Subgroups — #25000124

Order 11008.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19139513	C₂	1	1	yes	maximal, characteristic
2	#19134755	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134600	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134596	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582628	C₂	1	1	yes	maximal, characteristic
6	#19132479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13063301	—	2	1	no	—
9	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
10	C₂×#13063259	—	2	2	no	—
11	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×#13063249	—	2	1	no	—
13	C₂×#13063247	—	2	1	no	—
14	#14582821	—	2	2	no	—
15	#14582801	—	2	1	no	—
16	#14582797	—	2	1	no	—
17	#14582769	C₂²	1	1	yes	characteristic
18	#14582769	C₂²	1	1	yes	characteristic
19	#14582756	—	2	1	no	—
20	#14582662	—	2	1	no	—
21	#14582661	—	2	1	no	—
22	#14582628	—	2	2	no	—
23	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×Q₈⋊C₈	—	2	2	no	—
27	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
28	C₂²×C₄×D₄₃	—	2	1	no	—
29	C₂²×C₄₃⋊C₈	—	2	1	no	—
30	#13063301	—	4	2	no	—
31	#13063301	—	4	2	no	—
32	C₄×D₁₇₂	—	2	1	no	—
33	C₄×D₁₇₂	—	2	1	no	—
34	C₄×D₁₇₂	—	2	1	no	—
35	C₄×D₁₇₂	—	2	1	no	—
36	C₂×C₄⋊Dic₄₃	—	2	1	no	—
37	C₂×C₄⋊Dic₄₃	—	2	1	no	—
38	C₂×C₄⋊Dic₄₃	—	2	1	no	—
39	C₂×C₄⋊Dic₄₃	—	2	1	no	—
40	C₂×C₄⋊Dic₄₃	—	2	1	no	—
41	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
42	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
43	C₂×Dic₄₃⋊C₄	—	2	2	no	—
44	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
45	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
46	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
47	#13063259	—	4	4	no	—
48	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
49	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
50	#13063249	—	4	2	no	—
51	#13063247	—	4	2	no	—
52	C₄₃⋊#95	—	2	2	no	—
53	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₄₃	—	2	1	no	—
55	C₂²×C₈×C₄₃	—	2	1	no	—
56	C₄×Q₈×C₄₃	—	2	1	no	—
57	C₄×Q₈×C₄₃	—	2	1	no	—
58	C₄×Q₈×C₄₃	—	2	1	no	—
59	C₄×Q₈×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₃	—	2	1	no	—
63	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₄₃	—	2	1	no	—
65	C₄⋊C₈×C₄₃	—	2	1	no	—
66	C₄×C₈×C₄₃	—	2	1	no	—
67	C₄×C₈×C₄₃	D₄	1	2	yes	—
68	C₂³×D₄₃	—	2	1	no	—
69	C₂×Q₈×C₄₃	—	2	1	no	—
70	C₂×Q₈×C₄₃	—	2	1	no	—
71	C₂×Q₈×C₄₃	—	2	1	no	—
72	C₂×Q₈×C₄₃	—	2	1	no	—
73	C₂×Q₈×C₄₃	—	2	1	no	—
74	C₂×Q₈×C₄₃	D₈	1	2	yes	—
75	C₂²×C₄×C₄₃	—	2	1	no	—
76	C₂²×C₄×C₄₃	—	2	1	no	—
77	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×Dic₄₃	—	2	1	no	—
81	C₂²×Dic₄₃	—	2	2	no	—
82	C₂²×Dic₄₃	—	4	1	no	—
83	C₂×D₁₇₂	—	2	1	no	—
84	C₂×D₁₇₂	—	2	1	no	—
85	C₂×D₁₇₂	—	2	1	no	—
86	C₂×D₁₇₂	—	2	1	no	—
87	C₂×D₁₇₂	—	2	1	no	—
88	C₂×D₁₇₂	Q₁₆	1	2	yes	—
89	C₂×C₄×D₄₃	—	4	1	no	—
90	C₂×C₄×D₄₃	—	4	1	no	—
91	C₂×C₄×D₄₃	—	4	1	no	—
92	C₂×C₄×D₄₃	—	4	1	no	—
93	C₂×C₄×D₄₃	—	4	1	no	—
94	C₂×C₄×D₄₃	—	4	1	no	—
95	C₂×C₈×C₄₃	—	2	2	no	—
96	C₂×C₈×C₄₃	—	2	2	no	—
97	C₂×C₈×C₄₃	—	2	2	no	—
98	C₂×C₈×C₄₃	—	4	1	no	—
99	C₂×C₈×C₄₃	—	4	1	no	—
100	C₂×C₈×C₄₃	—	4	1	no	—
101	C₄⋊C₄×C₄₃	—	2	1	no	—
102	C₄⋊C₄×C₄₃	—	2	1	no	—
103	C₄⋊C₄×C₄₃	—	4	1	no	—
104	C₄⋊C₄×C₄₃	—	4	1	no	—
105	C₄²×C₄₃	—	4	1	no	—
106	C₄²×C₄₃	—	4	1	no	—
107	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₄₃	#41	1	1	yes	characteristic
109	C₄²×C₄₃	#41	1	1	yes	characteristic
110	C₄²×C₄₃	#41	1	1	yes	characteristic
111	(C₂×D₄₃)⋊C₄	—	4	4	no	—
112	(C₂×D₄₃)⋊C₄	—	4	1	no	—
113	(C₂×D₄₃)⋊C₄	—	4	1	no	—
114	(C₂×D₄₃)⋊C₄	—	8	2	no	—
115	C₄⋊Dic₄₃	—	2	1	no	—
116	C₄⋊Dic₄₃	—	2	1	no	—
117	C₄⋊Dic₄₃	—	4	1	no	—
118	C₄⋊Dic₄₃	—	4	1	no	—
119	C₄⋊Dic₄₃	—	4	1	no	—
120	C₄⋊Dic₄₃	—	4	1	no	—
121	C₄⋊Dic₄₃	—	4	2	no	—
122	C₄⋊Dic₄₃	—	4	2	no	—
123	C₄⋊Dic₄₃	—	4	1	no	—
124	C₄⋊Dic₄₃	—	4	1	no	—
125	C₄⋊Dic₄₃	—	4	1	no	—
126	C₄⋊Dic₄₃	—	4	1	no	—
127	Dic₄₃⋊C₄	—	4	4	no	—
128	C₂×C₄₃⋊C₈	—	4	1	no	—
129	C₂×C₄₃⋊C₈	—	4	1	no	—
130	C₂×C₄₃⋊C₈	—	4	1	no	—
131	C₂³×C₄₃	#120	1	1	yes	characteristic
132	C₂²×D₄₃	—	2	2	no	—
133	C₂²×D₄₃	—	4	1	no	—
134	C₂²×D₄₃	—	4	1	no	—
135	C₂²×D₄₃	—	4	1	no	—
136	C₂²×D₄₃	—	4	1	no	—
137	C₂²×D₄₃	—	4	1	no	—
138	C₂²×D₄₃	—	4	1	no	—
139	Q₈×C₄₃	—	2	2	no	—
140	Q₈×C₄₃	—	2	2	no	—
141	Q₈×C₄₃	—	4	1	no	—
142	Q₈×C₄₃	—	4	1	no	—
143	C₂×C₄×C₄₃	—	2	1	no	—
144	C₂×C₄×C₄₃	—	2	1	no	—
145	C₂×C₄×C₄₃	—	2	2	no	—
146	C₂×C₄×C₄₃	—	4	1	no	—
147	C₂×C₄×C₄₃	—	4	1	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	1	no	—
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
152	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
153	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
154	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
155	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
156	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
159	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
161	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
164	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
165	C₂×Dic₄₃	—	4	1	no	—
166	C₂×Dic₄₃	—	4	1	no	—
167	C₂×Dic₄₃	—	4	2	no	—
168	C₂×Dic₄₃	—	4	2	no	—
169	C₂×Dic₄₃	—	4	1	no	—
170	C₂×Dic₄₃	—	4	2	no	—
171	C₂×Dic₄₃	—	8	1	no	—
172	C₂×Dic₄₃	—	8	1	no	—
173	C₂×Dic₄₃	—	8	1	no	—
174	D₁₇₂	—	2	2	no	—
175	D₁₇₂	—	2	2	no	—
176	D₁₇₂	—	4	1	no	—
177	D₁₇₂	—	4	1	no	—
178	C₄×D₄₃	—	8	1	no	—
179	C₄×D₄₃	—	8	1	no	—
180	C₄×D₄₃	—	8	1	no	—
181	C₄×D₄₃	—	8	1	no	—
182	C₈×C₄₃	—	2	4	no	—
183	C₈×C₄₃	—	8	1	no	—
184	C₄₃⋊C₈	—	8	1	no	—
185	#10434	—	43	1	no	maximal, Sylow
186	C₂²×C₄₃	#394	1	1	yes	characteristic
187	C₂²×C₄₃	#447	1	1	yes	characteristic
188	C₂²×C₄₃	#449	1	1	yes	characteristic
189	C₂²×C₄₃	#451	1	1	yes	characteristic
190	C₂²×C₄₃	#452	1	1	yes	characteristic
191	C₂²×C₄₃	#453	1	1	yes	characteristic
192	C₂²×C₄₃	#456	1	1	yes	characteristic
193	C₂×D₄₃	—	4	2	no	—
194	C₂×D₄₃	—	4	2	no	—
195	C₂×D₄₃	—	4	2	no	—
196	C₂×D₄₃	—	8	1	no	—
197	C₂×D₄₃	—	8	1	no	—
198	C₂×D₄₃	—	8	1	no	—
199	C₂×D₄₃	—	8	1	no	—
200	C₄×C₄₃	—	2	1	no	—
201	C₄×C₄₃	—	2	1	no	—
202	C₄×C₄₃	—	4	2	no	—
203	C₄×C₄₃	—	8	1	no	—
204	C₄×C₄₃	#466	1	1	yes	characteristic
205	C₄×C₄₃	#467	1	1	yes	characteristic
206	C₄×C₄₃	#468	1	1	yes	characteristic
207	C₄×C₄₃	#468	1	1	yes	characteristic
208	C₄×C₄₃	#480	1	1	yes	characteristic
209	C₄×C₄₃	#482	1	1	yes	characteristic
210	C₄×C₄₃	#484	1	1	yes	characteristic
211	C₄×C₄₃	#485	1	1	yes	characteristic
212	Dic₄₃	—	8	2	no	—
213	Dic₄₃	—	8	1	no	—
214	Dic₄₃	—	16	1	no	—
215	#2538	—	43	1	no	—
216	#1845	—	43	1	no	—
217	#1803	—	43	1	no	—
218	#1802	—	43	1	no	—
219	C₂×Q₈⋊C₈	D₄₃	1	1	yes	characteristic, complemented
220	C₂×D₄⋊C₈	—	43	1	no	—
221	#1296	—	43	1	no	—
222	C₂×C₄₃	#1621	1	1	yes	characteristic
223	C₂×C₄₃	#1632	1	1	yes	characteristic
224	C₂×C₄₃	#1649	1	1	yes	characteristic
225	C₂×C₄₃	#1650	1	1	yes	characteristic
226	C₂×C₄₃	#2033	1	1	yes	characteristic
227	C₂×C₄₃	#2036	1	1	yes	characteristic
228	C₂×C₄₃	#2039	1	1	yes	characteristic
229	D₄₃	—	8	2	no	—
230	C₂×C₂²⋊Q₈	—	86	1	no	—
231	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
232	C₂×C₄×D₄	—	43	1	no	—
233	C₂×#107	—	86	2	no	—
234	C₂×C₄⋊C₈	—	43	1	no	—
235	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
236	C₂×#103	—	86	1	no	—
237	C₂×#102	—	86	1	no	—
238	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
239	#396	—	86	2	no	—
240	#390	—	86	1	no	—
241	#389	—	86	1	no	—
242	#384	—	43	1	no	—
243	#384	—	43	1	no	—
244	#380	—	86	1	no	—
245	#340	—	86	1	no	—
246	#340	—	86	1	no	—
247	Q₈⋊C₈	—	2	2	no	—
248	D₄⋊C₈	—	86	2	no	—
249	C₄₃	#10434	1	1	yes	characteristic, complemented, Sylow
250	C₂²×Q₈	D₁₇₂	1	1	yes	characteristic
251	C₂²×D₄	—	43	1	no	—
252	C₂³×C₄	—	86	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	86	1	no	—
256	C₂²⋊Q₈	—	172	2	no	—
257	C₂²⋊Q₈	—	172	2	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×D₄	—	86	1	no	—
263	C₄×D₄	—	86	1	no	—
264	C₄×D₄	—	86	1	no	—
265	C₄×D₄	—	86	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	43	1	no	—
268	C₂×C₄⋊C₄	—	43	2	no	—
269	C₂×C₄⋊C₄	—	86	2	no	—
270	C₂×C₄⋊C₄	—	86	1	no	—
271	C₂×C₄⋊C₄	—	86	1	no	—
272	C₂×C₄⋊C₄	—	86	1	no	—
273	C₂×C₄⋊C₄	—	86	1	no	—
274	C₂×C₄⋊C₄	—	86	1	no	—
275	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	—	86	2	no	—
277	C₂×C₂²⋊C₄	—	86	2	no	—
278	C₂×C₂²⋊C₄	—	86	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
281	#107	—	172	4	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	86	1	no	—
285	C₄⋊C₈	—	86	1	no	—
286	#103	—	172	2	no	—
287	#102	—	172	2	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
290	#95	—	86	2	no	—
291	C₂⁴	—	86	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	D₃₄₄	1	2	yes	—
298	C₂×D₄	—	43	2	no	—
299	C₂×D₄	—	86	1	no	—
300	C₂×D₄	—	86	1	no	—
301	C₂×D₄	—	86	1	no	—
302	C₂×D₄	—	86	1	no	—
303	C₂×D₄	—	86	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	86	1	no	—
307	C₂²×C₄	—	86	2	no	—
308	C₂²×C₄	—	172	1	no	—
309	C₂²×C₄	—	172	1	no	—
310	C₂²×C₄	—	172	1	no	—
311	C₂²×C₄	—	172	1	no	—
312	C₂²×C₄	—	172	1	no	—
313	C₂²×C₄	—	172	1	no	—
314	C₂²×C₄	—	172	1	no	—
315	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
316	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	172	1	no	—
325	C₂×C₈	—	172	1	no	—
326	C₂×C₈	—	172	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	86	1	no	—
332	C₄⋊C₄	—	86	1	no	—
333	C₄⋊C₄	—	172	2	no	—
334	C₄⋊C₄	—	172	2	no	—
335	C₄⋊C₄	—	172	4	no	—
336	C₄⋊C₄	—	172	1	no	—
337	C₄⋊C₄	—	172	1	no	—
338	C₄⋊C₄	—	172	1	no	—
339	C₄⋊C₄	—	172	1	no	—
340	C₄⋊C₄	—	172	1	no	—
341	C₄⋊C₄	—	172	1	no	—
342	C₄⋊C₄	—	172	1	no	—
343	C₄⋊C₄	—	172	1	no	—
344	C₂²⋊C₄	—	344	2	no	—
345	C₂²⋊C₄	—	172	4	no	—
346	C₂²⋊C₄	—	172	1	no	—
347	C₂²⋊C₄	—	172	1	no	—
348	C₄²	—	4	1	no	—
349	C₄²	—	4	1	no	—
350	C₄²	#10621898	1	1	yes	characteristic
351	C₄²	#10621900	1	1	yes	characteristic
352	C₄²	#10621900	1	1	yes	characteristic
353	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
354	C₂³	—	86	2	no	—
355	C₂³	—	172	1	no	—
356	C₂³	—	172	1	no	—
357	C₂³	—	172	1	no	—
358	C₂³	—	172	1	no	—
359	C₂³	—	172	1	no	—
360	C₂³	—	172	1	no	—
361	C₂³	#13063295	1	1	yes	characteristic
362	Q₈	—	2	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	4	1	no	—
366	D₄	—	86	2	no	—
367	D₄	—	86	2	no	—
368	D₄	—	172	1	no	—
369	D₄	—	172	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	344	1	no	—
379	C₂×C₄	—	344	1	no	—
380	C₂×C₄	—	344	1	no	—
381	C₂×C₄	—	344	1	no	—
382	C₂×C₄	—	344	1	no	—
383	C₂×C₄	—	344	1	no	—
384	C₂×C₄	—	344	1	no	—
385	C₂×C₄	—	172	2	no	—
386	C₂×C₄	—	172	1	no	—
387	C₂×C₄	—	172	2	no	—
388	C₂×C₄	—	172	1	no	—
389	C₂×C₄	—	172	2	no	—
390	C₂×C₄	—	172	1	no	—
391	C₂×C₄	#13063296	1	1	yes	characteristic
392	C₂×C₄	#13063297	1	1	yes	characteristic
393	C₂×C₄	#13063299	1	1	yes	characteristic
394	C₂×C₄	#13063307	1	1	yes	characteristic
395	C₂×C₄	#13063309	1	1	yes	characteristic
396	C₂×C₄	#13063311	1	1	yes	characteristic
397	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
398	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
399	C₂×C₄	#13063347	1	1	yes	characteristic
400	C₂×C₄	#13063348	1	1	yes	characteristic
401	C₂×C₄	#13063352	1	1	yes	characteristic
402	C₂×C₄	#13063353	1	1	yes	characteristic
403	C₂×C₄	#13063354	1	1	yes	characteristic
404	C₂×C₄	#13063358	1	1	yes	characteristic
405	C₈	—	2	4	no	—
406	C₈	—	8	1	no	—
407	C₈	—	344	1	no	—
408	C₂²	—	344	1	no	—
409	C₂²	—	344	1	no	—
410	C₂²	—	344	1	no	—
411	C₂²	—	344	1	no	—
412	C₂²	—	172	2	no	—
413	C₂²	—	172	2	no	—
414	C₂²	—	172	2	no	—
415	C₂²	#14582815	1	1	yes	characteristic
416	C₂²	#14583035	1	1	yes	characteristic
417	C₂²	#14583047	1	1	yes	characteristic
418	C₂²	#14583056	1	1	yes	characteristic
419	C₂²	#14583063	1	1	yes	characteristic
420	C₂²	#14583068	1	1	yes	characteristic
421	C₂²	#14583083	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	8	1	no	—
426	C₄	—	344	1	no	—
427	C₄	—	344	2	no	—
428	C₄	—	688	1	no	—
429	C₄	#14583135	1	1	yes	characteristic
430	C₄	#14583137	1	1	yes	characteristic
431	C₄	#14583142	1	1	yes	characteristic
432	C₄	#14583145	1	1	yes	characteristic
433	C₄	#14583213	1	1	yes	characteristic
434	C₄	#14583224	1	1	yes	characteristic
435	C₄	#14583233	1	1	yes	characteristic
436	C₄	#14583239	1	1	yes	characteristic
437	C₂	—	344	2	no	—
438	C₂	#19133662	1	1	yes	characteristic
439	C₂	#19133732	1	1	yes	characteristic
440	C₂	#19133846	1	1	yes	characteristic
441	C₂	#19133854	1	1	yes	characteristic
442	C₂	#19135778	1	1	yes	characteristic
443	C₂	#19135797	1	1	yes	characteristic
444	C₂	#19135818	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063295
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×Q₈⋊C₈	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂²×D₁₇₂	D₄
hypercenter	C₂×Q₈⋊C₈	D₄₃
hypocenter	C₄₃	#10434
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. #19134755	C₂	semidirect
3. #19134600	C₂	semidirect
6. #19132479	C₂	semidirect
7. C₂×C₄₃×Q₈⋊C₈	C₂	semidirect
219. C₂×Q₈⋊C₈	D₄₃	semidirect
249. C₄₃	#10434	semidirect

Maximal subgroups

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

subgroup	index
#19139513	2
#19134755	2
#19134600	2
#19134596	2
C₂×#14582628	2
#19132479	2
C₂×C₄₃×Q₈⋊C₈	2
#10434	43