Group #45719172 — subgroups

Subgroups — C₁₃₁×#33288 #45719172

Order 33536.

684 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 238 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	#2864×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#2861×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#1991×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#1958×C₁₃₁	C₂	1	2	yes	maximal
5	#1936×C₁₃₁	C₂	1	4	yes	maximal
6	#1935×C₁₃₁	C₂	1	4	yes	maximal, complemented
7	C₄×#97×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
9	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₂×#103×C₁₃₁	C₂²	1	4	yes	—
11	C₂×#102×C₁₃₁	C₂²	1	4	yes	—
12	C₂×#97×C₁₃₁	C₂²	1	4	yes	—
13	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
14	#391×C₁₃₁	C₂²	1	2	yes	—
15	#390×C₁₃₁	C₂²	1	2	yes	—
16	#389×C₁₃₁	C₂²	1	4	yes	—
17	#388×C₁₃₁	—	2	4	no	—
18	#387×C₁₃₁	—	2	4	no	—
19	#382×C₁₃₁	C₂²	1	2	yes	—
20	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
21	#340×C₁₃₁	C₂²	1	8	yes	—
22	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
23	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₁₃₁	C₂³	1	4	yes	—
25	#125×C₁₃₁	—	2	4	no	—
26	#124×C₁₃₁	—	2	4	no	—
27	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
29	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
30	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
31	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
32	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
33	C₂×C₄²×C₁₃₁	D₄	1	4	yes	—
34	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
35	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
36	#103×C₁₃₁	—	2	8	no	—
37	#102×C₁₃₁	—	2	8	no	—
38	#97×C₁₃₁	—	2	8	no	—
39	C₄×C₈×C₁₃₁	—	2	4	no	—
40	#95×C₁₃₁	—	2	4	no	—
41	#95×C₁₃₁	—	2	4	no	—
42	#95×C₁₃₁	—	2	4	no	—
43	C₂⁴×C₁₃₁	—	2	1	no	—
44	C₂×Q₈×C₁₃₁	—	2	4	no	—
45	C₂×Q₈×C₁₃₁	—	2	2	no	—
46	C₂×D₄×C₁₃₁	—	2	4	no	—
47	C₂×D₄×C₁₃₁	—	2	2	no	—
48	C₂²×C₄×C₁₃₁	—	2	1	no	—
49	C₂²×C₄×C₁₃₁	—	2	4	no	—
50	C₂²×C₄×C₁₃₁	—	2	2	no	—
51	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
52	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
53	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
54	C₂×C₈×C₁₃₁	—	2	4	no	—
55	C₂×C₈×C₁₃₁	—	2	4	no	—
56	C₂×C₈×C₁₃₁	#41	1	8	yes	—
57	C₄⋊C₄×C₁₃₁	—	2	4	no	—
58	C₄⋊C₄×C₁₃₁	—	2	4	no	—
59	C₄⋊C₄×C₁₃₁	—	2	4	no	—
60	C₄⋊C₄×C₁₃₁	—	4	8	no	—
61	C₄⋊C₄×C₁₃₁	—	4	4	no	—
62	C₂²⋊C₄×C₁₃₁	—	4	8	no	—
63	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
64	C₄²×C₁₃₁	—	2	4	no	—
65	C₄²×C₁₃₁	—	4	4	no	—
66	C₄²×C₁₃₁	#41	1	4	yes	—
67	C₂³×C₁₃₁	—	4	1	no	—
68	C₂³×C₁₃₁	—	4	2	no	—
69	C₂³×C₁₃₁	—	4	4	no	—
70	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
71	Q₈×C₁₃₁	—	4	4	no	—
72	D₄×C₁₃₁	—	4	4	no	—
73	C₂×C₄×C₁₃₁	—	2	4	no	—
74	C₂×C₄×C₁₃₁	—	2	4	no	—
75	C₂×C₄×C₁₃₁	—	2	4	no	—
76	C₂×C₄×C₁₃₁	—	2	4	no	—
77	C₂×C₄×C₁₃₁	—	4	1	no	—
78	C₂×C₄×C₁₃₁	—	4	2	no	—
79	C₂×C₄×C₁₃₁	—	4	4	no	—
80	C₂×C₄×C₁₃₁	—	4	2	no	—
81	C₂×C₄×C₁₃₁	—	4	4	no	—
82	C₂×C₄×C₁₃₁	—	4	8	no	—
83	C₂×C₄×C₁₃₁	#124	1	4	yes	—
84	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
85	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
86	C₈×C₁₃₁	—	2	8	no	—
87	C₂²×C₁₃₁	—	8	1	no	—
88	C₂²×C₁₃₁	—	8	2	no	—
89	C₂²×C₁₃₁	—	8	4	no	—
90	C₂²×C₁₃₁	C₂×#124	1	1	yes	characteristic
91	C₂²×C₁₃₁	#532	1	2	yes	—
92	C₂²×C₁₃₁	#575	1	4	yes	—
93	C₄×C₁₃₁	—	2	4	no	—
94	C₄×C₁₃₁	—	4	4	no	—
95	C₄×C₁₃₁	—	8	1	no	—
96	C₄×C₁₃₁	—	8	2	no	—
97	C₄×C₁₃₁	—	8	4	no	—
98	C₄×C₁₃₁	#529	1	4	yes	—
99	C₂×C₁₃₁	—	16	1	no	—
100	C₂×C₁₃₁	#2861	1	1	yes	characteristic
101	C₂×C₁₃₁	#3135	1	2	yes	—
102	C₂×C₁₃₁	#3183	1	4	yes	—
103	#33288	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₁₃₁	#33288	1	1	yes	characteristic, direct product factor, Sylow
105	#2864	C₂×C₁₃₁	1	1	yes	characteristic, complemented
106	#2861	C₂×C₁₃₁	1	1	yes	characteristic
107	#1991	C₂×C₁₃₁	1	2	yes	complemented
108	#1958	C₂×C₁₃₁	1	2	yes	—
109	#1936	C₂×C₁₃₁	1	4	yes	—
110	#1935	C₂×C₁₃₁	1	4	yes	complemented
111	C₄×#97	C₂×C₁₃₁	1	1	yes	characteristic, complemented
112	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
113	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
114	C₂×#103	C₂²×C₁₃₁	1	4	yes	—
115	C₂×#102	C₂²×C₁₃₁	1	4	yes	—
116	C₂×#97	C₂²×C₁₃₁	1	4	yes	—
117	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
118	#391	C₂²×C₁₃₁	1	2	yes	—
119	#390	C₂²×C₁₃₁	1	2	yes	—
120	#389	C₂²×C₁₃₁	1	4	yes	—
121	#388	—	2	4	no	—
122	#387	—	2	4	no	—
123	#382	C₂²×C₁₃₁	1	2	yes	—
124	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
125	#340	C₂²×C₁₃₁	1	8	yes	—
126	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
127	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
128	C₂²×C₈	C₂³×C₁₃₁	1	4	yes	—
129	#125	—	2	4	no	—
130	#124	—	2	4	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	—	2	4	no	—
133	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
134	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
135	C₂×C₂²⋊C₄	—	2	2	no	—
136	C₂×C₂²⋊C₄	—	2	4	no	—
137	C₂×C₄²	D₄×C₁₃₁	1	4	yes	—
138	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
139	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
140	#103	—	2	8	no	—
141	#102	—	2	8	no	—
142	#97	—	2	8	no	—
143	C₄×C₈	—	2	4	no	—
144	#95	—	2	4	no	—
145	#95	—	2	4	no	—
146	#95	—	2	4	no	—
147	C₂⁴	—	2	1	no	—
148	C₂×Q₈	—	2	4	no	—
149	C₂×Q₈	—	2	2	no	—
150	C₂×D₄	—	2	4	no	—
151	C₂×D₄	—	2	2	no	—
152	C₂²×C₄	—	2	1	no	—
153	C₂²×C₄	—	2	4	no	—
154	C₂²×C₄	—	2	2	no	—
155	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
156	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
157	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
158	C₂×C₈	—	2	4	no	—
159	C₂×C₈	—	2	4	no	—
160	C₂×C₈	#41×C₁₃₁	1	8	yes	—
161	C₄⋊C₄	—	2	4	no	—
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	—	2	4	no	—
164	C₄⋊C₄	—	4	8	no	—
165	C₄⋊C₄	—	4	4	no	—
166	C₂²⋊C₄	—	4	8	no	—
167	C₂²⋊C₄	—	4	4	no	—
168	C₄²	—	2	4	no	—
169	C₄²	—	4	4	no	—
170	C₄²	#41×C₁₃₁	1	4	yes	—
171	C₂³	—	4	1	no	—
172	C₂³	—	4	2	no	—
173	C₂³	—	4	4	no	—
174	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
175	Q₈	—	4	4	no	—
176	D₄	—	4	4	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	4	1	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	—	4	8	no	—
187	C₂×C₄	#124×C₁₃₁	1	4	yes	—
188	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
189	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
190	C₈	—	2	8	no	—
191	C₂²	—	8	1	no	—
192	C₂²	—	8	2	no	—
193	C₂²	—	8	4	no	—
194	C₂²	C₂×#124×C₁₃₁	1	1	yes	characteristic
195	C₂²	#532×C₁₃₁	1	2	yes	—
196	C₂²	#575×C₁₃₁	1	4	yes	—
197	C₄	—	2	4	no	—
198	C₄	—	4	4	no	—
199	C₄	—	8	1	no	—
200	C₄	—	8	2	no	—
201	C₄	—	8	4	no	—
202	C₄	#529×C₁₃₁	1	4	yes	—
203	C₂	—	16	1	no	—
204	C₂	#2861×C₁₃₁	1	1	yes	characteristic
205	C₂	#3135×C₁₃₁	1	2	yes	—
206	C₂	#3183×C₁₃₁	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#2864×C₁₃₁

C₂

yes

maximal, characteristic, complemented

#2861×C₁₃₁

C₂

yes

maximal, characteristic

#1991×C₁₃₁

C₂

yes

maximal, complemented

#1958×C₁₃₁

C₂

yes

maximal

#1936×C₁₃₁

C₂

yes

maximal

#1935×C₁₃₁

C₂

yes

maximal, complemented

C₄×#97×C₁₃₁

C₂

yes

maximal, characteristic, complemented

C₂×#125×C₁₃₁

C₂²

yes

characteristic

C₂×#124×C₁₃₁

C₂²

yes

characteristic

C₂×#103×C₁₃₁

C₂²

yes

—

C₂×#102×C₁₃₁

C₂²

yes

—

C₂×#97×C₁₃₁

C₂²

yes

—

C₂×C₄×C₈×C₁₃₁

C₂²

yes

—

#391×C₁₃₁

C₂²

yes

—

#390×C₁₃₁

C₂²

yes

—

#389×C₁₃₁

C₂²

yes

—

#388×C₁₃₁

—

#387×C₁₃₁

—

#382×C₁₃₁

C₂²

yes

—

C₄³×C₁₃₁

C₂²

yes

characteristic

#340×C₁₃₁

C₂²

yes

—

C₂²×Q₈×C₁₃₁

C₂³

yes

characteristic

C₂²×D₄×C₁₃₁

C₂³

yes

characteristic

C₂²×C₈×C₁₃₁

C₂³

yes

—

#125×C₁₃₁

—

#124×C₁₃₁

—

C₂×C₄⋊C₄×C₁₃₁

—

C₂×C₄⋊C₄×C₁₃₁

—

C₂×C₄⋊C₄×C₁₃₁

C₂³

yes

—

C₂×C₄⋊C₄×C₁₃₁

C₂³

yes

—

C₂×C₂²⋊C₄×C₁₃₁

—

C₂×C₂²⋊C₄×C₁₃₁

—

C₂×C₄²×C₁₃₁

D₄

yes

—

C₂×C₄²×C₁₃₁

C₂³

yes

—

C₂×C₄²×C₁₃₁

C₂³

yes

characteristic

#103×C₁₃₁

—

#102×C₁₃₁

—

#97×C₁₃₁

—

C₄×C₈×C₁₃₁

—

#95×C₁₃₁

—

#95×C₁₃₁

—

#95×C₁₃₁

—

C₂⁴×C₁₃₁

—

C₂×Q₈×C₁₃₁

—

C₂×Q₈×C₁₃₁

—

C₂×D₄×C₁₃₁

—

C₂×D₄×C₁₃₁

—

C₂²×C₄×C₁₃₁

—

C₂²×C₄×C₁₃₁

—

C₂²×C₄×C₁₃₁

—

C₂²×C₄×C₁₃₁

C₂×D₄

yes

—

C₂²×C₄×C₁₃₁

C₂×D₄

yes

—

C₂²×C₄×C₁₃₁

C₂⁴

yes

characteristic

C₂×C₈×C₁₃₁

—

C₂×C₈×C₁₃₁

—

C₂×C₈×C₁₃₁

#41

yes

—

C₄⋊C₄×C₁₃₁

—

C₄⋊C₄×C₁₃₁

—

C₄⋊C₄×C₁₃₁

—

C₄⋊C₄×C₁₃₁

—

C₄⋊C₄×C₁₃₁

—

C₂²⋊C₄×C₁₃₁

—

C₂²⋊C₄×C₁₃₁

—

C₄²×C₁₃₁

—

C₄²×C₁₃₁

—

C₄²×C₁₃₁

#41

yes

—

C₂³×C₁₃₁

—

C₂³×C₁₃₁

—

C₂³×C₁₃₁

—

C₂³×C₁₃₁

C₂²×D₄

yes

characteristic

Q₈×C₁₃₁

—

D₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

#124

yes

—

C₂×C₄×C₁₃₁

C₂×#41

yes

—

C₂×C₄×C₁₃₁

C₂×#41

yes

—

C₈×C₁₃₁

—

C₂²×C₁₃₁

—

C₂²×C₁₃₁

—

C₂²×C₁₃₁

—

C₂²×C₁₃₁

C₂×#124

yes

characteristic

C₂²×C₁₃₁

#532

yes

—

C₂²×C₁₃₁

#575

yes

—

C₄×C₁₃₁

—

C₄×C₁₃₁

—

C₄×C₁₃₁

—

C₄×C₁₃₁

—

C₄×C₁₃₁

—

C₄×C₁₃₁

#529

yes

—

C₂×C₁₃₁

—

100

C₂×C₁₃₁

#2861

yes

characteristic

101

C₂×C₁₃₁

#3135

yes

—

102

C₂×C₁₃₁

#3183

yes

—

103

#33288

C₁₃₁

yes

maximal, characteristic, direct product factor, Sylow

104

C₁₃₁

#33288

yes

characteristic, direct product factor, Sylow

105

#2864

C₂×C₁₃₁

yes

characteristic, complemented

106

#2861

C₂×C₁₃₁

yes

characteristic

107

#1991

C₂×C₁₃₁

yes

complemented

108

#1958

C₂×C₁₃₁

yes

—

109

#1936

C₂×C₁₃₁

yes

—

110

#1935

C₂×C₁₃₁

yes

complemented

111

C₄×#97

C₂×C₁₃₁

yes

characteristic, complemented

112

C₂×#125

C₂²×C₁₃₁

yes

characteristic

113

C₂×#124

C₂²×C₁₃₁

yes

characteristic

114

C₂×#103

C₂²×C₁₃₁

yes

—

115

C₂×#102

C₂²×C₁₃₁

yes

—

116

C₂×#97

C₂²×C₁₃₁

yes

—

117

C₂×C₄×C₈

C₂²×C₁₃₁

yes

—

118

#391

C₂²×C₁₃₁

yes

—

119

#390

C₂²×C₁₃₁

yes

—

120

#389

C₂²×C₁₃₁

yes

—

121

#388

—

122

#387

—

123

#382

C₂²×C₁₃₁

yes

—

124

C₄³

C₂²×C₁₃₁

yes

characteristic

125

#340

C₂²×C₁₃₁

yes

—

126

C₂²×Q₈

C₂³×C₁₃₁

yes

characteristic

127

C₂²×D₄

C₂³×C₁₃₁

yes

characteristic

128

C₂²×C₈

C₂³×C₁₃₁

yes

—

129

#125

—

130

#124

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

C₂³×C₁₃₁

yes

—

134

C₂×C₄⋊C₄

C₂³×C₁₃₁

yes

—

135

C₂×C₂²⋊C₄

—

136

C₂×C₂²⋊C₄

—

137

C₂×C₄²

D₄×C₁₃₁

yes

—

138

C₂×C₄²

C₂³×C₁₃₁

yes

—

139

C₂×C₄²

C₂³×C₁₃₁

yes

characteristic

140

#103

—

141

#102

—

142

#97

—

143

C₄×C₈

—

144

#95

—

145

#95

—

146

#95

—

147

C₂⁴

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

C₂×D₄×C₁₃₁

yes

—

156

C₂²×C₄

C₂×D₄×C₁₃₁

yes

—

157

C₂²×C₄

C₂⁴×C₁₃₁

yes

characteristic

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

#41×C₁₃₁

yes

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₂²⋊C₄

—

167

C₂²⋊C₄

—

168

C₄²

—

169

C₄²

—

170

C₄²

#41×C₁₃₁

yes

—

171

C₂³

—

172

C₂³

—

173

C₂³

—

174

C₂³

C₂²×D₄×C₁₃₁

yes

characteristic

175

Q₈

—

176

D₄

—

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

#124×C₁₃₁

yes

—

188

C₂×C₄

C₂×#41×C₁₃₁

yes

—

189

C₂×C₄

C₂×#41×C₁₃₁

yes

—

190

C₈

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

C₂×#124×C₁₃₁

yes

characteristic

195

C₂²

#532×C₁₃₁

yes

—

196

C₂²

#575×C₁₃₁

yes

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

#529×C₁₃₁

yes

—

203

C₂

—

204

C₂

#2861×C₁₃₁

yes

characteristic

205

C₂

#3135×C₁₃₁

yes

—

206

C₂

#3183×C₁₃₁

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂²×D₄×C₁₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄³×C₁₃₁ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₃₁

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₃₁

prime radical

C₂²×D₄×C₁₃₁

C₂³

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃₁ ◁ C₄³×C₁₃₁ ◁ G

N	H ≅ G/N	type
1. #2864×C₁₃₁	C₂	semidirect
3. #1991×C₁₃₁	C₂	semidirect
6. #1935×C₁₃₁	C₂	semidirect
7. C₄×#97×C₁₃₁	C₂	semidirect
103. #33288	C₁₃₁	direct (N × H)
104. C₁₃₁	#33288	direct (N × H)
105. #2864	C₂×C₁₃₁	semidirect
107. #1991	C₂×C₁₃₁	semidirect
110. #1935	C₂×C₁₃₁	semidirect
111. C₄×#97	C₂×C₁₃₁	semidirect

H ≅ G/N

type

1. #2864×C₁₃₁

C₂

semidirect

3. #1991×C₁₃₁

C₂

semidirect

6. #1935×C₁₃₁

C₂

semidirect

7. C₄×#97×C₁₃₁

C₂

semidirect

103. #33288

C₁₃₁

direct (N × H)

104. C₁₃₁

#33288

direct (N × H)

105. #2864

C₂×C₁₃₁

semidirect

107. #1991

C₂×C₁₃₁

semidirect

110. #1935

C₂×C₁₃₁

semidirect

111. C₄×#97

C₂×C₁₃₁

semidirect

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

subgroup	index
#2864×C₁₃₁	2
#2861×C₁₃₁	2
#1991×C₁₃₁	2
#1958×C₁₃₁	2
#1936×C₁₃₁	2
#1935×C₁₃₁	2
C₄×#97×C₁₃₁	2
#33288	131

subgroup

index

#2864×C₁₃₁

#2861×C₁₃₁

#1991×C₁₃₁

#1958×C₁₃₁

#1936×C₁₃₁

#1935×C₁₃₁

C₄×#97×C₁₃₁

#33288

131

Subgroups — C₁₃₁×#33288 #45719172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C131×#33288 #45719172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33288 #45719172