Subgroups — C₂×C₄×C₄⋊C₄×D₄₇ #26374454

Order 12032.

5758 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₄×D₄₇	C₂	1	2	yes	maximal
2	C₂²×C₄²×D₄₇	C₂	1	2	yes	maximal
3	C₂²×C₄²×D₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊C₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×Dic₄₇⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688974	C₂	1	2	yes	maximal, complemented
8	C₄×C₄⋊C₄×D₄₇	C₂	1	16	yes	maximal, direct product factor
9	C₂×#95×D₄₇	C₂	1	2	yes	maximal
10	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₄×D₄₇	C₂²	1	4	yes	—
12	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic
13	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic
14	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
16	C₂²×Dic₄₇⋊C₄	C₂²	1	4	yes	—
17	C₂×C₄⋊C₄×D₄₇	C₄	1	32	yes	direct product factor
18	C₂×C₄⋊C₄×D₄₇	C₂²	1	16	yes	—
19	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
20	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
21	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄²×D₄₇	—	2	16	no	—
25	C₂×C₄²×D₄₇	C₄	1	16	yes	complemented
26	C₂×C₄²×D₄₇	C₂²	1	16	yes	—
27	C₂×C₄²×D₄₇	C₂²	1	8	yes	—
28	C₄⋊C₄×Dic₄₇	C₂²	1	16	yes	complemented
29	C₄×Dic₄₇⋊C₄	C₂²	1	16	yes	complemented
30	C₄×C₄⋊Dic₄₇	C₂²	1	8	yes	complemented
31	#15688974	C₂²	1	16	yes	complemented
32	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
33	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
34	#95×D₄₇	C₂²	1	16	yes	—
35	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
36	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
37	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₄₇	C₂²	1	8	yes	complemented
39	C₂×#95×C₄₇	C₂²	1	2	yes	—
40	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
41	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
42	C₂³×Dic₄₇	C₂³	1	4	yes	—
43	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
44	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	—	2	16	no	—
46	C₂²×C₄×D₄₇	—	2	8	no	—
47	C₂²×C₄×D₄₇	—	2	16	no	—
48	C₂²×C₄×D₄₇	C₂×C₄	1	8	yes	—
49	C₂²×C₄×D₄₇	C₂×C₄	1	32	yes	—
50	C₂²×C₄×D₄₇	C₂×C₄	1	8	yes	—
51	C₂²×C₄×D₄₇	C₂×C₄	1	16	yes	—
52	C₂²×C₄×D₄₇	C₂×C₄	1	8	yes	—
53	C₂²×C₄×D₄₇	D₄	1	8	yes	—
54	C₂²×C₄×D₄₇	Q₈	1	8	yes	—
55	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
56	C₂²×C₄×D₄₇	C₂³	1	16	yes	—
57	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
58	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
59	C₂×C₄⋊Dic₄₇	C₂×C₄	1	16	yes	complemented
60	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
61	C₂×Dic₄₇⋊C₄	C₂×C₄	1	32	yes	complemented
62	C₂×Dic₄₇⋊C₄	C₂³	1	16	yes	—
63	C₄⋊C₄×D₄₇	C₂×C₄	1	128	yes	direct product factor
64	C₂×C₄×Dic₄₇	—	2	8	no	—
65	C₂×C₄×Dic₄₇	—	2	16	no	—
66	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	complemented
67	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	complemented
68	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	complemented
69	C₂×C₄×Dic₄₇	C₂³	1	16	yes	—
70	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
71	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
72	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
73	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
74	C₄²×D₄₇	—	2	64	no	—
75	C₄²×D₄₇	C₂×C₄	1	64	yes	complemented
76	C₄₇⋊#95	C₂³	1	8	yes	—
77	C₄₇⋊#95	C₂³	1	16	yes	—
78	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
80	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
84	C₂×C₄²×C₄₇	—	2	8	no	—
85	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
86	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
87	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
88	#95×C₄₇	C₂³	1	8	yes	—
89	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₂³×D₄₇	C₂²×C₄	1	4	yes	—
91	C₂³×D₄₇	C₂²×C₄	1	8	yes	—
92	C₂³×D₄₇	C₂×D₄	1	4	yes	—
93	C₂³×D₄₇	C₂×Q₈	1	4	yes	—
94	C₂³×D₄₇	#41	1	8	yes	—
95	C₂³×D₄₇	C₂⁴	1	2	yes	—
96	C₂²×C₄×C₄₇	—	2	8	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	8	no	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
107	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
110	C₂²×Dic₄₇	—	2	8	no	—
111	C₂²×Dic₄₇	—	2	4	no	—
112	C₂²×Dic₄₇	—	2	8	no	—
113	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
114	C₂²×Dic₄₇	C₂²×C₄	1	16	yes	—
115	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
116	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
117	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
118	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
119	C₂²×Dic₄₇	C₂×Q₈	1	4	yes	—
120	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
121	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
122	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
123	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
124	C₂×C₄×D₄₇	—	2	32	no	—
125	C₂×C₄×D₄₇	—	2	128	no	—
126	C₂×C₄×D₄₇	—	2	32	no	—
127	C₂×C₄×D₄₇	—	2	16	no	—
128	C₂×C₄×D₄₇	—	2	32	no	—
129	C₂×C₄×D₄₇	C₄²	1	64	yes	complemented
130	C₂×C₄×D₄₇	C₄⋊C₄	1	64	yes	direct product factor
131	C₂×C₄×D₄₇	C₂²×C₄	1	16	yes	—
132	C₂×C₄×D₄₇	C₂²×C₄	1	64	yes	—
133	C₂×C₄×D₄₇	C₂²×C₄	1	16	yes	—
134	C₂×C₄×D₄₇	C₂²×C₄	1	32	yes	—
135	C₂×C₄×D₄₇	C₂²×C₄	1	16	yes	—
136	C₂×C₄×D₄₇	C₂×D₄	1	16	yes	—
137	C₂×C₄×D₄₇	C₂×Q₈	1	16	yes	—
138	C₄⋊C₄×C₄₇	C₂²×C₄	1	32	yes	complemented
139	C₄²×C₄₇	—	2	16	no	—
140	C₄²×C₄₇	C₂²×C₄	1	16	yes	complemented
141	C₄⋊Dic₄₇	C₂²×C₄	1	32	yes	complemented
142	Dic₄₇⋊C₄	C₂²×C₄	1	64	yes	complemented
143	C₄×Dic₄₇	—	2	16	no	—
144	C₄×Dic₄₇	—	2	32	no	—
145	C₄×Dic₄₇	C₂²×C₄	1	16	yes	complemented
146	C₄×Dic₄₇	C₂²×C₄	1	16	yes	complemented
147	C₄×Dic₄₇	C₂²×C₄	1	16	yes	complemented
148	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
149	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
150	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
151	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
152	C₂³×C₄₇	C₂×#41	1	4	yes	—
153	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
154	C₂²×D₄₇	C₂×C₄²	1	16	yes	—
155	C₂²×D₄₇	C₂×C₄⋊C₄	1	16	yes	—
156	C₂²×D₄₇	#117	1	16	yes	—
157	C₂²×D₄₇	C₄×D₄	1	32	yes	—
158	C₂²×D₄₇	C₄×Q₈	1	32	yes	—
159	C₂²×D₄₇	C₂³×C₄	1	4	yes	—
160	C₂²×D₄₇	C₂³×C₄	1	8	yes	—
161	C₂²×D₄₇	C₂²×D₄	1	4	yes	—
162	C₂²×D₄₇	C₂²×Q₈	1	4	yes	—
163	C₂²×D₄₇	C₂×#41	1	8	yes	—
164	C₂×C₄×C₄₇	—	2	8	no	—
165	C₂×C₄×C₄₇	—	2	32	no	—
166	C₂×C₄×C₄₇	—	2	8	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	—	2	8	no	—
169	C₂×C₄×C₄₇	C₂×C₄²	1	16	yes	complemented
170	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	16	yes	complemented
171	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
172	C₂×C₄×C₄₇	C₂³×C₄	1	16	yes	—
173	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
174	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
175	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
177	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
178	C₂×Dic₄₇	—	2	8	no	—
179	C₂×Dic₄₇	—	2	32	no	—
180	C₂×Dic₄₇	—	2	8	no	—
181	C₂×Dic₄₇	—	2	4	no	—
182	C₂×Dic₄₇	—	2	8	no	—
183	C₂×Dic₄₇	C₂×C₄²	1	16	yes	complemented
184	C₂×Dic₄₇	C₂×C₄⋊C₄	1	16	yes	complemented
185	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
186	C₂×Dic₄₇	C₂³×C₄	1	16	yes	—
187	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
188	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
189	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
190	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
191	C₂×Dic₄₇	C₂²×Q₈	1	4	yes	—
192	C₄×D₄₇	—	2	32	no	—
193	C₄×D₄₇	—	2	128	no	—
194	C₄×D₄₇	C₂×C₄²	1	64	yes	complemented
195	C₄×D₄₇	C₂×C₄⋊C₄	1	64	yes	direct product factor
196	C₂²×C₄×C₄⋊C₄	—	47	1	no	maximal, Sylow
197	C₂²×C₄₇	C₂²×C₄²	1	4	yes	—
198	C₂²×C₄₇	C₂²×C₄⋊C₄	1	4	yes	—
199	C₂²×C₄₇	C₂×#117	1	4	yes	—
200	C₂²×C₄₇	C₂×C₄×D₄	1	8	yes	—
201	C₂²×C₄₇	C₂×C₄×Q₈	1	8	yes	—
202	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
203	C₂²×C₄₇	C₂⁴×C₄	1	2	yes	—
204	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
205	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
206	C₂²×C₄₇	C₂²×#41	1	2	yes	—
207	C₂×D₄₇	C₄×C₄⋊C₄	1	64	yes	direct product factor
208	C₂×D₄₇	C₂²×C₄²	1	8	yes	—
209	C₂×D₄₇	C₂²×C₄⋊C₄	1	8	yes	—
210	C₂×D₄₇	C₂×#117	1	8	yes	—
211	C₂×D₄₇	C₂×C₄×D₄	1	16	yes	—
212	C₂×D₄₇	C₂×C₄×Q₈	1	16	yes	—
213	C₄×C₄₇	—	2	4	no	—
214	C₄×C₄₇	—	2	16	no	—
215	C₄×C₄₇	C₂²×C₄²	1	8	yes	complemented
216	C₄×C₄₇	C₂²×C₄⋊C₄	1	8	yes	complemented
217	Dic₄₇	—	2	4	no	—
218	Dic₄₇	—	2	16	no	—
219	Dic₄₇	C₂²×C₄²	1	8	yes	complemented
220	Dic₄₇	C₂²×C₄⋊C₄	1	8	yes	complemented
221	C₂³×C₄⋊C₄	—	47	2	no	—
222	C₂³×C₄²	—	47	1	no	—
223	C₂³×C₄²	—	47	2	no	—
224	C₂×C₄×C₄⋊C₄	—	47	1	no	—
225	C₂×C₄×C₄⋊C₄	—	47	2	no	—
226	C₂×C₄×C₄⋊C₄	—	47	16	no	—
227	C₂×C₄×C₄⋊C₄	—	47	2	no	—
228	C₂×C₄×C₄⋊C₄	—	47	2	no	—
229	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic, direct product factor
230	C₂²×#95	—	47	2	no	—
231	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	8	yes	complemented
232	C₂×C₄₇	C₂³×C₄²	1	1	yes	characteristic
233	C₂×C₄₇	C₂³×C₄⋊C₄	1	1	yes	characteristic
234	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
235	C₂×C₄₇	C₂²×C₄×D₄	1	2	yes	—
236	C₂×C₄₇	C₂²×C₄×Q₈	1	2	yes	—
237	D₄₇	C₂×C₄×C₄⋊C₄	1	16	yes	direct product factor
238	C₂⁴×C₄	—	47	1	no	—
239	C₂⁴×C₄	—	47	1	no	—
240	C₂⁴×C₄	—	47	4	no	—
241	C₂⁴×C₄	—	47	1	no	—
242	C₂²×C₄⋊C₄	—	47	4	no	—
243	C₂²×C₄⋊C₄	—	47	2	no	—
244	C₂²×C₄⋊C₄	—	47	32	no	—
245	C₂²×C₄⋊C₄	—	47	16	no	—
246	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
247	C₂²×C₄²	—	47	1	no	—
248	C₂²×C₄²	—	47	1	no	—
249	C₂²×C₄²	—	47	1	no	—
250	C₂²×C₄²	—	47	16	no	—
251	C₂²×C₄²	—	47	8	no	—
252	C₂²×C₄²	—	47	4	no	—
253	C₂²×C₄²	—	47	2	no	—
254	C₂²×C₄²	—	47	16	no	—
255	C₂²×C₄²	—	94	16	no	—
256	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
257	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
258	C₄×C₄⋊C₄	—	47	16	no	—
259	C₄×C₄⋊C₄	—	47	8	no	—
260	C₄×C₄⋊C₄	—	47	16	no	—
261	C₄×C₄⋊C₄	—	47	16	no	—
262	C₄×C₄⋊C₄	C₂×D₄₇	1	8	yes	direct product factor
263	C₂×#95	—	47	2	no	—
264	C₂×#95	—	47	4	no	—
265	C₂×#95	—	47	16	no	—
266	C₂×#95	C₂×D₄₇	1	2	yes	—
267	C₄₇	C₂²×C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
268	C₂⁵	—	47	1	no	—
269	C₂³×C₄	—	47	1	no	—
270	C₂³×C₄	—	47	1	no	—
271	C₂³×C₄	—	47	16	no	—
272	C₂³×C₄	—	47	8	no	—
273	C₂³×C₄	—	47	8	no	—
274	C₂³×C₄	—	47	8	no	—
275	C₂³×C₄	—	47	8	no	—
276	C₂³×C₄	—	47	4	no	—
277	C₂³×C₄	—	47	4	no	—
278	C₂³×C₄	—	47	4	no	—
279	C₂³×C₄	—	47	1	no	—
280	C₂³×C₄	—	47	32	no	—
281	C₂³×C₄	—	47	8	no	—
282	C₂³×C₄	—	47	16	no	—
283	C₂³×C₄	—	47	4	no	—
284	C₂³×C₄	—	94	16	no	—
285	C₂³×C₄	—	94	8	no	—
286	C₂³×C₄	—	94	16	no	—
287	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
288	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
289	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
290	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	—	47	32	no	—
292	C₂×C₄⋊C₄	—	47	16	no	—
293	C₂×C₄⋊C₄	—	47	16	no	—
294	C₂×C₄⋊C₄	—	47	8	no	—
295	C₂×C₄⋊C₄	—	47	128	no	—
296	C₂×C₄⋊C₄	C₄×D₄₇	1	16	yes	direct product factor
297	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	—
298	C₂×C₄²	—	2	8	no	—
299	C₂×C₄²	—	47	8	no	—
300	C₂×C₄²	—	47	8	no	—
301	C₂×C₄²	—	47	8	no	—
302	C₂×C₄²	—	47	4	no	—
303	C₂×C₄²	—	47	4	no	—
304	C₂×C₄²	—	47	4	no	—
305	C₂×C₄²	—	47	64	no	—
306	C₂×C₄²	—	47	16	no	—
307	C₂×C₄²	—	47	8	no	—
308	C₂×C₄²	—	94	64	no	—
309	C₂×C₄²	—	94	16	no	—
310	C₂×C₄²	—	94	8	no	—
311	C₂×C₄²	C₄×D₄₇	1	8	yes	complemented
312	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
313	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
314	#95	—	47	16	no	—
315	#95	—	47	8	no	—
316	#95	C₂²×D₄₇	1	8	yes	—
317	C₂⁴	—	47	4	no	—
318	C₂⁴	—	47	8	no	—
319	C₂⁴	—	47	4	no	—
320	C₂⁴	—	47	4	no	—
321	C₂⁴	—	47	8	no	—
322	C₂⁴	—	47	2	no	—
323	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	47	4	no	—
328	C₂²×C₄	—	47	4	no	—
329	C₂²×C₄	—	47	8	no	—
330	C₂²×C₄	—	47	4	no	—
331	C₂²×C₄	—	47	4	no	—
332	C₂²×C₄	—	47	2	no	—
333	C₂²×C₄	—	47	2	no	—
334	C₂²×C₄	—	47	64	no	—
335	C₂²×C₄	—	47	64	no	—
336	C₂²×C₄	—	47	16	no	—
337	C₂²×C₄	—	47	16	no	—
338	C₂²×C₄	—	47	32	no	—
339	C₂²×C₄	—	47	16	no	—
340	C₂²×C₄	—	47	16	no	—
341	C₂²×C₄	—	47	4	no	—
342	C₂²×C₄	—	47	16	no	—
343	C₂²×C₄	—	47	2	no	—
344	C₂²×C₄	—	47	8	no	—
345	C₂²×C₄	—	47	16	no	—
346	C₂²×C₄	—	47	64	no	—
347	C₂²×C₄	—	94	32	no	—
348	C₂²×C₄	—	94	32	no	—
349	C₂²×C₄	—	94	128	no	—
350	C₂²×C₄	—	94	32	no	—
351	C₂²×C₄	—	94	16	no	—
352	C₂²×C₄	—	94	8	no	—
353	C₂²×C₄	—	94	4	no	—
354	C₂²×C₄	—	94	8	no	—
355	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
356	C₂²×C₄	C₂×C₄×D₄₇	1	16	yes	—
357	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
358	C₂²×C₄	C₂×C₄×D₄₇	1	8	yes	—
359	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
360	C₂²×C₄	D₄×D₄₇	1	4	yes	—
361	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
362	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
363	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
364	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
365	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
366	C₄⋊C₄	—	47	64	no	—
367	C₄⋊C₄	—	47	32	no	—
368	C₄⋊C₄	C₂×C₄×D₄₇	1	32	yes	direct product factor
369	C₄²	—	2	16	no	—
370	C₄²	—	47	16	no	—
371	C₄²	—	47	16	no	—
372	C₄²	—	47	16	no	—
373	C₄²	—	94	32	no	—
374	C₄²	—	94	16	no	—
375	C₄²	C₂×C₄×D₄₇	1	16	yes	complemented
376	C₂³	—	47	16	no	—
377	C₂³	—	47	16	no	—
378	C₂³	—	47	16	no	—
379	C₂³	—	47	32	no	—
380	C₂³	—	47	32	no	—
381	C₂³	—	47	4	no	—
382	C₂³	—	47	8	no	—
383	C₂³	—	47	4	no	—
384	C₂³	—	47	4	no	—
385	C₂³	—	47	8	no	—
386	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
387	C₂³	C₂²×C₄×D₄₇	1	4	yes	—
388	C₂³	C₂×D₄×D₄₇	1	2	yes	—
389	C₂³	C₂×Q₈×D₄₇	1	2	yes	—
390	C₂³	#41×D₄₇	1	4	yes	—
391	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	32	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	47	16	no	—
398	C₂×C₄	—	47	16	no	—
399	C₂×C₄	—	47	4	no	—
400	C₂×C₄	—	47	4	no	—
401	C₂×C₄	—	47	8	no	—
402	C₂×C₄	—	47	4	no	—
403	C₂×C₄	—	47	4	no	—
404	C₂×C₄	—	47	64	no	—
405	C₂×C₄	—	47	64	no	—
406	C₂×C₄	—	47	4	no	—
407	C₂×C₄	—	47	16	no	—
408	C₂×C₄	—	94	32	no	—
409	C₂×C₄	—	94	128	no	—
410	C₂×C₄	—	94	8	no	—
411	C₂×C₄	—	94	32	no	—
412	C₂×C₄	—	94	8	no	—
413	C₂×C₄	—	94	4	no	—
414	C₂×C₄	—	94	8	no	—
415	C₂×C₄	C₄²×D₄₇	1	16	yes	complemented
416	C₂×C₄	C₄⋊C₄×D₄₇	1	16	yes	direct product factor
417	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
418	C₂×C₄	C₂²×C₄×D₄₇	1	16	yes	—
419	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
420	C₂×C₄	C₂²×C₄×D₄₇	1	8	yes	—
421	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
422	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
423	C₂×C₄	C₂×Q₈×D₄₇	1	4	yes	—
424	C₂²	—	47	8	no	—
425	C₂²	—	47	8	no	—
426	C₂²	—	47	8	no	—
427	C₂²	—	47	16	no	—
428	C₂²	—	47	16	no	—
429	C₂²	—	47	64	no	—
430	C₂²	C₂×C₄²×D₄₇	1	4	yes	—
431	C₂²	C₂×C₄⋊C₄×D₄₇	1	4	yes	—
432	C₂²	#117×D₄₇	1	4	yes	—
433	C₂²	C₄×D₄×D₄₇	1	8	yes	—
434	C₂²	C₄×Q₈×D₄₇	1	8	yes	—
435	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
436	C₂²	C₂³×C₄×D₄₇	1	2	yes	—
437	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
438	C₂²	C₂²×Q₈×D₄₇	1	1	yes	characteristic
439	C₂²	C₂×#41×D₄₇	1	2	yes	—
440	C₄	—	2	4	no	—
441	C₄	—	2	16	no	—
442	C₄	—	47	8	no	—
443	C₄	—	47	8	no	—
444	C₄	—	94	4	no	—
445	C₄	—	94	16	no	—
446	C₄	C₂×C₄²×D₄₇	1	8	yes	complemented
447	C₄	C₂×C₄⋊C₄×D₄₇	1	8	yes	direct product factor
448	C₂	—	47	16	no	—
449	C₂	C₄×C₄⋊C₄×D₄₇	1	8	yes	direct product factor
450	C₂	C₂²×C₄²×D₄₇	1	1	yes	characteristic
451	C₂	C₂²×C₄⋊C₄×D₄₇	1	1	yes	characteristic
452	C₂	C₂×#117×D₄₇	1	1	yes	characteristic
453	C₂	C₂×C₄×D₄×D₄₇	1	2	yes	—
454	C₂	C₂×C₄×Q₈×D₄₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₂×C₄⋊C₄×Dic₄₇	C₂	semidirect
5. C₂×C₄×Dic₄₇⋊C₄	C₂	semidirect
6. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
7. C₂×#15688974	C₂	semidirect
8. C₄×C₄⋊C₄×D₄₇	C₂	direct (N × H)
10. C₂×C₄×C₄⋊C₄×C₄₇	C₂	semidirect
17. C₂×C₄⋊C₄×D₄₇	C₄	direct (N × H)
25. C₂×C₄²×D₄₇	C₄	semidirect
28. C₄⋊C₄×Dic₄₇	C₂²	semidirect
29. C₄×Dic₄₇⋊C₄	C₂²	semidirect
30. C₄×C₄⋊Dic₄₇	C₂²	semidirect
31. #15688974	C₂²	semidirect
38. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
59. C₂×C₄⋊Dic₄₇	C₂×C₄	semidirect
61. C₂×Dic₄₇⋊C₄	C₂×C₄	semidirect
63. C₄⋊C₄×D₄₇	C₂×C₄	direct (N × H)
66. C₂×C₄×Dic₄₇	C₂×C₄	semidirect
67. C₂×C₄×Dic₄₇	C₂×C₄	semidirect
68. C₂×C₄×Dic₄₇	C₂×C₄	semidirect
75. C₄²×D₄₇	C₂×C₄	semidirect
82. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
85. C₂×C₄²×C₄₇	C₂×C₄	semidirect
129. C₂×C₄×D₄₇	C₄²	semidirect
130. C₂×C₄×D₄₇	C₄⋊C₄	direct (N × H)
138. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
140. C₄²×C₄₇	C₂²×C₄	semidirect
141. C₄⋊Dic₄₇	C₂²×C₄	semidirect
142. Dic₄₇⋊C₄	C₂²×C₄	semidirect
145. C₄×Dic₄₇	C₂²×C₄	semidirect
146. C₄×Dic₄₇	C₂²×C₄	semidirect
147. C₄×Dic₄₇	C₂²×C₄	semidirect
169. C₂×C₄×C₄₇	C₂×C₄²	semidirect
170. C₂×C₄×C₄₇	C₂×C₄⋊C₄	semidirect
183. C₂×Dic₄₇	C₂×C₄²	semidirect
184. C₂×Dic₄₇	C₂×C₄⋊C₄	semidirect
194. C₄×D₄₇	C₂×C₄²	semidirect
195. C₄×D₄₇	C₂×C₄⋊C₄	direct (N × H)
207. C₂×D₄₇	C₄×C₄⋊C₄	direct (N × H)
215. C₄×C₄₇	C₂²×C₄²	semidirect
216. C₄×C₄₇	C₂²×C₄⋊C₄	semidirect
219. Dic₄₇	C₂²×C₄²	semidirect
220. Dic₄₇	C₂²×C₄⋊C₄	semidirect
229. C₂×C₄×C₄⋊C₄	D₄₇	direct (N × H)
231. C₂×C₄₇	C₂×C₄×C₄⋊C₄	semidirect
237. D₄₇	C₂×C₄×C₄⋊C₄	direct (N × H)
262. C₄×C₄⋊C₄	C₂×D₄₇	direct (N × H)
267. C₄₇	C₂²×C₄×C₄⋊C₄	semidirect
296. C₂×C₄⋊C₄	C₄×D₄₇	direct (N × H)
311. C₂×C₄²	C₄×D₄₇	semidirect
368. C₄⋊C₄	C₂×C₄×D₄₇	direct (N × H)
375. C₄²	C₂×C₄×D₄₇	semidirect
415. C₂×C₄	C₄²×D₄₇	semidirect
416. C₂×C₄	C₄⋊C₄×D₄₇	direct (N × H)
446. C₄	C₂×C₄²×D₄₇	semidirect
447. C₄	C₂×C₄⋊C₄×D₄₇	direct (N × H)
449. C₂	C₄×C₄⋊C₄×D₄₇	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×C₄⋊C₄×D₄₇	2
C₂²×C₄²×D₄₇	2
C₂×C₄⋊C₄×Dic₄₇	2
C₂×C₄×Dic₄₇⋊C₄	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×#15688974	2
C₄×C₄⋊C₄×D₄₇	2
C₂×#95×D₄₇	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₂²×C₄×C₄⋊C₄	47

Subgroups — C2×C4×C4⋊C4×D47 #26374454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₄⋊C₄×D₄₇ #26374454