Subgroups — #18083806

Order 4864.

654 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926947	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926825	C₂	1	1	yes	maximal, characteristic
3	#14568589	C₂	1	1	yes	maximal, characteristic
4	#14564557	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₂×#10597392	—	2	2	no	—
10	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
11	#11926947	—	2	2	no	—
12	#11926947	—	2	2	no	—
13	#11926825	—	2	2	no	—
14	#11926825	—	2	2	no	—
15	C₂×#10597275	—	2	1	no	—
16	C₂×#10597264	—	2	2	no	—
17	C₂×#10597273	—	2	2	no	—
18	C₂×#10597278	—	2	1	no	—
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#11926479	—	2	2	no	—
21	#11926445	—	2	1	no	—
22	#11926413	—	2	1	no	—
23	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
24	#11926271	—	2	2	no	—
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₉×#332	—	2	2	no	—
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×D₇₆	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₉	—	2	1	no	—
32	C₂²×Dic₃₈	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
41	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	#10597392	—	4	4	no	—
43	#10597392	—	4	4	no	—
44	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
45	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
46	C₂×C₄⋊Dic₁₉	—	2	1	no	—
47	C₂×C₄⋊Dic₁₉	—	2	1	no	—
48	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
50	C₂×Dic₁₉⋊C₄	—	2	4	no	—
51	C₂×C₄×Dic₁₉	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₄×D₇₆	—	2	1	no	—
54	C₄×D₇₆	—	2	1	no	—
55	C₄×D₇₆	—	2	1	no	—
56	C₄×D₇₆	—	2	1	no	—
57	#10597315	—	2	1	no	—
58	#10597315	—	2	1	no	—
59	#10597315	—	2	1	no	—
60	#10597315	D₄	1	2	yes	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	—	2	1	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
65	C₁₉⋊#95	—	2	1	no	—
66	#10597278	—	2	4	no	—
67	#10597275	—	2	4	no	—
68	#10597273	—	4	4	no	—
69	#10597264	—	2	8	no	—
70	C₄×C₁₉⋊C₈	—	2	1	no	—
71	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
72	C₂³×D₁₉	—	2	1	no	—
73	C₂×Q₈×C₁₉	—	4	1	no	—
74	C₂×Q₈×C₁₉	—	4	1	no	—
75	C₂×Q₈×C₁₉	—	4	2	no	—
76	C₂×Q₈×C₁₉	—	4	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×Dic₁₉	—	2	2	no	—
82	C₂²×Dic₁₉	—	2	1	no	—
83	C₂²×Dic₁₉	—	4	1	no	—
84	C₂×D₇₆	—	2	1	no	—
85	C₂×D₇₆	—	2	1	no	—
86	C₂×D₇₆	—	2	1	no	—
87	C₂×D₇₆	—	2	1	no	—
88	C₂×D₇₆	—	2	1	no	—
89	C₂×D₇₆	Q₁₆	1	2	yes	—
90	C₂×C₄×D₁₉	—	4	1	no	—
91	C₂×C₄×D₁₉	—	4	1	no	—
92	C₂×C₄×D₁₉	—	4	2	no	—
93	C₂×C₄×D₁₉	—	4	2	no	—
94	C₂×Dic₃₈	—	2	2	no	—
95	C₂×Dic₃₈	—	4	2	no	—
96	C₂×Dic₃₈	—	4	2	no	—
97	C₂×Dic₃₈	—	4	1	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₂×C₈×C₁₉	—	4	1	no	—
102	C₂×C₈×C₁₉	—	4	2	no	—
103	C₄⋊C₄×C₁₉	—	2	2	no	—
104	C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₄⋊C₄×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₉	#41	1	1	yes	characteristic
111	(C₂×D₁₉)⋊C₄	—	4	8	no	—
112	(C₂×D₁₉)⋊C₄	—	4	1	no	—
113	(C₂×D₁₉)⋊C₄	—	4	1	no	—
114	C₄⋊Dic₁₉	—	2	2	no	—
115	C₄⋊Dic₁₉	—	2	2	no	—
116	C₄⋊Dic₁₉	—	2	1	no	—
117	C₄⋊Dic₁₉	—	2	2	no	—
118	C₄⋊Dic₁₉	—	2	1	no	—
119	C₄⋊Dic₁₉	—	4	1	no	—
120	C₄⋊Dic₁₉	—	4	1	no	—
121	C₄⋊Dic₁₉	D₈	1	4	yes	—
122	Dic₁₉⋊C₄	—	4	8	no	—
123	C₄×Dic₁₉	—	4	1	no	—
124	C₄×Dic₁₉	—	4	1	no	—
125	C₂×C₁₉⋊C₈	—	2	4	no	—
126	C₂×C₁₉⋊C₈	—	2	2	no	—
127	#10076	—	19	1	no	maximal, Sylow
128	C₂³×C₁₉	#120	1	1	yes	characteristic
129	C₂²×D₁₉	—	2	2	no	—
130	C₂²×D₁₉	—	4	1	no	—
131	C₂²×D₁₉	—	4	2	no	—
132	C₂²×D₁₉	—	4	1	no	—
133	C₂²×D₁₉	—	4	2	no	—
134	Q₈×C₁₉	—	8	2	no	—
135	Q₈×C₁₉	—	8	1	no	—
136	Q₈×C₁₉	—	8	1	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	—	4	4	no	—
140	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
147	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
149	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
150	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
152	C₂×Dic₁₉	—	2	4	no	—
153	C₂×Dic₁₉	—	4	2	no	—
154	C₂×Dic₁₉	—	4	2	no	—
155	C₂×Dic₁₉	—	4	2	no	—
156	C₂×Dic₁₉	—	4	1	no	—
157	C₂×Dic₁₉	—	4	2	no	—
158	C₂×Dic₁₉	—	8	2	no	—
159	D₇₆	—	2	2	no	—
160	D₇₆	—	2	2	no	—
161	D₇₆	—	4	1	no	—
162	D₇₆	—	4	1	no	—
163	C₄×D₁₉	—	8	2	no	—
164	C₄×D₁₉	—	8	1	no	—
165	C₄×D₁₉	—	8	1	no	—
166	Dic₃₈	—	4	4	no	—
167	Dic₃₈	—	8	1	no	—
168	Dic₃₈	—	8	1	no	—
169	C₈×C₁₉	—	4	2	no	—
170	C₈×C₁₉	—	8	1	no	—
171	C₁₉⋊C₈	—	2	4	no	—
172	C₂×#500	—	19	1	no	—
173	C₂×#474	—	19	1	no	—
174	#2542	—	19	1	no	—
175	#1981	—	19	1	no	—
176	C₂×#332	D₁₉	1	1	yes	characteristic, complemented
177	C₂×D₄⋊C₈	—	19	1	no	—
178	#1279	—	19	1	no	—
179	C₂²×C₁₉	#392	1	1	yes	characteristic
180	C₂²×C₁₉	#447	1	2	yes	—
181	C₂²×C₁₉	#451	1	1	yes	characteristic
182	C₂²×C₁₉	#452	1	1	yes	characteristic
183	C₂²×C₁₉	#456	1	2	yes	—
184	C₂×D₁₉	—	4	4	no	—
185	C₂×D₁₉	—	4	2	no	—
186	C₂×D₁₉	—	8	2	no	—
187	C₂×D₁₉	—	8	1	no	—
188	C₂×D₁₉	—	8	1	no	—
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	8	2	no	—
192	C₄×C₁₉	#451	1	1	yes	characteristic
193	C₄×C₁₉	#452	1	1	yes	characteristic
194	C₄×C₁₉	#459	1	2	yes	—
195	C₄×C₁₉	#467	1	1	yes	characteristic
196	C₄×C₁₉	#470	1	1	yes	characteristic
197	C₄×C₁₉	#493	1	1	yes	characteristic
198	C₄×C₁₉	#496	1	1	yes	characteristic
199	Dic₁₉	—	4	4	no	—
200	Dic₁₉	—	8	2	no	—
201	Dic₁₉	—	8	1	no	—
202	C₂×C₄⋊Q₈	—	19	1	no	—
203	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
204	C₂×C₂²⋊Q₈	—	38	2	no	—
205	C₂×C₄×D₄	—	19	1	no	—
206	#500	—	38	2	no	—
207	#500	—	38	2	no	—
208	#474	—	38	2	no	—
209	#474	—	38	2	no	—
210	C₂×#107	—	38	1	no	—
211	C₂×#107	—	38	2	no	—
212	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
214	C₂×#103	—	38	2	no	—
215	C₂×#102	—	38	1	no	—
216	C₂×C₄×C₈	—	19	1	no	—
217	#399	—	38	2	no	—
218	#390	—	38	1	no	—
219	#384	—	38	1	no	—
220	C₄×C₄⋊C₄	—	19	1	no	—
221	#332	—	2	2	no	—
222	D₄⋊C₈	—	38	2	no	—
223	C₂×C₁₉	#1647	1	2	yes	—
224	C₂×C₁₉	#1649	1	2	yes	—
225	C₂×C₁₉	#2001	1	1	yes	characteristic
226	C₂×C₁₉	#2005	1	1	yes	characteristic
227	C₂×C₁₉	#2011	1	1	yes	characteristic
228	D₁₉	—	8	2	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	—	38	1	no	—
231	C₂²×D₄	—	19	1	no	—
232	C₂³×C₄	—	38	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	—	38	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	19	2	no	—
241	C₄⋊Q₈	—	38	1	no	—
242	C₄⋊Q₈	—	38	1	no	—
243	C₄⋊Q₈	—	38	1	no	—
244	C₂²⋊Q₈	—	76	4	no	—
245	C₂²⋊Q₈	—	76	4	no	—
246	C₄×D₄	—	38	1	no	—
247	C₄×D₄	—	38	1	no	—
248	C₄×D₄	—	38	1	no	—
249	C₄×D₄	—	38	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	19	2	no	—
252	C₂×C₄⋊C₄	—	19	1	no	—
253	C₂×C₄⋊C₄	—	38	1	no	—
254	C₂×C₄⋊C₄	—	38	1	no	—
255	C₂×C₄⋊C₄	—	38	4	no	—
256	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
257	C₂×C₂²⋊C₄	—	38	4	no	—
258	C₂×C₂²⋊C₄	—	38	1	no	—
259	C₂×C₄²	—	38	1	no	—
260	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
261	#107	—	38	8	no	—
262	#107	—	38	4	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
267	#103	—	76	4	no	—
268	#102	—	38	4	no	—
269	C₄×C₈	—	19	2	no	—
270	C₄×C₈	—	38	1	no	—
271	#95	—	38	1	no	—
272	C₁₉	#10076	1	1	yes	characteristic, complemented, Sylow
273	C₂⁴	—	38	1	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×Q₈	—	38	2	no	—
279	C₂×Q₈	—	76	1	no	—
280	C₂×Q₈	—	76	2	no	—
281	C₂×Q₈	—	76	2	no	—
282	C₂×D₄	—	19	2	no	—
283	C₂×D₄	—	38	1	no	—
284	C₂×D₄	—	38	1	no	—
285	C₂×D₄	—	38	1	no	—
286	C₂×D₄	—	38	1	no	—
287	C₂×D₄	—	38	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	38	2	no	—
290	C₂²×C₄	—	38	1	no	—
291	C₂²×C₄	—	76	1	no	—
292	C₂²×C₄	—	76	1	no	—
293	C₂²×C₄	—	76	1	no	—
294	C₂²×C₄	—	76	2	no	—
295	C₂²×C₄	—	76	2	no	—
296	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
297	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	38	4	no	—
305	C₂×C₈	—	38	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	19	4	no	—
311	C₄⋊C₄	—	38	2	no	—
312	C₄⋊C₄	—	38	2	no	—
313	C₄⋊C₄	—	38	1	no	—
314	C₄⋊C₄	—	38	2	no	—
315	C₄⋊C₄	—	38	1	no	—
316	C₄⋊C₄	—	76	8	no	—
317	C₄⋊C₄	—	76	1	no	—
318	C₄⋊C₄	—	76	1	no	—
319	C₂²⋊C₄	—	76	8	no	—
320	C₂²⋊C₄	—	76	1	no	—
321	C₂²⋊C₄	—	76	1	no	—
322	C₄²	—	76	1	no	—
323	C₄²	—	76	1	no	—
324	C₄²	#64541	1	1	yes	characteristic
325	C₄²	D₄×D₁₉	1	1	yes	characteristic
326	C₄²	D₄×D₁₉	1	1	yes	characteristic
327	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
328	C₂³	—	38	2	no	—
329	C₂³	—	76	2	no	—
330	C₂³	—	76	1	no	—
331	C₂³	—	76	1	no	—
332	C₂³	—	76	2	no	—
333	C₂³	#10597328	1	1	yes	characteristic
334	Q₈	—	8	1	no	—
335	Q₈	—	8	1	no	—
336	Q₈	—	8	2	no	—
337	Q₈	—	76	4	no	—
338	Q₈	—	152	1	no	—
339	Q₈	—	152	1	no	—
340	D₄	—	38	2	no	—
341	D₄	—	38	2	no	—
342	D₄	—	76	1	no	—
343	D₄	—	76	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	38	4	no	—
348	C₂×C₄	—	76	2	no	—
349	C₂×C₄	—	76	2	no	—
350	C₂×C₄	—	76	2	no	—
351	C₂×C₄	—	76	1	no	—
352	C₂×C₄	—	76	2	no	—
353	C₂×C₄	—	152	2	no	—
354	C₂×C₄	—	152	1	no	—
355	C₂×C₄	—	152	1	no	—
356	C₂×C₄	—	152	2	no	—
357	C₂×C₄	#10597328	1	1	yes	characteristic
358	C₂×C₄	#10597330	1	1	yes	characteristic
359	C₂×C₄	#10597330	1	1	yes	characteristic
360	C₂×C₄	D₈×D₁₉	1	2	yes	—
361	C₂×C₄	#10597360	1	2	yes	—
362	C₂×C₄	#10597361	1	1	yes	characteristic
363	C₂×C₄	#10597362	1	1	yes	characteristic
364	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
365	C₂×C₄	#10597364	1	1	yes	characteristic
366	C₂×C₄	#10597376	1	1	yes	characteristic
367	C₂×C₄	#10597383	1	1	yes	characteristic
368	C₂×C₄	#10597386	1	1	yes	characteristic
369	C₈	—	4	2	no	—
370	C₈	—	8	1	no	—
371	C₈	—	38	4	no	—
372	C₂²	—	76	2	no	—
373	C₂²	—	76	4	no	—
374	C₂²	—	152	2	no	—
375	C₂²	—	152	1	no	—
376	C₂²	—	152	1	no	—
377	C₂²	#11926453	1	1	yes	characteristic
378	C₂²	#11926679	1	2	yes	—
379	C₂²	#11926701	1	1	yes	characteristic
380	C₂²	#11926709	1	1	yes	characteristic
381	C₂²	#11926729	1	2	yes	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	76	4	no	—
386	C₄	—	152	1	no	—
387	C₄	—	152	2	no	—
388	C₄	#11926698	1	1	yes	characteristic
389	C₄	#11926703	1	1	yes	characteristic
390	C₄	#11926738	1	2	yes	—
391	C₄	#11926784	1	1	yes	characteristic
392	C₄	#11926801	1	1	yes	characteristic
393	C₄	#11926919	1	1	yes	characteristic
394	C₄	#11926930	1	1	yes	characteristic
395	C₂	—	152	2	no	—
396	C₂	#14562871	1	2	yes	—
397	C₂	#14562885	1	2	yes	—
398	C₂	#14564644	1	1	yes	characteristic
399	C₂	#14564673	1	1	yes	characteristic
400	C₂	#14564707	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#332	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₇₆	D₄
hypercenter	C₂×#332	D₁₉
hypocenter	C₁₉	#10076
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#332

Complements

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

N	H ≅ G/N	type
1. C₂×#11926947	C₂	semidirect
4. #14564557	C₂	semidirect
6. #14561474	C₂	semidirect
7. C₂×C₁₉×#332	C₂	semidirect
176. C₂×#332	D₁₉	semidirect
272. C₁₉	#10076	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926947	2
C₂×#11926825	2
#14568589	2
#14564557	2
C₂×#11926271	2
#14561474	2
C₂×C₁₉×#332	2
#10076	19