Subgroups — #19148643

Order 5504.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583609	C₂	1	2	yes	maximal, complemented
2	#14583588	C₂	1	2	yes	maximal, complemented
3	#14583574	C₂	1	4	yes	maximal, complemented
4	Q₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583559	C₂	1	2	yes	maximal, complemented
6	#14583554	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583552	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583542	C₂	1	2	yes	maximal, complemented
9	#14583518	C₂	1	2	yes	maximal, complemented
10	#14583490	C₂	1	4	yes	maximal, complemented
11	#14583454	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583436	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583411	C₂	1	2	yes	maximal, complemented
14	C₂²⋊Q₈×D₄₃	C₂	1	2	yes	maximal, complemented
15	#14583381	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621902	C₂²	1	2	yes	—
19	C₂×#10621898	C₂²	1	2	yes	complemented
20	C₂×Q₈×D₄₃	C₂²	1	2	yes	complemented
21	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₄₃	C₂²	1	2	yes	—
23	#13063325	C₂²	1	1	yes	characteristic, complemented
24	#13063325	C₂²	1	2	yes	complemented
25	#13063320	C₂²	1	2	yes	complemented
26	#13063318	C₂²	1	4	yes	complemented
27	#13063317	C₂²	1	4	yes	complemented
28	#13063316	C₂²	1	1	yes	characteristic, complemented
29	#13063316	C₂²	1	2	yes	complemented
30	#13063314	C₂²	1	1	yes	characteristic, complemented
31	#13063311	C₂²	1	4	yes	complemented
32	#13063310	C₂²	1	2	yes	—
33	#13063310	C₂²	1	4	yes	complemented
34	#13063309	C₂²	1	4	yes	complemented
35	#13063307	C₂²	1	4	yes	—
36	#13063307	C₂²	1	4	yes	complemented
37	#13063305	C₂²	1	2	yes	—
38	#13063305	C₂²	1	4	yes	complemented
39	#13063305	C₂²	1	2	yes	complemented
40	#13063304	C₂²	1	2	yes	complemented
41	#13063303	C₂²	1	4	yes	—
42	#13063303	C₂²	1	4	yes	complemented
43	#13063302	C₂²	1	4	yes	complemented
44	#13063301	C₂²	1	2	yes	—
45	#13063301	C₂²	1	1	yes	characteristic
46	#13063301	C₂²	1	2	yes	complemented
47	#13063300	C₂²	1	1	yes	characteristic
48	#13063300	C₂²	1	2	yes	complemented
49	#13063298	C₂²	1	4	yes	—
50	#13063296	C₂²	1	2	yes	—
51	#13063295	C₂²	1	4	yes	—
52	Q₈×Dic₄₃	C₂²	1	2	yes	complemented
53	#13063290	C₂²	1	2	yes	complemented
54	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
55	C₄×D₁₇₂	C₂²	1	2	yes	—
56	C₄×D₁₇₂	C₂²	1	4	yes	—
57	C₄×D₁₇₂	C₂²	1	2	yes	—
58	C₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
59	C₄×D₁₇₂	C₂²	1	4	yes	complemented
60	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
61	#13063287	C₂²	1	1	yes	characteristic
62	#13063287	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
64	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
65	#13063283	C₂²	1	2	yes	—
66	#13063282	C₂²	1	4	yes	complemented
67	#13063282	C₂²	1	2	yes	complemented
68	C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic
69	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₄₃	C₂²	1	4	yes	complemented
72	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	—
74	C₄²×D₄₃	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
76	#126×C₄₃	C₂²	1	4	yes	complemented
77	#124×C₄₃	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×Q₈×C₄₃	C₂²	1	2	yes	complemented
81	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
82	#117×C₄₃	C₂²	1	2	yes	complemented
83	C₂³×D₄₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
86	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
90	C₂²×Dic₄₃	C₂³	1	2	yes	—
91	#10621902	—	2	8	no	—
92	Q₈×D₄₃	—	4	4	no	—
93	D₄×D₄₃	—	2	4	no	—
94	#10621898	—	4	4	no	—
95	C₂×D₁₇₂	C₂³	1	4	yes	—
96	C₂×D₁₇₂	C₂³	1	2	yes	—
97	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
98	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₄₃	—	4	4	no	—
100	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₄₃	C₂³	1	4	yes	—
104	C₂×C₄×D₄₃	C₂³	1	2	yes	—
105	C₂×C₄×D₄₃	C₂³	1	2	yes	—
106	C₂×C₄×D₄₃	C₂³	1	2	yes	—
107	C₂×C₄×D₄₃	C₂³	1	4	yes	—
108	C₂×C₄×D₄₃	C₂³	1	2	yes	—
109	C₂×C₄×D₄₃	C₂³	1	4	yes	—
110	C₂×Dic₈₆	C₂³	1	2	yes	—
111	C₂×Dic₈₆	C₂³	1	4	yes	—
112	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
114	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
116	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
117	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
119	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
121	C₄²×C₄₃	C₂³	1	4	yes	—
122	C₄²×C₄₃	C₂³	1	1	yes	characteristic
123	C₄²×C₄₃	C₂³	1	2	yes	—
124	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
125	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
126	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
134	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
135	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
136	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₄₃	C₂³	1	2	yes	—
139	C₄⋊Dic₄₃	C₂³	1	4	yes	—
140	C₄⋊Dic₄₃	C₂³	1	2	yes	—
141	C₄⋊Dic₄₃	C₂³	1	4	yes	—
142	C₄⋊Dic₄₃	C₂³	1	2	yes	—
143	Dic₄₃⋊C₄	C₂³	1	2	yes	—
144	Dic₄₃⋊C₄	C₂³	1	2	yes	—
145	Dic₄₃⋊C₄	C₂³	1	4	yes	—
146	Dic₄₃⋊C₄	C₂³	1	4	yes	—
147	Dic₄₃⋊C₄	C₂³	1	2	yes	—
148	Dic₄₃⋊C₄	C₂³	1	4	yes	—
149	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
150	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
151	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
152	C₄×Dic₄₃	C₂³	1	4	yes	—
153	C₂³×C₄₃	C₂⁴	1	2	yes	—
154	C₂²×D₄₃	—	2	4	no	—
155	C₂²×D₄₃	—	2	4	no	—
156	C₂²×D₄₃	—	4	2	no	—
157	C₂²×D₄₃	C₂⁴	1	2	yes	—
158	C₂²×D₄₃	C₂⁴	1	2	yes	—
159	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
160	Q₈×C₄₃	—	2	4	no	—
161	Q₈×C₄₃	—	2	2	no	—
162	D₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
165	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₄₃	—	2	4	no	—
172	C₂²⋊D₄₃	—	4	4	no	—
173	C₂×Dic₄₃	—	4	2	no	—
174	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₄₃	C₂⁴	1	4	yes	—
178	C₂×Dic₄₃	C₂⁴	1	2	yes	—
179	C₂×Dic₄₃	C₂⁴	1	2	yes	—
180	D₁₇₂	—	2	8	no	—
181	D₁₇₂	—	2	4	no	—
182	D₁₇₂	—	2	2	no	—
183	D₁₇₂	#41	1	4	yes	complemented
184	C₄×D₄₃	—	2	8	no	—
185	C₄×D₄₃	—	2	2	no	—
186	C₄×D₄₃	—	2	2	no	—
187	C₄×D₄₃	—	2	4	no	—
188	C₄×D₄₃	—	2	2	no	—
189	C₄×D₄₃	—	2	4	no	—
190	C₄×D₄₃	—	4	2	no	—
191	C₄×D₄₃	—	4	2	no	—
192	C₄×D₄₃	—	4	4	no	—
193	C₄×D₄₃	—	4	4	no	—
194	Dic₈₆	—	2	4	no	—
195	Dic₈₆	—	4	4	no	—
196	C₂²×C₄₃	—	2	2	no	—
197	C₂²×C₄₃	—	2	2	no	—
198	C₂²×C₄₃	—	2	2	no	—
199	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
200	C₂×D₄₃	—	2	1	no	—
201	C₂×D₄₃	—	2	1	no	—
202	C₂×D₄₃	—	2	2	no	—
203	C₂×D₄₃	—	2	2	no	—
204	C₂×D₄₃	—	2	2	no	—
205	C₂×D₄₃	—	2	2	no	—
206	C₂×D₄₃	—	2	2	no	—
207	C₂×D₄₃	—	4	8	no	—
208	C₂×D₄₃	C₂×#41	1	4	yes	—
209	C₂×D₄₃	2₋¹⁺⁴	1	2	yes	—
210	C₄×C₄₃	—	2	4	no	—
211	C₄×C₄₃	—	2	2	no	—
212	C₄×C₄₃	—	2	2	no	—
213	C₄×C₄₃	—	2	1	no	—
214	C₄×C₄₃	—	2	2	no	—
215	C₄×C₄₃	C₂×#41	1	2	yes	—
216	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
217	Dic₄₃	—	2	2	no	—
218	Dic₄₃	—	2	1	no	—
219	Dic₄₃	—	2	4	no	—
220	Dic₄₃	—	2	2	no	—
221	Dic₄₃	—	2	1	no	—
222	Dic₄₃	—	2	1	no	—
223	#3520	—	43	1	no	maximal, Sylow
224	C₂×C₄₃	—	4	2	no	—
225	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
226	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
228	D₄₃	—	2	2	no	—
229	D₄₃	—	2	4	no	—
230	D₄₃	—	4	2	no	—
231	#556	D₄₃	1	1	yes	characteristic, complemented
232	#554	—	43	2	no	—
233	#552	—	43	2	no	—
234	#551	—	43	4	no	—
235	D₄×Q₈	—	43	1	no	—
236	#548	—	43	2	no	—
237	#547	—	43	1	no	—
238	#547	—	43	1	no	—
239	#546	—	43	2	no	—
240	#542	—	43	2	no	—
241	#539	—	43	4	no	—
242	#533	—	43	1	no	—
243	#529	—	43	1	no	—
244	#525	—	43	2	no	—
245	C₂×C₂²⋊Q₈	—	43	2	no	—
246	#520	—	43	2	no	—
247	C₂×C₄×D₄	—	43	1	no	—
248	C₄₃	#3520	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	—	43	2	no	—
250	C₂×#41	—	43	2	no	—
251	C₂²×Q₈	—	43	2	no	—
252	C₂²×D₄	—	43	1	no	—
253	C₂³×C₄	—	43	2	no	—
254	C₄⋊Q₈	—	43	1	no	—
255	C₄⋊Q₈	—	43	2	no	—
256	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
257	#126	—	43	2	no	—
258	#126	—	43	4	no	—
259	#126	C₂×D₄₃	1	4	yes	complemented
260	#125	—	43	1	no	—
261	#125	—	43	2	no	—
262	#125	—	43	4	no	—
263	#124	—	43	1	no	—
264	#124	—	43	4	no	—
265	#124	C₂×D₄₃	1	2	yes	—
266	#123	—	43	2	no	—
267	#123	—	43	4	no	—
268	#123	—	43	4	no	—
269	#123	—	43	4	no	—
270	#123	—	43	4	no	—
271	C₂²⋊Q₈	—	43	1	no	—
272	C₂²⋊Q₈	—	43	2	no	—
273	C₂²⋊Q₈	—	43	2	no	—
274	C₂²⋊Q₈	—	43	2	no	—
275	C₂²⋊Q₈	—	43	2	no	—
276	C₂²⋊Q₈	—	43	4	no	—
277	C₂²⋊Q₈	—	43	2	no	—
278	C₂²⋊Q₈	—	43	4	no	—
279	C₂²⋊Q₈	—	43	4	no	—
280	C₂²⋊Q₈	—	43	4	no	—
281	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	complemented
282	#121	—	43	2	no	—
283	#121	—	43	1	no	—
284	#121	—	43	2	no	—
285	#121	—	43	4	no	—
286	#120	—	43	4	no	—
287	C₄×Q₈	—	43	2	no	—
288	C₄×Q₈	—	43	2	no	—
289	C₄×Q₈	C₂×D₄₃	1	2	yes	complemented
290	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
291	C₄×D₄	—	43	1	no	—
292	C₄×D₄	—	43	2	no	—
293	C₄×D₄	—	43	1	no	—
294	C₄×D₄	—	43	4	no	—
295	C₄×D₄	—	43	2	no	—
296	C₄×D₄	—	43	1	no	—
297	C₄×D₄	—	43	4	no	—
298	C₄×D₄	—	43	2	no	—
299	C₄×D₄	—	43	4	no	—
300	C₄×D₄	—	43	2	no	—
301	C₄×D₄	—	43	1	no	—
302	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
303	#117	—	43	2	no	—
304	#117	—	43	2	no	—
305	#117	—	43	4	no	—
306	#117	C₂×D₄₃	1	2	yes	complemented
307	C₂×C₄⋊C₄	—	43	1	no	—
308	C₂×C₄⋊C₄	—	43	4	no	—
309	C₂×C₄⋊C₄	—	43	2	no	—
310	C₂×C₄⋊C₄	—	43	2	no	—
311	C₂×C₂²⋊C₄	—	43	2	no	—
312	C₂×C₂²⋊C₄	—	43	4	no	—
313	C₂×C₄²	—	43	1	no	—
314	C₂⁴	—	43	2	no	—
315	#41	—	86	8	no	—
316	#41	—	172	4	no	—
317	C₂×Q₈	—	43	2	no	—
318	C₂×Q₈	—	43	4	no	—
319	C₂×Q₈	—	172	4	no	—
320	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
321	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
322	C₂×D₄	—	43	2	no	—
323	C₂×D₄	—	43	4	no	—
324	C₂×D₄	—	43	1	no	—
325	C₂×D₄	—	43	2	no	—
326	C₂×D₄	—	43	4	no	—
327	C₂×D₄	—	43	1	no	—
328	C₂×D₄	—	86	4	no	—
329	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
330	C₂²×C₄	—	43	2	no	—
331	C₂²×C₄	—	43	1	no	—
332	C₂²×C₄	—	43	1	no	—
333	C₂²×C₄	—	43	1	no	—
334	C₂²×C₄	—	43	4	no	—
335	C₂²×C₄	—	43	2	no	—
336	C₂²×C₄	—	43	2	no	—
337	C₂²×C₄	—	43	4	no	—
338	C₂²×C₄	—	43	2	no	—
339	C₂²×C₄	—	43	2	no	—
340	C₂²×C₄	—	43	4	no	—
341	C₂²×C₄	—	172	4	no	—
342	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
343	C₄⋊C₄	—	43	2	no	—
344	C₄⋊C₄	—	43	4	no	—
345	C₄⋊C₄	—	43	1	no	—
346	C₄⋊C₄	—	43	2	no	—
347	C₄⋊C₄	—	43	1	no	—
348	C₄⋊C₄	—	43	2	no	—
349	C₄⋊C₄	—	43	4	no	—
350	C₄⋊C₄	—	43	4	no	—
351	C₄⋊C₄	—	43	2	no	—
352	C₄⋊C₄	—	43	2	no	—
353	C₄⋊C₄	—	43	4	no	—
354	C₄⋊C₄	—	43	2	no	—
355	C₄⋊C₄	—	43	4	no	—
356	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
358	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
359	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
360	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
361	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
362	C₂²⋊C₄	—	43	2	no	—
363	C₂²⋊C₄	—	43	4	no	—
364	C₂²⋊C₄	—	43	2	no	—
365	C₂²⋊C₄	—	43	2	no	—
366	C₂²⋊C₄	—	43	4	no	—
367	C₂²⋊C₄	—	43	2	no	—
368	C₂²⋊C₄	—	43	4	no	—
369	C₂²⋊C₄	—	43	2	no	—
370	C₂²⋊C₄	—	43	2	no	—
371	C₂²⋊C₄	—	43	2	no	—
372	C₂²⋊C₄	—	43	4	no	—
373	C₂²⋊C₄	—	43	2	no	—
374	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
376	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
377	C₄²	—	43	1	no	—
378	C₄²	—	43	1	no	—
379	C₄²	—	43	1	no	—
380	C₄²	—	43	4	no	—
381	C₄²	C₂²×D₄₃	1	1	yes	characteristic
382	C₄²	C₂²×D₄₃	1	4	yes	—
383	C₄²	C₂²×D₄₃	1	2	yes	—
384	C₂³	—	43	1	no	—
385	C₂³	—	43	2	no	—
386	C₂³	—	43	2	no	—
387	C₂³	—	86	4	no	—
388	C₂³	—	86	4	no	—
389	C₂³	—	172	2	no	—
390	C₂³	C₂³×D₄₃	1	2	yes	—
391	Q₈	—	2	4	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	86	4	no	—
394	Q₈	—	172	4	no	—
395	D₄	—	2	2	no	—
396	D₄	—	43	4	no	—
397	D₄	—	86	8	no	—
398	D₄	—	86	4	no	—
399	D₄	—	86	4	no	—
400	D₄	—	86	2	no	—
401	D₄	—	172	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	43	1	no	—
404	C₂×C₄	—	43	1	no	—
405	C₂×C₄	—	43	1	no	—
406	C₂×C₄	—	43	4	no	—
407	C₂×C₄	—	43	2	no	—
408	C₂×C₄	—	43	2	no	—
409	C₂×C₄	—	86	8	no	—
410	C₂×C₄	—	86	2	no	—
411	C₂×C₄	—	86	2	no	—
412	C₂×C₄	—	86	4	no	—
413	C₂×C₄	—	86	2	no	—
414	C₂×C₄	—	86	4	no	—
415	C₂×C₄	—	172	2	no	—
416	C₂×C₄	—	172	2	no	—
417	C₂×C₄	—	172	4	no	—
418	C₂×C₄	—	172	4	no	—
419	C₂×C₄	—	172	2	no	—
420	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₄₃	1	4	yes	—
422	C₂×C₄	C₂³×D₄₃	1	2	yes	—
423	C₂×C₄	C₂³×D₄₃	1	2	yes	—
424	C₂×C₄	C₂³×D₄₃	1	2	yes	—
425	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	43	4	no	—
431	C₂²	—	43	2	no	—
432	C₂²	—	86	1	no	—
433	C₂²	—	86	2	no	—
434	C₂²	—	86	1	no	—
435	C₂²	—	86	2	no	—
436	C₂²	—	86	2	no	—
437	C₂²	—	86	2	no	—
438	C₂²	—	86	2	no	—
439	C₂²	—	172	8	no	—
440	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	86	2	no	—
447	C₄	—	86	1	no	—
448	C₄	—	86	1	no	—
449	C₄	—	86	2	no	—
450	C₄	—	86	4	no	—
451	C₄	—	86	1	no	—
452	C₄	#41×D₄₃	1	2	yes	—
453	C₄	#13063371	1	2	yes	—
454	C₂	—	4	2	no	—
455	C₂	—	86	2	no	—
456	C₂	—	86	4	no	—
457	C₂	—	172	2	no	—
458	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
459	C₂	C₂×#13063371	1	1	yes	characteristic
460	C₂	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#556	C₂
hypercenter	#556	D₄₃
hypocenter	C₄₃	#3520
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #14583609	C₂	semidirect
2. #14583588	C₂	semidirect
3. #14583574	C₂	semidirect
4. Q₈×D₁₇₂	C₂	semidirect
5. #14583559	C₂	semidirect
6. #14583554	C₂	semidirect
7. #14583552	C₂	semidirect
8. #14583542	C₂	semidirect
9. #14583518	C₂	semidirect
10. #14583490	C₂	semidirect
11. #14583454	C₂	semidirect
12. #14583436	C₂	semidirect
13. #14583411	C₂	semidirect
14. C₂²⋊Q₈×D₄₃	C₂	semidirect
15. #14583381	C₂	semidirect
16. C₄×D₄×D₄₃	C₂	semidirect
17. C₄₃×#556	C₂	semidirect
19. C₂×#10621898	C₂²	semidirect
20. C₂×Q₈×D₄₃	C₂²	semidirect
23. #13063325	C₂²	semidirect
24. #13063325	C₂²	semidirect
25. #13063320	C₂²	semidirect
26. #13063318	C₂²	semidirect
27. #13063317	C₂²	semidirect
28. #13063316	C₂²	semidirect
29. #13063316	C₂²	semidirect
30. #13063314	C₂²	semidirect
31. #13063311	C₂²	semidirect
33. #13063310	C₂²	semidirect
34. #13063309	C₂²	semidirect
36. #13063307	C₂²	semidirect
38. #13063305	C₂²	semidirect
39. #13063305	C₂²	semidirect
40. #13063304	C₂²	semidirect
42. #13063303	C₂²	semidirect
43. #13063302	C₂²	semidirect
46. #13063301	C₂²	semidirect
48. #13063300	C₂²	semidirect
52. Q₈×Dic₄₃	C₂²	semidirect
53. #13063290	C₂²	semidirect
58. C₄×D₁₇₂	C₂²	semidirect
59. C₄×D₁₇₂	C₂²	semidirect
62. #13063287	C₂²	semidirect
66. #13063282	C₂²	semidirect
67. #13063282	C₂²	semidirect
69. C₄⋊C₄×D₄₃	C₂²	semidirect
70. C₄⋊C₄×D₄₃	C₂²	semidirect
71. C₄⋊C₄×D₄₃	C₂²	semidirect
75. C₄⋊Q₈×C₄₃	C₂²	semidirect
76. #126×C₄₃	C₂²	semidirect
78. C₂²⋊Q₈×C₄₃	C₂²	semidirect
79. C₄×Q₈×C₄₃	C₂²	semidirect
80. C₄×Q₈×C₄₃	C₂²	semidirect
82. #117×C₄₃	C₂²	semidirect
183. D₁₇₂	#41	semidirect
231. #556	D₄₃	semidirect
248. C₄₃	#3520	semidirect
256. C₄⋊Q₈	C₂×D₄₃	semidirect
259. #126	C₂×D₄₃	semidirect
281. C₂²⋊Q₈	C₂×D₄₃	semidirect
289. C₄×Q₈	C₂×D₄₃	semidirect
290. C₄×Q₈	C₂×D₄₃	semidirect
306. #117	C₂×D₄₃	semidirect