Subgroups — C₂×#11927341 #14578379

Order 2432.

1484 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₉	C₂	1	2	yes	maximal, complemented
2	#11927341	C₂	1	16	yes	maximal, direct product factor
3	C₂×#10597364	C₂	1	2	yes	maximal, complemented
4	C₂×#10597361	C₂	1	2	yes	maximal, complemented
5	C₂×#10597360	C₂	1	2	yes	maximal, complemented
6	C₂×#10597357	C₂	1	2	yes	maximal, complemented
7	C₂×#10597350	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597396	C₂	1	2	yes	maximal, complemented
9	C₂²×#64515	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#41×C₁₉	C₂²	1	2	yes	complemented
12	#41×D₁₉	—	2	8	no	—
13	#41×D₁₉	C₂²	1	16	yes	complemented
14	C₂×#64545	C₂²	1	2	yes	—
15	C₂×Q₈×D₁₉	C₂²	1	2	yes	complemented
16	C₂×#64543	—	2	2	no	—
17	C₂×#64543	C₂²	1	2	yes	—
18	C₂×D₄×D₁₉	—	2	2	no	—
19	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
20	C₂×#64541	—	2	2	no	—
21	C₂×#64541	C₂²	1	2	yes	complemented
22	C₂²×C₄×D₁₉	—	2	2	no	—
23	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#135	C₂²	1	8	yes	complemented
25	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
27	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
29	#10597396	C₂²	1	16	yes	complemented
30	C₂×#64528	C₂²	1	2	yes	complemented
31	C₂×#64527	C₂²	1	2	yes	complemented
32	C₂×#64526	C₂²	1	2	yes	complemented
33	C₂×#64525	C₂²	1	2	yes	complemented
34	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	#10597364	C₂²	1	16	yes	complemented
36	#10597361	C₂²	1	16	yes	complemented
37	#10597360	C₂²	1	16	yes	complemented
38	#10597357	C₂²	1	16	yes	complemented
39	C₂×Dic₇₆	C₂²	1	1	yes	characteristic, complemented
40	#10597350	C₂²	1	8	yes	complemented
41	C₂×D₁₅₂	C₂²	1	1	yes	characteristic, complemented
42	C₂×#64516	C₂²	1	2	yes	complemented
43	C₂×#64515	C₂²	1	2	yes	complemented
44	C₂×#64515	C₂²	1	2	yes	complemented
45	C₂×#64515	C₂²	1	8	yes	complemented
46	C₂³×D₁₉	—	2	2	no	—
47	C₂³×D₁₉	D₄	1	1	yes	characteristic
48	#41×C₁₉	—	2	4	no	—
49	#41×C₁₉	C₂³	1	8	yes	complemented
50	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
51	C₂×D₄×C₁₉	—	2	2	no	—
52	C₂×D₄×C₁₉	C₂³	1	2	yes	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×C₂²⋊D₁₉	—	2	2	no	—
56	C₂×C₂²⋊D₁₉	—	2	2	no	—
57	C₂×C₂²⋊D₁₉	—	2	2	no	—
58	C₂²×Dic₁₉	—	2	2	no	—
59	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
60	#64545	—	2	4	no	—
61	#64545	C₂³	1	8	yes	—
62	Q₈×D₁₉	—	2	4	no	—
63	Q₈×D₁₉	C₂³	1	8	yes	complemented
64	#64543	—	2	16	no	—
65	#64543	—	2	4	no	—
66	#64543	C₂³	1	8	yes	—
67	D₄×D₁₉	—	2	16	no	—
68	D₄×D₁₉	—	2	4	no	—
69	D₄×D₁₉	C₂³	1	8	yes	complemented
70	#64541	—	2	4	no	—
71	#64541	—	2	16	no	—
72	#64541	C₂³	1	8	yes	complemented
73	C₂×D₇₆	—	2	2	no	—
74	C₂×D₇₆	C₂³	1	2	yes	—
75	C₂×C₄×D₁₉	—	2	2	no	—
76	C₂×C₄×D₁₉	—	2	2	no	—
77	C₂×C₄×D₁₉	—	2	2	no	—
78	C₂×C₄×D₁₉	—	2	16	no	—
79	C₂×C₄×D₁₉	D₄	1	2	yes	—
80	C₂×C₄×D₁₉	D₄	1	4	yes	—
81	C₂×C₄×D₁₉	C₂³	1	2	yes	—
82	C₂×C₄×D₁₉	C₂³	1	4	yes	—
83	C₂×Dic₃₈	—	2	2	no	—
84	C₂×Dic₃₈	C₂³	1	2	yes	—
85	Q₁₆×C₁₉	C₂³	1	4	yes	complemented
86	SD₁₆×C₁₉	C₂³	1	8	yes	complemented
87	D₈×C₁₉	C₂³	1	4	yes	complemented
88	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₈×C₁₉	C₂³	1	4	yes	complemented
91	#64528	C₂³	1	8	yes	complemented
92	#64527	C₂³	1	8	yes	complemented
93	#64526	C₂³	1	8	yes	complemented
94	#64525	C₂³	1	8	yes	complemented
95	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
96	C₂×C₁₉⋊C₈	C₂³	1	4	yes	complemented
97	Dic₇₆	C₂³	1	4	yes	complemented
98	D₁₅₂	C₂³	1	4	yes	complemented
99	#64516	C₂³	1	8	yes	complemented
100	#64515	C₂³	1	8	yes	complemented
101	#64515	C₂³	1	8	yes	complemented
102	C₂³×C₁₉	—	2	2	no	—
103	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×D₁₉	—	2	2	no	—
105	C₂²×D₁₉	—	2	8	no	—
106	C₂²×D₁₉	—	4	2	no	—
107	C₂²×D₁₉	—	4	8	no	—
108	C₂²×D₁₉	C₂×D₄	1	2	yes	—
109	C₂²×D₁₉	C₂×D₄	1	4	yes	—
110	Q₈×C₁₉	—	2	2	no	—
111	Q₈×C₁₉	C₂⁴	1	4	yes	—
112	D₄×C₁₉	—	2	8	no	—
113	D₄×C₁₉	—	2	2	no	—
114	D₄×C₁₉	C₂⁴	1	4	yes	—
115	C₂×C₄×C₁₉	—	2	2	no	—
116	C₂×C₄×C₁₉	—	2	8	no	—
117	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
120	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
121	C₂²⋊D₁₉	—	2	8	no	—
122	C₂²⋊D₁₉	—	2	8	no	—
123	C₂²⋊D₁₉	—	2	8	no	—
124	C₂×Dic₁₉	—	2	2	no	—
125	C₂×Dic₁₉	—	2	8	no	—
126	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
127	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
128	D₇₆	—	2	8	no	—
129	D₇₆	—	2	2	no	—
130	D₇₆	C₂⁴	1	4	yes	—
131	C₄×D₁₉	—	2	8	no	—
132	C₄×D₁₉	—	2	8	no	—
133	C₄×D₁₉	—	2	8	no	—
134	C₄×D₁₉	C₂×D₄	1	8	yes	—
135	C₄×D₁₉	C₂×D₄	1	4	yes	—
136	C₄×D₁₉	C₂⁴	1	4	yes	—
137	Dic₃₈	—	2	2	no	—
138	Dic₃₈	—	2	8	no	—
139	Dic₃₈	C₂⁴	1	4	yes	—
140	C₈×C₁₉	C₂⁴	1	2	yes	—
141	C₈×C₁₉	C₂⁴	1	2	yes	—
142	C₁₉⋊C₈	C₂⁴	1	4	yes	—
143	C₂×#575	—	19	1	no	maximal, Sylow
144	C₂²×C₁₉	—	2	2	no	—
145	C₂²×C₁₉	—	2	4	no	—
146	C₂²×C₁₉	—	4	4	no	—
147	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
148	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
149	C₂×D₁₉	—	2	4	no	—
150	C₂×D₁₉	—	2	4	no	—
151	C₂×D₁₉	—	4	4	no	—
152	C₂×D₁₉	—	4	16	no	—
153	C₂×D₁₉	—	4	4	no	—
154	C₂×D₁₉	C₂²×D₄	1	4	yes	—
155	C₄×C₁₉	—	2	4	no	—
156	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
157	C₄×C₁₉	C₂²×D₄	1	2	yes	—
158	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
159	Dic₁₉	—	2	4	no	—
160	Dic₁₉	C₂²×D₄	1	4	yes	—
161	C₂²×#41	—	19	2	no	—
162	#575	—	19	16	no	—
163	C₂×#137	—	19	2	no	—
164	C₂×#137	—	19	2	no	—
165	C₂×AGL(1,ℤ/8)	—	19	2	no	—
166	C₂×AGL(1,ℤ/8)	—	19	2	no	—
167	C₂×#135	—	19	2	no	—
168	C₂×#135	—	19	1	no	—
169	C₂×#135	D₁₉	1	1	yes	characteristic, complemented
170	C₂²×M₁₆	—	19	1	no	—
171	C₂×C₁₉	—	2	2	no	—
172	C₂×C₁₉	—	4	4	no	—
173	C₂×C₁₉	#575	1	2	yes	complemented
174	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
175	D₁₉	—	2	4	no	—
176	D₁₉	—	4	4	no	—
177	C₂×#41	—	19	16	no	—
178	C₂×#41	—	19	2	no	—
179	C₂×#41	—	19	2	no	—
180	C₂×#41	—	19	2	no	—
181	C₂×#41	—	38	2	no	—
182	C₂×#41	—	38	2	no	—
183	C₂×#41	—	38	8	no	—
184	C₂×#41	C₂×D₁₉	1	2	yes	complemented
185	C₂²×Q₈	—	19	2	no	—
186	C₂²×D₄	—	19	2	no	—
187	C₂²×D₄	—	38	2	no	—
188	C₂³×C₄	—	19	1	no	—
189	C₂³×C₄	—	38	2	no	—
190	#137	—	19	16	no	—
191	#137	—	19	16	no	—
192	AGL(1,ℤ/8)	—	19	16	no	—
193	AGL(1,ℤ/8)	—	19	16	no	—
194	#135	—	19	16	no	—
195	#135	—	19	8	no	—
196	#135	C₂×D₁₉	1	8	yes	complemented
197	C₂×Q₁₆	—	19	2	no	—
198	C₂×Q₁₆	—	19	1	no	—
199	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
200	C₂×SD₁₆	—	19	2	no	—
201	C₂×SD₁₆	—	19	2	no	—
202	C₂×SD₁₆	—	19	2	no	—
203	C₂×SD₁₆	C₂×D₁₉	1	2	yes	complemented
204	C₂×D₈	—	19	2	no	—
205	C₂×D₈	—	19	1	no	—
206	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic, complemented
207	C₂×M₁₆	—	19	2	no	—
208	C₂×M₁₆	—	19	2	no	—
209	C₂×M₁₆	—	19	8	no	—
210	C₂²×C₈	—	19	1	no	—
211	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
212	C₁₉	C₂×#575	1	1	yes	characteristic, complemented, Sylow
213	C₂⁴	—	19	1	no	—
214	C₂⁴	—	38	2	no	—
215	#41	—	2	4	no	—
216	#41	—	19	8	no	—
217	#41	—	19	8	no	—
218	#41	—	19	8	no	—
219	#41	—	38	16	no	—
220	#41	—	38	16	no	—
221	#41	—	38	4	no	—
222	#41	—	38	4	no	—
223	#41	—	38	4	no	—
224	#41	C₂²×D₁₉	1	8	yes	complemented
225	C₂×Q₈	—	19	8	no	—
226	C₂×Q₈	—	19	2	no	—
227	C₂×Q₈	—	38	2	no	—
228	C₂×Q₈	—	38	4	no	—
229	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
230	C₂×D₄	—	2	2	no	—
231	C₂×D₄	—	19	8	no	—
232	C₂×D₄	—	19	2	no	—
233	C₂×D₄	—	38	2	no	—
234	C₂×D₄	—	38	4	no	—
235	C₂×D₄	—	38	2	no	—
236	C₂×D₄	—	38	16	no	—
237	C₂×D₄	—	38	2	no	—
238	C₂×D₄	—	38	2	no	—
239	C₂×D₄	C₂²×D₁₉	1	2	yes	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	19	1	no	—
242	C₂²×C₄	—	19	4	no	—
243	C₂²×C₄	—	19	2	no	—
244	C₂²×C₄	—	19	2	no	—
245	C₂²×C₄	—	19	4	no	—
246	C₂²×C₄	—	38	2	no	—
247	C₂²×C₄	—	38	16	no	—
248	C₂²×C₄	—	38	2	no	—
249	C₂²×C₄	—	38	2	no	—
250	C₂²×C₄	—	38	2	no	—
251	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
252	Q₁₆	—	19	8	no	—
253	Q₁₆	—	19	4	no	—
254	Q₁₆	C₂²×D₁₉	1	4	yes	complemented
255	SD₁₆	—	19	8	no	—
256	SD₁₆	—	19	8	no	—
257	SD₁₆	—	19	8	no	—
258	SD₁₆	C₂²×D₁₉	1	8	yes	complemented
259	D₈	—	19	8	no	—
260	D₈	—	19	4	no	—
261	D₈	C₂²×D₁₉	1	4	yes	complemented
262	M₁₆	—	19	8	no	—
263	M₁₆	—	19	8	no	—
264	C₂×C₈	—	19	2	no	—
265	C₂×C₈	—	19	4	no	—
266	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
267	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
268	C₂×C₈	C₂²×D₁₉	1	4	yes	complemented
269	C₂³	—	2	2	no	—
270	C₂³	—	19	2	no	—
271	C₂³	—	19	4	no	—
272	C₂³	—	38	8	no	—
273	C₂³	—	38	2	no	—
274	C₂³	—	76	2	no	—
275	C₂³	—	76	8	no	—
276	C₂³	D₄×D₁₉	1	1	yes	characteristic
277	Q₈	—	2	2	no	—
278	Q₈	—	19	4	no	—
279	Q₈	—	38	8	no	—
280	Q₈	—	38	2	no	—
281	Q₈	C₂³×D₁₉	1	4	yes	—
282	D₄	—	2	8	no	—
283	D₄	—	2	2	no	—
284	D₄	—	19	4	no	—
285	D₄	—	38	8	no	—
286	D₄	—	38	8	no	—
287	D₄	—	38	8	no	—
288	D₄	—	38	8	no	—
289	D₄	—	38	2	no	—
290	D₄	C₂³×D₁₉	1	4	yes	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	19	2	no	—
294	C₂×C₄	—	19	4	no	—
295	C₂×C₄	—	19	8	no	—
296	C₂×C₄	—	19	4	no	—
297	C₂×C₄	—	19	4	no	—
298	C₂×C₄	—	38	8	no	—
299	C₂×C₄	—	38	8	no	—
300	C₂×C₄	—	38	8	no	—
301	C₂×C₄	—	38	2	no	—
302	C₂×C₄	—	38	8	no	—
303	C₂×C₄	D₄×D₁₉	1	2	yes	—
304	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
305	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
306	C₂×C₄	C₂³×D₁₉	1	2	yes	—
307	C₈	—	19	4	no	—
308	C₈	C₂³×D₁₉	1	2	yes	—
309	C₈	C₂³×D₁₉	1	2	yes	—
310	C₂²	—	2	2	no	—
311	C₂²	—	2	4	no	—
312	C₂²	—	4	4	no	—
313	C₂²	—	19	4	no	—
314	C₂²	—	38	4	no	—
315	C₂²	—	38	4	no	—
316	C₂²	—	76	4	no	—
317	C₂²	—	76	16	no	—
318	C₂²	—	76	4	no	—
319	C₂²	C₂×D₄×D₁₉	1	2	yes	—
320	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
321	C₄	—	2	4	no	—
322	C₄	—	19	4	no	—
323	C₄	—	38	4	no	—
324	C₄	C₂×D₄×D₁₉	1	2	yes	—
325	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
326	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
327	C₂	—	2	2	no	—
328	C₂	—	4	4	no	—
329	C₂	—	38	4	no	—
330	C₂	—	76	4	no	—
331	C₂	#11927341	1	2	yes	direct product factor
332	C₂	C₂²×D₄×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₉
commutator, cosocle	C₄×C₁₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂×C₁₉×#135	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₂×#135	D₁₉
hypocenter	C₁₉	C₂×#575
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₉	C₂	semidirect
2. #11927341	C₂	direct (N × H)
3. C₂×#10597364	C₂	semidirect
4. C₂×#10597361	C₂	semidirect
5. C₂×#10597360	C₂	semidirect
6. C₂×#10597357	C₂	semidirect
7. C₂×#10597350	C₂	semidirect
8. C₂×#10597396	C₂	semidirect
9. C₂²×#64515	C₂	semidirect
10. C₂×C₁₉×#135	C₂	semidirect
11. C₂×#41×C₁₉	C₂²	semidirect
13. #41×D₁₉	C₂²	semidirect
15. C₂×Q₈×D₁₉	C₂²	semidirect
19. C₂×D₄×D₁₉	C₂²	semidirect
21. C₂×#64541	C₂²	semidirect
24. C₁₉×#135	C₂²	semidirect
25. C₂×Q₁₆×C₁₉	C₂²	semidirect
26. C₂×SD₁₆×C₁₉	C₂²	semidirect
27. C₂×D₈×C₁₉	C₂²	semidirect
28. C₂²×C₈×C₁₉	C₂²	semidirect
29. #10597396	C₂²	semidirect
30. C₂×#64528	C₂²	semidirect
31. C₂×#64527	C₂²	semidirect
32. C₂×#64526	C₂²	semidirect
33. C₂×#64525	C₂²	semidirect
34. C₂²×C₁₉⋊C₈	C₂²	semidirect
35. #10597364	C₂²	semidirect
36. #10597361	C₂²	semidirect
37. #10597360	C₂²	semidirect
38. #10597357	C₂²	semidirect
39. C₂×Dic₇₆	C₂²	semidirect
40. #10597350	C₂²	semidirect
41. C₂×D₁₅₂	C₂²	semidirect
42. C₂×#64516	C₂²	semidirect
43. C₂×#64515	C₂²	semidirect
44. C₂×#64515	C₂²	semidirect
45. C₂×#64515	C₂²	semidirect
49. #41×C₁₉	C₂³	semidirect
63. Q₈×D₁₉	C₂³	semidirect
69. D₄×D₁₉	C₂³	semidirect
72. #64541	C₂³	semidirect
85. Q₁₆×C₁₉	C₂³	semidirect
86. SD₁₆×C₁₉	C₂³	semidirect
87. D₈×C₁₉	C₂³	semidirect
90. C₂×C₈×C₁₉	C₂³	semidirect
91. #64528	C₂³	semidirect
92. #64527	C₂³	semidirect
93. #64526	C₂³	semidirect
94. #64525	C₂³	semidirect
96. C₂×C₁₉⋊C₈	C₂³	semidirect
97. Dic₇₆	C₂³	semidirect
98. D₁₅₂	C₂³	semidirect
99. #64516	C₂³	semidirect
100. #64515	C₂³	semidirect
101. #64515	C₂³	semidirect
169. C₂×#135	D₁₉	semidirect
173. C₂×C₁₉	#575	semidirect
184. C₂×#41	C₂×D₁₉	semidirect
196. #135	C₂×D₁₉	semidirect
199. C₂×Q₁₆	C₂×D₁₉	semidirect
203. C₂×SD₁₆	C₂×D₁₉	semidirect
206. C₂×D₈	C₂×D₁₉	semidirect
211. C₂²×C₈	C₂×D₁₉	semidirect
212. C₁₉	C₂×#575	semidirect
224. #41	C₂²×D₁₉	semidirect
254. Q₁₆	C₂²×D₁₉	semidirect
258. SD₁₆	C₂²×D₁₉	semidirect
261. D₈	C₂²×D₁₉	semidirect
268. C₂×C₈	C₂²×D₁₉	semidirect
331. C₂	#11927341	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×#41×D₁₉	2
#11927341	2
C₂×#10597364	2
C₂×#10597361	2
C₂×#10597360	2
C₂×#10597357	2
C₂×#10597350	2
C₂×#10597396	2
C₂²×#64515	2
C₂×C₁₉×#135	2
C₂×#575	19

Subgroups — C2×#11927341 #14578379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11927341 #14578379