Subgroups — #26200183

Order 12032.

716 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253533	C₂	1	2	yes	maximal, complemented
2	C₈×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242755	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242750	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242745	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242740	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242733	C₂	1	2	yes	maximal, complemented
8	#20242726	C₂	1	2	yes	maximal, complemented
9	#20242151	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242093	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10625350	C₂²	1	1	yes	characteristic
13	#15689444	—	2	2	no	—
14	#15689405	C₂²	1	2	yes	—
15	#15689400	C₂²	1	2	yes	—
16	#15689320	C₂²	1	2	yes	—
17	#15689315	C₂²	1	2	yes	—
18	#15689266	—	2	2	no	—
19	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
20	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
21	#15689233	—	2	2	no	—
22	#15689223	—	2	2	no	—
23	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
24	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₄₇	—	2	1	no	—
26	C₈×C₂²⋊D₄₇	—	2	1	no	—
27	#15689180	C₂²	1	2	yes	—
28	#15689176	C₂²	1	1	yes	characteristic
29	#15689174	—	2	1	no	—
30	C₄×C₈×D₄₇	—	2	1	no	—
31	#15688876	C₂²	1	1	yes	characteristic
32	#15688876	C₂²	1	1	yes	characteristic
33	#15688874	C₂²	1	2	yes	—
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	C₂×#135×C₄₇	—	2	1	no	—
39	C₂×#135×C₄₇	—	2	1	no	—
40	C₄₇×#532	C₂²	1	2	yes	—
41	C₄₇×#495	—	2	1	no	—
42	C₄₇×#495	—	2	1	no	—
43	C₄₇×#494	C₂²	1	1	yes	characteristic
44	C₄₇×#493	C₂²	1	1	yes	characteristic
45	C₄₇×#492	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	D₄	1	1	yes	characteristic
48	C₂×#10625335	—	2	2	no	—
49	C₂×#10625334	—	2	2	no	—
50	C₂×C₈×D₄₇	—	2	1	no	—
51	C₂×C₈×D₄₇	—	2	1	no	—
52	C₄×Dic₉₄	D₄	1	1	yes	characteristic
53	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
54	C₄×D₁₈₈	D₄	1	1	yes	characteristic
55	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
56	C₄×C₂²⋊D₄₇	—	2	1	no	—
57	C₄×C₂²⋊D₄₇	—	2	1	no	—
58	#13093983	D₄	1	1	yes	characteristic
59	#13093981	—	2	1	no	—
60	C₄²×D₄₇	—	2	1	no	—
61	#13093957	—	2	2	no	—
62	#13093955	—	2	2	no	—
63	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
64	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
67	Dic₄₇⋊C₈	—	2	1	no	—
68	Dic₄₇⋊C₈	—	2	1	no	—
69	#13093947	—	2	2	no	—
70	#13093945	—	2	2	no	—
71	#13093945	—	2	2	no	—
72	#13093944	—	2	2	no	—
73	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
74	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
75	(C₂×D₄₇)⋊C₈	—	2	1	no	—
76	(C₂×D₄₇)⋊C₈	—	2	1	no	—
77	#13093935	—	2	2	no	—
78	C₄×C₄₇⋊C₈	—	2	1	no	—
79	C₈×Dic₄₇	—	2	1	no	—
80	C₈×Dic₄₇	—	2	1	no	—
81	C₂×#41×C₄₇	—	2	2	no	—
82	#135×C₄₇	—	4	4	no	—
83	#135×C₄₇	—	4	4	no	—
84	C₂×Q₁₆×C₄₇	—	2	1	no	—
85	C₂×Q₁₆×C₄₇	—	2	1	no	—
86	C₂×SD₁₆×C₄₇	—	2	2	no	—
87	C₂×SD₁₆×C₄₇	—	2	2	no	—
88	C₂×D₈×C₄₇	—	2	1	no	—
89	C₂×D₈×C₄₇	—	2	1	no	—
90	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
92	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
93	#127×C₄₇	C₂³	1	2	yes	—
94	#124×C₄₇	—	2	2	no	—
95	#121×C₄₇	—	2	2	no	—
96	#121×C₄₇	—	2	2	no	—
97	C₄×D₄×C₄₇	—	2	2	no	—
98	C₄×D₄×C₄₇	—	2	2	no	—
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
101	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
102	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
104	#41×C₄₇	—	4	4	no	—
105	#41×C₄₇	—	4	4	no	—
106	C₂×Q₈×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	2	2	no	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	—	2	2	no	—
110	C₂×D₄×C₄₇	—	4	2	no	—
111	C₂²×C₄×C₄₇	—	4	2	no	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
115	C₂×C₂²⋊D₄₇	—	2	1	no	—
116	#10625350	—	2	2	no	—
117	#10625350	—	2	2	no	—
118	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₄₇	—	2	1	no	—
120	C₂×C₄×D₄₇	—	2	1	no	—
121	C₂×C₄×D₄₇	—	2	1	no	—
122	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
123	Q₁₆×C₄₇	—	4	2	no	—
124	Q₁₆×C₄₇	—	4	2	no	—
125	SD₁₆×C₄₇	—	4	4	no	—
126	SD₁₆×C₄₇	—	4	4	no	—
127	D₈×C₄₇	—	4	2	no	—
128	D₈×C₄₇	—	4	2	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	—	2	2	no	—
131	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	2	no	—
137	C₂²⋊C₄×C₄₇	—	4	2	no	—
138	C₂²⋊C₄×C₄₇	—	4	2	no	—
139	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₇	#41	1	1	yes	characteristic
142	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
143	C₂²⋊Dic₄₇	—	2	1	no	—
144	#10625335	—	4	4	no	—
145	#10625334	—	4	4	no	—
146	(C₂×D₄₇)⋊C₄	—	2	1	no	—
147	(C₂×D₄₇)⋊C₄	—	2	1	no	—
148	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
149	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
150	Dic₄₇⋊C₄	—	2	1	no	—
151	Dic₄₇⋊C₄	—	2	1	no	—
152	C₄×Dic₄₇	—	2	1	no	—
153	C₄×Dic₄₇	—	2	1	no	—
154	C₄×Dic₄₇	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	2	1	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₈×D₄₇	—	4	2	no	—
160	C₈×D₄₇	—	4	2	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	#121	1	1	yes	characteristic
163	C₂²×D₄₇	—	2	1	no	—
164	Q₈×C₄₇	—	4	2	no	—
165	Q₈×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	4	2	no	—
167	D₄×C₄₇	—	4	2	no	—
168	D₄×C₄₇	—	4	2	no	—
169	D₄×C₄₇	—	4	2	no	—
170	D₄×C₄₇	—	8	2	no	—
171	D₄×C₄₇	—	8	4	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	8	4	no	—
179	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
180	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
181	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
185	C₂²⋊D₄₇	—	2	4	no	—
186	C₂×Dic₄₇	—	2	1	no	—
187	C₂×Dic₄₇	—	2	1	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	D₁₈₈	—	2	1	no	—
190	D₁₈₈	#135	1	2	yes	complemented
191	C₄×D₄₇	—	2	4	no	—
192	C₄×D₄₇	—	4	2	no	—
193	C₄×D₄₇	—	4	1	no	—
194	C₄×D₄₇	—	4	1	no	—
195	Dic₉₄	—	2	1	no	—
196	Dic₉₄	#135	1	2	yes	complemented
197	C₈×C₄₇	—	2	1	no	—
198	C₈×C₄₇	—	2	1	no	—
199	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
200	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
201	C₄₇⋊C₈	—	4	2	no	—
202	C₄₇⋊C₈	—	4	2	no	—
203	C₄₇⋊C₈	—	4	1	no	—
204	C₄₇⋊C₈	—	4	1	no	—
205	#19269	—	47	1	no	maximal, Sylow
206	C₂²×C₄₇	—	2	1	no	—
207	C₂²×C₄₇	—	2	1	no	—
208	C₂²×C₄₇	—	2	1	no	—
209	C₂²×C₄₇	—	8	2	no	—
210	C₂²×C₄₇	—	8	2	no	—
211	C₂²×C₄₇	—	8	2	no	—
212	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
213	C₂×D₄₇	—	2	2	no	—
214	C₂×D₄₇	—	4	1	no	—
215	C₂×D₄₇	—	4	1	no	—
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	—	2	1	no	—
218	C₄×C₄₇	—	2	1	no	—
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	8	2	no	—
221	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
222	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
223	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
225	Dic₄₇	—	2	2	no	—
226	Dic₄₇	—	4	1	no	—
227	Dic₄₇	—	4	1	no	—
228	#3147	D₄₇	1	1	yes	characteristic, complemented
229	#3115	—	47	2	no	—
230	C₈×#41	—	47	1	no	—
231	#1670	—	47	1	no	—
232	#1669	—	47	1	no	—
233	#1668	—	47	1	no	—
234	#1667	—	47	1	no	—
235	#1666	—	47	2	no	—
236	#1665	—	47	2	no	—
237	#1568	—	47	1	no	—
238	#1553	—	47	2	no	—
239	C₂×C₄₇	—	4	1	no	—
240	C₂×C₄₇	—	16	2	no	—
241	C₂×C₄₇	#3038	1	1	yes	characteristic
242	C₂×C₄₇	#3050	1	1	yes	characteristic
243	C₂×C₄₇	#3067	1	1	yes	characteristic
244	D₄₇	—	4	2	no	—
245	C₂×#135	—	2	1	no	—
246	C₂×#135	—	2	1	no	—
247	#532	C₂×D₄₇	1	2	yes	—
248	C₄×#41	—	47	1	no	—
249	#495	—	2	1	no	—
250	#495	—	2	1	no	—
251	#494	C₂×D₄₇	1	1	yes	characteristic
252	#493	C₂×D₄₇	1	1	yes	characteristic
253	#492	C₂×D₄₇	1	2	yes	—
254	#482	—	94	2	no	—
255	#475	—	47	2	no	—
256	#474	—	47	2	no	—
257	#460	—	47	2	no	—
258	#459	—	47	2	no	—
259	#449	—	94	2	no	—
260	C₈×Q₈	—	47	1	no	—
261	C₈×Q₈	—	47	1	no	—
262	#442	—	94	2	no	—
263	#440	—	94	2	no	—
264	C₈×D₄	—	47	1	no	—
265	C₈×D₄	—	47	1	no	—
266	C₈×D₄	—	94	1	no	—
267	C₈×D₄	—	94	1	no	—
268	#432	—	47	2	no	—
269	#431	—	47	1	no	—
270	#431	—	94	1	no	—
271	C₂×C₄×C₈	—	94	1	no	—
272	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
273	#335	—	47	1	no	—
274	#335	—	47	1	no	—
275	#334	—	47	2	no	—
276	#332	—	47	2	no	—
277	#332	—	47	2	no	—
278	#331	—	47	2	no	—
279	#331	—	47	2	no	—
280	C₄₇	#19269	1	1	yes	characteristic, complemented, Sylow
281	C₂×#41	—	2	2	no	—
282	C₂×#41	—	47	1	no	—
283	#135	—	4	4	no	—
284	#135	—	4	4	no	—
285	C₂×Q₁₆	—	2	1	no	—
286	C₂×Q₁₆	—	2	1	no	—
287	C₂×SD₁₆	—	2	2	no	—
288	C₂×SD₁₆	—	2	2	no	—
289	C₂×SD₁₆	—	94	2	no	—
290	C₂×D₈	—	2	1	no	—
291	C₂×D₈	—	2	1	no	—
292	C₂×D₈	—	94	2	no	—
293	C₂²×C₈	—	94	1	no	—
294	C₂²×C₈	—	94	1	no	—
295	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
296	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
297	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
298	#127	C₂²×D₄₇	1	2	yes	—
299	#124	—	2	2	no	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	C₄×Q₈	—	47	1	no	—
303	C₄×Q₈	—	47	1	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	47	1	no	—
307	C₄×D₄	—	47	1	no	—
308	C₄×D₄	—	94	1	no	—
309	C₄×D₄	—	94	1	no	—
310	#117	—	47	1	no	—
311	#117	—	94	1	no	—
312	C₂×C₄²	—	94	1	no	—
313	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
314	#107	—	94	2	no	—
315	#106	—	94	2	no	—
316	C₄⋊C₈	—	47	1	no	—
317	C₄⋊C₈	—	47	1	no	—
318	C₄⋊C₈	—	47	2	no	—
319	C₄⋊C₈	—	47	2	no	—
320	C₄⋊C₈	—	94	1	no	—
321	C₄⋊C₈	—	94	1	no	—
322	#103	—	94	2	no	—
323	#102	—	94	2	no	—
324	#102	—	94	2	no	—
325	#102	—	94	2	no	—
326	C₂²⋊C₈	—	94	2	no	—
327	C₂²⋊C₈	—	94	1	no	—
328	C₂²⋊C₈	—	94	1	no	—
329	C₂²⋊C₈	—	94	1	no	—
330	#97	—	94	2	no	—
331	C₄×C₈	—	94	1	no	—
332	C₄×C₈	—	94	1	no	—
333	C₄×C₈	—	94	1	no	—
334	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
335	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
336	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
338	#41	—	4	4	no	—
339	#41	—	4	4	no	—
340	#41	—	94	2	no	—
341	#41	—	94	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	47	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	47	1	no	—
349	C₂×D₄	—	94	1	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	94	1	no	—
352	C₂²×C₄	—	94	1	no	—
353	C₂²×C₄	—	94	1	no	—
354	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
355	C₂²×C₄	#10625352	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
357	Q₁₆	—	4	2	no	—
358	Q₁₆	—	4	2	no	—
359	SD₁₆	—	4	4	no	—
360	SD₁₆	—	4	4	no	—
361	SD₁₆	—	188	4	no	—
362	D₈	—	4	2	no	—
363	D₈	—	4	2	no	—
364	D₈	—	188	4	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	94	2	no	—
368	C₂×C₈	—	94	2	no	—
369	C₂×C₈	—	94	1	no	—
370	C₂×C₈	—	94	1	no	—
371	C₂×C₈	—	188	2	no	—
372	C₂×C₈	—	188	2	no	—
373	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
374	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
375	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
376	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	47	1	no	—
380	C₄⋊C₄	—	47	1	no	—
381	C₄⋊C₄	—	94	1	no	—
382	C₄⋊C₄	—	94	1	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	4	2	no	—
385	C₂²⋊C₄	—	94	1	no	—
386	C₂²⋊C₄	—	94	1	no	—
387	C₂²⋊C₄	—	94	1	no	—
388	C₄²	—	94	1	no	—
389	C₄²	—	94	1	no	—
390	C₄²	—	94	1	no	—
391	C₄²	D₄×D₄₇	1	1	yes	characteristic
392	C₄²	#10625352	1	1	yes	characteristic
393	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
394	C₄²	C₂³×D₄₇	1	1	yes	characteristic
395	C₂³	—	4	2	no	—
396	C₂³	—	94	1	no	—
397	C₂³	#13093995	1	1	yes	characteristic
398	Q₈	—	4	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	47	2	no	—
401	Q₈	—	94	1	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	8	2	no	—
407	D₄	—	8	4	no	—
408	D₄	—	47	2	no	—
409	D₄	—	94	4	no	—
410	D₄	—	94	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	—	94	4	no	—
419	C₂×C₄	—	94	1	no	—
420	C₂×C₄	—	94	1	no	—
421	C₂×C₄	—	94	1	no	—
422	C₂×C₄	—	188	2	no	—
423	C₂×C₄	—	188	1	no	—
424	C₂×C₄	—	188	1	no	—
425	C₂×C₄	#13093995	1	1	yes	characteristic
426	C₂×C₄	#13093995	1	1	yes	characteristic
427	C₂×C₄	#13093995	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	188	2	no	—
434	C₈	—	188	2	no	—
435	C₈	—	188	1	no	—
436	C₈	—	188	1	no	—
437	C₈	#13094050	1	2	yes	—
438	C₈	#13094050	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	94	2	no	—
446	C₂²	—	188	1	no	—
447	C₂²	—	188	1	no	—
448	C₂²	C₂×#13093995	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	8	2	no	—
454	C₄	—	94	2	no	—
455	C₄	—	188	1	no	—
456	C₄	—	188	1	no	—
457	C₄	#135×D₄₇	1	1	yes	characteristic
458	C₄	#135×D₄₇	1	1	yes	characteristic
459	C₄	C₂×#13094050	1	1	yes	characteristic
460	C₄	C₂×#13094050	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	16	2	no	—
463	C₂	—	188	2	no	—
464	C₂	#20252864	1	1	yes	characteristic
465	C₂	#20252965	1	1	yes	characteristic
466	C₂	#20253104	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093995
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3147	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	#3147	D₄₇
hypocenter	C₄₇	#19269
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3147

Complements

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

N	H ≅ G/N	type
1. #20253533	C₂	semidirect
2. C₈×#10625350	C₂	semidirect
3. #20242755	C₂	semidirect
4. #20242750	C₂	semidirect
5. #20242745	C₂	semidirect
6. #20242740	C₂	semidirect
7. #20242733	C₂	semidirect
8. #20242726	C₂	semidirect
9. #20242151	C₂	semidirect
10. #20242093	C₂	semidirect
11. C₄₇×#3147	C₂	semidirect
190. D₁₈₈	#135	semidirect
196. Dic₉₄	#135	semidirect
228. #3147	D₄₇	semidirect
280. C₄₇	#19269	semidirect

Maximal subgroups

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

subgroup	index
#20253533	2
C₈×#10625350	2
#20242755	2
#20242750	2
#20242745	2
#20242740	2
#20242733	2
#20242726	2
#20242151	2
#20242093	2
C₄₇×#3147	2
#19269	47