Subgroups — #25080458

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145154	C₂	1	1	yes	maximal, characteristic
2	#19144726	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144718	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134054	C₂	1	2	yes	maximal, complemented
6	#19134040	C₂	1	2	yes	maximal, complemented
7	#19133978	C₂	1	2	yes	maximal, complemented
8	#19133944	C₂	1	2	yes	maximal, complemented
9	#19133296	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133291	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583456	C₂²	1	1	yes	characteristic
13	#14583449	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
15	#14583297	C₂²	1	1	yes	characteristic
16	#14583272	C₂²	1	1	yes	characteristic
17	#14583250	C₂²	1	1	yes	characteristic
18	#14583246	C₂²	1	1	yes	characteristic
19	#14583230	—	2	1	no	—
20	#14583213	—	2	1	no	—
21	#14583195	C₂²	1	2	yes	—
22	#14583185	C₂²	1	2	yes	—
23	#14583128	—	2	1	no	—
24	#14583128	—	2	1	no	—
25	#14583110	C₂²	1	2	yes	—
26	#14583100	C₂²	1	2	yes	—
27	#14583057	—	2	1	no	—
28	#14583040	—	2	1	no	—
29	C₈×Dic₈₆	—	2	1	no	—
30	C₈×Dic₈₆	—	2	1	no	—
31	C₈×Dic₈₆	C₂²	1	2	yes	—
32	C₈×Dic₈₆	C₂²	1	2	yes	—
33	#14583007	—	2	2	no	—
34	#14583001	—	2	2	no	—
35	C₄×#10621873	—	2	1	no	—
36	C₄×#10621873	—	2	1	no	—
37	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
38	C₂×Dic₄₃⋊C₈	—	2	1	no	—
39	C₂×C₈×Dic₄₃	—	2	1	no	—
40	#14582647	C₂²	1	2	yes	—
41	#14582646	C₂²	1	2	yes	—
42	#14582644	C₂²	1	2	yes	—
43	#14582642	C₂²	1	2	yes	—
44	C₄₃×#432	C₂²	1	1	yes	characteristic
45	C₄₃×#432	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#335	C₂²	1	2	yes	—
48	C₄₃×#334	C₂²	1	2	yes	—
49	C₂×#10621898	—	2	1	no	—
50	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
51	C₂×Dic₁₇₂	—	2	2	no	—
52	C₂×#10621873	—	2	2	no	—
53	C₂×#10621873	—	2	1	no	—
54	C₂×#10621873	—	2	1	no	—
55	C₂²×C₄₃⋊C₈	—	2	1	no	—
56	#13063325	C₂³	1	1	yes	characteristic
57	#13063325	C₂³	1	1	yes	characteristic
58	#13063325	C₂³	1	1	yes	characteristic
59	#13063322	C₂³	1	1	yes	characteristic
60	#13063317	—	2	1	no	—
61	#13063313	—	2	1	no	—
62	#13063304	—	2	1	no	—
63	#13063304	—	2	1	no	—
64	#13063299	—	2	1	no	—
65	#13063299	—	2	1	no	—
66	C₄×Dic₈₆	—	2	1	no	—
67	C₄×Dic₈₆	—	2	1	no	—
68	C₄×Dic₈₆	—	2	1	no	—
69	C₄×Dic₈₆	—	2	1	no	—
70	C₄×Dic₈₆	D₄	1	2	yes	—
71	C₄×Dic₈₆	C₂³	1	2	yes	—
72	C₄×D₁₇₂	—	2	1	no	—
73	C₄×D₁₇₂	—	2	1	no	—
74	#13063284	—	2	1	no	—
75	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
76	C₂×Dic₄₃⋊C₄	—	2	1	no	—
77	C₂×C₄×Dic₄₃	—	2	1	no	—
78	#13063259	—	2	2	no	—
79	#13063257	—	2	1	no	—
80	#13063257	—	2	1	no	—
81	#13063257	—	2	2	no	—
82	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
83	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
84	Dic₄₃⋊C₈	—	2	2	no	—
85	Dic₄₃⋊C₈	—	2	2	no	—
86	#13063250	—	2	2	no	—
87	#13063250	—	2	2	no	—
88	#13063250	—	2	1	no	—
89	#13063250	—	2	1	no	—
90	#13063250	—	2	2	no	—
91	#13063247	—	2	1	no	—
92	#13063247	—	2	1	no	—
93	#13063247	—	2	2	no	—
94	C₈×Dic₄₃	—	2	2	no	—
95	C₈×Dic₄₃	—	2	2	no	—
96	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
100	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
101	C₂²⋊C₈×C₄₃	—	2	1	no	—
102	C₂²⋊C₈×C₄₃	—	2	1	no	—
103	#97×C₄₃	—	2	1	no	—
104	#97×C₄₃	—	2	1	no	—
105	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
106	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
107	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₃	—	4	1	no	—
113	C₂²×Dic₄₃	—	2	1	no	—
114	C₂²×Dic₄₃	—	2	1	no	—
115	#10621898	—	8	2	no	—
116	C₂×D₁₇₂	—	2	1	no	—
117	C₂×D₁₇₂	—	2	1	no	—
118	C₂×D₁₇₂	—	2	1	no	—
119	C₂×C₄×D₄₃	—	4	1	no	—
120	C₂×Dic₈₆	—	2	1	no	—
121	C₂×Dic₈₆	—	2	4	no	—
122	C₂×Dic₈₆	—	2	1	no	—
123	C₂×Dic₈₆	—	2	1	no	—
124	C₂×Dic₈₆	—	2	1	no	—
125	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	4	1	no	—
130	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₃	#41	1	1	yes	characteristic
137	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
138	C₂²⋊Dic₄₃	—	4	1	no	—
139	(C₂×D₄₃)⋊C₄	—	4	1	no	—
140	(C₂×D₄₃)⋊C₄	—	4	1	no	—
141	C₄⋊Dic₄₃	—	2	1	no	—
142	C₄⋊Dic₄₃	—	2	1	no	—
143	C₄⋊Dic₄₃	—	2	1	no	—
144	C₄⋊Dic₄₃	—	2	1	no	—
145	C₄⋊Dic₄₃	—	2	1	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	—	2	1	no	—
148	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
149	Dic₄₃⋊C₄	—	2	2	no	—
150	Dic₄₃⋊C₄	—	2	2	no	—
151	Dic₄₃⋊C₄	—	4	1	no	—
152	Dic₄₃⋊C₄	—	4	1	no	—
153	C₄×Dic₄₃	—	2	2	no	—
154	C₄×Dic₄₃	—	2	2	no	—
155	C₄×Dic₄₃	—	4	1	no	—
156	C₂×C₄₃⋊C₈	—	2	2	no	—
157	C₂×C₄₃⋊C₈	—	4	2	no	—
158	Dic₁₇₂	—	4	4	no	—
159	#10621873	—	4	2	no	—
160	#10621873	—	4	4	no	—
161	#10621873	—	4	2	no	—
162	C₂³×C₄₃	#121	1	1	yes	characteristic
163	C₂²×D₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
169	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂²⋊D₄₃	—	8	2	no	—
175	C₂×Dic₄₃	—	2	4	no	—
176	C₂×Dic₄₃	—	2	2	no	—
177	C₂×Dic₄₃	—	2	2	no	—
178	C₂×Dic₄₃	—	4	2	no	—
179	C₂×Dic₄₃	—	4	1	no	—
180	C₂×Dic₄₃	—	4	1	no	—
181	C₂×Dic₄₃	—	4	1	no	—
182	D₁₇₂	—	4	2	no	—
183	D₁₇₂	—	4	1	no	—
184	D₁₇₂	—	4	1	no	—
185	D₁₇₂	—	8	1	no	—
186	C₄×D₄₃	—	8	2	no	—
187	Dic₈₆	—	2	4	no	—
188	Dic₈₆	—	2	2	no	—
189	Dic₈₆	—	4	2	no	—
190	Dic₈₆	—	4	1	no	—
191	Dic₈₆	—	4	1	no	—
192	Dic₈₆	—	8	1	no	—
193	Dic₈₆	#135	1	4	yes	—
194	C₈×C₄₃	—	2	1	no	—
195	C₈×C₄₃	—	2	1	no	—
196	C₈×C₄₃	—	2	1	no	—
197	C₈×C₄₃	—	4	2	no	—
198	C₈×C₄₃	—	4	2	no	—
199	C₈×C₄₃	#137	1	2	yes	—
200	C₄₃⋊C₈	—	4	2	no	—
201	#19263	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	2	1	no	—
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	#471	1	2	yes	—
205	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
206	C₂×D₄₃	—	8	1	no	—
207	C₂×D₄₃	—	8	1	no	—
208	C₂×D₄₃	—	8	1	no	—
209	C₄×C₄₃	—	2	1	no	—
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	—	2	1	no	—
213	C₄×C₄₃	C₂×#135	1	2	yes	—
214	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
215	C₄×C₄₃	#575	1	1	yes	characteristic
216	Dic₄₃	—	2	4	no	—
217	Dic₄₃	—	4	2	no	—
218	Dic₄₃	—	8	1	no	—
219	Dic₄₃	—	8	1	no	—
220	Dic₄₃	—	8	1	no	—
221	#3167	—	43	1	no	—
222	#3113	—	43	1	no	—
223	#3112	—	43	1	no	—
224	C₂×C₈×Q₈	—	43	1	no	—
225	#1684	—	43	2	no	—
226	#1682	—	43	2	no	—
227	#1672	—	43	2	no	—
228	#1666	—	43	2	no	—
229	#1568	D₄₃	1	1	yes	characteristic, complemented
230	#1552	—	43	1	no	—
231	#1551	—	43	1	no	—
232	C₂×C₄₃	—	2	2	no	—
233	C₂×C₄₃	#3037	1	1	yes	characteristic
234	C₂×C₄₃	#3050	1	1	yes	characteristic
235	C₂×C₄₃	C₂×#471	1	1	yes	characteristic
236	D₄₃	—	16	1	no	—
237	#533	—	43	1	no	—
238	#532	—	43	1	no	—
239	C₂×C₄×Q₈	—	43	1	no	—
240	#498	—	43	1	no	—
241	#492	—	43	1	no	—
242	#487	—	43	1	no	—
243	#486	—	43	1	no	—
244	#483	—	86	1	no	—
245	#480	—	86	1	no	—
246	#477	—	43	2	no	—
247	#475	—	43	2	no	—
248	#465	—	86	1	no	—
249	#465	—	86	1	no	—
250	#462	—	43	2	no	—
251	#460	—	43	2	no	—
252	#451	—	86	1	no	—
253	#448	—	86	1	no	—
254	C₈×Q₈	—	43	2	no	—
255	C₈×Q₈	—	43	2	no	—
256	C₈×Q₈	—	86	1	no	—
257	C₈×Q₈	—	86	1	no	—
258	#441	—	86	2	no	—
259	#440	—	86	2	no	—
260	C₄×SD₁₆	—	86	1	no	—
261	C₄×SD₁₆	—	86	1	no	—
262	#432	C₂×D₄₃	1	1	yes	characteristic
263	#432	C₂×D₄₃	1	1	yes	characteristic
264	C₂×C₄⋊C₈	—	43	1	no	—
265	C₂×C₄⋊C₈	—	86	1	no	—
266	C₂×C₄×C₈	—	86	1	no	—
267	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
268	#335	C₂×D₄₃	1	2	yes	—
269	#334	C₂×D₄₃	1	2	yes	—
270	#333	—	43	2	no	—
271	#332	—	43	2	no	—
272	#332	—	43	2	no	—
273	#331	—	43	2	no	—
274	C₄₃	#19263	1	1	yes	characteristic, complemented, Sylow
275	C₂×#41	—	86	1	no	—
276	C₂²×Q₈	—	43	1	no	—
277	C₂×Q₁₆	—	86	2	no	—
278	C₂×SD₁₆	—	86	2	no	—
279	C₂×SD₁₆	—	86	1	no	—
280	C₂×SD₁₆	—	86	1	no	—
281	C₂²×C₈	—	86	1	no	—
282	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
283	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
284	C₄⋊Q₈	—	43	1	no	—
285	C₄⋊Q₈	—	43	1	no	—
286	C₄⋊Q₈	—	43	1	no	—
287	#127	—	43	1	no	—
288	#125	—	86	1	no	—
289	#124	—	86	1	no	—
290	C₂²⋊Q₈	—	86	1	no	—
291	C₂²⋊Q₈	—	86	1	no	—
292	#121	—	86	1	no	—
293	#121	—	86	1	no	—
294	C₄×Q₈	—	43	2	no	—
295	C₄×Q₈	—	43	2	no	—
296	C₄×Q₈	—	86	1	no	—
297	C₄×Q₈	—	86	1	no	—
298	C₄×Q₈	—	86	1	no	—
299	C₄×Q₈	—	86	1	no	—
300	C₄×D₄	—	86	1	no	—
301	C₄×D₄	—	86	1	no	—
302	#117	—	86	1	no	—
303	C₂×C₄⋊C₄	—	43	1	no	—
304	C₂×C₄⋊C₄	—	86	1	no	—
305	C₂×C₄²	—	86	1	no	—
306	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
307	#107	—	86	2	no	—
308	#106	—	86	2	no	—
309	#106	—	86	1	no	—
310	#106	—	86	1	no	—
311	C₄⋊C₈	—	43	2	no	—
312	C₄⋊C₈	—	86	2	no	—
313	C₄⋊C₈	—	86	2	no	—
314	C₄⋊C₈	—	86	1	no	—
315	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
316	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
317	#103	—	86	2	no	—
318	#103	—	86	2	no	—
319	#103	—	86	2	no	—
320	#103	—	86	1	no	—
321	#103	—	86	1	no	—
322	#102	—	86	2	no	—
323	#102	—	86	1	no	—
324	#102	—	86	1	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	#97	—	2	1	no	—
328	#97	—	2	1	no	—
329	C₄×C₈	—	86	2	no	—
330	C₄×C₈	—	86	2	no	—
331	C₄×C₈	D₁₇₂	1	1	yes	characteristic
332	C₄×C₈	D₁₇₂	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
334	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
335	#41	—	344	2	no	—
336	C₂×Q₈	—	43	2	no	—
337	C₂×Q₈	—	86	4	no	—
338	C₂×Q₈	—	86	1	no	—
339	C₂×Q₈	—	86	1	no	—
340	C₂×Q₈	—	86	1	no	—
341	C₂×Q₈	—	86	1	no	—
342	C₂×D₄	—	86	1	no	—
343	C₂×D₄	—	86	1	no	—
344	C₂×D₄	—	86	1	no	—
345	C₂×D₄	—	172	1	no	—
346	C₂²×C₄	—	86	1	no	—
347	C₂²×C₄	—	86	1	no	—
348	C₂²×C₄	—	172	1	no	—
349	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
351	C₂²×C₄	#10621902	1	1	yes	characteristic
352	Q₁₆	—	172	4	no	—
353	SD₁₆	—	172	2	no	—
354	SD₁₆	—	172	4	no	—
355	SD₁₆	—	172	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	86	2	no	—
361	C₂×C₈	—	172	2	no	—
362	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
363	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
364	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
365	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
366	C₄⋊C₄	—	43	2	no	—
367	C₄⋊C₄	—	86	1	no	—
368	C₄⋊C₄	—	86	2	no	—
369	C₄⋊C₄	—	86	2	no	—
370	C₄⋊C₄	—	86	1	no	—
371	C₄⋊C₄	—	86	1	no	—
372	C₄⋊C₄	—	86	1	no	—
373	C₄⋊C₄	—	86	1	no	—
374	C₄⋊C₄	—	86	1	no	—
375	C₄⋊C₄	—	86	1	no	—
376	C₄⋊C₄	—	172	1	no	—
377	C₄⋊C₄	—	172	1	no	—
378	C₂²⋊C₄	—	172	1	no	—
379	C₂²⋊C₄	—	172	1	no	—
380	C₂²⋊C₄	—	172	1	no	—
381	C₄²	—	86	2	no	—
382	C₄²	—	86	2	no	—
383	C₄²	—	172	1	no	—
384	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
385	C₄²	D₄×D₄₃	1	1	yes	characteristic
386	C₄²	#10621902	1	1	yes	characteristic
387	C₄²	C₂³×D₄₃	1	1	yes	characteristic
388	C₂³	—	172	1	no	—
389	C₂³	#13063300	1	1	yes	characteristic
390	Q₈	—	43	4	no	—
391	Q₈	—	86	4	no	—
392	Q₈	—	86	2	no	—
393	Q₈	—	344	1	no	—
394	Q₈	—	172	2	no	—
395	Q₈	—	172	1	no	—
396	Q₈	—	172	1	no	—
397	D₄	—	344	1	no	—
398	D₄	—	344	2	no	—
399	D₄	—	172	2	no	—
400	D₄	—	172	1	no	—
401	D₄	—	172	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	86	4	no	—
407	C₂×C₄	—	86	2	no	—
408	C₂×C₄	—	86	2	no	—
409	C₂×C₄	—	344	2	no	—
410	C₂×C₄	—	172	1	no	—
411	C₂×C₄	—	172	1	no	—
412	C₂×C₄	—	172	1	no	—
413	C₂×C₄	—	172	2	no	—
414	C₂×C₄	#13063300	1	1	yes	characteristic
415	C₂×C₄	#13063300	1	1	yes	characteristic
416	C₂×C₄	#13063300	1	1	yes	characteristic
417	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
419	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	172	2	no	—
426	C₈	#13063358	1	2	yes	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	344	1	no	—
430	C₂²	—	344	1	no	—
431	C₂²	—	344	1	no	—
432	C₂²	#14583163	1	2	yes	—
433	C₂²	C₂×#13063300	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	86	4	no	—
439	C₄	—	344	1	no	—
440	C₄	—	344	1	no	—
441	C₄	—	344	1	no	—
442	C₄	—	172	2	no	—
443	C₄	#135×D₄₃	1	2	yes	—
444	C₄	C₂×#13063358	1	1	yes	characteristic
445	C₄	#14583699	1	1	yes	characteristic
446	C₂	—	2	2	no	—
447	C₂	—	688	1	no	—
448	C₂	#19144069	1	1	yes	characteristic
449	C₂	#19144177	1	1	yes	characteristic
450	C₂	C₂×#14583163	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063300
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1568	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	#1568	D₄₃
hypocenter	C₄₃	#19263
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
2. #19144726	C₂	semidirect
4. C₂×C₈×Dic₈₆	C₂	semidirect
5. #19134054	C₂	semidirect
6. #19134040	C₂	semidirect
7. #19133978	C₂	semidirect
8. #19133944	C₂	semidirect
9. #19133296	C₂	semidirect
11. C₄₃×#1568	C₂	semidirect
229. #1568	D₄₃	semidirect
274. C₄₃	#19263	semidirect

Maximal subgroups

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

subgroup	index
#19145154	2
#19144726	2
#19144718	2
C₂×C₈×Dic₈₆	2
#19134054	2
#19134040	2
#19133978	2
#19133944	2
#19133296	2
#19133291	2
C₄₃×#1568	2
#19263	43