Subgroups — #27092517

Order 12032.

2620 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258157	C₂	1	4	yes	maximal, complemented
2	#20255192	C₂	1	2	yes	maximal, complemented
3	#20255187	C₂	1	2	yes	maximal, complemented
4	#20255181	C₂	1	4	yes	maximal, complemented
5	#20255173	C₂	1	8	yes	maximal, complemented
6	#20253104	C₂	1	4	yes	maximal, complemented
7	#20252736	C₂	1	4	yes	maximal, complemented
8	C₂×#15689241	C₂	1	2	yes	maximal, complemented
9	C₄₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689959	C₂²	1	4	yes	complemented
11	#15689937	—	2	4	no	—
12	#15689936	C₂²	1	8	yes	complemented
13	#15689930	—	2	8	no	—
14	#15689929	C₂²	1	16	yes	complemented
15	#15689925	—	2	4	no	—
16	#15689924	C₂²	1	8	yes	complemented
17	#15689921	C₂²	1	8	yes	complemented
18	#15689920	—	2	8	no	—
19	C₂×#13094046	C₂²	1	2	yes	—
20	#135×D₄₇	—	2	8	no	—
21	C₂×#13094030	C₂²	1	4	yes	complemented
22	#15689395	C₂²	1	8	yes	complemented
23	#15689390	C₂²	1	8	yes	complemented
24	#15689383	C₂²	1	16	yes	complemented
25	#15689305	C₂²	1	8	yes	complemented
26	#15689300	C₂²	1	8	yes	complemented
27	#15689295	C₂²	1	8	yes	complemented
28	#15689290	C₂²	1	8	yes	complemented
29	#15689241	C₂²	1	4	yes	complemented
30	#15689241	C₂²	1	4	yes	complemented
31	#15689241	C₂²	1	4	yes	complemented
32	#15689241	C₂²	1	4	yes	complemented
33	C₂×#13093960	C₂²	1	2	yes	complemented
34	C₂×#13093952	C₂²	1	4	yes	complemented
35	#15689107	C₂²	1	4	yes	complemented
36	C₂×#135×C₄₇	C₂²	1	4	yes	complemented
37	C₄₇×#532	C₂²	1	2	yes	complemented
38	C₄₇×#495	C₂²	1	4	yes	complemented
39	C₄₇×#494	C₂²	1	1	yes	characteristic, complemented
40	C₄₇×#493	C₂²	1	1	yes	characteristic, complemented
41	C₄₇×#492	C₂²	1	2	yes	complemented
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
43	#13094072	C₂³	1	8	yes	—
44	#13094071	—	2	8	no	—
45	#13094070	—	2	8	no	—
46	#13094069	—	4	4	no	—
47	#13094069	C₂³	1	8	yes	—
48	C₂×#10625350	—	4	4	no	—
49	C₂×#10625350	C₂³	1	4	yes	—
50	#41×D₄₇	—	2	16	no	—
51	#13094056	—	2	16	no	—
52	#13094055	C₂³	1	16	yes	—
53	#13094054	—	2	8	no	—
54	#13094053	—	2	16	no	—
55	#13094051	—	2	16	no	—
56	#13094050	C₂³	1	16	yes	—
57	#13094049	—	2	8	no	—
58	#13094048	—	2	16	no	—
59	#13094047	—	2	8	no	—
60	#13094046	D₄	1	4	yes	complemented
61	#13094046	D₄	1	4	yes	complemented
62	#13094046	C₂³	1	4	yes	—
63	#13094046	C₂³	1	4	yes	—
64	#13094045	—	2	16	no	—
65	#13094044	—	2	16	no	—
66	#13094043	—	2	8	no	—
67	C₂×Dic₁₈₈	D₄	1	2	yes	complemented
68	Q₁₆×D₄₇	—	2	8	no	—
69	C₂×#10625325	D₄	1	4	yes	complemented
70	SD₁₆×D₄₇	—	2	16	no	—
71	C₂×D₃₇₆	D₄	1	2	yes	complemented
72	D₈×D₄₇	—	2	8	no	—
73	#13094030	—	2	4	no	—
74	#13094030	—	2	4	no	—
75	#13094030	C₂³	1	8	yes	—
76	#13094030	C₂³	1	8	yes	—
77	C₂×#10625329	C₂³	1	4	yes	—
78	C₂×#10625324	—	2	4	no	—
79	C₂×C₈×D₄₇	—	2	4	no	—
80	#13093960	C₂³	1	4	yes	—
81	#13093960	C₂³	1	4	yes	—
82	#13093952	C₂³	1	8	yes	—
83	#13093952	C₂³	1	8	yes	—
84	#13093943	C₂³	1	8	yes	—
85	#13093941	C₂³	1	8	yes	—
86	C₂×#41×C₄₇	C₂³	1	4	yes	—
87	#135×C₄₇	—	2	4	no	—
88	#135×C₄₇	—	2	4	no	—
89	#135×C₄₇	—	2	4	no	—
90	#135×C₄₇	—	2	4	no	—
91	C₂×Q₁₆×C₄₇	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
93	C₂×D₈×C₄₇	C₂³	1	4	yes	—
94	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
95	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
96	#127×C₄₇	C₂³	1	2	yes	—
97	#124×C₄₇	C₂³	1	4	yes	—
98	#121×C₄₇	—	4	2	no	—
99	C₄×D₄×C₄₇	—	4	2	no	—
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₄₇	C₂³	1	2	yes	—
104	#41×C₄₇	—	2	8	no	—
105	#41×C₄₇	—	2	8	no	—
106	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
107	C₂×D₄×C₄₇	—	2	4	no	—
108	C₂×D₄×C₄₇	—	4	2	no	—
109	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂×C₂²⋊D₄₇	—	2	4	no	—
114	C₂×C₂²⋊D₄₇	—	4	8	no	—
115	#10625354	—	2	16	no	—
116	Q₈×D₄₇	—	2	16	no	—
117	#10625352	—	2	16	no	—
118	#10625352	—	4	16	no	—
119	D₄×D₄₇	—	2	16	no	—
120	D₄×D₄₇	—	4	16	no	—
121	#10625350	—	2	4	no	—
122	#10625350	—	2	4	no	—
123	#10625350	—	4	8	no	—
124	#10625350	—	4	8	no	—
125	#10625350	—	4	8	no	—
126	#10625350	C₂×D₄	1	8	yes	—
127	#10625350	C₂⁴	1	8	yes	—
128	C₂×D₁₈₈	—	4	4	no	—
129	C₂×D₁₈₈	C₂×D₄	1	4	yes	—
130	C₂×C₄×D₄₇	—	2	4	no	—
131	C₂×C₄×D₄₇	—	4	8	no	—
132	C₂×Dic₉₄	—	4	4	no	—
133	C₂×Dic₉₄	C₂×D₄	1	4	yes	—
134	Q₁₆×C₄₇	—	2	4	no	—
135	Q₁₆×C₄₇	—	2	4	no	—
136	SD₁₆×C₄₇	—	2	8	no	—
137	SD₁₆×C₄₇	—	2	8	no	—
138	D₈×C₄₇	—	2	4	no	—
139	D₈×C₄₇	—	2	4	no	—
140	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
145	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
146	C₄⋊C₄×C₄₇	—	4	2	no	—
147	C₂²⋊C₄×C₄₇	—	4	4	no	—
148	C₄²×C₄₇	—	2	1	no	—
149	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
150	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
151	#10625337	—	2	16	no	—
152	#10625336	—	2	16	no	—
153	#10625335	—	2	16	no	—
154	#10625334	—	2	16	no	—
155	#10625329	—	2	4	no	—
156	#10625329	C₂⁴	1	8	yes	—
157	C₂×C₄₇⋊C₈	—	2	4	no	—
158	Dic₁₈₈	C₂×D₄	1	4	yes	—
159	Dic₁₈₈	C₂×D₄	1	4	yes	—
160	D₃₇₆	C₂×D₄	1	4	yes	—
161	D₃₇₆	C₂×D₄	1	4	yes	—
162	#10625325	C₂×D₄	1	8	yes	—
163	#10625325	C₂×D₄	1	8	yes	—
164	#10625324	—	2	8	no	—
165	#10625324	—	2	8	no	—
166	C₈×D₄₇	—	2	8	no	—
167	C₈×D₄₇	—	2	8	no	—
168	C₂³×C₄₇	—	2	4	no	—
169	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂²×D₄₇	—	2	4	no	—
171	C₂²×D₄₇	—	4	8	no	—
172	Q₈×C₄₇	—	2	8	no	—
173	D₄×C₄₇	—	2	8	no	—
174	D₄×C₄₇	—	4	8	no	—
175	D₄×C₄₇	—	8	4	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	4	no	—
181	C₂×C₄×C₄₇	—	4	4	no	—
182	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
186	C₂²⋊D₄₇	—	2	8	no	—
187	C₂²⋊D₄₇	—	2	8	no	—
188	C₂²⋊D₄₇	—	4	16	no	—
189	C₂×Dic₄₇	—	2	4	no	—
190	C₂×Dic₄₇	—	4	8	no	—
191	D₁₈₈	—	2	4	no	—
192	D₁₈₈	—	4	8	no	—
193	D₁₈₈	C₂²×D₄	1	8	yes	—
194	C₄×D₄₇	—	2	8	no	—
195	C₄×D₄₇	—	2	8	no	—
196	C₄×D₄₇	—	4	16	no	—
197	Dic₉₄	—	2	4	no	—
198	Dic₉₄	—	4	8	no	—
199	Dic₉₄	C₂²×D₄	1	8	yes	—
200	C₈×C₄₇	C₂²×D₄	1	2	yes	—
201	C₈×C₄₇	C₂²×D₄	1	2	yes	—
202	C₈×C₄₇	C₂²×D₄	1	2	yes	—
203	C₈×C₄₇	C₂²×D₄	1	2	yes	—
204	C₄₇⋊C₈	—	2	8	no	—
205	#61105	—	47	1	no	maximal, Sylow
206	C₂²×C₄₇	—	4	1	no	—
207	C₂²×C₄₇	—	4	4	no	—
208	C₂²×C₄₇	—	8	4	no	—
209	C₂²×C₄₇	D₄²	1	2	yes	—
210	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×D₄₇	—	2	8	no	—
212	C₂×D₄₇	—	8	4	no	—
213	C₂×D₄₇	—	16	8	no	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	4	1	no	—
216	C₄×C₄₇	—	4	4	no	—
217	C₄×C₄₇	D₄²	1	1	yes	characteristic
218	C₄×C₄₇	D₄²	1	1	yes	characteristic
219	C₄×C₄₇	C₂³×D₄	1	2	yes	—
220	Dic₄₇	—	2	8	no	—
221	#3584	—	47	4	no	—
222	#3293	—	47	2	no	—
223	#3292	—	47	2	no	—
224	#3291	—	47	4	no	—
225	#3290	—	47	8	no	—
226	#3147	D₄₇	1	1	yes	characteristic, complemented
227	#3067	—	47	4	no	—
228	#3018	—	47	4	no	—
229	C₂×#443	—	47	2	no	—
230	C₂×C₄₇	—	2	1	no	—
231	C₂×C₄₇	—	2	2	no	—
232	C₂×C₄₇	—	8	4	no	—
233	C₂×C₄₇	C₂×D₄²	1	1	yes	characteristic
234	D₄₇	—	4	8	no	—
235	#585	—	47	4	no	—
236	#578	—	47	8	no	—
237	#578	—	94	4	no	—
238	#577	—	47	16	no	—
239	#577	—	94	8	no	—
240	#576	—	47	8	no	—
241	#576	—	94	4	no	—
242	#575	—	47	8	no	—
243	#575	—	94	8	no	—
244	C₂×#135	—	47	2	no	—
245	C₂×#135	—	94	8	no	—
246	C₂×#135	C₂×D₄₇	1	4	yes	complemented
247	C₂×#131	—	47	4	no	—
248	#532	C₂×D₄₇	1	2	yes	complemented
249	#495	C₂×D₄₇	1	4	yes	complemented
250	#494	C₂×D₄₇	1	1	yes	characteristic, complemented
251	#493	C₂×D₄₇	1	1	yes	characteristic, complemented
252	#492	C₂×D₄₇	1	2	yes	complemented
253	#473	—	47	8	no	—
254	#472	—	47	8	no	—
255	#471	—	47	16	no	—
256	#456	—	47	8	no	—
257	#455	—	47	8	no	—
258	#454	—	47	8	no	—
259	#453	—	47	8	no	—
260	#443	—	47	4	no	—
261	#443	—	47	4	no	—
262	#443	—	47	4	no	—
263	#443	—	47	4	no	—
264	C₂×#108	—	47	2	no	—
265	C₂×#104	—	47	4	no	—
266	#413	—	47	4	no	—
267	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
268	C₄₇	#61105	1	1	yes	characteristic, complemented, Sylow
269	2₋¹⁺⁴	—	47	8	no	—
270	2₋¹⁺⁴	—	94	8	no	—
271	H(5,𝔽₂)	—	47	8	no	—
272	H(5,𝔽₂)	—	94	8	no	—
273	H(5,𝔽₂)	—	188	4	no	—
274	C₂×#41	—	47	4	no	—
275	C₂×#41	—	94	16	no	—
276	C₂×#41	—	188	4	no	—
277	C₂×#41	C₂²×D₄₇	1	4	yes	—
278	#137	—	47	16	no	—
279	#137	—	94	16	no	—
280	#137	—	94	16	no	—
281	#137	—	94	8	no	—
282	AGL(1,ℤ/8)	—	47	16	no	—
283	AGL(1,ℤ/8)	—	94	16	no	—
284	AGL(1,ℤ/8)	—	94	16	no	—
285	AGL(1,ℤ/8)	—	94	8	no	—
286	#135	—	2	4	no	—
287	#135	—	2	4	no	—
288	#135	—	2	4	no	—
289	#135	—	2	4	no	—
290	#135	—	47	4	no	—
291	#135	—	47	4	no	—
292	#135	—	47	4	no	—
293	#135	—	47	4	no	—
294	#135	—	94	8	no	—
295	#135	—	94	8	no	—
296	#135	—	94	16	no	—
297	#135	—	94	16	no	—
298	C₂×Q₁₆	—	47	2	no	—
299	C₂×Q₁₆	—	94	8	no	—
300	C₂×Q₁₆	C₂²×D₄₇	1	4	yes	—
301	C₂×SD₁₆	—	47	4	no	—
302	C₂×SD₁₆	—	94	16	no	—
303	C₂×SD₁₆	C₂²×D₄₇	1	8	yes	—
304	C₂×D₈	—	47	2	no	—
305	C₂×D₈	—	94	8	no	—
306	C₂×D₈	C₂²×D₄₇	1	4	yes	—
307	#131	—	47	8	no	—
308	#131	—	47	8	no	—
309	#131	—	94	4	no	—
310	#131	—	94	4	no	—
311	C₂×M₁₆	—	47	4	no	—
312	C₂×M₁₆	—	94	4	no	—
313	C₂²×C₈	—	94	4	no	—
314	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
315	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
316	#127	C₂²×D₄₇	1	2	yes	—
317	#124	C₂²×D₄₇	1	4	yes	—
318	#121	—	4	2	no	—
319	C₄×D₄	—	4	2	no	—
320	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
321	#108	—	47	4	no	—
322	#108	—	47	4	no	—
323	#104	—	47	8	no	—
324	#104	—	47	8	no	—
325	#101	—	47	8	no	—
326	#100	—	47	8	no	—
327	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₄₇	1	2	yes	—
330	#41	—	2	8	no	—
331	#41	—	2	8	no	—
332	#41	—	47	8	no	—
333	#41	—	47	8	no	—
334	#41	—	94	4	no	—
335	#41	—	94	4	no	—
336	#41	—	94	16	no	—
337	#41	—	94	16	no	—
338	#41	—	188	8	no	—
339	#41	—	188	8	no	—
340	#41	—	188	8	no	—
341	#41	—	188	16	no	—
342	C₂×Q₈	—	47	4	no	—
343	C₂×Q₈	—	94	16	no	—
344	C₂×Q₈	—	188	4	no	—
345	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	47	4	no	—
349	C₂×D₄	—	94	16	no	—
350	C₂×D₄	—	94	4	no	—
351	C₂×D₄	—	188	4	no	—
352	C₂×D₄	—	188	16	no	—
353	C₂×D₄	—	188	8	no	—
354	C₂×D₄	C₂³×D₄₇	1	4	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	94	4	no	—
358	C₂²×C₄	—	188	8	no	—
359	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
360	Q₁₆	—	2	4	no	—
361	Q₁₆	—	2	4	no	—
362	Q₁₆	—	47	4	no	—
363	Q₁₆	—	47	4	no	—
364	Q₁₆	—	94	16	no	—
365	SD₁₆	—	2	8	no	—
366	SD₁₆	—	2	8	no	—
367	SD₁₆	—	47	8	no	—
368	SD₁₆	—	47	8	no	—
369	SD₁₆	—	94	16	no	—
370	SD₁₆	—	94	16	no	—
371	D₈	—	2	4	no	—
372	D₈	—	2	4	no	—
373	D₈	—	47	4	no	—
374	D₈	—	47	4	no	—
375	D₈	—	94	16	no	—
376	M₁₆	—	47	8	no	—
377	M₁₆	—	94	4	no	—
378	M₁₆	—	94	8	no	—
379	M₁₆	—	94	8	no	—
380	C₂×C₈	—	94	4	no	—
381	C₂×C₈	—	94	8	no	—
382	C₂×C₈	—	94	8	no	—
383	C₂×C₈	D₄×D₄₇	1	2	yes	—
384	C₂×C₈	D₄×D₄₇	1	2	yes	—
385	C₂×C₈	D₄×D₄₇	1	2	yes	—
386	C₂×C₈	D₄×D₄₇	1	2	yes	—
387	C₂×C₈	C₂³×D₄₇	1	2	yes	—
388	C₂×C₈	C₂³×D₄₇	1	2	yes	—
389	C₄⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₄²	—	2	1	no	—
392	C₄²	C₂³×D₄₇	1	1	yes	characteristic
393	C₄²	C₂³×D₄₇	1	1	yes	characteristic
394	C₂³	—	2	4	no	—
395	C₂³	—	94	4	no	—
396	C₂³	—	188	8	no	—
397	C₂³	#13094069	1	1	yes	characteristic
398	Q₈	—	2	8	no	—
399	Q₈	—	47	8	no	—
400	Q₈	—	94	4	no	—
401	Q₈	—	188	8	no	—
402	D₄	—	2	8	no	—
403	D₄	—	4	8	no	—
404	D₄	—	8	4	no	—
405	D₄	—	47	8	no	—
406	D₄	—	94	8	no	—
407	D₄	—	94	8	no	—
408	D₄	—	94	4	no	—
409	D₄	—	188	8	no	—
410	D₄	—	188	16	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	94	4	no	—
418	C₂×C₄	—	94	8	no	—
419	C₂×C₄	—	94	8	no	—
420	C₂×C₄	—	188	16	no	—
421	C₂×C₄	—	188	8	no	—
422	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
423	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
424	C₂×C₄	#13094069	1	1	yes	characteristic
425	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
426	C₈	—	94	8	no	—
427	C₈	C₂×D₄×D₄₇	1	2	yes	—
428	C₈	C₂×D₄×D₄₇	1	2	yes	—
429	C₈	C₂×D₄×D₄₇	1	2	yes	—
430	C₈	C₂×D₄×D₄₇	1	2	yes	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	8	4	no	—
434	C₂²	—	94	8	no	—
435	C₂²	—	376	4	no	—
436	C₂²	—	752	8	no	—
437	C₂²	#15689758	1	2	yes	—
438	C₂²	C₂×#13094069	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	4	no	—
442	C₄	—	94	8	no	—
443	C₄	#15689758	1	1	yes	characteristic
444	C₄	#15689758	1	1	yes	characteristic
445	C₄	C₂²×D₄×D₄₇	1	2	yes	—
446	C₂	—	2	1	no	—
447	C₂	—	2	2	no	—
448	C₂	—	8	4	no	—
449	C₂	—	188	8	no	—
450	C₂	C₂×#15689758	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15689758
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3147	C₂
socle	C₂×C₄₇	C₂×D₄²
hypercenter	#3147	D₄₇
hypocenter	C₄₇	#61105
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3147

Complements

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

N	H ≅ G/N	type
1. #20258157	C₂	semidirect
2. #20255192	C₂	semidirect
3. #20255187	C₂	semidirect
4. #20255181	C₂	semidirect
5. #20255173	C₂	semidirect
6. #20253104	C₂	semidirect
7. #20252736	C₂	semidirect
8. C₂×#15689241	C₂	semidirect
9. C₄₇×#3147	C₂	semidirect
10. #15689959	C₂²	semidirect
12. #15689936	C₂²	semidirect
14. #15689929	C₂²	semidirect
16. #15689924	C₂²	semidirect
17. #15689921	C₂²	semidirect
21. C₂×#13094030	C₂²	semidirect
22. #15689395	C₂²	semidirect
23. #15689390	C₂²	semidirect
24. #15689383	C₂²	semidirect
25. #15689305	C₂²	semidirect
26. #15689300	C₂²	semidirect
27. #15689295	C₂²	semidirect
28. #15689290	C₂²	semidirect
29. #15689241	C₂²	semidirect
30. #15689241	C₂²	semidirect
31. #15689241	C₂²	semidirect
32. #15689241	C₂²	semidirect
33. C₂×#13093960	C₂²	semidirect
34. C₂×#13093952	C₂²	semidirect
35. #15689107	C₂²	semidirect
36. C₂×#135×C₄₇	C₂²	semidirect
37. C₄₇×#532	C₂²	semidirect
38. C₄₇×#495	C₂²	semidirect
39. C₄₇×#494	C₂²	semidirect
40. C₄₇×#493	C₂²	semidirect
41. C₄₇×#492	C₂²	semidirect
42. C₂×C₄×C₈×C₄₇	C₂²	semidirect
60. #13094046	D₄	semidirect
61. #13094046	D₄	semidirect
67. C₂×Dic₁₈₈	D₄	semidirect
69. C₂×#10625325	D₄	semidirect
71. C₂×D₃₇₆	D₄	semidirect
226. #3147	D₄₇	semidirect
246. C₂×#135	C₂×D₄₇	semidirect
248. #532	C₂×D₄₇	semidirect
249. #495	C₂×D₄₇	semidirect
250. #494	C₂×D₄₇	semidirect
251. #493	C₂×D₄₇	semidirect
252. #492	C₂×D₄₇	semidirect
267. C₂×C₄×C₈	C₂×D₄₇	semidirect
268. C₄₇	#61105	semidirect

Maximal subgroups

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

subgroup	index
#20258157	2
#20255192	2
#20255187	2
#20255181	2
#20255173	2
#20253104	2
#20252736	2
C₂×#15689241	2
C₄₇×#3147	2
#61105	47