Group #25015091 — subgroups

Subgroups — #25015091

Order 11008.

482 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 135 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	#19136351	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582715	C₂	1	2	yes	maximal, complemented
3	C₂×#14582712	C₂	1	2	yes	maximal
4	C₄×#13063261	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#495	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063265	C₂²	1	2	yes	—
7	C₂×#13063261	C₂²	1	2	yes	—
8	C₄×#10621877	—	2	1	no	—
9	C₄⋊(C₄₃⋊C₁₆)	—	2	2	no	—
10	#14582715	—	2	4	no	—
11	#14582712	—	2	4	no	—
12	#14582664	—	2	1	no	—
13	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₄₃	—	2	1	no	—
15	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₃	—	2	1	no	—
17	C₄₃×#495	—	2	2	no	—
18	C₄₃×#495	C₄	1	4	yes	—
19	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#10621877	—	2	2	no	—
21	#13063265	—	2	2	no	—
22	#13063265	—	2	2	no	—
23	C₂×C₄₃⋊C₁₆	—	2	2	no	—
24	#13063261	—	2	2	no	—
25	#13063261	D₄	1	4	yes	—
26	#13063236	—	4	1	no	—
27	C₄×C₄₃⋊C₈	—	4	1	no	—
28	C₂²×Q₈×C₄₃	—	2	1	no	—
29	C₂²×D₄×C₄₃	—	2	1	no	—
30	C₂×Q₁₆×C₄₃	—	2	2	no	—
31	C₂×Q₁₆×C₄₃	—	2	1	no	—
32	C₂×Q₁₆×C₄₃	—	2	2	no	—
33	C₂×Q₁₆×C₄₃	C₂×C₄	1	2	yes	—
34	C₂×SD₁₆×C₄₃	—	2	4	no	—
35	C₂×SD₁₆×C₄₃	—	4	4	no	—
36	C₂×D₈×C₄₃	—	2	2	no	—
37	C₂×D₈×C₄₃	—	2	1	no	—
38	C₂×D₈×C₄₃	—	2	2	no	—
39	C₂×D₈×C₄₃	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
42	#124×C₄₃	—	2	4	no	—
43	#124×C₄₃	—	4	1	no	—
44	#124×C₄₃	—	4	1	no	—
45	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
46	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
47	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
48	C₄×C₈×C₄₃	D₄	1	2	yes	—
49	C₂⁴×C₄₃	—	4	1	no	—
50	C₂×Q₈×C₄₃	—	2	2	no	—
51	C₂×Q₈×C₄₃	—	4	1	no	—
52	C₂×Q₈×C₄₃	—	4	2	no	—
53	C₂×Q₈×C₄₃	—	4	2	no	—
54	C₂×D₄×C₄₃	—	2	2	no	—
55	C₂×D₄×C₄₃	—	4	1	no	—
56	C₂×D₄×C₄₃	—	4	2	no	—
57	C₂×D₄×C₄₃	—	4	2	no	—
58	C₂²×C₄×C₄₃	—	4	1	no	—
59	C₂²×C₄×C₄₃	SD₁₆	1	2	yes	—
60	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
61	Q₁₆×C₄₃	—	2	4	no	—
62	Q₁₆×C₄₃	—	4	1	no	—
63	Q₁₆×C₄₃	—	4	1	no	—
64	SD₁₆×C₄₃	—	4	8	no	—
65	D₈×C₄₃	—	2	4	no	—
66	D₈×C₄₃	—	4	1	no	—
67	D₈×C₄₃	—	4	1	no	—
68	C₂×C₈×C₄₃	—	2	2	no	—
69	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
70	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₄₃	#41	1	2	yes	—
74	C₂²⋊C₄×C₄₃	—	4	4	no	—
75	C₂²⋊C₄×C₄₃	—	4	4	no	—
76	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
77	C₄²×C₄₃	D₈	1	1	yes	characteristic
78	C₄²×C₄₃	D₈	1	1	yes	characteristic
79	#10621877	—	2	4	no	—
80	#10621877	—	4	2	no	—
81	C₂×C₄₃⋊C₈	—	4	2	no	—
82	C₄₃⋊C₁₆	—	4	2	no	—
83	C₂³×C₄₃	—	4	2	no	—
84	C₂³×C₄₃	—	8	4	no	—
85	C₂³×C₄₃	—	8	2	no	—
86	C₂³×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
87	Q₈×C₄₃	—	4	2	no	—
88	Q₈×C₄₃	—	4	2	no	—
89	Q₈×C₄₃	—	8	2	no	—
90	D₄×C₄₃	—	4	2	no	—
91	D₄×C₄₃	—	4	2	no	—
92	D₄×C₄₃	—	8	2	no	—
93	C₂×C₄×C₄₃	—	4	2	no	—
94	C₂×C₄×C₄₃	—	4	2	no	—
95	C₂×C₄×C₄₃	—	8	2	no	—
96	C₂×C₄×C₄₃	#102	1	2	yes	—
97	C₂×C₄×C₄₃	#102	1	2	yes	—
98	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₄₃	#121	1	2	yes	—
100	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
102	C₈×C₄₃	—	2	2	no	—
103	C₈×C₄₃	C₄×D₄	1	2	yes	—
104	C₈×C₄₃	#124	1	1	yes	characteristic
105	C₈×C₄₃	#127	1	1	yes	characteristic
106	C₄₃⋊C₈	—	4	4	no	—
107	#13258	—	43	1	no	maximal, Sylow
108	C₂²×C₄₃	—	2	2	no	—
109	C₂²×C₄₃	—	8	4	no	—
110	C₂²×C₄₃	—	8	2	no	—
111	C₂²×C₄₃	—	16	4	no	—
112	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
113	C₂²×C₄₃	#460	1	2	yes	—
114	C₄×C₄₃	—	2	2	no	—
115	C₄×C₄₃	—	2	2	no	—
116	C₄×C₄₃	—	8	2	no	—
117	C₄×C₄₃	#390	1	1	yes	characteristic
118	C₄×C₄₃	#418	1	1	yes	characteristic
119	C₄×C₄₃	#459	1	2	yes	—
120	C₂×#495	D₄₃	1	1	yes	characteristic
121	#2150	—	43	1	no	—
122	C₂×#362	—	43	2	no	—
123	C₂×#361	—	43	2	no	—
124	C₄×#108	—	43	1	no	—
125	C₂×C₄₃	—	2	2	no	—
126	C₂×C₄₃	—	16	2	no	—
127	C₂×C₄₃	#1982	1	1	yes	characteristic
128	C₂×C₄₃	#2148	1	2	yes	—
129	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
130	C₂²×SD₁₆	—	2	1	no	—
131	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
132	C₂×#124	—	2	1	no	—
133	C₂×M₃₂	—	43	2	no	—
134	#495	—	2	2	no	—
135	#495	Dic₄₃	1	4	yes	—
136	C₂×#108	—	43	2	no	—
137	C₄×M₁₆	—	86	1	no	—
138	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
139	C₄⋊C₁₆	—	86	2	no	—
140	#362	—	86	4	no	—
141	#361	—	86	4	no	—
142	#341	—	86	1	no	—
143	C₄₃	#13258	1	1	yes	characteristic, complemented, Sylow
144	C₂²×Q₈	—	2	1	no	—
145	C₂²×D₄	—	2	1	no	—
146	C₂×Q₁₆	—	2	2	no	—
147	C₂×Q₁₆	—	2	2	no	—
148	C₂×Q₁₆	—	2	1	no	—
149	C₂×Q₁₆	C₂×Dic₄₃	1	2	yes	—
150	C₂×SD₁₆	—	2	4	no	—
151	C₂×SD₁₆	—	4	4	no	—
152	C₂×D₈	—	2	2	no	—
153	C₂×D₈	—	2	2	no	—
154	C₂×D₈	—	2	1	no	—
155	C₂×D₈	C₂×Dic₄₃	1	2	yes	—
156	C₂×M₁₆	—	86	2	no	—
157	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
159	#124	—	2	4	no	—
160	#124	—	4	1	no	—
161	#124	—	4	1	no	—
162	C₂×C₂²⋊C₄	—	4	2	no	—
163	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
164	M₃₂	—	86	2	no	—
165	M₃₂	—	86	2	no	—
166	C₂×C₁₆	—	86	2	no	—
167	#108	—	43	4	no	—
168	#108	—	86	2	no	—
169	#97	—	172	1	no	—
170	C₄×C₈	—	172	1	no	—
171	C₄×C₈	C₂×Dic₄₃	1	2	yes	—
172	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
173	C₂⁴	—	4	1	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	4	1	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	—	4	2	no	—
178	C₂×D₄	—	2	2	no	—
179	C₂×D₄	—	4	2	no	—
180	C₂×D₄	—	4	1	no	—
181	C₂×D₄	—	4	2	no	—
182	C₂²×C₄	—	4	1	no	—
183	C₂²×C₄	#10621883	1	2	yes	—
184	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
185	Q₁₆	—	2	4	no	—
186	Q₁₆	—	4	1	no	—
187	Q₁₆	—	4	1	no	—
188	SD₁₆	—	4	8	no	—
189	D₈	—	2	4	no	—
190	D₈	—	4	1	no	—
191	D₈	—	4	1	no	—
192	M₁₆	—	86	4	no	—
193	M₁₆	—	172	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	172	2	no	—
196	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
197	C₂×C₈	D₄×D₄₃	1	2	yes	—
198	C₂×C₈	#10621900	1	2	yes	—
199	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
200	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
201	C₂²⋊C₄	—	4	4	no	—
202	C₂²⋊C₄	—	4	4	no	—
203	C₄²	#10621882	1	1	yes	characteristic
204	C₄²	#10621882	1	1	yes	characteristic
205	C₄²	C₂²⋊Dic₄₃	1	2	yes	—
206	C₁₆	—	172	2	no	—
207	C₂³	—	4	2	no	—
208	C₂³	—	8	4	no	—
209	C₂³	—	8	2	no	—
210	C₂³	C₂×#10621883	1	1	yes	characteristic
211	Q₈	—	4	2	no	—
212	Q₈	—	4	2	no	—
213	Q₈	—	8	2	no	—
214	D₄	—	4	2	no	—
215	D₄	—	4	2	no	—
216	D₄	—	8	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	8	2	no	—
220	C₂×C₄	#13063246	1	2	yes	—
221	C₂×C₄	#13063246	1	2	yes	—
222	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
223	C₂×C₄	#13063296	1	2	yes	—
224	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
225	C₂×C₄	#13063351	1	2	yes	—
226	C₈	—	2	2	no	—
227	C₈	—	172	4	no	—
228	C₈	D₄×Dic₄₃	1	2	yes	—
229	C₈	#13063312	1	1	yes	characteristic
230	C₈	#13063321	1	1	yes	characteristic
231	C₂²	—	2	2	no	—
232	C₂²	—	8	2	no	—
233	C₂²	—	8	4	no	—
234	C₂²	—	16	4	no	—
235	C₂²	C₂×#13063246	1	1	yes	characteristic
236	C₂²	#14583096	1	2	yes	—
237	C₄	—	2	2	no	—
238	C₄	—	2	2	no	—
239	C₄	—	8	2	no	—
240	C₄	#14582802	1	1	yes	characteristic
241	C₄	#14582904	1	1	yes	characteristic
242	C₄	#14583091	1	2	yes	—
243	C₂	—	2	2	no	—
244	C₂	—	16	2	no	—
245	C₂	#19135523	1	1	yes	characteristic
246	C₂	#19136344	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19136351

C₂

yes

maximal, characteristic, complemented

C₂×#14582715

C₂

yes

maximal, complemented

C₂×#14582712

C₂

yes

maximal

C₄×#13063261

C₂

yes

maximal, characteristic, complemented

C₂×C₄₃×#495

C₂

yes

maximal, characteristic

C₂×#13063265

C₂²

yes

—

C₂×#13063261

C₂²

yes

—

C₄×#10621877

—

C₄⋊(C₄₃⋊C₁₆)

—

#14582715

—

#14582712

—

#14582664

—

C₂²×Q₁₆×C₄₃

C₂²

yes

characteristic

C₂²×SD₁₆×C₄₃

—

C₂²×D₈×C₄₃

C₂²

yes

characteristic

C₂×#124×C₄₃

—

C₄₃×#495

—

C₄₃×#495

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

—

—

—

C₂×C₄₃⋊C₁₆

—

#13063261

—

#13063261

D₄

yes

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₂²×Q₈×C₄₃

—

C₂²×D₄×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

C₂×C₄

yes

—

C₂×SD₁₆×C₄₃

—

C₂×SD₁₆×C₄₃

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

C₂×C₄

yes

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

#124×C₄₃

—

#124×C₄₃

—

#124×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂⁴×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

SD₁₆

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

SD₁₆×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂²⋊C₄

yes

—

C₄²×C₄₃

D₈

yes

characteristic

C₄²×C₄₃

D₈

yes

characteristic

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×SD₁₆

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#102

yes

—

C₂×C₄×C₄₃

#102

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#121

yes

—

100

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

101

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

102

C₈×C₄₃

—

103

C₈×C₄₃

C₄×D₄

yes

—

104

C₈×C₄₃

#124

yes

characteristic

105

C₈×C₄₃

#127

yes

characteristic

106

C₄₃⋊C₈

—

107

#13258

—

maximal, Sylow

108

C₂²×C₄₃

—

109

C₂²×C₄₃

—

110

C₂²×C₄₃

—

111

C₂²×C₄₃

—

112

C₂²×C₄₃

C₂×#102

yes

characteristic

113

C₂²×C₄₃

#460

yes

—

114

C₄×C₄₃

—

115

C₄×C₄₃

—

116

C₄×C₄₃

—

117

C₄×C₄₃

#390

yes

characteristic

118

C₄×C₄₃

#418

yes

characteristic

119

C₄×C₄₃

#459

yes

—

120

C₂×#495

D₄₃

yes

characteristic

121

#2150

—

122

C₂×#362

—

123

C₂×#361

—

124

C₄×#108

—

125

C₂×C₄₃

—

126

C₂×C₄₃

—

127

C₂×C₄₃

#1982

yes

characteristic

128

C₂×C₄₃

#2148

yes

—

129

C₂²×Q₁₆

C₂×D₄₃

yes

characteristic

130

C₂²×SD₁₆

—

131

C₂²×D₈

C₂×D₄₃

yes

characteristic

132

C₂×#124

—

133

C₂×M₃₂

—

134

#495

—

135

#495

Dic₄₃

yes

—

136

C₂×#108

—

137

C₄×M₁₆

—

138

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

139

C₄⋊C₁₆

—

140

#362

—

141

#361

—

142

#341

—

143

C₄₃

#13258

yes

characteristic, complemented, Sylow

144

C₂²×Q₈

—

145

C₂²×D₄

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

C₂×Q₁₆

—

149

C₂×Q₁₆

C₂×Dic₄₃

yes

—

150

C₂×SD₁₆

—

151

C₂×SD₁₆

—

152

C₂×D₈

—

153

C₂×D₈

—

154

C₂×D₈

—

155

C₂×D₈

C₂×Dic₄₃

yes

—

156

C₂×M₁₆

—

157

C₂²×C₈

C₂²⋊D₄₃

yes

characteristic

158

C₂²×C₈

C₂²×D₄₃

yes

characteristic

159

#124

—

160

#124

—

161

#124

—

162

C₂×C₂²⋊C₄

—

163

C₂×C₄²

C₂²⋊D₄₃

yes

characteristic

164

M₃₂

—

165

M₃₂

—

166

C₂×C₁₆

—

167

#108

—

168

#108

—

169

#97

—

172

—

170

C₄×C₈

—

172

—

171

C₄×C₈

C₂×Dic₄₃

yes

—

172

C₄×C₈

C₂²⋊D₄₃

yes

—

173

C₂⁴

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂²×C₄

—

183

C₂²×C₄

#10621883

yes

—

184

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

185

Q₁₆

—

186

Q₁₆

—

187

Q₁₆

—

188

SD₁₆

—

189

D₈

—

190

D₈

—

191

D₈

—

192

M₁₆

—

193

M₁₆

—

172

—

194

C₂×C₈

—

195

C₂×C₈

—

172

—

196

C₂×C₈

C₂²⋊Dic₄₃

yes

—

197

C₂×C₈

D₄×D₄₃

yes

—

198

C₂×C₈

#10621900

yes

—

199

C₂×C₈

C₂²×Dic₄₃

yes

characteristic

200

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

201

C₂²⋊C₄

—

202

C₂²⋊C₄

—

203

C₄²

#10621882

yes

characteristic

204

C₄²

#10621882

yes

characteristic

205

C₄²

C₂²⋊Dic₄₃

yes

—

206

C₁₆

—

172

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

C₂×#10621883

yes

characteristic

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

D₄

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

#13063246

yes

—

221

C₂×C₄

#13063246

yes

—

222

C₂×C₄

C₂×C₂²⋊Dic₄₃

yes

characteristic

223

C₂×C₄

#13063296

yes

—

224

C₂×C₄

C₂×#10621882

yes

characteristic

225

C₂×C₄

#13063351

yes

—

226

C₈

—

227

C₈

—

172

—

228

C₈

D₄×Dic₄₃

yes

—

229

C₈

#13063312

yes

characteristic

230

C₈

#13063321

yes

characteristic

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

C₂×#13063246

yes

characteristic

236

C₂²

#14583096

yes

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

#14582802

yes

characteristic

241

C₄

#14582904

yes

characteristic

242

C₄

#14583091

yes

—

243

C₂

—

244

C₂

—

245

C₂

#19135523

yes

characteristic

246

C₂

#19136344

yes

—

	subgroup	G/H
center	C₂²	C₂×#13063246
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#495	C₂
socle	C₂²×C₄₃	C₂×#102
prime radical	C₂²×D₈×C₄₃	C₂²
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#495	D₄₃
hypocenter	C₄₃	#13258
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#495

subgroup

G/H

center

C₂²

C₂×#13063246

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#495

C₂

socle

C₂²×C₄₃

C₂×#102

prime radical

C₂²×D₈×C₄₃

C₂²

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#495

N	H ≅ G/N	type
1. #19136351	C₂	semidirect
2. C₂×#14582715	C₂	semidirect
4. C₄×#13063261	C₂	semidirect
143. C₄₃	#13258	semidirect

H ≅ G/N

type

1. #19136351

C₂

semidirect

2. C₂×#14582715

C₂

semidirect

4. C₄×#13063261

C₂

semidirect

143. C₄₃

#13258

semidirect

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

subgroup	index
#19136351	2
C₂×#14582715	2
C₂×#14582712	2
C₄×#13063261	2
C₂×C₄₃×#495	2
#13258	43

subgroup

index

C₂×C₄₃×#495

Subgroups — #25015091

Conjugacy classes of subgroups

Complements

Maximal subgroups