Subgroups — #25966498

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147985	C₂	1	2	yes	maximal, complemented
2	#19145278	C₂	1	8	yes	maximal, complemented
3	#19145263	C₂	1	8	yes	maximal, complemented
4	#19145119	C₂	1	1	yes	maximal, characteristic, complemented
5	#19145041	C₂	1	1	yes	maximal, characteristic, complemented
6	#19144918	C₂	1	2	yes	maximal, complemented
7	#19144204	C₂	1	2	yes	maximal, complemented
8	#19144176	C₂	1	2	yes	maximal, complemented
9	#19143397	C₂	1	2	yes	maximal, complemented
10	C₄×#13063347	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	2	yes	—
13	C₂×#13063347	C₂²	1	2	yes	—
14	#14583520	C₂²	1	8	yes	—
15	#14583511	C₂²	1	4	yes	—
16	#14583504	C₂²	1	4	yes	—
17	#14583496	—	2	4	no	—
18	#14583487	—	2	4	no	—
19	#14583456	C₂²	1	2	yes	—
20	#14583449	C₂²	1	2	yes	—
21	#14583427	—	2	8	no	—
22	#14583410	C₂²	1	4	yes	—
23	C₄×#10621898	C₂²	1	4	yes	—
24	#14583308	C₂²	1	8	yes	complemented
25	#14583293	C₂²	1	4	yes	complemented
26	#14583288	C₂²	1	4	yes	complemented
27	#14583254	C₂²	1	8	yes	complemented
28	#14583250	C₂²	1	4	yes	complemented
29	#14583246	C₂²	1	4	yes	complemented
30	#14583157	C₂²	1	4	yes	—
31	#14583152	C₂²	1	4	yes	—
32	#14583145	C₂²	1	8	yes	—
33	#14583140	C₂²	1	4	yes	—
34	#14583135	C₂²	1	4	yes	—
35	#14583128	C₂²	1	8	yes	—
36	#14583012	C₂²	1	4	yes	complemented
37	#14583007	C₂²	1	4	yes	complemented
38	#14583001	C₂²	1	8	yes	complemented
39	C₄×Dic₁₇₂	C₂²	1	4	yes	complemented
40	C₄×#10621873	C₂²	1	8	yes	complemented
41	C₄×D₃₄₄	C₂²	1	4	yes	complemented
42	#14582937	C₂²	1	2	yes	—
43	#14582937	C₂²	1	2	yes	—
44	#14582896	C₂²	1	4	yes	—
45	#14582896	C₂²	1	4	yes	—
46	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
48	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
49	C₄₃×#405	C₂²	1	8	yes	—
50	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
51	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
54	C₂×#10621898	C₂³	1	4	yes	—
55	#13063347	—	2	8	no	—
56	#13063347	—	2	8	no	—
57	C₂×Dic₁₇₂	C₂³	1	2	yes	—
58	C₂×Dic₁₇₂	C₂³	1	2	yes	—
59	C₂×#10621873	C₂³	1	4	yes	—
60	C₂×#10621873	C₂³	1	4	yes	—
61	C₂×D₃₄₄	C₂³	1	2	yes	—
62	C₂×D₃₄₄	C₂³	1	2	yes	—
63	#13063325	C₂³	1	2	yes	—
64	#13063325	C₂³	1	4	yes	—
65	#13063322	C₂³	1	2	yes	—
66	#13063320	—	2	8	no	—
67	#13063318	—	2	8	no	—
68	#13063317	C₂³	1	4	yes	—
69	#13063315	—	2	8	no	—
70	#13063313	C₂³	1	4	yes	—
71	#13063311	—	2	8	no	—
72	#13063310	—	2	8	no	—
73	#13063308	—	2	4	no	—
74	#13063307	—	2	8	no	—
75	#13063304	—	2	4	no	—
76	#13063304	C₂³	1	8	yes	—
77	#13063303	—	2	8	no	—
78	#13063299	—	2	4	no	—
79	#13063299	C₂³	1	8	yes	—
80	#13063298	—	2	8	no	—
81	#13063294	—	2	4	no	—
82	C₄×Dic₈₆	—	2	4	no	—
83	C₄×Dic₈₆	C₂³	1	8	yes	—
84	C₄×D₁₇₂	—	2	4	no	—
85	C₄×D₁₇₂	C₂³	1	8	yes	—
86	C₄×C₂²⋊D₄₃	—	2	8	no	—
87	C₄×C₂²⋊D₄₃	—	2	8	no	—
88	#13063284	C₂³	1	4	yes	—
89	#13063282	—	2	4	no	—
90	C₄²×D₄₃	—	2	4	no	—
91	#13063259	C₂³	1	4	yes	—
92	#13063259	C₂³	1	4	yes	—
93	#13063257	C₂³	1	4	yes	—
94	#13063257	C₂³	1	4	yes	—
95	#13063250	C₂³	1	8	yes	—
96	#13063250	C₂³	1	8	yes	—
97	#13063247	C₂³	1	8	yes	—
98	#13063247	C₂³	1	8	yes	—
99	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₄₃	—	2	4	no	—
101	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
102	C₂²×C₈×C₄₃	—	2	4	no	—
103	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
104	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
108	#117×C₄₃	D₄	1	4	yes	—
109	#117×C₄₃	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
111	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
112	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
114	#97×C₄₃	C₂³	1	4	yes	—
115	#97×C₄₃	C₂³	1	4	yes	—
116	C₄×C₈×C₄₃	C₂³	1	4	yes	—
117	C₄×C₈×C₄₃	C₂³	1	4	yes	—
118	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
127	C₂×C₂²⋊D₄₃	—	2	4	no	—
128	C₂×C₂²⋊D₄₃	—	2	8	no	—
129	#10621898	—	2	8	no	—
130	#10621898	—	2	8	no	—
131	C₂×D₁₇₂	—	2	4	no	—
132	C₂×D₁₇₂	C₂⁴	1	4	yes	—
133	C₂×C₄×D₄₃	—	2	4	no	—
134	C₂×C₄×D₄₃	—	2	8	no	—
135	C₂×Dic₈₆	—	2	4	no	—
136	C₂×Dic₈₆	C₂⁴	1	4	yes	—
137	M₁₆×C₄₃	—	2	8	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	8	no	—
141	C₂×C₈×C₄₃	#41	1	4	yes	—
142	C₂×C₈×C₄₃	#41	1	4	yes	—
143	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
144	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
145	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
146	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
147	C₄⋊C₄×C₄₃	C₂×D₄	1	8	yes	—
148	C₂²⋊C₄×C₄₃	C₂×D₄	1	8	yes	—
149	C₄²×C₄₃	C₂×D₄	1	2	yes	—
150	C₄²×C₄₃	C₂×D₄	1	2	yes	—
151	C₄²×C₄₃	C₂⁴	1	2	yes	—
152	C₄²×C₄₃	C₂⁴	1	2	yes	—
153	C₂²⋊Dic₄₃	—	2	4	no	—
154	C₂²⋊Dic₄₃	—	2	8	no	—
155	(C₂×D₄₃)⋊C₄	—	2	8	no	—
156	(C₂×D₄₃)⋊C₄	—	2	8	no	—
157	(C₂×D₄₃)⋊C₄	—	2	8	no	—
158	C₄⋊Dic₄₃	—	2	4	no	—
159	C₄⋊Dic₄₃	—	2	4	no	—
160	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
161	Dic₄₃⋊C₄	—	2	8	no	—
162	Dic₄₃⋊C₄	—	2	8	no	—
163	Dic₄₃⋊C₄	—	2	8	no	—
164	C₄×Dic₄₃	—	2	4	no	—
165	C₄×Dic₄₃	—	2	8	no	—
166	Dic₁₇₂	—	2	4	no	—
167	Dic₁₇₂	—	2	4	no	—
168	D₃₄₄	—	2	4	no	—
169	D₃₄₄	—	2	4	no	—
170	#10621873	—	2	8	no	—
171	#10621873	—	2	8	no	—
172	C₂³×C₄₃	—	2	2	no	—
173	C₂³×C₄₃	—	4	2	no	—
174	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
175	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂²×D₄₃	—	2	4	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	4	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
184	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
186	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
188	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
189	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
190	C₂²⋊D₄₃	—	4	8	no	—
191	C₂²⋊D₄₃	—	8	8	no	—
192	C₂×Dic₄₃	—	2	4	no	—
193	C₂×Dic₄₃	—	2	8	no	—
194	D₁₇₂	—	2	4	no	—
195	D₁₇₂	—	2	4	no	—
196	D₁₇₂	—	8	4	no	—
197	C₄×D₄₃	—	4	8	no	—
198	C₄×D₄₃	—	8	8	no	—
199	Dic₈₆	—	2	4	no	—
200	Dic₈₆	—	2	4	no	—
201	Dic₈₆	—	8	4	no	—
202	C₈×C₄₃	—	2	2	no	—
203	C₈×C₄₃	—	2	2	no	—
204	C₈×C₄₃	C₂×#41	1	4	yes	—
205	C₈×C₄₃	C₂×#41	1	4	yes	—
206	#60685	—	43	1	no	maximal, Sylow
207	C₂²×C₄₃	—	2	2	no	—
208	C₂²×C₄₃	—	2	4	no	—
209	C₂²×C₄₃	—	2	2	no	—
210	C₂²×C₄₃	—	4	4	no	—
211	C₂²×C₄₃	#532	1	2	yes	—
212	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
213	C₂×D₄₃	—	4	8	no	—
214	C₂×D₄₃	—	4	4	no	—
215	C₄×C₄₃	—	2	4	no	—
216	C₄×C₄₃	—	2	4	no	—
217	C₄×C₄₃	—	2	2	no	—
218	C₄×C₄₃	#532	1	2	yes	—
219	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
220	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
221	Dic₄₃	—	4	8	no	—
222	Dic₄₃	—	4	4	no	—
223	#3455	—	43	2	no	—
224	#3179	—	43	8	no	—
225	#3178	—	43	8	no	—
226	#3162	—	43	1	no	—
227	#3150	—	43	1	no	—
228	#3131	—	43	2	no	—
229	#3054	—	43	2	no	—
230	#3050	—	43	2	no	—
231	#2943	—	43	2	no	—
232	C₄×#135	—	43	2	no	—
233	C₂×#405	D₄₃	1	1	yes	characteristic, complemented
234	C₂×C₄₃	—	2	2	no	—
235	C₂×C₄₃	—	4	2	no	—
236	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
237	C₂×C₄₃	#3584	1	2	yes	—
238	D₄₃	—	8	4	no	—
239	C₂×#135	—	43	2	no	—
240	C₂×#135	—	43	2	no	—
241	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
242	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
243	#542	—	43	8	no	—
244	#541	—	43	4	no	—
245	#540	—	43	4	no	—
246	#539	—	86	4	no	—
247	#538	—	86	4	no	—
248	#533	—	43	2	no	—
249	#532	—	43	2	no	—
250	#529	—	86	8	no	—
251	#525	—	43	4	no	—
252	C₄×#41	—	43	4	no	—
253	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
254	#501	—	43	8	no	—
255	#497	—	43	4	no	—
256	#496	—	43	4	no	—
257	#488	—	43	8	no	—
258	#487	—	43	4	no	—
259	#486	—	43	4	no	—
260	#470	—	43	4	no	—
261	#469	—	43	4	no	—
262	#468	—	43	8	no	—
263	#467	—	43	4	no	—
264	#466	—	43	4	no	—
265	#465	—	43	8	no	—
266	#442	—	43	4	no	—
267	#441	—	43	4	no	—
268	#440	—	43	8	no	—
269	C₄×Q₁₆	—	43	4	no	—
270	C₄×SD₁₆	—	43	8	no	—
271	C₄×D₈	—	43	4	no	—
272	#427	—	43	2	no	—
273	#427	—	43	2	no	—
274	#416	—	43	4	no	—
275	#416	—	43	4	no	—
276	#405	C₂×D₄₃	1	8	yes	—
277	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
278	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
281	C₄₃	#60685	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	—	43	4	no	—
283	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
284	#135	—	86	8	no	—
285	#135	—	86	8	no	—
286	C₂×Q₁₆	—	43	2	no	—
287	C₂×Q₁₆	—	43	2	no	—
288	C₂×SD₁₆	—	43	4	no	—
289	C₂×SD₁₆	—	43	4	no	—
290	C₂×D₈	—	43	2	no	—
291	C₂×D₈	—	43	2	no	—
292	C₂×M₁₆	—	2	4	no	—
293	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
294	C₂²×C₈	—	2	4	no	—
295	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
296	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
297	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
298	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
299	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
300	C₄⋊Q₈	—	43	4	no	—
301	C₄⋊Q₈	—	43	2	no	—
302	#127	—	43	2	no	—
303	#126	—	86	8	no	—
304	#126	—	86	8	no	—
305	#125	—	43	4	no	—
306	#125	—	86	8	no	—
307	#124	—	43	4	no	—
308	#124	—	86	8	no	—
309	#123	—	86	4	no	—
310	#123	—	86	8	no	—
311	#123	—	86	8	no	—
312	C₂²⋊Q₈	—	43	8	no	—
313	C₂²⋊Q₈	—	86	4	no	—
314	C₂²⋊Q₈	—	86	8	no	—
315	#121	—	43	8	no	—
316	#121	—	86	4	no	—
317	#121	—	86	8	no	—
318	#120	—	86	4	no	—
319	C₄×Q₈	—	43	8	no	—
320	C₄×Q₈	—	86	4	no	—
321	C₄×D₄	—	43	8	no	—
322	C₄×D₄	—	86	8	no	—
323	C₄×D₄	—	86	8	no	—
324	C₄×D₄	—	86	4	no	—
325	#117	—	43	4	no	—
326	#117	—	86	4	no	—
327	#117	D₁₇₂	1	4	yes	—
328	#117	C₂²×D₄₃	1	4	yes	—
329	C₂×C₄⋊C₄	D₁₇₂	1	2	yes	—
330	C₂×C₂²⋊C₄	D₁₇₂	1	2	yes	—
331	C₂×C₄²	—	86	4	no	—
332	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
334	#107	—	43	4	no	—
335	#107	—	43	4	no	—
336	#106	—	43	4	no	—
337	#106	—	43	4	no	—
338	#103	—	43	8	no	—
339	#103	—	43	8	no	—
340	#102	—	43	8	no	—
341	#102	—	43	8	no	—
342	#97	C₂²×D₄₃	1	4	yes	—
343	#97	C₂²×D₄₃	1	4	yes	—
344	C₄×C₈	C₂²×D₄₃	1	4	yes	—
345	C₄×C₈	C₂²×D₄₃	1	4	yes	—
346	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
347	#41	—	86	8	no	—
348	#41	—	86	8	no	—
349	C₂×Q₈	—	43	4	no	—
350	C₂×Q₈	—	86	4	no	—
351	C₂×D₄	—	43	4	no	—
352	C₂×D₄	—	86	8	no	—
353	C₂×D₄	—	86	4	no	—
354	C₂×D₄	—	86	4	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	86	8	no	—
358	C₂²×C₄	—	86	4	no	—
359	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
361	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
362	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
363	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
364	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
365	Q₁₆	—	86	4	no	—
366	Q₁₆	—	86	4	no	—
367	SD₁₆	—	86	8	no	—
368	SD₁₆	—	86	8	no	—
369	D₈	—	86	4	no	—
370	D₈	—	86	4	no	—
371	M₁₆	—	2	8	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	8	no	—
375	C₂×C₈	#10621898	1	4	yes	—
376	C₂×C₈	#10621898	1	4	yes	—
377	C₂×C₈	C₂³×D₄₃	1	2	yes	—
378	C₂×C₈	C₂³×D₄₃	1	2	yes	—
379	C₂×C₈	C₂³×D₄₃	1	2	yes	—
380	C₂×C₈	C₂³×D₄₃	1	2	yes	—
381	C₄⋊C₄	—	43	8	no	—
382	C₄⋊C₄	—	86	8	no	—
383	C₄⋊C₄	—	86	4	no	—
384	C₄⋊C₄	—	86	8	no	—
385	C₄⋊C₄	—	86	8	no	—
386	C₄⋊C₄	—	86	4	no	—
387	C₄⋊C₄	C₂×D₁₇₂	1	8	yes	—
388	C₂²⋊C₄	—	86	4	no	—
389	C₂²⋊C₄	—	86	8	no	—
390	C₂²⋊C₄	—	86	8	no	—
391	C₂²⋊C₄	—	86	8	no	—
392	C₂²⋊C₄	—	86	8	no	—
393	C₂²⋊C₄	C₂×D₁₇₂	1	8	yes	—
394	C₄²	—	86	8	no	—
395	C₄²	—	86	4	no	—
396	C₄²	C₂×D₁₇₂	1	2	yes	—
397	C₄²	C₂×D₁₇₂	1	2	yes	—
398	C₄²	C₂³×D₄₃	1	2	yes	—
399	C₄²	C₂³×D₄₃	1	2	yes	—
400	C₂³	—	2	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	86	4	no	—
403	C₂³	C₂²×D₁₇₂	1	2	yes	—
404	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
405	Q₈	—	86	4	no	—
406	Q₈	—	86	4	no	—
407	Q₈	—	344	4	no	—
408	D₄	—	86	4	no	—
409	D₄	—	86	4	no	—
410	D₄	—	344	4	no	—
411	D₄	—	344	8	no	—
412	D₄	—	172	8	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	86	8	no	—
420	C₂×C₄	—	86	4	no	—
421	C₂×C₄	—	344	8	no	—
422	C₂×C₄	—	172	8	no	—
423	C₂×C₄	C₂²×D₁₇₂	1	4	yes	—
424	C₂×C₄	C₂²×D₁₇₂	1	4	yes	—
425	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
426	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
427	C₂×C₄	C₂×#10621898	1	2	yes	—
428	C₂×C₄	C₂×#10621898	1	2	yes	—
429	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	2	2	no	—
432	C₈	C₂×#10621898	1	4	yes	—
433	C₈	C₂×#10621898	1	4	yes	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	172	8	no	—
439	C₂²	—	172	4	no	—
440	C₂²	#14583449	1	2	yes	—
441	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
442	C₄	—	2	4	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	2	no	—
445	C₄	—	172	8	no	—
446	C₄	—	172	4	no	—
447	C₄	#14583449	1	2	yes	—
448	C₄	C₂²×#10621898	1	1	yes	characteristic
449	C₄	C₂²×#10621898	1	1	yes	characteristic
450	C₂	—	2	2	no	—
451	C₂	—	4	2	no	—
452	C₂	—	344	4	no	—
453	C₂	C₂×#14583449	1	1	yes	characteristic
454	C₂	#19149369	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#60685
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
1. #19147985	C₂	semidirect
2. #19145278	C₂	semidirect
3. #19145263	C₂	semidirect
4. #19145119	C₂	semidirect
5. #19145041	C₂	semidirect
6. #19144918	C₂	semidirect
7. #19144204	C₂	semidirect
8. #19144176	C₂	semidirect
9. #19143397	C₂	semidirect
10. C₄×#13063347	C₂	semidirect
11. C₂×C₄₃×#405	C₂	semidirect
24. #14583308	C₂²	semidirect
25. #14583293	C₂²	semidirect
26. #14583288	C₂²	semidirect
27. #14583254	C₂²	semidirect
28. #14583250	C₂²	semidirect
29. #14583246	C₂²	semidirect
36. #14583012	C₂²	semidirect
37. #14583007	C₂²	semidirect
38. #14583001	C₂²	semidirect
39. C₄×Dic₁₇₂	C₂²	semidirect
40. C₄×#10621873	C₂²	semidirect
41. C₄×D₃₄₄	C₂²	semidirect
233. C₂×#405	D₄₃	semidirect
281. C₄₃	#60685	semidirect

Maximal subgroups

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

subgroup	index
#19147985	2
#19145278	2
#19145263	2
#19145119	2
#19145041	2
#19144918	2
#19144204	2
#19144176	2
#19143397	2
C₄×#13063347	2
C₂×C₄₃×#405	2
#60685	43