Subgroups — #25114823

Order 11008.

978 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582978	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582940	C₂	1	2	yes	maximal, complemented
3	#19137527	C₂	1	2	yes	maximal
4	#19135363	C₂	1	2	yes	maximal, complemented
5	#19134797	C₂	1	2	yes	maximal, complemented
6	#19134784	C₂	1	2	yes	maximal, complemented
7	#19134759	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134629	C₂	1	2	yes	maximal, complemented
9	C₄×#107×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#10621872	C₂²	1	2	yes	—
11	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
12	C₂×#13063283	C₂²	1	2	yes	—
13	C₂×C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
14	#14582978	C₄	1	8	yes	complemented
15	#14582940	—	2	8	no	—
16	C₂×#13063259	C₂²	1	1	yes	characteristic
17	C₂×#13063259	C₂²	1	1	yes	characteristic
18	C₂×#13063258	C₂²	1	2	yes	—
19	C₂×#13063257	C₂²	1	2	yes	—
20	C₂×#13063256	C₂²	1	2	yes	—
21	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
23	#14582790	—	2	2	no	—
24	#14582784	—	2	2	no	—
25	#14582777	—	2	2	no	—
26	#14582765	C₂²	1	2	yes	—
27	#14582756	C₂²	1	2	yes	—
28	#14582756	C₂²	1	2	yes	—
29	C₄×(C₂×D₄₃)⋊C₄	—	2	2	no	—
30	#14582661	C₂²	1	2	yes	—
31	#14582661	C₂²	1	2	yes	—
32	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
38	C₂²×C₄×D₄₃	—	2	2	no	—
39	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
40	C₂×#10621872	—	2	4	no	—
41	C₂×#10621872	—	2	4	no	—
42	C₂×#10621872	C₂×C₄	1	8	yes	complemented
43	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
44	C₄×D₁₇₂	C₂×C₄	1	4	yes	—
45	C₄×D₁₇₂	Q₈	1	4	yes	—
46	#13063283	—	2	4	no	—
47	#13063283	—	4	2	no	—
48	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
51	C₂×Dic₄₃⋊C₄	—	2	2	no	—
52	C₄⋊C₄×D₄₃	—	2	4	no	—
53	C₄⋊C₄×D₄₃	—	4	2	no	—
54	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
55	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
56	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
57	C₂×(C₂×D₄₃)⋊C₄	D₄	1	2	yes	—
58	C₂×C₄×Dic₄₃	—	2	2	no	—
59	#13063259	—	4	1	no	—
60	#13063259	—	4	1	no	—
61	#13063258	—	2	4	no	—
62	#13063257	—	2	4	no	—
63	#13063256	—	2	4	no	—
64	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	complemented
65	(C₂×D₄₃)⋊C₈	C₂×C₄	1	8	yes	complemented
66	C₄₃⋊#95	—	2	2	no	—
67	C₄₃⋊#95	—	2	2	no	—
68	C₄₃⋊#95	—	2	2	no	—
69	C₄₃⋊#95	—	2	2	no	—
70	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₃	—	2	2	no	—
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	#107×C₄₃	—	2	2	no	—
77	#107×C₄₃	D₄	1	4	yes	complemented
78	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
79	#95×C₄₃	—	2	2	no	—
80	C₂³×D₄₃	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
86	C₂²×Dic₄₃	—	2	2	no	—
87	C₂²×Dic₄₃	—	2	2	no	—
88	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
89	C₂×D₁₇₂	—	4	1	no	—
90	C₂×D₁₇₂	—	4	1	no	—
91	C₂×D₁₇₂	C₄⋊C₄	1	4	yes	—
92	C₂×C₄×D₄₃	—	2	2	no	—
93	C₂×C₄×D₄₃	—	2	2	no	—
94	C₂×C₄×D₄₃	—	2	2	no	—
95	C₂×C₄×D₄₃	—	2	2	no	—
96	C₂×C₄×D₄₃	—	4	4	no	—
97	C₂×C₄×D₄₃	—	4	4	no	—
98	C₂×C₄×D₄₃	—	8	2	no	—
99	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
100	C₂×C₄×D₄₃	C₂×Q₈	1	4	yes	—
101	C₂×C₈×C₄₃	—	2	1	no	—
102	C₂×C₈×C₄₃	—	2	1	no	—
103	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₄₃	#41	1	2	yes	—
107	C₄⋊C₄×C₄₃	—	2	2	no	—
108	C₄⋊C₄×C₄₃	—	2	2	no	—
109	C₄⋊C₄×C₄₃	—	2	2	no	—
110	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
111	C₄²×C₄₃	—	8	2	no	—
112	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
113	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
114	(C₂×D₄₃)⋊C₄	—	4	4	no	—
115	(C₂×D₄₃)⋊C₄	—	4	4	no	—
116	(C₂×D₄₃)⋊C₄	—	8	2	no	—
117	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	8	yes	—
118	C₄⋊Dic₄₃	—	2	2	no	—
119	C₄⋊Dic₄₃	—	2	2	no	—
120	C₄⋊Dic₄₃	—	2	2	no	—
121	C₄⋊Dic₄₃	—	2	2	no	—
122	C₄⋊Dic₄₃	C₄⋊C₄	1	4	yes	—
123	Dic₄₃⋊C₄	—	4	4	no	—
124	C₄×Dic₄₃	—	4	4	no	—
125	C₂×C₄₃⋊C₈	—	2	2	no	—
126	C₂×C₄₃⋊C₈	—	2	2	no	—
127	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
128	#10621872	—	2	16	no	—
129	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
130	C₂²×D₄₃	—	2	2	no	—
131	C₂²×D₄₃	—	2	2	no	—
132	C₂²×D₄₃	—	2	2	no	—
133	C₂²×D₄₃	—	2	2	no	—
134	C₂²×D₄₃	—	2	2	no	—
135	C₂²×D₄₃	—	2	2	no	—
136	C₂²×D₄₃	C₂×C₄⋊C₄	1	4	yes	—
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	4	no	—
142	C₂×C₄×C₄₃	—	4	2	no	—
143	C₂×C₄×C₄₃	—	4	2	no	—
144	C₂×C₄×C₄₃	—	4	2	no	—
145	C₂×C₄×C₄₃	—	4	2	no	—
146	C₂×C₄×C₄₃	—	4	2	no	—
147	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×Dic₄₃	—	2	2	no	—
156	C₂×Dic₄₃	—	2	2	no	—
157	C₂×Dic₄₃	—	4	2	no	—
158	C₂×Dic₄₃	—	4	2	no	—
159	C₂×Dic₄₃	—	4	2	no	—
160	C₂×Dic₄₃	—	4	2	no	—
161	C₂×Dic₄₃	—	4	2	no	—
162	C₂×Dic₄₃	—	4	2	no	—
163	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
164	D₁₇₂	—	4	4	no	—
165	C₄×D₄₃	—	2	4	no	—
166	C₄×D₄₃	—	2	4	no	—
167	C₄×D₄₃	—	2	4	no	—
168	C₄×D₄₃	—	2	4	no	—
169	C₄×D₄₃	—	8	8	no	—
170	C₈×C₄₃	—	2	2	no	—
171	C₈×C₄₃	C₄×D₄	1	4	yes	—
172	C₄₃⋊C₈	—	2	4	no	—
173	#22664	—	43	1	no	maximal, Sylow
174	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
175	C₂²×C₄₃	D₄²	1	1	yes	characteristic
176	C₂²×C₄₃	#547	1	1	yes	characteristic
177	C₂²×C₄₃	#575	1	1	yes	characteristic
178	C₂²×C₄₃	#575	1	1	yes	characteristic
179	C₂²×C₄₃	#576	1	1	yes	characteristic
180	C₂²×C₄₃	#578	1	1	yes	characteristic
181	C₂×D₄₃	—	2	4	no	—
182	C₂×D₄₃	—	2	4	no	—
183	C₂×D₄₃	—	2	4	no	—
184	C₂×D₄₃	—	4	2	no	—
185	C₂×D₄₃	—	4	2	no	—
186	C₂×D₄₃	—	4	2	no	—
187	C₂×D₄₃	—	4	2	no	—
188	C₄×C₄₃	—	2	2	no	—
189	C₄×C₄₃	—	2	2	no	—
190	C₄×C₄₃	—	4	4	no	—
191	C₄×C₄₃	—	8	2	no	—
192	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₄₃	#520	1	1	yes	characteristic
194	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
195	C₄×C₄₃	#554	1	1	yes	characteristic
196	Dic₄₃	—	2	4	no	—
197	Dic₄₃	—	8	2	no	—
198	Dic₄₃	—	8	2	no	—
199	C₂×#436	—	43	1	no	—
200	C₂×#428	—	43	2	no	—
201	#2352	—	43	2	no	—
202	#1949	—	43	2	no	—
203	#1854	—	43	2	no	—
204	#1852	—	43	2	no	—
205	#1846	—	43	1	no	—
206	#1809	—	43	2	no	—
207	C₄×#107	D₄₃	1	1	yes	characteristic, complemented
208	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄₃	#2911	1	1	yes	characteristic
210	C₂×C₄₃	#2913	1	1	yes	characteristic
211	C₂×C₄₃	#3273	1	1	yes	characteristic
212	C₂×C₄₃	#3277	1	1	yes	characteristic
213	C₂×C₄₃	#3352	1	1	yes	characteristic
214	C₂×C₄₃	#3355	1	1	yes	characteristic
215	D₄₃	—	4	4	no	—
216	C₂²×M₁₆	—	43	2	no	—
217	C₂×C₄×D₄	—	43	1	no	—
218	C₂×#117	—	43	2	no	—
219	C₂²×C₄⋊C₄	—	43	2	no	—
220	#436	—	43	8	no	—
221	#428	—	86	8	no	—
222	C₂×#107	—	43	2	no	—
223	C₂×#107	—	43	1	no	—
224	C₂×#107	—	43	1	no	—
225	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
226	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
227	C₂×#106	—	43	2	no	—
228	C₂×#106	—	43	2	no	—
229	C₂×C₄⋊C₈	—	43	1	no	—
230	C₂×C₂²⋊C₈	—	43	2	no	—
231	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
232	#388	—	86	2	no	—
233	#387	—	86	2	no	—
234	#386	—	86	2	no	—
235	#382	—	43	2	no	—
236	#380	—	43	2	no	—
237	#380	—	43	2	no	—
238	C₄×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
239	C₄×C₂²⋊C₄	—	86	2	no	—
240	#340	—	43	2	no	—
241	#340	—	43	2	no	—
242	#340	C₂×D₄₃	1	2	yes	—
243	C₄₃	#22664	1	1	yes	characteristic, complemented, Sylow
244	C₂²×D₄	—	43	1	no	—
245	C₂³×C₄	—	43	2	no	—
246	C₂³×C₄	—	86	2	no	—
247	C₂×M₁₆	—	43	8	no	—
248	C₂×M₁₆	—	86	4	no	—
249	C₂×M₁₆	—	86	4	no	—
250	C₂²×C₈	—	43	2	no	—
251	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
252	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
253	C₄×D₄	—	43	4	no	—
254	C₄×D₄	—	43	4	no	—
255	#117	—	86	4	no	—
256	#117	—	172	2	no	—
257	C₂×C₄⋊C₄	—	43	1	no	—
258	C₂×C₄⋊C₄	—	43	2	no	—
259	C₂×C₄⋊C₄	—	43	2	no	—
260	C₂×C₄⋊C₄	—	86	4	no	—
261	C₂×C₄⋊C₄	—	86	2	no	—
262	C₂×C₄⋊C₄	—	172	2	no	—
263	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
264	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
265	C₂×C₂²⋊C₄	—	43	2	no	—
266	C₂×C₂²⋊C₄	—	86	2	no	—
267	C₂×C₂²⋊C₄	—	86	2	no	—
268	C₂×C₂²⋊C₄	—	86	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	86	2	no	—
271	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
272	#107	—	2	2	no	—
273	#107	—	86	4	no	—
274	#107	—	172	1	no	—
275	#107	—	172	1	no	—
276	#107	D₁₇₂	1	4	yes	complemented
277	#106	—	86	4	no	—
278	#106	—	86	4	no	—
279	C₄⋊C₈	—	43	4	no	—
280	C₂²⋊C₈	—	43	8	no	—
281	C₄×C₈	C₄×D₄₃	1	4	yes	complemented
282	#95	—	2	2	no	—
283	#95	—	86	2	no	—
284	#95	—	86	2	no	—
285	#95	—	86	2	no	—
286	#95	—	86	2	no	—
287	C₂⁴	—	43	2	no	—
288	C₂×D₄	—	43	4	no	—
289	C₂×D₄	—	172	1	no	—
290	C₂×D₄	—	172	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	43	2	no	—
294	C₂²×C₄	—	43	4	no	—
295	C₂²×C₄	—	43	4	no	—
296	C₂²×C₄	—	86	2	no	—
297	C₂²×C₄	—	86	2	no	—
298	C₂²×C₄	—	86	2	no	—
299	C₂²×C₄	—	86	2	no	—
300	C₂²×C₄	—	86	2	no	—
301	C₂²×C₄	—	86	2	no	—
302	C₂²×C₄	—	344	2	no	—
303	C₂²×C₄	—	172	4	no	—
304	C₂²×C₄	—	172	4	no	—
305	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
306	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
307	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
308	M₁₆	—	86	16	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	43	4	no	—
312	C₂×C₈	—	86	2	no	—
313	C₂×C₈	—	86	2	no	—
314	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
315	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
316	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
317	C₂×C₈	#10621898	1	2	yes	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	43	4	no	—
322	C₄⋊C₄	—	86	2	no	—
323	C₄⋊C₄	—	86	2	no	—
324	C₄⋊C₄	—	86	2	no	—
325	C₄⋊C₄	—	86	2	no	—
326	C₄⋊C₄	—	172	4	no	—
327	C₄⋊C₄	C₂×D₁₇₂	1	4	yes	—
328	C₂²⋊C₄	—	43	8	no	—
329	C₂²⋊C₄	—	344	2	no	—
330	C₂²⋊C₄	—	172	4	no	—
331	C₂²⋊C₄	—	172	4	no	—
332	C₄²	—	8	2	no	—
333	C₄²	—	172	4	no	—
334	C₄²	C₂×C₄×D₄₃	1	2	yes	—
335	C₄²	Q₈×D₄₃	1	2	yes	—
336	C₂³	—	43	4	no	—
337	C₂³	—	86	2	no	—
338	C₂³	—	86	2	no	—
339	C₂³	—	86	2	no	—
340	C₂³	—	86	2	no	—
341	C₂³	—	86	2	no	—
342	C₂³	—	86	2	no	—
343	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
344	D₄	—	172	4	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	4	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	43	4	no	—
356	C₂×C₄	—	86	2	no	—
357	C₂×C₄	—	86	2	no	—
358	C₂×C₄	—	86	4	no	—
359	C₂×C₄	—	86	4	no	—
360	C₂×C₄	—	86	4	no	—
361	C₂×C₄	—	86	4	no	—
362	C₂×C₄	—	344	8	no	—
363	C₂×C₄	—	172	2	no	—
364	C₂×C₄	—	172	2	no	—
365	C₂×C₄	—	172	2	no	—
366	C₂×C₄	—	172	2	no	—
367	C₂×C₄	—	172	2	no	—
368	C₂×C₄	—	172	2	no	—
369	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
370	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
371	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
373	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
374	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
375	C₂×C₄	#13063371	1	1	yes	characteristic
376	C₂×C₄	#13063372	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	86	4	no	—
379	C₈	C₄×D₁₇₂	1	4	yes	—
380	C₂²	—	86	4	no	—
381	C₂²	—	86	4	no	—
382	C₂²	—	86	4	no	—
383	C₂²	—	172	2	no	—
384	C₂²	—	172	2	no	—
385	C₂²	—	172	2	no	—
386	C₂²	—	172	2	no	—
387	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
388	C₂²	D₄×D₁₇₂	1	1	yes	characteristic
389	C₂²	#14583554	1	1	yes	characteristic
390	C₂²	#14583696	1	1	yes	characteristic
391	C₂²	#14583696	1	1	yes	characteristic
392	C₂²	#14583700	1	1	yes	characteristic
393	C₂²	#14583712	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	4	4	no	—
397	C₄	—	8	2	no	—
398	C₄	—	86	4	no	—
399	C₄	—	344	2	no	—
400	C₄	—	344	2	no	—
401	C₄	C₂×C₄×D₁₇₂	1	1	yes	characteristic
402	C₄	#14583379	1	1	yes	characteristic
403	C₄	Q₈×D₁₇₂	1	1	yes	characteristic
404	C₄	#14583609	1	1	yes	characteristic
405	C₂	—	172	4	no	—
406	C₂	C₄⋊C₄×D₁₇₂	1	1	yes	characteristic
407	C₂	#19143183	1	1	yes	characteristic
408	C₂	#19143191	1	1	yes	characteristic
409	C₂	#19146205	1	1	yes	characteristic
410	C₂	#19146251	1	1	yes	characteristic
411	C₂	#19147171	1	1	yes	characteristic
412	C₂	#19147202	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#107×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₁₇₂	D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#107	D₄₃
hypocenter	C₄₃	#22664
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
2. C₂×#14582940	C₂	semidirect
4. #19135363	C₂	semidirect
5. #19134797	C₂	semidirect
6. #19134784	C₂	semidirect
7. #19134759	C₂	semidirect
8. #19134629	C₂	semidirect
9. C₄×#107×C₄₃	C₂	semidirect
14. #14582978	C₄	semidirect
42. C₂×#10621872	C₂×C₄	semidirect
64. C₄⋊(C₄₃⋊C₈)	C₂×C₄	semidirect
65. (C₂×D₄₃)⋊C₈	C₂×C₄	semidirect
77. #107×C₄₃	D₄	semidirect
78. C₄×C₈×C₄₃	C₂×C₄	semidirect
207. C₄×#107	D₄₃	semidirect
243. C₄₃	#22664	semidirect
276. #107	D₁₇₂	semidirect
281. C₄×C₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582978	2
C₂×#14582940	2
#19137527	2
#19135363	2
#19134797	2
#19134784	2
#19134759	2
#19134629	2
C₄×#107×C₄₃	2
#22664	43