Subgroups — #24991877

Order 11008.

618 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583247	C₂	1	1	yes	maximal, characteristic
2	#19137655	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135521	C₂	1	1	yes	maximal, characteristic
4	#19135521	C₂	1	1	yes	maximal, characteristic
5	#19132434	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13063322	C₂²	1	1	yes	characteristic
9	C₂×Q₈×Dic₄₃	—	2	1	no	—
10	#14583247	—	2	2	no	—
11	#14583247	C₄	1	4	yes	complemented
12	C₂×#13063247	—	2	1	no	—
13	C₂×#13063247	—	2	1	no	—
14	C₂×#13063247	—	2	1	no	—
15	C₂×#13063247	—	2	1	no	—
16	C₂×#13063245	—	2	2	no	—
17	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	#14582806	—	2	1	no	—
19	#14582798	—	2	1	no	—
20	#14582785	—	2	2	no	—
21	C₄⋊C₄×Dic₄₃	—	2	1	no	—
22	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#332	—	2	2	no	—
28	C₂²×D₁₇₂	—	2	1	no	—
29	C₂²×D₁₇₂	—	2	1	no	—
30	C₂²×D₁₇₂	—	2	1	no	—
31	C₂²×C₄₃⋊C₈	—	2	1	no	—
32	#13063322	—	2	1	no	—
33	#13063322	—	2	1	no	—
34	#13063322	—	2	1	no	—
35	#13063322	C₂×C₄	1	2	yes	—
36	Q₈×Dic₄₃	—	4	2	no	—
37	Q₈×Dic₄₃	—	4	2	no	—
38	C₂×C₄⋊Dic₄₃	—	2	2	no	—
39	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
42	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
43	C₂×C₄×Dic₄₃	—	2	2	no	—
44	C₂×C₄×Dic₄₃	—	2	1	no	—
45	C₂×C₄×Dic₄₃	—	2	1	no	—
46	#13063247	—	4	2	no	—
47	#13063247	—	4	2	no	—
48	#13063247	—	4	2	no	—
49	#13063247	—	4	2	no	—
50	#13063245	—	2	8	no	—
51	C₄×C₄₃⋊C₈	—	2	1	no	—
52	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
53	C₄₃⋊#95	—	2	2	no	—
54	C₄₃⋊#95	—	2	2	no	—
55	C₄₃⋊#95	—	2	1	no	—
56	C₄₃⋊#95	—	2	1	no	—
57	C₂²×Q₈×C₄₃	—	2	1	no	—
58	C₂²×C₈×C₄₃	—	2	1	no	—
59	C₂²×C₈×C₄₃	—	2	1	no	—
60	C₄⋊Q₈×C₄₃	—	2	1	no	—
61	C₄⋊Q₈×C₄₃	—	2	1	no	—
62	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
63	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
66	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₄₃	—	2	1	no	—
68	C₄⋊C₈×C₄₃	—	2	1	no	—
69	C₄⋊C₈×C₄₃	—	2	1	no	—
70	C₄⋊C₈×C₄₃	—	2	1	no	—
71	C₂³×D₄₃	—	4	1	no	—
72	C₂×Q₈×C₄₃	—	2	2	no	—
73	C₂×Q₈×C₄₃	—	2	2	no	—
74	C₂×Q₈×C₄₃	—	4	1	no	—
75	C₂×Q₈×C₄₃	—	4	1	no	—
76	C₂×Q₈×C₄₃	—	4	1	no	—
77	C₂×Q₈×C₄₃	—	4	1	no	—
78	C₂²×C₄×C₄₃	—	2	2	no	—
79	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×Dic₄₃	—	2	1	no	—
83	C₂²×Dic₄₃	—	2	1	no	—
84	C₂²×Dic₄₃	—	2	1	no	—
85	C₂²×Dic₄₃	—	2	1	no	—
86	C₂×D₁₇₂	—	2	2	no	—
87	C₂×D₁₇₂	—	2	2	no	—
88	C₂×D₁₇₂	—	2	2	no	—
89	C₂×D₁₇₂	—	4	1	no	—
90	C₂×D₁₇₂	—	4	1	no	—
91	C₂×D₁₇₂	—	4	1	no	—
92	C₂×D₁₇₂	—	4	2	no	—
93	C₂×D₁₇₂	—	4	2	no	—
94	C₂×D₁₇₂	—	4	1	no	—
95	C₂×D₁₇₂	—	4	1	no	—
96	C₂×D₁₇₂	—	4	1	no	—
97	C₂×D₁₇₂	—	4	1	no	—
98	C₂×D₁₇₂	—	4	1	no	—
99	C₂×D₁₇₂	—	4	1	no	—
100	C₂×D₁₇₂	—	4	1	no	—
101	C₂×D₁₇₂	—	4	1	no	—
102	C₂×C₈×C₄₃	—	4	1	no	—
103	C₂×C₈×C₄₃	—	4	1	no	—
104	C₂×C₈×C₄₃	—	4	1	no	—
105	C₂×C₈×C₄₃	—	4	1	no	—
106	C₂×C₈×C₄₃	—	4	1	no	—
107	C₂×C₈×C₄₃	—	4	1	no	—
108	C₄⋊C₄×C₄₃	—	2	2	no	—
109	C₄⋊C₄×C₄₃	—	2	2	no	—
110	C₄⋊C₄×C₄₃	—	2	2	no	—
111	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
112	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₄₃	#41	1	1	yes	characteristic
115	C₄²×C₄₃	#41	1	1	yes	characteristic
116	C₄⋊Dic₄₃	—	2	1	no	—
117	C₄⋊Dic₄₃	—	2	1	no	—
118	C₄⋊Dic₄₃	—	2	1	no	—
119	C₄⋊Dic₄₃	—	2	1	no	—
120	C₄⋊Dic₄₃	—	2	1	no	—
121	C₄⋊Dic₄₃	—	2	1	no	—
122	C₄⋊Dic₄₃	—	4	4	no	—
123	C₄⋊Dic₄₃	D₈	1	2	yes	—
124	C₄⋊Dic₄₃	SD₁₆	1	2	yes	—
125	C₄×Dic₄₃	—	4	4	no	—
126	C₄×Dic₄₃	—	4	1	no	—
127	C₄×Dic₄₃	—	4	1	no	—
128	C₄×Dic₄₃	—	4	1	no	—
129	C₄×Dic₄₃	—	4	1	no	—
130	C₂×C₄₃⋊C₈	—	2	2	no	—
131	C₂×C₄₃⋊C₈	—	4	1	no	—
132	C₂×C₄₃⋊C₈	—	4	1	no	—
133	C₂³×C₄₃	#120	1	1	yes	characteristic
134	C₂²×D₄₃	—	4	2	no	—
135	C₂²×D₄₃	—	8	1	no	—
136	C₂²×D₄₃	—	8	1	no	—
137	C₂²×D₄₃	—	8	1	no	—
138	C₂²×D₄₃	—	8	1	no	—
139	C₂²×D₄₃	—	8	1	no	—
140	C₂²×D₄₃	—	8	1	no	—
141	Q₈×C₄₃	—	4	2	no	—
142	Q₈×C₄₃	—	4	2	no	—
143	Q₈×C₄₃	—	4	2	no	—
144	Q₈×C₄₃	—	4	2	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	4	no	—
148	C₂×C₄×C₄₃	—	4	2	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
154	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
155	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
158	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
159	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
160	C₂×C₄×C₄₃	AGL(1,ℤ/8)	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×Dic₄₃	—	2	2	no	—
165	C₂×Dic₄₃	—	2	2	no	—
166	C₂×Dic₄₃	—	4	1	no	—
167	C₂×Dic₄₃	—	4	1	no	—
168	C₂×Dic₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	4	1	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	—	4	1	no	—
172	C₂×Dic₄₃	—	4	1	no	—
173	C₂×Dic₄₃	—	4	1	no	—
174	C₂×Dic₄₃	—	4	1	no	—
175	C₂×Dic₄₃	—	4	1	no	—
176	D₁₇₂	—	4	4	no	—
177	D₁₇₂	—	4	2	no	—
178	D₁₇₂	—	4	2	no	—
179	D₁₇₂	—	4	2	no	—
180	D₁₇₂	—	4	2	no	—
181	D₁₇₂	—	8	2	no	—
182	D₁₇₂	—	8	1	no	—
183	D₁₇₂	—	8	1	no	—
184	D₁₇₂	—	8	1	no	—
185	D₁₇₂	—	8	1	no	—
186	C₈×C₄₃	—	8	1	no	—
187	C₈×C₄₃	—	8	1	no	—
188	C₄₃⋊C₈	—	4	2	no	—
189	#9062	—	43	1	no	maximal, Sylow
190	C₂²×C₄₃	#386	1	1	yes	characteristic
191	C₂²×C₄₃	#447	1	1	yes	characteristic
192	C₂²×C₄₃	#448	1	1	yes	characteristic
193	C₂²×C₄₃	#449	1	1	yes	characteristic
194	C₂²×C₄₃	#449	1	1	yes	characteristic
195	C₂²×C₄₃	#454	1	1	yes	characteristic
196	C₂²×C₄₃	#454	1	1	yes	characteristic
197	C₂×D₄₃	—	8	2	no	—
198	C₂×D₄₃	—	8	2	no	—
199	C₂×D₄₃	—	8	2	no	—
200	C₂×D₄₃	—	16	1	no	—
201	C₂×D₄₃	—	16	1	no	—
202	C₂×D₄₃	—	16	1	no	—
203	C₂×D₄₃	—	16	1	no	—
204	C₄×C₄₃	—	2	1	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	4	4	no	—
207	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
208	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
209	C₄×C₄₃	#440	1	1	yes	characteristic
210	C₄×C₄₃	#442	1	1	yes	characteristic
211	C₄×C₄₃	#459	1	1	yes	characteristic
212	C₄×C₄₃	#460	1	1	yes	characteristic
213	C₄×C₄₃	#463	1	1	yes	characteristic
214	C₄×C₄₃	#464	1	1	yes	characteristic
215	Dic₄₃	—	4	2	no	—
216	Dic₄₃	—	4	2	no	—
217	Dic₄₃	—	8	1	no	—
218	Dic₄₃	—	8	1	no	—
219	C₂×#486	—	43	1	no	—
220	#2365	—	43	1	no	—
221	#1982	—	43	1	no	—
222	#1982	—	43	1	no	—
223	C₂×#332	D₄₃	1	1	yes	characteristic, complemented
224	#1279	—	43	1	no	—
225	#1279	—	43	1	no	—
226	C₂×C₄₃	#1625	1	1	yes	characteristic
227	C₂×C₄₃	#1626	1	1	yes	characteristic
228	C₂×C₄₃	#1627	1	1	yes	characteristic
229	C₂×C₄₃	#1628	1	1	yes	characteristic
230	C₂×C₄₃	#1879	1	1	yes	characteristic
231	C₂×C₄₃	#1880	1	1	yes	characteristic
232	C₂×C₄₃	#1888	1	1	yes	characteristic
233	D₄₃	—	16	2	no	—
234	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
235	C₂×#127	—	43	1	no	—
236	C₂×C₄×Q₈	—	86	1	no	—
237	#486	—	43	4	no	—
238	#486	—	86	2	no	—
239	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
241	C₂×#102	—	86	2	no	—
242	C₂×#102	—	86	1	no	—
243	C₂×#102	—	86	1	no	—
244	C₂×#102	—	86	1	no	—
245	C₂×#102	—	86	1	no	—
246	C₂×C₄×C₈	—	43	1	no	—
247	#391	—	86	1	no	—
248	#389	—	86	1	no	—
249	#387	—	86	2	no	—
250	C₄×C₄⋊C₄	—	43	1	no	—
251	C₄×C₄⋊C₄	—	43	1	no	—
252	C₄×C₄⋊C₄	—	86	1	no	—
253	#332	—	2	2	no	—
254	C₄₃	#9062	1	1	yes	characteristic, complemented, Sylow
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×D₄	—	86	1	no	—
257	C₂²×D₄	—	86	1	no	—
258	C₂²×D₄	—	86	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	86	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	C₄×D₄₃	1	2	yes	—
265	C₄⋊Q₈	C₂²⋊D₄₃	1	2	yes	—
266	#127	—	43	2	no	—
267	#127	—	86	1	no	—
268	#127	—	86	1	no	—
269	#127	—	86	1	no	—
270	C₄×Q₈	—	172	2	no	—
271	C₄×Q₈	—	172	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	43	1	no	—
274	C₂×C₄⋊C₄	—	43	1	no	—
275	C₂×C₄⋊C₄	—	43	1	no	—
276	C₂×C₄⋊C₄	—	43	1	no	—
277	C₂×C₄⋊C₄	—	86	2	no	—
278	C₂×C₄⋊C₄	D₁₇₂	1	2	yes	—
279	C₂×C₄²	—	86	2	no	—
280	C₂×C₄²	—	86	1	no	—
281	C₂×C₄²	—	86	1	no	—
282	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	#102	—	86	8	no	—
288	#102	—	172	2	no	—
289	#102	—	172	2	no	—
290	#102	—	172	2	no	—
291	#102	—	172	2	no	—
292	C₄×C₈	—	43	2	no	—
293	C₄×C₈	—	86	1	no	—
294	#95	—	86	2	no	—
295	#95	—	86	2	no	—
296	#95	—	86	1	no	—
297	#95	—	86	1	no	—
298	C₂⁴	—	172	1	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×D₄	—	86	2	no	—
306	C₂×D₄	—	86	2	no	—
307	C₂×D₄	—	86	2	no	—
308	C₂×D₄	—	172	2	no	—
309	C₂×D₄	—	172	2	no	—
310	C₂×D₄	—	172	1	no	—
311	C₂×D₄	—	172	1	no	—
312	C₂×D₄	—	172	1	no	—
313	C₂×D₄	—	172	1	no	—
314	C₂×D₄	—	172	1	no	—
315	C₂×D₄	—	172	1	no	—
316	C₂×D₄	—	172	1	no	—
317	C₂×D₄	—	172	1	no	—
318	C₂×D₄	—	172	1	no	—
319	C₂×D₄	—	172	1	no	—
320	C₂×D₄	—	172	1	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	86	1	no	—
323	C₂²×C₄	—	86	1	no	—
324	C₂²×C₄	—	86	1	no	—
325	C₂²×C₄	—	86	1	no	—
326	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
328	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	86	2	no	—
336	C₂×C₈	—	172	1	no	—
337	C₂×C₈	—	172	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	43	2	no	—
342	C₄⋊C₄	—	43	2	no	—
343	C₄⋊C₄	—	86	1	no	—
344	C₄⋊C₄	—	86	1	no	—
345	C₄⋊C₄	—	86	1	no	—
346	C₄⋊C₄	—	86	1	no	—
347	C₄⋊C₄	—	86	1	no	—
348	C₄⋊C₄	—	86	1	no	—
349	C₄⋊C₄	—	172	4	no	—
350	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
351	C₄²	—	172	4	no	—
352	C₄²	—	172	1	no	—
353	C₄²	—	172	1	no	—
354	C₄²	—	172	1	no	—
355	C₄²	—	172	1	no	—
356	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
357	C₄²	#10621900	1	1	yes	characteristic
358	C₄²	#10621900	1	1	yes	characteristic
359	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
360	C₂³	—	344	1	no	—
361	C₂³	—	344	1	no	—
362	C₂³	—	344	1	no	—
363	C₂³	—	344	1	no	—
364	C₂³	—	344	1	no	—
365	C₂³	—	344	1	no	—
366	C₂³	—	172	2	no	—
367	C₂³	#13063295	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	344	2	no	—
373	D₄	—	344	1	no	—
374	D₄	—	344	1	no	—
375	D₄	—	344	1	no	—
376	D₄	—	344	1	no	—
377	D₄	—	172	4	no	—
378	D₄	—	172	2	no	—
379	D₄	—	172	2	no	—
380	D₄	—	172	2	no	—
381	D₄	—	172	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	86	2	no	—
388	C₂×C₄	—	86	2	no	—
389	C₂×C₄	—	172	1	no	—
390	C₂×C₄	—	172	1	no	—
391	C₂×C₄	—	172	1	no	—
392	C₂×C₄	—	172	1	no	—
393	C₂×C₄	—	172	1	no	—
394	C₂×C₄	—	172	1	no	—
395	C₂×C₄	—	172	1	no	—
396	C₂×C₄	—	172	1	no	—
397	C₂×C₄	—	172	1	no	—
398	C₂×C₄	—	172	1	no	—
399	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
400	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
401	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
402	C₂×C₄	#13063297	1	1	yes	characteristic
403	C₂×C₄	#13063297	1	1	yes	characteristic
404	C₂×C₄	#13063309	1	1	yes	characteristic
405	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
406	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
407	C₂×C₄	#13063346	1	1	yes	characteristic
408	C₂×C₄	#13063348	1	1	yes	characteristic
409	C₂×C₄	#13063349	1	1	yes	characteristic
410	C₂×C₄	#13063352	1	1	yes	characteristic
411	C₂×C₄	#13063352	1	1	yes	characteristic
412	C₂×C₄	#13063357	1	1	yes	characteristic
413	C₈	—	8	1	no	—
414	C₈	—	8	1	no	—
415	C₈	—	172	2	no	—
416	C₂²	—	344	2	no	—
417	C₂²	—	344	2	no	—
418	C₂²	—	344	2	no	—
419	C₂²	—	688	1	no	—
420	C₂²	—	688	1	no	—
421	C₂²	—	688	1	no	—
422	C₂²	—	688	1	no	—
423	C₂²	#14582776	1	1	yes	characteristic
424	C₂²	#14583034	1	1	yes	characteristic
425	C₂²	#14583039	1	1	yes	characteristic
426	C₂²	#14583045	1	1	yes	characteristic
427	C₂²	#14583047	1	1	yes	characteristic
428	C₂²	#14583074	1	1	yes	characteristic
429	C₂²	#14583074	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	4	4	no	—
433	C₄	—	344	1	no	—
434	C₄	—	344	1	no	—
435	C₄	—	172	2	no	—
436	C₄	—	172	2	no	—
437	C₄	#14582979	1	1	yes	characteristic
438	C₄	#14582984	1	1	yes	characteristic
439	C₄	#14583002	1	1	yes	characteristic
440	C₄	#14583008	1	1	yes	characteristic
441	C₄	#14583092	1	1	yes	characteristic
442	C₄	#14583097	1	1	yes	characteristic
443	C₄	#14583116	1	1	yes	characteristic
444	C₄	#14583123	1	1	yes	characteristic
445	C₂	—	688	2	no	—
446	C₂	#19133685	1	1	yes	characteristic
447	C₂	#19133692	1	1	yes	characteristic
448	C₂	#19133699	1	1	yes	characteristic
449	C₂	#19133706	1	1	yes	characteristic
450	C₂	#19134941	1	1	yes	characteristic
451	C₂	#19134948	1	1	yes	characteristic
452	C₂	#19134996	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063295
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#332	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂×#13063322	C₂²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#332	D₄₃
hypocenter	C₄₃	#9062
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#332

Complements

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

N	H ≅ G/N	type
2. #19137655	C₂	semidirect
5. #19132434	C₂	semidirect
6. #19132434	C₂	semidirect
7. C₂×C₄₃×#332	C₂	semidirect
11. #14583247	C₄	semidirect
223. C₂×#332	D₄₃	semidirect
254. C₄₃	#9062	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583247	2
#19137655	2
#19135521	2
#19132434	2
C₂×C₄₃×#332	2
#9062	43