Subgroups — #25115414

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583027	C₂	1	2	yes	maximal
2	#19137072	C₂	1	1	yes	maximal, characteristic
3	#19135318	C₂	1	2	yes	maximal
4	#19135317	C₂	1	2	yes	maximal
5	#19135312	C₂	1	2	yes	maximal
6	#19134748	C₂	1	2	yes	maximal
7	#19134747	C₂	1	1	yes	maximal, characteristic
8	#19134454	C₂	1	2	yes	maximal
9	C₄₃×#1767	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
11	#14583027	—	2	8	no	—
12	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
17	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
19	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
20	C₂×#13063235	C₂²	1	2	yes	—
21	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
22	#14582805	C₄	1	1	yes	characteristic
23	#14582805	C₄	1	1	yes	characteristic
24	#14582797	C₄	1	1	yes	characteristic
25	#14582797	C₄	1	1	yes	characteristic
26	#14582783	C₄	1	2	yes	—
27	#14582783	C₄	1	2	yes	—
28	C₄×Dic₄₃⋊C₄	C₂²	1	2	yes	—
29	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
30	#14582745	C₂²	1	2	yes	—
31	#14582653	C₂²	1	2	yes	—
32	#14582653	C₂²	1	2	yes	—
33	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#97×C₄₃	C₂²	1	2	yes	—
36	C₄³×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#336	C₂²	1	2	yes	—
38	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
40	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
41	C₄×Dic₈₆	D₄	1	4	yes	—
42	C₄×Dic₈₆	Q₈	1	4	yes	—
43	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
50	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
51	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
52	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
53	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
54	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
55	Dic₄₃⋊C₈	—	2	4	no	—
56	Dic₄₃⋊C₈	—	2	4	no	—
57	Dic₄₃⋊C₈	—	4	2	no	—
58	Dic₄₃⋊C₈	—	4	2	no	—
59	#13063235	—	2	4	no	—
60	C₈×Dic₄₃	—	2	4	no	—
61	C₄₃⋊#95	C₂×C₄	1	2	yes	—
62	C₄₃⋊#95	C₂×C₄	1	2	yes	—
63	C₄₃⋊#95	C₂×C₄	1	2	yes	—
64	C₄₃⋊#95	C₂×C₄	1	2	yes	—
65	C₄₃⋊#95	C₂×C₄	1	2	yes	—
66	C₄₃⋊#95	C₂×C₄	1	2	yes	—
67	C₄₃⋊#95	C₂×C₄	1	2	yes	—
68	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
69	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
70	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₄₃	—	2	2	no	—
78	C₄⋊C₈×C₄₃	Q₈	1	4	yes	complemented
79	#97×C₄₃	—	2	4	no	—
80	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
87	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
88	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
89	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
90	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
91	C₂×Dic₈₆	—	4	1	no	—
92	C₂×Dic₈₆	—	4	1	no	—
93	C₂×Dic₈₆	C₄⋊C₄	1	4	yes	—
94	C₂×C₈×C₄₃	—	2	2	no	—
95	C₂×C₈×C₄₃	—	2	2	no	—
96	C₂×C₈×C₄₃	—	2	2	no	—
97	C₂×C₈×C₄₃	—	2	2	no	—
98	C₂×C₈×C₄₃	—	2	2	no	—
99	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
100	C₄²×C₄₃	—	2	2	no	—
101	C₄²×C₄₃	—	2	1	no	—
102	C₄²×C₄₃	—	2	1	no	—
103	C₄²×C₄₃	—	4	1	no	—
104	C₄²×C₄₃	—	4	1	no	—
105	C₄²×C₄₃	—	4	1	no	—
106	C₄²×C₄₃	C₂×D₄	1	2	yes	—
107	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
108	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
109	C₄²×C₄₃	#41	1	2	yes	—
110	C₄⋊Dic₄₃	—	4	1	no	—
111	C₄⋊Dic₄₃	—	4	1	no	—
112	C₄⋊Dic₄₃	C₄⋊C₄	1	4	yes	—
113	Dic₄₃⋊C₄	—	2	4	no	—
114	Dic₄₃⋊C₄	—	4	2	no	—
115	Dic₄₃⋊C₄	C₄⋊C₄	1	8	yes	—
116	C₄×Dic₄₃	—	2	2	no	—
117	C₄×Dic₄₃	—	2	2	no	—
118	C₄×Dic₄₃	C₂×D₄	1	4	yes	—
119	C₄×Dic₄₃	C₂×Q₈	1	4	yes	—
120	C₂×C₄₃⋊C₈	—	2	2	no	—
121	C₂×C₄₃⋊C₈	—	2	2	no	—
122	C₂×C₄₃⋊C₈	—	2	2	no	—
123	C₂×C₄₃⋊C₈	—	2	2	no	—
124	C₂×C₄₃⋊C₈	—	2	2	no	—
125	C₂×C₄₃⋊C₈	—	2	2	no	—
126	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
127	C₂×C₄×C₄₃	—	2	1	no	—
128	C₂×C₄×C₄₃	—	2	1	no	—
129	C₂×C₄×C₄₃	—	2	1	no	—
130	C₂×C₄×C₄₃	—	2	1	no	—
131	C₂×C₄×C₄₃	—	2	1	no	—
132	C₂×C₄×C₄₃	—	2	1	no	—
133	C₂×C₄×C₄₃	—	2	1	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	1	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
143	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
144	C₂×C₄×C₄₃	#131	1	2	yes	—
145	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
149	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
150	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
151	C₂×Dic₄₃	—	2	2	no	—
152	C₂×Dic₄₃	—	2	2	no	—
153	C₂×Dic₄₃	—	2	2	no	—
154	C₂×Dic₄₃	—	2	2	no	—
155	C₂×Dic₄₃	—	2	2	no	—
156	C₂×Dic₄₃	—	2	2	no	—
157	C₂×Dic₄₃	—	2	2	no	—
158	C₂×Dic₄₃	—	2	2	no	—
159	C₂×Dic₄₃	—	2	2	no	—
160	C₂×Dic₄₃	—	2	2	no	—
161	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
163	Dic₈₆	—	4	4	no	—
164	C₈×C₄₃	—	2	4	no	—
165	C₈×C₄₃	—	4	2	no	—
166	C₄₃⋊C₈	—	4	2	no	—
167	C₄₃⋊C₈	—	4	2	no	—
168	#22723	—	43	1	no	maximal, Sylow
169	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
170	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
171	C₂²×C₄₃	#520	1	1	yes	characteristic
172	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
173	C₂²×C₄₃	#568	1	1	yes	characteristic
174	C₂²×C₄₃	#568	1	1	yes	characteristic
175	C₂²×C₄₃	#568	1	1	yes	characteristic
176	C₄×C₄₃	—	2	2	no	—
177	C₄×C₄₃	—	2	2	no	—
178	C₄×C₄₃	—	2	2	no	—
179	C₄×C₄₃	—	2	2	no	—
180	C₄×C₄₃	—	2	2	no	—
181	C₄×C₄₃	—	4	1	no	—
182	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
183	C₄×C₄₃	#550	1	1	yes	characteristic
184	C₄×C₄₃	#557	1	1	yes	characteristic
185	C₄×C₄₃	Q₈²	1	1	yes	characteristic
186	Dic₄₃	—	2	4	no	—
187	Dic₄₃	—	2	4	no	—
188	Dic₄₃	—	4	2	no	—
189	Dic₄₃	—	4	2	no	—
190	C₂×#446	—	43	2	no	—
191	#2295	—	43	1	no	—
192	#1940	—	43	2	no	—
193	#1940	—	43	2	no	—
194	#1939	—	43	2	no	—
195	#1843	—	43	2	no	—
196	#1842	—	43	1	no	—
197	#1768	—	43	2	no	—
198	#1767	D₄₃	1	1	yes	characteristic
199	C₂×C₄₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
200	C₂×C₄₃	#2905	1	1	yes	characteristic
201	C₂×C₄₃	#2906	1	1	yes	characteristic
202	C₂×C₄₃	#2961	1	1	yes	characteristic
203	C₂×C₄₃	#2962	1	1	yes	characteristic
204	C₂×C₄₃	#2992	1	1	yes	characteristic
205	C₂×C₄₃	#2995	1	1	yes	characteristic
206	C₂×C₄×Q₈	—	43	1	no	—
207	#446	—	86	8	no	—
208	C₂×C₄⋊C₈	—	43	2	no	—
209	C₂×C₄⋊C₈	—	43	2	no	—
210	C₂×C₄⋊C₈	—	43	2	no	—
211	C₂×C₄⋊C₈	—	43	2	no	—
212	C₂×C₄⋊C₈	—	43	2	no	—
213	C₂×C₄⋊C₈	—	43	2	no	—
214	C₂×C₄⋊C₈	—	43	1	no	—
215	C₂×C₄⋊C₈	—	43	1	no	—
216	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
218	C₂×#97	—	43	2	no	—
219	C₂×#97	C₂×D₄₃	1	2	yes	—
220	C₂×C₄×C₈	—	43	2	no	—
221	#391	—	43	1	no	—
222	#391	—	43	1	no	—
223	#389	—	43	1	no	—
224	#389	—	43	1	no	—
225	#387	—	43	2	no	—
226	#387	—	43	2	no	—
227	C₄×C₄⋊C₄	—	43	2	no	—
228	C₄×C₄⋊C₄	—	43	1	no	—
229	#376	—	43	2	no	—
230	C₄³	C₂×D₄₃	1	1	yes	characteristic
231	#336	—	43	2	no	—
232	#336	—	43	2	no	—
233	#336	C₂×D₄₃	1	2	yes	—
234	C₄₃	#22723	1	1	yes	characteristic, complemented, Sylow
235	C₂²×Q₈	—	43	1	no	—
236	C₂²×C₈	—	43	2	no	—
237	C₂²×C₈	—	43	2	no	—
238	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
239	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
240	C₄×Q₈	—	43	4	no	—
241	C₄×Q₈	—	43	4	no	—
242	C₂×C₄⋊C₄	—	43	2	no	—
243	C₂×C₄⋊C₄	—	43	1	no	—
244	C₂×C₄⋊C₄	—	43	2	no	—
245	C₂×C₄⋊C₄	—	43	2	no	—
246	C₂×C₄⋊C₄	—	43	1	no	—
247	C₂×C₄⋊C₄	—	43	1	no	—
248	C₂×C₄²	—	43	2	no	—
249	C₂×C₄²	—	43	2	no	—
250	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
251	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
252	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
253	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
254	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
256	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	86	4	no	—
259	C₄⋊C₈	—	86	4	no	—
260	C₄⋊C₈	—	86	4	no	—
261	C₄⋊C₈	—	86	4	no	—
262	C₄⋊C₈	—	172	1	no	—
263	C₄⋊C₈	—	172	1	no	—
264	C₄⋊C₈	—	172	2	no	—
265	C₄⋊C₈	—	172	2	no	—
266	C₄⋊C₈	Dic₈₆	1	4	yes	complemented
267	#97	—	2	4	no	—
268	#97	—	86	4	no	—
269	C₄×C₈	—	86	4	no	—
270	#95	—	43	2	no	—
271	#95	—	43	2	no	—
272	#95	—	43	2	no	—
273	#95	—	43	2	no	—
274	#95	—	43	2	no	—
275	#95	—	43	2	no	—
276	#95	—	43	2	no	—
277	C₂×Q₈	—	43	4	no	—
278	C₂×Q₈	—	172	1	no	—
279	C₂×Q₈	—	172	1	no	—
280	C₂²×C₄	—	43	2	no	—
281	C₂²×C₄	—	43	2	no	—
282	C₂²×C₄	—	43	2	no	—
283	C₂²×C₄	—	43	2	no	—
284	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
290	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	86	2	no	—
297	C₂×C₈	—	86	2	no	—
298	C₂×C₈	—	86	2	no	—
299	C₂×C₈	—	86	2	no	—
300	C₂×C₈	—	86	2	no	—
301	C₂×C₈	—	86	2	no	—
302	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
303	C₄⋊C₄	—	43	8	no	—
304	C₄⋊C₄	—	43	4	no	—
305	C₄⋊C₄	—	86	4	no	—
306	C₄⋊C₄	—	172	2	no	—
307	C₄⋊C₄	—	172	1	no	—
308	C₄⋊C₄	—	172	1	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	4	1	no	—
313	C₄²	—	4	1	no	—
314	C₄²	—	4	1	no	—
315	C₄²	—	43	4	no	—
316	C₄²	—	43	4	no	—
317	C₄²	—	86	2	no	—
318	C₄²	—	86	2	no	—
319	C₄²	C₂×Dic₈₆	1	2	yes	—
320	C₄²	#10621898	1	2	yes	—
321	C₄²	D₄×D₄₃	1	2	yes	—
322	C₄²	Q₈×D₄₃	1	2	yes	—
323	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
324	Q₈	—	172	4	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	43	4	no	—
339	C₂×C₄	—	43	4	no	—
340	C₂×C₄	—	86	2	no	—
341	C₂×C₄	—	86	2	no	—
342	C₂×C₄	—	86	2	no	—
343	C₂×C₄	—	86	2	no	—
344	C₂×C₄	—	86	2	no	—
345	C₂×C₄	—	86	2	no	—
346	C₂×C₄	—	86	2	no	—
347	C₂×C₄	—	86	2	no	—
348	C₂×C₄	—	86	2	no	—
349	C₂×C₄	—	86	2	no	—
350	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
351	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
352	C₂×C₄	C₄×Dic₈₆	1	2	yes	—
353	C₂×C₄	C₄×Dic₈₆	1	2	yes	—
354	C₂×C₄	#13063333	1	2	yes	—
355	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
356	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
357	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
358	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
359	C₂×C₄	#13063371	1	1	yes	characteristic
360	C₂×C₄	#13063372	1	1	yes	characteristic
361	C₈	—	2	4	no	—
362	C₈	—	4	2	no	—
363	C₈	—	172	2	no	—
364	C₈	—	172	2	no	—
365	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
366	C₂²	C₂×C₄×Dic₈₆	1	1	yes	characteristic
367	C₂²	#14583379	1	1	yes	characteristic
368	C₂²	C₂×#13063333	1	1	yes	characteristic
369	C₂²	#14583665	1	1	yes	characteristic
370	C₂²	#14583665	1	1	yes	characteristic
371	C₂²	#14583665	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	1	no	—
378	C₄	—	86	4	no	—
379	C₄	—	86	4	no	—
380	C₄	—	172	2	no	—
381	C₄	—	172	2	no	—
382	C₄	D₄×Dic₈₆	1	1	yes	characteristic
383	C₄	#14583570	1	1	yes	characteristic
384	C₄	#14583627	1	1	yes	characteristic
385	C₄	Q₈×Dic₈₆	1	1	yes	characteristic
386	C₂	C₄⋊C₄×Dic₈₆	1	1	yes	characteristic
387	C₂	#19143157	1	1	yes	characteristic
388	C₂	#19143164	1	1	yes	characteristic
389	C₂	#19143535	1	1	yes	characteristic
390	C₂	#19143542	1	1	yes	characteristic
391	C₂	#19143736	1	1	yes	characteristic
392	C₂	#19143767	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle, prime radical	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1767	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1767	D₄₃
hypocenter	C₄₃	#22723
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1767

Complements

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

N	H ≅ G/N	type
78. C₄⋊C₈×C₄₃	Q₈	semidirect
234. C₄₃	#22723	semidirect
266. C₄⋊C₈	Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583027	2
#19137072	2
#19135318	2
#19135317	2
#19135312	2
#19134748	2
#19134747	2
#19134454	2
C₄₃×#1767	2
#22723	43