Subgroups — #20255002

Order 6016.

556 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094051	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689792	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689498	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689376	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689373	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689321	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689316	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689268	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689267	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689257	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689255	C₂	1	1	yes	maximal, characteristic, complemented
13	SD₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689199	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625354	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₄₇	—	2	1	no	—
18	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
19	#13094051	—	2	4	no	—
20	C₂×#10625336	C₂²	1	1	yes	characteristic, complemented
21	C₂×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×#10625334	C₂²	1	1	yes	characteristic
23	C₂×#10625334	C₂²	1	1	yes	characteristic, complemented
24	C₂×#10625334	C₂²	1	1	yes	characteristic, complemented
25	C₂×#10625324	C₂²	1	1	yes	characteristic, complemented
26	#13094020	—	2	1	no	—
27	#13094020	C₂²	1	1	yes	characteristic
28	#13094020	C₂²	1	1	yes	characteristic, complemented
29	#13093998	—	2	1	no	—
30	#13093998	C₂²	1	1	yes	characteristic
31	#13093998	C₂²	1	1	yes	characteristic, complemented
32	#13093996	—	2	1	no	—
33	#13093995	—	2	1	no	—
34	#13093995	C₂²	1	1	yes	characteristic
35	#13093995	C₂²	1	1	yes	characteristic, complemented
36	#13093993	—	2	1	no	—
37	#13093992	—	2	1	no	—
38	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
39	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₄₇	—	2	1	no	—
41	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
42	#13093956	C₂²	1	1	yes	characteristic, complemented
43	Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	#13093948	C₂²	1	1	yes	characteristic, complemented
45	#13093946	C₂²	1	1	yes	characteristic, complemented
46	#13093946	C₂²	1	1	yes	characteristic, complemented
47	#13093945	C₂²	1	1	yes	characteristic
48	#13093945	C₂²	1	1	yes	characteristic, complemented
49	#13093945	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
55	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
56	C₂×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×D₈×C₄₇	C₂²	1	1	yes	characteristic
59	C₂×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
60	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₄₇	—	2	1	no	—
62	C₂³×D₄₇	—	2	1	no	—
63	#41×C₄₇	—	2	2	no	—
64	#41×C₄₇	—	4	1	no	—
65	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₄₇	—	2	2	no	—
67	C₂×D₄×C₄₇	—	2	1	no	—
68	C₂×D₄×C₄₇	—	2	1	no	—
69	C₂×D₄×C₄₇	—	4	1	no	—
70	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	—	2	1	no	—
74	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊D₄₇	—	2	1	no	—
76	C₂×C₂²⋊D₄₇	—	2	1	no	—
77	C₂×C₂²⋊D₄₇	—	2	1	no	—
78	C₂×C₂²⋊D₄₇	—	2	1	no	—
79	C₂×C₂²⋊D₄₇	—	2	1	no	—
80	C₂×C₂²⋊D₄₇	—	2	1	no	—
81	C₂×C₂²⋊D₄₇	—	2	1	no	—
82	C₂×C₂²⋊D₄₇	—	2	1	no	—
83	C₂×C₂²⋊D₄₇	—	2	1	no	—
84	C₂×C₂²⋊D₄₇	—	4	4	no	—
85	C₂×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
86	C₂²×Dic₄₇	—	2	1	no	—
87	#10625354	—	2	2	no	—
88	#10625354	—	4	1	no	—
89	D₄×D₄₇	—	2	2	no	—
90	D₄×D₄₇	—	4	1	no	—
91	C₂×D₁₈₈	—	2	1	no	—
92	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
93	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₄₇	—	2	1	no	—
95	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
96	SD₁₆×C₄₇	—	2	2	no	—
97	SD₁₆×C₄₇	D₄	1	4	yes	complemented
98	D₈×C₄₇	—	2	2	no	—
99	D₈×C₄₇	—	2	2	no	—
100	M₁₆×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₂²⋊Dic₄₇	—	2	1	no	—
104	C₂²⋊Dic₄₇	—	2	1	no	—
105	C₂²⋊Dic₄₇	—	2	1	no	—
106	C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
107	#10625336	—	2	2	no	—
108	#10625334	—	2	2	no	—
109	#10625334	—	4	1	no	—
110	#10625334	—	4	1	no	—
111	(C₂×D₄₇)⋊C₄	—	2	1	no	—
112	(C₂×D₄₇)⋊C₄	—	2	1	no	—
113	(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
114	C₄⋊Dic₄₇	—	2	1	no	—
115	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
117	Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
118	C₄×Dic₄₇	—	2	1	no	—
119	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
120	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
122	D₃₇₆	—	2	2	no	—
123	#10625324	—	2	2	no	—
124	C₂³×C₄₇	—	2	1	no	—
125	C₂³×C₄₇	—	2	1	no	—
126	C₂³×C₄₇	—	2	1	no	—
127	C₂³×C₄₇	—	4	2	no	—
128	C₂³×C₄₇	—	4	2	no	—
129	C₂³×C₄₇	—	8	1	no	—
130	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₄₇	—	2	1	no	—
132	C₂²×D₄₇	—	2	1	no	—
133	C₂²×D₄₇	—	4	2	no	—
134	C₂²×D₄₇	—	4	2	no	—
135	C₂²×D₄₇	—	8	1	no	—
136	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
137	Q₈×C₄₇	—	2	1	no	—
138	Q₈×C₄₇	C₂×D₄	1	2	yes	complemented
139	D₄×C₄₇	—	2	1	no	—
140	D₄×C₄₇	—	2	1	no	—
141	D₄×C₄₇	—	2	1	no	—
142	D₄×C₄₇	—	2	1	no	—
143	D₄×C₄₇	—	2	1	no	—
144	D₄×C₄₇	—	4	2	no	—
145	D₄×C₄₇	—	4	2	no	—
146	D₄×C₄₇	C₂×D₄	1	2	yes	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
153	C₂²⋊D₄₇	—	2	2	no	—
154	C₂²⋊D₄₇	—	4	2	no	—
155	C₂²⋊D₄₇	—	4	2	no	—
156	C₂²⋊D₄₇	—	4	2	no	—
157	C₂²⋊D₄₇	—	4	2	no	—
158	C₂²⋊D₄₇	—	4	2	no	—
159	C₂²⋊D₄₇	—	8	1	no	—
160	C₂²⋊D₄₇	—	8	1	no	—
161	C₂²⋊D₄₇	—	8	1	no	—
162	C₂²⋊D₄₇	—	8	1	no	—
163	C₂×Dic₄₇	—	2	1	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
167	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
168	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
169	D₁₈₈	—	2	1	no	—
170	D₁₈₈	—	2	1	no	—
171	D₁₈₈	—	2	1	no	—
172	D₁₈₈	—	2	1	no	—
173	D₁₈₈	—	4	2	no	—
174	C₄×D₄₇	—	2	1	no	—
175	C₄×D₄₇	—	2	1	no	—
176	C₄×D₄₇	—	4	2	no	—
177	C₈×C₄₇	—	2	1	no	—
178	C₈×C₄₇	C₂×D₄	1	2	yes	complemented
179	C₄₇⋊C₈	—	2	1	no	—
180	C₄₇⋊C₈	—	2	1	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	4	1	no	—
186	C₂²×C₄₇	—	4	1	no	—
187	C₂²×C₄₇	—	4	1	no	—
188	C₂²×C₄₇	—	4	1	no	—
189	C₂²×C₄₇	—	4	1	no	—
190	C₂²×C₄₇	—	4	1	no	—
191	C₂²×C₄₇	—	4	1	no	—
192	C₂²×C₄₇	—	4	1	no	—
193	C₂²×C₄₇	—	8	4	no	—
194	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×D₄₇	—	2	1	no	—
196	C₂×D₄₇	—	2	1	no	—
197	C₂×D₄₇	—	2	1	no	—
198	C₂×D₄₇	—	4	1	no	—
199	C₂×D₄₇	—	4	1	no	—
200	C₂×D₄₇	—	4	1	no	—
201	C₂×D₄₇	—	4	1	no	—
202	C₂×D₄₇	—	4	1	no	—
203	C₂×D₄₇	—	4	1	no	—
204	C₂×D₄₇	—	8	4	no	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
208	C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
209	Dic₄₇	—	2	1	no	—
210	Dic₄₇	—	2	1	no	—
211	Dic₄₇	—	4	1	no	—
212	Dic₄₇	—	4	1	no	—
213	Dic₄₇	AGL(1,ℤ/8)	1	2	yes	complemented
214	#3274	—	47	1	no	maximal, Sylow
215	C₂×C₄₇	—	4	2	no	—
216	C₂×C₄₇	—	4	1	no	—
217	C₂×C₄₇	—	8	1	no	—
218	C₂×C₄₇	—	8	1	no	—
219	C₂×C₄₇	D₄²	1	1	yes	characteristic
220	C₂×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂×C₄₇	#576	1	1	yes	characteristic
222	D₄₇	—	4	1	no	—
223	D₄₇	—	8	1	no	—
224	D₄₇	—	8	1	no	—
225	C₂×AGL(1,ℤ/8)	—	47	1	no	—
226	C₂×AGL(1,ℤ/8)	D₄₇	1	1	yes	characteristic, complemented
227	#550	—	47	1	no	—
228	D₄²	—	47	1	no	—
229	#493	—	47	1	no	—
230	#469	—	47	1	no	—
231	#469	—	47	1	no	—
232	#460	—	47	1	no	—
233	#459	—	47	1	no	—
234	#449	—	47	1	no	—
235	#449	—	47	1	no	—
236	#447	—	47	1	no	—
237	#447	—	47	1	no	—
238	C₄×SD₁₆	—	47	1	no	—
239	#436	—	47	1	no	—
240	C₄₇	#3274	1	1	yes	characteristic, complemented, Sylow
241	C₂×#41	—	47	1	no	—
242	C₂×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
243	C₂²×D₄	—	47	1	no	—
244	C₂²×D₄	—	94	1	no	—
245	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
246	AGL(1,ℤ/8)	—	2	4	no	—
247	AGL(1,ℤ/8)	—	94	4	no	—
248	C₂×SD₁₆	—	47	1	no	—
249	C₂×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
250	C₂×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
251	C₂×D₈	—	47	1	no	—
252	C₂×D₈	—	47	1	no	—
253	C₂×D₈	—	47	1	no	—
254	C₂×D₈	—	47	1	no	—
255	C₂×D₈	C₂×D₄₇	1	1	yes	characteristic
256	C₂×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
257	C₂×M₁₆	—	47	1	no	—
258	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
259	#127	—	47	1	no	—
260	#127	—	47	1	no	—
261	#127	—	94	1	no	—
262	#121	—	47	1	no	—
263	#121	—	47	1	no	—
264	#121	—	47	1	no	—
265	#121	—	47	1	no	—
266	#121	—	94	1	no	—
267	#121	—	94	1	no	—
268	#121	—	94	1	no	—
269	#120	—	94	1	no	—
270	#120	—	94	1	no	—
271	C₄×Q₈	—	47	1	no	—
272	C₄×D₄	—	47	1	no	—
273	C₄×D₄	—	47	1	no	—
274	C₄×D₄	—	94	1	no	—
275	#106	—	47	1	no	—
276	C₄⋊C₈	—	47	1	no	—
277	#103	—	47	1	no	—
278	#102	—	47	1	no	—
279	#102	—	47	1	no	—
280	#102	—	47	1	no	—
281	#102	—	47	1	no	—
282	#102	—	47	1	no	—
283	C₂²⋊C₈	—	47	1	no	—
284	C₂²⋊C₈	—	47	1	no	—
285	C₄×C₈	—	47	1	no	—
286	C₂⁴	—	2	1	no	—
287	C₂⁴	—	94	1	no	—
288	#41	—	2	2	no	—
289	#41	—	4	1	no	—
290	#41	—	94	2	no	—
291	#41	—	188	1	no	—
292	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	47	1	no	—
298	C₂×D₄	—	47	1	no	—
299	C₂×D₄	—	47	1	no	—
300	C₂×D₄	—	94	1	no	—
301	C₂×D₄	—	94	1	no	—
302	C₂×D₄	—	94	1	no	—
303	C₂×D₄	—	94	1	no	—
304	C₂×D₄	—	94	1	no	—
305	C₂×D₄	—	94	1	no	—
306	C₂×D₄	—	94	2	no	—
307	C₂×D₄	—	94	1	no	—
308	C₂×D₄	—	94	1	no	—
309	C₂×D₄	—	94	1	no	—
310	C₂×D₄	—	94	1	no	—
311	C₂×D₄	—	188	1	no	—
312	C₂×D₄	—	188	4	no	—
313	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
314	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
315	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	47	1	no	—
318	C₂²×C₄	—	94	1	no	—
319	C₂²×C₄	—	94	1	no	—
320	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
321	SD₁₆	—	2	2	no	—
322	SD₁₆	—	94	2	no	—
323	SD₁₆	C₂²⋊D₄₇	1	4	yes	complemented
324	D₈	—	2	2	no	—
325	D₈	—	2	2	no	—
326	D₈	—	94	2	no	—
327	D₈	—	94	2	no	—
328	D₈	—	188	1	no	—
329	D₈	—	188	1	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	94	2	no	—
332	C₂×C₈	—	47	1	no	—
333	C₂×C₈	—	47	1	no	—
334	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
335	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
336	C₄⋊C₄	—	47	1	no	—
337	C₄⋊C₄	—	47	1	no	—
338	C₄⋊C₄	—	47	1	no	—
339	C₄⋊C₄	—	94	1	no	—
340	C₂²⋊C₄	—	47	1	no	—
341	C₂²⋊C₄	—	47	1	no	—
342	C₂²⋊C₄	—	94	1	no	—
343	C₂²⋊C₄	—	94	1	no	—
344	C₂²⋊C₄	—	94	1	no	—
345	C₂²⋊C₄	—	94	1	no	—
346	C₂²⋊C₄	—	94	1	no	—
347	C₄²	—	47	1	no	—
348	C₄²	—	94	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	8	1	no	—
355	C₂³	—	47	1	no	—
356	C₂³	—	94	1	no	—
357	C₂³	—	94	1	no	—
358	C₂³	—	376	1	no	—
359	C₂³	—	188	2	no	—
360	C₂³	—	188	2	no	—
361	C₂³	D₄×D₄₇	1	1	yes	characteristic
362	Q₈	—	2	1	no	—
363	Q₈	C₂×C₂²⋊D₄₇	1	2	yes	complemented
364	D₄	—	2	1	no	—
365	D₄	—	2	1	no	—
366	D₄	—	2	1	no	—
367	D₄	—	2	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	94	2	no	—
372	D₄	—	94	1	no	—
373	D₄	—	94	1	no	—
374	D₄	—	94	1	no	—
375	D₄	—	94	1	no	—
376	D₄	—	376	1	no	—
377	D₄	—	376	1	no	—
378	D₄	—	376	1	no	—
379	D₄	—	376	1	no	—
380	D₄	—	188	2	no	—
381	D₄	—	188	2	no	—
382	D₄	—	188	2	no	—
383	D₄	—	188	2	no	—
384	D₄	—	188	2	no	—
385	D₄	—	188	2	no	—
386	D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	47	1	no	—
392	C₂×C₄	—	47	1	no	—
393	C₂×C₄	—	47	1	no	—
394	C₂×C₄	—	94	1	no	—
395	C₂×C₄	—	94	1	no	—
396	C₂×C₄	—	94	1	no	—
397	C₂×C₄	—	94	1	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	94	1	no	—
404	C₈	—	94	1	no	—
405	C₈	C₂×C₂²⋊D₄₇	1	2	yes	complemented
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	8	4	no	—
419	C₂²	—	94	1	no	—
420	C₂²	—	94	1	no	—
421	C₂²	—	94	1	no	—
422	C₂²	—	376	4	no	—
423	C₂²	—	188	1	no	—
424	C₂²	—	188	1	no	—
425	C₂²	—	188	1	no	—
426	C₂²	—	188	1	no	—
427	C₂²	—	188	1	no	—
428	C₂²	—	188	1	no	—
429	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	—	47	2	no	—
433	C₄	—	94	1	no	—
434	C₄	—	94	1	no	—
435	C₄	—	188	1	no	—
436	C₄	—	188	1	no	—
437	C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
438	C₄	#13094069	1	1	yes	characteristic
439	C₂	—	4	1	no	—
440	C₂	—	4	2	no	—
441	C₂	—	8	1	no	—
442	C₂	—	8	1	no	—
443	C₂	—	376	1	no	—
444	C₂	—	376	1	no	—
445	C₂	—	188	1	no	—
446	C₂	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
447	C₂	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
448	C₂	#15689927	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂×AGL(1,ℤ/8)×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₄₇
hypocenter	C₄₇	#3274
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×#13094051	C₂	semidirect
2. #15689792	C₂	semidirect
3. D₄×C₂²⋊D₄₇	C₂	semidirect
4. #15689498	C₂	semidirect
5. #15689376	C₂	semidirect
6. #15689373	C₂	semidirect
7. #15689321	C₂	semidirect
8. #15689316	C₂	semidirect
9. #15689268	C₂	semidirect
10. #15689267	C₂	semidirect
11. #15689257	C₂	semidirect
12. #15689255	C₂	semidirect
13. SD₁₆×Dic₄₇	C₂	semidirect
14. #15689199	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₄₇	C₂	semidirect
16. C₂×#10625354	C₂²	semidirect
20. C₂×#10625336	C₂²	semidirect
21. C₂×D₃₇₆	C₂²	semidirect
23. C₂×#10625334	C₂²	semidirect
24. C₂×#10625334	C₂²	semidirect
25. C₂×#10625324	C₂²	semidirect
28. #13094020	C₂²	semidirect
31. #13093998	C₂²	semidirect
35. #13093995	C₂²	semidirect
38. Q₈×Dic₄₇	C₂²	semidirect
42. #13093956	C₂²	semidirect
43. Dic₄₇⋊C₈	C₂²	semidirect
44. #13093948	C₂²	semidirect
45. #13093946	C₂²	semidirect
46. #13093946	C₂²	semidirect
48. #13093945	C₂²	semidirect
49. #13093945	C₂²	semidirect
50. C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
51. (C₂×D₄₇)⋊C₈	C₂²	semidirect
52. C₈×Dic₄₇	C₂²	semidirect
53. C₂×#41×C₄₇	C₂²	semidirect
57. C₂×SD₁₆×C₄₇	C₂²	semidirect
59. C₂×D₈×C₄₇	C₂²	semidirect
60. C₂×M₁₆×C₄₇	C₂²	semidirect
97. SD₁₆×C₄₇	D₄	semidirect
138. Q₈×C₄₇	C₂×D₄	semidirect
178. C₈×C₄₇	C₂×D₄	semidirect
213. Dic₄₇	AGL(1,ℤ/8)	semidirect
226. C₂×AGL(1,ℤ/8)	D₄₇	semidirect
240. C₄₇	#3274	semidirect
242. C₂×#41	C₂×D₄₇	semidirect
250. C₂×SD₁₆	C₂×D₄₇	semidirect
256. C₂×D₈	C₂×D₄₇	semidirect
258. C₂×M₁₆	C₂×D₄₇	semidirect
323. SD₁₆	C₂²⋊D₄₇	semidirect
363. Q₈	C₂×C₂²⋊D₄₇	semidirect
405. C₈	C₂×C₂²⋊D₄₇	semidirect