Subgroups — #19143809

Order 5504.

764 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063345	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583406	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583060	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583058	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583053	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583048	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583043	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583041	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583036	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583031	C₂	1	1	yes	maximal, characteristic, complemented
12	#14582896	C₂	1	1	yes	maximal, characteristic, complemented
13	#14582895	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×(C₂×D₄₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#135×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10621902	C₂²	1	1	yes	characteristic
17	C₂×#10621898	—	2	1	no	—
18	C₂×#10621898	C₂²	1	1	yes	characteristic
19	C₂×#10621900	—	2	1	no	—
20	C₂×#10621900	C₂²	1	1	yes	characteristic
21	#41×D₄₃	—	2	4	no	—
22	#41×D₄₃	—	2	4	no	—
23	C₂×Q₈×D₄₃	C₂²	1	1	yes	characteristic
24	C₂×D₄×D₄₃	—	2	1	no	—
25	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₄₃	—	2	1	no	—
27	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
28	#13063345	—	2	4	no	—
29	C₂×#10621885	C₂²	1	1	yes	characteristic, complemented
30	C₂×#10621883	C₂²	1	1	yes	characteristic, complemented
31	C₂×#10621884	C₂²	1	1	yes	characteristic, complemented
32	C₂×#10621882	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	#13063306	—	2	1	no	—
35	#13063301	C₂²	1	1	yes	characteristic
36	#13063301	C₂²	1	1	yes	characteristic, complemented
37	#13063296	C₂²	1	1	yes	characteristic
38	#13063296	C₂²	1	1	yes	characteristic, complemented
39	#13063293	—	2	1	no	—
40	C₄×C₂²⋊D₄₃	—	2	1	no	—
41	C₄×C₂²⋊D₄₃	—	2	1	no	—
42	#13063284	C₂²	1	1	yes	characteristic, complemented
43	#13063250	C₂²	1	1	yes	characteristic, complemented
44	#13063250	C₂²	1	1	yes	characteristic, complemented
45	#13063249	C₂²	1	1	yes	characteristic, complemented
46	#13063249	C₂²	1	1	yes	characteristic, complemented
47	#13063247	C₂²	1	1	yes	characteristic, complemented
48	#13063247	C₂²	1	1	yes	characteristic, complemented
49	#13063246	C₂²	1	1	yes	characteristic, complemented
50	#13063246	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
52	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
53	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
57	#135×C₄₃	—	2	4	no	—
58	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
62	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₄₃	—	2	1	no	—
64	C₂³×D₄₃	D₄	1	1	yes	characteristic
65	#41×C₄₃	—	2	2	no	—
66	#41×C₄₃	—	2	2	no	—
67	#41×C₄₃	—	2	2	no	—
68	#41×C₄₃	D₄	1	4	yes	complemented
69	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₄₃	—	2	1	no	—
72	C₂×D₄×C₄₃	—	2	1	no	—
73	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	—	2	1	no	—
76	C₂²×C₄×C₄₃	—	2	1	no	—
77	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₂²⋊D₄₃	—	2	1	no	—
79	C₂×C₂²⋊D₄₃	—	2	1	no	—
80	C₂×C₂²⋊D₄₃	—	2	1	no	—
81	C₂×C₂²⋊D₄₃	—	2	1	no	—
82	C₂×C₂²⋊D₄₃	—	2	1	no	—
83	C₂²×Dic₄₃	—	2	1	no	—
84	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
85	#10621902	—	2	2	no	—
86	#10621902	—	2	2	no	—
87	Q₈×D₄₃	—	2	2	no	—
88	Q₈×D₄₃	—	2	2	no	—
89	#10621900	—	2	8	no	—
90	#10621900	—	2	2	no	—
91	#10621900	—	2	2	no	—
92	D₄×D₄₃	—	2	8	no	—
93	D₄×D₄₃	—	2	2	no	—
94	D₄×D₄₃	—	2	2	no	—
95	#10621898	—	2	8	no	—
96	#10621898	—	2	2	no	—
97	#10621898	D₄	1	4	yes	complemented
98	C₂×D₁₇₂	—	2	1	no	—
99	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₄₃	—	2	8	no	—
101	C₂×C₄×D₄₃	—	2	1	no	—
102	C₂×C₄×D₄₃	—	2	2	no	—
103	C₂×C₄×D₄₃	—	2	2	no	—
104	C₂×C₄×D₄₃	—	2	1	no	—
105	C₂×C₄×D₄₃	—	2	1	no	—
106	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
107	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
108	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
110	C₂×Dic₈₆	—	2	1	no	—
111	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
112	Q₁₆×C₄₃	—	2	2	no	—
113	SD₁₆×C₄₃	—	2	2	no	—
114	SD₁₆×C₄₃	—	2	2	no	—
115	D₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
118	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
119	C₂²⋊Dic₄₃	—	2	1	no	—
120	C₂²⋊Dic₄₃	—	2	1	no	—
121	C₂²⋊Dic₄₃	—	2	1	no	—
122	#10621885	—	2	2	no	—
123	#10621884	—	2	2	no	—
124	#10621883	—	2	2	no	—
125	#10621882	—	2	2	no	—
126	(C₂×D₄₃)⋊C₄	—	2	1	no	—
127	(C₂×D₄₃)⋊C₄	—	2	1	no	—
128	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
129	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
130	Dic₄₃⋊C₄	—	2	1	no	—
131	Dic₄₃⋊C₄	—	2	1	no	—
132	C₄×Dic₄₃	—	2	1	no	—
133	C₂×C₄₃⋊C₈	—	2	2	no	—
134	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
135	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
136	C₂³×C₄₃	—	2	1	no	—
137	C₂³×C₄₃	—	2	1	no	—
138	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×D₄₃	—	2	4	no	—
140	C₂²×D₄₃	—	2	2	no	—
141	C₂²×D₄₃	—	2	1	no	—
142	C₂²×D₄₃	—	2	2	no	—
143	C₂²×D₄₃	—	4	1	no	—
144	C₂²×D₄₃	—	4	2	no	—
145	C₂²×D₄₃	—	4	2	no	—
146	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
148	Q₈×C₄₃	—	2	1	no	—
149	Q₈×C₄₃	—	2	1	no	—
150	Q₈×C₄₃	—	2	1	no	—
151	Q₈×C₄₃	C₂×D₄	1	2	yes	—
152	D₄×C₄₃	—	2	4	no	—
153	D₄×C₄₃	—	2	1	no	—
154	D₄×C₄₃	—	2	1	no	—
155	D₄×C₄₃	—	2	1	no	—
156	D₄×C₄₃	—	4	2	no	—
157	D₄×C₄₃	C₂×D₄	1	2	yes	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
163	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
165	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₄₃	—	2	4	no	—
167	C₂²⋊D₄₃	—	2	4	no	—
168	C₂²⋊D₄₃	—	2	4	no	—
169	C₂²⋊D₄₃	—	4	2	no	—
170	C₂²⋊D₄₃	—	4	2	no	—
171	C₂×Dic₄₃	—	2	4	no	—
172	C₂×Dic₄₃	—	2	2	no	—
173	C₂×Dic₄₃	—	2	1	no	—
174	C₂×Dic₄₃	—	2	1	no	—
175	C₂×Dic₄₃	—	2	1	no	—
176	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
177	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
178	D₁₇₂	—	2	4	no	—
179	D₁₇₂	—	2	1	no	—
180	D₁₇₂	C₂×D₄	1	2	yes	—
181	C₄×D₄₃	—	2	4	no	—
182	C₄×D₄₃	—	2	4	no	—
183	C₄×D₄₃	—	2	2	no	—
184	C₄×D₄₃	—	2	4	no	—
185	C₄×D₄₃	—	2	2	no	—
186	C₄×D₄₃	—	2	1	no	—
187	C₄×D₄₃	—	2	1	no	—
188	C₄×D₄₃	—	2	1	no	—
189	C₄×D₄₃	—	2	1	no	—
190	Dic₈₆	—	2	4	no	—
191	Dic₈₆	—	2	1	no	—
192	Dic₈₆	C₂×D₄	1	2	yes	—
193	C₈×C₄₃	—	2	1	no	—
194	C₈×C₄₃	—	2	1	no	—
195	C₄₃⋊C₈	—	2	1	no	—
196	C₄₃⋊C₈	—	2	1	no	—
197	C₂²×C₄₃	—	2	1	no	—
198	C₂²×C₄₃	—	2	1	no	—
199	C₂²×C₄₃	—	2	2	no	—
200	C₂²×C₄₃	—	4	1	no	—
201	C₂²×C₄₃	—	4	1	no	—
202	C₂²×C₄₃	—	4	1	no	—
203	C₂²×C₄₃	—	4	1	no	—
204	C₂²×C₄₃	—	4	1	no	—
205	C₂²×C₄₃	#120	1	2	yes	—
206	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×D₄₃	—	2	1	no	—
208	C₂×D₄₃	—	2	1	no	—
209	C₂×D₄₃	—	2	2	no	—
210	C₂×D₄₃	—	2	1	no	—
211	C₂×D₄₃	—	2	1	no	—
212	C₂×D₄₃	—	2	1	no	—
213	C₂×D₄₃	—	4	4	no	—
214	C₂×D₄₃	—	4	8	no	—
215	C₂×D₄₃	—	4	1	no	—
216	C₂×D₄₃	—	4	1	no	—
217	C₂×D₄₃	#135	1	2	yes	complemented
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	4	1	no	—
220	C₄×C₄₃	#120	1	2	yes	—
221	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
222	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
223	Dic₄₃	—	2	1	no	—
224	Dic₄₃	—	2	2	no	—
225	Dic₄₃	—	2	1	no	—
226	Dic₄₃	—	4	1	no	—
227	Dic₄₃	—	4	1	no	—
228	#3002	—	43	1	no	maximal, Sylow
229	C₂×C₄₃	—	2	2	no	—
230	C₂×C₄₃	—	4	2	no	—
231	C₂×C₄₃	—	8	1	no	—
232	C₂×C₄₃	C₂×#120	1	1	yes	characteristic
233	C₂×C₄₃	C₂×#135	1	1	yes	characteristic
234	C₂×C₄₃	#575	1	1	yes	characteristic
235	D₄₃	—	2	2	no	—
236	D₄₃	—	4	1	no	—
237	D₄₃	—	4	2	no	—
238	C₂²×#41	—	43	1	no	—
239	C₂×#135	—	43	1	no	—
240	C₂×#135	D₄₃	1	1	yes	characteristic, complemented
241	#525	—	43	1	no	—
242	#452	—	43	1	no	—
243	#452	—	43	1	no	—
244	#451	—	43	1	no	—
245	#450	—	43	1	no	—
246	#449	—	43	1	no	—
247	#449	—	43	1	no	—
248	#448	—	43	1	no	—
249	#447	—	43	1	no	—
250	#416	—	43	1	no	—
251	#416	—	43	1	no	—
252	C₂×C₂²⋊C₈	—	43	1	no	—
253	C₄₃	#3002	1	1	yes	characteristic, complemented, Sylow
254	C₂×#41	—	43	1	no	—
255	C₂×#41	—	43	1	no	—
256	C₂×#41	—	43	1	no	—
257	C₂×#41	—	86	1	no	—
258	C₂×#41	—	86	1	no	—
259	C₂×#41	—	86	4	no	—
260	C₂×#41	—	86	4	no	—
261	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
262	C₂×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
263	C₂²×Q₈	—	43	1	no	—
264	C₂²×D₄	—	43	1	no	—
265	C₂²×D₄	—	86	1	no	—
266	C₂³×C₄	—	43	1	no	—
267	C₂³×C₄	—	86	1	no	—
268	#135	—	2	4	no	—
269	#135	—	86	4	no	—
270	C₂×Q₁₆	—	43	1	no	—
271	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
272	C₂×SD₁₆	—	43	1	no	—
273	C₂×SD₁₆	—	43	1	no	—
274	C₂×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
275	C₂×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
276	C₂×D₈	—	43	1	no	—
277	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
278	C₂²×C₈	—	43	1	no	—
279	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
280	#123	—	86	1	no	—
281	C₂²⋊Q₈	—	43	1	no	—
282	C₂²⋊Q₈	—	43	1	no	—
283	#121	—	43	1	no	—
284	#121	—	43	1	no	—
285	#120	—	86	1	no	—
286	C₄×D₄	—	86	1	no	—
287	C₄×D₄	—	86	1	no	—
288	#117	—	43	1	no	—
289	#103	—	43	1	no	—
290	#103	—	43	1	no	—
291	#103	—	43	1	no	—
292	#103	—	43	1	no	—
293	#102	—	43	1	no	—
294	#102	—	43	1	no	—
295	#102	—	43	1	no	—
296	#102	—	43	1	no	—
297	C₂²⋊C₈	—	43	1	no	—
298	C₂²⋊C₈	—	43	1	no	—
299	C₂²⋊C₈	—	43	1	no	—
300	C₂²⋊C₈	—	43	1	no	—
301	C₂⁴	—	43	1	no	—
302	C₂⁴	—	86	1	no	—
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	2	2	no	—
306	#41	—	43	4	no	—
307	#41	—	86	8	no	—
308	#41	—	86	2	no	—
309	#41	—	86	8	no	—
310	#41	—	86	2	no	—
311	#41	—	86	2	no	—
312	#41	—	86	2	no	—
313	#41	—	86	2	no	—
314	#41	C₂²⋊D₄₃	1	4	yes	complemented
315	C₂×Q₈	—	43	1	no	—
316	C₂×Q₈	—	86	1	no	—
317	C₂×Q₈	—	86	2	no	—
318	C₂×Q₈	—	86	2	no	—
319	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
320	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	43	1	no	—
324	C₂×D₄	—	86	1	no	—
325	C₂×D₄	—	86	1	no	—
326	C₂×D₄	—	86	2	no	—
327	C₂×D₄	—	86	8	no	—
328	C₂×D₄	—	86	1	no	—
329	C₂×D₄	—	86	1	no	—
330	C₂×D₄	—	86	2	no	—
331	C₂×D₄	—	86	1	no	—
332	C₂×D₄	—	86	1	no	—
333	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
334	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	43	1	no	—
338	C₂²×C₄	—	43	1	no	—
339	C₂²×C₄	—	43	1	no	—
340	C₂²×C₄	—	43	1	no	—
341	C₂²×C₄	—	43	1	no	—
342	C₂²×C₄	—	86	1	no	—
343	C₂²×C₄	—	86	1	no	—
344	C₂²×C₄	—	86	8	no	—
345	C₂²×C₄	—	86	1	no	—
346	C₂²×C₄	—	86	2	no	—
347	C₂²×C₄	—	86	1	no	—
348	C₂²×C₄	—	86	2	no	—
349	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
350	Q₁₆	—	2	2	no	—
351	Q₁₆	—	86	2	no	—
352	SD₁₆	—	2	2	no	—
353	SD₁₆	—	2	2	no	—
354	SD₁₆	—	86	2	no	—
355	SD₁₆	—	86	2	no	—
356	D₈	—	2	2	no	—
357	D₈	—	86	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	43	1	no	—
360	C₂×C₈	—	43	1	no	—
361	C₂×C₈	—	86	2	no	—
362	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
363	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
364	C₄⋊C₄	—	43	1	no	—
365	C₄⋊C₄	—	43	1	no	—
366	C₄⋊C₄	—	86	1	no	—
367	C₄⋊C₄	—	86	1	no	—
368	C₂²⋊C₄	—	86	1	no	—
369	C₂²⋊C₄	—	86	1	no	—
370	C₂²⋊C₄	—	86	1	no	—
371	C₂²⋊C₄	—	86	1	no	—
372	C₂²⋊C₄	—	86	1	no	—
373	C₄²	—	86	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	43	1	no	—
377	C₂³	—	43	1	no	—
378	C₂³	—	86	2	no	—
379	C₂³	—	86	4	no	—
380	C₂³	—	86	2	no	—
381	C₂³	—	86	1	no	—
382	C₂³	—	172	1	no	—
383	C₂³	—	172	2	no	—
384	C₂³	—	172	2	no	—
385	C₂³	D₄×D₄₃	1	1	yes	characteristic
386	Q₈	—	2	1	no	—
387	Q₈	—	2	1	no	—
388	Q₈	—	2	1	no	—
389	Q₈	—	43	2	no	—
390	Q₈	—	86	4	no	—
391	Q₈	—	86	1	no	—
392	Q₈	C₂×C₂²⋊D₄₃	1	2	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	1	no	—
395	D₄	—	2	1	no	—
396	D₄	—	2	1	no	—
397	D₄	—	4	2	no	—
398	D₄	—	43	2	no	—
399	D₄	—	86	4	no	—
400	D₄	—	86	4	no	—
401	D₄	—	86	4	no	—
402	D₄	—	86	4	no	—
403	D₄	—	86	1	no	—
404	D₄	—	172	2	no	—
405	D₄	—	172	2	no	—
406	D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	43	1	no	—
412	C₂×C₄	—	43	1	no	—
413	C₂×C₄	—	86	4	no	—
414	C₂×C₄	—	86	4	no	—
415	C₂×C₄	—	86	4	no	—
416	C₂×C₄	—	86	2	no	—
417	C₂×C₄	—	86	1	no	—
418	C₂×C₄	—	86	2	no	—
419	C₂×C₄	—	86	2	no	—
420	C₂×C₄	—	86	4	no	—
421	C₂×C₄	—	86	1	no	—
422	C₂×C₄	—	86	1	no	—
423	C₂×C₄	—	86	1	no	—
424	C₂×C₄	—	86	1	no	—
425	C₂×C₄	—	86	1	no	—
426	C₂×C₄	—	86	1	no	—
427	C₂×C₄	D₄×D₄₃	1	2	yes	—
428	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
430	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	86	1	no	—
434	C₈	—	86	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	43	2	no	—
444	C₂²	—	86	1	no	—
445	C₂²	—	86	1	no	—
446	C₂²	—	86	2	no	—
447	C₂²	—	86	1	no	—
448	C₂²	—	86	1	no	—
449	C₂²	—	86	1	no	—
450	C₂²	—	172	4	no	—
451	C₂²	—	172	8	no	—
452	C₂²	—	172	1	no	—
453	C₂²	—	172	1	no	—
454	C₂²	#13063293	1	2	yes	—
455	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	4	1	no	—
458	C₄	—	86	1	no	—
459	C₄	—	86	1	no	—
460	C₄	—	86	2	no	—
461	C₄	—	172	1	no	—
462	C₄	—	172	1	no	—
463	C₄	#13063293	1	2	yes	—
464	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
465	C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
466	C₂	—	2	2	no	—
467	C₂	—	4	2	no	—
468	C₂	—	8	1	no	—
469	C₂	—	86	2	no	—
470	C₂	—	172	1	no	—
471	C₂	—	172	2	no	—
472	C₂	C₂×#13063293	1	1	yes	characteristic
473	C₂	#135×D₄₃	1	1	yes	characteristic
474	C₂	#14583696	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×#135×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	C₂×#135	D₄₃
hypocenter	C₄₃	#3002
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₄₃	C₂	semidirect
2. C₂×#13063345	C₂	semidirect
3. #14583406	C₂	semidirect
4. #14583060	C₂	semidirect
5. #14583058	C₂	semidirect
6. #14583053	C₂	semidirect
7. #14583048	C₂	semidirect
8. #14583043	C₂	semidirect
9. #14583041	C₂	semidirect
10. #14583036	C₂	semidirect
11. #14583031	C₂	semidirect
12. #14582896	C₂	semidirect
13. #14582895	C₂	semidirect
14. C₂×(C₂×D₄₃)⋊C₈	C₂	semidirect
15. C₂×#135×C₄₃	C₂	semidirect
29. C₂×#10621885	C₂²	semidirect
30. C₂×#10621883	C₂²	semidirect
31. C₂×#10621884	C₂²	semidirect
32. C₂×#10621882	C₂²	semidirect
33. C₂²×C₄₃⋊C₈	C₂²	semidirect
36. #13063301	C₂²	semidirect
38. #13063296	C₂²	semidirect
42. #13063284	C₂²	semidirect
43. #13063250	C₂²	semidirect
44. #13063250	C₂²	semidirect
45. #13063249	C₂²	semidirect
46. #13063249	C₂²	semidirect
47. #13063247	C₂²	semidirect
48. #13063247	C₂²	semidirect
49. #13063246	C₂²	semidirect
50. #13063246	C₂²	semidirect
53. (C₂×D₄₃)⋊C₈	C₂²	semidirect
54. (C₂×D₄₃)⋊C₈	C₂²	semidirect
56. C₂×#41×C₄₃	C₂²	semidirect
58. C₂×Q₁₆×C₄₃	C₂²	semidirect
59. C₂×SD₁₆×C₄₃	C₂²	semidirect
60. C₂×SD₁₆×C₄₃	C₂²	semidirect
61. C₂×D₈×C₄₃	C₂²	semidirect
62. C₂²×C₈×C₄₃	C₂²	semidirect
68. #41×C₄₃	D₄	semidirect
97. #10621898	D₄	semidirect
217. C₂×D₄₃	#135	semidirect
240. C₂×#135	D₄₃	semidirect
253. C₄₃	#3002	semidirect
262. C₂×#41	C₂×D₄₃	semidirect
271. C₂×Q₁₆	C₂×D₄₃	semidirect
274. C₂×SD₁₆	C₂×D₄₃	semidirect
275. C₂×SD₁₆	C₂×D₄₃	semidirect
277. C₂×D₈	C₂×D₄₃	semidirect
279. C₂²×C₈	C₂×D₄₃	semidirect
314. #41	C₂²⋊D₄₃	semidirect