Group #25001337 — subgroups

Subgroups — #25001337

Order 11008.

402 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 119 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	#19135389	C₂	1	1	yes	maximal, characteristic
2	#19134592	C₂	1	2	yes	maximal
3	#19132478	C₂	1	2	yes	maximal, complemented
4	#19132430	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
9	C₂×#13063245	—	2	2	no	—
10	C₂×(C₂×D₄₃)⋊C₈	—	2	2	no	—
11	#14582661	—	2	2	no	—
12	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₄₃×#384	C₂²	1	2	yes	—
14	C₄₃×#340	—	2	2	no	—
15	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
16	C₂²×C₄×D₄₃	—	2	1	no	—
17	C₂²×C₄₃⋊C₈	—	2	1	no	—
18	C₂²×C₄₃⋊C₈	—	2	2	no	—
19	C₄×D₁₇₂	—	2	2	no	—
20	C₄×D₁₇₂	—	2	2	no	—
21	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
22	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
23	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
25	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
26	#13063245	—	4	4	no	—
27	(C₂×D₄₃)⋊C₈	—	4	4	no	—
28	C₂²×C₈×C₄₃	D₄	1	2	yes	—
29	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
30	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
31	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
32	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
33	C₄×C₈×C₄₃	—	2	2	no	—
34	C₂³×D₄₃	—	2	1	no	—
35	C₂²×C₄×C₄₃	—	4	2	no	—
36	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
39	C₂²×Dic₄₃	—	2	1	no	—
40	C₂×D₁₇₂	—	2	1	no	—
41	C₂×D₁₇₂	—	2	2	no	—
42	C₂×D₁₇₂	—	2	2	no	—
43	C₂×D₁₇₂	Q₁₆	1	2	yes	—
44	C₂×C₄×D₄₃	—	4	1	no	—
45	C₂×C₄×D₄₃	—	4	1	no	—
46	C₂×C₄×D₄₃	—	4	2	no	—
47	C₂×C₄×D₄₃	—	4	2	no	—
48	C₂×C₈×C₄₃	—	2	2	no	—
49	C₂×C₈×C₄₃	—	2	2	no	—
50	C₂×C₈×C₄₃	—	2	2	no	—
51	C₄⋊C₄×C₄₃	—	4	2	no	—
52	C₄⋊C₄×C₄₃	—	4	2	no	—
53	C₄⋊C₄×C₄₃	—	4	2	no	—
54	C₄⋊C₄×C₄₃	—	4	2	no	—
55	C₄⋊C₄×C₄₃	—	8	2	no	—
56	C₄²×C₄₃	#41	1	2	yes	—
57	C₄²×C₄₃	#41	1	2	yes	—
58	(C₂×D₄₃)⋊C₄	—	4	2	no	—
59	C₄⋊Dic₄₃	—	2	2	no	—
60	C₂×C₄₃⋊C₈	—	4	2	no	—
61	C₂×C₄₃⋊C₈	—	4	1	no	—
62	C₂×C₄₃⋊C₈	—	4	2	no	—
63	C₂×C₄₃⋊C₈	—	4	2	no	—
64	C₂×C₄₃⋊C₈	—	4	2	no	—
65	C₂³×C₄₃	#121	1	1	yes	characteristic
66	C₂²×D₄₃	—	2	2	no	—
67	C₂²×D₄₃	—	4	1	no	—
68	C₂²×D₄₃	—	4	2	no	—
69	C₂²×D₄₃	—	4	1	no	—
70	C₂²×D₄₃	—	4	2	no	—
71	C₂×C₄×C₄₃	—	2	2	no	—
72	C₂×C₄×C₄₃	—	8	2	no	—
73	C₂×C₄×C₄₃	—	8	2	no	—
74	C₂×C₄×C₄₃	—	8	2	no	—
75	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
76	C₂×C₄×C₄₃	#123	1	2	yes	—
77	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
78	C₂×C₄×C₄₃	#126	1	2	yes	—
79	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
80	C₂×C₄×C₄₃	#135	1	2	yes	—
81	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
82	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
83	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
84	C₂×Dic₄₃	—	4	1	no	—
85	C₂×Dic₄₃	—	4	2	no	—
86	D₁₇₂	—	2	4	no	—
87	D₁₇₂	—	4	2	no	—
88	C₄×D₄₃	—	8	2	no	—
89	C₄×D₄₃	—	8	1	no	—
90	C₄×D₄₃	—	8	1	no	—
91	C₈×C₄₃	—	4	2	no	—
92	C₄₃⋊C₈	—	8	2	no	—
93	C₄₃⋊C₈	—	8	1	no	—
94	#10622	—	43	1	no	maximal, Sylow
95	C₂²×C₄₃	#397	1	1	yes	characteristic
96	C₂²×C₄₃	#463	1	2	yes	—
97	C₂²×C₄₃	#467	1	1	yes	characteristic
98	C₂²×C₄₃	#469	1	1	yes	characteristic
99	C₂²×C₄₃	#471	1	2	yes	—
100	C₂×D₄₃	—	4	2	no	—
101	C₂×D₄₃	—	4	4	no	—
102	C₂×D₄₃	—	8	1	no	—
103	C₂×D₄₃	—	8	1	no	—
104	C₂×D₄₃	—	8	2	no	—
105	C₄×C₄₃	—	2	2	no	—
106	C₄×C₄₃	—	16	2	no	—
107	C₄×C₄₃	#482	1	2	yes	—
108	C₄×C₄₃	#482	1	2	yes	—
109	C₄×C₄₃	#484	1	2	yes	—
110	C₄×C₄₃	#488	1	1	yes	characteristic
111	C₄×C₄₃	#490	1	1	yes	characteristic
112	Dic₄₃	—	8	1	no	—
113	#1954	—	43	1	no	—
114	#1834	D₄₃	1	1	yes	characteristic, complemented
115	#1802	—	43	2	no	—
116	#1296	—	43	2	no	—
117	#1277	—	43	1	no	—
118	C₂×C₄₃	#1683	1	2	yes	—
119	C₂×C₄₃	#1701	1	2	yes	—
120	C₂×C₄₃	#2073	1	1	yes	characteristic
121	C₂×C₄₃	#2076	1	1	yes	characteristic
122	C₂×C₄₃	#2079	1	1	yes	characteristic
123	D₄₃	—	8	2	no	—
124	C₂×C₄×D₄	—	43	1	no	—
125	C₂×C₄⋊C₈	—	43	2	no	—
126	C₂×C₄⋊C₈	—	43	1	no	—
127	C₂×#102	—	86	2	no	—
128	C₂×C₂²⋊C₈	—	86	2	no	—
129	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
130	#384	C₂×D₄₃	1	2	yes	—
131	#340	—	2	2	no	—
132	#340	—	86	2	no	—
133	C₄₃	#10622	1	1	yes	characteristic, complemented, Sylow
134	C₂²×D₄	—	43	1	no	—
135	C₂³×C₄	—	86	1	no	—
136	C₂²×C₈	—	86	2	no	—
137	C₂²×C₈	—	86	1	no	—
138	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
139	C₄×D₄	—	86	2	no	—
140	C₄×D₄	—	86	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	43	1	no	—
145	C₂×C₂²⋊C₄	—	86	1	no	—
146	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
147	C₄⋊C₈	—	86	2	no	—
148	C₄⋊C₈	—	86	2	no	—
149	C₄⋊C₈	—	86	2	no	—
150	#102	—	172	4	no	—
151	C₂²⋊C₈	—	172	4	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂⁴	—	86	1	no	—
154	C₂×D₄	—	43	2	no	—
155	C₂×D₄	—	86	2	no	—
156	C₂×D₄	—	86	1	no	—
157	C₂×D₄	—	86	2	no	—
158	C₂²×C₄	—	4	2	no	—
159	C₂²×C₄	—	86	1	no	—
160	C₂²×C₄	—	172	1	no	—
161	C₂²×C₄	—	172	1	no	—
162	C₂²×C₄	—	172	2	no	—
163	C₂²×C₄	—	172	2	no	—
164	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
165	C₂²×C₄	#10621900	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	172	2	no	—
171	C₂×C₈	—	172	1	no	—
172	C₂×C₈	—	172	2	no	—
173	C₂×C₈	—	172	2	no	—
174	C₂×C₈	—	172	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	8	2	no	—
180	C₄⋊C₄	—	86	2	no	—
181	C₂²⋊C₄	—	172	2	no	—
182	C₄²	#10621898	1	2	yes	—
183	C₄²	#10621902	1	2	yes	—
184	C₂³	—	86	2	no	—
185	C₂³	—	172	1	no	—
186	C₂³	—	172	2	no	—
187	C₂³	—	172	1	no	—
188	C₂³	—	172	2	no	—
189	C₂³	#13063296	1	1	yes	characteristic
190	D₄	—	86	4	no	—
191	D₄	—	172	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	8	2	no	—
194	C₂×C₄	—	8	2	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	—	344	2	no	—
197	C₂×C₄	—	344	1	no	—
198	C₂×C₄	—	344	1	no	—
199	C₂×C₄	—	172	1	no	—
200	C₂×C₄	—	172	2	no	—
201	C₂×C₄	#13063308	1	1	yes	characteristic
202	C₂×C₄	#13063310	1	2	yes	—
203	C₂×C₄	#13063314	1	1	yes	characteristic
204	C₂×C₄	#13063320	1	2	yes	—
205	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
206	C₂×C₄	#13063345	1	2	yes	—
207	C₂×C₄	#13063348	1	1	yes	characteristic
208	C₂×C₄	#13063349	1	2	yes	—
209	C₂×C₄	#13063350	1	2	yes	—
210	C₈	—	4	2	no	—
211	C₈	—	344	2	no	—
212	C₈	—	344	1	no	—
213	C₂²	—	344	1	no	—
214	C₂²	—	344	1	no	—
215	C₂²	—	344	2	no	—
216	C₂²	—	172	2	no	—
217	C₂²	—	172	4	no	—
218	C₂²	#14582825	1	1	yes	characteristic
219	C₂²	#14583111	1	2	yes	—
220	C₂²	#14583137	1	1	yes	characteristic
221	C₂²	#14583149	1	1	yes	characteristic
222	C₂²	#14583159	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	16	2	no	—
225	C₄	—	344	1	no	—
226	C₄	#14583223	1	2	yes	—
227	C₄	#14583226	1	2	yes	—
228	C₄	#14583236	1	2	yes	—
229	C₄	#14583256	1	1	yes	characteristic
230	C₄	#14583265	1	1	yes	characteristic
231	C₂	—	344	2	no	—
232	C₂	#19134043	1	2	yes	—
233	C₂	#19134153	1	2	yes	—
234	C₂	#19136009	1	1	yes	characteristic
235	C₂	#19136024	1	1	yes	characteristic
236	C₂	#19136041	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19135389

C₂

yes

maximal, characteristic

#19134592

C₂

yes

maximal

#19132478

C₂

yes

maximal, complemented

#19132430

C₂

yes

maximal, characteristic, complemented

C₄₃×#1834

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₁₇₂

C₂²

yes

characteristic

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂×#13063245

—

C₂×(C₂×D₄₃)⋊C₈

—

#14582661

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#384

C₂²

yes

—

C₄₃×#340

—

C₂²×D₁₇₂

D₄

yes

characteristic

C₂²×C₄×D₄₃

—

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

—

C₄×D₁₇₂

—

C₄×D₁₇₂

—

C₂×C₄⋊Dic₄₃

D₄

yes

characteristic

C₂×(C₂×D₄₃)⋊C₄

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063245

—

(C₂×D₄₃)⋊C₈

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄×C₈×C₄₃

—

C₂³×D₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

characteristic

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

Q₁₆

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#121

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#123

yes

characteristic

C₂×C₄×C₄₃

#123

yes

—

C₂×C₄×C₄₃

#124

yes

characteristic

C₂×C₄×C₄₃

#126

yes

—

C₂×C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

#135

yes

characteristic

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

100

C₂×D₄₃

—

101

C₂×D₄₃

—

102

C₂×D₄₃

—

103

C₂×D₄₃

—

104

C₂×D₄₃

—

105

C₄×C₄₃

—

106

C₄×C₄₃

—

107

C₄×C₄₃

#482

yes

—

108

C₄×C₄₃

#482

yes

—

109

C₄×C₄₃

#484

yes

—

110

C₄×C₄₃

#488

yes

characteristic

111

C₄×C₄₃

#490

yes

characteristic

112

Dic₄₃

—

113

#1954

—

114

#1834

D₄₃

yes

characteristic, complemented

115

#1802

—

116

#1296

—

117

#1277

—

118

C₂×C₄₃

#1683

yes

—

119

C₂×C₄₃

#1701

yes

—

120

C₂×C₄₃

#2073

yes

characteristic

121

C₂×C₄₃

#2076

yes

characteristic

122

C₂×C₄₃

#2079

yes

characteristic

123

D₄₃

—

124

C₂×C₄×D₄

—

125

C₂×C₄⋊C₈

—

126

C₂×C₄⋊C₈

—

127

C₂×#102

—

128

C₂×C₂²⋊C₈

—

129

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

130

#384

C₂×D₄₃

yes

—

131

#340

—

132

#340

—

133

C₄₃

#10622

yes

characteristic, complemented, Sylow

134

C₂²×D₄

—

135

C₂³×C₄

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

C₂²⋊D₄₃

yes

—

139

C₄×D₄

—

140

C₄×D₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₂²⋊C₄

—

146

C₂×C₄²

C₂²×D₄₃

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#102

—

172

—

151

C₂²⋊C₈

—

172

—

152

C₄×C₈

—

153

C₂⁴

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

172

—

161

C₂²×C₄

—

172

—

162

C₂²×C₄

—

172

—

163

C₂²×C₄

—

172

—

164

C₂²×C₄

D₄×D₄₃

yes

characteristic

165

C₂²×C₄

#10621900

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

172

—

171

C₂×C₈

—

172

—

172

C₂×C₈

—

172

—

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

C₂²⋊C₄

—

172

—

182

C₄²

#10621898

yes

—

183

C₄²

#10621902

yes

—

184

C₂³

—

185

C₂³

—

172

—

186

C₂³

—

172

—

187

C₂³

—

172

—

188

C₂³

—

172

—

189

C₂³

#13063296

yes

characteristic

190

D₄

—

191

D₄

—

172

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

344

—

197

C₂×C₄

—

344

—

198

C₂×C₄

—

344

—

199

C₂×C₄

—

172

—

200

C₂×C₄

—

172

—

201

C₂×C₄

#13063308

yes

characteristic

202

C₂×C₄

#13063310

yes

—

203

C₂×C₄

#13063314

yes

characteristic

204

C₂×C₄

#13063320

yes

—

205

C₂×C₄

Q₁₆×D₄₃

yes

characteristic

206

C₂×C₄

#13063345

yes

—

207

C₂×C₄

#13063348

yes

characteristic

208

C₂×C₄

#13063349

yes

—

209

C₂×C₄

#13063350

yes

—

210

C₈

—

211

C₈

—

344

—

212

C₈

—

344

—

213

C₂²

—

344

—

214

C₂²

—

344

—

215

C₂²

—

344

—

216

C₂²

—

172

—

217

C₂²

—

172

—

218

C₂²

#14582825

yes

characteristic

219

C₂²

#14583111

yes

—

220

C₂²

#14583137

yes

characteristic

221

C₂²

#14583149

yes

characteristic

222

C₂²

#14583159

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

344

—

226

C₄

#14583223

yes

—

227

C₄

#14583226

yes

—

228

C₄

#14583236

yes

—

229

C₄

#14583256

yes

characteristic

230

C₄

#14583265

yes

characteristic

231

C₂

—

344

—

232

C₂

#19134043

yes

—

233

C₂

#19134153

yes

—

234

C₂

#19136009

yes

characteristic

235

C₂

#19136024

yes

characteristic

236

C₂

#19136041

yes

characteristic

	subgroup	G/H
center	C₂³	#13063296
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1834	C₂
socle	C₂³×C₄₃	#121
prime radical	C₂²×D₁₇₂	D₄
hypercenter	#1834	D₄₃
hypocenter	C₄₃	#10622
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

subgroup

G/H

center

C₂³

#13063296

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1834

C₂

socle

C₂³×C₄₃

#121

prime radical

C₂²×D₁₇₂

D₄

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

N	H ≅ G/N	type
3. #19132478	C₂	semidirect
4. #19132430	C₂	semidirect
5. C₄₃×#1834	C₂	semidirect
114. #1834	D₄₃	semidirect
133. C₄₃	#10622	semidirect

H ≅ G/N

type

3. #19132478

C₂

semidirect

4. #19132430

C₂

semidirect

5. C₄₃×#1834

C₂

semidirect

114. #1834

D₄₃

semidirect

133. C₄₃

#10622

semidirect

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

subgroup	index
#19135389	2
#19134592	2
#19132478	2
#19132430	2
C₄₃×#1834	2
#10622	43

subgroup

index

C₄₃×#1834

Subgroups — #25001337

Conjugacy classes of subgroups

Complements

Maximal subgroups