Subgroups — #25065749

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 376 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	#19133376	C₂	1	4	yes	maximal, complemented
4	#19133373	C₂	1	4	yes	maximal, complemented
5	#19133353	C₂	1	2	yes	maximal, complemented
6	#19133350	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2920	C₂	1	1	yes	maximal, characteristic
8	#14582956	—	2	1	no	—
9	#14582956	C₂²	1	2	yes	—
10	#14582952	—	2	1	no	—
11	#14582952	C₄	1	2	yes	—
12	#14582952	C₄	1	2	yes	—
13	#14582952	C₂²	1	2	yes	—
14	#14582952	C₂²	1	2	yes	—
15	#14582952	C₂²	1	2	yes	—
16	#14582923	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
18	#14582863	—	2	1	no	—
19	C₂×C₂²⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
20	C₄×#10621877	—	2	1	no	—
21	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	#14582651	C₂²	1	8	yes	complemented
24	#14582649	C₂²	1	8	yes	complemented
25	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#432	—	2	1	no	—
27	C₄₃×#432	C₂²	1	2	yes	—
28	C₄₃×#431	—	2	1	no	—
29	C₄₃×#431	C₂²	1	2	yes	—
30	C₄₃×#423	C₂²	1	2	yes	—
31	C₄₃×#407	—	2	1	no	—
32	C₄×M₁₆×C₄₃	—	2	1	no	—
33	C₂×#10621877	—	2	2	no	—
34	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
35	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
36	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
37	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
38	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
39	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
40	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
43	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
44	#13063236	—	2	2	no	—
45	C₄×C₄₃⋊C₈	—	2	2	no	—
46	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
47	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
48	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
49	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	Q₈	1	1	yes	characteristic
53	C₂×M₁₆×C₄₃	—	2	2	no	—
54	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₃	Q₈	1	1	yes	characteristic
61	C₂×C₄²×C₄₃	Q₈	1	1	yes	characteristic
62	C₂×C₄²×C₄₃	Q₈	1	1	yes	characteristic
63	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₄₃	—	2	2	no	—
67	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
68	C₂²⋊C₈×C₄₃	—	2	2	no	—
69	C₂²⋊C₈×C₄₃	—	2	2	no	—
70	#97×C₄₃	—	2	2	no	—
71	C₄×C₈×C₄₃	—	2	2	no	—
72	C₂⁴×C₄₃	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₃	—	2	4	no	—
74	C₂²×C₄×C₄₃	—	4	2	no	—
75	C₂²×C₄×C₄₃	—	4	2	no	—
76	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂×D₄	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	M₁₆×C₄₃	—	4	4	no	—
95	C₂×C₈×C₄₃	—	2	4	no	—
96	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
109	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
110	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
111	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
112	#10621877	—	4	4	no	—
113	C₂×C₄₃⋊C₈	—	2	4	no	—
114	C₂×C₄₃⋊C₈	—	4	2	no	—
115	C₂×C₄₃⋊C₈	—	4	2	no	—
116	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
117	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
118	C₂³×C₄₃	—	2	2	no	—
119	C₂³×C₄₃	—	4	1	no	—
120	C₂³×C₄₃	—	4	1	no	—
121	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₄₃	—	2	2	no	—
125	C₂×C₄×C₄₃	—	2	2	no	—
126	C₂×C₄×C₄₃	—	2	2	no	—
127	C₂×C₄×C₄₃	—	2	2	no	—
128	C₂×C₄×C₄₃	—	2	2	no	—
129	C₂×C₄×C₄₃	—	2	2	no	—
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	2	no	—
135	C₂×C₄×C₄₃	—	4	1	no	—
136	C₂×C₄×C₄₃	—	4	1	no	—
137	C₂×C₄×C₄₃	—	4	1	no	—
138	C₂×C₄×C₄₃	—	4	1	no	—
139	C₂×C₄×C₄₃	—	4	1	no	—
140	C₂×C₄×C₄₃	—	4	1	no	—
141	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₃	#135	1	4	yes	—
151	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
154	C₈×C₄₃	—	4	4	no	—
155	C₄₃⋊C₈	—	2	4	no	—
156	C₄₃⋊C₈	—	2	4	no	—
157	C₄₃⋊C₈	—	4	4	no	—
158	#17815	—	43	1	no	maximal, Sylow
159	C₂²×C₄₃	—	2	1	no	—
160	C₂²×C₄₃	—	2	1	no	—
161	C₂²×C₄₃	—	2	1	no	—
162	C₂²×C₄₃	—	2	1	no	—
163	C₂²×C₄₃	—	2	1	no	—
164	C₂²×C₄₃	—	2	1	no	—
165	C₂²×C₄₃	—	2	1	no	—
166	C₂²×C₄₃	—	2	1	no	—
167	C₂²×C₄₃	—	4	4	no	—
168	C₂²×C₄₃	#427	1	2	yes	—
169	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
170	C₄×C₄₃	—	2	1	no	—
171	C₄×C₄₃	—	2	1	no	—
172	C₄×C₄₃	—	2	1	no	—
173	C₄×C₄₃	—	2	1	no	—
174	C₄×C₄₃	—	2	1	no	—
175	C₄×C₄₃	—	2	1	no	—
176	C₄×C₄₃	—	2	1	no	—
177	C₄×C₄₃	—	2	1	no	—
178	C₄×C₄₃	#427	1	2	yes	—
179	C₄×C₄₃	#430	1	2	yes	—
180	C₄×C₄₃	#568	1	2	yes	—
181	C₄×C₄₃	C₂×#135	1	2	yes	—
182	#2920	—	43	1	no	—
183	#2920	D₄₃	1	1	yes	characteristic
184	C₂×#431	—	43	1	no	—
185	#1572	—	43	4	no	—
186	#1572	—	43	4	no	—
187	#1567	—	43	2	no	—
188	#1566	—	43	2	no	—
189	C₂×C₄₃	—	2	2	no	—
190	C₂×C₄₃	—	4	1	no	—
191	C₂×C₄₃	—	4	1	no	—
192	C₂×C₄₃	#2905	1	1	yes	characteristic
193	C₂×C₄₃	C₂×#427	1	1	yes	characteristic
194	C₂×C₄₃	C₂×#430	1	1	yes	characteristic
195	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
196	#432	—	2	1	no	—
197	#432	—	43	2	no	—
198	#432	—	86	1	no	—
199	#432	C₂×D₄₃	1	2	yes	—
200	#431	—	2	1	no	—
201	#431	—	43	2	no	—
202	#431	—	43	2	no	—
203	#431	—	43	2	no	—
204	#431	—	43	2	no	—
205	#431	—	43	2	no	—
206	#431	—	86	1	no	—
207	#431	C₂×D₄₃	1	2	yes	—
208	#423	—	43	2	no	—
209	#423	C₂×D₄₃	1	2	yes	—
210	C₂×C₄⋊C₈	—	43	2	no	—
211	#407	—	2	1	no	—
212	#407	—	86	1	no	—
213	C₂×C₂²⋊C₈	—	43	2	no	—
214	C₄×M₁₆	—	2	1	no	—
215	C₄×M₁₆	—	86	1	no	—
216	C₂×C₄×C₈	—	43	1	no	—
217	C₂×C₄×C₈	—	43	1	no	—
218	#335	—	43	8	no	—
219	#334	—	43	8	no	—
220	C₄₃	#17815	1	1	yes	characteristic, complemented, Sylow
221	C₂³×C₄	Dic₈₆	1	1	yes	characteristic
222	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
223	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	86	2	no	—
226	C₂²×C₈	—	43	2	no	—
227	C₂²×C₈	—	43	2	no	—
228	C₂×C₄²	Dic₈₆	1	1	yes	characteristic
229	C₂×C₄²	Dic₈₆	1	1	yes	characteristic
230	C₂×C₄²	Dic₈₆	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
234	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
235	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
236	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
238	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
239	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	43	4	no	—
242	C₄⋊C₈	—	43	4	no	—
243	C₄⋊C₈	—	43	4	no	—
244	C₄⋊C₈	—	86	2	no	—
245	C₄⋊C₈	C₂²×D₄₃	1	4	yes	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	43	4	no	—
249	C₂²⋊C₈	—	43	4	no	—
250	C₂²⋊C₈	—	86	2	no	—
251	C₂²⋊C₈	—	86	2	no	—
252	#97	—	2	2	no	—
253	#97	—	86	2	no	—
254	C₄×C₈	—	2	2	no	—
255	C₄×C₈	—	43	2	no	—
256	C₄×C₈	—	43	2	no	—
257	C₄×C₈	—	43	2	no	—
258	C₄×C₈	—	43	2	no	—
259	C₄×C₈	—	86	2	no	—
260	C₂⁴	Dic₄₃⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
274	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
275	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
282	M₁₆	—	4	4	no	—
283	M₁₆	—	172	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	43	4	no	—
286	C₂×C₈	—	43	4	no	—
287	C₂×C₈	—	86	4	no	—
288	C₂×C₈	—	172	2	no	—
289	C₂×C₈	—	172	2	no	—
290	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
291	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
292	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
293	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
294	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
295	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
296	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
297	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
298	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
299	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
300	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
302	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
303	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
304	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
305	C₄²	C₂³×D₄₃	1	1	yes	characteristic
306	C₂³	—	2	2	no	—
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
310	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
311	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
338	C₂×C₄	#13063345	1	4	yes	—
339	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
340	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
341	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
342	C₈	—	4	4	no	—
343	C₈	—	86	4	no	—
344	C₈	—	86	4	no	—
345	C₈	—	172	4	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	4	4	no	—
355	C₂²	#14582935	1	2	yes	—
356	C₂²	C₂²×Dic₄₃⋊C₄	1	1	yes	characteristic
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	#14582935	1	2	yes	—
366	C₄	#14582947	1	2	yes	—
367	C₄	#14583665	1	2	yes	—
368	C₄	C₂×#13063345	1	2	yes	—
369	C₂	—	2	2	no	—
370	C₂	—	4	1	no	—
371	C₂	—	4	1	no	—
372	C₂	#19143158	1	1	yes	characteristic
373	C₂	C₂×#14582935	1	1	yes	characteristic
374	C₂	C₂×#14582947	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2920	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₄₃	C₄⋊C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2920	D₄₃
hypocenter	C₄₃	#17815
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #19133376	C₂	semidirect
4. #19133373	C₂	semidirect
5. #19133353	C₂	semidirect
6. #19133350	C₂	semidirect
23. #14582651	C₂²	semidirect
24. #14582649	C₂²	semidirect
220. C₄₃	#17815	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
#19133376	2
#19133373	2
#19133353	2
#19133350	2
C₄₃×#2920	2
#17815	43