Group #24996481 — subgroups

Subgroups — #24996481

Order 11008.

478 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 139 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	#19135573	C₂	1	2	yes	maximal
2	C₄×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#19133354	C₂	1	1	yes	maximal, characteristic
4	#19133050	C₂	1	2	yes	maximal
5	C₄₃×#3170	C₂	1	1	yes	maximal, characteristic
6	#14582923	C₂²	1	2	yes	—
7	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₈×Dic₄₃	—	2	2	no	—
9	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
10	#14582658	—	2	4	no	—
11	#14582652	—	2	2	no	—
12	Q₈⋊(C₄₃⋊C₈)	—	2	4	no	—
13	C₄₃×#533	C₂²	1	2	yes	—
14	C₄₃×#500	C₄	1	1	yes	characteristic, complemented
15	C₄₃×#494	C₄	1	1	yes	characteristic, complemented
16	C₄₃×#487	C₄	1	2	yes	complemented
17	C₄₃×#467	—	2	2	no	—
18	C₄×Q₁₆×C₄₃	—	2	2	no	—
19	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#10621877	—	2	2	no	—
21	C₂²×C₄₃⋊C₈	—	2	1	no	—
22	C₂×C₄×Dic₄₃	—	2	1	no	—
23	C₂×C₄×Dic₄₃	—	2	1	no	—
24	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
25	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
26	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
27	C₄×C₄₃⋊C₈	—	2	1	no	—
28	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
29	C₈×Dic₄₃	—	2	8	no	—
30	C₂×Q₁₆×C₄₃	—	2	2	no	—
31	C₂²×C₈×C₄₃	D₄	1	2	yes	—
32	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
33	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
34	#125×C₄₃	—	2	2	no	—
35	C₂²⋊Q₈×C₄₃	—	2	2	no	—
36	C₂²⋊Q₈×C₄₃	—	2	2	no	—
37	C₄×Q₈×C₄₃	—	2	2	no	—
38	C₄×Q₈×C₄₃	—	2	2	no	—
39	#117×C₄₃	—	2	2	no	—
40	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
41	#107×C₄₃	—	2	2	no	—
42	#103×C₄₃	—	2	4	no	—
43	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₄₃	D₄	1	2	yes	—
46	C₂×Q₈×C₄₃	—	2	2	no	—
47	C₂×Q₈×C₄₃	—	2	2	no	—
48	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
51	C₂²×Dic₄₃	—	2	2	no	—
52	Q₁₆×C₄₃	—	4	4	no	—
53	C₂×C₈×C₄₃	—	2	4	no	—
54	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
56	C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₄⋊C₄×C₄₃	—	2	2	no	—
59	C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₄⋊C₄×C₄₃	—	4	2	no	—
61	C₄⋊C₄×C₄₃	—	4	2	no	—
62	C₂²⋊C₄×C₄₃	—	4	2	no	—
63	C₄²×C₄₃	—	4	2	no	—
64	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₄₃	#41	1	1	yes	characteristic
68	C₄×Dic₄₃	—	2	4	no	—
69	C₄×Dic₄₃	—	2	4	no	—
70	C₄×Dic₄₃	—	2	2	no	—
71	C₄×Dic₄₃	Q₁₆	1	4	yes	complemented
72	#10621877	—	4	4	no	—
73	C₂×C₄₃⋊C₈	—	2	4	no	—
74	C₂×C₄₃⋊C₈	—	2	2	no	—
75	C₂×C₄₃⋊C₈	—	4	2	no	—
76	C₂³×C₄₃	#121	1	1	yes	characteristic
77	Q₈×C₄₃	—	4	4	no	—
78	Q₈×C₄₃	—	4	4	no	—
79	C₂×C₄×C₄₃	—	2	2	no	—
80	C₂×C₄×C₄₃	—	2	2	no	—
81	C₂×C₄×C₄₃	—	4	2	no	—
82	C₂×C₄×C₄₃	—	4	2	no	—
83	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
87	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
88	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
89	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
90	C₂×C₄×C₄₃	#135	1	2	yes	—
91	C₂×Dic₄₃	—	2	4	no	—
92	C₂×Dic₄₃	—	2	4	no	—
93	C₂×Dic₄₃	—	2	4	no	—
94	C₈×C₄₃	—	2	2	no	—
95	C₈×C₄₃	#104	1	4	yes	—
96	C₄₃⋊C₈	—	2	4	no	—
97	C₄₃⋊C₈	—	8	2	no	—
98	#9845	—	43	1	no	maximal, Sylow
99	C₂²×C₄₃	—	2	1	no	—
100	C₂²×C₄₃	—	2	1	no	—
101	C₂²×C₄₃	#390	1	1	yes	characteristic
102	C₂²×C₄₃	#467	1	2	yes	—
103	C₄×C₄₃	—	2	1	no	—
104	C₄×C₄₃	—	2	1	no	—
105	C₄×C₄₃	—	8	2	no	—
106	C₄×C₄₃	—	8	2	no	—
107	C₄×C₄₃	C₂×#104	1	2	yes	—
108	C₄×C₄₃	C₄×Q₁₆	1	2	yes	—
109	C₄×C₄₃	#443	1	2	yes	—
110	C₄×C₄₃	#494	1	1	yes	characteristic
111	C₄×C₄₃	#495	1	1	yes	characteristic
112	Dic₄₃	—	2	8	no	—
113	#3170	D₄₃	1	1	yes	characteristic
114	#1994	—	43	2	no	—
115	C₄²×C₈	—	43	1	no	—
116	#1567	—	43	1	no	—
117	#1493	—	43	2	no	—
118	C₂×C₄₃	—	2	2	no	—
119	C₂×C₄₃	#1962	1	1	yes	characteristic
120	C₂×C₄₃	#1969	1	1	yes	characteristic
121	C₂×C₄₃	#1974	1	1	yes	characteristic
122	#533	C₂×D₄₃	1	2	yes	—
123	#500	Dic₄₃	1	1	yes	characteristic, complemented
124	#494	Dic₄₃	1	1	yes	characteristic, complemented
125	#487	Dic₄₃	1	2	yes	complemented
126	#467	—	2	2	no	—
127	C₄×Q₁₆	—	2	2	no	—
128	#423	—	43	2	no	—
129	C₂×C₄×C₈	—	43	1	no	—
130	C₂×C₄×C₈	—	86	2	no	—
131	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
132	C₄³	—	43	1	no	—
133	#339	—	86	4	no	—
134	#335	—	86	2	no	—
135	Q₈⋊C₈	—	86	4	no	—
136	C₄₃	#9845	1	1	yes	characteristic, complemented, Sylow
137	C₂×Q₁₆	—	2	2	no	—
138	C₂×M₁₆	—	86	2	no	—
139	C₂²×C₈	—	86	1	no	—
140	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
141	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
142	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
143	#125	—	2	2	no	—
144	C₂²⋊Q₈	—	2	2	no	—
145	C₂²⋊Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	#117	—	2	2	no	—
149	C₂×C₄²	—	43	2	no	—
150	C₂×C₄²	—	86	1	no	—
151	C₂×C₄²	—	86	1	no	—
152	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
153	#107	—	2	2	no	—
154	C₄⋊C₈	—	86	2	no	—
155	C₄⋊C₈	—	86	2	no	—
156	#103	—	2	4	no	—
157	C₄×C₈	—	43	2	no	—
158	C₄×C₈	—	86	8	no	—
159	C₄×C₈	—	86	1	no	—
160	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
161	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
162	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂²×C₄	—	86	2	no	—
166	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
167	C₂²×C₄	#10621900	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
169	Q₁₆	—	4	4	no	—
170	M₁₆	—	172	4	no	—
171	C₂×C₈	—	2	4	no	—
172	C₂×C₈	—	86	4	no	—
173	C₂×C₈	—	86	2	no	—
174	C₂×C₈	—	172	2	no	—
175	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
176	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₂²⋊C₄	—	4	2	no	—
184	C₄²	—	4	2	no	—
185	C₄²	—	43	4	no	—
186	C₄²	—	86	4	no	—
187	C₄²	—	86	4	no	—
188	C₄²	—	86	2	no	—
189	C₄²	D₄×D₄₃	1	1	yes	characteristic
190	C₄²	#10621900	1	1	yes	characteristic
191	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
192	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
193	C₂³	#13063296	1	1	yes	characteristic
194	Q₈	—	4	4	no	—
195	Q₈	—	4	4	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	86	4	no	—
201	C₂×C₄	—	86	4	no	—
202	C₂×C₄	—	86	4	no	—
203	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
204	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
205	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
206	C₂×C₄	#13063296	1	1	yes	characteristic
207	C₂×C₄	#13063312	1	1	yes	characteristic
208	C₂×C₄	#13063321	1	1	yes	characteristic
209	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
210	C₂×C₄	#13063348	1	2	yes	—
211	C₈	—	2	2	no	—
212	C₈	—	86	4	no	—
213	C₈	—	344	2	no	—
214	C₈	#13063252	1	4	yes	—
215	C₂²	—	2	1	no	—
216	C₂²	—	2	1	no	—
217	C₂²	#14582802	1	1	yes	characteristic
218	C₂²	#14583137	1	2	yes	—
219	C₄	—	2	1	no	—
220	C₄	—	2	1	no	—
221	C₄	—	8	2	no	—
222	C₄	—	8	2	no	—
223	C₄	—	86	8	no	—
224	C₄	C₂×#13063252	1	2	yes	—
225	C₄	Q₁₆×Dic₄₃	1	2	yes	—
226	C₄	#14583016	1	2	yes	—
227	C₄	#14583277	1	1	yes	characteristic
228	C₄	#14583284	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	#19135424	1	1	yes	characteristic
231	C₂	#19135457	1	1	yes	characteristic
232	C₂	#19135484	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19135573

C₂

yes

maximal

C₄×C₈×Dic₄₃

C₂

yes

maximal, characteristic

#19133354

C₂

yes

maximal, characteristic

#19133050

C₂

yes

maximal

C₄₃×#3170

C₂

yes

maximal, characteristic

#14582923

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₈×Dic₄₃

—

C₄²×Dic₄₃

C₂²

yes

characteristic

#14582658

—

#14582652

—

Q₈⋊(C₄₃⋊C₈)

—

C₄₃×#533

C₂²

yes

—

C₄₃×#500

C₄

yes

characteristic, complemented

C₄₃×#494

C₄

yes

characteristic, complemented

C₄₃×#487

C₄

yes

complemented

C₄₃×#467

—

C₄×Q₁₆×C₄₃

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×#10621877

—

C₂²×C₄₃⋊C₈

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

D₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₈×Dic₄₃

—

C₂×Q₁₆×C₄₃

—

C₂²×C₈×C₄₃

D₄

yes

—

C₄⋊Q₈×C₄₃

C₂×C₄

yes

—

C₄⋊Q₈×C₄₃

C₂×C₄

yes

—

#125×C₄₃

—

C₂²⋊Q₈×C₄₃

—

C₂²⋊Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

#117×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#107×C₄₃

—

#103×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

characteristic

C₂²×Dic₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

#41

yes

characteristic

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

Q₁₆

yes

complemented

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#121

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×Q₁₆

yes

—

C₂×C₄×C₄₃

#135

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#104

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#9845

—

maximal, Sylow

C₂²×C₄₃

—

100

C₂²×C₄₃

—

101

C₂²×C₄₃

#390

yes

characteristic

102

C₂²×C₄₃

#467

yes

—

103

C₄×C₄₃

—

104

C₄×C₄₃

—

105

C₄×C₄₃

—

106

C₄×C₄₃

—

107

C₄×C₄₃

C₂×#104

yes

—

108

C₄×C₄₃

C₄×Q₁₆

yes

—

109

C₄×C₄₃

#443

yes

—

110

C₄×C₄₃

#494

yes

characteristic

111

C₄×C₄₃

#495

yes

characteristic

112

Dic₄₃

—

113

#3170

D₄₃

yes

characteristic

114

#1994

—

115

C₄²×C₈

—

116

#1567

—

117

#1493

—

118

C₂×C₄₃

—

119

C₂×C₄₃

#1962

yes

characteristic

120

C₂×C₄₃

#1969

yes

characteristic

121

C₂×C₄₃

#1974

yes

characteristic

122

#533

C₂×D₄₃

yes

—

123

#500

Dic₄₃

yes

characteristic, complemented

124

#494

Dic₄₃

yes

characteristic, complemented

125

#487

Dic₄₃

yes

complemented

126

#467

—

127

C₄×Q₁₆

—

128

#423

—

129

C₂×C₄×C₈

—

130

C₂×C₄×C₈

—

131

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

132

C₄³

—

133

#339

—

134

#335

—

135

Q₈⋊C₈

—

136

C₄₃

#9845

yes

characteristic, complemented, Sylow

137

C₂×Q₁₆

—

138

C₂×M₁₆

—

139

C₂²×C₈

—

140

C₂²×C₈

C₂²⋊D₄₃

yes

—

141

C₄⋊Q₈

C₂×Dic₄₃

yes

—

142

C₄⋊Q₈

C₂×Dic₄₃

yes

—

143

#125

—

144

C₂²⋊Q₈

—

145

C₂²⋊Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

#117

—

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

—

152

C₂×C₄²

C₂²×D₄₃

yes

characteristic

153

#107

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

#103

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

C₂×Dic₄₃

yes

characteristic

161

C₄×C₈

C₂×Dic₄₃

yes

characteristic

162

C₄×C₈

C₂²⋊D₄₃

yes

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂²×C₄

—

166

C₂²×C₄

D₄×D₄₃

yes

characteristic

167

C₂²×C₄

#10621900

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

169

Q₁₆

—

170

M₁₆

—

172

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

172

—

175

C₂×C₈

C₂²⋊Dic₄₃

yes

—

176

C₂×C₈

C₂²⋊Dic₄₃

yes

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

189

C₄²

D₄×D₄₃

yes

characteristic

190

C₄²

#10621900

yes

characteristic

191

C₄²

C₂²×Dic₄₃

yes

characteristic

192

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

193

C₂³

#13063296

yes

characteristic

194

Q₈

—

195

Q₈

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

C₂×C₂²⋊Dic₄₃

yes

characteristic

204

C₂×C₄

D₄×Dic₄₃

yes

characteristic

205

C₂×C₄

D₄×Dic₄₃

yes

characteristic

206

C₂×C₄

#13063296

yes

characteristic

207

C₂×C₄

#13063312

yes

characteristic

208

C₂×C₄

#13063321

yes

characteristic

209

C₂×C₄

Q₁₆×D₄₃

yes

—

210

C₂×C₄

#13063348

yes

—

211

C₈

—

212

C₈

—

213

C₈

—

344

—

214

C₈

#13063252

yes

—

215

C₂²

—

216

C₂²

—

217

C₂²

#14582802

yes

characteristic

218

C₂²

#14583137

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

C₂×#13063252

yes

—

225

C₄

Q₁₆×Dic₄₃

yes

—

226

C₄

#14583016

yes

—

227

C₄

#14583277

yes

characteristic

228

C₄

#14583284

yes

characteristic

229

C₂

—

230

C₂

#19135424

yes

characteristic

231

C₂

#19135457

yes

characteristic

232

C₂

#19135484

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063321
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#3170	C₂
socle	C₂²×C₄₃	#390
prime radical	C₂³×C₄₃	#121
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#3170	D₄₃
hypocenter	C₄₃	#9845
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#13063321

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#3170

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
14. C₄₃×#500	C₄	semidirect
15. C₄₃×#494	C₄	semidirect
16. C₄₃×#487	C₄	semidirect
71. C₄×Dic₄₃	Q₁₆	semidirect
123. #500	Dic₄₃	semidirect
124. #494	Dic₄₃	semidirect
125. #487	Dic₄₃	semidirect
136. C₄₃	#9845	semidirect

H ≅ G/N

type

14. C₄₃×#500

C₄

semidirect

15. C₄₃×#494

C₄

semidirect

16. C₄₃×#487

C₄

semidirect

71. C₄×Dic₄₃

Q₁₆

semidirect

123. #500

Dic₄₃

semidirect

124. #494

Dic₄₃

semidirect

125. #487

Dic₄₃

semidirect

136. C₄₃

#9845

semidirect

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

subgroup	index
#19135573	2
C₄×C₈×Dic₄₃	2
#19133354	2
#19133050	2
C₄₃×#3170	2
#9845	43

subgroup

index

C₄×C₈×Dic₄₃

C₄₃×#3170

Subgroups — #24996481

Conjugacy classes of subgroups

Complements

Maximal subgroups