Group #24991062 — subgroups

Subgroups — #24991062

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	#19135398	C₂	1	1	yes	maximal, characteristic
2	#19135358	C₂	1	2	yes	maximal
3	C₂×#14582648	C₂	1	1	yes	maximal, characteristic
4	#19132436	C₂	1	2	yes	maximal
5	C₄₃×#2369	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063256	—	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	#14582648	C₄	1	4	yes	complemented
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#391	—	2	2	no	—
15	C₄₃×#389	—	2	2	no	—
16	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
17	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₄₃⋊C₈	—	2	1	no	—
19	C₂²×C₄₃⋊C₈	—	2	2	no	—
20	C₂×C₄⋊Dic₄₃	—	2	1	no	—
21	C₂×C₄⋊Dic₄₃	—	2	2	no	—
22	#13063256	—	4	4	no	—
23	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
25	#13063249	—	4	4	no	—
26	C₄×C₄₃⋊C₈	—	2	2	no	—
27	C₂²×Q₈×C₄₃	D₄	1	2	yes	—
28	C₄⋊Q₈×C₄₃	—	2	2	no	—
29	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
30	C₄⋊Q₈×C₄₃	Q₈	1	2	yes	—
31	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
32	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
35	C₂×C₄²×C₄₃	—	2	2	no	—
36	C₂×C₄²×C₄₃	—	2	2	no	—
37	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
38	#95×C₄₃	—	2	4	no	—
39	#95×C₄₃	—	2	2	no	—
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	—	2	2	no	—
46	C₂²×C₄×C₄₃	—	2	2	no	—
47	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
49	C₂²×Dic₄₃	—	4	1	no	—
50	C₄⋊C₄×C₄₃	—	2	4	no	—
51	C₄⋊C₄×C₄₃	—	2	4	no	—
52	C₄⋊C₄×C₄₃	—	2	2	no	—
53	C₄⋊C₄×C₄₃	—	2	2	no	—
54	C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₄⋊C₄×C₄₃	—	8	2	no	—
56	C₄⋊C₄×C₄₃	SD₁₆	1	4	yes	—
57	C₄²×C₄₃	—	4	2	no	—
58	C₄²×C₄₃	—	4	2	no	—
59	C₄²×C₄₃	—	8	2	no	—
60	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
61	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
62	C₄²×C₄₃	#41	1	2	yes	—
63	C₄⋊Dic₄₃	—	4	2	no	—
64	C₄⋊Dic₄₃	—	4	2	no	—
65	C₄⋊Dic₄₃	—	4	2	no	—
66	C₂×C₄₃⋊C₈	—	2	2	no	—
67	C₂×C₄₃⋊C₈	—	2	4	no	—
68	C₂×C₄₃⋊C₈	—	4	1	no	—
69	C₂×C₄₃⋊C₈	—	4	1	no	—
70	C₂×C₄₃⋊C₈	—	4	2	no	—
71	C₂×C₄₃⋊C₈	—	4	2	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	—	2	4	no	—
79	C₂×C₄×C₄₃	—	4	2	no	—
80	C₂×C₄×C₄₃	—	4	2	no	—
81	C₂×C₄×C₄₃	—	4	2	no	—
82	C₂×C₄×C₄₃	—	4	2	no	—
83	C₂×C₄×C₄₃	—	4	2	no	—
84	C₂×C₄×C₄₃	—	4	2	no	—
85	C₂×C₄×C₄₃	—	4	2	no	—
86	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
88	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
89	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
90	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
91	C₂×C₄×C₄₃	#135	1	2	yes	—
92	C₂×C₄×C₄₃	#137	1	2	yes	—
93	C₂×C₄×C₄₃	#137	1	2	yes	—
94	C₂×Dic₄₃	—	8	2	no	—
95	C₂×Dic₄₃	—	8	1	no	—
96	C₄₃⋊C₈	—	4	2	no	—
97	C₄₃⋊C₈	—	4	4	no	—
98	#8928	—	43	1	no	maximal, Sylow
99	C₂²×C₄₃	#385	1	1	yes	characteristic
100	C₂²×C₄₃	#448	1	2	yes	—
101	C₂²×C₄₃	#452	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	—	4	4	no	—
108	C₄×C₄₃	—	8	2	no	—
109	C₄×C₄₃	C₄×SD₁₆	1	2	yes	—
110	C₄×C₄₃	#441	1	2	yes	—
111	C₄×C₄₃	#475	1	2	yes	—
112	C₄×C₄₃	#479	1	2	yes	—
113	Dic₄₃	—	16	1	no	—
114	#2369	D₄₃	1	1	yes	characteristic
115	#1956	—	43	1	no	—
116	#1948	—	43	2	no	—
117	C₂×#333	—	43	1	no	—
118	#1279	—	43	2	no	—
119	C₂×C₄₃	#1623	1	1	yes	characteristic
120	C₂×C₄₃	#1634	1	1	yes	characteristic
121	C₂×C₄₃	#1643	1	2	yes	—
122	C₂×C₄₃	#1856	1	1	yes	characteristic
123	C₂×C₄₃	#1865	1	2	yes	—
124	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
125	C₂×#106	—	86	2	no	—
126	C₂×C₄⋊C₈	—	43	2	no	—
127	C₂×#103	—	86	2	no	—
128	C₂×C₄×C₈	—	43	1	no	—
129	#391	—	2	2	no	—
130	#389	—	2	2	no	—
131	#384	—	43	1	no	—
132	C₄×C₄⋊C₄	—	2	2	no	—
133	C₄×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
134	#340	—	86	2	no	—
135	#333	—	43	4	no	—
136	C₄₃	#8928	1	1	yes	characteristic, complemented, Sylow
137	C₂²×Q₈	C₂²⋊D₄₃	1	2	yes	—
138	C₂²×C₈	—	86	2	no	—
139	C₂²×C₈	—	86	1	no	—
140	C₄⋊Q₈	—	2	2	no	—
141	C₄⋊Q₈	Dic₈₆	1	2	yes	—
142	C₄⋊Q₈	C₄×D₄₃	1	2	yes	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	2	2	no	—
145	C₂×C₄⋊C₄	—	86	2	no	—
146	C₂×C₄⋊C₄	—	86	1	no	—
147	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
148	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
149	C₂×C₄²	—	2	2	no	—
150	C₂×C₄²	—	2	2	no	—
151	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
152	#106	—	172	4	no	—
153	C₄⋊C₈	—	43	4	no	—
154	C₄⋊C₈	—	86	2	no	—
155	#103	—	172	4	no	—
156	C₄×C₈	—	86	2	no	—
157	#95	—	2	4	no	—
158	#95	—	2	2	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	Dic₄₃⋊C₄	1	4	yes	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	172	1	no	—
167	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
169	C₂×C₈	—	86	2	no	—
170	C₂×C₈	—	86	4	no	—
171	C₂×C₈	—	172	1	no	—
172	C₂×C₈	—	172	1	no	—
173	C₂×C₈	—	172	2	no	—
174	C₂×C₈	—	172	2	no	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	8	2	no	—
181	C₄⋊C₄	—	172	2	no	—
182	C₄⋊C₄	—	172	2	no	—
183	C₄⋊C₄	—	172	2	no	—
184	C₄⋊C₄	#10621884	1	4	yes	—
185	C₄²	—	4	2	no	—
186	C₄²	—	4	2	no	—
187	C₄²	—	8	2	no	—
188	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
189	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
190	C₄²	#10621898	1	2	yes	—
191	C₂³	#13063294	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	—	2	4	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	344	1	no	—
206	C₂×C₄	—	344	2	no	—
207	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
208	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
209	C₂×C₄	#13063304	1	2	yes	—
210	C₂×C₄	#13063308	1	1	yes	characteristic
211	C₂×C₄	C₂×#10621884	1	2	yes	—
212	C₂×C₄	#13063345	1	2	yes	—
213	C₂×C₄	#13063355	1	2	yes	—
214	C₂×C₄	#13063356	1	2	yes	—
215	C₈	—	172	2	no	—
216	C₈	—	172	4	no	—
217	C₂²	#14582772	1	1	yes	characteristic
218	C₂²	#14583038	1	2	yes	—
219	C₂²	#14583061	1	2	yes	—
220	C₂²	#14583067	1	1	yes	characteristic
221	C₂²	#14583077	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	4	no	—
225	C₄	—	4	4	no	—
226	C₄	—	8	2	no	—
227	C₄	—	688	1	no	—
228	C₄	C₄×#10621884	1	2	yes	—
229	C₄	#14583004	1	2	yes	—
230	C₄	#14583184	1	2	yes	—
231	C₄	#14583206	1	2	yes	—
232	C₂	#19133673	1	1	yes	characteristic
233	C₂	#19133740	1	1	yes	characteristic
234	C₂	#19133802	1	2	yes	—
235	C₂	#19134805	1	1	yes	characteristic
236	C₂	#19134863	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19135398

C₂

yes

maximal, characteristic

#19135358

C₂

yes

maximal

C₂×#14582648

C₂

yes

maximal, characteristic

#19132436

C₂

yes

maximal

C₄₃×#2369

C₂

yes

maximal, characteristic

C₂×#13063256

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂×#13063249

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#14582769

C₂²

yes

characteristic

#14582661

—

#14582648

C₄

yes

complemented

C₂×C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄₃×#391

—

C₄₃×#389

—

C₄×C₄⋊C₄×C₄₃

—

C₄×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

#13063256

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

C₂×C₄

yes

—

#13063249

—

C₄×C₄₃⋊C₈

—

C₂²×Q₈×C₄₃

D₄

yes

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

C₂×C₄

yes

—

C₄⋊Q₈×C₄₃

Q₈

yes

—

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

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#95×C₄₃

—

#95×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₄⋊C₄

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

SD₁₆

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄²×C₄₃

#41

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

—

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

—

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×SD₁₆

yes

—

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

100

C₂²×C₄₃

#448

yes

—

101

C₂²×C₄₃

#452

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

—

108

C₄×C₄₃

—

109

C₄×C₄₃

C₄×SD₁₆

yes

—

110

C₄×C₄₃

#441

yes

—

111

C₄×C₄₃

#475

yes

—

112

C₄×C₄₃

#479

yes

—

113

Dic₄₃

—

114

#2369

D₄₃

yes

characteristic

115

#1956

—

116

#1948

—

117

C₂×#333

—

118

#1279

—

119

C₂×C₄₃

#1623

yes

characteristic

120

C₂×C₄₃

#1634

yes

characteristic

121

C₂×C₄₃

#1643

yes

—

122

C₂×C₄₃

#1856

yes

characteristic

123

C₂×C₄₃

#1865

yes

—

124

C₂×C₄⋊Q₈

C₂×D₄₃

yes

characteristic

125

C₂×#106

—

126

C₂×C₄⋊C₈

—

127

C₂×#103

—

128

C₂×C₄×C₈

—

129

#391

—

130

#389

—

131

#384

—

132

C₄×C₄⋊C₄

—

133

C₄×C₄⋊C₄

C₂×D₄₃

yes

—

134

#340

—

135

#333

—

136

C₄₃

#8928

yes

characteristic, complemented, Sylow

137

C₂²×Q₈

C₂²⋊D₄₃

yes

—

138

C₂²×C₈

—

139

C₂²×C₈

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

Dic₈₆

yes

—

142

C₄⋊Q₈

C₄×D₄₃

yes

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

148

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

C₂²×D₄₃

yes

characteristic

152

#106

—

172

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

#103

—

172

—

156

C₄×C₈

—

157

#95

—

158

#95

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

Dic₄₃⋊C₄

yes

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

172

—

167

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

169

C₂×C₈

—

170

C₂×C₈

—

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

C₄⋊C₄

—

172

—

182

C₄⋊C₄

—

172

—

183

C₄⋊C₄

—

172

—

184

C₄⋊C₄

#10621884

yes

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

C₂×Dic₈₆

yes

characteristic

189

C₄²

C₂×C₄×D₄₃

yes

characteristic

190

C₄²

#10621898

yes

—

191

C₂³

#13063294

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

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

344

—

206

C₂×C₄

—

344

—

207

C₂×C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

208

C₂×C₄

C₄×C₂²⋊D₄₃

yes

—

209

C₂×C₄

#13063304

yes

—

210

C₂×C₄

#13063308

yes

characteristic

211

C₂×C₄

C₂×#10621884

yes

—

212

C₂×C₄

#13063345

yes

—

213

C₂×C₄

#13063355

yes

—

214

C₂×C₄

#13063356

yes

—

215

C₈

—

172

—

216

C₈

—

172

—

217

C₂²

#14582772

yes

characteristic

218

C₂²

#14583038

yes

—

219

C₂²

#14583061

yes

—

220

C₂²

#14583067

yes

characteristic

221

C₂²

#14583077

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

688

—

228

C₄

C₄×#10621884

yes

—

229

C₄

#14583004

yes

—

230

C₄

#14583184

yes

—

231

C₄

#14583206

yes

—

232

C₂

#19133673

yes

characteristic

233

C₂

#19133740

yes

characteristic

234

C₂

#19133802

yes

—

235

C₂

#19134805

yes

characteristic

236

C₂

#19134863

yes

—

	subgroup	G/H
center	C₂³	#13063294
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2369	C₂
socle, prime radical	C₂³×C₄₃	#120
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#2369	D₄₃
hypocenter	C₄₃	#8928
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2369

subgroup

G/H

center

C₂³

#13063294

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2369

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 ◁ #2369

N	H ≅ G/N	type
12. #14582648	C₄	semidirect
136. C₄₃	#8928	semidirect

H ≅ G/N

type

12. #14582648

C₄

semidirect

136. C₄₃

#8928

semidirect

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

subgroup	index
#19135398	2
#19135358	2
C₂×#14582648	2
#19132436	2
C₄₃×#2369	2
#8928	43

subgroup

index

C₄₃×#2369

Subgroups — #24991062

Conjugacy classes of subgroups

Complements

Maximal subgroups