Subgroups — #20255001

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	C₂×#13094049	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689792	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689757	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689498	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689375	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689374	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689321	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689317	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689271	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689259	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689255	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689208	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689198	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#449	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625354	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₄₇	—	2	1	no	—
19	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
20	#13094051	—	2	4	no	—
21	#13094049	—	2	4	no	—
22	C₂×#10625336	C₂²	1	1	yes	characteristic
23	C₂×#10625336	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
25	C₂×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
26	C₂×#10625334	C₂²	1	1	yes	characteristic
27	C₂×#10625334	C₂²	1	1	yes	characteristic, complemented
28	C₂×#10625334	C₂²	1	1	yes	characteristic, complemented
29	C₂×#10625329	C₂²	1	1	yes	characteristic, complemented
30	C₂×#10625324	C₂²	1	1	yes	characteristic, complemented
31	#13094020	—	2	1	no	—
32	#13094020	C₂²	1	1	yes	characteristic
33	#13094020	C₂²	1	1	yes	characteristic, complemented
34	#13093999	C₂²	1	1	yes	characteristic
35	#13093998	—	2	1	no	—
36	#13093998	C₂²	1	1	yes	characteristic, complemented
37	#13093997	—	2	1	no	—
38	#13093995	—	2	1	no	—
39	#13093995	C₂²	1	1	yes	characteristic, complemented
40	#13093994	—	2	1	no	—
41	#13093992	—	2	1	no	—
42	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
43	#13093986	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊D₄₇	—	2	1	no	—
45	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
46	#13093955	C₂²	1	1	yes	characteristic, complemented
47	Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	#13093946	C₂²	1	1	yes	characteristic
49	#13093946	C₂²	1	1	yes	characteristic, complemented
50	#13093945	C₂²	1	1	yes	characteristic, complemented
51	#13093944	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
57	#121×C₄₇	C₂²	1	1	yes	characteristic
58	#103×C₄₇	C₂²	1	1	yes	characteristic, complemented
59	#102×C₄₇	C₂²	1	1	yes	characteristic, complemented
60	C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₄₇	—	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	1	no	—
67	C₂×D₄×C₄₇	—	2	1	no	—
68	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	—	2	1	no	—
71	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊D₄₇	—	2	1	no	—
73	C₂×C₂²⋊D₄₇	—	2	1	no	—
74	C₂×C₂²⋊D₄₇	—	2	1	no	—
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	D₄	1	1	yes	characteristic
80	#10625354	—	2	2	no	—
81	#10625354	—	4	1	no	—
82	D₄×D₄₇	—	2	2	no	—
83	D₄×D₄₇	—	4	1	no	—
84	D₄×D₄₇	—	4	4	no	—
85	C₂×D₁₈₈	—	2	2	no	—
86	C₂×D₁₈₈	—	2	1	no	—
87	C₂×D₁₈₈	—	2	1	no	—
88	C₂×D₁₈₈	—	2	1	no	—
89	C₂×D₁₈₈	—	4	1	no	—
90	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
91	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
92	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₄₇	—	2	1	no	—
94	C₂×C₄×D₄₇	—	2	1	no	—
95	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
96	SD₁₆×C₄₇	—	2	2	no	—
97	D₈×C₄₇	—	4	1	no	—
98	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
101	C₂²⋊C₄×C₄₇	—	2	1	no	—
102	C₂²⋊Dic₄₇	—	2	1	no	—
103	C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
104	#10625336	—	2	2	no	—
105	#10625336	D₄	1	4	yes	complemented
106	#10625334	—	2	2	no	—
107	#10625334	—	2	2	no	—
108	#10625334	—	2	2	no	—
109	(C₂×D₄₇)⋊C₄	—	2	1	no	—
110	(C₂×D₄₇)⋊C₄	—	2	1	no	—
111	(C₂×D₄₇)⋊C₄	—	2	1	no	—
112	(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
113	C₄⋊Dic₄₇	—	2	1	no	—
114	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
115	Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
116	C₄×Dic₄₇	—	2	1	no	—
117	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
118	#10625329	—	2	2	no	—
119	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
120	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
121	D₃₇₆	—	2	2	no	—
122	D₃₇₆	—	4	1	no	—
123	#10625324	—	2	2	no	—
124	C₂³×C₄₇	—	2	1	no	—
125	C₂³×C₄₇	—	2	1	no	—
126	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×D₄₇	—	2	1	no	—
128	C₂²×D₄₇	—	2	1	no	—
129	C₂²×D₄₇	—	2	1	no	—
130	C₂²×D₄₇	—	4	2	no	—
131	C₂²×D₄₇	—	4	2	no	—
132	C₂²×D₄₇	—	4	2	no	—
133	C₂²×D₄₇	—	4	2	no	—
134	C₂²×D₄₇	—	8	1	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	—	4	2	no	—
144	D₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
152	C₂²⋊D₄₇	—	2	2	no	—
153	C₂²⋊D₄₇	—	4	2	no	—
154	C₂²⋊D₄₇	—	4	2	no	—
155	C₂²⋊D₄₇	—	4	2	no	—
156	C₂²⋊D₄₇	—	8	1	no	—
157	C₂²⋊D₄₇	—	8	1	no	—
158	C₂²⋊D₄₇	—	8	1	no	—
159	C₂²⋊D₄₇	—	8	1	no	—
160	C₂×Dic₄₇	—	2	1	no	—
161	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
162	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
163	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
164	D₁₈₈	—	2	1	no	—
165	D₁₈₈	—	2	1	no	—
166	D₁₈₈	—	2	1	no	—
167	D₁₈₈	—	2	1	no	—
168	D₁₈₈	—	2	1	no	—
169	D₁₈₈	—	4	2	no	—
170	D₁₈₈	—	4	2	no	—
171	D₁₈₈	—	4	2	no	—
172	D₁₈₈	C₂×D₄	1	2	yes	—
173	C₄×D₄₇	—	2	1	no	—
174	C₄×D₄₇	—	2	1	no	—
175	C₄×D₄₇	—	4	2	no	—
176	C₄×D₄₇	—	4	2	no	—
177	C₈×C₄₇	—	2	1	no	—
178	C₈×C₄₇	—	2	1	no	—
179	C₄₇⋊C₈	—	2	1	no	—
180	C₄₇⋊C₈	C₂×D₄	1	2	yes	complemented
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	4	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	C₂²×D₄	1	1	yes	characteristic
191	C₂×D₄₇	—	2	1	no	—
192	C₂×D₄₇	—	2	2	no	—
193	C₂×D₄₇	—	2	1	no	—
194	C₂×D₄₇	—	2	1	no	—
195	C₂×D₄₇	—	4	1	no	—
196	C₂×D₄₇	—	4	1	no	—
197	C₂×D₄₇	—	4	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	—	8	4	no	—
204	C₂×D₄₇	—	8	4	no	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	4	1	no	—
208	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
209	C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
210	Dic₄₇	—	2	1	no	—
211	Dic₄₇	—	2	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	1	no	—
216	C₂×C₄₇	—	8	1	no	—
217	C₂×C₄₇	—	8	1	no	—
218	C₂×C₄₇	D₄²	1	1	yes	characteristic
219	C₂×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₂×C₄₇	#576	1	1	yes	characteristic
221	D₄₇	—	4	1	no	—
222	D₄₇	—	4	2	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)	—	47	1	no	—
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	D₄₇	1	1	yes	characteristic, complemented
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	—	47	1	no	—
245	C₂²×D₄	—	94	1	no	—
246	AGL(1,ℤ/8)	—	94	4	no	—
247	AGL(1,ℤ/8)	—	94	4	no	—
248	C₂×SD₁₆	—	47	1	no	—
249	C₂×SD₁₆	—	47	1	no	—
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	—	47	1	no	—
256	C₂×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
257	C₂×M₁₆	—	47	1	no	—
258	C₂×M₁₆	—	47	1	no	—
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	—	94	1	no	—
266	#121	—	94	1	no	—
267	#121	—	94	1	no	—
268	#121	C₂×D₄₇	1	1	yes	characteristic
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	C₂×D₄₇	1	1	yes	characteristic, complemented
278	#102	—	47	1	no	—
279	#102	—	47	1	no	—
280	#102	—	47	1	no	—
281	#102	—	47	1	no	—
282	#102	C₂×D₄₇	1	1	yes	characteristic, complemented
283	C₂²⋊C₈	—	47	1	no	—
284	C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
285	C₄×C₈	—	47	1	no	—
286	C₂⁴	—	94	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	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	47	1	no	—
296	C₂×D₄	—	47	1	no	—
297	C₂×D₄	—	47	1	no	—
298	C₂×D₄	—	47	1	no	—
299	C₂×D₄	—	94	2	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	1	no	—
307	C₂×D₄	—	94	2	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	1	no	—
313	C₂×D₄	—	188	4	no	—
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	—	47	4	no	—
323	SD₁₆	—	94	2	no	—
324	D₈	—	4	1	no	—
325	D₈	—	94	2	no	—
326	D₈	—	94	2	no	—
327	D₈	—	94	2	no	—
328	D₈	—	94	2	no	—
329	D₈	—	188	1	no	—
330	M₁₆	—	94	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	—	94	1	no	—
339	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	47	1	no	—
342	C₂²⋊C₄	—	47	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	—	47	1	no	—
352	C₂³	—	94	1	no	—
353	C₂³	—	94	1	no	—
354	C₂³	—	94	1	no	—
355	C₂³	—	376	1	no	—
356	C₂³	—	376	1	no	—
357	C₂³	—	188	2	no	—
358	C₂³	—	188	2	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	D₄×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	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	47	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	—	94	1	no	—
377	D₄	—	376	1	no	—
378	D₄	—	376	1	no	—
379	D₄	—	376	1	no	—
380	D₄	—	376	1	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	—	188	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	47	1	no	—
393	C₂×C₄	—	47	1	no	—
394	C₂×C₄	—	47	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	—	2	1	no	—
404	C₈	—	47	2	no	—
405	C₈	—	94	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	4	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	—	94	1	no	—
416	C₂²	—	94	2	no	—
417	C₂²	—	94	1	no	—
418	C₂²	—	94	1	no	—
419	C₂²	—	376	4	no	—
420	C₂²	—	376	4	no	—
421	C₂²	—	188	1	no	—
422	C₂²	—	188	1	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	—	4	1	no	—
433	C₄	—	47	2	no	—
434	C₄	—	94	1	no	—
435	C₄	—	94	1	no	—
436	C₄	—	188	1	no	—
437	C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
438	C₄	#13094069	1	1	yes	characteristic
439	C₂	—	4	1	no	—
440	C₂	—	8	1	no	—
441	C₂	—	8	1	no	—
442	C₂	—	376	1	no	—
443	C₂	—	376	1	no	—
444	C₂	—	188	1	no	—
445	C₂	—	188	2	no	—
446	C₂	#15689755	1	1	yes	characteristic
447	C₂	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
448	C₂	#15689925	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#449	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#449	D₄₇
hypocenter	C₄₇	#3274
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #449

Complements

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

N	H ≅ G/N	type
1. C₂×#13094051	C₂	semidirect
2. C₂×#13094049	C₂	semidirect
3. #15689792	C₂	semidirect
4. #15689757	C₂	semidirect
5. #15689498	C₂	semidirect
6. #15689375	C₂	semidirect
7. #15689374	C₂	semidirect
8. #15689321	C₂	semidirect
9. #15689317	C₂	semidirect
10. #15689271	C₂	semidirect
11. #15689259	C₂	semidirect
12. #15689255	C₂	semidirect
13. #15689208	C₂	semidirect
14. #15689198	C₂	semidirect
15. C₄₇×#449	C₂	semidirect
16. C₂×#10625354	C₂²	semidirect
23. C₂×#10625336	C₂²	semidirect
25. C₂×D₃₇₆	C₂²	semidirect
27. C₂×#10625334	C₂²	semidirect
28. C₂×#10625334	C₂²	semidirect
29. C₂×#10625329	C₂²	semidirect
30. C₂×#10625324	C₂²	semidirect
33. #13094020	C₂²	semidirect
36. #13093998	C₂²	semidirect
39. #13093995	C₂²	semidirect
42. Q₈×Dic₄₇	C₂²	semidirect
46. #13093955	C₂²	semidirect
47. Dic₄₇⋊C₈	C₂²	semidirect
49. #13093946	C₂²	semidirect
50. #13093945	C₂²	semidirect
51. #13093944	C₂²	semidirect
52. (C₂×D₄₇)⋊C₈	C₂²	semidirect
53. C₈×Dic₄₇	C₂²	semidirect
54. C₂×#41×C₄₇	C₂²	semidirect
55. C₂×SD₁₆×C₄₇	C₂²	semidirect
56. C₂×D₈×C₄₇	C₂²	semidirect
58. #103×C₄₇	C₂²	semidirect
59. #102×C₄₇	C₂²	semidirect
60. C₂²⋊C₈×C₄₇	C₂²	semidirect
105. #10625336	D₄	semidirect
138. Q₈×C₄₇	C₂×D₄	semidirect
180. C₄₇⋊C₈	C₂×D₄	semidirect
213. Dic₄₇	AGL(1,ℤ/8)	semidirect
235. #449	D₄₇	semidirect
240. C₄₇	#3274	semidirect
242. C₂×#41	C₂×D₄₇	semidirect
250. C₂×SD₁₆	C₂×D₄₇	semidirect
256. C₂×D₈	C₂×D₄₇	semidirect
277. #103	C₂×D₄₇	semidirect
282. #102	C₂×D₄₇	semidirect
284. C₂²⋊C₈	C₂×D₄₇	semidirect
363. Q₈	D₄×D₄₇	semidirect