Subgroups — #24999982

Order 11008.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19139769	C₂	1	1	yes	maximal, characteristic
2	#19135398	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135359	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134596	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582626	C₂	1	1	yes	maximal, characteristic
6	#19132434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#13063257	—	2	1	no	—
10	C₂×#13063249	—	2	2	no	—
11	C₂×#13063247	—	2	1	no	—
12	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	#14582810	—	2	2	no	—
14	#14582800	—	2	1	no	—
15	#14582769	C₂²	1	1	yes	characteristic
16	#14582764	—	2	1	no	—
17	#14582756	—	2	1	no	—
18	#14582756	—	2	1	no	—
19	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
20	#14582662	—	2	1	no	—
21	#14582662	—	2	1	no	—
22	#14582626	—	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×#333	—	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	C₄×D₁₇₂	—	2	1	no	—
31	C₄×D₁₇₂	—	2	1	no	—
32	C₄×D₁₇₂	—	2	1	no	—
33	C₄×D₁₇₂	—	2	1	no	—
34	C₂×C₄⋊Dic₄₃	—	2	1	no	—
35	C₂×C₄⋊Dic₄₃	—	2	1	no	—
36	C₂×C₄⋊Dic₄₃	—	2	1	no	—
37	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
38	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
40	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
41	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
42	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
43	C₂×C₄×Dic₄₃	—	2	1	no	—
44	#13063257	—	4	2	no	—
45	#13063249	—	4	4	no	—
46	#13063247	—	4	2	no	—
47	C₄×C₄₃⋊C₈	—	2	1	no	—
48	C₄×C₄₃⋊C₈	—	2	1	no	—
49	C₄₃⋊#95	—	2	2	no	—
50	C₄₃⋊#95	—	2	2	no	—
51	C₄₃⋊#95	—	2	1	no	—
52	C₂²×Q₈×C₄₃	D₄	1	2	yes	—
53	C₂²×C₈×C₄₃	—	2	1	no	—
54	C₂²×C₈×C₄₃	—	2	1	no	—
55	C₄⋊Q₈×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	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₄₃	—	2	1	no	—
63	C₄⋊C₈×C₄₃	—	2	1	no	—
64	C₄⋊C₈×C₄₃	—	2	1	no	—
65	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
66	C₂³×D₄₃	—	2	1	no	—
67	C₂×Q₈×C₄₃	—	2	2	no	—
68	C₂×Q₈×C₄₃	—	2	2	no	—
69	C₂×Q₈×C₄₃	—	4	2	no	—
70	C₂×Q₈×C₄₃	—	4	2	no	—
71	C₂²×C₄×C₄₃	—	2	2	no	—
72	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×Dic₄₃	—	2	1	no	—
76	C₂²×Dic₄₃	—	2	1	no	—
77	C₂²×Dic₄₃	—	2	1	no	—
78	C₂²×Dic₄₃	—	4	1	no	—
79	C₂×D₁₇₂	—	2	1	no	—
80	C₂×D₁₇₂	—	2	1	no	—
81	C₂×D₁₇₂	—	2	1	no	—
82	C₂×D₁₇₂	—	2	1	no	—
83	C₂×D₁₇₂	—	2	1	no	—
84	C₂×D₁₇₂	SD₁₆	1	2	yes	—
85	C₂×C₄×D₄₃	—	4	1	no	—
86	C₂×C₄×D₄₃	—	4	1	no	—
87	C₂×C₄×D₄₃	—	4	1	no	—
88	C₂×C₄×D₄₃	—	4	1	no	—
89	C₂×C₄×D₄₃	—	4	1	no	—
90	C₂×C₄×D₄₃	—	4	1	no	—
91	C₂×C₈×C₄₃	—	2	2	no	—
92	C₂×C₈×C₄₃	—	4	1	no	—
93	C₂×C₈×C₄₃	—	4	1	no	—
94	C₂×C₈×C₄₃	—	4	1	no	—
95	C₂×C₈×C₄₃	—	4	1	no	—
96	C₂×C₈×C₄₃	—	4	1	no	—
97	C₄⋊C₄×C₄₃	—	4	1	no	—
98	C₄⋊C₄×C₄₃	—	4	1	no	—
99	C₄⋊C₄×C₄₃	—	4	1	no	—
100	C₄⋊C₄×C₄₃	—	4	1	no	—
101	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₄₃	#41	1	1	yes	characteristic
103	C₄²×C₄₃	#41	1	1	yes	characteristic
104	C₄²×C₄₃	#41	1	1	yes	characteristic
105	(C₂×D₄₃)⋊C₄	—	4	1	no	—
106	(C₂×D₄₃)⋊C₄	—	4	1	no	—
107	(C₂×D₄₃)⋊C₄	—	8	2	no	—
108	(C₂×D₄₃)⋊C₄	—	8	2	no	—
109	C₄⋊Dic₄₃	—	2	1	no	—
110	C₄⋊Dic₄₃	—	2	1	no	—
111	C₄⋊Dic₄₃	—	2	1	no	—
112	C₄⋊Dic₄₃	—	2	1	no	—
113	C₄⋊Dic₄₃	—	2	1	no	—
114	C₄⋊Dic₄₃	—	2	1	no	—
115	C₄⋊Dic₄₃	—	4	2	no	—
116	C₄⋊Dic₄₃	—	4	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	1	no	—
122	C₂×C₄₃⋊C₈	—	2	2	no	—
123	C₂×C₄₃⋊C₈	—	4	1	no	—
124	C₂×C₄₃⋊C₈	—	4	1	no	—
125	C₂³×C₄₃	#120	1	1	yes	characteristic
126	C₂²×D₄₃	—	2	2	no	—
127	C₂²×D₄₃	—	4	1	no	—
128	C₂²×D₄₃	—	4	1	no	—
129	C₂²×D₄₃	—	4	1	no	—
130	C₂²×D₄₃	—	4	1	no	—
131	C₂²×D₄₃	—	4	1	no	—
132	C₂²×D₄₃	—	4	1	no	—
133	Q₈×C₄₃	—	4	4	no	—
134	Q₈×C₄₃	—	8	2	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	4	2	no	—
138	C₂×C₄×C₄₃	—	4	2	no	—
139	C₂×C₄×C₄₃	—	4	2	no	—
140	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
141	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
142	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
143	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
144	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
145	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
147	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
148	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
149	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
150	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
152	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
153	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
154	C₂×Dic₄₃	—	4	1	no	—
155	C₂×Dic₄₃	—	4	1	no	—
156	C₂×Dic₄₃	—	4	1	no	—
157	C₂×Dic₄₃	—	4	1	no	—
158	C₂×Dic₄₃	—	4	1	no	—
159	C₂×Dic₄₃	—	4	1	no	—
160	C₂×Dic₄₃	—	4	1	no	—
161	C₂×Dic₄₃	—	4	1	no	—
162	C₂×Dic₄₃	—	4	1	no	—
163	C₂×Dic₄₃	—	8	1	no	—
164	C₂×Dic₄₃	—	8	1	no	—
165	C₂×Dic₄₃	—	8	1	no	—
166	D₁₇₂	—	2	2	no	—
167	D₁₇₂	—	2	2	no	—
168	D₁₇₂	—	4	1	no	—
169	D₁₇₂	—	4	1	no	—
170	C₄×D₄₃	—	8	1	no	—
171	C₄×D₄₃	—	8	1	no	—
172	C₄×D₄₃	—	8	1	no	—
173	C₄×D₄₃	—	8	1	no	—
174	C₈×C₄₃	—	4	2	no	—
175	C₈×C₄₃	—	8	1	no	—
176	C₄₃⋊C₈	—	4	2	no	—
177	#10412	—	43	1	no	maximal, Sylow
178	C₂²×C₄₃	#394	1	1	yes	characteristic
179	C₂²×C₄₃	#448	1	1	yes	characteristic
180	C₂²×C₄₃	#449	1	1	yes	characteristic
181	C₂²×C₄₃	#452	1	1	yes	characteristic
182	C₂²×C₄₃	#452	1	1	yes	characteristic
183	C₂²×C₄₃	#453	1	1	yes	characteristic
184	C₂²×C₄₃	#455	1	1	yes	characteristic
185	C₂×D₄₃	—	4	2	no	—
186	C₂×D₄₃	—	4	2	no	—
187	C₂×D₄₃	—	4	2	no	—
188	C₂×D₄₃	—	8	1	no	—
189	C₂×D₄₃	—	8	1	no	—
190	C₂×D₄₃	—	8	1	no	—
191	C₂×D₄₃	—	8	1	no	—
192	C₄×C₄₃	—	2	1	no	—
193	C₄×C₄₃	—	2	1	no	—
194	C₄×C₄₃	—	8	2	no	—
195	C₄×C₄₃	#463	1	1	yes	characteristic
196	C₄×C₄₃	#464	1	1	yes	characteristic
197	C₄×C₄₃	#465	1	1	yes	characteristic
198	C₄×C₄₃	#470	1	1	yes	characteristic
199	C₄×C₄₃	#483	1	1	yes	characteristic
200	C₄×C₄₃	#485	1	1	yes	characteristic
201	C₄×C₄₃	#488	1	1	yes	characteristic
202	C₄×C₄₃	#489	1	1	yes	characteristic
203	Dic₄₃	—	8	1	no	—
204	Dic₄₃	—	8	1	no	—
205	Dic₄₃	—	8	1	no	—
206	Dic₄₃	—	16	1	no	—
207	#2563	—	43	1	no	—
208	#1956	—	43	1	no	—
209	#1948	—	43	1	no	—
210	#1802	—	43	1	no	—
211	C₂×#333	D₄₃	1	1	yes	characteristic, complemented
212	C₂×D₄⋊C₈	—	43	1	no	—
213	#1279	—	43	1	no	—
214	C₂×C₄₃	#1622	1	1	yes	characteristic
215	C₂×C₄₃	#1634	1	1	yes	characteristic
216	C₂×C₄₃	#1643	1	1	yes	characteristic
217	C₂×C₄₃	#1646	1	1	yes	characteristic
218	C₂×C₄₃	#2035	1	1	yes	characteristic
219	C₂×C₄₃	#2037	1	1	yes	characteristic
220	C₂×C₄₃	#2042	1	1	yes	characteristic
221	D₄₃	—	8	2	no	—
222	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
223	C₂×C₄×D₄	—	43	1	no	—
224	C₂×#106	—	86	1	no	—
225	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
227	C₂×#103	—	86	2	no	—
228	C₂×#102	—	86	1	no	—
229	C₂×C₄×C₈	—	43	1	no	—
230	#393	—	86	2	no	—
231	#390	—	86	1	no	—
232	#384	—	43	1	no	—
233	#382	—	86	1	no	—
234	#380	—	86	1	no	—
235	#380	—	86	1	no	—
236	C₄×C₄⋊C₄	—	43	1	no	—
237	#340	—	86	1	no	—
238	#340	—	86	1	no	—
239	#333	—	2	2	no	—
240	D₄⋊C₈	—	86	2	no	—
241	C₄₃	#10412	1	1	yes	characteristic, complemented, Sylow
242	C₂²×Q₈	D₁₇₂	1	2	yes	—
243	C₂²×D₄	—	43	1	no	—
244	C₂³×C₄	—	86	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	86	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄×D₄	—	86	1	no	—
253	C₄×D₄	—	86	1	no	—
254	C₄×D₄	—	86	1	no	—
255	C₄×D₄	—	86	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	43	1	no	—
259	C₂×C₄⋊C₄	—	43	1	no	—
260	C₂×C₄⋊C₄	—	43	1	no	—
261	C₂×C₄⋊C₄	—	86	1	no	—
262	C₂×C₄⋊C₄	—	86	1	no	—
263	C₂×C₄⋊C₄	—	86	1	no	—
264	C₂×C₂²⋊C₄	—	86	2	no	—
265	C₂×C₂²⋊C₄	—	86	2	no	—
266	C₂×C₂²⋊C₄	—	86	1	no	—
267	C₂×C₄²	—	86	1	no	—
268	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
269	#106	—	172	2	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	C₂²⋊D₄₃	1	2	yes	—
274	#103	—	172	4	no	—
275	#102	—	172	2	no	—
276	C₄×C₈	—	86	1	no	—
277	C₄×C₈	—	86	1	no	—
278	#95	—	86	2	no	—
279	#95	—	86	2	no	—
280	#95	—	86	1	no	—
281	C₂⁴	—	86	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×D₄	—	43	2	no	—
287	C₂×D₄	—	86	1	no	—
288	C₂×D₄	—	86	1	no	—
289	C₂×D₄	—	86	1	no	—
290	C₂×D₄	—	86	1	no	—
291	C₂×D₄	—	86	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	86	1	no	—
294	C₂²×C₄	—	86	1	no	—
295	C₂²×C₄	—	86	1	no	—
296	C₂²×C₄	—	172	1	no	—
297	C₂²×C₄	—	172	1	no	—
298	C₂²×C₄	—	172	1	no	—
299	C₂²×C₄	—	172	1	no	—
300	C₂²×C₄	—	172	1	no	—
301	C₂²×C₄	—	172	1	no	—
302	C₂²×C₄	—	172	1	no	—
303	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
304	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
305	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	86	2	no	—
313	C₂×C₈	—	172	1	no	—
314	C₂×C₈	—	172	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	86	1	no	—
320	C₄⋊C₄	—	86	1	no	—
321	C₄⋊C₄	—	86	1	no	—
322	C₄⋊C₄	—	86	1	no	—
323	C₄⋊C₄	—	86	1	no	—
324	C₄⋊C₄	—	86	1	no	—
325	C₄⋊C₄	—	172	2	no	—
326	C₄⋊C₄	—	172	1	no	—
327	C₄⋊C₄	—	172	1	no	—
328	C₄⋊C₄	—	172	1	no	—
329	C₄⋊C₄	—	172	1	no	—
330	C₂²⋊C₄	—	344	2	no	—
331	C₂²⋊C₄	—	344	2	no	—
332	C₂²⋊C₄	—	172	1	no	—
333	C₂²⋊C₄	—	172	1	no	—
334	C₄²	—	172	1	no	—
335	C₄²	—	172	1	no	—
336	C₄²	#10621898	1	1	yes	characteristic
337	C₄²	#10621900	1	1	yes	characteristic
338	C₄²	#10621900	1	1	yes	characteristic
339	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
340	C₂³	—	86	2	no	—
341	C₂³	—	172	1	no	—
342	C₂³	—	172	1	no	—
343	C₂³	—	172	1	no	—
344	C₂³	—	172	1	no	—
345	C₂³	—	172	1	no	—
346	C₂³	—	172	1	no	—
347	C₂³	#13063295	1	1	yes	characteristic
348	Q₈	—	4	4	no	—
349	Q₈	—	8	2	no	—
350	D₄	—	86	2	no	—
351	D₄	—	86	2	no	—
352	D₄	—	172	1	no	—
353	D₄	—	172	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	344	1	no	—
360	C₂×C₄	—	344	1	no	—
361	C₂×C₄	—	344	1	no	—
362	C₂×C₄	—	344	1	no	—
363	C₂×C₄	—	344	1	no	—
364	C₂×C₄	—	344	1	no	—
365	C₂×C₄	—	344	1	no	—
366	C₂×C₄	—	172	1	no	—
367	C₂×C₄	—	172	1	no	—
368	C₂×C₄	—	172	1	no	—
369	C₂×C₄	—	172	1	no	—
370	C₂×C₄	—	172	1	no	—
371	C₂×C₄	—	172	1	no	—
372	C₂×C₄	—	172	1	no	—
373	C₂×C₄	—	172	1	no	—
374	C₂×C₄	—	172	1	no	—
375	C₂×C₄	#13063296	1	1	yes	characteristic
376	C₂×C₄	#13063297	1	1	yes	characteristic
377	C₂×C₄	#13063299	1	1	yes	characteristic
378	C₂×C₄	#13063307	1	1	yes	characteristic
379	C₂×C₄	#13063309	1	1	yes	characteristic
380	C₂×C₄	#13063311	1	1	yes	characteristic
381	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
382	C₂×C₄	#13063346	1	1	yes	characteristic
383	C₂×C₄	#13063346	1	1	yes	characteristic
384	C₂×C₄	#13063348	1	1	yes	characteristic
385	C₂×C₄	#13063352	1	1	yes	characteristic
386	C₂×C₄	#13063357	1	1	yes	characteristic
387	C₂×C₄	#13063357	1	1	yes	characteristic
388	C₂×C₄	#13063357	1	1	yes	characteristic
389	C₈	—	4	2	no	—
390	C₈	—	8	1	no	—
391	C₈	—	172	2	no	—
392	C₂²	—	344	1	no	—
393	C₂²	—	344	1	no	—
394	C₂²	—	344	1	no	—
395	C₂²	—	344	1	no	—
396	C₂²	—	172	2	no	—
397	C₂²	—	172	2	no	—
398	C₂²	—	172	2	no	—
399	C₂²	#14582815	1	1	yes	characteristic
400	C₂²	#14583039	1	1	yes	characteristic
401	C₂²	#14583047	1	1	yes	characteristic
402	C₂²	#14583064	1	1	yes	characteristic
403	C₂²	#14583064	1	1	yes	characteristic
404	C₂²	#14583069	1	1	yes	characteristic
405	C₂²	#14583079	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	8	2	no	—
409	C₄	—	344	1	no	—
410	C₄	—	344	1	no	—
411	C₄	—	344	1	no	—
412	C₄	—	688	1	no	—
413	C₄	#14583116	1	1	yes	characteristic
414	C₄	#14583123	1	1	yes	characteristic
415	C₄	#14583125	1	1	yes	characteristic
416	C₄	#14583154	1	1	yes	characteristic
417	C₄	#14583228	1	1	yes	characteristic
418	C₄	#14583238	1	1	yes	characteristic
419	C₄	#14583255	1	1	yes	characteristic
420	C₄	#14583260	1	1	yes	characteristic
421	C₂	—	344	2	no	—
422	C₂	#19133668	1	1	yes	characteristic
423	C₂	#19133741	1	1	yes	characteristic
424	C₂	#19133803	1	1	yes	characteristic
425	C₂	#19133824	1	1	yes	characteristic
426	C₂	#19135790	1	1	yes	characteristic
427	C₂	#19135806	1	1	yes	characteristic
428	C₂	#19135833	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063295
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#333	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂²×D₁₇₂	D₄
hypercenter	C₂×#333	D₄₃
hypocenter	C₄₃	#10412
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

Complements

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

N	H ≅ G/N	type
2. #19135398	C₂	semidirect
3. #19135359	C₂	semidirect
6. #19132434	C₂	semidirect
7. C₂×C₄₃×#333	C₂	semidirect
211. C₂×#333	D₄₃	semidirect
241. C₄₃	#10412	semidirect

Maximal subgroups

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

subgroup	index
#19139769	2
#19135398	2
#19135359	2
#19134596	2
C₂×#14582626	2
#19132434	2
C₂×C₄₃×#333	2
#10412	43