Subgroups — #14574506

Order 2432.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927117	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927113	C₂	1	1	yes	maximal, characteristic
3	#11926885	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926871	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926870	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926793	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926791	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926776	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926774	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926697	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926694	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926684	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926684	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926509	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×#64541	C₂²	1	1	yes	characteristic
18	C₂²×D₇₆	C₂²	1	1	yes	characteristic
19	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#117	C₂²	1	1	yes	characteristic
21	#10597392	C₂²	1	1	yes	characteristic, complemented
22	C₂×#64527	C₂²	1	1	yes	characteristic
23	C₂×#64527	C₂²	1	1	yes	characteristic
24	#10597370	C₂²	1	1	yes	characteristic
25	C₂×#64516	C₂²	1	1	yes	characteristic
26	C₂×#64516	C₂²	1	1	yes	characteristic
27	C₂×#64515	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
29	#10597343	C₂²	1	1	yes	characteristic, complemented
30	#10597341	C₂²	1	1	yes	characteristic
31	#10597341	C₂²	1	1	yes	characteristic
32	#10597341	C₂²	1	1	yes	characteristic
33	#10597341	C₂²	1	1	yes	characteristic
34	#10597340	—	2	1	no	—
35	#10597338	C₂²	1	1	yes	characteristic, complemented
36	#10597334	—	2	1	no	—
37	#10597331	—	2	1	no	—
38	#10597329	—	2	1	no	—
39	#10597328	—	2	1	no	—
40	#10597328	—	2	1	no	—
41	#10597321	—	2	1	no	—
42	#10597320	—	2	1	no	—
43	C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
49	#10597278	C₂²	1	1	yes	characteristic
50	#10597278	C₂²	1	1	yes	characteristic
51	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	#10597267	C₂²	1	1	yes	characteristic, complemented
54	#10597267	C₂²	1	1	yes	characteristic, complemented
55	#10597266	C₂²	1	1	yes	characteristic
56	#10597266	C₂²	1	1	yes	characteristic
57	#10597265	C₂²	1	1	yes	characteristic, complemented
58	#10597264	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₉	—	2	1	no	—
60	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊D₁₉	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊D₁₉	D₄	1	1	yes	characteristic
64	Q₈×D₁₉	—	4	1	no	—
65	Q₈×D₁₉	—	4	1	no	—
66	#64541	—	4	1	no	—
67	#64541	—	4	1	no	—
68	C₂×D₇₆	—	2	1	no	—
69	C₂×D₇₆	—	2	1	no	—
70	C₂×D₇₆	—	2	1	no	—
71	C₂×D₇₆	—	2	1	no	—
72	C₂×D₇₆	—	2	1	no	—
73	C₂×D₇₆	—	4	1	no	—
74	C₂×D₇₆	—	4	1	no	—
75	C₂×D₇₆	D₄	1	1	yes	characteristic
76	C₂×D₇₆	C₂³	1	1	yes	characteristic
77	C₂×D₇₆	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₁₉	—	2	1	no	—
79	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
81	C₂×Dic₃₈	—	2	1	no	—
82	C₂×Dic₃₈	D₄	1	1	yes	characteristic
83	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₄²×C₁₉	—	2	1	no	—
93	C₂²⋊Dic₁₉	—	2	1	no	—
94	#64527	—	4	1	no	—
95	#64527	—	4	1	no	—
96	(C₂×D₁₉)⋊C₄	—	2	1	no	—
97	(C₂×D₁₉)⋊C₄	—	2	1	no	—
98	(C₂×D₁₉)⋊C₄	—	2	1	no	—
99	(C₂×D₁₉)⋊C₄	—	2	1	no	—
100	(C₂×D₁₉)⋊C₄	—	2	1	no	—
101	(C₂×D₁₉)⋊C₄	—	2	1	no	—
102	(C₂×D₁₉)⋊C₄	—	2	1	no	—
103	C₄⋊Dic₁₉	—	2	1	no	—
104	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
105	Dic₁₉⋊C₄	—	2	1	no	—
106	Dic₁₉⋊C₄	—	2	1	no	—
107	C₄×Dic₁₉	—	2	1	no	—
108	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
109	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
110	#64516	—	4	1	no	—
111	#64516	—	4	1	no	—
112	#64515	—	4	1	no	—
113	C₈×D₁₉	—	4	1	no	—
114	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×D₁₉	—	2	1	no	—
116	C₂²×D₁₉	—	2	1	no	—
117	C₂²×D₁₉	—	4	2	no	—
118	C₂²×D₁₉	—	8	1	no	—
119	C₂²×D₁₉	—	8	1	no	—
120	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
122	Q₈×C₁₉	—	2	1	no	—
123	Q₈×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
132	C₂²⋊D₁₉	—	4	1	no	—
133	C₂²⋊D₁₉	—	4	1	no	—
134	C₂×Dic₁₉	—	2	1	no	—
135	C₂×Dic₁₉	—	2	1	no	—
136	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
138	D₇₆	—	2	1	no	—
139	D₇₆	—	2	1	no	—
140	D₇₆	—	2	1	no	—
141	D₇₆	—	2	1	no	—
142	D₇₆	—	4	1	no	—
143	D₇₆	—	4	2	no	—
144	D₇₆	—	8	1	no	—
145	D₇₆	—	8	1	no	—
146	D₇₆	—	8	1	no	—
147	D₇₆	—	8	1	no	—
148	C₄×D₁₉	—	2	1	no	—
149	C₄×D₁₉	—	2	1	no	—
150	C₄×D₁₉	—	2	1	no	—
151	C₄×D₁₉	—	2	1	no	—
152	C₄×D₁₉	—	4	2	no	—
153	Dic₃₈	—	2	1	no	—
154	Dic₃₈	—	2	1	no	—
155	Dic₃₈	—	4	1	no	—
156	Dic₃₈	—	4	2	no	—
157	C₈×C₁₉	—	2	1	no	—
158	C₈×C₁₉	—	2	1	no	—
159	C₁₉⋊C₈	—	2	1	no	—
160	C₁₉⋊C₈	—	2	1	no	—
161	#3200	—	19	1	no	maximal, Sylow
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
166	C₂×D₁₉	—	2	1	no	—
167	C₂×D₁₉	—	2	1	no	—
168	C₂×D₁₉	—	2	1	no	—
169	C₂×D₁₉	—	2	1	no	—
170	C₂×D₁₉	—	2	1	no	—
171	C₂×D₁₉	—	2	1	no	—
172	C₂×D₁₉	—	4	1	no	—
173	C₂×D₁₉	—	4	1	no	—
174	C₂×D₁₉	—	4	1	no	—
175	C₂×D₁₉	—	4	1	no	—
176	C₂×D₁₉	—	4	1	no	—
177	C₂×D₁₉	—	4	1	no	—
178	C₂×D₁₉	—	8	4	no	—
179	C₄×C₁₉	—	2	1	no	—
180	C₄×C₁₉	—	4	1	no	—
181	C₄×C₁₉	—	4	1	no	—
182	C₄×C₁₉	—	4	1	no	—
183	C₄×C₁₉	—	4	1	no	—
184	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
185	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
186	Dic₁₉	—	2	1	no	—
187	Dic₁₉	—	2	1	no	—
188	Dic₁₉	—	4	1	no	—
189	Dic₁₉	—	4	1	no	—
190	#536	—	19	1	no	—
191	#535	—	19	1	no	—
192	#485	—	19	1	no	—
193	#485	D₁₉	1	1	yes	characteristic, complemented
194	#482	—	19	1	no	—
195	#482	—	19	1	no	—
196	#468	—	19	1	no	—
197	#468	—	19	1	no	—
198	#465	—	19	1	no	—
199	#465	—	19	1	no	—
200	#450	—	19	1	no	—
201	#450	—	19	1	no	—
202	#448	—	19	1	no	—
203	#448	—	19	1	no	—
204	#408	—	19	1	no	—
205	C₂×C₁₉	—	4	1	no	—
206	C₂×C₁₉	#534	1	1	yes	characteristic
207	C₂×C₁₉	#577	1	1	yes	characteristic
208	C₂×C₁₉	#577	1	1	yes	characteristic
209	D₁₉	—	4	1	no	—
210	D₁₉	—	4	1	no	—
211	D₁₉	—	8	1	no	—
212	D₁₉	—	8	1	no	—
213	C₂×#41	—	19	1	no	—
214	C₂²×Q₈	—	19	1	no	—
215	C₂²×D₄	—	19	1	no	—
216	C₂×SD₁₆	—	19	1	no	—
217	C₂×SD₁₆	—	19	1	no	—
218	C₂×SD₁₆	—	19	1	no	—
219	C₂×SD₁₆	—	19	1	no	—
220	C₂×M₁₆	—	19	1	no	—
221	C₂²×C₈	—	19	1	no	—
222	C₄⋊Q₈	—	38	1	no	—
223	#127	—	38	1	no	—
224	#124	—	38	1	no	—
225	#124	—	38	1	no	—
226	#123	—	38	1	no	—
227	#123	—	38	1	no	—
228	C₂²⋊Q₈	—	19	1	no	—
229	C₂²⋊Q₈	—	19	1	no	—
230	C₂²⋊Q₈	—	19	1	no	—
231	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
232	#121	—	19	1	no	—
233	#121	—	19	1	no	—
234	#121	—	19	1	no	—
235	#121	—	19	1	no	—
236	#120	—	38	1	no	—
237	#120	—	38	1	no	—
238	#117	—	19	1	no	—
239	#117	C₂×D₁₉	1	1	yes	characteristic
240	#107	—	19	1	no	—
241	#107	C₂×D₁₉	1	1	yes	characteristic, complemented
242	#106	—	19	1	no	—
243	#106	C₂×D₁₉	1	1	yes	characteristic, complemented
244	#103	—	19	1	no	—
245	#103	—	19	1	no	—
246	#103	C₂×D₁₉	1	1	yes	characteristic, complemented
247	#103	C₂×D₁₉	1	1	yes	characteristic, complemented
248	#102	—	19	1	no	—
249	#102	—	19	1	no	—
250	#102	—	19	1	no	—
251	#102	—	19	1	no	—
252	C₂²⋊C₈	—	19	1	no	—
253	C₂²⋊C₈	—	19	1	no	—
254	C₂²⋊C₈	—	19	1	no	—
255	C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
256	C₁₉	#3200	1	1	yes	characteristic, complemented, Sylow
257	C₂⁴	—	38	1	no	—
258	#41	—	76	1	no	—
259	#41	—	76	1	no	—
260	C₂×Q₈	—	19	1	no	—
261	C₂×Q₈	—	19	1	no	—
262	C₂×Q₈	—	38	1	no	—
263	C₂×Q₈	—	76	1	no	—
264	C₂×Q₈	—	76	1	no	—
265	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
266	C₂×D₄	—	19	1	no	—
267	C₂×D₄	—	19	1	no	—
268	C₂×D₄	—	19	1	no	—
269	C₂×D₄	—	19	1	no	—
270	C₂×D₄	—	19	1	no	—
271	C₂×D₄	—	38	1	no	—
272	C₂×D₄	—	38	1	no	—
273	C₂×D₄	—	38	1	no	—
274	C₂×D₄	—	38	1	no	—
275	C₂×D₄	—	38	1	no	—
276	C₂×D₄	—	76	1	no	—
277	C₂×D₄	—	76	1	no	—
278	C₂²×C₄	—	19	1	no	—
279	C₂²×C₄	—	19	1	no	—
280	C₂²×C₄	—	38	1	no	—
281	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
282	SD₁₆	—	76	1	no	—
283	SD₁₆	—	76	1	no	—
284	SD₁₆	—	76	1	no	—
285	SD₁₆	—	76	1	no	—
286	M₁₆	—	76	1	no	—
287	C₂×C₈	—	19	1	no	—
288	C₂×C₈	—	19	1	no	—
289	C₂×C₈	—	76	1	no	—
290	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
291	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	19	1	no	—
294	C₄⋊C₄	—	38	1	no	—
295	C₄⋊C₄	—	38	1	no	—
296	C₄⋊C₄	—	38	1	no	—
297	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
298	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
299	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
300	C₂²⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₂²⋊C₄	—	38	1	no	—
303	C₂²⋊C₄	—	38	1	no	—
304	C₂²⋊C₄	—	38	1	no	—
305	C₂²⋊C₄	—	38	1	no	—
306	C₂²⋊C₄	—	38	1	no	—
307	C₂²⋊C₄	—	38	1	no	—
308	C₂²⋊C₄	—	38	1	no	—
309	C₂²⋊C₄	—	38	1	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	38	1	no	—
312	C₂³	—	19	1	no	—
313	C₂³	—	19	1	no	—
314	C₂³	—	38	1	no	—
315	C₂³	—	38	1	no	—
316	C₂³	—	76	2	no	—
317	C₂³	—	152	1	no	—
318	C₂³	—	152	1	no	—
319	C₂³	D₄×D₁₉	1	1	yes	characteristic
320	Q₈	—	2	1	no	—
321	Q₈	—	2	1	no	—
322	Q₈	—	38	1	no	—
323	Q₈	—	38	1	no	—
324	Q₈	—	76	1	no	—
325	Q₈	—	76	2	no	—
326	D₄	—	38	1	no	—
327	D₄	—	38	1	no	—
328	D₄	—	38	1	no	—
329	D₄	—	38	1	no	—
330	D₄	—	76	1	no	—
331	D₄	—	76	2	no	—
332	D₄	—	76	1	no	—
333	D₄	—	76	1	no	—
334	D₄	—	152	1	no	—
335	D₄	—	152	1	no	—
336	D₄	—	152	1	no	—
337	D₄	—	152	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	19	1	no	—
345	C₂×C₄	—	19	1	no	—
346	C₂×C₄	—	38	1	no	—
347	C₂×C₄	—	38	1	no	—
348	C₂×C₄	—	38	1	no	—
349	C₂×C₄	—	38	1	no	—
350	C₂×C₄	—	38	1	no	—
351	C₂×C₄	—	38	1	no	—
352	C₂×C₄	—	76	2	no	—
353	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
354	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	38	1	no	—
358	C₈	—	38	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	38	1	no	—
363	C₂²	—	38	1	no	—
364	C₂²	—	38	1	no	—
365	C₂²	—	38	1	no	—
366	C₂²	—	38	1	no	—
367	C₂²	—	38	1	no	—
368	C₂²	—	76	1	no	—
369	C₂²	—	76	1	no	—
370	C₂²	—	76	1	no	—
371	C₂²	—	76	1	no	—
372	C₂²	—	76	1	no	—
373	C₂²	—	76	1	no	—
374	C₂²	—	152	4	no	—
375	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	38	1	no	—
382	C₄	—	38	1	no	—
383	C₄	—	76	1	no	—
384	C₄	—	76	1	no	—
385	C₄	#10597435	1	1	yes	characteristic
386	C₄	#10597435	1	1	yes	characteristic
387	C₂	—	4	1	no	—
388	C₂	—	76	1	no	—
389	C₂	—	76	1	no	—
390	C₂	—	152	1	no	—
391	C₂	—	152	1	no	—
392	C₂	#11927105	1	1	yes	characteristic
393	C₂	#11927351	1	1	yes	characteristic
394	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
prime radical	#11927113	C₂
hypercenter	#485	D₁₉
hypocenter	C₁₉	#3200
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. #11927117	C₂	semidirect
3. #11926885	C₂	semidirect
4. #11926871	C₂	semidirect
5. #11926870	C₂	semidirect
6. #11926793	C₂	semidirect
7. #11926791	C₂	semidirect
8. #11926776	C₂	semidirect
9. #11926774	C₂	semidirect
10. #11926697	C₂	semidirect
11. #11926694	C₂	semidirect
12. #11926684	C₂	semidirect
13. #11926684	C₂	semidirect
14. #11926509	C₂	semidirect
15. C₁₉×#485	C₂	semidirect
16. C₂×Q₈×D₁₉	C₂²	semidirect
21. #10597392	C₂²	semidirect
27. C₂×#64515	C₂²	semidirect
28. C₂×C₈×D₁₉	C₂²	semidirect
29. #10597343	C₂²	semidirect
35. #10597338	C₂²	semidirect
43. C₁₉×#107	C₂²	semidirect
44. C₁₉×#106	C₂²	semidirect
45. C₁₉×#103	C₂²	semidirect
46. C₁₉×#103	C₂²	semidirect
51. (C₂×D₁₉)⋊C₈	C₂²	semidirect
52. (C₂×D₁₉)⋊C₈	C₂²	semidirect
53. #10597267	C₂²	semidirect
54. #10597267	C₂²	semidirect
57. #10597265	C₂²	semidirect
58. #10597264	C₂²	semidirect
193. #485	D₁₉	semidirect
241. #107	C₂×D₁₉	semidirect
243. #106	C₂×D₁₉	semidirect
246. #103	C₂×D₁₉	semidirect
247. #103	C₂×D₁₉	semidirect
256. C₁₉	#3200	semidirect

Maximal subgroups

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

subgroup	index
#11927117	2
#11927113	2
#11926885	2
#11926871	2
#11926870	2
#11926793	2
#11926791	2
#11926776	2
#11926774	2
#11926697	2
#11926694	2
#11926684	2
#11926509	2
C₁₉×#485	2
#3200	19