Group #18086643 — subgroups

Subgroups — #18086643

Order 4864.

478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14574945	C₂	1	1	yes	maximal, characteristic
2	#14564463	C₂	1	2	yes	maximal, complemented
3	#14562310	C₂	1	2	yes	maximal, complemented
4	#14561510	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	2	yes	—
7	#11926825	—	2	2	no	—
8	#11926780	—	2	2	no	—
9	#11926740	—	2	2	no	—
10	#11926568	C₂²	1	2	yes	—
11	C₂×#10597262	—	2	2	no	—
12	C₂×#10597262	—	2	2	no	—
13	#11926289	—	2	2	no	—
14	#11926287	—	2	2	no	—
15	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×#64541	—	2	2	no	—
20	C₂²×C₈×C₁₉	—	2	1	no	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	—	2	1	no	—
23	C₂×C₄²×C₁₉	—	2	1	no	—
24	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	#10597376	—	2	2	no	—
28	#10597376	—	2	2	no	—
29	C₂×#64520	—	2	2	no	—
30	C₂×D₁₅₂	—	2	2	no	—
31	#10597321	—	2	2	no	—
32	#10597320	D₄	1	2	yes	—
33	C₄×D₇₆	—	2	2	no	—
34	C₄×D₇₆	—	2	2	no	—
35	#10597315	D₄	1	2	yes	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	4	4	no	—
39	#10597278	—	2	4	no	—
40	#10597275	—	2	2	no	—
41	#10597262	—	4	4	no	—
42	#10597262	—	4	4	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
50	C₂×C₂²⋊D₁₉	—	4	2	no	—
51	#64541	—	4	2	no	—
52	#64541	—	4	2	no	—
53	#64541	—	4	2	no	—
54	#64541	—	4	2	no	—
55	C₂×D₇₆	—	2	2	no	—
56	C₂×D₇₆	—	2	2	no	—
57	C₂×D₇₆	—	2	2	no	—
58	C₂×C₄×D₁₉	—	4	2	no	—
59	C₂×Dic₃₈	—	2	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	—	4	2	no	—
62	C₂×C₈×C₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	—	4	1	no	—
64	C₄²×C₁₉	—	2	2	no	—
65	C₄²×C₁₉	—	2	2	no	—
66	C₄²×C₁₉	—	2	1	no	—
67	C₄²×C₁₉	—	2	2	no	—
68	C₄²×C₁₉	—	4	2	no	—
69	C₄²×C₁₉	D₈	1	2	yes	complemented
70	C₄²×C₁₉	C₂×D₄	1	2	yes	—
71	C₄²×C₁₉	#41	1	2	yes	—
72	(C₂×D₁₉)⋊C₄	—	4	2	no	—
73	(C₂×D₁₉)⋊C₄	—	4	2	no	—
74	C₄⋊Dic₁₉	—	2	2	no	—
75	C₄⋊Dic₁₉	—	2	2	no	—
76	#64520	—	4	2	no	—
77	#64520	—	4	2	no	—
78	C₂×C₁₉⋊C₈	—	4	2	no	—
79	D₁₅₂	—	8	2	no	—
80	#10518	—	19	1	no	maximal, Sylow
81	C₂³×C₁₉	#121	1	1	yes	characteristic
82	C₂²×D₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	—	4	1	no	—
92	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#121	1	2	yes	—
94	C₂×C₄×C₁₉	#123	1	2	yes	—
95	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
98	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
99	C₂²⋊D₁₉	—	8	2	no	—
100	C₂²⋊D₁₉	—	8	2	no	—
101	C₂×Dic₁₉	—	4	2	no	—
102	D₇₆	—	4	2	no	—
103	D₇₆	—	4	2	no	—
104	D₇₆	—	4	2	no	—
105	D₇₆	—	4	2	no	—
106	D₇₆	—	8	2	no	—
107	C₄×D₁₉	—	8	2	no	—
108	C₄×D₁₉	—	8	2	no	—
109	Dic₃₈	—	4	2	no	—
110	Dic₃₈	—	4	2	no	—
111	C₈×C₁₉	—	4	2	no	—
112	C₈×C₁₉	—	8	1	no	—
113	C₁₉⋊C₈	—	8	2	no	—
114	#3245	—	19	1	no	—
115	#1962	—	19	2	no	—
116	#1842	D₁₉	1	1	yes	characteristic, complemented
117	#1547	—	19	2	no	—
118	#1292	—	19	1	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	#394	1	1	yes	characteristic
122	C₂²×C₁₉	#466	1	1	yes	characteristic
123	C₂²×C₁₉	#469	1	1	yes	characteristic
124	C₂×D₁₉	—	8	2	no	—
125	C₂×D₁₉	—	8	2	no	—
126	C₂×D₁₉	—	8	2	no	—
127	C₄×C₁₉	—	2	4	no	—
128	C₄×C₁₉	—	2	2	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	4	2	no	—
131	C₄×C₁₉	#453	1	1	yes	characteristic
132	C₄×C₁₉	#456	1	1	yes	characteristic
133	C₄×C₁₉	#459	1	2	yes	—
134	C₄×C₁₉	#463	1	2	yes	—
135	Dic₁₉	—	8	2	no	—
136	#532	—	19	2	no	—
137	#474	—	38	2	no	—
138	#466	—	38	2	no	—
139	#459	—	38	2	no	—
140	#423	—	19	2	no	—
141	C₂×C₄⋊C₈	—	2	2	no	—
142	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
143	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
144	C₂×#104	—	38	2	no	—
145	C₂×#104	—	38	2	no	—
146	C₄³	C₂×D₁₉	1	1	yes	characteristic
147	#332	—	38	2	no	—
148	#331	—	38	2	no	—
149	C₂×C₁₉	—	2	1	no	—
150	C₂×C₁₉	—	2	1	no	—
151	C₂×C₁₉	#2039	1	1	yes	characteristic
152	C₂×C₁₉	#2050	1	1	yes	characteristic
153	C₂×C₁₉	#2054	1	1	yes	characteristic
154	D₁₉	—	16	2	no	—
155	C₂×#41	—	38	2	no	—
156	C₂×D₈	—	38	2	no	—
157	C₂×M₁₆	—	38	2	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
160	C₄⋊Q₈	—	19	2	no	—
161	#127	—	19	2	no	—
162	#124	—	38	2	no	—
163	#121	—	38	2	no	—
164	#121	—	38	2	no	—
165	C₄×D₄	—	38	2	no	—
166	C₄×D₄	—	38	2	no	—
167	C₂×C₄²	—	2	1	no	—
168	C₂×C₄²	—	2	1	no	—
169	C₂×C₄²	D₇₆	1	1	yes	characteristic
170	C₂×C₄²	D₇₆	1	1	yes	characteristic
171	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
172	#107	—	38	2	no	—
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	—	4	4	no	—
176	C₄⋊C₈	—	38	2	no	—
177	C₄⋊C₈	—	38	2	no	—
178	#104	—	76	4	no	—
179	#104	—	76	4	no	—
180	#102	—	38	4	no	—
181	C₁₉	#10518	1	1	yes	characteristic, complemented, Sylow
182	#41	—	76	2	no	—
183	#41	—	76	2	no	—
184	#41	—	76	2	no	—
185	#41	—	76	2	no	—
186	C₂×Q₈	—	38	2	no	—
187	C₂×D₄	—	38	2	no	—
188	C₂×D₄	—	38	2	no	—
189	C₂×D₄	—	38	2	no	—
190	C₂×D₄	—	76	2	no	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	—	2	1	no	—
193	C₂²×C₄	—	76	2	no	—
194	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
195	C₂²×C₄	#64541	1	1	yes	characteristic
196	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
197	D₈	—	152	2	no	—
198	M₁₆	—	76	2	no	—
199	M₁₆	—	76	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	4	2	no	—
202	C₂×C₈	—	4	2	no	—
203	C₂×C₈	—	4	1	no	—
204	C₂×C₈	—	76	2	no	—
205	C₄⋊C₄	—	38	2	no	—
206	C₄⋊C₄	—	38	2	no	—
207	C₂²⋊C₄	—	76	2	no	—
208	C₂²⋊C₄	—	76	2	no	—
209	C₄²	—	2	2	no	—
210	C₄²	—	2	2	no	—
211	C₄²	—	2	1	no	—
212	C₄²	—	2	2	no	—
213	C₄²	—	4	2	no	—
214	C₄²	D₁₅₂	1	2	yes	complemented
215	C₄²	D₄×D₁₉	1	2	yes	—
216	C₄²	#64545	1	2	yes	—
217	C₂³	—	76	2	no	—
218	C₂³	#10597376	1	1	yes	characteristic
219	Q₈	—	76	2	no	—
220	Q₈	—	76	2	no	—
221	D₄	—	76	2	no	—
222	D₄	—	76	2	no	—
223	D₄	—	76	2	no	—
224	D₄	—	76	2	no	—
225	D₄	—	152	2	no	—
226	D₄	—	152	2	no	—
227	D₄	—	152	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	4	1	no	—
235	C₂×C₄	—	4	1	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	76	2	no	—
238	C₂×C₄	—	152	2	no	—
239	C₂×C₄	—	152	2	no	—
240	C₂×C₄	#10597340	1	2	yes	—
241	C₂×C₄	#10597341	1	2	yes	—
242	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
243	C₂×C₄	#10597350	1	1	yes	characteristic
244	C₂×C₄	#10597354	1	2	yes	—
245	C₂×C₄	#10597383	1	1	yes	characteristic
246	C₂×C₄	#10597393	1	1	yes	characteristic
247	C₈	—	4	2	no	—
248	C₈	—	8	1	no	—
249	C₈	—	152	2	no	—
250	C₂²	—	2	1	no	—
251	C₂²	—	2	1	no	—
252	C₂²	—	152	2	no	—
253	C₂²	—	152	2	no	—
254	C₂²	—	152	2	no	—
255	C₂²	#11926461	1	1	yes	characteristic
256	C₂²	#11926780	1	1	yes	characteristic
257	C₂²	#11926797	1	1	yes	characteristic
258	C₄	—	2	4	no	—
259	C₄	—	2	2	no	—
260	C₄	—	2	1	no	—
261	C₄	—	4	2	no	—
262	C₄	—	152	2	no	—
263	C₄	#11926711	1	1	yes	characteristic
264	C₄	#11926726	1	1	yes	characteristic
265	C₄	#11926740	1	2	yes	—
266	C₄	#11926760	1	2	yes	—
267	C₂	—	2	1	no	—
268	C₂	—	2	1	no	—
269	C₂	—	304	2	no	—
270	C₂	#14564859	1	1	yes	characteristic
271	C₂	#14564922	1	1	yes	characteristic
272	C₂	#14564946	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574945

C₂

yes

maximal, characteristic

#14564463

C₂

yes

maximal, complemented

#14562310

C₂

yes

maximal, complemented

#14561510

C₂

yes

maximal, characteristic, complemented

C₁₉×#1842

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

—

—

—

—

C₂²

yes

—

—

—

—

—

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₄³×C₁₉

C₂²

yes

characteristic

C₂×#64541

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×D₁₅₂

—

#10597321

—

#10597320

D₄

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

—

—

—

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₂²⋊D₁₉

—

—

—

—

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

complemented

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

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

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂²⋊D₁₉

—

100

C₂²⋊D₁₉

—

101

C₂×Dic₁₉

—

102

D₇₆

—

103

D₇₆

—

104

D₇₆

—

105

D₇₆

—

106

D₇₆

—

107

C₄×D₁₉

—

108

C₄×D₁₉

—

109

Dic₃₈

—

110

Dic₃₈

—

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₁₉⋊C₈

—

114

#3245

—

115

#1962

—

116

#1842

D₁₉

yes

characteristic, complemented

117

#1547

—

118

#1292

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#394

yes

characteristic

122

C₂²×C₁₉

#466

yes

characteristic

123

C₂²×C₁₉

#469

yes

characteristic

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₂×D₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

#453

yes

characteristic

132

C₄×C₁₉

#456

yes

characteristic

133

C₄×C₁₉

#459

yes

—

134

C₄×C₁₉

#463

yes

—

135

Dic₁₉

—

136

#532

—

137

#474

—

138

#466

—

139

#459

—

140

#423

—

141

C₂×C₄⋊C₈

—

142

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

143

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

144

C₂×#104

—

145

C₂×#104

—

146

C₄³

C₂×D₁₉

yes

characteristic

147

#332

—

148

#331

—

149

C₂×C₁₉

—

150

C₂×C₁₉

—

151

C₂×C₁₉

#2039

yes

characteristic

152

C₂×C₁₉

#2050

yes

characteristic

153

C₂×C₁₉

#2054

yes

characteristic

154

D₁₉

—

155

C₂×#41

—

156

C₂×D₈

—

157

C₂×M₁₆

—

158

C₂²×C₈

—

159

C₂²×C₈

C₂²⋊D₁₉

yes

—

160

C₄⋊Q₈

—

161

#127

—

162

#124

—

163

#121

—

164

#121

—

165

C₄×D₄

—

166

C₄×D₄

—

167

C₂×C₄²

—

168

C₂×C₄²

—

169

C₂×C₄²

D₇₆

yes

characteristic

170

C₂×C₄²

D₇₆

yes

characteristic

171

C₂×C₄²

C₂²×D₁₉

yes

characteristic

172

#107

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

#104

—

179

#104

—

180

#102

—

181

C₁₉

#10518

yes

characteristic, complemented, Sylow

182

#41

—

183

#41

—

184

#41

—

185

#41

—

186

C₂×Q₈

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

C₂×D₇₆

yes

characteristic

195

C₂²×C₄

#64541

yes

characteristic

196

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

197

D₈

—

152

—

198

M₁₆

—

199

M₁₆

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₂²⋊C₄

—

208

C₂²⋊C₄

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

D₁₅₂

yes

complemented

215

C₄²

D₄×D₁₉

yes

—

216

C₄²

#64545

yes

—

217

C₂³

—

218

C₂³

#10597376

yes

characteristic

219

Q₈

—

220

Q₈

—

221

D₄

—

222

D₄

—

223

D₄

—

224

D₄

—

225

D₄

—

152

—

226

D₄

—

152

—

227

D₄

—

152

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

152

—

239

C₂×C₄

—

152

—

240

C₂×C₄

#10597340

yes

—

241

C₂×C₄

#10597341

yes

—

242

C₂×C₄

C₂×D₁₅₂

yes

characteristic

243

C₂×C₄

#10597350

yes

characteristic

244

C₂×C₄

#10597354

yes

—

245

C₂×C₄

#10597383

yes

characteristic

246

C₂×C₄

#10597393

yes

characteristic

247

C₈

—

248

C₈

—

249

C₈

—

152

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

152

—

253

C₂²

—

152

—

254

C₂²

—

152

—

255

C₂²

#11926461

yes

characteristic

256

C₂²

#11926780

yes

characteristic

257

C₂²

#11926797

yes

characteristic

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

152

—

263

C₄

#11926711

yes

characteristic

264

C₄

#11926726

yes

characteristic

265

C₄

#11926740

yes

—

266

C₄

#11926760

yes

—

267

C₂

—

268

C₂

—

269

C₂

—

304

—

270

C₂

#14564859

yes

characteristic

271

C₂

#14564922

yes

characteristic

272

C₂

#14564946

yes

characteristic

	subgroup	G/H
center	C₂²	#11926461
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1842	C₂
socle	C₂²×C₁₉	#394
prime radical	#14574945	C₂
hypercenter	#1842	D₁₉
hypocenter	C₁₉	#10518
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1842

subgroup

G/H

center

C₂²

#11926461

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1842

C₂

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1842

N	H ≅ G/N	type
2. #14564463	C₂	semidirect
3. #14562310	C₂	semidirect
4. #14561510	C₂	semidirect
5. C₁₉×#1842	C₂	semidirect
69. C₄²×C₁₉	D₈	semidirect
116. #1842	D₁₉	semidirect
181. C₁₉	#10518	semidirect
214. C₄²	D₁₅₂	semidirect

H ≅ G/N

type

2. #14564463

C₂

semidirect

3. #14562310

C₂

semidirect

4. #14561510

C₂

semidirect

5. C₁₉×#1842

C₂

semidirect

69. C₄²×C₁₉

D₈

semidirect

116. #1842

D₁₉

semidirect

181. C₁₉

#10518

semidirect

214. C₄²

D₁₅₂

semidirect

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

subgroup	index
#14574945	2
#14564463	2
#14562310	2
#14561510	2
C₁₉×#1842	2
#10518	19

subgroup

index

C₁₉×#1842

Subgroups — #18086643

Conjugacy classes of subgroups

Complements

Maximal subgroups