Subgroups — #25110528

Order 11008.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145081	C₂	1	1	yes	maximal, characteristic
2	#19143513	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143448	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135505	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135493	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135126	C₂	1	2	yes	maximal, complemented
7	#19135121	C₂	1	2	yes	maximal, complemented
8	#19135083	C₂	1	2	yes	maximal, complemented
9	#19135076	C₂	1	2	yes	maximal, complemented
10	#19134719	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1747	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063353	C₂²	1	2	yes	—
13	C₂×#13063347	C₂²	1	1	yes	characteristic
14	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
15	#14583665	C₂²	1	2	yes	—
16	#14583468	C₂²	1	2	yes	—
17	#14583373	C₂²	1	2	yes	—
18	#14583288	C₄	1	4	yes	complemented
19	#14583283	C₄	1	2	yes	complemented
20	#14583276	C₄	1	2	yes	complemented
21	#14583022	—	2	2	no	—
22	#14583017	—	2	2	no	—
23	#14583012	—	2	2	no	—
24	C₄×D₃₄₄	—	2	2	no	—
25	C₂×#13063261	C₂²	1	1	yes	characteristic
26	#14582937	C₂²	1	1	yes	characteristic
27	#14582917	C₂²	1	2	yes	—
28	#14582915	C₂²	1	2	yes	—
29	#14582905	C₂²	1	2	yes	—
30	#14582903	C₂²	1	2	yes	—
31	C₂×#13063241	C₂²	1	2	yes	—
32	#14582872	C₂²	1	2	yes	—
33	#14582670	C₂²	1	2	yes	—
34	#14582655	C₂²	1	2	yes	—
35	C₄₃×#405	C₂²	1	1	yes	characteristic
36	C₄₃×#405	C₂²	1	1	yes	characteristic
37	C₄₃×#405	C₂²	1	1	yes	characteristic
38	C₄₃×#338	C₂²	1	1	yes	characteristic
39	C₄₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
40	C₄₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
41	C₄₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
42	C₂×#10621898	C₂³	1	2	yes	—
43	C₂²×D₁₇₂	C₂³	1	2	yes	—
44	#13063353	—	4	2	no	—
45	#13063353	—	4	2	no	—
46	#13063347	—	2	1	no	—
47	#13063347	—	2	1	no	—
48	#13063347	—	2	1	no	—
49	#13063347	—	2	1	no	—
50	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×#10621873	C₂×C₄	1	2	yes	complemented
52	C₂×#10621873	C₂×C₄	1	4	yes	complemented
53	C₂×D₃₄₄	—	2	1	no	—
54	C₂×D₃₄₄	—	2	1	no	—
55	C₂×D₃₄₄	—	2	1	no	—
56	C₂×D₃₄₄	—	2	1	no	—
57	C₂×D₃₄₄	C₂×C₄	1	2	yes	—
58	C₂×D₃₄₄	C₂×C₄	1	2	yes	—
59	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×D₃₄₄	C₂×C₄	1	4	yes	complemented
61	#13063333	—	4	2	no	—
62	#13063331	—	2	4	no	—
63	C₂×#10621877	C₂³	1	2	yes	—
64	M₁₆×D₄₃	—	4	2	no	—
65	#13063322	C₂×C₄	1	4	yes	complemented
66	#13063313	C₂×C₄	1	4	yes	complemented
67	#13063300	—	4	2	no	—
68	#13063295	—	4	2	no	—
69	C₄×D₁₇₂	—	2	4	no	—
70	#13063287	—	4	2	no	—
71	#13063284	C₂³	1	2	yes	—
72	C₂²⋊C₄×D₄₃	—	4	2	no	—
73	#13063261	—	2	1	no	—
74	#13063261	—	2	1	no	—
75	#13063259	—	2	1	no	—
76	#13063257	—	2	1	no	—
77	#13063253	—	2	4	no	—
78	#13063251	—	4	2	no	—
79	#13063247	—	2	4	no	—
80	#13063245	—	4	2	no	—
81	#13063241	—	4	2	no	—
82	#13063239	—	4	2	no	—
83	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
87	#117×C₄₃	C₂³	1	1	yes	characteristic
88	#117×C₄₃	C₂³	1	1	yes	characteristic
89	#117×C₄₃	C₂³	1	1	yes	characteristic
90	#97×C₄₃	—	2	1	no	—
91	#97×C₄₃	C₂×C₄	1	2	yes	complemented
92	#97×C₄₃	D₄	1	2	yes	complemented
93	C₄×C₈×C₄₃	—	2	1	no	—
94	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	complemented
95	C₄×C₈×C₄₃	D₄	1	2	yes	complemented
96	C₂³×D₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
98	C₂×C₂²⋊D₄₃	—	2	2	no	—
99	#10621898	—	2	2	no	—
100	#10621898	—	2	2	no	—
101	#10621898	—	2	2	no	—
102	#10621898	—	2	2	no	—
103	C₂×D₁₇₂	—	2	2	no	—
104	C₂×D₁₇₂	—	2	2	no	—
105	C₂×D₁₇₂	—	2	2	no	—
106	C₂×D₁₇₂	—	2	2	no	—
107	C₂×D₁₇₂	—	2	2	no	—
108	C₂×D₁₇₂	—	4	4	no	—
109	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
110	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₄₃	—	2	2	no	—
112	C₂×C₄×D₄₃	—	4	4	no	—
113	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
114	M₁₆×C₄₃	—	2	1	no	—
115	M₁₆×C₄₃	—	2	1	no	—
116	M₁₆×C₄₃	—	2	1	no	—
117	M₁₆×C₄₃	—	2	1	no	—
118	M₁₆×C₄₃	—	2	1	no	—
119	M₁₆×C₄₃	—	2	1	no	—
120	C₂×C₈×C₄₃	—	2	1	no	—
121	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
128	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₂²⋊C₄×C₄₃	—	2	1	no	—
133	C₂²⋊C₄×C₄₃	—	2	1	no	—
134	C₂²⋊C₄×C₄₃	—	2	1	no	—
135	C₄²×C₄₃	—	2	1	no	—
136	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₄₃	C₂×D₄	1	2	yes	—
138	C₂²⋊Dic₄₃	—	2	2	no	—
139	(C₂×D₄₃)⋊C₄	—	4	4	no	—
140	(C₂×D₄₃)⋊C₄	—	4	4	no	—
141	C₄⋊Dic₄₃	—	2	2	no	—
142	C₄×Dic₄₃	—	2	2	no	—
143	#10621877	—	2	2	no	—
144	#10621877	—	2	2	no	—
145	C₂×C₄₃⋊C₈	—	2	2	no	—
146	Dic₁₇₂	—	2	1	no	—
147	Dic₁₇₂	—	2	1	no	—
148	D₃₄₄	—	2	2	no	—
149	D₃₄₄	—	2	2	no	—
150	D₃₄₄	—	2	2	no	—
151	D₃₄₄	—	2	2	no	—
152	D₃₄₄	—	2	1	no	—
153	D₃₄₄	—	2	1	no	—
154	D₃₄₄	—	4	4	no	—
155	#10621873	—	2	2	no	—
156	#10621873	—	2	2	no	—
157	#10621873	—	4	4	no	—
158	#10621872	—	4	4	no	—
159	C₈×D₄₃	—	4	4	no	—
160	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₄₃	—	2	4	no	—
162	C₂²×D₄₃	—	2	2	no	—
163	C₂²×D₄₃	—	4	2	no	—
164	C₂²×D₄₃	—	4	2	no	—
165	C₂²×D₄₃	—	16	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂²⋊D₄₃	—	4	2	no	—
176	C₂²⋊D₄₃	—	4	2	no	—
177	C₂×Dic₄₃	—	2	2	no	—
178	C₂×Dic₄₃	—	4	2	no	—
179	D₁₇₂	—	2	2	no	—
180	D₁₇₂	—	2	4	no	—
181	D₁₇₂	—	2	4	no	—
182	D₁₇₂	—	2	2	no	—
183	D₁₇₂	—	4	2	no	—
184	D₁₇₂	—	4	2	no	—
185	D₁₇₂	—	16	4	no	—
186	C₄×D₄₃	—	4	2	no	—
187	C₄×D₄₃	—	4	2	no	—
188	C₄×D₄₃	—	16	4	no	—
189	Dic₈₆	—	2	2	no	—
190	Dic₈₆	—	2	2	no	—
191	C₈×C₄₃	—	2	2	no	—
192	C₈×C₄₃	—	2	2	no	—
193	C₈×C₄₃	—	4	1	no	—
194	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
195	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
196	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
197	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
198	C₄₃⋊C₈	—	4	2	no	—
199	#22286	—	43	1	no	maximal, Sylow
200	C₂²×C₄₃	—	4	1	no	—
201	C₂²×C₄₃	#518	1	1	yes	characteristic
202	C₂²×C₄₃	#535	1	1	yes	characteristic
203	C₂²×C₄₃	#540	1	1	yes	characteristic
204	C₂×D₄₃	—	4	4	no	—
205	C₂×D₄₃	—	4	2	no	—
206	C₂×D₄₃	—	8	4	no	—
207	C₂×D₄₃	—	8	4	no	—
208	C₂×D₄₃	—	8	2	no	—
209	C₂×D₄₃	—	16	2	no	—
210	C₄×C₄₃	—	4	2	no	—
211	C₄×C₄₃	—	4	2	no	—
212	C₄×C₄₃	—	8	1	no	—
213	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
214	C₄×C₄₃	#518	1	1	yes	characteristic
215	C₄×C₄₃	#535	1	1	yes	characteristic
216	C₄×C₄₃	#540	1	1	yes	characteristic
217	Dic₄₃	—	4	2	no	—
218	Dic₄₃	—	8	2	no	—
219	#3155	—	43	1	no	—
220	#2957	—	43	1	no	—
221	#2948	—	43	1	no	—
222	#1978	—	43	1	no	—
223	#1976	—	43	1	no	—
224	#1911	—	43	2	no	—
225	#1910	—	43	2	no	—
226	#1904	—	43	2	no	—
227	#1903	—	43	2	no	—
228	#1833	—	43	1	no	—
229	#1747	D₄₃	1	1	yes	characteristic, complemented
230	C₂×C₄₃	—	2	1	no	—
231	C₂×C₄₃	—	2	1	no	—
232	C₂×C₄₃	—	2	1	no	—
233	C₂×C₄₃	#2328	1	1	yes	characteristic
234	D₄₃	—	8	2	no	—
235	D₄₃	—	8	4	no	—
236	C₂×AGL(1,ℤ/8)	—	43	2	no	—
237	C₂×#135	—	43	1	no	—
238	C₂²×D₈	—	43	1	no	—
239	#568	—	43	2	no	—
240	#535	—	43	2	no	—
241	#518	—	43	2	no	—
242	#496	—	43	4	no	—
243	#495	—	43	2	no	—
244	#493	—	43	2	no	—
245	#444	—	86	2	no	—
246	#443	—	86	2	no	—
247	#442	—	86	2	no	—
248	C₄×D₈	—	86	2	no	—
249	C₂×#108	—	43	1	no	—
250	#427	—	43	1	no	—
251	#421	—	43	2	no	—
252	#421	—	43	2	no	—
253	#418	—	43	2	no	—
254	#418	—	43	2	no	—
255	C₂×#100	—	43	2	no	—
256	#410	—	43	2	no	—
257	#405	C₂×D₄₃	1	1	yes	characteristic
258	#405	C₂×D₄₃	1	1	yes	characteristic
259	#405	C₂×D₄₃	1	1	yes	characteristic
260	#344	—	43	2	no	—
261	#338	C₂×D₄₃	1	1	yes	characteristic
262	H(3,ℤ/4)	—	43	2	no	—
263	H(3,ℤ/4)	C₂×D₄₃	1	1	yes	characteristic
264	H(3,ℤ/4)	C₂×D₄₃	1	1	yes	characteristic
265	H(3,ℤ/4)	C₂×D₄₃	1	1	yes	characteristic
266	C₄₃	#22286	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	—	43	2	no	—
268	C₂²×D₄	—	43	2	no	—
269	AGL(1,ℤ/8)	—	172	2	no	—
270	AGL(1,ℤ/8)	—	172	2	no	—
271	#135	—	86	1	no	—
272	#135	—	86	1	no	—
273	#135	—	86	1	no	—
274	#135	—	86	1	no	—
275	C₂×Q₁₆	—	43	1	no	—
276	C₂×SD₁₆	—	43	2	no	—
277	C₂×SD₁₆	—	43	4	no	—
278	C₂×D₈	—	43	2	no	—
279	C₂×D₈	—	43	2	no	—
280	C₂×D₈	—	43	1	no	—
281	C₂×D₈	—	43	4	no	—
282	C₂×D₈	—	86	1	no	—
283	C₂×D₈	—	86	1	no	—
284	C₂×D₈	—	86	1	no	—
285	C₂×D₈	—	86	1	no	—
286	#131	—	86	4	no	—
287	#131	—	172	2	no	—
288	C₂×M₁₆	—	43	2	no	—
289	C₂×M₁₆	—	172	2	no	—
290	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
291	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
292	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
294	#127	—	43	4	no	—
295	#124	—	43	4	no	—
296	#121	—	172	2	no	—
297	#120	—	172	2	no	—
298	C₄×D₄	—	86	4	no	—
299	C₄×D₄	—	172	2	no	—
300	#117	—	43	2	no	—
301	#117	C₂²×D₄₃	1	1	yes	characteristic
302	#117	C₂²×D₄₃	1	1	yes	characteristic
303	#117	C₂²×D₄₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	172	2	no	—
305	#108	—	86	1	no	—
306	#108	—	86	1	no	—
307	#107	—	86	1	no	—
308	#106	—	86	1	no	—
309	#104	—	86	4	no	—
310	#104	—	172	2	no	—
311	#102	—	86	4	no	—
312	#102	—	172	2	no	—
313	#100	—	172	2	no	—
314	#99	—	172	2	no	—
315	#97	—	2	1	no	—
316	#97	C₄×D₄₃	1	2	yes	complemented
317	#97	D₁₇₂	1	2	yes	complemented
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	C₄×D₄₃	1	2	yes	complemented
320	C₄×C₈	D₁₇₂	1	2	yes	complemented
321	C₂⁴	—	86	2	no	—
322	#41	—	86	2	no	—
323	#41	—	86	2	no	—
324	#41	—	86	2	no	—
325	#41	—	86	2	no	—
326	C₂×Q₈	—	43	2	no	—
327	C₂×D₄	—	43	4	no	—
328	C₂×D₄	—	43	2	no	—
329	C₂×D₄	—	86	2	no	—
330	C₂×D₄	—	86	2	no	—
331	C₂×D₄	—	86	2	no	—
332	C₂×D₄	—	86	2	no	—
333	C₂×D₄	—	86	2	no	—
334	C₂×D₄	—	86	2	no	—
335	C₂×D₄	—	172	4	no	—
336	C₂²×C₄	—	86	2	no	—
337	C₂²×C₄	—	172	4	no	—
338	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
339	Q₁₆	—	86	1	no	—
340	Q₁₆	—	86	1	no	—
341	SD₁₆	—	86	2	no	—
342	SD₁₆	—	86	2	no	—
343	SD₁₆	—	172	4	no	—
344	D₈	—	86	2	no	—
345	D₈	—	86	2	no	—
346	D₈	—	86	2	no	—
347	D₈	—	86	2	no	—
348	D₈	—	86	1	no	—
349	D₈	—	86	1	no	—
350	D₈	—	172	4	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	86	2	no	—
358	M₁₆	—	86	2	no	—
359	M₁₆	—	172	4	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	86	2	no	—
362	C₂×C₈	—	172	4	no	—
363	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
364	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
365	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
366	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
367	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
368	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
369	C₂×C₈	#10621898	1	1	yes	characteristic
370	C₂×C₈	#10621898	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	86	2	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	86	2	no	—
379	C₂²⋊C₄	—	172	4	no	—
380	C₂²⋊C₄	—	172	4	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	86	2	no	—
383	C₄²	C₂×C₄×D₄₃	1	2	yes	—
384	C₄²	C₂×D₁₇₂	1	2	yes	—
385	C₂³	—	86	4	no	—
386	C₂³	—	86	2	no	—
387	C₂³	—	172	2	no	—
388	C₂³	—	172	2	no	—
389	C₂³	—	688	2	no	—
390	C₂³	#13063371	1	1	yes	characteristic
391	Q₈	—	86	2	no	—
392	Q₈	—	86	2	no	—
393	D₄	—	86	4	no	—
394	D₄	—	86	2	no	—
395	D₄	—	86	2	no	—
396	D₄	—	86	4	no	—
397	D₄	—	172	2	no	—
398	D₄	—	172	2	no	—
399	D₄	—	172	2	no	—
400	D₄	—	172	2	no	—
401	D₄	—	688	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	86	2	no	—
406	C₂×C₄	—	172	2	no	—
407	C₂×C₄	—	172	2	no	—
408	C₂×C₄	—	172	2	no	—
409	C₂×C₄	—	688	4	no	—
410	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
412	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
413	C₂×C₄	#13063371	1	1	yes	characteristic
414	C₂×C₄	#13063371	1	1	yes	characteristic
415	C₂×C₄	#13063371	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	172	2	no	—
420	C₈	C₄×D₁₇₂	1	1	yes	characteristic
421	C₈	C₄×D₁₇₂	1	1	yes	characteristic
422	C₈	C₄×D₁₇₂	1	1	yes	characteristic
423	C₈	C₄×D₁₇₂	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	344	2	no	—
426	C₂²	—	344	4	no	—
427	C₂²	—	344	4	no	—
428	C₂²	—	172	2	no	—
429	C₂²	—	172	4	no	—
430	C₂²	—	688	2	no	—
431	C₂²	#14583373	1	1	yes	characteristic
432	C₂²	#14583468	1	1	yes	characteristic
433	C₂²	#14583504	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	1	no	—
437	C₄	—	344	2	no	—
438	C₄	—	172	2	no	—
439	C₄	C₂×C₄×D₁₇₂	1	1	yes	characteristic
440	C₄	#14583373	1	1	yes	characteristic
441	C₄	#14583468	1	1	yes	characteristic
442	C₄	#14583504	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	344	4	no	—
447	C₂	—	344	2	no	—
448	C₂	#19137320	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19137320
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1747	C₂
socle	C₂×C₄₃	#2328
prime radical	#19145081	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1747	D₄₃
hypocenter	C₄₃	#22286
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1747

Complements

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

N	H ≅ G/N	type
2. #19143513	C₂	semidirect
3. #19143448	C₂	semidirect
4. #19135505	C₂	semidirect
5. #19135493	C₂	semidirect
6. #19135126	C₂	semidirect
7. #19135121	C₂	semidirect
8. #19135083	C₂	semidirect
9. #19135076	C₂	semidirect
10. #19134719	C₂	semidirect
11. C₄₃×#1747	C₂	semidirect
18. #14583288	C₄	semidirect
19. #14583283	C₄	semidirect
20. #14583276	C₄	semidirect
50. C₂×Dic₁₇₂	C₂×C₄	semidirect
51. C₂×#10621873	C₂×C₄	semidirect
52. C₂×#10621873	C₂×C₄	semidirect
59. C₂×D₃₄₄	C₂×C₄	semidirect
60. C₂×D₃₄₄	C₂×C₄	semidirect
65. #13063322	C₂×C₄	semidirect
66. #13063313	C₂×C₄	semidirect
91. #97×C₄₃	C₂×C₄	semidirect
92. #97×C₄₃	D₄	semidirect
94. C₄×C₈×C₄₃	C₂×C₄	semidirect
95. C₄×C₈×C₄₃	D₄	semidirect
229. #1747	D₄₃	semidirect
266. C₄₃	#22286	semidirect
316. #97	C₄×D₄₃	semidirect
317. #97	D₁₇₂	semidirect
319. C₄×C₈	C₄×D₄₃	semidirect
320. C₄×C₈	D₁₇₂	semidirect

Maximal subgroups

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

subgroup	index
#19145081	2
#19143513	2
#19143448	2
#19135505	2
#19135493	2
#19135126	2
#19135121	2
#19135083	2
#19135076	2
#19134719	2
C₄₃×#1747	2
#22286	43