Subgroups — #26234500

Order 12032.

978 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689202	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689162	C₂	1	2	yes	maximal, complemented
3	#20246314	C₂	1	2	yes	maximal
4	#20244154	C₂	1	2	yes	maximal, complemented
5	#20243584	C₂	1	2	yes	maximal, complemented
6	#20243574	C₂	1	2	yes	maximal, complemented
7	#20243418	C₂	1	2	yes	maximal, complemented
8	C₄×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#10625324	C₂²	1	2	yes	—
11	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
12	C₂×#13093982	C₂²	1	2	yes	—
13	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
14	#15689202	C₄	1	8	yes	complemented
15	#15689162	—	2	8	no	—
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093958	C₂²	1	1	yes	characteristic
18	C₂×#13093957	C₂²	1	2	yes	—
19	C₂×#13093955	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
22	#15689012	—	2	2	no	—
23	#15689006	—	2	2	no	—
24	#15689001	—	2	2	no	—
25	#15688980	C₂²	1	2	yes	—
26	#15688980	C₂²	1	2	yes	—
27	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
28	#15688970	—	2	2	no	—
29	#15688886	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#106×C₄₇	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#382	C₂²	1	2	yes	—
37	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
38	C₂²×C₄×D₄₇	—	2	2	no	—
39	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
40	C₂×#10625324	—	2	4	no	—
41	C₂×#10625324	—	2	4	no	—
42	C₂×#10625324	C₂×C₄	1	8	yes	complemented
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
45	C₄×D₁₈₈	Q₈	1	4	yes	—
46	#13093982	—	2	4	no	—
47	#13093982	—	4	2	no	—
48	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×Dic₄₇⋊C₄	—	2	2	no	—
52	C₄⋊C₄×D₄₇	—	2	4	no	—
53	C₄⋊C₄×D₄₇	—	4	2	no	—
54	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
55	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
56	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
57	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
58	C₂×C₄×Dic₄₇	—	2	2	no	—
59	C₂×C₄×Dic₄₇	—	2	2	no	—
60	#13093958	—	2	2	no	—
61	#13093958	D₄	1	4	yes	complemented
62	#13093957	—	2	4	no	—
63	#13093955	—	2	4	no	—
64	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
65	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	complemented
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	#107×C₄₇	—	4	1	no	—
75	#107×C₄₇	—	4	1	no	—
76	#106×C₄₇	—	2	4	no	—
77	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
78	#95×C₄₇	—	2	2	no	—
79	#95×C₄₇	—	2	2	no	—
80	C₂³×D₄₇	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
86	C₂²×Dic₄₇	—	2	2	no	—
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
89	C₂×D₁₈₈	—	4	1	no	—
90	C₂×D₁₈₈	—	4	1	no	—
91	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
92	C₂×C₄×D₄₇	—	2	2	no	—
93	C₂×C₄×D₄₇	—	2	2	no	—
94	C₂×C₄×D₄₇	—	2	2	no	—
95	C₂×C₄×D₄₇	—	2	2	no	—
96	C₂×C₄×D₄₇	—	4	4	no	—
97	C₂×C₄×D₄₇	—	4	4	no	—
98	C₂×C₄×D₄₇	—	8	2	no	—
99	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
100	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
101	C₂×C₈×C₄₇	—	2	1	no	—
102	C₂×C₈×C₄₇	—	2	1	no	—
103	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₄₇	#41	1	2	yes	—
107	C₄⋊C₄×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
112	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
113	(C₂×D₄₇)⋊C₄	—	4	4	no	—
114	(C₂×D₄₇)⋊C₄	—	4	4	no	—
115	(C₂×D₄₇)⋊C₄	—	8	2	no	—
116	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	8	yes	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	—	2	2	no	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
121	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
122	Dic₄₇⋊C₄	—	4	4	no	—
123	C₄×Dic₄₇	—	4	4	no	—
124	C₄×Dic₄₇	—	8	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
128	#10625324	—	2	16	no	—
129	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
130	C₂²×D₄₇	—	2	2	no	—
131	C₂²×D₄₇	—	2	2	no	—
132	C₂²×D₄₇	—	2	2	no	—
133	C₂²×D₄₇	—	2	2	no	—
134	C₂²×D₄₇	—	2	2	no	—
135	C₂²×D₄₇	—	2	2	no	—
136	C₂²×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	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×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×Dic₄₇	—	2	2	no	—
156	C₂×Dic₄₇	—	2	2	no	—
157	C₂×Dic₄₇	—	2	4	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
164	D₁₈₈	—	4	4	no	—
165	C₄×D₄₇	—	2	4	no	—
166	C₄×D₄₇	—	2	4	no	—
167	C₄×D₄₇	—	2	4	no	—
168	C₄×D₄₇	—	2	4	no	—
169	C₄×D₄₇	—	8	8	no	—
170	C₈×C₄₇	—	2	2	no	—
171	C₈×C₄₇	C₄×D₄	1	4	yes	—
172	C₄₇⋊C₈	—	2	4	no	—
173	#22664	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
175	C₂²×C₄₇	D₄²	1	1	yes	characteristic
176	C₂²×C₄₇	#547	1	1	yes	characteristic
177	C₂²×C₄₇	#575	1	1	yes	characteristic
178	C₂²×C₄₇	#575	1	1	yes	characteristic
179	C₂²×C₄₇	#576	1	1	yes	characteristic
180	C₂²×C₄₇	#578	1	1	yes	characteristic
181	C₂×D₄₇	—	2	4	no	—
182	C₂×D₄₇	—	2	4	no	—
183	C₂×D₄₇	—	2	4	no	—
184	C₂×D₄₇	—	4	2	no	—
185	C₂×D₄₇	—	4	2	no	—
186	C₂×D₄₇	—	4	2	no	—
187	C₂×D₄₇	—	4	2	no	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	8	2	no	—
191	C₄×C₄₇	—	8	2	no	—
192	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₄₇	#520	1	1	yes	characteristic
194	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
195	C₄×C₄₇	#554	1	1	yes	characteristic
196	Dic₄₇	—	2	4	no	—
197	Dic₄₇	—	4	4	no	—
198	Dic₄₇	—	8	2	no	—
199	C₂×#436	—	47	1	no	—
200	C₂×#428	—	47	2	no	—
201	#2352	—	47	2	no	—
202	#1949	—	47	2	no	—
203	#1854	—	47	2	no	—
204	#1852	—	47	2	no	—
205	#1846	D₄₇	1	1	yes	characteristic, complemented
206	#1809	—	47	2	no	—
207	C₄×#107	—	47	1	no	—
208	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄₇	#2911	1	1	yes	characteristic
210	C₂×C₄₇	#2913	1	1	yes	characteristic
211	C₂×C₄₇	#3273	1	1	yes	characteristic
212	C₂×C₄₇	#3277	1	1	yes	characteristic
213	C₂×C₄₇	#3352	1	1	yes	characteristic
214	C₂×C₄₇	#3355	1	1	yes	characteristic
215	D₄₇	—	4	4	no	—
216	C₂²×M₁₆	—	47	2	no	—
217	C₂×C₄×D₄	—	47	1	no	—
218	C₂×#117	—	47	2	no	—
219	C₂²×C₄⋊C₄	—	47	2	no	—
220	#436	—	47	8	no	—
221	#428	—	94	8	no	—
222	C₂×#107	—	47	1	no	—
223	C₂×#107	—	47	1	no	—
224	C₂×#107	—	47	2	no	—
225	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
226	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
227	C₂×#106	—	47	2	no	—
228	C₂×#106	C₂×D₄₇	1	2	yes	—
229	C₂×C₄⋊C₈	—	47	1	no	—
230	C₂×C₂²⋊C₈	—	47	2	no	—
231	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
232	#388	—	94	2	no	—
233	#387	—	94	2	no	—
234	#386	—	94	2	no	—
235	#382	C₂×D₄₇	1	2	yes	—
236	#380	—	47	2	no	—
237	#380	—	47	2	no	—
238	C₄×C₄⋊C₄	—	47	2	no	—
239	C₄×C₂²⋊C₄	—	94	2	no	—
240	#340	—	47	2	no	—
241	#340	—	47	2	no	—
242	#340	—	47	2	no	—
243	C₄₇	#22664	1	1	yes	characteristic, complemented, Sylow
244	C₂²×D₄	—	47	1	no	—
245	C₂³×C₄	—	47	2	no	—
246	C₂³×C₄	—	94	2	no	—
247	C₂×M₁₆	—	47	8	no	—
248	C₂×M₁₆	—	94	4	no	—
249	C₂×M₁₆	—	94	4	no	—
250	C₂²×C₈	—	47	2	no	—
251	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
252	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
253	C₄×D₄	—	47	4	no	—
254	C₄×D₄	—	47	4	no	—
255	#117	—	94	4	no	—
256	#117	—	188	2	no	—
257	C₂×C₄⋊C₄	—	47	1	no	—
258	C₂×C₄⋊C₄	—	47	2	no	—
259	C₂×C₄⋊C₄	—	47	2	no	—
260	C₂×C₄⋊C₄	—	94	4	no	—
261	C₂×C₄⋊C₄	—	94	2	no	—
262	C₂×C₄⋊C₄	—	188	2	no	—
263	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
265	C₂×C₂²⋊C₄	—	47	2	no	—
266	C₂×C₂²⋊C₄	—	94	2	no	—
267	C₂×C₂²⋊C₄	—	94	2	no	—
268	C₂×C₂²⋊C₄	—	94	2	no	—
269	C₂×C₄²	—	94	2	no	—
270	C₂×C₄²	—	94	2	no	—
271	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
272	#107	—	4	1	no	—
273	#107	—	4	1	no	—
274	#107	—	47	4	no	—
275	#107	—	94	4	no	—
276	#107	—	94	2	no	—
277	#106	—	2	4	no	—
278	#106	—	94	4	no	—
279	C₄⋊C₈	—	47	4	no	—
280	C₂²⋊C₈	—	47	8	no	—
281	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	94	2	no	—
285	#95	—	94	2	no	—
286	#95	—	94	2	no	—
287	C₂⁴	—	47	2	no	—
288	C₂×D₄	—	47	4	no	—
289	C₂×D₄	—	188	1	no	—
290	C₂×D₄	—	188	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	47	2	no	—
294	C₂²×C₄	—	47	4	no	—
295	C₂²×C₄	—	47	4	no	—
296	C₂²×C₄	—	94	2	no	—
297	C₂²×C₄	—	94	2	no	—
298	C₂²×C₄	—	94	2	no	—
299	C₂²×C₄	—	94	2	no	—
300	C₂²×C₄	—	94	2	no	—
301	C₂²×C₄	—	94	2	no	—
302	C₂²×C₄	—	376	2	no	—
303	C₂²×C₄	—	188	4	no	—
304	C₂²×C₄	—	188	4	no	—
305	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
306	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
308	M₁₆	—	94	16	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	47	4	no	—
312	C₂×C₈	—	94	2	no	—
313	C₂×C₈	—	94	2	no	—
314	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
315	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
316	C₂×C₈	D₄×D₄₇	1	2	yes	—
317	C₂×C₈	#10625354	1	2	yes	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	47	4	no	—
323	C₄⋊C₄	—	47	4	no	—
324	C₄⋊C₄	—	94	2	no	—
325	C₄⋊C₄	—	94	2	no	—
326	C₄⋊C₄	—	94	2	no	—
327	C₄⋊C₄	—	188	4	no	—
328	C₂²⋊C₄	—	47	8	no	—
329	C₂²⋊C₄	—	376	2	no	—
330	C₂²⋊C₄	—	188	4	no	—
331	C₂²⋊C₄	—	188	4	no	—
332	C₄²	—	376	2	no	—
333	C₄²	—	188	4	no	—
334	C₄²	C₂×C₄×D₄₇	1	2	yes	—
335	C₄²	Q₈×D₄₇	1	2	yes	—
336	C₂³	—	47	4	no	—
337	C₂³	—	94	2	no	—
338	C₂³	—	94	2	no	—
339	C₂³	—	94	2	no	—
340	C₂³	—	94	2	no	—
341	C₂³	—	94	2	no	—
342	C₂³	—	94	2	no	—
343	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
344	D₄	—	188	4	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	47	4	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	2	no	—
358	C₂×C₄	—	94	4	no	—
359	C₂×C₄	—	94	4	no	—
360	C₂×C₄	—	94	4	no	—
361	C₂×C₄	—	94	4	no	—
362	C₂×C₄	—	94	4	no	—
363	C₂×C₄	—	376	8	no	—
364	C₂×C₄	—	188	2	no	—
365	C₂×C₄	—	188	2	no	—
366	C₂×C₄	—	188	2	no	—
367	C₂×C₄	—	188	2	no	—
368	C₂×C₄	—	188	2	no	—
369	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
370	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
371	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
375	C₂×C₄	#13094069	1	1	yes	characteristic
376	C₂×C₄	#13094072	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	94	4	no	—
379	C₈	#13093986	1	4	yes	—
380	C₂²	—	94	4	no	—
381	C₂²	—	94	4	no	—
382	C₂²	—	94	4	no	—
383	C₂²	—	188	2	no	—
384	C₂²	—	188	2	no	—
385	C₂²	—	188	2	no	—
386	C₂²	—	188	2	no	—
387	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
388	C₂²	#15689758	1	1	yes	characteristic
389	C₂²	#15689776	1	1	yes	characteristic
390	C₂²	#15689920	1	1	yes	characteristic
391	C₂²	#15689920	1	1	yes	characteristic
392	C₂²	#15689925	1	1	yes	characteristic
393	C₂²	#15689937	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	94	4	no	—
399	C₄	—	376	2	no	—
400	C₄	—	188	4	no	—
401	C₄	C₂×#13093986	1	1	yes	characteristic
402	C₄	#15689604	1	1	yes	characteristic
403	C₄	#15689788	1	1	yes	characteristic
404	C₄	#15689834	1	1	yes	characteristic
405	C₂	—	188	4	no	—
406	C₂	#20246288	1	1	yes	characteristic
407	C₂	#20251976	1	1	yes	characteristic
408	C₂	#20251985	1	1	yes	characteristic
409	C₂	#20254997	1	1	yes	characteristic
410	C₂	#20255043	1	1	yes	characteristic
411	C₂	#20255961	1	1	yes	characteristic
412	C₂	#20255992	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1846	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1846	D₄₇
hypocenter	C₄₇	#22664
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1846

Complements

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

N	H ≅ G/N	type
2. C₂×#15689162	C₂	semidirect
4. #20244154	C₂	semidirect
5. #20243584	C₂	semidirect
6. #20243574	C₂	semidirect
7. #20243418	C₂	semidirect
8. C₄×#13093958	C₂	semidirect
9. C₄₇×#1846	C₂	semidirect
14. #15689202	C₄	semidirect
42. C₂×#10625324	C₂×C₄	semidirect
61. #13093958	D₄	semidirect
64. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
65. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
77. C₄×C₈×C₄₇	C₂×C₄	semidirect
205. #1846	D₄₇	semidirect
243. C₄₇	#22664	semidirect
281. C₄×C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689202	2
C₂×#15689162	2
#20246314	2
#20244154	2
#20243584	2
#20243574	2
#20243418	2
C₄×#13093958	2
C₄₇×#1846	2
#22664	47