Group #18081952 — subgroups

Subgroups — #18081952

Order 4864.

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

normal subgroups only

This group has 418 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	#14574221	C₂	1	1	yes	maximal, characteristic
2	#14562398	C₂	1	1	yes	maximal, characteristic
3	#14562249	C₂	1	2	yes	maximal
4	#14562146	C₂	1	2	yes	maximal
5	C₁₉×#1726	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	2	yes	—
7	#11926949	C₄	1	1	yes	characteristic, complemented
8	#11926924	C₄	1	1	yes	characteristic, complemented
9	#11926895	C₄	1	2	yes	complemented
10	#11926785	—	2	1	no	—
11	#11926785	—	2	1	no	—
12	C₄×Dic₇₆	—	2	1	no	—
13	C₄×Dic₇₆	—	2	1	no	—
14	#11926601	C₂²	1	2	yes	—
15	#11926297	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926285	—	2	4	no	—
18	#11926280	—	2	4	no	—
19	C₂×C₁₉×#97	—	2	1	no	—
20	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₉	—	2	1	no	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#376	C₂²	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	—	2	1	no	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	#10597372	—	2	2	no	—
30	#10597370	—	2	2	no	—
31	#10597370	—	2	2	no	—
32	C₂×Dic₇₆	—	2	1	no	—
33	C₂×Dic₇₆	—	2	1	no	—
34	#10597316	—	2	2	no	—
35	#10597315	C₂×C₄	1	2	yes	—
36	#10597315	C₂×C₄	1	2	yes	—
37	C₄×Dic₃₈	—	2	2	no	—
38	C₄×Dic₃₈	—	2	2	no	—
39	C₁₉×#97	—	2	4	no	—
40	C₁₉×#97	—	2	1	no	—
41	C₁₉×#97	D₄	1	2	yes	—
42	C₄×C₈×C₁₉	—	2	4	no	—
43	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
47	C₁₉×#95	—	2	1	no	—
48	C₁₉×#95	D₄	1	2	yes	—
49	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
50	#10597275	—	2	1	no	—
51	#10597275	—	2	1	no	—
52	#10597273	—	2	2	no	—
53	#10597273	—	2	2	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
55	#10597260	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
60	C₂×Dic₃₈	—	2	2	no	—
61	C₂×Dic₃₈	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	2	2	no	—
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	2	2	no	—
73	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₉	#41	1	1	yes	characteristic
77	C₂²⋊Dic₁₉	—	4	2	no	—
78	C₄⋊Dic₁₉	—	2	2	no	—
79	C₄⋊Dic₁₉	—	2	2	no	—
80	C₄⋊Dic₁₉	—	2	2	no	—
81	C₄⋊Dic₁₉	—	2	2	no	—
82	Dic₁₉⋊C₄	—	4	2	no	—
83	Dic₁₉⋊C₄	—	4	2	no	—
84	C₄×Dic₁₉	—	4	2	no	—
85	C₂×C₁₉⋊C₈	—	4	2	no	—
86	Dic₇₆	—	4	2	no	—
87	Dic₇₆	—	4	2	no	—
88	#9763	—	19	1	no	maximal, Sylow
89	C₂³×C₁₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	4	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
103	C₂×Dic₁₉	—	4	2	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	Dic₃₈	—	4	2	no	—
106	Dic₃₈	—	4	2	no	—
107	Dic₃₈	—	8	2	no	—
108	C₈×C₁₉	—	2	4	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	#104	1	2	yes	—
112	C₈×C₁₉	#104	1	2	yes	—
113	C₁₉⋊C₈	—	8	2	no	—
114	#3170	—	19	1	no	—
115	#1726	D₁₉	1	1	yes	characteristic
116	#1568	—	19	1	no	—
117	#1531	—	19	2	no	—
118	#1506	—	19	2	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	#390	1	1	yes	characteristic
122	C₂²×C₁₉	#473	1	2	yes	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	4	4	no	—
129	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
130	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
131	Dic₁₉	—	8	2	no	—
132	Dic₁₉	—	8	2	no	—
133	#533	—	19	2	no	—
134	#500	—	19	1	no	—
135	#494	—	19	1	no	—
136	#487	—	19	2	no	—
137	#467	—	38	1	no	—
138	#467	—	38	1	no	—
139	C₄×Q₁₆	—	38	1	no	—
140	C₄×Q₁₆	—	38	1	no	—
141	#432	—	19	2	no	—
142	C₂×#97	—	2	1	no	—
143	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
144	C₂×C₄×C₈	—	2	1	no	—
145	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
146	#376	C₂×D₁₉	1	1	yes	characteristic
147	#335	—	38	1	no	—
148	#334	—	38	1	no	—
149	#330	—	38	4	no	—
150	#328	—	38	4	no	—
151	C₂×C₁₉	—	2	2	no	—
152	C₂×C₁₉	#1962	1	1	yes	characteristic
153	C₂×C₁₉	#1976	1	1	yes	characteristic
154	C₂×C₁₉	#1979	1	1	yes	characteristic
155	C₂×Q₁₆	—	38	1	no	—
156	C₂×Q₁₆	—	38	1	no	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
159	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
160	C₄⋊Q₈	—	19	2	no	—
161	C₄⋊Q₈	—	19	2	no	—
162	#125	—	38	2	no	—
163	C₂²⋊Q₈	—	38	2	no	—
164	C₂²⋊Q₈	—	38	2	no	—
165	C₄×Q₈	—	38	2	no	—
166	C₄×Q₈	—	38	2	no	—
167	#117	—	38	2	no	—
168	C₂×C₄²	—	2	1	no	—
169	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
170	#107	—	38	1	no	—
171	#107	—	38	1	no	—
172	C₄⋊C₈	—	38	2	no	—
173	#103	—	38	2	no	—
174	#103	—	38	2	no	—
175	C₂²⋊C₈	—	38	2	no	—
176	#97	—	2	4	no	—
177	#97	—	2	1	no	—
178	#97	—	38	2	no	—
179	#97	D₇₆	1	2	yes	—
180	C₄×C₈	—	2	4	no	—
181	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
182	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
183	C₄×C₈	D₇₆	1	1	yes	characteristic
184	C₄×C₈	D₇₆	1	1	yes	characteristic
185	#95	—	2	1	no	—
186	#95	D₇₆	1	2	yes	—
187	C₁₉	#9763	1	1	yes	characteristic, complemented, Sylow
188	C₂×Q₈	—	38	2	no	—
189	C₂×Q₈	—	38	2	no	—
190	C₂²×C₄	—	2	2	no	—
191	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
192	C₂²×C₄	#64541	1	1	yes	characteristic
193	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
194	Q₁₆	—	76	2	no	—
195	Q₁₆	—	76	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	76	2	no	—
202	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
203	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
204	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
205	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
206	C₄⋊C₄	—	38	2	no	—
207	C₄⋊C₄	—	38	2	no	—
208	C₄⋊C₄	—	38	2	no	—
209	C₄⋊C₄	—	38	2	no	—
210	C₄⋊C₄	—	76	2	no	—
211	C₄⋊C₄	—	76	2	no	—
212	C₂²⋊C₄	—	76	2	no	—
213	C₄²	—	2	2	no	—
214	C₄²	—	2	2	no	—
215	C₄²	—	76	2	no	—
216	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
217	C₄²	C₂×D₇₆	1	1	yes	characteristic
218	C₄²	C₂×D₇₆	1	1	yes	characteristic
219	C₄²	#64541	1	1	yes	characteristic
220	C₂³	#10597376	1	1	yes	characteristic
221	Q₈	—	76	2	no	—
222	Q₈	—	76	2	no	—
223	Q₈	—	152	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	4	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	76	2	no	—
232	C₂×C₄	—	76	2	no	—
233	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
234	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
235	C₂×C₄	#10597320	1	1	yes	characteristic
236	C₂×C₄	#10597321	1	1	yes	characteristic
237	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
238	C₂×C₄	#10597376	1	1	yes	characteristic
239	C₈	—	2	4	no	—
240	C₈	—	2	1	no	—
241	C₈	—	2	1	no	—
242	C₈	—	152	2	no	—
243	C₈	#10597262	1	2	yes	—
244	C₈	#10597262	1	2	yes	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	1	no	—
247	C₂²	#11926446	1	1	yes	characteristic
248	C₂²	#11926819	1	2	yes	—
249	C₄	—	2	1	no	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	2	1	no	—
254	C₄	—	4	4	no	—
255	C₄	—	152	2	no	—
256	C₄	—	152	2	no	—
257	C₄	C₂×#10597262	1	1	yes	characteristic
258	C₄	C₂×#10597262	1	1	yes	characteristic
259	C₂	—	2	2	no	—
260	C₂	#14564463	1	1	yes	characteristic
261	C₂	#14564533	1	1	yes	characteristic
262	C₂	#14564550	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574221

C₂

yes

maximal, characteristic

#14562398

C₂

yes

maximal, characteristic

#14562249

C₂

yes

maximal

#14562146

C₂

yes

maximal

C₁₉×#1726

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

#11926949

C₄

yes

characteristic, complemented

#11926924

C₄

yes

characteristic, complemented

#11926895

C₄

yes

complemented

#11926785

—

#11926785

—

C₄×Dic₇₆

—

C₄×Dic₇₆

—

#11926601

C₂²

yes

—

—

—

—

—

C₂×C₁₉×#97

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#376

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

#10597316

—

#10597315

C₂×C₄

yes

—

#10597315

C₂×C₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×#97

—

C₁₉×#97

—

C₁₉×#97

D₄

yes

—

C₄×C₈×C₁₉

—

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

C₁₉×#95

—

C₁₉×#95

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

—

—

—

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×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

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

Dic₇₆

—

—

C₂³×C₁₉

yes

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×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

100

C₂×C₄×C₁₉

#121

yes

characteristic

101

C₂×C₄×C₁₉

#124

yes

characteristic

102

C₂×C₄×C₁₉

#127

yes

characteristic

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

Dic₃₈

—

106

Dic₃₈

—

107

Dic₃₈

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

#104

yes

—

112

C₈×C₁₉

#104

yes

—

113

C₁₉⋊C₈

—

114

#3170

—

115

#1726

D₁₉

yes

characteristic

116

#1568

—

117

#1531

—

118

#1506

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#390

yes

characteristic

122

C₂²×C₁₉

#473

yes

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

C₂×#104

yes

characteristic

130

C₄×C₁₉

C₂×#104

yes

characteristic

131

Dic₁₉

—

132

Dic₁₉

—

133

#533

—

134

#500

—

135

#494

—

136

#487

—

137

#467

—

138

#467

—

139

C₄×Q₁₆

—

140

C₄×Q₁₆

—

141

#432

—

142

C₂×#97

—

143

C₂×#97

C₂×D₁₉

yes

characteristic

144

C₂×C₄×C₈

—

145

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

146

#376

C₂×D₁₉

yes

characteristic

147

#335

—

148

#334

—

149

#330

—

150

#328

—

151

C₂×C₁₉

—

152

C₂×C₁₉

#1962

yes

characteristic

153

C₂×C₁₉

#1976

yes

characteristic

154

C₂×C₁₉

#1979

yes

characteristic

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂²×C₈

—

158

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

159

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

#125

—

163

C₂²⋊Q₈

—

164

C₂²⋊Q₈

—

165

C₄×Q₈

—

166

C₄×Q₈

—

167

#117

—

168

C₂×C₄²

—

169

C₂×C₄²

C₂²×D₁₉

yes

characteristic

170

#107

—

171

#107

—

172

C₄⋊C₈

—

173

#103

—

174

#103

—

175

C₂²⋊C₈

—

176

#97

—

177

#97

—

178

#97

—

179

#97

D₇₆

yes

—

180

C₄×C₈

—

181

C₄×C₈

C₄×D₁₉

yes

characteristic

182

C₄×C₈

C₄×D₁₉

yes

characteristic

183

C₄×C₈

D₇₆

yes

characteristic

184

C₄×C₈

D₇₆

yes

characteristic

185

#95

—

186

#95

D₇₆

yes

—

187

C₁₉

#9763

yes

characteristic, complemented, Sylow

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂²×C₄

—

191

C₂²×C₄

C₂×D₇₆

yes

characteristic

192

C₂²×C₄

#64541

yes

characteristic

193

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

194

Q₁₆

—

195

Q₁₆

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

203

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

204

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

205

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₂²⋊C₄

—

213

C₄²

—

214

C₄²

—

215

C₄²

—

216

C₄²

C₂×C₄×D₁₉

yes

characteristic

217

C₄²

C₂×D₇₆

yes

characteristic

218

C₄²

C₂×D₇₆

yes

characteristic

219

C₄²

#64541

yes

characteristic

220

C₂³

#10597376

yes

characteristic

221

Q₈

—

222

Q₈

—

223

Q₈

—

152

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

C₄×D₇₆

yes

characteristic

234

C₂×C₄

C₄×D₇₆

yes

characteristic

235

C₂×C₄

#10597320

yes

characteristic

236

C₂×C₄

#10597321

yes

characteristic

237

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

238

C₂×C₄

#10597376

yes

characteristic

239

C₈

—

240

C₈

—

241

C₈

—

242

C₈

—

152

—

243

C₈

#10597262

yes

—

244

C₈

#10597262

yes

—

245

C₂²

—

246

C₂²

—

247

C₂²

#11926446

yes

characteristic

248

C₂²

#11926819

yes

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

152

—

256

C₄

—

152

—

257

C₄

C₂×#10597262

yes

characteristic

258

C₄

C₂×#10597262

yes

characteristic

259

C₂

—

260

C₂

#14564463

yes

characteristic

261

C₂

#14564533

yes

characteristic

262

C₂

#14564550

yes

characteristic

	subgroup	G/H
center	C₂²	#11926446
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1726	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1726	D₁₉
hypocenter	C₁₉	#9763
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1726

subgroup

G/H

center

C₂²

#11926446

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1726

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1726

N	H ≅ G/N	type
7. #11926949	C₄	semidirect
8. #11926924	C₄	semidirect
9. #11926895	C₄	semidirect
187. C₁₉	#9763	semidirect

H ≅ G/N

type

7. #11926949

C₄

semidirect

8. #11926924

C₄

semidirect

9. #11926895

C₄

semidirect

187. C₁₉

#9763

semidirect

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

subgroup	index
#14574221	2
#14562398	2
#14562249	2
#14562146	2
C₁₉×#1726	2
#9763	19

subgroup

index

C₁₉×#1726

Subgroups — #18081952

Conjugacy classes of subgroups

Complements

Maximal subgroups