Group #18085168 — subgroups

Subgroups — #18085168

Order 4864.

950 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 950 conjugacy classes of subgroups — too many to draw. Only its 113 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	#14574553	C₂	1	2	yes	maximal, complemented
2	#14564463	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562303	C₂	1	2	yes	maximal, complemented
4	#14561468	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2867	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	1	yes	characteristic
7	#11926920	—	2	2	no	—
8	#11926890	—	2	2	no	—
9	#11926736	—	2	4	no	—
10	#11926678	—	2	4	no	—
11	#11926597	C₂²	1	2	yes	—
12	#11926568	C₂²	1	1	yes	characteristic
13	C₂×#10597262	—	2	2	no	—
14	#11926288	—	2	4	no	—
15	C₂×C₁₉×#127	—	2	4	no	—
16	C₂×C₁₉×#127	—	2	2	no	—
17	C₂×C₁₉×#127	C₂²	1	2	yes	—
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₁₉	—	2	8	no	—
20	C₂²×D₄×C₁₉	—	2	2	no	—
21	C₂²×D₄×C₁₉	—	2	2	no	—
22	C₂²×D₄×C₁₉	D₄	1	4	yes	—
23	C₂×#64541	—	2	1	no	—
24	C₁₉×#127	—	2	2	no	—
25	C₁₉×#127	—	2	2	no	—
26	C₁₉×#127	—	2	2	no	—
27	C₁₉×#127	—	2	2	no	—
28	C₁₉×#127	—	4	16	no	—
29	C₁₉×#127	—	4	4	no	—
30	C₁₉×#127	—	4	4	no	—
31	C₂×C₄²×C₁₉	—	2	2	no	—
32	C₂×C₄²×C₁₉	D₄	1	2	yes	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×#64525	—	2	8	no	—
35	#10597376	—	2	2	no	—
36	C₂×#64520	—	2	1	no	—
37	#10597321	—	2	1	no	—
38	#10597320	D₄	1	1	yes	characteristic, complemented
39	C₄×D₇₆	—	2	2	no	—
40	#10597315	D₄	1	1	yes	characteristic, complemented
41	#10597289	—	2	8	no	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
43	#10597262	—	4	4	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	complemented
46	C₄×C₁₉⋊C₈	—	2	2	no	—
47	C₂⁴×C₁₉	—	2	4	no	—
48	C₂×D₄×C₁₉	—	2	4	no	—
49	C₂×D₄×C₁₉	—	2	4	no	—
50	C₂×D₄×C₁₉	—	4	8	no	—
51	C₂×D₄×C₁₉	—	4	32	no	—
52	C₂×D₄×C₁₉	—	4	16	no	—
53	C₂×D₄×C₁₉	—	4	8	no	—
54	C₂×D₄×C₁₉	—	4	2	no	—
55	C₂×D₄×C₁₉	—	4	2	no	—
56	C₂×D₄×C₁₉	—	4	2	no	—
57	C₂×D₄×C₁₉	—	4	2	no	—
58	C₂×D₄×C₁₉	—	4	4	no	—
59	C₂×D₄×C₁₉	—	4	4	no	—
60	C₂²×C₄×C₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₂²⋊D₁₉	—	4	1	no	—
64	#64541	—	4	2	no	—
65	#64541	—	4	2	no	—
66	C₂×D₇₆	—	2	2	no	—
67	C₂×D₇₆	—	2	1	no	—
68	C₂×C₄×D₁₉	—	4	1	no	—
69	C₂×Dic₃₈	—	2	1	no	—
70	C₄²×C₁₉	—	2	8	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	D₈	1	4	yes	complemented
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂×D₄	1	2	yes	—
75	C₄²×C₁₉	#41	1	1	yes	characteristic
76	#64525	—	8	8	no	—
77	(C₂×D₁₉)⋊C₄	—	4	2	no	—
78	C₄⋊Dic₁₉	—	2	2	no	—
79	#64520	—	4	2	no	—
80	C₂×C₁₉⋊C₈	—	2	4	no	—
81	C₂×C₁₉⋊C₈	—	4	1	no	—
82	#10280	—	19	1	no	maximal, Sylow
83	C₂³×C₁₉	—	4	8	no	—
84	C₂³×C₁₉	—	4	8	no	—
85	C₂³×C₁₉	—	4	4	no	—
86	C₂³×C₁₉	—	4	8	no	—
87	C₂³×C₁₉	#120	1	1	yes	characteristic
88	C₂²×D₁₉	—	4	1	no	—
89	D₄×C₁₉	—	4	8	no	—
90	D₄×C₁₉	—	8	4	no	—
91	D₄×C₁₉	—	8	32	no	—
92	D₄×C₁₉	—	8	4	no	—
93	D₄×C₁₉	—	8	4	no	—
94	D₄×C₁₉	—	8	4	no	—
95	D₄×C₁₉	—	8	2	no	—
96	D₄×C₁₉	—	8	2	no	—
97	C₂×C₄×C₁₉	—	2	8	no	—
98	C₂×C₄×C₁₉	—	2	4	no	—
99	C₂×C₄×C₁₉	—	2	4	no	—
100	C₂×C₄×C₁₉	#120	1	2	yes	—
101	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#121	1	2	yes	—
103	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
105	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
106	C₂²⋊D₁₉	—	8	2	no	—
107	C₂×Dic₁₉	—	4	1	no	—
108	D₇₆	—	4	4	no	—
109	D₇₆	—	4	2	no	—
110	C₄×D₁₉	—	8	1	no	—
111	C₄×D₁₉	—	8	1	no	—
112	Dic₃₈	—	4	2	no	—
113	C₁₉⋊C₈	—	4	4	no	—
114	C₁₉⋊C₈	—	8	1	no	—
115	#3205	—	19	2	no	—
116	#2867	D₁₉	1	1	yes	characteristic, complemented
117	#1962	—	19	1	no	—
118	#1545	—	19	2	no	—
119	#1276	—	19	1	no	—
120	C₂²×C₁₉	—	2	2	no	—
121	C₂²×C₁₉	—	8	16	no	—
122	C₂²×C₁₉	—	8	4	no	—
123	C₂²×C₁₉	—	8	4	no	—
124	C₂²×C₁₉	—	8	4	no	—
125	C₂²×C₁₉	#392	1	1	yes	characteristic
126	C₂²×C₁₉	#447	1	2	yes	—
127	C₂×D₁₉	—	8	2	no	—
128	C₂×D₁₉	—	8	1	no	—
129	C₄×C₁₉	—	2	8	no	—
130	C₄×C₁₉	—	2	2	no	—
131	C₄×C₁₉	#453	1	4	yes	—
132	C₄×C₁₉	#459	1	2	yes	—
133	C₄×C₁₉	#493	1	1	yes	characteristic
134	C₄×C₁₉	#496	1	1	yes	characteristic
135	Dic₁₉	—	8	1	no	—
136	#532	—	19	1	no	—
137	C₂×#127	—	2	4	no	—
138	C₂×#127	—	2	2	no	—
139	C₂×#127	C₂×D₁₉	1	2	yes	—
140	#493	—	38	2	no	—
141	#486	—	38	2	no	—
142	#459	—	38	4	no	—
143	#447	—	38	4	no	—
144	#431	—	19	2	no	—
145	#423	—	19	1	no	—
146	C₂×#104	—	38	2	no	—
147	C₄³	C₂×D₁₉	1	1	yes	characteristic
148	#331	—	38	4	no	—
149	C₂×C₁₉	—	2	2	no	—
150	C₂×C₁₉	—	16	4	no	—
151	C₂×C₁₉	#2002	1	2	yes	—
152	C₂×C₁₉	#2011	1	1	yes	characteristic
153	D₁₉	—	16	1	no	—
154	C₂×#41	—	38	1	no	—
155	C₂²×D₄	—	2	8	no	—
156	C₂²×D₄	—	2	2	no	—
157	C₂²×D₄	—	2	2	no	—
158	C₂²×D₄	C₂²⋊D₁₉	1	4	yes	—
159	C₂×D₈	—	38	8	no	—
160	C₂×M₁₆	—	38	1	no	—
161	C₄⋊Q₈	—	19	1	no	—
162	#127	—	2	2	no	—
163	#127	—	2	2	no	—
164	#127	—	2	2	no	—
165	#127	—	2	2	no	—
166	#127	—	4	16	no	—
167	#127	—	4	4	no	—
168	#127	—	4	4	no	—
169	#127	—	19	1	no	—
170	#124	—	38	1	no	—
171	#121	—	38	2	no	—
172	C₄×D₄	—	38	2	no	—
173	C₂×C₄²	—	2	2	no	—
174	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
175	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
176	C₄⋊C₈	—	19	4	no	—
177	C₄⋊C₈	—	38	2	no	—
178	#104	—	76	4	no	—
179	#102	—	38	8	no	—
180	C₂²⋊C₈	—	38	2	no	—
181	C₄×C₈	—	38	2	no	—
182	C₁₉	#10280	1	1	yes	characteristic, complemented, Sylow
183	C₂⁴	—	2	4	no	—
184	#41	—	76	2	no	—
185	#41	—	76	2	no	—
186	C₂×Q₈	—	38	1	no	—
187	C₂×D₄	—	2	4	no	—
188	C₂×D₄	—	2	4	no	—
189	C₂×D₄	—	4	8	no	—
190	C₂×D₄	—	4	32	no	—
191	C₂×D₄	—	4	16	no	—
192	C₂×D₄	—	4	8	no	—
193	C₂×D₄	—	4	4	no	—
194	C₂×D₄	—	4	4	no	—
195	C₂×D₄	—	4	2	no	—
196	C₂×D₄	—	4	2	no	—
197	C₂×D₄	—	4	2	no	—
198	C₂×D₄	—	4	2	no	—
199	C₂×D₄	—	38	2	no	—
200	C₂×D₄	—	38	1	no	—
201	C₂×D₄	—	76	1	no	—
202	C₂²×C₄	—	2	2	no	—
203	C₂²×C₄	—	76	1	no	—
204	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
205	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
206	D₈	—	152	8	no	—
207	M₁₆	—	76	2	no	—
208	C₂×C₈	—	38	4	no	—
209	C₂×C₈	—	76	1	no	—
210	C₄⋊C₄	—	38	2	no	—
211	C₂²⋊C₄	—	76	2	no	—
212	C₄²	—	2	8	no	—
213	C₄²	—	2	2	no	—
214	C₄²	#64525	1	4	yes	complemented
215	C₄²	D₄×D₁₉	1	1	yes	characteristic
216	C₄²	D₄×D₁₉	1	2	yes	—
217	C₄²	#64543	1	1	yes	characteristic
218	C₂³	—	4	8	no	—
219	C₂³	—	4	8	no	—
220	C₂³	—	4	8	no	—
221	C₂³	—	4	4	no	—
222	C₂³	—	76	1	no	—
223	C₂³	#10597399	1	1	yes	characteristic
224	Q₈	—	76	2	no	—
225	D₄	—	4	8	no	—
226	D₄	—	8	4	no	—
227	D₄	—	8	32	no	—
228	D₄	—	8	4	no	—
229	D₄	—	8	2	no	—
230	D₄	—	8	2	no	—
231	D₄	—	8	4	no	—
232	D₄	—	8	4	no	—
233	D₄	—	76	4	no	—
234	D₄	—	76	2	no	—
235	D₄	—	152	2	no	—
236	C₂×C₄	—	2	8	no	—
237	C₂×C₄	—	2	4	no	—
238	C₂×C₄	—	2	4	no	—
239	C₂×C₄	—	76	1	no	—
240	C₂×C₄	—	152	1	no	—
241	C₂×C₄	—	152	1	no	—
242	C₂×C₄	C₂×#64525	1	2	yes	—
243	C₂×C₄	#10597378	1	2	yes	—
244	C₂×C₄	#10597383	1	2	yes	—
245	C₂×C₄	#10597384	1	1	yes	characteristic
246	C₂×C₄	#10597385	1	2	yes	—
247	C₂×C₄	#10597386	1	1	yes	characteristic
248	C₈	—	76	4	no	—
249	C₈	—	152	1	no	—
250	C₂²	—	2	2	no	—
251	C₂²	—	8	16	no	—
252	C₂²	—	8	4	no	—
253	C₂²	—	8	4	no	—
254	C₂²	—	8	4	no	—
255	C₂²	—	152	2	no	—
256	C₂²	—	152	1	no	—
257	C₂²	#11926452	1	1	yes	characteristic
258	C₂²	#11926678	1	2	yes	—
259	C₄	—	2	8	no	—
260	C₄	—	2	2	no	—
261	C₄	—	152	1	no	—
262	C₄	#11926711	1	4	yes	—
263	C₄	#11926736	1	2	yes	—
264	C₄	#11926920	1	1	yes	characteristic
265	C₄	#11926931	1	1	yes	characteristic
266	C₂	—	2	2	no	—
267	C₂	—	16	4	no	—
268	C₂	—	304	1	no	—
269	C₂	#14564650	1	2	yes	—
270	C₂	#14564706	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574553

C₂

yes

maximal, complemented

#14564463

C₂

yes

maximal, characteristic, complemented

#14562303

C₂

yes

maximal, complemented

#14561468

C₂

yes

maximal, characteristic, complemented

C₁₉×#2867

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

—

—

—

—

C₂²

yes

—

#11926568

C₂²

yes

characteristic

C₂×#10597262

—

#11926288

—

C₂×C₁₉×#127

—

C₂×C₁₉×#127

—

C₂×C₁₉×#127

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

—

C₂×#64541

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

D₄

yes

characteristic, complemented

C₄×D₇₆

—

#10597315

D₄

yes

characteristic, complemented

#10597289

—

C₂²⋊(C₁₉⋊C₈)

—

#10597262

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

complemented

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

complemented

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

#64525

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10280

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

#120

yes

—

101

C₂×C₄×C₁₉

#121

yes

characteristic

102

C₂×C₄×C₁₉

#121

yes

—

103

C₂×C₄×C₁₉

#127

yes

characteristic

104

C₂×C₄×C₁₉

C₂×D₈

yes

—

105

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

106

C₂²⋊D₁₉

—

107

C₂×Dic₁₉

—

108

D₇₆

—

109

D₇₆

—

110

C₄×D₁₉

—

111

C₄×D₁₉

—

112

Dic₃₈

—

113

C₁₉⋊C₈

—

114

C₁₉⋊C₈

—

115

#3205

—

116

#2867

D₁₉

yes

characteristic, complemented

117

#1962

—

118

#1545

—

119

#1276

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

#392

yes

characteristic

126

C₂²×C₁₉

#447

yes

—

127

C₂×D₁₉

—

128

C₂×D₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

#453

yes

—

132

C₄×C₁₉

#459

yes

—

133

C₄×C₁₉

#493

yes

characteristic

134

C₄×C₁₉

#496

yes

characteristic

135

Dic₁₉

—

136

#532

—

137

C₂×#127

—

138

C₂×#127

—

139

C₂×#127

C₂×D₁₉

yes

—

140

#493

—

141

#486

—

142

#459

—

143

#447

—

144

#431

—

145

#423

—

146

C₂×#104

—

147

C₄³

C₂×D₁₉

yes

characteristic

148

#331

—

149

C₂×C₁₉

—

150

C₂×C₁₉

—

151

C₂×C₁₉

#2002

yes

—

152

C₂×C₁₉

#2011

yes

characteristic

153

D₁₉

—

154

C₂×#41

—

155

C₂²×D₄

—

156

C₂²×D₄

—

157

C₂²×D₄

—

158

C₂²×D₄

C₂²⋊D₁₉

yes

—

159

C₂×D₈

—

160

C₂×M₁₆

—

161

C₄⋊Q₈

—

162

#127

—

163

#127

—

164

#127

—

165

#127

—

166

#127

—

167

#127

—

168

#127

—

169

#127

—

170

#124

—

171

#121

—

172

C₄×D₄

—

173

C₂×C₄²

—

174

C₂×C₄²

C₂²⋊D₁₉

yes

—

175

C₂×C₄²

C₂²×D₁₉

yes

characteristic

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

#104

—

179

#102

—

180

C₂²⋊C₈

—

181

C₄×C₈

—

182

C₁₉

#10280

yes

characteristic, complemented, Sylow

183

C₂⁴

—

184

#41

—

185

#41

—

186

C₂×Q₈

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂×D₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

205

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

206

D₈

—

152

—

207

M₁₆

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₄⋊C₄

—

211

C₂²⋊C₄

—

212

C₄²

—

213

C₄²

—

214

C₄²

#64525

yes

complemented

215

C₄²

D₄×D₁₉

yes

characteristic

216

C₄²

D₄×D₁₉

yes

—

217

C₄²

#64543

yes

characteristic

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

#10597399

yes

characteristic

224

Q₈

—

225

D₄

—

226

D₄

—

227

D₄

—

228

D₄

—

229

D₄

—

230

D₄

—

231

D₄

—

232

D₄

—

233

D₄

—

234

D₄

—

235

D₄

—

152

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

152

—

241

C₂×C₄

—

152

—

242

C₂×C₄

C₂×#64525

yes

—

243

C₂×C₄

#10597378

yes

—

244

C₂×C₄

#10597383

yes

—

245

C₂×C₄

#10597384

yes

characteristic

246

C₂×C₄

#10597385

yes

—

247

C₂×C₄

#10597386

yes

characteristic

248

C₈

—

249

C₈

—

152

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

152

—

256

C₂²

—

152

—

257

C₂²

#11926452

yes

characteristic

258

C₂²

#11926678

yes

—

259

C₄

—

260

C₄

—

261

C₄

—

152

—

262

C₄

#11926711

yes

—

263

C₄

#11926736

yes

—

264

C₄

#11926920

yes

characteristic

265

C₄

#11926931

yes

characteristic

266

C₂

—

267

C₂

—

268

C₂

—

304

—

269

C₂

#14564650

yes

—

270

C₂

#14564706

yes

characteristic

	subgroup	G/H
center	C₂²	#11926452
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2867	C₂
socle	C₂²×C₁₉	#392
hypercenter	#2867	D₁₉
hypocenter	C₁₉	#10280
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2867

subgroup

G/H

center

C₂²

#11926452

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2867

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2867

N	H ≅ G/N	type
1. #14574553	C₂	semidirect
2. #14564463	C₂	semidirect
3. #14562303	C₂	semidirect
4. #14561468	C₂	semidirect
5. C₁₉×#2867	C₂	semidirect
38. #10597320	D₄	semidirect
40. #10597315	D₄	semidirect
45. C₄⋊(C₁₉⋊C₈)	D₄	semidirect
72. C₄²×C₁₉	D₈	semidirect
116. #2867	D₁₉	semidirect
182. C₁₉	#10280	semidirect
214. C₄²	#64525	semidirect

H ≅ G/N

type

1. #14574553

C₂

semidirect

2. #14564463

C₂

semidirect

3. #14562303

C₂

semidirect

4. #14561468

C₂

semidirect

5. C₁₉×#2867

C₂

semidirect

38. #10597320

D₄

semidirect

40. #10597315

D₄

semidirect

45. C₄⋊(C₁₉⋊C₈)

D₄

semidirect

72. C₄²×C₁₉

D₈

semidirect

116. #2867

D₁₉

semidirect

182. C₁₉

#10280

semidirect

214. C₄²

#64525

semidirect

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

subgroup	index
#14574553	2
#14564463	2
#14562303	2
#14561468	2
C₁₉×#2867	2
#10280	19

subgroup

index

C₁₉×#2867

Subgroups — #18085168

Conjugacy classes of subgroups

Complements

Maximal subgroups