Group #24995634 — subgroups

Subgroups — #24995634

Order 11008.

478 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 159 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	#19142973	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582647	C₂	1	2	yes	maximal
4	C₂×#14582646	C₂	1	2	yes	maximal
5	C₄₃×#1831	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063325	C₂²	1	1	yes	characteristic
7	C₂×#13063325	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
10	#14582805	—	2	2	no	—
11	#14582805	C₄	1	4	yes	—
12	#14582765	—	2	1	no	—
13	#14582765	—	2	1	no	—
14	#14582654	—	2	1	no	—
15	#14582647	—	2	4	no	—
16	#14582646	—	2	4	no	—
17	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
18	C₄³×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#336	—	2	2	no	—
20	C₂²×Dic₈₆	—	2	1	no	—
21	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
22	C₂²×C₄₃⋊C₈	—	2	2	no	—
23	#13063325	—	2	2	no	—
24	#13063325	—	2	2	no	—
25	#13063325	—	2	2	no	—
26	#13063325	—	2	2	no	—
27	C₂×C₄⋊Dic₄₃	—	2	1	no	—
28	C₂×C₄⋊Dic₄₃	—	2	1	no	—
29	C₂×C₄⋊Dic₄₃	—	2	1	no	—
30	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
31	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
32	C₄⋊(C₄₃⋊C₈)	D₄	1	4	yes	—
33	C₄×C₄₃⋊C₈	—	4	2	no	—
34	C₄₃⋊#95	—	2	4	no	—
35	C₄₃⋊#95	—	2	4	no	—
36	C₂²×C₈×C₄₃	—	2	2	no	—
37	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₄₃	D₄	1	2	yes	—
41	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₄₃	—	2	2	no	—
43	C₄⋊C₈×C₄₃	—	2	2	no	—
44	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
45	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×Dic₄₃	—	2	2	no	—
50	C₂²×Dic₄₃	—	2	2	no	—
51	C₂×Dic₈₆	—	2	4	no	—
52	C₂×Dic₈₆	—	4	1	no	—
53	C₂×Dic₈₆	—	4	1	no	—
54	C₂×Dic₈₆	—	4	4	no	—
55	C₂×Dic₈₆	—	4	4	no	—
56	C₂×C₈×C₄₃	—	4	2	no	—
57	C₂×C₈×C₄₃	—	4	4	no	—
58	C₄²×C₄₃	—	2	4	no	—
59	C₄²×C₄₃	—	2	2	no	—
60	C₄²×C₄₃	—	4	2	no	—
61	C₄²×C₄₃	SD₁₆	1	2	yes	—
62	C₄²×C₄₃	Q₁₆	1	2	yes	—
63	C₄²×C₄₃	C₂×D₄	1	2	yes	—
64	C₄²×C₄₃	#41	1	2	yes	—
65	C₄⋊Dic₄₃	—	2	4	no	—
66	C₄⋊Dic₄₃	—	4	2	no	—
67	C₄⋊Dic₄₃	—	4	2	no	—
68	C₄⋊Dic₄₃	—	4	1	no	—
69	C₄⋊Dic₄₃	—	4	1	no	—
70	C₂×C₄₃⋊C₈	—	2	4	no	—
71	C₂×C₄₃⋊C₈	—	4	2	no	—
72	C₂×C₄₃⋊C₈	—	4	2	no	—
73	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₄₃	—	2	2	no	—
75	C₂×C₄×C₄₃	—	2	2	no	—
76	C₂×C₄×C₄₃	—	2	2	no	—
77	C₂×C₄×C₄₃	—	2	2	no	—
78	C₂×C₄×C₄₃	—	2	2	no	—
79	C₂×C₄×C₄₃	—	2	2	no	—
80	C₂×C₄×C₄₃	#103	1	4	yes	—
81	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₄₃	#121	1	2	yes	—
83	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
84	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
85	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
87	C₂×C₄×C₄₃	#135	1	4	yes	—
88	C₂×C₄×C₄₃	#137	1	2	yes	—
89	C₂×Dic₄₃	—	4	2	no	—
90	C₂×Dic₄₃	—	4	2	no	—
91	C₂×Dic₄₃	—	4	4	no	—
92	C₂×Dic₄₃	—	4	4	no	—
93	Dic₈₆	—	8	2	no	—
94	Dic₈₆	—	8	2	no	—
95	Dic₈₆	—	8	4	no	—
96	C₈×C₄₃	—	8	2	no	—
97	C₄₃⋊C₈	—	4	4	no	—
98	#9693	—	43	1	no	maximal, Sylow
99	C₂²×C₄₃	#390	1	1	yes	characteristic
100	C₂²×C₄₃	#413	1	2	yes	—
101	C₂²×C₄₃	C₂×#103	1	1	yes	characteristic
102	C₂²×C₄₃	#416	1	2	yes	—
103	C₂²×C₄₃	#419	1	1	yes	characteristic
104	C₄×C₄₃	—	2	4	no	—
105	C₄×C₄₃	—	2	2	no	—
106	C₄×C₄₃	—	4	2	no	—
107	C₄×C₄₃	#461	1	2	yes	—
108	C₄×C₄₃	#462	1	2	yes	—
109	C₄×C₄₃	#488	1	2	yes	—
110	C₄×C₄₃	#495	1	2	yes	—
111	Dic₄₃	—	8	2	no	—
112	Dic₄₃	—	8	2	no	—
113	#2862	—	43	1	no	—
114	#1831	D₄₃	1	1	yes	characteristic
115	C₄×C₄⋊C₈	—	43	1	no	—
116	C₂×#333	—	43	2	no	—
117	C₂×#332	—	43	2	no	—
118	C₂×C₄₃	#1542	1	2	yes	—
119	C₂×C₄₃	#1554	1	2	yes	—
120	C₂×C₄₃	#1958	1	1	yes	characteristic
121	C₂×C₄₃	#1967	1	1	yes	characteristic
122	C₂×C₄₃	#1981	1	1	yes	characteristic
123	C₂×C₄⋊Q₈	—	43	1	no	—
124	C₂×C₄⋊Q₈	—	43	1	no	—
125	C₂×C₄⋊C₈	—	43	2	no	—
126	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
127	C₂×C₄×C₈	—	86	1	no	—
128	#391	—	43	4	no	—
129	#391	—	86	2	no	—
130	#382	—	86	1	no	—
131	#382	—	86	1	no	—
132	C₄³	C₂×D₄₃	1	1	yes	characteristic
133	#336	—	2	2	no	—
134	#336	—	86	1	no	—
135	#333	—	86	4	no	—
136	#332	—	86	4	no	—
137	C₄₃	#9693	1	1	yes	characteristic, complemented, Sylow
138	C₂²×Q₈	—	43	2	no	—
139	C₂²×Q₈	—	86	1	no	—
140	C₂²×C₈	—	2	2	no	—
141	C₂²×C₈	—	86	2	no	—
142	C₄⋊Q₈	—	86	2	no	—
143	C₄⋊Q₈	—	86	2	no	—
144	C₄⋊Q₈	—	86	2	no	—
145	C₄⋊Q₈	—	86	2	no	—
146	C₂×C₄⋊C₄	—	43	2	no	—
147	C₂×C₄⋊C₄	—	86	1	no	—
148	C₂×C₄⋊C₄	—	86	1	no	—
149	C₂×C₄⋊C₄	—	86	1	no	—
150	C₂×C₄²	C₄×D₄₃	1	2	yes	—
151	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
152	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
153	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
154	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
155	C₄⋊C₈	—	2	2	no	—
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	43	4	no	—
158	C₄⋊C₈	—	86	2	no	—
159	C₄×C₈	—	172	2	no	—
160	#95	—	86	4	no	—
161	#95	—	86	4	no	—
162	C₂×Q₈	—	86	4	no	—
163	C₂×Q₈	—	172	4	no	—
164	C₂×Q₈	—	172	1	no	—
165	C₂×Q₈	—	172	1	no	—
166	C₂×Q₈	—	172	4	no	—
167	C₂²×C₄	—	86	2	no	—
168	C₂²×C₄	—	86	2	no	—
169	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
170	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
171	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
172	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
173	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
174	C₂×C₈	—	4	2	no	—
175	C₂×C₈	—	4	4	no	—
176	C₂×C₈	—	86	4	no	—
177	C₂×C₈	—	172	2	no	—
178	C₂×C₈	—	172	2	no	—
179	C₄⋊C₄	—	86	4	no	—
180	C₄⋊C₄	—	172	2	no	—
181	C₄⋊C₄	—	172	2	no	—
182	C₄⋊C₄	—	172	1	no	—
183	C₄⋊C₄	—	172	1	no	—
184	C₄²	—	2	4	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	4	2	no	—
187	C₄²	#10621873	1	2	yes	—
188	C₄²	Dic₁₇₂	1	2	yes	—
189	C₄²	D₄×D₄₃	1	2	yes	—
190	C₄²	#10621902	1	2	yes	—
191	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
192	Q₈	—	344	4	no	—
193	Q₈	—	344	2	no	—
194	Q₈	—	344	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	172	2	no	—
202	C₂×C₄	—	172	2	no	—
203	C₂×C₄	—	172	4	no	—
204	C₂×C₄	—	172	4	no	—
205	C₂×C₄	#13063250	1	4	yes	—
206	C₂×C₄	#13063287	1	2	yes	—
207	C₂×C₄	#13063300	1	2	yes	—
208	C₂×C₄	#13063314	1	1	yes	characteristic
209	C₂×C₄	#13063321	1	1	yes	characteristic
210	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
211	C₂×C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
212	C₂×C₄	#13063345	1	4	yes	—
213	C₂×C₄	#13063358	1	2	yes	—
214	C₈	—	8	2	no	—
215	C₈	—	172	4	no	—
216	C₂²	#14582800	1	1	yes	characteristic
217	C₂²	#14582881	1	2	yes	—
218	C₂²	C₂×#13063250	1	1	yes	characteristic
219	C₂²	#14582893	1	2	yes	—
220	C₂²	#14582909	1	1	yes	characteristic
221	C₄	—	2	4	no	—
222	C₄	—	2	2	no	—
223	C₄	—	4	2	no	—
224	C₄	—	344	2	no	—
225	C₄	—	344	2	no	—
226	C₄	#14583105	1	2	yes	—
227	C₄	#14583110	1	2	yes	—
228	C₄	#14583256	1	2	yes	—
229	C₄	#14583281	1	2	yes	—
230	C₂	#19133250	1	2	yes	—
231	C₂	#19133306	1	2	yes	—
232	C₂	#19135404	1	1	yes	characteristic
233	C₂	#19135442	1	1	yes	characteristic
234	C₂	#19135517	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19142973

C₂

yes

maximal, characteristic

C₄×C₄⋊(C₄₃⋊C₈)

C₂

yes

maximal, characteristic

C₂×#14582647

C₂

yes

maximal

C₂×#14582646

C₂

yes

maximal

C₄₃×#1831

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

characteristic

C₂×#13063325

C₂²

yes

characteristic

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

—

#14582805

—

#14582805

C₄

yes

—

—

—

—

—

—

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₄₃×#336

—

C₂²×Dic₈₆

—

C₂²×Dic₈₆

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

—

—

—

—

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

C₄×C₄₃⋊C₈

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

SD₁₆

yes

—

C₄²×C₄₃

Q₁₆

yes

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#103

yes

—

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

100

C₂²×C₄₃

#413

yes

—

101

C₂²×C₄₃

C₂×#103

yes

characteristic

102

C₂²×C₄₃

#416

yes

—

103

C₂²×C₄₃

#419

yes

characteristic

104

C₄×C₄₃

—

105

C₄×C₄₃

—

106

C₄×C₄₃

—

107

C₄×C₄₃

#461

yes

—

108

C₄×C₄₃

#462

yes

—

109

C₄×C₄₃

#488

yes

—

110

C₄×C₄₃

#495

yes

—

111

Dic₄₃

—

112

Dic₄₃

—

113

#2862

—

114

#1831

D₄₃

yes

characteristic

115

C₄×C₄⋊C₈

—

116

C₂×#333

—

117

C₂×#332

—

118

C₂×C₄₃

#1542

yes

—

119

C₂×C₄₃

#1554

yes

—

120

C₂×C₄₃

#1958

yes

characteristic

121

C₂×C₄₃

#1967

yes

characteristic

122

C₂×C₄₃

#1981

yes

characteristic

123

C₂×C₄⋊Q₈

—

124

C₂×C₄⋊Q₈

—

125

C₂×C₄⋊C₈

—

126

C₂×C₄⋊C₈

C₂×D₄₃

yes

—

127

C₂×C₄×C₈

—

128

#391

—

129

#391

—

130

#382

—

131

#382

—

132

C₄³

C₂×D₄₃

yes

characteristic

133

#336

—

134

#336

—

135

#333

—

136

#332

—

137

C₄₃

#9693

yes

characteristic, complemented, Sylow

138

C₂²×Q₈

—

139

C₂²×Q₈

—

140

C₂²×C₈

—

141

C₂²×C₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄²

C₄×D₄₃

yes

—

151

C₂×C₄²

D₁₇₂

yes

characteristic

152

C₂×C₄²

D₁₇₂

yes

characteristic

153

C₂×C₄²

C₂²⋊D₄₃

yes

—

154

C₂×C₄²

C₂²×D₄₃

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄×C₈

—

172

—

160

#95

—

161

#95

—

162

C₂×Q₈

—

163

C₂×Q₈

—

172

—

164

C₂×Q₈

—

172

—

165

C₂×Q₈

—

172

—

166

C₂×Q₈

—

172

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

170

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

171

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

172

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

173

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

172

—

178

C₂×C₈

—

172

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

172

—

181

C₄⋊C₄

—

172

—

182

C₄⋊C₄

—

172

—

183

C₄⋊C₄

—

172

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

#10621873

yes

—

188

C₄²

Dic₁₇₂

yes

—

189

C₄²

D₄×D₄₃

yes

—

190

C₄²

#10621902

yes

—

191

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

192

Q₈

—

344

—

193

Q₈

—

344

—

194

Q₈

—

344

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

172

—

202

C₂×C₄

—

172

—

203

C₂×C₄

—

172

—

204

C₂×C₄

—

172

—

205

C₂×C₄

#13063250

yes

—

206

C₂×C₄

#13063287

yes

—

207

C₂×C₄

#13063300

yes

—

208

C₂×C₄

#13063314

yes

characteristic

209

C₂×C₄

#13063321

yes

characteristic

210

C₂×C₄

C₂×#10621873

yes

characteristic

211

C₂×C₄

C₂×Dic₁₇₂

yes

characteristic

212

C₂×C₄

#13063345

yes

—

213

C₂×C₄

#13063358

yes

—

214

C₈

—

215

C₈

—

172

—

216

C₂²

#14582800

yes

characteristic

217

C₂²

#14582881

yes

—

218

C₂²

C₂×#13063250

yes

characteristic

219

C₂²

#14582893

yes

—

220

C₂²

#14582909

yes

characteristic

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

344

—

225

C₄

—

344

—

226

C₄

#14583105

yes

—

227

C₄

#14583110

yes

—

228

C₄

#14583256

yes

—

229

C₄

#14583281

yes

—

230

C₂

#19133250

yes

—

231

C₂

#19133306

yes

—

232

C₂

#19135404

yes

characteristic

233

C₂

#19135442

yes

characteristic

234

C₂

#19135517

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1831	C₂
socle, prime radical	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1831	D₄₃
hypocenter	C₄₃	#9693
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂³

C₂×(C₂×D₄₃)⋊C₄

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1831

C₂

socle, prime radical

C₂³×C₄₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
137. C₄₃	#9693	semidirect

H ≅ G/N

type

137. C₄₃

#9693

semidirect

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

subgroup	index
#19142973	2
C₄×C₄⋊(C₄₃⋊C₈)	2
C₂×#14582647	2
C₂×#14582646	2
C₄₃×#1831	2
#9693	43

subgroup

index

C₄×C₄⋊(C₄₃⋊C₈)

C₄₃×#1831

Subgroups — #24995634

Conjugacy classes of subgroups

Complements

Maximal subgroups