Group #18076408 — subgroups

Subgroups — #18076408

Order 4864.

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

normal subgroups only

This group has 410 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	#14572716	C₂	1	1	yes	maximal, characteristic
2	#14564572	C₂	1	1	yes	maximal, characteristic
3	#14562387	C₂	1	2	yes	maximal
4	#14561473	C₂	1	2	yes	maximal
5	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₁₉⋊C₈	—	2	2	no	—
7	Q₈×C₁₉⋊C₈	—	2	2	no	—
8	#11926597	—	2	2	no	—
9	#11926597	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	#11926299	—	2	2	no	—
13	#11926297	—	2	2	no	—
14	#11926295	—	2	2	no	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#101	C₄	1	1	yes	characteristic
17	C₂×C₁₉×#101	C₄	1	1	yes	characteristic
18	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#343	C₄	1	2	yes	—
20	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
23	C₄×Q₈×C₁₉	—	2	2	no	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
27	C₂×C₄²×C₁₉	D₄	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×C₁₉⋊C₈	—	2	1	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	C₁₉×#101	—	2	2	no	—
32	C₁₉×#101	C₈	1	4	yes	complemented
33	C₁₉×#97	—	2	2	no	—
34	C₄×C₈×C₁₉	—	2	2	no	—
35	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
40	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
41	C₄×C₁₉⋊C₈	—	2	4	no	—
42	C₄×C₁₉⋊C₈	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	2	no	—
44	C₂×Q₈×C₁₉	—	2	2	no	—
45	C₂×Q₈×C₁₉	—	2	2	no	—
46	C₂×Q₈×C₁₉	C₂×C₈	1	2	yes	—
47	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
48	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
53	M₁₆×C₁₉	—	2	2	no	—
54	M₁₆×C₁₉	—	2	2	no	—
55	M₁₆×C₁₉	—	2	2	no	—
56	M₁₆×C₁₉	C₂×C₈	1	4	yes	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₄²×C₁₉	—	2	2	no	—
62	C₄²×C₁₉	—	2	2	no	—
63	C₄²×C₁₉	C₂×D₄	1	2	yes	—
64	C₄²×C₁₉	#41	1	2	yes	—
65	C₂×C₁₉⋊C₈	—	2	2	no	—
66	C₂×C₁₉⋊C₈	—	2	2	no	—
67	C₂×C₁₉⋊C₈	—	2	2	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	1	no	—
72	#8836	—	19	1	no	maximal, Sylow
73	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
74	Q₈×C₁₉	—	2	4	no	—
75	Q₈×C₁₉	—	2	4	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	4	1	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	—
84	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
87	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#131	1	2	yes	—
91	C₈×C₁₉	—	2	4	no	—
92	C₈×C₁₉	—	4	2	no	—
93	C₁₉⋊C₈	—	4	2	no	—
94	C₁₉⋊C₈	—	4	2	no	—
95	C₁₉⋊C₈	—	4	2	no	—
96	C₁₉⋊C₈	—	8	1	no	—
97	#2982	—	19	1	no	—
98	#1984	—	19	1	no	—
99	C₄×#101	D₁₉	1	1	yes	characteristic
100	#1565	—	19	2	no	—
101	#1278	—	19	2	no	—
102	C₂²×C₁₉	—	2	1	no	—
103	C₂²×C₁₉	—	2	1	no	—
104	C₂²×C₁₉	#385	1	1	yes	characteristic
105	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
106	C₂²×C₁₉	#424	1	1	yes	characteristic
107	C₄×C₁₉	—	2	4	no	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	—	4	2	no	—
111	C₄×C₁₉	C₈×D₄	1	2	yes	—
112	C₄×C₁₉	#435	1	2	yes	—
113	C₄×C₁₉	#454	1	1	yes	characteristic
114	C₄×C₁₉	#456	1	1	yes	characteristic
115	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
116	C₈×Q₈	—	38	2	no	—
117	C₈×Q₈	—	38	2	no	—
118	#431	—	19	2	no	—
119	#431	—	38	2	no	—
120	C₂×C₄⋊C₈	—	19	1	no	—
121	C₂×#101	Dic₁₉	1	1	yes	characteristic
122	C₂×#101	Dic₁₉	1	1	yes	characteristic
123	C₄×M₁₆	C₂×D₁₉	1	2	yes	—
124	C₂×C₄×C₈	—	19	1	no	—
125	#343	Dic₁₉	1	2	yes	—
126	#336	—	38	2	no	—
127	#335	—	38	2	no	—
128	#334	—	38	2	no	—
129	C₂×C₁₉	—	2	1	no	—
130	C₂×C₁₉	—	2	1	no	—
131	C₂×C₁₉	#1850	1	1	yes	characteristic
132	C₂×C₁₉	#1857	1	1	yes	characteristic
133	C₂×C₁₉	#1858	1	1	yes	characteristic
134	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
135	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
136	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
137	C₂²×C₈	—	38	1	no	—
138	C₂²×C₈	—	38	1	no	—
139	C₄×Q₈	—	2	2	no	—
140	C₄×Q₈	—	2	2	no	—
141	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
142	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
143	C₂×C₄²	D₇₆	1	2	yes	—
144	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
145	C₄⋊C₈	—	19	2	no	—
146	C₄⋊C₈	—	19	2	no	—
147	C₄⋊C₈	—	38	2	no	—
148	C₄⋊C₈	—	38	2	no	—
149	C₄⋊C₈	—	38	2	no	—
150	#101	—	2	2	no	—
151	#101	C₁₉⋊C₈	1	4	yes	complemented
152	C₂²⋊C₈	—	38	2	no	—
153	#97	—	2	2	no	—
154	C₄×C₈	—	2	2	no	—
155	C₄×C₈	—	38	4	no	—
156	C₄×C₈	—	38	2	no	—
157	C₄×C₈	—	38	2	no	—
158	C₁₉	#8836	1	1	yes	characteristic, complemented, Sylow
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	C₂×C₁₉⋊C₈	1	2	yes	—
162	C₂×Q₈	#64520	1	2	yes	—
163	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
164	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
165	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
166	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
167	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
168	M₁₆	—	2	2	no	—
169	M₁₆	—	2	2	no	—
170	M₁₆	—	2	2	no	—
171	M₁₆	C₂×C₁₉⋊C₈	1	4	yes	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	38	2	no	—
175	C₂×C₈	—	38	2	no	—
176	C₂×C₈	—	38	2	no	—
177	C₂×C₈	—	76	1	no	—
178	C₂×C₈	—	76	1	no	—
179	C₂×C₈	—	76	2	no	—
180	C₂×C₈	—	76	1	no	—
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	4	no	—
183	C₄²	—	2	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	D₄×D₁₉	1	2	yes	—
186	C₄²	#64543	1	2	yes	—
187	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
188	Q₈	—	2	4	no	—
189	Q₈	—	2	4	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	4	yes	—
198	C₂×C₄	#10597324	1	2	yes	—
199	C₂×C₄	#10597328	1	1	yes	characteristic
200	C₂×C₄	#10597332	1	1	yes	characteristic
201	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
202	C₂×C₄	C₂×#64520	1	1	yes	characteristic
203	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
204	C₂×C₄	#10597394	1	2	yes	—
205	C₈	—	2	4	no	—
206	C₈	—	4	2	no	—
207	C₈	—	76	2	no	—
208	C₈	—	76	2	no	—
209	C₈	—	76	2	no	—
210	C₈	—	152	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	#11926419	1	1	yes	characteristic
214	C₂²	C₂×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
215	C₂²	#11926571	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	2	no	—
218	C₄	—	2	4	no	—
219	C₄	—	4	2	no	—
220	C₄	D₄×C₁₉⋊C₈	1	2	yes	—
221	C₄	#11926616	1	2	yes	—
222	C₄	#11926719	1	1	yes	characteristic
223	C₄	#11926729	1	1	yes	characteristic
224	C₂	—	2	1	no	—
225	C₂	—	2	1	no	—
226	C₂	#14563815	1	1	yes	characteristic
227	C₂	#14563852	1	1	yes	characteristic
228	C₂	#14563857	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572716

C₂

yes

maximal, characteristic

#14564572

C₂

yes

maximal, characteristic

#14562387

C₂

yes

maximal

#14561473

C₂

yes

maximal

C₄×C₁₉×#101

C₂

yes

maximal, characteristic

Q₈×C₁₉⋊C₈

—

Q₈×C₁₉⋊C₈

—

#11926597

—

#11926597

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#101

C₄

yes

characteristic

C₂×C₁₉×#101

C₄

yes

characteristic

C₄×M₁₆×C₁₉

C₂²

yes

—

C₁₉×#343

C₄

yes

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×#101

—

C₁₉×#101

C₈

yes

complemented

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₈

yes

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8836

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊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

C₄⋊C₈

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2982

—

#1984

—

C₄×#101

D₁₉

yes

characteristic

100

#1565

—

101

#1278

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

#385

yes

characteristic

105

C₂²×C₁₉

C₂×C₄⋊C₈

yes

characteristic

106

C₂²×C₁₉

#424

yes

characteristic

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

C₈×D₄

yes

—

112

C₄×C₁₉

#435

yes

—

113

C₄×C₁₉

#454

yes

characteristic

114

C₄×C₁₉

#456

yes

characteristic

115

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

116

C₈×Q₈

—

117

C₈×Q₈

—

118

#431

—

119

#431

—

120

C₂×C₄⋊C₈

—

121

C₂×#101

Dic₁₉

yes

characteristic

122

C₂×#101

Dic₁₉

yes

characteristic

123

C₄×M₁₆

C₂×D₁₉

yes

—

124

C₂×C₄×C₈

—

125

#343

Dic₁₉

yes

—

126

#336

—

127

#335

—

128

#334

—

129

C₂×C₁₉

—

130

C₂×C₁₉

—

131

C₂×C₁₉

#1850

yes

characteristic

132

C₂×C₁₉

#1857

yes

characteristic

133

C₂×C₁₉

#1858

yes

characteristic

134

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

135

C₂×M₁₆

C₂×Dic₁₉

yes

—

136

C₂×M₁₆

C₂×Dic₁₉

yes

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₄×Q₈

—

140

C₄×Q₈

—

141

C₂×C₄⋊C₄

Dic₃₈

yes

—

142

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

143

C₂×C₄²

D₇₆

yes

—

144

C₂×C₄²

C₂²×D₁₉

yes

characteristic

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#101

—

151

#101

C₁₉⋊C₈

yes

complemented

152

C₂²⋊C₈

—

153

#97

—

154

C₄×C₈

—

155

C₄×C₈

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₁₉

#8836

yes

characteristic, complemented, Sylow

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

C₂×C₁₉⋊C₈

yes

—

162

C₂×Q₈

#64520

yes

—

163

C₂²×C₄

C₄⋊Dic₁₉

yes

—

164

C₂²×C₄

C₄⋊Dic₁₉

yes

—

165

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

166

C₂²×C₄

C₂×D₇₆

yes

characteristic

167

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

168

M₁₆

—

169

M₁₆

—

170

M₁₆

—

171

M₁₆

C₂×C₁₉⋊C₈

yes

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄²

—

184

C₄²

—

185

C₄²

D₄×D₁₉

yes

—

186

C₄²

#64543

yes

—

187

C₂³

C₂×C₄⋊Dic₁₉

yes

characteristic

188

Q₈

—

189

Q₈

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

—

198

C₂×C₄

#10597324

yes

—

199

C₂×C₄

#10597328

yes

characteristic

200

C₂×C₄

#10597332

yes

characteristic

201

C₂×C₄

C₂²×C₁₉⋊C₈

yes

characteristic

202

C₂×C₄

C₂×#64520

yes

characteristic

203

C₂×C₄

D₄×Dic₁₉

yes

—

204

C₂×C₄

#10597394

yes

—

205

C₈

—

206

C₈

—

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

—

152

—

211

C₂²

—

212

C₂²

—

213

C₂²

#11926419

yes

characteristic

214

C₂²

C₂×C₄⋊(C₁₉⋊C₈)

yes

characteristic

215

C₂²

#11926571

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

D₄×C₁₉⋊C₈

yes

—

221

C₄

#11926616

yes

—

222

C₄

#11926719

yes

characteristic

223

C₄

#11926729

yes

characteristic

224

C₂

—

225

C₂

—

226

C₂

#14563815

yes

characteristic

227

C₂

#14563852

yes

characteristic

228

C₂

#14563857

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#101	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#101	D₁₉
hypocenter	C₁₉	#8836
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#101

subgroup

G/H

center

C₂×C₄

#10597328

commutator

C₂×C₄×C₁₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#101

C₂

socle

C₂²×C₁₉

#385

prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#101

N	H ≅ G/N	type
32. C₁₉×#101	C₈	semidirect
151. #101	C₁₉⋊C₈	semidirect
158. C₁₉	#8836	semidirect

H ≅ G/N

type

32. C₁₉×#101

C₈

semidirect

151. #101

C₁₉⋊C₈

semidirect

158. C₁₉

#8836

semidirect

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

subgroup	index
#14572716	2
#14564572	2
#14562387	2
#14561473	2
C₄×C₁₉×#101	2
#8836	19

subgroup

index

C₄×C₁₉×#101

Subgroups — #18076408

Conjugacy classes of subgroups

Complements

Maximal subgroups