Subgroups — #25065079

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148481	C₂	1	1	yes	maximal, characteristic
2	#19143261	C₂	1	1	yes	maximal, characteristic
3	#19133303	C₂	1	2	yes	maximal, complemented
4	#19133293	C₂	1	2	yes	maximal, complemented
5	#19133283	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133266	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133259	C₂	1	2	yes	maximal, complemented
8	#19133253	C₂	1	2	yes	maximal, complemented
9	#19133250	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582644	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2988	C₂	1	1	yes	maximal, characteristic
12	#14583627	—	2	1	no	—
13	#14583627	C₄	1	2	yes	—
14	#14583619	—	2	1	no	—
15	#14583619	C₄	1	2	yes	—
16	#14583589	—	2	2	no	—
17	#14583589	C₄	1	4	yes	—
18	#14583511	—	2	2	no	—
19	#14583470	—	2	1	no	—
20	#14583456	C₂²	1	1	yes	characteristic
21	#14583456	C₂²	1	2	yes	—
22	#14583456	C₂²	1	2	yes	—
23	C₂×#13063325	C₂²	1	1	yes	characteristic
24	#14583376	—	2	1	no	—
25	#14582960	—	2	2	no	—
26	#14582956	C₂²	1	2	yes	—
27	#14582952	C₂²	1	2	yes	—
28	#14582923	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
30	#14582866	—	2	1	no	—
31	#14582855	—	2	1	no	—
32	#14582647	C₂²	1	1	yes	characteristic
33	#14582647	C₂²	1	1	yes	characteristic
34	#14582647	C₂²	1	2	yes	—
35	#14582646	C₂²	1	1	yes	characteristic
36	#14582646	C₂²	1	1	yes	characteristic
37	#14582646	C₂²	1	2	yes	—
38	#14582644	C₂²	1	2	yes	—
39	#14582644	C₂²	1	2	yes	—
40	#14582644	C₂²	1	2	yes	—
41	#14582644	C₂²	1	2	yes	—
42	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
43	C₈×Q₈×C₄₃	—	2	1	no	—
44	C₈×D₄×C₄₃	—	2	2	no	—
45	C₈×D₄×C₄₃	—	2	1	no	—
46	C₄₃×#431	C₂²	1	1	yes	characteristic
47	C₄₃×#431	C₂²	1	2	yes	—
48	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
49	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
50	C₂²×Dic₈₆	—	2	1	no	—
51	C₂×#10621877	—	2	1	no	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	#13063325	—	2	1	no	—
54	#13063325	—	2	1	no	—
55	#13063325	C₂×C₄	1	2	yes	—
56	#13063325	C₂³	1	1	yes	characteristic
57	#13063325	C₂³	1	2	yes	—
58	#13063325	C₂³	1	1	yes	characteristic
59	#13063323	—	2	2	no	—
60	#13063318	—	2	4	no	—
61	#13063318	—	2	4	no	—
62	#13063317	—	2	2	no	—
63	#13063317	—	2	1	no	—
64	#13063317	C₂×C₄	1	4	yes	—
65	#13063315	—	2	4	no	—
66	#13063315	—	2	4	no	—
67	#13063312	—	2	2	no	—
68	#13063306	—	2	4	no	—
69	#13063304	—	2	1	no	—
70	#13063304	—	2	2	no	—
71	#13063304	—	2	2	no	—
72	#13063304	—	2	2	no	—
73	#13063304	C₂×C₄	1	2	yes	—
74	#13063304	C₂×C₄	1	4	yes	—
75	C₄×Dic₈₆	—	2	2	no	—
76	C₄×Dic₈₆	—	2	1	no	—
77	C₄×Dic₈₆	—	2	2	no	—
78	C₄×Dic₈₆	—	2	2	no	—
79	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
80	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
81	#13063290	—	2	2	no	—
82	#13063290	—	2	2	no	—
83	#13063284	—	2	2	no	—
84	#13063284	—	2	1	no	—
85	#13063284	C₂×C₄	1	4	yes	—
86	#13063281	—	2	4	no	—
87	C₂×C₄⋊Dic₄₃	—	2	1	no	—
88	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
89	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
90	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
91	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
92	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
93	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
94	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
95	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
96	#13063236	—	2	2	no	—
97	C₄×C₄₃⋊C₈	—	2	2	no	—
98	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₄₃	—	2	1	no	—
100	C₂²×C₈×C₄₃	—	2	2	no	—
101	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
102	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
103	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
104	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₄₃	D₄	1	2	yes	—
106	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
107	#117×C₄₃	D₄	1	1	yes	characteristic
108	#117×C₄₃	D₄	1	2	yes	—
109	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
111	C₄⋊C₈×C₄₃	—	2	2	no	—
112	C₄⋊C₈×C₄₃	—	2	1	no	—
113	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
114	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
115	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
116	C₂²⋊C₈×C₄₃	—	2	1	no	—
117	C₂²⋊C₈×C₄₃	—	2	2	no	—
118	C₄×C₈×C₄₃	—	2	2	no	—
119	C₄×C₈×C₄₃	—	2	1	no	—
120	#41×C₄₃	—	2	2	no	—
121	#41×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
124	C₂×D₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
131	C₂²×Dic₄₃	—	2	2	no	—
132	C₂×Dic₈₆	—	2	2	no	—
133	C₂×Dic₈₆	—	2	1	no	—
134	C₂×Dic₈₆	—	2	2	no	—
135	C₂×Dic₈₆	—	4	2	no	—
136	C₂×Dic₈₆	—	4	2	no	—
137	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₄₃	—	2	1	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	1	no	—
141	C₂×C₈×C₄₃	—	8	1	no	—
142	C₂×C₈×C₄₃	—	8	2	no	—
143	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
144	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
145	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
147	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
148	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
149	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
150	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
151	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₄₃	C₂×D₄	1	2	yes	—
153	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₄₃	C₂×D₄	1	2	yes	—
155	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
157	C₂²⋊Dic₄₃	—	2	2	no	—
158	C₂²⋊Dic₄₃	—	2	4	no	—
159	C₂²⋊Dic₄₃	—	2	4	no	—
160	C₄⋊Dic₄₃	—	2	2	no	—
161	C₄⋊Dic₄₃	—	2	2	no	—
162	C₄⋊Dic₄₃	—	2	2	no	—
163	C₄⋊Dic₄₃	—	2	1	no	—
164	C₄⋊Dic₄₃	—	2	1	no	—
165	C₄⋊Dic₄₃	—	2	1	no	—
166	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
167	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
168	Dic₄₃⋊C₄	—	2	4	no	—
169	Dic₄₃⋊C₄	—	2	4	no	—
170	Dic₄₃⋊C₄	—	2	4	no	—
171	Dic₄₃⋊C₄	—	2	2	no	—
172	Dic₄₃⋊C₄	—	2	4	no	—
173	Dic₄₃⋊C₄	—	2	2	no	—
174	C₄×Dic₄₃	—	2	4	no	—
175	C₄×Dic₄₃	—	2	4	no	—
176	C₄×Dic₄₃	—	2	2	no	—
177	#10621877	—	4	2	no	—
178	C₂×C₄₃⋊C₈	—	2	1	no	—
179	C₂×C₄₃⋊C₈	—	2	2	no	—
180	C₂×C₄₃⋊C₈	—	2	1	no	—
181	C₂×C₄₃⋊C₈	—	4	2	no	—
182	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	Q₈×C₄₃	—	2	2	no	—
185	D₄×C₄₃	—	2	4	no	—
186	D₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	4	1	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
198	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	#135	1	2	yes	—
202	C₂×C₄×C₄₃	#135	1	2	yes	—
203	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×Dic₄₃	—	2	2	no	—
207	C₂×Dic₄₃	—	2	2	no	—
208	C₂×Dic₄₃	—	2	4	no	—
209	C₂×Dic₄₃	—	4	4	no	—
210	Dic₈₆	—	4	2	no	—
211	Dic₈₆	—	4	2	no	—
212	Dic₈₆	—	4	1	no	—
213	Dic₈₆	—	4	1	no	—
214	Dic₈₆	—	4	4	no	—
215	Dic₈₆	—	4	2	no	—
216	C₈×C₄₃	—	4	2	no	—
217	C₈×C₄₃	—	4	1	no	—
218	C₈×C₄₃	—	4	1	no	—
219	C₄₃⋊C₈	—	4	1	no	—
220	C₄₃⋊C₈	—	4	1	no	—
221	C₄₃⋊C₈	—	4	2	no	—
222	#17725	—	43	1	no	maximal, Sylow
223	C₂²×C₄₃	—	2	1	no	—
224	C₂²×C₄₃	—	2	1	no	—
225	C₂²×C₄₃	—	2	2	no	—
226	C₂²×C₄₃	—	2	2	no	—
227	C₂²×C₄₃	—	2	2	no	—
228	C₂²×C₄₃	#416	1	2	yes	—
229	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
230	C₄×C₄₃	—	2	1	no	—
231	C₄×C₄₃	—	2	2	no	—
232	C₄×C₄₃	—	2	1	no	—
233	C₄×C₄₃	—	2	2	no	—
234	C₄×C₄₃	—	2	2	no	—
235	C₄×C₄₃	—	2	1	no	—
236	C₄×C₄₃	#416	1	2	yes	—
237	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
238	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
239	C₄×C₄₃	#577	1	1	yes	characteristic
240	C₄×C₄₃	#578	1	1	yes	characteristic
241	Dic₄₃	—	4	2	no	—
242	Dic₄₃	—	4	4	no	—
243	Dic₄₃	—	4	2	no	—
244	#3509	—	43	1	no	—
245	#2988	D₄₃	1	1	yes	characteristic
246	#2925	—	43	1	no	—
247	#1554	—	43	2	no	—
248	#1552	—	43	2	no	—
249	#1550	—	43	1	no	—
250	#1546	—	43	1	no	—
251	#1544	—	43	2	no	—
252	#1542	—	43	1	no	—
253	#1542	—	43	2	no	—
254	C₂×#332	—	43	1	no	—
255	C₂×C₄₃	—	2	2	no	—
256	C₂×C₄₃	—	4	2	no	—
257	C₂×C₄₃	#2889	1	1	yes	characteristic
258	C₂×C₄₃	C₂×#416	1	1	yes	characteristic
259	C₂×C₄₃	#2898	1	1	yes	characteristic
260	#557	—	43	2	no	—
261	#557	—	86	1	no	—
262	#556	—	43	2	no	—
263	#556	—	86	1	no	—
264	#552	—	43	4	no	—
265	#552	—	86	2	no	—
266	#541	—	86	2	no	—
267	#536	—	86	1	no	—
268	#533	—	43	2	no	—
269	#533	—	43	1	no	—
270	#533	—	43	2	no	—
271	C₂×C₄⋊Q₈	—	43	1	no	—
272	#519	—	86	1	no	—
273	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
274	C₈×Q₈	—	2	1	no	—
275	C₈×D₄	—	2	2	no	—
276	C₈×D₄	—	2	1	no	—
277	#433	—	86	2	no	—
278	#432	—	43	2	no	—
279	#431	—	43	2	no	—
280	#431	C₂×D₄₃	1	1	yes	characteristic
281	#431	C₂×D₄₃	1	2	yes	—
282	#423	—	43	1	no	—
283	C₂×C₄⋊C₈	—	43	1	no	—
284	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
285	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
286	#408	—	86	1	no	—
287	#405	—	86	1	no	—
288	#333	—	43	1	no	—
289	#333	—	43	2	no	—
290	#333	—	43	1	no	—
291	#332	—	43	2	no	—
292	#332	—	43	2	no	—
293	#332	—	43	1	no	—
294	#332	—	43	2	no	—
295	#332	—	43	1	no	—
296	#332	—	43	2	no	—
297	#332	—	43	2	no	—
298	C₄₃	#17725	1	1	yes	characteristic, complemented, Sylow
299	C₂×#41	D₁₇₂	1	1	yes	characteristic
300	C₂²×Q₈	—	86	1	no	—
301	C₂×M₁₆	—	86	1	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	—	86	1	no	—
305	C₄⋊Q₈	—	43	2	no	—
306	C₄⋊Q₈	—	43	2	no	—
307	C₄⋊Q₈	—	43	1	no	—
308	C₄⋊Q₈	—	43	1	no	—
309	C₄⋊Q₈	—	86	2	no	—
310	C₄⋊Q₈	—	86	1	no	—
311	C₄⋊Q₈	—	86	1	no	—
312	#126	—	86	4	no	—
313	#126	—	86	4	no	—
314	#125	—	43	4	no	—
315	#125	—	86	4	no	—
316	#125	—	86	4	no	—
317	#125	—	86	1	no	—
318	#125	—	86	2	no	—
319	#124	—	86	2	no	—
320	#123	—	86	4	no	—
321	C₂²⋊Q₈	—	43	2	no	—
322	C₂²⋊Q₈	—	43	4	no	—
323	C₂²⋊Q₈	—	86	2	no	—
324	C₂²⋊Q₈	—	86	2	no	—
325	C₂²⋊Q₈	—	86	1	no	—
326	C₂²⋊Q₈	—	86	2	no	—
327	C₄×Q₈	—	43	4	no	—
328	C₄×Q₈	—	43	2	no	—
329	C₄×Q₈	—	86	2	no	—
330	C₄×Q₈	—	86	2	no	—
331	C₄×Q₈	—	86	2	no	—
332	C₄×Q₈	—	86	2	no	—
333	C₄×Q₈	—	86	2	no	—
334	C₄×Q₈	—	86	1	no	—
335	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
336	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
337	C₄×D₄	C₄×D₄₃	1	2	yes	—
338	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
339	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
340	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
341	#117	—	43	4	no	—
342	#117	—	86	1	no	—
343	#117	—	86	2	no	—
344	#117	—	86	4	no	—
345	#117	D₁₇₂	1	1	yes	characteristic
346	#117	D₁₇₂	1	2	yes	—
347	C₂×C₄⋊C₄	—	43	2	no	—
348	C₂×C₄⋊C₄	—	86	1	no	—
349	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
350	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
351	C₄⋊C₈	—	2	2	no	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	—	43	1	no	—
354	C₄⋊C₈	—	43	1	no	—
355	C₄⋊C₈	—	43	2	no	—
356	C₄⋊C₈	—	86	1	no	—
357	C₄⋊C₈	—	86	1	no	—
358	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
359	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
360	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
361	C₂²⋊C₈	—	2	1	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	C₂²⋊C₈	—	86	2	no	—
364	C₂²⋊C₈	—	86	2	no	—
365	#97	—	86	2	no	—
366	C₄×C₈	—	2	2	no	—
367	C₄×C₈	—	2	1	no	—
368	C₄×C₈	—	86	2	no	—
369	#41	—	2	2	no	—
370	#41	—	2	2	no	—
371	C₂×Q₈	—	43	2	no	—
372	C₂×Q₈	—	86	2	no	—
373	C₂×Q₈	—	86	1	no	—
374	C₂×Q₈	—	86	2	no	—
375	C₂×Q₈	—	172	2	no	—
376	C₂×Q₈	—	172	2	no	—
377	C₂×Q₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
378	C₂×D₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
379	C₂×D₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
380	C₂²×C₄	—	86	2	no	—
381	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
383	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
384	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
387	M₁₆	—	172	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	8	1	no	—
392	C₂×C₈	—	8	2	no	—
393	C₂×C₈	—	86	1	no	—
394	C₂×C₈	—	86	2	no	—
395	C₂×C₈	—	86	1	no	—
396	C₂×C₈	—	172	2	no	—
397	C₄⋊C₄	—	43	4	no	—
398	C₄⋊C₄	—	43	2	no	—
399	C₄⋊C₄	—	86	2	no	—
400	C₄⋊C₄	—	86	2	no	—
401	C₄⋊C₄	—	86	4	no	—
402	C₄⋊C₄	—	86	4	no	—
403	C₄⋊C₄	—	86	4	no	—
404	C₄⋊C₄	—	86	2	no	—
405	C₄⋊C₄	—	86	2	no	—
406	C₄⋊C₄	—	86	4	no	—
407	C₄⋊C₄	—	86	2	no	—
408	C₄⋊C₄	—	86	1	no	—
409	C₄⋊C₄	—	86	1	no	—
410	C₄⋊C₄	—	86	1	no	—
411	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
412	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
413	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
414	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
415	C₂²⋊C₄	—	86	4	no	—
416	C₂²⋊C₄	—	86	2	no	—
417	C₂²⋊C₄	—	86	4	no	—
418	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
419	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
420	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
421	C₄²	—	86	4	no	—
422	C₄²	—	86	4	no	—
423	C₄²	—	86	2	no	—
424	C₄²	C₂×C₄×D₄₃	1	2	yes	—
425	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
426	C₄²	C₂×D₁₇₂	1	2	yes	—
427	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
428	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
429	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
430	C₄²	C₂³×D₄₃	1	1	yes	characteristic
431	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
432	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
433	Q₈	—	2	2	no	—
434	Q₈	—	172	2	no	—
435	Q₈	—	172	4	no	—
436	Q₈	—	172	2	no	—
437	Q₈	—	172	2	no	—
438	Q₈	—	172	1	no	—
439	Q₈	—	172	1	no	—
440	D₄	—	2	4	no	—
441	D₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	86	2	no	—
451	C₂×C₄	—	86	2	no	—
452	C₂×C₄	—	86	4	no	—
453	C₂×C₄	—	172	4	no	—
454	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
455	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
456	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
457	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
458	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
459	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
460	C₂×C₄	#13063347	1	2	yes	—
461	C₂×C₄	#13063347	1	2	yes	—
462	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
463	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
465	C₈	—	4	2	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	1	no	—
468	C₈	—	172	1	no	—
469	C₈	—	172	1	no	—
470	C₈	—	172	2	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	#14582896	1	2	yes	—
477	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	1	no	—
484	C₄	—	172	2	no	—
485	C₄	—	172	4	no	—
486	C₄	—	172	2	no	—
487	C₄	#14582896	1	2	yes	—
488	C₄	C₂×#13063347	1	1	yes	characteristic
489	C₄	C₂×#13063347	1	1	yes	characteristic
490	C₄	#14583710	1	1	yes	characteristic
491	C₄	#14583714	1	1	yes	characteristic
492	C₂	—	2	2	no	—
493	C₂	—	4	2	no	—
494	C₂	#19143077	1	1	yes	characteristic
495	C₂	C₂×#14582896	1	1	yes	characteristic
496	C₂	#19143125	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2988	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₂×#41×C₄₃	D₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2988	D₄₃
hypocenter	C₄₃	#17725
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #2988

Complements

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

N	H ≅ G/N	type
3. #19133303	C₂	semidirect
4. #19133293	C₂	semidirect
5. #19133283	C₂	semidirect
6. #19133266	C₂	semidirect
7. #19133259	C₂	semidirect
8. #19133253	C₂	semidirect
9. #19133250	C₂	semidirect
10. C₂×#14582644	C₂	semidirect
298. C₄₃	#17725	semidirect

Maximal subgroups

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

subgroup	index
#19148481	2
#19143261	2
#19133303	2
#19133293	2
#19133283	2
#19133266	2
#19133259	2
#19133253	2
#19133250	2
C₂×#14582644	2
C₄₃×#2988	2
#17725	43