Group #24994005 — subgroups

Subgroups — #24994005

Order 11008.

486 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 115 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	#19143680	C₂	1	1	yes	maximal, characteristic
2	#19139580	C₂	1	1	yes	maximal, characteristic
3	#19133268	C₂	1	2	yes	maximal
4	#19132496	C₂	1	2	yes	maximal
5	C₄₃×#1801	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063325	C₂²	1	1	yes	characteristic
7	C₂×#13063323	—	2	1	no	—
8	#14583030	—	2	4	no	—
9	#14582956	—	2	2	no	—
10	#14582952	C₂²	1	2	yes	—
11	#14582829	C₄	1	4	yes	—
12	#14582804	—	2	1	no	—
13	#14582797	—	2	2	no	—
14	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	#14582646	—	2	4	no	—
16	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#423	C₂²	1	2	yes	—
18	C₂×#101×C₄₃	—	2	1	no	—
19	C₄₃×#343	—	2	1	no	—
20	C₂²×Dic₈₆	—	2	1	no	—
21	#13063325	—	2	2	no	—
22	#13063325	—	2	2	no	—
23	#13063323	—	4	4	no	—
24	C₂×C₄⋊Dic₄₃	—	2	1	no	—
25	C₂×C₄⋊Dic₄₃	—	2	1	no	—
26	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
27	C₂×Dic₄₃⋊C₄	—	2	4	no	—
28	C₂×C₄×Dic₄₃	—	2	1	no	—
29	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
30	C₄⋊(C₄₃⋊C₈)	D₄	1	4	yes	—
31	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
32	#13063236	—	2	4	no	—
33	C₄×C₄₃⋊C₈	—	2	2	no	—
34	C₄₃⋊#95	—	2	4	no	—
35	C₄₃⋊#95	C₂×C₄	1	2	yes	—
36	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
37	C₂×M₁₆×C₄₃	—	2	2	no	—
38	C₄×Q₈×C₄₃	—	2	2	no	—
39	C₄×Q₈×C₄₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₄₃	D₄	1	2	yes	—
43	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₄₃	—	2	2	no	—
45	C₄⋊C₈×C₄₃	—	2	2	no	—
46	#101×C₄₃	—	4	2	no	—
47	C₂×Q₈×C₄₃	—	2	2	no	—
48	C₂×Q₈×C₄₃	—	2	1	no	—
49	C₂×Q₈×C₄₃	—	2	2	no	—
50	C₂×Q₈×C₄₃	—	2	1	no	—
51	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₄₃	—	2	2	no	—
57	C₂²×Dic₄₃	—	2	2	no	—
58	C₂×Dic₈₆	—	4	2	no	—
59	C₂×Dic₈₆	—	4	2	no	—
60	C₂×Dic₈₆	—	4	1	no	—
61	C₂×Dic₈₆	—	4	1	no	—
62	M₁₆×C₄₃	—	4	2	no	—
63	M₁₆×C₄₃	—	4	2	no	—
64	C₂×C₈×C₄₃	—	4	2	no	—
65	C₄⋊C₄×C₄₃	—	2	4	no	—
66	C₄⋊C₄×C₄₃	—	2	2	no	—
67	C₄²×C₄₃	—	2	2	no	—
68	C₄²×C₄₃	—	2	2	no	—
69	C₄²×C₄₃	C₂×D₄	1	2	yes	—
70	C₄²×C₄₃	#41	1	2	yes	—
71	C₄⋊Dic₄₃	—	2	4	no	—
72	C₄⋊Dic₄₃	—	2	4	no	—
73	C₄⋊Dic₄₃	—	4	1	no	—
74	C₄⋊Dic₄₃	—	4	1	no	—
75	Dic₄₃⋊C₄	—	4	8	no	—
76	C₄×Dic₄₃	—	4	2	no	—
77	C₂×C₄₃⋊C₈	—	2	4	no	—
78	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	Q₈×C₄₃	—	4	2	no	—
80	Q₈×C₄₃	—	4	2	no	—
81	C₂×C₄×C₄₃	—	2	2	no	—
82	C₂×C₄×C₄₃	—	2	2	no	—
83	C₂×C₄×C₄₃	—	2	2	no	—
84	C₂×C₄×C₄₃	—	2	2	no	—
85	C₂×C₄×C₄₃	—	2	2	no	—
86	C₂×C₄×C₄₃	—	4	1	no	—
87	C₂×C₄×C₄₃	—	4	2	no	—
88	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
89	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
90	C₂×C₄×C₄₃	#121	1	2	yes	—
91	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
92	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
93	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
95	C₂×Dic₄₃	—	2	4	no	—
96	C₂×Dic₄₃	—	4	2	no	—
97	C₂×Dic₄₃	—	4	2	no	—
98	C₂×Dic₄₃	—	4	2	no	—
99	C₂×Dic₄₃	—	4	2	no	—
100	C₂×Dic₄₃	—	4	2	no	—
101	Dic₈₆	—	8	2	no	—
102	Dic₈₆	—	8	2	no	—
103	C₈×C₄₃	—	8	2	no	—
104	C₄₃⋊C₈	—	4	4	no	—
105	#9402	—	43	1	no	maximal, Sylow
106	C₂²×C₄₃	—	2	1	no	—
107	C₂²×C₄₃	—	2	1	no	—
108	C₂²×C₄₃	#386	1	1	yes	characteristic
109	C₂²×C₄₃	#417	1	1	yes	characteristic
110	C₂²×C₄₃	#418	1	1	yes	characteristic
111	C₄×C₄₃	—	2	1	no	—
112	C₄×C₄₃	—	2	2	no	—
113	C₄×C₄₃	—	4	2	no	—
114	C₄×C₄₃	—	4	2	no	—
115	C₄×C₄₃	#456	1	2	yes	—
116	C₄×C₄₃	#468	1	2	yes	—
117	C₄×C₄₃	#469	1	2	yes	—
118	Dic₄₃	—	4	4	no	—
119	Dic₄₃	—	8	2	no	—
120	#2983	—	43	1	no	—
121	#2546	—	43	1	no	—
122	#1801	D₄₃	1	1	yes	characteristic
123	#1546	—	43	2	no	—
124	#1303	—	43	2	no	—
125	C₂×C₄₃	—	2	1	no	—
126	C₂×C₄₃	—	2	1	no	—
127	C₂×C₄₃	#1886	1	1	yes	characteristic
128	C₂×C₄₃	#1895	1	1	yes	characteristic
129	C₂×C₄₃	#1915	1	1	yes	characteristic
130	C₂×C₄⋊Q₈	—	43	1	no	—
131	C₂×C₄⋊Q₈	—	86	1	no	—
132	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
133	#446	—	86	4	no	—
134	#432	—	86	2	no	—
135	#431	—	43	2	no	—
136	#423	C₂×D₄₃	1	2	yes	—
137	C₂×#101	—	2	1	no	—
138	#398	—	43	4	no	—
139	#391	—	86	1	no	—
140	#389	—	86	2	no	—
141	C₄×C₄⋊C₄	—	43	1	no	—
142	#343	—	2	1	no	—
143	#332	—	86	4	no	—
144	C₄₃	#9402	1	1	yes	characteristic, complemented, Sylow
145	C₂²×Q₈	—	86	1	no	—
146	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
147	C₂×M₁₆	—	2	2	no	—
148	C₄⋊Q₈	—	86	2	no	—
149	C₄⋊Q₈	—	86	2	no	—
150	C₄⋊Q₈	—	172	4	no	—
151	C₄×Q₈	—	2	2	no	—
152	C₄×Q₈	—	2	2	no	—
153	C₂×C₄⋊C₄	—	43	2	no	—
154	C₂×C₄⋊C₄	—	86	1	no	—
155	C₂×C₄⋊C₄	—	86	4	no	—
156	C₂×C₄⋊C₄	—	86	1	no	—
157	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
158	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
159	C₂×C₄²	—	86	1	no	—
160	C₂×C₄²	D₁₇₂	1	2	yes	—
161	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	43	4	no	—
165	C₄⋊C₈	—	86	4	no	—
166	#101	—	4	2	no	—
167	C₂²⋊C₈	—	86	2	no	—
168	#97	—	86	4	no	—
169	C₄×C₈	—	86	2	no	—
170	#95	—	43	2	no	—
171	#95	—	86	4	no	—
172	C₂×Q₈	—	2	2	no	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	—	2	1	no	—
175	C₂×Q₈	—	2	1	no	—
176	C₂×Q₈	—	172	2	no	—
177	C₂×Q₈	—	172	2	no	—
178	C₂×Q₈	—	172	1	no	—
179	C₂×Q₈	—	172	1	no	—
180	C₂²×C₄	—	86	2	no	—
181	C₂²×C₄	—	86	2	no	—
182	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
183	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
184	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
185	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
187	M₁₆	—	4	2	no	—
188	M₁₆	—	4	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	86	4	no	—
191	C₄⋊C₄	—	2	4	no	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	86	4	no	—
194	C₄⋊C₄	—	86	4	no	—
195	C₄⋊C₄	—	172	8	no	—
196	C₄⋊C₄	—	172	1	no	—
197	C₄⋊C₄	—	172	1	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	172	2	no	—
201	C₄²	D₄×D₄₃	1	2	yes	—
202	C₄²	#10621900	1	2	yes	—
203	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
204	Q₈	—	4	2	no	—
205	Q₈	—	4	2	no	—
206	Q₈	—	344	2	no	—
207	Q₈	—	344	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	86	4	no	—
216	C₂×C₄	—	172	2	no	—
217	C₂×C₄	—	172	2	no	—
218	C₂×C₄	—	172	2	no	—
219	C₂×C₄	—	172	2	no	—
220	C₂×C₄	—	172	2	no	—
221	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
222	C₂×C₄	#13063295	1	1	yes	characteristic
223	C₂×C₄	#13063297	1	2	yes	—
224	C₂×C₄	#13063309	1	1	yes	characteristic
225	C₂×C₄	#13063350	1	2	yes	—
226	C₂×C₄	#13063351	1	1	yes	characteristic
227	C₂×C₄	#13063356	1	1	yes	characteristic
228	C₈	—	8	2	no	—
229	C₈	—	172	4	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	2	1	no	—
232	C₂²	#14582776	1	1	yes	characteristic
233	C₂²	#14582898	1	1	yes	characteristic
234	C₂²	#14582903	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	2	no	—
237	C₄	—	4	2	no	—
238	C₄	—	4	2	no	—
239	C₄	—	344	2	no	—
240	C₄	—	172	4	no	—
241	C₄	#14583084	1	2	yes	—
242	C₄	#14583147	1	2	yes	—
243	C₄	#14583150	1	2	yes	—
244	C₂	—	2	1	no	—
245	C₂	—	2	1	no	—
246	C₂	#19134986	1	1	yes	characteristic
247	C₂	#19135031	1	1	yes	characteristic
248	C₂	#19135145	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19143680

C₂

yes

maximal, characteristic

#19139580

C₂

yes

maximal, characteristic

#19133268

C₂

yes

maximal

#19132496

C₂

yes

maximal

C₄₃×#1801

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

—

—

—

C₂²

yes

—

#14582829

C₄

yes

—

#14582804

—

#14582797

—

C₄×C₄⋊Dic₄₃

C₂²

yes

characteristic

#14582646

—

C₂×C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₄₃×#423

C₂²

yes

—

C₂×#101×C₄₃

—

C₄₃×#343

—

C₂²×Dic₈₆

—

#13063325

—

#13063325

—

#13063323

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₄₃⋊#95

—

C₄₃⋊#95

C₂×C₄

yes

—

C₂²×Q₈×C₄₃

D₄

yes

characteristic

C₂×M₁₆×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

#101×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

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

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

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

—

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

#120

yes

characteristic

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

#123

yes

characteristic

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

100

C₂×Dic₄₃

—

101

Dic₈₆

—

102

Dic₈₆

—

103

C₈×C₄₃

—

104

C₄₃⋊C₈

—

105

#9402

—

maximal, Sylow

106

C₂²×C₄₃

—

107

C₂²×C₄₃

—

108

C₂²×C₄₃

#386

yes

characteristic

109

C₂²×C₄₃

#417

yes

characteristic

110

C₂²×C₄₃

#418

yes

characteristic

111

C₄×C₄₃

—

112

C₄×C₄₃

—

113

C₄×C₄₃

—

114

C₄×C₄₃

—

115

C₄×C₄₃

#456

yes

—

116

C₄×C₄₃

#468

yes

—

117

C₄×C₄₃

#469

yes

—

118

Dic₄₃

—

119

Dic₄₃

—

120

#2983

—

121

#2546

—

122

#1801

D₄₃

yes

characteristic

123

#1546

—

124

#1303

—

125

C₂×C₄₃

—

126

C₂×C₄₃

—

127

C₂×C₄₃

#1886

yes

characteristic

128

C₂×C₄₃

#1895

yes

characteristic

129

C₂×C₄₃

#1915

yes

characteristic

130

C₂×C₄⋊Q₈

—

131

C₂×C₄⋊Q₈

—

132

C₂×C₄×Q₈

C₂×D₄₃

yes

characteristic

133

#446

—

134

#432

—

135

#431

—

136

#423

C₂×D₄₃

yes

—

137

C₂×#101

—

138

#398

—

139

#391

—

140

#389

—

141

C₄×C₄⋊C₄

—

142

#343

—

143

#332

—

144

C₄₃

#9402

yes

characteristic, complemented, Sylow

145

C₂²×Q₈

—

146

C₂²×Q₈

C₂²⋊D₄₃

yes

characteristic

147

C₂×M₁₆

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

—

172

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

C₄×D₄₃

yes

—

158

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

characteristic

159

C₂×C₄²

—

160

C₂×C₄²

D₁₇₂

yes

—

161

C₂×C₄²

C₂²×D₄₃

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#101

—

167

C₂²⋊C₈

—

168

#97

—

169

C₄×C₈

—

170

#95

—

171

#95

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

172

—

177

C₂×Q₈

—

172

—

178

C₂×Q₈

—

172

—

179

C₂×Q₈

—

172

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

183

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

184

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

185

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

186

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

187

M₁₆

—

188

M₁₆

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

172

—

196

C₄⋊C₄

—

172

—

197

C₄⋊C₄

—

172

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

172

—

201

C₄²

D₄×D₄₃

yes

—

202

C₄²

#10621900

yes

—

203

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

204

Q₈

—

205

Q₈

—

206

Q₈

—

344

—

207

Q₈

—

344

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

172

—

217

C₂×C₄

—

172

—

218

C₂×C₄

—

172

—

219

C₂×C₄

—

172

—

220

C₂×C₄

—

172

—

221

C₂×C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

222

C₂×C₄

#13063295

yes

characteristic

223

C₂×C₄

#13063297

yes

—

224

C₂×C₄

#13063309

yes

characteristic

225

C₂×C₄

#13063350

yes

—

226

C₂×C₄

#13063351

yes

characteristic

227

C₂×C₄

#13063356

yes

characteristic

228

C₈

—

229

C₈

—

172

—

230

C₂²

—

231

C₂²

—

232

C₂²

#14582776

yes

characteristic

233

C₂²

#14582898

yes

characteristic

234

C₂²

#14582903

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

344

—

240

C₄

—

172

—

241

C₄

#14583084

yes

—

242

C₄

#14583147

yes

—

243

C₄

#14583150

yes

—

244

C₂

—

245

C₂

—

246

C₂

#19134986

yes

characteristic

247

C₂

#19135031

yes

characteristic

248

C₂

#19135145

yes

characteristic

	subgroup	G/H
center	C₂²	#14582776
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1801	C₂
socle	C₂²×C₄₃	#386
prime radical	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1801	D₄₃
hypocenter	C₄₃	#9402
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#14582776

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1801

C₂

socle

C₂²×C₄₃

#386

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 ◁ #1801

N	H ≅ G/N	type
144. C₄₃	#9402	semidirect

H ≅ G/N

type

144. C₄₃

#9402

semidirect

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

subgroup	index
#19143680	2
#19139580	2
#19133268	2
#19132496	2
C₄₃×#1801	2
#9402	43

subgroup

index

C₄₃×#1801

Subgroups — #24994005

Conjugacy classes of subgroups

Complements

Maximal subgroups