Subgroups — #19148431

Order 5504.

1152 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583601	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583598	C₂	1	2	yes	maximal, complemented
3	#14583595	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583592	C₂	1	2	yes	maximal, complemented
5	#14583590	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583583	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583579	C₂	1	2	yes	maximal, complemented
8	#14583576	C₂	1	2	yes	maximal, complemented
9	#14583560	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583542	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583537	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583495	C₂	1	2	yes	maximal, complemented
13	#14583483	C₂	1	2	yes	maximal, complemented
14	#14583457	C₂	1	2	yes	maximal, complemented
15	#14583436	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583428	C₂	1	1	yes	maximal, characteristic, complemented
17	#14583412	C₂	1	1	yes	maximal, characteristic, complemented
18	#14583406	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#13063301	C₂	1	1	yes	maximal, characteristic, complemented
20	#121×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#14583371	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10621902	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₄₃	C₂²	1	2	yes	—
27	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
30	#13063320	C₂²	1	2	yes	complemented
31	#13063320	C₂²	1	2	yes	complemented
32	#13063319	C₂²	1	2	yes	complemented
33	#13063318	C₂²	1	2	yes	complemented
34	#13063318	C₂²	1	2	yes	complemented
35	#13063318	C₂²	1	2	yes	complemented
36	#13063317	C₂²	1	1	yes	characteristic, complemented
37	#13063316	C₂²	1	1	yes	characteristic, complemented
38	#13063315	C₂²	1	2	yes	complemented
39	#13063315	C₂²	1	2	yes	complemented
40	#13063314	C₂²	1	2	yes	complemented
41	#13063314	C₂²	1	1	yes	characteristic, complemented
42	#13063310	C₂²	1	2	yes	—
43	#13063310	C₂²	1	2	yes	complemented
44	#13063310	C₂²	1	2	yes	complemented
45	#13063309	C₂²	1	2	yes	complemented
46	#13063308	C₂²	1	2	yes	complemented
47	#13063307	C₂²	1	2	yes	—
48	#13063307	C₂²	1	2	yes	complemented
49	#13063307	C₂²	1	2	yes	complemented
50	#13063307	C₂²	1	2	yes	complemented
51	#13063306	C₂²	1	2	yes	complemented
52	#13063301	C₂²	1	2	yes	complemented
53	#13063301	C₂²	1	1	yes	characteristic, complemented
54	#13063301	C₂²	1	2	yes	complemented
55	#13063301	C₂²	1	1	yes	characteristic, complemented
56	#13063301	C₂²	1	1	yes	characteristic, complemented
57	#13063301	C₂²	1	1	yes	characteristic, complemented
58	#13063301	C₂²	1	1	yes	characteristic, complemented
59	#13063301	C₂²	1	2	yes	complemented
60	#13063300	C₂²	1	1	yes	characteristic
61	#13063299	C₂²	1	1	yes	characteristic, complemented
62	#13063299	C₂²	1	2	yes	complemented
63	#13063299	C₂²	1	1	yes	characteristic, complemented
64	#13063298	C₂²	1	2	yes	—
65	#13063298	C₂²	1	2	yes	complemented
66	#13063297	C₂²	1	2	yes	complemented
67	#13063297	C₂²	1	2	yes	complemented
68	#13063297	C₂²	1	2	yes	complemented
69	#13063297	C₂²	1	2	yes	complemented
70	#13063296	C₂²	1	1	yes	characteristic
71	#13063296	C₂²	1	1	yes	characteristic, complemented
72	#13063295	C₂²	1	2	yes	—
73	#13063295	C₂²	1	2	yes	complemented
74	#13063293	C₂²	1	2	yes	—
75	#13063293	C₂²	1	2	yes	complemented
76	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
77	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
78	C₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₁₇₂	C₂²	1	2	yes	complemented
80	D₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
81	D₄×Dic₄₃	C₂²	1	2	yes	complemented
82	D₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
83	#13063287	C₂²	1	1	yes	characteristic
84	#13063287	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
89	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
90	(C₂²⋊D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
91	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
92	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
93	(C₂²⋊D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
94	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
95	#13063284	C₂²	1	1	yes	characteristic, complemented
96	#13063283	C₂²	1	2	yes	complemented
97	#13063283	C₂²	1	1	yes	characteristic, complemented
98	#13063282	C₂²	1	2	yes	complemented
99	#13063282	C₂²	1	2	yes	complemented
100	#13063281	C₂²	1	2	yes	complemented
101	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
102	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
105	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
106	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₄₃	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₄₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
113	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
114	#124×C₄₃	C₂²	1	2	yes	complemented
115	#124×C₄₃	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
118	#121×C₄₃	C₂²	1	2	yes	complemented
119	#121×C₄₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
123	C₂³×D₄₃	C₂³	1	2	yes	—
124	C₂³×D₄₃	C₂³	1	1	yes	characteristic
125	C₂³×D₄₃	C₂³	1	1	yes	characteristic
126	#41×C₄₃	—	4	2	no	—
127	C₂×Q₈×C₄₃	—	4	2	no	—
128	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
130	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
131	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₄₃	C₂³	1	2	yes	—
133	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₄₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
146	C₂²×Dic₄₃	C₂³	1	2	yes	—
147	C₂²×Dic₄₃	C₂³	1	2	yes	—
148	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
149	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
150	#10621902	—	4	2	no	—
151	D₄×D₄₃	—	2	4	no	—
152	D₄×D₄₃	—	2	8	no	—
153	D₄×D₄₃	—	4	2	no	—
154	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
155	C₂×D₁₇₂	C₂³	1	2	yes	—
156	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
157	C₂×D₁₇₂	C₂³	1	2	yes	—
158	C₂×C₄×D₄₃	—	4	2	no	—
159	C₂×C₄×D₄₃	—	4	2	no	—
160	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₄₃	C₂³	1	2	yes	—
163	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₄₃	C₂³	1	2	yes	—
170	C₂×C₄×D₄₃	C₂³	1	2	yes	—
171	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
174	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
177	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
178	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
182	C₄²×C₄₃	C₂³	1	1	yes	characteristic
183	C₄²×C₄₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
190	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
206	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₄₃	C₂³	1	2	yes	—
211	C₄⋊Dic₄₃	C₂³	1	2	yes	—
212	C₄⋊Dic₄₃	C₂³	1	2	yes	—
213	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₄₃⋊C₄	C₂³	1	2	yes	—
216	Dic₄₃⋊C₄	C₂³	1	2	yes	—
217	Dic₄₃⋊C₄	C₂³	1	2	yes	—
218	Dic₄₃⋊C₄	C₂³	1	2	yes	—
219	Dic₄₃⋊C₄	C₂³	1	2	yes	—
220	Dic₄₃⋊C₄	C₂³	1	2	yes	—
221	Dic₄₃⋊C₄	C₂³	1	2	yes	—
222	Dic₄₃⋊C₄	C₂³	1	2	yes	—
223	Dic₄₃⋊C₄	C₂³	1	2	yes	—
224	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₄₃	C₂³	1	2	yes	—
228	C₄×Dic₄₃	C₂³	1	2	yes	—
229	C₄×Dic₄₃	C₂³	1	2	yes	—
230	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
231	C₂³×C₄₃	C₂⁴	1	2	yes	—
232	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₄₃	—	2	2	no	—
234	C₂²×D₄₃	—	2	4	no	—
235	C₂²×D₄₃	—	4	1	no	—
236	C₂²×D₄₃	—	4	1	no	—
237	C₂²×D₄₃	—	4	1	no	—
238	C₂²×D₄₃	—	4	1	no	—
239	C₂²×D₄₃	—	4	2	no	—
240	C₂²×D₄₃	—	4	2	no	—
241	C₂²×D₄₃	#41	1	4	yes	complemented
242	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
243	C₂²×D₄₃	C₂⁴	1	2	yes	—
244	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
245	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
246	Q₈×C₄₃	—	2	2	no	—
247	Q₈×C₄₃	—	2	2	no	—
248	Q₈×C₄₃	—	4	2	no	—
249	D₄×C₄₃	—	2	2	no	—
250	D₄×C₄₃	—	2	4	no	—
251	D₄×C₄₃	—	2	2	no	—
252	D₄×C₄₃	—	4	2	no	—
253	C₂×C₄×C₄₃	—	2	2	no	—
254	C₂×C₄×C₄₃	—	2	2	no	—
255	C₂×C₄×C₄₃	—	4	2	no	—
256	C₂×C₄×C₄₃	—	4	2	no	—
257	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
260	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
261	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
263	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
265	C₂²⋊D₄₃	—	2	2	no	—
266	C₂²⋊D₄₃	—	2	4	no	—
267	C₂²⋊D₄₃	—	2	2	no	—
268	C₂²⋊D₄₃	—	2	4	no	—
269	C₂²⋊D₄₃	—	4	2	no	—
270	C₂²⋊D₄₃	—	4	2	no	—
271	C₂²⋊D₄₃	—	4	2	no	—
272	C₂×Dic₄₃	—	4	1	no	—
273	C₂×Dic₄₃	—	4	1	no	—
274	C₂×Dic₄₃	—	4	2	no	—
275	C₂×Dic₄₃	—	4	2	no	—
276	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₄₃	C₂⁴	1	2	yes	—
279	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₄₃	C₂⁴	1	2	yes	—
282	C₂×Dic₄₃	C₂⁴	1	2	yes	—
283	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
284	D₁₇₂	—	2	2	no	—
285	D₁₇₂	—	2	4	no	—
286	D₁₇₂	—	2	2	no	—
287	D₁₇₂	—	4	2	no	—
288	C₄×D₄₃	—	2	4	no	—
289	C₄×D₄₃	—	2	2	no	—
290	C₄×D₄₃	—	2	2	no	—
291	C₄×D₄₃	—	2	2	no	—
292	C₄×D₄₃	—	2	2	no	—
293	C₄×D₄₃	—	4	1	no	—
294	C₄×D₄₃	—	4	1	no	—
295	C₄×D₄₃	—	4	1	no	—
296	C₄×D₄₃	—	4	1	no	—
297	C₄×D₄₃	—	4	1	no	—
298	C₄×D₄₃	—	4	2	no	—
299	C₄×D₄₃	—	4	2	no	—
300	C₂²×C₄₃	—	2	1	no	—
301	C₂²×C₄₃	—	2	1	no	—
302	C₂²×C₄₃	—	2	1	no	—
303	C₂²×C₄₃	—	2	2	no	—
304	C₂²×C₄₃	—	2	1	no	—
305	C₂²×C₄₃	—	2	2	no	—
306	C₂²×C₄₃	—	2	2	no	—
307	C₂²×C₄₃	—	2	1	no	—
308	C₂²×C₄₃	C₂×#41	1	2	yes	—
309	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
310	C₂×D₄₃	—	2	1	no	—
311	C₂×D₄₃	—	2	1	no	—
312	C₂×D₄₃	—	2	1	no	—
313	C₂×D₄₃	—	2	1	no	—
314	C₂×D₄₃	—	2	1	no	—
315	C₂×D₄₃	—	2	2	no	—
316	C₂×D₄₃	—	2	1	no	—
317	C₂×D₄₃	—	2	2	no	—
318	C₂×D₄₃	—	2	2	no	—
319	C₂×D₄₃	—	2	1	no	—
320	C₂×D₄₃	—	4	4	no	—
321	C₂×D₄₃	—	4	4	no	—
322	C₂×D₄₃	—	8	4	no	—
323	C₂×D₄₃	C₂×#41	1	2	yes	—
324	C₂×D₄₃	C₂×#41	1	2	yes	—
325	C₄×C₄₃	—	2	2	no	—
326	C₄×C₄₃	—	2	1	no	—
327	C₄×C₄₃	—	2	1	no	—
328	C₄×C₄₃	—	2	1	no	—
329	C₄×C₄₃	—	2	2	no	—
330	C₄×C₄₃	—	2	2	no	—
331	C₄×C₄₃	—	2	1	no	—
332	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
333	Dic₄₃	—	2	2	no	—
334	Dic₄₃	—	2	1	no	—
335	Dic₄₃	—	2	1	no	—
336	Dic₄₃	—	2	1	no	—
337	Dic₄₃	—	2	1	no	—
338	Dic₄₃	—	2	1	no	—
339	Dic₄₃	—	2	2	no	—
340	Dic₄₃	—	2	2	no	—
341	#3505	—	43	1	no	maximal, Sylow
342	C₂×C₄₃	—	2	2	no	—
343	C₂×C₄₃	—	4	1	no	—
344	C₂×C₄₃	—	4	2	no	—
345	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
346	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₄₃	#585	1	1	yes	characteristic
348	D₄₃	—	2	2	no	—
349	D₄₃	—	2	2	no	—
350	D₄₃	—	4	1	no	—
351	D₄₃	—	4	2	no	—
352	#553	—	43	2	no	—
353	#553	—	43	1	no	—
354	#553	—	43	1	no	—
355	#553	—	43	2	no	—
356	#552	—	43	1	no	—
357	#552	—	43	1	no	—
358	#551	—	43	2	no	—
359	#551	—	43	2	no	—
360	#548	—	43	1	no	—
361	#548	D₄₃	1	1	yes	characteristic, complemented
362	#546	—	43	1	no	—
363	#546	—	43	1	no	—
364	#539	—	43	2	no	—
365	#538	—	43	2	no	—
366	#534	—	43	2	no	—
367	#529	—	43	1	no	—
368	#529	—	43	1	no	—
369	#525	—	43	1	no	—
370	#525	—	43	1	no	—
371	C₂×C₂²⋊Q₈	—	43	1	no	—
372	C₂×#121	—	43	1	no	—
373	#518	—	43	2	no	—
374	C₂×C₄×D₄	—	43	1	no	—
375	C₄₃	#3505	1	1	yes	characteristic, complemented, Sylow
376	C₂×#41	—	43	1	no	—
377	C₂×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
378	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
379	C₂²×D₄	—	43	1	no	—
380	C₂²×D₄	—	43	2	no	—
381	C₂²×D₄	—	43	1	no	—
382	C₂³×C₄	—	43	1	no	—
383	C₂³×C₄	—	43	1	no	—
384	#126	—	43	2	no	—
385	#126	—	43	2	no	—
386	#126	—	43	2	no	—
387	#126	—	43	2	no	—
388	#126	—	43	2	no	—
389	#126	—	43	2	no	—
390	#125	—	43	1	no	—
391	#125	—	43	2	no	—
392	#125	—	43	2	no	—
393	#125	—	43	1	no	—
394	#124	—	43	1	no	—
395	#124	—	43	2	no	—
396	#124	C₂×D₄₃	1	1	yes	characteristic, complemented
397	#124	C₂×D₄₃	1	2	yes	complemented
398	#123	—	43	2	no	—
399	#123	—	43	2	no	—
400	#123	—	43	2	no	—
401	#123	—	43	2	no	—
402	#123	—	43	2	no	—
403	#123	—	43	2	no	—
404	#123	—	43	2	no	—
405	#123	—	43	2	no	—
406	#123	—	43	2	no	—
407	#123	—	43	2	no	—
408	C₂²⋊Q₈	—	43	1	no	—
409	C₂²⋊Q₈	—	43	1	no	—
410	C₂²⋊Q₈	—	43	2	no	—
411	C₂²⋊Q₈	—	43	1	no	—
412	C₂²⋊Q₈	—	43	1	no	—
413	C₂²⋊Q₈	—	43	2	no	—
414	C₂²⋊Q₈	—	43	1	no	—
415	C₂²⋊Q₈	—	43	2	no	—
416	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
417	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	complemented
418	#121	—	43	1	no	—
419	#121	—	43	2	no	—
420	#121	—	43	1	no	—
421	#121	—	43	2	no	—
422	#121	—	43	2	no	—
423	#121	—	43	2	no	—
424	#121	—	43	1	no	—
425	#121	—	43	1	no	—
426	#121	—	43	2	no	—
427	#121	—	43	1	no	—
428	#121	—	43	2	no	—
429	#121	—	43	2	no	—
430	#121	C₂×D₄₃	1	1	yes	characteristic, complemented
431	#121	C₂×D₄₃	1	2	yes	complemented
432	#120	—	43	2	no	—
433	#120	—	43	2	no	—
434	#120	—	43	2	no	—
435	#120	—	43	2	no	—
436	C₄×Q₈	—	43	1	no	—
437	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
438	C₄×D₄	—	43	1	no	—
439	C₄×D₄	—	43	2	no	—
440	C₄×D₄	—	43	1	no	—
441	C₄×D₄	—	43	1	no	—
442	C₄×D₄	—	43	1	no	—
443	C₄×D₄	—	43	2	no	—
444	C₄×D₄	—	43	2	no	—
445	C₄×D₄	—	43	2	no	—
446	C₄×D₄	—	43	1	no	—
447	C₄×D₄	—	43	2	no	—
448	C₄×D₄	—	43	1	no	—
449	C₄×D₄	—	43	1	no	—
450	C₄×D₄	—	43	2	no	—
451	C₄×D₄	—	43	2	no	—
452	C₄×D₄	—	43	2	no	—
453	C₄×D₄	—	43	1	no	—
454	C₄×D₄	—	43	2	no	—
455	C₄×D₄	—	43	1	no	—
456	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
457	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
458	#117	—	43	1	no	—
459	#117	—	43	2	no	—
460	#117	—	43	1	no	—
461	#117	—	43	2	no	—
462	#117	—	43	2	no	—
463	#117	—	43	2	no	—
464	C₂×C₄⋊C₄	—	43	2	no	—
465	C₂×C₄⋊C₄	—	43	1	no	—
466	C₂×C₄⋊C₄	—	43	1	no	—
467	C₂×C₄⋊C₄	—	43	1	no	—
468	C₂×C₂²⋊C₄	—	43	2	no	—
469	C₂×C₂²⋊C₄	—	43	2	no	—
470	C₂×C₂²⋊C₄	—	43	1	no	—
471	C₂×C₂²⋊C₄	—	43	1	no	—
472	C₂×C₂²⋊C₄	—	43	2	no	—
473	C₂×C₂²⋊C₄	—	43	2	no	—
474	C₂×C₄²	—	43	1	no	—
475	C₂⁴	—	43	1	no	—
476	C₂⁴	—	43	2	no	—
477	C₂⁴	—	43	1	no	—
478	#41	—	4	2	no	—
479	#41	—	172	2	no	—
480	C₂×Q₈	—	4	2	no	—
481	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
482	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
483	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
484	C₂×D₄	—	43	1	no	—
485	C₂×D₄	—	43	2	no	—
486	C₂×D₄	—	43	1	no	—
487	C₂×D₄	—	43	2	no	—
488	C₂×D₄	—	43	2	no	—
489	C₂×D₄	—	43	2	no	—
490	C₂×D₄	—	43	2	no	—
491	C₂×D₄	—	43	1	no	—
492	C₂×D₄	—	43	2	no	—
493	C₂×D₄	—	43	1	no	—
494	C₂×D₄	—	43	2	no	—
495	C₂×D₄	—	86	8	no	—
496	C₂×D₄	—	86	4	no	—
497	C₂×D₄	—	172	2	no	—
498	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
499	C₂×D₄	C₂²×D₄₃	1	2	yes	—
500	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
501	C₂×D₄	C₂²×D₄₃	1	2	yes	—
502	C₂²×C₄	—	43	2	no	—
503	C₂²×C₄	—	43	2	no	—
504	C₂²×C₄	—	43	1	no	—
505	C₂²×C₄	—	43	1	no	—
506	C₂²×C₄	—	43	1	no	—
507	C₂²×C₄	—	43	1	no	—
508	C₂²×C₄	—	43	2	no	—
509	C₂²×C₄	—	43	1	no	—
510	C₂²×C₄	—	43	1	no	—
511	C₂²×C₄	—	43	1	no	—
512	C₂²×C₄	—	43	1	no	—
513	C₂²×C₄	—	43	1	no	—
514	C₂²×C₄	—	43	1	no	—
515	C₂²×C₄	—	43	2	no	—
516	C₂²×C₄	—	43	2	no	—
517	C₂²×C₄	—	43	1	no	—
518	C₂²×C₄	—	172	2	no	—
519	C₂²×C₄	—	172	2	no	—
520	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
521	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
522	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
523	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
524	C₄⋊C₄	—	43	1	no	—
525	C₄⋊C₄	—	43	1	no	—
526	C₄⋊C₄	—	43	2	no	—
527	C₄⋊C₄	—	43	2	no	—
528	C₄⋊C₄	—	43	1	no	—
529	C₄⋊C₄	—	43	1	no	—
530	C₄⋊C₄	—	43	1	no	—
531	C₄⋊C₄	—	43	1	no	—
532	C₄⋊C₄	—	43	2	no	—
533	C₄⋊C₄	—	43	2	no	—
534	C₄⋊C₄	—	43	2	no	—
535	C₄⋊C₄	—	43	2	no	—
536	C₄⋊C₄	—	43	2	no	—
537	C₄⋊C₄	—	43	2	no	—
538	C₄⋊C₄	—	43	2	no	—
539	C₄⋊C₄	—	43	2	no	—
540	C₄⋊C₄	—	43	2	no	—
541	C₄⋊C₄	—	43	2	no	—
542	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
545	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
546	C₂²⋊C₄	—	43	2	no	—
547	C₂²⋊C₄	—	43	1	no	—
548	C₂²⋊C₄	—	43	1	no	—
549	C₂²⋊C₄	—	43	2	no	—
550	C₂²⋊C₄	—	43	2	no	—
551	C₂²⋊C₄	—	43	2	no	—
552	C₂²⋊C₄	—	43	1	no	—
553	C₂²⋊C₄	—	43	1	no	—
554	C₂²⋊C₄	—	43	2	no	—
555	C₂²⋊C₄	—	43	2	no	—
556	C₂²⋊C₄	—	43	2	no	—
557	C₂²⋊C₄	—	43	2	no	—
558	C₂²⋊C₄	—	43	2	no	—
559	C₂²⋊C₄	—	43	1	no	—
560	C₂²⋊C₄	—	43	2	no	—
561	C₂²⋊C₄	—	43	2	no	—
562	C₂²⋊C₄	—	43	1	no	—
563	C₂²⋊C₄	—	43	2	no	—
564	C₂²⋊C₄	—	43	2	no	—
565	C₂²⋊C₄	—	43	2	no	—
566	C₂²⋊C₄	—	43	2	no	—
567	C₂²⋊C₄	—	43	2	no	—
568	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
569	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
571	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
574	C₄²	—	43	1	no	—
575	C₄²	—	43	1	no	—
576	C₄²	—	43	1	no	—
577	C₄²	—	43	2	no	—
578	C₄²	—	43	2	no	—
579	C₄²	—	43	2	no	—
580	C₄²	C₂²×D₄₃	1	1	yes	characteristic
581	C₄²	C₂²×D₄₃	1	2	yes	—
582	C₂³	—	43	1	no	—
583	C₂³	—	43	1	no	—
584	C₂³	—	43	4	no	—
585	C₂³	—	43	1	no	—
586	C₂³	—	43	2	no	—
587	C₂³	—	86	4	no	—
588	C₂³	—	86	2	no	—
589	C₂³	—	172	2	no	—
590	C₂³	—	172	2	no	—
591	C₂³	—	172	1	no	—
592	C₂³	—	172	1	no	—
593	C₂³	—	172	1	no	—
594	C₂³	—	172	1	no	—
595	C₂³	C₂³×D₄₃	1	1	yes	characteristic
596	C₂³	C₂³×D₄₃	1	2	yes	—
597	C₂³	C₂³×D₄₃	1	1	yes	characteristic
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	—	4	2	no	—
601	D₄	—	2	4	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	2	no	—
605	D₄	—	86	2	no	—
606	D₄	—	86	4	no	—
607	D₄	—	86	2	no	—
608	D₄	—	86	4	no	—
609	D₄	—	86	4	no	—
610	D₄	—	86	2	no	—
611	D₄	—	86	2	no	—
612	D₄	—	172	2	no	—
613	D₄	—	172	2	no	—
614	D₄	—	172	2	no	—
615	D₄	—	172	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	43	1	no	—
621	C₂×C₄	—	43	1	no	—
622	C₂×C₄	—	43	2	no	—
623	C₂×C₄	—	43	1	no	—
624	C₂×C₄	—	43	1	no	—
625	C₂×C₄	—	43	2	no	—
626	C₂×C₄	—	43	2	no	—
627	C₂×C₄	—	43	1	no	—
628	C₂×C₄	—	86	4	no	—
629	C₂×C₄	—	86	2	no	—
630	C₂×C₄	—	86	2	no	—
631	C₂×C₄	—	86	2	no	—
632	C₂×C₄	—	86	2	no	—
633	C₂×C₄	—	172	1	no	—
634	C₂×C₄	—	172	1	no	—
635	C₂×C₄	—	172	1	no	—
636	C₂×C₄	—	172	1	no	—
637	C₂×C₄	—	172	2	no	—
638	C₂×C₄	—	172	1	no	—
639	C₂×C₄	—	172	2	no	—
640	C₂×C₄	—	172	1	no	—
641	C₂×C₄	—	172	1	no	—
642	C₂×C₄	—	172	2	no	—
643	C₂×C₄	—	172	2	no	—
644	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
645	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₄₃	1	2	yes	—
648	C₂×C₄	C₂³×D₄₃	1	2	yes	—
649	C₂×C₄	C₂³×D₄₃	1	2	yes	—
650	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	43	2	no	—
661	C₂²	—	43	2	no	—
662	C₂²	—	86	1	no	—
663	C₂²	—	86	1	no	—
664	C₂²	—	86	1	no	—
665	C₂²	—	86	1	no	—
666	C₂²	—	86	2	no	—
667	C₂²	—	86	1	no	—
668	C₂²	—	86	1	no	—
669	C₂²	—	86	2	no	—
670	C₂²	—	86	2	no	—
671	C₂²	—	86	1	no	—
672	C₂²	—	344	4	no	—
673	C₂²	—	172	4	no	—
674	C₂²	—	172	4	no	—
675	C₂²	#41×D₄₃	1	2	yes	—
676	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	1	no	—
684	C₄	—	86	1	no	—
685	C₄	—	86	2	no	—
686	C₄	—	86	1	no	—
687	C₄	—	86	1	no	—
688	C₄	—	86	1	no	—
689	C₄	—	86	1	no	—
690	C₄	—	86	2	no	—
691	C₄	—	86	2	no	—
692	C₄	#13063370	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	4	1	no	—
696	C₂	—	86	2	no	—
697	C₂	—	86	2	no	—
698	C₂	—	172	2	no	—
699	C₂	—	172	1	no	—
700	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
701	C₂	C₂×#13063370	1	1	yes	characteristic
702	C₂	#14583736	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#548	C₂
hypercenter	#548	D₄₃
hypocenter	C₄₃	#3505
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. #14583601	C₂	semidirect
2. #14583598	C₂	semidirect
3. #14583595	C₂	semidirect
4. #14583592	C₂	semidirect
5. #14583590	C₂	semidirect
6. #14583583	C₂	semidirect
7. #14583579	C₂	semidirect
8. #14583576	C₂	semidirect
9. #14583560	C₂	semidirect
10. #14583542	C₂	semidirect
11. #14583537	C₂	semidirect
12. #14583495	C₂	semidirect
13. #14583483	C₂	semidirect
14. #14583457	C₂	semidirect
15. #14583436	C₂	semidirect
16. #14583428	C₂	semidirect
17. #14583412	C₂	semidirect
18. #14583406	C₂	semidirect
19. C₂×#13063301	C₂	semidirect
20. #121×D₄₃	C₂	semidirect
21. #14583371	C₂	semidirect
22. C₄×D₄×D₄₃	C₂	semidirect
23. C₄₃×#548	C₂	semidirect
24. C₂×#10621902	C₂²	semidirect
27. C₂×D₄×D₄₃	C₂²	semidirect
29. C₂²×C₄×D₄₃	C₂²	semidirect
30. #13063320	C₂²	semidirect
31. #13063320	C₂²	semidirect
32. #13063319	C₂²	semidirect
33. #13063318	C₂²	semidirect
34. #13063318	C₂²	semidirect
35. #13063318	C₂²	semidirect
36. #13063317	C₂²	semidirect
37. #13063316	C₂²	semidirect
38. #13063315	C₂²	semidirect
39. #13063315	C₂²	semidirect
40. #13063314	C₂²	semidirect
41. #13063314	C₂²	semidirect
43. #13063310	C₂²	semidirect
44. #13063310	C₂²	semidirect
45. #13063309	C₂²	semidirect
46. #13063308	C₂²	semidirect
48. #13063307	C₂²	semidirect
49. #13063307	C₂²	semidirect
50. #13063307	C₂²	semidirect
51. #13063306	C₂²	semidirect
52. #13063301	C₂²	semidirect
53. #13063301	C₂²	semidirect
54. #13063301	C₂²	semidirect
55. #13063301	C₂²	semidirect
56. #13063301	C₂²	semidirect
57. #13063301	C₂²	semidirect
58. #13063301	C₂²	semidirect
59. #13063301	C₂²	semidirect
61. #13063299	C₂²	semidirect
62. #13063299	C₂²	semidirect
63. #13063299	C₂²	semidirect
65. #13063298	C₂²	semidirect
66. #13063297	C₂²	semidirect
67. #13063297	C₂²	semidirect
68. #13063297	C₂²	semidirect
69. #13063297	C₂²	semidirect
71. #13063296	C₂²	semidirect
73. #13063295	C₂²	semidirect
75. #13063293	C₂²	semidirect
76. Q₈×Dic₄₃	C₂²	semidirect
78. C₄×D₁₇₂	C₂²	semidirect
79. C₄×D₁₇₂	C₂²	semidirect
80. D₄×Dic₄₃	C₂²	semidirect
81. D₄×Dic₄₃	C₂²	semidirect
82. D₄×Dic₄₃	C₂²	semidirect
84. #13063287	C₂²	semidirect
86. C₄×C₂²⋊D₄₃	C₂²	semidirect
87. C₄×C₂²⋊D₄₃	C₂²	semidirect
88. C₄×C₂²⋊D₄₃	C₂²	semidirect
89. C₄×C₂²⋊D₄₃	C₂²	semidirect
91. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
92. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
93. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
94. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
95. #13063284	C₂²	semidirect
96. #13063283	C₂²	semidirect
97. #13063283	C₂²	semidirect
98. #13063282	C₂²	semidirect
99. #13063282	C₂²	semidirect
100. #13063281	C₂²	semidirect
101. C₂×C₄⋊Dic₄₃	C₂²	semidirect
102. C₂×Dic₄₃⋊C₄	C₂²	semidirect
103. C₄⋊C₄×D₄₃	C₂²	semidirect
104. C₄⋊C₄×D₄₃	C₂²	semidirect
106. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
108. C₂²⋊C₄×D₄₃	C₂²	semidirect
109. C₂²⋊C₄×D₄₃	C₂²	semidirect
110. C₂²⋊C₄×D₄₃	C₂²	semidirect
111. C₄²×D₄₃	C₂²	semidirect
112. C₂×#41×C₄₃	C₂²	semidirect
113. C₂²×Q₈×C₄₃	C₂²	semidirect
114. #124×C₄₃	C₂²	semidirect
115. #124×C₄₃	C₂²	semidirect
116. C₂²⋊Q₈×C₄₃	C₂²	semidirect
117. C₂²⋊Q₈×C₄₃	C₂²	semidirect
118. #121×C₄₃	C₂²	semidirect
119. #121×C₄₃	C₂²	semidirect
120. C₄×Q₈×C₄₃	C₂²	semidirect
121. C₄×D₄×C₄₃	C₂²	semidirect
122. C₄×D₄×C₄₃	C₂²	semidirect
241. C₂²×D₄₃	#41	semidirect
361. #548	D₄₃	semidirect
375. C₄₃	#3505	semidirect
377. C₂×#41	C₂×D₄₃	semidirect
378. C₂²×Q₈	C₂×D₄₃	semidirect
396. #124	C₂×D₄₃	semidirect
397. #124	C₂×D₄₃	semidirect
416. C₂²⋊Q₈	C₂×D₄₃	semidirect
417. C₂²⋊Q₈	C₂×D₄₃	semidirect
430. #121	C₂×D₄₃	semidirect
431. #121	C₂×D₄₃	semidirect
437. C₄×Q₈	C₂×D₄₃	semidirect
456. C₄×D₄	C₂×D₄₃	semidirect
457. C₄×D₄	C₂×D₄₃	semidirect