Group #18077004 — subgroups

Subgroups — #18077004

Order 4864.

476 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 155 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	#14564438	C₂	1	1	yes	maximal, characteristic
2	#14564398	C₂	1	2	yes	maximal
3	C₂×#11926293	C₂	1	1	yes	maximal, characteristic
4	#14561476	C₂	1	2	yes	maximal
5	C₁₉×#2369	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597265	—	2	2	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×#10597292	—	2	2	no	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926414	C₂²	1	1	yes	characteristic
11	#11926306	—	2	2	no	—
12	#11926293	C₄	1	4	yes	complemented
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₉×#391	—	2	2	no	—
15	C₁₉×#389	—	2	2	no	—
16	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
17	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
19	C₁₉×C₄⋊Q₈	—	2	2	no	—
20	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
21	C₁₉×C₄⋊Q₈	Q₈	1	2	yes	—
22	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
25	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	—	2	2	no	—
27	C₂×C₄²×C₁₉	—	2	2	no	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	—	2	2	no	—
31	C₂²×C₁₉⋊C₈	—	2	1	no	—
32	C₂²×C₁₉⋊C₈	—	2	2	no	—
33	C₁₉×#95	—	2	4	no	—
34	C₁₉×#95	—	2	2	no	—
35	#10597292	—	4	4	no	—
36	#10597265	—	4	4	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
39	C₄×C₁₉⋊C₈	—	2	2	no	—
40	C₂×Q₈×C₁₉	—	2	2	no	—
41	C₂×Q₈×C₁₉	—	4	2	no	—
42	C₂×Q₈×C₁₉	—	4	2	no	—
43	C₂×Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂²×Dic₁₉	—	4	1	no	—
50	C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₄⋊C₄×C₁₉	—	8	2	no	—
56	C₄⋊C₄×C₁₉	SD₁₆	1	4	yes	—
57	C₄²×C₁₉	—	4	2	no	—
58	C₄²×C₁₉	—	4	2	no	—
59	C₄²×C₁₉	—	8	2	no	—
60	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
62	C₄²×C₁₉	#41	1	2	yes	—
63	C₄⋊Dic₁₉	—	4	2	no	—
64	C₄⋊Dic₁₉	—	4	2	no	—
65	C₄⋊Dic₁₉	—	4	2	no	—
66	C₂×C₁₉⋊C₈	—	2	2	no	—
67	C₂×C₁₉⋊C₈	—	2	4	no	—
68	C₂×C₁₉⋊C₈	—	4	1	no	—
69	C₂×C₁₉⋊C₈	—	4	1	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	2	no	—
72	#8928	—	19	1	no	maximal, Sylow
73	C₂³×C₁₉	#120	1	1	yes	characteristic
74	Q₈×C₁₉	—	4	4	no	—
75	Q₈×C₁₉	—	8	2	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	4	no	—
79	C₂×C₄×C₁₉	—	2	4	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
89	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
90	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
92	C₂×C₄×C₁₉	#135	1	2	yes	—
93	C₂×C₄×C₁₉	#137	1	2	yes	—
94	C₂×C₄×C₁₉	#137	1	2	yes	—
95	C₂×Dic₁₉	—	8	2	no	—
96	C₂×Dic₁₉	—	8	1	no	—
97	C₁₉⋊C₈	—	4	2	no	—
98	C₁₉⋊C₈	—	4	4	no	—
99	#2369	D₁₉	1	1	yes	characteristic
100	#1956	—	19	1	no	—
101	#1948	—	19	2	no	—
102	C₂×#333	—	19	1	no	—
103	#1279	—	19	2	no	—
104	C₂²×C₁₉	#385	1	1	yes	characteristic
105	C₂²×C₁₉	#448	1	2	yes	—
106	C₂²×C₁₉	#452	1	2	yes	—
107	C₂²×C₁₉	#453	1	1	yes	characteristic
108	C₂²×C₁₉	#455	1	1	yes	characteristic
109	C₄×C₁₉	—	2	1	no	—
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	—	4	4	no	—
112	C₄×C₁₉	—	4	4	no	—
113	C₄×C₁₉	—	8	2	no	—
114	C₄×C₁₉	C₄×SD₁₆	1	2	yes	—
115	C₄×C₁₉	#441	1	2	yes	—
116	C₄×C₁₉	#475	1	2	yes	—
117	C₄×C₁₉	#479	1	2	yes	—
118	Dic₁₉	—	16	1	no	—
119	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
120	C₂×#106	—	38	2	no	—
121	C₂×C₄⋊C₈	—	19	2	no	—
122	C₂×#103	—	38	2	no	—
123	C₂×C₄×C₈	—	19	1	no	—
124	#391	—	2	2	no	—
125	#389	—	2	2	no	—
126	#384	—	19	1	no	—
127	C₄×C₄⋊C₄	—	2	2	no	—
128	C₄×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
129	#340	—	38	2	no	—
130	#333	—	19	4	no	—
131	C₂×C₁₉	#1623	1	1	yes	characteristic
132	C₂×C₁₉	#1634	1	1	yes	characteristic
133	C₂×C₁₉	#1643	1	2	yes	—
134	C₂×C₁₉	#1856	1	1	yes	characteristic
135	C₂×C₁₉	#1865	1	2	yes	—
136	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
137	C₂²×C₈	—	38	2	no	—
138	C₂²×C₈	—	38	1	no	—
139	C₄⋊Q₈	—	2	2	no	—
140	C₄⋊Q₈	Dic₃₈	1	2	yes	—
141	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	38	2	no	—
145	C₂×C₄⋊C₄	—	38	1	no	—
146	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
147	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
148	C₂×C₄²	—	2	2	no	—
149	C₂×C₄²	—	2	2	no	—
150	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
151	#106	—	76	4	no	—
152	C₄⋊C₈	—	19	4	no	—
153	C₄⋊C₈	—	38	2	no	—
154	#103	—	76	4	no	—
155	C₄×C₈	—	38	2	no	—
156	#95	—	2	4	no	—
157	#95	—	2	2	no	—
158	C₁₉	#8928	1	1	yes	characteristic, complemented, Sylow
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	Dic₁₉⋊C₄	1	4	yes	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	76	1	no	—
167	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
169	C₂×C₈	—	38	2	no	—
170	C₂×C₈	—	38	4	no	—
171	C₂×C₈	—	76	1	no	—
172	C₂×C₈	—	76	2	no	—
173	C₂×C₈	—	76	2	no	—
174	C₂×C₈	—	76	1	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	2	4	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	8	2	no	—
181	C₄⋊C₄	—	76	2	no	—
182	C₄⋊C₄	—	76	2	no	—
183	C₄⋊C₄	—	76	2	no	—
184	C₄⋊C₄	#64527	1	4	yes	—
185	C₄²	—	4	2	no	—
186	C₄²	—	4	2	no	—
187	C₄²	—	8	2	no	—
188	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
189	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
190	C₄²	#64541	1	2	yes	—
191	C₂³	#10597399	1	1	yes	characteristic
192	Q₈	—	4	4	no	—
193	Q₈	—	8	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	152	2	no	—
206	C₂×C₄	—	152	1	no	—
207	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
208	C₂×C₄	#10597370	1	2	yes	—
209	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
210	C₂×C₄	#10597375	1	1	yes	characteristic
211	C₂×C₄	C₂×#64527	1	2	yes	—
212	C₂×C₄	#10597388	1	2	yes	—
213	C₂×C₄	#10597396	1	2	yes	—
214	C₂×C₄	#10597397	1	2	yes	—
215	C₈	—	76	2	no	—
216	C₈	—	76	4	no	—
217	C₂²	#11926417	1	1	yes	characteristic
218	C₂²	#11926683	1	2	yes	—
219	C₂²	#11926706	1	2	yes	—
220	C₂²	#11926712	1	1	yes	characteristic
221	C₂²	#11926722	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	4	no	—
225	C₄	—	4	4	no	—
226	C₄	—	8	2	no	—
227	C₄	—	304	1	no	—
228	C₄	C₄×#64527	1	2	yes	—
229	C₄	#11926649	1	2	yes	—
230	C₄	#11926829	1	2	yes	—
231	C₄	#11926851	1	2	yes	—
232	C₂	#14562713	1	1	yes	characteristic
233	C₂	#14562780	1	1	yes	characteristic
234	C₂	#14562842	1	2	yes	—
235	C₂	#14563845	1	1	yes	characteristic
236	C₂	#14563903	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564438

C₂

yes

maximal, characteristic

#14564398

C₂

yes

maximal

C₂×#11926293

C₂

yes

maximal, characteristic

#14561476

C₂

yes

maximal

C₁₉×#2369

C₂

yes

maximal, characteristic

C₂×#10597265

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597292

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926414

C₂²

yes

characteristic

#11926306

—

#11926293

C₄

yes

complemented

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#391

—

C₁₉×#389

—

C₄×C₄⋊C₄×C₁₉

—

C₄×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

Q₈

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

#10597292

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2369

D₁₉

yes

characteristic

100

#1956

—

101

#1948

—

102

C₂×#333

—

103

#1279

—

104

C₂²×C₁₉

#385

yes

characteristic

105

C₂²×C₁₉

#448

yes

—

106

C₂²×C₁₉

#452

yes

—

107

C₂²×C₁₉

#453

yes

characteristic

108

C₂²×C₁₉

#455

yes

characteristic

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

C₄×SD₁₆

yes

—

115

C₄×C₁₉

#441

yes

—

116

C₄×C₁₉

#475

yes

—

117

C₄×C₁₉

#479

yes

—

118

Dic₁₉

—

119

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

120

C₂×#106

—

121

C₂×C₄⋊C₈

—

122

C₂×#103

—

123

C₂×C₄×C₈

—

124

#391

—

125

#389

—

126

#384

—

127

C₄×C₄⋊C₄

—

128

C₄×C₄⋊C₄

C₂×D₁₉

yes

—

129

#340

—

130

#333

—

131

C₂×C₁₉

#1623

yes

characteristic

132

C₂×C₁₉

#1634

yes

characteristic

133

C₂×C₁₉

#1643

yes

—

134

C₂×C₁₉

#1856

yes

characteristic

135

C₂×C₁₉

#1865

yes

—

136

C₂²×Q₈

C₂²⋊D₁₉

yes

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

Dic₃₈

yes

—

141

C₄⋊Q₈

C₄×D₁₉

yes

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

147

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

C₂²×D₁₉

yes

characteristic

151

#106

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

#103

—

155

C₄×C₈

—

156

#95

—

157

#95

—

158

C₁₉

#8928

yes

characteristic, complemented, Sylow

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

Dic₁₉⋊C₄

yes

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

#64527

yes

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

C₂×Dic₃₈

yes

characteristic

189

C₄²

C₂×C₄×D₁₉

yes

characteristic

190

C₄²

#64541

yes

—

191

C₂³

#10597399

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

152

—

206

C₂×C₄

—

152

—

207

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

208

C₂×C₄

#10597370

yes

—

209

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

210

C₂×C₄

#10597375

yes

characteristic

211

C₂×C₄

C₂×#64527

yes

—

212

C₂×C₄

#10597388

yes

—

213

C₂×C₄

#10597396

yes

—

214

C₂×C₄

#10597397

yes

—

215

C₈

—

216

C₈

—

217

C₂²

#11926417

yes

characteristic

218

C₂²

#11926683

yes

—

219

C₂²

#11926706

yes

—

220

C₂²

#11926712

yes

characteristic

221

C₂²

#11926722

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

304

—

228

C₄

C₄×#64527

yes

—

229

C₄

#11926649

yes

—

230

C₄

#11926829

yes

—

231

C₄

#11926851

yes

—

232

C₂

#14562713

yes

characteristic

233

C₂

#14562780

yes

characteristic

234

C₂

#14562842

yes

—

235

C₂

#14563845

yes

characteristic

236

C₂

#14563903

yes

—

	subgroup	G/H
center	C₂³	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2369	C₂
socle, prime radical	C₂³×C₁₉	#120
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2369	D₁₉
hypocenter	C₁₉	#8928
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2369

subgroup

G/H

center

C₂³

#10597399

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2369

C₂

socle, prime radical

C₂³×C₁₉

#120

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2369

N	H ≅ G/N	type
12. #11926293	C₄	semidirect
158. C₁₉	#8928	semidirect

H ≅ G/N

type

12. #11926293

C₄

semidirect

158. C₁₉

#8928

semidirect

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

subgroup	index
#14564438	2
#14564398	2
C₂×#11926293	2
#14561476	2
C₁₉×#2369	2
#8928	19

subgroup

index

C₁₉×#2369

Subgroups — #18077004

Conjugacy classes of subgroups

Complements

Maximal subgroups