Subgroups — #26234732

Order 12032.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689244	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689239	C₂	1	1	yes	maximal, characteristic
3	#20252190	C₂	1	1	yes	maximal, characteristic
4	#20251957	C₂	1	2	yes	maximal, complemented
5	#20244139	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244134	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243660	C₂	1	2	yes	maximal, complemented
8	#20243660	C₂	1	2	yes	maximal, complemented
9	#20243405	C₂	1	2	yes	maximal, complemented
10	#20243260	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1849	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	C₂×#13094032	C₂²	1	2	yes	—
14	C₂×#13094032	C₂²	1	2	yes	—
15	C₄×#10625350	C₂²	1	2	yes	—
16	#15689244	—	2	4	no	—
17	#15689239	—	2	4	no	—
18	#15689236	C₄	1	2	yes	complemented
19	#15689231	C₄	1	2	yes	complemented
20	#15689225	C₄	1	2	yes	complemented
21	#15689225	C₄	1	2	yes	complemented
22	#15689161	C₂²	1	1	yes	characteristic
23	#15689151	C₂²	1	2	yes	—
24	#15689151	C₂²	1	2	yes	—
25	#15689148	—	2	2	no	—
26	#15689148	—	2	2	no	—
27	#15689145	—	2	2	no	—
28	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
29	C₄⋊C₈×D₄₇	—	2	2	no	—
30	C₂×#13093950	C₂²	1	2	yes	—
31	C₂×#13093950	C₂²	1	2	yes	—
32	#15689120	C₂²	1	2	yes	—
33	C₂×#13093934	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
36	#15688884	C₂²	1	2	yes	—
37	#15688884	C₂²	1	2	yes	—
38	#15688877	C₂²	1	1	yes	characteristic
39	#15688877	C₂²	1	1	yes	characteristic
40	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#108×C₄₇	C₂²	1	2	yes	—
43	C₄₇×#423	C₂²	1	2	yes	—
44	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#10625350	C₂³	1	2	yes	—
46	#13094046	D₄	1	4	yes	—
47	#13094046	Q₈	1	4	yes	—
48	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
49	C₂×#10625325	C₂×C₄	1	2	yes	—
50	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
51	#13094032	—	2	4	no	—
52	#13094032	—	2	4	no	—
53	#13094032	—	4	2	no	—
54	#13094032	—	4	2	no	—
55	C₂×#10625324	—	2	2	no	—
56	C₂×#10625324	—	2	2	no	—
57	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₄₇	—	2	2	no	—
60	C₂×C₈×D₄₇	—	2	2	no	—
61	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
62	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
63	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
64	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
65	C₄×C₂²⋊D₄₇	—	2	2	no	—
66	C₄×C₂²⋊D₄₇	—	2	2	no	—
67	#13093983	C₂³	1	2	yes	—
68	#13093981	—	2	2	no	—
69	C₂×C₄⋊Dic₄₇	—	2	1	no	—
70	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	C₄²×D₄₇	—	2	2	no	—
73	#13093958	C₂×C₄	1	1	yes	characteristic
74	#13093958	C₂×C₄	1	1	yes	characteristic
75	#13093956	C₂×C₄	1	2	yes	—
76	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
77	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
78	Dic₄₇⋊C₈	—	2	2	no	—
79	Dic₄₇⋊C₈	—	2	2	no	—
80	Dic₄₇⋊C₈	—	2	2	no	—
81	Dic₄₇⋊C₈	—	2	2	no	—
82	#13093950	—	2	4	no	—
83	#13093950	—	2	4	no	—
84	#13093949	C₂×C₄	1	2	yes	—
85	#13093949	C₂×C₄	1	2	yes	—
86	#13093946	C₂×C₄	1	2	yes	—
87	#13093946	C₂×C₄	1	2	yes	—
88	#13093934	—	2	2	no	—
89	C₈×Dic₄₇	—	2	2	no	—
90	C₄₇⋊#95	—	2	1	no	—
91	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
92	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
93	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	#108×C₄₇	—	2	2	no	—
97	#108×C₄₇	—	2	2	no	—
98	#108×C₄₇	—	4	2	no	—
99	C₄⋊C₈×C₄₇	—	2	2	no	—
100	C₄⋊C₈×C₄₇	—	2	2	no	—
101	#97×C₄₇	C₂×C₄	1	2	yes	—
102	#97×C₄₇	C₂×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₇	—	2	2	no	—
107	C₂²×Dic₄₇	—	2	1	no	—
108	C₂²×Dic₄₇	—	2	1	no	—
109	#10625350	—	2	2	no	—
110	#10625350	—	2	2	no	—
111	#10625350	C₂×D₄	1	4	yes	—
112	#10625350	C₂×Q₈	1	4	yes	—
113	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₄₇	—	2	2	no	—
115	C₂×C₄×D₄₇	—	2	2	no	—
116	C₂×C₄×D₄₇	—	2	2	no	—
117	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
118	M₁₆×C₄₇	—	2	2	no	—
119	M₁₆×C₄₇	—	2	2	no	—
120	M₁₆×C₄₇	—	2	2	no	—
121	M₁₆×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
131	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
132	C₄²×C₄₇	C₂×D₄	1	2	yes	—
133	C₂²⋊Dic₄₇	—	2	2	no	—
134	(C₂×D₄₇)⋊C₄	—	2	2	no	—
135	(C₂×D₄₇)⋊C₄	—	2	2	no	—
136	C₄⋊Dic₄₇	—	4	2	no	—
137	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
138	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
139	Dic₄₇⋊C₄	—	2	2	no	—
140	Dic₄₇⋊C₄	—	2	2	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	1	no	—
146	C₄×Dic₄₇	—	2	1	no	—
147	C₄×Dic₄₇	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
155	Dic₁₈₈	C₄⋊C₄	1	4	yes	complemented
156	D₃₇₆	C₄⋊C₄	1	4	yes	complemented
157	#10625325	C₄⋊C₄	1	8	yes	complemented
158	#10625324	—	4	4	no	—
159	#10625324	—	4	4	no	—
160	C₈×D₄₇	—	4	4	no	—
161	C₈×D₄₇	—	4	4	no	—
162	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂²×D₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
174	C₂²⋊D₄₇	—	2	4	no	—
175	C₂²⋊D₄₇	—	2	4	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	2	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	4	1	no	—
181	C₂×Dic₄₇	—	4	1	no	—
182	C₂×Dic₄₇	—	4	1	no	—
183	C₂×Dic₄₇	—	4	1	no	—
184	C₂×Dic₄₇	—	4	1	no	—
185	D₁₈₈	—	2	2	no	—
186	D₁₈₈	C₂×C₄⋊C₄	1	4	yes	—
187	C₄×D₄₇	—	2	4	no	—
188	C₄×D₄₇	—	2	4	no	—
189	C₄×D₄₇	—	4	4	no	—
190	C₄×D₄₇	—	8	2	no	—
191	Dic₉₄	—	2	2	no	—
192	Dic₉₄	C₂×C₄⋊C₄	1	4	yes	—
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	—	4	2	no	—
195	C₈×C₄₇	—	4	2	no	—
196	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
197	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
198	C₄₇⋊C₈	—	2	1	no	—
199	C₄₇⋊C₈	—	2	2	no	—
200	C₄₇⋊C₈	—	2	1	no	—
201	#22687	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	—	2	1	no	—
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₄₇	#547	1	1	yes	characteristic
206	C₂²×C₄₇	#554	1	1	yes	characteristic
207	C₂×D₄₇	—	2	4	no	—
208	C₂×D₄₇	—	4	2	no	—
209	C₂×D₄₇	—	4	2	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
213	C₄×C₄₇	#520	1	1	yes	characteristic
214	C₄×C₄₇	D₄²	1	1	yes	characteristic
215	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
216	Dic₄₇	—	2	4	no	—
217	Dic₄₇	—	4	2	no	—
218	Dic₄₇	—	4	2	no	—
219	Dic₄₇	—	4	2	no	—
220	Dic₄₇	—	8	1	no	—
221	C₂×#444	—	47	1	no	—
222	C₂×#443	—	47	1	no	—
223	#2943	—	47	1	no	—
224	#2906	—	47	2	no	—
225	#1946	—	47	1	no	—
226	#1945	—	47	1	no	—
227	#1866	—	47	2	no	—
228	#1866	—	47	2	no	—
229	#1849	D₄₇	1	1	yes	characteristic, complemented
230	#1806	—	47	2	no	—
231	#1771	—	47	1	no	—
232	C₂×C₄₇	—	2	1	no	—
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₄₇	#2955	1	1	yes	characteristic
236	C₂×C₄₇	#2956	1	1	yes	characteristic
237	D₄₇	—	4	4	no	—
238	C₂×#135	—	47	1	no	—
239	C₂×#131	—	47	2	no	—
240	C₂×#131	—	47	2	no	—
241	C₄×#41	—	47	2	no	—
242	#444	—	94	4	no	—
243	#443	—	94	4	no	—
244	#442	—	47	2	no	—
245	#441	—	47	2	no	—
246	#440	—	47	2	no	—
247	#440	—	47	2	no	—
248	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
249	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
250	C₂×#108	C₂×D₄₇	1	2	yes	—
251	#427	—	47	1	no	—
252	#424	—	47	2	no	—
253	#424	—	47	2	no	—
254	#424	—	94	2	no	—
255	#424	—	94	2	no	—
256	#423	—	94	2	no	—
257	#423	C₂×D₄₇	1	2	yes	—
258	C₂×C₄⋊C₈	—	47	1	no	—
259	C₂×C₄⋊C₈	—	94	2	no	—
260	C₂×#104	—	47	2	no	—
261	C₂×#104	—	47	2	no	—
262	#416	—	47	2	no	—
263	C₂×#97	—	47	1	no	—
264	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
265	C₂×C₄×C₈	—	47	1	no	—
266	C₄×C₄⋊C₄	—	47	1	no	—
267	#339	—	47	2	no	—
268	#339	—	47	2	no	—
269	#336	—	47	1	no	—
270	#336	—	47	1	no	—
271	C₄₇	#22687	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	47	2	no	—
273	#135	—	47	4	no	—
274	#135	—	47	4	no	—
275	C₂×Q₁₆	—	47	1	no	—
276	C₂×SD₁₆	—	47	2	no	—
277	C₂×D₈	—	47	1	no	—
278	#131	—	94	4	no	—
279	#131	—	94	4	no	—
280	#131	—	188	2	no	—
281	#131	—	188	2	no	—
282	C₂×M₁₆	—	94	2	no	—
283	C₂×M₁₆	—	94	2	no	—
284	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
285	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
286	C₂²×C₈	—	47	1	no	—
287	C₂²×C₈	—	47	1	no	—
288	C₂²×C₈	—	94	2	no	—
289	C₂²×C₈	—	94	2	no	—
290	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
292	C₄×Q₈	—	47	2	no	—
293	C₄×Q₈	—	47	2	no	—
294	C₄×D₄	—	47	2	no	—
295	C₄×D₄	—	47	2	no	—
296	C₄×D₄	—	94	2	no	—
297	C₄×D₄	—	94	2	no	—
298	#117	—	47	2	no	—
299	#117	—	94	2	no	—
300	C₂×C₄⋊C₄	—	94	1	no	—
301	C₂×C₄²	—	47	1	no	—
302	C₂×C₄²	—	47	1	no	—
303	C₂×C₄²	—	94	2	no	—
304	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
305	#108	—	2	2	no	—
306	#108	—	2	2	no	—
307	#108	—	4	2	no	—
308	#107	—	47	1	no	—
309	#107	—	47	1	no	—
310	#106	—	47	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	—	47	2	no	—
314	C₄⋊C₈	—	47	2	no	—
315	C₄⋊C₈	—	94	2	no	—
316	C₄⋊C₈	—	94	2	no	—
317	C₄⋊C₈	—	94	2	no	—
318	C₄⋊C₈	—	94	2	no	—
319	#104	—	94	4	no	—
320	#104	—	94	4	no	—
321	#103	—	47	2	no	—
322	#103	—	47	2	no	—
323	#102	—	47	2	no	—
324	#102	—	47	2	no	—
325	#97	—	94	2	no	—
326	#97	C₄×D₄₇	1	2	yes	—
327	#97	C₄×D₄₇	1	2	yes	—
328	C₄×C₈	—	94	2	no	—
329	#95	—	94	1	no	—
330	#41	—	47	4	no	—
331	#41	—	47	4	no	—
332	#41	—	94	2	no	—
333	#41	—	94	2	no	—
334	C₂×Q₈	—	47	2	no	—
335	C₂×D₄	—	47	2	no	—
336	C₂×D₄	—	94	2	no	—
337	C₂²×C₄	—	94	2	no	—
338	C₂²×C₄	—	94	1	no	—
339	C₂²×C₄	—	94	2	no	—
340	C₂²×C₄	—	94	2	no	—
341	C₂²×C₄	—	94	1	no	—
342	C₂²×C₄	#10625354	1	1	yes	characteristic
343	C₂²×C₄	#10625354	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
345	Q₁₆	—	47	4	no	—
346	SD₁₆	—	47	8	no	—
347	D₈	—	47	4	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	188	4	no	—
353	M₁₆	—	188	4	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	47	1	no	—
359	C₂×C₈	—	47	2	no	—
360	C₂×C₈	—	47	1	no	—
361	C₂×C₈	—	94	1	no	—
362	C₂×C₈	—	94	1	no	—
363	C₂×C₈	—	94	1	no	—
364	C₂×C₈	—	94	1	no	—
365	C₂×C₈	—	188	4	no	—
366	C₂×C₈	—	188	4	no	—
367	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
368	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
369	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
370	C₂×C₈	D₄×D₄₇	1	2	yes	—
371	C₂×C₈	Q₈×D₄₇	1	2	yes	—
372	C₄⋊C₄	—	47	2	no	—
373	C₄⋊C₄	—	47	2	no	—
374	C₄⋊C₄	—	94	2	no	—
375	C₄⋊C₄	—	94	2	no	—
376	C₄⋊C₄	—	188	2	no	—
377	C₂²⋊C₄	—	94	2	no	—
378	C₂²⋊C₄	—	94	2	no	—
379	C₂²⋊C₄	—	94	2	no	—
380	C₄²	—	94	2	no	—
381	C₄²	—	94	2	no	—
382	C₄²	—	94	2	no	—
383	C₄²	—	94	1	no	—
384	C₄²	—	94	1	no	—
385	C₄²	—	94	1	no	—
386	C₄²	—	94	1	no	—
387	C₄²	C₂×C₄×D₄₇	1	2	yes	—
388	C₄²	D₄×D₄₇	1	2	yes	—
389	C₂³	—	94	2	no	—
390	C₂³	C₂×#10625354	1	1	yes	characteristic
391	Q₈	—	47	4	no	—
392	Q₈	—	94	2	no	—
393	D₄	—	47	4	no	—
394	D₄	—	94	4	no	—
395	D₄	—	94	4	no	—
396	D₄	—	94	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	94	2	no	—
400	C₂×C₄	—	94	4	no	—
401	C₂×C₄	—	94	4	no	—
402	C₂×C₄	—	94	2	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	94	2	no	—
405	C₂×C₄	—	376	2	no	—
406	C₂×C₄	—	188	4	no	—
407	C₂×C₄	—	188	1	no	—
408	C₂×C₄	—	188	1	no	—
409	C₂×C₄	—	188	1	no	—
410	C₂×C₄	—	188	1	no	—
411	C₂×C₄	—	188	1	no	—
412	C₂×C₄	#13093986	1	2	yes	—
413	C₂×C₄	#13093986	1	2	yes	—
414	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
418	C₂×C₄	#13094069	1	1	yes	characteristic
419	C₂×C₄	#13094072	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₈	—	94	1	no	—
424	C₈	—	94	2	no	—
425	C₈	—	94	1	no	—
426	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
427	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	94	4	no	—
431	C₂²	—	188	2	no	—
432	C₂²	—	188	2	no	—
433	C₂²	C₂×#13093986	1	1	yes	characteristic
434	C₂²	#15689776	1	1	yes	characteristic
435	C₂²	#15689834	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	94	4	no	—
439	C₄	—	376	1	no	—
440	C₄	—	188	2	no	—
441	C₄	—	188	2	no	—
442	C₄	—	188	2	no	—
443	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
444	C₄	#15689604	1	1	yes	characteristic
445	C₄	#15689758	1	1	yes	characteristic
446	C₄	#15689788	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	188	4	no	—
450	C₂	#20246288	1	1	yes	characteristic
451	C₂	#20252290	1	1	yes	characteristic
452	C₂	#20252297	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1849	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094046	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1849	D₄₇
hypocenter	C₄₇	#22687
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1849

Complements

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

N	H ≅ G/N	type
4. #20251957	C₂	semidirect
5. #20244139	C₂	semidirect
6. #20244134	C₂	semidirect
7. #20243660	C₂	semidirect
8. #20243660	C₂	semidirect
9. #20243405	C₂	semidirect
10. #20243260	C₂	semidirect
11. C₄₇×#1849	C₂	semidirect
18. #15689236	C₄	semidirect
19. #15689231	C₄	semidirect
20. #15689225	C₄	semidirect
21. #15689225	C₄	semidirect
155. Dic₁₈₈	C₄⋊C₄	semidirect
156. D₃₇₆	C₄⋊C₄	semidirect
157. #10625325	C₄⋊C₄	semidirect
229. #1849	D₄₇	semidirect
271. C₄₇	#22687	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689244	2
C₂×#15689239	2
#20252190	2
#20251957	2
#20244139	2
#20244134	2
#20243660	2
#20243405	2
#20243260	2
C₄₇×#1849	2
#22687	47