Subgroups — C₂×#20252304 #27080598

Order 12032.

2642 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094046	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689889	C₂	1	2	yes	maximal, complemented
3	#20252304	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689244	C₂	1	4	yes	maximal, complemented
5	C₂×#15689239	C₂	1	4	yes	maximal, complemented
6	C₂×#15689139	C₂	1	2	yes	maximal, complemented
7	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#108×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625350	C₂²	1	2	yes	—
10	C₂×#13094046	C₄	1	2	yes	complemented
11	C₂×#13094046	C₄	1	2	yes	complemented
12	C₂×#13094046	C₄	1	8	yes	complemented
13	C₂×#13094046	C₂²	1	2	yes	—
14	C₂×#13094046	C₂²	1	2	yes	—
15	C₂×#13094046	C₂²	1	8	yes	—
16	C₂²×Dic₁₈₈	C₄	1	1	yes	characteristic, complemented
17	C₂²×#10625325	C₄	1	2	yes	complemented
18	C₂²×D₃₇₆	C₄	1	1	yes	characteristic, complemented
19	#15689889	—	2	8	no	—
20	#15689889	C₂²	1	16	yes	complemented
21	C₂×#13094032	C₂²	1	8	yes	complemented
22	C₂×#13094030	—	2	4	no	—
23	C₂²×#10625329	C₂²	1	1	yes	characteristic
24	C₂×M₁₆×D₄₇	—	2	4	no	—
25	C₂×#13093983	C₂²	1	1	yes	characteristic
26	#15689244	C₂²	1	32	yes	complemented
27	#15689239	C₂²	1	32	yes	complemented
28	#15689139	C₂²	1	16	yes	complemented
29	C₂×#13093950	C₂²	1	8	yes	complemented
30	#15689078	C₂²	1	8	yes	complemented
31	C₂×#13093934	C₂²	1	2	yes	complemented
32	C₂×C₈×Dic₄₇	C₂²	1	2	yes	complemented
33	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
34	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#108×C₄₇	C₂²	1	2	yes	complemented
36	C₂×#108×C₄₇	C₂²	1	2	yes	complemented
37	C₂×#108×C₄₇	C₂²	1	8	yes	complemented
38	C₂×#10625350	—	2	2	no	—
39	C₂×#10625350	—	2	4	no	—
40	C₂×#10625350	—	2	2	no	—
41	C₂×#10625350	—	2	4	no	—
42	C₂×#10625350	C₂×C₄	1	4	yes	—
43	C₂×#10625350	C₂×C₄	1	8	yes	—
44	C₂×#10625350	C₂³	1	4	yes	—
45	C₂×#10625350	C₂³	1	8	yes	—
46	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
47	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
48	C₂²×C₂²⋊D₄₇	—	2	2	no	—
49	C₂²×C₄×D₄₇	—	2	2	no	—
50	#13094046	C₂×C₄	1	8	yes	—
51	#13094046	C₂×C₄	1	8	yes	—
52	#13094046	C₂×C₄	1	16	yes	complemented
53	#13094046	C₂×C₄	1	16	yes	complemented
54	#13094046	C₂³	1	8	yes	—
55	#13094046	C₂³	1	8	yes	—
56	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
57	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
58	C₂×Dic₁₈₈	C₂×C₄	1	8	yes	complemented
59	C₂×#10625325	C₂×C₄	1	4	yes	—
60	C₂×#10625325	C₂×C₄	1	4	yes	—
61	C₂×#10625325	C₂×C₄	1	16	yes	complemented
62	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
63	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
64	C₂×D₃₇₆	C₂×C₄	1	8	yes	complemented
65	#13094032	—	2	16	no	—
66	#13094032	C₂³	1	32	yes	complemented
67	#13094030	—	2	32	no	—
68	C₂×#10625329	D₄	1	2	yes	—
69	C₂×#10625329	D₄	1	2	yes	—
70	C₂×#10625329	D₄	1	4	yes	—
71	C₂×#10625329	C₂³	1	4	yes	—
72	C₂×#10625324	—	2	8	no	—
73	M₁₆×D₄₇	—	2	32	no	—
74	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
75	C₂×C₈×D₄₇	—	2	8	no	—
76	#13093983	—	2	2	no	—
77	#13093983	C₂³	1	4	yes	—
78	C₂×C₄⋊Dic₄₇	—	2	1	no	—
79	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
80	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
81	#13093950	C₂³	1	32	yes	complemented
82	#13093934	C₂³	1	8	yes	complemented
83	C₈×Dic₄₇	C₂³	1	8	yes	complemented
84	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₄₇	—	2	2	no	—
86	C₂×M₁₆×C₄₇	—	2	4	no	—
87	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
88	C₂×M₁₆×C₄₇	C₂³	1	8	yes	—
89	C₂²×C₈×C₄₇	—	2	2	no	—
90	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
95	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
98	#108×C₄₇	C₂³	1	8	yes	complemented
99	#108×C₄₇	C₂³	1	8	yes	complemented
100	C₂⁴×C₄₇	#41	1	1	yes	characteristic
101	C₂³×D₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
112	C₂×C₂²⋊D₄₇	—	2	4	no	—
113	C₂×C₂²⋊D₄₇	—	2	8	no	—
114	C₂×C₂²⋊D₄₇	—	2	4	no	—
115	C₂×C₂²⋊D₄₇	—	2	8	no	—
116	C₂²×Dic₄₇	—	2	2	no	—
117	C₂²×Dic₄₇	—	2	2	no	—
118	#10625350	—	2	8	no	—
119	#10625350	—	2	8	no	—
120	#10625350	—	2	8	no	—
121	#10625350	—	2	8	no	—
122	#10625350	—	2	4	no	—
123	#10625350	—	2	4	no	—
124	#10625350	—	2	8	no	—
125	#10625350	C₂²×C₄	1	8	yes	—
126	#10625350	C₂²×C₄	1	16	yes	—
127	#10625350	C₂⁴	1	8	yes	—
128	C₂×D₁₈₈	—	2	2	no	—
129	C₂×D₁₈₈	—	2	4	no	—
130	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
131	C₂×D₁₈₈	C₂²×C₄	1	8	yes	—
132	C₂×C₄×D₄₇	—	2	4	no	—
133	C₂×C₄×D₄₇	—	2	8	no	—
134	C₂×C₄×D₄₇	—	2	4	no	—
135	C₂×C₄×D₄₇	—	2	8	no	—
136	C₂×Dic₉₄	—	2	2	no	—
137	C₂×Dic₉₄	—	2	4	no	—
138	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
139	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
140	M₁₆×C₄₇	—	2	8	no	—
141	M₁₆×C₄₇	—	2	4	no	—
142	M₁₆×C₄₇	C₂⁴	1	8	yes	—
143	C₂×C₈×C₄₇	—	2	4	no	—
144	C₂×C₈×C₄₇	—	2	8	no	—
145	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
148	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
151	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
154	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
155	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
156	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
157	C₂²⋊Dic₄₇	—	2	4	no	—
158	C₄⋊Dic₄₇	—	2	4	no	—
159	C₄×Dic₄₇	—	2	2	no	—
160	C₄×Dic₄₇	C₂⁴	1	4	yes	—
161	#10625329	C₂×D₄	1	8	yes	—
162	#10625329	C₂×D₄	1	8	yes	—
163	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
164	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
165	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
166	Dic₁₈₈	C₂²×C₄	1	8	yes	—
167	Dic₁₈₈	C₂²×C₄	1	8	yes	—
168	D₃₇₆	C₂²×C₄	1	8	yes	—
169	D₃₇₆	C₂²×C₄	1	8	yes	—
170	#10625325	C₂²×C₄	1	16	yes	—
171	#10625325	C₂²×C₄	1	16	yes	—
172	#10625324	—	2	32	no	—
173	C₈×D₄₇	—	2	32	no	—
174	C₂³×C₄₇	—	4	2	no	—
175	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
176	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
177	C₂³×C₄₇	C₄×D₄	1	2	yes	—
178	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
179	C₂³×C₄₇	C₂×#41	1	2	yes	—
180	C₂²×D₄₇	—	2	4	no	—
181	C₂²×D₄₇	—	2	8	no	—
182	C₂²×D₄₇	—	8	4	no	—
183	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
191	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
200	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
201	C₂²⋊D₄₇	—	2	16	no	—
202	C₂²⋊D₄₇	—	2	8	no	—
203	C₂²⋊D₄₇	—	2	8	no	—
204	C₂×Dic₄₇	—	2	8	no	—
205	C₂×Dic₄₇	—	2	4	no	—
206	C₂×Dic₄₇	—	2	4	no	—
207	C₂×Dic₄₇	—	4	4	no	—
208	D₁₈₈	—	2	4	no	—
209	D₁₈₈	—	2	8	no	—
210	D₁₈₈	C₂³×C₄	1	8	yes	—
211	C₄×D₄₇	—	2	8	no	—
212	C₄×D₄₇	—	2	16	no	—
213	C₄×D₄₇	—	2	8	no	—
214	Dic₉₄	—	2	4	no	—
215	Dic₉₄	—	2	8	no	—
216	Dic₉₄	C₂³×C₄	1	8	yes	—
217	C₈×C₄₇	—	2	8	no	—
218	C₈×C₄₇	C₂³×C₄	1	2	yes	—
219	C₈×C₄₇	C₂³×C₄	1	2	yes	—
220	C₈×C₄₇	C₂³×C₄	1	2	yes	—
221	C₈×C₄₇	C₂³×C₄	1	2	yes	—
222	C₄₇⋊C₈	C₂²×D₄	1	8	yes	—
223	C₂×#2957	—	47	1	no	maximal, Sylow
224	C₂²×C₄₇	—	2	2	no	—
225	C₂²×C₄₇	—	2	2	no	—
226	C₂²×C₄₇	—	2	2	no	—
227	C₂²×C₄₇	—	4	2	no	—
228	C₂²×C₄₇	—	4	2	no	—
229	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
230	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
231	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
232	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
233	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
234	C₂×D₄₇	—	2	8	no	—
235	C₂×D₄₇	—	4	8	no	—
236	C₂×D₄₇	—	8	8	no	—
237	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
238	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
239	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
240	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
242	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
243	Dic₄₇	—	2	8	no	—
244	Dic₄₇	—	4	4	no	—
245	C₂²×#135	—	47	1	no	—
246	C₂×#568	—	47	2	no	—
247	#2957	—	47	16	no	—
248	C₂×#444	—	47	4	no	—
249	C₂×#443	—	47	4	no	—
250	C₂²×#108	D₄₇	1	1	yes	characteristic, complemented
251	C₂×#421	—	47	2	no	—
252	C₂×#405	—	47	1	no	—
253	C₂×C₄₇	—	2	1	no	—
254	C₂×C₄₇	—	2	2	no	—
255	C₂×C₄₇	—	2	1	no	—
256	C₂×C₄₇	—	2	2	no	—
257	C₂×C₄₇	#2957	1	2	yes	complemented
258	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
259	D₄₇	—	4	8	no	—
260	C₂²×#41	—	47	2	no	—
261	C₂×#135	—	47	2	no	—
262	C₂×#135	—	47	2	no	—
263	C₂×#135	—	47	8	no	—
264	C₂×#135	—	47	2	no	—
265	C₂×#135	—	47	2	no	—
266	C₂×#135	—	47	8	no	—
267	C₂²×Q₁₆	—	47	1	no	—
268	C₂²×SD₁₆	—	47	2	no	—
269	C₂²×D₈	—	47	1	no	—
270	#568	—	47	16	no	—
271	#568	—	94	8	no	—
272	C₂×#131	—	47	8	no	—
273	C₂×#131	—	94	4	no	—
274	C₂²×M₁₆	—	47	1	no	—
275	C₂²×M₁₆	—	94	4	no	—
276	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
277	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
278	C₂×#117	—	47	1	no	—
279	#444	—	47	32	no	—
280	#443	—	47	32	no	—
281	C₂×#108	C₂×D₄₇	1	2	yes	complemented
282	C₂×#108	C₂×D₄₇	1	2	yes	complemented
283	C₂×#108	C₂×D₄₇	1	8	yes	complemented
284	#421	—	47	16	no	—
285	C₂×#104	—	47	8	no	—
286	#405	—	47	8	no	—
287	C₂×#97	—	47	2	no	—
288	C₂×C₄×C₈	—	47	2	no	—
289	C₄₇	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
290	C₂×#41	—	47	8	no	—
291	C₂×#41	—	47	4	no	—
292	C₂×#41	—	47	4	no	—
293	C₂×#41	—	47	8	no	—
294	C₂×#41	—	94	2	no	—
295	C₂×#41	—	94	4	no	—
296	C₂×#41	—	94	2	no	—
297	C₂×#41	—	94	4	no	—
298	C₂²×Q₈	—	47	2	no	—
299	C₂²×D₄	—	47	2	no	—
300	C₂²×D₄	—	94	2	no	—
301	C₂³×C₄	—	94	2	no	—
302	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
303	#135	—	47	8	no	—
304	#135	—	47	8	no	—
305	#135	—	47	16	no	—
306	#135	—	47	16	no	—
307	#135	—	47	8	no	—
308	#135	—	47	8	no	—
309	C₂×Q₁₆	—	47	2	no	—
310	C₂×Q₁₆	—	47	2	no	—
311	C₂×Q₁₆	—	47	8	no	—
312	C₂×SD₁₆	—	47	4	no	—
313	C₂×SD₁₆	—	47	4	no	—
314	C₂×SD₁₆	—	47	16	no	—
315	C₂×D₈	—	47	2	no	—
316	C₂×D₈	—	47	2	no	—
317	C₂×D₈	—	47	8	no	—
318	#131	—	47	32	no	—
319	#131	—	94	32	no	—
320	#131	—	94	16	no	—
321	C₂×M₁₆	—	2	2	no	—
322	C₂×M₁₆	—	2	4	no	—
323	C₂×M₁₆	—	47	2	no	—
324	C₂×M₁₆	—	47	2	no	—
325	C₂×M₁₆	—	47	4	no	—
326	C₂×M₁₆	—	47	4	no	—
327	C₂×M₁₆	—	94	8	no	—
328	C₂×M₁₆	—	94	32	no	—
329	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
330	C₂×M₁₆	C₂²×D₄₇	1	8	yes	—
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	—	47	2	no	—
333	C₂²×C₈	—	94	8	no	—
334	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
335	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
336	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
337	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
338	C₂²×C₈	C₄×D₄₇	1	4	yes	—
339	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
340	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
341	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
342	#117	—	47	4	no	—
343	#117	—	94	2	no	—
344	C₂×C₄⋊C₄	—	94	1	no	—
345	C₂×C₂²⋊C₄	—	94	1	no	—
346	C₂×C₄²	—	47	2	no	—
347	#108	C₂²×D₄₇	1	8	yes	complemented
348	#108	C₂²×D₄₇	1	8	yes	complemented
349	#104	—	47	32	no	—
350	#97	—	47	8	no	—
351	C₄×C₈	—	47	8	no	—
352	C₂⁴	—	94	2	no	—
353	C₂⁴	#10625354	1	1	yes	characteristic
354	#41	—	47	8	no	—
355	#41	—	47	16	no	—
356	#41	—	47	8	no	—
357	#41	—	94	8	no	—
358	#41	—	94	8	no	—
359	#41	—	94	8	no	—
360	#41	—	94	8	no	—
361	#41	—	94	4	no	—
362	#41	—	94	4	no	—
363	#41	—	94	8	no	—
364	C₂×Q₈	—	47	4	no	—
365	C₂×Q₈	—	47	8	no	—
366	C₂×Q₈	—	94	2	no	—
367	C₂×Q₈	—	94	4	no	—
368	C₂×D₄	—	47	8	no	—
369	C₂×D₄	—	47	4	no	—
370	C₂×D₄	—	94	8	no	—
371	C₂×D₄	—	94	4	no	—
372	C₂×D₄	—	94	8	no	—
373	C₂×D₄	—	94	4	no	—
374	C₂×D₄	—	94	4	no	—
375	C₂×D₄	—	94	2	no	—
376	C₂²×C₄	—	94	2	no	—
377	C₂²×C₄	—	94	8	no	—
378	C₂²×C₄	—	94	4	no	—
379	C₂²×C₄	—	94	8	no	—
380	C₂²×C₄	—	94	4	no	—
381	C₂²×C₄	—	94	2	no	—
382	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
385	C₂²×C₄	D₄×D₄₇	1	2	yes	—
386	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
387	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
388	C₂²×C₄	#10625354	1	1	yes	characteristic
389	C₂²×C₄	#10625354	1	2	yes	—
390	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
391	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
392	Q₁₆	—	47	8	no	—
393	Q₁₆	—	47	8	no	—
394	SD₁₆	—	47	16	no	—
395	SD₁₆	—	47	16	no	—
396	D₈	—	47	8	no	—
397	D₈	—	47	8	no	—
398	M₁₆	—	2	8	no	—
399	M₁₆	—	2	4	no	—
400	M₁₆	—	47	8	no	—
401	M₁₆	—	47	8	no	—
402	M₁₆	—	94	32	no	—
403	M₁₆	C₂³×D₄₇	1	8	yes	—
404	C₂×C₈	—	2	8	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	47	4	no	—
407	C₂×C₈	—	47	4	no	—
408	C₂×C₈	—	47	4	no	—
409	C₂×C₈	—	94	32	no	—
410	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
411	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
412	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
413	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
414	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
415	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
416	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
417	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
418	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
419	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
420	C₂×C₈	C₂³×D₄₇	1	2	yes	—
421	C₂×C₈	C₂³×D₄₇	1	2	yes	—
422	C₄⋊C₄	—	94	4	no	—
423	C₂²⋊C₄	—	94	4	no	—
424	C₄²	—	47	4	no	—
425	C₄²	—	94	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	94	8	no	—
428	C₂³	—	94	4	no	—
429	C₂³	—	376	4	no	—
430	C₂³	#13093986	1	1	yes	characteristic
431	C₂³	#13093986	1	1	yes	characteristic
432	C₂³	#13093986	1	2	yes	—
433	C₂³	C₂×#10625354	1	1	yes	characteristic
434	C₂³	C₂×#10625354	1	2	yes	—
435	Q₈	—	47	8	no	—
436	Q₈	—	94	8	no	—
437	Q₈	—	94	4	no	—
438	D₄	—	47	8	no	—
439	D₄	—	94	16	no	—
440	D₄	—	94	8	no	—
441	D₄	—	94	8	no	—
442	D₄	—	94	8	no	—
443	D₄	—	94	4	no	—
444	C₂×C₄	—	94	8	no	—
445	C₂×C₄	—	94	4	no	—
446	C₂×C₄	—	94	16	no	—
447	C₂×C₄	—	94	8	no	—
448	C₂×C₄	—	94	8	no	—
449	C₂×C₄	—	94	4	no	—
450	C₂×C₄	—	188	4	no	—
451	C₂×C₄	#13093986	1	1	yes	characteristic
452	C₂×C₄	#13093986	1	2	yes	—
453	C₂×C₄	#13093986	1	2	yes	—
454	C₂×C₄	#13093986	1	1	yes	characteristic
455	C₂×C₄	#13093986	1	2	yes	—
456	C₂×C₄	#13093986	1	2	yes	—
457	C₂×C₄	#13093986	1	2	yes	—
458	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
459	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
461	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
462	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
463	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
464	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
465	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
466	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
467	C₂×C₄	C₂×#10625354	1	2	yes	—
468	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
469	C₈	—	2	8	no	—
470	C₈	—	47	8	no	—
471	C₈	C₂²×C₄×D₄₇	1	2	yes	—
472	C₈	C₂²×C₄×D₄₇	1	2	yes	—
473	C₈	C₂²×C₄×D₄₇	1	2	yes	—
474	C₈	C₂²×C₄×D₄₇	1	2	yes	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	94	8	no	—
481	C₂²	—	376	8	no	—
482	C₂²	—	188	8	no	—
483	C₂²	C₂×#13093986	1	2	yes	—
484	C₂²	C₂×#13093986	1	2	yes	—
485	C₂²	C₂×#13093986	1	1	yes	characteristic
486	C₂²	C₂×#13093986	1	1	yes	characteristic
487	C₂²	C₂²×#10625354	1	1	yes	characteristic
488	C₄	—	94	8	no	—
489	C₄	—	188	4	no	—
490	C₄	C₂×#13093986	1	2	yes	—
491	C₄	C₂×#13093986	1	1	yes	characteristic
492	C₄	C₂×#13093986	1	2	yes	—
493	C₄	C₂×#13093986	1	1	yes	characteristic
494	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
495	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
496	C₂	—	2	1	no	—
497	C₂	—	2	2	no	—
498	C₂	—	2	1	no	—
499	C₂	—	2	2	no	—
500	C₂	—	188	8	no	—
501	C₂	#20252304	1	2	yes	direct product factor
502	C₂	C₂²×#13093986	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂²×#108×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂²×#13094046	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂²×#108	D₄₇
hypocenter	C₄₇	C₂×#2957
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
2. C₂×#15689889	C₂	semidirect
3. #20252304	C₂	direct (N × H)
4. C₂×#15689244	C₂	semidirect
5. C₂×#15689239	C₂	semidirect
6. C₂×#15689139	C₂	semidirect
7. C₂×#15689078	C₂	semidirect
8. C₂²×#108×C₄₇	C₂	semidirect
10. C₂×#13094046	C₄	semidirect
11. C₂×#13094046	C₄	semidirect
12. C₂×#13094046	C₄	semidirect
16. C₂²×Dic₁₈₈	C₄	semidirect
17. C₂²×#10625325	C₄	semidirect
18. C₂²×D₃₇₆	C₄	semidirect
20. #15689889	C₂²	semidirect
21. C₂×#13094032	C₂²	semidirect
26. #15689244	C₂²	semidirect
27. #15689239	C₂²	semidirect
28. #15689139	C₂²	semidirect
29. C₂×#13093950	C₂²	semidirect
30. #15689078	C₂²	semidirect
31. C₂×#13093934	C₂²	semidirect
32. C₂×C₈×Dic₄₇	C₂²	semidirect
35. C₂×#108×C₄₇	C₂²	semidirect
36. C₂×#108×C₄₇	C₂²	semidirect
37. C₂×#108×C₄₇	C₂²	semidirect
52. #13094046	C₂×C₄	semidirect
53. #13094046	C₂×C₄	semidirect
58. C₂×Dic₁₈₈	C₂×C₄	semidirect
61. C₂×#10625325	C₂×C₄	semidirect
64. C₂×D₃₇₆	C₂×C₄	semidirect
66. #13094032	C₂³	semidirect
81. #13093950	C₂³	semidirect
82. #13093934	C₂³	semidirect
83. C₈×Dic₄₇	C₂³	semidirect
98. #108×C₄₇	C₂³	semidirect
99. #108×C₄₇	C₂³	semidirect
250. C₂²×#108	D₄₇	semidirect
257. C₂×C₄₇	#2957	semidirect
281. C₂×#108	C₂×D₄₇	semidirect
282. C₂×#108	C₂×D₄₇	semidirect
283. C₂×#108	C₂×D₄₇	semidirect
289. C₄₇	C₂×#2957	semidirect
347. #108	C₂²×D₄₇	semidirect
348. #108	C₂²×D₄₇	semidirect
501. C₂	#20252304	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×#13094046	2
C₂×#15689889	2
#20252304	2
C₂×#15689244	2
C₂×#15689239	2
C₂×#15689139	2
C₂×#15689078	2
C₂²×#108×C₄₇	2
C₂×#2957	47

Subgroups — C2×#20252304 #27080598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252304 #27080598