Subgroups — C₂×#20243368 #26215632

Order 12032.

2222 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal, complemented
2	C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal
3	#20243368	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688878	C₂	1	2	yes	maximal, complemented
5	C₂³×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	4	yes	—
7	C₂×C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
8	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	8	yes	complemented
9	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
10	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	8	yes	—
11	#15688878	C₂²	1	8	yes	complemented
12	C₂⁴×C₄×C₄₇	C₄	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₇	C₄	1	1	yes	characteristic
14	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₇	—	2	8	no	—
16	C₂²×C₄²×C₄₇	C₄	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₄	1	1	yes	characteristic
18	C₂²×C₄²×C₄₇	C₄	1	4	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₇	C₂²	1	4	yes	—
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄₇⋊C₈	—	2	8	no	—
23	C₂²×C₄₇⋊C₈	—	2	8	no	—
24	C₂²×C₄₇⋊C₈	—	2	8	no	—
25	C₂²×C₄₇⋊C₈	C₂³	1	8	yes	—
26	C₄⋊(C₄₇⋊C₈)	—	2	16	no	—
27	C₂²⋊(C₄₇⋊C₈)	—	2	16	no	—
28	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₇	—	2	4	no	—
30	C₂³×C₄×C₄₇	—	2	4	no	—
31	C₂³×C₄×C₄₇	—	2	4	no	—
32	C₂³×C₄×C₄₇	—	2	4	no	—
33	C₂³×C₄×C₄₇	—	2	4	no	—
34	C₂³×C₄×C₄₇	—	2	4	no	—
35	C₂³×C₄×C₄₇	—	2	4	no	—
36	C₂³×C₄×C₄₇	C₈	1	8	yes	complemented
37	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
38	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	D₄	1	4	yes	—
46	C₂³×C₄×C₄₇	Q₈	1	4	yes	—
47	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₄₇	—	2	4	no	—
50	C₂×C₄²×C₄₇	—	2	4	no	—
51	C₂×C₄²×C₄₇	—	2	4	no	—
52	C₂×C₄²×C₄₇	—	2	16	no	—
53	C₂×C₄²×C₄₇	—	2	16	no	—
54	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
56	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₄₇	D₄	1	8	yes	—
59	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
60	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
61	C₂⁴×C₄₇	—	2	2	no	—
62	C₂⁴×C₄₇	—	2	2	no	—
63	C₂⁴×C₄₇	—	2	2	no	—
64	C₂⁴×C₄₇	—	2	2	no	—
65	C₂⁴×C₄₇	C₄⋊C₄	1	4	yes	—
66	C₂⁴×C₄₇	C₂×C₈	1	4	yes	—
67	C₂⁴×C₄₇	M₁₆	1	4	yes	—
68	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
69	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	—	2	32	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	8	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	32	no	—
81	C₂²×C₄×C₄₇	—	2	8	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	8	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	16	no	—
86	C₂²×C₄×C₄₇	—	2	16	no	—
87	C₂²×C₄×C₄₇	—	2	8	no	—
88	C₂²×C₄×C₄₇	—	2	8	no	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
93	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
94	C₂²×C₄×C₄₇	C₄⋊C₄	1	8	yes	—
95	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂×C₈	1	16	yes	complemented
98	C₂²×C₄×C₄₇	M₁₆	1	4	yes	—
99	C₂²×C₄×C₄₇	M₁₆	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₄₇	#41	1	4	yes	—
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₄²×C₄₇	—	2	8	no	—
114	C₄²×C₄₇	—	2	4	no	—
115	C₄²×C₄₇	—	2	8	no	—
116	C₄²×C₄₇	—	2	4	no	—
117	C₄²×C₄₇	C₂²⋊C₄	1	8	yes	—
118	C₄²×C₄₇	C₂×D₄	1	8	yes	—
119	C₂×C₄₇⋊C₈	—	2	8	no	—
120	C₂×C₄₇⋊C₈	—	2	8	no	—
121	C₂×C₄₇⋊C₈	—	2	8	no	—
122	C₂×C₄₇⋊C₈	—	4	16	no	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	8	no	—
128	C₂³×C₄₇	—	2	8	no	—
129	C₂³×C₄₇	—	2	8	no	—
130	C₂³×C₄₇	—	2	8	no	—
131	C₂³×C₄₇	—	2	8	no	—
132	C₂³×C₄₇	—	2	8	no	—
133	C₂³×C₄₇	C₄⋊C₈	1	16	yes	complemented
134	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
135	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
136	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
137	C₂³×C₄₇	#117	1	2	yes	—
138	C₂³×C₄₇	C₂²×C₈	1	4	yes	—
139	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
140	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
141	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
142	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
143	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
144	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	—	2	32	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	8	no	—
155	C₂×C₄×C₄₇	—	2	8	no	—
156	C₂×C₄×C₄₇	—	2	8	no	—
157	C₂×C₄×C₄₇	—	2	8	no	—
158	C₂×C₄×C₄₇	—	2	8	no	—
159	C₂×C₄×C₄₇	—	2	8	no	—
160	C₂×C₄×C₄₇	—	2	16	no	—
161	C₂×C₄×C₄₇	—	2	32	no	—
162	C₂×C₄×C₄₇	C₂²⋊C₈	1	16	yes	complemented
163	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
166	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
167	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₇	#117	1	2	yes	—
169	C₂×C₄×C₄₇	#121	1	8	yes	—
170	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
171	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
172	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
173	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
174	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
175	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
179	C₄₇⋊C₈	—	4	8	no	—
180	C₂×#1797	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	—	2	32	no	—
182	C₂²×C₄₇	—	2	4	no	—
183	C₂²×C₄₇	—	2	4	no	—
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	—	2	4	no	—
187	C₂²×C₄₇	—	2	4	no	—
188	C₂²×C₄₇	#380	1	4	yes	—
189	C₂²×C₄₇	C₂×C₂²⋊C₈	1	4	yes	—
190	C₂²×C₄₇	#407	1	4	yes	—
191	C₂²×C₄₇	C₂×C₄⋊C₈	1	4	yes	—
192	C₂²×C₄₇	C₂×C₄⋊C₈	1	8	yes	complemented
193	C₂²×C₄₇	#423	1	4	yes	—
194	C₂²×C₄₇	#431	1	4	yes	—
195	C₂²×C₄₇	#432	1	4	yes	—
196	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
199	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
200	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
201	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
202	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
203	C₄×C₄₇	—	2	4	no	—
204	C₄×C₄₇	—	2	4	no	—
205	C₄×C₄₇	—	2	4	no	—
206	C₄×C₄₇	—	2	4	no	—
207	C₄×C₄₇	#380	1	4	yes	—
208	C₄×C₄₇	C₂×C₂²⋊C₈	1	8	yes	complemented
209	C₄×C₄₇	C₂×#121	1	2	yes	—
210	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
211	C₂³×C₄²	D₄₇	1	1	yes	characteristic
212	C₂²×C₄⋊C₈	—	47	2	no	—
213	C₂²×C₂²⋊C₈	—	47	2	no	—
214	#1797	—	47	8	no	—
215	C₂×#336	—	47	2	no	—
216	C₂×C₄₇	—	2	8	no	—
217	C₂×C₄₇	#1797	1	8	yes	complemented
218	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
219	C₂×C₄₇	C₂²×C₂²⋊C₈	1	1	yes	characteristic
220	C₂×C₄₇	C₂×#407	1	1	yes	characteristic
221	C₂×C₄₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
222	C₂×C₄₇	C₂×#423	1	1	yes	characteristic
223	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
224	C₂×C₄₇	C₂×#432	1	1	yes	characteristic
225	C₂⁴×C₄	Dic₄₇	1	1	yes	characteristic
226	C₂⁴×C₄	Dic₄₇	1	1	yes	characteristic
227	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
228	C₂³×C₈	—	47	4	no	—
229	C₂²×C₄²	—	2	8	no	—
230	C₂²×C₄²	Dic₄₇	1	1	yes	characteristic
231	C₂²×C₄²	Dic₄₇	1	1	yes	characteristic
232	C₂²×C₄²	Dic₄₇	1	4	yes	—
233	C₂²×C₄²	C₂×D₄₇	1	4	yes	—
234	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
235	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
236	C₂×C₄⋊C₈	—	47	8	no	—
237	C₂×C₄⋊C₈	—	94	8	no	—
238	C₂×C₂²⋊C₈	—	47	8	no	—
239	C₂×C₂²⋊C₈	—	94	8	no	—
240	#336	—	47	8	no	—
241	C₄₇	C₂×#1797	1	1	yes	characteristic, complemented, Sylow
242	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
243	C₂³×C₄	—	2	4	no	—
244	C₂³×C₄	—	2	4	no	—
245	C₂³×C₄	—	2	4	no	—
246	C₂³×C₄	—	2	4	no	—
247	C₂³×C₄	—	2	4	no	—
248	C₂³×C₄	—	2	4	no	—
249	C₂³×C₄	—	2	4	no	—
250	C₂³×C₄	C₄₇⋊C₈	1	8	yes	complemented
251	C₂³×C₄	Dic₉₄	1	4	yes	—
252	C₂³×C₄	D₁₈₈	1	4	yes	—
253	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
254	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
255	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
256	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
257	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
258	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
259	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
260	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
261	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
262	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
263	C₂²×C₈	—	47	8	no	—
264	C₂²×C₈	—	94	8	no	—
265	C₂²×C₈	—	94	8	no	—
266	C₂²×C₈	—	94	8	no	—
267	C₂×C₄²	—	2	4	no	—
268	C₂×C₄²	—	2	4	no	—
269	C₂×C₄²	—	2	4	no	—
270	C₂×C₄²	—	2	16	no	—
271	C₂×C₄²	—	2	16	no	—
272	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
273	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
274	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
275	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
276	C₂×C₄²	C₂²⋊D₄₇	1	8	yes	—
277	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
278	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
279	C₄⋊C₈	—	94	16	no	—
280	C₂²⋊C₈	—	94	16	no	—
281	C₂⁴	—	2	2	no	—
282	C₂⁴	—	2	2	no	—
283	C₂⁴	—	2	2	no	—
284	C₂⁴	—	2	2	no	—
285	C₂⁴	C₂×C₄₇⋊C₈	1	4	yes	—
286	C₂⁴	#10625329	1	4	yes	—
287	C₂⁴	C₄⋊Dic₄₇	1	4	yes	—
288	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
289	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
290	C₂²×C₄	—	2	32	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	32	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	16	no	—
306	C₂²×C₄	—	2	16	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	C₂×C₄₇⋊C₈	1	4	yes	—
312	C₂²×C₄	C₂×C₄₇⋊C₈	1	4	yes	—
313	C₂²×C₄	C₂×C₄₇⋊C₈	1	16	yes	complemented
314	C₂²×C₄	#10625329	1	4	yes	—
315	C₂²×C₄	#10625329	1	4	yes	—
316	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
317	C₂²×C₄	C₄⋊Dic₄₇	1	8	yes	—
318	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
319	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
320	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
321	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
322	C₂²×C₄	C₂×D₁₈₈	1	4	yes	—
323	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
324	C₂²×C₄	#10625350	1	4	yes	—
325	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
326	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
327	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
328	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
329	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
331	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	C₂×C₈	—	94	8	no	—
334	C₂×C₈	—	94	8	no	—
335	C₂×C₈	—	94	8	no	—
336	C₂×C₈	—	188	16	no	—
337	C₄²	—	2	8	no	—
338	C₄²	—	2	4	no	—
339	C₄²	—	2	8	no	—
340	C₄²	—	2	4	no	—
341	C₄²	C₂²⋊Dic₄₇	1	8	yes	—
342	C₄²	C₂×C₂²⋊D₄₇	1	8	yes	—
343	C₂³	—	2	8	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	8	no	—
347	C₂³	—	2	8	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	8	no	—
351	C₂³	—	2	8	no	—
352	C₂³	—	2	8	no	—
353	C₂³	C₄⋊(C₄₇⋊C₈)	1	16	yes	complemented
354	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
355	C₂³	C₂×C₄⋊Dic₄₇	1	4	yes	—
356	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
357	C₂³	#13093983	1	2	yes	—
358	C₂³	C₂²×C₄₇⋊C₈	1	4	yes	—
359	C₂³	C₂²×C₄₇⋊C₈	1	2	yes	—
360	C₂³	C₂×#10625329	1	4	yes	—
361	C₂³	C₂×#10625329	1	2	yes	—
362	C₂³	C₂×#10625329	1	2	yes	—
363	C₂³	C₂×#10625329	1	2	yes	—
364	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
365	C₂×C₄	—	2	32	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	16	no	—
379	C₂×C₄	—	2	32	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	16	yes	complemented
383	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
384	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
385	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
386	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
387	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
388	C₂×C₄	#13093983	1	2	yes	—
389	C₂×C₄	#13093998	1	8	yes	—
390	C₂×C₄	#13094003	1	8	yes	—
391	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
392	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
393	C₂×C₄	C₂×#10625329	1	4	yes	—
394	C₂×C₄	C₂×#10625329	1	4	yes	—
395	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
396	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
397	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
398	C₂×C₄	C₂×#10625350	1	2	yes	—
399	C₈	—	188	8	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	32	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	#15688983	1	4	yes	—
408	C₂²	C₂×C₂²⋊(C₄₇⋊C₈)	1	4	yes	—
409	C₂²	#15689087	1	4	yes	—
410	C₂²	C₂×C₄⋊(C₄₇⋊C₈)	1	4	yes	—
411	C₂²	C₂×C₄⋊(C₄₇⋊C₈)	1	8	yes	complemented
412	C₂²	#15689147	1	4	yes	—
413	C₂²	#15689176	1	4	yes	—
414	C₂²	#15689180	1	4	yes	—
415	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
416	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
417	C₂²	C₂×#13093983	1	1	yes	characteristic
418	C₂²	C₂³×C₄₇⋊C₈	1	1	yes	characteristic
419	C₂²	C₂²×#10625329	1	1	yes	characteristic
420	C₂²	C₂²×#10625329	1	1	yes	characteristic
421	C₂²	C₂²×#10625329	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	4	no	—
426	C₄	#15688983	1	4	yes	—
427	C₄	C₂×C₂²⋊(C₄₇⋊C₈)	1	8	yes	complemented
428	C₄	C₂×#13093998	1	2	yes	—
429	C₄	C₂×#13094003	1	2	yes	—
430	C₂	—	2	8	no	—
431	C₂	#20243368	1	8	yes	direct product factor
432	C₂	C₂×#15688983	1	1	yes	characteristic
433	C₂	C₂²×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
434	C₂	C₂×#15689087	1	1	yes	characteristic
435	C₂	C₂²×C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
436	C₂	C₂×#15689147	1	1	yes	characteristic
437	C₂	C₂×#15689176	1	1	yes	characteristic
438	C₂	C₂×#15689180	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂³×C₄²×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂²×C₄
prime radical	C₂⁵×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂³×C₄²	D₄₇
hypocenter	C₄₇	C₂×#1797
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
3. #20243368	C₂	direct (N × H)
4. C₂×#15688878	C₂	semidirect
8. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
11. #15688878	C₂²	semidirect
36. C₂³×C₄×C₄₇	C₈	semidirect
97. C₂²×C₄×C₄₇	C₂×C₈	semidirect
133. C₂³×C₄₇	C₄⋊C₈	semidirect
162. C₂×C₄×C₄₇	C₂²⋊C₈	semidirect
192. C₂²×C₄₇	C₂×C₄⋊C₈	semidirect
208. C₄×C₄₇	C₂×C₂²⋊C₈	semidirect
217. C₂×C₄₇	#1797	semidirect
241. C₄₇	C₂×#1797	semidirect
250. C₂³×C₄	C₄₇⋊C₈	semidirect
313. C₂²×C₄	C₂×C₄₇⋊C₈	semidirect
353. C₂³	C₄⋊(C₄₇⋊C₈)	semidirect
382. C₂×C₄	C₂²⋊(C₄₇⋊C₈)	semidirect
411. C₂²	C₂×C₄⋊(C₄₇⋊C₈)	semidirect
427. C₄	C₂×C₂²⋊(C₄₇⋊C₈)	semidirect
431. C₂	#20243368	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⋊(C₄₇⋊C₈)	2
C₂²×C₂²⋊(C₄₇⋊C₈)	2
#20243368	2
C₂×#15688878	2
C₂³×C₄²×C₄₇	2
C₂×#1797	47

Subgroups — C2×#20243368 #26215632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243368 #26215632