Finite Group Databasebeta

← C137×#9436 #46858822

Subgroups — C137×#9436 #46858822

Order 35072.

400 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 126 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#3139×C137C211yesmaximal, characteristic
2#2986×C137C211yesmaximal, characteristic
3#1561×C137C211yesmaximal, characteristic
4#1549×C137C212yesmaximal
5#1299×C137C212yesmaximal
6#533×C137C2211yescharacteristic
7C2×C4⋊Q8×C137C2211yescharacteristic
8#491×C137C414yes—
9#487×C137—22no—
10#446×C137—22no—
11C8×Q8×C137—22no—
12#433×C137—22no—
13#431×C137C2212yes—
14#423×C137C2212yes—
15#419×C137—22no—
16C4×M16×C137C2211yescharacteristic
17#332×C137—22no—
18#332×C137—22no—
19#332×C137—22no—
20C22×Q8×C137—21no—
21C2×M16×C137—21no—
22C2×M16×C137—22no—
23C4⋊Q8×C137—22no—
24C4⋊Q8×C137—21no—
25C4⋊Q8×C137C2×C412yes—
26C4⋊Q8×C137D412yes—
27#125×C137C2×C412yes—
28C22⋊Q8×C137—22no—
29C4×Q8×C137—22no—
30#117×C137D412yes—
31C2×C4⋊C4×C137—22no—
32C2×C42×C137C2311yescharacteristic
33C4⋊C8×C137—24no—
34C4⋊C8×C137—22no—
35C4⋊C8×C137—22no—
36C4⋊C8×C137D412yes—
37C4⋊C8×C137D412yes—
38#103×C137—28no—
39C22⋊C8×C137—22no—
40#97×C137—22no—
41#97×C137C2×C412yes—
42C4×C8×C137—22no—
43C4×C8×C137—21no—
44C4×C8×C137—22no—
45C2×Q8×C137—22no—
46C2×Q8×C137—22no—
47C2×Q8×C137—44no—
48C2×Q8×C137—41no—
49C22×C4×C137—41no—
50C22×C4×C137C2×D411yescharacteristic
51C22×C4×C137#4112yes—
52M16×C137—42no—
53M16×C137—82no—
54C2×C8×C137—22no—
55C2×C8×C137—22no—
56C2×C8×C137—22no—
57C2×C8×C137—42no—
58C4⋊C4×C137—24no—
59C4⋊C4×C137—22no—
60C4⋊C4×C137—24no—
61C4⋊C4×C137—42no—
62C4⋊C4×C137C22⋊C414yes—
63C22⋊C4×C137—22no—
64C42×C137—22no—
65C42×C137C22×C411yescharacteristic
66C42×C137C2×D411yescharacteristic
67C42×C137C2×D412yes—
68C23×C137#12311yescharacteristic
69Q8×C137—44no—
70Q8×C137—42no—
71Q8×C137—42no—
72Q8×C137—82no—
73C2×C4×C137—22no—
74C2×C4×C137—22no—
75C2×C4×C137—22no—
76C2×C4×C137—24no—
77C2×C4×C137—42no—
78C2×C4×C137—82no—
79C2×C4×C137C2×C22⋊C411yescharacteristic
80C2×C4×C137C4×D412yes—
81C2×C4×C137#12011yescharacteristic
82C2×C4×C137#12112yes—
83C8×C137—42no—
84C8×C137—42no—
85C8×C137—42no—
86C8×C137—82no—
87C22×C137—21no—
88C22×C137—22no—
89C22×C137#38611yescharacteristic
90C4×C137—21no—
91C4×C137—22no—
92C4×C137—44no—
93C4×C137—82no—
94C4×C137#45412yes—
95C4×C137#47112yes—
96C4×C137#47312yes—
97C2×C137—41no—
98C2×C137#188811yescharacteristic
99C2×C137#190812yes—
100#9436C13711yesmaximal, characteristic, direct product factor, Sylow
101C137#943611yescharacteristic, direct product factor, Sylow
102#3139C2×C13711yescharacteristic
103#2986C2×C13711yescharacteristic
104#1561C2×C13711yescharacteristic
105#1549C2×C13712yes—
106#1299C2×C13712yes—
107#533C22×C13711yescharacteristic
108C2×C4⋊Q8C22×C13711yescharacteristic
109#491C4×C13714yes—
110#487—22no—
111#446—22no—
112C8×Q8—22no—
113#433—22no—
114#431C22×C13712yes—
115#423C22×C13712yes—
116#419—22no—
117C4×M16C22×C13711yescharacteristic
118#332—22no—
119#332—22no—
120#332—22no—
121C22×Q8—21no—
122C2×M16—21no—
123C2×M16—22no—
124C4⋊Q8—22no—
125C4⋊Q8—21no—
126C4⋊Q8C2×C4×C13712yes—
127C4⋊Q8D4×C13712yes—
128#125C2×C4×C13712yes—
129C22⋊Q8—22no—
130C4×Q8—22no—
131#117D4×C13712yes—
132C2×C4⋊C4—22no—
133C2×C42C23×C13711yescharacteristic
134C4⋊C8—24no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8D4×C13712yes—
138C4⋊C8D4×C13712yes—
139#103—28no—
140C22⋊C8—22no—
141#97—22no—
142#97C2×C4×C13712yes—
143C4×C8—22no—
144C4×C8—21no—
145C4×C8—22no—
146C2×Q8—22no—
147C2×Q8—22no—
148C2×Q8—44no—
149C2×Q8—41no—
150C22×C4—41no—
151C22×C4C2×D4×C13711yescharacteristic
152C22×C4#41×C13712yes—
153M16—42no—
154M16—82no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—22no—
158C2×C8—42no—
159C4⋊C4—24no—
160C4⋊C4—22no—
161C4⋊C4—24no—
162C4⋊C4—42no—
163C4⋊C4C22⋊C4×C13714yes—
164C22⋊C4—22no—
165C42—22no—
166C42C22×C4×C13711yescharacteristic
167C42C2×D4×C13711yescharacteristic
168C42C2×D4×C13712yes—
169C23#123×C13711yescharacteristic
170Q8—44no—
171Q8—42no—
172Q8—42no—
173Q8—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—42no—
179C2×C4—82no—
180C2×C4C2×C22⋊C4×C13711yescharacteristic
181C2×C4C4×D4×C13712yes—
182C2×C4#120×C13711yescharacteristic
183C2×C4#121×C13712yes—
184C8—42no—
185C8—42no—
186C8—42no—
187C8—82no—
188C22—21no—
189C22—22no—
190C22#386×C13711yescharacteristic
191C4—21no—
192C4—22no—
193C4—44no—
194C4—82no—
195C4#454×C13712yes—
196C4#471×C13712yes—
197C4#473×C13712yes—
198C2—41no—
199C2#1888×C13711yescharacteristic
200C2#1908×C13712yes—
subgroupG/H
center, socleC22×C137#386
commutatorC42C22×C4×C137
Frattini, cosocleC2×C42C23×C137
prime radicalC23×C137#123
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
100. #9436C137direct (N × H)
101. C137#9436direct (N × H)

Maximal subgroups

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

subgroupindex
#3139×C1372
#2986×C1372
#1561×C1372
#1549×C1372
#1299×C1372
#9436137