Subgroups — C₂×#20245749 #26374497

Order 12032.

4694 conjugacy classes of subgroups.

The subgroup lattice has 404 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	#20245749	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄⋊C₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂²⋊C₄×Dic₄₇	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
7	C₂×#15688969	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄₇⋊#95	C₂	1	2	yes	maximal, 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	complemented
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	C₂²	1	4	yes	—
16	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
17	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
18	C₄⋊C₄×Dic₄₇	C₂²	1	16	yes	complemented
19	C₄×C₄⋊Dic₄₇	C₂²	1	8	yes	complemented
20	C₂²⋊C₄×Dic₄₇	C₂²	1	32	yes	complemented
21	C₄×C₂²⋊Dic₄₇	C₂²	1	16	yes	complemented
22	#15688969	C₂²	1	8	yes	complemented
23	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
24	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
25	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
26	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
27	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
28	C₂×C₄₇⋊#95	C₂²	1	16	yes	complemented
29	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₄₇	C₄	1	16	yes	complemented
32	C₂×C₄×D₄×C₄₇	C₂²	1	8	yes	—
33	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
35	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
36	C₂³×Dic₄₇	—	4	8	no	—
37	C₂³×Dic₄₇	—	4	8	no	—
38	C₂³×Dic₄₇	C₂×C₄	1	32	yes	complemented
39	C₂³×Dic₄₇	C₂³	1	2	yes	—
40	C₂³×Dic₄₇	C₂³	1	2	yes	—
41	C₂³×Dic₄₇	C₂³	1	4	yes	—
42	C₂³×Dic₄₇	C₂³	1	16	yes	—
43	D₄×Dic₄₇	C₂×C₄	1	128	yes	complemented
44	C₂×C₄⋊Dic₄₇	C₂×C₄	1	16	yes	complemented
45	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
46	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	32	yes	complemented
47	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
48	C₂×C₄×Dic₄₇	—	4	8	no	—
49	C₂×C₄×Dic₄₇	—	4	4	no	—
50	C₂×C₄×Dic₄₇	C₂×C₄	1	16	yes	complemented
51	C₂×C₄×Dic₄₇	C₂³	1	16	yes	—
52	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
53	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
54	C₄₇⋊#95	C₂³	1	4	yes	—
55	C₄₇⋊#95	C₂³	1	8	yes	—
56	C₄₇⋊#95	C₂³	1	16	yes	—
57	C₄₇⋊#95	C₂³	1	4	yes	—
58	C₄₇⋊#95	C₂³	1	8	yes	—
59	C₂⁵×C₄₇	C₂³	1	2	yes	—
60	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	—
61	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
62	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
63	C₂³×C₄×C₄₇	—	4	8	no	—
64	C₂³×C₄×C₄₇	C₂×C₄	1	16	yes	complemented
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
68	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
69	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₄₇	C₂×C₄	1	64	yes	complemented
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
73	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
74	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
75	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
76	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
77	C₂⁴×C₄₇	—	2	8	no	—
78	C₂⁴×C₄₇	—	2	4	no	—
79	C₂⁴×C₄₇	—	2	4	no	—
80	C₂⁴×C₄₇	C₂²×C₄	1	16	yes	—
81	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
82	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
83	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
84	C₂×D₄×C₄₇	C₄²	1	64	yes	complemented
85	C₂×D₄×C₄₇	C₂²×C₄	1	32	yes	—
86	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	8	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	4	32	no	—
92	C₂²×C₄×C₄₇	—	4	16	no	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	32	yes	complemented
99	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
103	C₂²×Dic₄₇	—	2	4	no	—
104	C₂²×Dic₄₇	—	2	8	no	—
105	C₂²×Dic₄₇	—	2	8	no	—
106	C₂²×Dic₄₇	—	2	4	no	—
107	C₂²×Dic₄₇	—	2	4	no	—
108	C₂²×Dic₄₇	—	2	4	no	—
109	C₂²×Dic₄₇	—	4	64	no	—
110	C₂²×Dic₄₇	—	4	16	no	—
111	C₂²×Dic₄₇	—	4	16	no	—
112	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
113	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
114	C₂²×Dic₄₇	C₂²×C₄	1	16	yes	—
115	C₂²×Dic₄₇	C₂²×C₄	1	64	yes	complemented
116	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
117	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
118	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
119	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
120	C₂²⋊C₄×C₄₇	C₂²×C₄	1	32	yes	complemented
121	C₄²×C₄₇	C₂²×C₄	1	16	yes	complemented
122	C₂²⋊Dic₄₇	C₂²×C₄	1	64	yes	complemented
123	C₄⋊Dic₄₇	C₂²×C₄	1	32	yes	complemented
124	C₄×Dic₄₇	—	4	16	no	—
125	C₄×Dic₄₇	—	4	8	no	—
126	C₄×Dic₄₇	C₂²×C₄	1	32	yes	complemented
127	C₂³×C₄₇	—	2	32	no	—
128	C₂³×C₄₇	—	2	16	no	—
129	C₂³×C₄₇	—	2	32	no	—
130	C₂³×C₄₇	—	2	16	no	—
131	C₂³×C₄₇	—	2	4	no	—
132	C₂³×C₄₇	—	2	8	no	—
133	C₂³×C₄₇	—	2	4	no	—
134	C₂³×C₄₇	C₂×C₄²	1	32	yes	—
135	C₂³×C₄₇	C₂³×C₄	1	16	yes	—
136	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
137	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
138	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
139	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
140	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
141	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
142	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
143	D₄×C₄₇	C₂×C₄²	1	64	yes	complemented
144	C₂×C₄×C₄₇	—	2	8	no	—
145	C₂×C₄×C₄₇	—	2	16	no	—
146	C₂×C₄×C₄₇	—	2	8	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	8	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	4	32	no	—
152	C₂×C₄×C₄₇	C₂×C₄²	1	16	yes	—
153	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
154	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
155	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
156	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
157	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
158	C₂×Dic₄₇	—	2	16	no	—
159	C₂×Dic₄₇	—	2	32	no	—
160	C₂×Dic₄₇	—	2	16	no	—
161	C₂×Dic₄₇	—	2	4	no	—
162	C₂×Dic₄₇	—	2	8	no	—
163	C₂×Dic₄₇	—	2	8	no	—
164	C₂×Dic₄₇	—	2	4	no	—
165	C₂×Dic₄₇	—	2	4	no	—
166	C₂×Dic₄₇	—	2	4	no	—
167	C₂×Dic₄₇	—	4	64	no	—
168	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
169	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
170	C₂×Dic₄₇	C₂³×C₄	1	16	yes	—
171	C₂×#2275	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	—	2	16	no	—
173	C₂²×C₄₇	—	2	8	no	—
174	C₂²×C₄₇	—	2	16	no	—
175	C₂²×C₄₇	—	2	8	no	—
176	C₂²×C₄₇	—	2	64	no	—
177	C₂²×C₄₇	C₂²×C₄²	1	16	yes	—
178	C₂²×C₄₇	C₂²×C₄²	1	4	yes	—
179	C₂²×C₄₇	#518	1	8	yes	—
180	C₂²×C₄₇	#518	1	4	yes	—
181	C₂²×C₄₇	#520	1	8	yes	—
182	C₂²×C₄₇	#520	1	4	yes	—
183	C₂²×C₄₇	C₂⁴×C₄	1	2	yes	—
184	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
186	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
188	C₄×C₄₇	—	2	4	no	—
189	C₄×C₄₇	—	2	8	no	—
190	C₄×C₄₇	—	2	4	no	—
191	C₄×C₄₇	C₂²×C₄²	1	8	yes	—
192	Dic₄₇	—	2	8	no	—
193	Dic₄₇	—	2	16	no	—
194	Dic₄₇	—	2	8	no	—
195	C₂²×C₄×D₄	—	47	2	no	—
196	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
197	#2275	—	47	16	no	—
198	C₂×C₄×C₄⋊C₄	—	47	1	no	—
199	C₂×C₄×C₄⋊C₄	—	47	2	no	—
200	C₂×C₄×C₂²⋊C₄	—	47	2	no	—
201	C₂×C₄×C₂²⋊C₄	—	47	4	no	—
202	C₂×#376	—	47	1	no	—
203	C₂²×#95	—	47	2	no	—
204	C₂×C₄₇	—	2	16	no	—
205	C₂×C₄₇	#2275	1	8	yes	complemented
206	C₂×C₄₇	C₂³×C₄²	1	1	yes	characteristic
207	C₂×C₄₇	C₂×#518	1	2	yes	—
208	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
209	C₂×C₄₇	C₂×#520	1	2	yes	—
210	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
211	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
212	C₂⁴×C₄	—	47	4	no	—
213	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
214	C₂×C₄×D₄	—	47	32	no	—
215	C₂×C₄×D₄	—	47	16	no	—
216	C₂×C₄×D₄	Dic₄₇	1	16	yes	complemented
217	C₂×C₄×D₄	C₂×D₄₇	1	8	yes	—
218	C₂²×C₄⋊C₄	—	47	2	no	—
219	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
220	C₂²×C₂²⋊C₄	—	47	4	no	—
221	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
222	C₂²×C₄²	—	47	2	no	—
223	C₂²×C₄²	—	47	4	no	—
224	C₂²×C₄²	—	47	2	no	—
225	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
226	C₄×C₄⋊C₄	—	47	16	no	—
227	C₄×C₄⋊C₄	—	47	8	no	—
228	C₄×C₂²⋊C₄	—	47	16	no	—
229	C₄×C₂²⋊C₄	—	47	32	no	—
230	#376	—	47	8	no	—
231	C₂×#95	—	47	1	no	—
232	C₂×#95	—	47	2	no	—
233	C₂×#95	—	47	4	no	—
234	C₂×#95	—	47	1	no	—
235	C₂×#95	—	47	2	no	—
236	C₂×#95	—	47	16	no	—
237	C₄₇	C₂×#2275	1	1	yes	characteristic, complemented, Sylow
238	C₂⁵	C₂²×D₄₇	1	2	yes	—
239	C₂²×D₄	C₄×D₄₇	1	16	yes	—
240	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
241	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
242	C₂³×C₄	—	4	8	no	—
243	C₂³×C₄	—	47	2	no	—
244	C₂³×C₄	—	47	4	no	—
245	C₂³×C₄	—	47	2	no	—
246	C₂³×C₄	—	47	32	no	—
247	C₂³×C₄	—	47	16	no	—
248	C₂³×C₄	—	188	8	no	—
249	C₂³×C₄	—	188	8	no	—
250	C₂³×C₄	C₂×Dic₄₇	1	16	yes	complemented
251	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
252	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
253	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
254	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
255	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
256	C₄×D₄	—	47	128	no	—
257	C₄×D₄	C₂×Dic₄₇	1	64	yes	complemented
258	C₂×C₄⋊C₄	—	47	16	no	—
259	C₂×C₄⋊C₄	—	47	8	no	—
260	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
261	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
262	C₂×C₂²⋊C₄	—	47	32	no	—
263	C₂×C₂²⋊C₄	—	47	16	no	—
264	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
265	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
266	C₂×C₄²	—	47	16	no	—
267	C₂×C₄²	—	47	8	no	—
268	C₂×C₄²	—	47	16	no	—
269	C₂×C₄²	—	47	8	no	—
270	C₂×C₄²	—	188	8	no	—
271	C₂×C₄²	—	188	4	no	—
272	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
273	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
274	#95	—	47	4	no	—
275	#95	—	47	16	no	—
276	#95	—	47	8	no	—
277	#95	—	47	8	no	—
278	#95	—	47	4	no	—
279	C₂⁴	—	2	8	no	—
280	C₂⁴	—	2	4	no	—
281	C₂⁴	—	2	4	no	—
282	C₂⁴	C₂×C₄×D₄₇	1	16	yes	—
283	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
284	C₂⁴	C₂³×D₄₇	1	4	yes	—
285	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
286	C₂×D₄	C₄×Dic₄₇	1	64	yes	complemented
287	C₂×D₄	C₂×C₄×D₄₇	1	32	yes	—
288	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	32	no	—
294	C₂²×C₄	—	4	16	no	—
295	C₂²×C₄	—	47	8	no	—
296	C₂²×C₄	—	47	8	no	—
297	C₂²×C₄	—	47	16	no	—
298	C₂²×C₄	—	47	4	no	—
299	C₂²×C₄	—	47	4	no	—
300	C₂²×C₄	—	47	8	no	—
301	C₂²×C₄	—	47	64	no	—
302	C₂²×C₄	—	94	4	no	—
303	C₂²×C₄	—	94	8	no	—
304	C₂²×C₄	—	94	4	no	—
305	C₂²×C₄	—	94	8	no	—
306	C₂²×C₄	—	94	4	no	—
307	C₂²×C₄	—	94	4	no	—
308	C₂²×C₄	—	188	64	no	—
309	C₂²×C₄	—	188	16	no	—
310	C₂²×C₄	—	188	16	no	—
311	C₂²×C₄	C₂×C₄×D₄₇	1	8	yes	—
312	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
313	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
314	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
315	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
316	C₂²×C₄	C₂²×Dic₄₇	1	32	yes	complemented
317	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
318	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
319	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
320	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
321	C₄⋊C₄	—	47	32	no	—
322	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	complemented
323	C₂²⋊C₄	—	47	64	no	—
324	C₂²⋊C₄	C₂²×Dic₄₇	1	32	yes	complemented
325	C₄²	—	47	32	no	—
326	C₄²	—	188	16	no	—
327	C₄²	—	188	8	no	—
328	C₄²	C₂²×Dic₄₇	1	16	yes	complemented
329	C₂³	—	2	32	no	—
330	C₂³	—	2	16	no	—
331	C₂³	—	2	32	no	—
332	C₂³	—	2	16	no	—
333	C₂³	—	2	8	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	4	no	—
336	C₂³	C₂×C₄×Dic₄₇	1	32	yes	—
337	C₂³	C₂²×C₄×D₄₇	1	16	yes	—
338	C₂³	C₂²×C₄×D₄₇	1	4	yes	—
339	C₂³	C₂³×Dic₄₇	1	8	yes	—
340	C₂³	C₂³×Dic₄₇	1	2	yes	—
341	C₂³	#13094069	1	4	yes	—
342	C₂³	#13094070	1	2	yes	—
343	C₂³	#13094071	1	2	yes	—
344	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
345	D₄	C₂×C₄×Dic₄₇	1	64	yes	complemented
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	16	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	32	no	—
354	C₂×C₄	—	47	8	no	—
355	C₂×C₄	—	47	8	no	—
356	C₂×C₄	—	47	16	no	—
357	C₂×C₄	—	94	32	no	—
358	C₂×C₄	—	94	16	no	—
359	C₂×C₄	—	94	16	no	—
360	C₂×C₄	—	94	4	no	—
361	C₂×C₄	—	94	8	no	—
362	C₂×C₄	—	94	4	no	—
363	C₂×C₄	—	94	8	no	—
364	C₂×C₄	—	94	4	no	—
365	C₂×C₄	—	94	4	no	—
366	C₂×C₄	—	188	64	no	—
367	C₂×C₄	C₂×C₄×Dic₄₇	1	16	yes	—
368	C₂×C₄	C₂²×C₄×D₄₇	1	8	yes	—
369	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
370	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
371	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
372	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
373	C₂²	—	2	16	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	16	no	—
376	C₂²	—	2	8	no	—
377	C₂²	—	2	64	no	—
378	C₂²	C₂²×C₄×Dic₄₇	1	16	yes	—
379	C₂²	C₂²×C₄×Dic₄₇	1	4	yes	—
380	C₂²	#15689595	1	8	yes	—
381	C₂²	#15689598	1	4	yes	—
382	C₂²	#15689602	1	8	yes	—
383	C₂²	#15689606	1	4	yes	—
384	C₂²	C₂³×C₄×D₄₇	1	2	yes	—
385	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
386	C₂²	C₂×#13094069	1	2	yes	—
387	C₂²	C₂×#13094070	1	1	yes	characteristic
388	C₂²	C₂×#13094071	1	1	yes	characteristic
389	C₄	—	2	4	no	—
390	C₄	—	2	8	no	—
391	C₄	—	2	4	no	—
392	C₄	—	94	8	no	—
393	C₄	—	94	16	no	—
394	C₄	—	94	8	no	—
395	C₄	C₂²×C₄×Dic₄₇	1	8	yes	—
396	C₂	—	2	16	no	—
397	C₂	#20245749	1	8	yes	direct product factor
398	C₂	C₂³×C₄×Dic₄₇	1	1	yes	characteristic
399	C₂	C₂×#15689595	1	2	yes	—
400	C₂	C₂×#15689598	1	1	yes	characteristic
401	C₂	C₂×#15689602	1	2	yes	—
402	C₂	C₂×#15689606	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×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×#2275
LCS	G ▷ C₂×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. #20245749	C₂	direct (N × H)
3. C₂×C₄⋊C₄×Dic₄₇	C₂	semidirect
4. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
5. C₂×C₂²⋊C₄×Dic₄₇	C₂	semidirect
6. C₂×C₄×C₂²⋊Dic₄₇	C₂	semidirect
7. C₂×#15688969	C₂	semidirect
8. C₂²×C₄₇⋊#95	C₂	semidirect
11. C₂×D₄×Dic₄₇	C₄	semidirect
18. C₄⋊C₄×Dic₄₇	C₂²	semidirect
19. C₄×C₄⋊Dic₄₇	C₂²	semidirect
20. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
21. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
22. #15688969	C₂²	semidirect
28. C₂×C₄₇⋊#95	C₂²	semidirect
31. C₂×C₄×D₄×C₄₇	C₄	semidirect
38. C₂³×Dic₄₇	C₂×C₄	semidirect
43. D₄×Dic₄₇	C₂×C₄	semidirect
44. C₂×C₄⋊Dic₄₇	C₂×C₄	semidirect
46. C₂×C₂²⋊Dic₄₇	C₂×C₄	semidirect
50. C₂×C₄×Dic₄₇	C₂×C₄	semidirect
64. C₂³×C₄×C₄₇	C₂×C₄	semidirect
70. C₄×D₄×C₄₇	C₂×C₄	semidirect
71. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
73. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
75. C₂×C₄²×C₄₇	C₂×C₄	semidirect
84. C₂×D₄×C₄₇	C₄²	semidirect
98. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
115. C₂²×Dic₄₇	C₂²×C₄	semidirect
119. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
120. C₂²⋊C₄×C₄₇	C₂²×C₄	semidirect
121. C₄²×C₄₇	C₂²×C₄	semidirect
122. C₂²⋊Dic₄₇	C₂²×C₄	semidirect
123. C₄⋊Dic₄₇	C₂²×C₄	semidirect
126. C₄×Dic₄₇	C₂²×C₄	semidirect
143. D₄×C₄₇	C₂×C₄²	semidirect
205. C₂×C₄₇	#2275	semidirect
216. C₂×C₄×D₄	Dic₄₇	semidirect
237. C₄₇	C₂×#2275	semidirect
250. C₂³×C₄	C₂×Dic₄₇	semidirect
257. C₄×D₄	C₂×Dic₄₇	semidirect
260. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
264. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
272. C₂×C₄²	C₂×Dic₄₇	semidirect
286. C₂×D₄	C₄×Dic₄₇	semidirect
316. C₂²×C₄	C₂²×Dic₄₇	semidirect
322. C₄⋊C₄	C₂²×Dic₄₇	semidirect
324. C₂²⋊C₄	C₂²×Dic₄₇	semidirect
328. C₄²	C₂²×Dic₄₇	semidirect
345. D₄	C₂×C₄×Dic₄₇	semidirect
397. C₂	#20245749	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
#20245749	2
C₂×C₄⋊C₄×Dic₄₇	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₂²⋊C₄×Dic₄₇	2
C₂×C₄×C₂²⋊Dic₄₇	2
C₂×#15688969	2
C₂²×C₄₇⋊#95	2
C₂²×C₄×D₄×C₄₇	2
C₂×#2275	47

Subgroups — C2×#20245749 #26374497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245749 #26374497