Subgroups — C₂×C₄₃×#3002 #24980370

Order 11008.

5130 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#135×C₄₃	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#3002	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₄₃×#452	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₃×#449	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#416	C₂	1	2	yes	maximal, complemented
12	C₂²×C₂²⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₄₃	—	2	16	no	—
14	C₂²×#41×C₄₃	—	2	1	no	—
15	C₂²×#41×C₄₃	—	2	4	no	—
16	C₂²×#41×C₄₃	—	2	1	no	—
17	C₂²×#41×C₄₃	C₂²	1	2	yes	—
18	C₂²×#41×C₄₃	C₂²	1	2	yes	—
19	C₂²×#41×C₄₃	C₂²	1	8	yes	complemented
20	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₄₃	—	2	1	no	—
23	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₂⁴×C₄×C₄₃	—	2	1	no	—
25	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#135×C₄₃	—	2	16	no	—
27	C₂×#135×C₄₃	C₂²	1	16	yes	complemented
28	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	complemented
29	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
30	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
31	C₂²×D₈×C₄₃	C₂²	1	2	yes	complemented
32	C₂³×C₈×C₄₃	C₂²	1	2	yes	complemented
33	C₄₃×#525	—	2	4	no	—
34	C₄₃×#525	C₂²	1	8	yes	complemented
35	C₂×#123×C₄₃	—	2	1	no	—
36	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×#120×C₄₃	—	2	1	no	—
41	C₂×C₄×D₄×C₄₃	—	2	1	no	—
42	C₂×C₄×D₄×C₄₃	—	2	1	no	—
43	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic, complemented
44	C₄₃×#452	C₂²	1	16	yes	complemented
45	C₄₃×#451	C₂²	1	8	yes	complemented
46	C₄₃×#450	C₂²	1	8	yes	complemented
47	C₄₃×#449	C₂²	1	16	yes	complemented
48	C₄₃×#448	C₂²	1	8	yes	complemented
49	C₄₃×#447	C₂²	1	8	yes	complemented
50	C₄₃×#416	C₂²	1	16	yes	complemented
51	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
52	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
53	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
54	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
55	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊C₈×C₄₃	C₂²	1	8	yes	complemented
58	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	complemented
59	C₂⁵×C₄₃	—	2	1	no	—
60	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
61	C₂×#41×C₄₃	—	2	64	no	—
62	C₂×#41×C₄₃	—	2	16	no	—
63	C₂×#41×C₄₃	—	2	16	no	—
64	C₂×#41×C₄₃	—	2	64	no	—
65	C₂×#41×C₄₃	—	2	8	no	—
66	C₂×#41×C₄₃	—	2	8	no	—
67	C₂×#41×C₄₃	—	2	8	no	—
68	C₂×#41×C₄₃	—	2	4	no	—
69	C₂×#41×C₄₃	—	2	4	no	—
70	C₂×#41×C₄₃	—	2	8	no	—
71	C₂×#41×C₄₃	—	2	8	no	—
72	C₂×#41×C₄₃	—	2	2	no	—
73	C₂×#41×C₄₃	—	2	8	no	—
74	C₂×#41×C₄₃	D₄	1	16	yes	complemented
75	C₂×#41×C₄₃	C₂³	1	8	yes	—
76	C₂×#41×C₄₃	C₂³	1	8	yes	—
77	C₂×#41×C₄₃	C₂³	1	4	yes	complemented
78	C₂²×Q₈×C₄₃	—	2	8	no	—
79	C₂²×Q₈×C₄₃	—	2	1	no	—
80	C₂²×Q₈×C₄₃	—	2	2	no	—
81	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₄₃	C₂³	1	4	yes	—
83	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₄₃	—	2	16	no	—
85	C₂²×D₄×C₄₃	—	2	2	no	—
86	C₂²×D₄×C₄₃	—	2	2	no	—
87	C₂²×D₄×C₄₃	—	2	8	no	—
88	C₂²×D₄×C₄₃	—	2	8	no	—
89	C₂²×D₄×C₄₃	—	2	1	no	—
90	C₂²×D₄×C₄₃	—	2	1	no	—
91	C₂²×D₄×C₄₃	—	2	1	no	—
92	C₂²×D₄×C₄₃	—	2	1	no	—
93	C₂²×D₄×C₄₃	—	2	2	no	—
94	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
96	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
97	C₂³×C₄×C₄₃	—	2	16	no	—
98	C₂³×C₄×C₄₃	—	2	1	no	—
99	C₂³×C₄×C₄₃	—	2	2	no	—
100	C₂³×C₄×C₄₃	—	2	8	no	—
101	C₂³×C₄×C₄₃	—	2	8	no	—
102	C₂³×C₄×C₄₃	—	2	2	no	—
103	C₂³×C₄×C₄₃	—	2	1	no	—
104	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
105	C₂³×C₄×C₄₃	D₄	1	4	yes	—
106	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
111	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
112	#135×C₄₃	—	2	64	no	—
113	C₂×Q₁₆×C₄₃	—	2	8	no	—
114	C₂×Q₁₆×C₄₃	C₂³	1	8	yes	complemented
115	C₂×SD₁₆×C₄₃	—	2	8	no	—
116	C₂×SD₁₆×C₄₃	—	2	8	no	—
117	C₂×SD₁₆×C₄₃	C₂³	1	8	yes	complemented
118	C₂×SD₁₆×C₄₃	C₂³	1	8	yes	complemented
119	C₂×D₈×C₄₃	—	2	8	no	—
120	C₂×D₈×C₄₃	C₂³	1	8	yes	complemented
121	C₂²×C₈×C₄₃	—	2	8	no	—
122	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
123	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
124	C₂²×C₈×C₄₃	C₂³	1	8	yes	complemented
125	#123×C₄₃	—	2	8	no	—
126	C₂²⋊Q₈×C₄₃	—	2	2	no	—
127	C₂²⋊Q₈×C₄₃	—	2	2	no	—
128	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
129	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	complemented
130	#121×C₄₃	—	2	2	no	—
131	#121×C₄₃	—	2	2	no	—
132	#121×C₄₃	C₂³	1	4	yes	—
133	#121×C₄₃	C₂³	1	4	yes	complemented
134	#120×C₄₃	—	2	8	no	—
135	C₄×D₄×C₄₃	—	2	8	no	—
136	C₄×D₄×C₄₃	—	2	8	no	—
137	#117×C₄₃	—	2	2	no	—
138	#117×C₄₃	C₂³	1	4	yes	complemented
139	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
140	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
141	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
148	C₂×C₄²×C₄₃	—	2	1	no	—
149	#103×C₄₃	C₂³	1	8	yes	complemented
150	#103×C₄₃	C₂³	1	8	yes	complemented
151	#102×C₄₃	C₂³	1	8	yes	complemented
152	#102×C₄₃	C₂³	1	8	yes	complemented
153	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
154	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
155	C₂²⋊C₈×C₄₃	C₂³	1	8	yes	complemented
156	C₂⁴×C₄₃	—	2	8	no	—
157	C₂⁴×C₄₃	—	2	4	no	—
158	C₂⁴×C₄₃	—	2	4	no	—
159	C₂⁴×C₄₃	—	2	4	no	—
160	C₂⁴×C₄₃	—	2	2	no	—
161	C₂⁴×C₄₃	—	2	1	no	—
162	C₂⁴×C₄₃	—	4	2	no	—
163	C₂⁴×C₄₃	—	4	4	no	—
164	C₂⁴×C₄₃	—	4	4	no	—
165	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
167	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
169	#41×C₄₃	—	2	64	no	—
170	#41×C₄₃	—	2	32	no	—
171	#41×C₄₃	—	2	64	no	—
172	#41×C₄₃	—	2	16	no	—
173	#41×C₄₃	—	2	16	no	—
174	#41×C₄₃	—	2	32	no	—
175	#41×C₄₃	—	2	16	no	—
176	#41×C₄₃	—	2	16	no	—
177	#41×C₄₃	—	4	8	no	—
178	#41×C₄₃	C₂×D₄	1	32	yes	complemented
179	C₂×Q₈×C₄₃	—	2	16	no	—
180	C₂×Q₈×C₄₃	—	2	8	no	—
181	C₂×Q₈×C₄₃	—	2	16	no	—
182	C₂×Q₈×C₄₃	—	2	4	no	—
183	C₂×Q₈×C₄₃	—	2	4	no	—
184	C₂×Q₈×C₄₃	—	2	2	no	—
185	C₂×Q₈×C₄₃	—	2	1	no	—
186	C₂×Q₈×C₄₃	—	2	4	no	—
187	C₂×Q₈×C₄₃	C₂×D₄	1	8	yes	—
188	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
189	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
190	C₂×D₄×C₄₃	—	2	16	no	—
191	C₂×D₄×C₄₃	—	2	64	no	—
192	C₂×D₄×C₄₃	—	2	16	no	—
193	C₂×D₄×C₄₃	—	2	8	no	—
194	C₂×D₄×C₄₃	—	2	16	no	—
195	C₂×D₄×C₄₃	—	2	4	no	—
196	C₂×D₄×C₄₃	—	2	4	no	—
197	C₂×D₄×C₄₃	—	2	2	no	—
198	C₂×D₄×C₄₃	—	2	1	no	—
199	C₂×D₄×C₄₃	—	2	16	no	—
200	C₂×D₄×C₄₃	—	2	8	no	—
201	C₂×D₄×C₄₃	—	2	8	no	—
202	C₂×D₄×C₄₃	—	2	4	no	—
203	C₂×D₄×C₄₃	—	2	4	no	—
204	C₂×D₄×C₄₃	—	2	4	no	—
205	C₂×D₄×C₄₃	—	2	4	no	—
206	C₂×D₄×C₄₃	—	4	4	no	—
207	C₂×D₄×C₄₃	—	4	4	no	—
208	C₂×D₄×C₄₃	—	4	4	no	—
209	C₂×D₄×C₄₃	C₂×D₄	1	8	yes	—
210	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
211	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₄₃	—	2	8	no	—
213	C₂²×C₄×C₄₃	—	2	64	no	—
214	C₂²×C₄×C₄₃	—	2	16	no	—
215	C₂²×C₄×C₄₃	—	2	4	no	—
216	C₂²×C₄×C₄₃	—	2	16	no	—
217	C₂²×C₄×C₄₃	—	2	4	no	—
218	C₂²×C₄×C₄₃	—	2	16	no	—
219	C₂²×C₄×C₄₃	—	2	8	no	—
220	C₂²×C₄×C₄₃	—	2	8	no	—
221	C₂²×C₄×C₄₃	—	2	4	no	—
222	C₂²×C₄×C₄₃	—	2	4	no	—
223	C₂²×C₄×C₄₃	—	2	16	no	—
224	C₂²×C₄×C₄₃	—	2	4	no	—
225	C₂²×C₄×C₄₃	—	2	4	no	—
226	C₂²×C₄×C₄₃	—	2	4	no	—
227	C₂²×C₄×C₄₃	—	2	2	no	—
228	C₂²×C₄×C₄₃	—	2	1	no	—
229	C₂²×C₄×C₄₃	—	2	1	no	—
230	C₂²×C₄×C₄₃	—	2	1	no	—
231	C₂²×C₄×C₄₃	—	4	4	no	—
232	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
233	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
237	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
239	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
246	Q₁₆×C₄₃	—	2	16	no	—
247	SD₁₆×C₄₃	—	2	16	no	—
248	SD₁₆×C₄₃	—	2	16	no	—
249	D₈×C₄₃	—	2	16	no	—
250	C₂×C₈×C₄₃	—	2	4	no	—
251	C₂×C₈×C₄₃	—	2	4	no	—
252	C₂×C₈×C₄₃	—	2	16	no	—
253	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
254	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
255	C₄⋊C₄×C₄₃	—	2	4	no	—
256	C₄⋊C₄×C₄₃	—	2	4	no	—
257	C₄⋊C₄×C₄₃	—	2	1	no	—
258	C₄⋊C₄×C₄₃	—	2	1	no	—
259	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
261	C₂²⋊C₄×C₄₃	—	2	4	no	—
262	C₂²⋊C₄×C₄₃	—	2	4	no	—
263	C₂²⋊C₄×C₄₃	—	2	4	no	—
264	C₂²⋊C₄×C₄₃	—	2	4	no	—
265	C₂²⋊C₄×C₄₃	—	2	4	no	—
266	C₄²×C₄₃	—	2	4	no	—
267	C₂³×C₄₃	—	2	2	no	—
268	C₂³×C₄₃	—	2	2	no	—
269	C₂³×C₄₃	—	2	2	no	—
270	C₂³×C₄₃	—	2	2	no	—
271	C₂³×C₄₃	—	2	16	no	—
272	C₂³×C₄₃	—	2	8	no	—
273	C₂³×C₄₃	—	2	2	no	—
274	C₂³×C₄₃	—	2	8	no	—
275	C₂³×C₄₃	—	2	2	no	—
276	C₂³×C₄₃	—	2	8	no	—
277	C₂³×C₄₃	—	2	2	no	—
278	C₂³×C₄₃	—	2	4	no	—
279	C₂³×C₄₃	—	2	2	no	—
280	C₂³×C₄₃	—	4	4	no	—
281	C₂³×C₄₃	—	4	16	no	—
282	C₂³×C₄₃	—	4	32	no	—
283	C₂³×C₄₃	—	4	8	no	—
284	C₂³×C₄₃	—	4	4	no	—
285	C₂³×C₄₃	—	4	8	no	—
286	C₂³×C₄₃	—	4	4	no	—
287	C₂³×C₄₃	—	4	2	no	—
288	C₂³×C₄₃	—	4	2	no	—
289	C₂³×C₄₃	—	4	2	no	—
290	C₂³×C₄₃	#120	1	4	yes	—
291	C₂³×C₄₃	#135	1	4	yes	complemented
292	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
293	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
294	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
295	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
296	Q₈×C₄₃	—	2	16	no	—
297	Q₈×C₄₃	—	2	8	no	—
298	Q₈×C₄₃	—	2	4	no	—
299	Q₈×C₄₃	—	2	4	no	—
300	Q₈×C₄₃	—	4	2	no	—
301	Q₈×C₄₃	C₂²×D₄	1	8	yes	—
302	D₄×C₄₃	—	2	32	no	—
303	D₄×C₄₃	—	2	16	no	—
304	D₄×C₄₃	—	2	32	no	—
305	D₄×C₄₃	—	2	8	no	—
306	D₄×C₄₃	—	2	4	no	—
307	D₄×C₄₃	—	2	4	no	—
308	D₄×C₄₃	—	4	8	no	—
309	D₄×C₄₃	—	4	8	no	—
310	D₄×C₄₃	—	4	8	no	—
311	D₄×C₄₃	—	4	2	no	—
312	D₄×C₄₃	C₂²×D₄	1	8	yes	—
313	C₂×C₄×C₄₃	—	2	16	no	—
314	C₂×C₄×C₄₃	—	2	32	no	—
315	C₂×C₄×C₄₃	—	2	2	no	—
316	C₂×C₄×C₄₃	—	2	8	no	—
317	C₂×C₄×C₄₃	—	2	2	no	—
318	C₂×C₄×C₄₃	—	2	8	no	—
319	C₂×C₄×C₄₃	—	2	4	no	—
320	C₂×C₄×C₄₃	—	2	8	no	—
321	C₂×C₄×C₄₃	—	2	32	no	—
322	C₂×C₄×C₄₃	—	2	4	no	—
323	C₂×C₄×C₄₃	—	2	4	no	—
324	C₂×C₄×C₄₃	—	2	8	no	—
325	C₂×C₄×C₄₃	—	2	4	no	—
326	C₂×C₄×C₄₃	—	2	4	no	—
327	C₂×C₄×C₄₃	—	2	2	no	—
328	C₂×C₄×C₄₃	—	2	2	no	—
329	C₂×C₄×C₄₃	—	2	2	no	—
330	C₂×C₄×C₄₃	—	4	2	no	—
331	C₂×C₄×C₄₃	—	4	2	no	—
332	C₂×C₄×C₄₃	—	4	2	no	—
333	C₂×C₄×C₄₃	—	4	8	no	—
334	C₂×C₄×C₄₃	#120	1	4	yes	—
335	C₂×C₄×C₄₃	#120	1	8	yes	—
336	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
341	C₂×C₄×C₄₃	C₂²×D₄	1	8	yes	—
342	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
343	C₈×C₄₃	—	2	4	no	—
344	C₈×C₄₃	—	2	4	no	—
345	C₂×#3002	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂²×C₄₃	—	2	2	no	—
347	C₂²×C₄₃	—	2	8	no	—
348	C₂²×C₄₃	—	2	8	no	—
349	C₂²×C₄₃	—	2	2	no	—
350	C₂²×C₄₃	—	2	2	no	—
351	C₂²×C₄₃	—	2	2	no	—
352	C₂²×C₄₃	—	2	8	no	—
353	C₂²×C₄₃	—	2	2	no	—
354	C₂²×C₄₃	—	2	2	no	—
355	C₂²×C₄₃	—	2	2	no	—
356	C₂²×C₄₃	—	4	16	no	—
357	C₂²×C₄₃	—	4	32	no	—
358	C₂²×C₄₃	—	4	4	no	—
359	C₂²×C₄₃	—	4	16	no	—
360	C₂²×C₄₃	—	4	4	no	—
361	C₂²×C₄₃	—	4	4	no	—
362	C₂²×C₄₃	—	4	2	no	—
363	C₂²×C₄₃	—	4	2	no	—
364	C₂²×C₄₃	—	4	2	no	—
365	C₂²×C₄₃	—	8	4	no	—
366	C₂²×C₄₃	C₂×#120	1	4	yes	—
367	C₂²×C₄₃	C₂×#120	1	2	yes	—
368	C₂²×C₄₃	C₂×#135	1	2	yes	—
369	C₂²×C₄₃	C₂×#135	1	4	yes	complemented
370	C₂²×C₄₃	#575	1	2	yes	—
371	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
372	C₄×C₄₃	—	2	2	no	—
373	C₄×C₄₃	—	2	8	no	—
374	C₄×C₄₃	—	2	2	no	—
375	C₄×C₄₃	—	4	2	no	—
376	C₄×C₄₃	—	4	2	no	—
377	C₄×C₄₃	—	4	2	no	—
378	C₄×C₄₃	C₂×#120	1	4	yes	—
379	C₄×C₄₃	C₂×#120	1	2	yes	—
380	C₄×C₄₃	C₂³×D₄	1	2	yes	—
381	C₂³×#41	C₂×C₄₃	1	1	yes	characteristic, complemented
382	C₂²×#135	C₂×C₄₃	1	2	yes	complemented
383	C₂×#525	C₂×C₄₃	1	1	yes	characteristic, complemented
384	#3002	C₂×C₄₃	1	16	yes	direct product factor
385	C₂×#452	C₂×C₄₃	1	2	yes	complemented
386	C₂×#449	C₂×C₄₃	1	2	yes	complemented
387	C₂×#451	C₂×C₄₃	1	1	yes	characteristic, complemented
388	C₂×#448	C₂×C₄₃	1	1	yes	characteristic, complemented
389	C₂×#450	C₂×C₄₃	1	1	yes	characteristic, complemented
390	C₂×#447	C₂×C₄₃	1	1	yes	characteristic, complemented
391	C₂×#416	C₂×C₄₃	1	2	yes	complemented
392	C₂²×C₂²⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
393	C₂×C₄₃	—	2	4	no	—
394	C₂×C₄₃	—	2	4	no	—
395	C₂×C₄₃	—	4	2	no	—
396	C₂×C₄₃	—	4	8	no	—
397	C₂×C₄₃	—	8	2	no	—
398	C₂×C₄₃	#3002	1	4	yes	direct product factor
399	C₂×C₄₃	C₂²×#120	1	1	yes	characteristic
400	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
401	C₂×C₄₃	C₂×#575	1	1	yes	characteristic
402	C₂²×#41	—	2	16	no	—
403	C₂²×#41	—	2	1	no	—
404	C₂²×#41	—	2	1	no	—
405	C₂²×#41	—	2	4	no	—
406	C₂²×#41	C₂²×C₄₃	1	2	yes	—
407	C₂²×#41	C₂²×C₄₃	1	2	yes	—
408	C₂²×#41	C₂²×C₄₃	1	8	yes	complemented
409	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic, complemented
410	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
411	C₂³×D₄	—	2	1	no	—
412	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
413	C₂⁴×C₄	—	2	1	no	—
414	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
415	C₂×#135	—	2	16	no	—
416	C₂×#135	C₂²×C₄₃	1	16	yes	complemented
417	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	complemented
418	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	complemented
419	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	complemented
420	C₂²×D₈	C₂²×C₄₃	1	2	yes	complemented
421	C₂³×C₈	C₂²×C₄₃	1	2	yes	complemented
422	#525	—	2	4	no	—
423	#525	C₂²×C₄₃	1	8	yes	complemented
424	C₂×#123	—	2	1	no	—
425	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
426	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
427	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
428	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic, complemented
429	C₂×#120	—	2	1	no	—
430	C₂×C₄×D₄	—	2	1	no	—
431	C₂×C₄×D₄	—	2	1	no	—
432	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic, complemented
433	#452	C₂²×C₄₃	1	16	yes	complemented
434	#451	C₂²×C₄₃	1	8	yes	complemented
435	#450	C₂²×C₄₃	1	8	yes	complemented
436	#449	C₂²×C₄₃	1	16	yes	complemented
437	#448	C₂²×C₄₃	1	8	yes	complemented
438	#447	C₂²×C₄₃	1	8	yes	complemented
439	#416	C₂²×C₄₃	1	16	yes	complemented
440	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
441	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
442	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
443	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
444	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
446	C₂×C₂²⋊C₈	C₂²×C₄₃	1	8	yes	complemented
447	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	complemented
448	C₄₃	C₂×#3002	1	1	yes	characteristic, direct product factor, Sylow
449	C₂⁵	—	2	1	no	—
450	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
451	C₂×#41	—	2	16	no	—
452	C₂×#41	—	2	64	no	—
453	C₂×#41	—	2	16	no	—
454	C₂×#41	—	2	64	no	—
455	C₂×#41	—	2	8	no	—
456	C₂×#41	—	2	8	no	—
457	C₂×#41	—	2	8	no	—
458	C₂×#41	—	2	4	no	—
459	C₂×#41	—	2	4	no	—
460	C₂×#41	—	2	8	no	—
461	C₂×#41	—	2	8	no	—
462	C₂×#41	—	2	2	no	—
463	C₂×#41	—	2	8	no	—
464	C₂×#41	D₄×C₄₃	1	16	yes	complemented
465	C₂×#41	C₂³×C₄₃	1	8	yes	—
466	C₂×#41	C₂³×C₄₃	1	8	yes	—
467	C₂×#41	C₂³×C₄₃	1	4	yes	complemented
468	C₂²×Q₈	—	2	8	no	—
469	C₂²×Q₈	—	2	1	no	—
470	C₂²×Q₈	—	2	2	no	—
471	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₄₃	1	4	yes	—
473	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
474	C₂²×D₄	—	2	16	no	—
475	C₂²×D₄	—	2	2	no	—
476	C₂²×D₄	—	2	2	no	—
477	C₂²×D₄	—	2	8	no	—
478	C₂²×D₄	—	2	8	no	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	—	2	1	no	—
483	C₂²×D₄	—	2	2	no	—
484	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
486	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
487	C₂³×C₄	—	2	16	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	2	no	—
490	C₂³×C₄	—	2	2	no	—
491	C₂³×C₄	—	2	8	no	—
492	C₂³×C₄	—	2	8	no	—
493	C₂³×C₄	—	2	1	no	—
494	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
495	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
496	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
497	C₂³×C₄	D₄×C₄₃	1	4	yes	—
498	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
501	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
502	#135	—	2	64	no	—
503	C₂×Q₁₆	—	2	8	no	—
504	C₂×Q₁₆	C₂³×C₄₃	1	8	yes	complemented
505	C₂×SD₁₆	—	2	8	no	—
506	C₂×SD₁₆	—	2	8	no	—
507	C₂×SD₁₆	C₂³×C₄₃	1	8	yes	complemented
508	C₂×SD₁₆	C₂³×C₄₃	1	8	yes	complemented
509	C₂×D₈	—	2	8	no	—
510	C₂×D₈	C₂³×C₄₃	1	8	yes	complemented
511	C₂²×C₈	—	2	8	no	—
512	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
513	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
514	C₂²×C₈	C₂³×C₄₃	1	8	yes	complemented
515	#123	—	2	8	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
519	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	complemented
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	C₂³×C₄₃	1	4	yes	—
523	#121	C₂³×C₄₃	1	4	yes	complemented
524	#120	—	2	8	no	—
525	C₄×D₄	—	2	8	no	—
526	C₄×D₄	—	2	8	no	—
527	#117	—	2	2	no	—
528	#117	C₂³×C₄₃	1	4	yes	complemented
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₄²	—	2	1	no	—
539	#103	C₂³×C₄₃	1	8	yes	complemented
540	#103	C₂³×C₄₃	1	8	yes	complemented
541	#102	C₂³×C₄₃	1	8	yes	complemented
542	#102	C₂³×C₄₃	1	8	yes	complemented
543	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
544	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
545	C₂²⋊C₈	C₂³×C₄₃	1	8	yes	complemented
546	C₂⁴	—	2	8	no	—
547	C₂⁴	—	2	4	no	—
548	C₂⁴	—	2	4	no	—
549	C₂⁴	—	2	4	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	1	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	4	4	no	—
554	C₂⁴	—	4	4	no	—
555	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
556	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
557	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
558	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
559	#41	—	2	64	no	—
560	#41	—	2	32	no	—
561	#41	—	2	64	no	—
562	#41	—	2	16	no	—
563	#41	—	2	16	no	—
564	#41	—	2	32	no	—
565	#41	—	2	16	no	—
566	#41	—	2	16	no	—
567	#41	—	4	8	no	—
568	#41	C₂×D₄×C₄₃	1	32	yes	complemented
569	C₂×Q₈	—	2	16	no	—
570	C₂×Q₈	—	2	8	no	—
571	C₂×Q₈	—	2	16	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	4	no	—
577	C₂×Q₈	C₂×D₄×C₄₃	1	8	yes	—
578	C₂×Q₈	C₂⁴×C₄₃	1	2	yes	—
579	C₂×Q₈	C₂⁴×C₄₃	1	4	yes	—
580	C₂×D₄	—	2	64	no	—
581	C₂×D₄	—	2	16	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	16	no	—
584	C₂×D₄	—	2	16	no	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	16	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	C₂×D₄×C₄₃	1	8	yes	—
600	C₂×D₄	C₂⁴×C₄₃	1	2	yes	—
601	C₂×D₄	C₂⁴×C₄₃	1	4	yes	—
602	C₂²×C₄	—	2	8	no	—
603	C₂²×C₄	—	2	64	no	—
604	C₂²×C₄	—	2	16	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	16	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	16	no	—
612	C₂²×C₄	—	2	8	no	—
613	C₂²×C₄	—	2	8	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	16	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
625	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
626	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
627	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
628	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
629	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
631	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
636	Q₁₆	—	2	16	no	—
637	SD₁₆	—	2	16	no	—
638	SD₁₆	—	2	16	no	—
639	D₈	—	2	16	no	—
640	C₂×C₈	—	2	4	no	—
641	C₂×C₈	—	2	4	no	—
642	C₂×C₈	—	2	16	no	—
643	C₂×C₈	C₂⁴×C₄₃	1	4	yes	—
644	C₂×C₈	C₂⁴×C₄₃	1	4	yes	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂⁴×C₄₃	1	2	yes	—
650	C₄⋊C₄	C₂⁴×C₄₃	1	2	yes	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	16	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	8	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	8	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	4	4	no	—
671	C₂³	—	4	16	no	—
672	C₂³	—	4	32	no	—
673	C₂³	—	4	8	no	—
674	C₂³	—	4	4	no	—
675	C₂³	—	4	8	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	#120×C₄₃	1	4	yes	—
681	C₂³	#135×C₄₃	1	4	yes	complemented
682	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
683	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
684	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
685	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
686	Q₈	—	2	16	no	—
687	Q₈	—	2	8	no	—
688	Q₈	—	2	4	no	—
689	Q₈	—	2	4	no	—
690	Q₈	—	4	2	no	—
691	Q₈	C₂²×D₄×C₄₃	1	8	yes	—
692	D₄	—	2	32	no	—
693	D₄	—	2	16	no	—
694	D₄	—	2	32	no	—
695	D₄	—	2	8	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	4	no	—
698	D₄	—	4	8	no	—
699	D₄	—	4	8	no	—
700	D₄	—	4	8	no	—
701	D₄	—	4	2	no	—
702	D₄	C₂²×D₄×C₄₃	1	8	yes	—
703	C₂×C₄	—	2	16	no	—
704	C₂×C₄	—	2	32	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	8	no	—
711	C₂×C₄	—	2	32	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	8	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	#120×C₄₃	1	4	yes	—
725	C₂×C₄	#120×C₄₃	1	8	yes	—
726	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
731	C₂×C₄	C₂²×D₄×C₄₃	1	8	yes	—
732	C₂×C₄	C₂⁵×C₄₃	1	1	yes	characteristic
733	C₈	—	2	4	no	—
734	C₈	—	2	4	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	8	no	—
737	C₂²	—	2	8	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	8	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	4	16	no	—
746	C₂²	—	4	32	no	—
747	C₂²	—	4	4	no	—
748	C₂²	—	4	16	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	8	4	no	—
755	C₂²	C₂×#120×C₄₃	1	4	yes	—
756	C₂²	C₂×#120×C₄₃	1	2	yes	—
757	C₂²	C₂×#135×C₄₃	1	2	yes	—
758	C₂²	C₂×#135×C₄₃	1	4	yes	complemented
759	C₂²	C₄₃×#575	1	2	yes	—
760	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
761	C₄	—	2	2	no	—
762	C₄	—	2	8	no	—
763	C₄	—	2	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	C₂×#120×C₄₃	1	4	yes	—
768	C₄	C₂×#120×C₄₃	1	2	yes	—
769	C₄	C₂³×D₄×C₄₃	1	2	yes	—
770	C₂	—	2	4	no	—
771	C₂	—	2	4	no	—
772	C₂	—	4	2	no	—
773	C₂	—	4	8	no	—
774	C₂	—	8	2	no	—
775	C₂	C₄₃×#3002	1	4	yes	direct product factor
776	C₂	C₂²×#120×C₄₃	1	1	yes	characteristic
777	C₂	C₂²×#135×C₄₃	1	1	yes	characteristic
778	C₂	C₂×C₄₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₃
socle	C₂³×C₄₃	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₄₃	C₂	semidirect
2. C₂²×#135×C₄₃	C₂	semidirect
3. C₂×C₄₃×#525	C₂	semidirect
4. C₄₃×#3002	C₂	direct (N × H)
5. C₂×C₄₃×#452	C₂	semidirect
6. C₂×C₄₃×#449	C₂	semidirect
7. C₂×C₄₃×#451	C₂	semidirect
8. C₂×C₄₃×#448	C₂	semidirect
9. C₂×C₄₃×#450	C₂	semidirect
10. C₂×C₄₃×#447	C₂	semidirect
11. C₂×C₄₃×#416	C₂	semidirect
12. C₂²×C₂²⋊C₈×C₄₃	C₂	semidirect
19. C₂²×#41×C₄₃	C₂²	semidirect
20. C₂²×#41×C₄₃	C₂²	semidirect
27. C₂×#135×C₄₃	C₂²	semidirect
28. C₂²×Q₁₆×C₄₃	C₂²	semidirect
29. C₂²×SD₁₆×C₄₃	C₂²	semidirect
30. C₂²×SD₁₆×C₄₃	C₂²	semidirect
31. C₂²×D₈×C₄₃	C₂²	semidirect
32. C₂³×C₈×C₄₃	C₂²	semidirect
34. C₄₃×#525	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
39. C₂×#121×C₄₃	C₂²	semidirect
43. C₂×#117×C₄₃	C₂²	semidirect
44. C₄₃×#452	C₂²	semidirect
45. C₄₃×#451	C₂²	semidirect
46. C₄₃×#450	C₂²	semidirect
47. C₄₃×#449	C₂²	semidirect
48. C₄₃×#448	C₂²	semidirect
49. C₄₃×#447	C₂²	semidirect
50. C₄₃×#416	C₂²	semidirect
51. C₂×#103×C₄₃	C₂²	semidirect
52. C₂×#103×C₄₃	C₂²	semidirect
53. C₂×#102×C₄₃	C₂²	semidirect
54. C₂×#102×C₄₃	C₂²	semidirect
57. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
58. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
74. C₂×#41×C₄₃	D₄	semidirect
77. C₂×#41×C₄₃	C₂³	semidirect
114. C₂×Q₁₆×C₄₃	C₂³	semidirect
117. C₂×SD₁₆×C₄₃	C₂³	semidirect
118. C₂×SD₁₆×C₄₃	C₂³	semidirect
120. C₂×D₈×C₄₃	C₂³	semidirect
124. C₂²×C₈×C₄₃	C₂³	semidirect
129. C₂²⋊Q₈×C₄₃	C₂³	semidirect
133. #121×C₄₃	C₂³	semidirect
138. #117×C₄₃	C₂³	semidirect
149. #103×C₄₃	C₂³	semidirect
150. #103×C₄₃	C₂³	semidirect
151. #102×C₄₃	C₂³	semidirect
152. #102×C₄₃	C₂³	semidirect
155. C₂²⋊C₈×C₄₃	C₂³	semidirect
178. #41×C₄₃	C₂×D₄	semidirect
291. C₂³×C₄₃	#135	semidirect
345. C₂×#3002	C₄₃	direct (N × H)
369. C₂²×C₄₃	C₂×#135	semidirect
381. C₂³×#41	C₂×C₄₃	semidirect
382. C₂²×#135	C₂×C₄₃	semidirect
383. C₂×#525	C₂×C₄₃	semidirect
384. #3002	C₂×C₄₃	direct (N × H)
385. C₂×#452	C₂×C₄₃	semidirect
386. C₂×#449	C₂×C₄₃	semidirect
387. C₂×#451	C₂×C₄₃	semidirect
388. C₂×#448	C₂×C₄₃	semidirect
389. C₂×#450	C₂×C₄₃	semidirect
390. C₂×#447	C₂×C₄₃	semidirect
391. C₂×#416	C₂×C₄₃	semidirect
392. C₂²×C₂²⋊C₈	C₂×C₄₃	semidirect
398. C₂×C₄₃	#3002	direct (N × H)
408. C₂²×#41	C₂²×C₄₃	semidirect
409. C₂²×#41	C₂²×C₄₃	semidirect
416. C₂×#135	C₂²×C₄₃	semidirect
417. C₂²×Q₁₆	C₂²×C₄₃	semidirect
418. C₂²×SD₁₆	C₂²×C₄₃	semidirect
419. C₂²×SD₁₆	C₂²×C₄₃	semidirect
420. C₂²×D₈	C₂²×C₄₃	semidirect
421. C₂³×C₈	C₂²×C₄₃	semidirect
423. #525	C₂²×C₄₃	semidirect
426. C₂×C₂²⋊Q₈	C₂²×C₄₃	semidirect
428. C₂×#121	C₂²×C₄₃	semidirect
432. C₂×#117	C₂²×C₄₃	semidirect
433. #452	C₂²×C₄₃	semidirect
434. #451	C₂²×C₄₃	semidirect
435. #450	C₂²×C₄₃	semidirect
436. #449	C₂²×C₄₃	semidirect
437. #448	C₂²×C₄₃	semidirect
438. #447	C₂²×C₄₃	semidirect
439. #416	C₂²×C₄₃	semidirect
440. C₂×#103	C₂²×C₄₃	semidirect
441. C₂×#103	C₂²×C₄₃	semidirect
442. C₂×#102	C₂²×C₄₃	semidirect
443. C₂×#102	C₂²×C₄₃	semidirect
446. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
447. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
448. C₄₃	C₂×#3002	direct (N × H)
464. C₂×#41	D₄×C₄₃	semidirect
467. C₂×#41	C₂³×C₄₃	semidirect
504. C₂×Q₁₆	C₂³×C₄₃	semidirect
507. C₂×SD₁₆	C₂³×C₄₃	semidirect
508. C₂×SD₁₆	C₂³×C₄₃	semidirect
510. C₂×D₈	C₂³×C₄₃	semidirect
514. C₂²×C₈	C₂³×C₄₃	semidirect
519. C₂²⋊Q₈	C₂³×C₄₃	semidirect
523. #121	C₂³×C₄₃	semidirect
528. #117	C₂³×C₄₃	semidirect
539. #103	C₂³×C₄₃	semidirect
540. #103	C₂³×C₄₃	semidirect
541. #102	C₂³×C₄₃	semidirect
542. #102	C₂³×C₄₃	semidirect
545. C₂²⋊C₈	C₂³×C₄₃	semidirect
568. #41	C₂×D₄×C₄₃	semidirect
681. C₂³	#135×C₄₃	semidirect
758. C₂²	C₂×#135×C₄₃	semidirect
775. C₂	C₄₃×#3002	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₄₃	2
C₂²×#135×C₄₃	2
C₂×C₄₃×#525	2
C₄₃×#3002	2
C₂×C₄₃×#452	2
C₂×C₄₃×#449	2
C₂×C₄₃×#451	2
C₂×C₄₃×#448	2
C₂×C₄₃×#450	2
C₂×C₄₃×#447	2
C₂×C₄₃×#416	2
C₂²×C₂²⋊C₈×C₄₃	2
C₂×#3002	43

Subgroups — C2×C43×#3002 #24980370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#3002 #24980370