Subgroups — #25972912

Order 11008.

2600 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149378	C₂	1	4	yes	maximal, complemented
2	#19146399	C₂	1	4	yes	maximal, complemented
3	#19146388	C₂	1	4	yes	maximal, complemented
4	#19146370	C₂	1	8	yes	maximal, complemented
5	#19144328	C₂	1	4	yes	maximal, complemented
6	#19143943	C₂	1	2	yes	maximal, complemented
7	C₂×#14583081	C₂	1	2	yes	maximal, complemented
8	#19143506	C₂	1	2	yes	maximal, complemented
9	C₄₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583735	C₂²	1	2	yes	complemented
11	C₂×#13063373	C₂²	1	2	yes	—
12	#14583715	—	2	8	no	—
13	#14583712	C₂²	1	16	yes	complemented
14	#14583708	—	2	8	no	—
15	#14583705	C₂²	1	16	yes	complemented
16	#14583699	C₂²	1	2	yes	—
17	#14583698	—	2	8	no	—
18	#14583697	C₂²	1	4	yes	—
19	C₂×#13063356	C₂²	1	4	yes	complemented
20	#137×D₄₃	—	2	8	no	—
21	#14583665	C₂²	1	4	yes	complemented
22	#14583171	C₂²	1	16	yes	complemented
23	#14583159	C₂²	1	16	yes	complemented
24	#14583081	C₂²	1	8	yes	complemented
25	#14583081	C₂²	1	8	yes	complemented
26	#14583081	C₂²	1	4	yes	complemented
27	#14583076	C₂²	1	4	yes	complemented
28	#14583071	C₂²	1	4	yes	complemented
29	#14583066	C₂²	1	4	yes	complemented
30	#14583022	C₂²	1	8	yes	complemented
31	#14583017	C₂²	1	8	yes	complemented
32	#14582948	C₂²	1	2	yes	complemented
33	C₂×#13063253	C₂²	1	4	yes	complemented
34	#14582883	C₂²	1	2	yes	complemented
35	C₂×#13063244	C₂²	1	2	yes	complemented
36	C₂×#137×C₄₃	C₂²	1	4	yes	complemented
37	C₄₃×#532	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
39	C₄₃×#497	C₂²	1	4	yes	complemented
40	C₄₃×#494	C₂²	1	2	yes	complemented
41	C₄₃×#492	C₂²	1	2	yes	complemented
42	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
43	#13063373	—	2	8	no	—
44	#13063373	—	4	2	no	—
45	#13063373	C₂³	1	4	yes	—
46	#13063373	C₂³	1	8	yes	—
47	#13063372	—	2	4	no	—
48	#13063371	—	2	4	no	—
49	#13063370	—	4	2	no	—
50	#13063370	C₂³	1	4	yes	—
51	C₂×#10621902	—	2	4	no	—
52	C₂×#10621898	—	4	2	no	—
53	C₂×#10621898	—	4	2	no	—
54	C₂×#10621898	C₂³	1	4	yes	—
55	#41×D₄₃	—	2	8	no	—
56	C₂×Q₈×D₄₃	—	2	4	no	—
57	#13063358	D₄	1	8	yes	complemented
58	#13063357	—	2	16	no	—
59	#13063357	—	2	16	no	—
60	#13063356	—	2	8	no	—
61	#13063356	C₂³	1	8	yes	—
62	#13063356	C₂³	1	16	yes	—
63	#13063355	—	2	4	no	—
64	#13063354	—	2	16	no	—
65	#13063353	D₄	1	8	yes	complemented
66	#13063352	—	2	16	no	—
67	#13063351	C₂³	1	8	yes	—
68	#13063350	—	2	4	no	—
69	#13063348	—	2	16	no	—
70	#13063347	C₂³	1	8	yes	—
71	#13063346	—	2	16	no	—
72	#13063345	—	2	8	no	—
73	C₂×#10621885	—	2	4	no	—
74	Q₁₆×D₄₃	—	2	16	no	—
75	C₂×#10621884	—	2	4	no	—
76	SD₁₆×D₄₃	—	2	16	no	—
77	#13063333	—	2	8	no	—
78	#13063331	C₂³	1	16	yes	—
79	C₂×#10621877	C₂³	1	4	yes	—
80	M₁₆×D₄₃	—	2	8	no	—
81	#13063261	C₂³	1	8	yes	—
82	#13063253	C₂³	1	8	yes	—
83	#13063253	C₂³	1	8	yes	—
84	#13063244	C₂³	1	4	yes	—
85	#13063244	C₂³	1	8	yes	—
86	#13063242	C₂³	1	4	yes	—
87	C₂×#41×C₄₃	C₂³	1	2	yes	—
88	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
89	#137×C₄₃	—	2	8	no	—
90	#137×C₄₃	—	2	8	no	—
91	C₂×Q₁₆×C₄₃	C₂³	1	8	yes	—
92	C₂×SD₁₆×C₄₃	C₂³	1	8	yes	—
93	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
94	C₄⋊Q₈×C₄₃	—	4	1	no	—
95	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
96	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
97	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
98	#127×C₄₃	C₂³	1	1	yes	characteristic
99	#124×C₄₃	C₂³	1	2	yes	—
100	#121×C₄₃	—	4	1	no	—
101	C₄×D₄×C₄₃	—	4	1	no	—
102	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	#97×C₄₃	C₂³	1	2	yes	—
105	C₄×C₈×C₄₃	C₂³	1	2	yes	—
106	#41×C₄₃	—	2	4	no	—
107	#41×C₄₃	—	2	4	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	—	2	4	no	—
110	C₂×Q₈×C₄₃	—	2	4	no	—
111	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
112	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
113	C₂×D₄×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	—	4	1	no	—
115	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
120	C₂×C₂²⋊D₄₃	—	2	4	no	—
121	C₂×C₂²⋊D₄₃	—	4	4	no	—
122	#10621902	—	2	16	no	—
123	#10621902	—	2	8	no	—
124	#10621902	—	4	8	no	—
125	Q₈×D₄₃	—	2	16	no	—
126	Q₈×D₄₃	—	2	8	no	—
127	Q₈×D₄₃	—	4	8	no	—
128	#10621900	—	2	8	no	—
129	#10621900	—	4	8	no	—
130	D₄×D₄₃	—	2	8	no	—
131	D₄×D₄₃	—	4	8	no	—
132	#10621898	—	2	4	no	—
133	#10621898	—	2	4	no	—
134	#10621898	—	4	4	no	—
135	#10621898	—	4	4	no	—
136	#10621898	—	4	4	no	—
137	#10621898	—	4	8	no	—
138	#10621898	—	4	8	no	—
139	#10621898	C₂×D₄	1	8	yes	—
140	#10621898	C₂⁴	1	8	yes	—
141	C₂×D₁₇₂	—	4	2	no	—
142	C₂×D₁₇₂	—	4	2	no	—
143	C₂×D₁₇₂	C₂×D₄	1	4	yes	—
144	C₂×C₄×D₄₃	—	2	4	no	—
145	C₂×C₄×D₄₃	—	4	4	no	—
146	C₂×C₄×D₄₃	—	4	4	no	—
147	C₂×Dic₈₆	—	4	2	no	—
148	C₂×Dic₈₆	—	4	2	no	—
149	C₂×Dic₈₆	C₂×D₄	1	4	yes	—
150	Q₁₆×C₄₃	—	2	16	no	—
151	SD₁₆×C₄₃	—	2	16	no	—
152	M₁₆×C₄₃	C₂×D₄	1	8	yes	—
153	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
154	C₄⋊C₄×C₄₃	—	4	2	no	—
155	C₄⋊C₄×C₄₃	—	4	2	no	—
156	C₄⋊C₄×C₄₃	—	4	1	no	—
157	C₂²⋊C₄×C₄₃	—	4	2	no	—
158	C₄²×C₄₃	—	2	1	no	—
159	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
160	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
161	#10621885	—	2	8	no	—
162	#10621885	—	2	16	no	—
163	#10621884	—	2	16	no	—
164	#10621884	—	2	8	no	—
165	#10621883	—	2	8	no	—
166	#10621882	—	2	8	no	—
167	#10621877	—	2	4	no	—
168	#10621877	C₂⁴	1	8	yes	—
169	C₂×C₄₃⋊C₈	—	2	4	no	—
170	Dic₁₇₂	C₂×D₄	1	8	yes	—
171	D₃₄₄	C₂×D₄	1	8	yes	—
172	#10621873	C₂×D₄	1	16	yes	—
173	#10621872	—	2	16	no	—
174	C₈×D₄₃	—	2	16	no	—
175	C₂³×C₄₃	—	2	2	no	—
176	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²×D₄₃	—	2	4	no	—
178	C₂²×D₄₃	—	4	4	no	—
179	Q₈×C₄₃	—	2	8	no	—
180	Q₈×C₄₃	—	2	4	no	—
181	Q₈×C₄₃	—	4	4	no	—
182	D₄×C₄₃	—	2	4	no	—
183	D₄×C₄₃	—	4	4	no	—
184	D₄×C₄₃	—	8	2	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	4	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	4	2	no	—
192	C₂×C₄×C₄₃	—	4	2	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
197	C₂²⋊D₄₃	—	2	8	no	—
198	C₂²⋊D₄₃	—	2	8	no	—
199	C₂²⋊D₄₃	—	4	8	no	—
200	C₂×Dic₄₃	—	2	4	no	—
201	C₂×Dic₄₃	—	4	4	no	—
202	D₁₇₂	—	2	4	no	—
203	D₁₇₂	—	4	4	no	—
204	D₁₇₂	—	4	8	no	—
205	D₁₇₂	C₂²×D₄	1	8	yes	—
206	C₄×D₄₃	—	2	8	no	—
207	C₄×D₄₃	—	2	8	no	—
208	C₄×D₄₃	—	4	8	no	—
209	C₄×D₄₃	—	4	16	no	—
210	Dic₈₆	—	2	4	no	—
211	Dic₈₆	—	4	4	no	—
212	Dic₈₆	—	4	8	no	—
213	Dic₈₆	C₂²×D₄	1	8	yes	—
214	C₈×C₄₃	C₂²×D₄	1	8	yes	—
215	C₄₃⋊C₈	—	2	8	no	—
216	#61111	—	43	1	no	maximal, Sylow
217	C₂²×C₄₃	—	4	1	no	—
218	C₂²×C₄₃	—	4	2	no	—
219	C₂²×C₄₃	—	8	2	no	—
220	C₂²×C₄₃	D₄²	1	2	yes	—
221	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×D₄₃	—	2	8	no	—
223	C₂×D₄₃	—	8	4	no	—
224	C₂×D₄₃	—	16	4	no	—
225	C₄×C₄₃	—	2	2	no	—
226	C₄×C₄₃	—	4	1	no	—
227	C₄×C₄₃	—	4	2	no	—
228	C₄×C₄₃	—	4	4	no	—
229	C₄×C₄₃	D₄²	1	2	yes	—
230	C₄×C₄₃	C₂³×D₄	1	2	yes	—
231	Dic₄₃	—	2	8	no	—
232	#3586	—	43	4	no	—
233	#3293	—	43	4	no	—
234	#3291	—	43	4	no	—
235	#3289	—	43	8	no	—
236	#3152	D₄₃	1	1	yes	characteristic, complemented
237	#3069	—	43	4	no	—
238	#3018	—	43	2	no	—
239	C₂×#456	—	43	2	no	—
240	#2956	—	43	2	no	—
241	C₂×C₄₃	—	2	1	no	—
242	C₂×C₄₃	—	2	2	no	—
243	C₂×C₄₃	—	8	2	no	—
244	C₂×C₄₃	C₂×D₄²	1	1	yes	characteristic
245	D₄₃	—	4	8	no	—
246	#585	—	43	2	no	—
247	C₂×2₋¹⁺⁴	—	43	2	no	—
248	#578	—	43	16	no	—
249	#578	—	86	8	no	—
250	#577	—	43	16	no	—
251	#577	—	86	8	no	—
252	#575	—	43	4	no	—
253	#575	—	43	2	no	—
254	#575	—	86	8	no	—
255	C₂×#137	—	43	4	no	—
256	C₂×#137	—	86	8	no	—
257	C₂×#137	C₂×D₄₃	1	4	yes	complemented
258	#568	—	43	4	no	—
259	#532	C₂×D₄₃	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
261	#497	C₂×D₄₃	1	4	yes	complemented
262	#494	C₂×D₄₃	1	2	yes	complemented
263	#492	C₂×D₄₃	1	2	yes	complemented
264	#473	—	43	16	no	—
265	#471	—	43	16	no	—
266	#456	—	43	8	no	—
267	#456	—	43	8	no	—
268	#456	—	43	4	no	—
269	#455	—	43	4	no	—
270	#454	—	43	4	no	—
271	#453	—	43	4	no	—
272	#444	—	43	8	no	—
273	#443	—	43	8	no	—
274	#430	—	43	2	no	—
275	C₂×#104	—	43	4	no	—
276	#413	—	43	2	no	—
277	C₂×#101	—	43	2	no	—
278	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
279	C₄₃	#61111	1	1	yes	characteristic, complemented, Sylow
280	2₋¹⁺⁴	—	43	8	no	—
281	2₋¹⁺⁴	—	43	4	no	—
282	2₋¹⁺⁴	—	86	8	no	—
283	2₋¹⁺⁴	—	86	4	no	—
284	2₋¹⁺⁴	—	172	2	no	—
285	H(5,𝔽₂)	—	43	4	no	—
286	H(5,𝔽₂)	—	86	4	no	—
287	H(5,𝔽₂)	—	172	2	no	—
288	C₂×#41	—	43	4	no	—
289	C₂×#41	—	86	4	no	—
290	C₂×#41	—	86	8	no	—
291	C₂×#41	—	172	2	no	—
292	C₂×#41	—	172	2	no	—
293	C₂×#41	C₂²×D₄₃	1	2	yes	—
294	C₂²×Q₈	—	86	4	no	—
295	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
296	#137	—	2	8	no	—
297	#137	—	2	8	no	—
298	#137	—	43	16	no	—
299	#137	—	43	8	no	—
300	#137	—	43	8	no	—
301	#137	—	86	16	no	—
302	#137	—	86	16	no	—
303	#137	—	86	16	no	—
304	#137	—	86	8	no	—
305	#137	—	86	4	no	—
306	AGL(1,ℤ/8)	—	43	8	no	—
307	AGL(1,ℤ/8)	—	43	8	no	—
308	AGL(1,ℤ/8)	—	86	16	no	—
309	AGL(1,ℤ/8)	—	86	4	no	—
310	#135	—	43	8	no	—
311	#135	—	86	16	no	—
312	#135	—	86	16	no	—
313	#135	—	86	8	no	—
314	C₂×Q₁₆	—	86	16	no	—
315	C₂×Q₁₆	—	86	4	no	—
316	C₂×Q₁₆	C₂²×D₄₃	1	8	yes	—
317	C₂×SD₁₆	—	86	16	no	—
318	C₂×SD₁₆	—	86	4	no	—
319	C₂×SD₁₆	C₂²×D₄₃	1	8	yes	—
320	#131	—	43	16	no	—
321	#131	—	86	8	no	—
322	C₂×M₁₆	—	43	4	no	—
323	C₂×M₁₆	—	86	8	no	—
324	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
325	C₄⋊Q₈	—	4	1	no	—
326	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
327	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
328	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
329	#127	C₂²×D₄₃	1	1	yes	characteristic
330	#124	C₂²×D₄₃	1	2	yes	—
331	#121	—	4	1	no	—
332	C₄×D₄	—	4	1	no	—
333	C₂×C₄⋊C₄	—	4	1	no	—
334	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
335	#108	—	43	8	no	—
336	#104	—	43	8	no	—
337	#104	—	43	8	no	—
338	#101	—	43	8	no	—
339	#101	—	43	4	no	—
340	#100	—	43	4	no	—
341	#97	C₂²×D₄₃	1	2	yes	—
342	C₄×C₈	C₂²×D₄₃	1	2	yes	—
343	#41	—	2	4	no	—
344	#41	—	2	4	no	—
345	#41	—	43	8	no	—
346	#41	—	43	8	no	—
347	#41	—	86	4	no	—
348	#41	—	86	4	no	—
349	#41	—	86	8	no	—
350	#41	—	86	16	no	—
351	#41	—	86	8	no	—
352	#41	—	172	4	no	—
353	#41	—	172	8	no	—
354	#41	—	172	4	no	—
355	#41	—	172	8	no	—
356	#41	—	172	4	no	—
357	#41	—	172	8	no	—
358	#41	—	172	8	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	43	4	no	—
363	C₂×Q₈	—	86	16	no	—
364	C₂×Q₈	—	86	8	no	—
365	C₂×Q₈	—	172	2	no	—
366	C₂×Q₈	—	172	2	no	—
367	C₂×Q₈	—	172	8	no	—
368	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
369	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂×D₄	—	43	4	no	—
373	C₂×D₄	—	86	8	no	—
374	C₂×D₄	—	86	4	no	—
375	C₂×D₄	—	172	2	no	—
376	C₂×D₄	—	172	2	no	—
377	C₂×D₄	—	172	8	no	—
378	C₂×D₄	—	172	4	no	—
379	C₂×D₄	C₂³×D₄₃	1	2	yes	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	86	4	no	—
384	C₂²×C₄	—	172	4	no	—
385	C₂²×C₄	—	172	4	no	—
386	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
387	Q₁₆	—	2	16	no	—
388	Q₁₆	—	43	8	no	—
389	Q₁₆	—	86	16	no	—
390	Q₁₆	—	86	8	no	—
391	SD₁₆	—	2	16	no	—
392	SD₁₆	—	43	16	no	—
393	SD₁₆	—	86	8	no	—
394	SD₁₆	—	86	16	no	—
395	SD₁₆	—	86	8	no	—
396	D₈	—	43	8	no	—
397	D₈	—	86	8	no	—
398	M₁₆	—	43	8	no	—
399	M₁₆	—	86	4	no	—
400	M₁₆	—	86	16	no	—
401	M₁₆	D₄×D₄₃	1	8	yes	—
402	C₂×C₈	—	86	4	no	—
403	C₂×C₈	—	86	16	no	—
404	C₂×C₈	C₂³×D₄₃	1	4	yes	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	C₂³×D₄₃	1	1	yes	characteristic
411	C₄²	C₂³×D₄₃	1	1	yes	characteristic
412	C₂³	—	2	2	no	—
413	C₂³	—	86	4	no	—
414	C₂³	—	172	4	no	—
415	C₂³	#13063370	1	1	yes	characteristic
416	Q₈	—	2	8	no	—
417	Q₈	—	2	4	no	—
418	Q₈	—	4	4	no	—
419	Q₈	—	43	8	no	—
420	Q₈	—	86	4	no	—
421	Q₈	—	172	8	no	—
422	Q₈	—	172	4	no	—
423	D₄	—	2	4	no	—
424	D₄	—	4	4	no	—
425	D₄	—	8	2	no	—
426	D₄	—	43	8	no	—
427	D₄	—	86	8	no	—
428	D₄	—	86	8	no	—
429	D₄	—	86	4	no	—
430	D₄	—	172	4	no	—
431	D₄	—	172	8	no	—
432	D₄	—	172	8	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	86	4	no	—
443	C₂×C₄	—	86	8	no	—
444	C₂×C₄	—	86	8	no	—
445	C₂×C₄	—	172	8	no	—
446	C₂×C₄	—	172	16	no	—
447	C₂×C₄	—	172	4	no	—
448	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
449	C₂×C₄	#13063370	1	1	yes	characteristic
450	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
451	C₈	—	86	8	no	—
452	C₈	C₂×D₄×D₄₃	1	8	yes	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	86	8	no	—
457	C₂²	—	344	4	no	—
458	C₂²	—	688	4	no	—
459	C₂²	#14583534	1	2	yes	—
460	C₂²	C₂×#13063370	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	4	no	—
465	C₄	—	86	8	no	—
466	C₄	#14583534	1	2	yes	—
467	C₄	C₂²×D₄×D₄₃	1	2	yes	—
468	C₂	—	2	1	no	—
469	C₂	—	2	2	no	—
470	C₂	—	8	2	no	—
471	C₂	—	172	8	no	—
472	C₂	C₂×#14583534	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#14583534
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3152	C₂
socle	C₂×C₄₃	C₂×D₄²
hypercenter	#3152	D₄₃
hypocenter	C₄₃	#61111
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3152

Complements

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

N	H ≅ G/N	type
1. #19149378	C₂	semidirect
2. #19146399	C₂	semidirect
3. #19146388	C₂	semidirect
4. #19146370	C₂	semidirect
5. #19144328	C₂	semidirect
6. #19143943	C₂	semidirect
7. C₂×#14583081	C₂	semidirect
8. #19143506	C₂	semidirect
9. C₄₃×#3152	C₂	semidirect
10. #14583735	C₂²	semidirect
13. #14583712	C₂²	semidirect
15. #14583705	C₂²	semidirect
19. C₂×#13063356	C₂²	semidirect
21. #14583665	C₂²	semidirect
22. #14583171	C₂²	semidirect
23. #14583159	C₂²	semidirect
24. #14583081	C₂²	semidirect
25. #14583081	C₂²	semidirect
26. #14583081	C₂²	semidirect
27. #14583076	C₂²	semidirect
28. #14583071	C₂²	semidirect
29. #14583066	C₂²	semidirect
30. #14583022	C₂²	semidirect
31. #14583017	C₂²	semidirect
32. #14582948	C₂²	semidirect
33. C₂×#13063253	C₂²	semidirect
34. #14582883	C₂²	semidirect
35. C₂×#13063244	C₂²	semidirect
36. C₂×#137×C₄₃	C₂²	semidirect
38. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
39. C₄₃×#497	C₂²	semidirect
40. C₄₃×#494	C₂²	semidirect
41. C₄₃×#492	C₂²	semidirect
42. C₄×M₁₆×C₄₃	C₂²	semidirect
57. #13063358	D₄	semidirect
65. #13063353	D₄	semidirect
236. #3152	D₄₃	semidirect
257. C₂×#137	C₂×D₄₃	semidirect
260. C₂×C₄⋊Q₈	C₂×D₄₃	semidirect
261. #497	C₂×D₄₃	semidirect
262. #494	C₂×D₄₃	semidirect
263. #492	C₂×D₄₃	semidirect
278. C₄×M₁₆	C₂×D₄₃	semidirect
279. C₄₃	#61111	semidirect

Maximal subgroups

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

subgroup	index
#19149378	2
#19146399	2
#19146388	2
#19146370	2
#19144328	2
#19143943	2
C₂×#14583081	2
#19143506	2
C₄₃×#3152	2
#61111	43