Subgroups — #26200234

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×#15689471	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252868	C₂	1	1	yes	maximal, characteristic
3	#41×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242806	C₂	1	4	yes	maximal, complemented
5	#20242799	C₂	1	4	yes	maximal, complemented
6	#20242143	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242069	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242057	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13094049	—	2	1	no	—
11	C₂×#13094021	C₂²	1	1	yes	characteristic
12	#15689471	—	2	1	no	—
13	#15689471	—	2	1	no	—
14	#15689471	C₂²	1	4	yes	—
15	#15689323	—	2	1	no	—
16	#15689323	C₂²	1	2	yes	—
17	#15689318	—	2	1	no	—
18	#15689318	C₂²	1	2	yes	—
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	#15689147	C₂²	1	1	yes	characteristic
25	#15689127	—	2	1	no	—
26	C₂×#13093944	—	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	#15688872	C₂²	1	4	yes	complemented
31	#15688866	C₂²	1	4	yes	—
32	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#477	C₂²	1	2	yes	complemented
35	C₄₇×#476	C₂²	1	2	yes	complemented
36	C₄₇×#475	—	2	1	no	—
37	C₄₇×#474	—	2	1	no	—
38	C₄₇×#428	—	2	1	no	—
39	C₄₇×#423	C₂²	1	1	yes	characteristic
40	C₄₇×#417	—	2	1	no	—
41	C₂²×D₁₈₈	—	2	1	no	—
42	C₂²×D₁₈₈	—	2	1	no	—
43	C₂²×D₁₈₈	—	2	1	no	—
44	#13094049	—	4	4	no	—
45	C₂×#10625336	—	2	2	no	—
46	C₂×#10625334	—	2	2	no	—
47	C₂×#10625329	—	2	1	no	—
48	C₂²×C₄₇⋊C₈	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
50	#13094021	—	2	1	no	—
51	#13094021	—	2	1	no	—
52	#13094021	—	2	1	no	—
53	#13094021	C₂³	1	2	yes	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
58	#13093944	—	2	2	no	—
59	#13093944	—	2	2	no	—
60	#13093944	—	2	4	no	—
61	#13093944	—	2	4	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×Q₈×C₄₇	—	2	1	no	—
71	C₂×M₁₆×C₄₇	—	2	1	no	—
72	C₄⋊Q₈×C₄₇	—	2	1	no	—
73	C₄⋊Q₈×C₄₇	—	2	1	no	—
74	C₄⋊Q₈×C₄₇	—	2	1	no	—
75	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
76	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
77	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₄×D₄×C₄₇	—	2	1	no	—
79	C₄×D₄×C₄₇	—	2	1	no	—
80	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
81	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
82	#117×C₄₇	—	2	1	no	—
83	#117×C₄₇	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₄²×C₄₇	—	2	1	no	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	#107×C₄₇	—	2	2	no	—
89	#106×C₄₇	—	2	2	no	—
90	C₄⋊C₈×C₄₇	—	2	1	no	—
91	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
92	#103×C₄₇	—	2	2	no	—
93	#102×C₄₇	—	2	2	no	—
94	C₂³×D₄₇	—	4	1	no	—
95	#41×C₄₇	—	2	2	no	—
96	#41×C₄₇	SD₁₆	1	4	yes	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	4	1	no	—
99	C₂×Q₈×C₄₇	—	8	2	no	—
100	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	4	1	no	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
110	C₂×D₁₈₈	—	2	2	no	—
111	C₂×D₁₈₈	—	2	2	no	—
112	C₂×D₁₈₈	—	2	2	no	—
113	C₂×D₁₈₈	—	4	4	no	—
114	C₂×D₁₈₈	—	4	2	no	—
115	C₂×D₁₈₈	—	4	2	no	—
116	C₂×D₁₈₈	—	4	1	no	—
117	C₂×D₁₈₈	—	4	1	no	—
118	C₂×D₁₈₈	—	4	1	no	—
119	C₂×D₁₈₈	—	8	2	no	—
120	M₁₆×C₄₇	—	4	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	1	no	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	4	1	no	—
127	C₄⋊C₄×C₄₇	—	4	1	no	—
128	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²⋊C₄×C₄₇	—	2	1	no	—
131	C₂²⋊C₄×C₄₇	—	2	1	no	—
132	C₂²⋊C₄×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	—	2	1	no	—
135	C₄²×C₄₇	—	2	1	no	—
136	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₇	#41	1	1	yes	characteristic
139	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
140	#10625336	—	4	4	no	—
141	#10625334	—	4	4	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	#121	1	1	yes	characteristic
151	C₂²×D₄₇	—	4	2	no	—
152	C₂²×D₄₇	—	8	2	no	—
153	C₂²×D₄₇	—	8	2	no	—
154	C₂²×D₄₇	—	8	2	no	—
155	Q₈×C₄₇	—	2	1	no	—
156	Q₈×C₄₇	—	8	2	no	—
157	Q₈×C₄₇	—	8	2	no	—
158	Q₈×C₄₇	C₂×SD₁₆	1	2	yes	—
159	D₄×C₄₇	—	2	4	no	—
160	D₄×C₄₇	—	2	1	no	—
161	D₄×C₄₇	C₂×SD₁₆	1	2	yes	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	8	2	no	—
172	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
176	C₂×C₄×C₄₇	#135	1	2	yes	—
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	D₁₈₈	—	4	2	no	—
181	D₁₈₈	—	4	2	no	—
182	D₁₈₈	—	4	4	no	—
183	D₁₈₈	—	8	2	no	—
184	D₁₈₈	—	8	2	no	—
185	D₁₈₈	—	8	2	no	—
186	D₁₈₈	—	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	#465	1	2	yes	—
199	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
200	C₂×D₄₇	—	8	2	no	—
201	C₂×D₄₇	—	8	2	no	—
202	C₂×D₄₇	—	8	2	no	—
203	C₂×D₄₇	—	16	4	no	—
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	—	8	2	no	—
210	C₄×C₄₇	#465	1	2	yes	—
211	C₄×C₄₇	#472	1	2	yes	—
212	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
213	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
214	C₄×C₄₇	#575	1	2	yes	—
215	C₂×#486	—	47	1	no	—
216	#3079	D₄₇	1	1	yes	characteristic, complemented
217	#3038	—	47	1	no	—
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	#3040	1	1	yes	characteristic
227	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
228	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
229	D₄₇	—	16	2	no	—
230	C₂×AGL(1,ℤ/8)	—	94	1	no	—
231	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
232	C₂×#127	—	47	1	no	—
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	C₂×D₄₇	1	2	yes	complemented
238	#476	C₂×D₄₇	1	2	yes	complemented
239	#475	—	2	1	no	—
240	#474	—	2	1	no	—
241	#460	—	47	2	no	—
242	#460	—	94	1	no	—
243	#459	—	47	2	no	—
244	#459	—	94	1	no	—
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	—	2	1	no	—
251	#423	—	47	1	no	—
252	#423	C₂×D₄₇	1	1	yes	characteristic
253	#418	—	94	1	no	—
254	#417	—	2	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	—	2	1	no	—
264	C₂²×D₄	—	94	1	no	—
265	C₂²×D₄	—	94	1	no	—
266	C₂²×D₄	—	94	1	no	—
267	AGL(1,ℤ/8)	—	188	4	no	—
268	C₂×SD₁₆	—	94	2	no	—
269	C₂×D₈	—	94	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	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
278	#127	—	47	2	no	—
279	#127	—	94	1	no	—
280	#127	—	94	1	no	—
281	#127	—	94	1	no	—
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	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
294	#107	—	2	2	no	—
295	#106	—	2	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	—	2	2	no	—
303	#102	—	2	2	no	—
304	#102	—	94	4	no	—
305	#102	—	94	4	no	—
306	#102	—	94	2	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	—	188	1	no	—
316	#41	—	2	2	no	—
317	#41	#10625336	1	4	yes	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	8	2	no	—
321	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	94	2	no	—
324	C₂×D₄	—	94	2	no	—
325	C₂×D₄	—	94	2	no	—
326	C₂×D₄	—	376	2	no	—
327	C₂×D₄	—	188	4	no	—
328	C₂×D₄	—	188	1	no	—
329	C₂×D₄	—	188	1	no	—
330	C₂×D₄	—	188	1	no	—
331	C₂×D₄	—	188	2	no	—
332	C₂×D₄	—	188	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	—	4	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	—	188	4	no	—
342	D₈	—	188	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	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	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	—	376	2	no	—
372	C₂³	—	376	2	no	—
373	C₂³	—	376	2	no	—
374	C₂³	—	188	2	no	—
375	C₂³	#13093996	1	1	yes	characteristic
376	Q₈	—	2	1	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	8	2	no	—
379	Q₈	C₂×#10625336	1	2	yes	—
380	D₄	—	2	4	no	—
381	D₄	—	2	1	no	—
382	D₄	—	376	2	no	—
383	D₄	—	376	2	no	—
384	D₄	—	376	2	no	—
385	D₄	—	376	2	no	—
386	D₄	—	188	2	no	—
387	D₄	—	188	2	no	—
388	D₄	—	188	4	no	—
389	D₄	C₂×#10625336	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	—	4	2	no	—
399	C₂×C₄	—	8	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×#10625336	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	—	376	2	no	—
419	C₂²	—	376	2	no	—
420	C₂²	—	376	2	no	—
421	C₂²	—	752	4	no	—
422	C₂²	#15689354	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	—	8	2	no	—
430	C₄	#15689354	1	2	yes	—
431	C₄	#15689391	1	2	yes	—
432	C₄	C₂²×#10625336	1	1	yes	characteristic
433	C₄	C₂×#13094044	1	1	yes	characteristic
434	C₄	#15689922	1	2	yes	—
435	C₂	—	2	2	no	—
436	C₂	—	4	2	no	—
437	C₂	—	752	2	no	—
438	C₂	#20252884	1	1	yes	characteristic
439	C₂	C₂×#15689354	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	C₄₇×#3079	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	#20252868	C₂
hypercenter	#3079	D₄₇
hypocenter	C₄₇	#19274
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3079

Complements

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

N	H ≅ G/N	type
1. C₂×#15689471	C₂	semidirect
3. #41×C₄₇⋊C₈	C₂	semidirect
4. #20242806	C₂	semidirect
5. #20242799	C₂	semidirect
6. #20242143	C₂	semidirect
7. #20242069	C₂	semidirect
8. #20242057	C₂	semidirect
9. C₄₇×#3079	C₂	semidirect
19. Q₈×C₄₇⋊C₈	C₂²	semidirect
21. D₄×C₄₇⋊C₈	C₂²	semidirect
29. #15688873	C₂²	semidirect
30. #15688872	C₂²	semidirect
34. C₄₇×#477	C₂²	semidirect
35. C₄₇×#476	C₂²	semidirect
216. #3079	D₄₇	semidirect
237. #477	C₂×D₄₇	semidirect
238. #476	C₂×D₄₇	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×#15689471	2
#20252868	2
#41×C₄₇⋊C₈	2
#20242806	2
#20242799	2
#20242143	2
#20242069	2
#20242057	2
C₄₇×#3079	2
#19274	47