Subgroups — C₂×#20242919 #26198825

Order 12032.

778 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689469	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689413	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689201	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242919	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688875	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688871	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688867	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#459	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	—	2	1	no	—
10	C₂×#13094024	C₂²	1	1	yes	characteristic
11	#15689469	—	2	2	no	—
12	#15689469	C₂²	1	4	yes	complemented
13	#15689413	—	2	2	no	—
14	#15689413	C₂²	1	4	yes	complemented
15	#15689201	—	2	2	no	—
16	#15689201	C₂²	1	4	yes	complemented
17	C₂×#13093955	—	2	1	no	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093945	—	2	1	no	—
21	C₂×#13093945	—	2	1	no	—
22	C₂×#13093945	—	2	1	no	—
23	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15688875	C₂²	1	4	yes	complemented
26	#15688871	C₂²	1	4	yes	complemented
27	#15688867	C₂²	1	4	yes	complemented
28	C₂²×D₈×C₄₇	—	2	1	no	—
29	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#459	—	2	2	no	—
32	C₄₇×#459	C₂²	1	4	yes	—
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#102×C₄₇	—	2	1	no	—
35	C₂²×Dic₉₄	—	2	1	no	—
36	C₂×#10625329	—	2	4	no	—
37	C₂×#10625329	—	4	4	no	—
38	C₂²×C₄₇⋊C₈	—	2	1	no	—
39	C₂²×C₄₇⋊C₈	—	2	1	no	—
40	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
41	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
42	#13094024	—	2	1	no	—
43	#13094024	—	2	1	no	—
44	#13094024	—	2	1	no	—
45	#13094024	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₄₇	—	2	1	no	—
47	C₂×C₄⋊Dic₄₇	—	2	1	no	—
48	#13093955	—	2	4	no	—
49	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
50	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
51	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
52	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
53	#13093945	—	2	4	no	—
54	#13093945	—	2	4	no	—
55	#13093945	—	2	4	no	—
56	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
57	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
58	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
59	C₂²×D₄×C₄₇	—	2	1	no	—
60	C₂²×D₄×C₄₇	—	2	1	no	—
61	C₂²×D₄×C₄₇	—	2	1	no	—
62	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	—	2	1	no	—
64	C₂×D₈×C₄₇	—	2	4	no	—
65	C₂×D₈×C₄₇	—	4	4	no	—
66	C₂²×C₈×C₄₇	—	2	1	no	—
67	#127×C₄₇	—	2	1	no	—
68	#127×C₄₇	—	2	1	no	—
69	#127×C₄₇	—	2	1	no	—
70	#127×C₄₇	C₂³	1	2	yes	—
71	C₄×D₄×C₄₇	—	2	1	no	—
72	C₄×D₄×C₄₇	—	2	1	no	—
73	C₄×D₄×C₄₇	D₄	1	2	yes	—
74	C₄×D₄×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₄₇	—	2	1	no	—
79	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
80	#102×C₄₇	—	2	4	no	—
81	C₂⁴×C₄₇	—	2	1	no	—
82	C₂⁴×C₄₇	—	4	1	no	—
83	C₂×D₄×C₄₇	—	2	1	no	—
84	C₂×D₄×C₄₇	—	2	2	no	—
85	C₂×D₄×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	4	1	no	—
90	C₂×D₄×C₄₇	—	4	1	no	—
91	C₂×D₄×C₄₇	—	4	1	no	—
92	C₂×D₄×C₄₇	—	4	2	no	—
93	C₂×D₄×C₄₇	—	4	2	no	—
94	C₂×D₄×C₄₇	—	4	2	no	—
95	C₂×D₄×C₄₇	—	4	2	no	—
96	C₂×D₄×C₄₇	—	8	2	no	—
97	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	4	2	no	—
102	C₂²×C₄×C₄₇	—	4	2	no	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
106	C₂²×Dic₄₇	—	4	1	no	—
107	C₂×Dic₉₄	—	2	2	no	—
108	C₂×Dic₉₄	—	4	1	no	—
109	C₂×Dic₉₄	—	8	2	no	—
110	D₈×C₄₇	—	4	8	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	4	2	no	—
113	C₄⋊C₄×C₄₇	—	2	1	no	—
114	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
115	C₂²⋊C₄×C₄₇	—	2	2	no	—
116	C₂²⋊C₄×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₄₇	#41	1	1	yes	characteristic
120	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	4	1	no	—
124	C₄⋊Dic₄₇	—	4	1	no	—
125	#10625329	—	4	8	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	4	2	no	—
131	C₂×C₄₇⋊C₈	—	4	2	no	—
132	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
133	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	4	2	no	—
136	C₂³×C₄₇	—	4	2	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	8	2	no	—
140	C₂³×C₄₇	—	8	2	no	—
141	C₂³×C₄₇	—	8	2	no	—
142	C₂³×C₄₇	#121	1	1	yes	characteristic
143	D₄×C₄₇	—	2	2	no	—
144	D₄×C₄₇	—	2	2	no	—
145	D₄×C₄₇	—	4	2	no	—
146	D₄×C₄₇	—	4	2	no	—
147	D₄×C₄₇	—	4	2	no	—
148	D₄×C₄₇	—	4	2	no	—
149	D₄×C₄₇	—	4	2	no	—
150	D₄×C₄₇	—	8	2	no	—
151	D₄×C₄₇	—	8	2	no	—
152	D₄×C₄₇	—	8	2	no	—
153	D₄×C₄₇	—	8	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	4	no	—
160	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₇	#135	1	2	yes	—
164	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₄₇	#137	1	2	yes	—
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	8	2	no	—
172	Dic₉₄	—	8	2	no	—
173	Dic₉₄	—	8	2	no	—
174	C₈×C₄₇	—	4	2	no	—
175	C₄₇⋊C₈	—	2	2	no	—
176	C₄₇⋊C₈	—	2	2	no	—
177	C₄₇⋊C₈	—	4	2	no	—
178	C₄₇⋊C₈	—	4	2	no	—
179	C₂×#1697	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	—	4	2	no	—
181	C₂²×C₄₇	—	4	2	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	8	4	no	—
184	C₂²×C₄₇	—	8	2	no	—
185	C₂²×C₄₇	—	8	2	no	—
186	C₂²×C₄₇	—	8	2	no	—
187	C₂²×C₄₇	—	16	4	no	—
188	C₂²×C₄₇	#463	1	2	yes	—
189	C₂²×C₄₇	#468	1	2	yes	—
190	C₂²×C₄₇	#472	1	2	yes	—
191	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
192	C₄×C₄₇	—	2	1	no	—
193	C₄×C₄₇	—	2	1	no	—
194	C₄×C₄₇	—	4	2	no	—
195	C₄×C₄₇	#463	1	2	yes	—
196	C₄×C₄₇	#468	1	2	yes	—
197	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
198	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
201	Dic₄₇	—	8	2	no	—
202	C₂×#486	—	47	1	no	—
203	C₂×#476	—	47	1	no	—
204	C₂×#459	D₄₇	1	1	yes	characteristic
205	C₂×#436	—	47	1	no	—
206	#1697	—	47	8	no	—
207	C₂×#335	—	47	1	no	—
208	C₂×#333	—	47	1	no	—
209	C₂×#331	—	47	1	no	—
210	C₂×C₄₇	—	8	2	no	—
211	C₂×C₄₇	—	16	2	no	—
212	C₂×C₄₇	#1697	1	4	yes	complemented
213	C₂×C₄₇	C₂×#463	1	1	yes	characteristic
214	C₂×C₄₇	C₂×#468	1	1	yes	characteristic
215	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
216	C₂²×D₈	—	2	1	no	—
217	C₂²×M₁₆	—	94	1	no	—
218	C₂×C₄⋊Q₈	—	47	1	no	—
219	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
221	#486	—	47	4	no	—
222	#486	—	94	2	no	—
223	#476	—	47	4	no	—
224	#476	—	94	2	no	—
225	#459	—	2	2	no	—
226	#459	C₂×D₄₇	1	4	yes	—
227	#436	—	47	4	no	—
228	#436	—	94	2	no	—
229	C₂×#106	—	94	1	no	—
230	C₂×C₄⋊C₈	—	47	1	no	—
231	C₂×C₄⋊C₈	—	47	1	no	—
232	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
233	C₂×#102	—	2	1	no	—
234	C₂×#102	—	94	1	no	—
235	C₂×#102	—	94	1	no	—
236	C₂×#102	—	94	1	no	—
237	C₂×C₂²⋊C₈	—	94	1	no	—
238	C₂×C₄×C₈	—	47	1	no	—
239	#335	—	47	4	no	—
240	#333	—	47	4	no	—
241	#331	—	47	4	no	—
242	C₄₇	C₂×#1697	1	1	yes	characteristic, complemented, Sylow
243	C₂²×Q₈	—	94	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
248	C₂³×C₄	—	2	1	no	—
249	C₂×D₈	—	2	4	no	—
250	C₂×D₈	—	4	4	no	—
251	C₂×M₁₆	—	94	4	no	—
252	C₂×M₁₆	—	188	4	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	47	1	no	—
255	C₂²×C₈	—	47	1	no	—
256	C₂²×C₈	—	94	1	no	—
257	C₂²×C₈	—	94	1	no	—
258	C₄⋊Q₈	—	47	2	no	—
259	C₄⋊Q₈	—	94	1	no	—
260	C₄⋊Q₈	—	94	1	no	—
261	C₄⋊Q₈	—	94	1	no	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#127	—	2	1	no	—
265	#127	C₂²×D₄₇	1	2	yes	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
269	C₄×D₄	C₂²×D₄₇	1	2	yes	—
270	C₂×C₄⋊C₄	—	94	1	no	—
271	C₂×C₄⋊C₄	—	94	1	no	—
272	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	#106	—	94	4	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	47	2	no	—
278	C₄⋊C₈	—	47	2	no	—
279	C₄⋊C₈	—	94	1	no	—
280	C₄⋊C₈	—	94	1	no	—
281	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
282	#102	—	2	4	no	—
283	#102	—	94	4	no	—
284	#102	—	94	4	no	—
285	#102	—	94	4	no	—
286	C₂²⋊C₈	—	94	4	no	—
287	C₄×C₈	—	47	2	no	—
288	C₄×C₈	—	47	2	no	—
289	C₂⁴	—	2	1	no	—
290	C₂⁴	—	4	1	no	—
291	C₂×Q₈	—	94	2	no	—
292	C₂×Q₈	—	376	2	no	—
293	C₂×Q₈	—	188	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	8	2	no	—
308	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	188	1	no	—
315	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
316	C₂²×C₄	#10625352	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
318	D₈	—	4	8	no	—
319	M₁₆	—	188	8	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	47	2	no	—
323	C₂×C₈	—	47	2	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	—	188	2	no	—
329	C₂×C₈	—	188	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	94	2	no	—
332	C₄⋊C₄	—	94	2	no	—
333	C₄⋊C₄	—	188	1	no	—
334	C₄⋊C₄	—	188	1	no	—
335	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₄²	D₄×D₄₇	1	1	yes	characteristic
339	C₄²	#10625352	1	1	yes	characteristic
340	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
341	C₄²	C₂³×D₄₇	1	1	yes	characteristic
342	C₂³	—	2	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	8	2	no	—
348	C₂³	—	8	2	no	—
349	C₂³	—	8	2	no	—
350	C₂³	#13093996	1	1	yes	characteristic
351	Q₈	—	376	2	no	—
352	Q₈	—	376	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	8	2	no	—
363	D₄	—	8	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	376	2	no	—
371	C₂×C₄	—	188	2	no	—
372	C₂×C₄	#13093996	1	1	yes	characteristic
373	C₂×C₄	#13093996	1	1	yes	characteristic
374	C₂×C₄	#13093996	1	1	yes	characteristic
375	C₂×C₄	#13094043	1	2	yes	—
376	C₂×C₄	#13094048	1	2	yes	—
377	C₂×C₄	#13094050	1	2	yes	—
378	C₂×C₄	#13094054	1	2	yes	—
379	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	94	2	no	—
384	C₈	—	94	2	no	—
385	C₈	—	188	2	no	—
386	C₈	—	188	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	8	4	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	16	4	no	—
395	C₂²	#15689336	1	2	yes	—
396	C₂²	#15689367	1	2	yes	—
397	C₂²	#15689391	1	2	yes	—
398	C₂²	C₂×#13093996	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	376	2	no	—
403	C₄	#15689336	1	2	yes	—
404	C₄	#15689367	1	2	yes	—
405	C₄	C₂×#13094043	1	1	yes	characteristic
406	C₄	C₂×#13094048	1	1	yes	characteristic
407	C₄	C₂×#13094050	1	1	yes	characteristic
408	C₄	C₂×#13094054	1	1	yes	characteristic
409	C₂	—	8	2	no	—
410	C₂	—	16	2	no	—
411	C₂	#20242919	1	4	yes	direct product factor
412	C₂	C₂×#15689336	1	1	yes	characteristic
413	C₂	C₂×#15689367	1	1	yes	characteristic
414	C₂	C₂×#15689391	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#459	C₂
socle	C₂³×C₄₇	#121
hypercenter	C₂×#459	D₄₇
hypocenter	C₄₇	C₂×#1697
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#459

Complements

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

N	H ≅ G/N	type
1. C₂×#15689469	C₂	semidirect
2. C₂×#15689413	C₂	semidirect
3. C₂×#15689201	C₂	semidirect
4. #20242919	C₂	direct (N × H)
5. C₂×#15688875	C₂	semidirect
6. C₂×#15688871	C₂	semidirect
7. C₂×#15688867	C₂	semidirect
12. #15689469	C₂²	semidirect
14. #15689413	C₂²	semidirect
16. #15689201	C₂²	semidirect
25. #15688875	C₂²	semidirect
26. #15688871	C₂²	semidirect
27. #15688867	C₂²	semidirect
212. C₂×C₄₇	#1697	semidirect
242. C₄₇	C₂×#1697	semidirect
411. C₂	#20242919	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×#15689469	2
C₂×#15689413	2
C₂×#15689201	2
#20242919	2
C₂×#15688875	2
C₂×#15688871	2
C₂×#15688867	2
C₂×C₄₇×#459	2
C₂×#1697	47

Subgroups — C2×#20242919 #26198825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242919 #26198825