Finite Group Databasebeta

← C137×#7413 #46856799

Subgroups — C137×#7413 #46856799

Order 35072.

178 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 46 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#2074×C137C211yesmaximal, characteristic
2#1394×C137C211yesmaximal, characteristic
3#1319×C137C211yesmaximal, characteristic
4C2×#103×C137—21no—
5C2×#101×C137—21no—
6#391×C137C2211yescharacteristic
7#382×C137C411yescharacteristic
8#340×C137—21no—
9#336×C137C411yescharacteristic
10#324×C137—21no—
11C22×Q8×C137D411yescharacteristic
12C2×M16×C137—41no—
13C22×C8×C137—21no—
14C2×C4⋊C4×C137—21no—
15C2×C4⋊C4×C137D411yescharacteristic
16C2×C42×C137C2×C411yescharacteristic
17#103×C137—41no—
18#103×C137—41no—
19#101×C137—22no—
20#101×C137—41no—
21C22⋊C8×C137—41no—
22#95×C137—41no—
23#95×C137—41no—
24C2×Q8×C137—21no—
25C2×Q8×C137—41no—
26C2×Q8×C137—41no—
27C2×Q8×C137D811yescharacteristic
28C2×Q8×C137SD1611yescharacteristic
29C22×C4×C137—21no—
30C22×C4×C137—21no—
31C22×C4×C137—21no—
32C22×C4×C137—41no—
33C22×C4×C137C22⋊C411yescharacteristic
34M16×C137—42no—
35M16×C137—81no—
36C2×C8×C137—41no—
37C2×C8×C137—41no—
38C2×C8×C137—41no—
39C2×C8×C137—81no—
40C2×C8×C137—81no—
41C4⋊C4×C137—41no—
42C4⋊C4×C137—41no—
43C4⋊C4×C137—41no—
44C42×C137—41no—
45C23×C137#9911yescharacteristic
46Q8×C137—41no—
47Q8×C137—41no—
48Q8×C137—81no—
49C2×C4×C137—21no—
50C2×C4×C137—21no—
51C2×C4×C137—21no—
52C2×C4×C137—21no—
53C2×C4×C137—41no—
54C2×C4×C137—41no—
55C2×C4×C137—41no—
56C2×C4×C137—41no—
57C2×C4×C137—41no—
58C2×C4×C137—41no—
59C2×C4×C137—81no—
60C2×C4×C137—81no—
61C2×C4×C137—81no—
62C2×C4×C137—81no—
63C2×C4×C137#10211yescharacteristic
64C2×C4×C137#10411yescharacteristic
65C8×C137—81no—
66C8×C137—82no—
67C8×C137—161no—
68C22×C137—21no—
69C22×C137—21no—
70C22×C137#32711yescharacteristic
71C22×C137#35211yescharacteristic
72C22×C137#35411yescharacteristic
73C4×C137—21no—
74C4×C137—21no—
75C4×C137—41no—
76C4×C137—41no—
77C4×C137—81no—
78C4×C137—81no—
79C4×C137—161no—
80C2×C137—21no—
81C2×C137—21no—
82C2×C137#134411yescharacteristic
83C2×C137#141311yescharacteristic
84C2×C137#141411yescharacteristic
85#7413C13711yesmaximal, characteristic, direct product factor, Sylow
86C137#741311yescharacteristic, direct product factor, Sylow
87#2074C2×C13711yescharacteristic
88#1394C2×C13711yescharacteristic
89#1319C2×C13711yescharacteristic
90C2×#103—21no—
91C2×#101—21no—
92#391C22×C13711yescharacteristic
93#382C4×C13711yescharacteristic
94#340—21no—
95#336C4×C13711yescharacteristic
96#324—21no—
97C22×Q8D4×C13711yescharacteristic
98C2×M16—41no—
99C22×C8—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4D4×C13711yescharacteristic
102C2×C42C2×C4×C13711yescharacteristic
103#103—41no—
104#103—41no—
105#101—22no—
106#101—41no—
107C22⋊C8—41no—
108#95—41no—
109#95—41no—
110C2×Q8—21no—
111C2×Q8—41no—
112C2×Q8—41no—
113C2×Q8D8×C13711yescharacteristic
114C2×Q8SD16×C13711yescharacteristic
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—41no—
119C22×C4C22⋊C4×C13711yescharacteristic
120M16—42no—
121M16—81no—
122C2×C8—41no—
123C2×C8—41no—
124C2×C8—41no—
125C2×C8—81no—
126C2×C8—81no—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—41no—
130C42—41no—
131C23#99×C13711yescharacteristic
132Q8—41no—
133Q8—41no—
134Q8—81no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—81no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—81no—
149C2×C4#102×C13711yescharacteristic
150C2×C4#104×C13711yescharacteristic
151C8—81no—
152C8—82no—
153C8—161no—
154C22—21no—
155C22—21no—
156C22#327×C13711yescharacteristic
157C22#352×C13711yescharacteristic
158C22#354×C13711yescharacteristic
159C4—21no—
160C4—21no—
161C4—41no—
162C4—41no—
163C4—81no—
164C4—81no—
165C4—161no—
166C2—21no—
167C2—21no—
168C2#1344×C13711yescharacteristic
169C2#1413×C13711yescharacteristic
170C2#1414×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#354
commutatorC2×C42C2×C4×C137
Frattini, cosocle#391C22×C137
prime radicalC23×C137#99
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C137 ◁ C22×C4×C137 ◁ #391×C137 ◁ G

Complements

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

NH ≅ G/Ntype
85. #7413C137direct (N × H)
86. C137#7413direct (N × H)

Maximal subgroups

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

subgroupindex
#2074×C1372
#1394×C1372
#1319×C1372
#7413137