Group #18069631 — subgroups

Subgroups — #18069631

Order 4864.

280 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 87 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	#14564572	C₂	1	1	yes	maximal, characteristic
2	#14563631	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic
4	#11926568	—	2	1	no	—
5	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
6	C₂×#10597293	—	2	1	no	—
7	C₂×C₄×C₁₉⋊C₈	C₄	1	1	yes	characteristic
8	#11926313	C₄	1	2	yes	—
9	#11926299	—	2	1	no	—
10	#11926299	—	2	1	no	—
11	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#423	—	2	1	no	—
13	C₂×C₁₉×#101	—	2	1	no	—
14	C₁₉×#343	C₄	1	2	yes	—
15	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×M₁₆×C₁₉	—	2	2	no	—
17	C₄×Q₈×C₁₉	—	4	1	no	—
18	C₄×Q₈×C₁₉	—	4	1	no	—
19	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₂×#64520	—	2	2	no	—
26	C₂²×C₁₉⋊C₈	—	2	1	no	—
27	C₂²×C₁₉⋊C₈	—	2	1	no	—
28	C₁₉×C₄⋊C₈	—	4	1	no	—
29	C₁₉×C₄⋊C₈	—	4	1	no	—
30	C₁₉×#101	—	4	1	no	—
31	C₁₉×#101	—	4	1	no	—
32	#10597293	—	4	1	no	—
33	#10597293	—	4	1	no	—
34	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
35	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
36	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
37	C₄×C₁₉⋊C₈	—	4	1	no	—
38	C₂×Q₈×C₁₉	—	4	1	no	—
39	C₂×Q₈×C₁₉	—	4	1	no	—
40	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
41	C₂×Q₈×C₁₉	SD₁₆	1	1	yes	characteristic
42	C₂×Q₈×C₁₉	SD₁₆	1	1	yes	characteristic
43	C₂×Q₈×C₁₉	Q₁₆	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
51	M₁₆×C₁₉	—	4	2	no	—
52	M₁₆×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	—	4	2	no	—
54	C₄⋊C₄×C₁₉	—	4	1	no	—
55	C₄⋊C₄×C₁₉	—	4	1	no	—
56	C₄⋊C₄×C₁₉	—	4	1	no	—
57	C₄²×C₁₉	—	2	1	no	—
58	C₄²×C₁₉	—	2	1	no	—
59	C₄²×C₁₉	—	2	1	no	—
60	C₄²×C₁₉	—	2	1	no	—
61	C₄²×C₁₉	—	2	1	no	—
62	C₄²×C₁₉	—	2	1	no	—
63	#64520	—	4	2	no	—
64	#64520	—	4	2	no	—
65	C₂×C₁₉⋊C₈	—	2	2	no	—
66	C₂×C₁₉⋊C₈	—	4	1	no	—
67	C₂×C₁₉⋊C₈	—	4	1	no	—
68	C₂×C₁₉⋊C₈	—	4	2	no	—
69	C₂×C₁₉⋊C₈	—	4	2	no	—
70	C₂×C₁₉⋊C₈	—	4	1	no	—
71	#7238	—	19	1	no	maximal, Sylow
72	C₂³×C₁₉	#95	1	1	yes	characteristic
73	Q₈×C₁₉	—	4	1	no	—
74	Q₈×C₁₉	—	4	1	no	—
75	Q₈×C₁₉	—	4	1	no	—
76	Q₈×C₁₉	—	4	1	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
99	C₈×C₁₉	—	8	2	no	—
100	C₁₉⋊C₈	—	4	2	no	—
101	C₁₉⋊C₈	—	8	2	no	—
102	C₁₉⋊C₈	—	8	1	no	—
103	#1984	—	19	1	no	—
104	#1801	—	19	1	no	—
105	#1801	D₁₉	1	1	yes	characteristic
106	C₂²×C₁₉	—	2	1	no	—
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
109	C₂²×C₁₉	#340	1	1	yes	characteristic
110	C₂²×C₁₉	#342	1	1	yes	characteristic
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	1	no	—
118	C₄×C₁₉	—	4	1	no	—
119	C₄×C₁₉	—	4	1	no	—
120	C₄×C₁₉	—	4	1	no	—
121	C₄×C₁₉	#355	1	1	yes	characteristic
122	C₄×C₁₉	#356	1	1	yes	characteristic
123	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
124	#423	—	2	1	no	—
125	#423	—	38	1	no	—
126	C₂×C₄⋊C₈	—	19	1	no	—
127	C₂×#101	—	2	1	no	—
128	C₂×#101	—	38	1	no	—
129	C₂×C₄×C₈	—	19	1	no	—
130	#343	—	19	2	no	—
131	#343	Dic₁₉	1	2	yes	—
132	#336	—	38	1	no	—
133	#336	—	38	1	no	—
134	C₂×C₁₉	—	2	1	no	—
135	C₂×C₁₉	—	2	1	no	—
136	C₂×C₁₉	#1289	1	1	yes	characteristic
137	C₂×C₁₉	#1392	1	1	yes	characteristic
138	C₂×C₁₉	#1394	1	1	yes	characteristic
139	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
140	C₂×M₁₆	—	2	2	no	—
141	C₂×M₁₆	—	38	2	no	—
142	C₂²×C₈	—	38	1	no	—
143	C₂²×C₈	—	38	1	no	—
144	C₄×Q₈	—	4	1	no	—
145	C₄×Q₈	—	4	1	no	—
146	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
147	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
148	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
149	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
150	C₂×C₄²	D₇₆	1	1	yes	characteristic
151	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
152	C₄⋊C₈	—	4	1	no	—
153	C₄⋊C₈	—	4	1	no	—
154	C₄⋊C₈	—	76	1	no	—
155	C₄⋊C₈	—	76	1	no	—
156	C₄⋊C₈	—	76	1	no	—
157	#101	—	4	1	no	—
158	#101	—	4	1	no	—
159	#101	—	76	1	no	—
160	#101	—	76	1	no	—
161	C₄×C₈	—	76	1	no	—
162	C₁₉	#7238	1	1	yes	characteristic, complemented, Sylow
163	C₂×Q₈	—	4	1	no	—
164	C₂×Q₈	—	4	1	no	—
165	C₂×Q₈	#64525	1	1	yes	characteristic
166	C₂×Q₈	#64526	1	1	yes	characteristic
167	C₂×Q₈	#64527	1	1	yes	characteristic
168	C₂×Q₈	#64528	1	1	yes	characteristic
169	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
170	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
171	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
172	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
173	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
174	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
175	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
176	M₁₆	—	4	2	no	—
177	M₁₆	—	4	2	no	—
178	M₁₆	—	76	2	no	—
179	M₁₆	—	76	2	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	38	2	no	—
182	C₂×C₈	—	76	1	no	—
183	C₂×C₈	—	76	1	no	—
184	C₂×C₈	—	76	2	no	—
185	C₂×C₈	—	76	2	no	—
186	C₂×C₈	—	76	1	no	—
187	C₄⋊C₄	—	4	1	no	—
188	C₄⋊C₄	—	4	1	no	—
189	C₄⋊C₄	—	4	1	no	—
190	C₄²	—	2	1	no	—
191	C₄²	—	2	1	no	—
192	C₄²	—	2	1	no	—
193	C₄²	—	2	1	no	—
194	C₄²	—	2	1	no	—
195	C₄²	—	2	1	no	—
196	C₂³	C₁₉⋊#95	1	1	yes	characteristic
197	Q₈	—	4	1	no	—
198	Q₈	—	4	1	no	—
199	Q₈	—	4	1	no	—
200	Q₈	—	4	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	#10597263	1	1	yes	characteristic
216	C₂×C₄	#10597263	1	1	yes	characteristic
217	C₂×C₄	#10597264	1	1	yes	characteristic
218	C₂×C₄	#10597265	1	1	yes	characteristic
219	C₂×C₄	#10597266	1	1	yes	characteristic
220	C₂×C₄	#10597267	1	1	yes	characteristic
221	C₂×C₄	#10597289	1	1	yes	characteristic
222	C₂×C₄	#10597292	1	1	yes	characteristic
223	C₈	—	8	2	no	—
224	C₈	—	76	2	no	—
225	C₈	—	152	2	no	—
226	C₈	—	152	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	—	2	1	no	—
229	C₂²	#11926300	1	1	yes	characteristic
230	C₂²	#11926306	1	1	yes	characteristic
231	C₂²	#11926310	1	1	yes	characteristic
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	2	1	no	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	2	1	no	—
239	C₄	—	4	1	no	—
240	C₄	—	4	1	no	—
241	C₄	—	4	1	no	—
242	C₄	#11926340	1	1	yes	characteristic
243	C₄	#11926342	1	1	yes	characteristic
244	C₂	—	2	1	no	—
245	C₂	—	2	1	no	—
246	C₂	#14561502	1	1	yes	characteristic
247	C₂	#14561757	1	1	yes	characteristic
248	C₂	#14561761	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564572

C₂

yes

maximal, characteristic

#14563631

C₂

yes

maximal, characteristic

C₁₉×#1801

C₂

yes

maximal, characteristic

#11926568

—

C₂×C₄⋊(C₁₉⋊C₈)

C₄

yes

characteristic

C₂×#10597293

—

C₂×C₄×C₁₉⋊C₈

C₄

yes

characteristic

#11926313

C₄

yes

—

#11926299

—

#11926299

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#423

—

C₂×C₁₉×#101

—

C₁₉×#343

C₄

yes

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#101

—

C₁₉×#101

—

#10597293

—

#10597293

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

characteristic

C₂×Q₈×C₁₉

SD₁₆

yes

characteristic

C₂×Q₈×C₁₉

SD₁₆

yes

characteristic

C₂×Q₈×C₁₉

Q₁₆

yes

characteristic

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

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

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

100

C₁₉⋊C₈

—

101

C₁₉⋊C₈

—

102

C₁₉⋊C₈

—

103

#1984

—

104

#1801

—

105

#1801

D₁₉

yes

characteristic

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

H(3,ℤ/4)

yes

characteristic

109

C₂²×C₁₉

#340

yes

characteristic

110

C₂²×C₁₉

#342

yes

characteristic

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

#355

yes

characteristic

122

C₄×C₁₉

#356

yes

characteristic

123

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

124

#423

—

125

#423

—

126

C₂×C₄⋊C₈

—

127

C₂×#101

—

128

C₂×#101

—

129

C₂×C₄×C₈

—

130

#343

—

131

#343

Dic₁₉

yes

—

132

#336

—

133

#336

—

134

C₂×C₁₉

—

135

C₂×C₁₉

—

136

C₂×C₁₉

#1289

yes

characteristic

137

C₂×C₁₉

#1392

yes

characteristic

138

C₂×C₁₉

#1394

yes

characteristic

139

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

140

C₂×M₁₆

—

141

C₂×M₁₆

—

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₄×Q₈

—

145

C₄×Q₈

—

146

C₂×C₄⋊C₄

Dic₃₈

yes

characteristic

147

C₂×C₄⋊C₄

C₄×D₁₉

yes

characteristic

148

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

149

C₂×C₄²

C₄×D₁₉

yes

characteristic

150

C₂×C₄²

D₇₆

yes

characteristic

151

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

#101

—

158

#101

—

159

#101

—

160

#101

—

161

C₄×C₈

—

162

C₁₉

#7238

yes

characteristic, complemented, Sylow

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

#64525

yes

characteristic

166

C₂×Q₈

#64526

yes

characteristic

167

C₂×Q₈

#64527

yes

characteristic

168

C₂×Q₈

#64528

yes

characteristic

169

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

170

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

171

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

172

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

173

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

174

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

175

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

176

M₁₆

—

177

M₁₆

—

178

M₁₆

—

179

M₁₆

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

—

195

C₄²

—

196

C₂³

C₁₉⋊#95

yes

characteristic

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

#10597263

yes

characteristic

216

C₂×C₄

#10597263

yes

characteristic

217

C₂×C₄

#10597264

yes

characteristic

218

C₂×C₄

#10597265

yes

characteristic

219

C₂×C₄

#10597266

yes

characteristic

220

C₂×C₄

#10597267

yes

characteristic

221

C₂×C₄

#10597289

yes

characteristic

222

C₂×C₄

#10597292

yes

characteristic

223

C₈

—

224

C₈

—

225

C₈

—

152

—

226

C₈

—

152

—

227

C₂²

—

228

C₂²

—

229

C₂²

#11926300

yes

characteristic

230

C₂²

#11926306

yes

characteristic

231

C₂²

#11926310

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

#11926340

yes

characteristic

243

C₄

#11926342

yes

characteristic

244

C₂

—

245

C₂

—

246

C₂

#14561502

yes

characteristic

247

C₂

#14561757

yes

characteristic

248

C₂

#14561761

yes

characteristic

	subgroup	G/H
center	C₂²	#11926310
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂×C₄×Q₈	C₂×D₁₉
Fitting	C₁₉×#1801	C₂
socle	C₂²×C₁₉	#342
prime radical	C₂³×C₁₉	#95
cosocle	C₂×C₄×Q₈×C₁₉	C₂²
hypercenter	#1801	D₁₉
hypocenter	C₁₉	#7238
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×Q₈ ◁ #1801

subgroup

G/H

center

C₂²

#11926310

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₂×C₄×Q₈

C₂×D₁₉

Fitting

C₁₉×#1801

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄×Q₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×Q₈ ◁ #1801

N	H ≅ G/N	type
162. C₁₉	#7238	semidirect

H ≅ G/N

type

162. C₁₉

#7238

semidirect

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

subgroup	index
#14564572	2
#14563631	2
C₁₉×#1801	2
#7238	19

subgroup

index

#14564572

#14563631

C₁₉×#1801

#7238

Subgroups — #18069631

Conjugacy classes of subgroups

Complements

Maximal subgroups