Subgroups — #25002434

Order 11008.

898 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582923	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582667	C₂	1	4	yes	maximal
4	C₂×C₄₃×#423	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10621877	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₄₃	C₄	1	2	yes	—
8	#14582923	—	2	2	no	—
9	#14582923	C₄	1	4	yes	complemented
10	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
11	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
12	C₄×C₄⋊Dic₄₃	—	2	1	no	—
13	C₄×C₄⋊Dic₄₃	—	2	1	no	—
14	C₄×C₄⋊Dic₄₃	—	2	1	no	—
15	C₄×C₄⋊Dic₄₃	—	2	1	no	—
16	C₂×C₄₃⋊#95	C₄	1	2	yes	—
17	#14582667	—	2	8	no	—
18	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#423	—	2	2	no	—
21	C₄₃×#423	C₄	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
23	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
24	C₂³×Dic₄₃	C₂×C₄	1	4	yes	—
25	C₂×#10621877	—	2	2	no	—
26	C₂×#10621877	—	2	4	no	—
27	C₂×#10621877	—	2	4	no	—
28	C₂×#10621877	C₂×C₄	1	4	yes	—
29	C₂²×C₄₃⋊C₈	—	2	2	no	—
30	C₂×C₄⋊Dic₄₃	—	2	2	no	—
31	C₂×C₄⋊Dic₄₃	—	2	2	no	—
32	C₂×C₄⋊Dic₄₃	—	2	2	no	—
33	C₂×C₄⋊Dic₄₃	—	2	2	no	—
34	C₂×C₄⋊Dic₄₃	D₄	1	4	yes	—
35	C₂×C₄⋊Dic₄₃	Q₈	1	4	yes	—
36	C₂×C₄×Dic₄₃	—	2	2	no	—
37	C₂×C₄×Dic₄₃	—	2	2	no	—
38	C₂×C₄×Dic₄₃	—	4	4	no	—
39	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
40	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
41	C₄₃⋊#95	—	2	2	no	—
42	C₄₃⋊#95	—	2	2	no	—
43	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₄₃	—	2	2	no	—
47	C₂×M₁₆×C₄₃	—	2	4	no	—
48	C₂×M₁₆×C₄₃	—	2	4	no	—
49	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₄₃	—	2	2	no	—
51	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₃	D₄	1	2	yes	—
56	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₃	Q₈	1	2	yes	—
59	C₄⋊C₈×C₄₃	—	2	4	no	—
60	C₄⋊C₈×C₄₃	—	2	4	no	—
61	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₃	—	2	2	no	—
63	C₂²×C₄×C₄₃	—	2	2	no	—
64	C₂²×C₄×C₄₃	—	4	2	no	—
65	C₂²×C₄×C₄₃	C₄²	1	2	yes	—
66	C₂²×C₄×C₄₃	C₄²	1	2	yes	—
67	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₄₃	#41	1	2	yes	—
82	C₂²×C₄×C₄₃	#41	1	2	yes	—
83	C₂²×Dic₄₃	—	2	4	no	—
84	C₂²×Dic₄₃	—	2	4	no	—
85	C₂²×Dic₄₃	—	4	4	no	—
86	C₂²×Dic₄₃	—	4	4	no	—
87	C₂²×Dic₄₃	C₄⋊C₄	1	8	yes	—
88	M₁₆×C₄₃	—	2	8	no	—
89	M₁₆×C₄₃	—	4	2	no	—
90	M₁₆×C₄₃	—	4	2	no	—
91	C₂×C₈×C₄₃	—	2	4	no	—
92	C₂×C₈×C₄₃	—	4	4	no	—
93	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
96	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
97	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
98	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
99	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
100	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
101	C₄⋊Dic₄₃	—	2	4	no	—
102	C₄⋊Dic₄₃	—	2	4	no	—
103	C₄⋊Dic₄₃	—	2	4	no	—
104	C₄⋊Dic₄₃	—	2	4	no	—
105	C₄×Dic₄₃	—	4	4	no	—
106	C₄×Dic₄₃	—	4	4	no	—
107	#10621877	—	2	8	no	—
108	#10621877	—	4	2	no	—
109	#10621877	—	4	2	no	—
110	C₂×C₄₃⋊C₈	—	2	4	no	—
111	C₂×C₄₃⋊C₈	—	4	4	no	—
112	C₂³×C₄₃	—	2	1	no	—
113	C₂³×C₄₃	—	2	1	no	—
114	C₂³×C₄₃	—	2	2	no	—
115	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
116	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
118	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂³×C₄₃	#117	1	2	yes	—
120	C₂×C₄×C₄₃	—	2	1	no	—
121	C₂×C₄×C₄₃	—	2	1	no	—
122	C₂×C₄×C₄₃	—	2	2	no	—
123	C₂×C₄×C₄₃	—	2	2	no	—
124	C₂×C₄×C₄₃	—	2	4	no	—
125	C₂×C₄×C₄₃	—	2	4	no	—
126	C₂×C₄×C₄₃	—	4	2	no	—
127	C₂×C₄×C₄₃	—	4	2	no	—
128	C₂×C₄×C₄₃	#95	1	2	yes	—
129	C₂×C₄×C₄₃	#95	1	2	yes	—
130	C₂×C₄×C₄₃	#95	1	2	yes	—
131	C₂×C₄×C₄₃	#95	1	2	yes	—
132	C₂×C₄×C₄₃	#100	1	2	yes	—
133	C₂×C₄×C₄₃	#101	1	2	yes	—
134	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
140	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
141	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
142	C₂×C₄×C₄₃	#121	1	2	yes	—
143	C₂×C₄×C₄₃	#121	1	2	yes	—
144	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
145	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
147	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
148	C₂×C₄×C₄₃	#125	1	2	yes	—
149	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
150	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
152	C₂×Dic₄₃	—	2	8	no	—
153	C₂×Dic₄₃	—	4	8	no	—
154	C₂×Dic₄₃	—	4	4	no	—
155	C₂×Dic₄₃	—	4	4	no	—
156	C₂×Dic₄₃	—	4	8	no	—
157	C₈×C₄₃	—	4	4	no	—
158	C₄₃⋊C₈	—	4	4	no	—
159	#10847	—	43	1	no	maximal, Sylow
160	C₂²×C₄₃	—	2	2	no	—
161	C₂²×C₄₃	—	2	2	no	—
162	C₂²×C₄₃	—	2	2	no	—
163	C₂²×C₄₃	—	2	2	no	—
164	C₂²×C₄₃	—	2	1	no	—
165	C₂²×C₄₃	—	2	1	no	—
166	C₂²×C₄₃	—	2	1	no	—
167	C₂²×C₄₃	—	2	1	no	—
168	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
169	C₂²×C₄₃	C₄×C₄⋊C₄	1	2	yes	—
170	C₂²×C₄₃	#380	1	2	yes	—
171	C₂²×C₄₃	#382	1	1	yes	characteristic
172	C₂²×C₄₃	#384	1	1	yes	characteristic
173	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
174	C₂²×C₄₃	C₂×#101	1	1	yes	characteristic
175	C₂²×C₄₃	#413	1	2	yes	—
176	C₄×C₄₃	—	2	2	no	—
177	C₄×C₄₃	—	2	2	no	—
178	C₄×C₄₃	—	2	2	no	—
179	C₄×C₄₃	#343	1	4	yes	complemented
180	C₄×C₄₃	#389	1	2	yes	—
181	C₄×C₄₃	#389	1	2	yes	—
182	C₄×C₄₃	#390	1	1	yes	characteristic
183	C₄×C₄₃	#390	1	1	yes	characteristic
184	C₄×C₄₃	#391	1	1	yes	characteristic
185	C₄×C₄₃	#391	1	1	yes	characteristic
186	Dic₄₃	—	4	8	no	—
187	C₂×#423	—	43	1	no	—
188	C₂×#423	D₄₃	1	1	yes	characteristic
189	C₂×C₄×C₄⋊C₄	—	43	1	no	—
190	C₂×#343	—	43	4	no	—
191	C₂×C₄₃	—	2	2	no	—
192	C₂×C₄₃	—	2	1	no	—
193	C₂×C₄₃	—	2	1	no	—
194	C₂×C₄₃	C₄⋊#95	1	1	yes	characteristic
195	C₂×C₄₃	C₂×#343	1	1	yes	characteristic
196	C₂×C₄₃	#1742	1	1	yes	characteristic
197	C₂×C₄₃	#1800	1	2	yes	—
198	C₂×C₄₃	#1801	1	2	yes	—
199	C₂²×M₁₆	—	43	2	no	—
200	C₂²×M₁₆	C₂×D₄₃	1	2	yes	—
201	C₂²×C₄⋊C₄	—	43	2	no	—
202	C₂²×C₄²	—	43	2	no	—
203	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
204	#423	—	2	2	no	—
205	#423	—	43	4	no	—
206	#423	—	86	2	no	—
207	#423	Dic₄₃	1	4	yes	complemented
208	C₂×C₄⋊C₈	—	2	1	no	—
209	C₂×C₄⋊C₈	—	2	1	no	—
210	C₂×C₄⋊C₈	—	86	1	no	—
211	C₂×C₄⋊C₈	—	86	1	no	—
212	C₄×C₄⋊C₄	—	86	1	no	—
213	C₄×C₄⋊C₄	—	86	1	no	—
214	C₄×C₄⋊C₄	—	86	1	no	—
215	C₄×C₄⋊C₄	—	86	1	no	—
216	C₂×#95	—	43	2	no	—
217	#343	—	86	8	no	—
218	C₄₃	#10847	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₄	—	43	4	no	—
220	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
221	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	4	no	—
225	C₂×M₁₆	—	2	4	no	—
226	C₂×M₁₆	—	43	4	no	—
227	C₂×M₁₆	—	86	2	no	—
228	C₂×M₁₆	—	86	4	no	—
229	C₂×M₁₆	—	86	4	no	—
230	C₂×M₁₆	C₂×Dic₄₃	1	4	yes	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	86	2	no	—
233	C₂×C₄⋊C₄	—	43	4	no	—
234	C₂×C₄⋊C₄	—	43	4	no	—
235	C₂×C₄⋊C₄	—	86	2	no	—
236	C₂×C₄⋊C₄	—	86	2	no	—
237	C₂×C₄⋊C₄	—	86	2	no	—
238	C₂×C₄⋊C₄	—	86	2	no	—
239	C₂×C₄²	—	86	2	no	—
240	C₂×C₄²	—	86	2	no	—
241	C₂×C₄²	—	172	4	no	—
242	C₂×C₄²	Dic₈₆	1	2	yes	—
243	C₂×C₄²	C₄×D₄₃	1	2	yes	—
244	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
245	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
246	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
247	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
250	C₄⋊C₈	—	2	4	no	—
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	86	4	no	—
253	C₄⋊C₈	—	86	4	no	—
254	#95	—	86	2	no	—
255	#95	—	86	2	no	—
256	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	43	8	no	—
261	C₂²×C₄	—	86	4	no	—
262	C₂²×C₄	—	86	4	no	—
263	C₂²×C₄	—	172	4	no	—
264	C₂²×C₄	—	172	4	no	—
265	C₂²×C₄	C₄×Dic₄₃	1	2	yes	—
266	C₂²×C₄	C₄×Dic₄₃	1	2	yes	—
267	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
268	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
269	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
276	C₂²×C₄	D₄×D₄₃	1	2	yes	—
277	C₂²×C₄	#10621900	1	2	yes	—
278	C₂²×C₄	Q₈×D₄₃	1	2	yes	—
279	C₂²×C₄	#10621902	1	2	yes	—
280	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
283	M₁₆	—	2	8	no	—
284	M₁₆	—	4	2	no	—
285	M₁₆	—	4	2	no	—
286	M₁₆	—	86	8	no	—
287	M₁₆	—	172	2	no	—
288	M₁₆	—	172	2	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	4	4	no	—
291	C₂×C₈	—	86	4	no	—
292	C₂×C₈	—	172	4	no	—
293	C₄⋊C₄	—	86	4	no	—
294	C₄⋊C₄	—	86	4	no	—
295	C₄⋊C₄	—	86	4	no	—
296	C₄⋊C₄	—	86	4	no	—
297	C₄²	—	172	4	no	—
298	C₄²	—	172	4	no	—
299	C₄²	Dic₄₃⋊C₄	1	2	yes	—
300	C₄²	Dic₄₃⋊C₄	1	2	yes	—
301	C₄²	C₄⋊Dic₄₃	1	2	yes	—
302	C₄²	C₄⋊Dic₄₃	1	2	yes	—
303	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
304	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
305	C₄²	C₂²⋊Dic₄₃	1	2	yes	—
306	C₄²	C₂²⋊Dic₄₃	1	2	yes	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	2	no	—
310	C₂³	C₂×C₄×Dic₄₃	1	1	yes	characteristic
311	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
312	C₂³	C₄⋊C₄×D₄₃	1	2	yes	—
313	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
314	C₂³	#13063283	1	2	yes	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	86	8	no	—
324	C₂×C₄	—	172	8	no	—
325	C₂×C₄	—	172	4	no	—
326	C₂×C₄	—	172	4	no	—
327	C₂×C₄	—	172	8	no	—
328	C₂×C₄	C₄₃⋊#95	1	2	yes	—
329	C₂×C₄	C₄₃⋊#95	1	2	yes	—
330	C₂×C₄	C₄₃⋊#95	1	2	yes	—
331	C₂×C₄	C₄₃⋊#95	1	2	yes	—
332	C₂×C₄	#13063241	1	2	yes	—
333	C₂×C₄	#13063243	1	2	yes	—
334	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
336	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
338	C₂×C₄	#13063287	1	2	yes	—
339	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
340	C₂×C₄	#13063290	1	2	yes	—
341	C₂×C₄	Q₈×Dic₄₃	1	2	yes	—
342	C₂×C₄	#13063296	1	2	yes	—
343	C₂×C₄	#13063300	1	2	yes	—
344	C₂×C₄	#13063301	1	2	yes	—
345	C₂×C₄	#13063305	1	2	yes	—
346	C₂×C₄	#13063312	1	1	yes	characteristic
347	C₂×C₄	#13063314	1	1	yes	characteristic
348	C₂×C₄	#13063316	1	2	yes	—
349	C₂×C₄	#13063321	1	1	yes	characteristic
350	C₂×C₄	#13063323	1	1	yes	characteristic
351	C₂×C₄	#13063324	1	2	yes	—
352	C₈	—	4	4	no	—
353	C₈	—	172	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	C₂×C₄₃⋊#95	1	1	yes	characteristic
363	C₂²	C₄⋊C₄×Dic₄₃	1	2	yes	—
364	C₂²	#14582756	1	2	yes	—
365	C₂²	#14582764	1	1	yes	characteristic
366	C₂²	#14582768	1	1	yes	characteristic
367	C₂²	C₂×#13063241	1	1	yes	characteristic
368	C₂²	C₂×#13063243	1	1	yes	characteristic
369	C₂²	#14582881	1	2	yes	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	172	8	no	—
374	C₄	#14582667	1	4	yes	complemented
375	C₄	#14582795	1	2	yes	—
376	C₄	#14582798	1	2	yes	—
377	C₄	#14582800	1	1	yes	characteristic
378	C₄	#14582802	1	1	yes	characteristic
379	C₄	#14582804	1	1	yes	characteristic
380	C₄	#14582806	1	1	yes	characteristic
381	C₂	—	2	2	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	#19132824	1	1	yes	characteristic
385	C₂	C₂×#14582667	1	1	yes	characteristic
386	C₂	#19134333	1	1	yes	characteristic
387	C₂	#19134584	1	2	yes	—
388	C₂	#19134588	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂³×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#423	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#423	D₄₃
hypocenter	C₄₃	#10847
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
9. #14582923	C₄	semidirect
21. C₄₃×#423	C₄	semidirect
179. C₄×C₄₃	#343	semidirect
207. #423	Dic₄₃	semidirect
218. C₄₃	#10847	semidirect
374. C₄	#14582667	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582923	2
C₂×C₄×C₄⋊Dic₄₃	2
C₂×#14582667	2
C₂×C₄₃×#423	2
#10847	43