Group #18082349 — subgroups

Subgroups — #18082349

Order 4864.

694 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 163 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×#11926921	C₂	1	1	yes	maximal, characteristic
2	#14564440	C₂	1	2	yes	maximal, complemented
3	#14564440	C₂	1	2	yes	maximal, complemented
4	C₂×#11926266	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₅₂	—	2	2	no	—
7	C₂×#10597320	C₂²	1	2	yes	—
8	#11926921	—	2	2	no	—
9	#11926921	C₄	1	4	yes	complemented
10	C₂×#10597266	—	2	4	no	—
11	C₂×#10597266	—	2	4	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926266	—	2	2	no	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#384	C₂²	1	2	yes	—
17	C₁₉×#340	—	2	2	no	—
18	C₂²×D₇₆	—	2	2	no	—
19	C₂²×D₇₆	—	2	2	no	—
20	C₂²×D₇₆	—	2	2	no	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
27	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
28	C₂×D₁₅₂	—	2	8	no	—
29	C₂×D₁₅₂	—	4	8	no	—
30	#10597320	—	2	2	no	—
31	#10597320	—	2	2	no	—
32	#10597320	—	2	2	no	—
33	#10597320	C₂×C₄	1	4	yes	—
34	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₉	D₄	1	2	yes	—
36	#10597266	—	4	8	no	—
37	#10597266	—	4	8	no	—
38	C₄×C₁₉⋊C₈	—	2	1	no	—
39	C₄×C₁₉⋊C₈	—	2	1	no	—
40	C₄×C₁₉⋊C₈	—	2	1	no	—
41	C₄×C₁₉⋊C₈	—	2	1	no	—
42	C₂³×D₁₉	—	4	2	no	—
43	C₂²×C₄×C₁₉	—	4	2	no	—
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×D₇₆	—	2	4	no	—
48	C₂×D₇₆	—	2	4	no	—
49	C₂×D₇₆	—	2	4	no	—
50	C₂×D₇₆	—	4	4	no	—
51	C₂×D₇₆	—	4	4	no	—
52	C₂×D₇₆	—	4	4	no	—
53	C₂×D₇₆	—	4	4	no	—
54	C₂×D₇₆	—	4	4	no	—
55	C₂×D₇₆	—	4	4	no	—
56	C₂×D₇₆	—	4	2	no	—
57	C₂×D₇₆	—	4	2	no	—
58	C₂×D₇₆	—	4	2	no	—
59	C₂×C₈×C₁₉	—	2	4	no	—
60	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
61	C₄⋊C₄×C₁₉	—	4	4	no	—
62	C₄⋊C₄×C₁₉	—	4	4	no	—
63	C₄⋊C₄×C₁₉	—	4	4	no	—
64	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₉	#41	1	1	yes	characteristic
67	C₄²×C₁₉	#41	1	1	yes	characteristic
68	C₂×C₁₉⋊C₈	—	2	2	no	—
69	C₂×C₁₉⋊C₈	—	2	2	no	—
70	C₂×C₁₉⋊C₈	—	2	2	no	—
71	C₂×C₁₉⋊C₈	—	2	4	no	—
72	C₂×C₁₉⋊C₈	D₈	1	4	yes	complemented
73	D₁₅₂	—	4	16	no	—
74	#9832	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	#127	1	1	yes	characteristic
76	C₂²×D₁₉	—	4	4	no	—
77	C₂²×D₁₉	—	8	2	no	—
78	C₂²×D₁₉	—	8	2	no	—
79	C₂²×D₁₉	—	8	2	no	—
80	C₂²×D₁₉	—	8	2	no	—
81	C₂²×D₁₉	—	8	2	no	—
82	C₂²×D₁₉	—	8	2	no	—
83	C₂×C₄×C₁₉	—	8	2	no	—
84	C₂×C₄×C₁₉	—	8	2	no	—
85	C₂×C₄×C₁₉	—	8	2	no	—
86	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
93	C₂×C₄×C₁₉	#135	1	2	yes	—
94	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
95	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
96	D₇₆	—	4	8	no	—
97	D₇₆	—	4	8	no	—
98	D₇₆	—	4	8	no	—
99	D₇₆	—	8	4	no	—
100	D₇₆	—	8	4	no	—
101	D₇₆	—	8	4	no	—
102	C₈×C₁₉	—	2	4	no	—
103	C₁₉⋊C₈	—	2	4	no	—
104	C₁₉⋊C₈	—	4	2	no	—
105	C₂×#493	—	19	1	no	—
106	#1957	—	19	2	no	—
107	#1957	—	19	2	no	—
108	#1834	D₁₉	1	1	yes	characteristic, complemented
109	C₂×#322	—	19	1	no	—
110	C₂²×C₁₉	#390	1	1	yes	characteristic
111	C₂²×C₁₉	#493	1	1	yes	characteristic
112	C₂²×C₁₉	#495	1	1	yes	characteristic
113	C₂²×C₁₉	#496	1	2	yes	—
114	C₂²×C₁₉	#496	1	2	yes	—
115	C₂×D₁₉	—	8	4	no	—
116	C₂×D₁₉	—	8	4	no	—
117	C₂×D₁₉	—	8	4	no	—
118	C₂×D₁₉	—	16	2	no	—
119	C₂×D₁₉	—	16	2	no	—
120	C₂×D₁₉	—	16	2	no	—
121	C₂×D₁₉	—	16	2	no	—
122	C₄×C₁₉	—	16	2	no	—
123	C₄×C₁₉	#418	1	2	yes	—
124	C₄×C₁₉	C₄×D₈	1	2	yes	—
125	C₄×C₁₉	#442	1	2	yes	—
126	C₄×C₁₉	#466	1	2	yes	—
127	C₄×C₁₉	#469	1	2	yes	—
128	C₄×C₁₉	#490	1	2	yes	—
129	C₂²×D₈	—	38	2	no	—
130	C₂×#127	—	19	2	no	—
131	#493	—	19	4	no	—
132	#493	—	38	2	no	—
133	C₂×#102	—	38	4	no	—
134	C₂×#102	—	38	4	no	—
135	C₂×C₄×C₈	—	19	1	no	—
136	C₂×C₄×C₈	—	19	1	no	—
137	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
138	#384	C₂×D₁₉	1	2	yes	—
139	#340	—	2	2	no	—
140	#322	—	38	2	no	—
141	C₂×C₁₉	#1717	1	2	yes	—
142	C₂×C₁₉	#1721	1	2	yes	—
143	C₂×C₁₉	#1961	1	1	yes	characteristic
144	C₂×C₁₉	#1970	1	1	yes	characteristic
145	C₂×C₁₉	#1972	1	1	yes	characteristic
146	D₁₉	—	16	4	no	—
147	C₂²×D₄	—	38	2	no	—
148	C₂²×D₄	—	38	2	no	—
149	C₂²×D₄	—	38	2	no	—
150	C₂×D₈	—	38	8	no	—
151	C₂×D₈	—	76	8	no	—
152	C₂²×C₈	—	19	2	no	—
153	C₂²×C₈	—	19	2	no	—
154	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
155	#127	—	19	4	no	—
156	#127	—	38	2	no	—
157	#127	—	38	2	no	—
158	#127	—	38	2	no	—
159	C₂×C₄⋊C₄	—	2	2	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	—	2	2	no	—
162	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
163	#102	—	76	8	no	—
164	#102	—	76	8	no	—
165	C₄×C₈	—	38	1	no	—
166	C₄×C₈	—	38	1	no	—
167	C₄×C₈	—	38	1	no	—
168	C₄×C₈	—	38	1	no	—
169	C₄×C₈	C₄×D₁₉	1	2	yes	—
170	C₄×C₈	D₇₆	1	2	yes	—
171	C₁₉	#9832	1	1	yes	characteristic, complemented, Sylow
172	C₂⁴	—	76	2	no	—
173	C₂×D₄	—	38	4	no	—
174	C₂×D₄	—	38	4	no	—
175	C₂×D₄	—	38	4	no	—
176	C₂×D₄	—	76	2	no	—
177	C₂×D₄	—	76	4	no	—
178	C₂×D₄	—	76	4	no	—
179	C₂×D₄	—	76	2	no	—
180	C₂×D₄	—	76	2	no	—
181	C₂×D₄	—	76	4	no	—
182	C₂×D₄	—	76	4	no	—
183	C₂×D₄	—	76	4	no	—
184	C₂×D₄	—	76	4	no	—
185	C₂²×C₄	—	4	2	no	—
186	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
187	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
189	D₈	—	76	16	no	—
190	C₂×C₈	—	2	4	no	—
191	C₂×C₈	—	19	4	no	—
192	C₂×C₈	—	38	2	no	—
193	C₂×C₈	—	38	2	no	—
194	C₂×C₈	—	38	2	no	—
195	C₂×C₈	—	38	4	no	—
196	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
197	C₄⋊C₄	—	4	4	no	—
198	C₄⋊C₄	—	4	4	no	—
199	C₄⋊C₄	—	4	4	no	—
200	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
201	C₄²	C₂×D₇₆	1	1	yes	characteristic
202	C₄²	#64545	1	1	yes	characteristic
203	C₄²	#64545	1	1	yes	characteristic
204	C₂³	—	76	4	no	—
205	C₂³	—	152	2	no	—
206	C₂³	—	152	2	no	—
207	C₂³	—	152	2	no	—
208	C₂³	—	152	2	no	—
209	C₂³	—	152	2	no	—
210	C₂³	—	152	2	no	—
211	C₂³	#10597386	1	1	yes	characteristic
212	D₄	—	76	8	no	—
213	D₄	—	76	8	no	—
214	D₄	—	76	8	no	—
215	D₄	—	152	4	no	—
216	D₄	—	152	4	no	—
217	D₄	—	152	4	no	—
218	C₂×C₄	—	8	2	no	—
219	C₂×C₄	—	8	2	no	—
220	C₂×C₄	—	8	2	no	—
221	C₂×C₄	#10597339	1	1	yes	characteristic
222	C₂×C₄	#10597339	1	1	yes	characteristic
223	C₂×C₄	#10597341	1	1	yes	characteristic
224	C₂×C₄	#10597341	1	1	yes	characteristic
225	C₂×C₄	D₈×D₁₉	1	2	yes	—
226	C₂×C₄	#10597360	1	4	yes	—
227	C₂×C₄	#10597365	1	2	yes	—
228	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
229	C₂×C₄	#10597393	1	1	yes	characteristic
230	C₂×C₄	#10597395	1	4	yes	—
231	C₈	—	2	4	no	—
232	C₈	—	38	4	no	—
233	C₈	—	76	2	no	—
234	C₂²	—	304	2	no	—
235	C₂²	—	304	2	no	—
236	C₂²	—	304	2	no	—
237	C₂²	—	304	2	no	—
238	C₂²	—	152	4	no	—
239	C₂²	—	152	4	no	—
240	C₂²	—	152	4	no	—
241	C₂²	#11926445	1	1	yes	characteristic
242	C₂²	#11926919	1	1	yes	characteristic
243	C₂²	#11926929	1	1	yes	characteristic
244	C₂²	#11926930	1	2	yes	—
245	C₂²	#11926934	1	2	yes	—
246	C₄	—	16	2	no	—
247	C₄	#11926548	1	2	yes	—
248	C₄	#11926626	1	2	yes	—
249	C₄	#11926655	1	2	yes	—
250	C₄	#11926781	1	2	yes	—
251	C₄	#11926798	1	2	yes	—
252	C₄	#11926910	1	2	yes	—
253	C₂	—	304	4	no	—
254	C₂	#14563277	1	2	yes	—
255	C₂	#14563303	1	2	yes	—
256	C₂	#14564458	1	1	yes	characteristic
257	C₂	#14564499	1	1	yes	characteristic
258	C₂	#14564509	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926921

C₂

yes

maximal, characteristic

#14564440

C₂

yes

maximal, complemented

#14564440

C₂

yes

maximal, complemented

C₂×#11926266

C₂

yes

maximal, characteristic, complemented

C₁₉×#1834

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₅₂

—

C₂×#10597320

C₂²

yes

—

#11926921

—

#11926921

C₄

yes

complemented

C₂×#10597266

—

C₂×#10597266

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926266

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

—

C₁₉×#340

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

D₄

yes

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

—

—

—

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

#10597266

—

#10597266

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₈

yes

complemented

D₁₅₂

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

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

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

100

D₇₆

—

101

D₇₆

—

102

C₈×C₁₉

—

103

C₁₉⋊C₈

—

104

C₁₉⋊C₈

—

105

C₂×#493

—

106

#1957

—

107

#1957

—

108

#1834

D₁₉

yes

characteristic, complemented

109

C₂×#322

—

110

C₂²×C₁₉

#390

yes

characteristic

111

C₂²×C₁₉

#493

yes

characteristic

112

C₂²×C₁₉

#495

yes

characteristic

113

C₂²×C₁₉

#496

yes

—

114

C₂²×C₁₉

#496

yes

—

115

C₂×D₁₉

—

116

C₂×D₁₉

—

117

C₂×D₁₉

—

118

C₂×D₁₉

—

119

C₂×D₁₉

—

120

C₂×D₁₉

—

121

C₂×D₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

#418

yes

—

124

C₄×C₁₉

C₄×D₈

yes

—

125

C₄×C₁₉

#442

yes

—

126

C₄×C₁₉

#466

yes

—

127

C₄×C₁₉

#469

yes

—

128

C₄×C₁₉

#490

yes

—

129

C₂²×D₈

—

130

C₂×#127

—

131

#493

—

132

#493

—

133

C₂×#102

—

134

C₂×#102

—

135

C₂×C₄×C₈

—

136

C₂×C₄×C₈

—

137

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

138

#384

C₂×D₁₉

yes

—

139

#340

—

140

#322

—

141

C₂×C₁₉

#1717

yes

—

142

C₂×C₁₉

#1721

yes

—

143

C₂×C₁₉

#1961

yes

characteristic

144

C₂×C₁₉

#1970

yes

characteristic

145

C₂×C₁₉

#1972

yes

characteristic

146

D₁₉

—

147

C₂²×D₄

—

148

C₂²×D₄

—

149

C₂²×D₄

—

150

C₂×D₈

—

151

C₂×D₈

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

C₂²⋊D₁₉

yes

—

155

#127

—

156

#127

—

157

#127

—

158

#127

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄²

C₂²×D₁₉

yes

characteristic

163

#102

—

164

#102

—

165

C₄×C₈

—

166

C₄×C₈

—

167

C₄×C₈

—

168

C₄×C₈

—

169

C₄×C₈

C₄×D₁₉

yes

—

170

C₄×C₈

D₇₆

yes

—

171

C₁₉

#9832

yes

characteristic, complemented, Sylow

172

C₂⁴

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂²×C₄

—

186

C₂²×C₄

D₄×D₁₉

yes

characteristic

187

C₂²×C₄

D₄×D₁₉

yes

characteristic

188

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

189

D₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄²

C₂×C₄×D₁₉

yes

characteristic

201

C₄²

C₂×D₇₆

yes

characteristic

202

C₄²

#64545

yes

characteristic

203

C₄²

#64545

yes

characteristic

204

C₂³

—

205

C₂³

—

152

—

206

C₂³

—

152

—

207

C₂³

—

152

—

208

C₂³

—

152

—

209

C₂³

—

152

—

210

C₂³

—

152

—

211

C₂³

#10597386

yes

characteristic

212

D₄

—

213

D₄

—

214

D₄

—

215

D₄

—

152

—

216

D₄

—

152

—

217

D₄

—

152

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

#10597339

yes

characteristic

222

C₂×C₄

#10597339

yes

characteristic

223

C₂×C₄

#10597341

yes

characteristic

224

C₂×C₄

#10597341

yes

characteristic

225

C₂×C₄

D₈×D₁₉

yes

—

226

C₂×C₄

#10597360

yes

—

227

C₂×C₄

#10597365

yes

—

228

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

229

C₂×C₄

#10597393

yes

characteristic

230

C₂×C₄

#10597395

yes

—

231

C₈

—

232

C₈

—

233

C₈

—

234

C₂²

—

304

—

235

C₂²

—

304

—

236

C₂²

—

304

—

237

C₂²

—

304

—

238

C₂²

—

152

—

239

C₂²

—

152

—

240

C₂²

—

152

—

241

C₂²

#11926445

yes

characteristic

242

C₂²

#11926919

yes

characteristic

243

C₂²

#11926929

yes

characteristic

244

C₂²

#11926930

yes

—

245

C₂²

#11926934

yes

—

246

C₄

—

247

C₄

#11926548

yes

—

248

C₄

#11926626

yes

—

249

C₄

#11926655

yes

—

250

C₄

#11926781

yes

—

251

C₄

#11926798

yes

—

252

C₄

#11926910

yes

—

253

C₂

—

304

—

254

C₂

#14563277

yes

—

255

C₂

#14563303

yes

—

256

C₂

#14564458

yes

characteristic

257

C₂

#14564499

yes

characteristic

258

C₂

#14564509

yes

characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1834	C₂
socle	C₂³×C₁₉	#127
prime radical	C₂×#11926921	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1834	D₁₉
hypocenter	C₁₉	#9832
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

subgroup

G/H

center

C₂³

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1834

C₂

C₂³×C₁₉

C₂

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

N	H ≅ G/N	type
2. #14564440	C₂	semidirect
3. #14564440	C₂	semidirect
4. C₂×#11926266	C₂	semidirect
5. C₁₉×#1834	C₂	semidirect
9. #11926921	C₄	semidirect
72. C₂×C₁₉⋊C₈	D₈	semidirect
108. #1834	D₁₉	semidirect
171. C₁₉	#9832	semidirect

H ≅ G/N

type

2. #14564440

C₂

semidirect

3. #14564440

C₂

semidirect

4. C₂×#11926266

C₂

semidirect

5. C₁₉×#1834

C₂

semidirect

9. #11926921

C₄

semidirect

72. C₂×C₁₉⋊C₈

D₈

semidirect

108. #1834

D₁₉

semidirect

171. C₁₉

#9832

semidirect

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

subgroup	index
C₂×#11926921	2
#14564440	2
C₂×#11926266	2
C₁₉×#1834	2
#9832	19

subgroup

index

C₁₉×#1834

Subgroups — #18082349

Conjugacy classes of subgroups

Complements

Maximal subgroups