Subgroups — C₄×#14583704 #25960820

Order 11008.

2826 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	C₂×#14583704	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063371	C₂	1	2	yes	maximal, complemented
3	#19143472	C₂	1	3	yes	maximal, complemented
4	#19143448	C₂	1	3	yes	maximal, complemented
5	#19143429	C₂	1	6	yes	maximal, complemented
6	C₄×#13063353	C₂	1	6	yes	maximal, complemented
7	C₄×#13063347	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×D₃₄₄	C₂	1	3	yes	maximal, complemented
9	#19143195	C₂	1	1	yes	maximal, characteristic, complemented
10	#19143122	C₂	1	2	yes	maximal, complemented
11	C₄×#131×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063371	C₂²	1	2	yes	—
13	#14583704	C₄	1	16	yes	direct product factor
14	C₂×#13063353	C₂²	1	6	yes	—
15	C₂×#13063347	C₂²	1	3	yes	—
16	C₂²×D₃₄₄	C₂²	1	3	yes	—
17	#14583382	C₂²	1	2	yes	—
18	#14583381	—	2	2	no	—
19	#14583379	C₂²	1	6	yes	complemented
20	#14583373	C₂²	1	6	yes	complemented
21	#14583371	—	2	6	no	—
22	C₄×#10621902	—	2	2	no	—
23	C₄×#10621898	C₂²	1	6	yes	complemented
24	C₂×C₄×D₁₇₂	C₂²	1	6	yes	complemented
25	C₄×D₄×D₄₃	—	2	6	no	—
26	#14583012	C₂²	1	12	yes	complemented
27	#14583001	C₂²	1	12	yes	complemented
28	C₄×Dic₁₇₂	C₂²	1	3	yes	complemented
29	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
30	C₄×#10621873	C₂²	1	6	yes	complemented
31	C₄×#10621873	C₂²	1	6	yes	complemented
32	C₄×D₃₄₄	C₂²	1	6	yes	complemented
33	C₄×D₃₄₄	C₂²	1	3	yes	complemented
34	C₄×D₃₄₄	C₂²	1	6	yes	complemented
35	C₄×D₃₄₄	C₂²	1	3	yes	complemented
36	C₄×D₃₄₄	C₂²	1	6	yes	complemented
37	#14582941	C₂²	1	6	yes	complemented
38	#14582937	C₂²	1	3	yes	complemented
39	C₂×#13063259	C₂²	1	3	yes	complemented
40	#14582905	C₂²	1	6	yes	complemented
41	#14582901	C₂²	1	6	yes	complemented
42	#14582896	C₂²	1	6	yes	complemented
43	C₂×#13063247	C₂²	1	6	yes	complemented
44	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
46	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#405	C₂²	1	3	yes	complemented
48	C₄₃×#405	C₂²	1	3	yes	complemented
49	C₄×M₁₆×C₄₃	C₂²	1	3	yes	complemented
50	C₂×C₄×C₈×C₄₃	C₂²	1	3	yes	complemented
51	#13063371	—	2	8	no	—
52	#13063371	C₂×C₄	1	16	yes	complemented
53	C₂×#10621902	—	2	2	no	—
54	C₂×#10621898	C₂³	1	6	yes	—
55	C₂²×D₁₇₂	C₂³	1	6	yes	—
56	C₂×D₄×D₄₃	—	2	6	no	—
57	C₂²×C₄×D₄₃	—	2	6	no	—
58	#13063353	C₂×C₄	1	48	yes	complemented
59	#13063347	C₂×C₄	1	24	yes	complemented
60	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
61	C₂×#10621873	C₂³	1	6	yes	—
62	C₂×D₃₄₄	C₂×C₄	1	24	yes	complemented
63	C₂×D₃₄₄	C₂³	1	3	yes	—
64	C₂×D₃₄₄	C₂³	1	6	yes	—
65	Q₈×Dic₄₃	—	2	2	no	—
66	C₄×Dic₈₆	C₂³	1	2	yes	—
67	C₄×Dic₈₆	C₂³	1	6	yes	—
68	C₄×D₁₇₂	—	2	6	no	—
69	C₄×D₁₇₂	—	2	6	no	—
70	C₄×D₁₇₂	C₂³	1	6	yes	—
71	C₄×D₁₇₂	C₂³	1	12	yes	—
72	C₄×D₁₇₂	C₂³	1	6	yes	—
73	D₄×Dic₄₃	—	2	6	no	—
74	#13063287	—	2	6	no	—
75	#13063287	—	2	6	no	—
76	C₄×C₂²⋊D₄₃	—	2	6	no	—
77	C₄×C₂²⋊D₄₃	—	2	6	no	—
78	(C₂²⋊D₄₃)⋊C₄	—	2	12	no	—
79	#13063284	C₂³	1	6	yes	—
80	#13063283	—	2	6	no	—
81	#13063282	—	2	6	no	—
82	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
83	C₄⋊C₄×D₄₃	—	2	6	no	—
84	C₂×(C₂×D₄₃)⋊C₄	—	2	6	no	—
85	C₂²⋊C₄×D₄₃	—	2	12	no	—
86	C₄²×D₄₃	—	2	6	no	—
87	#13063259	C₂³	1	3	yes	—
88	#13063259	C₂³	1	6	yes	—
89	#13063259	C₂³	1	1	yes	characteristic
90	#13063257	C₂³	1	6	yes	—
91	#13063250	C₂³	1	2	yes	—
92	#13063250	C₂³	1	6	yes	—
93	#13063247	C₂³	1	6	yes	—
94	#13063247	C₂³	1	12	yes	—
95	#13063247	C₂³	1	6	yes	—
96	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
97	#131×C₄₃	—	2	4	no	—
98	#131×C₄₃	C₂×C₄	1	8	yes	complemented
99	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
100	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
101	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
102	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
103	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
104	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
105	C₄×D₄×C₄₃	D₄	1	3	yes	—
106	C₄×D₄×C₄₃	D₄	1	3	yes	—
107	#117×C₄₃	C₂³	1	3	yes	—
108	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
109	#97×C₄₃	C₂³	1	6	yes	—
110	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₄₃	C₂³	1	3	yes	—
112	C₄×C₈×C₄₃	C₂³	1	3	yes	—
113	C₄×C₈×C₄₃	C₂³	1	3	yes	—
114	C₂³×D₄₃	—	2	6	no	—
115	#41×C₄₃	C₂²×C₄	1	4	yes	—
116	#41×C₄₃	#41	1	4	yes	—
117	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂×D₄×C₄₃	C₂×D₄	1	3	yes	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
121	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
122	C₂×C₂²⋊D₄₃	—	2	6	no	—
123	C₂²×Dic₄₃	—	2	6	no	—
124	#10621902	—	2	16	no	—
125	D₄×D₄₃	—	2	48	no	—
126	#10621898	—	2	12	no	—
127	#10621898	C₂²×C₄	1	24	yes	complemented
128	C₂×D₁₇₂	—	2	6	no	—
129	C₂×D₁₇₂	—	2	12	no	—
130	C₂×D₁₇₂	C₂²×C₄	1	24	yes	complemented
131	C₂×D₁₇₂	C₂⁴	1	6	yes	—
132	C₂×C₄×D₄₃	—	2	6	no	—
133	C₂×C₄×D₄₃	—	2	6	no	—
134	C₂×C₄×D₄₃	—	2	6	no	—
135	C₂×C₄×D₄₃	—	2	12	no	—
136	C₂×C₄×D₄₃	—	8	12	no	—
137	C₂×Dic₈₆	C₂⁴	1	2	yes	—
138	M₁₆×C₄₃	—	2	6	no	—
139	M₁₆×C₄₃	C₂²×C₄	1	12	yes	complemented
140	C₂×C₈×C₄₃	—	2	6	no	—
141	C₂×C₈×C₄₃	C₂²×C₄	1	12	yes	complemented
142	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
143	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
144	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
145	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
146	C₄⋊C₄×C₄₃	C₂×D₄	1	3	yes	—
147	C₄⋊C₄×C₄₃	C₂×D₄	1	3	yes	—
148	C₂²⋊C₄×C₄₃	C₂×D₄	1	6	yes	—
149	C₄²×C₄₃	C₂×D₄	1	3	yes	—
150	C₄²×C₄₃	C₂×D₄	1	3	yes	—
151	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
152	C₄²×C₄₃	C₂⁴	1	3	yes	—
153	C₂²⋊Dic₄₃	—	2	6	no	—
154	(C₂×D₄₃)⋊C₄	—	2	6	no	—
155	(C₂×D₄₃)⋊C₄	—	2	12	no	—
156	(C₂×D₄₃)⋊C₄	—	2	6	no	—
157	C₄⋊Dic₄₃	—	2	6	no	—
158	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
159	C₄⋊Dic₄₃	C₂⁴	1	6	yes	—
160	Dic₄₃⋊C₄	—	2	6	no	—
161	Dic₄₃⋊C₄	—	2	2	no	—
162	C₄×Dic₄₃	—	2	2	no	—
163	C₄×Dic₄₃	—	2	6	no	—
164	C₄×Dic₄₃	—	2	6	no	—
165	Dic₁₇₂	C₂²×C₄	1	4	yes	complemented
166	D₃₄₄	C₂²×C₄	1	12	yes	complemented
167	D₃₄₄	C₂²×C₄	1	24	yes	complemented
168	#10621873	C₂²×C₄	1	24	yes	complemented
169	C₂³×C₄₃	C₂²×D₄	1	3	yes	—
170	C₂²×D₄₃	—	2	6	no	—
171	C₂²×D₄₃	—	2	24	no	—
172	C₂²×D₄₃	—	8	6	no	—
173	C₂²×D₄₃	—	8	6	no	—
174	Q₈×C₄₃	C₄×D₄	1	4	yes	—
175	D₄×C₄₃	C₄×D₄	1	12	yes	—
176	C₂×C₄×C₄₃	—	2	6	no	—
177	C₂×C₄×C₄₃	—	4	3	no	—
178	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
179	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
180	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
182	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
183	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂×#41	1	6	yes	—
185	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
186	C₂²⋊D₄₃	—	2	24	no	—
187	C₂×Dic₄₃	—	2	2	no	—
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	6	no	—
190	C₂×Dic₄₃	—	8	6	no	—
191	D₁₇₂	—	2	24	no	—
192	D₁₇₂	—	2	6	no	—
193	D₁₇₂	C₂³×C₄	1	12	yes	—
194	C₄×D₄₃	—	2	24	no	—
195	C₄×D₄₃	—	4	12	no	—
196	C₄×D₄₃	—	8	6	no	—
197	C₄×D₄₃	—	8	12	no	—
198	Dic₈₆	—	2	2	no	—
199	Dic₈₆	C₂³×C₄	1	4	yes	—
200	C₈×C₄₃	—	2	1	no	—
201	C₈×C₄₃	—	2	3	no	—
202	C₈×C₄₃	C₂³×C₄	1	6	yes	—
203	C₈×C₄₃	C₂³×C₄	1	2	yes	—
204	C₄×#576	—	43	1	no	maximal, Sylow
205	C₂²×C₄₃	—	2	3	no	—
206	C₂²×C₄₃	—	2	3	no	—
207	C₂²×C₄₃	C₂×C₄×D₄	1	6	yes	—
208	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
209	C₂×D₄₃	—	2	12	no	—
210	C₂×D₄₃	—	4	6	no	—
211	C₂×D₄₃	—	4	6	no	—
212	C₂×D₄₃	—	8	24	no	—
213	C₄×C₄₃	—	2	3	no	—
214	C₄×C₄₃	—	2	1	no	—
215	C₄×C₄₃	—	2	3	no	—
216	C₄×C₄₃	C₂×C₄×D₄	1	6	yes	—
217	C₄×C₄₃	#576	1	2	yes	complemented
218	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
219	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
220	Dic₄₃	—	2	4	no	—
221	Dic₄₃	—	4	2	no	—
222	Dic₄₃	—	4	6	no	—
223	C₂×#576	—	43	1	no	—
224	C₄×H(5,𝔽₂)	—	43	2	no	—
225	#2951	—	43	3	no	—
226	#2948	—	43	3	no	—
227	#2946	—	43	6	no	—
228	C₄×AGL(1,ℤ/8)	—	43	6	no	—
229	C₄×#135	—	43	3	no	—
230	C₂×C₄×D₈	—	43	3	no	—
231	#2913	—	43	1	no	—
232	#2897	—	43	2	no	—
233	C₄×#131	D₄₃	1	1	yes	characteristic, complemented
234	C₂×C₄₃	—	2	6	no	—
235	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
236	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
237	C₂×C₄₃	#3584	1	1	yes	characteristic
238	D₄₃	—	4	12	no	—
239	C₂×H(5,𝔽₂)	—	43	2	no	—
240	#576	—	43	16	no	—
241	C₂×AGL(1,ℤ/8)	—	43	6	no	—
242	C₂×#135	—	43	3	no	—
243	C₂²×D₈	—	43	3	no	—
244	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
245	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
246	#520	—	43	2	no	—
247	#520	—	43	6	no	—
248	#520	—	86	2	no	—
249	#518	—	43	6	no	—
250	#518	—	86	6	no	—
251	C₄×#41	—	43	6	no	—
252	C₄×#41	—	86	2	no	—
253	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
254	C₂×C₄×D₄	—	43	6	no	—
255	C₂×C₄×D₄	—	86	6	no	—
256	#442	—	43	12	no	—
257	#440	—	43	12	no	—
258	C₄×Q₁₆	—	43	1	no	—
259	C₄×Q₁₆	—	43	3	no	—
260	C₄×SD₁₆	—	43	6	no	—
261	C₄×SD₁₆	—	43	6	no	—
262	C₄×D₈	—	43	3	no	—
263	C₄×D₈	—	43	6	no	—
264	C₄×D₈	—	43	6	no	—
265	C₄×D₈	—	43	6	no	—
266	C₄×D₈	—	43	3	no	—
267	#428	—	43	6	no	—
268	#427	—	43	3	no	—
269	C₂×#107	—	43	3	no	—
270	#418	—	43	6	no	—
271	#417	—	43	6	no	—
272	#416	—	43	6	no	—
273	C₂×#102	—	43	6	no	—
274	#405	C₂×D₄₃	1	3	yes	complemented
275	#405	C₂×D₄₃	1	3	yes	complemented
276	C₄×M₁₆	C₂×D₄₃	1	3	yes	complemented
277	C₂×C₄×C₈	C₂×D₄₃	1	3	yes	complemented
278	C₄₃	C₄×#576	1	1	yes	characteristic, complemented, Sylow
279	H(5,𝔽₂)	—	43	16	no	—
280	H(5,𝔽₂)	—	86	8	no	—
281	C₂×#41	—	43	6	no	—
282	C₂×#41	—	86	2	no	—
283	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
284	C₂²×D₄	—	43	6	no	—
285	C₂²×D₄	—	86	6	no	—
286	C₂³×C₄	—	86	6	no	—
287	AGL(1,ℤ/8)	—	43	48	no	—
288	#135	—	43	24	no	—
289	C₂×Q₁₆	—	43	1	no	—
290	C₂×SD₁₆	—	43	6	no	—
291	C₂×D₈	—	43	24	no	—
292	C₂×D₈	—	43	3	no	—
293	C₂×D₈	—	43	6	no	—
294	#131	—	2	4	no	—
295	#131	C₄×D₄₃	1	8	yes	complemented
296	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
297	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
298	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
299	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
300	C₄×Q₈	—	43	2	no	—
301	C₄×Q₈	—	43	6	no	—
302	C₄×Q₈	—	86	2	no	—
303	C₄×Q₈	D₁₇₂	1	1	yes	characteristic
304	C₄×Q₈	D₁₇₂	1	1	yes	characteristic
305	C₄×D₄	—	43	6	no	—
306	C₄×D₄	—	43	12	no	—
307	C₄×D₄	—	43	6	no	—
308	C₄×D₄	—	86	6	no	—
309	C₄×D₄	—	86	6	no	—
310	C₄×D₄	—	86	6	no	—
311	C₄×D₄	—	86	6	no	—
312	C₄×D₄	—	86	6	no	—
313	C₄×D₄	—	86	12	no	—
314	C₄×D₄	—	86	6	no	—
315	C₄×D₄	—	86	6	no	—
316	C₄×D₄	D₁₇₂	1	3	yes	—
317	C₄×D₄	D₁₇₂	1	3	yes	—
318	#117	—	43	6	no	—
319	#117	—	86	6	no	—
320	#117	—	86	6	no	—
321	#117	C₂²×D₄₃	1	3	yes	—
322	C₂×C₄⋊C₄	—	43	6	no	—
323	C₂×C₄⋊C₄	—	86	6	no	—
324	C₂×C₂²⋊C₄	—	86	6	no	—
325	C₂×C₂²⋊C₄	—	86	12	no	—
326	C₂×C₄²	—	86	6	no	—
327	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
328	#107	—	43	3	no	—
329	#107	—	43	6	no	—
330	#107	—	43	1	no	—
331	#106	—	43	6	no	—
332	#103	—	43	2	no	—
333	#103	—	43	6	no	—
334	#102	—	43	6	no	—
335	#102	—	43	12	no	—
336	#102	—	43	6	no	—
337	#97	C₂²×D₄₃	1	6	yes	—
338	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
339	C₄×C₈	C₂²×D₄₃	1	3	yes	—
340	C₄×C₈	C₂²×D₄₃	1	3	yes	—
341	C₄×C₈	C₂²×D₄₃	1	3	yes	—
342	C₂⁴	—	86	6	no	—
343	#41	—	43	24	no	—
344	#41	—	86	16	no	—
345	#41	—	86	12	no	—
346	#41	C₂×C₄×D₄₃	1	4	yes	—
347	#41	#10621898	1	4	yes	—
348	C₂×Q₈	—	43	2	no	—
349	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
350	C₂×D₄	—	43	24	no	—
351	C₂×D₄	—	43	6	no	—
352	C₂×D₄	—	86	6	no	—
353	C₂×D₄	—	86	48	no	—
354	C₂×D₄	—	86	6	no	—
355	C₂×D₄	—	86	12	no	—
356	C₂×D₄	C₂×D₁₇₂	1	3	yes	—
357	C₂²×C₄	—	86	6	no	—
358	C₂²×C₄	—	86	6	no	—
359	C₂²×C₄	—	86	6	no	—
360	C₂²×C₄	—	86	12	no	—
361	C₂²×C₄	—	86	6	no	—
362	C₂²×C₄	—	344	12	no	—
363	C₂²×C₄	C₂×D₁₇₂	1	3	yes	—
364	C₂²×C₄	C₂×D₁₇₂	1	3	yes	—
365	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
366	Q₁₆	—	43	4	no	—
367	SD₁₆	—	43	24	no	—
368	D₈	—	43	12	no	—
369	D₈	—	43	24	no	—
370	M₁₆	—	2	6	no	—
371	M₁₆	C₂×C₄×D₄₃	1	12	yes	complemented
372	C₂×C₈	—	2	6	no	—
373	C₂×C₈	C₂×C₄×D₄₃	1	12	yes	complemented
374	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
375	C₂×C₈	C₂³×D₄₃	1	3	yes	—
376	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
377	C₂×C₈	C₂³×D₄₃	1	3	yes	—
378	C₄⋊C₄	—	43	2	no	—
379	C₄⋊C₄	—	43	6	no	—
380	C₄⋊C₄	—	86	6	no	—
381	C₄⋊C₄	—	86	6	no	—
382	C₄⋊C₄	—	86	2	no	—
383	C₄⋊C₄	C₂×D₁₇₂	1	3	yes	—
384	C₄⋊C₄	C₂×D₁₇₂	1	3	yes	—
385	C₂²⋊C₄	—	86	6	no	—
386	C₂²⋊C₄	—	86	6	no	—
387	C₂²⋊C₄	—	86	12	no	—
388	C₂²⋊C₄	—	86	6	no	—
389	C₂²⋊C₄	C₂×D₁₇₂	1	6	yes	—
390	C₄²	—	86	6	no	—
391	C₄²	—	86	6	no	—
392	C₄²	—	86	2	no	—
393	C₄²	C₂×D₁₇₂	1	3	yes	—
394	C₄²	C₂×D₁₇₂	1	3	yes	—
395	C₄²	C₂³×D₄₃	1	3	yes	—
396	C₄²	C₂³×D₄₃	1	1	yes	characteristic
397	C₂³	—	86	24	no	—
398	C₂³	—	86	6	no	—
399	C₂³	—	344	6	no	—
400	C₂³	—	344	6	no	—
401	C₂³	C₂²×D₁₇₂	1	3	yes	—
402	Q₈	—	43	4	no	—
403	Q₈	—	86	2	no	—
404	Q₈	C₄×D₁₇₂	1	4	yes	—
405	D₄	—	43	12	no	—
406	D₄	—	86	24	no	—
407	D₄	—	86	24	no	—
408	D₄	—	86	6	no	—
409	D₄	C₄×D₁₇₂	1	12	yes	—
410	C₂×C₄	—	2	6	no	—
411	C₂×C₄	—	4	3	no	—
412	C₂×C₄	—	86	2	no	—
413	C₂×C₄	—	86	24	no	—
414	C₂×C₄	—	86	2	no	—
415	C₂×C₄	—	86	6	no	—
416	C₂×C₄	—	344	12	no	—
417	C₂×C₄	—	344	6	no	—
418	C₂×C₄	—	344	6	no	—
419	C₂×C₄	—	172	12	no	—
420	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
421	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
422	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
424	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
425	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
426	C₂×C₄	C₂×#10621898	1	6	yes	—
427	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	3	no	—
430	C₈	C₂²×C₄×D₄₃	1	2	yes	—
431	C₈	C₂²×C₄×D₄₃	1	6	yes	—
432	C₂²	—	2	3	no	—
433	C₂²	—	2	3	no	—
434	C₂²	—	86	12	no	—
435	C₂²	—	344	24	no	—
436	C₂²	—	172	6	no	—
437	C₂²	—	172	6	no	—
438	C₂²	C₂×C₄×D₁₇₂	1	6	yes	—
439	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
440	C₄	—	2	3	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	3	no	—
443	C₄	—	86	4	no	—
444	C₄	—	172	6	no	—
445	C₄	—	172	2	no	—
446	C₄	C₂×C₄×D₁₇₂	1	6	yes	—
447	C₄	#14583704	1	2	yes	direct product factor
448	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
449	C₄	C₂²×#10621898	1	1	yes	characteristic
450	C₂	—	2	6	no	—
451	C₂	—	172	12	no	—
452	C₂	C₂²×C₄×D₁₇₂	1	1	yes	characteristic
453	C₂	C₂×#14583704	1	1	yes	characteristic
454	C₂	#19149369	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#131×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂×#14583704	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₄×#131	D₄₃
hypocenter	C₄₃	C₄×#576
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
2. C₄×#13063371	C₂	semidirect
3. #19143472	C₂	semidirect
4. #19143448	C₂	semidirect
5. #19143429	C₂	semidirect
6. C₄×#13063353	C₂	semidirect
7. C₄×#13063347	C₂	semidirect
8. C₂×C₄×D₃₄₄	C₂	semidirect
9. #19143195	C₂	semidirect
10. #19143122	C₂	semidirect
11. C₄×#131×C₄₃	C₂	semidirect
13. #14583704	C₄	direct (N × H)
19. #14583379	C₂²	semidirect
20. #14583373	C₂²	semidirect
23. C₄×#10621898	C₂²	semidirect
24. C₂×C₄×D₁₇₂	C₂²	semidirect
26. #14583012	C₂²	semidirect
27. #14583001	C₂²	semidirect
28. C₄×Dic₁₇₂	C₂²	semidirect
29. C₄×Dic₁₇₂	C₂²	semidirect
30. C₄×#10621873	C₂²	semidirect
31. C₄×#10621873	C₂²	semidirect
32. C₄×D₃₄₄	C₂²	semidirect
33. C₄×D₃₄₄	C₂²	semidirect
34. C₄×D₃₄₄	C₂²	semidirect
35. C₄×D₃₄₄	C₂²	semidirect
36. C₄×D₃₄₄	C₂²	semidirect
37. #14582941	C₂²	semidirect
38. #14582937	C₂²	semidirect
39. C₂×#13063259	C₂²	semidirect
40. #14582905	C₂²	semidirect
41. #14582901	C₂²	semidirect
42. #14582896	C₂²	semidirect
43. C₂×#13063247	C₂²	semidirect
47. C₄₃×#405	C₂²	semidirect
48. C₄₃×#405	C₂²	semidirect
49. C₄×M₁₆×C₄₃	C₂²	semidirect
50. C₂×C₄×C₈×C₄₃	C₂²	semidirect
52. #13063371	C₂×C₄	semidirect
58. #13063353	C₂×C₄	semidirect
59. #13063347	C₂×C₄	semidirect
62. C₂×D₃₄₄	C₂×C₄	semidirect
98. #131×C₄₃	C₂×C₄	semidirect
127. #10621898	C₂²×C₄	semidirect
130. C₂×D₁₇₂	C₂²×C₄	semidirect
139. M₁₆×C₄₃	C₂²×C₄	semidirect
141. C₂×C₈×C₄₃	C₂²×C₄	semidirect
165. Dic₁₇₂	C₂²×C₄	semidirect
166. D₃₄₄	C₂²×C₄	semidirect
167. D₃₄₄	C₂²×C₄	semidirect
168. #10621873	C₂²×C₄	semidirect
217. C₄×C₄₃	#576	semidirect
233. C₄×#131	D₄₃	semidirect
274. #405	C₂×D₄₃	semidirect
275. #405	C₂×D₄₃	semidirect
276. C₄×M₁₆	C₂×D₄₃	semidirect
277. C₂×C₄×C₈	C₂×D₄₃	semidirect
278. C₄₃	C₄×#576	semidirect
295. #131	C₄×D₄₃	semidirect
371. M₁₆	C₂×C₄×D₄₃	semidirect
373. C₂×C₈	C₂×C₄×D₄₃	semidirect
447. C₄	#14583704	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#14583704	2
C₄×#13063371	2
#19143472	2
#19143448	2
#19143429	2
C₄×#13063353	2
C₄×#13063347	2
C₂×C₄×D₃₄₄	2
#19143195	2
#19143122	2
C₄×#131×C₄₃	2
C₄×#576	43

Subgroups — C4×#14583704 #25960820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#14583704 #25960820