Group #18085147 — subgroups

Subgroups — #18085147

Order 4864.

574 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 139 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	C₂×#11926924	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926829	C₂	1	2	yes	maximal
3	C₂×#11926291	C₂	1	2	yes	maximal
4	#14561470	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₇₆	—	2	2	no	—
7	C₂×#10597315	C₂²	1	2	yes	—
8	#11926924	—	2	4	no	—
9	#11926829	—	2	4	no	—
10	#11926829	—	2	4	no	—
11	C₂×#10597265	—	2	2	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
13	C₂×#10597292	—	2	2	no	—
14	#11926291	—	2	4	no	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#336	—	2	2	no	—
19	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×Dic₃₈	—	2	2	no	—
21	C₂²×C₈×C₁₉	—	2	1	no	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₄×Q₈×C₁₉	—	2	2	no	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	—	2	1	no	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	—	2	2	no	—
30	C₂×C₄⋊Dic₁₉	—	2	2	no	—
31	C₂²×C₁₉⋊C₈	—	2	2	no	—
32	C₂×Dic₇₆	—	2	8	no	—
33	C₂×Dic₇₆	—	4	4	no	—
34	C₂×Dic₇₆	—	4	4	no	—
35	#10597315	—	2	2	no	—
36	#10597315	—	2	2	no	—
37	#10597315	—	2	2	no	—
38	#10597315	D₄	1	4	yes	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₄×C₈×C₁₉	—	2	2	no	—
41	#10597292	—	2	8	no	—
42	#10597265	—	2	8	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
45	C₂×Q₈×C₁₉	—	2	1	no	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	complemented
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	—	2	1	no	—
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂²×Dic₁₉	—	4	2	no	—
55	C₂×Dic₃₈	—	2	4	no	—
56	C₂×Dic₃₈	—	4	4	no	—
57	C₂×Dic₃₈	—	4	4	no	—
58	C₂×Dic₃₈	—	4	2	no	—
59	C₂×C₈×C₁₉	—	2	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	—	4	1	no	—
62	C₂×C₈×C₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
64	C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₄²×C₁₉	—	4	1	no	—
67	C₄²×C₁₉	—	4	1	no	—
68	C₄²×C₁₉	C₂×D₄	1	2	yes	—
69	C₄²×C₁₉	C₂×D₄	1	2	yes	—
70	C₄⋊Dic₁₉	—	2	4	no	—
71	C₄⋊Dic₁₉	—	2	4	no	—
72	C₄⋊Dic₁₉	—	4	2	no	—
73	C₄⋊Dic₁₉	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	2	4	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	Dic₇₆	—	4	16	no	—
78	#10276	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	#121	1	1	yes	characteristic
80	Q₈×C₁₉	—	2	4	no	—
81	Q₈×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	4	1	no	—
85	C₂×C₄×C₁₉	—	4	1	no	—
86	C₂×C₄×C₁₉	—	4	1	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#120	1	2	yes	—
90	C₂×C₄×C₁₉	#121	1	2	yes	—
91	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
93	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
95	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
96	C₂×C₄×C₁₉	#137	1	2	yes	—
97	C₂×Dic₁₉	—	4	4	no	—
98	C₂×Dic₁₉	—	8	4	no	—
99	Dic₃₈	—	4	8	no	—
100	Dic₃₈	—	8	2	no	—
101	Dic₃₈	—	8	2	no	—
102	C₈×C₁₉	—	2	4	no	—
103	C₈×C₁₉	—	8	1	no	—
104	C₁₉⋊C₈	—	4	4	no	—
105	C₂×#494	—	19	1	no	—
106	C₂×#475	—	19	2	no	—
107	#1984	D₁₉	1	1	yes	characteristic
108	C₂×#332	—	19	2	no	—
109	#1277	—	19	1	no	—
110	C₂²×C₁₉	#392	1	1	yes	characteristic
111	C₂²×C₁₉	#460	1	2	yes	—
112	C₂²×C₁₉	#467	1	1	yes	characteristic
113	C₂²×C₁₉	#470	1	1	yes	characteristic
114	C₂²×C₁₉	#473	1	2	yes	—
115	C₄×C₁₉	—	2	2	no	—
116	C₄×C₁₉	—	4	2	no	—
117	C₄×C₁₉	—	8	1	no	—
118	C₄×C₁₉	#450	1	2	yes	—
119	C₄×C₁₉	#451	1	2	yes	—
120	C₄×C₁₉	#452	1	2	yes	—
121	C₄×C₁₉	#492	1	1	yes	characteristic
122	C₄×C₁₉	#496	1	1	yes	characteristic
123	Dic₁₉	—	8	4	no	—
124	C₂²×Q₁₆	—	38	2	no	—
125	C₂×C₄⋊Q₈	—	19	2	no	—
126	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
127	#494	—	38	4	no	—
128	#475	—	38	4	no	—
129	#475	—	38	4	no	—
130	C₂×#106	—	38	2	no	—
131	C₂×C₄⋊C₈	—	19	2	no	—
132	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
133	C₂×#103	—	38	2	no	—
134	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
135	#336	—	2	2	no	—
136	#332	—	38	4	no	—
137	C₂×C₁₉	#1670	1	2	yes	—
138	C₂×C₁₉	#1690	1	2	yes	—
139	C₂×C₁₉	#2001	1	1	yes	characteristic
140	C₂×C₁₉	#2014	1	1	yes	characteristic
141	C₂×C₁₉	#2020	1	1	yes	characteristic
142	C₂²×Q₈	—	38	2	no	—
143	C₂²×Q₈	D₇₆	1	1	yes	characteristic
144	C₂×Q₁₆	—	38	8	no	—
145	C₂×Q₁₆	—	76	4	no	—
146	C₂×Q₁₆	—	76	4	no	—
147	C₂²×C₈	—	2	1	no	—
148	C₂²×C₈	—	38	2	no	—
149	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
150	C₄⋊Q₈	—	19	4	no	—
151	C₄⋊Q₈	—	38	2	no	—
152	C₄⋊Q₈	—	38	2	no	—
153	C₄⋊Q₈	—	38	2	no	—
154	C₄×Q₈	—	2	2	no	—
155	C₄×Q₈	—	2	2	no	—
156	C₂×C₄⋊C₄	—	2	1	no	—
157	C₂×C₄⋊C₄	—	38	2	no	—
158	C₂×C₄⋊C₄	—	38	2	no	—
159	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
160	C₂×C₄²	—	2	1	no	—
161	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
162	#106	—	38	8	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	19	4	no	—
165	C₄⋊C₈	—	38	2	no	—
166	#103	—	38	8	no	—
167	C₄×C₈	—	2	2	no	—
168	C₁₉	#10276	1	1	yes	characteristic, complemented, Sylow
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	—	38	4	no	—
173	C₂×Q₈	—	76	2	no	—
174	C₂×Q₈	—	76	4	no	—
175	C₂×Q₈	—	76	4	no	—
176	C₂×Q₈	Dic₇₆	1	2	yes	complemented
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	—	76	2	no	—
180	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
181	C₂²×C₄	#64541	1	1	yes	characteristic
182	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
183	Q₁₆	—	76	16	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	4	1	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	38	4	no	—
189	C₂×C₈	—	76	2	no	—
190	C₂×C₈	—	76	2	no	—
191	C₂×C₈	#64527	1	4	yes	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₄⋊C₄	—	38	4	no	—
195	C₄⋊C₄	—	38	4	no	—
196	C₄⋊C₄	—	76	2	no	—
197	C₄⋊C₄	—	76	2	no	—
198	C₄²	—	4	1	no	—
199	C₄²	—	4	1	no	—
200	C₄²	D₄×D₁₉	1	2	yes	—
201	C₄²	D₄×D₁₉	1	2	yes	—
202	C₂³	#10597376	1	1	yes	characteristic
203	Q₈	—	2	4	no	—
204	Q₈	—	4	2	no	—
205	Q₈	—	76	8	no	—
206	Q₈	—	152	2	no	—
207	Q₈	—	152	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	76	4	no	—
215	C₂×C₄	—	152	4	no	—
216	C₂×C₄	#10597328	1	2	yes	—
217	C₂×C₄	#10597330	1	2	yes	—
218	C₂×C₄	#10597350	1	1	yes	characteristic
219	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
220	C₂×C₄	#10597355	1	2	yes	—
221	C₂×C₄	#10597383	1	1	yes	characteristic
222	C₂×C₄	#10597386	1	1	yes	characteristic
223	C₂×C₄	C₂×#64527	1	2	yes	—
224	C₂×C₄	#10597395	1	2	yes	—
225	C₈	—	2	4	no	—
226	C₈	—	8	1	no	—
227	C₈	—	76	4	no	—
228	C₂²	#11926453	1	1	yes	characteristic
229	C₂²	#11926744	1	2	yes	—
230	C₂²	#11926785	1	1	yes	characteristic
231	C₂²	#11926802	1	1	yes	characteristic
232	C₂²	#11926819	1	2	yes	—
233	C₄	—	2	2	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	1	no	—
236	C₄	—	152	4	no	—
237	C₄	#11926694	1	2	yes	—
238	C₄	#11926702	1	2	yes	—
239	C₄	#11926708	1	2	yes	—
240	C₄	#11926918	1	1	yes	characteristic
241	C₄	#11926934	1	1	yes	characteristic
242	C₂	#14563005	1	2	yes	—
243	C₂	#14563129	1	2	yes	—
244	C₂	#14564645	1	1	yes	characteristic
245	C₂	#14564722	1	1	yes	characteristic
246	C₂	#14564756	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926924

C₂

yes

maximal, characteristic

C₂×#11926829

C₂

yes

maximal

C₂×#11926291

C₂

yes

maximal

#14561470

C₂

yes

maximal, characteristic

C₁₉×#1984

C₂

yes

maximal, characteristic

C₂²×Dic₇₆

—

C₂×#10597315

C₂²

yes

—

—

—

—

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597292

—

#11926291

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

—

—

—

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

—

#10597292

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

Q₁₆

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

—

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

#120

yes

characteristic

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

100

Dic₃₈

—

101

Dic₃₈

—

102

C₈×C₁₉

—

103

C₈×C₁₉

—

104

C₁₉⋊C₈

—

105

C₂×#494

—

106

C₂×#475

—

107

#1984

D₁₉

yes

characteristic

108

C₂×#332

—

109

#1277

—

110

C₂²×C₁₉

#392

yes

characteristic

111

C₂²×C₁₉

#460

yes

—

112

C₂²×C₁₉

#467

yes

characteristic

113

C₂²×C₁₉

#470

yes

characteristic

114

C₂²×C₁₉

#473

yes

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

#450

yes

—

119

C₄×C₁₉

#451

yes

—

120

C₄×C₁₉

#452

yes

—

121

C₄×C₁₉

#492

yes

characteristic

122

C₄×C₁₉

#496

yes

characteristic

123

Dic₁₉

—

124

C₂²×Q₁₆

—

125

C₂×C₄⋊Q₈

—

126

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

127

#494

—

128

#475

—

129

#475

—

130

C₂×#106

—

131

C₂×C₄⋊C₈

—

132

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

133

C₂×#103

—

134

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

135

#336

—

136

#332

—

137

C₂×C₁₉

#1670

yes

—

138

C₂×C₁₉

#1690

yes

—

139

C₂×C₁₉

#2001

yes

characteristic

140

C₂×C₁₉

#2014

yes

characteristic

141

C₂×C₁₉

#2020

yes

characteristic

142

C₂²×Q₈

—

143

C₂²×Q₈

D₇₆

yes

characteristic

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

147

C₂²×C₈

—

148

C₂²×C₈

—

149

C₂²×C₈

C₂²⋊D₁₉

yes

—

150

C₄⋊Q₈

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

153

C₄⋊Q₈

—

154

C₄×Q₈

—

155

C₄×Q₈

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

D₇₆

yes

characteristic

160

C₂×C₄²

—

161

C₂×C₄²

C₂²×D₁₉

yes

characteristic

162

#106

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#103

—

167

C₄×C₈

—

168

C₁₉

#10276

yes

characteristic, complemented, Sylow

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

Dic₇₆

yes

complemented

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

C₂×D₇₆

yes

characteristic

181

C₂²×C₄

#64541

yes

characteristic

182

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

183

Q₁₆

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

#64527

yes

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄²

—

199

C₄²

—

200

C₄²

D₄×D₁₉

yes

—

201

C₄²

D₄×D₁₉

yes

—

202

C₂³

#10597376

yes

characteristic

203

Q₈

—

204

Q₈

—

205

Q₈

—

206

Q₈

—

152

—

207

Q₈

—

152

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

152

—

216

C₂×C₄

#10597328

yes

—

217

C₂×C₄

#10597330

yes

—

218

C₂×C₄

#10597350

yes

characteristic

219

C₂×C₄

C₂×Dic₇₆

yes

characteristic

220

C₂×C₄

#10597355

yes

—

221

C₂×C₄

#10597383

yes

characteristic

222

C₂×C₄

#10597386

yes

characteristic

223

C₂×C₄

C₂×#64527

yes

—

224

C₂×C₄

#10597395

yes

—

225

C₈

—

226

C₈

—

227

C₈

—

228

C₂²

#11926453

yes

characteristic

229

C₂²

#11926744

yes

—

230

C₂²

#11926785

yes

characteristic

231

C₂²

#11926802

yes

characteristic

232

C₂²

#11926819

yes

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

152

—

237

C₄

#11926694

yes

—

238

C₄

#11926702

yes

—

239

C₄

#11926708

yes

—

240

C₄

#11926918

yes

characteristic

241

C₄

#11926934

yes

characteristic

242

C₂

#14563005

yes

—

243

C₂

#14563129

yes

—

244

C₂

#14564645

yes

characteristic

245

C₂

#14564722

yes

characteristic

246

C₂

#14564756

yes

characteristic

	subgroup	G/H
center	C₂³	#10597376
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1984	C₂
socle, prime radical	C₂³×C₁₉	#121
hypercenter	#1984	D₁₉
hypocenter	C₁₉	#10276
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

subgroup

G/H

center

C₂³

#10597376

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1984

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

N	H ≅ G/N	type
48. C₂×Q₈×C₁₉	Q₁₆	semidirect
168. C₁₉	#10276	semidirect
176. C₂×Q₈	Dic₇₆	semidirect

H ≅ G/N

type

48. C₂×Q₈×C₁₉

Q₁₆

semidirect

168. C₁₉

#10276

semidirect

176. C₂×Q₈

Dic₇₆

semidirect

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

subgroup	index
C₂×#11926924	2
C₂×#11926829	2
C₂×#11926291	2
#14561470	2
C₁₉×#1984	2
#10276	19

subgroup

index

C₁₉×#1984

Subgroups — #18085147

Conjugacy classes of subgroups

Complements

Maximal subgroups