Group #18075173 — subgroups

Subgroups — #18075173

Order 4864.

1026 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 163 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	#14563559	C₂	1	2	yes	maximal
2	#14561965	C₂	1	4	yes	maximal
3	C₂²×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597293	—	2	4	no	—
5	#11926508	C₂²	1	4	yes	—
6	#11926270	—	2	8	no	—
7	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₄⋊Q₈	—	2	4	no	—
10	C₂×C₁₉×C₄⋊Q₈	—	2	8	no	—
11	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic
14	C₂²×Q₈×C₁₉	—	2	4	no	—
15	C₂²×Q₈×C₁₉	—	2	2	no	—
16	C₂²×Q₈×C₁₉	—	2	4	no	—
17	C₂²×Q₈×C₁₉	—	4	4	no	—
18	C₂²×Q₈×C₁₉	—	4	4	no	—
19	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
20	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₁₉×C₄⋊Q₈	—	2	32	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
31	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	—
32	C₂×C₄²×C₁₉	—	2	2	no	—
33	C₂×C₄²×C₁₉	—	2	4	no	—
34	C₂×#64520	—	2	4	no	—
35	#10597293	—	4	8	no	—
36	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
37	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×Q₈×C₁₉	—	2	8	no	—
39	C₂×Q₈×C₁₉	—	2	8	no	—
40	C₂×Q₈×C₁₉	—	2	8	no	—
41	C₂×Q₈×C₁₉	—	4	4	no	—
42	C₂×Q₈×C₁₉	—	4	16	no	—
43	C₂×Q₈×C₁₉	—	4	16	no	—
44	C₂×Q₈×C₁₉	—	4	4	no	—
45	C₂×Q₈×C₁₉	—	4	4	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	4	no	—
50	C₂²×C₄×C₁₉	—	2	8	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	—	4	4	no	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
61	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
62	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
63	C₄⋊C₄×C₁₉	—	2	16	no	—
64	C₄⋊C₄×C₁₉	—	2	16	no	—
65	C₄²×C₁₉	—	2	8	no	—
66	#64520	—	4	8	no	—
67	C₂×C₁₉⋊C₈	—	4	4	no	—
68	#8551	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	—	2	2	no	—
70	C₂³×C₁₉	—	2	4	no	—
71	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
73	Q₈×C₁₉	—	4	16	no	—
74	Q₈×C₁₉	—	4	16	no	—
75	C₂×C₄×C₁₉	—	2	8	no	—
76	C₂×C₄×C₁₉	—	2	8	no	—
77	C₂×C₄×C₁₉	—	2	8	no	—
78	C₂×C₄×C₁₉	—	2	4	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	4	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	4	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	4	no	—
85	C₂×C₄×C₁₉	—	2	4	no	—
86	C₂×C₄×C₁₉	—	4	4	no	—
87	C₂×C₄×C₁₉	—	4	4	no	—
88	C₂×C₄×C₁₉	—	4	4	no	—
89	C₂×C₄×C₁₉	—	4	4	no	—
90	C₂×C₄×C₁₉	—	4	4	no	—
91	C₂×C₄×C₁₉	#99	1	4	yes	—
92	C₂×C₄×C₁₉	#101	1	8	yes	complemented
93	C₂×C₄×C₁₉	#120	1	4	yes	—
94	C₁₉⋊C₈	—	8	4	no	—
95	C₂²×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
96	#1784	—	19	2	no	—
97	#1463	—	19	4	no	—
98	C₂²×C₁₉	—	2	8	no	—
99	C₂²×C₁₉	—	2	2	no	—
100	C₂²×C₁₉	—	2	2	no	—
101	C₂²×C₁₉	—	2	2	no	—
102	C₂²×C₁₉	#379	1	1	yes	characteristic
103	C₂²×C₁₉	C₂×#99	1	2	yes	—
104	C₂²×C₁₉	C₂×#101	1	4	yes	—
105	C₄×C₁₉	—	2	4	no	—
106	C₄×C₁₉	—	2	4	no	—
107	C₄×C₁₉	—	2	8	no	—
108	C₄×C₁₉	—	4	2	no	—
109	C₄×C₁₉	—	4	4	no	—
110	C₂³×Q₈	Dic₁₉	1	1	yes	characteristic
111	C₂³×Q₈	C₂×D₁₉	1	1	yes	characteristic
112	C₂×C₄⋊Q₈	—	2	4	no	—
113	C₂×C₄⋊Q₈	—	2	8	no	—
114	C₂²×C₄⋊C₄	Dic₁₉	1	2	yes	—
115	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
116	C₂²×C₄²	Dic₁₉	1	1	yes	characteristic
117	C₂×#101	—	38	4	no	—
118	#407	—	19	4	no	—
119	#324	—	38	8	no	—
120	C₂×C₁₉	—	2	2	no	—
121	C₂×C₁₉	—	2	4	no	—
122	C₂×C₁₉	#1781	1	1	yes	characteristic
123	C₂×C₁₉	#1784	1	2	yes	—
124	C₂²×Q₈	—	2	4	no	—
125	C₂²×Q₈	—	2	2	no	—
126	C₂²×Q₈	—	2	4	no	—
127	C₂²×Q₈	—	4	4	no	—
128	C₂²×Q₈	—	4	4	no	—
129	C₂²×Q₈	C₂²⋊D₁₉	1	4	yes	—
130	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
131	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
132	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
133	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
134	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
135	C₂×M₁₆	—	38	4	no	—
136	C₄⋊Q₈	—	2	32	no	—
137	C₂×C₄⋊C₄	—	2	4	no	—
138	C₂×C₄⋊C₄	—	2	4	no	—
139	C₂×C₄⋊C₄	—	2	4	no	—
140	C₂×C₄⋊C₄	—	2	4	no	—
141	C₂×C₄⋊C₄	—	2	4	no	—
142	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	8	yes	—
143	C₂×C₄²	—	2	2	no	—
144	C₂×C₄²	—	2	4	no	—
145	#101	—	76	8	no	—
146	C₂²⋊C₈	—	38	8	no	—
147	C₁₉	#8551	1	1	yes	characteristic, complemented, Sylow
148	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
149	C₂×Q₈	—	2	8	no	—
150	C₂×Q₈	—	2	8	no	—
151	C₂×Q₈	—	2	8	no	—
152	C₂×Q₈	—	4	4	no	—
153	C₂×Q₈	—	4	16	no	—
154	C₂×Q₈	—	4	16	no	—
155	C₂×Q₈	—	4	4	no	—
156	C₂×Q₈	—	4	4	no	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	2	4	no	—
161	C₂²×C₄	—	2	8	no	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	4	2	no	—
166	C₂²×C₄	—	4	2	no	—
167	C₂²×C₄	—	4	4	no	—
168	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
169	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
170	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
171	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
172	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
173	C₂²×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
174	M₁₆	—	76	8	no	—
175	C₂×C₈	—	76	4	no	—
176	C₄⋊C₄	—	2	16	no	—
177	C₄⋊C₄	—	2	16	no	—
178	C₄²	—	2	8	no	—
179	C₂³	—	2	2	no	—
180	C₂³	—	2	4	no	—
181	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
182	C₂³	C₂×C₂²⋊Dic₁₉	1	2	yes	—
183	Q₈	—	4	16	no	—
184	Q₈	—	4	16	no	—
185	C₂×C₄	—	2	8	no	—
186	C₂×C₄	—	2	8	no	—
187	C₂×C₄	—	2	8	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	4	no	—
195	C₂×C₄	—	2	4	no	—
196	C₂×C₄	—	4	4	no	—
197	C₂×C₄	—	4	4	no	—
198	C₂×C₄	—	4	4	no	—
199	C₂×C₄	—	4	4	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	#10597291	1	4	yes	—
202	C₂×C₄	#10597293	1	8	yes	complemented
203	C₂×C₄	#10597399	1	4	yes	—
204	C₈	—	152	4	no	—
205	C₂²	—	2	8	no	—
206	C₂²	—	2	2	no	—
207	C₂²	—	2	2	no	—
208	C₂²	—	2	2	no	—
209	C₂²	#11926400	1	1	yes	characteristic
210	C₂²	C₂×#10597291	1	2	yes	—
211	C₂²	C₂×#10597293	1	4	yes	—
212	C₄	—	2	4	no	—
213	C₄	—	2	4	no	—
214	C₄	—	2	8	no	—
215	C₄	—	4	2	no	—
216	C₄	—	4	4	no	—
217	C₂	—	2	2	no	—
218	C₂	—	2	4	no	—
219	C₂	#14563550	1	1	yes	characteristic
220	C₂	#14563559	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563559

C₂

yes

maximal

#14561965

C₂

yes

maximal

C₂²×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂×#10597293

—

#11926508

C₂²

yes

—

#11926270

—

C₂³×Q₈×C₁₉

C₄

yes

characteristic

C₂³×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

—

C₂×C₁₉×C₄⋊Q₈

—

C₂²×C₄⋊C₄×C₁₉

C₄

yes

—

C₂²×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂²×C₄²×C₁₉

C₄

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×#64520

—

#10597293

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

#8551

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

C₂×C₂²⋊C₄

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×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

—

C₂×C₄×C₁₉

#101

yes

complemented

C₂×C₄×C₁₉

#120

yes

—

C₁₉⋊C₈

—

C₂²×C₄⋊Q₈

D₁₉

yes

characteristic

#1784

—

#1463

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

#379

yes

characteristic

103

C₂²×C₁₉

C₂×#99

yes

—

104

C₂²×C₁₉

C₂×#101

yes

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₂³×Q₈

Dic₁₉

yes

characteristic

111

C₂³×Q₈

C₂×D₁₉

yes

characteristic

112

C₂×C₄⋊Q₈

—

113

C₂×C₄⋊Q₈

—

114

C₂²×C₄⋊C₄

Dic₁₉

yes

—

115

C₂²×C₄⋊C₄

C₂×D₁₉

yes

—

116

C₂²×C₄²

Dic₁₉

yes

characteristic

117

C₂×#101

—

118

#407

—

119

#324

—

120

C₂×C₁₉

—

121

C₂×C₁₉

—

122

C₂×C₁₉

#1781

yes

characteristic

123

C₂×C₁₉

#1784

yes

—

124

C₂²×Q₈

—

125

C₂²×Q₈

—

126

C₂²×Q₈

—

127

C₂²×Q₈

—

128

C₂²×Q₈

—

129

C₂²×Q₈

C₂²⋊D₁₉

yes

—

130

C₂³×C₄

C₂×Dic₁₉

yes

—

131

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

132

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

133

C₂³×C₄

C₂×Dic₁₉

yes

—

134

C₂³×C₄

C₂²×D₁₉

yes

characteristic

135

C₂×M₁₆

—

136

C₄⋊Q₈

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

143

C₂×C₄²

—

144

C₂×C₄²

—

145

#101

—

146

C₂²⋊C₈

—

147

C₁₉

#8551

yes

characteristic, complemented, Sylow

148

C₂⁴

C₂²×Dic₁₉

yes

characteristic

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

169

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

170

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

171

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

172

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

173

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

174

M₁₆

—

175

C₂×C₈

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄²

—

179

C₂³

—

180

C₂³

—

181

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

182

C₂³

C₂×C₂²⋊Dic₁₉

yes

—

183

Q₈

—

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

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

#10597291

yes

—

202

C₂×C₄

#10597293

yes

complemented

203

C₂×C₄

#10597399

yes

—

204

C₈

—

152

—

205

C₂²

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

#11926400

yes

characteristic

210

C₂²

C₂×#10597291

yes

—

211

C₂²

C₂×#10597293

yes

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₂

—

218

C₂

—

219

C₂

#14563550

yes

characteristic

220

C₂

#14563559

yes

—

	subgroup	G/H
center	C₂²	#11926400
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×C₄⋊Q₈	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#8551
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×C₄⋊Q₈

subgroup

G/H

center

C₂²

#11926400

commutator, prime radical

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₂²×C₁₉×C₄⋊Q₈

C₂

socle

C₂²×C₁₉

#379

cosocle

C₂³×C₄×C₁₉

C₂³

hypercenter

C₂²×C₄⋊Q₈

D₁₉

hypocenter

C₁₉

#8551

LCS

G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×C₄⋊Q₈

N	H ≅ G/N	type
92. C₂×C₄×C₁₉	#101	semidirect
147. C₁₉	#8551	semidirect
202. C₂×C₄	#10597293	semidirect

H ≅ G/N

type

92. C₂×C₄×C₁₉

#101

semidirect

147. C₁₉

#8551

semidirect

202. C₂×C₄

#10597293

semidirect

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

subgroup	index
#14563559	2
#14561965	2
C₂²×C₁₉×C₄⋊Q₈	2
#8551	19

subgroup

index

#14563559

#14561965

C₂²×C₁₉×C₄⋊Q₈

#8551

Subgroups — #18075173

Conjugacy classes of subgroups

Complements

Maximal subgroups