Group #18075695 — subgroups

Subgroups — #18075695

Order 4864.

358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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×#11926674	C₂	1	1	yes	maximal, characteristic
2	#14562383	C₂	1	1	yes	maximal, characteristic
3	#14562063	C₂	1	2	yes	maximal
4	#14561530	C₂	1	2	yes	maximal
5	C₁₉×#1837	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
7	#11926674	—	2	1	no	—
8	#11926674	—	2	1	no	—
9	#11926674	C₄	1	2	yes	—
10	#11926674	C₄	1	2	yes	—
11	#11926597	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₈	—	2	1	no	—
14	C₂×#10597272	—	2	1	no	—
15	#11926297	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926274	—	2	4	no	—
18	C₁₉×#423	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#341	—	2	1	no	—
21	C₁₉×#341	—	2	1	no	—
22	C₂²×Dic₃₈	Q₈	1	1	yes	characteristic
23	C₂×M₁₆×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	Q₈	1	1	yes	characteristic
28	C₂×Dic₁₉⋊C₄	—	2	1	no	—
29	C₂×C₄×Dic₁₉	—	2	1	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	C₄×Dic₃₈	—	2	1	no	—
32	C₄×Dic₃₈	—	2	1	no	—
33	C₄×Dic₃₈	C₂×C₄	1	2	yes	—
34	C₄×Dic₃₈	D₄	1	2	yes	—
35	C₁₉×C₄⋊C₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
42	#10597272	—	2	2	no	—
43	#10597272	—	2	2	no	—
44	Dic₁₉⋊C₈	—	2	2	no	—
45	Dic₁₉⋊C₈	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
49	C₄×C₁₉⋊C₈	—	2	2	no	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂²×Dic₁₉	—	2	1	no	—
54	C₂²×Dic₁₉	—	2	1	no	—
55	C₂×Dic₃₈	—	2	1	no	—
56	C₂×Dic₃₈	—	4	2	no	—
57	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
58	M₁₆×C₁₉	—	4	2	no	—
59	M₁₆×C₁₉	—	4	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₉	#41	1	1	yes	characteristic
71	C₄⋊Dic₁₉	—	2	1	no	—
72	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
73	Dic₁₉⋊C₄	—	2	2	no	—
74	Dic₁₉⋊C₄	—	2	2	no	—
75	C₄×Dic₁₉	—	2	2	no	—
76	C₄×Dic₁₉	—	2	2	no	—
77	C₂×C₁₉⋊C₈	—	2	2	no	—
78	C₂×C₁₉⋊C₈	—	4	2	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	#8665	—	19	1	no	maximal, Sylow
81	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#135	1	2	yes	—
91	C₂×C₄×C₁₉	#137	1	2	yes	—
92	C₂×Dic₁₉	—	2	2	no	—
93	C₂×Dic₁₉	—	2	2	no	—
94	C₂×Dic₁₉	—	4	2	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	Dic₃₈	—	2	4	no	—
97	Dic₃₈	—	4	2	no	—
98	C₈×C₁₉	—	2	1	no	—
99	C₈×C₁₉	—	2	1	no	—
100	C₈×C₁₉	—	2	1	no	—
101	C₈×C₁₉	—	2	1	no	—
102	C₈×C₁₉	—	8	2	no	—
103	C₁₉⋊C₈	—	4	2	no	—
104	C₁₉⋊C₈	—	8	2	no	—
105	C₂×#446	—	19	1	no	—
106	#1837	D₁₉	1	1	yes	characteristic
107	#1564	—	19	1	no	—
108	#1487	—	19	2	no	—
109	#1301	—	19	2	no	—
110	C₂²×C₁₉	—	2	1	no	—
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	#380	1	1	yes	characteristic
113	C₂²×C₁₉	#479	1	2	yes	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	#416	1	1	yes	characteristic
118	C₄×C₁₉	#419	1	1	yes	characteristic
119	C₄×C₁₉	#430	1	2	yes	—
120	C₄×C₁₉	#464	1	2	yes	—
121	Dic₁₉	—	4	2	no	—
122	Dic₁₉	—	4	2	no	—
123	C₂×C₄×Q₈	—	19	1	no	—
124	#446	—	19	2	no	—
125	#446	—	19	2	no	—
126	#446	—	38	1	no	—
127	#446	—	38	1	no	—
128	#431	—	19	2	no	—
129	#423	C₂×D₁₉	1	2	yes	—
130	C₂×C₄⋊C₈	—	19	1	no	—
131	C₂×C₄⋊C₈	—	38	1	no	—
132	C₂×#97	—	38	1	no	—
133	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
134	#341	—	2	1	no	—
135	#341	—	2	1	no	—
136	#335	—	38	1	no	—
137	#334	—	38	1	no	—
138	Q₈⋊C₈	—	38	4	no	—
139	C₂×C₁₉	—	2	2	no	—
140	C₂×C₁₉	#1805	1	1	yes	characteristic
141	C₂×C₁₉	#1811	1	1	yes	characteristic
142	C₂×C₁₉	#1814	1	1	yes	characteristic
143	C₂²×Q₈	—	19	1	no	—
144	C₂×M₁₆	—	2	2	no	—
145	C₂²×C₈	—	38	1	no	—
146	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
147	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
148	C₄×Q₈	—	19	2	no	—
149	C₄×Q₈	—	19	2	no	—
150	C₄×Q₈	—	38	1	no	—
151	C₄×Q₈	—	38	1	no	—
152	C₂×C₄⋊C₄	—	19	1	no	—
153	C₂×C₄⋊C₄	—	38	1	no	—
154	C₂×C₄²	—	38	1	no	—
155	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	19	2	no	—
159	C₄⋊C₈	—	38	2	no	—
160	C₄⋊C₈	—	38	2	no	—
161	C₄⋊C₈	—	38	1	no	—
162	C₄⋊C₈	—	38	2	no	—
163	C₂²⋊C₈	—	38	2	no	—
164	#97	—	38	2	no	—
165	#97	—	38	2	no	—
166	C₄×C₈	—	38	2	no	—
167	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
168	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
169	C₄×C₈	D₇₆	1	1	yes	characteristic
170	C₄×C₈	D₇₆	1	1	yes	characteristic
171	C₁₉	#8665	1	1	yes	characteristic, complemented, Sylow
172	C₂×Q₈	—	19	2	no	—
173	C₂×Q₈	—	38	1	no	—
174	C₂×Q₈	—	76	2	no	—
175	C₂²×C₄	—	38	1	no	—
176	C₂²×C₄	—	38	1	no	—
177	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
178	C₂²×C₄	#64545	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
180	M₁₆	—	4	2	no	—
181	M₁₆	—	4	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	38	2	no	—
186	C₂×C₈	—	76	2	no	—
187	C₂×C₈	—	76	2	no	—
188	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
189	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
190	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
191	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
192	C₄⋊C₄	—	19	2	no	—
193	C₄⋊C₄	—	38	2	no	—
194	C₄⋊C₄	—	38	2	no	—
195	C₄⋊C₄	—	38	1	no	—
196	C₄²	—	38	2	no	—
197	C₄²	—	38	2	no	—
198	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
199	C₄²	C₂×D₇₆	1	1	yes	characteristic
200	C₄²	D₄×D₁₉	1	1	yes	characteristic
201	C₄²	#64543	1	1	yes	characteristic
202	C₂³	#10597392	1	1	yes	characteristic
203	Q₈	—	38	4	no	—
204	Q₈	—	76	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	38	2	no	—
208	C₂×C₄	—	38	2	no	—
209	C₂×C₄	—	76	2	no	—
210	C₂×C₄	—	76	2	no	—
211	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
212	C₂×C₄	#10597338	1	1	yes	characteristic
213	C₂×C₄	#10597341	1	1	yes	characteristic
214	C₂×C₄	#10597343	1	1	yes	characteristic
215	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
216	C₂×C₄	#10597384	1	1	yes	characteristic
217	C₂×C₄	#10597396	1	2	yes	—
218	C₂×C₄	#10597397	1	2	yes	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	8	2	no	—
224	C₈	—	76	2	no	—
225	C₈	—	152	2	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	#11926401	1	1	yes	characteristic
229	C₂²	#11926848	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	76	2	no	—
234	C₄	—	76	2	no	—
235	C₄	#11926538	1	1	yes	characteristic
236	C₄	#11926552	1	1	yes	characteristic
237	C₄	#11926591	1	2	yes	—
238	C₄	#11926763	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#14563647	1	1	yes	characteristic
241	C₂	#14563674	1	1	yes	characteristic
242	C₂	#14563690	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926674

C₂

yes

maximal, characteristic

#14562383

C₂

yes

maximal, characteristic

#14562063

C₂

yes

maximal

#14561530

C₂

yes

maximal

C₁₉×#1837

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂²

yes

—

—

C₄

yes

—

#11926674

C₄

yes

—

#11926597

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₈

—

—

—

—

—

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#341

—

C₁₉×#341

—

C₂²×Dic₃₈

Q₈

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

Q₈

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂×C₄

yes

—

C₄×Dic₃₈

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

#10597272

—

#10597272

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₄⋊C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8665

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

100

C₈×C₁₉

—

101

C₈×C₁₉

—

102

C₈×C₁₉

—

103

C₁₉⋊C₈

—

104

C₁₉⋊C₈

—

105

C₂×#446

—

106

#1837

D₁₉

yes

characteristic

107

#1564

—

108

#1487

—

109

#1301

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

#380

yes

characteristic

113

C₂²×C₁₉

#479

yes

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

#416

yes

characteristic

118

C₄×C₁₉

#419

yes

characteristic

119

C₄×C₁₉

#430

yes

—

120

C₄×C₁₉

#464

yes

—

121

Dic₁₉

—

122

Dic₁₉

—

123

C₂×C₄×Q₈

—

124

#446

—

125

#446

—

126

#446

—

127

#446

—

128

#431

—

129

#423

C₂×D₁₉

yes

—

130

C₂×C₄⋊C₈

—

131

C₂×C₄⋊C₈

—

132

C₂×#97

—

133

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

134

#341

—

135

#341

—

136

#335

—

137

#334

—

138

Q₈⋊C₈

—

139

C₂×C₁₉

—

140

C₂×C₁₉

#1805

yes

characteristic

141

C₂×C₁₉

#1811

yes

characteristic

142

C₂×C₁₉

#1814

yes

characteristic

143

C₂²×Q₈

—

144

C₂×M₁₆

—

145

C₂²×C₈

—

146

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

147

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄²

—

155

C₂×C₄²

C₂²×D₁₉

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₂²⋊C₈

—

164

#97

—

165

#97

—

166

C₄×C₈

—

167

C₄×C₈

C₄×D₁₉

yes

characteristic

168

C₄×C₈

C₄×D₁₉

yes

characteristic

169

C₄×C₈

D₇₆

yes

characteristic

170

C₄×C₈

D₇₆

yes

characteristic

171

C₁₉

#8665

yes

characteristic, complemented, Sylow

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

Q₈×D₁₉

yes

characteristic

178

C₂²×C₄

#64545

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

180

M₁₆

—

181

M₁₆

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

189

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

190

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

191

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄²

—

197

C₄²

—

198

C₄²

C₂×C₄×D₁₉

yes

characteristic

199

C₄²

C₂×D₇₆

yes

characteristic

200

C₄²

D₄×D₁₉

yes

characteristic

201

C₄²

#64543

yes

characteristic

202

C₂³

#10597392

yes

characteristic

203

Q₈

—

204

Q₈

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

212

C₂×C₄

#10597338

yes

characteristic

213

C₂×C₄

#10597341

yes

characteristic

214

C₂×C₄

#10597343

yes

characteristic

215

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

216

C₂×C₄

#10597384

yes

characteristic

217

C₂×C₄

#10597396

yes

—

218

C₂×C₄

#10597397

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

225

C₈

—

152

—

226

C₂²

—

227

C₂²

—

228

C₂²

#11926401

yes

characteristic

229

C₂²

#11926848

yes

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

#11926538

yes

characteristic

236

C₄

#11926552

yes

characteristic

237

C₄

#11926591

yes

—

238

C₄

#11926763

yes

—

239

C₂

—

240

C₂

#14563647

yes

characteristic

241

C₂

#14563674

yes

characteristic

242

C₂

#14563690

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597384
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1837	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	C₂²⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1837	D₁₉
hypocenter	C₁₉	#8665
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂×C₄

#10597384

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1837

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂³×C₁₉

C₂²⋊Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
171. C₁₉	#8665	semidirect

H ≅ G/N

type

171. C₁₉

#8665

semidirect

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

subgroup	index
C₂×#11926674	2
#14562383	2
#14562063	2
#14561530	2
C₁₉×#1837	2
#8665	19

subgroup

index

C₁₉×#1837

Subgroups — #18075695

Conjugacy classes of subgroups

Complements

Maximal subgroups