Group #24989753 — subgroups

Subgroups — #24989753

Order 11008.

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

normal subgroups only

This group has 358 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	C₂×#14583029	C₂	1	1	yes	maximal, characteristic
2	#19133343	C₂	1	1	yes	maximal, characteristic
3	#19133023	C₂	1	2	yes	maximal
4	#19132490	C₂	1	2	yes	maximal
5	C₄₃×#1837	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
7	#14583029	—	2	1	no	—
8	#14583029	—	2	1	no	—
9	#14583029	C₄	1	2	yes	—
10	#14583029	C₄	1	2	yes	—
11	#14582952	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₃⋊C₈	—	2	1	no	—
14	C₂×#13063235	—	2	1	no	—
15	#14582652	—	2	1	no	—
16	#14582650	—	2	1	no	—
17	#14582629	—	2	4	no	—
18	C₄₃×#423	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#341	—	2	1	no	—
21	C₄₃×#341	—	2	1	no	—
22	C₂²×Dic₈₆	Q₈	1	1	yes	characteristic
23	C₂²×C₄₃⋊C₈	—	2	1	no	—
24	C₄×Dic₈₆	—	2	1	no	—
25	C₄×Dic₈₆	—	2	1	no	—
26	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
27	C₄×Dic₈₆	D₄	1	2	yes	—
28	C₂×C₄⋊Dic₄₃	Q₈	1	1	yes	characteristic
29	C₂×Dic₄₃⋊C₄	—	2	1	no	—
30	C₂×C₄×Dic₄₃	—	2	1	no	—
31	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
32	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
33	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
34	Dic₄₃⋊C₈	—	2	2	no	—
35	Dic₄₃⋊C₈	—	2	2	no	—
36	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
37	#13063235	—	2	2	no	—
38	#13063235	—	2	2	no	—
39	C₄×C₄₃⋊C₈	—	2	2	no	—
40	C₂×M₁₆×C₄₃	—	2	2	no	—
41	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₄₃	—	2	2	no	—
45	C₄⋊C₈×C₄₃	—	2	2	no	—
46	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
49	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
53	C₂²×Dic₄₃	—	2	1	no	—
54	C₂²×Dic₄₃	—	2	1	no	—
55	C₂×Dic₈₆	—	2	1	no	—
56	C₂×Dic₈₆	—	4	2	no	—
57	C₂×Dic₈₆	C₄⋊C₄	1	2	yes	—
58	M₁₆×C₄₃	—	4	2	no	—
59	M₁₆×C₄₃	—	4	2	no	—
60	C₂×C₈×C₄₃	—	2	2	no	—
61	C₂×C₈×C₄₃	—	2	2	no	—
62	C₂×C₈×C₄₃	—	4	2	no	—
63	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₄₃	#41	1	1	yes	characteristic
71	C₄⋊Dic₄₃	—	2	1	no	—
72	C₄⋊Dic₄₃	C₄⋊C₄	1	2	yes	—
73	Dic₄₃⋊C₄	—	2	2	no	—
74	Dic₄₃⋊C₄	—	2	2	no	—
75	C₄×Dic₄₃	—	2	2	no	—
76	C₄×Dic₄₃	—	2	2	no	—
77	C₂×C₄₃⋊C₈	—	2	2	no	—
78	C₂×C₄₃⋊C₈	—	4	2	no	—
79	C₂×C₄₃⋊C₈	—	4	2	no	—
80	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₄₃	—	2	2	no	—
82	C₂×C₄×C₄₃	—	4	1	no	—
83	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
86	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
87	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
88	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₄₃	#135	1	2	yes	—
90	C₂×C₄×C₄₃	#137	1	2	yes	—
91	C₂×Dic₄₃	—	2	2	no	—
92	C₂×Dic₄₃	—	2	2	no	—
93	C₂×Dic₄₃	—	4	2	no	—
94	C₂×Dic₄₃	—	4	2	no	—
95	Dic₈₆	—	2	4	no	—
96	Dic₈₆	—	4	2	no	—
97	C₈×C₄₃	—	2	1	no	—
98	C₈×C₄₃	—	2	1	no	—
99	C₈×C₄₃	—	2	1	no	—
100	C₈×C₄₃	—	2	1	no	—
101	C₈×C₄₃	—	8	2	no	—
102	C₄₃⋊C₈	—	4	2	no	—
103	C₄₃⋊C₈	—	8	2	no	—
104	#8665	—	43	1	no	maximal, Sylow
105	C₂²×C₄₃	—	2	1	no	—
106	C₂²×C₄₃	—	2	1	no	—
107	C₂²×C₄₃	#380	1	1	yes	characteristic
108	C₂²×C₄₃	#479	1	2	yes	—
109	C₄×C₄₃	—	2	1	no	—
110	C₄×C₄₃	—	2	1	no	—
111	C₄×C₄₃	—	2	1	no	—
112	C₄×C₄₃	#416	1	1	yes	characteristic
113	C₄×C₄₃	#419	1	1	yes	characteristic
114	C₄×C₄₃	#430	1	2	yes	—
115	C₄×C₄₃	#464	1	2	yes	—
116	Dic₄₃	—	4	2	no	—
117	Dic₄₃	—	4	2	no	—
118	C₂×#446	—	43	1	no	—
119	#1837	D₄₃	1	1	yes	characteristic
120	#1564	—	43	1	no	—
121	#1487	—	43	2	no	—
122	#1301	—	43	2	no	—
123	C₂×C₄₃	—	2	2	no	—
124	C₂×C₄₃	#1805	1	1	yes	characteristic
125	C₂×C₄₃	#1811	1	1	yes	characteristic
126	C₂×C₄₃	#1814	1	1	yes	characteristic
127	C₂×C₄×Q₈	—	43	1	no	—
128	#446	—	43	2	no	—
129	#446	—	43	2	no	—
130	#446	—	86	1	no	—
131	#446	—	86	1	no	—
132	#431	—	43	2	no	—
133	#423	C₂×D₄₃	1	2	yes	—
134	C₂×C₄⋊C₈	—	43	1	no	—
135	C₂×C₄⋊C₈	—	86	1	no	—
136	C₂×#97	—	86	1	no	—
137	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
138	#341	—	2	1	no	—
139	#341	—	2	1	no	—
140	#335	—	86	1	no	—
141	#334	—	86	1	no	—
142	Q₈⋊C₈	—	86	4	no	—
143	C₄₃	#8665	1	1	yes	characteristic, complemented, Sylow
144	C₂²×Q₈	—	43	1	no	—
145	C₂×M₁₆	—	2	2	no	—
146	C₂²×C₈	—	86	1	no	—
147	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
148	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
149	C₄×Q₈	—	43	2	no	—
150	C₄×Q₈	—	43	2	no	—
151	C₄×Q₈	—	86	1	no	—
152	C₄×Q₈	—	86	1	no	—
153	C₂×C₄⋊C₄	—	43	1	no	—
154	C₂×C₄⋊C₄	—	86	1	no	—
155	C₂×C₄²	—	86	1	no	—
156	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	43	2	no	—
160	C₄⋊C₈	—	86	2	no	—
161	C₄⋊C₈	—	86	2	no	—
162	C₄⋊C₈	—	86	1	no	—
163	C₄⋊C₈	—	86	2	no	—
164	C₂²⋊C₈	—	86	2	no	—
165	#97	—	86	2	no	—
166	#97	—	86	2	no	—
167	C₄×C₈	—	86	2	no	—
168	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
169	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
170	C₄×C₈	D₁₇₂	1	1	yes	characteristic
171	C₄×C₈	D₁₇₂	1	1	yes	characteristic
172	C₂×Q₈	—	43	2	no	—
173	C₂×Q₈	—	86	1	no	—
174	C₂×Q₈	—	172	2	no	—
175	C₂²×C₄	—	86	1	no	—
176	C₂²×C₄	—	86	1	no	—
177	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
178	C₂²×C₄	#10621902	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
180	M₁₆	—	4	2	no	—
181	M₁₆	—	4	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	86	2	no	—
186	C₂×C₈	—	172	2	no	—
187	C₂×C₈	—	172	2	no	—
188	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
189	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
190	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
191	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
192	C₄⋊C₄	—	43	2	no	—
193	C₄⋊C₄	—	86	2	no	—
194	C₄⋊C₄	—	86	2	no	—
195	C₄⋊C₄	—	86	1	no	—
196	C₄²	—	86	2	no	—
197	C₄²	—	86	2	no	—
198	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
199	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
200	C₄²	D₄×D₄₃	1	1	yes	characteristic
201	C₄²	#10621900	1	1	yes	characteristic
202	C₂³	#13063301	1	1	yes	characteristic
203	Q₈	—	86	4	no	—
204	Q₈	—	172	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	86	2	no	—
208	C₂×C₄	—	86	2	no	—
209	C₂×C₄	—	172	2	no	—
210	C₂×C₄	—	172	2	no	—
211	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
212	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
213	C₂×C₄	#13063283	1	1	yes	characteristic
214	C₂×C₄	#13063296	1	1	yes	characteristic
215	C₂×C₄	#13063300	1	1	yes	characteristic
216	C₂×C₄	#13063305	1	1	yes	characteristic
217	C₂×C₄	#13063345	1	2	yes	—
218	C₂×C₄	#13063355	1	2	yes	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	8	2	no	—
224	C₈	—	344	2	no	—
225	C₈	—	172	2	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	#14582756	1	1	yes	characteristic
229	C₂²	#14583203	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	172	2	no	—
234	C₄	—	172	2	no	—
235	C₄	#14582893	1	1	yes	characteristic
236	C₄	#14582907	1	1	yes	characteristic
237	C₄	#14582946	1	2	yes	—
238	C₄	#14583118	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#19134607	1	1	yes	characteristic
241	C₂	#19134634	1	1	yes	characteristic
242	C₂	#19134650	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583029

C₂

yes

maximal, characteristic

#19133343

C₂

yes

maximal, characteristic

#19133023

C₂

yes

maximal

#19132490

C₂

yes

maximal

C₄₃×#1837

C₂

yes

maximal, characteristic

C₂×C₄×Dic₈₆

C₂²

yes

—

—

C₄

yes

—

#14583029

C₄

yes

—

#14582952

C₂²

yes

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₈

—

—

—

—

—

C₄₃×#423

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#341

—

C₄₃×#341

—

C₂²×Dic₈₆

Q₈

yes

characteristic

C₂²×C₄₃⋊C₈

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

C₄×Dic₈₆

C₂×C₄

yes

—

C₄×Dic₈₆

D₄

yes

—

C₂×C₄⋊Dic₄₃

Q₈

yes

characteristic

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

C₂×C₄

yes

—

Dic₄₃⋊C₈

—

Dic₄₃⋊C₈

—

C₂²⋊(C₄₃⋊C₈)

—

#13063235

—

#13063235

—

C₄×C₄₃⋊C₈

—

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₄⋊C₄

yes

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

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⋊C₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

100

C₈×C₄₃

—

101

C₈×C₄₃

—

102

C₄₃⋊C₈

—

103

C₄₃⋊C₈

—

104

#8665

—

maximal, Sylow

105

C₂²×C₄₃

—

106

C₂²×C₄₃

—

107

C₂²×C₄₃

#380

yes

characteristic

108

C₂²×C₄₃

#479

yes

—

109

C₄×C₄₃

—

110

C₄×C₄₃

—

111

C₄×C₄₃

—

112

C₄×C₄₃

#416

yes

characteristic

113

C₄×C₄₃

#419

yes

characteristic

114

C₄×C₄₃

#430

yes

—

115

C₄×C₄₃

#464

yes

—

116

Dic₄₃

—

117

Dic₄₃

—

118

C₂×#446

—

119

#1837

D₄₃

yes

characteristic

120

#1564

—

121

#1487

—

122

#1301

—

123

C₂×C₄₃

—

124

C₂×C₄₃

#1805

yes

characteristic

125

C₂×C₄₃

#1811

yes

characteristic

126

C₂×C₄₃

#1814

yes

characteristic

127

C₂×C₄×Q₈

—

128

#446

—

129

#446

—

130

#446

—

131

#446

—

132

#431

—

133

#423

C₂×D₄₃

yes

—

134

C₂×C₄⋊C₈

—

135

C₂×C₄⋊C₈

—

136

C₂×#97

—

137

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

138

#341

—

139

#341

—

140

#335

—

141

#334

—

142

Q₈⋊C₈

—

143

C₄₃

#8665

yes

characteristic, complemented, Sylow

144

C₂²×Q₈

—

145

C₂×M₁₆

—

146

C₂²×C₈

—

147

C₂²×C₈

C₂²⋊D₄₃

yes

characteristic

148

C₂²×C₈

C₂²⋊D₄₃

yes

characteristic

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄²

—

156

C₂×C₄²

C₂²×D₄₃

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₂²⋊C₈

—

165

#97

—

166

#97

—

167

C₄×C₈

—

168

C₄×C₈

C₄×D₄₃

yes

characteristic

169

C₄×C₈

C₄×D₄₃

yes

characteristic

170

C₄×C₈

D₁₇₂

yes

characteristic

171

C₄×C₈

D₁₇₂

yes

characteristic

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

172

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

Q₈×D₄₃

yes

characteristic

178

C₂²×C₄

#10621902

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

180

M₁₆

—

181

M₁₆

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

172

—

187

C₂×C₈

—

172

—

188

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

189

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

190

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

191

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄²

—

197

C₄²

—

198

C₄²

C₂×C₄×D₄₃

yes

characteristic

199

C₄²

C₂×D₁₇₂

yes

characteristic

200

C₄²

D₄×D₄₃

yes

characteristic

201

C₄²

#10621900

yes

characteristic

202

C₂³

#13063301

yes

characteristic

203

Q₈

—

204

Q₈

—

172

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

172

—

210

C₂×C₄

—

172

—

211

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

212

C₂×C₄

C₄⋊C₄×D₄₃

yes

characteristic

213

C₂×C₄

#13063283

yes

characteristic

214

C₂×C₄

#13063296

yes

characteristic

215

C₂×C₄

#13063300

yes

characteristic

216

C₂×C₄

#13063305

yes

characteristic

217

C₂×C₄

#13063345

yes

—

218

C₂×C₄

#13063355

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

344

—

225

C₈

—

172

—

226

C₂²

—

227

C₂²

—

228

C₂²

#14582756

yes

characteristic

229

C₂²

#14583203

yes

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

172

—

234

C₄

—

172

—

235

C₄

#14582893

yes

characteristic

236

C₄

#14582907

yes

characteristic

237

C₄

#14582946

yes

—

238

C₄

#14583118

yes

—

239

C₂

—

240

C₂

#19134607

yes

characteristic

241

C₂

#19134634

yes

characteristic

242

C₂

#19134650

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063296
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1837	C₂
socle	C₂²×C₄₃	#380
prime radical	C₂³×C₄₃	C₂²⋊Q₈
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1837	D₄₃
hypocenter	C₄₃	#8665
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂×C₄

#13063296

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1837

C₂

socle

C₂²×C₄₃

#380

prime radical

C₂³×C₄₃

C₂²⋊Q₈

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
143. C₄₃	#8665	semidirect

H ≅ G/N

type

143. C₄₃

#8665

semidirect

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

subgroup	index
C₂×#14583029	2
#19133343	2
#19133023	2
#19132490	2
C₄₃×#1837	2
#8665	43

subgroup

index

C₄₃×#1837

Subgroups — #24989753

Conjugacy classes of subgroups

Complements

Maximal subgroups