Subgroups — C₂×#20241255 #26106149

Order 12032.

1130 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688983	C₂	1	1	yes	maximal, characteristic
3	#20241255	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄₇⋊C₈	C₄	1	2	yes	complemented
6	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
7	C₂²×C₂²⋊Dic₄₇	—	2	1	no	—
8	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
9	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
10	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
11	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
12	C₂×C₂²⋊(C₄₇⋊C₈)	C₄	1	2	yes	complemented
13	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	#15688983	—	2	1	no	—
15	#15688983	—	2	1	no	—
16	#15688983	C₄	1	2	yes	complemented
17	#15688983	C₂²	1	2	yes	—
18	C₂×C₄₇⋊#95	C₄	1	2	yes	complemented
19	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
21	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
22	C₄₇×#380	—	2	1	no	—
23	C₄₇×#380	—	2	1	no	—
24	C₄₇×#380	C₄	1	2	yes	complemented
25	C₄₇×#380	C₂²	1	2	yes	—
26	C₂×#95×C₄₇	C₄	1	2	yes	complemented
27	C₂³×Dic₄₇	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	2	no	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂²×C₄₇⋊C₈	—	4	4	no	—
31	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	—	4	4	no	—
35	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
36	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
37	C₂×C₂²⋊Dic₄₇	—	4	2	no	—
38	C₂×C₂²⋊Dic₄₇	—	4	2	no	—
39	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
43	C₄₇⋊#95	—	2	2	no	—
44	C₄₇⋊#95	C₂×C₄	1	4	yes	complemented
45	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	—	2	2	no	—
47	C₂³×C₄×C₄₇	—	4	4	no	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₇	Q₈	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	Q₈	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
69	#95×C₄₇	—	2	2	no	—
70	#95×C₄₇	C₂×C₄	1	4	yes	complemented
71	C₂⁴×C₄₇	—	4	2	no	—
72	C₂⁴×C₄₇	—	4	2	no	—
73	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂⁴×C₄₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂⁴×C₄₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂⁴×C₄₇	D₈	1	2	yes	—
80	C₂⁴×C₄₇	SD₁₆	1	2	yes	—
81	C₂⁴×C₄₇	SD₁₆	1	2	yes	—
82	C₂⁴×C₄₇	Q₁₆	1	2	yes	—
83	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	—	4	2	no	—
90	C₂²×C₄×C₄₇	—	4	2	no	—
91	C₂²×C₄×C₄₇	—	4	2	no	—
92	C₂²×C₄×C₄₇	—	4	2	no	—
93	C₂²×C₄×C₄₇	—	4	2	no	—
94	C₂²×C₄×C₄₇	—	4	2	no	—
95	C₂²×C₄×C₄₇	—	4	2	no	—
96	C₂²×C₄×C₄₇	—	4	2	no	—
97	C₂²×C₄×C₄₇	—	4	2	no	—
98	C₂²×C₄×C₄₇	—	4	2	no	—
99	C₂²×C₄×C₄₇	—	4	4	no	—
100	C₂²×C₄×C₄₇	—	4	4	no	—
101	C₂²×C₄×C₄₇	—	4	4	no	—
102	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
130	C₂²×Dic₄₇	—	2	4	no	—
131	C₂²×Dic₄₇	—	4	4	no	—
132	C₂²×Dic₄₇	—	4	4	no	—
133	C₂²×Dic₄₇	—	4	4	no	—
134	C₄⋊C₄×C₄₇	—	4	4	no	—
135	C₄⋊C₄×C₄₇	—	4	4	no	—
136	C₂²⋊C₄×C₄₇	—	4	4	no	—
137	C₂²⋊C₄×C₄₇	—	4	2	no	—
138	C₂²⋊C₄×C₄₇	—	4	2	no	—
139	C₂²⋊Dic₄₇	—	4	4	no	—
140	C₂²⋊Dic₄₇	—	4	2	no	—
141	C₂²⋊Dic₄₇	—	4	2	no	—
142	C₄⋊Dic₄₇	—	4	4	no	—
143	C₄⋊Dic₄₇	—	4	4	no	—
144	C₂×C₄₇⋊C₈	—	2	4	no	—
145	C₂×C₄₇⋊C₈	—	4	4	no	—
146	C₂×C₄₇⋊C₈	—	4	4	no	—
147	C₂×C₄₇⋊C₈	—	4	4	no	—
148	C₂³×C₄₇	—	2	2	no	—
149	C₂³×C₄₇	—	2	2	no	—
150	C₂³×C₄₇	—	2	2	no	—
151	C₂³×C₄₇	—	2	2	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	4	1	no	—
155	C₂³×C₄₇	—	4	1	no	—
156	C₂³×C₄₇	—	4	1	no	—
157	C₂³×C₄₇	—	4	1	no	—
158	C₂³×C₄₇	—	4	1	no	—
159	C₂³×C₄₇	—	4	1	no	—
160	C₂³×C₄₇	—	4	1	no	—
161	C₂³×C₄₇	—	4	4	no	—
162	C₂³×C₄₇	—	4	4	no	—
163	C₂³×C₄₇	—	4	4	no	—
164	C₂³×C₄₇	—	4	4	no	—
165	C₂³×C₄₇	—	4	1	no	—
166	C₂³×C₄₇	#95	1	1	yes	characteristic
167	C₂³×C₄₇	#95	1	1	yes	characteristic
168	C₂³×C₄₇	#95	1	1	yes	characteristic
169	C₂³×C₄₇	#95	1	1	yes	characteristic
170	C₂³×C₄₇	#102	1	2	yes	—
171	C₂³×C₄₇	#102	1	2	yes	—
172	C₂³×C₄₇	#102	1	2	yes	—
173	C₂³×C₄₇	#102	1	2	yes	—
174	C₂³×C₄₇	#103	1	2	yes	—
175	C₂³×C₄₇	#103	1	2	yes	—
176	C₂³×C₄₇	#103	1	2	yes	—
177	C₂³×C₄₇	#103	1	2	yes	—
178	C₂³×C₄₇	#106	1	2	yes	—
179	C₂³×C₄₇	#106	1	2	yes	—
180	C₂³×C₄₇	#107	1	2	yes	—
181	C₂³×C₄₇	#107	1	2	yes	—
182	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
186	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
187	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
188	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	4	1	no	—
205	C₂×C₄×C₄₇	—	4	1	no	—
206	C₂×C₄×C₄₇	—	4	1	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	—	4	1	no	—
210	C₂×C₄×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	1	no	—
212	C₂×C₄×C₄₇	—	4	1	no	—
213	C₂×C₄×C₄₇	—	4	1	no	—
214	C₂×C₄×C₄₇	—	4	1	no	—
215	C₂×C₄×C₄₇	—	4	1	no	—
216	C₂×C₄×C₄₇	—	4	4	no	—
217	C₂×C₄×C₄₇	—	4	4	no	—
218	C₂×C₄×C₄₇	—	4	4	no	—
219	C₂×C₄×C₄₇	—	8	8	no	—
220	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
221	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
222	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
223	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
224	C₂×C₄×C₄₇	#99	1	4	yes	—
225	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×Dic₄₇	—	4	4	no	—
230	C₂×Dic₄₇	—	4	4	no	—
231	C₂×Dic₄₇	—	4	4	no	—
232	C₂×Dic₄₇	—	8	8	no	—
233	C₄₇⋊C₈	—	4	4	no	—
234	C₂×#1289	—	47	1	no	maximal, Sylow
235	C₂²×C₄₇	—	2	4	no	—
236	C₂²×C₄₇	—	2	4	no	—
237	C₂²×C₄₇	—	2	4	no	—
238	C₂²×C₄₇	—	2	4	no	—
239	C₂²×C₄₇	—	2	4	no	—
240	C₂²×C₄₇	—	2	4	no	—
241	C₂²×C₄₇	—	2	1	no	—
242	C₂²×C₄₇	—	2	1	no	—
243	C₂²×C₄₇	—	2	1	no	—
244	C₂²×C₄₇	—	2	1	no	—
245	C₂²×C₄₇	—	2	1	no	—
246	C₂²×C₄₇	—	2	1	no	—
247	C₂²×C₄₇	—	2	1	no	—
248	C₂²×C₄₇	—	2	1	no	—
249	C₂²×C₄₇	—	2	1	no	—
250	C₂²×C₄₇	—	2	1	no	—
251	C₂²×C₄₇	—	2	1	no	—
252	C₂²×C₄₇	—	2	1	no	—
253	C₂²×C₄₇	—	4	2	no	—
254	C₂²×C₄₇	—	4	2	no	—
255	C₂²×C₄₇	—	4	2	no	—
256	C₂²×C₄₇	—	4	2	no	—
257	C₂²×C₄₇	—	4	2	no	—
258	C₂²×C₄₇	—	4	2	no	—
259	C₂²×C₄₇	—	4	1	no	—
260	C₂²×C₄₇	—	4	1	no	—
261	C₂²×C₄₇	—	4	1	no	—
262	C₂²×C₄₇	—	4	1	no	—
263	C₂²×C₄₇	H(3,ℤ/4)	1	2	yes	—
264	C₂²×C₄₇	#340	1	2	yes	—
265	C₂²×C₄₇	#340	1	2	yes	—
266	C₂²×C₄₇	#340	1	2	yes	—
267	C₂²×C₄₇	#340	1	2	yes	—
268	C₂²×C₄₇	#342	1	2	yes	—
269	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
270	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
271	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
272	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
273	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
274	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
275	C₂²×C₄₇	C₂×#107	1	1	yes	characteristic
276	C₄×C₄₇	—	2	1	no	—
277	C₄×C₄₇	—	2	1	no	—
278	C₄×C₄₇	—	2	1	no	—
279	C₄×C₄₇	—	2	1	no	—
280	C₄×C₄₇	—	2	1	no	—
281	C₄×C₄₇	—	2	1	no	—
282	C₄×C₄₇	—	8	4	no	—
283	C₄×C₄₇	#342	1	2	yes	—
284	C₄×C₄₇	C₂×#99	1	2	yes	—
285	Dic₄₇	—	8	4	no	—
286	C₂²×C₂²⋊C₈	—	47	1	no	—
287	C₂×#380	—	47	1	no	—
288	C₂×#380	D₄₇	1	1	yes	characteristic
289	#1289	—	47	4	no	—
290	C₂×C₄₇	—	2	1	no	—
291	C₂×C₄₇	—	2	1	no	—
292	C₂×C₄₇	—	2	2	no	—
293	C₂×C₄₇	—	2	2	no	—
294	C₂×C₄₇	—	2	2	no	—
295	C₂×C₄₇	—	2	1	no	—
296	C₂×C₄₇	—	2	1	no	—
297	C₂×C₄₇	—	2	1	no	—
298	C₂×C₄₇	—	2	1	no	—
299	C₂×C₄₇	#1289	1	4	yes	complemented
300	C₂×C₄₇	C₂×H(3,ℤ/4)	1	1	yes	characteristic
301	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
302	C₂×C₄₇	C₂×#342	1	1	yes	characteristic
303	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
304	C₂³×C₈	—	47	2	no	—
305	C₂²×C₄⋊C₄	—	2	1	no	—
306	C₂²×C₄⋊C₄	—	94	1	no	—
307	C₂²×C₂²⋊C₄	—	2	1	no	—
308	C₂²×C₂²⋊C₄	—	94	1	no	—
309	C₂×C₂²⋊C₈	—	47	2	no	—
310	C₂×C₂²⋊C₈	—	47	2	no	—
311	C₂×C₂²⋊C₈	—	94	1	no	—
312	C₂×C₂²⋊C₈	—	94	1	no	—
313	C₂×C₂²⋊C₈	—	94	1	no	—
314	C₂×C₂²⋊C₈	—	94	1	no	—
315	#380	—	2	1	no	—
316	#380	—	2	1	no	—
317	#380	—	47	2	no	—
318	#380	—	47	2	no	—
319	#380	—	94	1	no	—
320	#380	—	94	1	no	—
321	#380	Dic₄₇	1	2	yes	complemented
322	#380	C₂×D₄₇	1	2	yes	—
323	C₂×#95	—	47	2	no	—
324	C₂×#95	Dic₄₇	1	2	yes	complemented
325	C₄₇	C₂×#1289	1	1	yes	characteristic, complemented, Sylow
326	C₂⁵	C₂²⋊D₄₇	1	1	yes	characteristic
327	C₂³×C₄	—	2	2	no	—
328	C₂³×C₄	—	4	4	no	—
329	C₂³×C₄	—	94	2	no	—
330	C₂³×C₄	Dic₉₄	1	1	yes	characteristic
331	C₂³×C₄	Dic₉₄	1	1	yes	characteristic
332	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
333	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
334	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
335	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
336	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
337	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
338	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
339	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
340	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
341	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
342	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
343	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
344	C₂²×C₈	—	47	4	no	—
345	C₂²×C₈	—	94	2	no	—
346	C₂²×C₈	—	94	2	no	—
347	C₂²×C₈	—	188	4	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	4	4	no	—
351	C₂×C₄⋊C₄	—	94	2	no	—
352	C₂×C₄⋊C₄	—	94	2	no	—
353	C₂×C₄⋊C₄	—	188	4	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	4	2	no	—
357	C₂×C₂²⋊C₄	—	4	2	no	—
358	C₂×C₂²⋊C₄	—	94	2	no	—
359	C₂×C₂²⋊C₄	—	94	2	no	—
360	C₂×C₂²⋊C₄	—	188	2	no	—
361	C₂×C₂²⋊C₄	—	188	2	no	—
362	C₂²⋊C₈	—	94	2	no	—
363	C₂²⋊C₈	—	94	2	no	—
364	C₂²⋊C₈	—	94	2	no	—
365	C₂²⋊C₈	—	94	2	no	—
366	#95	—	2	2	no	—
367	#95	—	47	4	no	—
368	#95	—	94	2	no	—
369	#95	C₂×Dic₄₇	1	4	yes	complemented
370	C₂⁴	—	4	2	no	—
371	C₂⁴	—	4	2	no	—
372	C₂⁴	Dic₄₇⋊C₄	1	1	yes	characteristic
373	C₂⁴	Dic₄₇⋊C₄	1	1	yes	characteristic
374	C₂⁴	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
375	C₂⁴	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
376	C₂⁴	#10625334	1	2	yes	—
377	C₂⁴	#10625335	1	2	yes	—
378	C₂⁴	#10625336	1	2	yes	—
379	C₂⁴	#10625337	1	2	yes	—
380	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
381	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
382	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	4	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	94	4	no	—
402	C₂²×C₄	—	188	4	no	—
403	C₂²×C₄	—	188	4	no	—
404	C₂²×C₄	—	188	4	no	—
405	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
406	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
407	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
408	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
409	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
410	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
411	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
412	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
413	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
414	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
415	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
416	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
417	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
418	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
419	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
420	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
421	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
422	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
423	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
424	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
425	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
426	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
427	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
428	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
431	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
433	C₂×C₈	—	94	4	no	—
434	C₂×C₈	—	188	4	no	—
435	C₂×C₈	—	188	4	no	—
436	C₂×C₈	—	188	4	no	—
437	C₄⋊C₄	—	4	4	no	—
438	C₄⋊C₄	—	4	4	no	—
439	C₄⋊C₄	—	188	4	no	—
440	C₄⋊C₄	—	188	4	no	—
441	C₂²⋊C₄	—	4	4	no	—
442	C₂²⋊C₄	—	4	2	no	—
443	C₂²⋊C₄	—	4	2	no	—
444	C₂²⋊C₄	—	188	4	no	—
445	C₂²⋊C₄	—	188	2	no	—
446	C₂²⋊C₄	—	188	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	4	4	no	—
461	C₂³	—	4	4	no	—
462	C₂³	—	4	4	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	C₄₇⋊#95	1	1	yes	characteristic
466	C₂³	C₄₇⋊#95	1	1	yes	characteristic
467	C₂³	C₄₇⋊#95	1	1	yes	characteristic
468	C₂³	C₄₇⋊#95	1	1	yes	characteristic
469	C₂³	#13093944	1	2	yes	—
470	C₂³	#13093944	1	2	yes	—
471	C₂³	#13093945	1	2	yes	—
472	C₂³	#13093945	1	2	yes	—
473	C₂³	#13093947	1	2	yes	—
474	C₂³	#13093947	1	2	yes	—
475	C₂³	#13093948	1	2	yes	—
476	C₂³	#13093948	1	2	yes	—
477	C₂³	#13093955	1	2	yes	—
478	C₂³	#13093955	1	2	yes	—
479	C₂³	#13093957	1	2	yes	—
480	C₂³	#13093957	1	2	yes	—
481	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
482	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
483	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
484	C₂³	C₂×#10625334	1	1	yes	characteristic
485	C₂³	C₂×#10625336	1	1	yes	characteristic
486	C₂³	C₂×#10625335	1	1	yes	characteristic
487	C₂³	C₂×#10625337	1	1	yes	characteristic
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	8	8	no	—
519	C₂×C₄	—	376	8	no	—
520	C₂×C₄	—	188	4	no	—
521	C₂×C₄	—	188	4	no	—
522	C₂×C₄	—	188	4	no	—
523	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
524	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
525	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
526	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
527	C₂×C₄	#13093938	1	4	yes	—
528	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
529	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
530	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
531	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
532	C₈	—	188	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	2	4	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	#15688879	1	2	yes	—
562	C₂²	#15688885	1	2	yes	—
563	C₂²	#15688885	1	2	yes	—
564	C₂²	#15688885	1	2	yes	—
565	C₂²	#15688885	1	2	yes	—
566	C₂²	#15688889	1	2	yes	—
567	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
568	C₂²	C₂×#13093944	1	1	yes	characteristic
569	C₂²	C₂×#13093945	1	1	yes	characteristic
570	C₂²	C₂×#13093947	1	1	yes	characteristic
571	C₂²	C₂×#13093948	1	1	yes	characteristic
572	C₂²	C₂×#13093955	1	1	yes	characteristic
573	C₂²	C₂×#13093957	1	1	yes	characteristic
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	8	4	no	—
581	C₄	—	376	4	no	—
582	C₄	#15688889	1	2	yes	—
583	C₄	C₂×#13093938	1	2	yes	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	2	no	—
589	C₂	—	2	2	no	—
590	C₂	—	2	2	no	—
591	C₂	—	2	1	no	—
592	C₂	—	2	1	no	—
593	C₂	#20241255	1	4	yes	direct product factor
594	C₂	C₂×#15688879	1	1	yes	characteristic
595	C₂	C₂×#15688885	1	1	yes	characteristic
596	C₂	C₂×#15688889	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₄₇⋊#95
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#380	C₂
socle	C₂³×C₄₇	#95
prime radical	C₂⁵×C₄₇	D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#380	D₄₇
hypocenter	C₄₇	C₂×#1289
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂×#380

Complements

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

N	H ≅ G/N	type
3. #20241255	C₂	direct (N × H)
5. C₂³×C₄₇⋊C₈	C₄	semidirect
12. C₂×C₂²⋊(C₄₇⋊C₈)	C₄	semidirect
16. #15688983	C₄	semidirect
18. C₂×C₄₇⋊#95	C₄	semidirect
24. C₄₇×#380	C₄	semidirect
26. C₂×#95×C₄₇	C₄	semidirect
31. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
44. C₄₇⋊#95	C₂×C₄	semidirect
70. #95×C₄₇	C₂×C₄	semidirect
299. C₂×C₄₇	#1289	semidirect
321. #380	Dic₄₇	semidirect
324. C₂×#95	Dic₄₇	semidirect
325. C₄₇	C₂×#1289	semidirect
369. #95	C₂×Dic₄₇	semidirect
593. C₂	#20241255	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×C₂²⋊(C₄₇⋊C₈)	2
C₂×#15688983	2
#20241255	2
C₂×C₄₇×#380	2
C₂×#1289	47

Subgroups — C2×#20241255 #26106149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241255 #26106149