Subgroups — #26200230

Order 12032.

722 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689469	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	#20242802	C₂	1	4	yes	maximal, complemented
5	#20242795	C₂	1	4	yes	maximal, complemented
6	#20242143	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242070	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	C₂×#13094024	C₂²	1	1	yes	characteristic
11	#15689469	—	2	1	no	—
12	#15689469	—	2	1	no	—
13	#15689469	C₂²	1	4	yes	—
14	#15689418	C₂²	1	2	yes	complemented
15	#15689413	C₂²	1	2	yes	complemented
16	#15689408	—	2	1	no	—
17	#15689403	—	2	1	no	—
18	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
19	D₄×C₄₇⋊C₈	—	2	2	no	—
20	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
21	#15689176	—	2	1	no	—
22	#15689176	C₂²	1	1	yes	characteristic
23	#15689166	—	2	1	no	—
24	#15689147	C₂²	1	1	yes	characteristic
25	#15689124	—	2	1	no	—
26	C₂×#13093945	—	2	2	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	#15688871	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×#10625329	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
45	#13094024	—	2	1	no	—
46	#13094024	—	2	1	no	—
47	#13094024	—	2	1	no	—
48	#13094024	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	#13093957	—	2	2	no	—
52	#13093955	—	2	2	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	#13093948	—	2	2	no	—
58	#13093945	—	2	2	no	—
59	#13093945	—	2	4	no	—
60	#13093945	—	2	4	no	—
61	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
62	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
63	C₄×C₄₇⋊C₈	—	2	1	no	—
64	C₄×C₄₇⋊C₈	—	2	2	no	—
65	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
66	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
67	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
68	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
69	C₂²×D₄×C₄₇	—	2	1	no	—
70	C₂²×D₄×C₄₇	—	2	1	no	—
71	C₂²×D₄×C₄₇	—	2	1	no	—
72	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
73	C₂×SD₁₆×C₄₇	—	2	2	no	—
74	C₂×D₈×C₄₇	—	2	2	no	—
75	C₂×M₁₆×C₄₇	—	2	1	no	—
76	#127×C₄₇	—	2	1	no	—
77	#127×C₄₇	—	2	1	no	—
78	#127×C₄₇	—	2	1	no	—
79	#127×C₄₇	C₂³	1	2	yes	—
80	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
81	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₄×D₄×C₄₇	—	2	1	no	—
83	C₄×D₄×C₄₇	—	2	1	no	—
84	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
85	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
86	#117×C₄₇	—	2	1	no	—
87	#117×C₄₇	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₇	—	2	1	no	—
91	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
92	#102×C₄₇	—	2	2	no	—
93	#102×C₄₇	—	2	2	no	—
94	C₂⁴×C₄₇	—	4	1	no	—
95	#41×C₄₇	—	2	2	no	—
96	#41×C₄₇	SD₁₆	1	4	yes	—
97	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₄₇	—	2	1	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	4	4	no	—
103	C₂×D₄×C₄₇	—	4	1	no	—
104	C₂×D₄×C₄₇	—	4	1	no	—
105	C₂×D₄×C₄₇	—	4	1	no	—
106	C₂×D₄×C₄₇	—	4	2	no	—
107	C₂×D₄×C₄₇	—	4	2	no	—
108	C₂×D₄×C₄₇	—	8	2	no	—
109	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
116	C₂²×Dic₄₇	—	4	1	no	—
117	C₂×Dic₉₄	—	2	2	no	—
118	C₂×Dic₉₄	—	4	1	no	—
119	C₂×Dic₉₄	—	8	2	no	—
120	SD₁₆×C₄₇	—	4	4	no	—
121	D₈×C₄₇	—	4	4	no	—
122	M₁₆×C₄₇	—	4	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	1	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₄₇	—	2	1	no	—
129	C₂²⋊C₄×C₄₇	—	2	1	no	—
130	C₂²⋊C₄×C₄₇	—	2	1	no	—
131	C₄²×C₄₇	—	2	1	no	—
132	C₄²×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₇	#41	1	1	yes	characteristic
137	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	—	2	2	no	—
140	C₄⋊Dic₄₇	—	4	1	no	—
141	C₄⋊Dic₄₇	—	4	1	no	—
142	#10625329	—	4	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	4	2	no	—
146	C₂×C₄₇⋊C₈	—	4	4	no	—
147	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
148	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
149	C₂³×C₄₇	—	2	1	no	—
150	C₂³×C₄₇	—	4	2	no	—
151	C₂³×C₄₇	—	8	2	no	—
152	C₂³×C₄₇	—	8	2	no	—
153	C₂³×C₄₇	—	8	2	no	—
154	C₂³×C₄₇	#121	1	1	yes	characteristic
155	Q₈×C₄₇	—	2	1	no	—
156	Q₈×C₄₇	C₂×SD₁₆	1	2	yes	—
157	D₄×C₄₇	—	2	4	no	—
158	D₄×C₄₇	—	2	1	no	—
159	D₄×C₄₇	—	4	2	no	—
160	D₄×C₄₇	—	4	2	no	—
161	D₄×C₄₇	—	4	4	no	—
162	D₄×C₄₇	—	8	2	no	—
163	D₄×C₄₇	—	8	2	no	—
164	D₄×C₄₇	—	8	2	no	—
165	D₄×C₄₇	—	8	2	no	—
166	D₄×C₄₇	C₂×SD₁₆	1	2	yes	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
176	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
177	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
179	C₂×C₄×C₄₇	#135	1	2	yes	—
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	8	2	no	—
185	Dic₉₄	—	8	2	no	—
186	Dic₉₄	—	8	2	no	—
187	C₈×C₄₇	—	4	2	no	—
188	C₄₇⋊C₈	—	2	2	no	—
189	C₄₇⋊C₈	—	2	2	no	—
190	C₄₇⋊C₈	—	4	2	no	—
191	C₄₇⋊C₈	—	4	2	no	—
192	#19274	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	4	1	no	—
197	C₂²×C₄₇	—	4	1	no	—
198	C₂²×C₄₇	—	8	2	no	—
199	C₂²×C₄₇	—	8	2	no	—
200	C₂²×C₄₇	—	8	2	no	—
201	C₂²×C₄₇	—	16	4	no	—
202	C₂²×C₄₇	#465	1	2	yes	—
203	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
204	C₄×C₄₇	—	2	1	no	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	4	1	no	—
208	C₄×C₄₇	—	4	1	no	—
209	C₄×C₄₇	#465	1	2	yes	—
210	C₄×C₄₇	#472	1	2	yes	—
211	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
212	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
213	C₄×C₄₇	#575	1	2	yes	—
214	Dic₄₇	—	8	2	no	—
215	C₂×#486	—	47	1	no	—
216	#3079	—	47	1	no	—
217	#3038	D₄₇	1	1	yes	characteristic
218	C₈×#41	—	47	1	no	—
219	#1678	—	47	4	no	—
220	#1677	—	47	4	no	—
221	#1566	—	47	1	no	—
222	#1548	—	47	1	no	—
223	#1545	—	47	1	no	—
224	C₂×C₄₇	—	2	2	no	—
225	C₂×C₄₇	—	4	2	no	—
226	C₂×C₄₇	—	16	2	no	—
227	C₂×C₄₇	#3040	1	1	yes	characteristic
228	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
229	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
230	C₂×AGL(1,ℤ/8)	—	2	1	no	—
231	C₂×C₄⋊Q₈	—	47	1	no	—
232	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
233	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
234	#486	—	47	4	no	—
235	#486	—	94	1	no	—
236	#486	—	94	1	no	—
237	#477	—	47	2	no	—
238	#476	—	47	2	no	—
239	#475	—	94	1	no	—
240	#474	—	94	1	no	—
241	#460	—	2	1	no	—
242	#460	C₂×D₄₇	1	2	yes	—
243	#459	—	2	1	no	—
244	#459	C₂×D₄₇	1	2	yes	—
245	C₈×Q₈	—	47	2	no	—
246	C₈×D₄	—	47	2	no	—
247	C₈×D₄	—	94	2	no	—
248	#431	—	47	1	no	—
249	#431	—	94	1	no	—
250	#428	—	94	1	no	—
251	#423	—	47	1	no	—
252	#423	C₂×D₄₇	1	1	yes	characteristic
253	#418	—	2	1	no	—
254	#417	—	94	1	no	—
255	C₂×#102	—	94	2	no	—
256	C₂×C₄×C₈	—	47	1	no	—
257	C₂×C₄×C₈	—	94	1	no	—
258	#334	—	47	4	no	—
259	#333	—	47	4	no	—
260	#331	—	47	4	no	—
261	C₄₇	#19274	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
263	C₂²×Q₈	—	94	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	1	no	—
267	AGL(1,ℤ/8)	—	4	4	no	—
268	C₂×SD₁₆	—	2	2	no	—
269	C₂×D₈	—	2	2	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	94	1	no	—
272	C₂²×C₈	—	47	2	no	—
273	C₂²×C₈	—	94	2	no	—
274	C₄⋊Q₈	—	47	2	no	—
275	C₄⋊Q₈	—	94	1	no	—
276	C₄⋊Q₈	—	94	1	no	—
277	C₄⋊Q₈	—	94	1	no	—
278	#127	—	2	1	no	—
279	#127	—	2	1	no	—
280	#127	—	2	1	no	—
281	#127	C₂²×D₄₇	1	2	yes	—
282	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
283	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
287	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
288	#117	—	2	1	no	—
289	#117	C₂²⋊D₄₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	—	94	1	no	—
291	C₂×C₄⋊C₄	—	94	1	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
294	#107	—	94	2	no	—
295	#106	—	94	2	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	47	2	no	—
298	C₄⋊C₈	—	47	2	no	—
299	C₄⋊C₈	—	94	2	no	—
300	C₄⋊C₈	—	94	1	no	—
301	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
302	#103	—	94	2	no	—
303	#102	—	2	2	no	—
304	#102	—	2	2	no	—
305	#102	—	94	4	no	—
306	#102	—	94	4	no	—
307	#102	—	94	2	no	—
308	C₂²⋊C₈	—	94	2	no	—
309	C₂²⋊C₈	—	94	1	no	—
310	C₄×C₈	—	47	1	no	—
311	C₄×C₈	—	47	1	no	—
312	C₄×C₈	—	47	2	no	—
313	C₄×C₈	—	94	2	no	—
314	C₄×C₈	—	94	1	no	—
315	C₂⁴	—	4	1	no	—
316	#41	—	2	2	no	—
317	#41	#10625335	1	4	yes	—
318	C₂×Q₈	—	94	2	no	—
319	C₂×Q₈	—	376	2	no	—
320	C₂×Q₈	—	188	1	no	—
321	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	8	2	no	—
333	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	188	1	no	—
338	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
339	C₂²×C₄	#10625352	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
341	SD₁₆	—	4	4	no	—
342	D₈	—	4	4	no	—
343	M₁₆	—	4	2	no	—
344	M₁₆	—	188	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	47	2	no	—
347	C₂×C₈	—	47	2	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	94	2	no	—
350	C₂×C₈	—	188	2	no	—
351	C₂×C₈	—	188	4	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	94	2	no	—
355	C₄⋊C₄	—	94	2	no	—
356	C₄⋊C₄	—	188	1	no	—
357	C₄⋊C₄	—	188	1	no	—
358	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
359	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	D₄×D₄₇	1	1	yes	characteristic
367	C₄²	#10625352	1	1	yes	characteristic
368	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
369	C₄²	C₂³×D₄₇	1	1	yes	characteristic
370	C₂³	—	2	1	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	8	2	no	—
375	C₂³	#13093996	1	1	yes	characteristic
376	Q₈	—	2	1	no	—
377	Q₈	—	376	2	no	—
378	Q₈	—	376	2	no	—
379	Q₈	C₂×#10625335	1	2	yes	—
380	D₄	—	2	4	no	—
381	D₄	—	2	1	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	4	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	D₄	C₂×#10625335	1	2	yes	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	376	2	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	#13093996	1	1	yes	characteristic
401	C₂×C₄	#13093996	1	1	yes	characteristic
402	C₂×C₄	#13093996	1	1	yes	characteristic
403	C₂×C₄	C₂×#10625335	1	2	yes	—
404	C₂×C₄	#13094044	1	2	yes	—
405	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
408	C₈	—	4	2	no	—
409	C₈	—	94	2	no	—
410	C₈	—	94	2	no	—
411	C₈	—	188	2	no	—
412	C₈	—	188	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	#15689350	1	2	yes	—
423	C₂²	C₂×#13093996	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	376	2	no	—
430	C₄	#15689350	1	2	yes	—
431	C₄	#15689391	1	2	yes	—
432	C₄	C₂²×#10625335	1	1	yes	characteristic
433	C₄	C₂×#13094044	1	1	yes	characteristic
434	C₄	#15689919	1	2	yes	—
435	C₂	—	2	2	no	—
436	C₂	—	4	2	no	—
437	C₂	—	16	2	no	—
438	C₂	#20252880	1	1	yes	characteristic
439	C₂	C₂×#15689350	1	1	yes	characteristic
440	C₂	C₂×#15689391	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	#19274
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×#15689469	C₂	semidirect
2. #20253203	C₂	semidirect
3. #41×C₄₇⋊C₈	C₂	semidirect
4. #20242802	C₂	semidirect
5. #20242795	C₂	semidirect
6. #20242143	C₂	semidirect
7. #20242070	C₂	semidirect
8. #20242056	C₂	semidirect
14. #15689418	C₂²	semidirect
15. #15689413	C₂²	semidirect
18. Q₈×C₄₇⋊C₈	C₂²	semidirect
20. D₄×C₄₇⋊C₈	C₂²	semidirect
29. #15688873	C₂²	semidirect
30. #15688871	C₂²	semidirect
261. C₄₇	#19274	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689469	2
#20253203	2
#41×C₄₇⋊C₈	2
#20242802	2
#20242795	2
#20242143	2
#20242070	2
#20242056	2
C₄₇×#3038	2
#19274	47