Subgroups — #26207546

Order 12032.

798 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	#20255736	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#20254989	C₂	1	2	yes	maximal, complemented
4	#20242980	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242854	C₂	1	2	yes	maximal, complemented
6	#20242777	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242743	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242569	C₂	1	2	yes	maximal, complemented
9	#20242479	C₂	1	2	yes	maximal, complemented
10	#20242274	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094048	—	2	2	no	—
13	C₂²×D₃₇₆	—	2	1	no	—
14	#15689777	C₂²	1	2	yes	complemented
15	D₄×D₁₈₈	C₂²	1	2	yes	—
16	#15689528	C₂²	1	1	yes	characteristic, complemented
17	#15689500	C₂²	1	1	yes	characteristic
18	#15689496	C₂²	1	2	yes	complemented
19	#15689470	C₂²	1	2	yes	complemented
20	#15689437	—	2	2	no	—
21	#15689404	C₂²	1	2	yes	complemented
22	#15689370	—	2	2	no	—
23	#15689359	—	2	1	no	—
24	#15689359	—	2	1	no	—
25	#15689328	C₂²	1	2	yes	—
26	#15689319	C₂²	1	2	yes	—
27	#15689318	C₂²	1	2	yes	complemented
28	#15689275	—	2	2	no	—
29	#15689269	—	2	2	no	—
30	#15689259	—	2	2	no	—
31	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
32	#15689202	C₂²	1	2	yes	complemented
33	C₂×#13093958	—	2	1	no	—
34	#15688876	C₂²	1	1	yes	characteristic, complemented
35	#15688868	C₂²	1	2	yes	complemented
36	#15688866	C₂²	1	2	yes	complemented
37	#15688852	C₂²	1	2	yes	complemented
38	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
41	C₄₇×#335	C₂²	1	1	yes	characteristic, complemented
42	C₄₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₄₇×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	C₈²×C₄₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×#10625352	—	2	2	no	—
46	C₂²×D₁₈₈	—	2	2	no	—
47	C₂×D₄×D₄₇	—	2	2	no	—
48	#13094048	—	4	8	no	—
49	C₂×#10625325	—	2	2	no	—
50	C₂×#10625325	—	2	2	no	—
51	C₂×#10625335	—	2	2	no	—
52	C₂×D₃₇₆	—	2	2	no	—
53	C₂×D₃₇₆	—	2	1	no	—
54	C₂×D₃₇₆	—	2	1	no	—
55	C₂×D₃₇₆	—	4	4	no	—
56	C₂×D₃₇₆	D₄	1	1	yes	characteristic
57	C₂×#10625334	—	2	2	no	—
58	C₂×#10625324	—	2	2	no	—
59	#13094024	C₂³	1	2	yes	—
60	#13094021	C₂³	1	2	yes	—
61	#13094008	—	4	2	no	—
62	#13094004	—	2	2	no	—
63	#13093999	—	2	2	no	—
64	#13093998	—	2	2	no	—
65	#13093998	—	2	2	no	—
66	#13093994	—	4	2	no	—
67	C₄×D₁₈₈	C₂³	1	2	yes	—
68	C₂×C₄⋊Dic₄₇	—	2	2	no	—
69	#13093958	—	2	1	no	—
70	#13093958	—	2	1	no	—
71	#13093958	—	2	2	no	—
72	#13093958	D₄	1	1	yes	characteristic
73	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
74	#13093947	—	2	2	no	—
75	#13093946	—	2	2	no	—
76	#13093946	—	2	2	no	—
77	#13093946	—	4	2	no	—
78	#13093946	D₄	1	2	yes	—
79	#13093944	—	2	2	no	—
80	(C₂×D₄₇)⋊C₈	—	2	2	no	—
81	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	—	2	1	no	—
83	C₂²×C₈×C₄₇	—	2	1	no	—
84	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
86	#107×C₄₇	D₄	1	1	yes	characteristic
87	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
89	#102×C₄₇	D₄	1	1	yes	characteristic
90	#102×C₄₇	D₄	1	1	yes	characteristic
91	C₂²⋊C₈×C₄₇	—	2	1	no	—
92	C₂²⋊C₈×C₄₇	—	2	1	no	—
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
96	C₂³×D₄₇	—	4	2	no	—
97	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂×C₂²⋊D₄₇	—	4	2	no	—
102	C₂×C₂²⋊D₄₇	—	4	2	no	—
103	C₂²×Dic₄₇	—	4	2	no	—
104	#10625352	—	4	4	no	—
105	#10625352	—	8	2	no	—
106	D₄×D₄₇	—	4	4	no	—
107	D₄×D₄₇	—	8	2	no	—
108	C₂×D₁₈₈	—	2	2	no	—
109	C₂×D₁₈₈	—	2	2	no	—
110	C₂×D₁₈₈	—	2	2	no	—
111	C₂×D₁₈₈	—	4	4	no	—
112	C₂×D₁₈₈	—	4	2	no	—
113	C₂×D₁₈₈	—	8	2	no	—
114	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
115	C₂×C₄×D₄₇	—	2	2	no	—
116	C₂×Dic₉₄	—	2	2	no	—
117	D₈×C₄₇	D₈	1	4	yes	complemented
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	4	2	no	—
122	C₂×C₈×C₄₇	—	4	2	no	—
123	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
132	#10625335	—	4	4	no	—
133	#10625334	—	4	4	no	—
134	(C₂×D₄₇)⋊C₄	—	2	2	no	—
135	(C₂×D₄₇)⋊C₄	—	4	2	no	—
136	(C₂×D₄₇)⋊C₄	—	4	2	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	—	4	2	no	—
140	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	D₃₇₆	—	2	2	no	—
143	D₃₇₆	—	4	4	no	—
144	D₃₇₆	—	4	2	no	—
145	D₃₇₆	—	8	1	no	—
146	#10625325	—	4	4	no	—
147	#10625325	—	8	2	no	—
148	#10625324	—	4	4	no	—
149	C₂³×C₄₇	—	2	1	no	—
150	C₂³×C₄₇	—	2	1	no	—
151	C₂²×D₄₇	—	2	2	no	—
152	C₂²×D₄₇	—	4	2	no	—
153	C₂²×D₄₇	—	8	4	no	—
154	C₂²×D₄₇	—	8	4	no	—
155	C₂²×D₄₇	—	16	2	no	—
156	D₄×C₄₇	—	2	1	no	—
157	D₄×C₄₇	—	2	1	no	—
158	D₄×C₄₇	C₂×D₈	1	2	yes	—
159	D₄×C₄₇	C₂×D₈	1	2	yes	complemented
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂²⋊D₄₇	—	8	4	no	—
170	C₂²⋊D₄₇	—	8	4	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	8	4	no	—
174	D₁₈₈	—	2	2	no	—
175	D₁₈₈	—	2	2	no	—
176	D₁₈₈	—	4	2	no	—
177	D₁₈₈	—	4	2	no	—
178	D₁₈₈	—	4	2	no	—
179	D₁₈₈	—	4	2	no	—
180	D₁₈₈	—	8	2	no	—
181	D₁₈₈	—	8	4	no	—
182	C₄×D₄₇	—	4	2	no	—
183	C₄×D₄₇	—	4	2	no	—
184	Dic₉₄	—	4	2	no	—
185	Dic₉₄	—	4	2	no	—
186	C₈×C₄₇	—	2	1	no	—
187	C₈×C₄₇	—	2	1	no	—
188	C₈×C₄₇	—	4	1	no	—
189	C₈×C₄₇	—	4	1	no	—
190	C₈×C₄₇	—	4	1	no	—
191	C₈×C₄₇	C₂×D₈	1	2	yes	complemented
192	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	complemented
193	C₄₇⋊C₈	—	4	2	no	—
194	#19883	—	47	1	no	maximal, Sylow
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	4	1	no	—
198	C₂²×C₄₇	—	4	1	no	—
199	C₂²×C₄₇	—	4	1	no	—
200	C₂²×C₄₇	—	4	1	no	—
201	C₂²×C₄₇	D₄²	1	1	yes	characteristic
202	C₂×D₄₇	—	4	2	no	—
203	C₂×D₄₇	—	4	2	no	—
204	C₂×D₄₇	—	4	2	no	—
205	C₂×D₄₇	—	8	2	no	—
206	C₂×D₄₇	—	8	2	no	—
207	C₂×D₄₇	—	8	2	no	—
208	C₂×D₄₇	—	16	8	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	4	1	no	—
211	C₄×C₄₇	—	4	1	no	—
212	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
213	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₄×C₄₇	#576	1	1	yes	characteristic
215	C₄×C₄₇	#577	1	1	yes	characteristic
216	Dic₄₇	—	4	2	no	—
217	Dic₄₇	—	8	2	no	—
218	#3334	—	47	1	no	—
219	D₄×D₈	—	47	1	no	—
220	#3272	—	47	2	no	—
221	#1706	—	47	1	no	—
222	#1685	—	47	2	no	—
223	#1673	—	47	1	no	—
224	#1667	—	47	1	no	—
225	#1639	—	47	2	no	—
226	#1625	—	47	2	no	—
227	#1589	—	47	1	no	—
228	C₈×D₈	D₄₇	1	1	yes	characteristic, complemented
229	C₂×C₄₇	—	4	2	no	—
230	C₂×C₄₇	—	4	2	no	—
231	C₂×C₄₇	#3272	1	1	yes	characteristic
232	C₂×C₄₇	D₄×D₈	1	1	yes	characteristic
233	C₂×C₄₇	#3290	1	1	yes	characteristic
234	D₄₇	—	8	2	no	—
235	D₄₇	—	16	2	no	—
236	C₂×AGL(1,ℤ/8)	—	94	2	no	—
237	C₂²×D₈	—	94	1	no	—
238	#547	—	47	2	no	—
239	D₄²	—	47	2	no	—
240	#500	—	47	1	no	—
241	#493	—	47	1	no	—
242	#492	—	47	2	no	—
243	#486	—	47	2	no	—
244	#480	—	94	2	no	—
245	#474	—	47	2	no	—
246	#468	—	94	2	no	—
247	#466	—	94	1	no	—
248	#466	—	94	1	no	—
249	#461	—	47	2	no	—
250	#459	—	47	2	no	—
251	#459	—	47	2	no	—
252	#450	—	94	2	no	—
253	#449	—	94	2	no	—
254	#447	—	94	2	no	—
255	C₄×D₈	—	47	1	no	—
256	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
257	#436	—	47	2	no	—
258	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
259	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
260	C₂×#107	—	94	1	no	—
261	#335	—	47	1	no	—
262	#335	C₂×D₄₇	1	1	yes	characteristic, complemented
263	#332	—	47	2	no	—
264	#331	—	47	2	no	—
265	D₄⋊C₈	—	47	2	no	—
266	D₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
267	D₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
268	C₈²	C₂×D₄₇	1	1	yes	characteristic, complemented
269	C₄₇	#19883	1	1	yes	characteristic, complemented, Sylow
270	C₂×#41	—	94	2	no	—
271	C₂²×D₄	—	94	2	no	—
272	C₂²×D₄	—	94	2	no	—
273	AGL(1,ℤ/8)	—	188	8	no	—
274	C₂×SD₁₆	—	94	2	no	—
275	C₂×SD₁₆	—	94	2	no	—
276	C₂×SD₁₆	—	94	2	no	—
277	C₂×D₈	—	47	1	no	—
278	C₂×D₈	—	94	2	no	—
279	C₂×D₈	—	94	2	no	—
280	C₂×D₈	—	94	1	no	—
281	C₂×D₈	—	94	1	no	—
282	C₂×D₈	—	188	4	no	—
283	C₂×D₈	D₁₈₈	1	1	yes	characteristic
284	C₂×M₁₆	—	94	2	no	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₄⋊Q₈	—	47	2	no	—
288	#127	—	47	2	no	—
289	#123	—	188	2	no	—
290	C₂²⋊Q₈	—	94	2	no	—
291	#121	—	94	2	no	—
292	#121	—	94	2	no	—
293	#121	—	94	2	no	—
294	#120	—	188	2	no	—
295	C₄×D₄	—	47	2	no	—
296	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
297	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	—	94	2	no	—
299	#107	—	47	1	no	—
300	#107	—	94	2	no	—
301	#107	—	94	1	no	—
302	#107	—	94	1	no	—
303	#107	D₁₈₈	1	1	yes	characteristic
304	C₄⋊C₈	—	47	2	no	—
305	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
306	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
307	#103	—	94	2	no	—
308	#102	—	47	2	no	—
309	#102	—	94	2	no	—
310	#102	—	94	2	no	—
311	#102	—	94	2	no	—
312	#102	—	188	2	no	—
313	#102	D₁₈₈	1	1	yes	characteristic
314	#102	D₁₈₈	1	1	yes	characteristic
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	94	2	no	—
318	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
321	C₂⁴	—	188	2	no	—
322	#41	—	376	2	no	—
323	#41	—	188	4	no	—
324	C₂×Q₈	—	94	2	no	—
325	C₂×D₄	—	47	2	no	—
326	C₂×D₄	—	94	2	no	—
327	C₂×D₄	—	94	2	no	—
328	C₂×D₄	—	94	2	no	—
329	C₂×D₄	—	376	2	no	—
330	C₂×D₄	—	376	2	no	—
331	C₂×D₄	—	188	2	no	—
332	C₂×D₄	—	188	4	no	—
333	C₂×D₄	—	188	2	no	—
334	C₂×D₄	—	188	2	no	—
335	C₂×D₄	—	188	4	no	—
336	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
337	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	94	2	no	—
341	C₂²×C₄	—	188	2	no	—
342	SD₁₆	—	376	2	no	—
343	SD₁₆	—	188	4	no	—
344	SD₁₆	—	188	4	no	—
345	D₈	—	94	2	no	—
346	D₈	—	376	1	no	—
347	D₈	—	188	4	no	—
348	D₈	—	188	4	no	—
349	D₈	—	188	2	no	—
350	D₈	D₃₇₆	1	4	yes	complemented
351	M₁₆	—	188	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	—	94	2	no	—
358	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
359	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
360	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
361	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
362	C₄⋊C₄	—	47	2	no	—
363	C₄⋊C₄	—	94	2	no	—
364	C₄⋊C₄	—	94	2	no	—
365	C₄⋊C₄	—	188	2	no	—
366	C₄⋊C₄	C₂×D₁₈₈	1	1	yes	characteristic
367	C₄⋊C₄	C₂×D₁₈₈	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	94	2	no	—
371	C₂²⋊C₄	—	188	2	no	—
372	C₂²⋊C₄	—	188	2	no	—
373	C₄²	C₂³×D₄₇	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	94	2	no	—
377	C₂³	—	376	4	no	—
378	C₂³	—	376	4	no	—
379	C₂³	—	188	2	no	—
380	C₂³	—	752	2	no	—
381	Q₈	—	188	2	no	—
382	Q₈	—	188	2	no	—
383	D₄	—	2	1	no	—
384	D₄	—	2	1	no	—
385	D₄	—	94	2	no	—
386	D₄	—	94	2	no	—
387	D₄	—	376	2	no	—
388	D₄	—	376	4	no	—
389	D₄	—	376	4	no	—
390	D₄	—	376	4	no	—
391	D₄	—	188	2	no	—
392	D₄	—	188	2	no	—
393	D₄	—	188	2	no	—
394	D₄	—	188	2	no	—
395	D₄	C₂×D₃₇₆	1	2	yes	—
396	D₄	C₂×D₃₇₆	1	2	yes	complemented
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	376	4	no	—
405	C₂×C₄	—	188	2	no	—
406	C₂×C₄	—	188	2	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
410	C₂×C₄	#13094070	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₈	—	188	2	no	—
417	C₈	C₂×D₃₇₆	1	2	yes	complemented
418	C₈	#13094048	1	2	yes	complemented
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	376	2	no	—
426	C₂²	—	376	2	no	—
427	C₂²	—	376	2	no	—
428	C₂²	—	188	2	no	—
429	C₂²	—	188	2	no	—
430	C₂²	—	188	2	no	—
431	C₂²	—	752	8	no	—
432	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	376	2	no	—
437	C₄	—	188	2	no	—
438	C₄	C₂²×D₃₇₆	1	1	yes	characteristic
439	C₄	C₂×#13094048	1	1	yes	characteristic
440	C₄	#15689928	1	1	yes	characteristic
441	C₄	#15689930	1	1	yes	characteristic
442	C₂	—	4	2	no	—
443	C₂	—	4	2	no	—
444	C₂	—	376	2	no	—
445	C₂	—	752	2	no	—
446	C₂	#20254989	1	1	yes	characteristic
447	C₂	D₄×D₃₇₆	1	1	yes	characteristic
448	C₂	#20255175	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₈₈
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×D₈×C₄₇	C₂
socle	C₂²×C₄₇	D₄²
hypercenter	C₈×D₈	D₄₇
hypocenter	C₄₇	#19883
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
1. #20255736	C₂	semidirect
2. D₄×D₃₇₆	C₂	semidirect
3. #20254989	C₂	semidirect
4. #20242980	C₂	semidirect
5. #20242854	C₂	semidirect
6. #20242777	C₂	semidirect
7. #20242743	C₂	semidirect
8. #20242569	C₂	semidirect
9. #20242479	C₂	semidirect
10. #20242274	C₂	semidirect
11. C₈×D₈×C₄₇	C₂	semidirect
14. #15689777	C₂²	semidirect
16. #15689528	C₂²	semidirect
18. #15689496	C₂²	semidirect
19. #15689470	C₂²	semidirect
21. #15689404	C₂²	semidirect
27. #15689318	C₂²	semidirect
32. #15689202	C₂²	semidirect
34. #15688876	C₂²	semidirect
35. #15688868	C₂²	semidirect
36. #15688866	C₂²	semidirect
37. #15688852	C₂²	semidirect
40. C₈×D₄×C₄₇	C₂²	semidirect
41. C₄₇×#335	C₂²	semidirect
43. C₄₇×D₄⋊C₈	C₂²	semidirect
44. C₈²×C₄₇	C₂²	semidirect
117. D₈×C₄₇	D₈	semidirect
159. D₄×C₄₇	C₂×D₈	semidirect
191. C₈×C₄₇	C₂×D₈	semidirect
192. C₈×C₄₇	AGL(1,ℤ/8)	semidirect
228. C₈×D₈	D₄₇	semidirect
259. C₈×D₄	C₂×D₄₇	semidirect
262. #335	C₂×D₄₇	semidirect
267. D₄⋊C₈	C₂×D₄₇	semidirect
268. C₈²	C₂×D₄₇	semidirect
269. C₄₇	#19883	semidirect
350. D₈	D₃₇₆	semidirect
396. D₄	C₂×D₃₇₆	semidirect
417. C₈	C₂×D₃₇₆	semidirect
418. C₈	#13094048	semidirect

Maximal subgroups

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

subgroup	index
#20255736	2
D₄×D₃₇₆	2
#20254989	2
#20242980	2
#20242854	2
#20242777	2
#20242743	2
#20242569	2
#20242479	2
#20242274	2
C₈×D₈×C₄₇	2
#19883	47