Subgroups — #14575561

Order 2432.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927257	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927196	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926893	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926887	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926833	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926775	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926774	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926748	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926692	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926691	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926626	C₂	1	1	yes	maximal, characteristic, complemented
12	(C₂²⋊D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926539	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926538	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#64545	C₂²	1	1	yes	characteristic
17	C₂×#64541	C₂²	1	1	yes	characteristic
18	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₁₉×#117	C₂²	1	1	yes	characteristic
20	#10597390	C₂²	1	1	yes	characteristic
21	C₂×#64527	C₂²	1	1	yes	characteristic
22	#10597376	C₂²	1	1	yes	characteristic
23	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×D₁₅₂	C₂²	1	1	yes	characteristic
26	C₂×#64516	C₂²	1	1	yes	characteristic
27	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
28	#10597343	C₂²	1	1	yes	characteristic
29	#10597341	C₂²	1	1	yes	characteristic
30	#10597340	—	2	1	no	—
31	#10597339	C₂²	1	1	yes	characteristic
32	#10597339	C₂²	1	1	yes	characteristic
33	#10597338	C₂²	1	1	yes	characteristic
34	C₄⋊C₄×D₁₉	—	2	1	no	—
35	#10597334	C₂²	1	1	yes	characteristic
36	#10597331	—	2	1	no	—
37	#10597330	—	2	1	no	—
38	#10597330	—	2	1	no	—
39	#10597329	—	2	1	no	—
40	#10597321	—	2	1	no	—
41	#10597318	—	2	1	no	—
42	C₁₉×#107	C₂²	1	1	yes	characteristic
43	C₁₉×#106	C₂²	1	1	yes	characteristic
44	C₁₉×#103	C₂²	1	1	yes	characteristic
45	C₁₉×#103	C₂²	1	1	yes	characteristic
46	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	#10597292	C₂²	1	1	yes	characteristic
48	#10597278	C₂²	1	1	yes	characteristic
49	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
50	#10597273	C₂²	1	1	yes	characteristic
51	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
52	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
53	#10597267	C₂²	1	1	yes	characteristic
54	#10597267	C₂²	1	1	yes	characteristic
55	#10597266	C₂²	1	1	yes	characteristic
56	#10597266	C₂²	1	1	yes	characteristic
57	#10597266	C₂²	1	1	yes	characteristic
58	#10597265	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊D₁₉	—	2	1	no	—
62	C₂×C₂²⋊D₁₉	—	2	1	no	—
63	C₂×C₂²⋊D₁₉	D₄	1	1	yes	characteristic
64	#64545	—	2	2	no	—
65	#64545	—	4	1	no	—
66	#64541	—	2	2	no	—
67	#64541	—	4	1	no	—
68	C₂×D₇₆	—	2	1	no	—
69	C₂×D₇₆	—	2	1	no	—
70	C₂×D₇₆	C₂³	1	1	yes	characteristic
71	C₂×D₇₆	C₂³	1	1	yes	characteristic
72	C₂×C₄×D₁₉	—	2	1	no	—
73	C₂×C₄×D₁₉	—	2	1	no	—
74	C₂×C₄×D₁₉	—	2	1	no	—
75	C₂×C₄×D₁₉	—	2	1	no	—
76	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
77	C₂×Dic₃₈	—	2	1	no	—
78	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
79	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₄²×C₁₉	—	2	1	no	—
88	C₂²⋊Dic₁₉	D₄	1	1	yes	characteristic
89	#64527	—	4	1	no	—
90	(C₂×D₁₉)⋊C₄	—	2	1	no	—
91	(C₂×D₁₉)⋊C₄	—	2	1	no	—
92	(C₂×D₁₉)⋊C₄	—	2	1	no	—
93	(C₂×D₁₉)⋊C₄	—	2	1	no	—
94	(C₂×D₁₉)⋊C₄	—	2	1	no	—
95	(C₂×D₁₉)⋊C₄	—	2	1	no	—
96	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
97	C₄⋊Dic₁₉	—	2	1	no	—
98	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
99	Dic₁₉⋊C₄	—	2	1	no	—
100	Dic₁₉⋊C₄	—	2	1	no	—
101	Dic₁₉⋊C₄	—	2	1	no	—
102	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
103	C₄×Dic₁₉	—	2	1	no	—
104	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₁₉⋊C₈	—	4	1	no	—
106	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
107	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
108	D₁₅₂	—	2	2	no	—
109	#64516	—	4	1	no	—
110	C₈×D₁₉	—	4	1	no	—
111	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×D₁₉	—	2	1	no	—
113	C₂²×D₁₉	—	2	1	no	—
114	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
115	Q₈×C₁₉	—	2	1	no	—
116	Q₈×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
125	C₂²⋊D₁₉	—	2	2	no	—
126	C₂²⋊D₁₉	—	4	2	no	—
127	C₂²⋊D₁₉	—	8	1	no	—
128	C₂×Dic₁₉	—	2	1	no	—
129	C₂×Dic₁₉	—	2	1	no	—
130	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
133	D₇₆	—	2	1	no	—
134	D₇₆	—	2	1	no	—
135	D₇₆	—	2	1	no	—
136	D₇₆	—	4	2	no	—
137	D₇₆	—	8	1	no	—
138	D₇₆	#41	1	2	yes	—
139	C₄×D₁₉	—	2	1	no	—
140	C₄×D₁₉	—	2	1	no	—
141	C₄×D₁₉	—	4	2	no	—
142	C₄×D₁₉	—	4	2	no	—
143	C₄×D₁₉	—	4	2	no	—
144	C₄×D₁₉	—	4	2	no	—
145	Dic₃₈	—	2	1	no	—
146	Dic₃₈	—	2	1	no	—
147	Dic₃₈	—	8	1	no	—
148	C₈×C₁₉	—	2	1	no	—
149	C₈×C₁₉	—	2	1	no	—
150	C₁₉⋊C₈	—	2	1	no	—
151	C₁₉⋊C₈	—	2	1	no	—
152	#3303	—	19	1	no	maximal, Sylow
153	C₂²×C₁₉	—	2	1	no	—
154	C₂²×C₁₉	—	2	1	no	—
155	C₂²×C₁₉	—	2	1	no	—
156	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×D₁₉	—	2	1	no	—
158	C₂×D₁₉	—	2	2	no	—
159	C₂×D₁₉	—	2	1	no	—
160	C₂×D₁₉	—	2	1	no	—
161	C₂×D₁₉	—	4	1	no	—
162	C₂×D₁₉	—	4	1	no	—
163	C₂×D₁₉	—	4	1	no	—
164	C₂×D₁₉	—	4	1	no	—
165	C₂×D₁₉	—	4	1	no	—
166	C₄×C₁₉	—	2	1	no	—
167	C₄×C₁₉	—	4	1	no	—
168	C₄×C₁₉	—	4	1	no	—
169	C₄×C₁₉	—	4	1	no	—
170	C₄×C₁₉	—	4	1	no	—
171	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
172	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
173	Dic₁₉	—	2	1	no	—
174	Dic₁₉	—	2	1	no	—
175	Dic₁₉	—	4	1	no	—
176	Dic₁₉	—	4	1	no	—
177	Dic₁₉	#135	1	2	yes	—
178	#555	—	19	1	no	—
179	#547	—	19	1	no	—
180	#487	—	19	1	no	—
181	#485	—	19	1	no	—
182	#485	D₁₉	1	1	yes	characteristic, complemented
183	#476	—	19	1	no	—
184	#465	—	19	1	no	—
185	#465	—	19	1	no	—
186	#461	—	19	1	no	—
187	#449	—	19	1	no	—
188	#449	—	19	1	no	—
189	C₄×D₈	—	19	1	no	—
190	C₈×D₄	—	19	1	no	—
191	#416	—	19	1	no	—
192	#416	—	19	1	no	—
193	C₂×C₁₉	—	4	1	no	—
194	C₂×C₁₉	#546	1	1	yes	characteristic
195	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
196	C₂×C₁₉	#577	1	1	yes	characteristic
197	D₁₉	—	4	1	no	—
198	D₁₉	—	4	2	no	—
199	D₁₉	—	8	1	no	—
200	C₂×#41	—	19	1	no	—
201	C₂×#41	—	19	1	no	—
202	C₂×SD₁₆	—	19	1	no	—
203	C₂×SD₁₆	—	19	1	no	—
204	C₂×D₈	—	19	1	no	—
205	C₂²×C₈	—	19	1	no	—
206	C₂²×C₈	—	19	1	no	—
207	C₄⋊Q₈	—	19	1	no	—
208	C₄⋊Q₈	—	19	1	no	—
209	#124	—	38	1	no	—
210	#124	—	38	1	no	—
211	#123	—	38	1	no	—
212	#123	—	38	1	no	—
213	C₂²⋊Q₈	—	19	1	no	—
214	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
215	#121	—	19	1	no	—
216	#121	—	19	1	no	—
217	#121	—	38	1	no	—
218	#121	—	38	1	no	—
219	C₄×D₄	—	19	1	no	—
220	C₄×D₄	—	19	1	no	—
221	C₄×D₄	—	19	1	no	—
222	#117	—	19	1	no	—
223	#117	—	38	1	no	—
224	#117	C₂×D₁₉	1	1	yes	characteristic
225	C₂×C₄⋊C₄	—	38	1	no	—
226	#107	C₂×D₁₉	1	1	yes	characteristic
227	#106	—	19	1	no	—
228	#106	C₂×D₁₉	1	1	yes	characteristic
229	C₄⋊C₈	—	19	1	no	—
230	#103	—	19	1	no	—
231	#103	—	19	1	no	—
232	#103	—	19	1	no	—
233	#103	—	19	1	no	—
234	#103	C₂×D₁₉	1	1	yes	characteristic
235	#103	C₂×D₁₉	1	1	yes	characteristic
236	#102	—	19	1	no	—
237	#102	—	19	1	no	—
238	#102	—	19	1	no	—
239	#102	—	19	1	no	—
240	C₂²⋊C₈	—	19	1	no	—
241	C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
242	C₄×C₈	—	19	1	no	—
243	C₁₉	#3303	1	1	yes	characteristic, complemented, Sylow
244	#41	—	38	2	no	—
245	#41	—	38	2	no	—
246	#41	—	76	1	no	—
247	#41	—	76	1	no	—
248	C₂×Q₈	—	19	1	no	—
249	C₂×Q₈	—	38	1	no	—
250	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
251	C₂×D₄	—	19	1	no	—
252	C₂×D₄	—	19	1	no	—
253	C₂×D₄	—	19	1	no	—
254	C₂×D₄	—	38	1	no	—
255	C₂×D₄	—	38	1	no	—
256	C₂×D₄	—	38	1	no	—
257	C₂×D₄	—	38	1	no	—
258	C₂²×C₄	—	19	1	no	—
259	C₂²×C₄	—	38	1	no	—
260	C₂²×C₄	—	38	1	no	—
261	C₂²×C₄	—	38	1	no	—
262	C₂²×C₄	—	38	1	no	—
263	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
264	SD₁₆	—	76	1	no	—
265	SD₁₆	—	76	1	no	—
266	D₈	—	38	2	no	—
267	C₂×C₈	—	19	1	no	—
268	C₂×C₈	—	19	1	no	—
269	C₂×C₈	—	76	1	no	—
270	C₂×C₈	—	76	1	no	—
271	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
272	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
273	C₄⋊C₄	—	2	1	no	—
274	C₄⋊C₄	—	19	1	no	—
275	C₄⋊C₄	—	19	1	no	—
276	C₄⋊C₄	—	38	1	no	—
277	C₄⋊C₄	—	38	1	no	—
278	C₄⋊C₄	—	38	1	no	—
279	C₄⋊C₄	—	38	1	no	—
280	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
281	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
282	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
283	C₂²⋊C₄	—	2	1	no	—
284	C₂²⋊C₄	—	2	1	no	—
285	C₂²⋊C₄	—	19	1	no	—
286	C₂²⋊C₄	—	19	1	no	—
287	C₂²⋊C₄	—	38	1	no	—
288	C₂²⋊C₄	—	38	1	no	—
289	C₂²⋊C₄	—	38	1	no	—
290	C₂²⋊C₄	—	38	1	no	—
291	C₂²⋊C₄	—	38	1	no	—
292	C₂²⋊C₄	—	38	1	no	—
293	C₄²	—	2	1	no	—
294	C₄²	—	19	1	no	—
295	C₄²	—	38	1	no	—
296	C₂³	—	19	1	no	—
297	C₂³	—	38	1	no	—
298	C₂³	—	38	1	no	—
299	C₂³	D₄×D₁₉	1	1	yes	characteristic
300	Q₈	—	2	1	no	—
301	Q₈	—	2	1	no	—
302	Q₈	—	38	1	no	—
303	Q₈	—	38	1	no	—
304	Q₈	—	152	1	no	—
305	D₄	—	19	2	no	—
306	D₄	—	38	2	no	—
307	D₄	—	38	1	no	—
308	D₄	—	38	1	no	—
309	D₄	—	38	1	no	—
310	D₄	—	76	2	no	—
311	D₄	—	76	2	no	—
312	D₄	—	152	1	no	—
313	D₄	—	152	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	19	1	no	—
321	C₂×C₄	—	19	1	no	—
322	C₂×C₄	—	19	1	no	—
323	C₂×C₄	—	38	1	no	—
324	C₂×C₄	—	38	1	no	—
325	C₂×C₄	—	38	1	no	—
326	C₂×C₄	—	38	1	no	—
327	C₂×C₄	—	76	2	no	—
328	C₂×C₄	—	76	2	no	—
329	C₂×C₄	—	76	2	no	—
330	C₂×C₄	—	76	2	no	—
331	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
332	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
333	C₈	—	2	1	no	—
334	C₈	—	2	1	no	—
335	C₈	—	38	1	no	—
336	C₈	—	38	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	38	1	no	—
341	C₂²	—	38	1	no	—
342	C₂²	—	38	1	no	—
343	C₂²	—	38	2	no	—
344	C₂²	—	76	1	no	—
345	C₂²	—	76	1	no	—
346	C₂²	—	76	1	no	—
347	C₂²	—	76	1	no	—
348	C₂²	—	76	1	no	—
349	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	4	1	no	—
352	C₄	—	4	1	no	—
353	C₄	—	4	1	no	—
354	C₄	—	4	1	no	—
355	C₄	—	19	2	no	—
356	C₄	—	38	1	no	—
357	C₄	—	38	1	no	—
358	C₄	—	76	1	no	—
359	C₄	—	76	1	no	—
360	C₄	#41×D₁₉	1	1	yes	characteristic
361	C₄	#10597435	1	1	yes	characteristic
362	C₂	—	4	1	no	—
363	C₂	—	76	1	no	—
364	C₂	—	76	2	no	—
365	C₂	—	152	1	no	—
366	C₂	#11927186	1	1	yes	characteristic
367	C₂	#135×D₁₉	1	1	yes	characteristic
368	C₂	#11927353	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#485	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#485	D₁₉
hypocenter	C₁₉	#3303
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #485

Complements

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

N	H ≅ G/N	type
1. #11927257	C₂	semidirect
2. #11927196	C₂	semidirect
3. #11926893	C₂	semidirect
4. #11926887	C₂	semidirect
5. #11926833	C₂	semidirect
6. #11926775	C₂	semidirect
7. #11926774	C₂	semidirect
8. #11926748	C₂	semidirect
9. #11926692	C₂	semidirect
10. #11926691	C₂	semidirect
11. #11926626	C₂	semidirect
12. (C₂²⋊D₁₉)⋊C₈	C₂	semidirect
13. #11926539	C₂	semidirect
14. #11926538	C₂	semidirect
15. C₁₉×#485	C₂	semidirect
182. #485	D₁₉	semidirect
243. C₁₉	#3303	semidirect

Maximal subgroups

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

subgroup	index
#11927257	2
#11927196	2
#11926893	2
#11926887	2
#11926833	2
#11926775	2
#11926774	2
#11926748	2
#11926692	2
#11926691	2
#11926626	2
(C₂²⋊D₁₉)⋊C₈	2
#11926539	2
#11926538	2
C₁₉×#485	2
#3303	19