Subgroups — C₂×#20242105 #26184797

Order 12032.

1182 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689180	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689180	C₂	1	1	yes	maximal, characteristic
3	#20242105	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688869	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	#15689180	—	2	2	no	—
7	#15689180	—	2	2	no	—
8	#15689180	C₂²	1	4	yes	—
9	#15689180	C₂²	1	4	yes	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
13	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
14	C₂×#13093935	—	2	1	no	—
15	C₂×#13093935	—	2	1	no	—
16	#15688869	C₂²	1	16	yes	complemented
17	C₂³×Q₈×C₄₇	—	2	1	no	—
18	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
19	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
20	C₂×C₄⋊Q₈×C₄₇	—	2	2	no	—
21	C₂×C₄⋊Q₈×C₄₇	—	2	2	no	—
22	C₂×C₄⋊Q₈×C₄₇	C₄	1	2	yes	—
23	C₂×C₄⋊Q₈×C₄₇	C₄	1	4	yes	—
24	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
25	C₂×C₄⋊Q₈×C₄₇	C₂²	1	4	yes	—
26	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
27	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
33	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
34	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
35	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
36	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
37	#13093935	—	2	4	no	—
38	#13093935	—	2	4	no	—
39	C₂²×Q₈×C₄₇	—	2	4	no	—
40	C₂²×Q₈×C₄₇	—	2	2	no	—
41	C₂²×Q₈×C₄₇	—	2	4	no	—
42	C₂²×Q₈×C₄₇	—	2	2	no	—
43	C₂²×Q₈×C₄₇	—	4	8	no	—
44	C₂³×C₄×C₄₇	—	2	2	no	—
45	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
48	C₄⋊Q₈×C₄₇	—	2	4	no	—
49	C₄⋊Q₈×C₄₇	—	2	4	no	—
50	C₄⋊Q₈×C₄₇	—	2	4	no	—
51	C₄⋊Q₈×C₄₇	—	2	4	no	—
52	C₄⋊Q₈×C₄₇	—	2	4	no	—
53	C₄⋊Q₈×C₄₇	—	2	2	no	—
54	C₄⋊Q₈×C₄₇	—	2	2	no	—
55	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
56	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
57	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
66	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	D₄	1	2	yes	—
71	C₂×C₄²×C₄₇	D₄	1	2	yes	—
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
74	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×Q₈×C₄₇	—	2	8	no	—
76	C₂×Q₈×C₄₇	—	2	4	no	—
77	C₂×Q₈×C₄₇	—	2	4	no	—
78	C₂×Q₈×C₄₇	—	4	8	no	—
79	C₂×Q₈×C₄₇	—	4	16	no	—
80	C₂×Q₈×C₄₇	—	4	16	no	—
81	C₂×Q₈×C₄₇	—	4	8	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	8	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	4	8	no	—
88	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₄⋊C₄×C₄₇	—	2	8	no	—
101	C₄⋊C₄×C₄₇	—	2	4	no	—
102	C₄⋊C₄×C₄₇	—	2	8	no	—
103	C₄⋊C₄×C₄₇	—	2	4	no	—
104	C₄⋊C₄×C₄₇	—	2	4	no	—
105	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
106	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
107	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
108	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
109	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
110	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₄₇	C₂×D₄	1	2	yes	—
112	C₄²×C₄₇	C₂×D₄	1	2	yes	—
113	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₄₇⋊C₈	—	2	4	no	—
117	C₂×C₄₇⋊C₈	—	2	4	no	—
118	C₂×C₄₇⋊C₈	—	4	4	no	—
119	C₂×C₄₇⋊C₈	—	4	4	no	—
120	C₂³×C₄₇	—	2	2	no	—
121	C₂³×C₄₇	—	2	2	no	—
122	C₂³×C₄₇	#101	1	4	yes	—
123	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
124	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	Q₈×C₄₇	—	4	16	no	—
126	Q₈×C₄₇	—	4	8	no	—
127	Q₈×C₄₇	—	4	8	no	—
128	C₂×C₄×C₄₇	—	2	4	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	4	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	8	no	—
139	C₂×C₄×C₄₇	—	4	16	no	—
140	C₂×C₄×C₄₇	—	4	8	no	—
141	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
148	C₂×C₄×C₄₇	#137	1	4	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
152	C₄₇⋊C₈	—	4	4	no	—
153	C₄₇⋊C₈	—	4	4	no	—
154	C₂×#1556	—	47	1	no	maximal, Sylow
155	C₂²×C₄₇	—	2	8	no	—
156	C₂²×C₄₇	—	2	2	no	—
157	C₂²×C₄₇	—	2	2	no	—
158	C₂²×C₄₇	C₂×#101	1	4	yes	—
159	C₂²×C₄₇	C₂×#101	1	2	yes	—
160	C₂²×C₄₇	#418	1	2	yes	—
161	C₂²×C₄₇	#419	1	2	yes	—
162	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
163	C₄×C₄₇	—	2	1	no	—
164	C₄×C₄₇	—	2	2	no	—
165	C₄×C₄₇	—	2	1	no	—
166	C₄×C₄₇	—	2	2	no	—
167	C₄×C₄₇	—	2	2	no	—
168	C₄×C₄₇	—	4	8	no	—
169	C₄×C₄₇	#418	1	2	yes	—
170	C₄×C₄₇	#419	1	2	yes	—
171	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
172	C₄×C₄₇	C₂×#137	1	2	yes	—
173	C₂²×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
174	C₂×#432	—	47	1	no	—
175	C₂×#432	—	47	1	no	—
176	#1556	—	47	8	no	—
177	C₂×#332	—	47	4	no	—
178	C₂×C₄₇	—	2	4	no	—
179	C₂×C₄₇	#1556	1	4	yes	complemented
180	C₂×C₄₇	C₂²×#101	1	1	yes	characteristic
181	C₂×C₄₇	C₂×#418	1	1	yes	characteristic
182	C₂×C₄₇	C₂×#419	1	1	yes	characteristic
183	C₂³×Q₈	—	2	1	no	—
184	C₂×C₄⋊Q₈	—	2	1	no	—
185	C₂×C₄⋊Q₈	—	2	1	no	—
186	C₂×C₄⋊Q₈	—	2	2	no	—
187	C₂×C₄⋊Q₈	—	2	2	no	—
188	C₂×C₄⋊Q₈	Dic₄₇	1	4	yes	—
189	C₂×C₄⋊Q₈	Dic₄₇	1	2	yes	—
190	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
191	C₂×C₄⋊Q₈	C₂×D₄₇	1	4	yes	—
192	C₂²×C₄⋊C₄	—	2	1	no	—
193	C₂²×C₄⋊C₄	Dic₄₇	1	2	yes	—
194	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
195	#432	—	47	4	no	—
196	#432	—	47	4	no	—
197	#432	—	94	2	no	—
198	#432	—	94	2	no	—
199	C₂×C₄⋊C₈	—	47	2	no	—
200	C₂×C₄⋊C₈	—	47	2	no	—
201	C₂×C₂²⋊C₈	—	94	1	no	—
202	C₂×C₂²⋊C₈	—	94	1	no	—
203	C₂×#97	—	94	1	no	—
204	C₂×#97	—	94	1	no	—
205	#332	—	47	16	no	—
206	C₄₇	C₂×#1556	1	1	yes	characteristic, complemented, Sylow
207	C₂²×Q₈	—	2	4	no	—
208	C₂²×Q₈	—	2	2	no	—
209	C₂²×Q₈	—	2	4	no	—
210	C₂²×Q₈	—	2	2	no	—
211	C₂²×Q₈	—	4	8	no	—
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
214	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
215	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
216	C₂²×C₈	—	94	2	no	—
217	C₂²×C₈	—	94	2	no	—
218	C₄⋊Q₈	—	2	4	no	—
219	C₄⋊Q₈	—	2	4	no	—
220	C₄⋊Q₈	—	2	4	no	—
221	C₄⋊Q₈	—	2	4	no	—
222	C₄⋊Q₈	—	2	4	no	—
223	C₄⋊Q₈	—	2	2	no	—
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
226	C₄⋊Q₈	C₂×Dic₄₇	1	8	yes	—
227	C₄⋊Q₈	C₂²×D₄₇	1	4	yes	—
228	C₂×C₄⋊C₄	—	2	4	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
235	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
236	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
237	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
240	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
241	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
242	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
244	C₄⋊C₈	—	47	4	no	—
245	C₄⋊C₈	—	47	4	no	—
246	C₄⋊C₈	—	94	2	no	—
247	C₄⋊C₈	—	94	2	no	—
248	C₂²⋊C₈	—	94	4	no	—
249	C₂²⋊C₈	—	94	4	no	—
250	#97	—	94	4	no	—
251	#97	—	94	4	no	—
252	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
253	C₂×Q₈	—	2	8	no	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	4	8	no	—
257	C₂×Q₈	—	4	16	no	—
258	C₂×Q₈	—	4	16	no	—
259	C₂×Q₈	—	4	8	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	4	8	no	—
266	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
267	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
268	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
269	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
272	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
273	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
275	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
276	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
278	C₂×C₈	—	94	4	no	—
279	C₂×C₈	—	94	4	no	—
280	C₂×C₈	—	188	4	no	—
281	C₂×C₈	—	188	4	no	—
282	C₄⋊C₄	—	2	8	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	8	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
288	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
289	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
290	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
291	C₄²	C₂²×Dic₄₇	1	2	yes	—
292	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
293	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
294	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
295	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
296	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
297	C₄²	C₂³×D₄₇	1	1	yes	characteristic
298	C₂³	—	2	2	no	—
299	C₂³	—	2	2	no	—
300	C₂³	#13093943	1	4	yes	—
301	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
302	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
303	Q₈	—	4	16	no	—
304	Q₈	—	4	8	no	—
305	Q₈	—	4	8	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	4	16	no	—
318	C₂×C₄	—	4	8	no	—
319	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
320	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
321	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
322	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
323	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
324	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
325	C₂×C₄	#13094050	1	4	yes	—
326	C₂×C₄	#13094055	1	4	yes	—
327	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
328	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
330	C₈	—	188	4	no	—
331	C₈	—	188	4	no	—
332	C₂²	—	2	8	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	C₂×#13093943	1	4	yes	—
336	C₂²	C₂×#13093943	1	2	yes	—
337	C₂²	#15689128	1	2	yes	—
338	C₂²	#15689132	1	2	yes	—
339	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
340	C₄	—	2	1	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	4	8	no	—
346	C₄	#15689128	1	2	yes	—
347	C₄	#15689132	1	2	yes	—
348	C₄	C₂×#13094050	1	2	yes	—
349	C₄	C₂×#13094055	1	2	yes	—
350	C₂	—	2	4	no	—
351	C₂	#20242105	1	4	yes	direct product factor
352	C₂	C₂²×#13093943	1	1	yes	characteristic
353	C₂	C₂×#15689128	1	1	yes	characteristic
354	C₂	C₂×#15689132	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂²×C₄⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂²×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	C₂×#1556
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
3. #20242105	C₂	direct (N × H)
4. C₂×#15688869	C₂	semidirect
16. #15688869	C₂²	semidirect
179. C₂×C₄₇	#1556	semidirect
206. C₄₇	C₂×#1556	semidirect
351. C₂	#20242105	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#15689180	2
#20242105	2
C₂×#15688869	2
C₂²×C₄⋊Q₈×C₄₇	2
C₂×#1556	47

Subgroups — C2×#20242105 #26184797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242105 #26184797