Subgroups — C₂×#20241266 #26106261

Order 12032.

1454 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
3	#20241266	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×Dic₄₇	—	2	1	no	—
6	C₂³×C₄₇⋊C₈	—	2	1	no	—
7	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
8	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
9	C₂×C₂²⋊(C₄₇⋊C₈)	C₄	1	4	yes	complemented
10	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
11	C₂×C₄₇⋊#95	—	2	1	no	—
12	C₂×C₄₇⋊#95	—	2	2	no	—
13	C₂×C₄₇⋊#95	C₄	1	4	yes	complemented
14	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	complemented
17	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
18	C₄₇×#380	—	2	1	no	—
19	C₄₇×#380	—	2	1	no	—
20	C₄₇×#380	C₄	1	2	yes	complemented
21	C₄₇×#380	C₂²	1	2	yes	—
22	C₂×#95×C₄₇	—	2	1	no	—
23	C₂³×Dic₄₇	—	2	8	no	—
24	C₂³×Dic₄₇	—	2	4	no	—
25	C₂³×Dic₄₇	—	2	2	no	—
26	C₂³×Dic₄₇	—	4	4	no	—
27	C₂³×Dic₄₇	—	4	2	no	—
28	C₂³×Dic₄₇	—	4	2	no	—
29	C₂²×C₄₇⋊C₈	—	2	4	no	—
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇⋊C₈	—	4	4	no	—
32	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
33	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
34	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
35	C₄₇⋊#95	—	2	4	no	—
36	C₄₇⋊#95	—	2	2	no	—
37	C₄₇⋊#95	C₂×C₄	1	4	yes	complemented
38	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	—	2	2	no	—
40	C₂³×C₄×C₄₇	—	4	4	no	—
41	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	D₄	1	2	yes	—
48	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	Q₈	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
53	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	complemented
54	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
57	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
58	#95×C₄₇	—	2	2	no	—
59	#95×C₄₇	—	2	2	no	—
60	C₂⁴×C₄₇	—	2	4	no	—
61	C₂⁴×C₄₇	—	2	4	no	—
62	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
63	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
64	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
66	C₂⁴×C₄₇	D₈	1	2	yes	—
67	C₂⁴×C₄₇	SD₁₆	1	2	yes	—
68	C₂⁴×C₄₇	SD₁₆	1	2	yes	—
69	C₂⁴×C₄₇	Q₁₆	1	2	yes	—
70	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	—	2	4	no	—
72	C₂²×C₄×C₄₇	—	2	4	no	—
73	C₂²×C₄×C₄₇	—	2	4	no	—
74	C₂²×C₄×C₄₇	—	4	4	no	—
75	C₂²×C₄×C₄₇	—	4	4	no	—
76	C₂²×C₄×C₄₇	—	4	2	no	—
77	C₂²×C₄×C₄₇	—	4	4	no	—
78	C₂²×C₄×C₄₇	—	4	2	no	—
79	C₂²×C₄×C₄₇	—	4	2	no	—
80	C₂²×C₄×C₄₇	—	4	4	no	—
81	C₂²×C₄×C₄₇	—	4	2	no	—
82	C₂²×C₄×C₄₇	—	4	4	no	—
83	C₂²×C₄×C₄₇	—	4	4	no	—
84	C₂²×C₄×C₄₇	—	4	4	no	—
85	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
86	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
103	C₂²×Dic₄₇	—	2	16	no	—
104	C₂²×Dic₄₇	—	2	8	no	—
105	C₂²×Dic₄₇	—	2	4	no	—
106	C₂²×Dic₄₇	—	4	16	no	—
107	C₂²×Dic₄₇	—	4	16	no	—
108	C₂²×Dic₄₇	—	4	8	no	—
109	C₂²×Dic₄₇	—	4	4	no	—
110	C₂²×Dic₄₇	—	4	8	no	—
111	C₂²×Dic₄₇	—	4	2	no	—
112	C₂²×Dic₄₇	—	4	2	no	—
113	C₄⋊C₄×C₄₇	—	4	4	no	—
114	C₄⋊C₄×C₄₇	—	4	4	no	—
115	C₂²⋊C₄×C₄₇	—	4	4	no	—
116	C₂²⋊C₄×C₄₇	—	4	2	no	—
117	C₂²⋊C₄×C₄₇	—	4	2	no	—
118	C₂×C₄₇⋊C₈	—	2	4	no	—
119	C₂×C₄₇⋊C₈	—	4	8	no	—
120	C₂×C₄₇⋊C₈	—	4	4	no	—
121	C₂³×C₄₇	—	2	8	no	—
122	C₂³×C₄₇	—	2	8	no	—
123	C₂³×C₄₇	—	2	8	no	—
124	C₂³×C₄₇	—	2	8	no	—
125	C₂³×C₄₇	—	2	4	no	—
126	C₂³×C₄₇	—	2	4	no	—
127	C₂³×C₄₇	—	2	4	no	—
128	C₂³×C₄₇	—	2	4	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	#95	1	2	yes	—
134	C₂³×C₄₇	#95	1	2	yes	—
135	C₂³×C₄₇	#99	1	4	yes	—
136	C₂³×C₄₇	#102	1	4	yes	—
137	C₂³×C₄₇	#102	1	2	yes	—
138	C₂³×C₄₇	#102	1	2	yes	—
139	C₂³×C₄₇	#103	1	4	yes	—
140	C₂³×C₄₇	#103	1	2	yes	—
141	C₂³×C₄₇	#103	1	2	yes	—
142	C₂³×C₄₇	#104	1	4	yes	—
143	C₂³×C₄₇	#106	1	4	yes	—
144	C₂³×C₄₇	#107	1	4	yes	—
145	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
149	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
150	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
151	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	4	no	—
171	C₂×C₄×C₄₇	—	4	4	no	—
172	C₂×C₄×C₄₇	—	4	4	no	—
173	C₂×C₄×C₄₇	—	8	8	no	—
174	C₂×C₄×C₄₇	#95	1	2	yes	—
175	C₂×C₄×C₄₇	#95	1	2	yes	—
176	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₄₇	—	2	8	no	—
181	C₂×Dic₄₇	—	4	32	no	—
182	C₂×Dic₄₇	—	4	4	no	—
183	C₂×Dic₄₇	—	4	8	no	—
184	C₂×Dic₄₇	—	4	8	no	—
185	C₂×Dic₄₇	—	4	4	no	—
186	C₄₇⋊C₈	—	4	4	no	—
187	C₂×#1294	—	47	1	no	maximal, Sylow
188	C₂²×C₄₇	—	2	8	no	—
189	C₂²×C₄₇	—	2	8	no	—
190	C₂²×C₄₇	—	2	8	no	—
191	C₂²×C₄₇	—	2	8	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	—	2	4	no	—
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	2	no	—
202	C₂²×C₄₇	—	2	4	no	—
203	C₂²×C₄₇	—	2	2	no	—
204	C₂²×C₄₇	#327	1	8	yes	—
205	C₂²×C₄₇	#328	1	8	yes	—
206	C₂²×C₄₇	#339	1	4	yes	—
207	C₂²×C₄₇	#340	1	4	yes	—
208	C₂²×C₄₇	#340	1	4	yes	—
209	C₂²×C₄₇	#342	1	4	yes	—
210	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×#99	1	2	yes	—
212	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
214	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
215	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
216	C₂²×C₄₇	C₂×#104	1	2	yes	—
217	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#107	1	1	yes	characteristic
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	2	2	no	—
221	C₄×C₄₇	—	2	2	no	—
222	C₄×C₄₇	—	2	1	no	—
223	C₄×C₄₇	—	2	1	no	—
224	C₄×C₄₇	—	2	1	no	—
225	C₄×C₄₇	—	8	4	no	—
226	Dic₄₇	—	4	8	no	—
227	C₂²×C₂²⋊C₈	—	47	1	no	—
228	C₂×#380	D₄₇	1	1	yes	characteristic
229	C₂²×#95	—	47	1	no	—
230	#1294	—	47	4	no	—
231	C₂×C₄₇	—	2	1	no	—
232	C₂×C₄₇	—	2	4	no	—
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	—	2	1	no	—
235	C₂×C₄₇	—	2	1	no	—
236	C₂×C₄₇	#1294	1	8	yes	complemented
237	C₂×C₄₇	C₂×#327	1	2	yes	—
238	C₂×C₄₇	C₂×#328	1	2	yes	—
239	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
240	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
241	C₂×C₄₇	C₂×#342	1	1	yes	characteristic
242	C₂⁴×C₄	—	94	1	no	—
243	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
244	C₂³×C₈	—	94	1	no	—
245	C₂²×C₄⋊C₄	Dic₄₇	1	2	yes	complemented
246	C₂²×C₂²⋊C₄	—	2	1	no	—
247	C₂×C₂²⋊C₈	—	47	4	no	—
248	C₂×C₂²⋊C₈	—	47	2	no	—
249	C₂×C₂²⋊C₈	—	94	2	no	—
250	C₂×C₂²⋊C₈	—	94	1	no	—
251	#380	—	2	1	no	—
252	#380	—	2	1	no	—
253	#380	Dic₄₇	1	2	yes	complemented
254	#380	C₂×D₄₇	1	2	yes	—
255	C₂×#95	—	2	1	no	—
256	C₂×#95	—	47	4	no	—
257	C₂×#95	—	47	2	no	—
258	C₂×#95	—	94	2	no	—
259	C₂×#95	—	94	1	no	—
260	C₄₇	C₂×#1294	1	1	yes	characteristic, complemented, Sylow
261	C₂⁵	C₂²⋊D₄₇	1	1	yes	characteristic
262	C₂³×C₄	—	2	2	no	—
263	C₂³×C₄	—	4	4	no	—
264	C₂³×C₄	—	94	8	no	—
265	C₂³×C₄	—	94	4	no	—
266	C₂³×C₄	—	94	2	no	—
267	C₂³×C₄	—	188	4	no	—
268	C₂³×C₄	—	188	2	no	—
269	C₂³×C₄	—	188	2	no	—
270	C₂³×C₄	Dic₉₄	1	2	yes	—
271	C₂³×C₄	C₄×D₄₇	1	2	yes	—
272	C₂³×C₄	C₄×D₄₇	1	2	yes	—
273	C₂³×C₄	D₁₈₈	1	2	yes	—
274	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
275	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
276	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
277	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
278	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
279	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
280	C₂²×C₈	—	94	4	no	—
281	C₂²×C₈	—	94	2	no	—
282	C₂²×C₈	—	188	4	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	4	4	no	—
285	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	complemented
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	4	2	no	—
289	C₂×C₂²⋊C₄	—	4	2	no	—
290	C₂²⋊C₈	—	47	4	no	—
291	C₂²⋊C₈	—	94	4	no	—
292	C₂²⋊C₈	—	94	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	47	4	no	—
296	#95	—	94	4	no	—
297	#95	—	94	2	no	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	Dic₄₇⋊C₄	1	2	yes	—
301	C₂⁴	(C₂×D₄₇)⋊C₄	1	2	yes	—
302	C₂⁴	#10625334	1	2	yes	—
303	C₂⁴	#10625335	1	2	yes	—
304	C₂⁴	#10625336	1	2	yes	—
305	C₂⁴	#10625337	1	2	yes	—
306	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
307	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
308	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	—	4	4	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	4	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	94	8	no	—
324	C₂²×C₄	—	94	16	no	—
325	C₂²×C₄	—	94	4	no	—
326	C₂²×C₄	—	188	4	no	—
327	C₂²×C₄	—	188	16	no	—
328	C₂²×C₄	—	188	16	no	—
329	C₂²×C₄	—	188	8	no	—
330	C₂²×C₄	—	188	8	no	—
331	C₂²×C₄	—	188	2	no	—
332	C₂²×C₄	—	188	2	no	—
333	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
334	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
335	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
336	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
337	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
338	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
339	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
340	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
341	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
342	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
343	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
344	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
345	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
349	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
351	C₂×C₈	—	94	4	no	—
352	C₂×C₈	—	188	4	no	—
353	C₂×C₈	—	188	8	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	4	no	—
371	C₂³	C₄₇⋊#95	1	2	yes	—
372	C₂³	C₄₇⋊#95	1	2	yes	—
373	C₂³	#13093939	1	4	yes	—
374	C₂³	#13093944	1	4	yes	—
375	C₂³	#13093945	1	2	yes	—
376	C₂³	#13093945	1	2	yes	—
377	C₂³	#13093947	1	4	yes	—
378	C₂³	#13093948	1	2	yes	—
379	C₂³	#13093948	1	2	yes	—
380	C₂³	#13093951	1	4	yes	—
381	C₂³	#13093955	1	4	yes	—
382	C₂³	#13093957	1	4	yes	—
383	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
384	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
385	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
386	C₂³	C₂×#10625334	1	1	yes	characteristic
387	C₂³	C₂×#10625336	1	1	yes	characteristic
388	C₂³	C₂×#10625335	1	1	yes	characteristic
389	C₂³	C₂×#10625337	1	1	yes	characteristic
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	8	8	no	—
412	C₂×C₄	—	94	8	no	—
413	C₂×C₄	—	188	32	no	—
414	C₂×C₄	—	188	4	no	—
415	C₂×C₄	—	188	8	no	—
416	C₂×C₄	—	188	8	no	—
417	C₂×C₄	—	188	4	no	—
418	C₂×C₄	C₄₇⋊#95	1	2	yes	—
419	C₂×C₄	C₄₇⋊#95	1	2	yes	—
420	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
422	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
423	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
424	C₈	—	188	4	no	—
425	C₂²	—	2	8	no	—
426	C₂²	—	2	8	no	—
427	C₂²	—	2	8	no	—
428	C₂²	—	2	8	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	2	no	—
441	C₂²	#15688857	1	8	yes	—
442	C₂²	#15688860	1	8	yes	—
443	C₂²	#15688882	1	4	yes	—
444	C₂²	#15688885	1	4	yes	—
445	C₂²	#15688885	1	4	yes	—
446	C₂²	#15688890	1	4	yes	—
447	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
448	C₂²	C₂×#13093939	1	2	yes	—
449	C₂²	C₂×#13093944	1	1	yes	characteristic
450	C₂²	C₂×#13093945	1	1	yes	characteristic
451	C₂²	C₂×#13093947	1	1	yes	characteristic
452	C₂²	C₂×#13093948	1	1	yes	characteristic
453	C₂²	C₂×#13093951	1	2	yes	—
454	C₂²	C₂×#13093955	1	1	yes	characteristic
455	C₂²	C₂×#13093957	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	8	4	no	—
463	C₄	—	188	8	no	—
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	2	4	no	—
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	#20241266	1	8	yes	direct product factor
470	C₂	C₂×#15688857	1	2	yes	—
471	C₂	C₂×#15688860	1	2	yes	—
472	C₂	C₂×#15688882	1	1	yes	characteristic
473	C₂	C₂×#15688885	1	1	yes	characteristic
474	C₂	C₂×#15688890	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#380	C₂
socle	C₂⁴×C₄₇	C₂²⋊C₄
prime radical	C₂⁵×C₄₇	D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#380	D₄₇
hypocenter	C₄₇	C₂×#1294
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂×#380

Complements

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

N	H ≅ G/N	type
3. #20241266	C₂	direct (N × H)
9. C₂×C₂²⋊(C₄₇⋊C₈)	C₄	semidirect
13. C₂×C₄₇⋊#95	C₄	semidirect
16. C₂²×C₄⋊C₄×C₄₇	C₄	semidirect
20. C₄₇×#380	C₄	semidirect
34. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
37. C₄₇⋊#95	C₂×C₄	semidirect
53. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
236. C₂×C₄₇	#1294	semidirect
245. C₂²×C₄⋊C₄	Dic₄₇	semidirect
253. #380	Dic₄₇	semidirect
260. C₄₇	C₂×#1294	semidirect
285. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
469. C₂	#20241266	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×C₂²⋊(C₄₇⋊C₈)	2
C₂²×C₄₇⋊#95	2
#20241266	2
C₂×C₄₇×#380	2
C₂×#1294	47

Subgroups — C2×#20241266 #26106261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241266 #26106261