Group #18086209 — subgroups

Subgroups — #18086209

Order 4864.

376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926836	C₂	1	1	yes	maximal, characteristic
2	#14563628	C₂	1	1	yes	maximal, characteristic
3	#14562410	C₂	1	1	yes	maximal, characteristic
4	#14562320	C₂	1	1	yes	maximal, characteristic
5	#14562029	C₂	1	1	yes	maximal, characteristic
6	#14561530	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1548	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
9	#11926836	—	2	2	no	—
10	#11926836	—	2	2	no	—
11	#11926597	C₂²	1	1	yes	characteristic
12	C₂×#10597264	—	2	1	no	—
13	#11926568	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#10597267	—	2	1	no	—
16	C₂×#10597281	—	2	1	no	—
17	#11926312	—	2	1	no	—
18	#11926297	—	2	2	no	—
19	#11926290	—	2	2	no	—
20	#11926274	—	2	2	no	—
21	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₁₉×#431	C₂²	1	1	yes	characteristic
23	C₁₉×#423	C₂²	1	1	yes	characteristic
24	C₁₉×#333	—	2	2	no	—
25	C₂²×Q₈×C₁₉	—	2	1	no	—
26	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
27	C₂×M₁₆×C₁₉	—	2	1	no	—
28	C₁₉×C₄⋊Q₈	—	2	1	no	—
29	C₁₉×C₄⋊Q₈	—	2	1	no	—
30	C₁₉×C₄⋊Q₈	—	2	1	no	—
31	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
36	C₂×Dic₁₉⋊C₄	—	2	1	no	—
37	C₂×C₄×Dic₁₉	—	2	1	no	—
38	C₂×#64520	—	2	1	no	—
39	C₂²×C₁₉⋊C₈	—	2	1	no	—
40	C₄×Dic₃₈	—	2	1	no	—
41	C₄×Dic₃₈	—	2	1	no	—
42	C₄×Dic₃₈	—	2	1	no	—
43	C₄×Dic₃₈	—	2	1	no	—
44	C₁₉×C₄⋊C₈	—	2	1	no	—
45	C₁₉×C₄⋊C₈	—	2	1	no	—
46	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
47	C₁₉×C₂²⋊C₈	—	2	1	no	—
48	C₄×C₈×C₁₉	—	2	1	no	—
49	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
50	#10597281	—	4	2	no	—
51	#10597267	—	2	4	no	—
52	#10597264	—	2	4	no	—
53	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
56	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
57	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
58	C₄×C₁₉⋊C₈	—	2	1	no	—
59	C₂×Q₈×C₁₉	—	2	2	no	—
60	C₂×Q₈×C₁₉	—	4	1	no	—
61	C₂×Q₈×C₁₉	—	8	2	no	—
62	C₂²×C₄×C₁₉	—	4	1	no	—
63	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
66	C₂²×Dic₁₉	—	2	1	no	—
67	C₂²×Dic₁₉	—	2	1	no	—
68	C₂×Dic₃₈	—	2	1	no	—
69	C₂×Dic₃₈	—	2	1	no	—
70	C₂×Dic₃₈	—	2	1	no	—
71	C₂×Dic₃₈	—	2	1	no	—
72	C₂×Dic₃₈	—	2	1	no	—
73	C₂×Dic₃₈	Q₁₆	1	2	yes	—
74	M₁₆×C₁₉	—	4	1	no	—
75	M₁₆×C₁₉	—	4	1	no	—
76	C₂×C₈×C₁₉	—	2	2	no	—
77	C₂×C₈×C₁₉	—	4	1	no	—
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₄⋊C₄×C₁₉	—	4	1	no	—
81	C₄⋊C₄×C₁₉	—	4	1	no	—
82	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₁₉	#41	1	1	yes	characteristic
86	C₄⋊Dic₁₉	—	2	1	no	—
87	C₄⋊Dic₁₉	—	2	1	no	—
88	Dic₁₉⋊C₄	—	4	1	no	—
89	Dic₁₉⋊C₄	—	4	1	no	—
90	C₄×Dic₁₉	—	4	1	no	—
91	C₄×Dic₁₉	—	4	1	no	—
92	#64520	—	4	1	no	—
93	#64520	—	4	1	no	—
94	C₂×C₁₉⋊C₈	—	2	2	no	—
95	C₂×C₁₉⋊C₈	—	4	1	no	—
96	C₂×C₁₉⋊C₈	—	4	1	no	—
97	C₂×C₁₉⋊C₈	—	4	1	no	—
98	C₂×C₁₉⋊C₈	—	4	1	no	—
99	#10455	—	19	1	no	maximal, Sylow
100	C₂³×C₁₉	#123	1	1	yes	characteristic
101	Q₈×C₁₉	—	8	2	no	—
102	Q₈×C₁₉	—	8	2	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	8	2	no	—
107	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
110	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
111	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
112	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
115	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
116	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
117	C₂×Dic₁₉	—	2	2	no	—
118	C₂×Dic₁₉	—	4	1	no	—
119	C₂×Dic₁₉	—	4	1	no	—
120	C₂×Dic₁₉	—	4	1	no	—
121	C₂×Dic₁₉	—	8	1	no	—
122	Dic₃₈	—	2	2	no	—
123	Dic₃₈	—	2	2	no	—
124	Dic₃₈	—	4	1	no	—
125	Dic₃₈	—	4	1	no	—
126	C₈×C₁₉	—	4	2	no	—
127	C₈×C₁₉	—	8	1	no	—
128	C₁₉⋊C₈	—	4	2	no	—
129	C₁₉⋊C₈	—	8	1	no	—
130	C₁₉⋊C₈	—	8	1	no	—
131	C₂×#477	—	19	1	no	—
132	#1801	—	19	1	no	—
133	#1571	—	19	1	no	—
134	#1549	—	19	1	no	—
135	#1548	D₁₉	1	1	yes	characteristic
136	#1479	—	19	1	no	—
137	#1301	—	19	1	no	—
138	C₂²×C₁₉	—	2	1	no	—
139	C₂²×C₁₉	—	2	1	no	—
140	C₂²×C₁₉	#394	1	1	yes	characteristic
141	C₂²×C₁₉	#484	1	1	yes	characteristic
142	C₂²×C₁₉	#485	1	1	yes	characteristic
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	—	2	1	no	—
146	C₄×C₁₉	—	8	2	no	—
147	C₄×C₁₉	#449	1	1	yes	characteristic
148	C₄×C₁₉	#451	1	1	yes	characteristic
149	C₄×C₁₉	#467	1	1	yes	characteristic
150	C₄×C₁₉	#468	1	1	yes	characteristic
151	C₄×C₁₉	#473	1	2	yes	—
152	Dic₁₉	—	4	2	no	—
153	Dic₁₉	—	8	1	no	—
154	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
155	C₂×C₄×Q₈	—	19	1	no	—
156	#477	—	38	2	no	—
157	#477	—	38	2	no	—
158	#431	—	19	1	no	—
159	#431	C₂×D₁₉	1	1	yes	characteristic
160	C₂×#107	—	38	1	no	—
161	#423	—	19	1	no	—
162	#423	C₂×D₁₉	1	1	yes	characteristic
163	C₂×C₄⋊C₈	—	19	1	no	—
164	C₂×#103	—	38	1	no	—
165	C₂×#101	—	38	1	no	—
166	#343	—	38	1	no	—
167	#335	—	38	2	no	—
168	#333	—	2	2	no	—
169	#332	—	38	2	no	—
170	Q₈⋊C₈	—	38	2	no	—
171	C₂×C₁₉	—	2	1	no	—
172	C₂×C₁₉	—	2	1	no	—
173	C₂×C₁₉	#2036	1	1	yes	characteristic
174	C₂×C₁₉	#2047	1	1	yes	characteristic
175	C₂×C₁₉	#2048	1	1	yes	characteristic
176	C₂²×Q₈	—	2	1	no	—
177	C₂²×Q₈	—	19	1	no	—
178	C₂×M₁₆	—	2	1	no	—
179	C₂×M₁₆	—	38	1	no	—
180	C₂²×C₈	—	38	1	no	—
181	C₄⋊Q₈	—	2	1	no	—
182	C₄⋊Q₈	—	2	1	no	—
183	C₄⋊Q₈	—	2	1	no	—
184	C₄⋊Q₈	D₇₆	1	2	yes	—
185	C₄×Q₈	—	38	1	no	—
186	C₄×Q₈	—	38	1	no	—
187	C₄×Q₈	—	38	1	no	—
188	C₄×Q₈	—	38	1	no	—
189	C₂×C₄⋊C₄	—	2	1	no	—
190	C₂×C₄⋊C₄	—	2	1	no	—
191	C₂×C₄⋊C₄	—	19	1	no	—
192	C₂×C₄⋊C₄	—	38	1	no	—
193	C₂×C₄²	—	38	1	no	—
194	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
195	#107	—	38	4	no	—
196	C₄⋊C₈	—	2	1	no	—
197	C₄⋊C₈	—	2	1	no	—
198	C₄⋊C₈	—	19	2	no	—
199	C₄⋊C₈	—	38	1	no	—
200	C₄⋊C₈	—	38	1	no	—
201	C₄⋊C₈	—	38	1	no	—
202	C₄⋊C₈	—	38	1	no	—
203	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
204	#103	—	38	4	no	—
205	#101	—	76	2	no	—
206	C₂²⋊C₈	—	2	1	no	—
207	C₂²⋊C₈	—	38	1	no	—
208	C₄×C₈	—	2	1	no	—
209	C₄×C₈	—	38	1	no	—
210	C₁₉	#10455	1	1	yes	characteristic, complemented, Sylow
211	C₂×Q₈	—	2	2	no	—
212	C₂×Q₈	—	4	1	no	—
213	C₂×Q₈	—	8	2	no	—
214	C₂×Q₈	—	19	2	no	—
215	C₂×Q₈	—	38	1	no	—
216	C₂×Q₈	—	38	1	no	—
217	C₂×Q₈	—	38	1	no	—
218	C₂×Q₈	—	38	1	no	—
219	C₂×Q₈	—	38	1	no	—
220	C₂²×C₄	—	4	1	no	—
221	C₂²×C₄	—	38	1	no	—
222	C₂²×C₄	—	38	1	no	—
223	C₂²×C₄	#64541	1	1	yes	characteristic
224	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
225	C₂²×C₄	#64543	1	1	yes	characteristic
226	M₁₆	—	4	1	no	—
227	M₁₆	—	4	1	no	—
228	M₁₆	—	76	1	no	—
229	M₁₆	—	76	1	no	—
230	C₂×C₈	—	2	2	no	—
231	C₂×C₈	—	4	1	no	—
232	C₂×C₈	—	38	2	no	—
233	C₂×C₈	—	76	1	no	—
234	C₂×C₈	—	76	1	no	—
235	C₂×C₈	—	76	1	no	—
236	C₂×C₈	—	76	1	no	—
237	C₄⋊C₄	—	2	2	no	—
238	C₄⋊C₄	—	2	2	no	—
239	C₄⋊C₄	—	4	1	no	—
240	C₄⋊C₄	—	4	1	no	—
241	C₄⋊C₄	—	38	1	no	—
242	C₄⋊C₄	—	38	1	no	—
243	C₄⋊C₄	—	76	1	no	—
244	C₄⋊C₄	—	76	1	no	—
245	C₄²	—	76	1	no	—
246	C₄²	—	76	1	no	—
247	C₄²	C₂×D₇₆	1	1	yes	characteristic
248	C₄²	D₄×D₁₉	1	1	yes	characteristic
249	C₄²	#64543	1	1	yes	characteristic
250	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
251	C₂³	#10597329	1	1	yes	characteristic
252	Q₈	—	8	2	no	—
253	Q₈	—	8	2	no	—
254	Q₈	—	38	2	no	—
255	Q₈	—	38	2	no	—
256	Q₈	—	76	1	no	—
257	Q₈	—	76	1	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	4	1	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	8	2	no	—
262	C₂×C₄	—	38	2	no	—
263	C₂×C₄	—	76	1	no	—
264	C₂×C₄	—	76	1	no	—
265	C₂×C₄	—	76	1	no	—
266	C₂×C₄	—	152	1	no	—
267	C₂×C₄	#10597328	1	1	yes	characteristic
268	C₂×C₄	#10597331	1	1	yes	characteristic
269	C₂×C₄	#10597332	1	1	yes	characteristic
270	C₂×C₄	#10597360	1	1	yes	characteristic
271	C₂×C₄	#10597361	1	1	yes	characteristic
272	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
273	C₂×C₄	#10597365	1	1	yes	characteristic
274	C₂×C₄	#10597376	1	1	yes	characteristic
275	C₂×C₄	#10597384	1	1	yes	characteristic
276	C₂×C₄	#10597385	1	1	yes	characteristic
277	C₈	—	4	2	no	—
278	C₈	—	8	1	no	—
279	C₈	—	76	2	no	—
280	C₈	—	152	1	no	—
281	C₈	—	152	1	no	—
282	C₂²	—	2	1	no	—
283	C₂²	—	2	1	no	—
284	C₂²	#11926460	1	1	yes	characteristic
285	C₂²	#11926878	1	1	yes	characteristic
286	C₂²	#11926884	1	1	yes	characteristic
287	C₄	—	2	1	no	—
288	C₄	—	2	1	no	—
289	C₄	—	2	1	no	—
290	C₄	—	8	2	no	—
291	C₄	—	76	2	no	—
292	C₄	—	152	1	no	—
293	C₄	#11926692	1	1	yes	characteristic
294	C₄	#11926701	1	1	yes	characteristic
295	C₄	#11926782	1	1	yes	characteristic
296	C₄	#11926787	1	1	yes	characteristic
297	C₄	#11926817	1	2	yes	—
298	C₂	—	2	1	no	—
299	C₂	—	2	1	no	—
300	C₂	#14564837	1	1	yes	characteristic
301	C₂	#14564902	1	1	yes	characteristic
302	C₂	#14564907	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926836

C₂

yes

maximal, characteristic

#14563628

C₂

yes

maximal, characteristic

#14562410

C₂

yes

maximal, characteristic

#14562320

C₂

yes

maximal, characteristic

#14562029

C₂

yes

maximal, characteristic

#14561530

C₂

yes

maximal, characteristic

C₁₉×#1548

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#10597264

—

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

—

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#333

—

C₂²×Q₈×C₁₉

—

C₂²×Dic₃₈

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

#10597281

—

#10597267

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₁₆

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10455

—

maximal, Sylow

100

C₂³×C₁₉

#123

yes

characteristic

101

Q₈×C₁₉

—

102

Q₈×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

#120

yes

characteristic

108

C₂×C₄×C₁₉

#121

yes

characteristic

109

C₂×C₄×C₁₉

#121

yes

characteristic

110

C₂×C₄×C₁₉

#121

yes

characteristic

111

C₂×C₄×C₁₉

#123

yes

characteristic

112

C₂×C₄×C₁₉

#124

yes

characteristic

113

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

114

C₂×C₄×C₁₉

#135

yes

characteristic

115

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

116

C₂×C₄×C₁₉

#137

yes

characteristic

117

C₂×Dic₁₉

—

118

C₂×Dic₁₉

—

119

C₂×Dic₁₉

—

120

C₂×Dic₁₉

—

121

C₂×Dic₁₉

—

122

Dic₃₈

—

123

Dic₃₈

—

124

Dic₃₈

—

125

Dic₃₈

—

126

C₈×C₁₉

—

127

C₈×C₁₉

—

128

C₁₉⋊C₈

—

129

C₁₉⋊C₈

—

130

C₁₉⋊C₈

—

131

C₂×#477

—

132

#1801

—

133

#1571

—

134

#1549

—

135

#1548

D₁₉

yes

characteristic

136

#1479

—

137

#1301

—

138

C₂²×C₁₉

—

139

C₂²×C₁₉

—

140

C₂²×C₁₉

#394

yes

characteristic

141

C₂²×C₁₉

#484

yes

characteristic

142

C₂²×C₁₉

#485

yes

characteristic

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

#449

yes

characteristic

148

C₄×C₁₉

#451

yes

characteristic

149

C₄×C₁₉

#467

yes

characteristic

150

C₄×C₁₉

#468

yes

characteristic

151

C₄×C₁₉

#473

yes

—

152

Dic₁₉

—

153

Dic₁₉

—

154

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

155

C₂×C₄×Q₈

—

156

#477

—

157

#477

—

158

#431

—

159

#431

C₂×D₁₉

yes

characteristic

160

C₂×#107

—

161

#423

—

162

#423

C₂×D₁₉

yes

characteristic

163

C₂×C₄⋊C₈

—

164

C₂×#103

—

165

C₂×#101

—

166

#343

—

167

#335

—

168

#333

—

169

#332

—

170

Q₈⋊C₈

—

171

C₂×C₁₉

—

172

C₂×C₁₉

—

173

C₂×C₁₉

#2036

yes

characteristic

174

C₂×C₁₉

#2047

yes

characteristic

175

C₂×C₁₉

#2048

yes

characteristic

176

C₂²×Q₈

—

177

C₂²×Q₈

—

178

C₂×M₁₆

—

179

C₂×M₁₆

—

180

C₂²×C₈

—

181

C₄⋊Q₈

—

182

C₄⋊Q₈

—

183

C₄⋊Q₈

—

184

C₄⋊Q₈

D₇₆

yes

—

185

C₄×Q₈

—

186

C₄×Q₈

—

187

C₄×Q₈

—

188

C₄×Q₈

—

189

C₂×C₄⋊C₄

—

190

C₂×C₄⋊C₄

—

191

C₂×C₄⋊C₄

—

192

C₂×C₄⋊C₄

—

193

C₂×C₄²

—

194

C₂×C₄²

C₂²×D₁₉

yes

characteristic

195

#107

—

196

C₄⋊C₈

—

197

C₄⋊C₈

—

198

C₄⋊C₈

—

199

C₄⋊C₈

—

200

C₄⋊C₈

—

201

C₄⋊C₈

—

202

C₄⋊C₈

—

203

C₄⋊C₈

C₂²⋊D₁₉

yes

—

204

#103

—

205

#101

—

206

C₂²⋊C₈

—

207

C₂²⋊C₈

—

208

C₄×C₈

—

209

C₄×C₈

—

210

C₁₉

#10455

yes

characteristic, complemented, Sylow

211

C₂×Q₈

—

212

C₂×Q₈

—

213

C₂×Q₈

—

214

C₂×Q₈

—

215

C₂×Q₈

—

216

C₂×Q₈

—

217

C₂×Q₈

—

218

C₂×Q₈

—

219

C₂×Q₈

—

220

C₂²×C₄

—

221

C₂²×C₄

—

222

C₂²×C₄

—

223

C₂²×C₄

#64541

yes

characteristic

224

C₂²×C₄

D₄×D₁₉

yes

characteristic

225

C₂²×C₄

#64543

yes

characteristic

226

M₁₆

—

227

M₁₆

—

228

M₁₆

—

229

M₁₆

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

—

233

C₂×C₈

—

234

C₂×C₈

—

235

C₂×C₈

—

236

C₂×C₈

—

237

C₄⋊C₄

—

238

C₄⋊C₄

—

239

C₄⋊C₄

—

240

C₄⋊C₄

—

241

C₄⋊C₄

—

242

C₄⋊C₄

—

243

C₄⋊C₄

—

244

C₄⋊C₄

—

245

C₄²

—

246

C₄²

—

247

C₄²

C₂×D₇₆

yes

characteristic

248

C₄²

D₄×D₁₉

yes

characteristic

249

C₄²

#64543

yes

characteristic

250

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

251

C₂³

#10597329

yes

characteristic

252

Q₈

—

253

Q₈

—

254

Q₈

—

255

Q₈

—

256

Q₈

—

257

Q₈

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

266

C₂×C₄

—

152

—

267

C₂×C₄

#10597328

yes

characteristic

268

C₂×C₄

#10597331

yes

characteristic

269

C₂×C₄

#10597332

yes

characteristic

270

C₂×C₄

#10597360

yes

characteristic

271

C₂×C₄

#10597361

yes

characteristic

272

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

273

C₂×C₄

#10597365

yes

characteristic

274

C₂×C₄

#10597376

yes

characteristic

275

C₂×C₄

#10597384

yes

characteristic

276

C₂×C₄

#10597385

yes

characteristic

277

C₈

—

278

C₈

—

279

C₈

—

280

C₈

—

152

—

281

C₈

—

152

—

282

C₂²

—

283

C₂²

—

284

C₂²

#11926460

yes

characteristic

285

C₂²

#11926878

yes

characteristic

286

C₂²

#11926884

yes

characteristic

287

C₄

—

288

C₄

—

289

C₄

—

290

C₄

—

291

C₄

—

292

C₄

—

152

—

293

C₄

#11926692

yes

characteristic

294

C₄

#11926701

yes

characteristic

295

C₄

#11926782

yes

characteristic

296

C₄

#11926787

yes

characteristic

297

C₄

#11926817

yes

—

298

C₂

—

299

C₂

—

300

C₂

#14564837

yes

characteristic

301

C₂

#14564902

yes

characteristic

302

C₂

#14564907

yes

characteristic

	subgroup	G/H
center	C₂²	#11926460
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1548	C₂
socle	C₂²×C₁₉	#394
prime radical	C₂³×C₁₉	#123
hypercenter	#1548	D₁₉
hypocenter	C₁₉	#10455
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

subgroup

G/H

center

C₂²

#11926460

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1548

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

N	H ≅ G/N	type
210. C₁₉	#10455	semidirect

H ≅ G/N

type

210. C₁₉

#10455

semidirect

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

subgroup	index
C₂×#11926836	2
#14563628	2
#14562410	2
#14562320	2
#14562029	2
#14561530	2
C₁₉×#1548	2
#10455	19

subgroup

index

C₁₉×#1548

Subgroups — #18086209

Conjugacy classes of subgroups

Complements

Maximal subgroups