Subgroups — C₂×C₄×D₄×Dic₄₇ #26374470

Order 12032.

5694 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×Dic₄₇	C₂	1	2	yes	maximal
2	C₂³×C₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
3	C₄×D₄×Dic₄₇	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂²⋊C₄×Dic₄₇	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
8	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂⁴×Dic₄₇	C₂²	1	4	yes	—
11	C₂×D₄×Dic₄₇	C₄	1	32	yes	direct product factor
12	C₂×D₄×Dic₄₇	C₂²	1	16	yes	—
13	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
15	C₂²×C₄×Dic₄₇	—	2	16	no	—
16	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
17	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
18	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
20	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
21	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄×Dic₄₇	C₂²	1	16	yes	complemented
23	C₄⋊C₄×Dic₄₇	C₂²	1	16	yes	complemented
24	C₄×C₄⋊Dic₄₇	C₂²	1	8	yes	complemented
25	C₂²⋊C₄×Dic₄₇	C₂²	1	32	yes	complemented
26	C₄×C₂²⋊Dic₄₇	C₂²	1	16	yes	complemented
27	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
28	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
29	C₄²×Dic₄₇	C₂²	1	8	yes	complemented
30	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₄₇	C₄	1	16	yes	complemented
33	C₂×C₄×D₄×C₄₇	C₂²	1	8	yes	—
34	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
36	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
37	C₂³×Dic₄₇	—	2	16	no	—
38	C₂³×Dic₄₇	—	2	16	no	—
39	C₂³×Dic₄₇	C₂×C₄	1	32	yes	complemented
40	C₂³×Dic₄₇	C₂³	1	2	yes	—
41	C₂³×Dic₄₇	C₂³	1	4	yes	—
42	C₂³×Dic₄₇	C₂³	1	16	yes	—
43	C₂³×Dic₄₇	C₂³	1	2	yes	—
44	D₄×Dic₄₇	C₂×C₄	1	128	yes	direct product factor
45	C₂×C₄⋊Dic₄₇	C₂×C₄	1	16	yes	complemented
46	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
47	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	32	yes	complemented
48	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
49	C₂×C₄×Dic₄₇	—	2	8	no	—
50	C₂×C₄×Dic₄₇	—	2	4	no	—
51	C₂×C₄×Dic₄₇	—	2	16	no	—
52	C₂×C₄×Dic₄₇	—	2	8	no	—
53	C₂×C₄×Dic₄₇	—	2	64	no	—
54	C₂×C₄×Dic₄₇	C₂×C₄	1	16	yes	complemented
55	C₂×C₄×Dic₄₇	D₄	1	8	yes	direct product factor
56	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
57	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
58	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
59	C₂×C₄×Dic₄₇	C₂³	1	16	yes	—
60	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
61	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
62	C₄₇⋊#95	C₂³	1	16	yes	—
63	C₄₇⋊#95	C₂³	1	8	yes	—
64	C₂⁵×C₄₇	C₂³	1	2	yes	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	—
66	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
67	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
68	C₂³×C₄×C₄₇	—	2	8	no	—
69	C₂³×C₄×C₄₇	—	2	8	no	—
70	C₂³×C₄×C₄₇	C₂×C₄	1	16	yes	complemented
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
73	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
74	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₄₇	C₂×C₄	1	64	yes	complemented
77	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
80	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
81	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
82	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
83	C₂⁴×C₄₇	—	2	4	no	—
84	C₂⁴×C₄₇	—	2	4	no	—
85	C₂⁴×C₄₇	—	2	8	no	—
86	C₂⁴×C₄₇	C₂²×C₄	1	16	yes	—
87	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
88	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
89	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₂×D₄×C₄₇	C₄²	1	64	yes	complemented
91	C₂×D₄×C₄₇	C₂²×C₄	1	32	yes	—
92	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	64	no	—
97	C₂²×C₄×C₄₇	—	2	16	no	—
98	C₂²×C₄×C₄₇	—	2	16	no	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	32	yes	complemented
105	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₄₇	#41	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
111	C₂²×Dic₄₇	—	2	8	no	—
112	C₂²×Dic₄₇	—	2	4	no	—
113	C₂²×Dic₄₇	—	2	4	no	—
114	C₂²×Dic₄₇	—	2	8	no	—
115	C₂²×Dic₄₇	—	2	128	no	—
116	C₂²×Dic₄₇	—	2	32	no	—
117	C₂²×Dic₄₇	—	2	32	no	—
118	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
119	C₂²×Dic₄₇	C₂²×C₄	1	16	yes	—
120	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
121	C₂²×Dic₄₇	C₂²×C₄	1	64	yes	complemented
122	C₂²×Dic₄₇	C₂×D₄	1	8	yes	—
123	C₂²×Dic₄₇	#41	1	8	yes	—
124	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
125	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
126	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
127	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
128	C₂²⋊C₄×C₄₇	C₂²×C₄	1	32	yes	complemented
129	C₄²×C₄₇	C₂²×C₄	1	16	yes	complemented
130	C₂²⋊Dic₄₇	C₂²×C₄	1	64	yes	complemented
131	C₄⋊Dic₄₇	C₂²×C₄	1	32	yes	complemented
132	C₄×Dic₄₇	—	2	16	no	—
133	C₄×Dic₄₇	—	2	8	no	—
134	C₄×Dic₄₇	—	2	32	no	—
135	C₄×Dic₄₇	—	2	16	no	—
136	C₄×Dic₄₇	C₂²×C₄	1	32	yes	complemented
137	C₄×Dic₄₇	C₂×D₄	1	16	yes	direct product factor
138	C₂³×C₄₇	—	2	32	no	—
139	C₂³×C₄₇	—	2	16	no	—
140	C₂³×C₄₇	—	2	32	no	—
141	C₂³×C₄₇	—	2	16	no	—
142	C₂³×C₄₇	—	2	4	no	—
143	C₂³×C₄₇	—	2	8	no	—
144	C₂³×C₄₇	—	2	4	no	—
145	C₂³×C₄₇	C₂×C₄²	1	32	yes	complemented
146	C₂³×C₄₇	C₂³×C₄	1	16	yes	—
147	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
148	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
149	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
150	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
151	C₂³×C₄₇	C₂×#41	1	4	yes	—
152	C₂³×C₄₇	C₂×#41	1	2	yes	—
153	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
154	D₄×C₄₇	C₂×C₄²	1	64	yes	complemented
155	C₂×C₄×C₄₇	—	2	16	no	—
156	C₂×C₄×C₄₇	—	2	8	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	64	no	—
161	C₂×C₄×C₄₇	C₂×C₄²	1	16	yes	complemented
162	C₂×C₄×C₄₇	C₄×D₄	1	16	yes	complemented
163	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
164	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
165	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
166	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
167	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
168	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
169	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
170	C₂×Dic₄₇	—	2	32	no	—
171	C₂×Dic₄₇	—	2	16	no	—
172	C₂×Dic₄₇	—	2	8	no	—
173	C₂×Dic₄₇	—	2	4	no	—
174	C₂×Dic₄₇	—	2	4	no	—
175	C₂×Dic₄₇	—	2	8	no	—
176	C₂×Dic₄₇	—	2	128	no	—
177	C₂×Dic₄₇	C₄×D₄	1	32	yes	direct product factor
178	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
179	C₂×Dic₄₇	C₂³×C₄	1	16	yes	—
180	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
181	C₂×Dic₄₇	C₂²×D₄	1	8	yes	—
182	C₂×Dic₄₇	C₂×#41	1	8	yes	—
183	C₂×C₄²×D₄	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	2	16	no	—
185	C₂²×C₄₇	—	2	8	no	—
186	C₂²×C₄₇	—	2	16	no	—
187	C₂²×C₄₇	—	2	8	no	—
188	C₂²×C₄₇	—	2	64	no	—
189	C₂²×C₄₇	C₂²×C₄²	1	4	yes	—
190	C₂²×C₄₇	C₂²×C₄²	1	16	yes	complemented
191	C₂²×C₄₇	C₂×C₄×D₄	1	8	yes	—
192	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
193	C₂²×C₄₇	C₄×#41	1	8	yes	—
194	C₂²×C₄₇	C₄×#41	1	4	yes	—
195	C₂²×C₄₇	C₂⁴×C₄	1	2	yes	—
196	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
197	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
198	C₂²×C₄₇	C₂²×#41	1	2	yes	—
199	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
200	C₄×C₄₇	—	2	8	no	—
201	C₄×C₄₇	—	2	4	no	—
202	C₄×C₄₇	C₂²×C₄²	1	8	yes	complemented
203	C₄×C₄₇	C₂×C₄×D₄	1	8	yes	complemented
204	Dic₄₇	—	2	16	no	—
205	Dic₄₇	—	2	8	no	—
206	Dic₄₇	C₂×C₄×D₄	1	16	yes	direct product factor
207	C₂²×C₄×D₄	—	47	2	no	—
208	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
209	C₂³×C₄²	—	47	2	no	—
210	C₄²×D₄	—	47	16	no	—
211	C₂×C₄×C₄⋊C₄	—	47	1	no	—
212	C₂×C₄×C₄⋊C₄	—	47	2	no	—
213	C₂×C₄×C₂²⋊C₄	—	47	2	no	—
214	C₂×C₄×C₂²⋊C₄	—	47	4	no	—
215	C₂×C₄³	—	47	1	no	—
216	C₂×C₄₇	—	2	16	no	—
217	C₂×C₄₇	C₄²×D₄	1	8	yes	complemented
218	C₂×C₄₇	C₂³×C₄²	1	1	yes	characteristic
219	C₂×C₄₇	C₂²×C₄×D₄	1	2	yes	—
220	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
221	C₂×C₄₇	C₂×C₄×#41	1	2	yes	—
222	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
223	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
224	C₂⁴×C₄	—	47	4	no	—
225	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
226	C₂×C₄×D₄	—	47	32	no	—
227	C₂×C₄×D₄	—	47	16	no	—
228	C₂×C₄×D₄	Dic₄₇	1	16	yes	direct product factor
229	C₂×C₄×D₄	C₂×D₄₇	1	8	yes	—
230	C₂²×C₄⋊C₄	—	47	2	no	—
231	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
232	C₂²×C₂²⋊C₄	—	47	4	no	—
233	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
234	C₂²×C₄²	—	47	2	no	—
235	C₂²×C₄²	—	47	1	no	—
236	C₂²×C₄²	—	47	4	no	—
237	C₂²×C₄²	—	47	16	no	—
238	C₂²×C₄²	—	47	2	no	—
239	C₂²×C₄²	—	47	2	no	—
240	C₂²×C₄²	—	47	1	no	—
241	C₂²×C₄²	—	94	16	no	—
242	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
243	C₄×C₄⋊C₄	—	47	16	no	—
244	C₄×C₄⋊C₄	—	47	8	no	—
245	C₄×C₂²⋊C₄	—	47	16	no	—
246	C₄×C₂²⋊C₄	—	47	32	no	—
247	C₂×#95	—	47	4	no	—
248	C₂×#95	—	47	2	no	—
249	C₄³	—	47	8	no	—
250	C₄₇	C₂×C₄²×D₄	1	1	yes	characteristic, complemented, Sylow
251	C₂⁵	C₂²×D₄₇	1	2	yes	—
252	C₂²×D₄	C₄×D₄₇	1	16	yes	—
253	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
254	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
255	C₂³×C₄	—	2	8	no	—
256	C₂³×C₄	—	2	8	no	—
257	C₂³×C₄	—	47	2	no	—
258	C₂³×C₄	—	47	32	no	—
259	C₂³×C₄	—	47	2	no	—
260	C₂³×C₄	—	47	4	no	—
261	C₂³×C₄	—	47	16	no	—
262	C₂³×C₄	—	94	16	no	—
263	C₂³×C₄	—	94	16	no	—
264	C₂³×C₄	C₂×Dic₄₇	1	16	yes	complemented
265	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
266	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
267	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
268	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
269	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
270	C₄×D₄	—	47	128	no	—
271	C₄×D₄	C₂×Dic₄₇	1	64	yes	direct product factor
272	C₂×C₄⋊C₄	—	47	16	no	—
273	C₂×C₄⋊C₄	—	47	8	no	—
274	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
275	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
276	C₂×C₂²⋊C₄	—	47	32	no	—
277	C₂×C₂²⋊C₄	—	47	16	no	—
278	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
279	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
280	C₂×C₄²	—	47	16	no	—
281	C₂×C₄²	—	47	8	no	—
282	C₂×C₄²	—	47	8	no	—
283	C₂×C₄²	—	47	4	no	—
284	C₂×C₄²	—	47	8	no	—
285	C₂×C₄²	—	47	4	no	—
286	C₂×C₄²	—	47	16	no	—
287	C₂×C₄²	—	47	8	no	—
288	C₂×C₄²	—	94	64	no	—
289	C₂×C₄²	—	94	8	no	—
290	C₂×C₄²	—	94	16	no	—
291	C₂×C₄²	—	94	8	no	—
292	C₂×C₄²	—	94	4	no	—
293	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
294	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
295	#95	—	47	16	no	—
296	#95	—	47	8	no	—
297	C₂⁴	—	2	4	no	—
298	C₂⁴	—	2	8	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	C₂×C₄×D₄₇	1	16	yes	—
301	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
302	C₂⁴	C₂³×D₄₇	1	4	yes	—
303	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
304	C₂×D₄	C₄×Dic₄₇	1	64	yes	direct product factor
305	C₂×D₄	C₂×C₄×D₄₇	1	32	yes	—
306	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	64	no	—
311	C₂²×C₄	—	2	16	no	—
312	C₂²×C₄	—	2	16	no	—
313	C₂²×C₄	—	47	8	no	—
314	C₂²×C₄	—	47	8	no	—
315	C₂²×C₄	—	47	8	no	—
316	C₂²×C₄	—	47	4	no	—
317	C₂²×C₄	—	47	8	no	—
318	C₂²×C₄	—	47	16	no	—
319	C₂²×C₄	—	47	64	no	—
320	C₂²×C₄	—	47	4	no	—
321	C₂²×C₄	—	47	8	no	—
322	C₂²×C₄	—	94	32	no	—
323	C₂²×C₄	—	94	128	no	—
324	C₂²×C₄	—	94	32	no	—
325	C₂²×C₄	—	94	8	no	—
326	C₂²×C₄	—	94	4	no	—
327	C₂²×C₄	—	94	8	no	—
328	C₂²×C₄	—	94	4	no	—
329	C₂²×C₄	C₂×C₄×D₄₇	1	8	yes	—
330	C₂²×C₄	D₄×D₄₇	1	4	yes	—
331	C₂²×C₄	#10625352	1	4	yes	—
332	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
333	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
334	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
335	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
336	C₂²×C₄	C₂²×Dic₄₇	1	32	yes	complemented
337	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
338	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
339	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
340	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
341	C₄⋊C₄	—	47	32	no	—
342	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	complemented
343	C₂²⋊C₄	—	47	64	no	—
344	C₂²⋊C₄	C₂²×Dic₄₇	1	32	yes	complemented
345	C₄²	—	47	32	no	—
346	C₄²	—	47	16	no	—
347	C₄²	—	94	16	no	—
348	C₄²	—	94	32	no	—
349	C₄²	—	94	16	no	—
350	C₄²	—	94	8	no	—
351	C₄²	C₂²×Dic₄₇	1	16	yes	complemented
352	C₂³	—	2	32	no	—
353	C₂³	—	2	16	no	—
354	C₂³	—	2	32	no	—
355	C₂³	—	2	16	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	4	no	—
359	C₂³	C₂×C₄×Dic₄₇	1	32	yes	complemented
360	C₂³	C₂²×C₄×D₄₇	1	16	yes	—
361	C₂³	C₂²×C₄×D₄₇	1	4	yes	—
362	C₂³	C₂³×Dic₄₇	1	8	yes	—
363	C₂³	C₂³×Dic₄₇	1	2	yes	—
364	C₂³	C₂×D₄×D₄₇	1	2	yes	—
365	C₂³	#41×D₄₇	1	4	yes	—
366	C₂³	C₂×#10625352	1	2	yes	—
367	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
368	D₄	C₂×C₄×Dic₄₇	1	64	yes	direct product factor
369	C₂×C₄	—	2	16	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	64	no	—
375	C₂×C₄	—	47	32	no	—
376	C₂×C₄	—	47	8	no	—
377	C₂×C₄	—	47	8	no	—
378	C₂×C₄	—	47	8	no	—
379	C₂×C₄	—	47	8	no	—
380	C₂×C₄	—	47	16	no	—
381	C₂×C₄	—	94	128	no	—
382	C₂×C₄	—	94	32	no	—
383	C₂×C₄	—	94	16	no	—
384	C₂×C₄	—	94	8	no	—
385	C₂×C₄	—	94	4	no	—
386	C₂×C₄	—	94	8	no	—
387	C₂×C₄	—	94	4	no	—
388	C₂×C₄	C₂×C₄×Dic₄₇	1	16	yes	complemented
389	C₂×C₄	D₄×Dic₄₇	1	16	yes	direct product factor
390	C₂×C₄	C₂²×C₄×D₄₇	1	8	yes	—
391	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
392	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
393	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
394	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
395	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
396	C₂×C₄	C₂×#10625352	1	4	yes	—
397	C₂²	—	2	16	no	—
398	C₂²	—	2	8	no	—
399	C₂²	—	2	16	no	—
400	C₂²	—	2	8	no	—
401	C₂²	—	2	64	no	—
402	C₂²	C₂²×C₄×Dic₄₇	1	4	yes	—
403	C₂²	C₂²×C₄×Dic₄₇	1	16	yes	complemented
404	C₂²	C₄×D₄×D₄₇	1	8	yes	—
405	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
406	C₂²	C₄×#10625352	1	8	yes	—
407	C₂²	#41×Dic₄₇	1	4	yes	—
408	C₂²	C₂³×C₄×D₄₇	1	2	yes	—
409	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
410	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
411	C₂²	C₂×#41×D₄₇	1	2	yes	—
412	C₂²	C₂²×#10625352	1	1	yes	characteristic
413	C₄	—	2	8	no	—
414	C₄	—	2	4	no	—
415	C₄	—	47	16	no	—
416	C₄	—	94	16	no	—
417	C₄	—	94	8	no	—
418	C₄	C₂²×C₄×Dic₄₇	1	8	yes	complemented
419	C₄	C₂×D₄×Dic₄₇	1	8	yes	direct product factor
420	C₂	—	2	16	no	—
421	C₂	C₄×D₄×Dic₄₇	1	8	yes	direct product factor
422	C₂	C₂³×C₄×Dic₄₇	1	1	yes	characteristic
423	C₂	C₂×C₄×D₄×D₄₇	1	2	yes	—
424	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
425	C₂	C₂×C₄×#10625352	1	2	yes	—
426	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×Dic₄₇	C₂	semidirect
3. C₄×D₄×Dic₄₇	C₂	direct (N × H)
4. C₂×C₄⋊C₄×Dic₄₇	C₂	semidirect
5. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
6. C₂×C₂²⋊C₄×Dic₄₇	C₂	semidirect
7. C₂×C₄×C₂²⋊Dic₄₇	C₂	semidirect
8. C₂×C₄²×Dic₄₇	C₂	semidirect
11. C₂×D₄×Dic₄₇	C₄	direct (N × H)
22. C₂²×C₄×Dic₄₇	C₂²	semidirect
23. C₄⋊C₄×Dic₄₇	C₂²	semidirect
24. C₄×C₄⋊Dic₄₇	C₂²	semidirect
25. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
26. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
29. C₄²×Dic₄₇	C₂²	semidirect
32. C₂×C₄×D₄×C₄₇	C₄	semidirect
39. C₂³×Dic₄₇	C₂×C₄	semidirect
44. D₄×Dic₄₇	C₂×C₄	direct (N × H)
45. C₂×C₄⋊Dic₄₇	C₂×C₄	semidirect
47. C₂×C₂²⋊Dic₄₇	C₂×C₄	semidirect
54. C₂×C₄×Dic₄₇	C₂×C₄	semidirect
55. C₂×C₄×Dic₄₇	D₄	direct (N × H)
70. C₂³×C₄×C₄₇	C₂×C₄	semidirect
76. C₄×D₄×C₄₇	C₂×C₄	semidirect
77. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
79. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
81. C₂×C₄²×C₄₇	C₂×C₄	semidirect
90. C₂×D₄×C₄₇	C₄²	semidirect
104. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
121. C₂²×Dic₄₇	C₂²×C₄	semidirect
127. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
128. C₂²⋊C₄×C₄₇	C₂²×C₄	semidirect
129. C₄²×C₄₇	C₂²×C₄	semidirect
130. C₂²⋊Dic₄₇	C₂²×C₄	semidirect
131. C₄⋊Dic₄₇	C₂²×C₄	semidirect
136. C₄×Dic₄₇	C₂²×C₄	semidirect
137. C₄×Dic₄₇	C₂×D₄	direct (N × H)
145. C₂³×C₄₇	C₂×C₄²	semidirect
154. D₄×C₄₇	C₂×C₄²	semidirect
161. C₂×C₄×C₄₇	C₂×C₄²	semidirect
162. C₂×C₄×C₄₇	C₄×D₄	semidirect
177. C₂×Dic₄₇	C₄×D₄	direct (N × H)
190. C₂²×C₄₇	C₂²×C₄²	semidirect
202. C₄×C₄₇	C₂²×C₄²	semidirect
203. C₄×C₄₇	C₂×C₄×D₄	semidirect
206. Dic₄₇	C₂×C₄×D₄	direct (N × H)
217. C₂×C₄₇	C₄²×D₄	semidirect
228. C₂×C₄×D₄	Dic₄₇	direct (N × H)
250. C₄₇	C₂×C₄²×D₄	semidirect
264. C₂³×C₄	C₂×Dic₄₇	semidirect
271. C₄×D₄	C₂×Dic₄₇	direct (N × H)
274. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
278. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
293. C₂×C₄²	C₂×Dic₄₇	semidirect
304. C₂×D₄	C₄×Dic₄₇	direct (N × H)
336. C₂²×C₄	C₂²×Dic₄₇	semidirect
342. C₄⋊C₄	C₂²×Dic₄₇	semidirect
344. C₂²⋊C₄	C₂²×Dic₄₇	semidirect
351. C₄²	C₂²×Dic₄₇	semidirect
359. C₂³	C₂×C₄×Dic₄₇	semidirect
368. D₄	C₂×C₄×Dic₄₇	direct (N × H)
388. C₂×C₄	C₂×C₄×Dic₄₇	semidirect
389. C₂×C₄	D₄×Dic₄₇	direct (N × H)
403. C₂²	C₂²×C₄×Dic₄₇	semidirect
418. C₄	C₂²×C₄×Dic₄₇	semidirect
419. C₄	C₂×D₄×Dic₄₇	direct (N × H)
421. C₂	C₄×D₄×Dic₄₇	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×D₄×Dic₄₇	2
C₂³×C₄×Dic₄₇	2
C₄×D₄×Dic₄₇	2
C₂×C₄⋊C₄×Dic₄₇	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₂²⋊C₄×Dic₄₇	2
C₂×C₄×C₂²⋊Dic₄₇	2
C₂×C₄²×Dic₄₇	2
C₂²×C₄×D₄×C₄₇	2
C₂×C₄²×D₄	47

Subgroups — C2×C4×D4×Dic47 #26374470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₄×Dic₄₇ #26374470