Subgroups — #25107221

Order 11008.

724 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143228	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582952	C₂	1	1	yes	maximal, characteristic
3	#19135368	C₂	1	4	yes	maximal, complemented
4	#19134800	C₂	1	4	yes	maximal
5	#19134766	C₂	1	2	yes	maximal, complemented
6	#19134732	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₃×#423	C₂	1	1	yes	maximal, characteristic
8	#14582956	—	2	1	no	—
9	#14582956	—	2	1	no	—
10	#14582952	—	2	1	no	—
11	#14582952	—	2	1	no	—
12	#14582952	C₄	1	2	yes	—
13	#14582952	C₄	1	2	yes	—
14	#14582952	C₄	1	2	yes	—
15	#14582952	C₄	1	2	yes	—
16	C₂×#13063260	C₂²	1	8	yes	—
17	#14582923	C₂²	1	1	yes	characteristic
18	#14582923	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
20	#14582863	C₂²	1	2	yes	—
21	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
22	C₄×#10621877	C₂²	1	2	yes	—
23	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
24	#14582663	C₂²	1	8	yes	—
25	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
26	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#423	—	2	1	no	—
28	C₄₃×#423	—	2	1	no	—
29	C₄₃×#423	C₂²	1	2	yes	—
30	C₄₃×#423	C₂²	1	2	yes	—
31	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
32	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
33	C₂×#10621877	C₂³	1	2	yes	—
34	C₂×#10621877	C₂³	1	2	yes	—
35	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
36	#13063260	—	4	8	no	—
37	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
38	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
39	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
40	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
41	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
42	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
43	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
44	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
45	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
46	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
47	#13063236	—	2	2	no	—
48	C₄×C₄₃⋊C₈	—	2	2	no	—
49	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
50	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
51	C₂³×C₄×C₄₃	Q₈	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	Q₈	1	1	yes	characteristic
53	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₄₃	—	2	2	no	—
55	C₂×M₁₆×C₄₃	—	4	4	no	—
56	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
57	C₂²×C₈×C₄₃	—	2	2	no	—
58	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₃	Q₈	1	1	yes	characteristic
67	C₂×C₄²×C₄₃	Q₈	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₄₃	—	2	2	no	—
71	C₄⋊C₈×C₄₃	—	2	2	no	—
72	C₄⋊C₈×C₄₃	—	2	2	no	—
73	C₄⋊C₈×C₄₃	—	2	2	no	—
74	C₂⁴×C₄₃	C₂×Q₈	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	—	2	4	no	—
76	C₂²×C₄×C₄₃	—	2	2	no	—
77	C₂²×C₄×C₄₃	—	2	2	no	—
78	C₂²×C₄×C₄₃	—	4	2	no	—
79	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
97	M₁₆×C₄₃	—	2	8	no	—
98	M₁₆×C₄₃	—	4	4	no	—
99	C₂×C₈×C₄₃	—	2	4	no	—
100	C₂×C₈×C₄₃	—	4	4	no	—
101	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
117	#10621877	—	2	4	no	—
118	#10621877	—	2	4	no	—
119	C₂×C₄₃⋊C₈	—	2	4	no	—
120	C₂×C₄₃⋊C₈	—	2	4	no	—
121	C₂×C₄₃⋊C₈	—	2	2	no	—
122	C₂×C₄₃⋊C₈	—	2	2	no	—
123	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
124	C₂³×C₄₃	—	2	2	no	—
125	C₂³×C₄₃	—	2	2	no	—
126	C₂³×C₄₃	—	4	1	no	—
127	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
130	C₂×C₄×C₄₃	—	2	2	no	—
131	C₂×C₄×C₄₃	—	2	2	no	—
132	C₂×C₄×C₄₃	—	2	2	no	—
133	C₂×C₄×C₄₃	—	2	2	no	—
134	C₂×C₄×C₄₃	—	2	1	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	2	2	no	—
139	C₂×C₄×C₄₃	—	2	2	no	—
140	C₂×C₄×C₄₃	—	2	2	no	—
141	C₂×C₄×C₄₃	—	2	2	no	—
142	C₂×C₄×C₄₃	—	2	2	no	—
143	C₂×C₄×C₄₃	—	2	2	no	—
144	C₂×C₄×C₄₃	—	2	2	no	—
145	C₂×C₄×C₄₃	—	4	1	no	—
146	C₂×C₄×C₄₃	—	4	1	no	—
147	C₂×C₄×C₄₃	—	4	1	no	—
148	C₂×C₄×C₄₃	#108	1	4	yes	complemented
149	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
162	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
163	C₈×C₄₃	—	4	4	no	—
164	C₄₃⋊C₈	—	2	8	no	—
165	C₄₃⋊C₈	—	4	2	no	—
166	C₄₃⋊C₈	—	4	2	no	—
167	#21993	—	43	1	no	maximal, Sylow
168	C₂²×C₄₃	—	2	1	no	—
169	C₂²×C₄₃	—	2	1	no	—
170	C₂²×C₄₃	—	2	1	no	—
171	C₂²×C₄₃	—	2	1	no	—
172	C₂²×C₄₃	—	2	1	no	—
173	C₂²×C₄₃	—	2	1	no	—
174	C₂²×C₄₃	—	2	1	no	—
175	C₂²×C₄₃	—	4	4	no	—
176	C₂²×C₄₃	C₂×#108	1	2	yes	—
177	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×C₄₃	#544	1	2	yes	—
179	C₄×C₄₃	—	2	1	no	—
180	C₄×C₄₃	—	2	1	no	—
181	C₄×C₄₃	—	2	1	no	—
182	C₄×C₄₃	—	2	1	no	—
183	C₄×C₄₃	—	2	1	no	—
184	C₄×C₄₃	—	2	1	no	—
185	C₄×C₄₃	—	2	1	no	—
186	C₄×C₄₃	C₂×#108	1	2	yes	—
187	C₄×C₄₃	C₂×#108	1	2	yes	—
188	C₄×C₄₃	#430	1	2	yes	—
189	C₄×C₄₃	#520	1	2	yes	—
190	C₄×C₄₃	#535	1	1	yes	characteristic
191	C₄×C₄₃	#536	1	1	yes	characteristic
192	#2920	—	43	1	no	—
193	C₂×#431	—	43	1	no	—
194	C₂×#423	D₄₃	1	1	yes	characteristic
195	#1950	—	43	4	no	—
196	#1855	—	43	4	no	—
197	#1848	—	43	2	no	—
198	#1837	—	43	2	no	—
199	C₂×C₄₃	—	2	2	no	—
200	C₂×C₄₃	—	2	2	no	—
201	C₂×C₄₃	—	4	1	no	—
202	C₂×C₄₃	#2317	1	1	yes	characteristic
203	C₂×C₄₃	C₂²×#108	1	1	yes	characteristic
204	C₂×C₄₃	C₂×#430	1	1	yes	characteristic
205	C₂²×M₁₆	C₂×D₄₃	1	2	yes	—
206	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
207	#432	—	86	1	no	—
208	#432	—	86	1	no	—
209	#431	—	43	2	no	—
210	#431	—	43	2	no	—
211	#431	—	43	2	no	—
212	#431	—	43	2	no	—
213	#431	—	86	1	no	—
214	#431	—	86	1	no	—
215	C₂×#108	—	43	8	no	—
216	#423	—	2	1	no	—
217	#423	—	2	1	no	—
218	#423	—	43	1	no	—
219	#423	—	43	1	no	—
220	#423	C₂×D₄₃	1	2	yes	—
221	#423	C₂×D₄₃	1	2	yes	—
222	C₂×C₄⋊C₈	—	2	1	no	—
223	C₂×C₄⋊C₈	—	2	1	no	—
224	C₂×C₄⋊C₈	—	43	2	no	—
225	#407	—	43	2	no	—
226	C₂×C₂²⋊C₈	—	43	2	no	—
227	C₄×M₁₆	—	43	2	no	—
228	C₂×C₄×C₈	—	43	2	no	—
229	#341	—	43	8	no	—
230	C₄₃	#21993	1	1	yes	characteristic, complemented, Sylow
231	C₂³×C₄	Dic₈₆	1	1	yes	characteristic
232	C₂³×C₄	Dic₈₆	1	1	yes	characteristic
233	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	4	4	no	—
236	C₂×M₁₆	—	43	2	no	—
237	C₂×M₁₆	—	43	2	no	—
238	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	43	4	no	—
241	C₂×C₄²	Dic₈₆	1	1	yes	characteristic
242	C₂×C₄²	Dic₈₆	1	1	yes	characteristic
243	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
244	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
247	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
250	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
251	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
252	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
253	#108	—	172	8	no	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	43	4	no	—
259	C₄⋊C₈	—	43	4	no	—
260	C₄⋊C₈	—	86	1	no	—
261	C₄⋊C₈	—	86	1	no	—
262	C₄⋊C₈	—	86	1	no	—
263	C₄⋊C₈	—	86	1	no	—
264	C₂²⋊C₈	—	43	4	no	—
265	C₂²⋊C₈	—	43	4	no	—
266	C₂²⋊C₈	—	86	2	no	—
267	C₂²⋊C₈	—	86	2	no	—
268	#97	—	86	2	no	—
269	C₄×C₈	—	43	4	no	—
270	C₄×C₈	—	43	4	no	—
271	C₄×C₈	—	86	2	no	—
272	C₂⁴	C₂×Dic₈₆	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
281	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
286	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
287	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
288	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
289	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
294	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
295	M₁₆	—	2	8	no	—
296	M₁₆	—	4	4	no	—
297	M₁₆	—	86	4	no	—
298	M₁₆	—	86	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	—	43	8	no	—
302	C₂×C₈	—	86	4	no	—
303	C₂×C₈	—	86	4	no	—
304	C₂×C₈	—	86	2	no	—
305	C₂×C₈	—	86	2	no	—
306	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
307	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
308	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
309	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
310	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
311	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
312	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
313	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
314	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
315	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
316	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
317	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
318	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
319	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
320	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
321	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	4	1	no	—
325	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
326	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
327	C₂³	C₂²×Dic₈₆	1	1	yes	characteristic
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	#13063260	1	4	yes	complemented
347	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
348	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
352	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
359	C₂×C₄	#13063370	1	2	yes	—
360	C₂×C₄	#13063373	1	2	yes	—
361	C₈	—	4	4	no	—
362	C₈	—	86	8	no	—
363	C₈	—	172	2	no	—
364	C₈	—	172	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	4	no	—
373	C₂²	C₂×#13063260	1	2	yes	—
374	C₂²	C₂²×Dic₄₃⋊C₄	1	1	yes	characteristic
375	C₂²	#14583530	1	2	yes	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	C₂×#13063260	1	2	yes	—
384	C₄	C₂×#13063260	1	2	yes	—
385	C₄	#14582947	1	2	yes	—
386	C₄	#14583380	1	2	yes	—
387	C₄	#14583466	1	1	yes	characteristic
388	C₄	#14583473	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	—	4	1	no	—
392	C₂	#19137219	1	1	yes	characteristic
393	C₂	C₂²×#13063260	1	1	yes	characteristic
394	C₂	C₂×#14582947	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#423	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₄₃	C₂×Q₈
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#423	D₄₃
hypocenter	C₄₃	#21993
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #19135368	C₂	semidirect
5. #19134766	C₂	semidirect
6. #19134732	C₂	semidirect
148. C₂×C₄×C₄₃	#108	semidirect
230. C₄₃	#21993	semidirect
346. C₂×C₄	#13063260	semidirect

Maximal subgroups

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

subgroup	index
#19143228	2
C₂×#14582952	2
#19135368	2
#19134800	2
#19134766	2
#19134732	2
C₂×C₄₃×#423	2
#21993	43