Group #18070521 — subgroups

Subgroups — #18070521

Order 4864.

516 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 207 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	C₄×C₄⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal
2	#14561461	C₂	1	4	yes	maximal
3	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
5	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
6	#11926299	C₂²	1	4	yes	—
7	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
9	C₁₉×#391	C₂²	1	2	yes	—
10	C₁₉×#389	—	2	2	no	—
11	C₁₉×#384	C₄	1	1	yes	characteristic
12	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
13	C₄³×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
15	C₁₉×C₄⋊Q₈	—	2	2	no	—
16	C₁₉×C₄⋊Q₈	C₈	1	4	yes	complemented
17	C₄×Q₈×C₁₉	—	4	4	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	D₄	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₁₉⋊C₈	—	2	4	no	—
29	C₁₉×#95	—	2	4	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
31	C₄×C₁₉⋊C₈	—	4	4	no	—
32	C₂×Q₈×C₁₉	—	2	2	no	—
33	C₂×Q₈×C₁₉	—	4	2	no	—
34	C₂×Q₈×C₁₉	—	4	2	no	—
35	C₂×Q₈×C₁₉	C₂×C₈	1	4	yes	—
36	C₂²×C₄×C₁₉	—	2	2	no	—
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₄⋊C₄×C₁₉	—	2	8	no	—
44	C₄⋊C₄×C₁₉	—	4	2	no	—
45	C₄⋊C₄×C₁₉	—	4	4	no	—
46	C₄⋊C₄×C₁₉	—	4	4	no	—
47	C₄²×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	—	2	4	no	—
49	C₄²×C₁₉	—	4	1	no	—
50	C₄²×C₁₉	—	4	4	no	—
51	C₄²×C₁₉	C₂×C₈	1	2	yes	—
52	C₄²×C₁₉	M₁₆	1	2	yes	—
53	C₄²×C₁₉	SD₁₆	1	4	yes	—
54	C₄²×C₁₉	Q₁₆	1	4	yes	—
55	C₂×C₁₉⋊C₈	—	2	8	no	—
56	C₂×C₁₉⋊C₈	—	4	4	no	—
57	C₂×C₁₉⋊C₈	—	4	4	no	—
58	#7571	—	19	1	no	maximal, Sylow
59	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	Q₈×C₁₉	—	4	4	no	—
61	Q₈×C₁₉	—	4	4	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	1	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	4	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	4	2	no	—
70	C₂×C₄×C₁₉	—	4	2	no	—
71	C₂×C₄×C₁₉	—	4	2	no	—
72	C₂×C₄×C₁₉	—	4	4	no	—
73	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
74	C₂×C₄×C₁₉	#100	1	2	yes	—
75	C₂×C₄×C₁₉	#103	1	4	yes	—
76	C₂×C₄×C₁₉	#103	1	4	yes	—
77	C₂×C₄×C₁₉	#104	1	4	yes	—
78	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
81	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
82	C₁₉⋊C₈	—	4	8	no	—
83	C₄×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
84	C₄×C₄⋊C₈	—	19	2	no	—
85	#1272	—	19	4	no	—
86	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
87	C₂²×C₁₉	#410	1	1	yes	characteristic
88	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
89	C₂²×C₁₉	C₂×#103	1	2	yes	—
90	C₂²×C₁₉	C₂×#104	1	2	yes	—
91	C₄×C₁₉	—	2	1	no	—
92	C₄×C₁₉	—	2	1	no	—
93	C₄×C₁₉	—	2	2	no	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	4	4	no	—
96	C₄×C₁₉	—	4	1	no	—
97	C₄×C₁₉	—	8	2	no	—
98	C₄×C₁₉	Q₈⋊C₈	1	8	yes	—
99	C₄×C₁₉	#333	1	4	yes	—
100	C₂×C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
101	C₂×C₄×Q₈	Dic₁₉	1	2	yes	—
102	C₂×C₄⋊C₈	—	38	2	no	—
103	C₂×C₄×C₈	—	38	2	no	—
104	#391	C₂×D₁₉	1	2	yes	—
105	#389	—	2	2	no	—
106	#384	Dic₁₉	1	1	yes	characteristic
107	C₄×C₄⋊C₄	—	2	2	no	—
108	C₄³	C₂×D₁₉	1	1	yes	characteristic
109	#336	—	19	4	no	—
110	C₂×C₁₉	#1460	1	1	yes	characteristic
111	C₂×C₁₉	C₂×Q₈⋊C₈	1	2	yes	—
112	C₂×C₁₉	#1503	1	2	yes	—
113	C₂×C₁₉	#1525	1	1	yes	characteristic
114	C₂×C₁₉	C₂×#333	1	1	yes	characteristic
115	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
116	C₂²×C₈	—	38	4	no	—
117	C₄⋊Q₈	—	2	2	no	—
118	C₄⋊Q₈	C₁₉⋊C₈	1	4	yes	complemented
119	C₄×Q₈	—	4	4	no	—
120	C₂×C₄⋊C₄	—	2	2	no	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₄⋊C₄	—	2	2	no	—
123	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
124	C₂×C₄²	—	2	2	no	—
125	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
126	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
127	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
128	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
129	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
130	C₄⋊C₈	—	38	8	no	—
131	C₄×C₈	—	76	4	no	—
132	#95	—	2	4	no	—
133	C₁₉	#7571	1	1	yes	characteristic, complemented, Sylow
134	C₂×Q₈	—	2	2	no	—
135	C₂×Q₈	—	4	2	no	—
136	C₂×Q₈	—	4	2	no	—
137	C₂×Q₈	C₂×C₁₉⋊C₈	1	4	yes	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	2	2	no	—
140	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
141	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
142	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
143	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
144	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
145	C₂×C₈	—	38	8	no	—
146	C₂×C₈	—	76	4	no	—
147	C₂×C₈	—	76	4	no	—
148	C₄⋊C₄	—	2	8	no	—
149	C₄⋊C₄	—	4	2	no	—
150	C₄⋊C₄	—	4	4	no	—
151	C₄⋊C₄	—	4	4	no	—
152	C₄²	—	2	2	no	—
153	C₄²	—	2	4	no	—
154	C₄²	—	4	1	no	—
155	C₄²	—	4	4	no	—
156	C₄²	C₂×C₁₉⋊C₈	1	2	yes	—
157	C₄²	#64520	1	2	yes	—
158	C₄²	#64527	1	4	yes	—
159	C₄²	#64528	1	4	yes	—
160	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
161	Q₈	—	4	4	no	—
162	Q₈	—	4	4	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	4	no	—
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	—	4	2	no	—
171	C₂×C₄	—	4	2	no	—
172	C₂×C₄	—	4	4	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
175	C₂×C₄	#10597290	1	2	yes	—
176	C₂×C₄	#10597292	1	4	yes	—
177	C₂×C₄	#10597292	1	4	yes	—
178	C₂×C₄	#10597294	1	4	yes	—
179	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
180	C₂×C₄	C₂×#64520	1	1	yes	characteristic
181	C₂×C₄	C₂×#64527	1	2	yes	—
182	C₂×C₄	C₂×#64528	1	2	yes	—
183	C₈	—	76	8	no	—
184	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
185	C₂²	#11926518	1	1	yes	characteristic
186	C₂²	C₂×#10597290	1	1	yes	characteristic
187	C₂²	C₂×#10597292	1	2	yes	—
188	C₂²	C₂×#10597294	1	2	yes	—
189	C₄	—	2	2	no	—
190	C₄	—	2	2	no	—
191	C₄	—	2	1	no	—
192	C₄	—	2	1	no	—
193	C₄	—	4	4	no	—
194	C₄	—	4	1	no	—
195	C₄	—	8	2	no	—
196	C₄	Q₈⋊(C₁₉⋊C₈)	1	8	yes	—
197	C₄	#11926293	1	4	yes	—
198	C₂	#14561956	1	1	yes	characteristic
199	C₂	C₂×Q₈⋊(C₁₉⋊C₈)	1	2	yes	—
200	C₂	#14562134	1	2	yes	—
201	C₂	#14562227	1	1	yes	characteristic
202	C₂	C₂×#11926293	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal

#14561461

C₂

yes

maximal

C₄×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄×C₁₉⋊C₈

—

#11926299

C₂²

yes

—

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₄

yes

—

C₁₉×#391

C₂²

yes

—

C₁₉×#389

—

C₁₉×#384

C₄

yes

characteristic

C₄×C₄⋊C₄×C₁₉

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₈

yes

complemented

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

—

C₄²×C₁₉

M₁₆

yes

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

Q₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7571

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

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

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

#100

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₁₉⋊C₈

—

C₄×C₄⋊Q₈

D₁₉

yes

characteristic

C₄×C₄⋊C₈

—

#1272

—

C₂²×C₁₉

C₂×C₂²⋊C₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

C₂×#104

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

Q₈⋊C₈

yes

—

C₄×C₁₉

#333

yes

—

100

C₂×C₄⋊Q₈

Dic₁₉

yes

characteristic

101

C₂×C₄×Q₈

Dic₁₉

yes

—

102

C₂×C₄⋊C₈

—

103

C₂×C₄×C₈

—

104

#391

C₂×D₁₉

yes

—

105

#389

—

106

#384

Dic₁₉

yes

characteristic

107

C₄×C₄⋊C₄

—

108

C₄³

C₂×D₁₉

yes

characteristic

109

#336

—

110

C₂×C₁₉

#1460

yes

characteristic

111

C₂×C₁₉

C₂×Q₈⋊C₈

yes

—

112

C₂×C₁₉

#1503

yes

—

113

C₂×C₁₉

#1525

yes

characteristic

114

C₂×C₁₉

C₂×#333

yes

characteristic

115

C₂²×Q₈

C₂×Dic₁₉

yes

—

116

C₂²×C₈

—

117

C₄⋊Q₈

—

118

C₄⋊Q₈

C₁₉⋊C₈

yes

complemented

119

C₄×Q₈

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

124

C₂×C₄²

—

125

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

126

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

127

C₂×C₄²

C₂²⋊D₁₉

yes

—

128

C₂×C₄²

C₂²⋊D₁₉

yes

—

129

C₂×C₄²

C₂²×D₁₉

yes

characteristic

130

C₄⋊C₈

—

131

C₄×C₈

—

132

#95

—

133

C₁₉

#7571

yes

characteristic, complemented, Sylow

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

C₂×C₁₉⋊C₈

yes

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

141

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

142

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

143

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

144

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄²

—

153

C₄²

—

154

C₄²

—

155

C₄²

—

156

C₄²

C₂×C₁₉⋊C₈

yes

—

157

C₄²

#64520

yes

—

158

C₄²

#64527

yes

—

159

C₄²

#64528

yes

—

160

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

161

Q₈

—

162

Q₈

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

—

175

C₂×C₄

#10597290

yes

—

176

C₂×C₄

#10597292

yes

—

177

C₂×C₄

#10597292

yes

—

178

C₂×C₄

#10597294

yes

—

179

C₂×C₄

C₂²×C₁₉⋊C₈

yes

characteristic

180

C₂×C₄

C₂×#64520

yes

characteristic

181

C₂×C₄

C₂×#64527

yes

—

182

C₂×C₄

C₂×#64528

yes

—

183

C₈

—

184

C₂²

C₂×C₂²⋊(C₁₉⋊C₈)

yes

characteristic

185

C₂²

#11926518

yes

characteristic

186

C₂²

C₂×#10597290

yes

characteristic

187

C₂²

C₂×#10597292

yes

—

188

C₂²

C₂×#10597294

yes

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

Q₈⋊(C₁₉⋊C₈)

yes

—

197

C₄

#11926293

yes

—

198

C₂

#14561956

yes

characteristic

199

C₂

C₂×Q₈⋊(C₁₉⋊C₈)

yes

—

200

C₂

#14562134

yes

—

201

C₂

#14562227

yes

characteristic

202

C₂

C₂×#11926293

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#7571
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

subgroup

G/H

center

C₂²×C₄

C₂²⋊Dic₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×C₄⋊Q₈

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₄×C₄⋊Q₈

D₁₉

hypocenter

C₁₉

#7571

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

N	H ≅ G/N	type
16. C₁₉×C₄⋊Q₈	C₈	semidirect
118. C₄⋊Q₈	C₁₉⋊C₈	semidirect
133. C₁₉	#7571	semidirect

H ≅ G/N

type

16. C₁₉×C₄⋊Q₈

C₈

semidirect

118. C₄⋊Q₈

C₁₉⋊C₈

semidirect

133. C₁₉

#7571

semidirect

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

subgroup	index
C₄×C₄⋊(C₁₉⋊C₈)	2
#14561461	2
C₄×C₁₉×C₄⋊Q₈	2
#7571	19

subgroup

index

C₄×C₄⋊(C₁₉⋊C₈)

#14561461

C₄×C₁₉×C₄⋊Q₈

#7571

Subgroups — #18070521

Conjugacy classes of subgroups

Complements

Maximal subgroups