Group #18087335 — subgroups

Subgroups — #18087335

Order 4864.

310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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	#14564456	C₂	1	1	yes	maximal, characteristic
2	#14563809	C₂	1	1	yes	maximal, characteristic
3	#14562307	C₂	1	1	yes	maximal, characteristic
4	#14561495	C₂	1	1	yes	maximal, characteristic
5	#14561494	C₂	1	1	yes	maximal, characteristic
6	#14561479	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	C₂×#10597279	—	2	1	no	—
10	C₂×#10597279	—	2	1	no	—
11	#11926568	C₂²	1	1	yes	characteristic
12	C₂×#10597292	—	2	1	no	—
13	C₂×#10597292	—	2	1	no	—
14	C₂×#10597260	C₂²	1	1	yes	characteristic
15	#11926410	C₂²	1	1	yes	characteristic
16	#11926290	—	2	2	no	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×#431	C₂²	1	1	yes	characteristic
19	C₁₉×#423	C₂²	1	1	yes	characteristic
20	C₁₉×#332	—	2	2	no	—
21	C₂²×Q₈×C₁₉	—	2	1	no	—
22	C₂×M₁₆×C₁₉	—	2	1	no	—
23	C₁₉×C₄⋊Q₈	—	2	1	no	—
24	C₁₉×C₄⋊Q₈	—	2	1	no	—
25	C₁₉×C₄⋊Q₈	—	2	1	no	—
26	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×#64520	—	2	1	no	—
32	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
33	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	—	2	1	no	—
36	C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×C₂²⋊C₈	—	2	1	no	—
38	C₄×C₈×C₁₉	—	2	1	no	—
39	#10597292	—	4	2	no	—
40	#10597292	—	4	2	no	—
41	C₁₉⋊#95	—	2	1	no	—
42	C₁₉⋊#95	—	2	1	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
44	#10597279	—	4	2	no	—
45	#10597279	—	4	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	#10597260	—	2	1	no	—
50	#10597260	—	2	1	no	—
51	C₄×C₁₉⋊C₈	—	2	1	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	4	1	no	—
54	C₂×Q₈×C₁₉	—	4	1	no	—
55	C₂×Q₈×C₁₉	—	4	1	no	—
56	C₂×Q₈×C₁₉	—	4	1	no	—
57	C₂×Q₈×C₁₉	—	4	1	no	—
58	C₂²×C₄×C₁₉	—	4	1	no	—
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
62	C₂²×Dic₁₉	—	4	1	no	—
63	M₁₆×C₁₉	—	4	1	no	—
64	M₁₆×C₁₉	—	4	1	no	—
65	C₂×C₈×C₁₉	—	4	1	no	—
66	C₂×C₈×C₁₉	—	4	1	no	—
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₄⋊C₄×C₁₉	—	4	1	no	—
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	#41	1	1	yes	characteristic
73	C₄²×C₁₉	#41	1	1	yes	characteristic
74	C₄²×C₁₉	#41	1	1	yes	characteristic
75	C₄⋊Dic₁₉	—	4	1	no	—
76	C₄⋊Dic₁₉	—	4	1	no	—
77	#64520	—	4	1	no	—
78	#64520	—	4	1	no	—
79	C₂×C₁₉⋊C₈	—	2	1	no	—
80	C₂×C₁₉⋊C₈	—	2	1	no	—
81	C₂×C₁₉⋊C₈	—	2	1	no	—
82	C₂×C₁₉⋊C₈	—	2	1	no	—
83	C₂×C₁₉⋊C₈	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	4	1	no	—
85	C₂×C₁₉⋊C₈	D₈	1	2	yes	—
86	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	—
87	#10632	—	19	1	no	maximal, Sylow
88	C₂³×C₁₉	#124	1	1	yes	characteristic
89	Q₈×C₁₉	—	4	2	no	—
90	Q₈×C₁₉	—	4	2	no	—
91	Q₈×C₁₉	—	8	1	no	—
92	Q₈×C₁₉	—	8	1	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	8	1	no	—
97	C₂×C₄×C₁₉	—	8	1	no	—
98	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
108	C₂×Dic₁₉	—	8	1	no	—
109	C₂×Dic₁₉	—	8	1	no	—
110	C₂×Dic₁₉	—	8	1	no	—
111	C₈×C₁₉	—	8	1	no	—
112	C₈×C₁₉	—	8	1	no	—
113	C₁₉⋊C₈	—	2	2	no	—
114	C₁₉⋊C₈	—	2	2	no	—
115	C₁₉⋊C₈	—	8	1	no	—
116	C₁₉⋊C₈	—	8	1	no	—
117	#1960	—	19	1	no	—
118	#1849	—	19	1	no	—
119	#1546	—	19	1	no	—
120	#1546	D₁₉	1	1	yes	characteristic
121	#1286	—	19	1	no	—
122	#1286	—	19	1	no	—
123	#1281	—	19	1	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	#397	1	1	yes	characteristic
127	C₂²×C₁₉	#486	1	1	yes	characteristic
128	C₂²×C₁₉	#489	1	1	yes	characteristic
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	—	8	2	no	—
134	C₄×C₁₉	#459	1	1	yes	characteristic
135	C₄×C₁₉	#461	1	1	yes	characteristic
136	C₄×C₁₉	#480	1	1	yes	characteristic
137	C₄×C₁₉	#481	1	1	yes	characteristic
138	Dic₁₉	—	16	1	no	—
139	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
140	#431	—	19	1	no	—
141	#431	C₂×D₁₉	1	1	yes	characteristic
142	C₂×#108	—	38	1	no	—
143	C₂×#108	—	38	1	no	—
144	#423	—	19	1	no	—
145	#423	C₂×D₁₉	1	1	yes	characteristic
146	C₂×#103	—	38	1	no	—
147	C₂×#103	—	38	1	no	—
148	C₂×#97	—	19	1	no	—
149	#382	—	19	1	no	—
150	#332	—	2	2	no	—
151	#332	—	38	2	no	—
152	C₂×C₁₉	—	2	1	no	—
153	C₂×C₁₉	—	2	1	no	—
154	C₂×C₁₉	#2071	1	1	yes	characteristic
155	C₂×C₁₉	#2082	1	1	yes	characteristic
156	C₂×C₁₉	#2082	1	1	yes	characteristic
157	C₂²×Q₈	—	2	1	no	—
158	C₂×M₁₆	—	2	1	no	—
159	C₂×M₁₆	—	38	1	no	—
160	C₂²×C₈	—	19	1	no	—
161	C₂²×C₈	—	19	1	no	—
162	C₄⋊Q₈	—	2	1	no	—
163	C₄⋊Q₈	—	2	1	no	—
164	C₄⋊Q₈	—	2	1	no	—
165	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
166	C₂×C₄⋊C₄	—	2	1	no	—
167	C₂×C₄⋊C₄	—	2	1	no	—
168	C₂×C₄⋊C₄	—	38	1	no	—
169	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
170	#108	—	76	2	no	—
171	#108	—	76	2	no	—
172	C₄⋊C₈	—	2	1	no	—
173	C₄⋊C₈	—	2	1	no	—
174	C₄⋊C₈	—	2	1	no	—
175	C₄⋊C₈	—	38	1	no	—
176	C₄⋊C₈	—	38	1	no	—
177	C₄⋊C₈	—	38	1	no	—
178	#103	—	76	2	no	—
179	#103	—	76	2	no	—
180	C₂²⋊C₈	—	2	1	no	—
181	C₂²⋊C₈	—	38	1	no	—
182	#97	—	38	1	no	—
183	#97	—	38	1	no	—
184	C₄×C₈	—	2	1	no	—
185	C₄×C₈	—	38	1	no	—
186	#95	—	38	1	no	—
187	#95	—	38	1	no	—
188	C₁₉	#10632	1	1	yes	characteristic, complemented, Sylow
189	C₂×Q₈	—	2	2	no	—
190	C₂×Q₈	—	4	1	no	—
191	C₂×Q₈	—	4	1	no	—
192	C₂×Q₈	—	4	1	no	—
193	C₂×Q₈	—	4	1	no	—
194	C₂×Q₈	—	4	1	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	—	76	1	no	—
197	C₂²×C₄	#64541	1	1	yes	characteristic
198	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
199	C₂²×C₄	#64543	1	1	yes	characteristic
200	M₁₆	—	4	1	no	—
201	M₁₆	—	4	1	no	—
202	M₁₆	—	76	1	no	—
203	M₁₆	—	76	1	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	4	1	no	—
206	C₂×C₈	—	19	2	no	—
207	C₂×C₈	—	19	2	no	—
208	C₂×C₈	—	38	1	no	—
209	C₂×C₈	—	38	1	no	—
210	C₂×C₈	—	38	1	no	—
211	C₂×C₈	—	38	1	no	—
212	C₂×C₈	—	76	1	no	—
213	C₂×C₈	—	76	1	no	—
214	C₄⋊C₄	—	2	2	no	—
215	C₄⋊C₄	—	2	2	no	—
216	C₄⋊C₄	—	4	1	no	—
217	C₄⋊C₄	—	4	1	no	—
218	C₄⋊C₄	—	76	1	no	—
219	C₄⋊C₄	—	76	1	no	—
220	C₄²	#64541	1	1	yes	characteristic
221	C₄²	#64543	1	1	yes	characteristic
222	C₄²	#64543	1	1	yes	characteristic
223	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
224	C₂³	#10597331	1	1	yes	characteristic
225	Q₈	—	4	2	no	—
226	Q₈	—	4	2	no	—
227	Q₈	—	8	1	no	—
228	Q₈	—	8	1	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	4	1	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	8	1	no	—
233	C₂×C₄	—	8	1	no	—
234	C₂×C₄	—	152	1	no	—
235	C₂×C₄	—	152	1	no	—
236	C₂×C₄	—	152	1	no	—
237	C₂×C₄	#10597325	1	1	yes	characteristic
238	C₂×C₄	#10597325	1	1	yes	characteristic
239	C₂×C₄	#10597329	1	1	yes	characteristic
240	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
241	C₂×C₄	#10597357	1	1	yes	characteristic
242	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
243	C₂×C₄	#10597361	1	1	yes	characteristic
244	C₂×C₄	#10597375	1	1	yes	characteristic
245	C₂×C₄	#10597381	1	1	yes	characteristic
246	C₂×C₄	#10597385	1	1	yes	characteristic
247	C₈	—	8	1	no	—
248	C₈	—	8	1	no	—
249	C₈	—	38	2	no	—
250	C₈	—	38	2	no	—
251	C₈	—	152	1	no	—
252	C₈	—	152	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	#11926472	1	1	yes	characteristic
256	C₂²	#11926889	1	1	yes	characteristic
257	C₂²	#11926902	1	1	yes	characteristic
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	8	2	no	—
263	C₄	—	304	1	no	—
264	C₄	#11926737	1	1	yes	characteristic
265	C₄	#11926747	1	1	yes	characteristic
266	C₄	#11926856	1	1	yes	characteristic
267	C₄	#11926861	1	1	yes	characteristic
268	C₂	—	2	1	no	—
269	C₂	—	2	1	no	—
270	C₂	#14565041	1	1	yes	characteristic
271	C₂	#14565102	1	1	yes	characteristic
272	C₂	#14565103	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564456

C₂

yes

maximal, characteristic

#14563809

C₂

yes

maximal, characteristic

#14562307

C₂

yes

maximal, characteristic

#14561495

C₂

yes

maximal, characteristic

#14561494

C₂

yes

maximal, characteristic

#14561479

C₂

yes

maximal, characteristic

C₁₉×#1546

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

—

C₂²

yes

—

—

C₂²

yes

characteristic

#11926410

C₂²

yes

characteristic

#11926290

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#332

—

C₂²×Q₈×C₁₉

—

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

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

#10597292

—

#10597292

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597279

—

#10597279

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

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

—

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

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₈

yes

—

C₂×C₁₉⋊C₈

SD₁₆

yes

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

100

C₂×C₄×C₁₉

#123

yes

characteristic

101

C₂×C₄×C₁₉

#123

yes

characteristic

102

C₂×C₄×C₁₉

#126

yes

characteristic

103

C₂×C₄×C₁₉

#126

yes

characteristic

104

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

105

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

106

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

107

C₂×C₄×C₁₉

#137

yes

characteristic

108

C₂×Dic₁₉

—

109

C₂×Dic₁₉

—

110

C₂×Dic₁₉

—

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₁₉⋊C₈

—

114

C₁₉⋊C₈

—

115

C₁₉⋊C₈

—

116

C₁₉⋊C₈

—

117

#1960

—

118

#1849

—

119

#1546

—

120

#1546

D₁₉

yes

characteristic

121

#1286

—

122

#1286

—

123

#1281

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

#397

yes

characteristic

127

C₂²×C₁₉

#486

yes

characteristic

128

C₂²×C₁₉

#489

yes

characteristic

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

#459

yes

characteristic

135

C₄×C₁₉

#461

yes

characteristic

136

C₄×C₁₉

#480

yes

characteristic

137

C₄×C₁₉

#481

yes

characteristic

138

Dic₁₉

—

139

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

140

#431

—

141

#431

C₂×D₁₉

yes

characteristic

142

C₂×#108

—

143

C₂×#108

—

144

#423

—

145

#423

C₂×D₁₉

yes

characteristic

146

C₂×#103

—

147

C₂×#103

—

148

C₂×#97

—

149

#382

—

150

#332

—

151

#332

—

152

C₂×C₁₉

—

153

C₂×C₁₉

—

154

C₂×C₁₉

#2071

yes

characteristic

155

C₂×C₁₉

#2082

yes

characteristic

156

C₂×C₁₉

#2082

yes

characteristic

157

C₂²×Q₈

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂²×C₈

—

161

C₂²×C₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

—

164

C₄⋊Q₈

—

165

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄²

C₂²×D₁₉

yes

characteristic

170

#108

—

171

#108

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

#103

—

179

#103

—

180

C₂²⋊C₈

—

181

C₂²⋊C₈

—

182

#97

—

183

#97

—

184

C₄×C₈

—

185

C₄×C₈

—

186

#95

—

187

#95

—

188

C₁₉

#10632

yes

characteristic, complemented, Sylow

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×Q₈

—

194

C₂×Q₈

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

#64541

yes

characteristic

198

C₂²×C₄

D₄×D₁₉

yes

characteristic

199

C₂²×C₄

#64543

yes

characteristic

200

M₁₆

—

201

M₁₆

—

202

M₁₆

—

203

M₁₆

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄²

#64541

yes

characteristic

221

C₄²

#64543

yes

characteristic

222

C₄²

#64543

yes

characteristic

223

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

224

C₂³

#10597331

yes

characteristic

225

Q₈

—

226

Q₈

—

227

Q₈

—

228

Q₈

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

152

—

235

C₂×C₄

—

152

—

236

C₂×C₄

—

152

—

237

C₂×C₄

#10597325

yes

characteristic

238

C₂×C₄

#10597325

yes

characteristic

239

C₂×C₄

#10597329

yes

characteristic

240

C₂×C₄

D₈×D₁₉

yes

characteristic

241

C₂×C₄

#10597357

yes

characteristic

242

C₂×C₄

SD₁₆×D₁₉

yes

characteristic

243

C₂×C₄

#10597361

yes

characteristic

244

C₂×C₄

#10597375

yes

characteristic

245

C₂×C₄

#10597381

yes

characteristic

246

C₂×C₄

#10597385

yes

characteristic

247

C₈

—

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

152

—

252

C₈

—

152

—

253

C₂²

—

254

C₂²

—

255

C₂²

#11926472

yes

characteristic

256

C₂²

#11926889

yes

characteristic

257

C₂²

#11926902

yes

characteristic

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

304

—

264

C₄

#11926737

yes

characteristic

265

C₄

#11926747

yes

characteristic

266

C₄

#11926856

yes

characteristic

267

C₄

#11926861

yes

characteristic

268

C₂

—

269

C₂

—

270

C₂

#14565041

yes

characteristic

271

C₂

#14565102

yes

characteristic

272

C₂

#14565103

yes

characteristic

	subgroup	G/H
center	C₂²	#11926472
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1546	C₂
socle	C₂²×C₁₉	#397
prime radical	C₂³×C₁₉	#124
hypercenter	#1546	D₁₉
hypocenter	C₁₉	#10632
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1546

subgroup

G/H

center

C₂²

#11926472

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1546

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1546

N	H ≅ G/N	type
188. C₁₉	#10632	semidirect

H ≅ G/N

type

188. C₁₉

#10632

semidirect

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

subgroup	index
#14564456	2
#14563809	2
#14562307	2
#14561495	2
#14561494	2
#14561479	2
C₁₉×#1546	2
#10632	19

subgroup

index

C₁₉×#1546

Subgroups — #18087335

Conjugacy classes of subgroups

Complements

Maximal subgroups