Subgroups — #19148341

Order 5504.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583620	C₂	1	2	yes	maximal, complemented
2	#14583607	C₂	1	2	yes	maximal, complemented
3	#14583591	C₂	1	2	yes	maximal, complemented
4	#14583584	C₂	1	4	yes	maximal, complemented
5	#14583583	C₂	1	2	yes	maximal, complemented
6	#14583575	C₂	1	4	yes	maximal, complemented
7	#14583530	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583522	C₂	1	2	yes	maximal, complemented
9	#14583509	C₂	1	2	yes	maximal, complemented
10	#14583473	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583451	C₂	1	2	yes	maximal, complemented
12	#14583435	C₂	1	2	yes	maximal, complemented
13	#14583410	C₂	1	1	yes	maximal, characteristic
14	#14583380	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583377	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063284	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂²⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621898	C₂²	1	1	yes	characteristic
19	#13063324	C₂²	1	2	yes	complemented
20	#13063324	C₂²	1	2	yes	complemented
21	#13063323	C₂²	1	2	yes	complemented
22	#13063320	C₂²	1	4	yes	complemented
23	#13063320	C₂²	1	4	yes	complemented
24	#13063318	C₂²	1	4	yes	—
25	#13063318	C₂²	1	4	yes	—
26	#13063316	C₂²	1	2	yes	complemented
27	#13063316	C₂²	1	4	yes	complemented
28	#13063316	C₂²	1	2	yes	complemented
29	#13063315	C₂²	1	4	yes	complemented
30	#13063315	C₂²	1	4	yes	complemented
31	#13063314	C₂²	1	2	yes	complemented
32	#13063311	C₂²	1	4	yes	—
33	#13063309	C₂²	1	4	yes	—
34	#13063308	C₂²	1	4	yes	—
35	#13063308	C₂²	1	2	yes	—
36	#13063307	C₂²	1	4	yes	—
37	#13063305	C₂²	1	4	yes	complemented
38	#13063304	C₂²	1	4	yes	—
39	#13063304	C₂²	1	1	yes	characteristic
40	#13063304	C₂²	1	1	yes	characteristic
41	#13063302	C₂²	1	4	yes	—
42	#13063301	C₂²	1	2	yes	complemented
43	#13063301	C₂²	1	2	yes	complemented
44	#13063299	C₂²	1	1	yes	characteristic
45	#13063299	C₂²	1	1	yes	characteristic
46	#13063294	C₂²	1	2	yes	—
47	Q₈×Dic₄₃	C₂²	1	2	yes	complemented
48	Q₈×Dic₄₃	C₂²	1	2	yes	complemented
49	Q₈×Dic₄₃	C₂²	1	2	yes	complemented
50	Q₈×Dic₄₃	C₂²	1	2	yes	complemented
51	#13063290	C₂²	1	4	yes	complemented
52	#13063290	C₂²	1	2	yes	complemented
53	#13063287	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
55	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
57	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	—
58	#13063284	C₂²	1	4	yes	—
59	#13063284	C₂²	1	1	yes	characteristic
60	#13063284	C₂²	1	2	yes	—
61	#13063284	C₂²	1	1	yes	characteristic
62	#13063284	C₂²	1	1	yes	characteristic
63	#13063284	C₂²	1	1	yes	characteristic
64	#13063284	C₂²	1	2	yes	—
65	#13063284	C₂²	1	1	yes	characteristic
66	#13063283	C₂²	1	4	yes	complemented
67	#13063283	C₂²	1	2	yes	complemented
68	#13063281	C₂²	1	4	yes	—
69	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
70	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
71	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
72	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
73	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
74	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
75	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
76	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
77	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
79	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
83	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×Q₈×C₄₃	—	2	4	no	—
85	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
86	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
87	C₂²×C₄×C₄₃	—	2	4	no	—
88	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
89	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
95	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
98	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
99	C₂²×Dic₄₃	C₂³	1	2	yes	—
100	C₂²×Dic₄₃	C₂³	1	2	yes	—
101	#10621898	—	2	4	no	—
102	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₄₃	C₂³	1	2	yes	—
104	C₂×C₄×D₄₃	C₂³	1	4	yes	—
105	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
106	C₂×Dic₈₆	C₂³	1	4	yes	—
107	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
108	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
109	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
110	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
111	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
112	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
113	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
114	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
115	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
116	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
117	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
118	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
119	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
120	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
121	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
125	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
126	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
127	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
128	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
129	C₄⋊Dic₄₃	C₂³	1	2	yes	—
130	C₄⋊Dic₄₃	C₂³	1	2	yes	—
131	C₄⋊Dic₄₃	C₂³	1	4	yes	—
132	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₄₃	C₂³	1	4	yes	—
135	C₄⋊Dic₄₃	C₂³	1	4	yes	—
136	Dic₄₃⋊C₄	C₂³	1	4	yes	—
137	Dic₄₃⋊C₄	C₂³	1	4	yes	—
138	Dic₄₃⋊C₄	C₂³	1	4	yes	—
139	Dic₄₃⋊C₄	C₂³	1	4	yes	—
140	Dic₄₃⋊C₄	C₂³	1	2	yes	—
141	Dic₄₃⋊C₄	C₂³	1	2	yes	—
142	Dic₄₃⋊C₄	C₂³	1	4	yes	—
143	C₄×Dic₄₃	C₂³	1	2	yes	—
144	C₄×Dic₄₃	C₂³	1	2	yes	—
145	C₄×Dic₄₃	C₂³	1	2	yes	—
146	C₄×Dic₄₃	C₂³	1	2	yes	—
147	C₄×Dic₄₃	C₂³	1	4	yes	—
148	C₄×Dic₄₃	C₂³	1	4	yes	—
149	C₄×Dic₄₃	C₂³	1	4	yes	—
150	C₄×Dic₄₃	C₂³	1	2	yes	—
151	C₂³×C₄₃	—	2	2	no	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	—	4	1	no	—
154	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
155	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
156	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
157	C₂²×D₄₃	C₂⁴	1	2	yes	—
158	Q₈×C₄₃	—	2	4	no	—
159	Q₈×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	#41	1	4	yes	—
168	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
170	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
171	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
174	C₂²⋊D₄₃	—	2	4	no	—
175	C₂²⋊D₄₃	—	2	4	no	—
176	C₂²⋊D₄₃	—	4	2	no	—
177	C₂×Dic₄₃	—	2	4	no	—
178	C₂×Dic₄₃	—	4	2	no	—
179	C₂×Dic₄₃	C₂⁴	1	2	yes	—
180	C₂×Dic₄₃	C₂⁴	1	2	yes	—
181	C₂×Dic₄₃	C₂⁴	1	2	yes	—
182	C₂×Dic₄₃	C₂⁴	1	2	yes	—
183	C₂×Dic₄₃	C₂⁴	1	2	yes	—
184	C₂×Dic₄₃	C₂⁴	1	2	yes	—
185	C₂×Dic₄₃	C₂⁴	1	2	yes	—
186	D₁₇₂	—	2	2	no	—
187	C₄×D₄₃	—	2	4	no	—
188	C₄×D₄₃	—	4	4	no	—
189	Dic₈₆	—	2	2	no	—
190	Dic₈₆	—	4	4	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	—	2	1	no	—
194	C₂²×C₄₃	—	2	1	no	—
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	—	2	1	no	—
198	C₂²×C₄₃	—	4	4	no	—
199	C₂²×C₄₃	C₂×#41	1	2	yes	—
200	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
201	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
202	C₂×D₄₃	—	2	2	no	—
203	C₂×D₄₃	—	2	2	no	—
204	C₂×D₄₃	—	2	2	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	4	no	—
208	C₄×C₄₃	—	2	4	no	—
209	C₄×C₄₃	C₂×#41	1	2	yes	—
210	C₄×C₄₃	C₂×#41	1	2	yes	—
211	Dic₄₃	—	2	2	no	—
212	Dic₄₃	—	2	2	no	—
213	Dic₄₃	—	2	2	no	—
214	Dic₄₃	—	2	2	no	—
215	Dic₄₃	—	2	2	no	—
216	Dic₄₃	—	2	2	no	—
217	Dic₄₃	—	2	2	no	—
218	#3495	—	43	1	no	maximal, Sylow
219	C₂×C₄₃	—	2	2	no	—
220	C₂×C₄₃	—	2	2	no	—
221	C₂×C₄₃	—	4	1	no	—
222	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
223	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
224	C₂×C₄₃	#585	1	1	yes	characteristic
225	D₄₃	—	4	2	no	—
226	#556	—	43	2	no	—
227	#554	—	43	2	no	—
228	#552	—	43	2	no	—
229	#552	—	43	2	no	—
230	#552	—	43	4	no	—
231	#551	—	43	4	no	—
232	#544	—	43	1	no	—
233	#542	—	43	2	no	—
234	#541	—	43	2	no	—
235	#536	—	43	1	no	—
236	#533	—	43	2	no	—
237	#529	—	43	2	no	—
238	#525	—	43	1	no	—
239	C₂×C₂²⋊Q₈	D₄₃	1	1	yes	characteristic, complemented
240	#520	—	43	1	no	—
241	#519	—	43	1	no	—
242	C₂×#117	—	43	1	no	—
243	C₄₃	#3495	1	1	yes	characteristic, complemented, Sylow
244	C₂×#41	—	43	1	no	—
245	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
246	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
247	C₄⋊Q₈	—	43	2	no	—
248	C₄⋊Q₈	—	43	2	no	—
249	C₄⋊Q₈	—	43	2	no	—
250	#126	—	43	4	no	—
251	#126	—	43	4	no	—
252	#126	—	43	4	no	—
253	#126	—	43	4	no	—
254	#125	—	43	2	no	—
255	#125	—	43	4	no	—
256	#125	—	43	4	no	—
257	#125	—	43	4	no	—
258	#125	—	43	2	no	—
259	#124	—	43	2	no	—
260	#124	—	43	4	no	—
261	#123	—	43	2	no	—
262	#123	—	43	4	no	—
263	#123	—	43	4	no	—
264	#123	—	43	4	no	—
265	C₂²⋊Q₈	—	43	2	no	—
266	C₂²⋊Q₈	—	43	2	no	—
267	C₂²⋊Q₈	—	43	1	no	—
268	C₂²⋊Q₈	—	43	1	no	—
269	C₂²⋊Q₈	—	43	4	no	—
270	C₂²⋊Q₈	—	43	4	no	—
271	C₂²⋊Q₈	—	43	4	no	—
272	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
273	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
274	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
275	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
276	#121	—	43	1	no	—
277	#121	—	43	1	no	—
278	#120	—	43	2	no	—
279	C₄×Q₈	—	43	2	no	—
280	C₄×Q₈	—	43	2	no	—
281	C₄×Q₈	—	43	2	no	—
282	C₄×Q₈	—	43	2	no	—
283	C₄×Q₈	—	43	2	no	—
284	C₄×Q₈	—	43	4	no	—
285	C₄×D₄	—	43	4	no	—
286	C₄×D₄	—	43	2	no	—
287	C₄×D₄	—	43	2	no	—
288	C₄×D₄	—	43	2	no	—
289	C₄×D₄	—	43	4	no	—
290	#117	—	43	1	no	—
291	#117	—	43	1	no	—
292	#117	—	43	2	no	—
293	#117	—	43	1	no	—
294	#117	—	43	2	no	—
295	#117	—	43	1	no	—
296	#117	—	43	1	no	—
297	#117	—	43	4	no	—
298	#117	—	43	2	no	—
299	#117	—	43	4	no	—
300	#117	—	43	4	no	—
301	C₂×C₄⋊C₄	—	43	1	no	—
302	C₂×C₄⋊C₄	—	43	1	no	—
303	C₂×C₄⋊C₄	—	43	2	no	—
304	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
306	C₂×C₂²⋊C₄	—	43	2	no	—
307	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
308	C₂×C₄²	—	43	2	no	—
309	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
310	#41	—	86	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	43	1	no	—
313	C₂×Q₈	—	43	4	no	—
314	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
315	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
316	C₂×D₄	—	43	2	no	—
317	C₂×D₄	—	43	2	no	—
318	C₂×D₄	—	43	2	no	—
319	C₂×D₄	—	43	1	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	43	2	no	—
322	C₂²×C₄	—	43	2	no	—
323	C₂²×C₄	—	43	2	no	—
324	C₂²×C₄	—	43	4	no	—
325	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
327	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
328	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
329	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
330	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
332	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
333	C₄⋊C₄	—	43	1	no	—
334	C₄⋊C₄	—	43	1	no	—
335	C₄⋊C₄	—	43	2	no	—
336	C₄⋊C₄	—	43	1	no	—
337	C₄⋊C₄	—	43	1	no	—
338	C₄⋊C₄	—	43	2	no	—
339	C₄⋊C₄	—	43	4	no	—
340	C₄⋊C₄	—	43	1	no	—
341	C₄⋊C₄	—	43	1	no	—
342	C₄⋊C₄	—	43	4	no	—
343	C₄⋊C₄	—	43	4	no	—
344	C₄⋊C₄	—	43	4	no	—
345	C₄⋊C₄	—	43	4	no	—
346	C₄⋊C₄	—	43	4	no	—
347	C₄⋊C₄	—	43	2	no	—
348	C₄⋊C₄	—	43	2	no	—
349	C₄⋊C₄	—	43	4	no	—
350	C₄⋊C₄	—	43	4	no	—
351	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
352	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
353	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
354	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
355	C₂²⋊C₄	—	43	2	no	—
356	C₂²⋊C₄	—	43	2	no	—
357	C₂²⋊C₄	—	43	2	no	—
358	C₂²⋊C₄	—	43	2	no	—
359	C₂²⋊C₄	—	43	2	no	—
360	C₂²⋊C₄	—	43	2	no	—
361	C₂²⋊C₄	—	43	2	no	—
362	C₂²⋊C₄	—	43	2	no	—
363	C₂²⋊C₄	—	43	4	no	—
364	C₂²⋊C₄	—	43	4	no	—
365	C₂²⋊C₄	—	43	2	no	—
366	C₂²⋊C₄	—	43	4	no	—
367	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
368	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
369	C₄²	—	43	2	no	—
370	C₄²	—	43	2	no	—
371	C₄²	—	43	2	no	—
372	C₄²	—	43	2	no	—
373	C₄²	—	43	4	no	—
374	C₄²	—	43	4	no	—
375	C₄²	—	43	4	no	—
376	C₄²	—	43	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	43	2	no	—
381	C₂³	C₂³×D₄₃	1	1	yes	characteristic
382	C₂³	C₂³×D₄₃	1	1	yes	characteristic
383	C₂³	C₂³×D₄₃	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	86	2	no	—
387	Q₈	—	172	4	no	—
388	D₄	—	86	4	no	—
389	D₄	—	86	4	no	—
390	D₄	—	86	2	no	—
391	D₄	—	172	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	43	2	no	—
400	C₂×C₄	—	43	2	no	—
401	C₂×C₄	—	43	2	no	—
402	C₂×C₄	—	43	2	no	—
403	C₂×C₄	—	43	2	no	—
404	C₂×C₄	—	43	2	no	—
405	C₂×C₄	—	43	2	no	—
406	C₂×C₄	—	86	4	no	—
407	C₂×C₄	—	86	4	no	—
408	C₂×C₄	—	172	4	no	—
409	C₂×C₄	—	172	2	no	—
410	C₂×C₄	#10621900	1	4	yes	—
411	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₄₃	1	4	yes	—
413	C₂×C₄	C₂³×D₄₃	1	4	yes	—
414	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	86	2	no	—
426	C₂²	—	86	2	no	—
427	C₂²	—	86	2	no	—
428	C₂²	C₂×#10621900	1	2	yes	—
429	C₂²	#13063373	1	2	yes	—
430	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	4	no	—
435	C₄	—	86	2	no	—
436	C₄	—	86	2	no	—
437	C₄	—	86	2	no	—
438	C₄	—	86	2	no	—
439	C₄	—	86	2	no	—
440	C₄	—	86	2	no	—
441	C₄	—	86	2	no	—
442	C₄	C₂×#10621900	1	2	yes	—
443	C₄	C₂×#10621900	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	2	2	no	—
446	C₂	—	4	1	no	—
447	C₂	—	172	2	no	—
448	C₂	C₂²×#10621900	1	1	yes	characteristic
449	C₂	C₂×#13063373	1	1	yes	characteristic
450	C₂	#14583735	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₂×C₂²⋊Q₈×C₄₃	C₂
hypercenter	C₂×C₂²⋊Q₈	D₄₃
hypocenter	C₄₃	#3495
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #14583620	C₂	semidirect
2. #14583607	C₂	semidirect
3. #14583591	C₂	semidirect
4. #14583584	C₂	semidirect
5. #14583583	C₂	semidirect
6. #14583575	C₂	semidirect
7. #14583530	C₂	semidirect
8. #14583522	C₂	semidirect
9. #14583509	C₂	semidirect
10. #14583473	C₂	semidirect
11. #14583451	C₂	semidirect
12. #14583435	C₂	semidirect
14. #14583380	C₂	semidirect
15. #14583377	C₂	semidirect
16. C₂×#13063284	C₂	semidirect
17. C₂×C₂²⋊Q₈×C₄₃	C₂	semidirect
19. #13063324	C₂²	semidirect
20. #13063324	C₂²	semidirect
21. #13063323	C₂²	semidirect
22. #13063320	C₂²	semidirect
23. #13063320	C₂²	semidirect
26. #13063316	C₂²	semidirect
27. #13063316	C₂²	semidirect
28. #13063316	C₂²	semidirect
29. #13063315	C₂²	semidirect
30. #13063315	C₂²	semidirect
31. #13063314	C₂²	semidirect
37. #13063305	C₂²	semidirect
42. #13063301	C₂²	semidirect
43. #13063301	C₂²	semidirect
47. Q₈×Dic₄₃	C₂²	semidirect
48. Q₈×Dic₄₃	C₂²	semidirect
49. Q₈×Dic₄₃	C₂²	semidirect
50. Q₈×Dic₄₃	C₂²	semidirect
51. #13063290	C₂²	semidirect
52. #13063290	C₂²	semidirect
53. #13063287	C₂²	semidirect
66. #13063283	C₂²	semidirect
67. #13063283	C₂²	semidirect
71. C₄⋊C₄×D₄₃	C₂²	semidirect
239. C₂×C₂²⋊Q₈	D₄₃	semidirect
243. C₄₃	#3495	semidirect