Group #24987163 — subgroups

Subgroups — #24987163

Order 11008.

454 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 177 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×Q₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063244	C₂	1	1	yes	maximal, characteristic
3	#19132876	C₂	1	2	yes	maximal
4	#19132444	C₂	1	2	yes	maximal
5	C₄₃×#1461	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₄₃⋊C₈	—	2	2	no	—
7	Q₈×C₄₃⋊C₈	—	2	2	no	—
8	C₂×C₄⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
9	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×#13063244	C₄	1	2	yes	—
11	C₄×#10621877	C₂²	1	2	yes	—
12	C₂×C₄×C₄₃⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	#14582668	C₄	1	2	yes	—
15	#14582621	—	2	2	no	—
16	C₈×C₄₃⋊C₈	—	2	2	no	—
17	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#431	C₂²	1	2	yes	—
19	C₄₃×#324	C₄	1	4	yes	—
20	C₂×#10621877	C₂×C₄	1	4	yes	—
21	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
23	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
25	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
26	#13063244	C₈	1	8	yes	complemented
27	#13063236	—	2	2	no	—
28	C₄×C₄₃⋊C₈	—	2	2	no	—
29	C₄×C₄₃⋊C₈	—	2	2	no	—
30	C₄×C₄₃⋊C₈	—	2	2	no	—
31	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
32	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
33	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
34	C₄×Q₈×C₄₃	—	2	2	no	—
35	C₄×Q₈×C₄₃	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₄₃	—	2	2	no	—
41	C₂²⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
42	C₄×C₈×C₄₃	—	2	2	no	—
43	C₂×Q₈×C₄₃	—	2	2	no	—
44	C₂×Q₈×C₄₃	—	2	2	no	—
45	C₂×Q₈×C₄₃	C₂×C₈	1	4	yes	—
46	C₂²×C₄×C₄₃	C₄²	1	2	yes	—
47	C₂²×C₄×C₄₃	C₄²	1	2	yes	—
48	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₈×C₄₃	—	2	4	no	—
52	C₄⋊C₄×C₄₃	—	2	2	no	—
53	C₄⋊C₄×C₄₃	—	2	4	no	—
54	C₄²×C₄₃	—	2	2	no	—
55	C₄²×C₄₃	—	2	2	no	—
56	C₄²×C₄₃	C₂×D₄	1	2	yes	—
57	C₄²×C₄₃	#41	1	2	yes	—
58	#10621877	—	2	4	no	—
59	#10621877	C₂×C₈	1	8	yes	—
60	C₂×C₄₃⋊C₈	—	2	4	no	—
61	C₂×C₄₃⋊C₈	—	2	2	no	—
62	C₂×C₄₃⋊C₈	—	2	2	no	—
63	C₂×C₄₃⋊C₈	—	4	1	no	—
64	C₂×C₄₃⋊C₈	—	4	2	no	—
65	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
67	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
68	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
69	Q₈×C₄₃	—	2	8	no	—
70	C₂×C₄×C₄₃	—	2	2	no	—
71	C₂×C₄×C₄₃	—	2	2	no	—
72	C₂×C₄×C₄₃	—	2	1	no	—
73	C₂×C₄×C₄₃	—	2	1	no	—
74	C₂×C₄×C₄₃	—	2	2	no	—
75	C₂×C₄×C₄₃	—	4	1	no	—
76	C₂×C₄×C₄₃	—	4	2	no	—
77	C₂×C₄×C₄₃	C₄×C₈	1	4	yes	—
78	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
80	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
81	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
83	C₂×C₄×C₄₃	#131	1	2	yes	—
84	C₈×C₄₃	—	4	4	no	—
85	C₄₃⋊C₈	—	2	1	no	—
86	C₄₃⋊C₈	—	2	2	no	—
87	C₄₃⋊C₈	—	2	8	no	—
88	C₄₃⋊C₈	—	4	2	no	—
89	C₄₃⋊C₈	#101	1	2	yes	complemented
90	C₈×#101	—	43	1	no	maximal, Sylow
91	C₂²×C₄₃	—	2	1	no	—
92	C₂²×C₄₃	—	2	1	no	—
93	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
95	C₂²×C₄₃	#405	1	1	yes	characteristic
96	C₄×C₄₃	—	2	4	no	—
97	C₄×C₄₃	—	2	1	no	—
98	C₄×C₄₃	—	2	2	no	—
99	C₄×C₄₃	—	4	2	no	—
100	C₄×C₄₃	C₂×#101	1	1	yes	characteristic
101	C₄×C₄₃	#413	1	1	yes	characteristic
102	C₄×C₄₃	C₈×D₄	1	4	yes	—
103	C₂×C₈×Q₈	—	43	1	no	—
104	C₄×#101	—	43	1	no	—
105	#1461	D₄₃	1	1	yes	characteristic
106	C₈×M₁₆	—	43	2	no	—
107	#1283	—	43	2	no	—
108	C₂×C₄₃	—	2	1	no	—
109	C₂×C₄₃	—	2	1	no	—
110	C₂×C₄₃	C₈×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄₃	C₄×#101	1	1	yes	characteristic
112	C₂×C₄₃	#1757	1	1	yes	characteristic
113	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
114	C₈×Q₈	—	86	2	no	—
115	C₈×Q₈	—	86	2	no	—
116	#431	C₂×D₄₃	1	2	yes	—
117	C₂×C₄⋊C₈	—	43	1	no	—
118	C₂×C₄⋊C₈	—	43	2	no	—
119	C₂×#101	—	43	2	no	—
120	C₄×M₁₆	—	43	2	no	—
121	C₂×C₄×C₈	—	43	1	no	—
122	C₂×C₄×C₈	—	43	2	no	—
123	#343	—	43	2	no	—
124	#324	Dic₄₃	1	4	yes	—
125	#322	—	86	2	no	—
126	C₈²	—	86	2	no	—
127	C₄₃	C₈×#101	1	1	yes	characteristic, complemented, Sylow
128	C₂²×Q₈	C₄×D₄₃	1	1	yes	characteristic
129	C₂×M₁₆	—	43	4	no	—
130	C₂²×C₈	—	43	1	no	—
131	C₂²×C₈	—	43	1	no	—
132	C₂²×C₈	—	43	2	no	—
133	C₄×Q₈	—	2	2	no	—
134	C₄×Q₈	—	2	2	no	—
135	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
136	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
137	C₂×C₄²	C₄×D₄₃	1	2	yes	—
138	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
139	C₄⋊C₈	—	2	2	no	—
140	C₄⋊C₈	—	86	4	no	—
141	C₄⋊C₈	—	86	2	no	—
142	#101	—	43	8	no	—
143	C₂²⋊C₈	C₂×Dic₄₃	1	4	yes	—
144	#97	—	86	2	no	—
145	C₄×C₈	—	2	2	no	—
146	C₄×C₈	—	43	2	no	—
147	C₄×C₈	—	43	2	no	—
148	C₄×C₈	—	86	2	no	—
149	C₄×C₈	—	86	2	no	—
150	C₄×C₈	—	86	2	no	—
151	C₂×Q₈	—	2	2	no	—
152	C₂×Q₈	—	2	2	no	—
153	C₂×Q₈	C₈×D₄₃	1	4	yes	—
154	C₂²×C₄	C₄×Dic₄₃	1	2	yes	—
155	C₂²×C₄	C₄×Dic₄₃	1	2	yes	—
156	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
158	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
159	M₁₆	—	43	8	no	—
160	M₁₆	—	86	4	no	—
161	C₂×C₈	—	2	4	no	—
162	C₂×C₈	—	43	1	no	—
163	C₂×C₈	—	43	1	no	—
164	C₂×C₈	—	43	2	no	—
165	C₂×C₈	—	86	2	no	—
166	C₂×C₈	—	86	4	no	—
167	C₂×C₈	—	86	2	no	—
168	C₂×C₈	—	172	1	no	—
169	C₂×C₈	—	172	2	no	—
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	2	4	no	—
172	C₄²	—	2	2	no	—
173	C₄²	—	2	2	no	—
174	C₄²	D₄×D₄₃	1	2	yes	—
175	C₄²	#10621900	1	2	yes	—
176	C₂³	C₂×C₄×Dic₄₃	1	1	yes	characteristic
177	Q₈	—	2	8	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	4	1	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	C₈×Dic₄₃	1	4	yes	—
186	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
187	C₂×C₄	#13063281	1	1	yes	characteristic
188	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
189	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
190	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
191	C₂×C₄	#13063333	1	2	yes	—
192	C₈	—	4	4	no	—
193	C₈	—	43	2	no	—
194	C₈	—	86	1	no	—
195	C₈	—	86	2	no	—
196	C₈	—	86	8	no	—
197	C₈	—	172	2	no	—
198	C₂²	—	2	1	no	—
199	C₂²	—	2	1	no	—
200	C₂²	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
201	C₂²	C₂×C₈×Dic₄₃	1	1	yes	characteristic
202	C₂²	#14582857	1	1	yes	characteristic
203	C₄	—	2	4	no	—
204	C₄	—	2	1	no	—
205	C₄	—	2	2	no	—
206	C₄	—	4	2	no	—
207	C₄	#101×D₄₃	1	1	yes	characteristic
208	C₄	#14582882	1	1	yes	characteristic
209	C₄	(C₂²⋊D₄₃)⋊C₈	1	4	yes	—
210	C₂	—	2	1	no	—
211	C₂	—	2	1	no	—
212	C₂	#19134369	1	1	yes	characteristic
213	C₂	#101×Dic₄₃	1	1	yes	characteristic
214	C₂	#19134397	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic

C₄×#13063244

C₂

yes

maximal, characteristic

#19132876

C₂

yes

maximal

#19132444

C₂

yes

maximal

C₄₃×#1461

C₂

yes

maximal, characteristic

Q₈×C₄₃⋊C₈

—

Q₈×C₄₃⋊C₈

—

C₂×C₄⋊(C₄₃⋊C₈)

C₄

yes

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂×#13063244

C₄

yes

—

C₄×#10621877

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₄

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#14582668

C₄

yes

—

#14582621

—

C₈×C₄₃⋊C₈

—

C₂×C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₄₃×#431

C₂²

yes

—

C₄₃×#324

C₄

yes

—

C₂×#10621877

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063244

C₈

yes

complemented

#13063236

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₂²×Q₈×C₄₃

C₂×C₄

yes

characteristic

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₈

yes

—

C₂²×C₄×C₄₃

C₄²

yes

—

C₂²×C₄×C₄₃

C₄²

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

#10621877

—

#10621877

C₂×C₈

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₂³×C₄₃

C₂×C₄²

yes

characteristic

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×C₈

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#117

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

C₂²×C₈

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

C₂×C₄×C₈

yes

characteristic

C₂²×C₄₃

#405

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

100

C₄×C₄₃

C₂×#101

yes

characteristic

101

C₄×C₄₃

#413

yes

characteristic

102

C₄×C₄₃

C₈×D₄

yes

—

103

C₂×C₈×Q₈

—

104

C₄×#101

—

105

#1461

D₄₃

yes

characteristic

106

C₈×M₁₆

—

107

#1283

—

108

C₂×C₄₃

—

109

C₂×C₄₃

—

110

C₂×C₄₃

C₈×C₂²⋊C₄

yes

characteristic

111

C₂×C₄₃

C₄×#101

yes

characteristic

112

C₂×C₄₃

#1757

yes

characteristic

113

C₂×C₄×Q₈

C₂×D₄₃

yes

characteristic

114

C₈×Q₈

—

115

C₈×Q₈

—

116

#431

C₂×D₄₃

yes

—

117

C₂×C₄⋊C₈

—

118

C₂×C₄⋊C₈

—

119

C₂×#101

—

120

C₄×M₁₆

—

121

C₂×C₄×C₈

—

122

C₂×C₄×C₈

—

123

#343

—

124

#324

Dic₄₃

yes

—

125

#322

—

126

C₈²

—

127

C₄₃

C₈×#101

yes

characteristic, complemented, Sylow

128

C₂²×Q₈

C₄×D₄₃

yes

characteristic

129

C₂×M₁₆

—

130

C₂²×C₈

—

131

C₂²×C₈

—

132

C₂²×C₈

—

133

C₄×Q₈

—

134

C₄×Q₈

—

135

C₂×C₄⋊C₄

C₄×D₄₃

yes

characteristic

136

C₂×C₄⋊C₄

C₂×Dic₄₃

yes

—

137

C₂×C₄²

C₄×D₄₃

yes

—

138

C₂×C₄²

C₂²×D₄₃

yes

characteristic

139

C₄⋊C₈

—

140

C₄⋊C₈

—

141

C₄⋊C₈

—

142

#101

—

143

C₂²⋊C₈

C₂×Dic₄₃

yes

—

144

#97

—

145

C₄×C₈

—

146

C₄×C₈

—

147

C₄×C₈

—

148

C₄×C₈

—

149

C₄×C₈

—

150

C₄×C₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

C₈×D₄₃

yes

—

154

C₂²×C₄

C₄×Dic₄₃

yes

—

155

C₂²×C₄

C₄×Dic₄₃

yes

—

156

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

157

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

158

C₂²×C₄

C₂²×Dic₄₃

yes

characteristic

159

M₁₆

—

160

M₁₆

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

172

—

169

C₂×C₈

—

172

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄²

—

173

C₄²

—

174

C₄²

D₄×D₄₃

yes

—

175

C₄²

#10621900

yes

—

176

C₂³

C₂×C₄×Dic₄₃

yes

characteristic

177

Q₈

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

C₈×Dic₄₃

yes

—

186

C₂×C₄

C₂²⋊C₄×D₄₃

yes

characteristic

187

C₂×C₄

#13063281

yes

characteristic

188

C₂×C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

189

C₂×C₄

D₄×Dic₄₃

yes

—

190

C₂×C₄

C₂×C₈×D₄₃

yes

—

191

C₂×C₄

#13063333

yes

—

192

C₈

—

193

C₈

—

194

C₈

—

195

C₈

—

196

C₈

—

197

C₈

—

172

—

198

C₂²

—

199

C₂²

—

200

C₂²

C₂²⋊C₄×Dic₄₃

yes

characteristic

201

C₂²

C₂×C₈×Dic₄₃

yes

characteristic

202

C₂²

#14582857

yes

characteristic

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

#101×D₄₃

yes

characteristic

208

C₄

#14582882

yes

characteristic

209

C₄

(C₂²⋊D₄₃)⋊C₈

yes

—

210

C₂

—

211

C₂

—

212

C₂

#19134369

yes

characteristic

213

C₂

#101×Dic₄₃

yes

characteristic

214

C₂

#19134397

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₃
commutator	C₂²×C₄₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1461	C₂
socle	C₂²×C₄₃	C₄×C₂²⋊C₄
prime radical	C₂³×C₄₃	C₂×C₄²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1461	D₄₃
hypocenter	C₄₃	C₈×#101
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1461

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₄₃

commutator

C₂²×C₄₃

C₂×C₄×C₈

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1461

C₂

socle

C₂²×C₄₃

C₄×C₂²⋊C₄

prime radical

C₂³×C₄₃

C₂×C₄²

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1461

N	H ≅ G/N	type
26. #13063244	C₈	semidirect
89. C₄₃⋊C₈	#101	semidirect
127. C₄₃	C₈×#101	semidirect

H ≅ G/N

type

26. #13063244

C₈

semidirect

89. C₄₃⋊C₈

#101

semidirect

127. C₄₃

C₈×#101

semidirect

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

subgroup	index
C₂×Q₈×C₄₃⋊C₈	2
C₄×#13063244	2
#19132876	2
#19132444	2
C₄₃×#1461	2
C₈×#101	43

subgroup

index

C₂×Q₈×C₄₃⋊C₈

C₄₃×#1461

Subgroups — #24987163

Conjugacy classes of subgroups

Complements

Maximal subgroups