	47	32	no	—
661	C₂³	—	47	8	no	—
662	C₂³	—	94	64	no	—
663	C₂³	—	94	8	no	—
664	C₂³	—	94	8	no	—
665	C₂³	—	94	8	no	—
666	C₂³	—	94	8	no	—
667	C₂³	—	94	8	no	—
668	C₂³	—	376	64	no	—
669	C₂³	—	188	32	no	—
670	C₂³	—	188	32	no	—
671	C₂³	—	188	8	no	—
672	C₂³	—	188	32	no	—
673	C₂³	—	188	8	no	—
674	C₂³	C₂×D₄×D₄₇	1	4	yes	—
675	C₂³	C₂⁴×D₄₇	1	8	yes	—
676	C₂³	C₂⁴×D₄₇	1	2	yes	—
677	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
678	Q₈	—	2	16	no	—
679	Q₈	—	94	16	no	—
680	D₄	—	2	32	no	—
681	D₄	—	2	16	no	—
682	D₄	—	2	16	no	—
683	D₄	—	4	8	no	—
684	D₄	—	47	32	no	—
685	D₄	—	47	32	no	—
686	D₄	—	94	64	no	—
687	D₄	—	94	64	no	—
688	D₄	—	94	32	no	—
689	D₄	—	94	16	no	—
690	D₄	—	94	16	no	—
691	D₄	—	188	8	no	—
692	D₄	—	188	32	no	—
693	C₂×C₄	—	2	8	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	32	no	—
698	C₂×C₄	—	2	8	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	47	8	no	—
701	C₂×C₄	—	47	8	no	—
702	C₂×C₄	—	94	64	no	—
703	C₂×C₄	—	94	8	no	—
704	C₂×C₄	—	94	8	no	—
705	C₂×C₄	—	94	32	no	—
706	C₂×C₄	—	94	32	no	—
707	C₂×C₄	—	188	16	no	—
708	C₂×C₄	—	188	8	no	—
709	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
710	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
711	C₂×C₄	C₂×D₄×D₄₇	1	16	yes	complemented
712	C₂×C₄	#13094070	1	4	yes	complemented
713	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
714	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
715	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
716	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
717	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
718	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
719	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
720	C₂²	—	2	8	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	8	no	—
724	C₂²	—	2	8	no	—
725	C₂²	—	2	8	no	—
726	C₂²	—	4	16	no	—
727	C₂²	—	47	16	no	—
728	C₂²	—	94	32	no	—
729	C₂²	—	94	8	no	—
730	C₂²	—	94	8	no	—
731	C₂²	—	94	8	no	—
732	C₂²	—	94	8	no	—
733	C₂²	—	94	8	no	—
734	C₂²	—	376	64	no	—
735	C₂²	—	188	32	no	—
736	C₂²	—	188	16	no	—
737	C₂²	C₂²×D₄×D₄₇	1	4	yes	—
738	C₂²	C₂²×D₄×D₄₇	1	2	yes	—
739	C₂²	C₂×#13094070	1	2	yes	—
740	C₂²	#15689959	1	2	yes	—
741	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
742	C₄	—	2	8	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	94	8	no	—
747	C₄	—	94	8	no	—
748	C₄	C₂²×D₄×D₄₇	1	4	yes	—
749	C₄	C₂²×D₄×D₄₇	1	4	yes	—
750	C₄	C₂×#13094070	1	4	yes	complemented
751	C₂	—	2	4	no	—
752	C₂	—	4	8	no	—
753	C₂	—	94	16	no	—
754	C₂	—	188	8	no	—
755	C₂	#20257150	1	4	yes	direct product factor
756	C₂	C₂³×D₄×D₄₇	1	1	yes	characteristic
757	C₂	C₂²×#13094070	1	1	yes	characteristic
758	C₂	C₂×#15689959	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×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×#3496
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂²×#13094070	C₂	semidirect
2. #20257150	C₂	direct (N × H)
3. C₂×#15689778	C₂	semidirect
4. C₂×#15689776	C₂	semidirect
5. C₂×#15689769	C₂	semidirect
6. C₂×#15689766	C₂	semidirect
7. C₂×D₄×D₁₈₈	C₂	semidirect
8. C₂×#15689758	C₂	semidirect
9. C₂×#15689701	C₂	semidirect
10. C₂×#15689681	C₂	semidirect
11. C₂×#15689673	C₂	semidirect
12. C₂×#121×D₄₇	C₂	semidirect
13. C₂²×C₄×D₁₈₈	C₂	semidirect
14. C₂×C₄₇×#532	C₂	semidirect
16. C₂×#13094070	C₂²	semidirect
17. C₂²×#10625354	C₂²	semidirect
18. C₂²×#10625350	C₂²	semidirect
19. C₂²×#10625350	C₂²	semidirect
21. C₂³×D₁₈₈	C₂²	semidirect
22. C₂²×D₄×D₄₇	C₂²	semidirect
23. C₂²×D₄×D₄₇	C₂²	semidirect
24. C₂²×D₄×D₄₇	C₂²	semidirect
25. C₂³×C₄×D₄₇	C₂²	semidirect
26. #15689778	C₂²	semidirect
27. #15689776	C₂²	semidirect
28. #15689769	C₂²	semidirect
29. #15689766	C₂²	semidirect
30. D₄×D₁₈₈	C₂²	semidirect
31. #15689758	C₂²	semidirect
32. #15689701	C₂²	semidirect
33. #15689681	C₂²	semidirect
34. #15689673	C₂²	semidirect
35. C₂×#13094024	C₂²	semidirect
36. C₂×#13094021	C₂²	semidirect
37. C₂×#13094012	C₂²	semidirect
38. C₂×#13094009	C₂²	semidirect
39. C₂×#13094006	C₂²	semidirect
40. C₂×#13094003	C₂²	semidirect
41. C₂×#13094000	C₂²	semidirect
42. C₂×#13093999	C₂²	semidirect
43. C₂×#13093998	C₂²	semidirect
44. C₂×#13093998	C₂²	semidirect
45. C₂×#13093998	C₂²	semidirect
46. C₂×#13093997	C₂²	semidirect
47. C₂×#13093996	C₂²	semidirect
48. C₂×#13093995	C₂²	semidirect
49. C₂×#13093995	C₂²	semidirect
50. #121×D₄₇	C₂²	semidirect
51. C₂×#13093994	C₂²	semidirect
52. C₂×#13093992	C₂²	semidirect
53. C₂×C₄×D₁₈₈	C₂²	semidirect
54. C₂×C₄×D₁₈₈	C₂²	semidirect
55. C₂×C₄×D₁₈₈	C₂²	semidirect
56. C₂×C₄×D₁₈₈	C₂²	semidirect
57. C₂×C₄×D₁₈₈	C₂²	semidirect
58. C₂×C₄×D₁₈₈	C₂²	semidirect
59. C₂×C₄×D₁₈₈	C₂²	semidirect
60. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
61. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
62. C₂²×(C₂×D₄₇)⋊C₄	C₂²	semidirect
63. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
64. C₂²×#41×C₄₇	C₂²	semidirect
65. C₄₇×#532	C₂²	semidirect
66. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
67. C₂×#127×C₄₇	C₂²	semidirect
68. C₂×#124×C₄₇	C₂²	semidirect
69. C₂×#121×C₄₇	C₂²	semidirect
70. C₂×#121×C₄₇	C₂²	semidirect
71. C₂×C₄×D₄×C₄₇	C₂²	semidirect
72. C₂×C₄×D₄×C₄₇	C₂²	semidirect
73. C₂²×C₄²×C₄₇	C₂²	semidirect
78. C₂×#10625354	C₂³	semidirect
81. C₂×#10625350	C₂³	semidirect
82. C₂×#10625350	C₂³	semidirect
85. C₂²×D₁₈₈	D₄	semidirect
93. C₂²×D₁₈₈	C₂³	semidirect
100. C₂×D₄×D₄₇	C₂³	semidirect
101. C₂×D₄×D₄₇	C₂³	semidirect
102. C₂×D₄×D₄₇	C₂³	semidirect
109. C₂²×C₄×D₄₇	C₂³	semidirect
110. #13094024	C₂³	semidirect
111. #13094021	C₂³	semidirect
112. #13094012	C₂³	semidirect
113. #13094009	C₂³	semidirect
114. #13094006	C₂³	semidirect
115. #13094003	C₂³	semidirect
116. #13094000	C₂³	semidirect
117. #13093999	C₂³	semidirect
118. #13093998	C₂³	semidirect
119. #13093998	C₂³	semidirect
120. #13093998	C₂³	semidirect
121. #13093997	C₂³	semidirect
122. #13093996	C₂³	semidirect
123. #13093995	C₂³	semidirect
124. #13093995	C₂³	semidirect
125. #13093994	C₂³	semidirect
126. #13093992	C₂³	semidirect
127. C₄×D₁₈₈	C₂³	semidirect
128. C₄×D₁₈₈	C₂³	semidirect
129. C₄×D₁₈₈	C₂³	semidirect
130. C₄×D₁₈₈	C₂³	semidirect
131. C₄×D₁₈₈	C₂³	semidirect
132. C₄×D₁₈₈	C₂³	semidirect
137. C₂×C₄⋊Dic₄₇	C₂³	semidirect
139. C₄⋊C₄×D₄₇	C₂³	semidirect
146. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
147. C₂²⋊C₄×D₄₇	C₂³	semidirect
149. C₂×#41×C₄₇	C₂³	semidirect
159. C₄⋊Q₈×C₄₇	C₂³	semidirect
160. #127×C₄₇	C₂³	semidirect
161. #124×C₄₇	C₂³	semidirect
162. #121×C₄₇	C₂³	semidirect
163. #121×C₄₇	C₂³	semidirect
164. C₄×D₄×C₄₇	C₂³	semidirect
165. C₄×D₄×C₄₇	C₂³	semidirect
174. C₂×C₄²×C₄₇	C₂³	semidirect
182. C₂³×D₄₇	C₂×D₄	semidirect
201. C₂²×C₄×C₄₇	C₂×D₄	semidirect
234. C₂×D₁₈₈	C₂×D₄	semidirect
235. C₂×D₁₈₈	C₂×D₄	semidirect
236. C₂×D₁₈₈	C₂×D₄	semidirect
295. C₂²×D₄₇	C₂²×D₄	semidirect
312. C₂×C₄×C₄₇	C₂²×D₄	semidirect
313. C₂×C₄×C₄₇	H(5,𝔽₂)	semidirect
333. D₁₈₈	C₂²×D₄	semidirect
334. D₁₈₈	C₂²×D₄	semidirect
369. C₄×C₄₇	C₂×H(5,𝔽₂)	semidirect
383. C₂×#532	D₄₇	semidirect
388. C₂×C₄₇	#3496	semidirect
399. C₂²×#41	C₂×D₄₇	semidirect
415. #532	C₂×D₄₇	semidirect
417. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
419. C₂×#127	C₂×D₄₇	semidirect
421. C₂×#124	C₂×D₄₇	semidirect
435. C₂×#121	C₂×D₄₇	semidirect
436. C₂×#121	C₂×D₄₇	semidirect
446. C₂×C₄×D₄	C₂×D₄₇	semidirect
447. C₂×C₄×D₄	C₂×D₄₇	semidirect
452. C₂²×C₄²	C₂×D₄₇	semidirect
453. C₄₇	C₂×#3496	semidirect
464. C₂×#41	C₂²×D₄₇	semidirect
502. C₄⋊Q₈	C₂²×D₄₇	semidirect
504. #127	C₂²×D₄₇	semidirect
506. #124	C₂²×D₄₇	semidirect
519. #121	C₂²×D₄₇	semidirect
520. #121	C₂²×D₄₇	semidirect
529. C₄×D₄	C₂²×D₄₇	semidirect
530. C₄×D₄	C₂²×D₄₇	semidirect
554. C₂×C₄²	C₂²×D₄₇	semidirect
622. C₂²×C₄	D₄×D₄₇	semidirect
711. C₂×C₄	C₂×D₄×D₄₇	semidirect
712. C₂×C₄	#13094070	semidirect
750. C₄	C₂×#13094070	semidirect
755. C₂	#20257150	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×#13094070	2
#20257150	2
C₂×#15689778	2
C₂×#15689776	2
C₂×#15689769	2
C₂×#15689766	2
C₂×D₄×D₁₈₈	2
C₂×#15689758	2
C₂×#15689701	2
C₂×#15689681	2
C₂×#15689673	2
C₂×#121×D₄₇	2
C₂²×C₄×D₁₈₈	2
C₂×C₄₇×#532	2
C₂×#3496	47

Subgroups — C2×#20257150 #27124167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257150 #27124167