Group #24989519 — subgroups

Subgroups — #24989519

Order 11008.

398 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 137 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	#19134591	C₂	1	1	yes	maximal, characteristic
3	#19133350	C₂	1	2	yes	maximal
4	#19132469	C₂	1	2	yes	maximal
5	C₄₃×#1801	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₄₃⋊C₈	—	2	2	no	—
7	Q₈×C₄₃⋊C₈	—	2	2	no	—
8	#14582923	C₂²	1	2	yes	—
9	C₂×C₄⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
10	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#13063244	—	2	1	no	—
12	C₂×C₄×C₄₃⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	#14582668	—	2	1	no	—
15	#14582649	—	2	2	no	—
16	#14582649	—	2	2	no	—
17	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#423	C₂²	1	2	yes	—
19	C₂×#101×C₄₃	—	2	1	no	—
20	C₄₃×#343	—	2	1	no	—
21	C₂×#10621877	—	2	2	no	—
22	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
24	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
26	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
27	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
28	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
29	#13063244	—	4	2	no	—
30	C₄×C₄₃⋊C₈	—	2	2	no	—
31	C₄×C₄₃⋊C₈	—	2	2	no	—
32	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
33	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
34	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
35	C₂×M₁₆×C₄₃	—	2	2	no	—
36	C₄×Q₈×C₄₃	—	2	2	no	—
37	C₄×Q₈×C₄₃	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₄₃	Q₈	1	2	yes	—
40	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₄₃	—	2	2	no	—
43	C₄⋊C₈×C₄₃	—	2	2	no	—
44	#101×C₄₃	—	4	2	no	—
45	C₂×Q₈×C₄₃	—	2	2	no	—
46	C₂×Q₈×C₄₃	—	2	2	no	—
47	C₂×Q₈×C₄₃	SD₁₆	1	2	yes	—
48	C₂×Q₈×C₄₃	SD₁₆	1	2	yes	—
49	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
51	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
54	M₁₆×C₄₃	—	4	2	no	—
55	M₁₆×C₄₃	—	4	2	no	—
56	C₂×C₈×C₄₃	—	4	2	no	—
57	C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₄⋊C₄×C₄₃	—	2	4	no	—
59	C₄²×C₄₃	—	2	2	no	—
60	C₄²×C₄₃	—	2	2	no	—
61	C₄²×C₄₃	C₂×D₄	1	2	yes	—
62	C₄²×C₄₃	#41	1	2	yes	—
63	#10621877	—	4	2	no	—
64	#10621877	—	4	2	no	—
65	C₂×C₄₃⋊C₈	—	2	2	no	—
66	C₂×C₄₃⋊C₈	—	2	2	no	—
67	C₂×C₄₃⋊C₈	—	4	1	no	—
68	C₂×C₄₃⋊C₈	—	4	2	no	—
69	C₂×C₄₃⋊C₈	—	4	2	no	—
70	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
72	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
73	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
74	Q₈×C₄₃	—	2	4	no	—
75	Q₈×C₄₃	—	2	4	no	—
76	C₂×C₄×C₄₃	—	2	2	no	—
77	C₂×C₄×C₄₃	—	2	2	no	—
78	C₂×C₄×C₄₃	—	2	1	no	—
79	C₂×C₄×C₄₃	—	2	1	no	—
80	C₂×C₄×C₄₃	—	2	2	no	—
81	C₂×C₄×C₄₃	—	4	1	no	—
82	C₂×C₄×C₄₃	—	4	2	no	—
83	C₂×C₄×C₄₃	#106	1	4	yes	—
84	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
86	C₂×C₄×C₄₃	#121	1	2	yes	—
87	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
88	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
89	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
90	C₂×C₄×C₄₃	#135	1	2	yes	—
91	C₈×C₄₃	—	8	2	no	—
92	C₄₃⋊C₈	—	2	1	no	—
93	C₄₃⋊C₈	—	2	2	no	—
94	C₄₃⋊C₈	—	4	2	no	—
95	C₄₃⋊C₈	—	8	2	no	—
96	C₄₃⋊C₈	#101	1	2	yes	complemented
97	#8615	—	43	1	no	maximal, Sylow
98	C₂²×C₄₃	—	2	1	no	—
99	C₂²×C₄₃	—	2	1	no	—
100	C₂²×C₄₃	#380	1	1	yes	characteristic
101	C₂²×C₄₃	C₂×#106	1	1	yes	characteristic
102	C₂²×C₄₃	#427	1	1	yes	characteristic
103	C₄×C₄₃	—	2	1	no	—
104	C₄×C₄₃	—	2	4	no	—
105	C₄×C₄₃	—	2	2	no	—
106	C₄×C₄₃	—	4	2	no	—
107	C₄×C₄₃	C₂×#101	1	1	yes	characteristic
108	C₄×C₄₃	#413	1	1	yes	characteristic
109	C₄×C₄₃	#465	1	2	yes	—
110	C₄×C₄₃	#465	1	2	yes	—
111	C₂×C₈×Q₈	—	43	1	no	—
112	#1801	—	43	1	no	—
113	#1801	D₄₃	1	1	yes	characteristic
114	#1566	—	43	2	no	—
115	#1292	—	43	2	no	—
116	C₂×C₄₃	—	2	1	no	—
117	C₂×C₄₃	—	2	1	no	—
118	C₂×C₄₃	#1801	1	1	yes	characteristic
119	C₂×C₄₃	#1807	1	1	yes	characteristic
120	C₂×C₄₃	#1813	1	1	yes	characteristic
121	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
122	C₈×Q₈	—	86	2	no	—
123	C₈×Q₈	—	86	2	no	—
124	#423	—	43	2	no	—
125	#423	C₂×D₄₃	1	2	yes	—
126	C₂×C₄⋊C₈	—	43	1	no	—
127	C₂×C₄⋊C₈	—	43	2	no	—
128	C₂×#101	—	2	1	no	—
129	C₂×#101	—	86	1	no	—
130	C₂×C₄×C₈	—	43	1	no	—
131	C₂×C₄×C₈	—	43	2	no	—
132	#343	—	2	1	no	—
133	#343	—	86	1	no	—
134	#334	—	86	2	no	—
135	#334	—	86	2	no	—
136	C₄₃	#8615	1	1	yes	characteristic, complemented, Sylow
137	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
138	C₂×M₁₆	—	2	2	no	—
139	C₂×M₁₆	—	86	2	no	—
140	C₂²×C₈	—	43	1	no	—
141	C₂²×C₈	—	43	1	no	—
142	C₂²×C₈	—	43	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₂×C₄⋊C₄	Dic₈₆	1	2	yes	—
146	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
147	C₂×C₄²	C₄×D₄₃	1	2	yes	—
148	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
149	C₄⋊C₈	—	2	2	no	—
150	C₄⋊C₈	—	2	2	no	—
151	C₄⋊C₈	—	86	4	no	—
152	C₄⋊C₈	—	86	2	no	—
153	C₄⋊C₈	—	86	2	no	—
154	C₄⋊C₈	—	86	2	no	—
155	#101	—	4	2	no	—
156	#101	—	172	2	no	—
157	C₄×C₈	—	43	2	no	—
158	C₄×C₈	—	43	2	no	—
159	C₄×C₈	—	86	2	no	—
160	C₄×C₈	—	86	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	2	2	no	—
163	C₂×Q₈	#10621883	1	2	yes	—
164	C₂×Q₈	#10621884	1	2	yes	—
165	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
166	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
167	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
169	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
170	M₁₆	—	4	2	no	—
171	M₁₆	—	4	2	no	—
172	M₁₆	—	172	2	no	—
173	M₁₆	—	172	2	no	—
174	C₂×C₈	—	4	2	no	—
175	C₂×C₈	—	43	1	no	—
176	C₂×C₈	—	43	1	no	—
177	C₂×C₈	—	43	2	no	—
178	C₂×C₈	—	86	2	no	—
179	C₂×C₈	—	86	2	no	—
180	C₂×C₈	—	172	1	no	—
181	C₂×C₈	—	172	2	no	—
182	C₂×C₈	—	172	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	2	2	no	—
187	C₄²	D₄×D₄₃	1	2	yes	—
188	C₄²	#10621900	1	2	yes	—
189	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
190	Q₈	—	2	4	no	—
191	Q₈	—	2	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	#13063256	1	4	yes	—
200	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
201	C₂×C₄	#13063281	1	1	yes	characteristic
202	C₂×C₄	#13063297	1	2	yes	—
203	C₂×C₄	#13063302	1	2	yes	—
204	C₂×C₄	C₂×#10621884	1	1	yes	characteristic
205	C₂×C₄	C₂×#10621883	1	1	yes	characteristic
206	C₂×C₄	#13063345	1	2	yes	—
207	C₈	—	8	2	no	—
208	C₈	—	43	2	no	—
209	C₈	—	86	1	no	—
210	C₈	—	86	2	no	—
211	C₈	—	344	2	no	—
212	C₈	—	172	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	#14582757	1	1	yes	characteristic
216	C₂²	C₂×#13063256	1	1	yes	characteristic
217	C₂²	#14582935	1	1	yes	characteristic
218	C₄	—	2	1	no	—
219	C₄	—	2	4	no	—
220	C₄	—	2	2	no	—
221	C₄	—	4	2	no	—
222	C₄	#101×D₄₃	1	1	yes	characteristic
223	C₄	#14582882	1	1	yes	characteristic
224	C₄	#14583126	1	2	yes	—
225	C₄	#14583130	1	2	yes	—
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	#19134589	1	1	yes	characteristic
229	C₂	#19134618	1	1	yes	characteristic
230	C₂	#19134643	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic

#19134591

C₂

yes

maximal, characteristic

#19133350

C₂

yes

maximal

#19132469

C₂

yes

maximal

C₄₃×#1801

C₂

yes

maximal, characteristic

Q₈×C₄₃⋊C₈

—

Q₈×C₄₃⋊C₈

—

#14582923

C₂²

yes

—

C₂×C₄⋊(C₄₃⋊C₈)

C₄

yes

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂×#13063244

—

C₂×C₄×C₄₃⋊C₈

C₄

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

—

—

C₂×C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₄₃×#423

C₂²

yes

—

C₂×#101×C₄₃

—

C₄₃×#343

—

C₂×#10621877

—

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)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063244

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₂²×Q₈×C₄₃

D₄

yes

characteristic

C₂×M₁₆×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₂×C₄⋊C₄×C₄₃

Q₈

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

#101×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

SD₁₆

yes

—

C₂×Q₈×C₄₃

SD₁₆

yes

—

C₂²×C₄×C₄₃

C₄⋊C₄

yes

—

C₂²×C₄×C₄₃

C₄⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×Q₈

yes

characteristic

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

—

#10621877

—

#10621877

—

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×C₄⋊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

#106

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

#135

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

100

C₂²×C₄₃

#380

yes

characteristic

101

C₂²×C₄₃

C₂×#106

yes

characteristic

102

C₂²×C₄₃

#427

yes

characteristic

103

C₄×C₄₃

—

104

C₄×C₄₃

—

105

C₄×C₄₃

—

106

C₄×C₄₃

—

107

C₄×C₄₃

C₂×#101

yes

characteristic

108

C₄×C₄₃

#413

yes

characteristic

109

C₄×C₄₃

#465

yes

—

110

C₄×C₄₃

#465

yes

—

111

C₂×C₈×Q₈

—

112

#1801

—

113

#1801

D₄₃

yes

characteristic

114

#1566

—

115

#1292

—

116

C₂×C₄₃

—

117

C₂×C₄₃

—

118

C₂×C₄₃

#1801

yes

characteristic

119

C₂×C₄₃

#1807

yes

characteristic

120

C₂×C₄₃

#1813

yes

characteristic

121

C₂×C₄×Q₈

C₂×D₄₃

yes

characteristic

122

C₈×Q₈

—

123

C₈×Q₈

—

124

#423

—

125

#423

C₂×D₄₃

yes

—

126

C₂×C₄⋊C₈

—

127

C₂×C₄⋊C₈

—

128

C₂×#101

—

129

C₂×#101

—

130

C₂×C₄×C₈

—

131

C₂×C₄×C₈

—

132

#343

—

133

#343

—

134

#334

—

135

#334

—

136

C₄₃

#8615

yes

characteristic, complemented, Sylow

137

C₂²×Q₈

C₂²⋊D₄₃

yes

characteristic

138

C₂×M₁₆

—

139

C₂×M₁₆

—

140

C₂²×C₈

—

141

C₂²×C₈

—

142

C₂²×C₈

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

C₂×C₄⋊C₄

Dic₈₆

yes

—

146

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

characteristic

147

C₂×C₄²

C₄×D₄₃

yes

—

148

C₂×C₄²

C₂²×D₄₃

yes

characteristic

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

#101

—

156

#101

—

172

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

#10621883

yes

—

164

C₂×Q₈

#10621884

yes

—

165

C₂²×C₄

Dic₄₃⋊C₄

yes

—

166

C₂²×C₄

Dic₄₃⋊C₄

yes

—

167

C₂²×C₄

C₂×Dic₈₆

yes

characteristic

168

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

169

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

170

M₁₆

—

171

M₁₆

—

172

M₁₆

—

172

—

173

M₁₆

—

172

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

172

—

181

C₂×C₈

—

172

—

182

C₂×C₈

—

172

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄²

—

186

C₄²

—

187

C₄²

D₄×D₄₃

yes

—

188

C₄²

#10621900

yes

—

189

C₂³

C₂×Dic₄₃⋊C₄

yes

characteristic

190

Q₈

—

191

Q₈

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

#13063256

yes

—

200

C₂×C₄

C₂²⋊C₄×D₄₃

yes

characteristic

201

C₂×C₄

#13063281

yes

characteristic

202

C₂×C₄

#13063297

yes

—

203

C₂×C₄

#13063302

yes

—

204

C₂×C₄

C₂×#10621884

yes

characteristic

205

C₂×C₄

C₂×#10621883

yes

characteristic

206

C₂×C₄

#13063345

yes

—

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

—

211

C₈

—

344

—

212

C₈

—

172

—

213

C₂²

—

214

C₂²

—

215

C₂²

#14582757

yes

characteristic

216

C₂²

C₂×#13063256

yes

characteristic

217

C₂²

#14582935

yes

characteristic

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

#101×D₄₃

yes

characteristic

223

C₄

#14582882

yes

characteristic

224

C₄

#14583126

yes

—

225

C₄

#14583130

yes

—

226

C₂

—

227

C₂

—

228

C₂

#19134589

yes

characteristic

229

C₂

#19134618

yes

characteristic

230

C₂

#19134643

yes

characteristic

	subgroup	G/H
center	C₂²	#14582757
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1801	C₂
socle	C₂²×C₄₃	#380
prime radical	C₂³×C₄₃	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1801	D₄₃
hypocenter	C₄₃	#8615
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#14582757

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1801

C₂

socle

C₂²×C₄₃

#380

prime radical

C₂³×C₄₃

C₂×C₄⋊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
96. C₄₃⋊C₈	#101	semidirect
136. C₄₃	#8615	semidirect

H ≅ G/N

type

96. C₄₃⋊C₈

#101

semidirect

136. C₄₃

#8615

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
#19134591	2
#19133350	2
#19132469	2
C₄₃×#1801	2
#8615	43

subgroup

index

C₂×Q₈×C₄₃⋊C₈

C₄₃×#1801

Subgroups — #24989519

Conjugacy classes of subgroups

Complements

Maximal subgroups