Subgroups — #25154676

Order 11008.

786 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137542	C₂	1	1	yes	maximal, characteristic
2	#19135980	C₂	1	2	yes	maximal
3	#19135728	C₂	1	2	yes	maximal
4	#19135548	C₂	1	2	yes	maximal, complemented
5	#19135353	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135314	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135163	C₂	1	2	yes	maximal, complemented
8	#19134722	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134592	C₂	1	1	yes	maximal, characteristic
10	C₄×#13063245	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#2551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
13	C₂×#13063283	—	2	1	no	—
14	C₂×#13063258	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
17	C₂×#13063245	C₂²	1	1	yes	characteristic
18	C₂×#13063245	C₂²	1	1	yes	characteristic
19	C₂×#13063245	C₂²	1	2	yes	—
20	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	#14582801	C₂²	1	2	yes	—
22	#14582791	—	2	2	no	—
23	#14582769	C₂²	1	1	yes	characteristic
24	#14582756	—	2	1	no	—
25	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
26	#14582661	C₂²	1	2	yes	—
27	#14582661	C₂²	1	2	yes	—
28	#14582661	C₂²	1	1	yes	characteristic
29	#14582661	C₂²	1	2	yes	—
30	#14582661	C₂²	1	2	yes	—
31	#14582661	C₂²	1	1	yes	characteristic
32	#14582654	C₂²	1	2	yes	—
33	C₂×C₄⋊Q₈×C₄₃	—	2	1	no	—
34	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
35	C₄₃×#395	—	2	2	no	—
36	C₄₃×#389	—	2	1	no	—
37	C₄₃×#389	C₂²	1	2	yes	—
38	C₄₃×#384	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
42	C₂²×C₄×D₄₃	—	2	1	no	—
43	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
46	C₄×D₁₇₂	—	2	2	no	—
47	C₄×D₁₇₂	Q₈	1	4	yes	complemented
48	#13063283	—	4	4	no	—
49	C₂×C₄⋊Dic₄₃	—	2	1	no	—
50	C₂×C₄⋊Dic₄₃	—	2	1	no	—
51	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
53	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
54	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
55	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
56	C₂×C₄×Dic₄₃	—	2	2	no	—
57	#13063258	—	2	4	no	—
58	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
60	#13063245	—	2	2	no	—
61	#13063245	—	2	2	no	—
62	#13063245	—	4	2	no	—
63	C₄×C₄₃⋊C₈	—	2	2	no	—
64	C₄₃⋊#95	—	2	2	no	—
65	C₂²×Q₈×C₄₃	—	2	2	no	—
66	C₄⋊Q₈×C₄₃	—	2	4	no	—
67	C₄⋊Q₈×C₄₃	—	4	2	no	—
68	C₄⋊Q₈×C₄₃	—	4	4	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₃	—	2	1	no	—
79	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	#95×C₄₃	—	2	1	no	—
82	#95×C₄₃	—	2	2	no	—
83	#95×C₄₃	D₄	1	2	yes	—
84	C₂³×D₄₃	—	2	1	no	—
85	C₂×Q₈×C₄₃	—	4	4	no	—
86	C₂×Q₈×C₄₃	—	4	4	no	—
87	C₂×Q₈×C₄₃	—	8	2	no	—
88	C₂²×C₄×C₄₃	—	2	1	no	—
89	C₂²×C₄×C₄₃	—	2	1	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₃	—	2	1	no	—
97	C₂²×Dic₄₃	—	2	2	no	—
98	C₂×D₁₇₂	—	2	1	no	—
99	C₂×D₁₇₂	—	2	1	no	—
100	C₂×D₁₇₂	—	2	1	no	—
101	C₂×D₁₇₂	—	2	1	no	—
102	C₂×D₁₇₂	—	2	1	no	—
103	C₂×D₁₇₂	C₂×Q₈	1	2	yes	—
104	C₂×C₄×D₄₃	—	2	4	no	—
105	C₂×C₄×D₄₃	—	4	2	no	—
106	C₂×C₄×D₄₃	—	4	2	no	—
107	C₄⋊C₄×C₄₃	—	2	2	no	—
108	C₄⋊C₄×C₄₃	—	2	1	no	—
109	C₄⋊C₄×C₄₃	—	2	1	no	—
110	C₄⋊C₄×C₄₃	—	2	2	no	—
111	C₄⋊C₄×C₄₃	—	2	2	no	—
112	C₄⋊C₄×C₄₃	—	4	4	no	—
113	C₄⋊C₄×C₄₃	—	4	4	no	—
114	C₄⋊C₄×C₄₃	—	4	2	no	—
115	C₄⋊C₄×C₄₃	—	8	1	no	—
116	C₄⋊C₄×C₄₃	D₈	1	4	yes	—
117	C₄⋊C₄×C₄₃	#41	1	2	yes	—
118	C₄⋊C₄×C₄₃	#41	1	2	yes	—
119	C₄²×C₄₃	—	2	2	no	—
120	C₄²×C₄₃	—	2	2	no	—
121	C₄²×C₄₃	—	4	2	no	—
122	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
123	C₄²×C₄₃	#41	1	2	yes	—
124	(C₂×D₄₃)⋊C₄	—	2	4	no	—
125	(C₂×D₄₃)⋊C₄	—	4	4	no	—
126	(C₂×D₄₃)⋊C₄	—	8	2	no	—
127	C₄⋊Dic₄₃	—	2	1	no	—
128	C₄⋊Dic₄₃	—	2	2	no	—
129	C₄⋊Dic₄₃	—	2	2	no	—
130	C₄⋊Dic₄₃	—	4	2	no	—
131	C₄⋊Dic₄₃	—	8	1	no	—
132	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
133	C₄×Dic₄₃	—	4	4	no	—
134	C₂×C₄₃⋊C₈	—	2	1	no	—
135	C₂×C₄₃⋊C₈	—	2	1	no	—
136	C₂×C₄₃⋊C₈	—	2	1	no	—
137	C₂×C₄₃⋊C₈	—	2	1	no	—
138	C₂×C₄₃⋊C₈	—	2	2	no	—
139	C₂×C₄₃⋊C₈	—	2	2	no	—
140	C₂×C₄₃⋊C₈	—	2	2	no	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	1	no	—
143	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
144	C₂²×D₄₃	—	2	2	no	—
145	C₂²×D₄₃	—	4	1	no	—
146	C₂²×D₄₃	—	4	1	no	—
147	C₂²×D₄₃	—	4	1	no	—
148	C₂²×D₄₃	—	4	1	no	—
149	C₂²×D₄₃	—	4	1	no	—
150	C₂²×D₄₃	—	4	1	no	—
151	Q₈×C₄₃	—	8	8	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
169	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
170	C₂×C₄×C₄₃	C₂×D₈	1	4	yes	—
171	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
172	C₂×C₄×C₄₃	#137	1	2	yes	—
173	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
179	C₂×Dic₄₃	—	2	2	no	—
180	C₂×Dic₄₃	—	4	1	no	—
181	C₂×Dic₄₃	—	4	1	no	—
182	C₂×Dic₄₃	—	4	2	no	—
183	C₂×Dic₄₃	—	4	2	no	—
184	C₂×Dic₄₃	—	4	2	no	—
185	D₁₇₂	—	2	2	no	—
186	D₁₇₂	—	2	2	no	—
187	D₁₇₂	—	4	1	no	—
188	D₁₇₂	—	4	1	no	—
189	C₄×D₄₃	—	4	8	no	—
190	C₄₃⋊C₈	—	4	1	no	—
191	C₄₃⋊C₈	—	4	2	no	—
192	C₄₃⋊C₈	—	4	1	no	—
193	#26020	—	43	1	no	maximal, Sylow
194	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
195	C₂²×C₄₃	#546	1	1	yes	characteristic
196	C₂²×C₄₃	#548	1	1	yes	characteristic
197	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
198	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
199	C₂²×C₄₃	#577	1	1	yes	characteristic
200	C₂²×C₄₃	#577	1	1	yes	characteristic
201	C₂×D₄₃	—	4	2	no	—
202	C₂×D₄₃	—	4	2	no	—
203	C₂×D₄₃	—	4	2	no	—
204	C₂×D₄₃	—	8	1	no	—
205	C₂×D₄₃	—	8	1	no	—
206	C₂×D₄₃	—	8	1	no	—
207	C₂×D₄₃	—	8	1	no	—
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	2	4	no	—
210	C₄×C₄₃	—	4	2	no	—
211	C₄×C₄₃	—	4	2	no	—
212	C₄×C₄₃	—	4	2	no	—
213	C₄×C₄₃	—	8	2	no	—
214	C₄×C₄₃	#474	1	4	yes	—
215	C₄×C₄₃	#533	1	1	yes	characteristic
216	C₄×C₄₃	#544	1	1	yes	characteristic
217	C₄×C₄₃	#555	1	1	yes	characteristic
218	C₄×C₄₃	#556	1	1	yes	characteristic
219	Dic₄₃	—	4	2	no	—
220	Dic₄₃	—	8	2	no	—
221	#2551	D₄₃	1	1	yes	characteristic, complemented
222	#2354	—	43	1	no	—
223	#2067	—	43	2	no	—
224	#2023	—	43	2	no	—
225	#1988	—	43	2	no	—
226	#1947	—	43	1	no	—
227	#1939	—	43	1	no	—
228	#1918	—	43	2	no	—
229	#1834	—	43	1	no	—
230	#1802	—	43	1	no	—
231	C₄×#102	—	43	1	no	—
232	C₂×C₄₃	#2439	1	1	yes	characteristic
233	C₂×C₄₃	C₂×#474	1	1	yes	characteristic
234	C₂×C₄₃	#3084	1	1	yes	characteristic
235	C₂×C₄₃	#3294	1	1	yes	characteristic
236	C₂×C₄₃	#3329	1	1	yes	characteristic
237	C₂×C₄₃	#3358	1	1	yes	characteristic
238	C₂×C₄₃	#3369	1	1	yes	characteristic
239	D₄₃	—	8	2	no	—
240	C₂×C₄⋊Q₈	—	2	1	no	—
241	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
242	C₂×C₄×D₄	—	43	1	no	—
243	C₂×#117	—	86	1	no	—
244	C₂×#107	—	43	2	no	—
245	C₂×C₄⋊C₈	—	43	1	no	—
246	C₂×C₄⋊C₈	—	43	2	no	—
247	C₂×#102	—	43	1	no	—
248	C₂×#102	—	43	1	no	—
249	C₂×#102	—	43	2	no	—
250	C₂×C₄×C₈	—	43	1	no	—
251	#395	—	2	2	no	—
252	#390	—	43	2	no	—
253	#389	—	2	1	no	—
254	#389	C₂×D₄₃	1	2	yes	—
255	#388	—	86	2	no	—
256	#384	—	43	1	no	—
257	#384	C₂×D₄₃	1	1	yes	characteristic
258	#380	—	86	1	no	—
259	C₄×C₄⋊C₄	—	43	2	no	—
260	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
262	#340	—	43	2	no	—
263	#340	—	43	2	no	—
264	#340	—	43	2	no	—
265	#340	—	43	1	no	—
266	#340	—	43	2	no	—
267	#340	—	43	1	no	—
268	#336	—	43	2	no	—
269	C₄₃	#26020	1	1	yes	characteristic, complemented, Sylow
270	C₂²×Q₈	—	2	2	no	—
271	C₂²×D₄	—	43	1	no	—
272	C₂³×C₄	—	86	1	no	—
273	C₂²×C₈	—	43	1	no	—
274	C₂²×C₈	—	43	2	no	—
275	C₂²×C₈	—	43	1	no	—
276	C₄⋊Q₈	—	2	4	no	—
277	C₄⋊Q₈	—	4	2	no	—
278	C₄⋊Q₈	—	4	4	no	—
279	C₄×D₄	—	43	4	no	—
280	C₄×D₄	—	86	2	no	—
281	#117	—	172	4	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	43	1	no	—
287	C₂×C₄⋊C₄	—	43	2	no	—
288	C₂×C₄⋊C₄	—	86	1	no	—
289	C₂×C₄⋊C₄	—	86	1	no	—
290	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	86	1	no	—
296	C₂×C₂²⋊C₄	—	86	2	no	—
297	C₂×C₂²⋊C₄	—	86	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	86	2	no	—
300	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
301	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
302	#107	—	86	4	no	—
303	C₄⋊C₈	—	86	2	no	—
304	C₄⋊C₈	—	172	2	no	—
305	#102	—	86	2	no	—
306	#102	—	86	2	no	—
307	#102	—	172	2	no	—
308	C₄×C₈	—	86	2	no	—
309	#95	—	2	1	no	—
310	#95	—	2	2	no	—
311	#95	—	86	2	no	—
312	#95	C₂²⋊D₄₃	1	2	yes	—
313	C₂⁴	—	86	1	no	—
314	C₂×Q₈	—	4	4	no	—
315	C₂×Q₈	—	4	4	no	—
316	C₂×Q₈	—	8	2	no	—
317	C₂×D₄	—	43	2	no	—
318	C₂×D₄	—	86	1	no	—
319	C₂×D₄	—	86	1	no	—
320	C₂×D₄	—	86	1	no	—
321	C₂×D₄	—	86	1	no	—
322	C₂×D₄	—	86	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	86	1	no	—
327	C₂²×C₄	—	86	4	no	—
328	C₂²×C₄	—	86	2	no	—
329	C₂²×C₄	—	172	2	no	—
330	C₂²×C₄	—	172	2	no	—
331	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
332	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
334	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
335	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
336	C₂×C₈	—	86	1	no	—
337	C₂×C₈	—	86	1	no	—
338	C₂×C₈	—	86	1	no	—
339	C₂×C₈	—	86	1	no	—
340	C₂×C₈	—	86	2	no	—
341	C₂×C₈	—	86	2	no	—
342	C₂×C₈	—	86	2	no	—
343	C₂×C₈	—	86	1	no	—
344	C₂×C₈	—	86	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	4	4	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	8	1	no	—
354	C₄⋊C₄	—	43	2	no	—
355	C₄⋊C₄	—	86	1	no	—
356	C₄⋊C₄	—	86	2	no	—
357	C₄⋊C₄	—	86	2	no	—
358	C₄⋊C₄	—	344	1	no	—
359	C₄⋊C₄	—	172	2	no	—
360	C₄⋊C₄	#10621882	1	4	yes	—
361	C₄⋊C₄	#10621900	1	2	yes	—
362	C₄⋊C₄	#10621902	1	2	yes	—
363	C₂²⋊C₄	—	86	4	no	—
364	C₂²⋊C₄	—	344	2	no	—
365	C₂²⋊C₄	—	172	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	—	172	4	no	—
370	C₄²	Q₈×D₄₃	1	2	yes	—
371	C₄²	#10621902	1	2	yes	—
372	C₂³	—	86	2	no	—
373	C₂³	—	172	1	no	—
374	C₂³	—	172	1	no	—
375	C₂³	—	172	1	no	—
376	C₂³	—	172	1	no	—
377	C₂³	—	172	1	no	—
378	C₂³	—	172	1	no	—
379	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
380	Q₈	—	8	8	no	—
381	D₄	—	86	2	no	—
382	D₄	—	86	2	no	—
383	D₄	—	172	1	no	—
384	D₄	—	172	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	86	2	no	—
402	C₂×C₄	—	172	2	no	—
403	C₂×C₄	—	172	2	no	—
404	C₂×C₄	—	172	2	no	—
405	C₂×C₄	—	172	1	no	—
406	C₂×C₄	—	172	1	no	—
407	C₂×C₄	—	172	8	no	—
408	C₂×C₄	#13063301	1	2	yes	—
409	C₂×C₄	#13063301	1	2	yes	—
410	C₂×C₄	C₂×#10621882	1	4	yes	—
411	C₂×C₄	C₂×#10621882	1	2	yes	—
412	C₂×C₄	#13063356	1	2	yes	—
413	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
414	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
415	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
416	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
417	C₂×C₄	#13063370	1	1	yes	characteristic
418	C₂×C₄	#13063373	1	1	yes	characteristic
419	C₈	—	172	1	no	—
420	C₈	—	172	2	no	—
421	C₈	—	172	1	no	—
422	C₂²	—	344	1	no	—
423	C₂²	—	344	1	no	—
424	C₂²	—	344	1	no	—
425	C₂²	—	344	1	no	—
426	C₂²	—	172	2	no	—
427	C₂²	—	172	2	no	—
428	C₂²	—	172	2	no	—
429	C₂²	C₂×#13063301	1	1	yes	characteristic
430	C₂²	#14583543	1	1	yes	characteristic
431	C₂²	#14583560	1	1	yes	characteristic
432	C₂²	C₂²×#10621882	1	1	yes	characteristic
433	C₂²	C₂×#13063356	1	1	yes	characteristic
434	C₂²	#14583707	1	1	yes	characteristic
435	C₂²	#14583710	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	4	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	8	2	no	—
442	C₄	—	344	2	no	—
443	C₄	—	172	2	no	—
444	C₄	#14583176	1	4	yes	—
445	C₄	#14583454	1	1	yes	characteristic
446	C₄	#14583526	1	1	yes	characteristic
447	C₄	#14583615	1	1	yes	characteristic
448	C₄	#14583623	1	1	yes	characteristic
449	C₂	—	344	2	no	—
450	C₂	#19138282	1	1	yes	characteristic
451	C₂	C₂×#14583176	1	1	yes	characteristic
452	C₂	#19144453	1	1	yes	characteristic
453	C₂	#19146408	1	1	yes	characteristic
454	C₂	#19146889	1	1	yes	characteristic
455	C₂	#19147230	1	1	yes	characteristic
456	C₂	#19147335	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2551	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₁₇₂	C₂³
hypercenter	#2551	D₄₃
hypocenter	C₄₃	#26020
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2551

Complements

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

N	H ≅ G/N	type
4. #19135548	C₂	semidirect
5. #19135353	C₂	semidirect
6. #19135314	C₂	semidirect
7. #19135163	C₂	semidirect
8. #19134722	C₂	semidirect
11. C₄₃×#2551	C₂	semidirect
47. C₄×D₁₇₂	Q₈	semidirect
221. #2551	D₄₃	semidirect
269. C₄₃	#26020	semidirect

Maximal subgroups

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

subgroup	index
#19137542	2
#19135980	2
#19135728	2
#19135548	2
#19135353	2
#19135314	2
#19135163	2
#19134722	2
#19134592	2
C₄×#13063245	2
C₄₃×#2551	2
#26020	43