Group #14569405 — subgroups

Subgroups — #14569405

Order 2432.

528 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10597390	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597370	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597372	C₂	1	1	yes	maximal, characteristic
4	#11926477	C₂	1	4	yes	maximal, complemented
5	#11926472	C₂	1	4	yes	maximal
6	#11926451	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926449	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926409	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
13	C₁₉×C₂²⋊Q₈	—	2	4	no	—
14	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
18	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
19	#10597390	—	2	4	no	—
20	#10597372	—	2	4	no	—
21	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
23	#10597370	—	2	4	no	—
24	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
25	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
26	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
28	C₁₉⋊#95	C₂²	1	4	yes	—
29	C₁₉⋊#95	C₂²	1	4	yes	—
30	C₁₉⋊#95	C₂²	1	4	yes	—
31	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×Q₈×C₁₉	—	2	2	no	—
33	C₂×Q₈×C₁₉	—	2	2	no	—
34	C₂×Q₈×C₁₉	—	2	2	no	—
35	C₂²×C₄×C₁₉	—	2	2	no	—
36	C₂²×C₄×C₁₉	—	2	2	no	—
37	C₂²×C₄×C₁₉	D₄	1	4	yes	—
38	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×Dic₁₉	C₂³	1	2	yes	—
43	C₂²×Dic₁₉	C₂³	1	2	yes	—
44	C₂²×Dic₁₉	C₂³	1	2	yes	—
45	C₂²×Dic₁₉	C₂³	1	2	yes	—
46	C₂×Dic₃₈	—	2	2	no	—
47	C₂×Dic₃₈	—	2	2	no	—
48	C₂×Dic₃₈	—	2	2	no	—
49	C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₂²⋊C₄×C₁₉	—	2	4	no	—
52	C₂²⋊Dic₁₉	—	2	4	no	—
53	C₂²⋊Dic₁₉	—	2	4	no	—
54	C₄⋊Dic₁₉	—	2	2	no	—
55	C₄⋊Dic₁₉	—	2	4	no	—
56	Dic₁₉⋊C₄	—	2	4	no	—
57	Dic₁₉⋊C₄	—	2	8	no	—
58	C₄×Dic₁₉	—	2	2	no	—
59	C₄×Dic₁₉	D₄	1	4	yes	—
60	C₂³×C₁₉	—	2	1	no	—
61	C₂³×C₁₉	—	2	1	no	—
62	C₂³×C₁₉	—	2	2	no	—
63	C₂³×C₁₉	—	2	2	no	—
64	C₂³×C₁₉	C₂×D₄	1	2	yes	—
65	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
66	Q₈×C₁₉	—	4	4	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	8	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	—	2	4	no	—
75	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
76	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
77	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₁₉	#41	1	2	yes	—
79	C₂×Dic₁₉	—	2	2	no	—
80	C₂×Dic₁₉	—	2	2	no	—
81	C₂×Dic₁₉	—	2	2	no	—
82	C₂×Dic₁₉	—	2	2	no	—
83	C₂×Dic₁₉	—	2	2	no	—
84	C₂×Dic₁₉	—	2	2	no	—
85	C₂×Dic₁₉	—	2	2	no	—
86	C₂×Dic₁₉	—	2	2	no	—
87	C₂×Dic₁₉	—	2	4	no	—
88	C₂×Dic₁₉	—	2	2	no	—
89	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
90	Dic₃₈	—	4	4	no	—
91	#2621	—	19	1	no	maximal, Sylow
92	C₂²×C₁₉	—	2	2	no	—
93	C₂²×C₁₉	—	2	2	no	—
94	C₂²×C₁₉	—	2	2	no	—
95	C₂²×C₁₉	—	4	2	no	—
96	C₂²×C₁₉	—	4	2	no	—
97	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
98	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
99	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
100	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
101	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
102	C₄×C₁₉	—	2	2	no	—
103	C₄×C₁₉	—	4	2	no	—
104	C₄×C₁₉	—	4	2	no	—
105	C₄×C₁₉	#121	1	4	yes	—
106	Dic₁₉	—	2	4	no	—
107	Dic₁₉	—	4	2	no	—
108	Dic₁₉	—	4	2	no	—
109	Dic₁₉	—	4	2	no	—
110	C₂×C₄⋊Q₈	—	19	1	no	—
111	C₂×C₂²⋊Q₈	—	19	1	no	—
112	C₂×C₂²⋊Q₈	D₁₉	1	1	yes	characteristic
113	C₂×#117	—	19	1	no	—
114	#398	—	19	4	no	—
115	#397	—	19	4	no	—
116	#391	—	19	1	no	—
117	#391	—	19	1	no	—
118	#382	—	19	1	no	—
119	C₂×C₁₉	—	4	2	no	—
120	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
121	C₂×C₁₉	#536	1	1	yes	characteristic
122	C₂×C₁₉	#536	1	2	yes	—
123	C₂×C₁₉	#536	1	1	yes	characteristic
124	C₂×C₁₉	#541	1	2	yes	—
125	C₂²×Q₈	—	19	1	no	—
126	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
127	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
128	C₄⋊Q₈	—	38	4	no	—
129	C₂²⋊Q₈	—	2	4	no	—
130	C₂²⋊Q₈	—	38	4	no	—
131	#117	—	38	4	no	—
132	C₂×C₄⋊C₄	—	19	2	no	—
133	C₂×C₄⋊C₄	—	19	1	no	—
134	C₂×C₄⋊C₄	—	19	2	no	—
135	C₂×C₄⋊C₄	—	19	4	no	—
136	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
137	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
138	C₂×C₂²⋊C₄	—	19	2	no	—
139	C₂×C₂²⋊C₄	—	19	2	no	—
140	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
141	C₂×C₄²	—	19	1	no	—
142	C₂×C₄²	—	19	1	no	—
143	#95	—	19	4	no	—
144	#95	—	19	4	no	—
145	#95	—	19	4	no	—
146	C₁₉	#2621	1	1	yes	characteristic, complemented, Sylow
147	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
148	C₂×Q₈	—	2	2	no	—
149	C₂×Q₈	—	2	2	no	—
150	C₂×Q₈	—	2	2	no	—
151	C₂×Q₈	—	38	2	no	—
152	C₂×Q₈	—	38	2	no	—
153	C₂×Q₈	—	38	2	no	—
154	C₂²×C₄	—	2	2	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	19	2	no	—
157	C₂²×C₄	—	19	2	no	—
158	C₂²×C₄	—	19	2	no	—
159	C₂²×C₄	—	19	2	no	—
160	C₂²×C₄	C₂²⋊D₁₉	1	4	yes	—
161	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
162	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
163	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
164	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
165	C₄⋊C₄	—	2	2	no	—
166	C₄⋊C₄	—	2	4	no	—
167	C₄⋊C₄	—	38	8	no	—
168	C₄⋊C₄	—	38	4	no	—
169	C₄⋊C₄	—	38	4	no	—
170	C₄⋊C₄	—	38	2	no	—
171	C₂²⋊C₄	—	2	4	no	—
172	C₂²⋊C₄	—	38	4	no	—
173	C₂²⋊C₄	—	38	4	no	—
174	C₄²	—	19	4	no	—
175	C₄²	—	38	2	no	—
176	C₂³	—	2	1	no	—
177	C₂³	—	2	1	no	—
178	C₂³	—	2	2	no	—
179	C₂³	—	2	2	no	—
180	C₂³	C₂×C₂²⋊D₁₉	1	2	yes	—
181	C₂³	C₂³×D₁₉	1	1	yes	characteristic
182	Q₈	—	4	4	no	—
183	Q₈	—	76	4	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	8	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	4	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	19	4	no	—
193	C₂×C₄	—	38	2	no	—
194	C₂×C₄	—	38	2	no	—
195	C₂×C₄	—	38	2	no	—
196	C₂×C₄	—	38	2	no	—
197	C₂×C₄	—	38	2	no	—
198	C₂×C₄	—	38	2	no	—
199	C₂×C₄	—	38	4	no	—
200	C₂×C₄	—	38	2	no	—
201	C₂×C₄	—	38	2	no	—
202	C₂×C₄	—	38	2	no	—
203	C₂×C₄	D₄×D₁₉	1	2	yes	—
204	C₂×C₄	#64543	1	2	yes	—
205	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
206	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
207	C₂²	—	2	2	no	—
208	C₂²	—	2	2	no	—
209	C₂²	—	2	2	no	—
210	C₂²	—	4	2	no	—
211	C₂²	—	4	2	no	—
212	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
213	C₂²	C₂×#64543	1	1	yes	characteristic
214	C₂²	#10597433	1	2	yes	—
215	C₂²	#10597436	1	2	yes	—
216	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
217	C₄	—	2	2	no	—
218	C₄	—	4	2	no	—
219	C₄	—	4	2	no	—
220	C₄	—	38	4	no	—
221	C₄	—	76	2	no	—
222	C₄	—	76	2	no	—
223	C₄	—	76	2	no	—
224	C₄	#10597385	1	4	yes	—
225	C₂	—	4	2	no	—
226	C₂	C₂×#10597385	1	1	yes	characteristic
227	C₂	#11927115	1	1	yes	characteristic
228	C₂	#11927117	1	2	yes	—
229	C₂	#11927118	1	1	yes	characteristic
230	C₂	#11927154	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597390

C₂

yes

maximal, characteristic, complemented

C₂×#10597370

C₂

yes

maximal, characteristic

C₂×#10597372

C₂

yes

maximal, characteristic

#11926477

C₂

yes

maximal, complemented

#11926472

C₂

yes

maximal

#11926451

C₂

yes

maximal, characteristic, complemented

#11926449

C₂

yes

maximal, characteristic, complemented

#11926409

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×C₂²⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₂²⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597390

—

#10597372

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597370

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

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×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

Dic₃₈

—

#2621

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

characteristic

100

C₂²×C₁₉

2₋¹⁺⁴

yes

—

101

C₂²×C₁₉

2₋¹⁺⁴

yes

—

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

#121

yes

—

106

Dic₁₉

—

107

Dic₁₉

—

108

Dic₁₉

—

109

Dic₁₉

—

110

C₂×C₄⋊Q₈

—

111

C₂×C₂²⋊Q₈

—

112

C₂×C₂²⋊Q₈

D₁₉

yes

characteristic

113

C₂×#117

—

114

#398

—

115

#397

—

116

#391

—

117

#391

—

118

#382

—

119

C₂×C₁₉

—

120

C₂×C₁₉

C₂×#121

yes

characteristic

121

C₂×C₁₉

#536

yes

characteristic

122

C₂×C₁₉

#536

yes

—

123

C₂×C₁₉

#536

yes

characteristic

124

C₂×C₁₉

#541

yes

—

125

C₂²×Q₈

—

126

C₂²×Q₈

C₂×D₁₉

yes

characteristic

127

C₂³×C₄

C₂×D₁₉

yes

characteristic

128

C₄⋊Q₈

—

129

C₂²⋊Q₈

—

130

C₂²⋊Q₈

—

131

#117

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

137

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

138

C₂×C₂²⋊C₄

—

139

C₂×C₂²⋊C₄

—

140

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

141

C₂×C₄²

—

142

C₂×C₄²

—

143

#95

—

144

#95

—

145

#95

—

146

C₁₉

#2621

yes

characteristic, complemented, Sylow

147

C₂⁴

C₂²×D₁₉

yes

characteristic

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

C₂²⋊D₁₉

yes

—

161

C₂²×C₄

C₂²×D₁₉

yes

—

162

C₂²×C₄

C₂²×D₁₉

yes

—

163

C₂²×C₄

C₂²×D₁₉

yes

characteristic

164

C₂²×C₄

C₂²×D₁₉

yes

characteristic

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₂²⋊C₄

—

172

C₂²⋊C₄

—

173

C₂²⋊C₄

—

174

C₄²

—

175

C₄²

—

176

C₂³

—

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

C₂×C₂²⋊D₁₉

yes

—

181

C₂³

C₂³×D₁₉

yes

characteristic

182

Q₈

—

183

Q₈

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

D₄×D₁₉

yes

—

204

C₂×C₄

#64543

yes

—

205

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

206

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

C₂×D₄×D₁₉

yes

characteristic

213

C₂²

C₂×#64543

yes

characteristic

214

C₂²

#10597433

yes

—

215

C₂²

#10597436

yes

—

216

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

#10597385

yes

—

225

C₂

—

226

C₂

C₂×#10597385

yes

characteristic

227

C₂

#11927115

yes

characteristic

228

C₂

#11927117

yes

—

229

C₂

#11927118

yes

characteristic

230

C₂

#11927154

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×C₂²⋊Q₈	C₂
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	C₂×C₂²⋊Q₈	D₁₉
hypocenter	C₁₉	#2621
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×C₂²⋊Q₈

C₂

prime radical

C₂⁴×C₁₉

C₂³

hypercenter

C₂×C₂²⋊Q₈

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

N	H ≅ G/N	type
1. C₂×#10597390	C₂	semidirect
4. #11926477	C₂	semidirect
6. #11926451	C₂	semidirect
7. #11926449	C₂	semidirect
8. #11926409	C₂	semidirect
146. C₁₉	#2621	semidirect

H ≅ G/N

type

1. C₂×#10597390

C₂

semidirect

4. #11926477

C₂

semidirect

6. #11926451

C₂

semidirect

7. #11926449

C₂

semidirect

8. #11926409

C₂

semidirect

146. C₁₉

#2621

semidirect

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

subgroup	index
C₂×#10597390	2
C₂×#10597370	2
C₂×#10597372	2
#11926477	2
#11926472	2
#11926451	2
#11926449	2
#11926409	2
C₂×C₁₉×C₂²⋊Q₈	2
#2621	19

subgroup

index

C₂×C₁₉×C₂²⋊Q₈

Subgroups — #14569405

Conjugacy classes of subgroups

Complements

Maximal subgroups