Subgroups — #25107159

Order 11008.

902 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582769	C₂	1	1	yes	maximal, characteristic
2	#19136993	C₂	1	1	yes	maximal, characteristic
3	#19135359	C₂	1	2	yes	maximal, complemented
4	#19135354	C₂	1	2	yes	maximal, complemented
5	#19134790	C₂	1	2	yes	maximal
6	#19134785	C₂	1	2	yes	maximal
7	#19134763	C₂	1	2	yes	maximal, complemented
8	#19134729	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₃×#432	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄⋊Dic₄₃	—	2	1	no	—
11	C₂²×C₄⋊Dic₄₃	—	2	1	no	—
12	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	C₂×#13063259	C₂²	1	4	yes	—
14	C₂×#13063257	C₂²	1	4	yes	—
15	#14582769	—	2	1	no	—
16	#14582769	—	2	1	no	—
17	#14582769	C₂²	1	2	yes	—
18	#14582769	C₂²	1	2	yes	—
19	#14582767	—	2	1	no	—
20	#14582765	C₂²	1	1	yes	characteristic
21	#14582765	C₂²	1	1	yes	characteristic
22	#14582762	—	2	1	no	—
23	#14582759	C₂²	1	1	yes	characteristic
24	#14582759	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
27	C₄×C₂²⋊Dic₄₃	—	2	1	no	—
28	#14582745	—	2	1	no	—
29	#14582662	C₂²	1	4	yes	—
30	#14582662	C₂²	1	4	yes	—
31	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#432	C₄	1	8	yes	complemented
33	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
35	C₂×#97×C₄₃	C₂²	1	2	yes	—
36	C₂³×Dic₄₃	—	2	2	no	—
37	C₂×C₄⋊Dic₄₃	—	2	2	no	—
38	C₂×C₄⋊Dic₄₃	—	2	2	no	—
39	C₂×C₄⋊Dic₄₃	—	2	2	no	—
40	C₂×C₄⋊Dic₄₃	—	2	2	no	—
41	C₂×C₄⋊Dic₄₃	—	2	2	no	—
42	C₂×C₄⋊Dic₄₃	—	4	4	no	—
43	C₂×C₄⋊Dic₄₃	—	4	4	no	—
44	C₂×C₄⋊Dic₄₃	—	4	4	no	—
45	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
46	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
47	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
50	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
51	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
52	C₂×C₄×Dic₄₃	—	2	1	no	—
53	C₂×C₄×Dic₄₃	—	2	1	no	—
54	#13063259	—	4	4	no	—
55	#13063257	—	4	4	no	—
56	C₄₃⋊#95	—	2	1	no	—
57	C₄₃⋊#95	—	2	1	no	—
58	C₄₃⋊#95	—	2	1	no	—
59	C₄₃⋊#95	—	2	1	no	—
60	C₄₃⋊#95	—	2	1	no	—
61	C₄₃⋊#95	—	2	1	no	—
62	C₄₃⋊#95	—	2	1	no	—
63	C₄₃⋊#95	—	2	1	no	—
64	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
68	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
69	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₃	Q₈	1	4	yes	—
72	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₃	C₂×C₄	1	8	yes	complemented
75	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	—
76	#97×C₄₃	C₂×C₄	1	8	yes	complemented
77	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₃	—	2	2	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
86	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₃	—	2	1	no	—
95	C₂²×Dic₄₃	—	2	1	no	—
96	C₂²×Dic₄₃	—	2	1	no	—
97	C₂²×Dic₄₃	—	2	1	no	—
98	C₂²×Dic₄₃	—	2	4	no	—
99	C₂²×Dic₄₃	—	4	4	no	—
100	C₂²×Dic₄₃	—	4	4	no	—
101	C₂²×Dic₄₃	—	4	4	no	—
102	C₂×C₈×C₄₃	—	2	4	no	—
103	C₂×C₈×C₄₃	—	2	4	no	—
104	C₂×C₈×C₄₃	C₂²×C₄	1	8	yes	—
105	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
106	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
107	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
108	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
109	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
110	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
111	C₂²⋊Dic₄₃	—	4	2	no	—
112	C₂²⋊Dic₄₃	—	4	2	no	—
113	C₄⋊Dic₄₃	—	2	2	no	—
114	C₄⋊Dic₄₃	—	2	4	no	—
115	C₄⋊Dic₄₃	—	2	2	no	—
116	C₄⋊Dic₄₃	—	2	4	no	—
117	C₄⋊Dic₄₃	—	2	2	no	—
118	C₄⋊Dic₄₃	—	2	2	no	—
119	C₄⋊Dic₄₃	—	4	4	no	—
120	C₄⋊Dic₄₃	—	4	4	no	—
121	C₄⋊Dic₄₃	—	4	4	no	—
122	C₄⋊Dic₄₃	—	4	4	no	—
123	C₄⋊Dic₄₃	—	4	4	no	—
124	C₄×Dic₄₃	—	4	2	no	—
125	C₄×Dic₄₃	—	4	2	no	—
126	C₂³×C₄₃	—	2	1	no	—
127	C₂³×C₄₃	—	2	1	no	—
128	C₂³×C₄₃	—	2	1	no	—
129	C₂³×C₄₃	—	2	1	no	—
130	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
131	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
132	C₂³×C₄₃	#137	1	2	yes	—
133	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₄₃	—	2	1	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	2	1	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	2	1	no	—
141	C₂×C₄×C₄₃	—	2	1	no	—
142	C₂×C₄×C₄₃	—	2	8	no	—
143	C₂×C₄×C₄₃	—	2	4	no	—
144	C₂×C₄×C₄₃	—	2	4	no	—
145	C₂×C₄×C₄₃	—	2	8	no	—
146	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
152	C₂×C₄×C₄₃	#137	1	2	yes	—
153	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
156	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
157	C₂×Dic₄₃	—	4	4	no	—
158	C₂×Dic₄₃	—	4	1	no	—
159	C₂×Dic₄₃	—	4	1	no	—
160	C₂×Dic₄₃	—	4	1	no	—
161	C₂×Dic₄₃	—	4	1	no	—
162	C₂×Dic₄₃	—	4	1	no	—
163	C₂×Dic₄₃	—	4	1	no	—
164	C₂×Dic₄₃	—	4	4	no	—
165	C₂×Dic₄₃	—	4	4	no	—
166	C₂×Dic₄₃	—	4	1	no	—
167	C₂×Dic₄₃	—	4	1	no	—
168	C₂×Dic₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	4	1	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	—	4	1	no	—
172	C₂×Dic₄₃	—	8	8	no	—
173	C₈×C₄₃	—	2	8	no	—
174	#21987	—	43	1	no	maximal, Sylow
175	C₂²×C₄₃	—	2	2	no	—
176	C₂²×C₄₃	—	2	2	no	—
177	C₂²×C₄₃	—	2	2	no	—
178	C₂²×C₄₃	—	2	2	no	—
179	C₂²×C₄₃	—	2	2	no	—
180	C₂²×C₄₃	—	2	2	no	—
181	C₂²×C₄₃	#428	1	4	yes	—
182	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₄₃	#535	1	1	yes	characteristic
184	C₂²×C₄₃	#536	1	1	yes	characteristic
185	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
188	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
189	C₄×C₄₃	—	2	2	no	—
190	C₄×C₄₃	—	2	2	no	—
191	C₄×C₄₃	—	2	2	no	—
192	C₄×C₄₃	—	2	2	no	—
193	C₄×C₄₃	#428	1	4	yes	—
194	C₄×C₄₃	#520	1	2	yes	—
195	C₄×C₄₃	#544	1	2	yes	—
196	Dic₄₃	—	8	1	no	—
197	Dic₄₃	—	8	4	no	—
198	Dic₄₃	—	8	1	no	—
199	Dic₄₃	—	8	1	no	—
200	Dic₄₃	—	8	1	no	—
201	C₂×#432	D₄₃	1	1	yes	characteristic
202	C₂×#384	—	43	1	no	—
203	#2283	—	43	1	no	—
204	#1948	—	43	2	no	—
205	#1947	—	43	2	no	—
206	#1853	—	43	2	no	—
207	#1852	—	43	2	no	—
208	#1847	—	43	2	no	—
209	#1836	—	43	2	no	—
210	C₂×C₄₃	—	2	4	no	—
211	C₂×C₄₃	#2317	1	1	yes	characteristic
212	C₂×C₄₃	C₂×#428	1	1	yes	characteristic
213	C₂×C₄₃	C₂×#428	1	1	yes	characteristic
214	C₂×C₄₃	#3217	1	1	yes	characteristic
215	C₂×C₄₃	#3218	1	1	yes	characteristic
216	C₂×C₄₃	#3238	1	1	yes	characteristic
217	C₂×C₄₃	#3239	1	1	yes	characteristic
218	C₂²×C₄⋊C₄	—	43	2	no	—
219	C₂²×C₄⋊C₄	—	86	1	no	—
220	C₂²×C₄⋊C₄	—	86	1	no	—
221	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
222	#432	Dic₄₃	1	8	yes	complemented
223	C₂×#107	—	43	4	no	—
224	C₂×#106	—	43	4	no	—
225	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
226	C₂×C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
227	C₂×#97	C₂×D₄₃	1	2	yes	—
228	#384	—	43	2	no	—
229	#384	—	43	2	no	—
230	#384	—	86	1	no	—
231	#384	—	86	1	no	—
232	#383	—	86	1	no	—
233	#382	—	43	1	no	—
234	#382	—	43	1	no	—
235	#381	—	86	1	no	—
236	#380	—	43	1	no	—
237	#380	—	43	1	no	—
238	C₄×C₄⋊C₄	—	43	1	no	—
239	C₄×C₄⋊C₄	—	43	1	no	—
240	C₄×C₂²⋊C₄	—	86	1	no	—
241	#376	—	86	1	no	—
242	#340	—	43	4	no	—
243	#340	—	43	4	no	—
244	C₄₃	#21987	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₄	—	86	2	no	—
246	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
247	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
248	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
249	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
250	C₂×C₄⋊C₄	—	43	4	no	—
251	C₂×C₄⋊C₄	—	43	1	no	—
252	C₂×C₄⋊C₄	—	43	1	no	—
253	C₂×C₄⋊C₄	—	43	1	no	—
254	C₂×C₄⋊C₄	—	43	1	no	—
255	C₂×C₄⋊C₄	—	86	2	no	—
256	C₂×C₄⋊C₄	—	86	2	no	—
257	C₂×C₄⋊C₄	—	86	2	no	—
258	C₂×C₄⋊C₄	—	86	2	no	—
259	C₂×C₄⋊C₄	—	86	2	no	—
260	C₂×C₄⋊C₄	—	172	4	no	—
261	C₂×C₄⋊C₄	—	172	4	no	—
262	C₂×C₄⋊C₄	—	172	4	no	—
263	C₂×C₂²⋊C₄	—	86	1	no	—
264	C₂×C₂²⋊C₄	—	86	1	no	—
265	C₂×C₄²	—	86	1	no	—
266	C₂×C₄²	—	86	1	no	—
267	C₂×C₄²	Dic₈₆	1	4	yes	—
268	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
269	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
270	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
271	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
272	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
273	#107	—	172	4	no	—
274	#106	—	172	4	no	—
275	C₄⋊C₈	C₂×Dic₄₃	1	8	yes	complemented
276	C₂²⋊C₈	C₂×Dic₄₃	1	8	yes	—
277	#97	C₂×Dic₄₃	1	8	yes	complemented
278	#95	—	86	1	no	—
279	#95	—	86	1	no	—
280	#95	—	86	1	no	—
281	#95	—	86	1	no	—
282	#95	—	86	1	no	—
283	#95	—	86	1	no	—
284	#95	—	86	1	no	—
285	#95	—	86	1	no	—
286	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	86	1	no	—
294	C₂²×C₄	—	86	1	no	—
295	C₂²×C₄	—	86	1	no	—
296	C₂²×C₄	—	86	1	no	—
297	C₂²×C₄	—	86	4	no	—
298	C₂²×C₄	—	172	4	no	—
299	C₂²×C₄	—	172	4	no	—
300	C₂²×C₄	—	172	4	no	—
301	C₂²×C₄	C₄⋊Dic₄₃	1	4	yes	—
302	C₂²×C₄	C₄⋊Dic₄₃	1	4	yes	—
303	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
304	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
309	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
310	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	C₂²×Dic₄₃	1	8	yes	—
314	C₄⋊C₄	—	86	2	no	—
315	C₄⋊C₄	—	86	4	no	—
316	C₄⋊C₄	—	86	2	no	—
317	C₄⋊C₄	—	86	4	no	—
318	C₄⋊C₄	—	86	2	no	—
319	C₄⋊C₄	—	86	2	no	—
320	C₄⋊C₄	—	172	4	no	—
321	C₄⋊C₄	—	172	4	no	—
322	C₄⋊C₄	—	172	4	no	—
323	C₄⋊C₄	—	172	4	no	—
324	C₄⋊C₄	—	172	4	no	—
325	C₂²⋊C₄	—	172	2	no	—
326	C₂²⋊C₄	—	172	2	no	—
327	C₄²	—	172	2	no	—
328	C₄²	—	172	2	no	—
329	C₄²	C₄⋊Dic₄₃	1	4	yes	—
330	C₄²	C₄⋊Dic₄₃	1	4	yes	—
331	C₄²	C₂×Dic₈₆	1	2	yes	—
332	C₄²	C₂×Dic₈₆	1	2	yes	—
333	C₄²	C₂²×Dic₄₃	1	2	yes	—
334	C₄²	C₂²×Dic₄₃	1	2	yes	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	C₂×C₄⋊Dic₄₃	1	2	yes	—
340	C₂³	#13063353	1	2	yes	—
341	C₂³	#13063358	1	2	yes	—
342	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	344	8	no	—
356	C₂×C₄	—	172	1	no	—
357	C₂×C₄	—	172	1	no	—
358	C₂×C₄	—	172	1	no	—
359	C₂×C₄	—	172	1	no	—
360	C₂×C₄	—	172	4	no	—
361	C₂×C₄	—	172	4	no	—
362	C₂×C₄	—	172	1	no	—
363	C₂×C₄	—	172	1	no	—
364	C₂×C₄	—	172	1	no	—
365	C₂×C₄	—	172	1	no	—
366	C₂×C₄	—	172	4	no	—
367	C₂×C₄	—	172	1	no	—
368	C₂×C₄	—	172	1	no	—
369	C₂×C₄	—	172	1	no	—
370	C₂×C₄	—	172	1	no	—
371	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
372	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
373	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
374	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
375	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
376	C₂×C₄	#13063353	1	2	yes	—
377	C₂×C₄	#13063358	1	2	yes	—
378	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
379	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
380	C₂×C₄	#13063371	1	2	yes	—
381	C₂×C₄	#13063372	1	2	yes	—
382	C₈	—	2	8	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	#14582941	1	4	yes	—
390	C₂²	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
391	C₂²	#14583468	1	1	yes	characteristic
392	C₂²	#14583475	1	1	yes	characteristic
393	C₂²	C₂×#13063353	1	1	yes	characteristic
394	C₂²	C₂×#13063353	1	1	yes	characteristic
395	C₂²	C₂×#13063358	1	1	yes	characteristic
396	C₂²	C₂×#13063358	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	344	1	no	—
402	C₄	—	344	1	no	—
403	C₄	—	344	4	no	—
404	C₄	—	344	1	no	—
405	C₄	—	344	1	no	—
406	C₄	#14582941	1	4	yes	—
407	C₄	#14583382	1	2	yes	—
408	C₄	#14583527	1	2	yes	—
409	C₂	—	2	4	no	—
410	C₂	#19137218	1	1	yes	characteristic
411	C₂	C₂×#14582941	1	1	yes	characteristic
412	C₂	C₂×#14582941	1	1	yes	characteristic
413	C₂	#19145615	1	1	yes	characteristic
414	C₂	#19145624	1	1	yes	characteristic
415	C₂	#19145818	1	1	yes	characteristic
416	C₂	#19145827	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#432	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#432	D₄₃
hypocenter	C₄₃	#21987
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#432

Complements

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

N	H ≅ G/N	type
3. #19135359	C₂	semidirect
4. #19135354	C₂	semidirect
7. #19134763	C₂	semidirect
8. #19134729	C₂	semidirect
32. C₄₃×#432	C₄	semidirect
74. C₄⋊C₈×C₄₃	C₂×C₄	semidirect
76. #97×C₄₃	C₂×C₄	semidirect
222. #432	Dic₄₃	semidirect
244. C₄₃	#21987	semidirect
275. C₄⋊C₈	C₂×Dic₄₃	semidirect
277. #97	C₂×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582769	2
#19136993	2
#19135359	2
#19135354	2
#19134790	2
#19134785	2
#19134763	2
#19134729	2
C₂×C₄₃×#432	2
#21987	43