Subgroups — #25105223

Order 11008.

998 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145021	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583019	C₂	1	2	yes	maximal, complemented
3	C₂×#14583014	C₂	1	2	yes	maximal, complemented
4	#19143314	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135487	C₂	1	2	yes	maximal, complemented
6	#19135482	C₂	1	2	yes	maximal, complemented
7	#19135428	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135426	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134766	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063345	C₂²	1	2	yes	—
13	C₂×#13063345	C₂²	1	2	yes	—
14	C₂×#13063331	C₂²	1	2	yes	—
15	#14583449	C₂²	1	1	yes	characteristic
16	#14583281	C₄	1	2	yes	complemented
17	#14583281	C₄	1	2	yes	complemented
18	#14583278	C₄	1	1	yes	characteristic, complemented
19	#14583275	C₄	1	1	yes	characteristic, complemented
20	#14583273	C₄	1	1	yes	characteristic, complemented
21	#14583271	C₄	1	1	yes	characteristic, complemented
22	#14583019	—	2	8	no	—
23	#14583014	—	2	8	no	—
24	#14582972	—	2	4	no	—
25	C₂×#13063260	C₂²	1	2	yes	—
26	C₂×#13063260	C₂²	1	2	yes	—
27	#14582923	C₂²	1	1	yes	characteristic
28	C₂×#13063252	C₂²	1	2	yes	—
29	C₂×#13063252	C₂²	1	2	yes	—
30	C₂×#13063251	C₂²	1	2	yes	—
31	C₂×#13063251	C₂²	1	2	yes	—
32	#14582865	C₂²	1	2	yes	—
33	C₂×#13063235	C₂²	1	1	yes	characteristic
34	C₂×#13063235	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
38	#14582745	C₂²	1	1	yes	characteristic
39	C₂×#131×C₄₃	C₂²	1	2	yes	—
40	C₄₃×#532	C₂²	1	1	yes	characteristic
41	C₄₃×#435	—	2	4	no	—
42	C₄₃×#423	C₂²	1	1	yes	characteristic
43	C₄₃×#408	C₂²	1	2	yes	—
44	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×#10621898	C₂³	1	2	yes	—
46	#13063345	—	2	4	no	—
47	#13063345	—	2	4	no	—
48	#13063345	—	2	4	no	—
49	#13063345	—	2	4	no	—
50	C₂×#10621885	C₂×C₄	1	2	yes	—
51	C₂×#10621885	C₂×C₄	1	2	yes	—
52	C₂×#10621883	C₂×C₄	1	2	yes	—
53	C₂×#10621883	C₂×C₄	1	2	yes	—
54	C₂×#10621884	C₂×C₄	1	2	yes	—
55	C₂×#10621884	C₂×C₄	1	2	yes	—
56	C₂×#10621882	C₂×C₄	1	2	yes	—
57	C₂×#10621882	C₂×C₄	1	2	yes	—
58	#13063331	—	2	4	no	—
59	#13063331	—	2	4	no	—
60	C₂×#10621877	C₂³	1	2	yes	—
61	C₂×#10621872	—	2	2	no	—
62	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
64	C₂×C₈×D₄₃	—	2	2	no	—
65	#13063325	C₂×C₄	1	1	yes	characteristic
66	#13063322	C₂×C₄	1	1	yes	characteristic
67	#13063313	C₂×C₄	1	2	yes	—
68	#13063299	—	2	2	no	—
69	C₄×D₁₇₂	—	2	2	no	—
70	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
71	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
72	#13063260	—	2	4	no	—
73	#13063260	—	2	4	no	—
74	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
75	#13063252	—	2	4	no	—
76	#13063252	—	2	4	no	—
77	#13063251	—	2	4	no	—
78	#13063251	—	2	4	no	—
79	(C₂×D₄₃)⋊C₈	—	2	4	no	—
80	#13063235	—	2	2	no	—
81	#13063235	D₄	1	4	yes	complemented
82	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₄₃	—	2	2	no	—
87	C₈×Dic₄₃	D₄	1	4	yes	complemented
88	C₄₃⋊#95	—	2	2	no	—
89	C₂×#41×C₄₃	C₂³	1	2	yes	—
90	#131×C₄₃	—	2	4	no	—
91	#131×C₄₃	—	2	4	no	—
92	C₂×M₁₆×C₄₃	—	2	2	no	—
93	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
94	C₂²×C₈×C₄₃	—	2	2	no	—
95	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
98	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
99	#124×C₄₃	C₂×C₄	1	2	yes	—
100	#121×C₄₃	—	2	2	no	—
101	C₄×D₄×C₄₃	—	2	2	no	—
102	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₄₃	—	2	2	no	—
104	C₂²⋊C₈×C₄₃	—	2	4	no	—
105	#97×C₄₃	D₄	1	4	yes	—
106	#41×C₄₃	—	2	2	no	—
107	#41×C₄₃	—	2	2	no	—
108	#41×C₄₃	—	2	2	no	—
109	#41×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	#41	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
117	C₂×C₂²⋊D₄₃	—	2	2	no	—
118	C₂²×Dic₄₃	—	2	1	no	—
119	C₂²×Dic₄₃	—	2	1	no	—
120	#10621898	—	2	2	no	—
121	#10621898	—	2	2	no	—
122	#10621898	—	2	2	no	—
123	#10621898	—	2	2	no	—
124	C₂×D₁₇₂	—	2	2	no	—
125	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
126	C₂×C₄×D₄₃	—	2	2	no	—
127	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
128	M₁₆×C₄₃	—	2	2	no	—
129	M₁₆×C₄₃	—	2	2	no	—
130	M₁₆×C₄₃	—	4	4	no	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	1	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	4	4	no	—
135	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₂²⋊C₄×C₄₃	—	2	4	no	—
141	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₄₃	C₂×D₄	1	2	yes	—
144	#10621885	—	2	4	no	—
145	#10621885	—	2	4	no	—
146	#10621884	—	2	4	no	—
147	#10621884	—	2	4	no	—
148	#10621883	—	2	4	no	—
149	#10621883	—	2	4	no	—
150	#10621882	—	2	4	no	—
151	#10621882	—	2	4	no	—
152	(C₂×D₄₃)⋊C₄	—	2	4	no	—
153	C₄⋊Dic₄₃	—	2	2	no	—
154	C₄×Dic₄₃	—	2	1	no	—
155	C₄×Dic₄₃	—	2	1	no	—
156	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
157	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
158	#10621877	—	2	2	no	—
159	#10621877	—	2	2	no	—
160	C₂×C₄₃⋊C₈	—	2	2	no	—
161	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
166	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
167	C₂×C₄₃⋊C₈	#41	1	2	yes	—
168	C₂×C₄₃⋊C₈	#41	1	2	yes	—
169	#10621872	—	4	4	no	—
170	C₈×D₄₃	—	4	4	no	—
171	C₂³×C₄₃	—	2	2	no	—
172	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
173	C₂²×D₄₃	—	2	2	no	—
174	Q₈×C₄₃	—	2	2	no	—
175	Q₈×C₄₃	—	2	2	no	—
176	D₄×C₄₃	—	2	2	no	—
177	D₄×C₄₃	—	2	2	no	—
178	D₄×C₄₃	—	4	2	no	—
179	D₄×C₄₃	—	4	2	no	—
180	D₄×C₄₃	—	8	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂²×D₄	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	C₂²⋊D₄₃	—	4	2	no	—
194	C₂²⋊D₄₃	—	4	2	no	—
195	C₂×Dic₄₃	—	2	2	no	—
196	C₂×Dic₄₃	—	2	2	no	—
197	C₂×Dic₄₃	—	2	2	no	—
198	C₂×Dic₄₃	—	4	2	no	—
199	C₂×Dic₄₃	—	4	2	no	—
200	D₁₇₂	—	2	2	no	—
201	D₁₇₂	—	2	2	no	—
202	D₁₇₂	—	8	2	no	—
203	C₄×D₄₃	—	4	2	no	—
204	C₄×D₄₃	—	4	2	no	—
205	Dic₈₆	—	2	2	no	—
206	Dic₈₆	—	2	2	no	—
207	C₈×C₄₃	—	2	2	no	—
208	C₈×C₄₃	—	4	2	no	—
209	C₈×C₄₃	#127	1	4	yes	—
210	C₄₃⋊C₈	—	4	2	no	—
211	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
212	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
213	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
214	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
215	#21707	—	43	1	no	maximal, Sylow
216	C₂²×C₄₃	—	2	2	no	—
217	C₂²×C₄₃	—	4	2	no	—
218	C₂²×C₄₃	—	4	4	no	—
219	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₄₃	#532	1	1	yes	characteristic
221	C₂²×C₄₃	#532	1	1	yes	characteristic
222	C₂×D₄₃	—	4	2	no	—
223	C₂×D₄₃	—	4	4	no	—
224	C₄×C₄₃	—	2	2	no	—
225	C₄×C₄₃	—	2	2	no	—
226	C₄×C₄₃	—	4	2	no	—
227	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
228	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
229	C₄×C₄₃	C₂×#127	1	1	yes	characteristic
230	C₄×C₄₃	#532	1	1	yes	characteristic
231	Dic₄₃	—	4	2	no	—
232	Dic₄₃	—	4	2	no	—
233	Dic₄₃	—	4	2	no	—
234	#3147	—	43	1	no	—
235	C₂×#444	—	43	2	no	—
236	C₂×#443	—	43	2	no	—
237	#2932	—	43	1	no	—
238	#2932	D₄₃	1	1	yes	characteristic, complemented
239	#1975	—	43	2	no	—
240	#1974	—	43	2	no	—
241	#1963	—	43	1	no	—
242	#1963	—	43	1	no	—
243	#1848	—	43	1	no	—
244	#1726	—	43	1	no	—
245	C₂×C₄₃	—	2	1	no	—
246	C₂×C₄₃	—	2	1	no	—
247	C₂×C₄₃	—	8	2	no	—
248	C₂×C₄₃	C₄×#127	1	1	yes	characteristic
249	C₂×C₄₃	#2957	1	2	yes	—
250	D₄₃	—	8	2	no	—
251	C₂×#135	—	43	2	no	—
252	C₂×#135	—	43	2	no	—
253	C₂×#131	—	43	2	no	—
254	C₂×#131	C₂×D₄₃	1	2	yes	—
255	#532	—	43	1	no	—
256	#532	C₂×D₄₃	1	1	yes	characteristic
257	#495	—	43	2	no	—
258	#495	—	43	2	no	—
259	#494	—	43	1	no	—
260	#493	—	43	1	no	—
261	#492	—	43	1	no	—
262	#492	—	43	1	no	—
263	#444	—	86	8	no	—
264	#443	—	86	8	no	—
265	#435	—	2	4	no	—
266	#435	—	86	4	no	—
267	C₂×#108	—	43	2	no	—
268	C₂×#108	—	43	2	no	—
269	#423	—	43	1	no	—
270	#423	C₂×D₄₃	1	1	yes	characteristic
271	C₂×#104	—	43	2	no	—
272	C₂×#104	—	43	2	no	—
273	C₂×#104	—	43	2	no	—
274	C₂×#104	—	43	2	no	—
275	#408	—	43	2	no	—
276	#408	C₂×D₄₃	1	2	yes	—
277	C₂×#97	—	43	1	no	—
278	C₂×#97	—	43	1	no	—
279	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
280	C₂×C₄×C₈	—	43	1	no	—
281	C₂×C₄×C₈	—	43	1	no	—
282	C₂×C₄×C₈	—	43	1	no	—
283	#376	—	43	1	no	—
284	C₄₃	#21707	1	1	yes	characteristic, complemented, Sylow
285	C₂×#41	—	43	2	no	—
286	C₂×#41	C₂²×D₄₃	1	2	yes	—
287	#135	—	86	4	no	—
288	#135	—	86	4	no	—
289	#135	—	86	4	no	—
290	#135	—	86	4	no	—
291	C₂×Q₁₆	—	43	2	no	—
292	C₂×Q₁₆	—	43	2	no	—
293	C₂×SD₁₆	—	43	2	no	—
294	C₂×SD₁₆	—	43	2	no	—
295	C₂×SD₁₆	—	43	2	no	—
296	C₂×SD₁₆	—	43	2	no	—
297	C₂×D₈	—	43	2	no	—
298	C₂×D₈	—	43	2	no	—
299	#131	—	2	4	no	—
300	#131	—	2	4	no	—
301	#131	—	86	4	no	—
302	#131	—	86	4	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	43	2	no	—
305	C₂×M₁₆	—	86	2	no	—
306	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	43	1	no	—
309	C₂²×C₈	—	43	1	no	—
310	C₂²×C₈	—	86	2	no	—
311	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
312	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
313	C₄⋊Q₈	—	43	1	no	—
314	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
315	#127	—	43	1	no	—
316	#127	C₄×D₄₃	1	1	yes	characteristic
317	#124	—	43	2	no	—
318	#124	C₄×D₄₃	1	2	yes	—
319	#121	—	2	2	no	—
320	#121	—	86	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	86	2	no	—
323	C₂×C₄²	—	43	1	no	—
324	C₂×C₄²	—	43	1	no	—
325	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
326	#108	—	86	4	no	—
327	#108	—	86	4	no	—
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	86	2	no	—
330	#104	—	86	4	no	—
331	#104	—	86	4	no	—
332	#104	—	86	4	no	—
333	#104	—	86	4	no	—
334	C₂²⋊C₈	—	2	4	no	—
335	C₂²⋊C₈	—	86	4	no	—
336	#97	—	43	4	no	—
337	#97	—	86	2	no	—
338	#97	C₂²⋊D₄₃	1	4	yes	—
339	C₄×C₈	—	43	4	no	—
340	C₄×C₈	—	43	1	no	—
341	C₄×C₈	—	43	1	no	—
342	C₄×C₈	—	43	1	no	—
343	C₄×C₈	—	43	1	no	—
344	C₄×C₈	—	86	2	no	—
345	#95	—	86	2	no	—
346	#41	—	2	2	no	—
347	#41	—	2	2	no	—
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	#41	—	86	2	no	—
351	#41	—	86	2	no	—
352	#41	—	86	2	no	—
353	#41	—	86	2	no	—
354	C₂×Q₈	—	43	2	no	—
355	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	43	2	no	—
359	C₂×D₄	—	86	2	no	—
360	C₂×D₄	—	86	2	no	—
361	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	86	1	no	—
364	C₂²×C₄	—	86	1	no	—
365	C₂²×C₄	—	86	2	no	—
366	C₂²×C₄	#10621898	1	2	yes	—
367	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
368	Q₁₆	—	86	4	no	—
369	Q₁₆	—	86	4	no	—
370	SD₁₆	—	86	4	no	—
371	SD₁₆	—	86	4	no	—
372	SD₁₆	—	86	4	no	—
373	SD₁₆	—	86	4	no	—
374	D₈	—	86	4	no	—
375	D₈	—	86	4	no	—
376	M₁₆	—	2	2	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	4	4	no	—
379	M₁₆	—	86	2	no	—
380	M₁₆	—	86	2	no	—
381	M₁₆	—	172	4	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	4	4	no	—
386	C₂×C₈	—	43	1	no	—
387	C₂×C₈	—	43	1	no	—
388	C₂×C₈	—	43	1	no	—
389	C₂×C₈	—	43	1	no	—
390	C₂×C₈	—	43	2	no	—
391	C₂×C₈	—	43	2	no	—
392	C₂×C₈	—	43	2	no	—
393	C₂×C₈	—	43	2	no	—
394	C₂×C₈	—	86	2	no	—
395	C₂×C₈	—	172	4	no	—
396	C₂×C₈	D₄×D₄₃	1	2	yes	—
397	C₂×C₈	D₄×D₄₃	1	2	yes	—
398	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
399	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	86	2	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	86	4	no	—
404	C₄²	—	43	2	no	—
405	C₄²	—	43	2	no	—
406	C₄²	—	86	1	no	—
407	C₄²	—	86	1	no	—
408	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
409	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
410	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
411	C₂³	—	2	2	no	—
412	C₂³	—	86	2	no	—
413	C₂³	C₂×#10621898	1	1	yes	characteristic
414	Q₈	—	2	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	86	2	no	—
417	Q₈	—	86	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	8	2	no	—
423	D₄	—	86	2	no	—
424	D₄	—	86	2	no	—
425	D₄	—	344	2	no	—
426	D₄	—	172	2	no	—
427	D₄	—	172	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	86	2	no	—
433	C₂×C₄	—	86	2	no	—
434	C₂×C₄	—	86	2	no	—
435	C₂×C₄	—	172	2	no	—
436	C₂×C₄	—	172	2	no	—
437	C₂×C₄	—	172	2	no	—
438	C₂×C₄	—	172	2	no	—
439	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
440	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
441	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
442	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
443	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
445	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
446	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
447	C₈	—	2	2	no	—
448	C₈	—	4	2	no	—
449	C₈	—	43	2	no	—
450	C₈	—	43	2	no	—
451	C₈	—	43	2	no	—
452	C₈	—	43	2	no	—
453	C₈	—	172	2	no	—
454	C₈	#13063321	1	4	yes	—
455	C₂²	—	2	2	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	172	4	no	—
459	C₂²	—	172	2	no	—
460	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
461	C₂²	#14583446	1	1	yes	characteristic
462	C₂²	#14583446	1	1	yes	characteristic
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	172	2	no	—
467	C₄	—	172	2	no	—
468	C₄	—	172	2	no	—
469	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
470	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
471	C₄	C₂×#13063321	1	1	yes	characteristic
472	C₄	#14583445	1	1	yes	characteristic
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	8	2	no	—
476	C₂	—	344	2	no	—
477	C₂	C₄×#13063321	1	1	yes	characteristic
478	C₂	#19143510	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2932	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19145021	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2932	D₄₃
hypocenter	C₄₃	#21707
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #2932

Complements

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

N	H ≅ G/N	type
2. C₂×#14583019	C₂	semidirect
3. C₂×#14583014	C₂	semidirect
4. #19143314	C₂	semidirect
5. #19135487	C₂	semidirect
6. #19135482	C₂	semidirect
7. #19135428	C₂	semidirect
8. #19135426	C₂	semidirect
9. #19134766	C₂	semidirect
10. #19134283	C₂	semidirect
11. C₄₃×#2932	C₂	semidirect
16. #14583281	C₄	semidirect
17. #14583281	C₄	semidirect
18. #14583278	C₄	semidirect
19. #14583275	C₄	semidirect
20. #14583273	C₄	semidirect
21. #14583271	C₄	semidirect
81. #13063235	D₄	semidirect
87. C₈×Dic₄₃	D₄	semidirect
238. #2932	D₄₃	semidirect
284. C₄₃	#21707	semidirect

Maximal subgroups

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

subgroup	index
#19145021	2
C₂×#14583019	2
C₂×#14583014	2
#19143314	2
#19135487	2
#19135482	2
#19135428	2
#19135426	2
#19134766	2
#19134283	2
C₄₃×#2932	2
#21707	43