Group #24990174 — subgroups

Subgroups — #24990174

Order 11008.

422 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 123 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	#19137516	C₂	1	1	yes	maximal, characteristic
2	#19134591	C₂	1	1	yes	maximal, characteristic
3	#19132497	C₂	1	2	yes	maximal
4	#19132454	C₂	1	2	yes	maximal
5	C₄₃×#1461	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×Dic₄₃	—	2	1	no	—
7	#14582923	C₂²	1	2	yes	—
8	C₂×#13063244	—	2	1	no	—
9	#14582798	—	2	1	no	—
10	#14582798	—	2	2	no	—
11	#14582765	C₄	1	2	yes	—
12	#14582765	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊Dic₄₃	C₄	1	2	yes	—
14	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	#14582668	—	2	1	no	—
16	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#431	C₂²	1	2	yes	—
18	C₄₃×#324	—	2	2	no	—
19	C₂×#10621877	—	2	2	no	—
20	Q₈×Dic₄₃	—	4	2	no	—
21	Q₈×Dic₄₃	—	4	2	no	—
22	C₂×C₄⋊Dic₄₃	—	2	2	no	—
23	C₂×C₄⋊Dic₄₃	—	2	2	no	—
24	C₂×C₄⋊Dic₄₃	—	2	1	no	—
25	C₂×C₄⋊Dic₄₃	—	2	1	no	—
26	C₂×C₄×Dic₄₃	—	2	2	no	—
27	C₂×C₄×Dic₄₃	—	2	1	no	—
28	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
29	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
30	#13063244	—	4	2	no	—
31	C₄₃⋊#95	—	2	2	no	—
32	C₄₃⋊#95	—	2	1	no	—
33	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
34	C₄₃⋊#95	C₂×C₄	1	2	yes	—
35	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
36	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
37	C₄×Q₈×C₄₃	—	2	2	no	—
38	C₄×Q₈×C₄₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
41	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₃	—	2	2	no	—
44	C₂²⋊C₈×C₄₃	—	2	2	no	—
45	C₄×C₈×C₄₃	—	2	2	no	—
46	C₂×Q₈×C₄₃	—	2	2	no	—
47	C₂×Q₈×C₄₃	—	2	2	no	—
48	C₂×Q₈×C₄₃	D₈	1	2	yes	—
49	C₂×Q₈×C₄₃	SD₁₆	1	2	yes	—
50	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×Dic₄₃	—	2	1	no	—
56	C₂²×Dic₄₃	—	2	1	no	—
57	C₂²×Dic₄₃	—	2	2	no	—
58	C₂×C₈×C₄₃	—	4	2	no	—
59	C₄⋊C₄×C₄₃	—	2	4	no	—
60	C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₄²×C₄₃	—	2	2	no	—
62	C₄²×C₄₃	—	2	2	no	—
63	C₄²×C₄₃	#41	1	2	yes	—
64	C₄²×C₄₃	#41	1	2	yes	—
65	C₄⋊Dic₄₃	—	4	2	no	—
66	C₄⋊Dic₄₃	—	4	4	no	—
67	C₄⋊Dic₄₃	—	4	4	no	—
68	C₄⋊Dic₄₃	—	4	1	no	—
69	C₄⋊Dic₄₃	—	4	1	no	—
70	C₄×Dic₄₃	—	4	4	no	—
71	C₄×Dic₄₃	—	4	1	no	—
72	C₄×Dic₄₃	—	4	1	no	—
73	#10621877	—	4	2	no	—
74	#10621877	—	4	2	no	—
75	C₂×C₄₃⋊C₈	—	4	2	no	—
76	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	Q₈×C₄₃	—	2	4	no	—
78	Q₈×C₄₃	—	2	4	no	—
79	C₂×C₄×C₄₃	—	2	2	no	—
80	C₂×C₄×C₄₃	—	2	2	no	—
81	C₂×C₄×C₄₃	—	2	2	no	—
82	C₂×C₄×C₄₃	—	4	1	no	—
83	C₂×C₄×C₄₃	—	4	1	no	—
84	C₂×C₄×C₄₃	—	4	2	no	—
85	C₂×C₄×C₄₃	#102	1	4	yes	—
86	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
87	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
88	C₂×C₄×C₄₃	#123	1	2	yes	—
89	C₂×C₄×C₄₃	#123	1	2	yes	—
90	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
92	C₂×C₄×C₄₃	#137	1	2	yes	—
93	C₂×Dic₄₃	—	2	2	no	—
94	C₂×Dic₄₃	—	4	1	no	—
95	C₂×Dic₄₃	—	4	1	no	—
96	C₂×Dic₄₃	—	4	1	no	—
97	C₂×Dic₄₃	—	4	2	no	—
98	C₂×Dic₄₃	—	4	1	no	—
99	C₂×Dic₄₃	—	4	2	no	—
100	C₂×Dic₄₃	—	4	2	no	—
101	C₂×Dic₄₃	—	4	1	no	—
102	C₈×C₄₃	—	8	2	no	—
103	C₄₃⋊C₈	—	8	2	no	—
104	#8766	—	43	1	no	maximal, Sylow
105	C₂²×C₄₃	—	2	1	no	—
106	C₂²×C₄₃	—	2	1	no	—
107	C₂²×C₄₃	#381	1	1	yes	characteristic
108	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
109	C₂²×C₄₃	#419	1	1	yes	characteristic
110	C₄×C₄₃	—	2	4	no	—
111	C₄×C₄₃	—	2	2	no	—
112	C₄×C₄₃	—	2	1	no	—
113	C₄×C₄₃	—	2	1	no	—
114	C₄×C₄₃	—	4	2	no	—
115	C₄×C₄₃	#480	1	2	yes	—
116	C₄×C₄₃	#483	1	2	yes	—
117	Dic₄₃	—	4	2	no	—
118	Dic₄₃	—	8	2	no	—
119	Dic₄₃	—	8	1	no	—
120	#2351	—	43	1	no	—
121	#1801	—	43	1	no	—
122	#1461	D₄₃	1	1	yes	characteristic
123	#1303	—	43	2	no	—
124	#1286	—	43	2	no	—
125	C₂×C₄₃	—	2	1	no	—
126	C₂×C₄₃	—	2	1	no	—
127	C₂×C₄₃	#1823	1	1	yes	characteristic
128	C₂×C₄₃	#1827	1	1	yes	characteristic
129	C₂×C₄₃	#1830	1	1	yes	characteristic
130	C₂×C₄×Q₈	—	86	1	no	—
131	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
132	#431	C₂×D₄₃	1	2	yes	—
133	#423	—	43	2	no	—
134	C₂×#101	—	86	1	no	—
135	#389	—	86	1	no	—
136	#389	—	86	2	no	—
137	#382	—	43	1	no	—
138	#382	—	43	2	no	—
139	C₄×C₄⋊C₄	—	43	1	no	—
140	C₄×C₄⋊C₄	—	43	2	no	—
141	#343	—	86	1	no	—
142	#324	—	2	2	no	—
143	C₄₃	#8766	1	1	yes	characteristic, complemented, Sylow
144	C₂²×Q₈	D₁₇₂	1	1	yes	characteristic
145	C₂×M₁₆	—	86	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₄×Q₈	—	172	2	no	—
149	C₄×Q₈	—	172	2	no	—
150	C₂×C₄⋊C₄	—	86	2	no	—
151	C₂×C₄⋊C₄	—	86	2	no	—
152	C₂×C₄⋊C₄	—	86	1	no	—
153	C₂×C₄⋊C₄	—	86	1	no	—
154	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
155	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
156	C₂×C₄²	—	86	2	no	—
157	C₂×C₄²	—	86	1	no	—
158	C₂×C₄²	C₄×D₄₃	1	2	yes	—
159	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
160	C₄⋊C₈	—	2	2	no	—
161	C₄⋊C₈	—	86	2	no	—
162	C₄⋊C₈	—	86	2	no	—
163	#101	—	172	2	no	—
164	C₂²⋊C₈	—	2	2	no	—
165	C₄×C₈	—	2	2	no	—
166	#95	—	43	1	no	—
167	#95	—	43	2	no	—
168	#95	—	43	1	no	—
169	#95	—	86	2	no	—
170	#95	—	86	1	no	—
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	—	2	2	no	—
173	C₂×Q₈	#10621873	1	2	yes	—
174	C₂×Q₈	D₃₄₄	1	2	yes	—
175	C₂²×C₄	—	86	1	no	—
176	C₂²×C₄	—	86	1	no	—
177	C₂²×C₄	—	86	2	no	—
178	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
179	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
180	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
181	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
182	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
183	M₁₆	—	172	2	no	—
184	M₁₆	—	172	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	172	2	no	—
187	C₄⋊C₄	—	2	4	no	—
188	C₄⋊C₄	—	2	2	no	—
189	C₄⋊C₄	—	172	2	no	—
190	C₄⋊C₄	—	172	4	no	—
191	C₄⋊C₄	—	172	4	no	—
192	C₄⋊C₄	—	172	1	no	—
193	C₄⋊C₄	—	172	1	no	—
194	C₄²	—	2	2	no	—
195	C₄²	—	2	2	no	—
196	C₄²	—	172	4	no	—
197	C₄²	—	172	1	no	—
198	C₄²	—	172	1	no	—
199	C₄²	#10621900	1	2	yes	—
200	C₄²	#10621900	1	2	yes	—
201	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
202	Q₈	—	2	4	no	—
203	Q₈	—	2	4	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	86	2	no	—
211	C₂×C₄	—	172	1	no	—
212	C₂×C₄	—	172	2	no	—
213	C₂×C₄	—	172	1	no	—
214	C₂×C₄	—	172	2	no	—
215	C₂×C₄	—	172	2	no	—
216	C₂×C₄	—	172	1	no	—
217	C₂×C₄	—	172	1	no	—
218	C₂×C₄	—	172	1	no	—
219	C₂×C₄	#13063247	1	4	yes	—
220	C₂×C₄	#13063281	1	1	yes	characteristic
221	C₂×C₄	#13063281	1	1	yes	characteristic
222	C₂×C₄	#13063306	1	2	yes	—
223	C₂×C₄	#13063309	1	2	yes	—
224	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
225	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
226	C₂×C₄	#13063358	1	2	yes	—
227	C₈	—	8	2	no	—
228	C₈	—	344	2	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	#14582760	1	1	yes	characteristic
232	C₂²	C₂×#13063247	1	1	yes	characteristic
233	C₂²	#14582909	1	1	yes	characteristic
234	C₄	—	2	4	no	—
235	C₄	—	2	2	no	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	4	2	no	—
239	C₄	—	344	2	no	—
240	C₄	—	344	1	no	—
241	C₄	—	172	2	no	—
242	C₄	#14583213	1	2	yes	—
243	C₄	#14583230	1	2	yes	—
244	C₂	—	2	1	no	—
245	C₂	—	2	1	no	—
246	C₂	#19134682	1	1	yes	characteristic
247	C₂	#19134696	1	1	yes	characteristic
248	C₂	#19134707	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19137516

C₂

yes

maximal, characteristic

#19134591

C₂

yes

maximal, characteristic

#19132497

C₂

yes

maximal

#19132454

C₂

yes

maximal

C₄₃×#1461

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₄₃

—

#14582923

C₂²

yes

—

—

—

—

C₄

yes

—

#14582765

C₂²

yes

characteristic

C₄×C₄⋊Dic₄₃

C₄

yes

—

C₄×C₄⋊Dic₄₃

C₂²

yes

characteristic

#14582668

—

C₂×C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₄₃×#431

C₂²

yes

—

C₄₃×#324

—

C₂×#10621877

—

Q₈×Dic₄₃

—

Q₈×Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063244

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

C₂×C₄

yes

characteristic

C₄₃⋊#95

C₂×C₄

yes

—

C₄₃⋊#95

C₂×C₄

yes

characteristic

C₂²×Q₈×C₄₃

D₄

yes

characteristic

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

D₈

yes

—

C₂×Q₈×C₄₃

SD₁₆

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#102

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

#123

yes

—

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

100

C₂×Dic₄₃

—

101

C₂×Dic₄₃

—

102

C₈×C₄₃

—

103

C₄₃⋊C₈

—

104

#8766

—

maximal, Sylow

105

C₂²×C₄₃

—

106

C₂²×C₄₃

—

107

C₂²×C₄₃

#381

yes

characteristic

108

C₂²×C₄₃

C₂×#102

yes

characteristic

109

C₂²×C₄₃

#419

yes

characteristic

110

C₄×C₄₃

—

111

C₄×C₄₃

—

112

C₄×C₄₃

—

113

C₄×C₄₃

—

114

C₄×C₄₃

—

115

C₄×C₄₃

#480

yes

—

116

C₄×C₄₃

#483

yes

—

117

Dic₄₃

—

118

Dic₄₃

—

119

Dic₄₃

—

120

#2351

—

121

#1801

—

122

#1461

D₄₃

yes

characteristic

123

#1303

—

124

#1286

—

125

C₂×C₄₃

—

126

C₂×C₄₃

—

127

C₂×C₄₃

#1823

yes

characteristic

128

C₂×C₄₃

#1827

yes

characteristic

129

C₂×C₄₃

#1830

yes

characteristic

130

C₂×C₄×Q₈

—

131

C₂×C₄×Q₈

C₂×D₄₃

yes

characteristic

132

#431

C₂×D₄₃

yes

—

133

#423

—

134

C₂×#101

—

135

#389

—

136

#389

—

137

#382

—

138

#382

—

139

C₄×C₄⋊C₄

—

140

C₄×C₄⋊C₄

—

141

#343

—

142

#324

—

143

C₄₃

#8766

yes

characteristic, complemented, Sylow

144

C₂²×Q₈

D₁₇₂

yes

characteristic

145

C₂×M₁₆

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

172

—

149

C₄×Q₈

—

172

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

D₁₇₂

yes

characteristic

155

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

156

C₂×C₄²

—

157

C₂×C₄²

—

158

C₂×C₄²

C₄×D₄₃

yes

—

159

C₂×C₄²

C₂²×D₄₃

yes

characteristic

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

#101

—

172

—

164

C₂²⋊C₈

—

165

C₄×C₈

—

166

#95

—

167

#95

—

168

#95

—

169

#95

—

170

#95

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

#10621873

yes

—

174

C₂×Q₈

D₃₄₄

yes

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

179

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

180

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

181

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

182

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

183

M₁₆

—

172

—

184

M₁₆

—

172

—

185

C₂×C₈

—

186

C₂×C₈

—

172

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

172

—

190

C₄⋊C₄

—

172

—

191

C₄⋊C₄

—

172

—

192

C₄⋊C₄

—

172

—

193

C₄⋊C₄

—

172

—

194

C₄²

—

195

C₄²

—

196

C₄²

—

172

—

197

C₄²

—

172

—

198

C₄²

—

172

—

199

C₄²

#10621900

yes

—

200

C₄²

#10621900

yes

—

201

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

202

Q₈

—

203

Q₈

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

172

—

212

C₂×C₄

—

172

—

213

C₂×C₄

—

172

—

214

C₂×C₄

—

172

—

215

C₂×C₄

—

172

—

216

C₂×C₄

—

172

—

217

C₂×C₄

—

172

—

218

C₂×C₄

—

172

—

219

C₂×C₄

#13063247

yes

—

220

C₂×C₄

#13063281

yes

characteristic

221

C₂×C₄

#13063281

yes

characteristic

222

C₂×C₄

#13063306

yes

—

223

C₂×C₄

#13063309

yes

—

224

C₂×C₄

C₂×D₃₄₄

yes

characteristic

225

C₂×C₄

C₂×#10621873

yes

characteristic

226

C₂×C₄

#13063358

yes

—

227

C₈

—

228

C₈

—

344

—

229

C₂²

—

230

C₂²

—

231

C₂²

#14582760

yes

characteristic

232

C₂²

C₂×#13063247

yes

characteristic

233

C₂²

#14582909

yes

characteristic

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

344

—

240

C₄

—

344

—

241

C₄

—

172

—

242

C₄

#14583213

yes

—

243

C₄

#14583230

yes

—

244

C₂

—

245

C₂

—

246

C₂

#19134682

yes

characteristic

247

C₂

#19134696

yes

characteristic

248

C₂

#19134707

yes

characteristic

	subgroup	G/H
center	C₂²	#14582760
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1461	C₂
socle	C₂²×C₄₃	#381
prime radical	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1461	D₄₃
hypocenter	C₄₃	#8766
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1461

subgroup

G/H

center

C₂²

#14582760

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1461

C₂

socle

C₂²×C₄₃

#381

prime radical

C₂³×C₄₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1461

N	H ≅ G/N	type
143. C₄₃	#8766	semidirect

H ≅ G/N

type

143. C₄₃

#8766

semidirect

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

subgroup	index
#19137516	2
#19134591	2
#19132497	2
#19132454	2
C₄₃×#1461	2
#8766	43

subgroup

index

C₄₃×#1461

Subgroups — #24990174

Conjugacy classes of subgroups

Complements

Maximal subgroups