Subgroups — C₂²×#14583445 #26003291

Order 11008.

12878 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14583445	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#13063323	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13063321	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13063314	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13063312	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13063297	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×C₂²⋊D₄₃	C₂	1	4	yes	maximal, complemented
9	C₂³×C₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#10621898	—	2	16	no	—
12	C₂²×#10621898	C₂²	1	24	yes	complemented
13	C₂³×Dic₈₆	C₂²	1	1	yes	characteristic
14	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic
15	C₂³×C₂²⋊D₄₃	C₂²	1	2	yes	—
16	C₂³×C₂²⋊D₄₃	C₂²	1	4	yes	—
17	C₂⁴×Dic₄₃	C₂²	1	2	yes	—
18	C₂³×C₄×D₄₃	C₂²	1	2	yes	—
19	#14583445	C₂²	1	256	yes	direct product factor
20	C₂×#13063323	C₂²	1	24	yes	complemented
21	C₂×#13063321	C₂²	1	24	yes	complemented
22	C₂×#13063314	C₂²	1	24	yes	complemented
23	C₂×#13063312	C₂²	1	24	yes	complemented
24	C₂×#13063297	C₂²	1	96	yes	complemented
25	C₂×C₄×C₂²⋊D₄₃	C₂²	1	96	yes	complemented
26	C₂²×Dic₄₃⋊C₄	C₂²	1	4	yes	—
27	C₂²×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
28	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
29	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄×Dic₄₃	C₂²	1	2	yes	—
32	C₂²×C₄×Dic₄₃	C₂²	1	24	yes	complemented
33	C₂²×#41×C₄₃	—	2	16	no	—
34	C₂²×#41×C₄₃	C₂²	1	24	yes	complemented
35	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂³×D₄×C₄₃	C₂²	1	2	yes	—
37	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
38	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
39	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
40	C₂⁴×D₄₃	C₂³	1	2	yes	—
41	C₂×#10621898	—	2	192	no	—
42	C₂×#10621898	C₂³	1	64	yes	complemented
43	C₂²×Dic₈₆	—	2	8	no	—
44	C₂²×Dic₈₆	C₂³	1	12	yes	—
45	C₂²×D₁₇₂	—	2	8	no	—
46	C₂²×D₁₇₂	C₂³	1	12	yes	—
47	C₂²×C₂²⋊D₄₃	—	2	16	no	—
48	C₂²×C₂²⋊D₄₃	—	2	32	no	—
49	C₂²×C₂²⋊D₄₃	C₂³	1	48	yes	—
50	C₂²×C₂²⋊D₄₃	C₂³	1	24	yes	—
51	C₂³×Dic₄₃	—	2	16	no	—
52	C₂³×Dic₄₃	C₂³	1	2	yes	—
53	C₂³×Dic₄₃	C₂³	1	24	yes	—
54	C₂³×Dic₄₃	C₂³	1	2	yes	—
55	C₂³×Dic₄₃	C₂³	1	2	yes	—
56	C₂²×C₄×D₄₃	—	2	16	no	—
57	C₂²×C₄×D₄₃	C₂³	1	24	yes	—
58	#13063323	C₂³	1	64	yes	complemented
59	#13063321	C₂³	1	64	yes	complemented
60	#13063314	C₂³	1	64	yes	complemented
61	#13063312	C₂³	1	64	yes	complemented
62	#13063297	C₂³	1	256	yes	complemented
63	C₄×C₂²⋊D₄₃	C₂³	1	256	yes	complemented
64	C₂×Dic₄₃⋊C₄	C₂³	1	48	yes	—
65	C₂×C₂²⋊Dic₄₃	C₂³	1	48	yes	—
66	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	48	yes	—
67	C₂×C₄×Dic₄₃	C₂³	1	24	yes	—
68	C₂×C₄×Dic₄₃	C₂³	1	12	yes	—
69	C₂×C₄×Dic₄₃	C₂³	1	12	yes	—
70	C₂×C₄×Dic₄₃	C₂³	1	64	yes	complemented
71	C₂⁵×C₄₃	C₂³	1	2	yes	—
72	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×#41×C₄₃	—	2	192	no	—
74	C₂×#41×C₄₃	C₂³	1	64	yes	complemented
75	C₂²×Q₈×C₄₃	—	2	8	no	—
76	C₂²×Q₈×C₄₃	C₂³	1	12	yes	—
77	C₂²×D₄×C₄₃	—	2	16	no	—
78	C₂²×D₄×C₄₃	—	2	8	no	—
79	C₂²×D₄×C₄₃	C₂³	1	24	yes	—
80	C₂²×D₄×C₄₃	C₂³	1	12	yes	—
81	C₂³×C₄×C₄₃	—	2	16	no	—
82	C₂³×C₄×C₄₃	D₄	1	16	yes	complemented
83	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₄₃	C₂³	1	24	yes	—
85	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₃	C₂³	1	12	yes	—
87	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂⁴×C₄₃	—	2	8	no	—
89	C₂⁴×C₄₃	—	2	8	no	—
90	C₂⁴×C₄₃	—	2	16	no	—
91	C₂⁴×C₄₃	C₂×D₄	1	8	yes	—
92	C₂⁴×C₄₃	C₂⁴	1	12	yes	—
93	C₂⁴×C₄₃	C₂⁴	1	6	yes	—
94	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
95	C₂³×D₄₃	—	2	8	no	—
96	C₂³×D₄₃	—	2	16	no	—
97	C₂³×D₄₃	C₂⁴	1	12	yes	—
98	#41×C₄₃	—	2	256	no	—
99	C₂×Q₈×C₄₃	—	2	48	no	—
100	C₂×Q₈×C₄₃	C₂⁴	1	16	yes	—
101	C₂×D₄×C₄₃	—	2	48	no	—
102	C₂×D₄×C₄₃	—	2	96	no	—
103	C₂×D₄×C₄₃	C₂⁴	1	32	yes	—
104	C₂×D₄×C₄₃	C₂⁴	1	16	yes	—
105	C₂²×C₄×C₄₃	—	2	96	no	—
106	C₂²×C₄×C₄₃	—	2	8	no	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
108	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	96	yes	complemented
110	C₂²×C₄×C₄₃	C₂⁴	1	12	yes	—
111	C₂²×C₄×C₄₃	C₂⁴	1	32	yes	—
112	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
113	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
114	C₂²×C₄×C₄₃	C₂⁴	1	16	yes	—
115	C₂×C₂²⋊D₄₃	—	2	192	no	—
116	C₂×C₂²⋊D₄₃	—	2	96	no	—
117	C₂×C₂²⋊D₄₃	C₂⁴	1	64	yes	—
118	C₂×C₂²⋊D₄₃	C₂⁴	1	32	yes	—
119	C₂²×Dic₄₃	—	2	96	no	—
120	C₂²×Dic₄₃	—	2	8	no	—
121	C₂²×Dic₄₃	—	2	8	no	—
122	C₂²×Dic₄₃	#41	1	16	yes	complemented
123	C₂²×Dic₄₃	C₂⁴	1	12	yes	—
124	C₂²×Dic₄₃	C₂⁴	1	32	yes	—
125	C₂²×Dic₄₃	C₂⁴	1	12	yes	—
126	C₂²×Dic₄₃	C₂⁴	1	12	yes	—
127	#10621898	—	2	256	no	—
128	C₂×D₁₇₂	—	2	48	no	—
129	C₂×D₁₇₂	C₂⁴	1	16	yes	—
130	C₂×C₄×D₄₃	—	2	96	no	—
131	C₂×C₄×D₄₃	C₂⁴	1	32	yes	—
132	C₂×Dic₈₆	—	2	48	no	—
133	C₂×Dic₈₆	C₂⁴	1	16	yes	—
134	C₂²⋊Dic₄₃	C₂⁴	1	64	yes	—
135	(C₂×D₄₃)⋊C₄	C₂⁴	1	64	yes	—
136	Dic₄₃⋊C₄	C₂⁴	1	64	yes	—
137	C₄×Dic₄₃	C₂⁴	1	32	yes	—
138	C₄×Dic₄₃	C₂⁴	1	16	yes	—
139	C₄×Dic₄₃	C₂⁴	1	16	yes	—
140	C₂³×C₄₃	—	2	32	no	—
141	C₂³×C₄₃	—	2	24	no	—
142	C₂³×C₄₃	—	2	24	no	—
143	C₂³×C₄₃	—	2	48	no	—
144	C₂³×C₄₃	—	4	32	no	—
145	C₂³×C₄₃	C₂²×D₄	1	24	yes	—
146	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
147	C₂³×C₄₃	C₂×#41	1	8	yes	—
148	C₂³×C₄₃	C₂⁵	1	8	yes	—
149	C₂³×C₄₃	C₂⁵	1	4	yes	—
150	C₂³×C₄₃	C₂⁵	1	3	yes	—
151	C₂²×D₄₃	—	2	24	no	—
152	C₂²×D₄₃	—	2	48	no	—
153	C₂²×D₄₃	—	4	32	no	—
154	C₂²×D₄₃	C₂⁵	1	8	yes	—
155	Q₈×C₄₃	—	2	32	no	—
156	D₄×C₄₃	—	2	64	no	—
157	D₄×C₄₃	—	2	32	no	—
158	C₂×C₄×C₄₃	—	2	24	no	—
159	C₂×C₄×C₄₃	—	2	64	no	—
160	C₂×C₄×C₄₃	C₂²×D₄	1	24	yes	—
161	C₂×C₄×C₄₃	C₂²×D₄	1	24	yes	—
162	C₂×C₄×C₄₃	C₂²×D₄	1	64	yes	complemented
163	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
164	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
165	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
166	C₂²⋊D₄₃	—	2	64	no	—
167	C₂²⋊D₄₃	—	2	128	no	—
168	C₂×Dic₄₃	—	2	24	no	—
169	C₂×Dic₄₃	—	2	24	no	—
170	C₂×Dic₄₃	—	2	64	no	—
171	C₂×Dic₄₃	C₂×#41	1	48	yes	complemented
172	C₂×Dic₄₃	C₂⁵	1	8	yes	—
173	C₂×Dic₄₃	C₂⁵	1	8	yes	—
174	C₂×Dic₄₃	C₂⁵	1	8	yes	—
175	D₁₇₂	—	2	32	no	—
176	C₄×D₄₃	—	2	64	no	—
177	Dic₈₆	—	2	32	no	—
178	C₂²×#532	—	43	1	no	maximal, Sylow
179	C₂²×C₄₃	—	2	8	no	—
180	C₂²×C₄₃	—	2	48	no	—
181	C₂²×C₄₃	—	2	8	no	—
182	C₂²×C₄₃	—	2	16	no	—
183	C₂²×C₄₃	—	4	48	no	—
184	C₂²×C₄₃	#532	1	16	yes	complemented
185	C₂²×C₄₃	C₂³×D₄	1	8	yes	—
186	C₂²×C₄₃	C₂³×D₄	1	6	yes	—
187	C₂²×C₄₃	C₂²×#41	1	12	yes	—
188	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
189	C₂×D₄₃	—	2	8	no	—
190	C₂×D₄₃	—	2	16	no	—
191	C₂×D₄₃	—	4	48	no	—
192	C₄×C₄₃	—	2	8	no	—
193	C₄×C₄₃	C₂³×D₄	1	8	yes	—
194	C₄×C₄₃	C₂³×D₄	1	8	yes	—
195	Dic₄₃	—	2	8	no	—
196	Dic₄₃	—	2	8	no	—
197	Dic₄₃	C₂²×#41	1	16	yes	complemented
198	C₂³×#41	—	43	1	no	—
199	C₂³×#41	D₄₃	1	1	yes	characteristic, complemented
200	C₂×#532	—	43	48	no	—
201	C₂²×C₄⋊Q₈	—	43	1	no	—
202	C₂²×#127	—	43	1	no	—
203	C₂²×#124	—	43	1	no	—
204	C₂²×#124	—	43	1	no	—
205	C₂²×#121	—	43	4	no	—
206	C₂²×C₄×D₄	—	43	4	no	—
207	C₂³×C₄²	—	43	1	no	—
208	C₂×C₄₃	—	2	8	no	—
209	C₂×C₄₃	—	4	8	no	—
210	C₂×C₄₃	C₂×#532	1	12	yes	complemented
211	C₂×C₄₃	C₂⁴×D₄	1	1	yes	characteristic
212	C₂×C₄₃	C₂³×#41	1	2	yes	—
213	D₄₃	—	4	8	no	—
214	C₂²×#41	—	2	16	no	—
215	C₂²×#41	—	43	24	no	—
216	C₂²×#41	—	86	16	no	—
217	C₂²×#41	C₂×D₄₃	1	24	yes	complemented
218	C₂³×Q₈	—	43	1	no	—
219	C₂³×Q₈	C₂×D₄₃	1	1	yes	characteristic
220	C₂³×D₄	—	43	2	no	—
221	C₂³×D₄	—	43	4	no	—
222	C₂³×D₄	—	43	1	no	—
223	C₂³×D₄	C₂×D₄₃	1	2	yes	—
224	C₂³×D₄	C₂×D₄₃	1	1	yes	characteristic
225	C₂⁴×C₄	—	43	2	no	—
226	C₂⁴×C₄	—	43	2	no	—
227	C₂⁴×C₄	C₂×D₄₃	1	2	yes	—
228	C₂⁴×C₄	C₂×D₄₃	1	1	yes	characteristic
229	#532	—	43	256	no	—
230	C₂×C₄⋊Q₈	—	43	24	no	—
231	C₂×#127	—	43	24	no	—
232	C₂×#124	—	43	24	no	—
233	C₂×#124	—	43	24	no	—
234	C₂×#121	—	43	96	no	—
235	C₂×C₄×D₄	—	43	96	no	—
236	C₂²×C₄⋊C₄	—	43	4	no	—
237	C₂²×C₂²⋊C₄	—	43	4	no	—
238	C₂²×C₂²⋊C₄	—	43	4	no	—
239	C₂²×C₄²	—	43	1	no	—
240	C₂²×C₄²	—	43	1	no	—
241	C₂²×C₄²	—	43	24	no	—
242	C₂²×C₄²	—	43	2	no	—
243	C₄₃	C₂²×#532	1	1	yes	characteristic, complemented, Sylow
244	C₂⁵	—	43	2	no	—
245	C₂⁵	C₂²×D₄₃	1	2	yes	—
246	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
247	C₂×#41	—	2	192	no	—
248	C₂×#41	—	43	64	no	—
249	C₂×#41	—	86	192	no	—
250	C₂×#41	C₂²×D₄₃	1	64	yes	complemented
251	C₂²×Q₈	—	2	8	no	—
252	C₂²×Q₈	—	43	12	no	—
253	C₂²×Q₈	—	86	8	no	—
254	C₂²×Q₈	C₂²×D₄₃	1	12	yes	—
255	C₂²×D₄	—	2	16	no	—
256	C₂²×D₄	—	2	8	no	—
257	C₂²×D₄	—	43	48	no	—
258	C₂²×D₄	—	43	24	no	—
259	C₂²×D₄	—	43	12	no	—
260	C₂²×D₄	—	86	32	no	—
261	C₂²×D₄	—	86	16	no	—
262	C₂²×D₄	—	86	8	no	—
263	C₂²×D₄	C₂²×D₄₃	1	24	yes	—
264	C₂²×D₄	C₂²×D₄₃	1	12	yes	—
265	C₂³×C₄	—	2	16	no	—
266	C₂³×C₄	—	43	2	no	—
267	C₂³×C₄	—	43	2	no	—
268	C₂³×C₄	—	43	2	no	—
269	C₂³×C₄	—	43	24	no	—
270	C₂³×C₄	—	43	24	no	—
271	C₂³×C₄	—	86	16	no	—
272	C₂³×C₄	—	86	16	no	—
273	C₂³×C₄	C₂²⋊D₄₃	1	16	yes	complemented
274	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
275	C₂³×C₄	C₂²×D₄₃	1	24	yes	—
276	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
277	C₂³×C₄	C₂²×D₄₃	1	12	yes	—
278	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
279	C₄⋊Q₈	—	43	64	no	—
280	#127	—	43	64	no	—
281	#124	—	43	64	no	—
282	#124	—	43	64	no	—
283	#121	—	43	256	no	—
284	C₄×D₄	—	43	256	no	—
285	C₂×C₄⋊C₄	—	43	48	no	—
286	C₂×C₂²⋊C₄	—	43	48	no	—
287	C₂×C₂²⋊C₄	—	43	48	no	—
288	C₂×C₄²	—	43	24	no	—
289	C₂×C₄²	—	43	12	no	—
290	C₂×C₄²	—	43	12	no	—
291	C₂×C₄²	—	43	64	no	—
292	C₂⁴	—	2	8	no	—
293	C₂⁴	—	2	8	no	—
294	C₂⁴	—	2	16	no	—
295	C₂⁴	—	43	12	no	—
296	C₂⁴	—	86	8	no	—
297	C₂⁴	—	86	16	no	—
298	C₂⁴	C₂×C₂²⋊D₄₃	1	8	yes	—
299	C₂⁴	C₂³×D₄₃	1	12	yes	—
300	C₂⁴	C₂³×D₄₃	1	6	yes	—
301	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
302	#41	—	2	256	no	—
303	#41	—	86	256	no	—
304	C₂×Q₈	—	2	48	no	—
305	C₂×Q₈	—	43	16	no	—
306	C₂×Q₈	—	86	48	no	—
307	C₂×Q₈	C₂³×D₄₃	1	16	yes	—
308	C₂×D₄	—	2	96	no	—
309	C₂×D₄	—	2	48	no	—
310	C₂×D₄	—	43	64	no	—
311	C₂×D₄	—	43	32	no	—
312	C₂×D₄	—	43	16	no	—
313	C₂×D₄	—	86	192	no	—
314	C₂×D₄	—	86	96	no	—
315	C₂×D₄	—	86	48	no	—
316	C₂×D₄	C₂³×D₄₃	1	32	yes	—
317	C₂×D₄	C₂³×D₄₃	1	16	yes	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	96	no	—
320	C₂²×C₄	—	43	16	no	—
321	C₂²×C₄	—	43	12	no	—
322	C₂²×C₄	—	43	12	no	—
323	C₂²×C₄	—	43	32	no	—
324	C₂²×C₄	—	43	12	no	—
325	C₂²×C₄	—	43	32	no	—
326	C₂²×C₄	—	86	96	no	—
327	C₂²×C₄	—	86	8	no	—
328	C₂²×C₄	—	86	8	no	—
329	C₂²×C₄	—	86	96	no	—
330	C₂²×C₄	C₂×C₂²⋊D₄₃	1	8	yes	—
331	C₂²×C₄	C₂×C₂²⋊D₄₃	1	8	yes	—
332	C₂²×C₄	C₂×C₂²⋊D₄₃	1	96	yes	complemented
333	C₂²×C₄	C₂³×D₄₃	1	12	yes	—
334	C₂²×C₄	C₂³×D₄₃	1	32	yes	—
335	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
336	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
337	C₂²×C₄	C₂³×D₄₃	1	16	yes	—
338	C₄⋊C₄	—	43	64	no	—
339	C₂²⋊C₄	—	43	64	no	—
340	C₂²⋊C₄	—	43	64	no	—
341	C₄²	—	43	32	no	—
342	C₄²	—	43	16	no	—
343	C₄²	—	43	16	no	—
344	C₂³	—	2	32	no	—
345	C₂³	—	2	24	no	—
346	C₂³	—	2	24	no	—
347	C₂³	—	2	48	no	—
348	C₂³	—	4	32	no	—
349	C₂³	—	43	8	no	—
350	C₂³	—	86	24	no	—
351	C₂³	—	86	48	no	—
352	C₂³	—	172	32	no	—
353	C₂³	C₂²×C₂²⋊D₄₃	1	24	yes	—
354	C₂³	C₂²×C₂²⋊D₄₃	1	4	yes	—
355	C₂³	#41×D₄₃	1	8	yes	—
356	C₂³	C₂⁴×D₄₃	1	8	yes	—
357	C₂³	C₂⁴×D₄₃	1	4	yes	—
358	C₂³	C₂⁴×D₄₃	1	3	yes	—
359	Q₈	—	2	32	no	—
360	Q₈	—	86	32	no	—
361	D₄	—	2	64	no	—
362	D₄	—	2	32	no	—
363	D₄	—	86	128	no	—
364	D₄	—	86	64	no	—
365	D₄	—	86	32	no	—
366	C₂×C₄	—	2	24	no	—
367	C₂×C₄	—	2	64	no	—
368	C₂×C₄	—	43	48	no	—
369	C₂×C₄	—	43	8	no	—
370	C₂×C₄	—	43	8	no	—
371	C₂×C₄	—	43	8	no	—
372	C₂×C₄	—	86	64	no	—
373	C₂×C₄	—	86	24	no	—
374	C₂×C₄	—	86	24	no	—
375	C₂×C₄	—	86	64	no	—
376	C₂×C₄	C₂²×C₂²⋊D₄₃	1	24	yes	—
377	C₂×C₄	C₂²×C₂²⋊D₄₃	1	24	yes	—
378	C₂×C₄	C₂²×C₂²⋊D₄₃	1	64	yes	complemented
379	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
380	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
381	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
382	C₂²	—	2	8	no	—
383	C₂²	—	2	48	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	2	16	no	—
386	C₂²	—	4	48	no	—
387	C₂²	—	86	8	no	—
388	C₂²	—	86	16	no	—
389	C₂²	—	172	48	no	—
390	C₂²	#14583445	1	16	yes	direct product factor
391	C₂²	C₂³×C₂²⋊D₄₃	1	8	yes	—
392	C₂²	C₂³×C₂²⋊D₄₃	1	6	yes	—
393	C₂²	C₂×#41×D₄₃	1	12	yes	—
394	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
395	C₄	—	2	8	no	—
396	C₄	—	43	16	no	—
397	C₄	—	86	8	no	—
398	C₄	—	86	8	no	—
399	C₄	C₂³×C₂²⋊D₄₃	1	8	yes	—
400	C₄	C₂³×C₂²⋊D₄₃	1	8	yes	—
401	C₂	—	2	8	no	—
402	C₂	—	4	8	no	—
403	C₂	—	172	8	no	—
404	C₂	C₂×#14583445	1	12	yes	direct product factor
405	C₂	C₂⁴×C₂²⋊D₄₃	1	1	yes	characteristic
406	C₂	C₂²×#41×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂³×#41×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂³×#41	D₄₃
hypocenter	C₄₃	C₂²×#532
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂³×#10621898	C₂	semidirect
2. C₂×#14583445	C₂	direct (N × H)
3. C₂²×#13063323	C₂	semidirect
4. C₂²×#13063321	C₂	semidirect
5. C₂²×#13063314	C₂	semidirect
6. C₂²×#13063312	C₂	semidirect
7. C₂²×#13063297	C₂	semidirect
8. C₂²×C₄×C₂²⋊D₄₃	C₂	semidirect
9. C₂³×C₄×Dic₄₃	C₂	semidirect
10. C₂³×#41×C₄₃	C₂	semidirect
12. C₂²×#10621898	C₂²	semidirect
19. #14583445	C₂²	direct (N × H)
20. C₂×#13063323	C₂²	semidirect
21. C₂×#13063321	C₂²	semidirect
22. C₂×#13063314	C₂²	semidirect
23. C₂×#13063312	C₂²	semidirect
24. C₂×#13063297	C₂²	semidirect
25. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
32. C₂²×C₄×Dic₄₃	C₂²	semidirect
34. C₂²×#41×C₄₃	C₂²	semidirect
42. C₂×#10621898	C₂³	semidirect
58. #13063323	C₂³	semidirect
59. #13063321	C₂³	semidirect
60. #13063314	C₂³	semidirect
61. #13063312	C₂³	semidirect
62. #13063297	C₂³	semidirect
63. C₄×C₂²⋊D₄₃	C₂³	semidirect
70. C₂×C₄×Dic₄₃	C₂³	semidirect
74. C₂×#41×C₄₃	C₂³	semidirect
82. C₂³×C₄×C₄₃	D₄	semidirect
109. C₂²×C₄×C₄₃	C₂×D₄	semidirect
122. C₂²×Dic₄₃	#41	semidirect
162. C₂×C₄×C₄₃	C₂²×D₄	semidirect
171. C₂×Dic₄₃	C₂×#41	semidirect
184. C₂²×C₄₃	#532	semidirect
197. Dic₄₃	C₂²×#41	semidirect
199. C₂³×#41	D₄₃	semidirect
210. C₂×C₄₃	C₂×#532	semidirect
217. C₂²×#41	C₂×D₄₃	semidirect
243. C₄₃	C₂²×#532	semidirect
250. C₂×#41	C₂²×D₄₃	semidirect
273. C₂³×C₄	C₂²⋊D₄₃	semidirect
332. C₂²×C₄	C₂×C₂²⋊D₄₃	semidirect
378. C₂×C₄	C₂²×C₂²⋊D₄₃	semidirect
390. C₂²	#14583445	direct (N × H)
404. C₂	C₂×#14583445	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×#10621898	2
C₂×#14583445	2
C₂²×#13063323	2
C₂²×#13063321	2
C₂²×#13063314	2
C₂²×#13063312	2
C₂²×#13063297	2
C₂²×C₄×C₂²⋊D₄₃	2
C₂³×C₄×Dic₄₃	2
C₂³×#41×C₄₃	2
C₂²×#532	43

Subgroups — C22×#14583445 #26003291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#14583445 #26003291