Subgroups — C₂×D₄×C₄⋊Dic₄₇ #26375565

Order 12032.

4718 conjugacy classes of subgroups.

The subgroup lattice has 472 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	D₄×C₄⋊Dic₄₇	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689022	C₂	1	2	yes	maximal, complemented
5	C₂×#15688998	C₂	1	4	yes	maximal, complemented
6	C₂×#15688993	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688983	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₄⋊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	—	2	16	no	—
12	C₂×D₄×Dic₄₇	C₂²	1	16	yes	—
13	C₂²×C₄⋊Dic₄₇	—	2	16	no	—
14	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
16	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
17	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	—
18	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
19	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊Dic₄₇	C₂²	1	16	yes	complemented
21	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
22	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
23	#15689022	C₂²	1	16	yes	complemented
24	#15688998	C₂²	1	32	yes	complemented
25	#15688993	C₂²	1	8	yes	complemented
26	#15688983	C₂²	1	16	yes	complemented
27	C₄×C₄⋊Dic₄₇	C₂²	1	8	yes	complemented
28	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
29	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
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	—	4	8	no	—
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	—	2	64	no	—
45	C₂×C₄⋊Dic₄₇	—	2	8	no	—
46	C₂×C₄⋊Dic₄₇	—	2	8	no	—
47	C₂×C₄⋊Dic₄₇	—	2	4	no	—
48	C₂×C₄⋊Dic₄₇	—	2	16	no	—
49	C₂×C₄⋊Dic₄₇	—	2	64	no	—
50	C₂×C₄⋊Dic₄₇	—	4	4	no	—
51	C₂×C₄⋊Dic₄₇	D₄	1	8	yes	direct product factor
52	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
53	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
58	C₂×C₂²⋊Dic₄₇	—	2	16	no	—
59	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
60	C₂×C₄×Dic₄₇	—	2	8	no	—
61	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
62	C₄₇⋊#95	C₂³	1	8	yes	—
63	C₄₇⋊#95	C₂³	1	16	yes	—
64	C₂⁵×C₄₇	C₂³	1	2	yes	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
66	C₂²×D₄×C₄₇	D₄	1	8	yes	—
67	C₂²×D₄×C₄₇	Q₈	1	8	yes	—
68	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
69	C₂³×C₄×C₄₇	—	2	8	no	—
70	C₂³×C₄×C₄₇	—	2	8	no	—
71	C₂³×C₄×C₄₇	C₂×C₄	1	16	yes	complemented
72	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
74	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
75	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
77	C₄×D₄×C₄₇	C₂×C₄	1	64	yes	complemented
78	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
81	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
82	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
83	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
84	C₂⁴×C₄₇	—	2	4	no	—
85	C₂⁴×C₄₇	—	2	4	no	—
86	C₂⁴×C₄₇	—	2	4	no	—
87	C₂⁴×C₄₇	—	2	4	no	—
88	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
89	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
90	C₂⁴×C₄₇	C₂×Q₈	1	8	yes	—
91	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
92	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₂×D₄×C₄₇	C₄⋊C₄	1	64	yes	complemented
94	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
95	C₂×D₄×C₄₇	C₂×D₄	1	16	yes	—
96	C₂×D₄×C₄₇	C₂×Q₈	1	16	yes	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	64	no	—
102	C₂²×C₄×C₄₇	—	2	16	no	—
103	C₂²×C₄×C₄₇	—	2	16	no	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	32	yes	complemented
109	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
112	C₂²×C₄×C₄₇	#41	1	4	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
117	C₂²×Dic₄₇	—	2	4	no	—
118	C₂²×Dic₄₇	—	2	4	no	—
119	C₂²×Dic₄₇	—	2	4	no	—
120	C₂²×Dic₄₇	—	2	8	no	—
121	C₂²×Dic₄₇	—	2	8	no	—
122	C₂²×Dic₄₇	—	2	32	no	—
123	C₂²×Dic₄₇	—	2	4	no	—
124	C₂²×Dic₄₇	—	2	8	no	—
125	C₂²×Dic₄₇	—	2	4	no	—
126	C₂²×Dic₄₇	—	2	32	no	—
127	C₂²×Dic₄₇	—	4	16	no	—
128	C₂²×Dic₄₇	—	4	64	no	—
129	C₂²×Dic₄₇	C₂×D₄	1	8	yes	—
130	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
131	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
132	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
133	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
134	C₂²⋊C₄×C₄₇	C₂²×C₄	1	32	yes	complemented
135	C₄²×C₄₇	C₂²×C₄	1	16	yes	complemented
136	C₂²⋊Dic₄₇	—	2	32	no	—
137	C₄⋊Dic₄₇	—	2	16	no	—
138	C₄⋊Dic₄₇	—	2	16	no	—
139	C₄⋊Dic₄₇	—	2	8	no	—
140	C₄⋊Dic₄₇	—	2	32	no	—
141	C₄⋊Dic₄₇	—	4	8	no	—
142	C₄⋊Dic₄₇	C₂×D₄	1	16	yes	direct product factor
143	C₄×Dic₄₇	—	2	16	no	—
144	C₂³×C₄₇	—	2	16	no	—
145	C₂³×C₄₇	—	2	16	no	—
146	C₂³×C₄₇	—	2	16	no	—
147	C₂³×C₄₇	—	2	16	no	—
148	C₂³×C₄₇	—	2	16	no	—
149	C₂³×C₄₇	—	2	16	no	—
150	C₂³×C₄₇	—	2	4	no	—
151	C₂³×C₄₇	—	2	4	no	—
152	C₂³×C₄₇	—	2	4	no	—
153	C₂³×C₄₇	—	2	4	no	—
154	C₂³×C₄₇	C₂×C₄⋊C₄	1	32	yes	complemented
155	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
156	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
157	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
158	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
159	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
160	C₂³×C₄₇	C₂²×Q₈	1	8	yes	—
161	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
162	C₂³×C₄₇	C₂×#41	1	2	yes	—
163	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
164	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
165	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
166	D₄×C₄₇	C₂×C₄⋊C₄	1	64	yes	complemented
167	C₂×C₄×C₄₇	—	2	16	no	—
168	C₂×C₄×C₄₇	—	2	8	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	64	no	—
174	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	16	yes	complemented
175	C₂×C₄×C₄₇	C₄×D₄	1	16	yes	complemented
176	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
177	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
178	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
179	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
180	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
181	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
182	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
183	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
184	C₂×Dic₄₇	—	2	16	no	—
185	C₂×Dic₄₇	—	2	4	no	—
186	C₂×Dic₄₇	—	2	4	no	—
187	C₂×Dic₄₇	—	2	4	no	—
188	C₂×Dic₄₇	—	2	8	no	—
189	C₂×Dic₄₇	—	2	8	no	—
190	C₂×Dic₄₇	—	2	4	no	—
191	C₂×Dic₄₇	—	2	8	no	—
192	C₂×Dic₄₇	—	2	4	no	—
193	C₂×Dic₄₇	—	4	64	no	—
194	C₂×Dic₄₇	—	4	16	no	—
195	C₂×Dic₄₇	—	4	8	no	—
196	C₂×Dic₄₇	C₂²×D₄	1	8	yes	—
197	C₂×D₄×C₄⋊C₄	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	—	2	64	no	—
199	C₂²×C₄₇	—	2	8	no	—
200	C₂²×C₄₇	—	2	8	no	—
201	C₂²×C₄₇	—	2	8	no	—
202	C₂²×C₄₇	—	2	8	no	—
203	C₂²×C₄₇	—	2	8	no	—
204	C₂²×C₄₇	—	2	8	no	—
205	C₂²×C₄₇	C₂²×C₄⋊C₄	1	4	yes	—
206	C₂²×C₄₇	C₂²×C₄⋊C₄	1	16	yes	complemented
207	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
208	C₂²×C₄₇	#520	1	4	yes	—
209	C₂²×C₄₇	D₄²	1	4	yes	—
210	C₂²×C₄₇	#547	1	4	yes	—
211	C₂²×C₄₇	D₄×Q₈	1	4	yes	—
212	C₂²×C₄₇	#554	1	4	yes	—
213	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
214	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
215	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
216	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
217	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
220	C₄×C₄₇	—	2	8	no	—
221	C₄×C₄₇	—	2	4	no	—
222	C₄×C₄₇	C₂²×C₄⋊C₄	1	8	yes	complemented
223	C₄×C₄₇	C₂×C₄×D₄	1	8	yes	complemented
224	Dic₄₇	—	2	8	no	—
225	Dic₄₇	—	4	8	no	—
226	Dic₄₇	—	4	4	no	—
227	C₂²×C₄×D₄	—	47	2	no	—
228	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
229	C₂³×C₄⋊C₄	—	47	2	no	—
230	D₄×C₄⋊C₄	—	47	16	no	—
231	C₂×#389	—	47	2	no	—
232	C₂×#385	—	47	4	no	—
233	C₂×#384	—	47	1	no	—
234	C₂×#380	—	47	2	no	—
235	C₂×C₄×C₄⋊C₄	—	47	1	no	—
236	C₂×C₄₇	—	2	16	no	—
237	C₂×C₄₇	D₄×C₄⋊C₄	1	8	yes	complemented
238	C₂×C₄₇	C₂³×C₄⋊C₄	1	1	yes	characteristic
239	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
240	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
241	C₂×C₄₇	C₂×D₄²	1	1	yes	characteristic
242	C₂×C₄₇	C₂×#547	1	1	yes	characteristic
243	C₂×C₄₇	C₂×D₄×Q₈	1	1	yes	characteristic
244	C₂×C₄₇	C₂×#554	1	1	yes	characteristic
245	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
246	C₂⁴×C₄	—	47	4	no	—
247	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
248	C₂×C₄×D₄	—	47	16	no	—
249	C₂×C₄×D₄	—	94	16	no	—
250	C₂×C₄×D₄	Dic₄₇	1	16	yes	complemented
251	C₂×C₄×D₄	C₂×D₄₇	1	8	yes	—
252	C₂²×C₄⋊C₄	—	47	1	no	—
253	C₂²×C₄⋊C₄	—	47	16	no	—
254	C₂²×C₄⋊C₄	—	47	2	no	—
255	C₂²×C₄⋊C₄	—	47	4	no	—
256	C₂²×C₄⋊C₄	—	47	2	no	—
257	C₂²×C₄⋊C₄	—	47	1	no	—
258	C₂²×C₄⋊C₄	—	47	2	no	—
259	C₂²×C₄⋊C₄	—	94	16	no	—
260	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
261	C₂²×C₂²⋊C₄	—	47	4	no	—
262	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
263	C₂²×C₄²	—	47	2	no	—
264	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
265	#389	—	47	16	no	—
266	#385	—	47	32	no	—
267	#384	—	47	8	no	—
268	#380	—	47	16	no	—
269	C₄×C₄⋊C₄	—	47	8	no	—
270	C₂×#95	—	47	2	no	—
271	C₂×#95	—	47	4	no	—
272	C₄₇	C₂×D₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
273	C₂⁵	C₂²×D₄₇	1	2	yes	—
274	C₂²×D₄	Dic₉₄	1	8	yes	—
275	C₂²×D₄	D₁₈₈	1	8	yes	—
276	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
277	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
278	C₂³×C₄	—	2	8	no	—
279	C₂³×C₄	—	2	8	no	—
280	C₂³×C₄	—	47	2	no	—
281	C₂³×C₄	—	47	2	no	—
282	C₂³×C₄	—	47	4	no	—
283	C₂³×C₄	—	47	16	no	—
284	C₂³×C₄	—	94	16	no	—
285	C₂³×C₄	—	94	16	no	—
286	C₂³×C₄	—	188	8	no	—
287	C₂³×C₄	C₂×Dic₄₇	1	16	yes	complemented
288	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
289	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
290	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
291	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
292	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
293	C₄×D₄	—	94	64	no	—
294	C₄×D₄	C₂×Dic₄₇	1	64	yes	complemented
295	C₂×C₄⋊C₄	—	47	8	no	—
296	C₂×C₄⋊C₄	—	47	4	no	—
297	C₂×C₄⋊C₄	—	47	8	no	—
298	C₂×C₄⋊C₄	—	47	16	no	—
299	C₂×C₄⋊C₄	—	47	8	no	—
300	C₂×C₄⋊C₄	—	47	4	no	—
301	C₂×C₄⋊C₄	—	47	8	no	—
302	C₂×C₄⋊C₄	—	94	64	no	—
303	C₂×C₄⋊C₄	—	94	16	no	—
304	C₂×C₄⋊C₄	—	94	8	no	—
305	C₂×C₄⋊C₄	—	94	8	no	—
306	C₂×C₄⋊C₄	—	94	4	no	—
307	C₂×C₄⋊C₄	—	188	4	no	—
308	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
309	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
310	C₂×C₂²⋊C₄	—	47	16	no	—
311	C₂×C₂²⋊C₄	—	94	16	no	—
312	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
313	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
314	C₂×C₄²	—	47	8	no	—
315	C₂×C₄²	—	94	8	no	—
316	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
317	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
318	#95	—	47	8	no	—
319	#95	—	47	16	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	4	no	—
323	C₂⁴	—	2	4	no	—
324	C₂⁴	C₂×Dic₉₄	1	8	yes	—
325	C₂⁴	C₂×D₁₈₈	1	8	yes	—
326	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
327	C₂⁴	C₂³×D₄₇	1	4	yes	—
328	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
329	C₂×D₄	C₄⋊Dic₄₇	1	64	yes	direct product factor
330	C₂×D₄	C₂×Dic₉₄	1	16	yes	—
331	C₂×D₄	C₂×D₁₈₈	1	16	yes	—
332	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	64	no	—
338	C₂²×C₄	—	2	16	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	47	8	no	—
341	C₂²×C₄	—	47	4	no	—
342	C₂²×C₄	—	47	4	no	—
343	C₂²×C₄	—	47	8	no	—
344	C₂²×C₄	—	94	32	no	—
345	C₂²×C₄	—	94	4	no	—
346	C₂²×C₄	—	94	4	no	—
347	C₂²×C₄	—	94	8	no	—
348	C₂²×C₄	—	94	4	no	—
349	C₂²×C₄	—	94	8	no	—
350	C₂²×C₄	—	94	32	no	—
351	C₂²×C₄	—	94	4	no	—
352	C₂²×C₄	—	94	8	no	—
353	C₂²×C₄	—	94	4	no	—
354	C₂²×C₄	—	188	16	no	—
355	C₂²×C₄	—	188	64	no	—
356	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
357	C₂²×C₄	C₂×D₁₈₈	1	4	yes	—
358	C₂²×C₄	D₄×D₄₇	1	4	yes	—
359	C₂²×C₄	#10625352	1	4	yes	—
360	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
361	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
362	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
363	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
364	C₂²×C₄	C₂²×Dic₄₇	1	32	yes	complemented
365	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
366	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
367	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
368	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
369	C₄⋊C₄	—	47	16	no	—
370	C₄⋊C₄	—	94	32	no	—
371	C₄⋊C₄	—	94	16	no	—
372	C₄⋊C₄	—	94	16	no	—
373	C₄⋊C₄	—	94	8	no	—
374	C₄⋊C₄	—	188	8	no	—
375	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	complemented
376	C₂²⋊C₄	—	94	32	no	—
377	C₂²⋊C₄	C₂²×Dic₄₇	1	32	yes	complemented
378	C₄²	—	94	16	no	—
379	C₄²	C₂²×Dic₄₇	1	16	yes	complemented
380	C₂³	—	2	16	no	—
381	C₂³	—	2	16	no	—
382	C₂³	—	2	16	no	—
383	C₂³	—	2	16	no	—
384	C₂³	—	2	16	no	—
385	C₂³	—	2	16	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	C₂×C₄⋊Dic₄₇	1	32	yes	complemented
391	C₂³	C₂³×Dic₄₇	1	8	yes	—
392	C₂³	C₂³×Dic₄₇	1	2	yes	—
393	C₂³	C₂×D₄×D₄₇	1	2	yes	—
394	C₂³	C₂²×D₁₈₈	1	8	yes	—
395	C₂³	C₂²×D₁₈₈	1	2	yes	—
396	C₂³	C₂²×Dic₉₄	1	8	yes	—
397	C₂³	C₂²×Dic₉₄	1	2	yes	—
398	C₂³	C₂×#10625352	1	2	yes	—
399	C₂³	#13094070	1	2	yes	—
400	C₂³	#13094071	1	2	yes	—
401	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
402	D₄	C₂×C₄⋊Dic₄₇	1	64	yes	direct product factor
403	C₂×C₄	—	2	16	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	64	no	—
410	C₂×C₄	—	47	8	no	—
411	C₂×C₄	—	94	16	no	—
412	C₂×C₄	—	94	4	no	—
413	C₂×C₄	—	94	4	no	—
414	C₂×C₄	—	94	8	no	—
415	C₂×C₄	—	94	4	no	—
416	C₂×C₄	—	94	8	no	—
417	C₂×C₄	—	94	4	no	—
418	C₂×C₄	—	94	8	no	—
419	C₂×C₄	—	94	4	no	—
420	C₂×C₄	—	188	64	no	—
421	C₂×C₄	—	188	16	no	—
422	C₂×C₄	—	188	8	no	—
423	C₂×C₄	C₂×C₄⋊Dic₄₇	1	16	yes	complemented
424	C₂×C₄	D₄×Dic₄₇	1	16	yes	complemented
425	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
426	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
427	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
428	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
429	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
430	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
431	C₂×C₄	C₂²×Dic₉₄	1	4	yes	—
432	C₂×C₄	C₂×#10625352	1	4	yes	—
433	C₂²	—	2	64	no	—
434	C₂²	—	2	8	no	—
435	C₂²	—	2	8	no	—
436	C₂²	—	2	8	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	8	no	—
440	C₂²	C₂²×C₄⋊Dic₄₇	1	4	yes	—
441	C₂²	C₂²×C₄⋊Dic₄₇	1	16	yes	complemented
442	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
443	C₂²	#15689606	1	4	yes	—
444	C₂²	D₄×D₁₈₈	1	4	yes	—
445	C₂²	#15689777	1	4	yes	—
446	C₂²	D₄×Dic₉₄	1	4	yes	—
447	C₂²	#15689830	1	4	yes	—
448	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
449	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
450	C₂²	C₂³×D₁₈₈	1	1	yes	characteristic
451	C₂²	C₂³×Dic₉₄	1	1	yes	characteristic
452	C₂²	C₂²×#10625352	1	1	yes	characteristic
453	C₂²	C₂×#13094070	1	1	yes	characteristic
454	C₂²	C₂×#13094071	1	1	yes	characteristic
455	C₄	—	2	8	no	—
456	C₄	—	2	4	no	—
457	C₄	—	94	8	no	—
458	C₄	—	188	8	no	—
459	C₄	—	188	4	no	—
460	C₄	C₂²×C₄⋊Dic₄₇	1	8	yes	complemented
461	C₄	C₂×D₄×Dic₄₇	1	8	yes	complemented
462	C₂	—	2	16	no	—
463	C₂	D₄×C₄⋊Dic₄₇	1	8	yes	direct product factor
464	C₂	C₂³×C₄⋊Dic₄₇	1	1	yes	characteristic
465	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
466	C₂	C₂×#15689606	1	1	yes	characteristic
467	C₂	C₂×D₄×D₁₈₈	1	1	yes	characteristic
468	C₂	C₂×#15689777	1	1	yes	characteristic
469	C₂	C₂×D₄×Dic₉₄	1	1	yes	characteristic
470	C₂	C₂×#15689830	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
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×D₄×C₄⋊C₄
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ 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. D₄×C₄⋊Dic₄₇	C₂	direct (N × H)
4. C₂×#15689022	C₂	semidirect
5. C₂×#15688998	C₂	semidirect
6. C₂×#15688993	C₂	semidirect
7. C₂×#15688983	C₂	semidirect
8. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
20. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
23. #15689022	C₂²	semidirect
24. #15688998	C₂²	semidirect
25. #15688993	C₂²	semidirect
26. #15688983	C₂²	semidirect
27. C₄×C₄⋊Dic₄₇	C₂²	semidirect
32. C₂×C₄×D₄×C₄₇	C₄	semidirect
51. C₂×C₄⋊Dic₄₇	D₄	direct (N × H)
71. C₂³×C₄×C₄₇	C₂×C₄	semidirect
77. C₄×D₄×C₄₇	C₂×C₄	semidirect
78. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
80. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
82. C₂×C₄²×C₄₇	C₂×C₄	semidirect
93. C₂×D₄×C₄₇	C₄⋊C₄	semidirect
108. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
133. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
134. C₂²⋊C₄×C₄₇	C₂²×C₄	semidirect
135. C₄²×C₄₇	C₂²×C₄	semidirect
142. C₄⋊Dic₄₇	C₂×D₄	direct (N × H)
154. C₂³×C₄₇	C₂×C₄⋊C₄	semidirect
166. D₄×C₄₇	C₂×C₄⋊C₄	semidirect
174. C₂×C₄×C₄₇	C₂×C₄⋊C₄	semidirect
175. C₂×C₄×C₄₇	C₄×D₄	semidirect
206. C₂²×C₄₇	C₂²×C₄⋊C₄	semidirect
222. C₄×C₄₇	C₂²×C₄⋊C₄	semidirect
223. C₄×C₄₇	C₂×C₄×D₄	semidirect
237. C₂×C₄₇	D₄×C₄⋊C₄	semidirect
250. C₂×C₄×D₄	Dic₄₇	semidirect
272. C₄₇	C₂×D₄×C₄⋊C₄	semidirect
287. C₂³×C₄	C₂×Dic₄₇	semidirect
294. C₄×D₄	C₂×Dic₄₇	semidirect
308. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
312. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
316. C₂×C₄²	C₂×Dic₄₇	semidirect
329. C₂×D₄	C₄⋊Dic₄₇	direct (N × H)
364. C₂²×C₄	C₂²×Dic₄₇	semidirect
375. C₄⋊C₄	C₂²×Dic₄₇	semidirect
377. C₂²⋊C₄	C₂²×Dic₄₇	semidirect
379. C₄²	C₂²×Dic₄₇	semidirect
390. C₂³	C₂×C₄⋊Dic₄₇	semidirect
402. D₄	C₂×C₄⋊Dic₄₇	direct (N × H)
423. C₂×C₄	C₂×C₄⋊Dic₄₇	semidirect
424. C₂×C₄	D₄×Dic₄₇	semidirect
441. C₂²	C₂²×C₄⋊Dic₄₇	semidirect
460. C₄	C₂²×C₄⋊Dic₄₇	semidirect
461. C₄	C₂×D₄×Dic₄₇	semidirect
463. C₂	D₄×C₄⋊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
D₄×C₄⋊Dic₄₇	2
C₂×#15689022	2
C₂×#15688998	2
C₂×#15688993	2
C₂×#15688983	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂²×C₄×D₄×C₄₇	2
C₂×D₄×C₄⋊C₄	47

Subgroups — C2×D4×C4⋊Dic47 #26375565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₄⋊Dic₄₇ #26375565