Subgroups — #26230198

Order 12032.

772 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253882	C₂	1	1	yes	maximal, characteristic
2	#20252306	C₂	1	1	yes	maximal, characteristic
3	#20252257	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244303	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244286	C₂	1	1	yes	maximal, characteristic
6	#20243924	C₂	1	2	yes	maximal, complemented
7	#20243909	C₂	1	2	yes	maximal, complemented
8	#20243883	C₂	1	2	yes	maximal, complemented
9	#20243862	C₂	1	2	yes	maximal, complemented
10	#20243512	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1747	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094057	C₂²	1	2	yes	—
13	C₂×#13094046	C₂²	1	1	yes	characteristic
14	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic
15	#15689889	C₂²	1	2	yes	—
16	#15689699	C₂²	1	2	yes	—
17	#15689600	C₂²	1	2	yes	—
18	#15689517	C₄	1	4	yes	complemented
19	#15689507	C₄	1	2	yes	complemented
20	#15689503	C₄	1	2	yes	complemented
21	#15689246	—	2	2	no	—
22	#15689241	—	2	2	no	—
23	#15689231	—	2	2	no	—
24	C₄×Dic₁₈₈	—	2	2	no	—
25	C₂×#13093960	C₂²	1	1	yes	characteristic
26	#15689161	C₂²	1	1	yes	characteristic
27	#15689141	C₂²	1	2	yes	—
28	#15689139	C₂²	1	2	yes	—
29	#15689133	C₂²	1	2	yes	—
30	#15689131	C₂²	1	2	yes	—
31	C₂×#13093942	C₂²	1	2	yes	—
32	#15689096	C₂²	1	2	yes	—
33	#15688894	C₂²	1	2	yes	—
34	#15688879	C₂²	1	2	yes	—
35	C₄₇×#405	C₂²	1	1	yes	characteristic
36	C₄₇×#405	C₂²	1	1	yes	characteristic
37	C₄₇×#405	C₂²	1	1	yes	characteristic
38	C₄₇×#338	C₂²	1	1	yes	characteristic
39	C₄₇×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
40	C₄₇×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
41	C₄₇×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
42	C₂×#10625350	C₂³	1	2	yes	—
43	C₂²×Dic₉₄	C₂³	1	2	yes	—
44	#13094057	—	4	2	no	—
45	#13094057	—	4	2	no	—
46	#13094046	—	2	1	no	—
47	#13094046	—	2	1	no	—
48	#13094046	—	2	1	no	—
49	#13094046	—	2	1	no	—
50	C₂×Dic₁₈₈	—	2	1	no	—
51	C₂×Dic₁₈₈	—	2	1	no	—
52	C₂×Dic₁₈₈	—	2	1	no	—
53	C₂×Dic₁₈₈	—	2	1	no	—
54	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
55	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
56	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
57	C₂×Dic₁₈₈	C₂×C₄	1	4	yes	—
58	C₂×#10625325	C₂×C₄	1	2	yes	—
59	C₂×#10625325	C₂×C₄	1	4	yes	—
60	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
61	#13094032	—	4	2	no	—
62	#13094030	—	2	4	no	—
63	C₂×#10625329	C₂³	1	2	yes	—
64	M₁₆×D₄₇	—	4	2	no	—
65	#13094024	C₂×C₄	1	4	yes	—
66	#13094012	C₂×C₄	1	4	yes	—
67	#13094008	—	4	2	no	—
68	#13094004	—	4	2	no	—
69	C₄×Dic₉₄	—	2	4	no	—
70	#13093989	—	4	2	no	—
71	#13093983	C₂³	1	2	yes	—
72	#13093980	—	4	2	no	—
73	#13093960	—	2	1	no	—
74	#13093960	—	2	1	no	—
75	#13093958	—	2	1	no	—
76	#13093956	—	2	1	no	—
77	#13093952	—	2	4	no	—
78	#13093950	—	4	2	no	—
79	#13093949	—	2	4	no	—
80	#13093947	—	4	2	no	—
81	#13093942	—	4	2	no	—
82	#13093938	—	4	2	no	—
83	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	#117×C₄₇	C₂³	1	1	yes	characteristic
88	#117×C₄₇	C₂³	1	1	yes	characteristic
89	#117×C₄₇	C₂³	1	1	yes	characteristic
90	#97×C₄₇	—	2	1	no	—
91	#97×C₄₇	C₂×C₄	1	2	yes	—
92	#97×C₄₇	D₄	1	2	yes	—
93	C₄×C₈×C₄₇	—	2	1	no	—
94	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₄₇	D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂×C₂²⋊D₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	#10625350	—	2	2	no	—
100	#10625350	—	2	2	no	—
101	#10625350	—	2	2	no	—
102	#10625350	—	2	2	no	—
103	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×Dic₉₄	—	2	2	no	—
106	C₂×Dic₉₄	—	2	2	no	—
107	C₂×Dic₉₄	—	2	2	no	—
108	C₂×Dic₉₄	—	2	2	no	—
109	C₂×Dic₉₄	—	2	2	no	—
110	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
111	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
112	M₁₆×C₄₇	—	2	1	no	—
113	M₁₆×C₄₇	—	2	1	no	—
114	M₁₆×C₄₇	—	2	1	no	—
115	M₁₆×C₄₇	—	2	1	no	—
116	M₁₆×C₄₇	—	2	1	no	—
117	M₁₆×C₄₇	—	2	1	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
126	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₂²⋊C₄×C₄₇	—	2	1	no	—
131	C₂²⋊C₄×C₄₇	—	2	1	no	—
132	C₂²⋊C₄×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
135	C₄²×C₄₇	C₂×D₄	1	2	yes	—
136	C₂²⋊Dic₄₇	—	2	2	no	—
137	(C₂×D₄₇)⋊C₄	—	4	4	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	—	4	4	no	—
140	Dic₄₇⋊C₄	—	4	4	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	4	4	no	—
143	#10625329	—	2	2	no	—
144	#10625329	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	Dic₁₈₈	—	2	2	no	—
147	Dic₁₈₈	—	2	2	no	—
148	Dic₁₈₈	—	2	2	no	—
149	Dic₁₈₈	—	2	2	no	—
150	Dic₁₈₈	—	2	1	no	—
151	Dic₁₈₈	—	2	1	no	—
152	Dic₁₈₈	—	4	4	no	—
153	D₃₇₆	—	2	1	no	—
154	D₃₇₆	—	2	1	no	—
155	#10625325	—	2	2	no	—
156	#10625325	—	2	2	no	—
157	#10625325	—	4	4	no	—
158	#10625324	—	4	4	no	—
159	C₈×D₄₇	—	4	4	no	—
160	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂²⋊D₄₇	—	4	2	no	—
172	C₂²⋊D₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	4	no	—
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	D₁₈₈	—	2	2	no	—
179	D₁₈₈	—	2	2	no	—
180	C₄×D₄₇	—	4	2	no	—
181	C₄×D₄₇	—	4	2	no	—
182	Dic₉₄	—	2	2	no	—
183	Dic₉₄	—	2	4	no	—
184	Dic₉₄	—	2	4	no	—
185	Dic₉₄	—	2	2	no	—
186	Dic₉₄	—	4	2	no	—
187	Dic₉₄	—	4	2	no	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	—	2	2	no	—
190	C₈×C₄₇	—	4	1	no	—
191	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
192	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
193	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
194	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
195	C₄₇⋊C₈	—	4	2	no	—
196	#22285	—	47	1	no	maximal, Sylow
197	C₂²×C₄₇	—	4	1	no	—
198	C₂²×C₄₇	#518	1	1	yes	characteristic
199	C₂²×C₄₇	#535	1	1	yes	characteristic
200	C₂²×C₄₇	#540	1	1	yes	characteristic
201	C₂×D₄₇	—	4	2	no	—
202	C₂×D₄₇	—	8	2	no	—
203	C₄×C₄₇	—	4	2	no	—
204	C₄×C₄₇	—	4	2	no	—
205	C₄×C₄₇	—	8	1	no	—
206	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₄₇	#518	1	1	yes	characteristic
208	C₄×C₄₇	#535	1	1	yes	characteristic
209	C₄×C₄₇	#540	1	1	yes	characteristic
210	Dic₄₇	—	4	4	no	—
211	Dic₄₇	—	4	2	no	—
212	Dic₄₇	—	8	2	no	—
213	#3156	—	47	1	no	—
214	#2957	—	47	1	no	—
215	#2950	—	47	1	no	—
216	#1979	—	47	1	no	—
217	#1976	—	47	1	no	—
218	#1912	—	47	2	no	—
219	#1909	—	47	2	no	—
220	#1905	—	47	2	no	—
221	#1902	—	47	2	no	—
222	#1833	—	47	1	no	—
223	#1747	D₄₇	1	1	yes	characteristic, complemented
224	C₂×C₄₇	—	2	1	no	—
225	C₂×C₄₇	—	2	1	no	—
226	C₂×C₄₇	—	2	1	no	—
227	C₂×C₄₇	#2328	1	1	yes	characteristic
228	D₄₇	—	8	2	no	—
229	C₂×#137	—	47	2	no	—
230	C₂×#135	—	47	1	no	—
231	C₂²×Q₁₆	—	47	1	no	—
232	#568	—	47	2	no	—
233	#536	—	47	2	no	—
234	#519	—	47	2	no	—
235	#497	—	47	4	no	—
236	#495	—	47	2	no	—
237	#494	—	47	2	no	—
238	#444	—	94	2	no	—
239	#443	—	94	2	no	—
240	#441	—	94	2	no	—
241	C₄×Q₁₆	—	94	2	no	—
242	C₂×#108	—	47	1	no	—
243	#427	—	47	1	no	—
244	#421	—	47	2	no	—
245	#421	—	47	2	no	—
246	#419	—	47	2	no	—
247	#419	—	47	2	no	—
248	C₂×#101	—	47	2	no	—
249	#410	—	47	2	no	—
250	#405	C₂×D₄₇	1	1	yes	characteristic
251	#405	C₂×D₄₇	1	1	yes	characteristic
252	#405	C₂×D₄₇	1	1	yes	characteristic
253	#344	—	47	2	no	—
254	#338	C₂×D₄₇	1	1	yes	characteristic
255	H(3,ℤ/4)	—	47	2	no	—
256	H(3,ℤ/4)	C₂×D₄₇	1	1	yes	characteristic
257	H(3,ℤ/4)	C₂×D₄₇	1	1	yes	characteristic
258	H(3,ℤ/4)	C₂×D₄₇	1	1	yes	characteristic
259	C₄₇	#22285	1	1	yes	characteristic, complemented, Sylow
260	C₂×#41	—	47	2	no	—
261	C₂²×Q₈	—	47	2	no	—
262	#137	—	188	2	no	—
263	#137	—	188	2	no	—
264	#135	—	94	1	no	—
265	#135	—	94	1	no	—
266	#135	—	94	1	no	—
267	#135	—	94	1	no	—
268	C₂×Q₁₆	—	47	2	no	—
269	C₂×Q₁₆	—	47	2	no	—
270	C₂×Q₁₆	—	47	1	no	—
271	C₂×Q₁₆	—	47	4	no	—
272	C₂×Q₁₆	—	94	1	no	—
273	C₂×Q₁₆	—	94	1	no	—
274	C₂×Q₁₆	—	94	1	no	—
275	C₂×Q₁₆	—	94	1	no	—
276	C₂×SD₁₆	—	47	2	no	—
277	C₂×SD₁₆	—	47	4	no	—
278	C₂×D₈	—	47	1	no	—
279	#131	—	94	4	no	—
280	#131	—	188	2	no	—
281	C₂×M₁₆	—	47	2	no	—
282	C₂×M₁₆	—	188	2	no	—
283	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
284	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
285	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
287	C₄⋊Q₈	—	47	4	no	—
288	#124	—	47	4	no	—
289	#123	—	188	2	no	—
290	C₂²⋊Q₈	—	188	2	no	—
291	C₄×Q₈	—	94	4	no	—
292	C₄×Q₈	—	188	2	no	—
293	#117	—	47	2	no	—
294	#117	—	188	2	no	—
295	#117	C₂²×D₄₇	1	1	yes	characteristic
296	#117	C₂²×D₄₇	1	1	yes	characteristic
297	#117	C₂²×D₄₇	1	1	yes	characteristic
298	#108	—	94	1	no	—
299	#108	—	94	1	no	—
300	#107	—	94	1	no	—
301	#106	—	94	1	no	—
302	#104	—	94	4	no	—
303	#104	—	188	2	no	—
304	#103	—	94	4	no	—
305	#103	—	188	2	no	—
306	#101	—	188	2	no	—
307	#99	—	188	2	no	—
308	#97	—	2	1	no	—
309	#97	C₄×D₄₇	1	2	yes	—
310	#97	D₁₈₈	1	2	yes	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	C₄×D₄₇	1	2	yes	—
313	C₄×C₈	D₁₈₈	1	2	yes	—
314	#41	—	94	2	no	—
315	#41	—	94	2	no	—
316	#41	—	94	2	no	—
317	#41	—	94	2	no	—
318	C₂×Q₈	—	47	4	no	—
319	C₂×Q₈	—	47	2	no	—
320	C₂×Q₈	—	94	2	no	—
321	C₂×Q₈	—	94	2	no	—
322	C₂×Q₈	—	94	2	no	—
323	C₂×Q₈	—	94	2	no	—
324	C₂×Q₈	—	94	2	no	—
325	C₂×D₄	—	47	2	no	—
326	C₂×D₄	—	94	2	no	—
327	C₂²×C₄	—	94	2	no	—
328	C₂²×C₄	—	94	2	no	—
329	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
330	Q₁₆	—	94	2	no	—
331	Q₁₆	—	94	2	no	—
332	Q₁₆	—	94	2	no	—
333	Q₁₆	—	94	2	no	—
334	Q₁₆	—	94	1	no	—
335	Q₁₆	—	94	1	no	—
336	Q₁₆	—	188	4	no	—
337	SD₁₆	—	94	2	no	—
338	SD₁₆	—	94	2	no	—
339	SD₁₆	—	188	4	no	—
340	D₈	—	94	1	no	—
341	D₈	—	94	1	no	—
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	2	1	no	—
347	M₁₆	—	2	1	no	—
348	M₁₆	—	94	2	no	—
349	M₁₆	—	94	2	no	—
350	M₁₆	—	188	4	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	94	2	no	—
353	C₂×C₈	—	188	4	no	—
354	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
355	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
356	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
357	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
358	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
359	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
360	C₂×C₈	#10625350	1	1	yes	characteristic
361	C₂×C₈	#10625350	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	94	2	no	—
366	C₄⋊C₄	—	188	4	no	—
367	C₄⋊C₄	—	188	4	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	94	2	no	—
372	C₂²⋊C₄	—	188	4	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	94	2	no	—
375	C₄²	—	188	4	no	—
376	C₄²	C₂×C₄×D₄₇	1	2	yes	—
377	C₄²	C₂×D₁₈₈	1	2	yes	—
378	C₂³	—	94	2	no	—
379	C₂³	#13094070	1	1	yes	characteristic
380	Q₈	—	94	2	no	—
381	Q₈	—	94	4	no	—
382	Q₈	—	94	4	no	—
383	Q₈	—	94	2	no	—
384	Q₈	—	188	2	no	—
385	Q₈	—	188	2	no	—
386	D₄	—	94	2	no	—
387	D₄	—	94	2	no	—
388	D₄	—	188	2	no	—
389	D₄	—	188	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	94	4	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	—	188	2	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
402	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
403	C₂×C₄	#13094070	1	1	yes	characteristic
404	C₂×C₄	#13094070	1	1	yes	characteristic
405	C₂×C₄	#13094070	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	188	2	no	—
410	C₈	C₄×D₁₈₈	1	1	yes	characteristic
411	C₈	C₄×D₁₈₈	1	1	yes	characteristic
412	C₈	C₄×D₁₈₈	1	1	yes	characteristic
413	C₈	C₄×D₁₈₈	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	376	2	no	—
416	C₂²	—	188	2	no	—
417	C₂²	#15689597	1	1	yes	characteristic
418	C₂²	#15689692	1	1	yes	characteristic
419	C₂²	#15689728	1	1	yes	characteristic
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	1	no	—
423	C₄	—	376	2	no	—
424	C₄	—	188	2	no	—
425	C₄	—	188	4	no	—
426	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
427	C₄	#15689597	1	1	yes	characteristic
428	C₄	#15689692	1	1	yes	characteristic
429	C₄	#15689728	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	376	2	no	—
434	C₂	#20246113	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20246113
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1747	C₂
socle	C₂×C₄₇	#2328
prime radical	C₂×#13094046	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1747	D₄₇
hypocenter	C₄₇	#22285
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1747

Complements

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

N	H ≅ G/N	type
3. #20252257	C₂	semidirect
4. #20244303	C₂	semidirect
6. #20243924	C₂	semidirect
7. #20243909	C₂	semidirect
8. #20243883	C₂	semidirect
9. #20243862	C₂	semidirect
10. #20243512	C₂	semidirect
11. C₄₇×#1747	C₂	semidirect
18. #15689517	C₄	semidirect
19. #15689507	C₄	semidirect
20. #15689503	C₄	semidirect
223. #1747	D₄₇	semidirect
259. C₄₇	#22285	semidirect

Maximal subgroups

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

subgroup	index
#20253882	2
#20252306	2
#20252257	2
#20244303	2
#20244286	2
#20243924	2
#20243909	2
#20243883	2
#20243862	2
#20243512	2
C₄₇×#1747	2
#22285	47