Subgroups — C₂×#20244039 #26218780

Order 12032.

1082 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093959	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689119	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689090	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689081	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244039	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688883	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688878	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#104×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×#13093983	C₂²	1	1	yes	characteristic
13	C₂×#13093959	—	2	4	no	—
14	C₂×#13093959	C₂²	1	4	yes	complemented
15	#15689119	C₄	1	4	yes	complemented
16	#15689119	C₂²	1	4	yes	—
17	C₂×#13093948	C₄	1	1	yes	characteristic, complemented
18	C₂×#13093948	C₄	1	1	yes	characteristic, complemented
19	C₂×#13093945	C₄	1	1	yes	characteristic, complemented
20	C₂×#13093945	C₄	1	1	yes	characteristic, complemented
21	#15689090	—	2	2	no	—
22	#15689090	C₂²	1	4	yes	—
23	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
24	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
25	#15689081	—	2	2	no	—
26	#15689081	C₂²	1	4	yes	complemented
27	C₂×#13093934	—	2	1	no	—
28	C₂×C₈×Dic₄₇	—	2	1	no	—
29	#15688883	C₂²	1	4	yes	complemented
30	#15688878	C₂²	1	4	yes	complemented
31	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#104×C₄₇	—	2	4	no	—
35	C₂×#104×C₄₇	C₂²	1	4	yes	—
36	C₂×#10625329	—	2	1	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	C₂³	1	2	yes	—
40	C₂²×C₄₇⋊C₈	—	2	2	no	—
41	C₂²×C₄₇⋊C₈	—	2	2	no	—
42	C₂²×C₄₇⋊C₈	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	—	2	1	no	—
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
48	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
52	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
53	#13093983	—	2	1	no	—
54	#13093983	—	2	1	no	—
55	#13093983	C₂×C₄	1	2	yes	—
56	#13093983	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
60	C₂×C₄×Dic₄₇	—	2	1	no	—
61	#13093959	—	2	8	no	—
62	#13093948	C₂×C₄	1	4	yes	complemented
63	#13093948	C₂×C₄	1	4	yes	complemented
64	#13093945	C₂×C₄	1	4	yes	complemented
65	#13093945	C₂×C₄	1	4	yes	complemented
66	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
68	#13093934	—	2	4	no	—
69	C₈×Dic₄₇	—	2	4	no	—
70	C₂×#41×C₄₇	—	2	1	no	—
71	C₂×#41×C₄₇	—	2	1	no	—
72	C₂×#41×C₄₇	—	2	2	no	—
73	C₂×#41×C₄₇	—	2	2	no	—
74	C₂×#41×C₄₇	—	2	2	no	—
75	C₂×#41×C₄₇	—	2	2	no	—
76	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×#41×C₄₇	C₂³	1	2	yes	—
78	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂²×D₄×C₄₇	—	2	1	no	—
80	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂³×C₄×C₄₇	—	2	1	no	—
82	C₂³×C₄×C₄₇	—	2	1	no	—
83	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₄₇	—	2	1	no	—
85	C₂×M₁₆×C₄₇	—	2	2	no	—
86	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
87	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
88	C₂²×C₈×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	—	2	2	no	—
90	C₂×C₄²×C₄₇	—	2	2	no	—
91	C₂×C₄²×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
93	#104×C₄₇	—	2	8	no	—
94	C₂⁴×C₄₇	—	2	1	no	—
95	C₂⁴×C₄₇	#41	1	1	yes	characteristic
96	#41×C₄₇	—	2	4	no	—
97	#41×C₄₇	—	2	4	no	—
98	#41×C₄₇	—	2	2	no	—
99	#41×C₄₇	—	2	2	no	—
100	#41×C₄₇	—	2	2	no	—
101	#41×C₄₇	—	2	2	no	—
102	#41×C₄₇	—	4	2	no	—
103	#41×C₄₇	—	4	2	no	—
104	#41×C₄₇	—	4	2	no	—
105	#41×C₄₇	—	4	2	no	—
106	C₂×Q₈×C₄₇	—	2	1	no	—
107	C₂×Q₈×C₄₇	—	2	2	no	—
108	C₂×Q₈×C₄₇	—	2	2	no	—
109	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂×D₄×C₄₇	—	2	2	no	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	2	no	—
114	C₂×D₄×C₄₇	—	2	1	no	—
115	C₂×D₄×C₄₇	—	4	2	no	—
116	C₂×D₄×C₄₇	—	4	2	no	—
117	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₄₇	—	2	4	no	—
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	4	2	no	—
124	C₂²×C₄×C₄₇	—	4	2	no	—
125	C₂²×C₄×C₄₇	—	4	2	no	—
126	C₂²×C₄×C₄₇	—	4	2	no	—
127	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	#41	1	2	yes	—
133	C₂²×C₄×C₄₇	#41	1	2	yes	—
134	C₂²×C₄×C₄₇	#41	1	2	yes	—
135	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
137	C₂²×Dic₄₇	—	2	1	no	—
138	C₂²×Dic₄₇	—	2	1	no	—
139	M₁₆×C₄₇	—	2	4	no	—
140	M₁₆×C₄₇	—	2	2	no	—
141	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
142	C₂×C₈×C₄₇	—	2	4	no	—
143	C₂×C₈×C₄₇	—	2	2	no	—
144	C₄²×C₄₇	—	2	2	no	—
145	C₄²×C₄₇	—	2	2	no	—
146	C₄²×C₄₇	—	4	2	no	—
147	C₂²⋊Dic₄₇	—	2	2	no	—
148	C₂²⋊Dic₄₇	—	2	2	no	—
149	C₄⋊Dic₄₇	—	2	1	no	—
150	C₄⋊Dic₄₇	—	2	1	no	—
151	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
152	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
153	C₄×Dic₄₇	—	2	2	no	—
154	C₄×Dic₄₇	—	2	2	no	—
155	#10625329	—	2	2	no	—
156	#10625329	—	2	2	no	—
157	#10625329	—	4	2	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂×C₄₇⋊C₈	—	2	4	no	—
161	C₂×C₄₇⋊C₈	—	2	2	no	—
162	C₂×C₄₇⋊C₈	—	2	2	no	—
163	C₂×C₄₇⋊C₈	—	2	4	no	—
164	C₂×C₄₇⋊C₈	—	2	2	no	—
165	C₂×C₄₇⋊C₈	—	2	2	no	—
166	C₂×C₄₇⋊C₈	—	2	2	no	—
167	C₂×C₄₇⋊C₈	—	2	2	no	—
168	C₂×C₄₇⋊C₈	—	2	2	no	—
169	C₂×C₄₇⋊C₈	—	4	2	no	—
170	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
171	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
172	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
173	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
174	C₂³×C₄₇	—	2	2	no	—
175	C₂³×C₄₇	—	2	2	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	4	2	no	—
178	C₂³×C₄₇	—	4	2	no	—
179	C₂³×C₄₇	—	4	2	no	—
180	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
181	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
182	C₂³×C₄₇	#124	1	2	yes	—
183	C₂³×C₄₇	#126	1	2	yes	—
184	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
185	Q₈×C₄₇	—	2	2	no	—
186	Q₈×C₄₇	—	2	2	no	—
187	Q₈×C₄₇	—	4	2	no	—
188	D₄×C₄₇	—	2	2	no	—
189	D₄×C₄₇	—	2	2	no	—
190	D₄×C₄₇	—	4	2	no	—
191	D₄×C₄₇	—	4	2	no	—
192	D₄×C₄₇	—	4	4	no	—
193	D₄×C₄₇	—	4	2	no	—
194	C₂×C₄×C₄₇	—	2	4	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	4	8	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	2	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	4	4	no	—
203	C₂×C₄×C₄₇	#117	1	2	yes	—
204	C₂×C₄×C₄₇	#117	1	2	yes	—
205	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
209	C₂×C₄×C₄₇	#121	1	2	yes	—
210	C₂×C₄×C₄₇	#121	1	2	yes	—
211	C₂×C₄×C₄₇	#123	1	2	yes	—
212	C₂×C₄×C₄₇	#123	1	2	yes	—
213	C₂×C₄×C₄₇	#124	1	2	yes	—
214	C₂×C₄×C₄₇	#126	1	2	yes	—
215	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
221	C₂×Dic₄₇	—	2	2	no	—
222	C₂×Dic₄₇	—	2	2	no	—
223	C₂×Dic₄₇	—	4	2	no	—
224	C₂×Dic₄₇	—	4	2	no	—
225	C₈×C₄₇	—	2	4	no	—
226	C₄₇⋊C₈	—	2	2	no	—
227	C₄₇⋊C₈	—	2	2	no	—
228	C₄₇⋊C₈	—	2	2	no	—
229	C₄₇⋊C₈	—	2	2	no	—
230	C₄₇⋊C₈	—	4	2	no	—
231	C₂×#1929	—	47	1	no	maximal, Sylow
232	C₂²×C₄₇	—	2	4	no	—
233	C₂²×C₄₇	—	2	4	no	—
234	C₂²×C₄₇	—	2	1	no	—
235	C₂²×C₄₇	—	2	1	no	—
236	C₂²×C₄₇	—	2	1	no	—
237	C₂²×C₄₇	—	2	1	no	—
238	C₂²×C₄₇	—	4	2	no	—
239	C₂²×C₄₇	—	4	2	no	—
240	C₂²×C₄₇	—	4	2	no	—
241	C₂²×C₄₇	—	8	4	no	—
242	C₂²×C₄₇	#388	1	2	yes	—
243	C₂²×C₄₇	#388	1	2	yes	—
244	C₂²×C₄₇	#443	1	2	yes	—
245	C₂²×C₄₇	#444	1	2	yes	—
246	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
248	C₂²×C₄₇	C₂×#126	1	1	yes	characteristic
249	C₄×C₄₇	—	4	4	no	—
250	C₄×C₄₇	—	4	2	no	—
251	C₄×C₄₇	#388	1	2	yes	—
252	C₄×C₄₇	#388	1	2	yes	—
253	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
254	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
256	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
257	Dic₄₇	—	4	2	no	—
258	Dic₄₇	—	4	2	no	—
259	C₂²×#108	—	47	1	no	—
260	C₂²×#104	D₄₇	1	1	yes	characteristic
261	C₂×#416	—	47	1	no	—
262	C₂×#408	—	47	1	no	—
263	C₂×#405	—	47	1	no	—
264	#1929	—	47	8	no	—
265	C₂×#339	—	47	1	no	—
266	C₂×#336	—	47	1	no	—
267	C₂×C₄₇	—	2	1	no	—
268	C₂×C₄₇	—	2	1	no	—
269	C₂×C₄₇	—	2	2	no	—
270	C₂×C₄₇	—	8	2	no	—
271	C₂×C₄₇	#1929	1	4	yes	complemented
272	C₂×C₄₇	C₂×#388	1	1	yes	characteristic
273	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
274	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
275	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
276	C₂²×M₁₆	—	47	1	no	—
277	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
278	C₂³×C₈	—	47	1	no	—
279	C₂³×C₈	—	47	1	no	—
280	C₂×#117	—	47	1	no	—
281	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
282	C₂×#108	—	47	4	no	—
283	C₂×#108	—	94	4	no	—
284	C₂×#104	—	2	4	no	—
285	C₂×#104	C₂×D₄₇	1	4	yes	—
286	#416	—	47	4	no	—
287	#416	—	47	4	no	—
288	C₂×#103	—	47	1	no	—
289	C₂×#103	—	47	1	no	—
290	C₂×#102	—	47	1	no	—
291	C₂×#102	—	47	1	no	—
292	#408	—	47	4	no	—
293	#408	—	94	2	no	—
294	C₂×C₂²⋊C₈	—	94	1	no	—
295	C₂×C₂²⋊C₈	—	94	1	no	—
296	#405	—	47	4	no	—
297	#405	—	94	2	no	—
298	C₂×#97	—	94	1	no	—
299	C₂×C₄×C₈	—	94	1	no	—
300	#339	—	47	4	no	—
301	#336	—	47	4	no	—
302	C₄₇	C₂×#1929	1	1	yes	characteristic, complemented, Sylow
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	2	2	no	—
306	C₂×#41	—	2	2	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	C₄×D₄₇	1	2	yes	—
310	C₂×#41	C₂²×D₄₇	1	2	yes	—
311	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
317	C₂×M₁₆	—	2	1	no	—
318	C₂×M₁₆	—	2	2	no	—
319	C₂×M₁₆	—	47	2	no	—
320	C₂×M₁₆	—	94	1	no	—
321	C₂×M₁₆	—	94	2	no	—
322	C₂×M₁₆	—	94	2	no	—
323	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
324	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
325	C₂²×C₈	—	2	1	no	—
326	C₂²×C₈	—	47	1	no	—
327	C₂²×C₈	—	47	1	no	—
328	C₂²×C₈	—	47	2	no	—
329	C₂²×C₈	—	47	2	no	—
330	C₂²×C₈	—	47	1	no	—
331	C₂²×C₈	—	47	1	no	—
332	C₂²×C₈	—	47	2	no	—
333	C₂²×C₈	—	47	2	no	—
334	C₂²×C₈	—	94	2	no	—
335	C₂²×C₈	—	94	2	no	—
336	C₂²×C₈	—	94	2	no	—
337	C₂²×C₈	—	94	2	no	—
338	C₂²×C₈	—	94	1	no	—
339	#117	—	47	2	no	—
340	#117	—	47	2	no	—
341	#117	—	94	1	no	—
342	#117	—	94	1	no	—
343	C₂×C₄⋊C₄	—	47	1	no	—
344	C₂×C₄⋊C₄	—	47	1	no	—
345	C₂×C₂²⋊C₄	—	94	1	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	94	1	no	—
350	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
351	#108	—	94	8	no	—
352	#104	—	2	8	no	—
353	#103	—	47	4	no	—
354	#103	—	47	4	no	—
355	#102	—	47	4	no	—
356	#102	—	47	4	no	—
357	C₂²⋊C₈	—	94	4	no	—
358	C₂²⋊C₈	—	94	4	no	—
359	#97	—	94	4	no	—
360	C₄×C₈	—	94	4	no	—
361	C₂⁴	—	2	1	no	—
362	C₂⁴	#10625352	1	1	yes	characteristic
363	#41	—	2	4	no	—
364	#41	—	2	4	no	—
365	#41	—	2	2	no	—
366	#41	—	2	2	no	—
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	#41	—	4	2	no	—
372	#41	—	4	2	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	94	1	no	—
395	C₂²×C₄	—	94	1	no	—
396	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
398	C₂²×C₄	#10625350	1	2	yes	—
399	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
400	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
401	C₂²×C₄	#10625352	1	2	yes	—
402	C₂²×C₄	#10625352	1	2	yes	—
403	C₂²×C₄	#10625352	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
405	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
406	M₁₆	—	2	4	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	94	2	no	—
409	M₁₆	—	94	2	no	—
410	M₁₆	—	188	2	no	—
411	M₁₆	C₂×C₂²⋊D₄₇	1	4	yes	—
412	C₂×C₈	—	2	4	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	47	2	no	—
415	C₂×C₈	—	47	2	no	—
416	C₂×C₈	—	47	2	no	—
417	C₂×C₈	—	47	2	no	—
418	C₂×C₈	—	94	2	no	—
419	C₂×C₈	—	94	2	no	—
420	C₂×C₈	—	94	4	no	—
421	C₂×C₈	—	94	2	no	—
422	C₂×C₈	—	94	2	no	—
423	C₂×C₈	—	94	4	no	—
424	C₂×C₈	—	94	2	no	—
425	C₂×C₈	—	94	2	no	—
426	C₂×C₈	—	94	2	no	—
427	C₂×C₈	—	94	2	no	—
428	C₂×C₈	—	94	2	no	—
429	C₂×C₈	—	188	2	no	—
430	C₄⋊C₄	—	47	2	no	—
431	C₄⋊C₄	—	47	2	no	—
432	C₄⋊C₄	—	94	1	no	—
433	C₄⋊C₄	—	94	1	no	—
434	C₂²⋊C₄	—	94	2	no	—
435	C₂²⋊C₄	—	94	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	4	2	no	—
439	C₄²	—	94	2	no	—
440	C₄²	—	94	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
448	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
449	C₂³	#13094011	1	2	yes	—
450	C₂³	#13094017	1	2	yes	—
451	C₂³	C₂×#10625352	1	1	yes	characteristic
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	4	4	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	94	2	no	—
471	C₂×C₄	—	94	2	no	—
472	C₂×C₄	—	188	2	no	—
473	C₂×C₄	—	188	2	no	—
474	C₂×C₄	#13093980	1	2	yes	—
475	C₂×C₄	#13093980	1	2	yes	—
476	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
477	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
478	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
479	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
480	C₂×C₄	#13093996	1	2	yes	—
481	C₂×C₄	#13093996	1	2	yes	—
482	C₂×C₄	#13094006	1	2	yes	—
483	C₂×C₄	#13094006	1	2	yes	—
484	C₂×C₄	#13094011	1	2	yes	—
485	C₂×C₄	#13094017	1	2	yes	—
486	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
487	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
488	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
489	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
490	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
491	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
492	C₈	—	2	4	no	—
493	C₈	—	94	2	no	—
494	C₈	—	94	2	no	—
495	C₈	—	94	2	no	—
496	C₈	—	94	2	no	—
497	C₈	—	188	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	8	4	no	—
508	C₂²	#15689017	1	2	yes	—
509	C₂²	#15689017	1	2	yes	—
510	C₂²	#15689237	1	2	yes	—
511	C₂²	#15689242	1	2	yes	—
512	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
513	C₂²	C₂×#13094011	1	1	yes	characteristic
514	C₂²	C₂×#13094017	1	1	yes	characteristic
515	C₄	—	4	4	no	—
516	C₄	—	4	2	no	—
517	C₄	—	188	2	no	—
518	C₄	—	188	2	no	—
519	C₄	#15689017	1	2	yes	—
520	C₄	#15689017	1	2	yes	—
521	C₄	C₂×#13093980	1	1	yes	characteristic
522	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
523	C₄	C₂×#13093996	1	1	yes	characteristic
524	C₄	C₂×#13094006	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	2	2	no	—
527	C₂	—	2	1	no	—
528	C₂	—	8	2	no	—
529	C₂	#20244039	1	4	yes	direct product factor
530	C₂	C₂×#15689017	1	1	yes	characteristic
531	C₂	C₂×#15689237	1	1	yes	characteristic
532	C₂	C₂×#15689242	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#104×C₄₇	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#104	D₄₇
hypocenter	C₄₇	C₂×#1929
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#104

Complements

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

N	H ≅ G/N	type
1. C₂²×#13093959	C₂	semidirect
4. C₂×#15689081	C₂	semidirect
5. #20244039	C₂	direct (N × H)
6. C₂×#15688883	C₂	semidirect
7. C₂×#15688878	C₂	semidirect
14. C₂×#13093959	C₂²	semidirect
15. #15689119	C₄	semidirect
17. C₂×#13093948	C₄	semidirect
18. C₂×#13093948	C₄	semidirect
19. C₂×#13093945	C₄	semidirect
20. C₂×#13093945	C₄	semidirect
26. #15689081	C₂²	semidirect
29. #15688883	C₂²	semidirect
30. #15688878	C₂²	semidirect
62. #13093948	C₂×C₄	semidirect
63. #13093948	C₂×C₄	semidirect
64. #13093945	C₂×C₄	semidirect
65. #13093945	C₂×C₄	semidirect
271. C₂×C₄₇	#1929	semidirect
302. C₄₇	C₂×#1929	semidirect
529. C₂	#20244039	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×#13093959	2
C₂×#15689119	2
C₂×#15689090	2
C₂×#15689081	2
#20244039	2
C₂×#15688883	2
C₂×#15688878	2
C₂²×#104×C₄₇	2
C₂×#1929	47

Subgroups — C2×#20244039 #26218780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244039 #26218780