Subgroups — C₂²×#14583706 #26010412

Order 11008.

11118 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063372	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13063371	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14583706	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#13063357	C₂	1	2	yes	maximal, complemented
5	C₂²×#13063355	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13063350	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13063349	C₂	1	2	yes	maximal, complemented
8	C₂²×#13063346	C₂	1	2	yes	maximal, complemented
9	C₂³×#10621873	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×D₄₃	C₂	1	2	yes	maximal, complemented
11	C₂²×#13063331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#135×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13063372	—	2	12	no	—
14	C₂×#13063372	C₂²	1	24	yes	complemented
15	C₂×#13063371	—	2	12	no	—
16	C₂×#13063371	C₂²	1	24	yes	complemented
17	C₂²×#10621902	C₂²	1	2	yes	—
18	C₂²×#10621898	—	2	1	no	—
19	C₂²×#10621898	—	2	1	no	—
20	C₂²×#10621898	C₂²	1	1	yes	characteristic
21	C₂²×#10621900	—	2	2	no	—
22	C₂²×#10621900	C₂²	1	2	yes	complemented
23	C₂³×Dic₈₆	—	2	1	no	—
24	C₂³×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
25	C₂²×Q₈×D₄₃	C₂²	1	2	yes	complemented
26	C₂³×D₁₇₂	—	2	1	no	—
27	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic
28	C₂²×D₄×D₄₃	—	2	2	no	—
29	C₂²×D₄×D₄₃	C₂²	1	2	yes	—
30	#14583706	C₂²	1	256	yes	direct product factor
31	C₂×#13063357	C₂²	1	48	yes	complemented
32	C₂×#13063355	C₂²	1	24	yes	complemented
33	C₂×#13063350	C₂²	1	24	yes	complemented
34	C₂×#13063349	C₂²	1	48	yes	complemented
35	C₂×#13063346	C₂²	1	48	yes	complemented
36	C₂²×#10621885	C₂²	1	2	yes	complemented
37	C₂²×#10621873	C₂²	1	2	yes	complemented
38	C₂²×#10621873	C₂²	1	2	yes	complemented
39	C₂²×#10621873	C₂²	1	24	yes	complemented
40	C₂²×#10621883	C₂²	1	2	yes	complemented
41	C₂²×#10621884	C₂²	1	2	yes	complemented
42	C₂×SD₁₆×D₄₃	C₂²	1	48	yes	complemented
43	C₂²×#10621882	C₂²	1	2	yes	complemented
44	C₂×#13063331	C₂²	1	24	yes	complemented
45	C₂²×#10621877	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#10621872	C₂²	1	2	yes	complemented
47	C₂²×C₈×D₄₃	C₂²	1	2	yes	complemented
48	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
49	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×#135×C₄₃	C₂²	1	24	yes	complemented
51	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
52	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
53	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
55	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
56	C₂⁴×D₄₃	—	2	1	no	—
57	C₂⁴×D₄₃	—	2	2	no	—
58	#13063372	—	2	96	no	—
59	#13063372	C₂³	1	64	yes	complemented
60	#13063371	—	2	96	no	—
61	#13063371	C₂³	1	64	yes	complemented
62	C₂×#10621902	—	2	12	no	—
63	C₂×#10621902	C₂³	1	24	yes	—
64	C₂×#10621898	—	2	24	no	—
65	C₂×#10621898	—	2	24	no	—
66	C₂×#10621898	D₄	1	12	yes	—
67	C₂×#10621898	C₂³	1	12	yes	—
68	C₂×#10621900	—	2	48	no	—
69	C₂×#10621900	—	2	12	no	—
70	C₂×#10621900	C₂³	1	24	yes	complemented
71	C₂²×Dic₈₆	—	2	1	no	—
72	C₂²×Dic₈₆	—	2	6	no	—
73	C₂²×Dic₈₆	—	2	2	no	—
74	C₂²×Dic₈₆	—	2	24	no	—
75	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
76	C₂²×Dic₈₆	C₂³	1	2	yes	—
77	C₂²×Dic₈₆	C₂³	1	12	yes	complemented
78	C₂×Q₈×D₄₃	—	2	12	no	—
79	C₂×Q₈×D₄₃	C₂³	1	24	yes	complemented
80	C₂²×D₁₇₂	—	2	2	no	—
81	C₂²×D₁₇₂	—	2	1	no	—
82	C₂²×D₁₇₂	—	2	6	no	—
83	C₂²×D₁₇₂	—	2	24	no	—
84	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
85	C₂²×D₁₇₂	C₂³	1	2	yes	—
86	C₂²×D₁₇₂	C₂³	1	12	yes	—
87	C₂²×C₂²⋊D₄₃	—	2	2	no	—
88	C₂²×C₂²⋊D₄₃	—	2	2	no	—
89	C₂²×C₂²⋊D₄₃	D₄	1	2	yes	—
90	C₂×D₄×D₄₃	—	2	48	no	—
91	C₂×D₄×D₄₃	—	2	12	no	—
92	C₂×D₄×D₄₃	C₂³	1	24	yes	—
93	C₂³×Dic₄₃	—	2	1	no	—
94	C₂³×Dic₄₃	—	2	2	no	—
95	C₂²×C₄×D₄₃	—	2	2	no	—
96	C₂²×C₄×D₄₃	—	2	2	no	—
97	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
98	#13063357	C₂³	1	128	yes	complemented
99	#13063355	C₂³	1	64	yes	complemented
100	#13063350	C₂³	1	64	yes	complemented
101	#13063349	C₂³	1	128	yes	complemented
102	#13063346	C₂³	1	128	yes	complemented
103	C₂×#10621885	C₂³	1	24	yes	complemented
104	C₂×#10621873	C₂³	1	24	yes	complemented
105	C₂×#10621873	C₂³	1	24	yes	complemented
106	C₂×#10621873	C₂³	1	64	yes	complemented
107	C₂×#10621883	C₂³	1	24	yes	complemented
108	C₂×#10621884	C₂³	1	24	yes	complemented
109	SD₁₆×D₄₃	C₂³	1	128	yes	complemented
110	C₂×#10621882	C₂³	1	24	yes	complemented
111	#13063331	C₂³	1	64	yes	complemented
112	C₂×#10621877	C₂³	1	12	yes	complemented
113	C₂×#10621872	C₂³	1	24	yes	complemented
114	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
115	C₂×C₈×D₄₃	C₂³	1	24	yes	complemented
116	C₂×#41×C₄₃	—	2	6	no	—
117	C₂×#41×C₄₃	—	2	6	no	—
118	C₂×#41×C₄₃	C₂³	1	12	yes	—
119	C₂×#41×C₄₃	C₂³	1	12	yes	complemented
120	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₄₃	—	2	1	no	—
123	C₂²×D₄×C₄₃	—	2	1	no	—
124	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₄₃	—	2	1	no	—
127	C₂³×C₄×C₄₃	—	2	1	no	—
128	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
129	#135×C₄₃	C₂³	1	64	yes	complemented
130	C₂×Q₁₆×C₄₃	C₂³	1	12	yes	complemented
131	C₂×SD₁₆×C₄₃	C₂³	1	12	yes	complemented
132	C₂×SD₁₆×C₄₃	C₂³	1	12	yes	complemented
133	C₂×D₈×C₄₃	C₂³	1	12	yes	complemented
134	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₄₃	C₂³	1	12	yes	complemented
137	C₂⁴×C₄₃	—	2	1	no	—
138	C₂⁴×C₄₃	—	2	1	no	—
139	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂³×D₄₃	—	2	2	no	—
141	C₂³×D₄₃	—	2	12	no	—
142	C₂³×D₄₃	—	2	24	no	—
143	C₂³×D₄₃	—	8	8	no	—
144	C₂³×D₄₃	—	8	4	no	—
145	C₂³×D₄₃	C₂×D₄	1	2	yes	—
146	#41×C₄₃	—	2	24	no	—
147	#41×C₄₃	—	2	24	no	—
148	#41×C₄₃	C₂⁴	1	16	yes	—
149	#41×C₄₃	C₂⁴	1	16	yes	complemented
150	C₂×Q₈×C₄₃	—	2	3	no	—
151	C₂×Q₈×C₄₃	—	2	3	no	—
152	C₂×Q₈×C₄₃	C₂⁴	1	6	yes	—
153	C₂×Q₈×C₄₃	C₂⁴	1	6	yes	—
154	C₂×D₄×C₄₃	—	2	3	no	—
155	C₂×D₄×C₄₃	—	2	3	no	—
156	C₂×D₄×C₄₃	—	2	12	no	—
157	C₂×D₄×C₄₃	—	2	12	no	—
158	C₂×D₄×C₄₃	C₂⁴	1	6	yes	—
159	C₂×D₄×C₄₃	C₂⁴	1	6	yes	—
160	C₂²×C₄×C₄₃	—	2	12	no	—
161	C₂²×C₄×C₄₃	—	2	12	no	—
162	C₂²×C₄×C₄₃	—	2	1	no	—
163	C₂²×C₄×C₄₃	—	2	1	no	—
164	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
166	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
168	C₂×C₂²⋊D₄₃	—	2	24	no	—
169	C₂×C₂²⋊D₄₃	—	2	24	no	—
170	C₂×C₂²⋊D₄₃	C₂×D₄	1	24	yes	—
171	C₂²×Dic₄₃	—	2	24	no	—
172	C₂²×Dic₄₃	—	2	2	no	—
173	C₂²×Dic₄₃	—	2	12	no	—
174	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
175	#10621902	—	2	48	no	—
176	#10621902	C₂⁴	1	32	yes	—
177	Q₈×D₄₃	—	2	48	no	—
178	Q₈×D₄₃	C₂⁴	1	32	yes	complemented
179	#10621900	—	2	128	no	—
180	#10621900	—	2	48	no	—
181	#10621900	C₂⁴	1	32	yes	complemented
182	D₄×D₄₃	—	2	128	no	—
183	D₄×D₄₃	—	2	48	no	—
184	D₄×D₄₃	C₂⁴	1	32	yes	—
185	#10621898	—	2	64	no	—
186	#10621898	—	2	64	no	—
187	#10621898	C₂×D₄	1	48	yes	—
188	#10621898	C₂⁴	1	16	yes	—
189	C₂×D₁₇₂	—	2	6	no	—
190	C₂×D₁₇₂	—	2	12	no	—
191	C₂×D₁₇₂	—	2	24	no	—
192	C₂×D₁₇₂	—	2	64	no	—
193	C₂×D₁₇₂	—	2	24	no	—
194	C₂×D₁₇₂	C₂×D₄	1	12	yes	—
195	C₂×D₁₇₂	C₂⁴	1	12	yes	—
196	C₂×D₁₇₂	C₂⁴	1	16	yes	—
197	C₂×C₄×D₄₃	—	2	24	no	—
198	C₂×C₄×D₄₃	—	2	24	no	—
199	C₂×C₄×D₄₃	C₂×D₄	1	12	yes	—
200	C₂×C₄×D₄₃	C₂⁴	1	12	yes	—
201	C₂×Dic₈₆	—	2	6	no	—
202	C₂×Dic₈₆	—	2	12	no	—
203	C₂×Dic₈₆	—	2	24	no	—
204	C₂×Dic₈₆	—	2	24	no	—
205	C₂×Dic₈₆	—	2	64	no	—
206	C₂×Dic₈₆	C₂×D₄	1	12	yes	—
207	C₂×Dic₈₆	C₂⁴	1	12	yes	—
208	C₂×Dic₈₆	C₂⁴	1	16	yes	complemented
209	Q₁₆×C₄₃	C₂⁴	1	16	yes	complemented
210	SD₁₆×C₄₃	C₂⁴	1	16	yes	complemented
211	SD₁₆×C₄₃	C₂⁴	1	16	yes	complemented
212	D₈×C₄₃	C₂⁴	1	16	yes	complemented
213	C₂×C₈×C₄₃	C₂⁴	1	6	yes	—
214	C₂×C₈×C₄₃	C₂⁴	1	6	yes	—
215	C₂×C₈×C₄₃	C₂⁴	1	16	yes	complemented
216	#10621885	C₂⁴	1	32	yes	complemented
217	#10621884	C₂⁴	1	32	yes	complemented
218	#10621883	C₂⁴	1	32	yes	complemented
219	#10621882	C₂⁴	1	32	yes	complemented
220	#10621877	C₂⁴	1	16	yes	complemented
221	C₂×C₄₃⋊C₈	C₂⁴	1	12	yes	—
222	#10621873	C₂⁴	1	32	yes	complemented
223	#10621873	C₂⁴	1	32	yes	complemented
224	#10621872	C₂⁴	1	32	yes	complemented
225	C₈×D₄₃	C₂⁴	1	32	yes	complemented
226	C₂³×C₄₃	—	2	4	no	—
227	C₂³×C₄₃	—	2	6	no	—
228	C₂³×C₄₃	—	2	6	no	—
229	C₂³×C₄₃	—	4	4	no	—
230	C₂³×C₄₃	—	4	4	no	—
231	C₂³×C₄₃	C₂²×D₄	1	6	yes	—
232	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
233	C₂²×D₄₃	—	2	8	no	—
234	C₂²×D₄₃	—	2	12	no	—
235	C₂²×D₄₃	—	2	16	no	—
236	C₂²×D₄₃	—	2	32	no	—
237	C₂²×D₄₃	—	4	8	no	—
238	C₂²×D₄₃	—	8	48	no	—
239	C₂²×D₄₃	—	8	24	no	—
240	C₂²×D₄₃	C₂²×D₄	1	12	yes	—
241	Q₈×C₄₃	—	2	6	no	—
242	Q₈×C₄₃	—	2	6	no	—
243	Q₈×C₄₃	C₂⁵	1	4	yes	—
244	Q₈×C₄₃	C₂⁵	1	4	yes	—
245	D₄×C₄₃	—	2	16	no	—
246	D₄×C₄₃	—	2	16	no	—
247	D₄×C₄₃	—	2	6	no	—
248	D₄×C₄₃	—	2	6	no	—
249	D₄×C₄₃	C₂⁵	1	4	yes	—
250	D₄×C₄₃	C₂⁵	1	4	yes	—
251	C₂×C₄×C₄₃	—	2	6	no	—
252	C₂×C₄×C₄₃	—	2	6	no	—
253	C₂×C₄×C₄₃	—	2	16	no	—
254	C₂×C₄×C₄₃	—	2	16	no	—
255	C₂×C₄×C₄₃	C₂²×D₄	1	6	yes	—
256	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
257	C₂×C₄×C₄₃	C₂²×D₄	1	12	yes	—
258	C₂×C₄×C₄₃	C₂⁵	1	3	yes	—
259	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
260	C₂²⋊D₄₃	—	2	32	no	—
261	C₂²⋊D₄₃	—	2	32	no	—
262	C₂²⋊D₄₃	C₂²×D₄	1	32	yes	—
263	C₂×Dic₄₃	—	2	12	no	—
264	C₂×Dic₄₃	—	2	16	no	—
265	C₂×Dic₄₃	—	2	32	no	—
266	C₂×Dic₄₃	C₂²×D₄	1	12	yes	—
267	D₁₇₂	—	2	32	no	—
268	D₁₇₂	—	2	16	no	—
269	D₁₇₂	—	2	12	no	—
270	D₁₇₂	C₂²×D₄	1	16	yes	—
271	D₁₇₂	C₂⁵	1	8	yes	—
272	C₄×D₄₃	—	2	32	no	—
273	C₄×D₄₃	—	2	32	no	—
274	C₄×D₄₃	C₂²×D₄	1	24	yes	—
275	C₄×D₄₃	C₂⁵	1	8	yes	—
276	Dic₈₆	—	2	16	no	—
277	Dic₈₆	—	2	12	no	—
278	Dic₈₆	—	2	32	no	—
279	Dic₈₆	C₂²×D₄	1	16	yes	—
280	Dic₈₆	C₂⁵	1	8	yes	—
281	C₈×C₄₃	C₂⁵	1	4	yes	—
282	C₈×C₄₃	C₂⁵	1	4	yes	—
283	C₄₃⋊C₈	C₂⁵	1	8	yes	—
284	C₂²×#577	—	43	1	no	maximal, Sylow
285	C₂²×C₄₃	—	2	12	no	—
286	C₂²×C₄₃	—	2	4	no	—
287	C₂²×C₄₃	—	2	4	no	—
288	C₂²×C₄₃	—	4	12	no	—
289	C₂²×C₄₃	—	4	12	no	—
290	C₂²×C₄₃	#577	1	4	yes	complemented
291	C₂²×C₄₃	C₂³×D₄	1	4	yes	—
292	C₂²×C₄₃	C₂³×D₄	1	3	yes	—
293	C₂×D₄₃	—	2	24	no	—
294	C₂×D₄₃	—	2	8	no	—
295	C₂×D₄₃	—	4	24	no	—
296	C₂×D₄₃	—	8	32	no	—
297	C₂×D₄₃	—	8	16	no	—
298	C₂×D₄₃	C₂³×D₄	1	8	yes	—
299	C₄×C₄₃	—	2	4	no	—
300	C₄×C₄₃	—	2	4	no	—
301	C₄×C₄₃	C₂³×D₄	1	4	yes	—
302	C₄×C₄₃	C₂³×D₄	1	3	yes	—
303	C₄×C₄₃	C₂⁶	1	1	yes	characteristic
304	Dic₄₃	—	2	8	no	—
305	Dic₄₃	C₂³×D₄	1	8	yes	—
306	C₂²×2₋¹⁺⁴	—	43	1	no	—
307	C₂²×H(5,𝔽₂)	—	43	1	no	—
308	C₂×#577	—	43	48	no	—
309	C₂²×#137	—	43	1	no	—
310	C₂²×#137	—	43	2	no	—
311	C₂²×AGL(1,ℤ/8)	—	43	1	no	—
312	C₂²×AGL(1,ℤ/8)	—	43	2	no	—
313	C₂²×#135	—	43	2	no	—
314	C₂²×#135	D₄₃	1	1	yes	characteristic, complemented
315	C₂³×SD₁₆	—	43	2	no	—
316	C₂³×SD₁₆	—	43	1	no	—
317	C₂²×#131	—	43	1	no	—
318	C₂×C₄₃	—	2	4	no	—
319	C₂×C₄₃	—	4	4	no	—
320	C₂×C₄₃	—	4	4	no	—
321	C₂×C₄₃	C₂×#577	1	6	yes	complemented
322	C₂×C₄₃	C₂⁴×D₄	1	1	yes	characteristic
323	D₄₃	—	2	8	no	—
324	D₄₃	—	4	8	no	—
325	C₂×2₋¹⁺⁴	—	43	24	no	—
326	C₂×2₋¹⁺⁴	—	86	12	no	—
327	C₂×H(5,𝔽₂)	—	43	24	no	—
328	C₂×H(5,𝔽₂)	—	86	12	no	—
329	C₂²×#41	—	43	1	no	—
330	C₂²×#41	—	43	2	no	—
331	C₂²×#41	—	43	2	no	—
332	C₂²×#41	—	86	1	no	—
333	C₂²×#41	—	86	1	no	—
334	C₂²×#41	—	86	2	no	—
335	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
336	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
337	C₂³×Q₈	—	43	2	no	—
338	C₂³×Q₈	—	43	1	no	—
339	C₂³×Q₈	—	86	1	no	—
340	C₂³×D₄	—	43	2	no	—
341	C₂³×D₄	—	43	1	no	—
342	C₂³×D₄	—	86	1	no	—
343	C₂³×D₄	—	86	2	no	—
344	#577	—	43	256	no	—
345	C₂×#137	—	43	24	no	—
346	C₂×#137	—	43	48	no	—
347	C₂×AGL(1,ℤ/8)	—	43	24	no	—
348	C₂×AGL(1,ℤ/8)	—	43	48	no	—
349	C₂×#135	—	43	48	no	—
350	C₂×#135	C₂×D₄₃	1	24	yes	complemented
351	C₂²×Q₁₆	—	43	2	no	—
352	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
353	C₂²×SD₁₆	—	43	2	no	—
354	C₂²×SD₁₆	—	43	2	no	—
355	C₂²×SD₁₆	—	43	48	no	—
356	C₂²×SD₁₆	—	43	2	no	—
357	C₂²×SD₁₆	—	43	2	no	—
358	C₂²×SD₁₆	—	43	24	no	—
359	C₂²×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
360	C₂²×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
361	C₂²×D₈	—	43	2	no	—
362	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
363	C₂×#131	—	43	24	no	—
364	C₂²×M₁₆	—	43	1	no	—
365	C₂²×M₁₆	—	43	2	no	—
366	C₂³×C₈	—	43	2	no	—
367	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
368	C₄₃	C₂²×#577	1	1	yes	characteristic, complemented, Sylow
369	C₂⁵	—	86	2	no	—
370	C₂⁵	—	86	1	no	—
371	2₋¹⁺⁴	—	43	64	no	—
372	2₋¹⁺⁴	—	86	96	no	—
373	H(5,𝔽₂)	—	43	64	no	—
374	H(5,𝔽₂)	—	86	96	no	—
375	C₂×#41	—	2	6	no	—
376	C₂×#41	—	2	6	no	—
377	C₂×#41	—	43	12	no	—
378	C₂×#41	—	43	12	no	—
379	C₂×#41	—	43	24	no	—
380	C₂×#41	—	43	24	no	—
381	C₂×#41	—	86	24	no	—
382	C₂×#41	—	86	24	no	—
383	C₂×#41	—	86	12	no	—
384	C₂×#41	—	86	12	no	—
385	C₂×#41	—	86	48	no	—
386	C₂×#41	C₂²×D₄₃	1	12	yes	—
387	C₂×#41	C₂²×D₄₃	1	12	yes	complemented
388	C₂²×Q₈	—	43	1	no	—
389	C₂²×Q₈	—	43	24	no	—
390	C₂²×Q₈	—	43	2	no	—
391	C₂²×Q₈	—	43	12	no	—
392	C₂²×Q₈	—	86	2	no	—
393	C₂²×Q₈	—	86	24	no	—
394	C₂²×Q₈	—	86	12	no	—
395	C₂²×Q₈	—	86	1	no	—
396	C₂²×Q₈	—	86	6	no	—
397	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
398	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
399	C₂²×D₄	—	2	1	no	—
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	—	43	2	no	—
402	C₂²×D₄	—	43	24	no	—
403	C₂²×D₄	—	43	1	no	—
404	C₂²×D₄	—	43	2	no	—
405	C₂²×D₄	—	43	12	no	—
406	C₂²×D₄	—	86	24	no	—
407	C₂²×D₄	—	86	2	no	—
408	C₂²×D₄	—	86	12	no	—
409	C₂²×D₄	—	86	2	no	—
410	C₂²×D₄	—	86	48	no	—
411	C₂²×D₄	—	86	2	no	—
412	C₂²×D₄	—	86	1	no	—
413	C₂²×D₄	—	86	6	no	—
414	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
415	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
416	C₂³×C₄	—	2	1	no	—
417	C₂³×C₄	—	2	1	no	—
418	C₂³×C₄	—	43	2	no	—
419	C₂³×C₄	—	86	2	no	—
420	C₂³×C₄	—	86	2	no	—
421	C₂³×C₄	—	86	2	no	—
422	C₂³×C₄	—	86	1	no	—
423	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
424	#137	—	43	64	no	—
425	#137	—	43	128	no	—
426	AGL(1,ℤ/8)	—	43	64	no	—
427	AGL(1,ℤ/8)	—	43	128	no	—
428	#135	—	43	128	no	—
429	#135	C₂²×D₄₃	1	64	yes	complemented
430	C₂×Q₁₆	—	43	24	no	—
431	C₂×Q₁₆	C₂²×D₄₃	1	12	yes	complemented
432	C₂×SD₁₆	—	43	24	no	—
433	C₂×SD₁₆	—	43	24	no	—
434	C₂×SD₁₆	—	43	128	no	—
435	C₂×SD₁₆	—	43	24	no	—
436	C₂×SD₁₆	—	43	24	no	—
437	C₂×SD₁₆	—	43	64	no	—
438	C₂×SD₁₆	C₂²×D₄₃	1	12	yes	complemented
439	C₂×SD₁₆	C₂²×D₄₃	1	12	yes	complemented
440	C₂×D₈	—	43	24	no	—
441	C₂×D₈	C₂²×D₄₃	1	12	yes	complemented
442	#131	—	43	64	no	—
443	C₂×M₁₆	—	43	12	no	—
444	C₂×M₁₆	—	43	24	no	—
445	C₂²×C₈	—	43	2	no	—
446	C₂²×C₈	—	43	24	no	—
447	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
448	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
449	C₂²×C₈	C₂²×D₄₃	1	12	yes	complemented
450	C₂⁴	—	2	1	no	—
451	C₂⁴	—	2	1	no	—
452	C₂⁴	—	43	2	no	—
453	C₂⁴	—	86	24	no	—
454	C₂⁴	—	86	12	no	—
455	C₂⁴	—	86	2	no	—
456	C₂⁴	—	344	4	no	—
457	C₂⁴	—	344	8	no	—
458	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
459	#41	—	2	24	no	—
460	#41	—	2	24	no	—
461	#41	—	43	48	no	—
462	#41	—	43	16	no	—
463	#41	—	43	32	no	—
464	#41	—	43	32	no	—
465	#41	—	86	64	no	—
466	#41	—	86	64	no	—
467	#41	—	86	48	no	—
468	#41	—	86	48	no	—
469	#41	—	86	128	no	—
470	#41	C₂³×D₄₃	1	16	yes	—
471	#41	C₂³×D₄₃	1	16	yes	complemented
472	C₂×Q₈	—	2	3	no	—
473	C₂×Q₈	—	2	3	no	—
474	C₂×Q₈	—	43	12	no	—
475	C₂×Q₈	—	43	32	no	—
476	C₂×Q₈	—	43	12	no	—
477	C₂×Q₈	—	43	16	no	—
478	C₂×Q₈	—	86	24	no	—
479	C₂×Q₈	—	86	64	no	—
480	C₂×Q₈	—	86	48	no	—
481	C₂×Q₈	—	86	12	no	—
482	C₂×Q₈	—	86	6	no	—
483	C₂×Q₈	—	86	24	no	—
484	C₂×Q₈	C₂³×D₄₃	1	6	yes	—
485	C₂×Q₈	C₂³×D₄₃	1	6	yes	—
486	C₂×D₄	—	2	12	no	—
487	C₂×D₄	—	2	12	no	—
488	C₂×D₄	—	2	3	no	—
489	C₂×D₄	—	2	3	no	—
490	C₂×D₄	—	43	24	no	—
491	C₂×D₄	—	43	32	no	—
492	C₂×D₄	—	43	12	no	—
493	C₂×D₄	—	43	12	no	—
494	C₂×D₄	—	43	16	no	—
495	C₂×D₄	—	86	64	no	—
496	C₂×D₄	—	86	24	no	—
497	C₂×D₄	—	86	48	no	—
498	C₂×D₄	—	86	24	no	—
499	C₂×D₄	—	86	128	no	—
500	C₂×D₄	—	86	24	no	—
501	C₂×D₄	—	86	12	no	—
502	C₂×D₄	—	86	6	no	—
503	C₂×D₄	—	86	24	no	—
504	C₂×D₄	C₂³×D₄₃	1	6	yes	—
505	C₂×D₄	C₂³×D₄₃	1	6	yes	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	12	no	—
509	C₂²×C₄	—	2	12	no	—
510	C₂²×C₄	—	43	2	no	—
511	C₂²×C₄	—	43	12	no	—
512	C₂²×C₄	—	43	12	no	—
513	C₂²×C₄	—	86	24	no	—
514	C₂²×C₄	—	86	24	no	—
515	C₂²×C₄	—	86	24	no	—
516	C₂²×C₄	—	86	12	no	—
517	C₂²×C₄	—	86	2	no	—
518	C₂²×C₄	D₄×D₄₃	1	6	yes	—
519	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
520	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
521	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
522	Q₁₆	—	43	32	no	—
523	Q₁₆	C₂³×D₄₃	1	16	yes	complemented
524	SD₁₆	—	43	32	no	—
525	SD₁₆	—	43	32	no	—
526	SD₁₆	—	43	32	no	—
527	SD₁₆	—	43	32	no	—
528	SD₁₆	C₂³×D₄₃	1	16	yes	complemented
529	SD₁₆	C₂³×D₄₃	1	16	yes	complemented
530	D₈	—	43	32	no	—
531	D₈	C₂³×D₄₃	1	16	yes	complemented
532	M₁₆	—	43	16	no	—
533	M₁₆	—	43	32	no	—
534	C₂×C₈	—	43	12	no	—
535	C₂×C₈	—	43	32	no	—
536	C₂×C₈	C₂³×D₄₃	1	6	yes	—
537	C₂×C₈	C₂³×D₄₃	1	6	yes	—
538	C₂×C₈	C₂³×D₄₃	1	16	yes	complemented
539	C₂³	—	2	4	no	—
540	C₂³	—	2	6	no	—
541	C₂³	—	2	6	no	—
542	C₂³	—	4	4	no	—
543	C₂³	—	4	4	no	—
544	C₂³	—	43	12	no	—
545	C₂³	—	86	32	no	—
546	C₂³	—	86	8	no	—
547	C₂³	—	86	16	no	—
548	C₂³	—	86	12	no	—
549	C₂³	—	344	24	no	—
550	C₂³	—	344	48	no	—
551	C₂³	—	172	8	no	—
552	C₂³	C₂×D₄×D₄₃	1	6	yes	—
553	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
554	Q₈	—	2	6	no	—
555	Q₈	—	2	6	no	—
556	Q₈	—	43	16	no	—
557	Q₈	—	43	8	no	—
558	Q₈	—	86	32	no	—
559	Q₈	—	86	16	no	—
560	Q₈	—	86	12	no	—
561	Q₈	C₂⁴×D₄₃	1	4	yes	—
562	Q₈	C₂⁴×D₄₃	1	4	yes	—
563	D₄	—	2	16	no	—
564	D₄	—	2	16	no	—
565	D₄	—	2	6	no	—
566	D₄	—	2	6	no	—
567	D₄	—	43	32	no	—
568	D₄	—	43	16	no	—
569	D₄	—	43	8	no	—
570	D₄	—	86	32	no	—
571	D₄	—	86	32	no	—
572	D₄	—	86	32	no	—
573	D₄	—	86	16	no	—
574	D₄	—	86	12	no	—
575	D₄	C₂⁴×D₄₃	1	4	yes	—
576	D₄	C₂⁴×D₄₃	1	4	yes	—
577	C₂×C₄	—	2	6	no	—
578	C₂×C₄	—	2	6	no	—
579	C₂×C₄	—	2	16	no	—
580	C₂×C₄	—	2	16	no	—
581	C₂×C₄	—	43	12	no	—
582	C₂×C₄	—	43	24	no	—
583	C₂×C₄	—	43	8	no	—
584	C₂×C₄	—	86	32	no	—
585	C₂×C₄	—	86	32	no	—
586	C₂×C₄	—	86	32	no	—
587	C₂×C₄	—	86	12	no	—
588	C₂×C₄	—	86	16	no	—
589	C₂×C₄	C₂×D₄×D₄₃	1	6	yes	—
590	C₂×C₄	C₂×D₄×D₄₃	1	3	yes	—
591	C₂×C₄	C₂×D₄×D₄₃	1	12	yes	—
592	C₂×C₄	C₂⁴×D₄₃	1	3	yes	—
593	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
594	C₈	—	43	8	no	—
595	C₈	C₂⁴×D₄₃	1	4	yes	—
596	C₈	C₂⁴×D₄₃	1	4	yes	—
597	C₂²	—	2	12	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	4	12	no	—
601	C₂²	—	4	12	no	—
602	C₂²	—	43	8	no	—
603	C₂²	—	86	24	no	—
604	C₂²	—	86	8	no	—
605	C₂²	—	344	16	no	—
606	C₂²	—	344	32	no	—
607	C₂²	—	172	24	no	—
608	C₂²	#14583706	1	4	yes	direct product factor
609	C₂²	C₂²×D₄×D₄₃	1	4	yes	—
610	C₂²	C₂²×D₄×D₄₃	1	3	yes	—
611	C₄	—	2	4	no	—
612	C₄	—	2	4	no	—
613	C₄	—	43	8	no	—
614	C₄	—	86	8	no	—
615	C₄	C₂²×D₄×D₄₃	1	4	yes	—
616	C₄	C₂²×D₄×D₄₃	1	3	yes	—
617	C₄	C₂⁵×D₄₃	1	1	yes	characteristic
618	C₂	—	2	4	no	—
619	C₂	—	4	4	no	—
620	C₂	—	4	4	no	—
621	C₂	—	86	8	no	—
622	C₂	—	172	8	no	—
623	C₂	C₂×#14583706	1	6	yes	direct product factor
624	C₂	C₂³×D₄×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator, cosocle	C₄×C₄₃	C₂⁶
Frattini	C₄	C₂⁵×D₄₃
Fitting	C₂²×#135×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
hypercenter	C₂²×#135	D₄₃
hypocenter	C₄₃	C₂²×#577
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂²×#13063372	C₂	semidirect
2. C₂²×#13063371	C₂	semidirect
3. C₂×#14583706	C₂	direct (N × H)
4. C₂²×#13063357	C₂	semidirect
5. C₂²×#13063355	C₂	semidirect
6. C₂²×#13063350	C₂	semidirect
7. C₂²×#13063349	C₂	semidirect
8. C₂²×#13063346	C₂	semidirect
9. C₂³×#10621873	C₂	semidirect
10. C₂²×SD₁₆×D₄₃	C₂	semidirect
11. C₂²×#13063331	C₂	semidirect
12. C₂²×#135×C₄₃	C₂	semidirect
14. C₂×#13063372	C₂²	semidirect
16. C₂×#13063371	C₂²	semidirect
22. C₂²×#10621900	C₂²	semidirect
24. C₂³×Dic₈₆	C₂²	semidirect
25. C₂²×Q₈×D₄₃	C₂²	semidirect
30. #14583706	C₂²	direct (N × H)
31. C₂×#13063357	C₂²	semidirect
32. C₂×#13063355	C₂²	semidirect
33. C₂×#13063350	C₂²	semidirect
34. C₂×#13063349	C₂²	semidirect
35. C₂×#13063346	C₂²	semidirect
36. C₂²×#10621885	C₂²	semidirect
37. C₂²×#10621873	C₂²	semidirect
38. C₂²×#10621873	C₂²	semidirect
39. C₂²×#10621873	C₂²	semidirect
40. C₂²×#10621883	C₂²	semidirect
41. C₂²×#10621884	C₂²	semidirect
42. C₂×SD₁₆×D₄₃	C₂²	semidirect
43. C₂²×#10621882	C₂²	semidirect
44. C₂×#13063331	C₂²	semidirect
45. C₂²×#10621877	C₂²	semidirect
46. C₂²×#10621872	C₂²	semidirect
47. C₂²×C₈×D₄₃	C₂²	semidirect
49. C₂²×#41×C₄₃	C₂²	semidirect
50. C₂×#135×C₄₃	C₂²	semidirect
51. C₂²×Q₁₆×C₄₃	C₂²	semidirect
52. C₂²×SD₁₆×C₄₃	C₂²	semidirect
53. C₂²×SD₁₆×C₄₃	C₂²	semidirect
54. C₂²×D₈×C₄₃	C₂²	semidirect
55. C₂³×C₈×C₄₃	C₂²	semidirect
59. #13063372	C₂³	semidirect
61. #13063371	C₂³	semidirect
70. C₂×#10621900	C₂³	semidirect
77. C₂²×Dic₈₆	C₂³	semidirect
79. C₂×Q₈×D₄₃	C₂³	semidirect
98. #13063357	C₂³	semidirect
99. #13063355	C₂³	semidirect
100. #13063350	C₂³	semidirect
101. #13063349	C₂³	semidirect
102. #13063346	C₂³	semidirect
103. C₂×#10621885	C₂³	semidirect
104. C₂×#10621873	C₂³	semidirect
105. C₂×#10621873	C₂³	semidirect
106. C₂×#10621873	C₂³	semidirect
107. C₂×#10621883	C₂³	semidirect
108. C₂×#10621884	C₂³	semidirect
109. SD₁₆×D₄₃	C₂³	semidirect
110. C₂×#10621882	C₂³	semidirect
111. #13063331	C₂³	semidirect
112. C₂×#10621877	C₂³	semidirect
113. C₂×#10621872	C₂³	semidirect
115. C₂×C₈×D₄₃	C₂³	semidirect
119. C₂×#41×C₄₃	C₂³	semidirect
129. #135×C₄₃	C₂³	semidirect
130. C₂×Q₁₆×C₄₃	C₂³	semidirect
131. C₂×SD₁₆×C₄₃	C₂³	semidirect
132. C₂×SD₁₆×C₄₃	C₂³	semidirect
133. C₂×D₈×C₄₃	C₂³	semidirect
136. C₂²×C₈×C₄₃	C₂³	semidirect
149. #41×C₄₃	C₂⁴	semidirect
178. Q₈×D₄₃	C₂⁴	semidirect
181. #10621900	C₂⁴	semidirect
208. C₂×Dic₈₆	C₂⁴	semidirect
209. Q₁₆×C₄₃	C₂⁴	semidirect
210. SD₁₆×C₄₃	C₂⁴	semidirect
211. SD₁₆×C₄₃	C₂⁴	semidirect
212. D₈×C₄₃	C₂⁴	semidirect
215. C₂×C₈×C₄₃	C₂⁴	semidirect
216. #10621885	C₂⁴	semidirect
217. #10621884	C₂⁴	semidirect
218. #10621883	C₂⁴	semidirect
219. #10621882	C₂⁴	semidirect
220. #10621877	C₂⁴	semidirect
222. #10621873	C₂⁴	semidirect
223. #10621873	C₂⁴	semidirect
224. #10621872	C₂⁴	semidirect
225. C₈×D₄₃	C₂⁴	semidirect
290. C₂²×C₄₃	#577	semidirect
314. C₂²×#135	D₄₃	semidirect
321. C₂×C₄₃	C₂×#577	semidirect
336. C₂²×#41	C₂×D₄₃	semidirect
350. C₂×#135	C₂×D₄₃	semidirect
352. C₂²×Q₁₆	C₂×D₄₃	semidirect
359. C₂²×SD₁₆	C₂×D₄₃	semidirect
360. C₂²×SD₁₆	C₂×D₄₃	semidirect
362. C₂²×D₈	C₂×D₄₃	semidirect
367. C₂³×C₈	C₂×D₄₃	semidirect
368. C₄₃	C₂²×#577	semidirect
387. C₂×#41	C₂²×D₄₃	semidirect
429. #135	C₂²×D₄₃	semidirect
431. C₂×Q₁₆	C₂²×D₄₃	semidirect
438. C₂×SD₁₆	C₂²×D₄₃	semidirect
439. C₂×SD₁₆	C₂²×D₄₃	semidirect
441. C₂×D₈	C₂²×D₄₃	semidirect
449. C₂²×C₈	C₂²×D₄₃	semidirect
471. #41	C₂³×D₄₃	semidirect
523. Q₁₆	C₂³×D₄₃	semidirect
528. SD₁₆	C₂³×D₄₃	semidirect
529. SD₁₆	C₂³×D₄₃	semidirect
531. D₈	C₂³×D₄₃	semidirect
538. C₂×C₈	C₂³×D₄₃	semidirect
608. C₂²	#14583706	direct (N × H)
623. C₂	C₂×#14583706	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13063372	2
C₂²×#13063371	2
C₂×#14583706	2
C₂²×#13063357	2
C₂²×#13063355	2
C₂²×#13063350	2
C₂²×#13063349	2
C₂²×#13063346	2
C₂³×#10621873	2
C₂²×SD₁₆×D₄₃	2
C₂²×#13063331	2
C₂²×#135×C₄₃	2
C₂²×#577	43

Subgroups — C22×#14583706 #26010412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#14583706 #26010412