Subgroups — #25257137

Order 11008.

2138 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137701	C₂	1	4	yes	maximal, complemented
2	#19137680	C₂	1	4	yes	maximal
3	#19137560	C₂	1	4	yes	maximal, complemented
4	#19137455	C₂	1	4	yes	maximal
5	#19137344	C₂	1	2	yes	maximal, complemented
6	#19137315	C₂	1	2	yes	maximal, complemented
7	#19137246	C₂	1	2	yes	maximal, complemented
8	C₂²⋊Q₈×Dic₄₃	C₂	1	4	yes	maximal
9	#19136993	C₂	1	1	yes	maximal, characteristic
10	#19136960	C₂	1	2	yes	maximal, complemented
11	C₂×#14582745	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄₃×#533	C₂	1	1	yes	maximal, characteristic
13	C₂×Q₈×Dic₄₃	C₂²	1	4	yes	—
14	C₂²×C₄×Dic₄₃	C₂²	1	2	yes	—
15	#14582806	C₂²	1	8	yes	—
16	#14582806	C₂²	1	4	yes	—
17	#14582798	C₂²	1	4	yes	—
18	#14582785	C₂²	1	8	yes	—
19	#14582785	C₂²	1	8	yes	—
20	#14582785	C₂²	1	8	yes	—
21	#14582785	C₂²	1	8	yes	—
22	#14582785	C₂²	1	8	yes	—
23	#14582774	C₂²	1	8	yes	—
24	#14582767	C₂²	1	2	yes	—
25	#14582767	C₂²	1	4	yes	—
26	#14582765	C₂²	1	4	yes	—
27	#14582765	C₂²	1	2	yes	—
28	#14582762	C₂²	1	2	yes	—
29	#14582759	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₃	C₂²	1	8	yes	—
31	C₄⋊C₄×Dic₄₃	C₂²	1	4	yes	—
32	C₄⋊C₄×Dic₄₃	C₂²	1	8	yes	—
33	C₄×C₄⋊Dic₄₃	C₂²	1	4	yes	—
34	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
35	C₂²⋊C₄×Dic₄₃	C₂²	1	8	yes	—
36	C₄×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
37	#14582745	C₂²	1	2	yes	—
38	#14582745	C₂²	1	4	yes	—
39	#14582745	C₂²	1	2	yes	—
40	#14582745	C₂²	1	2	yes	—
41	#14582745	C₂²	1	1	yes	characteristic
42	#14582745	C₂²	1	1	yes	characteristic
43	#14582745	C₂²	1	2	yes	—
44	C₂×C₄₃⋊#95	C₂²	1	2	yes	—
45	C₂×C₄₃⋊#95	C₂²	1	2	yes	—
46	C₄₃×#533	C₄	1	16	yes	complemented
47	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
49	C₂×#125×C₄₃	C₂²	1	2	yes	—
50	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
51	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
52	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
53	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
54	C₂×#117×C₄₃	C₂²	1	2	yes	—
55	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
56	C₂³×Dic₄₃	C₂³	1	4	yes	—
57	Q₈×Dic₄₃	—	2	16	no	—
58	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
59	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
60	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
61	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
62	C₂×C₄×Dic₄₃	—	2	8	no	—
63	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
64	C₂×C₄×Dic₄₃	C₂³	1	8	yes	—
65	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
66	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
67	C₂×C₄×Dic₄₃	C₂³	1	8	yes	—
68	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
69	C₄₃⋊#95	C₂³	1	8	yes	—
70	C₄₃⋊#95	C₂³	1	2	yes	—
71	C₄₃⋊#95	C₂³	1	4	yes	—
72	C₄₃⋊#95	C₂³	1	4	yes	—
73	C₄₃⋊#95	C₂³	1	8	yes	—
74	C₄₃⋊#95	C₂³	1	8	yes	—
75	C₄₃⋊#95	C₂³	1	4	yes	—
76	C₄₃⋊#95	C₂³	1	4	yes	—
77	C₄₃⋊#95	C₂³	1	8	yes	—
78	C₄₃⋊#95	C₂³	1	4	yes	—
79	C₄₃⋊#95	C₂³	1	2	yes	—
80	C₄₃⋊#95	C₂³	1	2	yes	—
81	C₄₃⋊#95	C₂³	1	2	yes	—
82	C₄₃⋊#95	C₂³	1	4	yes	—
83	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
84	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₄⋊Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
89	C₄⋊Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
90	#125×C₄₃	C₂×C₄	1	16	yes	complemented
91	C₂²⋊Q₈×C₄₃	C₂×C₄	1	16	yes	—
92	C₂²⋊Q₈×C₄₃	C₂×C₄	1	16	yes	—
93	C₄×Q₈×C₄₃	C₂×C₄	1	16	yes	complemented
94	C₄×Q₈×C₄₃	C₂×C₄	1	16	yes	complemented
95	#117×C₄₃	C₂×C₄	1	16	yes	—
96	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
102	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
103	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
109	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
110	C₂×Q₈×C₄₃	—	2	8	no	—
111	C₂×Q₈×C₄₃	—	4	4	no	—
112	C₂×Q₈×C₄₃	C₂²×C₄	1	8	yes	—
113	C₂×Q₈×C₄₃	C₂²×C₄	1	8	yes	—
114	C₂²×C₄×C₄₃	—	2	4	no	—
115	C₂²×C₄×C₄₃	—	2	4	no	—
116	C₂²×C₄×C₄₃	—	4	2	no	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
128	C₂²×Dic₄₃	—	2	8	no	—
129	C₂²×Dic₄₃	—	2	8	no	—
130	C₂²×Dic₄₃	—	4	4	no	—
131	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
132	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
133	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
134	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
135	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
136	C₄⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
137	C₄⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
138	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
139	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
140	C₂²⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
141	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
142	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
143	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
144	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
145	C₄²×C₄₃	C₂²×C₄	1	16	yes	—
146	C₂²⋊Dic₄₃	—	2	8	no	—
147	C₄⋊Dic₄₃	—	2	8	no	—
148	C₄⋊Dic₄₃	—	2	16	no	—
149	C₄⋊Dic₄₃	—	4	8	no	—
150	C₄×Dic₄₃	—	2	4	no	—
151	C₄×Dic₄₃	—	2	8	no	—
152	C₄×Dic₄₃	—	2	16	no	—
153	C₄×Dic₄₃	—	4	8	no	—
154	C₄×Dic₄₃	—	4	4	no	—
155	C₄×Dic₄₃	#41	1	8	yes	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
159	C₂³×C₄₃	2₋¹⁺⁴	1	4	yes	—
160	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
161	Q₈×C₄₃	—	2	16	no	—
162	Q₈×C₄₃	—	4	8	no	—
163	C₂×C₄×C₄₃	—	2	8	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	8	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	4	no	—
170	C₂×C₄×C₄₃	—	2	4	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	8	no	—
173	C₂×C₄×C₄₃	—	4	4	no	—
174	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
175	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
176	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
177	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
179	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
180	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
181	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
182	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
183	C₂×Dic₄₃	—	2	4	no	—
184	C₂×Dic₄₃	—	2	4	no	—
185	C₂×Dic₄₃	—	2	4	no	—
186	C₂×Dic₄₃	—	2	8	no	—
187	C₂×Dic₄₃	—	2	8	no	—
188	C₂×Dic₄₃	—	2	4	no	—
189	C₂×Dic₄₃	—	2	8	no	—
190	C₂×Dic₄₃	—	2	4	no	—
191	C₂×Dic₄₃	—	4	16	no	—
192	C₂×Dic₄₃	C₂×#41	1	8	yes	—
193	#34221	—	43	1	no	maximal, Sylow
194	C₂²×C₄₃	—	2	2	no	—
195	C₂²×C₄₃	—	2	2	no	—
196	C₂²×C₄₃	—	2	8	no	—
197	C₂²×C₄₃	#519	1	4	yes	—
198	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
199	C₂²×C₄₃	C₂²×#41	1	2	yes	—
200	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
201	C₂²×C₄₃	#585	1	2	yes	—
202	C₄×C₄₃	—	2	2	no	—
203	C₄×C₄₃	—	2	8	no	—
204	C₄×C₄₃	—	2	2	no	—
205	C₄×C₄₃	—	2	2	no	—
206	C₄×C₄₃	—	2	2	no	—
207	C₄×C₄₃	—	2	2	no	—
208	C₄×C₄₃	—	2	8	no	—
209	C₄×C₄₃	C₄×#41	1	4	yes	—
210	Dic₄₃	—	2	8	no	—
211	Dic₄₃	—	4	8	no	—
212	Dic₄₃	—	4	4	no	—
213	C₂×#533	D₄₃	1	1	yes	characteristic
214	#2371	—	43	4	no	—
215	#2368	—	43	4	no	—
216	#2356	—	43	4	no	—
217	#2343	—	43	4	no	—
218	#2331	—	43	2	no	—
219	#2327	—	43	2	no	—
220	#2320	—	43	2	no	—
221	C₄×C₂²⋊Q₈	—	43	4	no	—
222	#2283	—	43	1	no	—
223	#2276	—	43	2	no	—
224	C₂×#376	—	43	1	no	—
225	C₂×C₄₃	—	2	4	no	—
226	C₂×C₄₃	C₂×C₄×#41	1	1	yes	characteristic
227	C₂×C₄₃	C₂×#519	1	1	yes	characteristic
228	C₂×C₄₃	#3428	1	1	yes	characteristic
229	C₂×C₄₃	#3495	1	4	yes	—
230	#533	Dic₄₃	1	16	yes	complemented
231	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
233	C₂×#125	C₂×D₄₃	1	2	yes	—
234	C₂×C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
235	C₂×C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
236	C₂×C₄×Q₈	—	43	4	no	—
237	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
238	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
239	C₂×#117	C₂×D₄₃	1	2	yes	—
240	C₂²×C₄²	—	43	2	no	—
241	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
242	#391	—	43	4	no	—
243	#391	—	43	8	no	—
244	#389	—	43	4	no	—
245	#387	—	43	8	no	—
246	#387	—	43	8	no	—
247	#387	—	43	8	no	—
248	#387	—	43	8	no	—
249	#387	—	43	8	no	—
250	#385	—	43	8	no	—
251	#383	—	43	4	no	—
252	#383	—	43	2	no	—
253	#382	—	43	4	no	—
254	#382	—	43	2	no	—
255	#381	—	43	2	no	—
256	#380	—	43	2	no	—
257	C₄×C₄⋊C₄	—	43	4	no	—
258	C₄×C₄⋊C₄	—	43	8	no	—
259	C₄×C₄⋊C₄	—	43	8	no	—
260	C₄×C₄⋊C₄	—	43	2	no	—
261	C₄×C₄⋊C₄	—	43	4	no	—
262	C₄×C₂²⋊C₄	—	43	2	no	—
263	C₄×C₂²⋊C₄	—	43	8	no	—
264	#376	—	43	1	no	—
265	#376	—	43	2	no	—
266	#376	—	43	4	no	—
267	#376	—	43	2	no	—
268	#376	—	43	2	no	—
269	#376	—	43	2	no	—
270	#376	—	43	1	no	—
271	C₂×#95	—	43	2	no	—
272	C₂×#95	—	43	2	no	—
273	C₄₃	#34221	1	1	yes	characteristic, complemented, Sylow
274	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
275	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
276	C₂³×C₄	—	43	4	no	—
277	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
278	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
279	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
280	C₄⋊Q₈	C₂×Dic₄₃	1	8	yes	complemented
281	C₄⋊Q₈	C₂×Dic₄₃	1	8	yes	complemented
282	#125	C₂×Dic₄₃	1	16	yes	complemented
283	C₂²⋊Q₈	C₂×Dic₄₃	1	16	yes	—
284	C₂²⋊Q₈	C₂×Dic₄₃	1	16	yes	—
285	C₄×Q₈	—	86	16	no	—
286	C₄×Q₈	C₂×Dic₄₃	1	16	yes	complemented
287	C₄×Q₈	C₂×Dic₄₃	1	16	yes	complemented
288	#117	C₂×Dic₄₃	1	16	yes	—
289	C₂×C₄⋊C₄	—	43	4	no	—
290	C₂×C₄⋊C₄	—	43	8	no	—
291	C₂×C₄⋊C₄	—	43	8	no	—
292	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
295	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
296	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
297	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
298	C₂×C₂²⋊C₄	—	43	4	no	—
299	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
300	C₂×C₄²	—	43	2	no	—
301	C₂×C₄²	—	43	8	no	—
302	C₂×C₄²	—	43	4	no	—
303	C₂×C₄²	—	43	2	no	—
304	C₂×C₄²	—	43	4	no	—
305	C₂×C₄²	—	43	8	no	—
306	C₂×C₄²	—	86	8	no	—
307	C₂×C₄²	C₂×Dic₄₃	1	8	yes	—
308	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
309	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
310	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
311	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
312	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
313	#95	—	43	2	no	—
314	#95	—	43	2	no	—
315	#95	—	43	2	no	—
316	#95	—	43	4	no	—
317	#95	—	43	2	no	—
318	#95	—	43	4	no	—
319	#95	—	43	4	no	—
320	#95	—	43	4	no	—
321	#95	—	43	8	no	—
322	#95	—	43	4	no	—
323	#95	—	43	4	no	—
324	#95	—	43	8	no	—
325	#95	—	43	8	no	—
326	#95	—	43	8	no	—
327	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
328	C₂×Q₈	—	2	8	no	—
329	C₂×Q₈	—	4	4	no	—
330	C₂×Q₈	C₂²×Dic₄₃	1	8	yes	—
331	C₂×Q₈	C₂²×Dic₄₃	1	8	yes	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	43	4	no	—
336	C₂²×C₄	—	43	4	no	—
337	C₂²×C₄	—	43	8	no	—
338	C₂²×C₄	—	86	8	no	—
339	C₂²×C₄	—	86	8	no	—
340	C₂²×C₄	—	172	4	no	—
341	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
342	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
343	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
344	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
345	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
346	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
347	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
348	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
349	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
350	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
351	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
352	C₄⋊C₄	—	86	16	no	—
353	C₄⋊C₄	—	86	8	no	—
354	C₄⋊C₄	—	172	8	no	—
355	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
356	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
357	C₄⋊C₄	C₂²×Dic₄₃	1	16	yes	—
358	C₄⋊C₄	C₂²×Dic₄₃	1	16	yes	—
359	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
360	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
361	C₂²⋊C₄	—	86	8	no	—
362	C₂²⋊C₄	C₂²×Dic₄₃	1	16	yes	—
363	C₄²	—	43	8	no	—
364	C₄²	—	86	8	no	—
365	C₄²	—	86	16	no	—
366	C₄²	—	86	4	no	—
367	C₄²	—	172	4	no	—
368	C₄²	—	172	8	no	—
369	C₄²	C₂²×Dic₄₃	1	4	yes	—
370	C₄²	C₂²×Dic₄₃	1	4	yes	—
371	C₄²	C₂²×Dic₄₃	1	4	yes	—
372	C₄²	C₂²×Dic₄₃	1	4	yes	—
373	C₄²	C₂²×Dic₄₃	1	16	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	C₂³×Dic₄₃	1	2	yes	—
377	C₂³	#13063373	1	4	yes	—
378	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
379	Q₈	—	2	16	no	—
380	Q₈	—	4	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	43	8	no	—
393	C₂×C₄	—	86	4	no	—
394	C₂×C₄	—	86	4	no	—
395	C₂×C₄	—	86	4	no	—
396	C₂×C₄	—	86	8	no	—
397	C₂×C₄	—	86	8	no	—
398	C₂×C₄	—	86	4	no	—
399	C₂×C₄	—	86	8	no	—
400	C₂×C₄	—	86	4	no	—
401	C₂×C₄	—	172	16	no	—
402	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
403	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
404	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
405	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
406	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
407	C₂×C₄	C₂³×Dic₄₃	1	8	yes	—
408	C₂×C₄	C₂³×Dic₄₃	1	8	yes	—
409	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
410	C₂×C₄	#41×D₄₃	1	4	yes	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	8	no	—
414	C₂²	#14583377	1	4	yes	—
415	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
416	C₂²	C₂×#41×D₄₃	1	2	yes	—
417	C₂²	C₂×#13063373	1	2	yes	—
418	C₂²	#14583735	1	2	yes	—
419	C₄	—	2	2	no	—
420	C₄	—	2	8	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	8	no	—
426	C₄	—	86	8	no	—
427	C₄	—	172	4	no	—
428	C₄	—	172	8	no	—
429	C₄	#41×Dic₄₃	1	4	yes	—
430	C₂	—	2	4	no	—
431	C₂	C₂×#41×Dic₄₃	1	1	yes	characteristic
432	C₂	C₂×#14583377	1	1	yes	characteristic
433	C₂	#19147798	1	1	yes	characteristic
434	C₂	#19148342	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₂×C₄₃×#533	C₂
socle, cosocle	C₂³×C₄₃	C₂⁵
prime radical	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂×#533	D₄₃
hypocenter	C₄₃	#34221
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. #19137701	C₂	semidirect
3. #19137560	C₂	semidirect
5. #19137344	C₂	semidirect
6. #19137315	C₂	semidirect
7. #19137246	C₂	semidirect
10. #19136960	C₂	semidirect
46. C₄₃×#533	C₄	semidirect
88. C₄⋊Q₈×C₄₃	C₂×C₄	semidirect
89. C₄⋊Q₈×C₄₃	C₂×C₄	semidirect
90. #125×C₄₃	C₂×C₄	semidirect
93. C₄×Q₈×C₄₃	C₂×C₄	semidirect
94. C₄×Q₈×C₄₃	C₂×C₄	semidirect
230. #533	Dic₄₃	semidirect
273. C₄₃	#34221	semidirect
280. C₄⋊Q₈	C₂×Dic₄₃	semidirect
281. C₄⋊Q₈	C₂×Dic₄₃	semidirect
282. #125	C₂×Dic₄₃	semidirect
286. C₄×Q₈	C₂×Dic₄₃	semidirect
287. C₄×Q₈	C₂×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19137701	2
#19137680	2
#19137560	2
#19137455	2
#19137344	2
#19137315	2
#19137246	2
C₂²⋊Q₈×Dic₄₃	2
#19136993	2
#19136960	2
C₂×#14582745	2
C₂×C₄₃×#533	2
#34221	43