Subgroups — #26003710

Order 11008.

7812 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148217	C₂	1	6	yes	maximal, complemented
2	#19148203	C₂	1	9	yes	maximal, complemented
3	#19148194	C₂	1	6	yes	maximal, complemented
4	Q₈×#10621902	C₂	1	2	yes	maximal, complemented
5	#19148152	C₂	1	18	yes	maximal, complemented
6	#19148085	C₂	1	6	yes	maximal, complemented
7	#19147890	C₂	1	9	yes	maximal, complemented
8	C₄×#41×D₄₃	C₂	1	6	yes	maximal, complemented
9	C₄₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#41×D₄₃	C₂²	1	6	yes	—
11	#14583635	C₂²	1	9	yes	complemented
12	#14583628	C₂²	1	6	yes	complemented
13	#14583619	C₂²	1	18	yes	complemented
14	#14583610	C₂²	1	18	yes	complemented
15	#14583596	C₂²	1	36	yes	complemented
16	#14583588	C₂²	1	36	yes	complemented
17	#14583579	C₂²	1	36	yes	complemented
18	Q₈×D₁₇₂	C₂²	1	6	yes	complemented
19	#14583556	C₂²	1	12	yes	complemented
20	#14583554	C₂²	1	18	yes	complemented
21	#14583546	C₂²	1	36	yes	complemented
22	#14583534	C₂²	1	9	yes	complemented
23	#14583456	C₂²	1	9	yes	complemented
24	#14583454	C₂²	1	18	yes	complemented
25	#14583447	C₂²	1	18	yes	complemented
26	#14583431	C₂²	1	36	yes	complemented
27	#14583430	C₂²	1	36	yes	complemented
28	#14583428	C₂²	1	36	yes	complemented
29	#14583409	C₂²	1	36	yes	complemented
30	#14583406	C₂²	1	18	yes	complemented
31	#41×Dic₄₃	C₂²	1	6	yes	complemented
32	#41×Dic₄₃	C₂²	1	6	yes	complemented
33	C₄×#10621902	C₂²	1	6	yes	—
34	C₄×#10621902	C₂²	1	2	yes	—
35	C₄×#10621898	C₂²	1	18	yes	complemented
36	#14583367	C₂²	1	18	yes	complemented
37	C₄×#10621900	C₂²	1	18	yes	complemented
38	C₄×#10621900	C₂²	1	18	yes	complemented
39	C₄×Q₈×D₄₃	C₂²	1	6	yes	complemented
40	C₄×Q₈×D₄₃	C₂²	1	6	yes	complemented
41	C₄×D₄×D₄₃	C₂²	1	18	yes	complemented
42	C₄×D₄×D₄₃	C₂²	1	18	yes	complemented
43	#117×D₄₃	C₂²	1	18	yes	complemented
44	C₂×C₄²×D₄₃	C₂²	1	9	yes	complemented
45	Q₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
46	C₄₃×#555	C₂²	1	9	yes	complemented
47	C₄₃×#550	C₂²	1	6	yes	complemented
48	C₄₃×#532	C₂²	1	9	yes	complemented
49	C₄×#41×C₄₃	C₂²	1	6	yes	complemented
50	C₂×#10621902	C₂³	1	2	yes	—
51	C₂×#10621898	C₂³	1	18	yes	—
52	C₂×#10621900	C₂³	1	18	yes	—
53	#41×D₄₃	—	2	48	no	—
54	C₂×Q₈×D₄₃	C₂³	1	6	yes	—
55	C₂×D₄×D₄₃	C₂³	1	18	yes	—
56	C₂²×C₄×D₄₃	C₂³	1	18	yes	—
57	C₂²×C₄×D₄₃	C₂³	1	9	yes	—
58	#13063325	C₂³	1	18	yes	—
59	#13063318	C₂³	1	72	yes	—
60	#13063317	C₂³	1	18	yes	—
61	#13063316	C₂³	1	36	yes	—
62	#13063312	C₂³	1	36	yes	—
63	#13063307	C₂³	1	72	yes	—
64	#13063306	C₂³	1	36	yes	—
65	#13063305	C₂³	1	36	yes	—
66	#13063304	C₂³	1	36	yes	—
67	#13063301	C₂³	1	36	yes	—
68	#13063296	C₂³	1	36	yes	—
69	#13063296	C₂³	1	36	yes	—
70	#13063293	C₂³	1	36	yes	—
71	Q₈×Dic₄₃	C₂³	1	6	yes	—
72	Q₈×Dic₄₃	C₂³	1	2	yes	—
73	Q₈×Dic₄₃	C₂³	1	12	yes	—
74	C₄×Dic₈₆	C₂³	1	18	yes	—
75	C₄×Dic₈₆	C₂³	1	18	yes	—
76	#13063290	C₂³	1	18	yes	—
77	#13063290	C₂³	1	18	yes	—
78	C₄×D₁₇₂	C₂³	1	18	yes	—
79	C₄×D₁₇₂	C₂³	1	6	yes	—
80	D₄×Dic₄₃	C₂³	1	18	yes	—
81	D₄×Dic₄₃	C₂³	1	18	yes	—
82	D₄×Dic₄₃	C₂³	1	36	yes	—
83	#13063287	C₂³	1	18	yes	—
84	#13063287	C₂³	1	6	yes	—
85	C₄×C₂²⋊D₄₃	C₂³	1	36	yes	—
86	C₄×C₂²⋊D₄₃	C₂³	1	36	yes	—
87	(C₂²⋊D₄₃)⋊C₄	C₂³	1	36	yes	—
88	(C₂²⋊D₄₃)⋊C₄	C₂³	1	36	yes	—
89	#13063284	C₂³	1	18	yes	—
90	#13063284	C₂³	1	18	yes	—
91	#13063283	C₂³	1	6	yes	—
92	#13063283	C₂³	1	18	yes	—
93	#13063282	C₂³	1	36	yes	—
94	#13063281	C₂³	1	36	yes	—
95	C₄⋊C₄×D₄₃	C₂³	1	18	yes	—
96	C₄⋊C₄×D₄₃	C₂³	1	18	yes	—
97	C₂²⋊C₄×D₄₃	C₂³	1	36	yes	—
98	C₂×C₄×Dic₄₃	C₂³	1	9	yes	—
99	C₂×C₄×Dic₄₃	C₂³	1	18	yes	—
100	C₄²×D₄₃	C₂³	1	6	yes	—
101	C₄²×D₄₃	C₂³	1	18	yes	—
102	C₄²×D₄₃	C₂³	1	18	yes	—
103	C₄²×D₄₃	C₂³	1	18	yes	—
104	C₂×#41×C₄₃	C₂³	1	6	yes	—
105	C₂×#41×C₄₃	C₂³	1	6	yes	—
106	C₄⋊Q₈×C₄₃	C₂³	1	9	yes	—
107	#127×C₄₃	C₂³	1	9	yes	—
108	#124×C₄₃	C₂³	1	18	yes	—
109	#121×C₄₃	C₂³	1	36	yes	—
110	C₄×Q₈×C₄₃	C₂³	1	6	yes	—
111	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
112	C₄×D₄×C₄₃	C₂³	1	18	yes	—
113	C₄×D₄×C₄₃	C₂³	1	18	yes	—
114	#117×C₄₃	C₂³	1	18	yes	—
115	C₂×C₄²×C₄₃	C₂³	1	9	yes	—
116	C₂³×D₄₃	C₂⁴	1	9	yes	—
117	#41×C₄₃	—	2	24	no	—
118	#41×C₄₃	—	4	12	no	—
119	C₂×Q₈×C₄₃	C₂⁴	1	6	yes	—
120	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
121	C₂×D₄×C₄₃	C₂⁴	1	18	yes	—
122	C₂×D₄×C₄₃	C₂⁴	1	18	yes	—
123	C₂²×C₄×C₄₃	C₂⁴	1	18	yes	—
124	C₂²×C₄×C₄₃	C₂⁴	1	9	yes	—
125	C₂×C₂²⋊D₄₃	C₂⁴	1	36	yes	—
126	C₂²×Dic₄₃	C₂⁴	1	18	yes	—
127	C₂²×Dic₄₃	C₂⁴	1	9	yes	—
128	#10621902	#41	1	16	yes	complemented
129	Q₈×D₄₃	—	2	24	no	—
130	#10621900	—	2	72	no	—
131	D₄×D₄₃	—	2	72	no	—
132	#10621898	—	2	72	no	—
133	C₂×D₁₇₂	C₂⁴	1	6	yes	—
134	C₂×C₄×D₄₃	—	2	72	no	—
135	C₂×C₄×D₄₃	—	4	18	no	—
136	C₂×C₄×D₄₃	C₂⁴	1	6	yes	—
137	C₂×C₄×D₄₃	C₂⁴	1	6	yes	—
138	C₂×C₄×D₄₃	C₂⁴	1	18	yes	—
139	C₂×C₄×D₄₃	C₂⁴	1	18	yes	—
140	C₂×C₄×D₄₃	C₂⁴	1	18	yes	—
141	C₂×C₄×D₄₃	C₂⁴	1	6	yes	—
142	C₂×Dic₈₆	C₂⁴	1	18	yes	—
143	C₄⋊C₄×C₄₃	C₂⁴	1	6	yes	—
144	C₄⋊C₄×C₄₃	C₂⁴	1	18	yes	—
145	C₂²⋊C₄×C₄₃	C₂⁴	1	36	yes	—
146	C₄²×C₄₃	C₂⁴	1	6	yes	—
147	C₄²×C₄₃	C₂⁴	1	9	yes	—
148	C₄²×C₄₃	C₂⁴	1	9	yes	—
149	C₂²⋊Dic₄₃	C₂⁴	1	36	yes	—
150	C₂²⋊Dic₄₃	C₂⁴	1	36	yes	—
151	(C₂×D₄₃)⋊C₄	C₂⁴	1	12	yes	—
152	(C₂×D₄₃)⋊C₄	C₂⁴	1	36	yes	—
153	C₄⋊Dic₄₃	C₂⁴	1	6	yes	—
154	C₄⋊Dic₄₃	C₂⁴	1	18	yes	—
155	C₄⋊Dic₄₃	C₂⁴	1	36	yes	—
156	Dic₄₃⋊C₄	C₂⁴	1	36	yes	—
157	Dic₄₃⋊C₄	C₂⁴	1	36	yes	—
158	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
159	C₄×Dic₄₃	C₂⁴	1	6	yes	—
160	C₄×Dic₄₃	C₂⁴	1	6	yes	—
161	C₄×Dic₄₃	C₂⁴	1	18	yes	—
162	C₄×Dic₄₃	C₂⁴	1	18	yes	—
163	C₄×Dic₄₃	C₂⁴	1	9	yes	—
164	C₄×Dic₄₃	C₂⁴	1	18	yes	—
165	C₂³×C₄₃	C₂⁵	1	9	yes	—
166	C₂²×D₄₃	—	2	36	no	—
167	C₂²×D₄₃	—	4	9	no	—
168	C₂²×D₄₃	C₂⁵	1	6	yes	—
169	Q₈×C₄₃	—	4	6	no	—
170	Q₈×C₄₃	C₂×#41	1	8	yes	complemented
171	D₄×C₄₃	—	2	36	no	—
172	D₄×C₄₃	—	4	18	no	—
173	C₂×C₄×C₄₃	—	2	36	no	—
174	C₂×C₄×C₄₃	—	2	18	no	—
175	C₂×C₄×C₄₃	C₂⁵	1	6	yes	—
176	C₂×C₄×C₄₃	C₂⁵	1	9	yes	—
177	C₂×C₄×C₄₃	C₂⁵	1	6	yes	—
178	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
179	C₂²⋊D₄₃	—	2	72	no	—
180	C₂×Dic₄₃	—	2	36	no	—
181	C₂×Dic₄₃	—	4	9	no	—
182	C₂×Dic₄₃	C₂⁵	1	6	yes	—
183	C₂×Dic₄₃	C₂⁵	1	18	yes	—
184	C₂×Dic₄₃	C₂⁵	1	2	yes	—
185	D₁₇₂	C₂×#41	1	24	yes	complemented
186	C₄×D₄₃	—	2	36	no	—
187	C₄×D₄₃	—	2	36	no	—
188	C₄×D₄₃	—	2	12	no	—
189	C₄×D₄₃	—	2	12	no	—
190	C₄×D₄₃	—	4	18	no	—
191	C₄×D₄₃	C₂×#41	1	24	yes	complemented
192	Dic₈₆	—	2	36	no	—
193	#41²	—	43	1	no	maximal, Sylow
194	C₂²×C₄₃	—	2	18	no	—
195	C₂²×C₄₃	—	2	9	no	—
196	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
197	C₂×D₄₃	—	2	6	no	—
198	C₂×D₄₃	—	2	6	no	—
199	C₂×D₄₃	—	4	36	no	—
200	C₂×D₄₃	C₂²×#41	1	12	yes	—
201	C₄×C₄₃	—	2	6	no	—
202	C₄×C₄₃	—	2	9	no	—
203	C₄×C₄₃	C₂²×#41	1	12	yes	—
204	C₄×C₄₃	#585	1	2	yes	—
205	Dic₄₃	—	2	18	no	—
206	Dic₄₃	—	2	6	no	—
207	Dic₄₃	C₂²×#41	1	4	yes	—
208	#3483	D₄₃	1	1	yes	characteristic, complemented
209	#3482	—	43	6	no	—
210	#3481	—	43	9	no	—
211	#3480	—	43	6	no	—
212	Q₈×#41	—	43	2	no	—
213	#3475	—	43	18	no	—
214	D₄×#41	—	43	6	no	—
215	#3444	—	43	9	no	—
216	C₂×C₄×#41	—	43	6	no	—
217	C₂×C₄₃	—	4	9	no	—
218	C₂×C₄₃	C₂³×#41	1	2	yes	—
219	C₂×C₄₃	C₂×#585	1	1	yes	characteristic
220	D₄₃	—	2	12	no	—
221	C₂²×#41	—	43	6	no	—
222	#559	—	43	9	no	—
223	Q₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
224	#557	—	43	6	no	—
225	#556	—	43	18	no	—
226	#555	C₂×D₄₃	1	9	yes	complemented
227	#554	—	43	18	no	—
228	#553	—	43	36	no	—
229	#552	—	43	36	no	—
230	#551	—	43	36	no	—
231	#550	C₂×D₄₃	1	6	yes	complemented
232	D₄×Q₈	—	43	6	no	—
233	#548	—	43	12	no	—
234	#547	—	43	18	no	—
235	#546	—	43	36	no	—
236	D₄²	—	43	9	no	—
237	#533	—	43	18	no	—
238	#533	—	43	9	no	—
239	#532	—	43	18	no	—
240	#532	C₂×D₄₃	1	9	yes	complemented
241	#529	—	43	36	no	—
242	#529	—	43	36	no	—
243	#529	—	43	36	no	—
244	#525	—	43	18	no	—
245	#525	—	43	36	no	—
246	C₄×#41	—	43	6	no	—
247	C₄×#41	—	43	6	no	—
248	C₄×#41	—	43	2	no	—
249	C₄×#41	—	43	6	no	—
250	C₄×#41	—	43	18	no	—
251	C₄×#41	—	43	18	no	—
252	C₄×#41	—	43	18	no	—
253	C₄×#41	—	43	18	no	—
254	C₄×#41	C₂×D₄₃	1	6	yes	complemented
255	C₂×C₄×Q₈	—	43	6	no	—
256	C₂×C₄×Q₈	—	43	6	no	—
257	C₂×C₄×D₄	—	43	18	no	—
258	C₂×C₄×D₄	—	43	18	no	—
259	C₂×#117	—	43	18	no	—
260	C₂²×C₄²	—	43	9	no	—
261	C₄₃	#41²	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	43	2	no	—
263	C₂×#41	—	43	18	no	—
264	C₂×#41	—	43	18	no	—
265	C₂×#41	—	86	48	no	—
266	C₂×#41	C₂²×D₄₃	1	6	yes	—
267	C₂×#41	C₂²×D₄₃	1	6	yes	—
268	C₂²×Q₈	—	43	6	no	—
269	C₂²×D₄	—	43	18	no	—
270	C₂³×C₄	—	43	18	no	—
271	C₂³×C₄	—	43	9	no	—
272	C₄⋊Q₈	—	43	18	no	—
273	C₄⋊Q₈	C₂²×D₄₃	1	9	yes	—
274	#127	C₂²×D₄₃	1	9	yes	—
275	#126	—	43	72	no	—
276	#125	—	43	36	no	—
277	#125	—	43	18	no	—
278	#124	—	43	36	no	—
279	#124	C₂²×D₄₃	1	18	yes	—
280	#123	—	43	36	no	—
281	#123	—	43	72	no	—
282	C₂²⋊Q₈	—	43	36	no	—
283	C₂²⋊Q₈	—	43	36	no	—
284	C₂²⋊Q₈	—	43	36	no	—
285	#121	—	43	36	no	—
286	#121	—	43	36	no	—
287	#121	C₂²×D₄₃	1	36	yes	—
288	#120	—	43	36	no	—
289	C₄×Q₈	—	43	2	no	—
290	C₄×Q₈	—	43	6	no	—
291	C₄×Q₈	—	43	12	no	—
292	C₄×Q₈	—	43	18	no	—
293	C₄×Q₈	—	43	18	no	—
294	C₄×Q₈	—	43	18	no	—
295	C₄×Q₈	—	43	18	no	—
296	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
297	C₄×Q₈	C₂²×D₄₃	1	6	yes	—
298	C₄×D₄	—	43	18	no	—
299	C₄×D₄	—	43	18	no	—
300	C₄×D₄	—	43	36	no	—
301	C₄×D₄	—	43	36	no	—
302	C₄×D₄	—	43	36	no	—
303	C₄×D₄	—	43	6	no	—
304	C₄×D₄	—	43	18	no	—
305	C₄×D₄	—	43	36	no	—
306	C₄×D₄	—	43	36	no	—
307	C₄×D₄	—	43	6	no	—
308	C₄×D₄	—	43	18	no	—
309	C₄×D₄	C₂²×D₄₃	1	18	yes	—
310	C₄×D₄	C₂²×D₄₃	1	18	yes	—
311	#117	—	43	18	no	—
312	#117	—	43	18	no	—
313	#117	—	43	6	no	—
314	#117	—	43	18	no	—
315	#117	—	43	36	no	—
316	#117	—	43	36	no	—
317	#117	C₂²×D₄₃	1	18	yes	—
318	C₂×C₄⋊C₄	—	43	18	no	—
319	C₂×C₄⋊C₄	—	43	18	no	—
320	C₂×C₂²⋊C₄	—	43	36	no	—
321	C₂×C₄²	—	43	9	no	—
322	C₂×C₄²	—	43	18	no	—
323	C₂×C₄²	—	43	18	no	—
324	C₂×C₄²	—	43	18	no	—
325	C₂×C₄²	—	43	18	no	—
326	C₂×C₄²	—	43	6	no	—
327	C₂×C₄²	C₂²×D₄₃	1	9	yes	—
328	C₂⁴	—	43	9	no	—
329	#41	—	2	24	no	—
330	#41	—	4	12	no	—
331	#41	—	43	16	no	—
332	#41	—	86	72	no	—
333	#41	—	86	72	no	—
334	C₂×Q₈	—	43	18	no	—
335	C₂×Q₈	—	86	24	no	—
336	C₂×Q₈	C₂³×D₄₃	1	6	yes	—
337	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
338	C₂×D₄	—	43	36	no	—
339	C₂×D₄	—	43	6	no	—
340	C₂×D₄	—	86	72	no	—
341	C₂×D₄	C₂³×D₄₃	1	18	yes	—
342	C₂×D₄	C₂³×D₄₃	1	18	yes	—
343	C₂²×C₄	—	43	6	no	—
344	C₂²×C₄	—	43	18	no	—
345	C₂²×C₄	—	43	9	no	—
346	C₂²×C₄	—	43	6	no	—
347	C₂²×C₄	—	43	18	no	—
348	C₂²×C₄	—	43	18	no	—
349	C₂²×C₄	—	43	6	no	—
350	C₂²×C₄	—	43	18	no	—
351	C₂²×C₄	—	86	72	no	—
352	C₂²×C₄	—	172	18	no	—
353	C₂²×C₄	C₂³×D₄₃	1	18	yes	—
354	C₂²×C₄	C₂³×D₄₃	1	9	yes	—
355	C₄⋊C₄	—	43	6	no	—
356	C₄⋊C₄	—	43	18	no	—
357	C₄⋊C₄	—	43	36	no	—
358	C₄⋊C₄	—	43	36	no	—
359	C₄⋊C₄	—	43	36	no	—
360	C₄⋊C₄	C₂³×D₄₃	1	6	yes	—
361	C₄⋊C₄	C₂³×D₄₃	1	18	yes	—
362	C₂²⋊C₄	—	43	36	no	—
363	C₂²⋊C₄	—	43	36	no	—
364	C₂²⋊C₄	—	43	12	no	—
365	C₂²⋊C₄	—	43	36	no	—
366	C₂²⋊C₄	C₂³×D₄₃	1	36	yes	—
367	C₄²	—	43	6	no	—
368	C₄²	—	43	6	no	—
369	C₄²	—	43	18	no	—
370	C₄²	—	43	18	no	—
371	C₄²	—	43	18	no	—
372	C₄²	—	43	1	no	—
373	C₄²	—	43	9	no	—
374	C₄²	C₂³×D₄₃	1	9	yes	—
375	C₄²	C₂³×D₄₃	1	9	yes	—
376	C₄²	C₂³×D₄₃	1	6	yes	—
377	C₂³	—	43	6	no	—
378	C₂³	—	86	36	no	—
379	C₂³	—	172	9	no	—
380	C₂³	C₂⁴×D₄₃	1	9	yes	—
381	Q₈	—	4	6	no	—
382	Q₈	—	86	36	no	—
383	Q₈	#41×D₄₃	1	8	yes	complemented
384	D₄	—	2	36	no	—
385	D₄	—	4	18	no	—
386	D₄	—	43	24	no	—
387	D₄	—	86	72	no	—
388	C₂×C₄	—	2	36	no	—
389	C₂×C₄	—	2	18	no	—
390	C₂×C₄	—	43	2	no	—
391	C₂×C₄	—	43	24	no	—
392	C₂×C₄	—	43	6	no	—
393	C₂×C₄	—	43	18	no	—
394	C₂×C₄	—	86	12	no	—
395	C₂×C₄	—	86	36	no	—
396	C₂×C₄	—	86	36	no	—
397	C₂×C₄	—	86	36	no	—
398	C₂×C₄	—	86	12	no	—
399	C₂×C₄	—	172	18	no	—
400	C₂×C₄	—	172	9	no	—
401	C₂×C₄	C₂⁴×D₄₃	1	6	yes	—
402	C₂×C₄	C₂⁴×D₄₃	1	9	yes	—
403	C₂×C₄	C₂⁴×D₄₃	1	6	yes	—
404	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
405	C₂²	—	2	18	no	—
406	C₂²	—	2	9	no	—
407	C₂²	—	43	12	no	—
408	C₂²	—	86	6	no	—
409	C₂²	—	86	6	no	—
410	C₂²	—	172	36	no	—
411	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
412	C₄	—	2	6	no	—
413	C₄	—	2	9	no	—
414	C₄	—	43	4	no	—
415	C₄	—	86	18	no	—
416	C₄	—	86	6	no	—
417	C₄	C₂×#41×D₄₃	1	12	yes	—
418	C₄	#14583734	1	2	yes	—
419	C₂	—	4	9	no	—
420	C₂	—	86	12	no	—
421	C₂	C₂²×#41×D₄₃	1	2	yes	—
422	C₂	C₂×#14583734	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₄₃×#3483	C₂
hypercenter	#3483	D₄₃
hypocenter	C₄₃	#41²
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #3483

Complements

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

N	H ≅ G/N	type
1. #19148217	C₂	semidirect
2. #19148203	C₂	semidirect
3. #19148194	C₂	semidirect
4. Q₈×#10621902	C₂	semidirect
5. #19148152	C₂	semidirect
6. #19148085	C₂	semidirect
7. #19147890	C₂	semidirect
8. C₄×#41×D₄₃	C₂	semidirect
9. C₄₃×#3483	C₂	semidirect
11. #14583635	C₂²	semidirect
12. #14583628	C₂²	semidirect
13. #14583619	C₂²	semidirect
14. #14583610	C₂²	semidirect
15. #14583596	C₂²	semidirect
16. #14583588	C₂²	semidirect
17. #14583579	C₂²	semidirect
18. Q₈×D₁₇₂	C₂²	semidirect
19. #14583556	C₂²	semidirect
20. #14583554	C₂²	semidirect
21. #14583546	C₂²	semidirect
22. #14583534	C₂²	semidirect
23. #14583456	C₂²	semidirect
24. #14583454	C₂²	semidirect
25. #14583447	C₂²	semidirect
26. #14583431	C₂²	semidirect
27. #14583430	C₂²	semidirect
28. #14583428	C₂²	semidirect
29. #14583409	C₂²	semidirect
30. #14583406	C₂²	semidirect
31. #41×Dic₄₃	C₂²	semidirect
32. #41×Dic₄₃	C₂²	semidirect
35. C₄×#10621898	C₂²	semidirect
36. #14583367	C₂²	semidirect
37. C₄×#10621900	C₂²	semidirect
38. C₄×#10621900	C₂²	semidirect
39. C₄×Q₈×D₄₃	C₂²	semidirect
40. C₄×Q₈×D₄₃	C₂²	semidirect
41. C₄×D₄×D₄₃	C₂²	semidirect
42. C₄×D₄×D₄₃	C₂²	semidirect
43. #117×D₄₃	C₂²	semidirect
44. C₂×C₄²×D₄₃	C₂²	semidirect
45. Q₈²×C₄₃	C₂²	semidirect
46. C₄₃×#555	C₂²	semidirect
47. C₄₃×#550	C₂²	semidirect
48. C₄₃×#532	C₂²	semidirect
49. C₄×#41×C₄₃	C₂²	semidirect
128. #10621902	#41	semidirect
170. Q₈×C₄₃	C₂×#41	semidirect
185. D₁₇₂	C₂×#41	semidirect
191. C₄×D₄₃	C₂×#41	semidirect
208. #3483	D₄₃	semidirect
223. Q₈²	C₂×D₄₃	semidirect
226. #555	C₂×D₄₃	semidirect
231. #550	C₂×D₄₃	semidirect
240. #532	C₂×D₄₃	semidirect
254. C₄×#41	C₂×D₄₃	semidirect
261. C₄₃	#41²	semidirect
383. Q₈	#41×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19148217	2
#19148203	2
#19148194	2
Q₈×#10621902	2
#19148152	2
#19148085	2
#19147890	2
C₄×#41×D₄₃	2
C₄₃×#3483	2
#41²	43