Subgroups — C₂²×#15689016 #26374607

Order 12032.

5966 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15689016	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂⁴×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂⁴×Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂⁴×Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂⁴×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊Dic₄₇	—	2	8	no	—
14	C₂²×C₄⋊Dic₄₇	C₂²	1	12	yes	complemented
15	C₂²×C₂²⋊Dic₄₇	—	2	8	no	—
16	C₂²×C₂²⋊Dic₄₇	—	2	8	no	—
17	C₂²×C₂²⋊Dic₄₇	C₂²	1	12	yes	—
18	C₂²×C₂²⋊Dic₄₇	C₂²	1	12	yes	—
19	C₂²×C₄×Dic₄₇	—	2	8	no	—
20	C₂²×C₄×Dic₄₇	C₂²	1	12	yes	complemented
21	#15689016	C₂²	1	64	yes	direct product factor
22	C₂×C₄₇⋊#95	C₂²	1	12	yes	complemented
23	C₂×C₄₇⋊#95	C₂²	1	12	yes	complemented
24	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₄₇	C₄	1	16	yes	complemented
28	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	12	yes	—
29	C₂³×Dic₄₇	—	2	4	no	—
30	C₂³×Dic₄₇	—	2	4	no	—
31	C₂³×Dic₄₇	—	2	4	no	—
32	C₂³×Dic₄₇	—	2	4	no	—
33	C₂³×Dic₄₇	—	2	4	no	—
34	C₂³×Dic₄₇	—	2	4	no	—
35	C₂³×Dic₄₇	—	2	4	no	—
36	C₂³×Dic₄₇	—	2	4	no	—
37	C₂³×Dic₄₇	—	2	4	no	—
38	C₂³×Dic₄₇	—	2	4	no	—
39	C₂³×Dic₄₇	D₄	1	8	yes	—
40	C₂³×Dic₄₇	D₄	1	8	yes	—
41	C₂³×Dic₄₇	C₂³	1	6	yes	—
42	C₂³×Dic₄₇	C₂³	1	6	yes	—
43	C₂³×Dic₄₇	C₂³	1	6	yes	—
44	C₂³×Dic₄₇	C₂³	1	6	yes	—
45	C₂×C₄⋊Dic₄₇	—	2	48	no	—
46	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	complemented
47	C₂×C₂²⋊Dic₄₇	—	2	48	no	—
48	C₂×C₂²⋊Dic₄₇	—	2	48	no	—
49	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
50	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
51	C₂×C₄×Dic₄₇	—	2	48	no	—
52	C₂×C₄×Dic₄₇	C₂³	1	16	yes	complemented
53	C₄₇⋊#95	C₂³	1	16	yes	complemented
54	C₄₇⋊#95	C₂³	1	16	yes	complemented
55	C₂⁵×C₄₇	—	2	4	no	—
56	C₂⁵×C₄₇	—	2	4	no	—
57	C₂⁵×C₄₇	—	2	4	no	—
58	C₂⁵×C₄₇	—	2	4	no	—
59	C₂⁵×C₄₇	—	2	4	no	—
60	C₂⁵×C₄₇	—	2	4	no	—
61	C₂⁵×C₄₇	C₂×C₄	1	8	yes	—
62	C₂⁵×C₄₇	C₂³	1	6	yes	—
63	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	—	2	4	no	—
65	C₂³×C₄×C₄₇	—	2	4	no	—
66	C₂³×C₄×C₄₇	—	2	4	no	—
67	C₂³×C₄×C₄₇	—	2	4	no	—
68	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
69	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
70	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
71	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
72	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	96	yes	complemented
73	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
74	C₂⁴×C₄₇	—	2	32	no	—
75	C₂⁴×C₄₇	—	2	32	no	—
76	C₂⁴×C₄₇	—	2	32	no	—
77	C₂⁴×C₄₇	—	2	12	no	—
78	C₂⁴×C₄₇	—	2	12	no	—
79	C₂⁴×C₄₇	—	2	12	no	—
80	C₂⁴×C₄₇	—	2	12	no	—
81	C₂⁴×C₄₇	—	2	12	no	—
82	C₂⁴×C₄₇	—	2	12	no	—
83	C₂⁴×C₄₇	—	4	16	no	—
84	C₂⁴×C₄₇	—	4	16	no	—
85	C₂⁴×C₄₇	—	4	16	no	—
86	C₂⁴×C₄₇	—	4	16	no	—
87	C₂⁴×C₄₇	C₂²×C₄	1	24	yes	—
88	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
89	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
90	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
91	C₂⁴×C₄₇	#41	1	4	yes	—
92	C₂⁴×C₄₇	#41	1	4	yes	—
93	C₂⁴×C₄₇	#41	1	4	yes	—
94	C₂⁴×C₄₇	#41	1	4	yes	—
95	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
96	C₂⁴×C₄₇	C₂⁴	1	3	yes	—
97	C₂²×C₄×C₄₇	—	2	32	no	—
98	C₂²×C₄×C₄₇	—	2	32	no	—
99	C₂²×C₄×C₄₇	—	2	12	no	—
100	C₂²×C₄×C₄₇	—	2	12	no	—
101	C₂²×C₄×C₄₇	—	2	12	no	—
102	C₂²×C₄×C₄₇	—	2	12	no	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
105	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
107	C₂²×Dic₄₇	—	2	32	no	—
108	C₂²×Dic₄₇	—	2	32	no	—
109	C₂²×Dic₄₇	—	2	12	no	—
110	C₂²×Dic₄₇	—	2	12	no	—
111	C₂²×Dic₄₇	—	2	12	no	—
112	C₂²×Dic₄₇	—	2	12	no	—
113	C₂²×Dic₄₇	—	2	12	no	—
114	C₂²×Dic₄₇	—	2	12	no	—
115	C₂²×Dic₄₇	—	2	12	no	—
116	C₂²×Dic₄₇	—	2	12	no	—
117	C₂²×Dic₄₇	—	2	12	no	—
118	C₂²×Dic₄₇	—	2	12	no	—
119	C₂²×Dic₄₇	—	4	16	no	—
120	C₂²×Dic₄₇	—	4	16	no	—
121	C₂²×Dic₄₇	C₂×D₄	1	24	yes	—
122	C₂²×Dic₄₇	C₂×D₄	1	24	yes	—
123	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
124	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
125	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
126	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
127	C₂²⋊C₄×C₄₇	C₂²×C₄	1	64	yes	complemented
128	C₂²⋊Dic₄₇	—	2	32	no	—
129	C₂²⋊Dic₄₇	—	2	32	no	—
130	C₄⋊Dic₄₇	—	2	32	no	—
131	C₄×Dic₄₇	—	2	32	no	—
132	C₂³×C₄₇	—	2	48	no	—
133	C₂³×C₄₇	—	2	48	no	—
134	C₂³×C₄₇	—	2	48	no	—
135	C₂³×C₄₇	—	2	4	no	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	—	2	4	no	—
138	C₂³×C₄₇	—	2	4	no	—
139	C₂³×C₄₇	—	2	4	no	—
140	C₂³×C₄₇	—	2	4	no	—
141	C₂³×C₄₇	—	4	24	no	—
142	C₂³×C₄₇	—	4	24	no	—
143	C₂³×C₄₇	—	4	24	no	—
144	C₂³×C₄₇	—	4	24	no	—
145	C₂³×C₄₇	—	4	128	no	—
146	C₂³×C₄₇	#117	1	16	yes	—
147	C₂³×C₄₇	C₄×D₄	1	16	yes	—
148	C₂³×C₄₇	C₄×D₄	1	16	yes	—
149	C₂³×C₄₇	#121	1	16	yes	—
150	C₂³×C₄₇	#123	1	16	yes	—
151	C₂³×C₄₇	#124	1	16	yes	—
152	C₂³×C₄₇	#126	1	16	yes	—
153	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
154	C₂³×C₄₇	C₂³×C₄	1	6	yes	—
155	C₂³×C₄₇	C₂²×D₄	1	6	yes	—
156	C₂³×C₄₇	C₂²×D₄	1	6	yes	—
157	C₂³×C₄₇	C₂×#41	1	6	yes	—
158	C₂³×C₄₇	C₂×#41	1	6	yes	—
159	C₂³×C₄₇	C₂×#41	1	6	yes	—
160	C₂³×C₄₇	C₂×#41	1	6	yes	—
161	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
162	C₂×C₄×C₄₇	—	2	48	no	—
163	C₂×C₄×C₄₇	—	2	48	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
169	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
170	C₂×Dic₄₇	—	2	48	no	—
171	C₂×Dic₄₇	—	2	48	no	—
172	C₂×Dic₄₇	—	2	4	no	—
173	C₂×Dic₄₇	—	2	4	no	—
174	C₂×Dic₄₇	—	2	4	no	—
175	C₂×Dic₄₇	—	2	4	no	—
176	C₂×Dic₄₇	—	2	4	no	—
177	C₂×Dic₄₇	—	2	4	no	—
178	C₂×Dic₄₇	—	2	4	no	—
179	C₂×Dic₄₇	—	2	4	no	—
180	C₂×Dic₄₇	—	2	4	no	—
181	C₂×Dic₄₇	—	2	4	no	—
182	C₂×Dic₄₇	—	4	24	no	—
183	C₂×Dic₄₇	—	4	24	no	—
184	C₂×Dic₄₇	C₂²×D₄	1	8	yes	—
185	C₂×Dic₄₇	C₂²×D₄	1	8	yes	—
186	C₂²×#388	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	2	8	no	—
188	C₂²×C₄₇	—	2	8	no	—
189	C₂²×C₄₇	—	2	8	no	—
190	C₂²×C₄₇	—	4	4	no	—
191	C₂²×C₄₇	—	4	4	no	—
192	C₂²×C₄₇	—	4	4	no	—
193	C₂²×C₄₇	—	4	4	no	—
194	C₂²×C₄₇	—	4	96	no	—
195	C₂²×C₄₇	#388	1	64	yes	complemented
196	C₂²×C₄₇	C₂×#117	1	12	yes	—
197	C₂²×C₄₇	C₂×C₄×D₄	1	12	yes	—
198	C₂²×C₄₇	C₂×C₄×D₄	1	12	yes	—
199	C₂²×C₄₇	C₂×#121	1	12	yes	—
200	C₂²×C₄₇	C₂×#123	1	12	yes	—
201	C₂²×C₄₇	C₂×#124	1	12	yes	—
202	C₂²×C₄₇	C₂×#126	1	12	yes	—
203	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
204	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
205	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
206	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
207	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
208	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
209	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
210	C₄×C₄₇	—	2	8	no	—
211	C₄×C₄₇	—	2	8	no	—
212	Dic₄₇	—	2	8	no	—
213	Dic₄₇	—	2	8	no	—
214	Dic₄₇	—	4	4	no	—
215	Dic₄₇	—	4	4	no	—
216	C₂³×C₄⋊C₄	—	47	1	no	—
217	C₂³×C₂²⋊C₄	—	47	1	no	—
218	C₂³×C₂²⋊C₄	—	47	1	no	—
219	C₂³×C₂²⋊C₄	D₄₇	1	1	yes	characteristic
220	C₂³×C₄²	—	47	1	no	—
221	C₂×#388	—	47	24	no	—
222	C₂²×#95	—	47	1	no	—
223	C₂²×#95	—	47	1	no	—
224	C₂×C₄₇	—	4	8	no	—
225	C₂×C₄₇	C₂×#388	1	24	yes	complemented
226	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
227	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
228	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
229	C₂×C₄₇	C₂²×#121	1	1	yes	characteristic
230	C₂×C₄₇	C₂²×#123	1	1	yes	characteristic
231	C₂×C₄₇	C₂²×#124	1	1	yes	characteristic
232	C₂×C₄₇	C₂²×#126	1	1	yes	characteristic
233	C₂⁶	C₂×D₄₇	1	1	yes	characteristic
234	C₂⁴×C₄	—	47	1	no	—
235	C₂⁴×C₄	—	47	1	no	—
236	C₂⁴×C₄	—	47	1	no	—
237	C₂⁴×C₄	—	47	1	no	—
238	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
239	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	—	47	12	no	—
241	C₂²×C₄⋊C₄	—	94	8	no	—
242	C₂²×C₂²⋊C₄	—	47	12	no	—
243	C₂²×C₂²⋊C₄	—	47	12	no	—
244	C₂²×C₂²⋊C₄	—	94	8	no	—
245	C₂²×C₂²⋊C₄	—	94	8	no	—
246	C₂²×C₂²⋊C₄	Dic₄₇	1	16	yes	complemented
247	C₂²×C₂²⋊C₄	C₂×D₄₇	1	12	yes	—
248	C₂²×C₄²	—	47	12	no	—
249	C₂²×C₄²	—	94	8	no	—
250	#388	—	47	64	no	—
251	C₂×#95	—	47	12	no	—
252	C₂×#95	—	47	12	no	—
253	C₄₇	C₂²×#388	1	1	yes	characteristic, complemented, Sylow
254	C₂⁵	—	2	4	no	—
255	C₂⁵	—	2	4	no	—
256	C₂⁵	—	2	4	no	—
257	C₂⁵	—	2	4	no	—
258	C₂⁵	—	2	4	no	—
259	C₂⁵	—	2	4	no	—
260	C₂⁵	C₂×Dic₄₇	1	8	yes	—
261	C₂⁵	C₂²×D₄₇	1	6	yes	—
262	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
263	C₂³×C₄	—	2	4	no	—
264	C₂³×C₄	—	2	4	no	—
265	C₂³×C₄	—	2	4	no	—
266	C₂³×C₄	—	2	4	no	—
267	C₂³×C₄	—	47	8	no	—
268	C₂³×C₄	—	47	8	no	—
269	C₂³×C₄	—	47	6	no	—
270	C₂³×C₄	—	47	6	no	—
271	C₂³×C₄	—	47	6	no	—
272	C₂³×C₄	—	47	6	no	—
273	C₂³×C₄	—	94	4	no	—
274	C₂³×C₄	—	94	4	no	—
275	C₂³×C₄	—	94	4	no	—
276	C₂³×C₄	—	94	4	no	—
277	C₂³×C₄	—	94	4	no	—
278	C₂³×C₄	—	94	4	no	—
279	C₂³×C₄	—	94	4	no	—
280	C₂³×C₄	—	94	4	no	—
281	C₂³×C₄	—	94	4	no	—
282	C₂³×C₄	—	94	4	no	—
283	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
284	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
285	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
286	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
287	C₂×C₄⋊C₄	—	47	16	no	—
288	C₂×C₄⋊C₄	—	94	48	no	—
289	C₂×C₂²⋊C₄	—	47	16	no	—
290	C₂×C₂²⋊C₄	—	47	16	no	—
291	C₂×C₂²⋊C₄	—	94	48	no	—
292	C₂×C₂²⋊C₄	—	94	48	no	—
293	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	96	yes	complemented
294	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	—
295	C₂×C₄²	—	47	16	no	—
296	C₂×C₄²	—	94	48	no	—
297	#95	—	47	16	no	—
298	#95	—	47	16	no	—
299	C₂⁴	—	2	32	no	—
300	C₂⁴	—	2	32	no	—
301	C₂⁴	—	2	32	no	—
302	C₂⁴	—	2	12	no	—
303	C₂⁴	—	2	12	no	—
304	C₂⁴	—	2	12	no	—
305	C₂⁴	—	2	12	no	—
306	C₂⁴	—	2	12	no	—
307	C₂⁴	—	2	12	no	—
308	C₂⁴	—	4	16	no	—
309	C₂⁴	—	4	16	no	—
310	C₂⁴	—	4	16	no	—
311	C₂⁴	—	4	16	no	—
312	C₂⁴	#10625350	1	4	yes	—
313	C₂⁴	#10625350	1	4	yes	—
314	C₂⁴	D₄×D₄₇	1	4	yes	—
315	C₂⁴	D₄×D₄₇	1	4	yes	—
316	C₂⁴	#10625352	1	4	yes	—
317	C₂⁴	#10625352	1	4	yes	—
318	C₂⁴	C₂²×Dic₄₇	1	24	yes	—
319	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
320	C₂⁴	C₂³×D₄₇	1	4	yes	—
321	C₂⁴	C₂³×D₄₇	1	3	yes	—
322	C₂²×C₄	—	2	32	no	—
323	C₂²×C₄	—	2	32	no	—
324	C₂²×C₄	—	2	12	no	—
325	C₂²×C₄	—	2	12	no	—
326	C₂²×C₄	—	2	12	no	—
327	C₂²×C₄	—	2	12	no	—
328	C₂²×C₄	—	47	24	no	—
329	C₂²×C₄	—	47	24	no	—
330	C₂²×C₄	—	47	4	no	—
331	C₂²×C₄	—	47	4	no	—
332	C₂²×C₄	—	47	4	no	—
333	C₂²×C₄	—	47	4	no	—
334	C₂²×C₄	—	94	32	no	—
335	C₂²×C₄	—	94	32	no	—
336	C₂²×C₄	—	94	12	no	—
337	C₂²×C₄	—	94	12	no	—
338	C₂²×C₄	—	94	12	no	—
339	C₂²×C₄	—	94	12	no	—
340	C₂²×C₄	—	94	12	no	—
341	C₂²×C₄	—	94	12	no	—
342	C₂²×C₄	—	94	12	no	—
343	C₂²×C₄	—	94	12	no	—
344	C₂²×C₄	—	94	12	no	—
345	C₂²×C₄	—	94	12	no	—
346	C₂²×C₄	—	188	16	no	—
347	C₂²×C₄	—	188	16	no	—
348	C₂²×C₄	C₂²×Dic₄₇	1	24	yes	—
349	C₂²×C₄	C₂²×Dic₄₇	1	24	yes	—
350	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
351	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
352	C₄⋊C₄	—	94	32	no	—
353	C₂²⋊C₄	—	94	32	no	—
354	C₂²⋊C₄	—	94	32	no	—
355	C₂²⋊C₄	C₂²×Dic₄₇	1	64	yes	complemented
356	C₄²	—	94	32	no	—
357	C₂³	—	2	48	no	—
358	C₂³	—	2	48	no	—
359	C₂³	—	2	48	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	4	128	no	—
367	C₂³	—	4	24	no	—
368	C₂³	—	4	24	no	—
369	C₂³	—	4	24	no	—
370	C₂³	—	4	24	no	—
371	C₂³	#13093983	1	16	yes	—
372	C₂³	D₄×Dic₄₇	1	16	yes	—
373	C₂³	D₄×Dic₄₇	1	16	yes	—
374	C₂³	#13093997	1	16	yes	—
375	C₂³	#13094006	1	16	yes	—
376	C₂³	#13094010	1	16	yes	—
377	C₂³	#13094017	1	16	yes	—
378	C₂³	C₂³×Dic₄₇	1	8	yes	—
379	C₂³	C₂³×Dic₄₇	1	6	yes	—
380	C₂³	C₂×D₄×D₄₇	1	6	yes	—
381	C₂³	C₂×D₄×D₄₇	1	6	yes	—
382	C₂³	C₂×#10625352	1	6	yes	—
383	C₂³	C₂×#10625352	1	6	yes	—
384	C₂³	C₂×#10625350	1	6	yes	—
385	C₂³	C₂×#10625350	1	6	yes	—
386	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
387	C₂×C₄	—	2	48	no	—
388	C₂×C₄	—	2	48	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	47	8	no	—
394	C₂×C₄	—	47	8	no	—
395	C₂×C₄	—	94	48	no	—
396	C₂×C₄	—	94	48	no	—
397	C₂×C₄	—	94	4	no	—
398	C₂×C₄	—	94	4	no	—
399	C₂×C₄	—	94	4	no	—
400	C₂×C₄	—	94	4	no	—
401	C₂×C₄	—	94	4	no	—
402	C₂×C₄	—	94	4	no	—
403	C₂×C₄	—	94	4	no	—
404	C₂×C₄	—	94	4	no	—
405	C₂×C₄	—	94	4	no	—
406	C₂×C₄	—	94	4	no	—
407	C₂×C₄	—	188	24	no	—
408	C₂×C₄	—	188	24	no	—
409	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
410	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
411	C₂²	—	2	8	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	2	8	no	—
414	C₂²	—	4	96	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	#15689016	1	64	yes	direct product factor
420	C₂²	C₂×#13093983	1	12	yes	—
421	C₂²	C₂×D₄×Dic₄₇	1	12	yes	—
422	C₂²	C₂×D₄×Dic₄₇	1	12	yes	—
423	C₂²	C₂×#13093997	1	12	yes	—
424	C₂²	C₂×#13094006	1	12	yes	—
425	C₂²	C₂×#13094010	1	12	yes	—
426	C₂²	C₂×#13094017	1	12	yes	—
427	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
428	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
429	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
430	C₂²	C₂²×#10625352	1	1	yes	characteristic
431	C₂²	C₂²×#10625352	1	1	yes	characteristic
432	C₂²	C₂²×#10625350	1	1	yes	characteristic
433	C₂²	C₂²×#10625350	1	1	yes	characteristic
434	C₄	—	2	8	no	—
435	C₄	—	2	8	no	—
436	C₄	—	94	8	no	—
437	C₄	—	94	8	no	—
438	C₄	—	188	4	no	—
439	C₄	—	188	4	no	—
440	C₂	—	4	8	no	—
441	C₂	C₂×#15689016	1	24	yes	direct product factor
442	C₂	C₂²×#13093983	1	1	yes	characteristic
443	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
444	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
445	C₂	C₂²×#13093997	1	1	yes	characteristic
446	C₂	C₂²×#13094006	1	1	yes	characteristic
447	C₂	C₂²×#13094010	1	1	yes	characteristic
448	C₂	C₂²×#13094017	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂³×C₂²⋊C₄×C₄₇	C₂
socle	C₂⁵×C₄₇	C₂³
prime radical	C₂⁶×C₄₇	C₂²
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂³×C₂²⋊C₄	D₄₇
hypocenter	C₄₇	C₂²×#388
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁵ ◁ C₂³×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₄⋊Dic₄₇	C₂	semidirect
4. C₂³×C₄×Dic₄₇	C₂	semidirect
5. C₂×#15689016	C₂	direct (N × H)
6. C₂²×C₄₇⋊#95	C₂	semidirect
7. C₂²×C₄₇⋊#95	C₂	semidirect
14. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
20. C₂²×C₄×Dic₄₇	C₂²	semidirect
21. #15689016	C₂²	direct (N × H)
22. C₂×C₄₇⋊#95	C₂²	semidirect
23. C₂×C₄₇⋊#95	C₂²	semidirect
27. C₂²×C₂²⋊C₄×C₄₇	C₄	semidirect
46. C₂×C₄⋊Dic₄₇	C₂³	semidirect
52. C₂×C₄×Dic₄₇	C₂³	semidirect
53. C₄₇⋊#95	C₂³	semidirect
54. C₄₇⋊#95	C₂³	semidirect
72. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
127. C₂²⋊C₄×C₄₇	C₂²×C₄	semidirect
195. C₂²×C₄₇	#388	semidirect
225. C₂×C₄₇	C₂×#388	semidirect
246. C₂²×C₂²⋊C₄	Dic₄₇	semidirect
253. C₄₇	C₂²×#388	semidirect
293. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
355. C₂²⋊C₄	C₂²×Dic₄₇	semidirect
419. C₂²	#15689016	direct (N × H)
441. C₂	C₂×#15689016	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊Dic₄₇	2
C₂³×C₂²⋊Dic₄₇	2
C₂³×C₄×Dic₄₇	2
C₂×#15689016	2
C₂²×C₄₇⋊#95	2
C₂³×C₂²⋊C₄×C₄₇	2
C₂²×#388	47

Subgroups — C22×#15689016 #26374607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689016 #26374607