Subgroups — #24991890

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583272	C₂	1	1	yes	maximal, characteristic
2	#19137659	C₂	1	1	yes	maximal, characteristic
3	#19135543	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582642	C₂	1	1	yes	maximal, characteristic
6	#19132435	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621873	—	2	2	no	—
9	C₂×#13063325	C₂²	1	1	yes	characteristic
10	C₂×#13063322	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₁₇₂	—	2	1	no	—
12	C₂×#13063287	—	2	1	no	—
13	#14583272	—	2	2	no	—
14	#14583272	C₄	1	4	yes	complemented
15	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
16	#14582801	—	2	1	no	—
17	#14582800	—	2	1	no	—
18	#14582777	—	2	2	no	—
19	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
20	#14582662	—	2	1	no	—
21	#14582662	—	2	1	no	—
22	#14582661	—	2	1	no	—
23	#14582661	—	2	1	no	—
24	#14582642	—	2	2	no	—
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
28	C₂²×Dic₈₆	—	2	1	no	—
29	C₂²×D₁₇₂	—	2	1	no	—
30	C₂²×D₁₇₂	—	2	1	no	—
31	C₂²×D₁₇₂	D₄	1	2	yes	—
32	C₂²×C₄×D₄₃	—	2	2	no	—
33	C₂×#10621873	—	2	8	no	—
34	C₂×#10621873	—	4	4	no	—
35	C₂×#10621873	—	4	4	no	—
36	C₂²×C₄₃⋊C₈	—	2	1	no	—
37	#13063325	—	2	1	no	—
38	#13063325	—	2	1	no	—
39	#13063325	—	2	1	no	—
40	#13063325	C₂×C₄	1	2	yes	complemented
41	#13063322	—	2	1	no	—
42	#13063322	—	2	1	no	—
43	#13063322	C₂×C₄	1	2	yes	—
44	#13063322	D₄	1	2	yes	—
45	C₄×D₁₇₂	—	4	2	no	—
46	C₄×D₁₇₂	—	4	2	no	—
47	#13063287	—	4	2	no	—
48	#13063287	—	4	2	no	—
49	C₂×C₄⋊Dic₄₃	—	2	1	no	—
50	C₂×C₄⋊Dic₄₃	—	2	1	no	—
51	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
53	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
54	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
55	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
56	C₂×C₄×Dic₄₃	—	2	1	no	—
57	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
59	C₄₃⋊#95	—	2	1	no	—
60	C₂²×C₈×C₄₃	—	2	1	no	—
61	C₂²×C₈×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₃	—	2	1	no	—
65	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₄₃	—	2	1	no	—
67	C₄⋊C₈×C₄₃	—	2	1	no	—
68	C₄×C₈×C₄₃	—	2	1	no	—
69	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	complemented
70	#95×C₄₃	—	2	1	no	—
71	C₂³×D₄₃	—	2	2	no	—
72	C₂²×C₄×C₄₃	—	2	1	no	—
73	C₂²×C₄×C₄₃	—	2	1	no	—
74	C₂²×C₄×C₄₃	C₂×D₄	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×Dic₄₃	—	2	1	no	—
78	C₂²×Dic₄₃	—	2	1	no	—
79	C₂²×Dic₄₃	—	4	1	no	—
80	C₂×D₁₇₂	—	2	2	no	—
81	C₂×D₁₇₂	—	2	2	no	—
82	C₂×D₁₇₂	—	2	2	no	—
83	C₂×D₁₇₂	—	2	2	no	—
84	C₂×D₁₇₂	—	2	2	no	—
85	C₂×D₁₇₂	—	4	1	no	—
86	C₂×D₁₇₂	—	4	1	no	—
87	C₂×D₁₇₂	—	4	1	no	—
88	C₂×D₁₇₂	—	4	1	no	—
89	C₂×D₁₇₂	—	4	1	no	—
90	C₂×D₁₇₂	—	4	1	no	—
91	C₂×D₁₇₂	—	4	1	no	—
92	C₂×D₁₇₂	—	4	1	no	—
93	C₂×D₁₇₂	—	4	2	no	—
94	C₂×D₁₇₂	—	4	2	no	—
95	C₂×D₁₇₂	C₂²⋊C₄	1	4	yes	—
96	C₂×C₄×D₄₃	—	4	4	no	—
97	C₂×C₄×D₄₃	—	4	4	no	—
98	C₂×C₄×D₄₃	—	8	2	no	—
99	C₂×Dic₈₆	—	2	2	no	—
100	C₂×Dic₈₆	—	4	2	no	—
101	C₂×Dic₈₆	—	4	2	no	—
102	C₂×Dic₈₆	—	4	1	no	—
103	C₂×C₈×C₄₃	—	2	2	no	—
104	C₂×C₈×C₄₃	—	2	2	no	—
105	C₂×C₈×C₄₃	—	2	2	no	—
106	C₂×C₈×C₄₃	—	4	1	no	—
107	C₂×C₈×C₄₃	—	4	1	no	—
108	C₂×C₈×C₄₃	—	4	1	no	—
109	C₄⋊C₄×C₄₃	—	2	1	no	—
110	C₄⋊C₄×C₄₃	—	2	1	no	—
111	C₄⋊C₄×C₄₃	—	2	1	no	—
112	C₄⋊C₄×C₄₃	SD₁₆	1	2	yes	complemented
113	C₄²×C₄₃	—	4	1	no	—
114	C₄²×C₄₃	—	4	1	no	—
115	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₃	#41	1	1	yes	characteristic
118	C₄²×C₄₃	#41	1	1	yes	characteristic
119	(C₂×D₄₃)⋊C₄	—	4	4	no	—
120	(C₂×D₄₃)⋊C₄	—	4	4	no	—
121	(C₂×D₄₃)⋊C₄	—	8	2	no	—
122	C₄⋊Dic₄₃	—	2	1	no	—
123	C₄⋊Dic₄₃	—	2	2	no	—
124	C₄⋊Dic₄₃	—	2	2	no	—
125	C₄⋊Dic₄₃	—	2	1	no	—
126	C₄⋊Dic₄₃	—	2	1	no	—
127	C₄⋊Dic₄₃	—	4	1	no	—
128	C₄⋊Dic₄₃	—	4	1	no	—
129	C₄⋊Dic₄₃	SD₁₆	1	2	yes	complemented
130	C₄×Dic₄₃	—	4	1	no	—
131	C₄×Dic₄₃	—	4	1	no	—
132	C₂×C₄₃⋊C₈	—	4	1	no	—
133	C₂×C₄₃⋊C₈	—	4	1	no	—
134	C₂×C₄₃⋊C₈	—	4	1	no	—
135	#10621873	—	4	16	no	—
136	C₂³×C₄₃	#120	1	1	yes	characteristic
137	C₂²×D₄₃	—	2	4	no	—
138	C₂²×D₄₃	—	4	2	no	—
139	C₂²×D₄₃	—	4	2	no	—
140	C₂²×D₄₃	—	4	2	no	—
141	C₂²×D₄₃	—	4	2	no	—
142	C₂²×D₄₃	—	4	2	no	—
143	C₂²×D₄₃	—	4	2	no	—
144	C₂×C₄×C₄₃	—	2	1	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	2	no	—
147	C₂×C₄×C₄₃	—	4	1	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	1	no	—
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
156	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
157	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
161	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
162	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
165	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
166	C₂×Dic₄₃	—	2	2	no	—
167	C₂×Dic₄₃	—	4	1	no	—
168	C₂×Dic₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	4	2	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	—	4	1	no	—
172	C₂×Dic₄₃	—	4	1	no	—
173	C₂×Dic₄₃	—	8	1	no	—
174	C₂×Dic₄₃	—	8	1	no	—
175	D₁₇₂	—	4	4	no	—
176	D₁₇₂	—	4	2	no	—
177	D₁₇₂	—	4	2	no	—
178	D₁₇₂	—	4	2	no	—
179	D₁₇₂	—	4	2	no	—
180	D₁₇₂	—	4	2	no	—
181	D₁₇₂	—	4	2	no	—
182	D₁₇₂	—	4	2	no	—
183	D₁₇₂	—	4	2	no	—
184	D₁₇₂	—	8	2	no	—
185	C₄×D₄₃	—	8	8	no	—
186	Dic₈₆	—	4	4	no	—
187	Dic₈₆	—	8	2	no	—
188	C₈×C₄₃	—	2	4	no	—
189	C₈×C₄₃	—	8	1	no	—
190	C₄₃⋊C₈	—	8	1	no	—
191	#9064	—	43	1	no	maximal, Sylow
192	C₂²×C₄₃	#386	1	1	yes	characteristic
193	C₂²×C₄₃	#450	1	1	yes	characteristic
194	C₂²×C₄₃	#450	1	1	yes	characteristic
195	C₂²×C₄₃	#452	1	1	yes	characteristic
196	C₂²×C₄₃	#452	1	1	yes	characteristic
197	C₂²×C₄₃	#453	1	1	yes	characteristic
198	C₂²×C₄₃	#453	1	1	yes	characteristic
199	C₂×D₄₃	—	4	4	no	—
200	C₂×D₄₃	—	4	4	no	—
201	C₂×D₄₃	—	4	4	no	—
202	C₂×D₄₃	—	8	2	no	—
203	C₂×D₄₃	—	8	2	no	—
204	C₂×D₄₃	—	8	2	no	—
205	C₂×D₄₃	—	8	2	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	4	2	no	—
209	C₄×C₄₃	—	8	1	no	—
210	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
211	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
212	C₄×C₄₃	#440	1	1	yes	characteristic
213	C₄×C₄₃	#440	1	1	yes	characteristic
214	C₄×C₄₃	#461	1	1	yes	characteristic
215	C₄×C₄₃	#461	1	1	yes	characteristic
216	C₄×C₄₃	#463	1	1	yes	characteristic
217	C₄×C₄₃	#463	1	1	yes	characteristic
218	Dic₄₃	—	4	2	no	—
219	Dic₄₃	—	8	1	no	—
220	Dic₄₃	—	8	2	no	—
221	C₂×#492	—	43	1	no	—
222	#2366	—	43	1	no	—
223	#1987	—	43	1	no	—
224	#1987	—	43	1	no	—
225	C₂×#331	—	43	1	no	—
226	#1279	—	43	1	no	—
227	#1279	D₄₃	1	1	yes	characteristic, complemented
228	C₂×C₄₃	#1629	1	1	yes	characteristic
229	C₂×C₄₃	#1630	1	1	yes	characteristic
230	C₂×C₄₃	#1631	1	1	yes	characteristic
231	C₂×C₄₃	#1631	1	1	yes	characteristic
232	C₂×C₄₃	#1877	1	1	yes	characteristic
233	C₂×C₄₃	#1877	1	1	yes	characteristic
234	C₂×C₄₃	#1887	1	1	yes	characteristic
235	D₄₃	—	8	4	no	—
236	C₂²×SD₁₆	—	86	2	no	—
237	C₂×C₄⋊Q₈	—	43	1	no	—
238	C₂×#127	—	43	1	no	—
239	C₂×C₄×D₄	—	86	1	no	—
240	C₂×C₄×D₄	—	86	1	no	—
241	#492	—	43	4	no	—
242	#492	—	86	2	no	—
243	C₂×C₄⋊C₈	—	43	1	no	—
244	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
246	#390	—	86	1	no	—
247	#390	—	86	1	no	—
248	#386	—	86	2	no	—
249	C₄×C₄⋊C₄	—	43	1	no	—
250	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
251	#340	—	86	1	no	—
252	#340	—	86	1	no	—
253	#340	—	86	1	no	—
254	#340	—	86	1	no	—
255	#331	—	86	2	no	—
256	C₄₃	#9064	1	1	yes	characteristic, complemented, Sylow
257	C₂²×Q₈	—	86	1	no	—
258	C₂²×D₄	—	43	2	no	—
259	C₂²×D₄	—	86	1	no	—
260	C₂²×D₄	—	86	1	no	—
261	C₂³×C₄	—	86	2	no	—
262	C₂×SD₁₆	—	86	8	no	—
263	C₂×SD₁₆	—	172	4	no	—
264	C₂×SD₁₆	—	172	4	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	86	1	no	—
268	C₄⋊Q₈	—	43	2	no	—
269	C₄⋊Q₈	—	86	1	no	—
270	C₄⋊Q₈	—	86	1	no	—
271	C₄⋊Q₈	—	86	1	no	—
272	#127	—	43	2	no	—
273	#127	—	43	2	no	—
274	#127	—	86	1	no	—
275	#127	—	86	1	no	—
276	C₄×D₄	—	172	2	no	—
277	C₄×D₄	—	172	2	no	—
278	C₄×D₄	—	172	2	no	—
279	C₄×D₄	—	172	2	no	—
280	C₂×C₄⋊C₄	—	43	1	no	—
281	C₂×C₄⋊C₄	—	43	1	no	—
282	C₂×C₄⋊C₄	—	86	1	no	—
283	C₂×C₄⋊C₄	—	86	1	no	—
284	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
285	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	86	2	no	—
287	C₂×C₂²⋊C₄	—	86	2	no	—
288	C₂×C₂²⋊C₄	—	86	2	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	86	1	no	—
291	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	86	1	no	—
295	C₄⋊C₈	—	86	1	no	—
296	C₄×C₈	—	2	1	no	—
297	C₄×C₈	C₄×D₄₃	1	2	yes	complemented
298	#95	—	2	1	no	—
299	#95	—	86	1	no	—
300	C₂⁴	—	86	2	no	—
301	C₂×Q₈	—	86	2	no	—
302	C₂×Q₈	—	172	2	no	—
303	C₂×Q₈	—	172	2	no	—
304	C₂×Q₈	—	172	1	no	—
305	C₂×D₄	—	43	4	no	—
306	C₂×D₄	—	86	2	no	—
307	C₂×D₄	—	86	2	no	—
308	C₂×D₄	—	86	2	no	—
309	C₂×D₄	—	86	2	no	—
310	C₂×D₄	—	86	2	no	—
311	C₂×D₄	—	172	2	no	—
312	C₂×D₄	—	172	2	no	—
313	C₂×D₄	—	172	1	no	—
314	C₂×D₄	—	172	1	no	—
315	C₂×D₄	—	172	1	no	—
316	C₂×D₄	—	172	1	no	—
317	C₂×D₄	—	172	1	no	—
318	C₂×D₄	—	172	1	no	—
319	C₂×D₄	—	172	1	no	—
320	C₂×D₄	—	172	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	86	1	no	—
324	C₂²×C₄	—	86	1	no	—
325	C₂²×C₄	—	344	2	no	—
326	C₂²×C₄	—	172	4	no	—
327	C₂²×C₄	—	172	4	no	—
328	C₂²×C₄	—	172	1	no	—
329	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
330	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
332	SD₁₆	—	172	16	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	172	1	no	—
340	C₂×C₈	—	172	1	no	—
341	C₂×C₈	—	172	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	43	2	no	—
346	C₄⋊C₄	—	86	1	no	—
347	C₄⋊C₄	—	86	2	no	—
348	C₄⋊C₄	—	86	2	no	—
349	C₄⋊C₄	—	86	1	no	—
350	C₄⋊C₄	—	86	1	no	—
351	C₄⋊C₄	—	172	1	no	—
352	C₄⋊C₄	—	172	1	no	—
353	C₄⋊C₄	#10621873	1	2	yes	complemented
354	C₂²⋊C₄	—	344	2	no	—
355	C₂²⋊C₄	—	172	4	no	—
356	C₂²⋊C₄	—	172	4	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	4	1	no	—
359	C₄²	—	172	1	no	—
360	C₄²	—	172	1	no	—
361	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
362	C₄²	#10621898	1	1	yes	characteristic
363	C₄²	D₄×D₄₃	1	1	yes	characteristic
364	C₄²	#10621902	1	1	yes	characteristic
365	C₂³	—	86	4	no	—
366	C₂³	—	172	2	no	—
367	C₂³	—	172	2	no	—
368	C₂³	—	172	2	no	—
369	C₂³	—	172	2	no	—
370	C₂³	—	172	2	no	—
371	C₂³	—	172	2	no	—
372	C₂³	#13063295	1	1	yes	characteristic
373	Q₈	—	344	2	no	—
374	Q₈	—	172	4	no	—
375	D₄	—	344	2	no	—
376	D₄	—	172	4	no	—
377	D₄	—	172	2	no	—
378	D₄	—	172	2	no	—
379	D₄	—	172	2	no	—
380	D₄	—	172	2	no	—
381	D₄	—	172	2	no	—
382	D₄	—	172	2	no	—
383	D₄	—	172	2	no	—
384	D₄	—	172	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	86	2	no	—
394	C₂×C₄	—	344	8	no	—
395	C₂×C₄	—	344	1	no	—
396	C₂×C₄	—	344	1	no	—
397	C₂×C₄	—	172	1	no	—
398	C₂×C₄	—	172	1	no	—
399	C₂×C₄	—	172	1	no	—
400	C₂×C₄	—	172	2	no	—
401	C₂×C₄	—	172	1	no	—
402	C₂×C₄	—	172	1	no	—
403	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
404	C₂×C₄	#13063287	1	1	yes	characteristic
405	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
406	C₂×C₄	#13063298	1	1	yes	characteristic
407	C₂×C₄	#13063300	1	1	yes	characteristic
408	C₂×C₄	#13063310	1	1	yes	characteristic
409	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
410	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
411	C₂×C₄	#13063346	1	1	yes	characteristic
412	C₂×C₄	#13063347	1	1	yes	characteristic
413	C₂×C₄	#13063349	1	1	yes	characteristic
414	C₂×C₄	#13063353	1	1	yes	characteristic
415	C₂×C₄	#13063357	1	1	yes	characteristic
416	C₂×C₄	#13063358	1	1	yes	characteristic
417	C₈	—	2	4	no	—
418	C₈	—	8	1	no	—
419	C₈	—	344	1	no	—
420	C₂²	—	344	2	no	—
421	C₂²	—	344	2	no	—
422	C₂²	—	344	2	no	—
423	C₂²	—	344	2	no	—
424	C₂²	—	172	4	no	—
425	C₂²	—	172	4	no	—
426	C₂²	—	172	4	no	—
427	C₂²	#14582777	1	1	yes	characteristic
428	C₂²	#14583051	1	1	yes	characteristic
429	C₂²	#14583052	1	1	yes	characteristic
430	C₂²	#14583063	1	1	yes	characteristic
431	C₂²	#14583064	1	1	yes	characteristic
432	C₂²	#14583068	1	1	yes	characteristic
433	C₂²	#14583068	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	1	no	—
438	C₄	—	344	2	no	—
439	C₄	—	344	1	no	—
440	C₄	—	172	2	no	—
441	C₄	#14582986	1	1	yes	characteristic
442	C₄	C₄×#10621873	1	1	yes	characteristic
443	C₄	#14582998	1	1	yes	characteristic
444	C₄	#14583001	1	1	yes	characteristic
445	C₄	#14583103	1	1	yes	characteristic
446	C₄	#14583105	1	1	yes	characteristic
447	C₄	#14583113	1	1	yes	characteristic
448	C₄	#14583115	1	1	yes	characteristic
449	C₂	—	344	4	no	—
450	C₂	#19133713	1	1	yes	characteristic
451	C₂	#19133718	1	1	yes	characteristic
452	C₂	#19133724	1	1	yes	characteristic
453	C₂	#19133725	1	1	yes	characteristic
454	C₂	#19134928	1	1	yes	characteristic
455	C₂	#19134930	1	1	yes	characteristic
456	C₂	#19134992	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063295
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1279	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂×#13063322	C₂²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1279	D₄₃
hypocenter	C₄₃	#9064
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
3. #19135543	C₂	semidirect
4. #19135542	C₂	semidirect
6. #19132435	C₂	semidirect
7. C₄₃×#1279	C₂	semidirect
14. #14583272	C₄	semidirect
40. #13063325	C₂×C₄	semidirect
69. C₄×C₈×C₄₃	C₂×C₄	semidirect
112. C₄⋊C₄×C₄₃	SD₁₆	semidirect
129. C₄⋊Dic₄₃	SD₁₆	semidirect
227. #1279	D₄₃	semidirect
256. C₄₃	#9064	semidirect
297. C₄×C₈	C₄×D₄₃	semidirect
353. C₄⋊C₄	#10621873	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583272	2
#19137659	2
#19135543	2
#19135542	2
C₂×#14582642	2
#19132435	2
C₄₃×#1279	2
#9064	43