Subgroups — #26198752

Order 12032.

664 conjugacy classes of subgroups.

The subgroup lattice has 452 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	#20253448	C₂	1	2	yes	maximal, complemented
3	#20242804	C₂	1	2	yes	maximal, complemented
4	#20242797	C₂	1	2	yes	maximal, complemented
5	#20242792	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242787	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242748	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242743	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242136	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242048	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689673	C₂²	1	2	yes	—
13	#15689528	C₂²	1	1	yes	characteristic
14	#15689500	C₂²	1	1	yes	characteristic
15	#15689470	C₂²	1	2	yes	—
16	#15689447	—	2	2	no	—
17	#15689418	C₂²	1	2	yes	—
18	#15689413	C₂²	1	2	yes	—
19	#15689359	—	2	1	no	—
20	#15689359	—	2	1	no	—
21	#15689323	C₂²	1	2	yes	—
22	#15689318	C₂²	1	2	yes	—
23	#15689268	—	2	2	no	—
24	C₄×#10625336	—	2	2	no	—
25	C₄×D₃₇₆	—	2	1	no	—
26	C₄×D₃₇₆	—	2	1	no	—
27	C₄×#10625334	—	2	2	no	—
28	#15689176	C₂²	1	2	yes	—
29	#15688876	C₂²	1	1	yes	characteristic
30	#15688876	C₂²	1	1	yes	characteristic
31	#15688874	C₂²	1	2	yes	—
32	#15688871	C₂²	1	2	yes	—
33	#15688871	C₂²	1	2	yes	—
34	#15688866	C₂²	1	2	yes	—
35	#15688866	C₂²	1	2	yes	—
36	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₄₇	—	2	1	no	—
40	C₈×D₄×C₄₇	—	2	1	no	—
41	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#431	—	2	1	no	—
44	C₄₇×#431	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₄₇	—	2	1	no	—
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	—	2	2	no	—
48	C₂×#10625336	—	2	2	no	—
49	C₂×D₃₇₆	—	2	1	no	—
50	C₂×D₃₇₆	—	2	1	no	—
51	C₂×#10625334	—	2	2	no	—
52	#13094024	C₂³	1	2	yes	—
53	#13094021	C₂³	1	2	yes	—
54	#13094012	—	2	2	no	—
55	#13093998	—	2	2	no	—
56	#13093998	—	2	2	no	—
57	C₄×D₁₈₈	—	2	2	no	—
58	C₄×D₁₈₈	—	2	2	no	—
59	#13093958	—	2	1	no	—
60	#13093958	—	2	1	no	—
61	#13093957	—	2	2	no	—
62	#13093955	—	2	2	no	—
63	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
64	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
65	#13093948	—	2	2	no	—
66	#13093946	—	2	2	no	—
67	#13093946	—	2	2	no	—
68	#13093945	—	2	2	no	—
69	#13093944	—	2	2	no	—
70	#13093944	—	2	2	no	—
71	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
72	C₄×C₄₇⋊C₈	—	2	2	no	—
73	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	—	2	1	no	—
75	C₂²×C₈×C₄₇	—	2	1	no	—
76	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₄₇	—	2	1	no	—
81	C₄×D₄×C₄₇	—	2	1	no	—
82	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
83	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
84	#117×C₄₇	—	2	1	no	—
85	#117×C₄₇	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	—	2	1	no	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	—	2	1	no	—
89	C₄⋊C₈×C₄₇	—	2	1	no	—
90	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₄₇	—	2	1	no	—
93	C₂²⋊C₈×C₄₇	—	2	1	no	—
94	C₂²⋊C₈×C₄₇	—	2	1	no	—
95	C₄×C₈×C₄₇	—	2	1	no	—
96	C₄×C₈×C₄₇	—	2	1	no	—
97	C₄×C₈×C₄₇	—	2	1	no	—
98	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	#41×C₄₇	—	2	2	no	—
103	#41×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₄₇	—	2	1	no	—
106	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₄₇	—	4	2	no	—
114	#10625350	—	8	4	no	—
115	C₂×D₁₈₈	—	2	2	no	—
116	C₂×D₁₈₈	—	2	2	no	—
117	C₂×D₁₈₈	—	2	2	no	—
118	C₂×C₄×D₄₇	—	4	2	no	—
119	C₂×Dic₉₄	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	4	1	no	—
124	C₂×C₈×C₄₇	—	4	2	no	—
125	C₂×C₈×C₄₇	—	4	2	no	—
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	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄⋊C₄×C₄₇	—	2	1	no	—
131	C₄⋊C₄×C₄₇	—	2	1	no	—
132	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂²⋊C₄×C₄₇	—	2	1	no	—
135	C₂²⋊C₄×C₄₇	—	2	1	no	—
136	C₂²⋊C₄×C₄₇	—	2	1	no	—
137	C₄²×C₄₇	—	2	1	no	—
138	C₄²×C₄₇	—	2	1	no	—
139	C₄²×C₄₇	—	2	1	no	—
140	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₄₇	#41	1	1	yes	characteristic
143	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
144	#10625336	—	4	4	no	—
145	#10625334	—	4	4	no	—
146	(C₂×D₄₇)⋊C₄	—	4	2	no	—
147	(C₂×D₄₇)⋊C₄	—	4	2	no	—
148	C₄⋊Dic₄₇	—	2	2	no	—
149	C₄⋊Dic₄₇	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	D₃₇₆	—	4	2	no	—
153	D₃₇₆	—	4	2	no	—
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	#121	1	1	yes	characteristic
156	C₂²×D₄₇	—	4	2	no	—
157	Q₈×C₄₇	—	2	1	no	—
158	Q₈×C₄₇	#135	1	2	yes	—
159	D₄×C₄₇	—	2	4	no	—
160	D₄×C₄₇	—	2	1	no	—
161	D₄×C₄₇	#135	1	2	yes	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	2	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	1	no	—
173	C₂×C₄×C₄₇	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₄₇	—	8	4	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	D₁₈₈	—	4	2	no	—
183	D₁₈₈	—	4	2	no	—
184	D₁₈₈	—	4	2	no	—
185	D₁₈₈	—	4	2	no	—
186	D₁₈₈	—	8	2	no	—
187	C₄×D₄₇	—	8	4	no	—
188	Dic₉₄	—	8	2	no	—
189	C₈×C₄₇	—	2	1	no	—
190	C₈×C₄₇	—	2	1	no	—
191	C₈×C₄₇	—	2	1	no	—
192	C₈×C₄₇	—	4	1	no	—
193	C₈×C₄₇	—	4	1	no	—
194	C₈×C₄₇	#135	1	2	yes	—
195	C₄₇⋊C₈	—	4	2	no	—
196	C₄₇⋊C₈	—	4	2	no	—
197	#19128	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	4	1	no	—
203	C₂²×C₄₇	—	4	1	no	—
204	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
205	C₂×D₄₇	—	8	2	no	—
206	C₂×D₄₇	—	8	2	no	—
207	C₂×D₄₇	—	8	2	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	4	1	no	—
213	C₄×C₄₇	—	4	1	no	—
214	C₄×C₄₇	#472	1	2	yes	—
215	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
216	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
217	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
218	C₄×C₄₇	#575	1	1	yes	characteristic
219	Dic₄₇	—	8	2	no	—
220	#3169	—	47	1	no	—
221	#3106	—	47	2	no	—
222	C₈×#41	D₄₇	1	1	yes	characteristic, complemented
223	#1678	—	47	2	no	—
224	#1677	—	47	2	no	—
225	#1676	—	47	1	no	—
226	#1675	—	47	1	no	—
227	#1668	—	47	1	no	—
228	#1667	—	47	1	no	—
229	#1564	—	47	1	no	—
230	#1543	—	47	2	no	—
231	C₂×C₄₇	—	4	1	no	—
232	C₂×C₄₇	—	4	2	no	—
233	C₂×C₄₇	#3035	1	1	yes	characteristic
234	C₂×C₄₇	#3050	1	1	yes	characteristic
235	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
236	D₄₇	—	16	2	no	—
237	#532	—	47	2	no	—
238	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
239	#500	—	47	1	no	—
240	#493	—	47	1	no	—
241	#486	—	47	2	no	—
242	#482	—	94	2	no	—
243	#477	—	47	2	no	—
244	#476	—	47	2	no	—
245	#466	—	94	1	no	—
246	#466	—	94	1	no	—
247	#460	—	47	2	no	—
248	#459	—	47	2	no	—
249	#449	—	94	2	no	—
250	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic
251	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic
252	C₄×SD₁₆	—	94	2	no	—
253	C₄×D₈	—	94	2	no	—
254	C₄×D₈	—	94	1	no	—
255	C₄×D₈	—	94	1	no	—
256	C₈×D₄	—	2	1	no	—
257	C₈×D₄	—	2	1	no	—
258	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
259	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
260	#431	—	2	1	no	—
261	#431	—	47	2	no	—
262	#431	C₂×D₄₇	1	1	yes	characteristic
263	C₂×C₄×C₈	—	2	1	no	—
264	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
265	#335	—	47	1	no	—
266	#335	—	47	1	no	—
267	#334	—	47	2	no	—
268	#333	—	47	2	no	—
269	#333	—	47	2	no	—
270	#331	—	47	2	no	—
271	#331	—	47	2	no	—
272	C₄₇	#19128	1	1	yes	characteristic, complemented, Sylow
273	C₂×#41	—	94	2	no	—
274	C₂×#41	D₁₈₈	1	1	yes	characteristic
275	C₂×SD₁₆	—	94	2	no	—
276	C₂×D₈	—	94	2	no	—
277	C₂×D₈	—	94	1	no	—
278	C₂×D₈	—	94	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
282	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
283	C₄⋊Q₈	—	47	2	no	—
284	#127	—	47	2	no	—
285	#124	—	94	2	no	—
286	#121	—	94	2	no	—
287	#121	—	94	2	no	—
288	C₄×Q₈	D₁₈₈	1	1	yes	characteristic
289	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	94	2	no	—
293	C₄×D₄	—	94	2	no	—
294	C₄×D₄	D₁₈₈	1	1	yes	characteristic
295	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	#117	D₁₈₈	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
300	#107	—	94	1	no	—
301	#107	—	94	1	no	—
302	#107	—	94	2	no	—
303	#106	—	94	2	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	47	2	no	—
307	C₄⋊C₈	—	47	2	no	—
308	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
309	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
310	#103	—	94	2	no	—
311	#102	—	94	2	no	—
312	#102	—	94	2	no	—
313	#102	—	94	2	no	—
314	#102	—	94	2	no	—
315	#102	—	94	2	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	94	2	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	94	2	no	—
324	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
325	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
327	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	376	4	no	—
331	C₂×Q₈	—	94	2	no	—
332	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	94	2	no	—
335	C₂×D₄	—	94	2	no	—
336	C₂×D₄	—	94	2	no	—
337	C₂×D₄	—	188	2	no	—
338	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	188	2	no	—
343	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
344	C₂²×C₄	#10625350	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
346	SD₁₆	—	188	4	no	—
347	D₈	—	188	2	no	—
348	D₈	—	188	4	no	—
349	D₈	—	188	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	94	2	no	—
358	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	94	2	no	—
365	C₄⋊C₄	—	94	2	no	—
366	C₄⋊C₄	C₂×D₁₈₈	1	1	yes	characteristic
367	C₄⋊C₄	C₂×D₁₈₈	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	188	2	no	—
372	C₂²⋊C₄	—	188	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
377	C₄²	#10625350	1	1	yes	characteristic
378	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
379	C₄²	C₂³×D₄₇	1	1	yes	characteristic
380	C₂³	—	2	1	no	—
381	C₂³	—	188	2	no	—
382	C₂³	#13093998	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	376	2	no	—
385	Q₈	#13094046	1	2	yes	—
386	D₄	—	2	4	no	—
387	D₄	—	2	1	no	—
388	D₄	—	376	2	no	—
389	D₄	—	376	4	no	—
390	D₄	—	188	2	no	—
391	D₄	—	188	2	no	—
392	D₄	—	188	2	no	—
393	D₄	—	188	2	no	—
394	D₄	#13094046	1	2	yes	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	376	4	no	—
408	C₂×C₄	—	188	2	no	—
409	C₂×C₄	#13093998	1	1	yes	characteristic
410	C₂×C₄	#13093998	1	1	yes	characteristic
411	C₂×C₄	#13093998	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
414	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	188	2	no	—
421	C₈	—	188	2	no	—
422	C₈	#13094044	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	376	2	no	—
430	C₂²	—	376	2	no	—
431	C₂²	—	376	2	no	—
432	C₂²	C₂×#13093998	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	376	2	no	—
440	C₄	#15689393	1	2	yes	—
441	C₄	C₂×#13094044	1	1	yes	characteristic
442	C₄	C₂×#13094046	1	1	yes	characteristic
443	C₄	C₂×#13094046	1	1	yes	characteristic
444	C₄	#15689921	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	4	2	no	—
447	C₂	—	752	2	no	—
448	C₂	#20252843	1	1	yes	characteristic
449	C₂	#20252969	1	1	yes	characteristic
450	C₂	C₂×#15689393	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093998
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×#41×C₄₇	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	C₈×#41	D₄₇
hypocenter	C₄₇	#19128
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #20253967	C₂	semidirect
2. #20253448	C₂	semidirect
3. #20242804	C₂	semidirect
4. #20242797	C₂	semidirect
5. #20242792	C₂	semidirect
6. #20242787	C₂	semidirect
7. #20242748	C₂	semidirect
8. #20242743	C₂	semidirect
9. #20242136	C₂	semidirect
10. #20242048	C₂	semidirect
11. C₈×#41×C₄₇	C₂	semidirect
222. C₈×#41	D₄₇	semidirect
272. C₄₇	#19128	semidirect

Maximal subgroups

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

subgroup	index
#20253967	2
#20253448	2
#20242804	2
#20242797	2
#20242792	2
#20242787	2
#20242748	2
#20242743	2
#20242136	2
#20242048	2
C₈×#41×C₄₇	2
#19128	47