Group #45719111 — subgroups

Subgroups — C₁₃₁×#33227 #45719111

Order 33536.

986 conjugacy classes of subgroups; only the 318 normal subgroups are shown.

normal subgroups only

This group has 986 conjugacy classes of subgroups — too many to draw. Only its 318 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×#487×C₁₃₁	C₂	1	2	yes	maximal, complemented
2	C₂×#486×C₁₃₁	C₂	1	2	yes	maximal
3	#2862×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2858×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#1958×C₁₃₁	C₂	1	8	yes	maximal, complemented
6	C₄²×C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
9	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₂×#124×C₁₃₁	C₂²	1	4	yes	—
11	#487×C₁₃₁	—	2	8	no	—
12	#486×C₁₃₁	—	2	8	no	—
13	C₂×#103×C₁₃₁	C₂²	1	8	yes	—
14	C₂×#102×C₁₃₁	C₂²	1	8	yes	—
15	C₂×C₄×C₈×C₁₃₁	C₂²	1	4	yes	—
16	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
17	#391×C₁₃₁	—	2	4	no	—
18	#390×C₁₃₁	—	2	4	no	—
19	#382×C₁₃₁	C₂²	1	4	yes	—
20	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂²×Q₈×C₁₃₁	—	2	2	no	—
22	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
23	C₂²×D₄×C₁₃₁	—	2	2	no	—
24	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
25	C₂²×C₈×C₁₃₁	C₂³	1	4	yes	—
26	C₄⋊Q₈×C₁₃₁	—	2	4	no	—
27	C₄⋊Q₈×C₁₃₁	—	2	4	no	—
28	C₄⋊Q₈×C₁₃₁	—	2	4	no	—
29	#127×C₁₃₁	—	2	4	no	—
30	#124×C₁₃₁	—	2	16	no	—
31	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
34	C₂×C₂²⋊C₄×C₁₃₁	—	2	8	no	—
35	C₂×C₄²×C₁₃₁	D₄	1	4	yes	—
36	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
37	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
38	#103×C₁₃₁	—	2	16	no	—
39	#102×C₁₃₁	—	2	16	no	—
40	C₄×C₈×C₁₃₁	—	2	8	no	—
41	C₄×C₈×C₁₃₁	D₄	1	8	yes	—
42	#95×C₁₃₁	—	2	8	no	—
43	C₂⁴×C₁₃₁	—	2	2	no	—
44	C₂×Q₈×C₁₃₁	—	2	4	no	—
45	C₂×Q₈×C₁₃₁	—	2	8	no	—
46	C₂×Q₈×C₁₃₁	—	4	4	no	—
47	C₂×Q₈×C₁₃₁	—	4	8	no	—
48	C₂×D₄×C₁₃₁	—	2	4	no	—
49	C₂×D₄×C₁₃₁	—	2	8	no	—
50	C₂×D₄×C₁₃₁	—	4	4	no	—
51	C₂×D₄×C₁₃₁	—	4	8	no	—
52	C₂²×C₄×C₁₃₁	—	2	4	no	—
53	C₂²×C₄×C₁₃₁	—	2	2	no	—
54	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
55	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
56	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
57	C₂×C₈×C₁₃₁	—	2	8	no	—
58	C₂×C₈×C₁₃₁	C₂×D₄	1	8	yes	—
59	C₄⋊C₄×C₁₃₁	—	2	4	no	—
60	C₄⋊C₄×C₁₃₁	—	2	4	no	—
61	C₄⋊C₄×C₁₃₁	—	4	4	no	—
62	C₄⋊C₄×C₁₃₁	—	4	4	no	—
63	C₂²⋊C₄×C₁₃₁	—	4	16	no	—
64	C₄²×C₁₃₁	—	2	8	no	—
65	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
66	C₄²×C₁₃₁	#41	1	8	yes	—
67	C₂³×C₁₃₁	—	4	4	no	—
68	C₂³×C₁₃₁	—	4	2	no	—
69	C₂³×C₁₃₁	—	4	8	no	—
70	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
71	Q₈×C₁₃₁	—	4	8	no	—
72	Q₈×C₁₃₁	—	8	8	no	—
73	D₄×C₁₃₁	—	4	8	no	—
74	D₄×C₁₃₁	—	8	8	no	—
75	C₂×C₄×C₁₃₁	—	2	8	no	—
76	C₂×C₄×C₁₃₁	—	4	4	no	—
77	C₂×C₄×C₁₃₁	—	4	4	no	—
78	C₂×C₄×C₁₃₁	—	4	2	no	—
79	C₂×C₄×C₁₃₁	—	4	8	no	—
80	C₂×C₄×C₁₃₁	#124	1	8	yes	—
81	C₂×C₄×C₁₃₁	#127	1	4	yes	—
82	C₂×C₄×C₁₃₁	#135	1	8	yes	—
83	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
84	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
85	C₈×C₁₃₁	—	2	8	no	—
86	C₂²×C₁₃₁	—	8	2	no	—
87	C₂²×C₁₃₁	—	8	8	no	—
88	C₂²×C₁₃₁	—	8	4	no	—
89	C₂²×C₁₃₁	C₂×#124	1	2	yes	—
90	C₂²×C₁₃₁	C₂×#127	1	1	yes	characteristic
91	C₂²×C₁₃₁	C₂×#135	1	4	yes	—
92	C₄×C₁₃₁	—	2	8	no	—
93	C₄×C₁₃₁	—	8	2	no	—
94	C₄×C₁₃₁	—	8	4	no	—
95	C₄×C₁₃₁	#495	1	8	yes	—
96	C₄×C₁₃₁	#532	1	4	yes	—
97	C₂×C₁₃₁	—	16	2	no	—
98	C₂×C₁₃₁	#2858	1	1	yes	characteristic
99	C₂×C₁₃₁	#3131	1	4	yes	—
100	C₂×C₁₃₁	C₂×#495	1	2	yes	—
101	#33227	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₁₃₁	#33227	1	1	yes	characteristic, direct product factor, Sylow
103	C₂×#487	C₂×C₁₃₁	1	2	yes	complemented
104	C₂×#486	C₂×C₁₃₁	1	2	yes	—
105	#2862	C₂×C₁₃₁	1	1	yes	characteristic, complemented
106	#2858	C₂×C₁₃₁	1	1	yes	characteristic
107	#1958	C₂×C₁₃₁	1	8	yes	complemented
108	C₄²×C₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
109	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
110	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
111	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
112	C₂×#124	C₂²×C₁₃₁	1	4	yes	—
113	#487	—	2	8	no	—
114	#486	—	2	8	no	—
115	C₂×#103	C₂²×C₁₃₁	1	8	yes	—
116	C₂×#102	C₂²×C₁₃₁	1	8	yes	—
117	C₂×C₄×C₈	C₂²×C₁₃₁	1	4	yes	—
118	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
119	#391	—	2	4	no	—
120	#390	—	2	4	no	—
121	#382	C₂²×C₁₃₁	1	4	yes	—
122	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
123	C₂²×Q₈	—	2	2	no	—
124	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
125	C₂²×D₄	—	2	2	no	—
126	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
127	C₂²×C₈	C₂³×C₁₃₁	1	4	yes	—
128	C₄⋊Q₈	—	2	4	no	—
129	C₄⋊Q₈	—	2	4	no	—
130	C₄⋊Q₈	—	2	4	no	—
131	#127	—	2	4	no	—
132	#124	—	2	16	no	—
133	C₂×C₄⋊C₄	—	2	2	no	—
134	C₂×C₄⋊C₄	—	2	2	no	—
135	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
136	C₂×C₂²⋊C₄	—	2	8	no	—
137	C₂×C₄²	D₄×C₁₃₁	1	4	yes	—
138	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
139	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
140	#103	—	2	16	no	—
141	#102	—	2	16	no	—
142	C₄×C₈	—	2	8	no	—
143	C₄×C₈	D₄×C₁₃₁	1	8	yes	—
144	#95	—	2	8	no	—
145	C₂⁴	—	2	2	no	—
146	C₂×Q₈	—	2	4	no	—
147	C₂×Q₈	—	2	8	no	—
148	C₂×Q₈	—	4	4	no	—
149	C₂×Q₈	—	4	8	no	—
150	C₂×D₄	—	2	4	no	—
151	C₂×D₄	—	2	8	no	—
152	C₂×D₄	—	4	4	no	—
153	C₂×D₄	—	4	8	no	—
154	C₂²×C₄	—	2	4	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
157	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
158	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
159	C₂×C₈	—	2	8	no	—
160	C₂×C₈	C₂×D₄×C₁₃₁	1	8	yes	—
161	C₄⋊C₄	—	2	4	no	—
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	—	4	4	no	—
164	C₄⋊C₄	—	4	4	no	—
165	C₂²⋊C₄	—	4	16	no	—
166	C₄²	—	2	8	no	—
167	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
168	C₄²	#41×C₁₃₁	1	8	yes	—
169	C₂³	—	4	4	no	—
170	C₂³	—	4	2	no	—
171	C₂³	—	4	8	no	—
172	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
173	Q₈	—	4	8	no	—
174	Q₈	—	8	8	no	—
175	D₄	—	4	8	no	—
176	D₄	—	8	8	no	—
177	C₂×C₄	—	2	8	no	—
178	C₂×C₄	—	4	4	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	—	4	8	no	—
182	C₂×C₄	#124×C₁₃₁	1	8	yes	—
183	C₂×C₄	#127×C₁₃₁	1	4	yes	—
184	C₂×C₄	#135×C₁₃₁	1	8	yes	—
185	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
186	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
187	C₈	—	2	8	no	—
188	C₂²	—	8	2	no	—
189	C₂²	—	8	8	no	—
190	C₂²	—	8	4	no	—
191	C₂²	C₂×#124×C₁₃₁	1	2	yes	—
192	C₂²	C₂×#127×C₁₃₁	1	1	yes	characteristic
193	C₂²	C₂×#135×C₁₃₁	1	4	yes	—
194	C₄	—	2	8	no	—
195	C₄	—	8	2	no	—
196	C₄	—	8	4	no	—
197	C₄	#495×C₁₃₁	1	8	yes	—
198	C₄	#532×C₁₃₁	1	4	yes	—
199	C₂	—	16	2	no	—
200	C₂	#2858×C₁₃₁	1	1	yes	characteristic
201	C₂	#3131×C₁₃₁	1	4	yes	—
202	C₂	C₂×#495×C₁₃₁	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#487×C₁₃₁

C₂

yes

maximal, complemented

C₂×#486×C₁₃₁

C₂

yes

maximal

#2862×C₁₃₁

C₂

yes

maximal, characteristic, complemented

#2858×C₁₃₁

C₂

yes

maximal, characteristic

#1958×C₁₃₁

C₂

yes

maximal, complemented

C₄²×C₈×C₁₃₁

C₂

yes

maximal, characteristic, complemented

C₂×C₄⋊Q₈×C₁₃₁

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₁₃₁

C₂²

yes

—

C₂×#127×C₁₃₁

C₂²

yes

characteristic

C₂×#124×C₁₃₁

C₂²

yes

—

#487×C₁₃₁

—

#486×C₁₃₁

—

C₂×#103×C₁₃₁

C₂²

yes

—

C₂×#102×C₁₃₁

C₂²

yes

—

C₂×C₄×C₈×C₁₃₁

C₂²

yes

—

C₂×C₄×C₈×C₁₃₁

C₂²

yes

—

#391×C₁₃₁

—

#390×C₁₃₁

—

#382×C₁₃₁

C₂²

yes

—

C₄³×C₁₃₁

C₂²

yes

characteristic

C₂²×Q₈×C₁₃₁

—

C₂²×Q₈×C₁₃₁

C₂³

yes

—

C₂²×D₄×C₁₃₁

—

C₂²×D₄×C₁₃₁

C₂³

yes

—

C₂²×C₈×C₁₃₁

C₂³

yes

—

C₄⋊Q₈×C₁₃₁

—

C₄⋊Q₈×C₁₃₁

—

C₄⋊Q₈×C₁₃₁

—

#127×C₁₃₁

—

#124×C₁₃₁

—

C₂×C₄⋊C₄×C₁₃₁

—

C₂×C₄⋊C₄×C₁₃₁

—

C₂×C₄⋊C₄×C₁₃₁

C₂³

yes

—

C₂×C₂²⋊C₄×C₁₃₁

—

C₂×C₄²×C₁₃₁

D₄

yes

—

C₂×C₄²×C₁₃₁

C₂³

yes

characteristic

C₂×C₄²×C₁₃₁

C₂³

yes

—

#103×C₁₃₁

—

#102×C₁₃₁

—

C₄×C₈×C₁₃₁

—

C₄×C₈×C₁₃₁

D₄

yes

—

#95×C₁₃₁

—

C₂⁴×C₁₃₁

—

C₂×Q₈×C₁₃₁

—

C₂×Q₈×C₁₃₁

—

C₂×Q₈×C₁₃₁

—

C₂×Q₈×C₁₃₁

—

C₂×D₄×C₁₃₁

—

C₂×D₄×C₁₃₁

—

C₂×D₄×C₁₃₁

—

C₂×D₄×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×D₄

yes

—

C₄⋊C₄×C₁₃₁

—

C₄⋊C₄×C₁₃₁

—

C₄⋊C₄×C₁₃₁

—

C₄⋊C₄×C₁₃₁

—

C₂²⋊C₄×C₁₃₁

—

C₄²×C₁₃₁

—

C₄²×C₁₃₁

C₂×D₄

yes

—

C₄²×C₁₃₁

#41

yes

—

C₂³×C₁₃₁

—

C₂³×C₁₃₁

—

C₂³×C₁₃₁

—

C₂³×C₁₃₁

C₂²×D₄

yes

characteristic

Q₈×C₁₃₁

—

Q₈×C₁₃₁

—

D₄×C₁₃₁

—

D₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

#124

yes

—

C₂×C₄×C₁₃₁

#127

yes

—

C₂×C₄×C₁₃₁

#135

yes

—

C₂×C₄×C₁₃₁

C₂²×D₄

yes

—

C₂×C₄×C₁₃₁

C₂×#41

yes

—

C₈×C₁₃₁

—

C₂²×C₁₃₁

—

C₂²×C₁₃₁

—

C₂²×C₁₃₁

—

C₂²×C₁₃₁

C₂×#124

yes

—

C₂²×C₁₃₁

C₂×#127

yes

characteristic

C₂²×C₁₃₁

C₂×#135

yes

—

C₄×C₁₃₁

—

C₄×C₁₃₁

—

C₄×C₁₃₁

—

C₄×C₁₃₁

#495

yes

—

C₄×C₁₃₁

#532

yes

—

C₂×C₁₃₁

—

C₂×C₁₃₁

#2858

yes

characteristic

C₂×C₁₃₁

#3131

yes

—

100

C₂×C₁₃₁

C₂×#495

yes

—

101

#33227

C₁₃₁

yes

maximal, characteristic, direct product factor, Sylow

102

C₁₃₁

#33227

yes

characteristic, direct product factor, Sylow

103

C₂×#487

C₂×C₁₃₁

yes

complemented

104

C₂×#486

C₂×C₁₃₁

yes

—

105

#2862

C₂×C₁₃₁

yes

characteristic, complemented

106

#2858

C₂×C₁₃₁

yes

characteristic

107

#1958

C₂×C₁₃₁

yes

complemented

108

C₄²×C₈

C₂×C₁₃₁

yes

characteristic, complemented

109

C₂×C₄⋊Q₈

C₂²×C₁₃₁

yes

characteristic

110

C₂×C₄⋊Q₈

C₂²×C₁₃₁

yes

—

111

C₂×#127

C₂²×C₁₃₁

yes

characteristic

112

C₂×#124

C₂²×C₁₃₁

yes

—

113

#487

—

114

#486

—

115

C₂×#103

C₂²×C₁₃₁

yes

—

116

C₂×#102

C₂²×C₁₃₁

yes

—

117

C₂×C₄×C₈

C₂²×C₁₃₁

yes

—

118

C₂×C₄×C₈

C₂²×C₁₃₁

yes

—

119

#391

—

120

#390

—

121

#382

C₂²×C₁₃₁

yes

—

122

C₄³

C₂²×C₁₃₁

yes

characteristic

123

C₂²×Q₈

—

124

C₂²×Q₈

C₂³×C₁₃₁

yes

—

125

C₂²×D₄

—

126

C₂²×D₄

C₂³×C₁₃₁

yes

—

127

C₂²×C₈

C₂³×C₁₃₁

yes

—

128

C₄⋊Q₈

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

#127

—

132

#124

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

C₂³×C₁₃₁

yes

—

136

C₂×C₂²⋊C₄

—

137

C₂×C₄²

D₄×C₁₃₁

yes

—

138

C₂×C₄²

C₂³×C₁₃₁

yes

characteristic

139

C₂×C₄²

C₂³×C₁₃₁

yes

—

140

#103

—

141

#102

—

142

C₄×C₈

—

143

C₄×C₈

D₄×C₁₃₁

yes

—

144

#95

—

145

C₂⁴

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

C₂²×C₄

C₂×D₄×C₁₃₁

yes

—

157

C₂²×C₄

C₂×D₄×C₁₃₁

yes

—

158

C₂²×C₄

C₂⁴×C₁₃₁

yes

characteristic

159

C₂×C₈

—

160

C₂×C₈

C₂×D₄×C₁₃₁

yes

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₂²⋊C₄

—

166

C₄²

—

167

C₄²

C₂×D₄×C₁₃₁

yes

—

168

C₄²

#41×C₁₃₁

yes

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

C₂²×D₄×C₁₃₁

yes

characteristic

173

Q₈

—

174

Q₈

—

175

D₄

—

176

D₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

#124×C₁₃₁

yes

—

183

C₂×C₄

#127×C₁₃₁

yes

—

184

C₂×C₄

#135×C₁₃₁

yes

—

185

C₂×C₄

C₂²×D₄×C₁₃₁

yes

—

186

C₂×C₄

C₂×#41×C₁₃₁

yes

—

187

C₈

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

C₂×#124×C₁₃₁

yes

—

192

C₂²

C₂×#127×C₁₃₁

yes

characteristic

193

C₂²

C₂×#135×C₁₃₁

yes

—

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

#495×C₁₃₁

yes

—

198

C₄

#532×C₁₃₁

yes

—

199

C₂

—

200

C₂

#2858×C₁₃₁

yes

characteristic

201

C₂

#3131×C₁₃₁

yes

—

202

C₂

C₂×#495×C₁₃₁

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×#127×C₁₃₁	C₂²
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

C₂×#127×C₁₃₁

C₂²

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃₁ ◁ C₄³×C₁₃₁ ◁ G

N	H ≅ G/N	type
1. C₂×#487×C₁₃₁	C₂	semidirect
3. #2862×C₁₃₁	C₂	semidirect
5. #1958×C₁₃₁	C₂	semidirect
6. C₄²×C₈×C₁₃₁	C₂	semidirect
101. #33227	C₁₃₁	direct (N × H)
102. C₁₃₁	#33227	direct (N × H)
103. C₂×#487	C₂×C₁₃₁	semidirect
105. #2862	C₂×C₁₃₁	semidirect
107. #1958	C₂×C₁₃₁	semidirect
108. C₄²×C₈	C₂×C₁₃₁	semidirect

H ≅ G/N

type

1. C₂×#487×C₁₃₁

C₂

semidirect

3. #2862×C₁₃₁

C₂

semidirect

5. #1958×C₁₃₁

C₂

semidirect

6. C₄²×C₈×C₁₃₁

C₂

semidirect

101. #33227

C₁₃₁

direct (N × H)

102. C₁₃₁

#33227

direct (N × H)

103. C₂×#487

C₂×C₁₃₁

semidirect

105. #2862

C₂×C₁₃₁

semidirect

107. #1958

C₂×C₁₃₁

semidirect

108. C₄²×C₈

C₂×C₁₃₁

semidirect

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

subgroup	index
C₂×#487×C₁₃₁	2
C₂×#486×C₁₃₁	2
#2862×C₁₃₁	2
#2858×C₁₃₁	2
#1958×C₁₃₁	2
C₄²×C₈×C₁₃₁	2
#33227	131

subgroup

index

C₂×#487×C₁₃₁

C₂×#486×C₁₃₁

#2862×C₁₃₁

#2858×C₁₃₁

#1958×C₁₃₁

C₄²×C₈×C₁₃₁

#33227

131

Subgroups — C₁₃₁×#33227 #45719111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C131×#33227 #45719111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33227 #45719111