Finite Group Databasebeta

← C137×#10299 #46859685

Subgroups — C137×#10299 #46859685

Order 35072.

576 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 130 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#3229×C137C212yesmaximal
2#2868×C137C211yesmaximal, characteristic
3#1994×C137C211yesmaximal, characteristic
4#1546×C137C212yesmaximal
5#1276×C137C211yesmaximal, characteristic
6#533×C137C2211yescharacteristic
7C2×C4⋊Q8×C137—22no—
8C2×C4⋊Q8×C137C2212yes—
9#498×C137—22no—
10#487×C137—22no—
11#483×C137—24no—
12#475×C137—24no—
13#431×C137C2212yes—
14#423×C137C2211yescharacteristic
15#384×C137—24no—
16C43×C137C2211yescharacteristic
17#339×C137—22no—
18#332×C137—24no—
19C22×Q8×C137—22no—
20C2×M16×C137—21no—
21C4⋊Q8×C137—22no—
22C4⋊Q8×C137—22no—
23C4⋊Q8×C137—22no—
24C4⋊Q8×C137—22no—
25C4⋊Q8×C137—44no—
26C4⋊Q8×C137—44no—
27C4⋊Q8×C137D412yes—
28#125×C137—21no—
29C22⋊Q8×C137—22no—
30C4×Q8×C137—22no—
31#117×C137—21no—
32C2×C4⋊C4×C137—28no—
33C2×C4⋊C4×C137—22no—
34C2×C4⋊C4×C137D414yes—
35C2×C42×C137—22no—
36C2×C42×C137D412yes—
37C2×C42×C137C2311yescharacteristic
38#106×C137—28no—
39C4⋊C8×C137—22no—
40C4⋊C8×C137D414yes—
41#103×C137—28no—
42C22⋊C8×C137—22no—
43C4×C8×C137—22no—
44C2×Q8×C137—22no—
45C2×Q8×C137—42no—
46C2×Q8×C137—42no—
47C2×Q8×C137—44no—
48C2×Q8×C137—44no—
49C22×C4×C137—22no—
50C22×C4×C137—24no—
51C22×C4×C137C2×D412yes—
52C22×C4×C137C2×D411yescharacteristic
53M16×C137—42no—
54C2×C8×C137—24no—
55C2×C8×C137—41no—
56C4⋊C4×C137—24no—
57C4⋊C4×C137—22no—
58C4⋊C4×C137—24no—
59C4⋊C4×C137—22no—
60C4⋊C4×C137—416no—
61C4⋊C4×C137—42no—
62C4⋊C4×C137—42no—
63C4⋊C4×C137—42no—
64C22⋊C4×C137—41no—
65C42×C137—28no—
66C42×C137—22no—
67C42×C137—41no—
68C42×C137SD1614yes—
69C42×C137C2×D411yescharacteristic
70C42×C137C2×D412yes—
71C42×C137#4111yescharacteristic
72C23×C137#12011yescharacteristic
73Q8×C137—44no—
74Q8×C137—84no—
75Q8×C137—82no—
76Q8×C137—82no—
77C2×C4×C137—28no—
78C2×C4×C137—24no—
79C2×C4×C137—24no—
80C2×C4×C137—42no—
81C2×C4×C137—44no—
82C2×C4×C137—48no—
83C2×C4×C137#12012yes—
84C2×C4×C137#12112yes—
85C2×C4×C137#12111yescharacteristic
86C2×C4×C137#12711yescharacteristic
87C2×C4×C137C2×SD1612yes—
88C2×C4×C137AGL(1,ℤ/8)12yes—
89C8×C137—44no—
90C8×C137—81no—
91C22×C137—22no—
92C22×C137#39211yescharacteristic
93C22×C137#45012yes—
94C4×C137—28no—
95C4×C137—22no—
96C4×C137—82no—
97C4×C137—84no—
98C4×C137#45614yes—
99C4×C137#46012yes—
100C4×C137#49211yescharacteristic
101C4×C137#49611yescharacteristic
102C2×C137—22no—
103C2×C137#200512yes—
104C2×C137#201411yescharacteristic
105#10299C13711yesmaximal, characteristic, direct product factor, Sylow
106C137#1029911yescharacteristic, direct product factor, Sylow
107#3229C2×C13712yes—
108#2868C2×C13711yescharacteristic
109#1994C2×C13711yescharacteristic
110#1546C2×C13712yes—
111#1276C2×C13711yescharacteristic
112#533C22×C13711yescharacteristic
113C2×C4⋊Q8—22no—
114C2×C4⋊Q8C22×C13712yes—
115#498—22no—
116#487—22no—
117#483—24no—
118#475—24no—
119#431C22×C13712yes—
120#423C22×C13711yescharacteristic
121#384—24no—
122C43C22×C13711yescharacteristic
123#339—22no—
124#332—24no—
125C22×Q8—22no—
126C2×M16—21no—
127C4⋊Q8—22no—
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4⋊Q8—22no—
131C4⋊Q8—44no—
132C4⋊Q8—44no—
133C4⋊Q8D4×C13712yes—
134#125—21no—
135C22⋊Q8—22no—
136C4×Q8—22no—
137#117—21no—
138C2×C4⋊C4—28no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4D4×C13714yes—
141C2×C42—22no—
142C2×C42D4×C13712yes—
143C2×C42C23×C13711yescharacteristic
144#106—28no—
145C4⋊C8—22no—
146C4⋊C8D4×C13714yes—
147#103—28no—
148C22⋊C8—22no—
149C4×C8—22no—
150C2×Q8—22no—
151C2×Q8—42no—
152C2×Q8—42no—
153C2×Q8—44no—
154C2×Q8—44no—
155C22×C4—22no—
156C22×C4—24no—
157C22×C4C2×D4×C13712yes—
158C22×C4C2×D4×C13711yescharacteristic
159M16—42no—
160C2×C8—24no—
161C2×C8—41no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—24no—
165C4⋊C4—22no—
166C4⋊C4—416no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C22⋊C4—41no—
171C42—28no—
172C42—22no—
173C42—41no—
174C42SD16×C13714yes—
175C42C2×D4×C13711yescharacteristic
176C42C2×D4×C13712yes—
177C42#41×C13711yescharacteristic
178C23#120×C13711yescharacteristic
179Q8—44no—
180Q8—84no—
181Q8—82no—
182Q8—82no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—48no—
189C2×C4#120×C13712yes—
190C2×C4#121×C13712yes—
191C2×C4#121×C13711yescharacteristic
192C2×C4#127×C13711yescharacteristic
193C2×C4C2×SD16×C13712yes—
194C2×C4AGL(1,ℤ/8)×C13712yes—
195C8—44no—
196C8—81no—
197C22—22no—
198C22#392×C13711yescharacteristic
199C22#450×C13712yes—
200C4—28no—
201C4—22no—
202C4—84no—
203C4—82no—
204C4#456×C13714yes—
205C4#460×C13712yes—
206C4#492×C13711yescharacteristic
207C4#496×C13711yescharacteristic
208C2—22no—
209C2#2005×C13712yes—
210C2#2014×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#392
commutator, Frattini, cosocleC2×C42C23×C137
prime radicalC23×C137#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
105. #10299C137direct (N × H)
106. C137#10299direct (N × H)

Maximal subgroups

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

subgroupindex
#3229×C1372
#2868×C1372
#1994×C1372
#1546×C1372
#1276×C1372
#10299137