Group #34176390 — subgroups

Subgroups — #34176390

Order 20224.

608 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 143 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	#23763543	C₂	1	2	yes	maximal, complemented
2	#23761221	C₂	1	4	yes	maximal, complemented
3	C₄×#127×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#19098318	—	2	2	no	—
5	#19098318	—	2	2	no	—
6	#19098318	C₂²	1	4	yes	—
7	C₂×#127×C₇₉	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄×C₇₉	—	2	2	no	—
9	C₂×C₄×D₄×C₇₉	C₄	1	2	yes	—
10	#390×C₇₉	—	2	2	no	—
11	#390×C₇₉	C₂²	1	2	yes	—
12	#384×C₇₉	C₄	1	1	yes	characteristic
13	C₄³×C₇₉	C₂²	1	1	yes	characteristic
14	C₂²×C₇₉⋊C₈	—	2	4	no	—
15	C₂²×D₄×C₇₉	—	2	2	no	—
16	C₂²×D₄×C₇₉	C₂×C₄	1	2	yes	—
17	C₂³×C₄×C₇₉	—	2	2	no	—
18	#127×C₇₉	—	2	2	no	—
19	#127×C₇₉	C₈	1	4	yes	complemented
20	C₄×D₄×C₇₉	—	4	8	no	—
21	C₄×D₄×C₇₉	—	4	4	no	—
22	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
24	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
25	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
26	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₇₉	D₄	1	2	yes	—
29	C₂×C₄²×C₇₉	D₄	1	2	yes	—
30	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
31	C₂×C₇₉⋊C₈	—	4	4	no	—
32	C₂×C₇₉⋊C₈	—	4	4	no	—
33	C₂×C₇₉⋊C₈	—	4	4	no	—
34	C₂⁴×C₇₉	—	2	2	no	—
35	C₂×D₄×C₇₉	—	2	8	no	—
36	C₂×D₄×C₇₉	—	2	2	no	—
37	C₂×D₄×C₇₉	—	4	4	no	—
38	C₂×D₄×C₇₉	—	4	4	no	—
39	C₂×D₄×C₇₉	—	4	2	no	—
40	C₂×D₄×C₇₉	—	4	2	no	—
41	C₂×D₄×C₇₉	C₂×C₈	1	4	yes	—
42	C₂²×C₄×C₇₉	—	2	2	no	—
43	C₂²×C₄×C₇₉	—	4	8	no	—
44	C₂²×C₄×C₇₉	—	4	4	no	—
45	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
50	C₄⋊C₄×C₇₉	—	4	4	no	—
51	C₄⋊C₄×C₇₉	—	4	2	no	—
52	C₂²⋊C₄×C₇₉	—	4	4	no	—
53	C₂²⋊C₄×C₇₉	—	4	8	no	—
54	C₄²×C₇₉	—	2	2	no	—
55	C₄²×C₇₉	—	2	4	no	—
56	C₄²×C₇₉	—	4	2	no	—
57	C₄²×C₇₉	—	4	1	no	—
58	C₄²×C₇₉	C₂×C₈	1	2	yes	—
59	C₄²×C₇₉	M₁₆	1	2	yes	—
60	C₂³×C₇₉	—	2	4	no	—
61	C₂³×C₇₉	—	4	2	no	—
62	C₂³×C₇₉	—	4	2	no	—
63	C₂³×C₇₉	—	4	4	no	—
64	C₂³×C₇₉	—	4	4	no	—
65	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	D₄×C₇₉	—	4	4	no	—
67	D₄×C₇₉	—	4	4	no	—
68	D₄×C₇₉	—	4	16	no	—
69	C₂×C₄×C₇₉	—	2	2	no	—
70	C₂×C₄×C₇₉	—	2	1	no	—
71	C₂×C₄×C₇₉	—	2	1	no	—
72	C₂×C₄×C₇₉	—	2	2	no	—
73	C₂×C₄×C₇₉	—	2	2	no	—
74	C₂×C₄×C₇₉	—	2	2	no	—
75	C₂×C₄×C₇₉	—	2	2	no	—
76	C₂×C₄×C₇₉	—	2	1	no	—
77	C₂×C₄×C₇₉	—	2	2	no	—
78	C₂×C₄×C₇₉	—	4	2	no	—
79	C₂×C₄×C₇₉	—	4	4	no	—
80	C₂×C₄×C₇₉	—	8	8	no	—
81	C₂×C₄×C₇₉	C₂²⋊C₈	1	4	yes	—
82	C₂×C₄×C₇₉	#100	1	2	yes	—
83	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
84	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
85	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	4	yes	—
86	C₇₉⋊C₈	—	8	4	no	—
87	C₂²×C₇₉	—	4	4	no	—
88	C₂²×C₇₉	—	4	8	no	—
89	C₂²×C₇₉	—	8	2	no	—
90	C₂²×C₇₉	—	8	2	no	—
91	C₂²×C₇₉	—	8	4	no	—
92	C₂²×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
93	C₂²×C₇₉	#410	1	1	yes	characteristic
94	C₂²×C₇₉	C₂×#100	1	1	yes	characteristic
95	C₂²×C₇₉	#418	1	2	yes	—
96	C₂²×C₇₉	#421	1	2	yes	—
97	C₄×C₇₉	—	2	2	no	—
98	C₄×C₇₉	—	2	1	no	—
99	C₄×C₇₉	—	2	1	no	—
100	C₄×C₇₉	—	2	4	no	—
101	C₄×C₇₉	—	2	4	no	—
102	C₄×C₇₉	—	4	1	no	—
103	C₄×C₇₉	—	8	2	no	—
104	#7603	—	79	1	no	maximal, Sylow
105	C₂×C₇₉	—	8	4	no	—
106	C₂×C₇₉	#1460	1	1	yes	characteristic
107	C₂×C₇₉	#1478	1	2	yes	—
108	C₂×C₇₉	#1514	1	2	yes	—
109	C₂×C₇₉	#1536	1	1	yes	characteristic
110	C₂×C₇₉	#1555	1	1	yes	characteristic
111	C₄×#127	D₇₉	1	1	yes	characteristic
112	#1839	—	79	2	no	—
113	#1270	—	79	4	no	—
114	C₇₉	#7603	1	1	yes	characteristic, complemented, Sylow
115	C₂×#127	Dic₇₉	1	1	yes	characteristic
116	C₂×C₄×D₄	—	2	2	no	—
117	C₂×C₄×D₄	Dic₇₉	1	2	yes	—
118	#390	—	2	2	no	—
119	#390	C₂×D₇₉	1	2	yes	—
120	#384	Dic₇₉	1	1	yes	characteristic
121	C₄³	C₂×D₇₉	1	1	yes	characteristic
122	#336	—	79	4	no	—
123	#336	—	158	2	no	—
124	#336	—	158	2	no	—
125	C₂²×D₄	—	2	2	no	—
126	C₂²×D₄	C₂×Dic₇₉	1	2	yes	—
127	C₂³×C₄	—	2	2	no	—
128	C₂²×C₈	—	158	4	no	—
129	#127	—	2	2	no	—
130	#127	C₇₉⋊C₈	1	4	yes	complemented
131	C₄×D₄	—	4	8	no	—
132	C₄×D₄	—	4	4	no	—
133	C₂×C₄⋊C₄	—	2	2	no	—
134	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
135	C₂×C₂²⋊C₄	—	2	2	no	—
136	C₂×C₂²⋊C₄	—	2	4	no	—
137	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
138	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
139	C₂×C₄²	C₂²⋊D₇₉	1	2	yes	—
140	C₂×C₄²	C₂²⋊D₇₉	1	2	yes	—
141	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
142	C₂⁴	—	2	2	no	—
143	C₂×D₄	—	2	8	no	—
144	C₂×D₄	—	2	2	no	—
145	C₂×D₄	—	4	2	no	—
146	C₂×D₄	—	4	2	no	—
147	C₂×D₄	—	4	4	no	—
148	C₂×D₄	—	4	4	no	—
149	C₂×D₄	C₂×C₇₉⋊C₈	1	4	yes	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	4	8	no	—
152	C₂²×C₄	—	4	4	no	—
153	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
154	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
155	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
156	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
158	C₂×C₈	—	316	4	no	—
159	C₂×C₈	—	316	4	no	—
160	C₂×C₈	—	316	4	no	—
161	C₄⋊C₄	—	4	2	no	—
162	C₄⋊C₄	—	4	4	no	—
163	C₂²⋊C₄	—	4	4	no	—
164	C₂²⋊C₄	—	4	8	no	—
165	C₄²	—	2	2	no	—
166	C₄²	—	2	4	no	—
167	C₄²	—	4	2	no	—
168	C₄²	—	4	1	no	—
169	C₄²	C₂×C₇₉⋊C₈	1	2	yes	—
170	C₄²	#11929608	1	2	yes	—
171	C₂³	—	2	4	no	—
172	C₂³	—	4	2	no	—
173	C₂³	—	4	2	no	—
174	C₂³	—	4	4	no	—
175	C₂³	—	4	4	no	—
176	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
177	D₄	—	4	4	no	—
178	D₄	—	4	4	no	—
179	D₄	—	4	16	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	—	4	4	no	—
191	C₂×C₄	—	8	8	no	—
192	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	4	yes	—
193	C₂×C₄	#14579078	1	2	yes	—
194	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
195	C₂×C₄	C₂×#11929608	1	1	yes	characteristic
196	C₂×C₄	#14579187	1	4	yes	—
197	C₈	—	632	4	no	—
198	C₂²	—	4	4	no	—
199	C₂²	—	4	8	no	—
200	C₂²	—	8	4	no	—
201	C₂²	—	8	2	no	—
202	C₂²	—	8	2	no	—
203	C₂²	C₂×C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
204	C₂²	#19098537	1	1	yes	characteristic
205	C₂²	C₂×#14579078	1	1	yes	characteristic
206	C₂²	#19098568	1	2	yes	—
207	C₂²	#19098580	1	2	yes	—
208	C₄	—	2	4	no	—
209	C₄	—	2	1	no	—
210	C₄	—	2	1	no	—
211	C₄	—	2	4	no	—
212	C₄	—	2	2	no	—
213	C₄	—	4	1	no	—
214	C₄	—	8	2	no	—
215	C₂	—	8	4	no	—
216	C₂	#23761721	1	1	yes	characteristic
217	C₂	#23761791	1	2	yes	—
218	C₂	#23761947	1	2	yes	—
219	C₂	#23762035	1	1	yes	characteristic
220	C₂	#23762114	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23763543

C₂

yes

maximal, complemented

#23761221

C₂

yes

maximal, complemented

C₄×#127×C₇₉

C₂

yes

maximal, characteristic

#19098318

—

#19098318

—

#19098318

C₂²

yes

—

C₂×#127×C₇₉

C₄

yes

characteristic

C₂×C₄×D₄×C₇₉

—

C₂×C₄×D₄×C₇₉

C₄

yes

—

#390×C₇₉

—

#390×C₇₉

C₂²

yes

—

#384×C₇₉

C₄

yes

characteristic

C₄³×C₇₉

C₂²

yes

characteristic

C₂²×C₇₉⋊C₈

—

C₂²×D₄×C₇₉

—

C₂²×D₄×C₇₉

C₂×C₄

yes

—

C₂³×C₄×C₇₉

—

#127×C₇₉

—

#127×C₇₉

C₈

yes

complemented

C₄×D₄×C₇₉

—

C₄×D₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₇₉

—

C₂×C₂²⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂⁴×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

C₂×C₈

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×C₈

yes

—

C₄²×C₇₉

M₁₆

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₈

yes

—

C₂×C₄×C₇₉

#100

yes

—

C₂×C₄×C₇₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₂²⋊C₈

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

—

C₂²×C₇₉

#421

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

100

C₄×C₇₉

—

101

C₄×C₇₉

—

102

C₄×C₇₉

—

103

C₄×C₇₉

—

104

#7603

—

maximal, Sylow

105

C₂×C₇₉

—

106

C₂×C₇₉

#1460

yes

characteristic

107

C₂×C₇₉

#1478

yes

—

108

C₂×C₇₉

#1514

yes

—

109

C₂×C₇₉

#1536

yes

characteristic

110

C₂×C₇₉

#1555

yes

characteristic

111

C₄×#127

D₇₉

yes

characteristic

112

#1839

—

113

#1270

—

114

C₇₉

#7603

yes

characteristic, complemented, Sylow

115

C₂×#127

Dic₇₉

yes

characteristic

116

C₂×C₄×D₄

—

117

C₂×C₄×D₄

Dic₇₉

yes

—

118

#390

—

119

#390

C₂×D₇₉

yes

—

120

#384

Dic₇₉

yes

characteristic

121

C₄³

C₂×D₇₉

yes

characteristic

122

#336

—

123

#336

—

158

—

124

#336

—

158

—

125

C₂²×D₄

—

126

C₂²×D₄

C₂×Dic₇₉

yes

—

127

C₂³×C₄

—

128

C₂²×C₈

—

158

—

129

#127

—

130

#127

C₇₉⋊C₈

yes

complemented

131

C₄×D₄

—

132

C₄×D₄

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

C₂×Dic₇₉

yes

—

135

C₂×C₂²⋊C₄

—

136

C₂×C₂²⋊C₄

—

137

C₂×C₄²

C₂×Dic₇₉

yes

characteristic

138

C₂×C₄²

C₂×Dic₇₉

yes

characteristic

139

C₂×C₄²

C₂²⋊D₇₉

yes

—

140

C₂×C₄²

C₂²⋊D₇₉

yes

—

141

C₂×C₄²

C₂²×D₇₉

yes

characteristic

142

C₂⁴

—

143

C₂×D₄

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂×D₄

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

C₂×C₇₉⋊C₈

yes

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

C₂²⋊Dic₇₉

yes

characteristic

154

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

155

C₂²×C₄

C₂²⋊Dic₇₉

yes

characteristic

156

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

157

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

—

158

C₂×C₈

—

316

—

159

C₂×C₈

—

316

—

160

C₂×C₈

—

316

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₂²⋊C₄

—

164

C₂²⋊C₄

—

165

C₄²

—

166

C₄²

—

167

C₄²

—

168

C₄²

—

169

C₄²

C₂×C₇₉⋊C₈

yes

—

170

C₄²

#11929608

yes

—

171

C₂³

—

172

C₂³

—

173

C₂³

—

174

C₂³

—

175

C₂³

—

176

C₂³

C₂×C₂²⋊Dic₇₉

yes

characteristic

177

D₄

—

178

D₄

—

179

D₄

—

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

—

192

C₂×C₄

C₂²⋊(C₇₉⋊C₈)

yes

—

193

C₂×C₄

#14579078

yes

—

194

C₂×C₄

C₂²×C₇₉⋊C₈

yes

characteristic

195

C₂×C₄

C₂×#11929608

yes

characteristic

196

C₂×C₄

#14579187

yes

—

197

C₈

—

632

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

C₂×C₂²⋊(C₇₉⋊C₈)

yes

characteristic

204

C₂²

#19098537

yes

characteristic

205

C₂²

C₂×#14579078

yes

characteristic

206

C₂²

#19098568

yes

—

207

C₂²

#19098580

yes

—

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₂

—

216

C₂

#23761721

yes

characteristic

217

C₂

#23761791

yes

—

218

C₂

#23761947

yes

—

219

C₂

#23762035

yes

characteristic

220

C₂

#23762114

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₄×#127×C₇₉	C₂
socle	C₂³×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂×#127×C₇₉	C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₄×#127	D₇₉
hypocenter	C₇₉	#7603
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₄×#127×C₇₉

C₂

socle

C₂³×C₇₉

C₂×C₂²⋊C₄

prime radical

C₂×#127×C₇₉

C₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#127

N	H ≅ G/N	type
1. #23763543	C₂	semidirect
2. #23761221	C₂	semidirect
19. #127×C₇₉	C₈	semidirect
114. C₇₉	#7603	semidirect
130. #127	C₇₉⋊C₈	semidirect

H ≅ G/N

type

1. #23763543

C₂

semidirect

2. #23761221

C₂

semidirect

19. #127×C₇₉

C₈

semidirect

114. C₇₉

#7603

semidirect

130. #127

C₇₉⋊C₈

semidirect

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

subgroup	index
#23763543	2
#23761221	2
C₄×#127×C₇₉	2
#7603	79

subgroup

index

#23763543

#23761221

C₄×#127×C₇₉

#7603

Subgroups — #34176390

Conjugacy classes of subgroups

Complements

Maximal subgroups