Subgroups — #26187480

Order 12032.

638 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	#20253448	C₂	1	1	yes	maximal, characteristic
2	#20252520	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252454	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242270	C₂	1	2	yes	maximal, complemented
5	#20242263	C₂	1	2	yes	maximal, complemented
6	#20242255	C₂	1	2	yes	maximal, complemented
7	#20242185	C₂	1	2	yes	maximal, complemented
8	#20242176	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241840	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241671	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689673	C₂²	1	1	yes	characteristic
13	#15689447	C₄	1	2	yes	—
14	#15689418	C₄	1	1	yes	characteristic
15	#15689413	C₄	1	1	yes	characteristic
16	#15689323	C₄	1	1	yes	characteristic
17	#15689318	C₄	1	1	yes	characteristic
18	#15689268	C₄	1	2	yes	—
19	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	—
20	C₄×#10625336	C₂²	1	2	yes	—
21	C₄×#10625334	C₂²	1	2	yes	—
22	#15689202	—	2	1	no	—
23	#15689201	—	2	2	no	—
24	#15689201	C₂²	1	2	yes	—
25	#15689200	C₂²	1	2	yes	—
26	C₈×D₁₈₈	—	2	1	no	—
27	#15689188	C₂²	1	2	yes	—
28	#15689176	—	2	1	no	—
29	#15689176	C₂²	1	1	yes	characteristic
30	#15689176	C₂²	1	1	yes	characteristic
31	#15689147	—	2	1	no	—
32	#15689147	C₂²	1	1	yes	characteristic
33	#15689088	—	2	2	no	—
34	#15688875	C₂²	1	2	yes	—
35	#15688873	C₂²	1	2	yes	—
36	#15688852	C₂²	1	2	yes	—
37	#15688852	C₂²	1	2	yes	—
38	#15688844	C₂²	1	2	yes	—
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
40	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#431	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
44	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
45	C₄₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₄₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×#10625350	—	2	1	no	—
48	C₂×#10625336	C₂×C₄	1	2	yes	—
49	C₂×#10625334	C₂×C₄	1	2	yes	—
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	—	2	2	no	—
52	C₂×#10625324	—	2	2	no	—
53	C₂×C₈×D₄₇	—	2	2	no	—
54	#13094024	C₂×C₄	1	1	yes	characteristic
55	#13094021	C₂×C₄	1	1	yes	characteristic
56	#13094012	—	2	1	no	—
57	#13093998	—	2	1	no	—
58	#13093998	C₂×C₄	1	2	yes	—
59	C₄×D₁₈₈	—	2	1	no	—
60	C₄×D₁₈₈	C₂³	1	2	yes	—
61	#13093957	C₂×C₄	1	2	yes	—
62	#13093955	C₂×C₄	1	2	yes	—
63	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
64	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
66	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
68	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
69	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
70	#13093948	C₂×C₄	1	2	yes	—
71	#13093945	C₂×C₄	1	2	yes	—
72	#13093944	C₂×C₄	1	2	yes	—
73	#13093944	C₂×C₄	1	2	yes	—
74	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
75	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
76	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
77	(C₂×D₄₇)⋊C₈	—	2	2	no	—
78	(C₂×D₄₇)⋊C₈	—	2	2	no	—
79	C₄×C₄₇⋊C₈	—	2	2	no	—
80	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
81	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
82	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	—	2	1	no	—
84	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₄₇	—	2	1	no	—
87	C₄×D₄×C₄₇	—	2	1	no	—
88	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
90	#117×C₄₇	—	2	1	no	—
91	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	—	2	1	no	—
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
96	C₂²⋊C₈×C₄₇	—	2	1	no	—
97	C₄×C₈×C₄₇	—	2	1	no	—
98	C₄×C₈×C₄₇	—	2	1	no	—
99	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	#41×C₄₇	—	2	2	no	—
102	#41×C₄₇	—	4	1	no	—
103	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×D₄×C₄₇	—	2	1	no	—
105	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₇	—	2	2	no	—
113	#10625350	—	8	1	no	—
114	#10625350	—	8	1	no	—
115	C₂×D₁₈₈	—	2	1	no	—
116	C₂×D₁₈₈	—	2	1	no	—
117	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
118	C₂×C₄×D₄₇	—	2	2	no	—
119	C₂×Dic₉₄	—	2	1	no	—
120	C₂×C₈×C₄₇	—	2	4	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₄₇	—	2	1	no	—
130	C₂²⋊C₄×C₄₇	—	2	1	no	—
131	C₂²⋊C₄×C₄₇	—	2	1	no	—
132	C₄²×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	—	2	1	no	—
135	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₇	#41	1	1	yes	characteristic
138	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
139	#10625336	—	2	4	no	—
140	#10625334	—	4	2	no	—
141	(C₂×D₄₇)⋊C₄	—	2	2	no	—
142	(C₂×D₄₇)⋊C₄	—	2	2	no	—
143	C₄⋊Dic₄₇	—	2	1	no	—
144	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
145	#10625329	—	8	2	no	—
146	#10625329	—	8	1	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
152	#10625324	—	8	2	no	—
153	C₈×D₄₇	—	8	2	no	—
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
156	C₂²×D₄₇	—	2	2	no	—
157	Q₈×C₄₇	—	2	1	no	—
158	Q₈×C₄₇	#131	1	2	yes	—
159	D₄×C₄₇	—	2	1	no	—
160	D₄×C₄₇	—	2	1	no	—
161	D₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	2	1	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	2	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	4	2	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	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂³×C₄	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	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	D₁₈₈	—	2	2	no	—
183	D₁₈₈	—	2	2	no	—
184	D₁₈₈	—	4	2	no	—
185	D₁₈₈	—	8	1	no	—
186	C₄×D₄₇	—	4	2	no	—
187	C₄×D₄₇	—	4	2	no	—
188	Dic₉₄	—	8	1	no	—
189	C₈×C₄₇	—	2	2	no	—
190	C₈×C₄₇	—	2	2	no	—
191	C₈×C₄₇	—	4	1	no	—
192	C₈×C₄₇	—	4	1	no	—
193	C₄₇⋊C₈	—	2	2	no	—
194	C₄₇⋊C₈	—	2	2	no	—
195	C₄₇⋊C₈	—	2	2	no	—
196	C₄₇⋊C₈	—	2	2	no	—
197	C₄₇⋊C₈	—	4	2	no	—
198	#18018	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	4	1	no	—
203	C₂²×C₄₇	—	4	1	no	—
204	C₂²×C₄₇	—	4	1	no	—
205	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂×D₄₇	—	4	2	no	—
207	C₂×D₄₇	—	4	2	no	—
208	C₂×D₄₇	—	4	2	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	4	1	no	—
214	C₄×C₄₇	—	4	1	no	—
215	C₄×C₄₇	#443	1	2	yes	—
216	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
217	C₄×C₄₇	#568	1	1	yes	characteristic
218	C₄×C₄₇	#576	1	1	yes	characteristic
219	C₄×C₄₇	#577	1	1	yes	characteristic
220	Dic₄₇	—	4	2	no	—
221	#3106	—	47	1	no	—
222	#2991	—	47	1	no	—
223	#2979	—	47	1	no	—
224	#1589	—	47	2	no	—
225	#1588	—	47	2	no	—
226	#1586	—	47	2	no	—
227	C₈×SD₁₆	—	47	2	no	—
228	#1574	—	47	1	no	—
229	#1492	—	47	1	no	—
230	#1476	D₄₇	1	1	yes	characteristic, complemented
231	#1450	—	47	1	no	—
232	C₂×C₄₇	—	4	1	no	—
233	C₂×C₄₇	—	8	1	no	—
234	C₂×C₄₇	#2933	1	1	yes	characteristic
235	C₂×C₄₇	#2946	1	1	yes	characteristic
236	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
237	D₄₇	—	8	2	no	—
238	#532	—	47	1	no	—
239	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
240	#482	—	47	2	no	—
241	#477	—	47	1	no	—
242	#476	—	47	1	no	—
243	#460	—	47	1	no	—
244	#459	—	47	1	no	—
245	#449	—	47	2	no	—
246	C₈×Q₈	—	47	2	no	—
247	C₄×SD₁₆	—	47	2	no	—
248	C₄×D₈	—	47	2	no	—
249	#436	—	47	2	no	—
250	#436	—	47	2	no	—
251	#436	—	94	1	no	—
252	#436	—	94	2	no	—
253	C₈×D₄	—	47	2	no	—
254	C₈×D₄	—	94	1	no	—
255	#431	—	47	1	no	—
256	#431	—	47	1	no	—
257	#431	—	94	1	no	—
258	#431	C₂×D₄₇	1	1	yes	characteristic
259	#423	—	47	1	no	—
260	#423	—	94	1	no	—
261	#408	—	94	2	no	—
262	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
263	#335	—	47	2	no	—
264	#334	—	47	2	no	—
265	Q₈⋊C₈	C₂×D₄₇	1	1	yes	characteristic
266	Q₈⋊C₈	C₂×D₄₇	1	1	yes	characteristic
267	D₄⋊C₈	—	47	2	no	—
268	D₄⋊C₈	—	47	2	no	—
269	D₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
270	D₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
271	#322	—	47	2	no	—
272	C₈²	—	47	2	no	—
273	C₄₇	#18018	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	94	1	no	—
275	C₂×#41	C₄×D₄₇	1	1	yes	characteristic
276	C₂×SD₁₆	—	47	2	no	—
277	C₂×D₈	—	47	2	no	—
278	C₂×M₁₆	—	94	2	no	—
279	C₂×M₁₆	—	94	2	no	—
280	C₂×M₁₆	—	94	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	94	2	no	—
283	C₄⋊Q₈	—	47	1	no	—
284	#127	—	47	1	no	—
285	#124	—	94	1	no	—
286	#121	—	47	2	no	—
287	#121	—	94	1	no	—
288	C₄×Q₈	C₄×D₄₇	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	—	47	2	no	—
293	C₄×D₄	—	94	1	no	—
294	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
295	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	#117	C₄×D₄₇	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
300	#107	—	47	2	no	—
301	#106	—	47	2	no	—
302	C₄⋊C₈	—	47	1	no	—
303	C₄⋊C₈	—	47	1	no	—
304	C₄⋊C₈	—	47	1	no	—
305	C₄⋊C₈	—	47	1	no	—
306	C₄⋊C₈	—	47	2	no	—
307	C₄⋊C₈	—	94	2	no	—
308	C₄⋊C₈	—	94	1	no	—
309	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
310	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
311	#103	—	47	2	no	—
312	#102	—	47	2	no	—
313	#102	—	47	2	no	—
314	#102	—	47	2	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	47	2	no	—
317	C₂²⋊C₈	—	47	2	no	—
318	C₂²⋊C₈	—	94	2	no	—
319	C₂²⋊C₈	—	94	2	no	—
320	C₂²⋊C₈	—	94	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	47	2	no	—
324	C₄×C₈	—	47	2	no	—
325	C₄×C₈	—	94	2	no	—
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	—	4	1	no	—
330	#41	—	376	1	no	—
331	#41	—	376	1	no	—
332	C₂×Q₈	—	94	1	no	—
333	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	47	2	no	—
336	C₂×D₄	—	94	2	no	—
337	C₂×D₄	—	94	1	no	—
338	C₂×D₄	—	94	1	no	—
339	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	94	2	no	—
344	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
346	C₂²×C₄	#10625352	1	1	yes	characteristic
347	SD₁₆	—	94	4	no	—
348	D₈	—	188	2	no	—
349	M₁₆	—	376	2	no	—
350	M₁₆	—	376	2	no	—
351	M₁₆	—	376	1	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	47	2	no	—
358	C₂×C₈	—	47	2	no	—
359	C₂×C₈	—	47	2	no	—
360	C₂×C₈	—	47	2	no	—
361	C₂×C₈	—	94	2	no	—
362	C₂×C₈	—	376	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	47	2	no	—
366	C₄⋊C₄	—	94	1	no	—
367	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
368	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	94	2	no	—
373	C₂²⋊C₄	—	94	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
378	C₄²	D₄×D₄₇	1	1	yes	characteristic
379	C₄²	#10625352	1	1	yes	characteristic
380	C₄²	C₂³×D₄₇	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	—	94	2	no	—
383	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	376	1	no	—
386	Q₈	#13094030	1	2	yes	—
387	D₄	—	2	1	no	—
388	D₄	—	2	1	no	—
389	D₄	—	4	2	no	—
390	D₄	—	94	2	no	—
391	D₄	—	94	2	no	—
392	D₄	—	376	1	no	—
393	D₄	—	376	2	no	—
394	D₄	—	188	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	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	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	188	2	no	—
409	C₂×C₄	—	188	2	no	—
410	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
411	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
412	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	94	2	no	—
421	C₈	—	94	2	no	—
422	C₈	—	94	2	no	—
423	C₈	—	94	2	no	—
424	C₈	—	188	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	188	2	no	—
432	C₂²	—	188	2	no	—
433	C₂²	—	188	2	no	—
434	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	188	2	no	—
442	C₄	#15689237	1	2	yes	—
443	C₄	C₂×#13094030	1	1	yes	characteristic
444	C₄	#15689889	1	1	yes	characteristic
445	C₄	#15689925	1	1	yes	characteristic
446	C₄	#15689930	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	8	1	no	—
449	C₂	—	376	2	no	—
450	C₂	#20252109	1	1	yes	characteristic
451	C₂	#20252223	1	1	yes	characteristic
452	C₂	C₂×#15689237	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1476	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253448	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1476	D₄₇
hypocenter	C₄₇	#18018
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1476

Complements

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

N	H ≅ G/N	type
2. #20252520	C₂	semidirect
3. #20252454	C₂	semidirect
4. #20242270	C₂	semidirect
5. #20242263	C₂	semidirect
6. #20242255	C₂	semidirect
7. #20242185	C₂	semidirect
8. #20242176	C₂	semidirect
9. #20241840	C₂	semidirect
10. #20241671	C₂	semidirect
11. C₄₇×#1476	C₂	semidirect
230. #1476	D₄₇	semidirect
273. C₄₇	#18018	semidirect

Maximal subgroups

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

subgroup	index
#20253448	2
#20252520	2
#20252454	2
#20242270	2
#20242263	2
#20242255	2
#20242185	2
#20242176	2
#20241840	2
#20241671	2
C₄₇×#1476	2
#18018	47