Group #18075494 — subgroups

Subgroups — #18075494

Order 4864.

362 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 111 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×C₈×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	#14562398	C₂	1	1	yes	maximal, characteristic
3	#14561978	C₂	1	2	yes	maximal
4	#14561504	C₂	1	2	yes	maximal
5	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₈×Dic₃₈	—	2	1	no	—
8	C₈×Dic₃₈	—	2	1	no	—
9	C₈×Dic₃₈	—	2	1	no	—
10	C₈×Dic₃₈	—	2	1	no	—
11	#11926601	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₈	C₄	1	2	yes	—
14	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
15	#11926297	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926269	—	2	4	no	—
18	C₁₉×#432	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#335	—	2	1	no	—
21	C₁₉×#334	—	2	1	no	—
22	C₂²×Dic₃₈	Q₈	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×C₄⋊Dic₁₉	Q₈	1	1	yes	characteristic
27	C₂×Dic₁₉⋊C₄	D₄	1	2	yes	—
28	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
30	C₄×Dic₃₈	—	2	1	no	—
31	C₄×Dic₃₈	—	2	1	no	—
32	C₄×Dic₃₈	—	2	1	no	—
33	C₄×Dic₃₈	—	2	1	no	—
34	C₁₉×C₄⋊C₈	—	2	2	no	—
35	C₁₉×C₂²⋊C₈	—	2	2	no	—
36	C₁₉×#97	—	2	2	no	—
37	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
38	C₄×C₈×C₁₉	D₄	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	Dic₁₉⋊C₈	—	2	2	no	—
43	Dic₁₉⋊C₈	—	2	2	no	—
44	C₈×Dic₁₉	—	2	2	no	—
45	C₈×Dic₁₉	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	#10597260	—	2	2	no	—
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	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
54	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
55	C₂×Dic₃₈	—	2	1	no	—
56	C₂×Dic₃₈	—	2	1	no	—
57	C₂×Dic₃₈	—	2	4	no	—
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₂×C₈×C₁₉	—	4	1	no	—
60	C₂×C₈×C₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₉	#41	1	1	yes	characteristic
68	C₄²×C₁₉	#41	1	1	yes	characteristic
69	C₄⋊Dic₁₉	—	2	1	no	—
70	C₄⋊Dic₁₉	—	2	1	no	—
71	Dic₁₉⋊C₄	—	2	2	no	—
72	Dic₁₉⋊C₄	—	2	2	no	—
73	C₄×Dic₁₉	—	2	2	no	—
74	C₄×Dic₁₉	—	2	2	no	—
75	C₂×C₁₉⋊C₈	—	2	2	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	C₂×C₁₉⋊C₈	—	4	2	no	—
78	#8623	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×Dic₁₉	—	2	2	no	—
91	C₂×Dic₁₉	—	2	2	no	—
92	C₂×Dic₁₉	—	2	2	no	—
93	C₂×Dic₁₉	—	4	2	no	—
94	C₂×Dic₁₉	#108	1	4	yes	—
95	Dic₃₈	—	2	4	no	—
96	Dic₃₈	—	2	4	no	—
97	C₈×C₁₉	—	2	1	no	—
98	C₈×C₁₉	—	2	1	no	—
99	C₈×C₁₉	—	2	1	no	—
100	C₈×C₁₉	—	8	2	no	—
101	C₈×C₁₉	#101	1	2	yes	—
102	C₁₉⋊C₈	—	4	2	no	—
103	C₁₉⋊C₈	—	8	2	no	—
104	C₂×C₈×Q₈	—	19	1	no	—
105	#1568	—	19	1	no	—
106	#1568	D₁₉	1	1	yes	characteristic
107	#1467	—	19	2	no	—
108	#1290	—	19	2	no	—
109	C₂²×C₁₉	—	2	1	no	—
110	C₂²×C₁₉	—	2	1	no	—
111	C₂²×C₁₉	#380	1	1	yes	characteristic
112	C₂²×C₁₉	C₂×#108	1	2	yes	—
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	C₂×#101	1	1	yes	characteristic
119	C₄×C₁₉	#413	1	1	yes	characteristic
120	Dic₁₉	—	2	4	no	—
121	Dic₁₉	—	4	2	no	—
122	C₂×C₄×Q₈	—	19	1	no	—
123	C₈×Q₈	—	38	1	no	—
124	C₈×Q₈	—	38	1	no	—
125	C₈×Q₈	—	38	1	no	—
126	C₈×Q₈	—	38	1	no	—
127	#432	—	19	2	no	—
128	#432	C₂×D₁₉	1	2	yes	—
129	C₂×C₄⋊C₈	—	19	2	no	—
130	C₂×C₄⋊C₈	—	19	1	no	—
131	C₂×C₄×C₈	—	19	2	no	—
132	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
133	#335	—	2	1	no	—
134	#335	—	38	1	no	—
135	#334	—	2	1	no	—
136	#334	—	38	1	no	—
137	#324	—	38	4	no	—
138	C₂×C₁₉	—	2	2	no	—
139	C₂×C₁₉	#1801	1	1	yes	characteristic
140	C₂×C₁₉	#1810	1	1	yes	characteristic
141	C₂×C₁₉	#1812	1	1	yes	characteristic
142	C₂²×Q₈	—	19	1	no	—
143	C₂²×C₈	—	19	2	no	—
144	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
145	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
146	C₄×Q₈	—	38	1	no	—
147	C₄×Q₈	—	38	1	no	—
148	C₄×Q₈	—	38	1	no	—
149	C₄×Q₈	—	38	1	no	—
150	C₂×C₄⋊C₄	—	19	2	no	—
151	C₂×C₄⋊C₄	—	19	1	no	—
152	C₂×C₄²	—	19	2	no	—
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	2	2	no	—
155	C₄⋊C₈	—	38	2	no	—
156	C₄⋊C₈	—	38	2	no	—
157	C₄⋊C₈	—	38	1	no	—
158	C₄⋊C₈	—	38	2	no	—
159	C₄⋊C₈	—	38	1	no	—
160	C₂²⋊C₈	—	2	2	no	—
161	C₂²⋊C₈	—	38	2	no	—
162	#97	—	2	2	no	—
163	#97	—	38	2	no	—
164	C₄×C₈	—	38	2	no	—
165	C₄×C₈	—	38	2	no	—
166	C₄×C₈	D₇₆	1	1	yes	characteristic
167	C₄×C₈	D₇₆	1	1	yes	characteristic
168	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
169	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
170	C₁₉	#8623	1	1	yes	characteristic, complemented, Sylow
171	C₂×Q₈	—	38	4	no	—
172	C₂×Q₈	—	38	1	no	—
173	C₂×Q₈	—	38	1	no	—
174	C₂²×C₄	—	19	2	no	—
175	C₂²×C₄	—	19	2	no	—
176	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
177	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
178	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	4	1	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	38	2	no	—
183	C₂×C₈	—	76	2	no	—
184	C₂×C₈	—	76	2	no	—
185	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
186	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
187	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
188	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
189	C₄⋊C₄	—	38	2	no	—
190	C₄⋊C₄	—	38	1	no	—
191	C₄⋊C₄	—	38	2	no	—
192	C₄⋊C₄	—	38	1	no	—
193	C₄²	—	38	2	no	—
194	C₄²	—	38	2	no	—
195	C₄²	C₂×D₇₆	1	1	yes	characteristic
196	C₄²	#64543	1	1	yes	characteristic
197	C₄²	#64545	1	1	yes	characteristic
198	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
199	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
200	Q₈	—	38	4	no	—
201	Q₈	—	38	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	19	4	no	—
207	C₂×C₄	—	38	2	no	—
208	C₂×C₄	—	38	2	no	—
209	C₂×C₄	—	38	2	no	—
210	C₂×C₄	—	76	2	no	—
211	C₂×C₄	#10597338	1	1	yes	characteristic
212	C₂×C₄	#10597341	1	1	yes	characteristic
213	C₂×C₄	#10597343	1	1	yes	characteristic
214	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
215	C₂×C₄	#10597384	1	1	yes	characteristic
216	C₂×C₄	#10597392	1	1	yes	characteristic
217	C₈	—	2	1	no	—
218	C₈	—	2	1	no	—
219	C₈	—	2	1	no	—
220	C₈	—	8	2	no	—
221	C₈	—	76	2	no	—
222	C₈	—	152	2	no	—
223	C₈	#10597281	1	2	yes	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	#11926401	1	1	yes	characteristic
227	C₂²	#108×D₁₉	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	38	4	no	—
234	C₄	—	76	2	no	—
235	C₄	C₂×#10597281	1	1	yes	characteristic
236	C₄	#11926526	1	1	yes	characteristic
237	C₂	—	2	2	no	—
238	C₂	#14563628	1	1	yes	characteristic
239	C₂	#14563670	1	1	yes	characteristic
240	C₂	#14563678	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₃₈

C₂

yes

maximal, characteristic

#14562398

C₂

yes

maximal, characteristic

#14561978

C₂

yes

maximal

#14561504

C₂

yes

maximal

C₁₉×#1568

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂²

yes

characteristic

C₈×Dic₃₈

—

C₈×Dic₃₈

—

C₈×Dic₃₈

—

C₈×Dic₃₈

—

#11926601

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₈

C₄

yes

—

C₂×C₈×Dic₁₉

C₄

yes

—

#11926297

—

#11926295

—

#11926269

—

C₁₉×#432

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂²×Dic₃₈

Q₈

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

Q₈

yes

characteristic

C₂×Dic₁₉⋊C₄

D₄

yes

—

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

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

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8623

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#108

yes

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

100

C₈×C₁₉

—

101

C₈×C₁₉

#101

yes

—

102

C₁₉⋊C₈

—

103

C₁₉⋊C₈

—

104

C₂×C₈×Q₈

—

105

#1568

—

106

#1568

D₁₉

yes

characteristic

107

#1467

—

108

#1290

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

#380

yes

characteristic

112

C₂²×C₁₉

C₂×#108

yes

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

C₂×#101

yes

characteristic

119

C₄×C₁₉

#413

yes

characteristic

120

Dic₁₉

—

121

Dic₁₉

—

122

C₂×C₄×Q₈

—

123

C₈×Q₈

—

124

C₈×Q₈

—

125

C₈×Q₈

—

126

C₈×Q₈

—

127

#432

—

128

#432

C₂×D₁₉

yes

—

129

C₂×C₄⋊C₈

—

130

C₂×C₄⋊C₈

—

131

C₂×C₄×C₈

—

132

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

133

#335

—

134

#335

—

135

#334

—

136

#334

—

137

#324

—

138

C₂×C₁₉

—

139

C₂×C₁₉

#1801

yes

characteristic

140

C₂×C₁₉

#1810

yes

characteristic

141

C₂×C₁₉

#1812

yes

characteristic

142

C₂²×Q₈

—

143

C₂²×C₈

—

144

C₂²×C₈

C₄×D₁₉

yes

characteristic

145

C₂²×C₈

C₄×D₁₉

yes

characteristic

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄²

—

153

C₂×C₄²

C₂²×D₁₉

yes

characteristic

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₂²⋊C₈

—

161

C₂²⋊C₈

—

162

#97

—

163

#97

—

164

C₄×C₈

—

165

C₄×C₈

—

166

C₄×C₈

D₇₆

yes

characteristic

167

C₄×C₈

D₇₆

yes

characteristic

168

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

169

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

170

C₁₉

#8623

yes

characteristic, complemented, Sylow

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

177

C₂²×C₄

D₄×D₁₉

yes

characteristic

178

C₂²×C₄

Q₈×D₁₉

yes

characteristic

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

186

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

187

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

188

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄²

—

194

C₄²

—

195

C₄²

C₂×D₇₆

yes

characteristic

196

C₄²

#64543

yes

characteristic

197

C₄²

#64545

yes

characteristic

198

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

199

C₂³

C₄⋊C₄×D₁₉

yes

characteristic

200

Q₈

—

201

Q₈

—

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

#10597338

yes

characteristic

212

C₂×C₄

#10597341

yes

characteristic

213

C₂×C₄

#10597343

yes

characteristic

214

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

215

C₂×C₄

#10597384

yes

characteristic

216

C₂×C₄

#10597392

yes

characteristic

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

152

—

223

C₈

#10597281

yes

—

224

C₂²

—

225

C₂²

—

226

C₂²

#11926401

yes

characteristic

227

C₂²

#108×D₁₉

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

C₂×#10597281

yes

characteristic

236

C₄

#11926526

yes

characteristic

237

C₂

—

238

C₂

#14563628

yes

characteristic

239

C₂

#14563670

yes

characteristic

240

C₂

#14563678

yes

characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1568	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1568	D₁₉
hypocenter	C₁₉	#8623
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#11926401

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1568

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
170. C₁₉	#8623	semidirect

H ≅ G/N

type

170. C₁₉

#8623

semidirect

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

subgroup	index
C₂×C₈×Dic₃₈	2
#14562398	2
#14561978	2
#14561504	2
C₁₉×#1568	2
#8623	19

subgroup

index

C₂×C₈×Dic₃₈

C₁₉×#1568

Subgroups — #18075494

Conjugacy classes of subgroups

Complements

Maximal subgroups