Group #24991069 — subgroups

Subgroups — #24991069

Order 11008.

476 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 155 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	#19137685	C₂	1	1	yes	maximal, characteristic
2	#19135398	C₂	1	1	yes	maximal, characteristic
3	#19135354	C₂	1	2	yes	maximal
4	#19132434	C₂	1	2	yes	maximal
5	C₂×C₄₃×#333	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063259	—	2	2	no	—
7	C₂×#13063249	—	2	2	no	—
8	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	#14582806	—	2	2	no	—
10	#14582798	—	2	2	no	—
11	#14582769	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×Dic₄₃	—	2	2	no	—
13	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
14	#14582662	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
17	C₄₃×#333	C₄	1	4	yes	complemented
18	C₂²×C₄₃⋊C₈	—	2	1	no	—
19	C₂×C₄⋊Dic₄₃	—	2	1	no	—
20	C₂×C₄⋊Dic₄₃	—	2	2	no	—
21	C₂×C₄⋊Dic₄₃	—	2	2	no	—
22	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
23	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
24	C₂×C₄×Dic₄₃	—	2	2	no	—
25	C₂×C₄×Dic₄₃	—	2	2	no	—
26	#13063259	—	4	4	no	—
27	#13063249	—	4	4	no	—
28	C₄×C₄₃⋊C₈	—	2	2	no	—
29	C₄₃⋊#95	—	2	4	no	—
30	C₄₃⋊#95	—	2	2	no	—
31	C₂²×Q₈×C₄₃	D₄	1	2	yes	—
32	C₂²×C₈×C₄₃	—	2	2	no	—
33	C₄⋊Q₈×C₄₃	—	2	2	no	—
34	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
35	C₄⋊Q₈×C₄₃	Q₈	1	2	yes	—
36	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
37	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
38	C₄⋊C₈×C₄₃	—	2	2	no	—
39	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
40	C₂×Q₈×C₄₃	—	2	2	no	—
41	C₂×Q₈×C₄₃	—	4	2	no	—
42	C₂×Q₈×C₄₃	—	4	2	no	—
43	C₂×Q₈×C₄₃	C₄⋊C₄	1	4	yes	—
44	C₂²×C₄×C₄₃	—	2	2	no	—
45	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
47	C₂²×Dic₄₃	—	2	2	no	—
48	C₂²×Dic₄₃	—	2	2	no	—
49	C₂²×Dic₄₃	—	4	1	no	—
50	C₂×C₈×C₄₃	—	2	4	no	—
51	C₂×C₈×C₄₃	—	4	2	no	—
52	C₂×C₈×C₄₃	—	4	2	no	—
53	C₄⋊C₄×C₄₃	—	2	4	no	—
54	C₄⋊C₄×C₄₃	—	2	4	no	—
55	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
57	C₄²×C₄₃	#41	1	2	yes	—
58	C₄⋊Dic₄₃	—	2	2	no	—
59	C₄⋊Dic₄₃	—	2	2	no	—
60	C₄⋊Dic₄₃	—	2	2	no	—
61	C₄⋊Dic₄₃	—	4	2	no	—
62	C₄⋊Dic₄₃	—	4	2	no	—
63	C₄⋊Dic₄₃	—	4	2	no	—
64	C₄⋊Dic₄₃	—	8	2	no	—
65	C₄⋊Dic₄₃	Q₁₆	1	4	yes	—
66	C₄×Dic₄₃	—	4	2	no	—
67	C₄×Dic₄₃	—	4	2	no	—
68	C₄×Dic₄₃	—	8	2	no	—
69	C₂×C₄₃⋊C₈	—	2	2	no	—
70	C₂×C₄₃⋊C₈	—	4	1	no	—
71	C₂×C₄₃⋊C₈	—	4	1	no	—
72	C₂³×C₄₃	#120	1	1	yes	characteristic
73	Q₈×C₄₃	—	4	4	no	—
74	Q₈×C₄₃	—	8	2	no	—
75	C₂×C₄×C₄₃	—	2	1	no	—
76	C₂×C₄×C₄₃	—	2	1	no	—
77	C₂×C₄×C₄₃	—	2	4	no	—
78	C₂×C₄×C₄₃	—	4	2	no	—
79	C₂×C₄×C₄₃	—	4	2	no	—
80	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
83	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
84	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
85	C₂×C₄×C₄₃	#135	1	2	yes	—
86	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
87	C₂×C₄×C₄₃	#137	1	2	yes	—
88	C₂×Dic₄₃	—	2	4	no	—
89	C₂×Dic₄₃	—	4	2	no	—
90	C₂×Dic₄₃	—	4	2	no	—
91	C₂×Dic₄₃	—	4	2	no	—
92	C₂×Dic₄₃	—	4	2	no	—
93	C₂×Dic₄₃	—	4	2	no	—
94	C₂×Dic₄₃	—	8	2	no	—
95	C₂×Dic₄₃	—	8	1	no	—
96	C₈×C₄₃	—	4	4	no	—
97	C₄₃⋊C₈	—	4	2	no	—
98	#8929	—	43	1	no	maximal, Sylow
99	C₂²×C₄₃	#385	1	1	yes	characteristic
100	C₂²×C₄₃	#449	1	2	yes	—
101	C₂²×C₄₃	#451	1	2	yes	—
102	C₂²×C₄₃	#453	1	1	yes	characteristic
103	C₂²×C₄₃	#455	1	1	yes	characteristic
104	C₄×C₄₃	—	2	1	no	—
105	C₄×C₄₃	—	2	1	no	—
106	C₄×C₄₃	—	4	4	no	—
107	C₄×C₄₃	C₄×Q₁₆	1	2	yes	—
108	C₄×C₄₃	#440	1	2	yes	—
109	C₄×C₄₃	#477	1	2	yes	—
110	C₄×C₄₃	#479	1	2	yes	—
111	Dic₄₃	—	4	4	no	—
112	Dic₄₃	—	8	2	no	—
113	Dic₄₃	—	16	1	no	—
114	#2369	—	43	1	no	—
115	#1956	—	43	1	no	—
116	#1947	—	43	2	no	—
117	C₂×#333	D₄₃	1	1	yes	characteristic
118	#1279	—	43	2	no	—
119	C₂×C₄₃	#1624	1	1	yes	characteristic
120	C₂×C₄₃	#1633	1	1	yes	characteristic
121	C₂×C₄₃	#1644	1	2	yes	—
122	C₂×C₄₃	#1856	1	1	yes	characteristic
123	C₂×C₄₃	#1863	1	2	yes	—
124	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
125	C₂×#107	—	86	2	no	—
126	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
127	C₂×#103	—	86	2	no	—
128	C₂×C₄×C₈	—	43	1	no	—
129	#391	—	86	2	no	—
130	#389	—	86	2	no	—
131	#384	—	43	1	no	—
132	C₄×C₄⋊C₄	—	43	2	no	—
133	C₄×C₄⋊C₄	—	86	2	no	—
134	#340	—	86	2	no	—
135	#333	Dic₄₃	1	4	yes	complemented
136	C₄₃	#8929	1	1	yes	characteristic, complemented, Sylow
137	C₂²×Q₈	D₁₇₂	1	2	yes	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	—	86	1	no	—
140	C₄⋊Q₈	—	2	2	no	—
141	C₄⋊Q₈	Dic₈₆	1	2	yes	—
142	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	43	2	no	—
145	C₂×C₄⋊C₄	—	43	2	no	—
146	C₂×C₄⋊C₄	—	86	2	no	—
147	C₂×C₄⋊C₄	—	86	1	no	—
148	C₂×C₄⋊C₄	—	86	2	no	—
149	C₂×C₄²	—	86	2	no	—
150	C₂×C₄²	—	86	2	no	—
151	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
152	#107	—	172	4	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	C₂×Dic₄₃	1	4	yes	—
155	#103	—	172	4	no	—
156	C₄×C₈	—	86	2	no	—
157	#95	—	86	4	no	—
158	#95	—	86	2	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	C₄⋊Dic₄₃	1	4	yes	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	86	2	no	—
165	C₂²×C₄	—	86	2	no	—
166	C₂²×C₄	—	172	1	no	—
167	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
168	C₂²×C₄	D₄×D₄₃	1	2	yes	—
169	C₂×C₈	—	2	4	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	86	2	no	—
173	C₂×C₈	—	172	1	no	—
174	C₂×C₈	—	172	1	no	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	43	4	no	—
178	C₄⋊C₄	—	86	2	no	—
179	C₄⋊C₄	—	86	2	no	—
180	C₄⋊C₄	—	86	2	no	—
181	C₄⋊C₄	—	344	2	no	—
182	C₄⋊C₄	—	172	2	no	—
183	C₄⋊C₄	—	172	2	no	—
184	C₄⋊C₄	—	172	2	no	—
185	C₄²	—	344	2	no	—
186	C₄²	—	172	2	no	—
187	C₄²	—	172	2	no	—
188	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
189	C₄²	#10621900	1	2	yes	—
190	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
191	C₂³	#13063295	1	1	yes	characteristic
192	Q₈	—	4	4	no	—
193	Q₈	—	8	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	86	4	no	—
200	C₂×C₄	—	344	2	no	—
201	C₂×C₄	—	344	1	no	—
202	C₂×C₄	—	172	2	no	—
203	C₂×C₄	—	172	2	no	—
204	C₂×C₄	—	172	2	no	—
205	C₂×C₄	—	172	2	no	—
206	C₂×C₄	—	172	2	no	—
207	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
208	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
209	C₂×C₄	#13063302	1	2	yes	—
210	C₂×C₄	#13063309	1	1	yes	characteristic
211	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
212	C₂×C₄	#13063348	1	2	yes	—
213	C₂×C₄	#13063352	1	2	yes	—
214	C₂×C₄	#13063354	1	2	yes	—
215	C₈	—	4	4	no	—
216	C₈	—	172	2	no	—
217	C₂²	#14582774	1	1	yes	characteristic
218	C₂²	#14583047	1	2	yes	—
219	C₂²	#14583056	1	2	yes	—
220	C₂²	#14583069	1	1	yes	characteristic
221	C₂²	#14583079	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	4	no	—
225	C₄	—	344	2	no	—
226	C₄	—	172	4	no	—
227	C₄	—	688	1	no	—
228	C₄	Q₁₆×Dic₄₃	1	2	yes	—
229	C₄	#14583000	1	2	yes	—
230	C₄	#14583192	1	2	yes	—
231	C₄	#14583208	1	2	yes	—
232	C₂	#19133679	1	1	yes	characteristic
233	C₂	#19133736	1	1	yes	characteristic
234	C₂	#19133810	1	2	yes	—
235	C₂	#19134807	1	1	yes	characteristic
236	C₂	#19134851	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19137685

C₂

yes

maximal, characteristic

#19135398

C₂

yes

maximal, characteristic

#19135354

C₂

yes

maximal

#19132434

C₂

yes

maximal

C₂×C₄₃×#333

C₂

yes

maximal, characteristic

C₂×#13063259

—

C₂×#13063249

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

—

C₂²

yes

characteristic

C₄⋊C₄×Dic₄₃

—

C₄×C₄⋊Dic₄₃

C₂²

yes

—

#14582662

—

C₂×C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₄₃×#333

C₄

yes

complemented

C₂²×C₄₃⋊C₈

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

D₄

yes

—

C₂×C₄⋊Dic₄₃

D₄

yes

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

—

#13063259

—

#13063249

—

C₄×C₄₃⋊C₈

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂²×Q₈×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

C₂×C₄

yes

—

C₄⋊Q₈×C₄₃

Q₈

yes

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

C₂×C₄

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₄⋊C₄

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄²×C₄₃

#41

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

Q₁₆

yes

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#120

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⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

#123

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₁₆

yes

—

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

100

C₂²×C₄₃

#449

yes

—

101

C₂²×C₄₃

#451

yes

—

102

C₂²×C₄₃

#453

yes

characteristic

103

C₂²×C₄₃

#455

yes

characteristic

104

C₄×C₄₃

—

105

C₄×C₄₃

—

106

C₄×C₄₃

—

107

C₄×C₄₃

C₄×Q₁₆

yes

—

108

C₄×C₄₃

#440

yes

—

109

C₄×C₄₃

#477

yes

—

110

C₄×C₄₃

#479

yes

—

111

Dic₄₃

—

112

Dic₄₃

—

113

Dic₄₃

—

114

#2369

—

115

#1956

—

116

#1947

—

117

C₂×#333

D₄₃

yes

characteristic

118

#1279

—

119

C₂×C₄₃

#1624

yes

characteristic

120

C₂×C₄₃

#1633

yes

characteristic

121

C₂×C₄₃

#1644

yes

—

122

C₂×C₄₃

#1856

yes

characteristic

123

C₂×C₄₃

#1863

yes

—

124

C₂×C₄⋊Q₈

C₂×D₄₃

yes

characteristic

125

C₂×#107

—

126

C₂×C₄⋊C₈

C₂×D₄₃

yes

—

127

C₂×#103

—

128

C₂×C₄×C₈

—

129

#391

—

130

#389

—

131

#384

—

132

C₄×C₄⋊C₄

—

133

C₄×C₄⋊C₄

—

134

#340

—

135

#333

Dic₄₃

yes

complemented

136

C₄₃

#8929

yes

characteristic, complemented, Sylow

137

C₂²×Q₈

D₁₇₂

yes

—

138

C₂²×C₈

—

139

C₂²×C₈

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

Dic₈₆

yes

—

142

C₄⋊Q₈

C₂×Dic₄₃

yes

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

C₂²×D₄₃

yes

characteristic

152

#107

—

172

—

153

C₄⋊C₈

—

154

C₄⋊C₈

C₂×Dic₄₃

yes

—

155

#103

—

172

—

156

C₄×C₈

—

157

#95

—

158

#95

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

C₄⋊Dic₄₃

yes

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

172

—

167

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

168

C₂²×C₄

D₄×D₄₃

yes

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

172

—

174

C₂×C₈

—

172

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

344

—

182

C₄⋊C₄

—

172

—

183

C₄⋊C₄

—

172

—

184

C₄⋊C₄

—

172

—

185

C₄²

—

344

—

186

C₄²

—

172

—

187

C₄²

—

172

—

188

C₄²

C₂×Dic₈₆

yes

characteristic

189

C₄²

#10621900

yes

—

190

C₄²

C₂²×Dic₄₃

yes

characteristic

191

C₂³

#13063295

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

344

—

201

C₂×C₄

—

344

—

202

C₂×C₄

—

172

—

203

C₂×C₄

—

172

—

204

C₂×C₄

—

172

—

205

C₂×C₄

—

172

—

206

C₂×C₄

—

172

—

207

C₂×C₄

C₂×C₄⋊Dic₄₃

yes

characteristic

208

C₂×C₄

D₄×Dic₄₃

yes

—

209

C₂×C₄

#13063302

yes

—

210

C₂×C₄

#13063309

yes

characteristic

211

C₂×C₄

Q₁₆×D₄₃

yes

—

212

C₂×C₄

#13063348

yes

—

213

C₂×C₄

#13063352

yes

—

214

C₂×C₄

#13063354

yes

—

215

C₈

—

216

C₈

—

172

—

217

C₂²

#14582774

yes

characteristic

218

C₂²

#14583047

yes

—

219

C₂²

#14583056

yes

—

220

C₂²

#14583069

yes

characteristic

221

C₂²

#14583079

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

344

—

226

C₄

—

172

—

227

C₄

—

688

—

228

C₄

Q₁₆×Dic₄₃

yes

—

229

C₄

#14583000

yes

—

230

C₄

#14583192

yes

—

231

C₄

#14583208

yes

—

232

C₂

#19133679

yes

characteristic

233

C₂

#19133736

yes

characteristic

234

C₂

#19133810

yes

—

235

C₂

#19134807

yes

characteristic

236

C₂

#19134851

yes

—

	subgroup	G/H
center	C₂³	#13063295
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#333	C₂
socle, prime radical	C₂³×C₄₃	#120
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#333	D₄₃
hypocenter	C₄₃	#8929
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

subgroup

G/H

center

C₂³

#13063295

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₂×C₄₃×#333

C₂

socle, prime radical

C₂³×C₄₃

#120

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

N	H ≅ G/N	type
17. C₄₃×#333	C₄	semidirect
135. #333	Dic₄₃	semidirect
136. C₄₃	#8929	semidirect

H ≅ G/N

type

17. C₄₃×#333

C₄

semidirect

135. #333

Dic₄₃

semidirect

136. C₄₃

#8929

semidirect

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

subgroup	index
#19137685	2
#19135398	2
#19135354	2
#19132434	2
C₂×C₄₃×#333	2
#8929	43

subgroup

index

C₂×C₄₃×#333

Subgroups — #24991069

Conjugacy classes of subgroups

Complements

Maximal subgroups