Subgroups — #26198717

Order 12032.

726 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253967	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252845	C₂	1	2	yes	maximal, complemented
3	C₈×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242833	C₂	1	2	yes	maximal, complemented
5	#20242826	C₂	1	2	yes	maximal, complemented
6	#20242783	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242778	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242749	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242744	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242038	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#335	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	—	2	2	no	—
13	#15689673	C₂²	1	2	yes	—
14	C₄×#10625350	C₂²	1	1	yes	characteristic
15	#15689528	C₂²	1	1	yes	characteristic
16	#15689500	C₂²	1	1	yes	characteristic
17	#15689470	C₂²	1	2	yes	—
18	#15689359	—	2	1	no	—
19	#15689359	—	2	1	no	—
20	#15689346	—	2	2	no	—
21	#15689339	—	2	2	no	—
22	#15689334	C₂²	1	2	yes	—
23	#15689329	C₂²	1	2	yes	—
24	#15689324	C₂²	1	2	yes	—
25	#15689319	C₂²	1	2	yes	—
26	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
27	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
28	C₄×D₃₇₆	—	2	1	no	—
29	C₄×D₃₇₆	—	2	1	no	—
30	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
31	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
32	C₈×C₂²⋊D₄₇	—	2	1	no	—
33	C₈×C₂²⋊D₄₇	—	2	1	no	—
34	#15689176	C₂²	1	1	yes	characteristic
35	#15689174	—	2	1	no	—
36	#15689120	—	2	2	no	—
37	C₄×C₈×D₄₇	—	2	1	no	—
38	#15688870	C₂²	1	2	yes	—
39	#15688870	C₂²	1	2	yes	—
40	#15688866	C₂²	1	2	yes	—
41	#15688866	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#335	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	1	yes	characteristic
46	C₄₇×#335	C₂²	1	2	yes	—
47	C₂×#10625350	—	2	2	no	—
48	C₂×#10625350	D₄	1	1	yes	characteristic
49	#13094046	—	4	8	no	—
50	C₂×Dic₁₈₈	—	2	2	no	—
51	C₂×#10625325	—	2	2	no	—
52	C₂×#10625325	—	2	2	no	—
53	C₂×D₃₇₆	—	2	2	no	—
54	C₂×D₃₇₆	—	2	1	no	—
55	C₂×D₃₇₆	—	2	1	no	—
56	C₂×C₈×D₄₇	—	2	1	no	—
57	C₂×C₈×D₄₇	—	2	1	no	—
58	#13094024	C₂³	1	2	yes	—
59	#13094021	C₂³	1	2	yes	—
60	#13094012	—	2	2	no	—
61	#13093998	—	2	2	no	—
62	#13093998	—	2	2	no	—
63	C₄×Dic₉₄	D₄	1	1	yes	characteristic
64	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
65	C₄×D₁₈₈	—	2	2	no	—
66	C₄×D₁₈₈	—	2	2	no	—
67	C₄×D₁₈₈	D₄	1	1	yes	characteristic
68	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₄₇	—	2	1	no	—
70	C₄×C₂²⋊D₄₇	—	2	1	no	—
71	#13093983	D₄	1	1	yes	characteristic
72	#13093981	—	2	1	no	—
73	C₄²×D₄₇	—	2	1	no	—
74	#13093958	—	2	1	no	—
75	#13093958	—	2	1	no	—
76	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
77	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
78	Dic₄₇⋊C₈	—	2	1	no	—
79	Dic₄₇⋊C₈	—	2	1	no	—
80	#13093949	—	2	2	no	—
81	#13093949	—	2	2	no	—
82	#13093946	—	2	2	no	—
83	#13093946	—	2	2	no	—
84	#13093946	—	2	2	no	—
85	#13093946	—	2	2	no	—
86	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
87	(C₂×D₄₇)⋊C₈	—	2	1	no	—
88	(C₂×D₄₇)⋊C₈	—	2	1	no	—
89	C₄×C₄₇⋊C₈	—	2	1	no	—
90	C₈×Dic₄₇	—	2	1	no	—
91	C₈×Dic₄₇	—	2	1	no	—
92	C₂²×C₈×C₄₇	—	2	2	no	—
93	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₇	—	2	2	no	—
97	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
98	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
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	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₇	—	2	1	no	—
107	C₂×C₂²⋊D₄₇	—	4	2	no	—
108	#10625350	—	2	2	no	—
109	#10625350	—	4	4	no	—
110	#10625350	—	4	4	no	—
111	#10625350	D₈	1	4	yes	complemented
112	C₂×D₁₈₈	—	2	2	no	—
113	C₂×D₁₈₈	—	2	2	no	—
114	C₂×D₁₈₈	—	2	2	no	—
115	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₄₇	—	2	1	no	—
117	C₂×C₄×D₄₇	—	2	1	no	—
118	C₂×C₄×D₄₇	—	2	1	no	—
119	C₂×C₄×D₄₇	—	4	2	no	—
120	C₂×Dic₉₄	—	2	2	no	—
121	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	4	1	no	—
126	C₂×C₈×C₄₇	—	4	4	no	—
127	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₇	#41	1	1	yes	characteristic
134	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₄₇	—	2	1	no	—
136	(C₂×D₄₇)⋊C₄	—	2	1	no	—
137	(C₂×D₄₇)⋊C₄	—	2	1	no	—
138	(C₂×D₄₇)⋊C₄	—	4	2	no	—
139	(C₂×D₄₇)⋊C₄	—	4	2	no	—
140	C₄⋊Dic₄₇	—	2	2	no	—
141	C₄⋊Dic₄₇	—	2	2	no	—
142	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
143	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
144	Dic₄₇⋊C₄	—	2	1	no	—
145	Dic₄₇⋊C₄	—	2	1	no	—
146	C₄×Dic₄₇	—	2	1	no	—
147	C₄×Dic₄₇	—	2	1	no	—
148	C₄×Dic₄₇	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	Dic₁₈₈	—	4	4	no	—
152	D₃₇₆	—	4	2	no	—
153	D₃₇₆	—	4	4	no	—
154	D₃₇₆	—	4	2	no	—
155	#10625325	—	4	4	no	—
156	#10625325	—	4	4	no	—
157	C₈×D₄₇	—	4	2	no	—
158	C₈×D₄₇	—	4	2	no	—
159	C₂³×C₄₇	#121	1	1	yes	characteristic
160	C₂²×D₄₇	—	2	1	no	—
161	C₂²×D₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
169	C₂×C₄×C₄₇	#135	1	2	yes	—
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂²⋊D₄₇	—	2	4	no	—
174	C₂²⋊D₄₇	—	8	4	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	D₁₈₈	—	2	1	no	—
180	D₁₈₈	—	4	2	no	—
181	D₁₈₈	—	4	2	no	—
182	D₁₈₈	—	4	2	no	—
183	D₁₈₈	—	4	2	no	—
184	D₁₈₈	—	8	2	no	—
185	D₁₈₈	C₂×D₈	1	2	yes	—
186	C₄×D₄₇	—	2	4	no	—
187	C₄×D₄₇	—	4	2	no	—
188	C₄×D₄₇	—	4	1	no	—
189	C₄×D₄₇	—	4	1	no	—
190	C₄×D₄₇	—	8	4	no	—
191	Dic₉₄	—	2	1	no	—
192	Dic₉₄	—	4	2	no	—
193	Dic₉₄	—	4	2	no	—
194	Dic₉₄	C₂×D₈	1	2	yes	—
195	C₈×C₄₇	—	2	1	no	—
196	C₈×C₄₇	—	2	1	no	—
197	C₈×C₄₇	—	2	1	no	—
198	C₈×C₄₇	—	4	2	no	—
199	C₈×C₄₇	—	4	2	no	—
200	C₈×C₄₇	#135	1	2	yes	complemented
201	C₄₇⋊C₈	—	4	1	no	—
202	C₄₇⋊C₈	—	4	1	no	—
203	#19125	—	47	1	no	maximal, Sylow
204	C₂²×C₄₇	—	2	1	no	—
205	C₂²×C₄₇	—	2	1	no	—
206	C₂²×C₄₇	#466	1	2	yes	—
207	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
208	C₂×D₄₇	—	2	2	no	—
209	C₂×D₄₇	—	4	1	no	—
210	C₂×D₄₇	—	4	1	no	—
211	C₂×D₄₇	—	8	2	no	—
212	C₂×D₄₇	—	8	2	no	—
213	C₂×D₄₇	—	8	2	no	—
214	C₄×C₄₇	—	2	1	no	—
215	C₄×C₄₇	—	2	1	no	—
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	#466	1	2	yes	—
218	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
219	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
220	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
221	C₄×C₄₇	#575	1	1	yes	characteristic
222	Dic₄₇	—	2	2	no	—
223	Dic₄₇	—	4	1	no	—
224	Dic₄₇	—	4	1	no	—
225	Dic₄₇	—	8	2	no	—
226	#3169	—	47	1	no	—
227	#3035	—	47	2	no	—
228	C₈×#41	—	47	1	no	—
229	#1682	—	47	2	no	—
230	#1681	—	47	2	no	—
231	#1674	—	47	1	no	—
232	#1673	—	47	1	no	—
233	#1668	—	47	1	no	—
234	#1667	—	47	1	no	—
235	C₂×#335	D₄₇	1	1	yes	characteristic, complemented
236	#1540	—	47	2	no	—
237	C₂×C₄₇	—	2	2	no	—
238	C₂×C₄₇	#3035	1	1	yes	characteristic
239	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
240	C₂×C₄₇	#3067	1	1	yes	characteristic
241	D₄₇	—	4	2	no	—
242	D₄₇	—	16	2	no	—
243	C₂×#135	—	94	2	no	—
244	#532	—	47	2	no	—
245	C₄×#41	—	47	1	no	—
246	#500	—	47	1	no	—
247	#493	—	47	1	no	—
248	#486	—	47	2	no	—
249	#466	—	94	1	no	—
250	#466	—	94	1	no	—
251	#464	—	94	2	no	—
252	#463	—	94	2	no	—
253	#462	—	47	2	no	—
254	#461	—	47	2	no	—
255	#460	—	47	2	no	—
256	#459	—	47	2	no	—
257	C₈×Q₈	—	47	1	no	—
258	C₈×Q₈	—	47	1	no	—
259	C₄×D₈	—	94	1	no	—
260	C₄×D₈	—	94	1	no	—
261	C₈×D₄	—	47	1	no	—
262	C₈×D₄	—	47	1	no	—
263	C₈×D₄	—	94	1	no	—
264	C₈×D₄	—	94	1	no	—
265	#431	—	47	1	no	—
266	#431	—	94	1	no	—
267	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
268	#416	—	94	2	no	—
269	C₂×C₄×C₈	—	94	1	no	—
270	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
271	#335	C₂×D₄₇	1	1	yes	characteristic
272	#335	C₂×D₄₇	1	1	yes	characteristic
273	#335	C₂×D₄₇	1	2	yes	—
274	#332	—	47	2	no	—
275	#332	—	47	2	no	—
276	#331	—	47	2	no	—
277	#331	—	47	2	no	—
278	C₄₇	#19125	1	1	yes	characteristic, complemented, Sylow
279	C₂×#41	—	47	1	no	—
280	C₂×#41	—	94	2	no	—
281	#135	—	188	8	no	—
282	C₂×Q₁₆	—	94	2	no	—
283	C₂×SD₁₆	—	94	2	no	—
284	C₂×SD₁₆	—	94	2	no	—
285	C₂×D₈	—	94	2	no	—
286	C₂×D₈	—	94	1	no	—
287	C₂×D₈	—	94	1	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	94	1	no	—
290	C₂²×C₈	—	94	1	no	—
291	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
292	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
293	C₄⋊Q₈	—	47	2	no	—
294	#127	—	47	2	no	—
295	#124	—	94	2	no	—
296	#121	—	94	2	no	—
297	#121	—	94	2	no	—
298	C₄×Q₈	—	47	1	no	—
299	C₄×Q₈	—	47	1	no	—
300	C₄×D₄	—	47	1	no	—
301	C₄×D₄	—	47	1	no	—
302	C₄×D₄	—	94	1	no	—
303	C₄×D₄	—	94	1	no	—
304	C₄×D₄	—	94	2	no	—
305	C₄×D₄	—	94	2	no	—
306	#117	—	47	1	no	—
307	#117	—	94	1	no	—
308	C₂×C₄²	—	94	1	no	—
309	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
310	#107	—	94	1	no	—
311	#107	—	94	1	no	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	—	47	1	no	—
314	C₄⋊C₈	—	47	1	no	—
315	C₄⋊C₈	—	94	1	no	—
316	C₄⋊C₈	—	94	1	no	—
317	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
318	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
319	#103	—	94	2	no	—
320	#103	—	94	2	no	—
321	#102	—	94	2	no	—
322	#102	—	94	2	no	—
323	#102	—	94	2	no	—
324	#102	—	94	2	no	—
325	C₂²⋊C₈	—	94	1	no	—
326	C₂²⋊C₈	—	94	1	no	—
327	C₂²⋊C₈	—	94	1	no	—
328	C₄×C₈	—	94	1	no	—
329	C₄×C₈	—	94	1	no	—
330	C₄×C₈	—	94	1	no	—
331	C₄×C₈	D₁₈₈	1	1	yes	characteristic
332	C₄×C₈	D₁₈₈	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
334	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
335	#41	—	47	4	no	—
336	#41	—	94	2	no	—
337	#41	—	188	4	no	—
338	#41	—	188	4	no	—
339	C₂×Q₈	—	47	1	no	—
340	C₂×Q₈	—	94	2	no	—
341	C₂×D₄	—	47	1	no	—
342	C₂×D₄	—	94	1	no	—
343	C₂×D₄	—	94	2	no	—
344	C₂×D₄	—	94	2	no	—
345	C₂×D₄	—	94	2	no	—
346	C₂×D₄	—	188	2	no	—
347	C₂²×C₄	—	94	1	no	—
348	C₂²×C₄	—	94	1	no	—
349	C₂²×C₄	—	94	1	no	—
350	C₂²×C₄	—	188	2	no	—
351	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
352	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
353	C₂²×C₄	#10625354	1	1	yes	characteristic
354	Q₁₆	—	188	4	no	—
355	SD₁₆	—	188	4	no	—
356	SD₁₆	—	188	4	no	—
357	D₈	—	188	2	no	—
358	D₈	—	188	4	no	—
359	D₈	—	188	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	4	no	—
365	C₂×C₈	—	94	1	no	—
366	C₂×C₈	—	94	1	no	—
367	C₂×C₈	—	188	2	no	—
368	C₂×C₈	—	188	2	no	—
369	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
370	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
371	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
372	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
373	C₄⋊C₄	—	47	1	no	—
374	C₄⋊C₄	—	47	1	no	—
375	C₄⋊C₄	—	94	1	no	—
376	C₄⋊C₄	—	94	1	no	—
377	C₄⋊C₄	—	94	2	no	—
378	C₄⋊C₄	—	94	2	no	—
379	C₂²⋊C₄	—	94	1	no	—
380	C₂²⋊C₄	—	94	1	no	—
381	C₂²⋊C₄	—	94	1	no	—
382	C₂²⋊C₄	—	188	2	no	—
383	C₂²⋊C₄	—	188	2	no	—
384	C₄²	—	94	1	no	—
385	C₄²	—	94	1	no	—
386	C₄²	—	94	1	no	—
387	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
388	C₄²	D₄×D₄₇	1	1	yes	characteristic
389	C₄²	#10625354	1	1	yes	characteristic
390	C₄²	C₂³×D₄₇	1	1	yes	characteristic
391	C₂³	—	94	1	no	—
392	C₂³	—	188	2	no	—
393	C₂³	#13093999	1	1	yes	characteristic
394	Q₈	—	47	2	no	—
395	Q₈	—	94	1	no	—
396	Q₈	—	188	2	no	—
397	Q₈	—	188	2	no	—
398	D₄	—	47	2	no	—
399	D₄	—	94	4	no	—
400	D₄	—	94	1	no	—
401	D₄	—	376	2	no	—
402	D₄	—	376	4	no	—
403	D₄	—	188	2	no	—
404	D₄	—	188	2	no	—
405	D₄	—	188	2	no	—
406	D₄	—	188	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	94	1	no	—
411	C₂×C₄	—	94	4	no	—
412	C₂×C₄	—	94	1	no	—
413	C₂×C₄	—	94	1	no	—
414	C₂×C₄	—	376	4	no	—
415	C₂×C₄	—	188	2	no	—
416	C₂×C₄	—	188	2	no	—
417	C₂×C₄	—	188	1	no	—
418	C₂×C₄	—	188	1	no	—
419	C₂×C₄	#13093999	1	1	yes	characteristic
420	C₂×C₄	#13093999	1	1	yes	characteristic
421	C₂×C₄	#13093999	1	1	yes	characteristic
422	C₂×C₄	D₈×D₄₇	1	2	yes	—
423	C₂×C₄	#13094047	1	2	yes	—
424	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
426	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	4	2	no	—
432	C₈	—	188	1	no	—
433	C₈	—	188	1	no	—
434	C₈	#13094046	1	2	yes	complemented
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	94	2	no	—
438	C₂²	—	376	2	no	—
439	C₂²	—	376	2	no	—
440	C₂²	—	376	2	no	—
441	C₂²	—	188	1	no	—
442	C₂²	—	188	1	no	—
443	C₂²	#15689360	1	2	yes	—
444	C₂²	C₂×#13093999	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	94	2	no	—
449	C₄	—	376	2	no	—
450	C₄	—	188	1	no	—
451	C₄	—	188	1	no	—
452	C₄	#15689360	1	2	yes	—
453	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
454	C₄	C₂×#13094046	1	1	yes	characteristic
455	C₄	C₂×#13094047	1	1	yes	characteristic
456	C₄	#15689923	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	188	2	no	—
459	C₂	—	752	2	no	—
460	C₂	#20252845	1	1	yes	characteristic
461	C₂	C₂×#15689360	1	1	yes	characteristic
462	C₂	#20253109	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093999
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#335	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	C₂×#335	D₄₇
hypocenter	C₄₇	#19125
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
1. #20253967	C₂	semidirect
2. #20252845	C₂	semidirect
3. C₈×#10625350	C₂	semidirect
4. #20242833	C₂	semidirect
5. #20242826	C₂	semidirect
6. #20242783	C₂	semidirect
7. #20242778	C₂	semidirect
8. #20242749	C₂	semidirect
9. #20242744	C₂	semidirect
10. #20242038	C₂	semidirect
11. C₂×C₄₇×#335	C₂	semidirect
111. #10625350	D₈	semidirect
200. C₈×C₄₇	#135	semidirect
235. C₂×#335	D₄₇	semidirect
278. C₄₇	#19125	semidirect
434. C₈	#13094046	semidirect

Maximal subgroups

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

subgroup	index
#20253967	2
#20252845	2
C₈×#10625350	2
#20242833	2
#20242826	2
#20242783	2
#20242778	2
#20242749	2
#20242744	2
#20242038	2
C₂×C₄₇×#335	2
#19125	47