Group #26226465 — subgroups

Subgroups — #26226465

Order 12032.

628 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 211 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	#20245883	C₂	1	1	yes	maximal, characteristic
2	#20244002	C₂	1	4	yes	maximal
3	#20243955	C₂	1	4	yes	maximal, complemented
4	#20243542	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243369	C₂	1	2	yes	maximal
6	#20243243	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1832	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13093981	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
11	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	4	yes	—
12	C₂×#13093934	C₂²	1	4	yes	—
13	#15689012	C₄	1	4	yes	—
14	#15689005	C₄	1	4	yes	—
15	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
16	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
17	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
18	#15688877	C₂²	1	4	yes	—
19	#15688877	C₂²	1	4	yes	—
20	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
21	C₄₇×#376	C₂²	1	1	yes	characteristic
22	C₄₇×#336	C₂²	1	4	yes	—
23	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
24	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
25	#13093981	—	2	2	no	—
26	#13093981	—	2	2	no	—
27	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
28	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
29	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
30	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
31	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
32	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
33	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
34	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
35	C₄⋊(C₄₇⋊C₈)	—	4	4	no	—
36	(C₂×D₄₇)⋊C₈	—	4	4	no	—
37	#13093934	—	4	4	no	—
38	C₄₇⋊#95	C₂×C₄	1	4	yes	—
39	C₄₇⋊#95	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
41	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
42	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₇	—	2	4	no	—
44	#95×C₄₇	C₂×C₄	1	4	yes	—
45	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
47	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
48	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
49	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
50	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
51	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
52	C₂×C₄×D₄₇	—	2	1	no	—
53	C₂×C₄×D₄₇	—	2	1	no	—
54	C₂×C₄×D₄₇	—	2	2	no	—
55	C₂×C₄×D₄₇	—	2	2	no	—
56	C₂×C₈×C₄₇	—	2	4	no	—
57	C₂×C₈×C₄₇	—	2	4	no	—
58	C₂×C₈×C₄₇	—	2	4	no	—
59	C₄²×C₄₇	—	2	2	no	—
60	C₄²×C₄₇	—	2	2	no	—
61	C₄²×C₄₇	#41	1	2	yes	—
62	C₄²×C₄₇	#41	1	2	yes	—
63	(C₂×D₄₇)⋊C₄	—	2	4	no	—
64	(C₂×D₄₇)⋊C₄	—	4	4	no	—
65	Dic₄₇⋊C₄	—	2	4	no	—
66	Dic₄₇⋊C₄	—	4	4	no	—
67	C₄×Dic₄₇	—	2	1	no	—
68	C₄×Dic₄₇	—	2	1	no	—
69	C₄×Dic₄₇	—	2	2	no	—
70	C₄×Dic₄₇	—	2	2	no	—
71	C₄×Dic₄₇	—	4	4	no	—
72	C₂×C₄₇⋊C₈	—	2	4	no	—
73	C₂×C₄₇⋊C₈	—	2	4	no	—
74	C₂×C₄₇⋊C₈	—	2	4	no	—
75	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
76	C₂²×D₄₇	—	2	1	no	—
77	C₂²×D₄₇	—	2	2	no	—
78	C₂²×D₄₇	—	2	4	no	—
79	C₂×C₄×C₄₇	—	2	4	no	—
80	C₂×C₄×C₄₇	—	2	4	no	—
81	C₂×C₄×C₄₇	—	2	4	no	—
82	C₂×C₄×C₄₇	—	2	4	no	—
83	C₂×C₄×C₄₇	#117	1	4	yes	—
84	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
85	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
86	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
87	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
88	C₂×Dic₄₇	—	2	2	no	—
89	C₂×Dic₄₇	—	2	1	no	—
90	C₂×Dic₄₇	—	2	4	no	—
91	C₂×Dic₄₇	—	2	2	no	—
92	C₂×Dic₄₇	—	2	4	no	—
93	C₂×Dic₄₇	—	2	4	no	—
94	C₂×Dic₄₇	—	2	4	no	—
95	C₄×D₄₇	—	4	1	no	—
96	C₄×D₄₇	—	4	1	no	—
97	C₄×D₄₇	—	4	2	no	—
98	C₈×C₄₇	—	4	4	no	—
99	C₄₇⋊C₈	—	4	4	no	—
100	#21927	—	47	1	no	maximal, Sylow
101	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
102	C₂²×C₄₇	#520	1	2	yes	—
103	C₂²×C₄₇	#568	1	4	yes	—
104	C₂×D₄₇	—	4	1	no	—
105	C₂×D₄₇	—	4	2	no	—
106	C₂×D₄₇	—	4	4	no	—
107	C₄×C₄₇	—	2	4	no	—
108	C₄×C₄₇	—	4	4	no	—
109	C₄×C₄₇	#540	1	1	yes	characteristic
110	C₄×C₄₇	#541	1	1	yes	characteristic
111	C₄×C₄₇	#542	1	2	yes	—
112	Dic₄₇	—	4	1	no	—
113	Dic₄₇	—	4	2	no	—
114	Dic₄₇	—	4	4	no	—
115	#2298	—	47	1	no	—
116	#1924	—	47	4	no	—
117	#1917	—	47	4	no	—
118	#1843	—	47	1	no	—
119	#1832	D₄₇	1	1	yes	characteristic, complemented
120	#1798	—	47	2	no	—
121	#1767	—	47	2	no	—
122	C₂×C₄₇	#2314	1	1	yes	characteristic
123	C₂×C₄₇	#2923	1	2	yes	—
124	C₂×C₄₇	#2995	1	4	yes	—
125	D₄₇	—	8	1	no	—
126	C₂×#117	—	47	1	no	—
127	C₂×C₄⋊C₈	—	47	2	no	—
128	C₂×C₄⋊C₈	—	47	4	no	—
129	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
130	C₂×C₂²⋊C₈	—	47	4	no	—
131	C₂×#97	—	47	4	no	—
132	#388	—	47	4	no	—
133	#387	—	47	4	no	—
134	C₄×C₄⋊C₄	—	47	2	no	—
135	C₄×C₂²⋊C₄	—	47	2	no	—
136	#376	C₂×D₄₇	1	1	yes	characteristic
137	C₄³	—	47	1	no	—
138	#336	—	47	4	no	—
139	#336	—	47	4	no	—
140	#336	C₂×D₄₇	1	4	yes	—
141	C₄₇	#21927	1	1	yes	characteristic, complemented, Sylow
142	C₂³×C₄	—	47	1	no	—
143	C₂²×C₈	—	47	4	no	—
144	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
145	#117	—	94	2	no	—
146	#117	—	94	2	no	—
147	C₂×C₄⋊C₄	—	47	2	no	—
148	C₂×C₄⋊C₄	—	47	4	no	—
149	C₂×C₂²⋊C₄	—	47	2	no	—
150	C₂×C₂²⋊C₄	—	47	4	no	—
151	C₂×C₄²	—	47	1	no	—
152	C₂×C₄²	—	47	2	no	—
153	C₂×C₄²	—	47	4	no	—
154	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
155	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
156	C₄⋊C₈	—	2	4	no	—
157	C₄⋊C₈	—	94	4	no	—
158	C₄⋊C₈	—	188	4	no	—
159	C₂²⋊C₈	—	188	4	no	—
160	#97	—	188	4	no	—
161	#95	—	47	4	no	—
162	#95	—	47	4	no	—
163	#95	C₄×D₄₇	1	4	yes	—
164	C₂⁴	—	47	1	no	—
165	C₂²×C₄	—	47	1	no	—
166	C₂²×C₄	—	47	4	no	—
167	C₂²×C₄	—	47	2	no	—
168	C₂²×C₄	—	94	1	no	—
169	C₂²×C₄	—	94	1	no	—
170	C₂²×C₄	—	94	2	no	—
171	C₂²×C₄	—	94	2	no	—
172	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
173	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
174	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
175	C₂×C₈	—	2	4	no	—
176	C₂×C₈	—	2	4	no	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	94	4	no	—
179	C₂×C₈	—	94	4	no	—
180	C₂×C₈	—	94	4	no	—
181	C₄⋊C₄	—	94	4	no	—
182	C₄⋊C₄	—	188	4	no	—
183	C₂²⋊C₄	—	94	4	no	—
184	C₂²⋊C₄	—	188	4	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	2	2	no	—
187	C₄²	—	94	1	no	—
188	C₄²	—	94	1	no	—
189	C₄²	—	94	2	no	—
190	C₄²	—	94	2	no	—
191	C₄²	—	188	4	no	—
192	C₄²	#10625352	1	2	yes	—
193	C₄²	#10625354	1	2	yes	—
194	C₂³	—	94	1	no	—
195	C₂³	—	94	2	no	—
196	C₂³	—	94	4	no	—
197	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	94	2	no	—
203	C₂×C₄	—	94	1	no	—
204	C₂×C₄	—	94	4	no	—
205	C₂×C₄	—	94	2	no	—
206	C₂×C₄	—	94	4	no	—
207	C₂×C₄	—	94	4	no	—
208	C₂×C₄	—	94	4	no	—
209	C₂×C₄	—	188	1	no	—
210	C₂×C₄	—	188	1	no	—
211	C₂×C₄	—	188	2	no	—
212	C₂×C₄	#13093982	1	4	yes	—
213	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
214	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
215	C₂×C₄	#13094070	1	2	yes	—
216	C₂×C₄	#13094071	1	2	yes	—
217	C₈	—	4	4	no	—
218	C₈	—	188	4	no	—
219	C₂²	—	188	2	no	—
220	C₂²	—	188	4	no	—
221	C₂²	—	188	1	no	—
222	C₂²	C₂×#13093982	1	1	yes	characteristic
223	C₂²	#15689603	1	2	yes	—
224	C₂²	#15689888	1	4	yes	—
225	C₄	—	2	4	no	—
226	C₄	—	4	4	no	—
227	C₄	—	188	2	no	—
228	C₄	—	188	4	no	—
229	C₄	—	188	1	no	—
230	C₄	#15689729	1	1	yes	characteristic
231	C₄	#15689736	1	1	yes	characteristic
232	C₄	#15689742	1	2	yes	—
233	C₂	—	376	1	no	—
234	C₂	#20245998	1	1	yes	characteristic
235	C₂	#20252038	1	2	yes	—
236	C₂	#20252553	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20245883

C₂

yes

maximal, characteristic

#20244002

C₂

yes

maximal

#20243955

C₂

yes

maximal, complemented

#20243542

C₂

yes

maximal, characteristic, complemented

#20243369

C₂

yes

maximal

#20243243

C₂

yes

maximal, complemented

C₄₇×#1832

C₂

yes

maximal, characteristic, complemented

C₂×#13093981

C₂²

yes

characteristic

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₈

C₂²

yes

—

C₂×#13093934

C₂²

yes

—

#15689012

C₄

yes

—

#15689005

C₄

yes

—

C₄×Dic₄₇⋊C₄

C₂²

yes

—

C₄×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₄²×Dic₄₇

C₂²

yes

characteristic

#15688877

C₂²

yes

—

#15688877

C₂²

yes

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#376

C₂²

yes

characteristic

C₄₇×#336

C₂²

yes

—

C₂²×C₄×D₄₇

C₂³

yes

characteristic

C₂²×C₄₇⋊C₈

C₂³

yes

—

#13093981

—

#13093981

—

C₂×Dic₄₇⋊C₄

C₂×C₄

yes

—

C₂×Dic₄₇⋊C₄

C₂×C₄

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂×C₄

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂×C₄

yes

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

—

C₂×C₄×Dic₄₇

C₂³

yes

—

C₂×C₄×Dic₄₇

C₂³

yes

characteristic

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

(C₂×D₄₇)⋊C₈

—

#13093934

—

C₄₇⋊#95

C₂×C₄

yes

—

C₄₇⋊#95

C₂×C₄

yes

—

C₂²×C₈×C₄₇

C₂³

yes

—

C₂×C₄²×C₄₇

C₂³

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

#95×C₄₇

C₂×C₄

yes

—

C₂³×D₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²×C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

—

C₂²×C₄×C₄₇

C₂⁴

yes

characteristic

C₂²×Dic₄₇

C₂²×C₄

yes

characteristic

C₂²×Dic₄₇

C₂²×C₄

yes

—

C₂²×Dic₄₇

C₂²×C₄

yes

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

#41

yes

—

C₄²×C₄₇

#41

yes

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂³×C₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#117

yes

—

C₂×C₄×C₄₇

C₂×#41

yes

characteristic

C₂×C₄×C₄₇

C₂×#41

yes

characteristic

C₂×C₄×C₄₇

H(5,𝔽₂)

yes

—

C₂×C₄×C₄₇

2₋¹⁺⁴

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

100

#21927

—

maximal, Sylow

101

C₂²×C₄₇

C₂×#117

yes

characteristic

102

C₂²×C₄₇

#520

yes

—

103

C₂²×C₄₇

#568

yes

—

104

C₂×D₄₇

—

105

C₂×D₄₇

—

106

C₂×D₄₇

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

#540

yes

characteristic

110

C₄×C₄₇

#541

yes

characteristic

111

C₄×C₄₇

#542

yes

—

112

Dic₄₇

—

113

Dic₄₇

—

114

Dic₄₇

—

115

#2298

—

116

#1924

—

117

#1917

—

118

#1843

—

119

#1832

D₄₇

yes

characteristic, complemented

120

#1798

—

121

#1767

—

122

C₂×C₄₇

#2314

yes

characteristic

123

C₂×C₄₇

#2923

yes

—

124

C₂×C₄₇

#2995

yes

—

125

D₄₇

—

126

C₂×#117

—

127

C₂×C₄⋊C₈

—

128

C₂×C₄⋊C₈

—

129

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

130

C₂×C₂²⋊C₈

—

131

C₂×#97

—

132

#388

—

133

#387

—

134

C₄×C₄⋊C₄

—

135

C₄×C₂²⋊C₄

—

136

#376

C₂×D₄₇

yes

characteristic

137

C₄³

—

138

#336

—

139

#336

—

140

#336

C₂×D₄₇

yes

—

141

C₄₇

#21927

yes

characteristic, complemented, Sylow

142

C₂³×C₄

—

143

C₂²×C₈

—

144

C₂²×C₈

C₂²×D₄₇

yes

—

145

#117

—

146

#117

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₂²⋊C₄

—

150

C₂×C₂²⋊C₄

—

151

C₂×C₄²

—

152

C₂×C₄²

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂²×D₄₇

yes

—

155

C₂×C₄²

C₂²×D₄₇

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

188

—

159

C₂²⋊C₈

—

188

—

160

#97

—

188

—

161

#95

—

162

#95

—

163

#95

C₄×D₄₇

yes

—

164

C₂⁴

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

C₂×C₄×D₄₇

yes

—

173

C₂²×C₄

C₂×C₄×D₄₇

yes

—

174

C₂²×C₄

C₂³×D₄₇

yes

characteristic

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

188

—

183

C₂²⋊C₄

—

184

C₂²⋊C₄

—

188

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

188

—

192

C₄²

#10625352

yes

—

193

C₄²

#10625354

yes

—

194

C₂³

—

195

C₂³

—

196

C₂³

—

197

C₂³

C₂²×C₄×D₄₇

yes

characteristic

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

188

—

210

C₂×C₄

—

188

—

211

C₂×C₄

—

188

—

212

C₂×C₄

#13093982

yes

—

213

C₂×C₄

C₂×#10625352

yes

characteristic

214

C₂×C₄

C₂×#10625354

yes

characteristic

215

C₂×C₄

#13094070

yes

—

216

C₂×C₄

#13094071

yes

—

217

C₈

—

218

C₈

—

188

—

219

C₂²

—

188

—

220

C₂²

—

188

—

221

C₂²

—

188

—

222

C₂²

C₂×#13093982

yes

characteristic

223

C₂²

#15689603

yes

—

224

C₂²

#15689888

yes

—

225

C₄

—

226

C₄

—

227

C₄

—

188

—

228

C₄

—

188

—

229

C₄

—

188

—

230

C₄

#15689729

yes

characteristic

231

C₄

#15689736

yes

characteristic

232

C₄

#15689742

yes

—

233

C₂

—

376

—

234

C₂

#20245998

yes

characteristic

235

C₂

#20252038

yes

—

236

C₂

#20252553

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1832	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1832	D₄₇
hypocenter	C₄₇	#21927
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1832

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂³×C₄

Fitting

C₄₇×#1832

C₂

prime radical

C₂³×D₄₇

C₂²×C₄

cosocle

C₂²×C₄×C₄₇

C₂⁴

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ #1832

N	H ≅ G/N	type
3. #20243955	C₂	semidirect
4. #20243542	C₂	semidirect
6. #20243243	C₂	semidirect
7. C₄₇×#1832	C₂	semidirect
119. #1832	D₄₇	semidirect
141. C₄₇	#21927	semidirect

H ≅ G/N

type

3. #20243955

C₂

semidirect

4. #20243542

C₂

semidirect

6. #20243243

C₂

semidirect

7. C₄₇×#1832

C₂

semidirect

119. #1832

D₄₇

semidirect

141. C₄₇

#21927

semidirect

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

subgroup	index
#20245883	2
#20244002	2
#20243955	2
#20243542	2
#20243369	2
#20243243	2
C₄₇×#1832	2
#21927	47

subgroup

index

C₄₇×#1832

Subgroups — #26226465

Conjugacy classes of subgroups

Complements

Maximal subgroups