Group #23784900 — subgroups

Subgroups — C₄₁×#8699 #23784900

Order 10496.

598 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 182 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×C₄₁×#376	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1817	C₂	1	2	yes	maximal
3	C₄₁×#1280	C₂	1	4	yes	maximal
4	C₂²×C₄²×C₄₁	C₄	1	1	yes	characteristic
5	C₂²×C₄²×C₄₁	C₄	1	1	yes	characteristic
6	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	—
8	C₄₁×#376	—	2	4	no	—
9	C₂×#95×C₄₁	C₄	1	2	yes	—
10	C₂×#95×C₄₁	C₂²	1	2	yes	—
11	C₄₁×#336	—	2	4	no	—
12	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
13	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
15	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
16	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
17	C₂²×C₈×C₄₁	—	2	4	no	—
18	C₂×C₄²×C₄₁	—	2	2	no	—
19	C₂×C₄²×C₄₁	—	2	2	no	—
20	C₂×C₄²×C₄₁	—	2	4	no	—
21	C₂×C₄²×C₄₁	—	2	2	no	—
22	C₂×C₄²×C₄₁	—	2	4	no	—
23	C₂×C₄²×C₄₁	C₈	1	4	yes	complemented
24	C₂×C₄²×C₄₁	D₄	1	4	yes	—
25	C₂²⋊C₈×C₄₁	—	2	8	no	—
26	#95×C₄₁	—	2	4	no	—
27	#95×C₄₁	—	2	4	no	—
28	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₄₁	—	2	2	no	—
30	C₂²×C₄×C₄₁	—	2	2	no	—
31	C₂²×C₄×C₄₁	—	2	2	no	—
32	C₂²×C₄×C₄₁	—	2	2	no	—
33	C₂²×C₄×C₄₁	—	2	2	no	—
34	C₂²×C₄×C₄₁	—	2	2	no	—
35	C₂²×C₄×C₄₁	—	2	2	no	—
36	C₂²×C₄×C₄₁	—	4	2	no	—
37	C₂²×C₄×C₄₁	—	4	2	no	—
38	C₂²×C₄×C₄₁	—	4	2	no	—
39	C₂²×C₄×C₄₁	—	4	2	no	—
40	C₂²×C₄×C₄₁	—	4	2	no	—
41	C₂²×C₄×C₄₁	—	4	2	no	—
42	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
43	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
44	C₂²×C₄×C₄₁	C₂×C₈	1	2	yes	—
45	C₂²×C₄×C₄₁	C₂×C₈	1	4	yes	—
46	C₂²×C₄×C₄₁	M₁₆	1	2	yes	—
47	C₂²×C₄×C₄₁	M₁₆	1	4	yes	—
48	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₄₁	#41	1	4	yes	—
50	C₂×C₈×C₄₁	—	4	8	no	—
51	C₂×C₈×C₄₁	—	4	4	no	—
52	C₄²×C₄₁	—	2	8	no	—
53	C₄²×C₄₁	—	2	8	no	—
54	C₄²×C₄₁	—	2	8	no	—
55	C₂³×C₄₁	—	2	2	no	—
56	C₂³×C₄₁	—	2	2	no	—
57	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂³×C₄₁	#117	1	2	yes	—
59	C₂³×C₄₁	C₂²×C₈	1	1	yes	characteristic
60	C₂³×C₄₁	C₂×M₁₆	1	1	yes	characteristic
61	C₂³×C₄₁	C₂×M₁₆	1	2	yes	—
62	C₂×C₄×C₄₁	—	2	2	no	—
63	C₂×C₄×C₄₁	—	2	2	no	—
64	C₂×C₄×C₄₁	—	2	4	no	—
65	C₂×C₄×C₄₁	—	2	4	no	—
66	C₂×C₄×C₄₁	—	2	4	no	—
67	C₂×C₄×C₄₁	—	2	2	no	—
68	C₂×C₄×C₄₁	—	2	4	no	—
69	C₂×C₄×C₄₁	—	2	4	no	—
70	C₂×C₄×C₄₁	—	2	4	no	—
71	C₂×C₄×C₄₁	—	4	4	no	—
72	C₂×C₄×C₄₁	—	4	4	no	—
73	C₂×C₄×C₄₁	—	4	4	no	—
74	C₂×C₄×C₄₁	—	4	4	no	—
75	C₂×C₄×C₄₁	—	4	2	no	—
76	C₂×C₄×C₄₁	—	4	2	no	—
77	C₂×C₄×C₄₁	—	4	2	no	—
78	C₂×C₄×C₄₁	—	4	2	no	—
79	C₂×C₄×C₄₁	—	4	4	no	—
80	C₂×C₄×C₄₁	—	4	4	no	—
81	C₂×C₄×C₄₁	C₂²⋊C₈	1	4	yes	—
82	C₂×C₄×C₄₁	#123	1	4	yes	—
83	C₈×C₄₁	—	8	4	no	—
84	#8699	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂²×C₄₁	—	2	2	no	—
86	C₂²×C₄₁	—	2	2	no	—
87	C₂²×C₄₁	—	2	2	no	—
88	C₂²×C₄₁	—	2	2	no	—
89	C₂²×C₄₁	—	2	2	no	—
90	C₂²×C₄₁	—	2	2	no	—
91	C₂²×C₄₁	#381	1	1	yes	characteristic
92	C₂²×C₄₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
93	C₂²×C₄₁	#407	1	1	yes	characteristic
94	C₂²×C₄₁	#410	1	2	yes	—
95	C₂²×C₄₁	#413	1	2	yes	—
96	C₂²×C₄₁	#431	1	2	yes	—
97	C₂²×C₄₁	#432	1	2	yes	—
98	C₄×C₄₁	—	2	4	no	—
99	C₄×C₄₁	—	2	4	no	—
100	C₄×C₄₁	—	4	2	no	—
101	C₄×C₄₁	—	4	4	no	—
102	C₄×C₄₁	—	4	4	no	—
103	C₂×#376	C₂×C₄₁	1	1	yes	characteristic
104	#1817	C₂×C₄₁	1	2	yes	—
105	#1280	C₂×C₄₁	1	4	yes	—
106	C₂×C₄₁	—	2	2	no	—
107	C₂×C₄₁	—	2	2	no	—
108	C₂×C₄₁	#1458	1	2	yes	—
109	C₂×C₄₁	#1464	1	2	yes	—
110	C₂×C₄₁	#1817	1	1	yes	characteristic
111	C₂×C₄₁	#1820	1	1	yes	characteristic
112	C₂×C₄₁	#1822	1	1	yes	characteristic
113	C₂²×C₄²	C₄×C₄₁	1	1	yes	characteristic
114	C₂²×C₄²	C₄×C₄₁	1	1	yes	characteristic
115	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
116	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	—
117	#376	—	2	4	no	—
118	C₂×#95	C₄×C₄₁	1	2	yes	—
119	C₂×#95	C₂²×C₄₁	1	2	yes	—
120	#336	—	2	4	no	—
121	C₄₁	#8699	1	1	yes	characteristic, direct product factor, Sylow
122	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
123	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
124	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
125	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
126	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
127	C₂²×C₈	—	2	4	no	—
128	C₂×C₄²	—	2	2	no	—
129	C₂×C₄²	—	2	2	no	—
130	C₂×C₄²	—	2	4	no	—
131	C₂×C₄²	—	2	2	no	—
132	C₂×C₄²	—	2	4	no	—
133	C₂×C₄²	C₈×C₄₁	1	4	yes	complemented
134	C₂×C₄²	D₄×C₄₁	1	4	yes	—
135	C₂²⋊C₈	—	2	8	no	—
136	#95	—	2	4	no	—
137	#95	—	2	4	no	—
138	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
139	C₂²×C₄	—	2	2	no	—
140	C₂²×C₄	—	2	2	no	—
141	C₂²×C₄	—	2	2	no	—
142	C₂²×C₄	—	2	2	no	—
143	C₂²×C₄	—	2	2	no	—
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	4	2	no	—
147	C₂²×C₄	—	4	2	no	—
148	C₂²×C₄	—	4	2	no	—
149	C₂²×C₄	—	4	2	no	—
150	C₂²×C₄	—	4	2	no	—
151	C₂²×C₄	—	4	2	no	—
152	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
153	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
154	C₂²×C₄	C₂×C₈×C₄₁	1	2	yes	—
155	C₂²×C₄	C₂×C₈×C₄₁	1	4	yes	—
156	C₂²×C₄	M₁₆×C₄₁	1	2	yes	—
157	C₂²×C₄	M₁₆×C₄₁	1	4	yes	—
158	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
159	C₂²×C₄	#41×C₄₁	1	4	yes	—
160	C₂×C₈	—	4	8	no	—
161	C₂×C₈	—	4	4	no	—
162	C₄²	—	2	8	no	—
163	C₄²	—	2	8	no	—
164	C₄²	—	2	8	no	—
165	C₂³	—	2	2	no	—
166	C₂³	—	2	2	no	—
167	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
168	C₂³	#117×C₄₁	1	2	yes	—
169	C₂³	C₂²×C₈×C₄₁	1	1	yes	characteristic
170	C₂³	C₂×M₁₆×C₄₁	1	1	yes	characteristic
171	C₂³	C₂×M₁₆×C₄₁	1	2	yes	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	2	4	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	4	4	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	4	4	no	—
185	C₂×C₄	—	4	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	4	4	no	—
190	C₂×C₄	—	4	4	no	—
191	C₂×C₄	C₂²⋊C₈×C₄₁	1	4	yes	—
192	C₂×C₄	#123×C₄₁	1	4	yes	—
193	C₈	—	8	4	no	—
194	C₂²	—	2	2	no	—
195	C₂²	—	2	2	no	—
196	C₂²	—	2	2	no	—
197	C₂²	—	2	2	no	—
198	C₂²	—	2	2	no	—
199	C₂²	—	2	2	no	—
200	C₂²	C₄₁×#381	1	1	yes	characteristic
201	C₂²	C₂×C₂²⋊C₈×C₄₁	1	1	yes	characteristic
202	C₂²	C₄₁×#407	1	1	yes	characteristic
203	C₂²	C₄₁×#410	1	2	yes	—
204	C₂²	C₄₁×#413	1	2	yes	—
205	C₂²	C₄₁×#431	1	2	yes	—
206	C₂²	C₄₁×#432	1	2	yes	—
207	C₄	—	2	4	no	—
208	C₄	—	2	4	no	—
209	C₄	—	4	2	no	—
210	C₄	—	4	4	no	—
211	C₄	—	4	4	no	—
212	C₂	—	2	2	no	—
213	C₂	—	2	2	no	—
214	C₂	C₄₁×#1458	1	2	yes	—
215	C₂	C₄₁×#1464	1	2	yes	—
216	C₂	C₄₁×#1817	1	1	yes	characteristic
217	C₂	C₄₁×#1820	1	1	yes	characteristic
218	C₂	C₄₁×#1822	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄₁×#376

C₂

yes

maximal, characteristic

C₄₁×#1817

C₂

yes

maximal

C₄₁×#1280

C₂

yes

maximal

C₂²×C₄²×C₄₁

C₄

yes

characteristic

C₂²×C₄²×C₄₁

C₄

yes

characteristic

C₂²×C₄²×C₄₁

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₄₁

C₂²

yes

—

C₄₁×#376

—

C₂×#95×C₄₁

C₄

yes

—

C₂×#95×C₄₁

C₂²

yes

—

C₄₁×#336

—

C₂³×C₄×C₄₁

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₁

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₁

C₂×C₄

yes

—

C₂³×C₄×C₄₁

C₂×C₄

yes

—

C₂³×C₄×C₄₁

C₂³

yes

characteristic

C₂²×C₈×C₄₁

—

C₂×C₄²×C₄₁

—

C₂×C₄²×C₄₁

—

C₂×C₄²×C₄₁

—

C₂×C₄²×C₄₁

—

C₂×C₄²×C₄₁

—

C₂×C₄²×C₄₁

C₈

yes

complemented

C₂×C₄²×C₄₁

D₄

yes

—

C₂²⋊C₈×C₄₁

—

#95×C₄₁

—

#95×C₄₁

—

C₂⁴×C₄₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₁

C₂×C₈

yes

—

C₂²×C₄×C₄₁

C₂×C₈

yes

—

C₂²×C₄×C₄₁

M₁₆

yes

—

C₂²×C₄×C₄₁

M₁₆

yes

—

C₂²×C₄×C₄₁

C₂×D₄

yes

—

C₂²×C₄×C₄₁

#41

yes

—

C₂×C₈×C₄₁

—

C₂×C₈×C₄₁

—

C₄²×C₄₁

—

C₄²×C₄₁

—

C₄²×C₄₁

—

C₂³×C₄₁

—

C₂³×C₄₁

—

C₂³×C₄₁

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₄₁

#117

yes

—

C₂³×C₄₁

C₂²×C₈

yes

characteristic

C₂³×C₄₁

C₂×M₁₆

yes

characteristic

C₂³×C₄₁

C₂×M₁₆

yes

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

C₂²⋊C₈

yes

—

C₂×C₄×C₄₁

#123

yes

—

C₈×C₄₁

—

#8699

C₄₁

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄₁

—

C₂²×C₄₁

—

C₂²×C₄₁

—

C₂²×C₄₁

—

C₂²×C₄₁

—

C₂²×C₄₁

—

C₂²×C₄₁

#381

yes

characteristic

C₂²×C₄₁

C₂×C₂²⋊C₈

yes

C₂²×C₄₁

yes

C₂²×C₄₁

yes

—

C₂²×C₄₁

#413

yes

—

C₂²×C₄₁

#431

yes

—

C₂²×C₄₁

#432

yes

—

C₄×C₄₁

—

C₄×C₄₁

—

100

C₄×C₄₁

—

101

C₄×C₄₁

—

102

C₄×C₄₁

—

103

C₂×#376

C₂×C₄₁

yes

characteristic

104

#1817

C₂×C₄₁

yes

—

105

#1280

C₂×C₄₁

yes

—

106

C₂×C₄₁

—

107

C₂×C₄₁

—

108

C₂×C₄₁

#1458

yes

—

109

C₂×C₄₁

#1464

yes

—

110

C₂×C₄₁

#1817

yes

characteristic

111

C₂×C₄₁

#1820

yes

characteristic

112

C₂×C₄₁

#1822

yes

characteristic

113

C₂²×C₄²

C₄×C₄₁

yes

characteristic

114

C₂²×C₄²

C₄×C₄₁

yes

characteristic

115

C₂²×C₄²

C₂²×C₄₁

yes

characteristic

116

C₂×C₂²⋊C₈

C₂²×C₄₁

yes

—

117

#376

—

118

C₂×#95

C₄×C₄₁

yes

—

119

C₂×#95

C₂²×C₄₁

yes

—

120

#336

—

121

C₄₁

#8699

yes

characteristic, direct product factor, Sylow

122

C₂³×C₄

C₂×C₄×C₄₁

yes

characteristic

123

C₂³×C₄

C₂×C₄×C₄₁

yes

characteristic

124

C₂³×C₄

C₂×C₄×C₄₁

yes

—

125

C₂³×C₄

C₂×C₄×C₄₁

yes

—

126

C₂³×C₄

C₂³×C₄₁

yes

characteristic

127

C₂²×C₈

—

128

C₂×C₄²

—

129

C₂×C₄²

—

130

C₂×C₄²

—

131

C₂×C₄²

—

132

C₂×C₄²

—

133

C₂×C₄²

C₈×C₄₁

yes

complemented

134

C₂×C₄²

D₄×C₄₁

yes

—

135

C₂²⋊C₈

—

136

#95

—

137

#95

—

138

C₂⁴

C₂²×C₄×C₄₁

yes

characteristic

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

C₂²⋊C₄×C₄₁

yes

—

153

C₂²×C₄

C₂²⋊C₄×C₄₁

yes

—

154

C₂²×C₄

C₂×C₈×C₄₁

yes

—

155

C₂²×C₄

C₂×C₈×C₄₁

yes

—

156

C₂²×C₄

M₁₆×C₄₁

yes

—

157

C₂²×C₄

M₁₆×C₄₁

yes

—

158

C₂²×C₄

C₂×D₄×C₄₁

yes

—

159

C₂²×C₄

#41×C₄₁

yes

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₄²

—

163

C₄²

—

164

C₄²

—

165

C₂³

—

166

C₂³

—

167

C₂³

C₂×C₂²⋊C₄×C₄₁

yes

characteristic

168

C₂³

#117×C₄₁

yes

—

169

C₂³

C₂²×C₈×C₄₁

yes

characteristic

170

C₂³

C₂×M₁₆×C₄₁

yes

characteristic

171

C₂³

C₂×M₁₆×C₄₁

yes

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

C₂²⋊C₈×C₄₁

yes

—

192

C₂×C₄

#123×C₄₁

yes

—

193

C₈

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

—

199

C₂²

—

200

C₂²

C₄₁×#381

yes

characteristic

201

C₂²

C₂×C₂²⋊C₈×C₄₁

yes

characteristic

202

C₂²

C₄₁×#407

yes

characteristic

203

C₂²

C₄₁×#410

yes

—

204

C₂²

C₄₁×#413

yes

—

205

C₂²

C₄₁×#431

yes

—

206

C₂²

C₄₁×#432

yes

—

207

C₄

—

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

—

212

C₂

—

213

C₂

—

214

C₂

C₄₁×#1458

yes

—

215

C₂

C₄₁×#1464

yes

—

216

C₂

C₄₁×#1817

yes

characteristic

217

C₂

C₄₁×#1820

yes

characteristic

218

C₂

C₄₁×#1822

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
prime radical	C₂⁴×C₄₁	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

subgroup

G/H

center, socle

C₂³×C₄₁

C₂×C₂²⋊C₄

commutator

C₂³

C₂²×C₈×C₄₁

Frattini, cosocle

C₂³×C₄

C₂³×C₄₁

prime radical

C₂⁴×C₄₁

C₂²×C₄

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

N	H ≅ G/N	type
23. C₂×C₄²×C₄₁	C₈	semidirect
84. #8699	C₄₁	direct (N × H)
121. C₄₁	#8699	direct (N × H)
133. C₂×C₄²	C₈×C₄₁	semidirect

H ≅ G/N

type

23. C₂×C₄²×C₄₁

C₈

semidirect

84. #8699

C₄₁

direct (N × H)

121. C₄₁

#8699

direct (N × H)

133. C₂×C₄²

C₈×C₄₁

semidirect

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

subgroup	index
C₂×C₄₁×#376	2
C₄₁×#1817	2
C₄₁×#1280	2
#8699	41

subgroup

index

C₂×C₄₁×#376

C₄₁×#1817

C₄₁×#1280

#8699

Subgroups — C₄₁×#8699 #23784900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C41×#8699 #23784900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#8699 #23784900