Subgroups — #26200162

Order 12032.

786 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689495	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253203	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242734	C₂	1	4	yes	maximal, complemented
5	#20242727	C₂	1	4	yes	maximal, complemented
6	#20242143	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242074	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#3038	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625335	—	2	2	no	—
11	C₂×#13094024	C₂²	1	1	yes	characteristic
12	#15689495	—	2	1	no	—
13	#15689495	—	2	1	no	—
14	#15689495	C₂²	1	4	yes	—
15	#15689418	—	2	1	no	—
16	#15689413	—	2	1	no	—
17	#15689408	C₂²	1	2	yes	complemented
18	#15689403	C₂²	1	2	yes	complemented
19	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
20	D₄×C₄₇⋊C₈	—	2	2	no	—
21	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
22	#15689176	—	2	1	no	—
23	#15689176	C₂²	1	1	yes	characteristic
24	#15689166	—	2	1	no	—
25	#15689147	C₂²	1	1	yes	characteristic
26	#15689124	—	2	1	no	—
27	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	#15688873	C₂²	1	4	yes	complemented
30	#15688868	C₂²	1	4	yes	complemented
31	#15688867	C₂²	1	4	yes	—
32	C₂×AGL(1,ℤ/8)×C₄₇	—	2	1	no	—
33	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
34	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#460	—	2	1	no	—
36	C₄₇×#460	C₂²	1	2	yes	—
37	C₄₇×#459	—	2	1	no	—
38	C₄₇×#459	C₂²	1	2	yes	—
39	C₄₇×#423	C₂²	1	1	yes	characteristic
40	C₄₇×#418	—	2	1	no	—
41	C₂²×Dic₉₄	—	2	1	no	—
42	C₂×#10625335	—	2	4	no	—
43	C₂×#10625335	—	2	4	no	—
44	C₂×#10625335	—	4	8	no	—
45	C₂×#10625329	—	2	1	no	—
46	C₂²×C₄₇⋊C₈	—	2	2	no	—
47	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
48	#13094024	—	2	1	no	—
49	#13094024	—	2	1	no	—
50	#13094024	—	2	1	no	—
51	#13094024	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₇	—	2	1	no	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	#13093957	—	2	2	no	—
55	#13093955	—	2	2	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
58	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
59	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
60	#13093948	—	2	2	no	—
61	#13093945	—	2	2	no	—
62	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
64	C₄×C₄₇⋊C₈	—	2	1	no	—
65	C₄×C₄₇⋊C₈	—	2	2	no	—
66	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
67	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
68	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
69	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₄₇	—	2	1	no	—
71	C₂²×D₄×C₄₇	—	2	1	no	—
72	C₂²×D₄×C₄₇	—	2	1	no	—
73	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
74	C₂×SD₁₆×C₄₇	—	2	2	no	—
75	C₂×D₈×C₄₇	—	2	2	no	—
76	C₂×M₁₆×C₄₇	—	2	1	no	—
77	#127×C₄₇	—	2	1	no	—
78	#127×C₄₇	—	2	1	no	—
79	#127×C₄₇	—	2	1	no	—
80	#127×C₄₇	C₂³	1	2	yes	—
81	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₄₇	—	2	1	no	—
84	C₄×D₄×C₄₇	—	2	1	no	—
85	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
86	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
87	#117×C₄₇	—	2	1	no	—
88	#117×C₄₇	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	—	2	1	no	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	—	2	1	no	—
92	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
93	#102×C₄₇	—	2	2	no	—
94	#102×C₄₇	—	2	2	no	—
95	C₂⁴×C₄₇	—	4	1	no	—
96	#41×C₄₇	—	2	2	no	—
97	#41×C₄₇	SD₁₆	1	4	yes	complemented
98	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₄₇	—	2	1	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	4	4	no	—
104	C₂×D₄×C₄₇	—	4	1	no	—
105	C₂×D₄×C₄₇	—	4	1	no	—
106	C₂×D₄×C₄₇	—	4	1	no	—
107	C₂×D₄×C₄₇	—	4	2	no	—
108	C₂×D₄×C₄₇	—	4	2	no	—
109	C₂×D₄×C₄₇	—	8	2	no	—
110	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	C₂²×Dic₄₇	—	4	1	no	—
118	C₂×Dic₉₄	—	2	2	no	—
119	C₂×Dic₉₄	—	4	4	no	—
120	C₂×Dic₉₄	—	4	1	no	—
121	SD₁₆×C₄₇	—	4	4	no	—
122	D₈×C₄₇	—	4	4	no	—
123	M₁₆×C₄₇	—	4	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₄₇	C₂×D₄	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	C₂×D₄	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	#10625335	—	4	8	no	—
140	#10625335	—	4	8	no	—
141	C₄⋊Dic₄₇	—	2	2	no	—
142	C₄⋊Dic₄₇	—	2	2	no	—
143	C₄⋊Dic₄₇	—	4	1	no	—
144	C₄⋊Dic₄₇	—	4	1	no	—
145	#10625329	—	4	2	no	—
146	C₂×C₄₇⋊C₈	—	2	4	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	4	4	no	—
150	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
152	C₂³×C₄₇	—	2	1	no	—
153	C₂³×C₄₇	—	4	2	no	—
154	C₂³×C₄₇	—	8	2	no	—
155	C₂³×C₄₇	—	8	2	no	—
156	C₂³×C₄₇	—	8	2	no	—
157	C₂³×C₄₇	#121	1	1	yes	characteristic
158	Q₈×C₄₇	—	2	1	no	—
159	Q₈×C₄₇	C₂×SD₁₆	1	2	yes	complemented
160	D₄×C₄₇	—	2	4	no	—
161	D₄×C₄₇	—	2	1	no	—
162	D₄×C₄₇	—	4	2	no	—
163	D₄×C₄₇	—	4	2	no	—
164	D₄×C₄₇	—	4	4	no	—
165	D₄×C₄₇	—	8	2	no	—
166	D₄×C₄₇	—	8	2	no	—
167	D₄×C₄₇	—	8	2	no	—
168	D₄×C₄₇	—	8	2	no	—
169	D₄×C₄₇	C₂×SD₁₆	1	2	yes	complemented
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
179	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
180	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
182	C₂×C₄×C₄₇	#135	1	2	yes	—
183	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	8	2	no	—
188	Dic₉₄	—	4	4	no	—
189	Dic₉₄	—	8	2	no	—
190	C₈×C₄₇	—	4	2	no	—
191	C₄₇⋊C₈	—	2	2	no	—
192	C₄₇⋊C₈	—	4	2	no	—
193	C₄₇⋊C₈	—	4	2	no	—
194	C₄₇⋊C₈	AGL(1,ℤ/8)	1	4	yes	complemented
195	#19266	—	47	1	no	maximal, Sylow
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	—	4	1	no	—
200	C₂²×C₄₇	—	4	1	no	—
201	C₂²×C₄₇	—	8	2	no	—
202	C₂²×C₄₇	—	8	2	no	—
203	C₂²×C₄₇	—	8	2	no	—
204	C₂²×C₄₇	—	16	4	no	—
205	C₂²×C₄₇	#465	1	2	yes	—
206	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	4	1	no	—
211	C₄×C₄₇	—	4	1	no	—
212	C₄×C₄₇	#465	1	2	yes	—
213	C₄×C₄₇	#471	1	2	yes	—
214	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
215	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
216	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
217	Dic₄₇	—	8	2	no	—
218	C₂×#492	—	47	1	no	—
219	#3079	—	47	1	no	—
220	#3038	D₄₇	1	1	yes	characteristic
221	C₈×#41	—	47	1	no	—
222	#1666	—	47	4	no	—
223	#1665	—	47	4	no	—
224	#1566	—	47	1	no	—
225	#1549	—	47	1	no	—
226	#1545	—	47	1	no	—
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	—	4	2	no	—
229	C₂×C₄₇	—	16	2	no	—
230	C₂×C₄₇	#3038	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
232	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
233	C₂×AGL(1,ℤ/8)	—	2	1	no	—
234	C₂²×SD₁₆	—	94	2	no	—
235	C₂×C₄⋊Q₈	—	47	1	no	—
236	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
237	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
238	#492	—	47	4	no	—
239	#492	—	94	1	no	—
240	#492	—	94	1	no	—
241	#477	—	94	1	no	—
242	#476	—	94	1	no	—
243	#475	—	47	2	no	—
244	#474	—	47	2	no	—
245	#460	—	2	1	no	—
246	#460	C₂×D₄₇	1	2	yes	—
247	#459	—	2	1	no	—
248	#459	C₂×D₄₇	1	2	yes	—
249	C₈×Q₈	—	47	2	no	—
250	C₈×D₄	—	47	2	no	—
251	C₈×D₄	—	94	2	no	—
252	#431	—	47	1	no	—
253	#431	—	94	1	no	—
254	#428	—	94	1	no	—
255	#423	—	47	1	no	—
256	#423	C₂×D₄₇	1	1	yes	characteristic
257	#418	—	2	1	no	—
258	#417	—	94	1	no	—
259	C₂×C₄×C₈	—	47	1	no	—
260	C₂×C₄×C₈	—	94	1	no	—
261	#334	—	47	4	no	—
262	#332	—	47	4	no	—
263	#331	—	47	4	no	—
264	C₄₇	#19266	1	1	yes	characteristic, complemented, Sylow
265	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
266	C₂²×Q₈	—	94	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	AGL(1,ℤ/8)	—	4	4	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	94	4	no	—
273	C₂×SD₁₆	—	94	4	no	—
274	C₂×SD₁₆	—	188	8	no	—
275	C₂×D₈	—	2	2	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	94	1	no	—
278	C₂²×C₈	—	47	2	no	—
279	C₂²×C₈	—	94	2	no	—
280	C₄⋊Q₈	—	47	2	no	—
281	C₄⋊Q₈	—	94	1	no	—
282	C₄⋊Q₈	—	94	1	no	—
283	C₄⋊Q₈	—	94	1	no	—
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	—	2	1	no	—
287	#127	C₂²×D₄₇	1	2	yes	—
288	C₄×Q₈	C₂²⋊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	C₂²⋊D₄₇	1	1	yes	characteristic
293	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
294	#117	—	2	1	no	—
295	#117	C₂²⋊D₄₇	1	1	yes	characteristic
296	C₂×C₄⋊C₄	—	94	1	no	—
297	C₂×C₄⋊C₄	—	94	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
300	#107	—	94	2	no	—
301	#106	—	94	2	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	—	47	2	no	—
304	C₄⋊C₈	—	47	2	no	—
305	C₄⋊C₈	—	94	2	no	—
306	C₄⋊C₈	—	94	1	no	—
307	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
308	#103	—	94	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	94	2	no	—
312	C₂²⋊C₈	—	94	2	no	—
313	C₂²⋊C₈	—	94	1	no	—
314	C₄×C₈	—	47	1	no	—
315	C₄×C₈	—	47	1	no	—
316	C₄×C₈	—	47	2	no	—
317	C₄×C₈	—	94	2	no	—
318	C₄×C₈	—	94	1	no	—
319	C₂⁴	—	4	1	no	—
320	#41	—	2	2	no	—
321	#41	#10625335	1	4	yes	complemented
322	C₂×Q₈	—	94	2	no	—
323	C₂×Q₈	—	188	4	no	—
324	C₂×Q₈	—	188	1	no	—
325	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	8	2	no	—
337	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	188	1	no	—
342	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
343	C₂²×C₄	#10625352	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
345	SD₁₆	—	4	4	no	—
346	SD₁₆	—	188	8	no	—
347	SD₁₆	—	188	8	no	—
348	D₈	—	4	4	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	—	188	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	47	2	no	—
353	C₂×C₈	—	47	2	no	—
354	C₂×C₈	—	94	4	no	—
355	C₂×C₈	—	94	2	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	188	4	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	94	2	no	—
361	C₄⋊C₄	—	94	2	no	—
362	C₄⋊C₄	—	188	1	no	—
363	C₄⋊C₄	—	188	1	no	—
364	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
365	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	D₄×D₄₇	1	1	yes	characteristic
373	C₄²	#10625352	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
375	C₄²	C₂³×D₄₇	1	1	yes	characteristic
376	C₂³	—	2	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	#13093996	1	1	yes	characteristic
382	Q₈	—	2	1	no	—
383	Q₈	—	376	2	no	—
384	Q₈	—	188	4	no	—
385	Q₈	C₂×#10625335	1	2	yes	complemented
386	D₄	—	2	4	no	—
387	D₄	—	2	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	4	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	D₄	C₂×#10625335	1	2	yes	complemented
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	376	2	no	—
405	C₂×C₄	—	188	2	no	—
406	C₂×C₄	#13093996	1	1	yes	characteristic
407	C₂×C₄	#13093996	1	1	yes	characteristic
408	C₂×C₄	#13093996	1	1	yes	characteristic
409	C₂×C₄	C₂×#10625335	1	2	yes	—
410	C₂×C₄	#13094044	1	2	yes	—
411	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
414	C₈	—	4	2	no	—
415	C₈	—	47	4	no	—
416	C₈	—	94	2	no	—
417	C₈	—	188	2	no	—
418	C₈	—	188	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	16	4	no	—
428	C₂²	#15689350	1	2	yes	—
429	C₂²	C₂×#13093996	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	376	2	no	—
436	C₄	#15689350	1	2	yes	—
437	C₄	#15689384	1	2	yes	—
438	C₄	C₂²×#10625335	1	1	yes	characteristic
439	C₄	C₂×#13094044	1	1	yes	characteristic
440	C₄	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
441	C₂	—	2	2	no	—
442	C₂	—	4	2	no	—
443	C₂	—	16	2	no	—
444	C₂	#20252866	1	1	yes	characteristic
445	C₂	C₂×#15689350	1	1	yes	characteristic
446	C₂	C₂×#15689384	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3038	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	#3038	D₄₇
hypocenter	C₄₇	#19266
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3038

Complements

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

N	H ≅ G/N	type
1. C₂×#15689495	C₂	semidirect
2. #20253203	C₂	semidirect
3. #41×C₄₇⋊C₈	C₂	semidirect
4. #20242734	C₂	semidirect
5. #20242727	C₂	semidirect
6. #20242143	C₂	semidirect
7. #20242074	C₂	semidirect
8. #20242056	C₂	semidirect
17. #15689408	C₂²	semidirect
18. #15689403	C₂²	semidirect
19. Q₈×C₄₇⋊C₈	C₂²	semidirect
21. D₄×C₄₇⋊C₈	C₂²	semidirect
29. #15688873	C₂²	semidirect
30. #15688868	C₂²	semidirect
97. #41×C₄₇	SD₁₆	semidirect
159. Q₈×C₄₇	C₂×SD₁₆	semidirect
169. D₄×C₄₇	C₂×SD₁₆	semidirect
194. C₄₇⋊C₈	AGL(1,ℤ/8)	semidirect
264. C₄₇	#19266	semidirect
321. #41	#10625335	semidirect
385. Q₈	C₂×#10625335	semidirect
395. D₄	C₂×#10625335	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689495	2
#20253203	2
#41×C₄₇⋊C₈	2
#20242734	2
#20242727	2
#20242143	2
#20242074	2
#20242056	2
C₄₇×#3038	2
#19266	47