Subgroups — #26223102

Order 12032.

914 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252993	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689240	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252085	C₂	1	2	yes	maximal, complemented
4	C₂×#15689080	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244141	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244102	C₂	1	2	yes	maximal, complemented
7	#20243833	C₂	1	2	yes	maximal, complemented
8	#20243427	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243270	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243226	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1975	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094031	C₂²	1	2	yes	—
13	C₂²×#10625324	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
15	#15689630	C₂²	1	2	yes	—
16	C₂×#13093981	C₂²	1	1	yes	characteristic
17	#15689378	C₄	1	2	yes	complemented
18	#15689373	C₄	1	2	yes	complemented
19	#15689366	C₄	1	4	yes	complemented
20	#15689240	—	2	4	no	—
21	#15689197	—	2	4	no	—
22	(C₂²⋊D₄₇)⋊C₈	—	2	4	no	—
23	C₂×#13093960	C₂²	1	1	yes	characteristic
24	#15689161	C₂²	1	1	yes	characteristic
25	#15689149	C₂²	1	2	yes	—
26	C₂×#13093951	C₂²	1	2	yes	—
27	#15689119	C₂²	1	2	yes	—
28	#15689086	C₂²	1	2	yes	—
29	#15689081	C₂²	1	2	yes	—
30	#15689080	—	2	4	no	—
31	C₂×#13093934	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	#15688887	C₂²	1	2	yes	—
35	#15688884	C₂²	1	2	yes	—
36	#15688883	C₂²	1	2	yes	—
37	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#104×C₄₇	C₂²	1	2	yes	—
40	C₄₇×#408	C₂²	1	2	yes	—
41	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
43	#13094031	—	2	4	no	—
44	#13094031	—	2	4	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂×#10625329	C₂³	1	2	yes	—
47	C₂×#10625324	—	2	2	no	—
48	C₂×#10625324	—	2	2	no	—
49	C₂×#10625324	C₂×C₄	1	2	yes	—
50	C₂×#10625324	C₂×C₄	1	2	yes	—
51	C₂²×C₄₇⋊C₈	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₄₇	—	2	2	no	—
55	C₂×C₈×D₄₇	—	2	2	no	—
56	C₂×C₈×D₄₇	D₄	1	2	yes	—
57	C₂×C₈×D₄₇	D₄	1	2	yes	—
58	#13094005	—	2	2	no	—
59	#13094000	C₂×C₄	1	4	yes	—
60	#13093995	C₂×C₄	1	4	yes	—
61	#13093992	—	2	2	no	—
62	C₄×C₂²⋊D₄₇	—	2	4	no	—
63	#13093983	C₂³	1	2	yes	—
64	#13093981	—	2	2	no	—
65	#13093981	—	2	2	no	—
66	C₂×Dic₄₇⋊C₄	—	2	1	no	—
67	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
68	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
69	#13093960	—	2	2	no	—
70	#13093958	C₂×C₄	1	2	yes	—
71	#13093956	C₂×C₄	1	2	yes	—
72	Dic₄₇⋊C₈	—	2	4	no	—
73	#13093951	—	2	4	no	—
74	#13093948	C₂×C₄	1	4	yes	—
75	#13093945	C₂×C₄	1	4	yes	—
76	(C₂×D₄₇)⋊C₈	—	2	4	no	—
77	#13093934	—	2	2	no	—
78	#13093934	—	2	2	no	—
79	C₄×C₄₇⋊C₈	—	2	2	no	—
80	C₈×Dic₄₇	—	2	2	no	—
81	C₈×Dic₄₇	D₄	1	4	yes	complemented
82	C₂×#41×C₄₇	C₂³	1	2	yes	—
83	#135×C₄₇	—	2	2	no	—
84	#135×C₄₇	—	2	2	no	—
85	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
87	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
89	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	#108×C₄₇	—	2	2	no	—
93	#104×C₄₇	—	2	4	no	—
94	C₂²⋊C₈×C₄₇	—	2	4	no	—
95	#97×C₄₇	—	2	2	no	—
96	C₂³×D₄₇	#41	1	1	yes	characteristic
97	#41×C₄₇	—	2	2	no	—
98	#41×C₄₇	—	2	2	no	—
99	#41×C₄₇	—	2	2	no	—
100	#41×C₄₇	—	2	2	no	—
101	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₂×C₂²⋊D₄₇	—	2	4	no	—
108	C₂²×Dic₄₇	—	2	1	no	—
109	C₂²×Dic₄₇	#41	1	1	yes	characteristic
110	C₂×C₄×D₄₇	—	2	1	no	—
111	C₂×C₄×D₄₇	—	2	1	no	—
112	C₂×C₄×D₄₇	—	2	1	no	—
113	C₂×C₄×D₄₇	—	2	1	no	—
114	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
115	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
116	Q₁₆×C₄₇	—	2	2	no	—
117	SD₁₆×C₄₇	—	2	4	no	—
118	D₈×C₄₇	—	2	2	no	—
119	M₁₆×C₄₇	—	2	2	no	—
120	M₁₆×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₇	#41	1	2	yes	—
129	C₄²×C₄₇	—	2	1	no	—
130	C₄²×C₄₇	#41	1	2	yes	—
131	C₂²⋊Dic₄₇	—	2	2	no	—
132	C₂²⋊Dic₄₇	—	2	4	no	—
133	(C₂×D₄₇)⋊C₄	—	2	4	no	—
134	(C₂×D₄₇)⋊C₄	—	2	4	no	—
135	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
136	Dic₄₇⋊C₄	—	2	4	no	—
137	Dic₄₇⋊C₄	—	2	4	no	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	1	no	—
140	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
141	#10625329	—	2	2	no	—
142	#10625329	—	2	2	no	—
143	#10625329	—	4	4	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	4	4	no	—
148	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄₇⋊C₈	#41	1	2	yes	—
153	#10625324	—	2	4	no	—
154	#10625324	—	2	4	no	—
155	C₈×D₄₇	—	2	4	no	—
156	C₈×D₄₇	—	2	4	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂²×D₄₇	—	2	1	no	—
160	C₂²×D₄₇	—	2	1	no	—
161	C₂²×D₄₇	—	4	2	no	—
162	C₂²×D₄₇	C₄×D₄	1	2	yes	—
163	Q₈×C₄₇	—	2	2	no	—
164	Q₈×C₄₇	—	2	2	no	—
165	D₄×C₄₇	—	2	2	no	—
166	D₄×C₄₇	—	2	2	no	—
167	D₄×C₄₇	—	4	2	no	—
168	D₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₄₇	—	4	8	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	1	no	—
183	C₂×Dic₄₇	—	2	4	no	—
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
187	C₄×D₄₇	—	2	2	no	—
188	C₄×D₄₇	—	2	2	no	—
189	C₄×D₄₇	—	2	2	no	—
190	C₄×D₄₇	—	2	2	no	—
191	C₈×C₄₇	—	2	2	no	—
192	C₈×C₄₇	—	4	2	no	—
193	C₈×C₄₇	C₄×D₄	1	2	yes	—
194	C₈×C₄₇	C₄×D₄	1	2	yes	—
195	C₄₇⋊C₈	—	2	2	no	—
196	C₄₇⋊C₈	—	4	2	no	—
197	C₄₇⋊C₈	#121	1	2	yes	—
198	C₄₇⋊C₈	#121	1	2	yes	—
199	#21548	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	4	4	no	—
202	C₂²×C₄₇	—	4	2	no	—
203	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂²×C₄₇	#525	1	1	yes	characteristic
205	C₂²×C₄₇	#529	1	1	yes	characteristic
206	C₂×D₄₇	—	2	4	no	—
207	C₂×D₄₇	—	2	2	no	—
208	C₂×D₄₇	—	4	2	no	—
209	C₂×D₄₇	—	4	2	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
214	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
215	C₄×C₄₇	#532	1	1	yes	characteristic
216	Dic₄₇	—	2	2	no	—
217	Dic₄₇	—	4	2	no	—
218	Dic₄₇	—	4	4	no	—
219	#3054	—	47	1	no	—
220	C₂×#443	—	47	1	no	—
221	#2929	—	47	2	no	—
222	C₂×#405	—	47	1	no	—
223	#1975	D₄₇	1	1	yes	characteristic, complemented
224	#1946	—	47	1	no	—
225	#1938	—	47	2	no	—
226	#1897	—	47	2	no	—
227	#1811	—	47	1	no	—
228	#1772	—	47	1	no	—
229	#1764	—	47	2	no	—
230	C₂×C₄₇	—	2	1	no	—
231	C₂×C₄₇	—	2	1	no	—
232	C₂×C₄₇	—	8	2	no	—
233	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
234	C₂×C₄₇	#2955	1	2	yes	—
235	D₄₇	—	4	2	no	—
236	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
237	C₂×#131	—	47	2	no	—
238	C₂²×M₁₆	—	47	1	no	—
239	C₂³×C₈	—	47	1	no	—
240	#525	—	47	2	no	—
241	C₂×#117	—	47	1	no	—
242	#470	—	47	2	no	—
243	#469	—	47	2	no	—
244	#468	—	47	4	no	—
245	#443	—	94	4	no	—
246	#435	—	94	4	no	—
247	C₈×D₄	—	94	4	no	—
248	C₂×#108	—	47	1	no	—
249	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
250	#427	—	47	1	no	—
251	#424	—	47	2	no	—
252	C₂×#104	—	47	2	no	—
253	C₂×#104	C₂×D₄₇	1	2	yes	—
254	#416	—	47	2	no	—
255	#408	C₂×D₄₇	1	2	yes	—
256	#407	—	47	2	no	—
257	#405	—	47	2	no	—
258	#405	—	94	4	no	—
259	C₂×#97	—	47	1	no	—
260	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
261	C₂×C₄×C₈	—	47	1	no	—
262	C₂×C₄×C₈	—	47	1	no	—
263	#341	—	47	2	no	—
264	#339	—	47	2	no	—
265	#339	—	47	2	no	—
266	C₄₇	#21548	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	C₂²×D₄₇	1	2	yes	—
268	C₂³×C₄	—	47	1	no	—
269	#135	—	2	2	no	—
270	#135	—	2	2	no	—
271	C₂×Q₁₆	C₄×D₄₇	1	1	yes	characteristic
272	C₂×SD₁₆	C₄×D₄₇	1	2	yes	—
273	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic
274	#131	—	94	4	no	—
275	#131	—	94	4	no	—
276	C₂×M₁₆	—	47	2	no	—
277	C₂×M₁₆	—	47	2	no	—
278	C₂×M₁₆	—	47	2	no	—
279	C₂×M₁₆	—	94	2	no	—
280	C₂×M₁₆	—	94	2	no	—
281	C₂×M₁₆	—	94	2	no	—
282	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
283	C₂²×C₈	—	47	1	no	—
284	C₂²×C₈	—	47	1	no	—
285	C₂²×C₈	—	47	2	no	—
286	C₂²×C₈	—	47	2	no	—
287	C₂²×C₈	—	94	2	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	#123	—	94	2	no	—
293	C₂²⋊Q₈	—	47	4	no	—
294	#121	—	47	4	no	—
295	#120	—	94	2	no	—
296	C₄×D₄	—	94	4	no	—
297	#117	—	47	2	no	—
298	#117	—	94	2	no	—
299	#117	—	94	2	no	—
300	C₂×C₄⋊C₄	—	94	1	no	—
301	C₂×C₂²⋊C₄	—	94	1	no	—
302	C₂×C₄²	—	47	1	no	—
303	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
304	#108	—	2	2	no	—
305	#108	—	94	2	no	—
306	#107	—	47	2	no	—
307	#106	—	47	2	no	—
308	C₄⋊C₈	—	94	4	no	—
309	#104	—	2	4	no	—
310	#104	—	94	4	no	—
311	#103	—	47	4	no	—
312	#102	—	47	4	no	—
313	C₂²⋊C₈	—	2	4	no	—
314	C₂²⋊C₈	—	94	4	no	—
315	#97	—	2	2	no	—
316	#97	—	94	2	no	—
317	#97	—	94	2	no	—
318	C₄×C₈	—	47	4	no	—
319	C₄×C₈	—	94	2	no	—
320	C₄×C₈	—	94	2	no	—
321	C₂⁴	—	47	1	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	94	4	no	—
329	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	47	1	no	—
333	C₂²×C₄	—	47	2	no	—
334	C₂²×C₄	—	47	2	no	—
335	C₂²×C₄	—	94	1	no	—
336	C₂²×C₄	—	94	1	no	—
337	C₂²×C₄	—	94	1	no	—
338	C₂²×C₄	—	94	1	no	—
339	C₂²×C₄	—	94	1	no	—
340	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
341	Q₁₆	—	2	2	no	—
342	SD₁₆	—	2	4	no	—
343	D₈	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	94	4	no	—
347	M₁₆	—	94	4	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	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	47	2	no	—
355	C₂×C₈	—	47	1	no	—
356	C₂×C₈	—	47	1	no	—
357	C₂×C₈	—	47	2	no	—
358	C₂×C₈	—	47	2	no	—
359	C₂×C₈	—	94	4	no	—
360	C₂×C₈	—	94	4	no	—
361	C₂×C₈	—	94	1	no	—
362	C₂×C₈	—	94	1	no	—
363	C₂×C₈	—	94	2	no	—
364	C₂×C₈	—	188	4	no	—
365	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₂×C₈	D₄×D₄₇	1	2	yes	—
368	C₂×C₈	D₄×D₄₇	1	2	yes	—
369	C₂×C₈	#10625352	1	2	yes	—
370	C₄⋊C₄	—	47	4	no	—
371	C₄⋊C₄	—	94	4	no	—
372	C₄⋊C₄	—	94	4	no	—
373	C₂²⋊C₄	—	94	4	no	—
374	C₂²⋊C₄	—	94	4	no	—
375	C₂²⋊C₄	—	94	4	no	—
376	C₂²⋊C₄	—	94	2	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	47	2	no	—
379	C₄²	—	94	2	no	—
380	C₄²	—	94	1	no	—
381	C₄²	#10625352	1	2	yes	—
382	C₂³	—	2	2	no	—
383	C₂³	—	47	2	no	—
384	C₂³	—	94	1	no	—
385	C₂³	—	94	1	no	—
386	C₂³	—	188	2	no	—
387	C₂³	#41×D₄₇	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	188	8	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	47	2	no	—
401	C₂×C₄	—	94	1	no	—
402	C₂×C₄	—	94	1	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	94	2	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	94	2	no	—
407	C₂×C₄	—	94	4	no	—
408	C₂×C₄	—	94	2	no	—
409	C₂×C₄	—	188	2	no	—
410	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
413	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
415	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	47	2	no	—
419	C₈	—	47	2	no	—
420	C₈	—	94	2	no	—
421	C₈	—	188	2	no	—
422	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
423	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
424	C₂²	—	2	2	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	94	4	no	—
428	C₂²	—	94	2	no	—
429	C₂²	—	188	2	no	—
430	C₂²	—	188	2	no	—
431	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
432	C₂²	#15689633	1	1	yes	characteristic
433	C₂²	#15689652	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	94	2	no	—
437	C₄	—	188	2	no	—
438	C₄	—	188	4	no	—
439	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
440	C₄	C₄×#10625352	1	1	yes	characteristic
441	C₄	#121×D₄₇	1	1	yes	characteristic
442	C₄	#15689671	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	8	2	no	—
446	C₂	—	188	2	no	—
447	C₂	#20245904	1	1	yes	characteristic
448	C₂	#20252288	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1975	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20252993	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1975	D₄₇
hypocenter	C₄₇	#21548
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1975

Complements

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

N	H ≅ G/N	type
2. C₂×#15689240	C₂	semidirect
3. #20252085	C₂	semidirect
4. C₂×#15689080	C₂	semidirect
5. #20244141	C₂	semidirect
6. #20244102	C₂	semidirect
7. #20243833	C₂	semidirect
8. #20243427	C₂	semidirect
9. #20243270	C₂	semidirect
10. #20243226	C₂	semidirect
11. C₄₇×#1975	C₂	semidirect
17. #15689378	C₄	semidirect
18. #15689373	C₄	semidirect
19. #15689366	C₄	semidirect
81. C₈×Dic₄₇	D₄	semidirect
223. #1975	D₄₇	semidirect
266. C₄₇	#21548	semidirect

Maximal subgroups

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

subgroup	index
#20252993	2
C₂×#15689240	2
#20252085	2
C₂×#15689080	2
#20244141	2
#20244102	2
#20243833	2
#20243427	2
#20243270	2
#20243226	2
C₄₇×#1975	2
#21548	47