Group #25000155 — subgroups

Subgroups — #25000155

Order 11008.

478 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 133 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	#19134754	C₂	1	1	yes	maximal, characteristic
2	#19134600	C₂	1	2	yes	maximal
3	C₂×Q₈⋊(C₄₃⋊C₈)	C₂	1	2	yes	maximal
4	#19132478	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2582	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063258	—	2	2	no	—
7	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
8	C₂×#13063249	—	2	2	no	—
9	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	#14582769	C₂²	1	1	yes	characteristic
11	#14582661	—	2	2	no	—
12	Q₈⋊(C₄₃⋊C₈)	—	2	4	no	—
13	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
14	C₄₃×#398	—	2	2	no	—
15	C₄₃×#391	—	2	2	no	—
16	C₄₃×#389	—	2	2	no	—
17	C₄₃×#384	C₂²	1	1	yes	characteristic
18	C₂²×C₄₃⋊C₈	—	2	1	no	—
19	C₂²×C₄₃⋊C₈	—	2	2	no	—
20	C₂×C₄⋊Dic₄₃	—	2	2	no	—
21	C₂×C₄⋊Dic₄₃	—	2	1	no	—
22	#13063258	—	4	4	no	—
23	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
25	#13063249	—	4	4	no	—
26	C₄×C₄₃⋊C₈	—	2	1	no	—
27	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
28	C₂²×Q₈×C₄₃	D₄	1	2	yes	—
29	C₄×Q₈×C₄₃	—	2	2	no	—
30	C₄×Q₈×C₄₃	—	2	2	no	—
31	C₄×Q₈×C₄₃	—	2	2	no	—
32	C₄×Q₈×C₄₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
34	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
35	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
37	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
38	C₂×C₄²×C₄₃	—	2	2	no	—
39	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
40	#95×C₄₃	—	2	4	no	—
41	#95×C₄₃	—	2	2	no	—
42	C₂×Q₈×C₄₃	—	2	2	no	—
43	C₂×Q₈×C₄₃	—	2	2	no	—
44	C₂×Q₈×C₄₃	—	2	2	no	—
45	C₂×Q₈×C₄₃	—	2	2	no	—
46	C₂×Q₈×C₄₃	—	2	2	no	—
47	C₂×Q₈×C₄₃	Q₁₆	1	4	yes	—
48	C₂²×C₄×C₄₃	—	2	2	no	—
49	C₂²×C₄×C₄₃	—	2	2	no	—
50	C₂²×C₄×C₄₃	—	2	2	no	—
51	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
53	C₂²×Dic₄₃	—	4	1	no	—
54	C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₄⋊C₄×C₄₃	—	2	2	no	—
56	C₄⋊C₄×C₄₃	—	4	2	no	—
57	C₄⋊C₄×C₄₃	—	4	2	no	—
58	C₄⋊C₄×C₄₃	—	4	2	no	—
59	C₄⋊C₄×C₄₃	—	4	2	no	—
60	C₄⋊C₄×C₄₃	—	4	2	no	—
61	C₄⋊C₄×C₄₃	—	8	2	no	—
62	C₄²×C₄₃	—	4	2	no	—
63	C₄²×C₄₃	—	4	2	no	—
64	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₄₃	#41	1	1	yes	characteristic
66	C₄²×C₄₃	#41	1	2	yes	—
67	C₄⋊Dic₄₃	—	4	2	no	—
68	C₄⋊Dic₄₃	—	4	2	no	—
69	C₄⋊Dic₄₃	—	4	2	no	—
70	C₂×C₄₃⋊C₈	—	2	2	no	—
71	C₂×C₄₃⋊C₈	—	2	2	no	—
72	C₂×C₄₃⋊C₈	—	2	2	no	—
73	C₂×C₄₃⋊C₈	—	4	2	no	—
74	C₂×C₄₃⋊C₈	—	4	2	no	—
75	C₂×C₄₃⋊C₈	—	4	2	no	—
76	C₂³×C₄₃	#120	1	1	yes	characteristic
77	Q₈×C₄₃	—	2	4	no	—
78	Q₈×C₄₃	—	2	4	no	—
79	Q₈×C₄₃	—	4	2	no	—
80	Q₈×C₄₃	—	4	2	no	—
81	C₂×C₄×C₄₃	—	2	1	no	—
82	C₂×C₄×C₄₃	—	2	1	no	—
83	C₂×C₄×C₄₃	—	2	4	no	—
84	C₂×C₄×C₄₃	—	4	2	no	—
85	C₂×C₄×C₄₃	—	4	2	no	—
86	C₂×C₄×C₄₃	—	4	2	no	—
87	C₂×C₄×C₄₃	—	4	4	no	—
88	C₂×C₄×C₄₃	—	4	2	no	—
89	C₂×C₄×C₄₃	—	4	2	no	—
90	C₂×C₄×C₄₃	—	4	2	no	—
91	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
92	C₂×C₄×C₄₃	#121	1	2	yes	—
93	C₂×C₄×C₄₃	#123	1	2	yes	—
94	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
95	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
96	C₂×C₄×C₄₃	#135	1	2	yes	—
97	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
98	C₂×C₄×C₄₃	#137	1	2	yes	—
99	C₂×Dic₄₃	—	8	2	no	—
100	C₂×Dic₄₃	—	8	1	no	—
101	C₄₃⋊C₈	—	2	4	no	—
102	C₄₃⋊C₈	—	8	2	no	—
103	#10439	—	43	1	no	maximal, Sylow
104	C₂²×C₄₃	#394	1	1	yes	characteristic
105	C₂²×C₄₃	#449	1	2	yes	—
106	C₂²×C₄₃	#451	1	2	yes	—
107	C₂²×C₄₃	#453	1	1	yes	characteristic
108	C₂²×C₄₃	#456	1	1	yes	characteristic
109	C₄×C₄₃	—	2	1	no	—
110	C₄×C₄₃	—	2	1	no	—
111	C₄×C₄₃	—	4	4	no	—
112	C₄×C₄₃	—	8	2	no	—
113	C₄×C₄₃	—	8	2	no	—
114	C₄×C₄₃	#467	1	2	yes	—
115	C₄×C₄₃	#468	1	2	yes	—
116	C₄×C₄₃	#484	1	2	yes	—
117	C₄×C₄₃	#485	1	2	yes	—
118	Dic₄₃	—	16	1	no	—
119	#2582	D₄₃	1	1	yes	characteristic
120	#1845	—	43	1	no	—
121	#1803	—	43	2	no	—
122	C₂×Q₈⋊C₈	—	43	2	no	—
123	#1296	—	43	1	no	—
124	C₂×C₄₃	#1620	1	1	yes	characteristic
125	C₂×C₄₃	#1633	1	1	yes	characteristic
126	C₂×C₄₃	#1648	1	2	yes	—
127	C₂×C₄₃	#2036	1	2	yes	—
128	C₂×C₄₃	#2039	1	1	yes	characteristic
129	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
130	C₂×#107	—	86	2	no	—
131	C₂×C₄⋊C₈	—	43	2	no	—
132	C₂×#103	—	86	2	no	—
133	C₂×C₄×C₈	—	43	1	no	—
134	#398	—	2	2	no	—
135	#391	—	2	2	no	—
136	#389	—	2	2	no	—
137	#384	—	43	1	no	—
138	#384	C₂×D₄₃	1	1	yes	characteristic
139	#340	—	86	2	no	—
140	Q₈⋊C₈	—	86	4	no	—
141	C₄₃	#10439	1	1	yes	characteristic, complemented, Sylow
142	C₂²×Q₈	C₂²⋊D₄₃	1	2	yes	—
143	C₂²×C₈	—	86	1	no	—
144	C₂²×C₈	—	86	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₄×Q₈	—	2	2	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄⋊C₄	—	86	2	no	—
153	C₂×C₄⋊C₄	—	86	1	no	—
154	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
155	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
156	C₂×C₄²	—	2	2	no	—
157	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
158	#107	—	172	4	no	—
159	C₄⋊C₈	—	86	2	no	—
160	C₄⋊C₈	—	86	2	no	—
161	#103	—	172	4	no	—
162	C₄×C₈	—	43	2	no	—
163	C₄×C₈	—	86	1	no	—
164	#95	—	2	4	no	—
165	#95	—	2	2	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	#10621885	1	4	yes	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	172	1	no	—
176	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
178	C₂×C₈	—	86	2	no	—
179	C₂×C₈	—	86	2	no	—
180	C₂×C₈	—	86	2	no	—
181	C₂×C₈	—	172	2	no	—
182	C₂×C₈	—	172	2	no	—
183	C₂×C₈	—	172	2	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	2	no	—
190	C₄⋊C₄	—	4	2	no	—
191	C₄⋊C₄	—	8	2	no	—
192	C₄⋊C₄	—	172	2	no	—
193	C₄⋊C₄	—	172	2	no	—
194	C₄⋊C₄	—	172	2	no	—
195	C₄²	—	4	2	no	—
196	C₄²	—	4	2	no	—
197	C₄²	D₄×D₄₃	1	1	yes	characteristic
198	C₄²	#10621900	1	1	yes	characteristic
199	C₄²	#10621900	1	2	yes	—
200	C₂³	#13063294	1	1	yes	characteristic
201	Q₈	—	2	4	no	—
202	Q₈	—	2	4	no	—
203	Q₈	—	4	2	no	—
204	Q₈	—	4	2	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	4	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	344	2	no	—
216	C₂×C₄	—	344	1	no	—
217	C₂×C₄	#13063296	1	1	yes	characteristic
218	C₂×C₄	#13063297	1	2	yes	—
219	C₂×C₄	#13063306	1	2	yes	—
220	C₂×C₄	#13063312	1	1	yes	characteristic
221	C₂×C₄	C₂×#10621885	1	2	yes	—
222	C₂×C₄	#13063345	1	2	yes	—
223	C₂×C₄	#13063350	1	2	yes	—
224	C₂×C₄	#13063356	1	2	yes	—
225	C₈	—	86	4	no	—
226	C₈	—	344	2	no	—
227	C₂²	#14582813	1	1	yes	characteristic
228	C₂²	#14583044	1	2	yes	—
229	C₂²	#14583055	1	2	yes	—
230	C₂²	#14583067	1	1	yes	characteristic
231	C₂²	#14583082	1	1	yes	characteristic
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	4	no	—
235	C₄	—	8	2	no	—
236	C₄	—	8	2	no	—
237	C₄	—	688	1	no	—
238	C₄	#14583138	1	2	yes	—
239	C₄	#14583147	1	2	yes	—
240	C₄	#14583232	1	2	yes	—
241	C₄	#14583237	1	2	yes	—
242	C₂	#19133654	1	1	yes	characteristic
243	C₂	#19133735	1	1	yes	characteristic
244	C₂	#19133837	1	2	yes	—
245	C₂	#19135795	1	2	yes	—
246	C₂	#19135816	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134754

C₂

yes

maximal, characteristic

#19134600

C₂

yes

maximal

C₂×Q₈⋊(C₄₃⋊C₈)

C₂

yes

maximal

#19132478

C₂

yes

maximal, characteristic

C₄₃×#2582

C₂

yes

maximal, characteristic

C₂×#13063258

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂×#13063249

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#14582769

C₂²

yes

characteristic

#14582661

—

Q₈⋊(C₄₃⋊C₈)

—

C₂×C₄×Q₈×C₄₃

C₂²

yes

—

C₄₃×#398

—

C₄₃×#391

—

C₄₃×#389

—

C₄₃×#384

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

#13063258

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063249

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₂²×Q₈×C₄₃

D₄

yes

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#95×C₄₃

—

#95×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

Q₁₆

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

C₄²×C₄₃

yes

C₄²×C₄₃

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#120

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

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

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#121

yes

characteristic

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

#123

yes

—

C₂×C₄×C₄₃

#124

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

—

100

C₂×Dic₄₃

—

101

C₄₃⋊C₈

—

102

C₄₃⋊C₈

—

103

#10439

—

maximal, Sylow

104

C₂²×C₄₃

#394

yes

characteristic

105

C₂²×C₄₃

#449

yes

—

106

C₂²×C₄₃

#451

yes

—

107

C₂²×C₄₃

#453

yes

characteristic

108

C₂²×C₄₃

#456

yes

characteristic

109

C₄×C₄₃

—

110

C₄×C₄₃

—

111

C₄×C₄₃

—

112

C₄×C₄₃

—

113

C₄×C₄₃

—

114

C₄×C₄₃

#467

yes

—

115

C₄×C₄₃

#468

yes

—

116

C₄×C₄₃

#484

yes

—

117

C₄×C₄₃

#485

yes

—

118

Dic₄₃

—

119

#2582

D₄₃

yes

characteristic

120

#1845

—

121

#1803

—

122

C₂×Q₈⋊C₈

—

123

#1296

—

124

C₂×C₄₃

#1620

yes

characteristic

125

C₂×C₄₃

#1633

yes

characteristic

126

C₂×C₄₃

#1648

yes

—

127

C₂×C₄₃

#2036

yes

—

128

C₂×C₄₃

#2039

yes

characteristic

129

C₂×C₄×Q₈

C₂×D₄₃

yes

—

130

C₂×#107

—

131

C₂×C₄⋊C₈

—

132

C₂×#103

—

133

C₂×C₄×C₈

—

134

#398

—

135

#391

—

136

#389

—

137

#384

—

138

#384

C₂×D₄₃

yes

characteristic

139

#340

—

140

Q₈⋊C₈

—

141

C₄₃

#10439

yes

characteristic, complemented, Sylow

142

C₂²×Q₈

C₂²⋊D₄₃

yes

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

155

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

156

C₂×C₄²

—

157

C₂×C₄²

C₂²×D₄₃

yes

characteristic

158

#107

—

172

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

#103

—

172

—

162

C₄×C₈

—

163

C₄×C₈

—

164

#95

—

165

#95

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

#10621885

yes

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

172

—

176

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

177

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

172

—

182

C₂×C₈

—

172

—

183

C₂×C₈

—

172

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

172

—

193

C₄⋊C₄

—

172

—

194

C₄⋊C₄

—

172

—

195

C₄²

—

196

C₄²

—

197

C₄²

D₄×D₄₃

yes

characteristic

198

C₄²

#10621900

yes

characteristic

199

C₄²

#10621900

yes

—

200

C₂³

#13063294

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

344

—

216

C₂×C₄

—

344

—

217

C₂×C₄

#13063296

yes

characteristic

218

C₂×C₄

#13063297

yes

—

219

C₂×C₄

#13063306

yes

—

220

C₂×C₄

#13063312

yes

characteristic

221

C₂×C₄

C₂×#10621885

yes

—

222

C₂×C₄

#13063345

yes

—

223

C₂×C₄

#13063350

yes

—

224

C₂×C₄

#13063356

yes

—

225

C₈

—

226

C₈

—

344

—

227

C₂²

#14582813

yes

characteristic

228

C₂²

#14583044

yes

—

229

C₂²

#14583055

yes

—

230

C₂²

#14583067

yes

characteristic

231

C₂²

#14583082

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

688

—

238

C₄

#14583138

yes

—

239

C₄

#14583147

yes

—

240

C₄

#14583232

yes

—

241

C₄

#14583237

yes

—

242

C₂

#19133654

yes

characteristic

243

C₂

#19133735

yes

characteristic

244

C₂

#19133837

yes

—

245

C₂

#19135795

yes

—

246

C₂

#19135816

yes

characteristic

	subgroup	G/H
center	C₂³	#13063294
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2582	C₂
socle, prime radical	C₂³×C₄₃	#120
hypercenter	#2582	D₄₃
hypocenter	C₄₃	#10439
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2582

subgroup

G/H

center

C₂³

#13063294

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2582

C₂

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2582

N	H ≅ G/N	type
141. C₄₃	#10439	semidirect

H ≅ G/N

type

141. C₄₃

#10439

semidirect

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

subgroup	index
#19134754	2
#19134600	2
C₂×Q₈⋊(C₄₃⋊C₈)	2
#19132478	2
C₄₃×#2582	2
#10439	43

subgroup

index

C₂×Q₈⋊(C₄₃⋊C₈)

C₄₃×#2582

Subgroups — #25000155

Conjugacy classes of subgroups

Complements

Maximal subgroups