Subgroups — C₂×#20245462 #26370656

Order 12032.

790 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689240	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245462	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688943	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688937	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
10	C₂²×#10625334	—	2	1	no	—
11	C₂×#13094031	—	2	1	no	—
12	C₂×#13094020	—	2	1	no	—
13	#15689558	—	2	2	no	—
14	#15689558	C₂²	1	4	yes	complemented
15	C₂×#13093967	—	2	1	no	—
16	C₂×#13093965	—	2	1	no	—
17	C₂×#13093964	C₂²	1	1	yes	characteristic
18	#15689498	—	2	2	no	—
19	#15689498	C₂²	1	4	yes	complemented
20	#15689240	—	2	2	no	—
21	#15689240	C₂²	1	4	yes	complemented
22	C₂×#13093960	C₂²	1	1	yes	characteristic
23	C₂×#13093951	—	2	1	no	—
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	#15688943	C₂²	1	4	yes	complemented
26	#15688937	C₂²	1	4	yes	complemented
27	#15688936	C₂²	1	4	yes	complemented
28	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#509	—	2	2	no	—
31	C₄₇×#509	C₂²	1	4	yes	complemented
32	C₂×SD₃₂×C₄₇	—	2	1	no	—
33	C₂×D₁₆×C₄₇	—	2	1	no	—
34	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×D₁₈₈	—	2	1	no	—
36	C₂²×C₂²⋊D₄₇	—	4	2	no	—
37	C₂×D₃₇₆	—	2	1	no	—
38	C₂×D₃₇₆	—	2	1	no	—
39	C₂×D₃₇₆	—	2	1	no	—
40	C₂×D₃₇₆	—	2	1	no	—
41	C₂×D₃₇₆	—	2	1	no	—
42	C₂×D₃₇₆	C₂³	1	2	yes	—
43	C₂×#10625334	—	2	4	no	—
44	C₂×#10625334	—	4	1	no	—
45	C₂×#10625334	—	4	1	no	—
46	C₂×#10625334	—	4	2	no	—
47	#13094031	—	2	4	no	—
48	#13094031	—	4	2	no	—
49	C₂×#10625329	—	2	1	no	—
50	C₂×#10625329	—	4	1	no	—
51	C₂²×C₄₇⋊C₈	—	4	1	no	—
52	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
53	#13094020	—	2	4	no	—
54	#13094020	—	4	2	no	—
55	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
56	#13093967	—	2	4	no	—
57	#13093965	—	2	4	no	—
58	#13093964	—	2	1	no	—
59	#13093964	C₂³	1	2	yes	—
60	C₂×C₄₇⋊C₁₆	—	2	1	no	—
61	#13093960	—	2	1	no	—
62	#13093960	C₂³	1	2	yes	—
63	#13093951	—	2	4	no	—
64	C₈×Dic₄₇	D₄	1	2	yes	—
65	C₈×Dic₄₇	C₂³	1	2	yes	—
66	C₂×#41×C₄₇	—	2	1	no	—
67	C₂²×D₄×C₄₇	—	2	1	no	—
68	#135×C₄₇	—	2	1	no	—
69	#135×C₄₇	—	2	1	no	—
70	#135×C₄₇	D₄	1	2	yes	complemented
71	#135×C₄₇	C₂³	1	2	yes	—
72	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic, complemented
73	C₂×SD₁₆×C₄₇	—	2	1	no	—
74	C₂×D₈×C₄₇	—	2	1	no	—
75	C₂×D₈×C₄₇	—	2	1	no	—
76	C₂×D₈×C₄₇	—	2	1	no	—
77	C₂×D₈×C₄₇	—	2	1	no	—
78	C₂×D₈×C₄₇	—	2	1	no	—
79	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic, complemented
80	C₂×D₈×C₄₇	C₂³	1	2	yes	—
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	SD₃₂×C₄₇	—	2	4	no	—
83	D₁₆×C₄₇	—	2	4	no	—
84	M₃₂×C₄₇	—	2	1	no	—
85	M₃₂×C₄₇	C₂³	1	2	yes	—
86	C₂×C₁₆×C₄₇	—	2	1	no	—
87	C₂⁴×C₄₇	—	4	1	no	—
88	C₂³×D₄₇	—	4	1	no	—
89	#41×C₄₇	—	2	2	no	—
90	#41×C₄₇	—	2	2	no	—
91	#41×C₄₇	—	4	1	no	—
92	#41×C₄₇	—	4	1	no	—
93	C₂×Q₈×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	—	2	1	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	4	1	no	—
97	C₂×D₄×C₄₇	—	4	1	no	—
98	C₂×D₄×C₄₇	—	4	1	no	—
99	C₂×D₄×C₄₇	—	4	1	no	—
100	C₂×D₄×C₄₇	—	4	1	no	—
101	C₂×D₄×C₄₇	—	4	1	no	—
102	C₂²×C₄×C₄₇	—	4	1	no	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₂²⋊D₄₇	—	4	8	no	—
105	C₂×C₂²⋊D₄₇	—	8	8	no	—
106	C₂²×Dic₄₇	—	2	1	no	—
107	C₂×D₁₈₈	—	2	2	no	—
108	C₂×D₁₈₈	—	4	1	no	—
109	C₂×D₁₈₈	—	4	1	no	—
110	C₂×D₁₈₈	—	4	1	no	—
111	C₂×D₁₈₈	—	4	1	no	—
112	C₂×D₁₈₈	—	4	1	no	—
113	Q₁₆×C₄₇	—	2	1	no	—
114	Q₁₆×C₄₇	C₂×D₄	1	2	yes	complemented
115	SD₁₆×C₄₇	—	2	2	no	—
116	SD₁₆×C₄₇	—	2	2	no	—
117	D₈×C₄₇	—	2	1	no	—
118	D₈×C₄₇	—	2	2	no	—
119	D₈×C₄₇	—	2	2	no	—
120	D₈×C₄₇	—	4	1	no	—
121	D₈×C₄₇	—	4	1	no	—
122	D₈×C₄₇	C₂×D₄	1	2	yes	complemented
123	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
127	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
129	#10625334	—	4	4	no	—
130	#10625334	—	4	4	no	—
131	C₄×Dic₄₇	—	2	1	no	—
132	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
133	#10625329	—	2	2	no	—
134	#10625329	—	4	1	no	—
135	#10625329	—	4	4	no	—
136	C₂×C₄₇⋊C₈	—	4	1	no	—
137	C₂×C₄₇⋊C₈	—	4	4	no	—
138	C₂×C₄₇⋊C₈	D₈	1	1	yes	characteristic
139	C₂×C₄₇⋊C₈	D₈	1	1	yes	characteristic
140	C₂×C₄₇⋊C₈	D₈	1	2	yes	—
141	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
142	D₃₇₆	—	2	2	no	—
143	D₃₇₆	—	2	2	no	—
144	D₃₇₆	—	4	1	no	—
145	D₃₇₆	—	4	1	no	—
146	C₁₆×C₄₇	—	2	2	no	—
147	C₄₇⋊C₁₆	—	2	2	no	—
148	C₂³×C₄₇	—	4	1	no	—
149	C₂³×C₄₇	—	4	2	no	—
150	C₂³×C₄₇	—	8	4	no	—
151	C₂³×C₄₇	—	8	1	no	—
152	C₂³×C₄₇	—	8	1	no	—
153	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂²×D₄₇	—	4	2	no	—
155	C₂²×D₄₇	—	8	4	no	—
156	C₂²×D₄₇	—	8	1	no	—
157	C₂²×D₄₇	—	8	1	no	—
158	Q₈×C₄₇	—	2	2	no	—
159	Q₈×C₄₇	—	4	1	no	—
160	D₄×C₄₇	—	2	2	no	—
161	D₄×C₄₇	—	4	2	no	—
162	D₄×C₄₇	—	4	2	no	—
163	D₄×C₄₇	—	4	2	no	—
164	D₄×C₄₇	—	4	2	no	—
165	D₄×C₄₇	—	4	1	no	—
166	D₄×C₄₇	—	8	1	no	—
167	D₄×C₄₇	—	8	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂²⋊D₄₇	—	8	16	no	—
178	C₂×Dic₄₇	—	2	4	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	D₁₈₈	—	4	2	no	—
181	D₁₈₈	—	4	2	no	—
182	D₁₈₈	—	8	1	no	—
183	D₁₈₈	—	8	1	no	—
184	C₈×C₄₇	#121	1	1	yes	characteristic
185	C₈×C₄₇	#121	1	1	yes	characteristic
186	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
188	C₄₇⋊C₈	—	4	2	no	—
189	C₄₇⋊C₈	C₂×D₈	1	2	yes	—
190	C₄₇⋊C₈	C₂×D₈	1	2	yes	—
191	C₂×#2213	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	2	2	no	—
193	C₂²×C₄₇	—	4	2	no	—
194	C₂²×C₄₇	—	8	4	no	—
195	C₂²×C₄₇	—	8	2	no	—
196	C₂²×C₄₇	—	8	2	no	—
197	C₂²×C₄₇	—	16	2	no	—
198	C₂²×C₄₇	—	16	2	no	—
199	C₂²×C₄₇	#459	1	1	yes	characteristic
200	C₂²×C₄₇	#459	1	1	yes	characteristic
201	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂×D₄₇	—	8	4	no	—
203	C₂×D₄₇	—	8	2	no	—
204	C₂×D₄₇	—	16	2	no	—
205	C₂×D₄₇	—	16	2	no	—
206	C₄×C₄₇	—	4	2	no	—
207	C₄×C₄₇	#459	1	1	yes	characteristic
208	C₄×C₄₇	#459	1	1	yes	characteristic
209	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
210	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
211	Dic₄₇	—	2	4	no	—
212	C₂×#509	—	47	1	no	—
213	C₂×#509	D₄₇	1	1	yes	characteristic, complemented
214	C₂×#493	—	47	1	no	—
215	C₂×#443	—	47	1	no	—
216	#2213	—	47	8	no	—
217	C₂×#364	—	47	1	no	—
218	C₂×#361	—	47	1	no	—
219	C₂×#361	—	47	1	no	—
220	C₂×C₄₇	—	2	1	no	—
221	C₂×C₄₇	—	2	1	no	—
222	C₂×C₄₇	—	8	2	no	—
223	C₂×C₄₇	—	16	2	no	—
224	C₂×C₄₇	#2213	1	2	yes	complemented
225	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
226	D₄₇	—	16	2	no	—
227	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
228	C₂²×D₈	—	47	1	no	—
229	C₂²×D₈	—	94	1	no	—
230	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
231	C₂×#131	—	94	1	no	—
232	C₂×#127	—	94	1	no	—
233	#509	—	2	2	no	—
234	#509	—	47	4	no	—
235	#509	—	94	2	no	—
236	#509	C₂×D₄₇	1	4	yes	complemented
237	C₂×SD₃₂	—	2	1	no	—
238	C₂×SD₃₂	—	94	1	no	—
239	C₂×D₁₆	—	2	1	no	—
240	C₂×D₁₆	—	94	1	no	—
241	C₂×M₃₂	—	47	1	no	—
242	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
243	#493	—	47	4	no	—
244	#493	—	94	2	no	—
245	#443	—	47	4	no	—
246	#443	—	94	2	no	—
247	C₂×#108	—	47	1	no	—
248	C₂×#104	—	94	1	no	—
249	C₂×C₄×C₈	—	47	1	no	—
250	#364	—	47	4	no	—
251	#361	—	47	4	no	—
252	#361	—	47	4	no	—
253	C₄₇	C₂×#2213	1	1	yes	characteristic, complemented, Sylow
254	C₂×#41	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	94	1	no	—
257	C₂²×D₄	—	188	2	no	—
258	#135	—	2	1	no	—
259	#135	—	2	1	no	—
260	#135	C₂²⋊D₄₇	1	2	yes	complemented
261	#135	C₂²×D₄₇	1	2	yes	—
262	C₂×Q₁₆	C₂²⋊D₄₇	1	1	yes	characteristic, complemented
263	C₂×SD₁₆	—	2	1	no	—
264	C₂×D₈	—	2	1	no	—
265	C₂×D₈	—	2	1	no	—
266	C₂×D₈	—	2	1	no	—
267	C₂×D₈	—	2	1	no	—
268	C₂×D₈	—	2	1	no	—
269	C₂×D₈	—	47	2	no	—
270	C₂×D₈	—	94	4	no	—
271	C₂×D₈	—	94	1	no	—
272	C₂×D₈	—	94	1	no	—
273	C₂×D₈	—	94	1	no	—
274	C₂×D₈	—	94	1	no	—
275	C₂×D₈	—	94	1	no	—
276	C₂×D₈	—	188	1	no	—
277	C₂×D₈	—	188	1	no	—
278	C₂×D₈	—	188	2	no	—
279	C₂×D₈	C₂²⋊D₄₇	1	1	yes	characteristic, complemented
280	C₂×D₈	C₂²×D₄₇	1	2	yes	—
281	#131	—	94	4	no	—
282	#131	—	188	2	no	—
283	C₂×M₁₆	—	94	1	no	—
284	C₂×M₁₆	—	188	1	no	—
285	C₂²×C₈	—	47	1	no	—
286	C₂²×C₈	—	188	1	no	—
287	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
288	#127	—	94	4	no	—
289	#127	—	188	2	no	—
290	C₂×C₄²	—	47	1	no	—
291	SD₃₂	—	2	4	no	—
292	SD₃₂	—	94	4	no	—
293	D₁₆	—	2	4	no	—
294	D₁₆	—	94	4	no	—
295	M₃₂	—	2	1	no	—
296	M₃₂	—	47	2	no	—
297	M₃₂	—	94	1	no	—
298	M₃₂	C₂²×D₄₇	1	2	yes	—
299	C₂×C₁₆	—	2	1	no	—
300	C₂×C₁₆	—	94	1	no	—
301	#108	—	47	2	no	—
302	#108	—	94	1	no	—
303	#104	—	94	4	no	—
304	C₄×C₈	—	47	2	no	—
305	C₄×C₈	—	47	2	no	—
306	C₂⁴	—	4	1	no	—
307	C₂⁴	—	188	1	no	—
308	#41	—	2	2	no	—
309	#41	—	2	2	no	—
310	#41	—	4	1	no	—
311	#41	—	4	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	94	2	no	—
322	C₂×D₄	—	376	8	no	—
323	C₂×D₄	—	188	8	no	—
324	C₂×D₄	—	188	1	no	—
325	C₂×D₄	—	188	1	no	—
326	C₂×D₄	—	188	1	no	—
327	C₂×D₄	—	188	1	no	—
328	C₂×D₄	—	188	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	94	1	no	—
331	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
332	Q₁₆	—	2	1	no	—
333	Q₁₆	C₂×C₂²⋊D₄₇	1	2	yes	complemented
334	SD₁₆	—	2	2	no	—
335	SD₁₆	—	2	2	no	—
336	D₈	—	2	1	no	—
337	D₈	—	2	2	no	—
338	D₈	—	2	2	no	—
339	D₈	—	4	1	no	—
340	D₈	—	4	1	no	—
341	D₈	—	94	2	no	—
342	D₈	—	94	2	no	—
343	D₈	—	188	4	no	—
344	D₈	—	188	4	no	—
345	D₈	—	188	1	no	—
346	D₈	—	188	1	no	—
347	D₈	C₂×C₂²⋊D₄₇	1	2	yes	complemented
348	M₁₆	—	94	2	no	—
349	M₁₆	—	188	4	no	—
350	M₁₆	—	188	1	no	—
351	C₂×C₈	—	47	1	no	—
352	C₂×C₈	—	47	1	no	—
353	C₂×C₈	—	47	2	no	—
354	C₂×C₈	—	47	2	no	—
355	C₂×C₈	—	188	4	no	—
356	C₂×C₈	—	188	1	no	—
357	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
358	C₂×C₈	#10625352	1	1	yes	characteristic
359	C₂×C₈	#10625352	1	1	yes	characteristic
360	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
362	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
363	C₄²	—	47	2	no	—
364	C₄²	—	94	1	no	—
365	C₁₆	—	2	2	no	—
366	C₁₆	—	94	2	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	8	4	no	—
370	C₂³	—	8	1	no	—
371	C₂³	—	8	1	no	—
372	C₂³	—	376	4	no	—
373	C₂³	—	376	1	no	—
374	C₂³	—	376	1	no	—
375	C₂³	—	188	2	no	—
376	C₂³	#13094048	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	4	1	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	1	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	8	1	no	—
386	D₄	—	8	1	no	—
387	D₄	—	376	16	no	—
388	D₄	—	376	1	no	—
389	D₄	—	376	1	no	—
390	D₄	—	188	2	no	—
391	D₄	—	188	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	94	4	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	#13093996	1	1	yes	characteristic
398	C₂×C₄	#13093996	1	1	yes	characteristic
399	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
400	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
401	C₂×C₄	#13094048	1	1	yes	characteristic
402	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
403	C₈	—	47	2	no	—
404	C₈	—	47	2	no	—
405	C₈	—	188	2	no	—
406	C₈	#13093996	1	1	yes	characteristic
407	C₈	#13093996	1	1	yes	characteristic
408	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
409	C₈	C₂×#10625352	1	1	yes	characteristic
410	C₂²	—	2	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	8	4	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	16	2	no	—
416	C₂²	—	16	2	no	—
417	C₂²	—	376	4	no	—
418	C₂²	—	376	2	no	—
419	C₂²	—	752	2	no	—
420	C₂²	—	752	2	no	—
421	C₂²	#15689316	1	1	yes	characteristic
422	C₂²	#15689316	1	1	yes	characteristic
423	C₂²	C₂×#13094048	1	1	yes	characteristic
424	C₄	—	4	2	no	—
425	C₄	—	94	4	no	—
426	C₄	#15689316	1	1	yes	characteristic
427	C₄	#15689316	1	1	yes	characteristic
428	C₄	C₂×#13093996	1	1	yes	characteristic
429	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	8	2	no	—
433	C₂	—	16	2	no	—
434	C₂	—	752	2	no	—
435	C₂	#20245462	1	2	yes	direct product factor
436	C₂	C₂×#15689316	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15689316
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₂×C₄₇×#509	C₂
socle	C₂²×C₄₇	#459
hypercenter	C₂×#509	D₄₇
hypocenter	C₄₇	C₂×#2213
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#509

Complements

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

N	H ≅ G/N	type
1. C₂×#15689558	C₂	semidirect
2. C₂×#15689498	C₂	semidirect
3. C₂×#15689240	C₂	semidirect
4. #20245462	C₂	direct (N × H)
5. C₂×#15688943	C₂	semidirect
6. C₂×#15688937	C₂	semidirect
7. C₂×#15688936	C₂	semidirect
8. C₂×C₄₇×#509	C₂	semidirect
14. #15689558	C₂²	semidirect
19. #15689498	C₂²	semidirect
21. #15689240	C₂²	semidirect
25. #15688943	C₂²	semidirect
26. #15688937	C₂²	semidirect
27. #15688936	C₂²	semidirect
31. C₄₇×#509	C₂²	semidirect
70. #135×C₄₇	D₄	semidirect
72. C₂×Q₁₆×C₄₇	D₄	semidirect
79. C₂×D₈×C₄₇	D₄	semidirect
114. Q₁₆×C₄₇	C₂×D₄	semidirect
122. D₈×C₄₇	C₂×D₄	semidirect
213. C₂×#509	D₄₇	semidirect
224. C₂×C₄₇	#2213	semidirect
236. #509	C₂×D₄₇	semidirect
253. C₄₇	C₂×#2213	semidirect
260. #135	C₂²⋊D₄₇	semidirect
262. C₂×Q₁₆	C₂²⋊D₄₇	semidirect
279. C₂×D₈	C₂²⋊D₄₇	semidirect
333. Q₁₆	C₂×C₂²⋊D₄₇	semidirect
347. D₈	C₂×C₂²⋊D₄₇	semidirect
435. C₂	#20245462	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×#15689558	2
C₂×#15689498	2
C₂×#15689240	2
#20245462	2
C₂×#15688943	2
C₂×#15688937	2
C₂×#15688936	2
C₂×C₄₇×#509	2
C₂×#2213	47

Subgroups — C2×#20245462 #26370656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245462 #26370656