Group #18086973 — subgroups

Subgroups — #18086973

Order 4864.

494 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 145 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	#14564393	C₂	1	2	yes	maximal
2	#14563794	C₂	1	1	yes	maximal, characteristic
3	#14561518	C₂	1	1	yes	maximal, characteristic
4	#14561476	C₂	1	2	yes	maximal
5	C₁₉×#2551	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597264	—	2	2	no	—
7	C₂×#10597264	—	2	2	no	—
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926414	C₂²	1	1	yes	characteristic
11	#11926306	—	2	2	no	—
12	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
13	C₁₉×#395	—	2	2	no	—
14	C₁₉×#389	—	2	2	no	—
15	C₁₉×#384	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×Q₈×C₁₉	—	2	2	no	—
18	C₁₉×C₄⋊Q₈	—	4	4	no	—
19	C₁₉×C₄⋊Q₈	—	4	4	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
21	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
23	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
24	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	—	2	2	no	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×C₄⋊Dic₁₉	—	2	1	no	—
29	C₂²×C₁₉⋊C₈	—	2	1	no	—
30	C₂²×C₁₉⋊C₈	—	2	2	no	—
31	C₁₉×#95	—	2	2	no	—
32	C₁₉×#95	—	2	2	no	—
33	#10597264	—	4	4	no	—
34	#10597264	—	4	4	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	Q₈	1	4	yes	complemented
37	C₄×C₁₉⋊C₈	—	2	1	no	—
38	C₄×C₁₉⋊C₈	Q₈	1	2	yes	complemented
39	C₂×Q₈×C₁₉	—	4	8	no	—
40	C₂×Q₈×C₁₉	—	8	2	no	—
41	C₂²×C₄×C₁₉	—	2	2	no	—
42	C₂²×C₄×C₁₉	—	2	2	no	—
43	C₂²×C₄×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₂²×Dic₁₉	—	4	1	no	—
47	C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₄⋊C₄×C₁₉	—	4	2	no	—
50	C₄⋊C₄×C₁₉	—	4	8	no	—
51	C₄⋊C₄×C₁₉	—	4	2	no	—
52	C₄⋊C₄×C₁₉	—	4	2	no	—
53	C₄⋊C₄×C₁₉	D₈	1	4	yes	—
54	C₄⋊C₄×C₁₉	Q₁₆	1	4	yes	—
55	C₄²×C₁₉	—	4	2	no	—
56	C₄²×C₁₉	—	4	2	no	—
57	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
58	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
59	C₄²×C₁₉	#41	1	1	yes	characteristic
60	C₄⋊Dic₁₉	—	4	2	no	—
61	C₄⋊Dic₁₉	—	4	2	no	—
62	C₄⋊Dic₁₉	—	4	2	no	—
63	C₂×C₁₉⋊C₈	—	2	2	no	—
64	C₂×C₁₉⋊C₈	—	2	2	no	—
65	C₂×C₁₉⋊C₈	—	2	2	no	—
66	C₂×C₁₉⋊C₈	—	2	4	no	—
67	C₂×C₁₉⋊C₈	—	4	2	no	—
68	C₂×C₁₉⋊C₈	—	4	2	no	—
69	#10573	—	19	1	no	maximal, Sylow
70	C₂³×C₁₉	#120	1	1	yes	characteristic
71	Q₈×C₁₉	—	8	8	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	4	no	—
75	C₂×C₄×C₁₉	—	2	4	no	—
76	C₂×C₄×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	4	2	no	—
80	C₂×C₄×C₁₉	—	4	4	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
84	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
86	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
87	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
88	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
89	C₂×C₄×C₁₉	#137	1	2	yes	—
90	C₂×Dic₁₉	—	8	2	no	—
91	C₂×Dic₁₉	—	8	1	no	—
92	C₁₉⋊C₈	—	2	4	no	—
93	C₁₉⋊C₈	—	4	4	no	—
94	#2551	D₁₉	1	1	yes	characteristic
95	#1947	—	19	2	no	—
96	#1845	—	19	1	no	—
97	#1296	—	19	1	no	—
98	#1279	—	19	2	no	—
99	C₂²×C₁₉	#395	1	1	yes	characteristic
100	C₂²×C₁₉	#447	1	2	yes	—
101	C₂²×C₁₉	#451	1	2	yes	—
102	C₂²×C₁₉	#453	1	1	yes	characteristic
103	C₂²×C₁₉	#456	1	1	yes	characteristic
104	C₄×C₁₉	—	2	1	no	—
105	C₄×C₁₉	—	2	1	no	—
106	C₄×C₁₉	—	4	4	no	—
107	C₄×C₁₉	—	4	4	no	—
108	C₄×C₁₉	—	8	2	no	—
109	C₄×C₁₉	#474	1	2	yes	—
110	C₄×C₁₉	#477	1	2	yes	—
111	C₄×C₁₉	#500	1	2	yes	—
112	C₄×C₁₉	#501	1	2	yes	—
113	Dic₁₉	—	16	1	no	—
114	C₂×C₄⋊Q₈	—	2	2	no	—
115	C₂×#107	—	38	2	no	—
116	C₂×#107	—	38	2	no	—
117	C₂×C₄⋊C₈	—	19	2	no	—
118	C₂×C₄×C₈	—	19	1	no	—
119	#395	—	2	2	no	—
120	#389	—	2	2	no	—
121	#384	—	19	1	no	—
122	#384	C₂×D₁₉	1	1	yes	characteristic
123	C₄×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
124	#340	—	38	2	no	—
125	C₂×C₁₉	#1619	1	1	yes	characteristic
126	C₂×C₁₉	#1633	1	1	yes	characteristic
127	C₂×C₁₉	#1649	1	2	yes	—
128	C₂×C₁₉	#2057	1	2	yes	—
129	C₂×C₁₉	#2060	1	1	yes	characteristic
130	C₂²×Q₈	—	2	2	no	—
131	C₂²×C₈	—	38	1	no	—
132	C₂²×C₈	—	38	2	no	—
133	C₄⋊Q₈	—	4	4	no	—
134	C₄⋊Q₈	—	4	4	no	—
135	C₂×C₄⋊C₄	—	2	4	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	—	38	2	no	—
138	C₂×C₄⋊C₄	—	38	1	no	—
139	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
140	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
141	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
142	C₂×C₄²	—	2	2	no	—
143	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	#107	—	76	4	no	—
145	#107	—	76	4	no	—
146	C₄⋊C₈	—	19	4	no	—
147	C₄⋊C₈	—	38	2	no	—
148	C₄×C₈	—	19	2	no	—
149	C₄×C₈	—	38	1	no	—
150	#95	—	2	2	no	—
151	#95	—	2	2	no	—
152	C₁₉	#10573	1	1	yes	characteristic, complemented, Sylow
153	C₂×Q₈	—	4	8	no	—
154	C₂×Q₈	—	8	2	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	2	2	no	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	76	1	no	—
159	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
160	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
161	C₂×C₈	—	38	2	no	—
162	C₂×C₈	—	38	2	no	—
163	C₂×C₈	—	38	2	no	—
164	C₂×C₈	—	38	4	no	—
165	C₂×C₈	—	76	2	no	—
166	C₂×C₈	—	76	2	no	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	2	2	no	—
169	C₄⋊C₄	—	4	2	no	—
170	C₄⋊C₄	—	4	8	no	—
171	C₄⋊C₄	—	4	2	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	76	2	no	—
174	C₄⋊C₄	—	76	2	no	—
175	C₄⋊C₄	—	76	2	no	—
176	C₄⋊C₄	#64525	1	4	yes	—
177	C₄⋊C₄	#64528	1	4	yes	—
178	C₄²	—	4	2	no	—
179	C₄²	—	4	2	no	—
180	C₄²	Q₈×D₁₉	1	1	yes	characteristic
181	C₄²	Q₈×D₁₉	1	2	yes	—
182	C₄²	#64545	1	1	yes	characteristic
183	C₂³	#10597399	1	1	yes	characteristic
184	Q₈	—	8	8	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	4	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	152	2	no	—
196	C₂×C₄	—	152	1	no	—
197	C₂×C₄	C₂×#64525	1	2	yes	—
198	C₂×C₄	#10597378	1	2	yes	—
199	C₂×C₄	#10597388	1	2	yes	—
200	C₂×C₄	C₂×#64528	1	2	yes	—
201	C₂×C₄	#10597390	1	1	yes	characteristic
202	C₂×C₄	#10597390	1	2	yes	—
203	C₂×C₄	#10597392	1	1	yes	characteristic
204	C₂×C₄	#10597392	1	2	yes	—
205	C₈	—	38	4	no	—
206	C₈	—	76	4	no	—
207	C₂²	#11926463	1	1	yes	characteristic
208	C₂²	#11926678	1	2	yes	—
209	C₂²	#11926700	1	2	yes	—
210	C₂²	#11926712	1	1	yes	characteristic
211	C₂²	#11926727	1	1	yes	characteristic
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	4	4	no	—
215	C₄	—	4	4	no	—
216	C₄	—	8	2	no	—
217	C₄	—	304	1	no	—
218	C₄	#11926821	1	2	yes	—
219	C₄	#11926836	1	2	yes	—
220	C₄	#11926947	1	2	yes	—
221	C₄	#11926950	1	2	yes	—
222	C₂	#14562689	1	1	yes	characteristic
223	C₂	#14562775	1	1	yes	characteristic
224	C₂	#14562884	1	2	yes	—
225	C₂	#14564960	1	2	yes	—
226	C₂	#14564977	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564393

C₂

yes

maximal

#14563794

C₂

yes

maximal, characteristic

#14561518

C₂

yes

maximal, characteristic

#14561476

C₂

yes

maximal

C₁₉×#2551

C₂

yes

maximal, characteristic

C₂×#10597264

—

C₂×#10597264

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926414

C₂²

yes

characteristic

#11926306

—

C₂×C₁₉×C₄⋊Q₈

—

C₁₉×#395

—

C₁₉×#389

—

C₁₉×#384

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂²×Q₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

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

—

#10597264

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

Q₈

yes

complemented

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

Q₈

yes

complemented

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

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

D₈

yes

—

C₄⋊C₄×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

—

C₄²×C₁₉

#41

yes

characteristic

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

—

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

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2551

D₁₉

yes

—

—

—

—

C₂²×C₁₉

#395

yes

characteristic

100

C₂²×C₁₉

#447

yes

—

101

C₂²×C₁₉

#451

yes

—

102

C₂²×C₁₉

#453

yes

characteristic

103

C₂²×C₁₉

#456

yes

characteristic

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

#474

yes

—

110

C₄×C₁₉

#477

yes

—

111

C₄×C₁₉

#500

yes

—

112

C₄×C₁₉

#501

yes

—

113

Dic₁₉

—

114

C₂×C₄⋊Q₈

—

115

C₂×#107

—

116

C₂×#107

—

117

C₂×C₄⋊C₈

—

118

C₂×C₄×C₈

—

119

#395

—

120

#389

—

121

#384

—

122

#384

C₂×D₁₉

yes

characteristic

123

C₄×C₄⋊C₄

C₂×D₁₉

yes

—

124

#340

—

125

C₂×C₁₉

#1619

yes

characteristic

126

C₂×C₁₉

#1633

yes

characteristic

127

C₂×C₁₉

#1649

yes

—

128

C₂×C₁₉

#2057

yes

—

129

C₂×C₁₉

#2060

yes

characteristic

130

C₂²×Q₈

—

131

C₂²×C₈

—

132

C₂²×C₈

—

133

C₄⋊Q₈

—

134

C₄⋊Q₈

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

140

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

141

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

142

C₂×C₄²

—

143

C₂×C₄²

C₂²×D₁₉

yes

characteristic

144

#107

—

145

#107

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄×C₈

—

149

C₄×C₈

—

150

#95

—

151

#95

—

152

C₁₉

#10573

yes

characteristic, complemented, Sylow

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

160

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

#64525

yes

—

177

C₄⋊C₄

#64528

yes

—

178

C₄²

—

179

C₄²

—

180

C₄²

Q₈×D₁₉

yes

characteristic

181

C₄²

Q₈×D₁₉

yes

—

182

C₄²

#64545

yes

characteristic

183

C₂³

#10597399

yes

characteristic

184

Q₈

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

152

—

196

C₂×C₄

—

152

—

197

C₂×C₄

C₂×#64525

yes

—

198

C₂×C₄

#10597378

yes

—

199

C₂×C₄

#10597388

yes

—

200

C₂×C₄

C₂×#64528

yes

—

201

C₂×C₄

#10597390

yes

characteristic

202

C₂×C₄

#10597390

yes

—

203

C₂×C₄

#10597392

yes

characteristic

204

C₂×C₄

#10597392

yes

—

205

C₈

—

206

C₈

—

207

C₂²

#11926463

yes

characteristic

208

C₂²

#11926678

yes

—

209

C₂²

#11926700

yes

—

210

C₂²

#11926712

yes

characteristic

211

C₂²

#11926727

yes

characteristic

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

304

—

218

C₄

#11926821

yes

—

219

C₄

#11926836

yes

—

220

C₄

#11926947

yes

—

221

C₄

#11926950

yes

—

222

C₂

#14562689

yes

characteristic

223

C₂

#14562775

yes

characteristic

224

C₂

#14562884

yes

—

225

C₂

#14564960

yes

—

226

C₂

#14564977

yes

characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2551	C₂
socle, prime radical	C₂³×C₁₉	#120
hypercenter	#2551	D₁₉
hypocenter	C₁₉	#10573
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

subgroup

G/H

center

C₂³

#10597399

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2551

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

N	H ≅ G/N	type
36. C₄⋊(C₁₉⋊C₈)	Q₈	semidirect
38. C₄×C₁₉⋊C₈	Q₈	semidirect
152. C₁₉	#10573	semidirect

H ≅ G/N

type

36. C₄⋊(C₁₉⋊C₈)

Q₈

semidirect

38. C₄×C₁₉⋊C₈

Q₈

semidirect

152. C₁₉

#10573

semidirect

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

subgroup	index
#14564393	2
#14563794	2
#14561518	2
#14561476	2
C₁₉×#2551	2
#10573	19

subgroup

index

C₁₉×#2551

Subgroups — #18086973

Conjugacy classes of subgroups

Complements

Maximal subgroups