Finite Group Databasebeta

← C137×#19073 #46868459

Subgroups — C137×#19073 #46868459

Order 35072.

1252 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3549×C137C211yesmaximal, characteristic, complemented
2#3151×C137C213yesmaximal, complemented
3#1655×C137C218yesmaximal, complemented
4#1525×C137C213yesmaximal, complemented
5C2×AGL(1,ℤ/8)×C137—26no—
6H(3,𝔽4)×C137C2214yescomplemented
7#555×C137—23no—
8D42×C137—23no—
9#535×C137—26no—
10#532×C137C2213yes—
11C2×#127×C137C2211yescharacteristic, complemented
12#496×C137C22112yescomplemented
13#493×C137—23no—
14#492×C137—23no—
15C4×M16×C137C2213yescomplemented
16#329×C137C22112yescomplemented
17C2×#41×C137D416yes—
18C22×D4×C137—26no—
19C22×D4×C137—23no—
20AGL(1,ℤ/8)×C137—424no—
21C2×SD16×C137—212no—
22C2×D8×C137—212no—
23C2×M16×C137—23no—
24C4⋊Q8×C137D413yes—
25#127×C137—24no—
26#127×C137—23no—
27#127×C137D413yes—
28#127×C137C2312yes—
29#124×C137—212no—
30#124×C137C2316yes—
31#121×C137—212no—
32#121×C137—26no—
33#120×C137—24no—
34#120×C137—212no—
35C4×D4×C137—26no—
36#117×C137—26no—
37C2×C42×C137C2311yescharacteristic
38#97×C137C2316yes—
39C4×C8×C137—23no—
40C24×C137—24no—
41C24×C137—41no—
42#41×C137—412no—
43C2×Q8×C137C2×D416yes—
44C2×D4×C137—212no—
45C2×D4×C137—26no—
46C2×D4×C137—26no—
47C2×D4×C137—26no—
48C2×D4×C137—412no—
49C2×D4×C137—43no—
50C2×D4×C137—812no—
51C2×D4×C137C2×D416yes—
52C22×C4×C137—26no—
53C22×C4×C137C2×D413yes—
54SD16×C137—424no—
55D8×C137—424no—
56M16×C137—212no—
57C2×C8×C137—26no—
58C4⋊C4×C137—26no—
59C22⋊C4×C137—212no—
60C22⋊C4×C137—212no—
61C42×C137—24no—
62C42×C137C2×D413yes—
63C42×C137C2411yescharacteristic
64C23×C137—26no—
65C23×C137—42no—
66C23×C137—86no—
67C23×C137—812no—
68C23×C137#12011yescharacteristic
69Q8×C137—46no—
70D4×C137—46no—
71D4×C137—412no—
72D4×C137—412no—
73D4×C137—86no—
74D4×C137—812no—
75D4×C137—86no—
76C2×C4×C137—26no—
77C2×C4×C137—26no—
78C2×C4×C137—412no—
79C2×C4×C137#12013yes—
80C2×C4×C137C22×D413yes—
81C8×C137—212no—
82C22×C137—23no—
83C22×C137—46no—
84C22×C137—412no—
85C22×C137—86no—
86C22×C137—164no—
87C22×C137—168no—
88C22×C137C2×#12011yescharacteristic
89C4×C137—23no—
90C4×C137—46no—
91C4×C137#45316yes—
92C2×C137—41no—
93C2×C137—86no—
94C2×C137—162no—
95C2×C137C2×#45313yes—
96#19073C13711yesmaximal, characteristic, direct product factor, Sylow
97C137#1907311yescharacteristic, direct product factor, Sylow
98#3549C2×C13711yescharacteristic, complemented
99#3151C2×C13713yescomplemented
100#1655C2×C13718yescomplemented
101#1525C2×C13713yescomplemented
102C2×AGL(1,ℤ/8)—26no—
103H(3,𝔽4)C22×C13714yescomplemented
104#555—23no—
105D42—23no—
106#535—26no—
107#532C22×C13713yes—
108C2×#127C22×C13711yescharacteristic, complemented
109#496C22×C137112yescomplemented
110#493—23no—
111#492—23no—
112C4×M16C22×C13713yescomplemented
113#329C22×C137112yescomplemented
114C2×#41D4×C13716yes—
115C22×D4—26no—
116C22×D4—23no—
117AGL(1,ℤ/8)—424no—
118C2×SD16—212no—
119C2×D8—212no—
120C2×M16—23no—
121C4⋊Q8D4×C13713yes—
122#127—24no—
123#127—23no—
124#127D4×C13713yes—
125#127C23×C13712yes—
126#124—212no—
127#124C23×C13716yes—
128#121—212no—
129#121—26no—
130#120—24no—
131#120—212no—
132C4×D4—26no—
133#117—26no—
134C2×C42C23×C13711yescharacteristic
135#97C23×C13716yes—
136C4×C8—23no—
137C24—24no—
138C24—41no—
139#41—412no—
140C2×Q8C2×D4×C13716yes—
141C2×D4—212no—
142C2×D4—26no—
143C2×D4—26no—
144C2×D4—26no—
145C2×D4—412no—
146C2×D4—43no—
147C2×D4—812no—
148C2×D4C2×D4×C13716yes—
149C22×C4—26no—
150C22×C4C2×D4×C13713yes—
151SD16—424no—
152D8—424no—
153M16—212no—
154C2×C8—26no—
155C4⋊C4—26no—
156C22⋊C4—212no—
157C22⋊C4—212no—
158C42—24no—
159C42C2×D4×C13713yes—
160C42C24×C13711yescharacteristic
161C23—26no—
162C23—42no—
163C23—86no—
164C23—812no—
165C23#120×C13711yescharacteristic
166Q8—46no—
167D4—46no—
168D4—412no—
169D4—412no—
170D4—86no—
171D4—812no—
172D4—86no—
173C2×C4—26no—
174C2×C4—26no—
175C2×C4—412no—
176C2×C4#120×C13713yes—
177C2×C4C22×D4×C13713yes—
178C8—212no—
179C22—23no—
180C22—46no—
181C22—412no—
182C22—86no—
183C22—164no—
184C22—168no—
185C22C2×#120×C13711yescharacteristic
186C4—23no—
187C4—46no—
188C4#453×C13716yes—
189C2—41no—
190C2—86no—
191C2—162no—
192C2C2×#453×C13713yes—
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC42C24×C137
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3549×C137C2semidirect
2. #3151×C137C2semidirect
3. #1655×C137C2semidirect
4. #1525×C137C2semidirect
6. H(3,𝔽4)×C137C22semidirect
11. C2×#127×C137C22semidirect
12. #496×C137C22semidirect
15. C4×M16×C137C22semidirect
16. #329×C137C22semidirect
96. #19073C137direct (N × H)
97. C137#19073direct (N × H)
98. #3549C2×C137semidirect
99. #3151C2×C137semidirect
100. #1655C2×C137semidirect
101. #1525C2×C137semidirect
103. H(3,𝔽4)C22×C137semidirect
108. C2×#127C22×C137semidirect
109. #496C22×C137semidirect
112. C4×M16C22×C137semidirect
113. #329C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3549×C1372
#3151×C1372
#1655×C1372
#1525×C1372
#19073137