Subgroups — #25087865

Order 11008.

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	#19146943	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#19146196	C₂	1	2	yes	maximal, complemented
4	#19134187	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134061	C₂	1	2	yes	maximal, complemented
6	#19133984	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133950	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133776	C₂	1	2	yes	maximal, complemented
9	#19133686	C₂	1	2	yes	maximal, complemented
10	#19133481	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063349	—	2	2	no	—
13	C₂²×D₃₄₄	—	2	1	no	—
14	#14583553	C₂²	1	2	yes	complemented
15	D₄×D₁₇₂	C₂²	1	2	yes	—
16	#14583304	C₂²	1	1	yes	characteristic, complemented
17	#14583276	C₂²	1	1	yes	characteristic
18	#14583272	C₂²	1	2	yes	complemented
19	#14583246	C₂²	1	2	yes	complemented
20	#14583213	—	2	2	no	—
21	#14583180	C₂²	1	2	yes	complemented
22	#14583146	—	2	2	no	—
23	#14583135	—	2	1	no	—
24	#14583135	—	2	1	no	—
25	#14583104	C₂²	1	2	yes	—
26	#14583095	C₂²	1	2	yes	—
27	#14583094	C₂²	1	2	yes	complemented
28	#14583051	—	2	2	no	—
29	#14583045	—	2	2	no	—
30	#14583035	—	2	2	no	—
31	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
32	#14582978	C₂²	1	2	yes	complemented
33	C₂×#13063259	—	2	1	no	—
34	#14582652	C₂²	1	1	yes	characteristic, complemented
35	#14582644	C₂²	1	2	yes	complemented
36	#14582642	C₂²	1	2	yes	complemented
37	#14582628	C₂²	1	2	yes	complemented
38	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
41	C₄₃×#335	C₂²	1	1	yes	characteristic, complemented
42	C₄₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₄₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	C₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#10621900	—	2	2	no	—
46	C₂²×D₁₇₂	—	2	2	no	—
47	C₂×D₄×D₄₃	—	2	2	no	—
48	#13063349	—	4	8	no	—
49	C₂×#10621873	—	2	2	no	—
50	C₂×#10621873	—	2	2	no	—
51	C₂×#10621883	—	2	2	no	—
52	C₂×D₃₄₄	—	2	2	no	—
53	C₂×D₃₄₄	—	2	1	no	—
54	C₂×D₃₄₄	—	2	1	no	—
55	C₂×D₃₄₄	—	4	4	no	—
56	C₂×D₃₄₄	D₄	1	1	yes	characteristic
57	C₂×#10621882	—	2	2	no	—
58	C₂×#10621872	—	2	2	no	—
59	#13063325	C₂³	1	2	yes	—
60	#13063322	C₂³	1	2	yes	—
61	#13063309	—	4	2	no	—
62	#13063305	—	2	2	no	—
63	#13063300	—	2	2	no	—
64	#13063299	—	2	2	no	—
65	#13063299	—	2	2	no	—
66	#13063295	—	4	2	no	—
67	C₄×D₁₇₂	C₂³	1	2	yes	—
68	C₂×C₄⋊Dic₄₃	—	2	2	no	—
69	#13063259	—	2	1	no	—
70	#13063259	—	2	1	no	—
71	#13063259	—	2	2	no	—
72	#13063259	D₄	1	1	yes	characteristic
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
74	#13063248	—	2	2	no	—
75	#13063247	—	2	2	no	—
76	#13063247	—	2	2	no	—
77	#13063247	—	4	2	no	—
78	#13063247	D₄	1	2	yes	—
79	#13063245	—	2	2	no	—
80	(C₂×D₄₃)⋊C₈	—	2	2	no	—
81	C₂×D₈×C₄₃	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₄₃	—	2	1	no	—
83	C₂²×C₈×C₄₃	—	2	1	no	—
84	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
86	#107×C₄₃	D₄	1	1	yes	characteristic
87	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
89	#102×C₄₃	D₄	1	1	yes	characteristic
90	#102×C₄₃	D₄	1	1	yes	characteristic
91	C₂²⋊C₈×C₄₃	—	2	1	no	—
92	C₂²⋊C₈×C₄₃	—	2	1	no	—
93	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₂³×D₄₃	—	4	2	no	—
97	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	—	2	1	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂×C₂²⋊D₄₃	—	4	2	no	—
102	C₂×C₂²⋊D₄₃	—	4	2	no	—
103	C₂²×Dic₄₃	—	4	2	no	—
104	#10621900	—	4	4	no	—
105	#10621900	—	8	2	no	—
106	D₄×D₄₃	—	4	4	no	—
107	D₄×D₄₃	—	8	2	no	—
108	C₂×D₁₇₂	—	2	2	no	—
109	C₂×D₁₇₂	—	2	2	no	—
110	C₂×D₁₇₂	—	2	2	no	—
111	C₂×D₁₇₂	—	4	2	no	—
112	C₂×D₁₇₂	—	4	4	no	—
113	C₂×D₁₇₂	—	8	2	no	—
114	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
115	C₂×C₄×D₄₃	—	2	2	no	—
116	C₂×Dic₈₆	—	2	2	no	—
117	D₈×C₄₃	D₈	1	4	yes	complemented
118	C₂×C₈×C₄₃	—	2	1	no	—
119	C₂×C₈×C₄₃	—	2	1	no	—
120	C₂×C₈×C₄₃	—	2	1	no	—
121	C₂×C₈×C₄₃	—	4	2	no	—
122	C₂×C₈×C₄₃	—	4	2	no	—
123	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₄₃	—	2	1	no	—
130	C₂²⋊C₄×C₄₃	—	2	1	no	—
131	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
132	#10621883	—	4	4	no	—
133	#10621882	—	4	4	no	—
134	(C₂×D₄₃)⋊C₄	—	2	2	no	—
135	(C₂×D₄₃)⋊C₄	—	4	2	no	—
136	(C₂×D₄₃)⋊C₄	—	4	2	no	—
137	C₄⋊Dic₄₃	—	2	2	no	—
138	C₄⋊Dic₄₃	—	2	2	no	—
139	C₄⋊Dic₄₃	—	4	2	no	—
140	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
141	C₂×C₄₃⋊C₈	—	2	2	no	—
142	D₃₄₄	—	2	2	no	—
143	D₃₄₄	—	4	4	no	—
144	D₃₄₄	—	4	2	no	—
145	D₃₄₄	—	8	1	no	—
146	#10621873	—	4	4	no	—
147	#10621873	—	8	2	no	—
148	#10621872	—	4	4	no	—
149	C₂³×C₄₃	—	2	1	no	—
150	C₂³×C₄₃	—	2	1	no	—
151	C₂²×D₄₃	—	2	2	no	—
152	C₂²×D₄₃	—	4	2	no	—
153	C₂²×D₄₃	—	8	4	no	—
154	C₂²×D₄₃	—	8	4	no	—
155	C₂²×D₄₃	—	16	2	no	—
156	D₄×C₄₃	—	2	1	no	—
157	D₄×C₄₃	—	2	1	no	—
158	D₄×C₄₃	C₂×D₈	1	2	yes	—
159	D₄×C₄₃	C₂×D₈	1	2	yes	complemented
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂²⋊D₄₃	—	8	4	no	—
170	C₂²⋊D₄₃	—	8	4	no	—
171	C₂×Dic₄₃	—	2	2	no	—
172	C₂×Dic₄₃	—	4	2	no	—
173	C₂×Dic₄₃	—	8	4	no	—
174	D₁₇₂	—	2	2	no	—
175	D₁₇₂	—	2	2	no	—
176	D₁₇₂	—	4	2	no	—
177	D₁₇₂	—	4	2	no	—
178	D₁₇₂	—	4	2	no	—
179	D₁₇₂	—	4	2	no	—
180	D₁₇₂	—	8	2	no	—
181	D₁₇₂	—	8	4	no	—
182	C₄×D₄₃	—	4	2	no	—
183	C₄×D₄₃	—	4	2	no	—
184	Dic₈₆	—	4	2	no	—
185	Dic₈₆	—	4	2	no	—
186	C₈×C₄₃	—	2	1	no	—
187	C₈×C₄₃	—	2	1	no	—
188	C₈×C₄₃	—	4	1	no	—
189	C₈×C₄₃	—	4	1	no	—
190	C₈×C₄₃	—	4	1	no	—
191	C₈×C₄₃	C₂×D₈	1	2	yes	complemented
192	C₈×C₄₃	AGL(1,ℤ/8)	1	2	yes	complemented
193	C₄₃⋊C₈	—	4	2	no	—
194	#19883	—	43	1	no	maximal, Sylow
195	C₂²×C₄₃	—	2	2	no	—
196	C₂²×C₄₃	—	2	2	no	—
197	C₂²×C₄₃	—	4	1	no	—
198	C₂²×C₄₃	—	4	1	no	—
199	C₂²×C₄₃	—	4	1	no	—
200	C₂²×C₄₃	—	4	1	no	—
201	C₂²×C₄₃	D₄²	1	1	yes	characteristic
202	C₂×D₄₃	—	4	2	no	—
203	C₂×D₄₃	—	4	2	no	—
204	C₂×D₄₃	—	4	2	no	—
205	C₂×D₄₃	—	8	2	no	—
206	C₂×D₄₃	—	8	2	no	—
207	C₂×D₄₃	—	8	2	no	—
208	C₂×D₄₃	—	16	8	no	—
209	C₄×C₄₃	—	2	1	no	—
210	C₄×C₄₃	—	4	1	no	—
211	C₄×C₄₃	—	4	1	no	—
212	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
213	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₄×C₄₃	#576	1	1	yes	characteristic
215	C₄×C₄₃	#577	1	1	yes	characteristic
216	Dic₄₃	—	4	2	no	—
217	Dic₄₃	—	8	2	no	—
218	#3334	—	43	1	no	—
219	D₄×D₈	—	43	1	no	—
220	#3272	—	43	2	no	—
221	#1706	—	43	1	no	—
222	#1685	—	43	2	no	—
223	#1673	—	43	1	no	—
224	#1667	—	43	1	no	—
225	#1639	—	43	2	no	—
226	#1625	—	43	2	no	—
227	#1589	—	43	1	no	—
228	C₈×D₈	D₄₃	1	1	yes	characteristic, complemented
229	C₂×C₄₃	—	4	2	no	—
230	C₂×C₄₃	—	4	2	no	—
231	C₂×C₄₃	#3272	1	1	yes	characteristic
232	C₂×C₄₃	D₄×D₈	1	1	yes	characteristic
233	C₂×C₄₃	#3290	1	1	yes	characteristic
234	D₄₃	—	8	2	no	—
235	D₄₃	—	16	2	no	—
236	C₂×AGL(1,ℤ/8)	—	86	2	no	—
237	C₂²×D₈	—	86	1	no	—
238	#547	—	43	2	no	—
239	D₄²	—	43	2	no	—
240	#500	—	43	1	no	—
241	#493	—	43	1	no	—
242	#492	—	43	2	no	—
243	#486	—	43	2	no	—
244	#480	—	86	2	no	—
245	#474	—	43	2	no	—
246	#468	—	86	2	no	—
247	#466	—	86	1	no	—
248	#466	—	86	1	no	—
249	#461	—	43	2	no	—
250	#459	—	43	2	no	—
251	#459	—	43	2	no	—
252	#450	—	86	2	no	—
253	#449	—	86	2	no	—
254	#447	—	86	2	no	—
255	C₄×D₈	—	43	1	no	—
256	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
257	#436	—	43	2	no	—
258	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
259	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
260	C₂×#107	—	86	1	no	—
261	#335	—	43	1	no	—
262	#335	C₂×D₄₃	1	1	yes	characteristic, complemented
263	#332	—	43	2	no	—
264	#331	—	43	2	no	—
265	D₄⋊C₈	—	43	2	no	—
266	D₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
267	D₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
268	C₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
269	C₄₃	#19883	1	1	yes	characteristic, complemented, Sylow
270	C₂×#41	—	86	2	no	—
271	C₂²×D₄	—	86	2	no	—
272	C₂²×D₄	—	86	2	no	—
273	AGL(1,ℤ/8)	—	172	8	no	—
274	C₂×SD₁₆	—	86	2	no	—
275	C₂×SD₁₆	—	86	2	no	—
276	C₂×SD₁₆	—	86	2	no	—
277	C₂×D₈	—	43	1	no	—
278	C₂×D₈	—	86	2	no	—
279	C₂×D₈	—	86	2	no	—
280	C₂×D₈	—	86	1	no	—
281	C₂×D₈	—	86	1	no	—
282	C₂×D₈	—	172	4	no	—
283	C₂×D₈	D₁₇₂	1	1	yes	characteristic
284	C₂×M₁₆	—	86	2	no	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₄⋊Q₈	—	43	2	no	—
288	#127	—	43	2	no	—
289	#123	—	172	2	no	—
290	C₂²⋊Q₈	—	86	2	no	—
291	#121	—	86	2	no	—
292	#121	—	86	2	no	—
293	#121	—	86	2	no	—
294	#120	—	172	2	no	—
295	C₄×D₄	—	43	2	no	—
296	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
297	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	—	86	2	no	—
299	#107	—	43	1	no	—
300	#107	—	86	2	no	—
301	#107	—	86	1	no	—
302	#107	—	86	1	no	—
303	#107	D₁₇₂	1	1	yes	characteristic
304	C₄⋊C₈	—	43	2	no	—
305	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
306	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
307	#103	—	86	2	no	—
308	#102	—	43	2	no	—
309	#102	—	86	2	no	—
310	#102	—	86	2	no	—
311	#102	—	86	2	no	—
312	#102	—	172	2	no	—
313	#102	D₁₇₂	1	1	yes	characteristic
314	#102	D₁₇₂	1	1	yes	characteristic
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	86	2	no	—
318	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
321	C₂⁴	—	172	2	no	—
322	#41	—	344	2	no	—
323	#41	—	172	4	no	—
324	C₂×Q₈	—	86	2	no	—
325	C₂×D₄	—	43	2	no	—
326	C₂×D₄	—	86	2	no	—
327	C₂×D₄	—	86	2	no	—
328	C₂×D₄	—	86	2	no	—
329	C₂×D₄	—	344	2	no	—
330	C₂×D₄	—	344	2	no	—
331	C₂×D₄	—	172	2	no	—
332	C₂×D₄	—	172	4	no	—
333	C₂×D₄	—	172	2	no	—
334	C₂×D₄	—	172	2	no	—
335	C₂×D₄	—	172	4	no	—
336	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
337	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	86	2	no	—
341	C₂²×C₄	—	172	2	no	—
342	SD₁₆	—	344	2	no	—
343	SD₁₆	—	172	4	no	—
344	SD₁₆	—	172	4	no	—
345	D₈	—	86	2	no	—
346	D₈	—	344	1	no	—
347	D₈	—	172	4	no	—
348	D₈	—	172	4	no	—
349	D₈	—	172	2	no	—
350	D₈	D₃₄₄	1	4	yes	complemented
351	M₁₆	—	172	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	—	86	2	no	—
358	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
359	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
360	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
361	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
362	C₄⋊C₄	—	43	2	no	—
363	C₄⋊C₄	—	86	2	no	—
364	C₄⋊C₄	—	86	2	no	—
365	C₄⋊C₄	—	172	2	no	—
366	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
367	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	86	2	no	—
371	C₂²⋊C₄	—	172	2	no	—
372	C₂²⋊C₄	—	172	2	no	—
373	C₄²	C₂³×D₄₃	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	86	2	no	—
377	C₂³	—	344	4	no	—
378	C₂³	—	344	4	no	—
379	C₂³	—	172	2	no	—
380	C₂³	—	688	2	no	—
381	Q₈	—	172	2	no	—
382	Q₈	—	172	2	no	—
383	D₄	—	2	1	no	—
384	D₄	—	2	1	no	—
385	D₄	—	86	2	no	—
386	D₄	—	86	2	no	—
387	D₄	—	344	2	no	—
388	D₄	—	344	4	no	—
389	D₄	—	344	4	no	—
390	D₄	—	344	4	no	—
391	D₄	—	172	2	no	—
392	D₄	—	172	2	no	—
393	D₄	—	172	2	no	—
394	D₄	—	172	2	no	—
395	D₄	C₂×D₃₄₄	1	2	yes	—
396	D₄	C₂×D₃₄₄	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	—	86	2	no	—
404	C₂×C₄	—	344	4	no	—
405	C₂×C₄	—	172	2	no	—
406	C₂×C₄	—	172	2	no	—
407	C₂×C₄	—	172	2	no	—
408	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
410	C₂×C₄	#13063371	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	—	172	2	no	—
417	C₈	C₂×D₃₄₄	1	2	yes	complemented
418	C₈	#13063349	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	—	344	2	no	—
426	C₂²	—	344	2	no	—
427	C₂²	—	344	2	no	—
428	C₂²	—	172	2	no	—
429	C₂²	—	172	2	no	—
430	C₂²	—	172	2	no	—
431	C₂²	—	688	8	no	—
432	C₂²	D₄×D₁₇₂	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	344	2	no	—
437	C₄	—	172	2	no	—
438	C₄	C₂²×D₃₄₄	1	1	yes	characteristic
439	C₄	C₂×#13063349	1	1	yes	characteristic
440	C₄	#14583704	1	1	yes	characteristic
441	C₄	#14583706	1	1	yes	characteristic
442	C₂	—	4	2	no	—
443	C₂	—	4	2	no	—
444	C₂	—	344	2	no	—
445	C₂	—	688	2	no	—
446	C₂	#19146196	1	1	yes	characteristic
447	C₂	D₄×D₃₄₄	1	1	yes	characteristic
448	C₂	#19146382	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₇₂
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₈×D₈×C₄₃	C₂
socle	C₂²×C₄₃	D₄²
hypercenter	C₈×D₈	D₄₃
hypocenter	C₄₃	#19883
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
1. #19146943	C₂	semidirect
2. D₄×D₃₄₄	C₂	semidirect
3. #19146196	C₂	semidirect
4. #19134187	C₂	semidirect
5. #19134061	C₂	semidirect
6. #19133984	C₂	semidirect
7. #19133950	C₂	semidirect
8. #19133776	C₂	semidirect
9. #19133686	C₂	semidirect
10. #19133481	C₂	semidirect
11. C₈×D₈×C₄₃	C₂	semidirect
14. #14583553	C₂²	semidirect
16. #14583304	C₂²	semidirect
18. #14583272	C₂²	semidirect
19. #14583246	C₂²	semidirect
21. #14583180	C₂²	semidirect
27. #14583094	C₂²	semidirect
32. #14582978	C₂²	semidirect
34. #14582652	C₂²	semidirect
35. #14582644	C₂²	semidirect
36. #14582642	C₂²	semidirect
37. #14582628	C₂²	semidirect
40. C₈×D₄×C₄₃	C₂²	semidirect
41. C₄₃×#335	C₂²	semidirect
43. C₄₃×D₄⋊C₈	C₂²	semidirect
44. C₈²×C₄₃	C₂²	semidirect
117. D₈×C₄₃	D₈	semidirect
159. D₄×C₄₃	C₂×D₈	semidirect
191. C₈×C₄₃	C₂×D₈	semidirect
192. C₈×C₄₃	AGL(1,ℤ/8)	semidirect
228. C₈×D₈	D₄₃	semidirect
259. C₈×D₄	C₂×D₄₃	semidirect
262. #335	C₂×D₄₃	semidirect
267. D₄⋊C₈	C₂×D₄₃	semidirect
268. C₈²	C₂×D₄₃	semidirect
269. C₄₃	#19883	semidirect
350. D₈	D₃₄₄	semidirect
396. D₄	C₂×D₃₄₄	semidirect
417. C₈	C₂×D₃₄₄	semidirect
418. C₈	#13063349	semidirect

Maximal subgroups

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

subgroup	index
#19146943	2
D₄×D₃₄₄	2
#19146196	2
#19134187	2
#19134061	2
#19133984	2
#19133950	2
#19133776	2
#19133686	2
#19133481	2
C₈×D₈×C₄₃	2
#19883	43