Subgroups — #25146371

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144977	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144388	C₂	1	1	yes	maximal, characteristic
3	C₂×#14583105	C₂	1	1	yes	maximal, characteristic
4	#19135961	C₂	1	2	yes	maximal, complemented
5	#19135858	C₂	1	2	yes	maximal
6	#19135498	C₂	1	2	yes	maximal
7	#19135439	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135371	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135250	C₂	1	2	yes	maximal, complemented
10	C₄×#13063241	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621873	C₂²	1	2	yes	—
13	C₂×#13063325	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
15	#14583269	—	2	2	no	—
16	#14583251	—	2	1	no	—
17	#14583251	—	2	1	no	—
18	#14583196	—	2	2	no	—
19	#14583186	—	2	1	no	—
20	#14583176	—	2	1	no	—
21	#14583105	—	2	1	no	—
22	#14583105	—	2	1	no	—
23	#14583105	—	2	2	no	—
24	C₂×#13063261	C₂²	1	2	yes	—
25	#14582942	C₂²	1	2	yes	—
26	#14582923	C₂²	1	1	yes	characteristic
27	#14582907	C₂²	1	2	yes	—
28	#14582907	C₂²	1	2	yes	—
29	#14582903	C₂²	1	2	yes	—
30	C₂×#13063250	C₂²	1	2	yes	—
31	C₂×#13063243	C₂²	1	2	yes	—
32	C₂×#13063243	C₂²	1	2	yes	—
33	C₂×#13063241	C₂²	1	1	yes	characteristic
34	C₂×#13063241	C₂²	1	1	yes	characteristic
35	C₄×#10621877	C₂²	1	1	yes	characteristic
36	#14582667	C₂²	1	1	yes	characteristic
37	#14582667	C₂²	1	1	yes	characteristic
38	#14582664	C₂²	1	2	yes	—
39	C₄₃×#533	C₂²	1	1	yes	characteristic
40	C₄₃×#446	—	2	2	no	—
41	C₄₃×#446	—	2	1	no	—
42	C₈×Q₈×C₄₃	—	2	1	no	—
43	C₄₃×#424	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#405	C₂²	1	2	yes	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂²×Dic₈₆	C₂³	1	2	yes	—
48	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
49	C₂²×C₄×D₄₃	—	2	1	no	—
50	C₂×#10621873	—	2	4	no	—
51	C₂×#10621873	—	2	2	no	—
52	C₂×#10621873	—	2	2	no	—
53	C₂×#10621873	—	4	2	no	—
54	C₂×#10621877	C₂³	1	1	yes	characteristic
55	C₂×#10621877	C₂³	1	1	yes	characteristic
56	C₂×#10621877	C₂³	1	2	yes	—
57	#13063325	—	2	1	no	—
58	#13063325	—	2	1	no	—
59	#13063325	—	2	1	no	—
60	#13063325	—	2	1	no	—
61	C₄×D₁₇₂	—	2	1	no	—
62	C₄×D₁₇₂	—	2	1	no	—
63	C₄×D₁₇₂	—	2	1	no	—
64	C₄×D₁₇₂	—	2	1	no	—
65	C₂×C₄⋊Dic₄₃	—	2	1	no	—
66	C₂×C₄⋊Dic₄₃	—	2	1	no	—
67	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
68	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
69	#13063261	—	4	2	no	—
70	#13063258	—	2	2	no	—
71	#13063256	—	2	2	no	—
72	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
73	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
74	#13063250	—	2	2	no	—
75	#13063250	—	2	2	no	—
76	#13063248	—	2	2	no	—
77	#13063248	—	2	2	no	—
78	#13063248	—	2	2	no	—
79	#13063248	—	2	2	no	—
80	#13063245	—	2	2	no	—
81	#13063245	—	2	2	no	—
82	#13063243	—	2	4	no	—
83	#13063243	—	4	2	no	—
84	#13063241	—	2	2	no	—
85	#13063241	—	2	2	no	—
86	#13063236	—	2	1	no	—
87	C₄×C₄₃⋊C₈	—	2	1	no	—
88	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
91	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
92	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
93	#125×C₄₃	D₄	1	2	yes	—
94	C₂²⋊Q₈×C₄₃	—	2	1	no	—
95	C₂²⋊Q₈×C₄₃	—	2	1	no	—
96	C₄×Q₈×C₄₃	—	2	1	no	—
97	C₄×Q₈×C₄₃	—	2	1	no	—
98	#117×C₄₃	C₂³	1	2	yes	—
99	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₄₃	—	2	2	no	—
101	C₄⋊C₈×C₄₃	—	2	2	no	—
102	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
103	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
104	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
105	#97×C₄₃	—	2	2	no	—
106	#97×C₄₃	—	2	1	no	—
107	C₄×C₈×C₄₃	—	2	2	no	—
108	C₄×C₈×C₄₃	—	2	1	no	—
109	C₂³×D₄₃	—	2	1	no	—
110	C₂×Q₈×C₄₃	—	2	1	no	—
111	C₂×Q₈×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
115	C₂²×Dic₄₃	—	2	2	no	—
116	C₂²×Dic₄₃	—	2	1	no	—
117	C₂×D₁₇₂	—	2	1	no	—
118	C₂×D₁₇₂	—	2	1	no	—
119	C₂×D₁₇₂	—	2	1	no	—
120	C₂×D₁₇₂	—	2	1	no	—
121	C₂×D₁₇₂	—	2	1	no	—
122	C₂×D₁₇₂	#41	1	2	yes	—
123	C₂×C₄×D₄₃	—	4	1	no	—
124	C₂×C₄×D₄₃	—	4	1	no	—
125	C₂×C₄×D₄₃	—	8	2	no	—
126	C₂×Dic₈₆	—	2	2	no	—
127	C₂×Dic₈₆	—	2	2	no	—
128	C₂×Dic₈₆	—	2	2	no	—
129	C₂×Dic₈₆	—	2	2	no	—
130	C₂×Dic₈₆	—	2	2	no	—
131	C₂×Dic₈₆	—	2	2	no	—
132	M₁₆×C₄₃	—	2	1	no	—
133	M₁₆×C₄₃	—	2	1	no	—
134	M₁₆×C₄₃	—	2	1	no	—
135	M₁₆×C₄₃	#41	1	2	yes	—
136	C₂×C₈×C₄₃	—	2	1	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	—	2	1	no	—
140	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
142	C₄⋊C₄×C₄₃	—	2	2	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	2	1	no	—
145	C₄⋊C₄×C₄₃	—	2	1	no	—
146	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₄₃	—	2	2	no	—
149	C₄²×C₄₃	—	2	2	no	—
150	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
154	(C₂×D₄₃)⋊C₄	—	4	1	no	—
155	(C₂×D₄₃)⋊C₄	—	4	1	no	—
156	C₄⋊Dic₄₃	—	2	1	no	—
157	C₄⋊Dic₄₃	—	2	1	no	—
158	C₄⋊Dic₄₃	—	4	1	no	—
159	C₄⋊Dic₄₃	—	4	1	no	—
160	C₄⋊Dic₄₃	—	4	1	no	—
161	C₄⋊Dic₄₃	—	4	1	no	—
162	#10621877	—	2	1	no	—
163	#10621877	—	2	1	no	—
164	#10621877	—	2	2	no	—
165	#10621877	—	2	2	no	—
166	#10621877	—	2	1	no	—
167	#10621877	—	2	1	no	—
168	C₂×C₄₃⋊C₈	—	2	1	no	—
169	C₂×C₄₃⋊C₈	—	2	1	no	—
170	C₂×C₄₃⋊C₈	—	2	2	no	—
171	#10621873	—	4	4	no	—
172	#10621873	—	4	4	no	—
173	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂²×D₄₃	—	2	2	no	—
175	C₂²×D₄₃	—	4	1	no	—
176	C₂²×D₄₃	—	4	1	no	—
177	C₂²×D₄₃	—	8	1	no	—
178	C₂²×D₄₃	—	8	1	no	—
179	Q₈×C₄₃	—	4	2	no	—
180	Q₈×C₄₃	—	8	1	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	4	1	no	—
185	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
188	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
195	C₂×Dic₄₃	—	4	1	no	—
196	C₂×Dic₄₃	—	4	2	no	—
197	C₂×Dic₄₃	—	4	2	no	—
198	C₂×Dic₄₃	—	4	2	no	—
199	C₂×Dic₄₃	—	8	1	no	—
200	D₁₇₂	—	2	2	no	—
201	D₁₇₂	—	2	2	no	—
202	D₁₇₂	—	4	1	no	—
203	D₁₇₂	—	4	1	no	—
204	C₄×D₄₃	—	8	2	no	—
205	C₄×D₄₃	—	8	2	no	—
206	Dic₈₆	—	4	2	no	—
207	Dic₈₆	—	4	2	no	—
208	Dic₈₆	—	4	2	no	—
209	Dic₈₆	—	4	2	no	—
210	C₈×C₄₃	—	2	2	no	—
211	C₈×C₄₃	—	2	2	no	—
212	C₈×C₄₃	—	2	2	no	—
213	C₈×C₄₃	—	4	1	no	—
214	C₄₃⋊C₈	—	4	1	no	—
215	C₄₃⋊C₈	—	4	1	no	—
216	C₄₃⋊C₈	—	4	2	no	—
217	#25313	—	43	1	no	maximal, Sylow
218	C₂²×C₄₃	—	2	1	no	—
219	C₂²×C₄₃	—	2	1	no	—
220	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
221	C₂²×C₄₃	#529	1	1	yes	characteristic
222	C₂²×C₄₃	#542	1	1	yes	characteristic
223	C₂×D₄₃	—	4	2	no	—
224	C₂×D₄₃	—	8	2	no	—
225	C₂×D₄₃	—	8	1	no	—
226	C₂×D₄₃	—	8	1	no	—
227	C₂×D₄₃	—	8	2	no	—
228	C₄×C₄₃	—	2	1	no	—
229	C₄×C₄₃	—	2	1	no	—
230	C₄×C₄₃	—	2	1	no	—
231	C₄×C₄₃	—	4	2	no	—
232	C₄×C₄₃	—	4	2	no	—
233	C₄×C₄₃	#471	1	2	yes	—
234	C₄×C₄₃	#546	1	1	yes	characteristic
235	C₄×C₄₃	#548	1	1	yes	characteristic
236	C₄×C₄₃	#548	1	1	yes	characteristic
237	C₄×C₄₃	#550	1	1	yes	characteristic
238	Dic₄₃	—	8	2	no	—
239	Dic₄₃	—	8	1	no	—
240	#3139	—	43	1	no	—
241	#3077	—	43	1	no	—
242	C₂×#461	—	43	1	no	—
243	#2962	D₄₃	1	1	yes	characteristic, complemented
244	#2064	—	43	2	no	—
245	#2046	—	43	2	no	—
246	#1977	—	43	2	no	—
247	#1966	—	43	1	no	—
248	#1950	—	43	1	no	—
249	#1930	—	43	2	no	—
250	C₄×#100	—	43	1	no	—
251	C₂×C₄₃	—	2	1	no	—
252	C₂×C₄₃	—	2	1	no	—
253	C₂×C₄₃	#2426	1	1	yes	characteristic
254	C₂×C₄₃	C₂×#471	1	1	yes	characteristic
255	C₂×C₄₃	#3069	1	1	yes	characteristic
256	D₄₃	—	8	2	no	—
257	C₂²×SD₁₆	—	43	2	no	—
258	#533	C₂×D₄₃	1	1	yes	characteristic
259	C₂×C₄⋊Q₈	—	43	1	no	—
260	C₂×C₄×D₄	—	43	1	no	—
261	#491	—	86	2	no	—
262	#487	—	86	1	no	—
263	#487	—	86	1	no	—
264	#478	—	86	2	no	—
265	#476	—	86	1	no	—
266	#474	—	86	1	no	—
267	#461	—	86	1	no	—
268	#461	—	86	2	no	—
269	#461	—	86	1	no	—
270	#446	—	2	2	no	—
271	#446	—	2	1	no	—
272	C₈×Q₈	—	2	1	no	—
273	C₂×#108	—	43	2	no	—
274	#428	—	43	2	no	—
275	#424	C₂×D₄₃	1	2	yes	—
276	#423	—	43	1	no	—
277	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
278	#419	—	43	2	no	—
279	#419	—	43	2	no	—
280	#418	—	43	2	no	—
281	C₂×#103	—	43	2	no	—
282	C₂×#101	—	43	2	no	—
283	C₂×#101	—	43	2	no	—
284	C₂×#100	—	43	1	no	—
285	C₂×#100	—	43	1	no	—
286	#405	C₂×D₄₃	1	2	yes	—
287	C₄×M₁₆	—	43	1	no	—
288	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
289	#343	—	43	1	no	—
290	#343	—	43	1	no	—
291	#341	—	43	2	no	—
292	C₄₃	#25313	1	1	yes	characteristic, complemented, Sylow
293	C₂²×Q₈	—	43	2	no	—
294	C₂²×D₄	—	43	1	no	—
295	C₂³×C₄	—	86	1	no	—
296	C₂×SD₁₆	—	86	4	no	—
297	C₂×SD₁₆	—	86	2	no	—
298	C₂×SD₁₆	—	86	2	no	—
299	C₂×SD₁₆	—	172	2	no	—
300	C₂×M₁₆	—	43	1	no	—
301	C₂×M₁₆	—	43	2	no	—
302	C₂×M₁₆	—	43	1	no	—
303	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
304	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
305	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
306	C₄⋊Q₈	—	86	1	no	—
307	C₄⋊Q₈	—	86	1	no	—
308	C₄⋊Q₈	—	86	1	no	—
309	C₄⋊Q₈	—	86	1	no	—
310	C₄⋊Q₈	D₁₇₂	1	1	yes	characteristic
311	C₄⋊Q₈	D₁₇₂	1	1	yes	characteristic
312	#125	D₁₇₂	1	2	yes	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×Q₈	—	2	1	no	—
317	C₄×D₄	—	86	1	no	—
318	C₄×D₄	—	86	1	no	—
319	C₄×D₄	—	86	1	no	—
320	C₄×D₄	—	86	1	no	—
321	#117	C₂²×D₄₃	1	2	yes	—
322	C₂×C₄⋊C₄	—	43	1	no	—
323	C₂×C₄⋊C₄	—	86	1	no	—
324	C₂×C₄⋊C₄	—	86	1	no	—
325	C₂×C₂²⋊C₄	—	86	1	no	—
326	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
327	#108	—	172	2	no	—
328	#107	—	86	2	no	—
329	#106	—	86	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	—	86	1	no	—
333	C₄⋊C₈	—	86	1	no	—
334	C₄⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
335	C₄⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
336	C₄⋊C₈	C₂²⋊D₄₃	1	2	yes	—
337	#103	—	86	2	no	—
338	#103	—	86	2	no	—
339	#103	—	86	2	no	—
340	#103	—	86	2	no	—
341	#103	—	86	2	no	—
342	#103	—	86	2	no	—
343	#102	—	86	2	no	—
344	#102	—	86	2	no	—
345	#101	—	86	4	no	—
346	#101	—	172	2	no	—
347	#100	—	86	2	no	—
348	#100	—	86	2	no	—
349	#97	—	2	2	no	—
350	#97	—	2	1	no	—
351	#97	—	86	1	no	—
352	C₄×C₈	—	2	2	no	—
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	—	86	1	no	—
355	C₂⁴	—	86	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	86	2	no	—
359	C₂×Q₈	—	86	2	no	—
360	C₂×Q₈	—	86	2	no	—
361	C₂×Q₈	—	86	2	no	—
362	C₂×Q₈	—	86	2	no	—
363	C₂×Q₈	—	86	2	no	—
364	C₂×D₄	—	43	2	no	—
365	C₂×D₄	—	86	1	no	—
366	C₂×D₄	—	86	1	no	—
367	C₂×D₄	—	86	1	no	—
368	C₂×D₄	—	86	1	no	—
369	C₂×D₄	—	86	1	no	—
370	C₂²×C₄	—	86	1	no	—
371	C₂²×C₄	—	86	2	no	—
372	C₂²×C₄	—	344	2	no	—
373	C₂²×C₄	—	172	1	no	—
374	C₂²×C₄	—	172	1	no	—
375	C₂²×C₄	#10621898	1	1	yes	characteristic
376	C₂²×C₄	#10621898	1	1	yes	characteristic
377	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
378	SD₁₆	—	172	4	no	—
379	SD₁₆	—	172	4	no	—
380	M₁₆	—	2	1	no	—
381	M₁₆	—	2	1	no	—
382	M₁₆	—	2	1	no	—
383	M₁₆	—	86	1	no	—
384	M₁₆	—	86	1	no	—
385	M₁₆	—	86	2	no	—
386	M₁₆	—	86	2	no	—
387	M₁₆	—	86	1	no	—
388	M₁₆	—	86	1	no	—
389	M₁₆	#10621902	1	2	yes	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	86	1	no	—
395	C₂×C₈	—	86	1	no	—
396	C₂×C₈	—	86	2	no	—
397	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
398	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	86	1	no	—
404	C₄⋊C₄	—	86	1	no	—
405	C₄⋊C₄	—	172	1	no	—
406	C₄⋊C₄	—	172	1	no	—
407	C₄⋊C₄	—	172	1	no	—
408	C₄⋊C₄	—	172	1	no	—
409	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
410	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	172	1	no	—
413	C₂²⋊C₄	—	172	1	no	—
414	C₄²	—	2	2	no	—
415	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
416	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
417	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
418	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
419	C₂³	—	86	2	no	—
420	C₂³	—	344	1	no	—
421	C₂³	—	344	1	no	—
422	C₂³	—	172	1	no	—
423	C₂³	—	172	1	no	—
424	C₂³	C₂×#10621898	1	1	yes	characteristic
425	Q₈	—	4	2	no	—
426	Q₈	—	8	1	no	—
427	Q₈	—	172	2	no	—
428	Q₈	—	172	2	no	—
429	Q₈	—	172	2	no	—
430	Q₈	—	172	2	no	—
431	D₄	—	86	2	no	—
432	D₄	—	86	2	no	—
433	D₄	—	172	1	no	—
434	D₄	—	172	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	344	2	no	—
440	C₂×C₄	—	344	2	no	—
441	C₂×C₄	—	344	1	no	—
442	C₂×C₄	—	172	1	no	—
443	C₂×C₄	—	172	2	no	—
444	C₂×C₄	—	172	2	no	—
445	C₂×C₄	—	172	2	no	—
446	C₂×C₄	#13063299	1	1	yes	characteristic
447	C₂×C₄	#13063299	1	1	yes	characteristic
448	C₂×C₄	#13063299	1	1	yes	characteristic
449	C₂×C₄	#13063299	1	1	yes	characteristic
450	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
452	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
453	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
454	C₂×C₄	#13063371	1	1	yes	characteristic
455	C₂×C₄	#13063373	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	—	4	1	no	—
460	C₈	—	172	1	no	—
461	C₈	—	172	1	no	—
462	C₈	—	172	2	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	344	2	no	—
466	C₂²	—	344	2	no	—
467	C₂²	—	344	1	no	—
468	C₂²	—	344	1	no	—
469	C₂²	—	172	2	no	—
470	C₂²	C₂×#13063299	1	1	yes	characteristic
471	C₂²	#14583436	1	1	yes	characteristic
472	C₂²	#14583521	1	1	yes	characteristic
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	344	1	no	—
479	C₄	—	344	2	no	—
480	C₄	#14583162	1	2	yes	—
481	C₄	#14583537	1	1	yes	characteristic
482	C₄	#14583560	1	1	yes	characteristic
483	C₄	#14583561	1	1	yes	characteristic
484	C₄	#14583571	1	1	yes	characteristic
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	344	2	no	—
488	C₂	#19138155	1	1	yes	characteristic
489	C₂	C₂×#14583162	1	1	yes	characteristic
490	C₂	#19144332	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063299
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2962	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂²×D₁₇₂	C₂³
hypercenter	#2962	D₄₃
hypocenter	C₄₃	#25313
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2962

Complements

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

N	H ≅ G/N	type
1. #19144977	C₂	semidirect
4. #19135961	C₂	semidirect
7. #19135439	C₂	semidirect
8. #19135371	C₂	semidirect
9. #19135250	C₂	semidirect
11. C₄₃×#2962	C₂	semidirect
243. #2962	D₄₃	semidirect
292. C₄₃	#25313	semidirect

Maximal subgroups

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

subgroup	index
#19144977	2
#19144388	2
C₂×#14583105	2
#19135961	2
#19135858	2
#19135498	2
#19135439	2
#19135371	2
#19135250	2
C₄×#13063241	2
C₄₃×#2962	2
#25313	43