Subgroups — #26198981

Order 12032.

704 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	#20252837	C₂	1	2	yes	maximal, complemented
2	#20252354	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242953	C₂	1	2	yes	maximal, complemented
4	#20242946	C₂	1	2	yes	maximal, complemented
5	#20242903	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242898	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242869	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242864	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15688874	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242037	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094044	—	2	2	no	—
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	#15689342	—	2	2	no	—
15	#15689335	—	2	2	no	—
16	#15689330	C₂²	1	2	yes	—
17	#15689325	C₂²	1	2	yes	—
18	#15689320	C₂²	1	2	yes	—
19	#15689315	C₂²	1	2	yes	—
20	#15689253	C₂²	1	1	yes	characteristic
21	#15689253	C₂²	1	1	yes	characteristic
22	#15689202	C₂²	1	1	yes	characteristic
23	#15689202	C₂²	1	1	yes	characteristic
24	#15689194	—	2	1	no	—
25	#15689194	—	2	1	no	—
26	#15689176	C₂²	1	1	yes	characteristic
27	#15689174	—	2	1	no	—
28	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
29	#15689119	—	2	2	no	—
30	C₄×#10625324	—	2	1	no	—
31	#15688874	C₂²	1	2	yes	—
32	#15688874	C₂²	1	1	yes	characteristic
33	#15688874	C₂²	1	1	yes	characteristic
34	#15688869	C₂²	1	2	yes	—
35	#15688869	C₂²	1	2	yes	—
36	#15688867	C₂²	1	2	yes	—
37	#15688867	C₂²	1	2	yes	—
38	C₄₇×#532	C₂²	1	2	yes	—
39	C₄₇×#500	C₂²	1	1	yes	characteristic
40	C₄₇×#493	C₂²	1	1	yes	characteristic
41	C₄₇×#486	C₂²	1	2	yes	—
42	C₄₇×#466	—	2	1	no	—
43	C₄₇×#466	—	2	1	no	—
44	C₄×D₈×C₄₇	—	2	1	no	—
45	C₄×D₈×C₄₇	—	2	1	no	—
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	D₄	1	1	yes	characteristic
48	#13094044	—	4	8	no	—
49	C₂×#10625337	—	2	2	no	—
50	C₂×#10625335	—	2	2	no	—
51	C₂×#10625336	—	2	2	no	—
52	C₂×#10625334	—	2	2	no	—
53	C₂×#10625324	—	2	1	no	—
54	C₂×#10625324	—	2	1	no	—
55	C₂²×C₄₇⋊C₈	—	2	2	no	—
56	C₄×Dic₉₄	D₄	1	1	yes	characteristic
57	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
58	C₄×D₁₈₈	D₄	1	1	yes	characteristic
59	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
60	C₄×C₂²⋊D₄₇	—	2	1	no	—
61	C₄×C₂²⋊D₄₇	—	2	1	no	—
62	#13093983	D₄	1	1	yes	characteristic
63	#13093981	—	2	1	no	—
64	C₄²×D₄₇	—	2	1	no	—
65	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
66	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
69	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
70	Dic₄₇⋊C₈	—	2	1	no	—
71	Dic₄₇⋊C₈	—	2	1	no	—
72	#13093948	—	2	2	no	—
73	#13093948	—	2	2	no	—
74	#13093945	—	2	2	no	—
75	#13093945	—	2	2	no	—
76	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
77	(C₂×D₄₇)⋊C₈	—	2	1	no	—
78	(C₂×D₄₇)⋊C₈	—	2	1	no	—
79	#13093934	—	2	1	no	—
80	#13093934	—	2	1	no	—
81	C₄×C₄₇⋊C₈	—	2	1	no	—
82	C₂×#41×C₄₇	—	2	2	no	—
83	C₂×D₈×C₄₇	—	2	1	no	—
84	C₂×D₈×C₄₇	—	2	1	no	—
85	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
87	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
88	#127×C₄₇	C₂³	1	2	yes	—
89	#124×C₄₇	—	2	2	no	—
90	#121×C₄₇	—	2	2	no	—
91	#121×C₄₇	—	2	2	no	—
92	C₄×D₄×C₄₇	—	2	2	no	—
93	C₄×D₄×C₄₇	—	2	2	no	—
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	#107×C₄₇	—	2	1	no	—
96	#107×C₄₇	—	2	1	no	—
97	#102×C₄₇	—	2	2	no	—
98	#102×C₄₇	—	2	2	no	—
99	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	#41×C₄₇	—	4	4	no	—
104	#41×C₄₇	—	4	4	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	2	2	no	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	—	4	2	no	—
110	C₂²×C₄×C₄₇	—	4	2	no	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₇	—	2	1	no	—
115	#10625350	—	2	4	no	—
116	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₄₇	—	2	1	no	—
118	C₂×C₄×D₄₇	—	2	1	no	—
119	C₂×C₄×D₄₇	—	2	1	no	—
120	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
121	D₈×C₄₇	—	4	2	no	—
122	D₈×C₄₇	—	4	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	4	1	no	—
125	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₂²⋊C₄×C₄₇	—	4	2	no	—
132	C₂²⋊C₄×C₄₇	—	4	2	no	—
133	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	#41	1	1	yes	characteristic
136	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
137	C₂²⋊Dic₄₇	—	2	1	no	—
138	#10625337	—	4	4	no	—
139	#10625336	—	4	4	no	—
140	#10625335	—	4	4	no	—
141	#10625334	—	4	4	no	—
142	(C₂×D₄₇)⋊C₄	—	2	1	no	—
143	(C₂×D₄₇)⋊C₄	—	2	1	no	—
144	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
145	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
146	Dic₄₇⋊C₄	—	2	1	no	—
147	Dic₄₇⋊C₄	—	2	1	no	—
148	C₄×Dic₄₇	—	2	1	no	—
149	C₄×Dic₄₇	—	2	1	no	—
150	C₄×Dic₄₇	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	4	4	no	—
156	#10625324	—	4	2	no	—
157	#10625324	—	4	2	no	—
158	C₂³×C₄₇	—	4	2	no	—
159	C₂³×C₄₇	#121	1	1	yes	characteristic
160	C₂²×D₄₇	—	2	1	no	—
161	Q₈×C₄₇	—	4	2	no	—
162	Q₈×C₄₇	—	4	2	no	—
163	D₄×C₄₇	—	4	2	no	—
164	D₄×C₄₇	—	4	2	no	—
165	D₄×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	4	2	no	—
167	D₄×C₄₇	—	8	2	no	—
168	D₄×C₄₇	—	8	4	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	8	4	no	—
174	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
175	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
176	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
177	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	2	1	no	—
183	C₂×Dic₄₇	—	2	1	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	D₁₈₈	—	2	2	no	—
186	C₄×D₄₇	—	4	2	no	—
187	C₄×D₄₇	—	4	1	no	—
188	C₄×D₄₇	—	4	1	no	—
189	C₄×D₄₇	—	4	2	no	—
190	Dic₉₄	—	2	2	no	—
191	C₈×C₄₇	—	2	1	no	—
192	C₈×C₄₇	—	2	1	no	—
193	C₈×C₄₇	—	2	1	no	—
194	C₈×C₄₇	#135	1	2	yes	complemented
195	C₄₇⋊C₈	—	4	1	no	—
196	C₄₇⋊C₈	—	4	2	no	—
197	C₄₇⋊C₈	—	4	2	no	—
198	C₄₇⋊C₈	—	4	1	no	—
199	#19157	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	8	2	no	—
203	C₂²×C₄₇	—	8	2	no	—
204	C₂²×C₄₇	—	8	2	no	—
205	C₂²×C₄₇	#469	1	2	yes	—
206	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
207	C₂×D₄₇	—	4	1	no	—
208	C₂×D₄₇	—	4	1	no	—
209	C₂×D₄₇	—	4	1	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	8	2	no	—
214	C₄×C₄₇	#469	1	2	yes	—
215	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
216	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
217	C₄×C₄₇	#575	1	1	yes	characteristic
218	Dic₄₇	—	4	1	no	—
219	Dic₄₇	—	4	1	no	—
220	Dic₄₇	—	4	1	no	—
221	#3169	D₄₇	1	1	yes	characteristic, complemented
222	#3035	—	47	2	no	—
223	#2965	—	47	1	no	—
224	#1702	—	47	2	no	—
225	#1701	—	47	2	no	—
226	#1694	—	47	1	no	—
227	#1693	—	47	1	no	—
228	#1688	—	47	1	no	—
229	#1687	—	47	1	no	—
230	C₂×#334	—	47	1	no	—
231	#1540	—	47	2	no	—
232	C₂×C₄₇	—	2	2	no	—
233	C₂×C₄₇	—	16	2	no	—
234	C₂×C₄₇	#3035	1	1	yes	characteristic
235	C₂×C₄₇	C₂×#469	1	1	yes	characteristic
236	C₂×C₄₇	#3067	1	1	yes	characteristic
237	D₄₇	—	8	1	no	—
238	C₂×#135	—	94	2	no	—
239	#532	C₂×D₄₇	1	2	yes	—
240	C₄×#41	—	47	1	no	—
241	#500	C₂×D₄₇	1	1	yes	characteristic
242	#493	C₂×D₄₇	1	1	yes	characteristic
243	#486	C₂×D₄₇	1	2	yes	—
244	#466	—	2	1	no	—
245	#466	—	2	1	no	—
246	#464	—	94	2	no	—
247	#463	—	94	2	no	—
248	#462	—	47	2	no	—
249	#461	—	47	2	no	—
250	#460	—	47	2	no	—
251	#459	—	47	2	no	—
252	#446	—	47	1	no	—
253	#446	—	47	1	no	—
254	C₄×D₈	—	2	1	no	—
255	C₄×D₈	—	2	1	no	—
256	#436	—	47	1	no	—
257	#436	—	47	1	no	—
258	#435	—	94	1	no	—
259	#435	—	94	1	no	—
260	#431	—	47	1	no	—
261	#431	—	94	1	no	—
262	C₂×C₄⋊C₈	—	47	2	no	—
263	#416	—	94	2	no	—
264	C₄×M₁₆	—	94	1	no	—
265	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
266	#334	—	47	1	no	—
267	#334	—	47	1	no	—
268	#334	—	47	2	no	—
269	#332	—	47	2	no	—
270	#332	—	47	2	no	—
271	#331	—	47	2	no	—
272	#331	—	47	2	no	—
273	C₄₇	#19157	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	47	1	no	—
276	#135	—	188	8	no	—
277	C₂×Q₁₆	—	94	2	no	—
278	C₂×SD₁₆	—	94	2	no	—
279	C₂×SD₁₆	—	94	2	no	—
280	C₂×D₈	—	2	1	no	—
281	C₂×D₈	—	2	1	no	—
282	C₂×D₈	—	94	2	no	—
283	C₂×M₁₆	—	94	1	no	—
284	C₂×M₁₆	—	94	1	no	—
285	C₂²×C₈	—	94	2	no	—
286	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
287	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
288	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
289	#127	C₂²×D₄₇	1	2	yes	—
290	#124	—	2	2	no	—
291	#121	—	2	2	no	—
292	#121	—	2	2	no	—
293	C₄×Q₈	—	47	1	no	—
294	C₄×Q₈	—	47	1	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	—	47	1	no	—
298	C₄×D₄	—	47	1	no	—
299	C₄×D₄	—	94	1	no	—
300	C₄×D₄	—	94	1	no	—
301	#117	—	47	1	no	—
302	#117	—	94	1	no	—
303	C₂×C₄²	—	94	1	no	—
304	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
305	#107	—	2	1	no	—
306	#107	—	2	1	no	—
307	C₄⋊C₈	—	47	1	no	—
308	C₄⋊C₈	—	47	1	no	—
309	C₄⋊C₈	—	47	2	no	—
310	C₄⋊C₈	—	47	2	no	—
311	C₄⋊C₈	—	94	1	no	—
312	C₄⋊C₈	—	94	1	no	—
313	C₄⋊C₈	—	94	2	no	—
314	#103	—	94	2	no	—
315	#103	—	94	2	no	—
316	#102	—	2	2	no	—
317	#102	—	2	2	no	—
318	#102	—	94	2	no	—
319	#102	—	94	2	no	—
320	C₂²⋊C₈	—	94	1	no	—
321	C₂²⋊C₈	—	94	1	no	—
322	C₂²⋊C₈	—	94	1	no	—
323	#97	—	94	1	no	—
324	#97	—	94	1	no	—
325	C₄×C₈	—	94	1	no	—
326	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
327	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
330	#41	—	4	4	no	—
331	#41	—	4	4	no	—
332	#41	—	94	4	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	47	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	47	1	no	—
340	C₂×D₄	—	94	1	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	94	1	no	—
343	C₂²×C₄	—	94	1	no	—
344	C₂²×C₄	—	94	1	no	—
345	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
346	C₂²×C₄	#10625352	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
348	Q₁₆	—	188	4	no	—
349	SD₁₆	—	188	4	no	—
350	SD₁₆	—	188	4	no	—
351	D₈	—	4	2	no	—
352	D₈	—	4	2	no	—
353	D₈	—	188	4	no	—
354	M₁₆	—	188	2	no	—
355	M₁₆	—	188	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	94	2	no	—
359	C₂×C₈	—	94	2	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	—	94	1	no	—
362	C₂×C₈	—	188	4	no	—
363	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
364	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
365	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
366	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	47	1	no	—
370	C₄⋊C₄	—	47	1	no	—
371	C₄⋊C₄	—	94	1	no	—
372	C₄⋊C₄	—	94	1	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	—	94	1	no	—
376	C₂²⋊C₄	—	94	1	no	—
377	C₂²⋊C₄	—	94	1	no	—
378	C₄²	—	94	1	no	—
379	C₄²	—	94	1	no	—
380	C₄²	—	94	1	no	—
381	C₄²	D₄×D₄₇	1	1	yes	characteristic
382	C₄²	#10625352	1	1	yes	characteristic
383	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
384	C₄²	C₂³×D₄₇	1	1	yes	characteristic
385	C₂³	—	4	2	no	—
386	C₂³	—	94	1	no	—
387	C₂³	#13093995	1	1	yes	characteristic
388	Q₈	—	4	2	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	94	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	4	no	—
397	D₄	—	94	2	no	—
398	D₄	—	188	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	4	no	—
404	C₂×C₄	—	94	1	no	—
405	C₂×C₄	—	94	1	no	—
406	C₂×C₄	—	94	1	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	—	188	2	no	—
409	C₂×C₄	—	188	1	no	—
410	C₂×C₄	—	188	1	no	—
411	C₂×C₄	#13093995	1	1	yes	characteristic
412	C₂×C₄	#13093995	1	1	yes	characteristic
413	C₂×C₄	#13093995	1	1	yes	characteristic
414	C₂×C₄	#13094048	1	4	yes	—
415	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	188	1	no	—
422	C₈	—	188	2	no	—
423	C₈	—	188	2	no	—
424	C₈	—	188	1	no	—
425	C₈	#13094044	1	2	yes	complemented
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	188	1	no	—
432	C₂²	—	188	1	no	—
433	C₂²	—	188	1	no	—
434	C₂²	#15689373	1	2	yes	—
435	C₂²	C₂×#13093995	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	8	2	no	—
440	C₄	—	188	1	no	—
441	C₄	—	188	1	no	—
442	C₄	—	188	1	no	—
443	C₄	#15689373	1	2	yes	—
444	C₄	C₂×#13094044	1	1	yes	characteristic
445	C₄	C₂×#13094048	1	2	yes	—
446	C₄	#15689921	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	16	2	no	—
449	C₂	—	376	1	no	—
450	C₂	#20252837	1	1	yes	characteristic
451	C₂	C₂×#15689373	1	1	yes	characteristic
452	C₂	#20253104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093995
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3169	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	#3169	D₄₇
hypocenter	C₄₇	#19157
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #20252837	C₂	semidirect
2. #20252354	C₂	semidirect
3. #20242953	C₂	semidirect
4. #20242946	C₂	semidirect
5. #20242903	C₂	semidirect
6. #20242898	C₂	semidirect
7. #20242869	C₂	semidirect
8. #20242864	C₂	semidirect
9. C₂×#15688874	C₂	semidirect
10. #20242037	C₂	semidirect
11. C₄₇×#3169	C₂	semidirect
194. C₈×C₄₇	#135	semidirect
221. #3169	D₄₇	semidirect
273. C₄₇	#19157	semidirect
425. C₈	#13094044	semidirect

Maximal subgroups

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

subgroup	index
#20252837	2
#20252354	2
#20242953	2
#20242946	2
#20242903	2
#20242898	2
#20242869	2
#20242864	2
C₂×#15688874	2
#20242037	2
C₄₇×#3169	2
#19157	47