Finite Group Databasebeta

← C137×#10295 #46859681

Subgroups — C137×#10295 #46859681

Order 35072.

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

normal subgroups only

This group has 504 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#3230×C137C212yesmaximal
2#2862×C137C211yesmaximal, characteristic
3#1994×C137C211yesmaximal, characteristic
4#1549×C137C212yesmaximal
5#1276×C137C211yesmaximal, characteristic
6#533×C137C2211yescharacteristic
7C2×C4⋊Q8×C137C2212yes—
8#500×C137—22no—
9#487×C137—22no—
10#484×C137—24no—
11#477×C137—24no—
12#431×C137C2212yes—
13#423×C137C2211yescharacteristic
14#391×C137—24no—
15#382×C137—22no—
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×C137D412yes—
26#125×C137—21no—
27C22⋊Q8×C137—22no—
28C4×Q8×C137—22no—
29#117×C137—21no—
30C2×C4⋊C4×C137—22no—
31C2×C4⋊C4×C137D414yes—
32C2×C42×C137—22no—
33C2×C42×C137D412yes—
34C2×C42×C137C2311yescharacteristic
35#107×C137—28no—
36C4⋊C8×C137—22no—
37C4⋊C8×C137D414yes—
38#103×C137—28no—
39C22⋊C8×C137—22no—
40C4×C8×C137—22no—
41#95×C137—28no—
42C2×Q8×C137—22no—
43C2×Q8×C137—48no—
44C2×Q8×C137—42no—
45C2×Q8×C137—42no—
46C22×C4×C137—22no—
47C22×C4×C137—24no—
48C22×C4×C137C2×D412yes—
49C22×C4×C137C2×D411yescharacteristic
50M16×C137—42no—
51C2×C8×C137—24no—
52C2×C8×C137—41no—
53C4⋊C4×C137—24no—
54C4⋊C4×C137—22no—
55C4⋊C4×C137—24no—
56C4⋊C4×C137—22no—
57C4⋊C4×C137—42no—
58C4⋊C4×C137—42no—
59C4⋊C4×C137—42no—
60C22⋊C4×C137—41no—
61C42×C137—22no—
62C42×C137—44no—
63C42×C137—41no—
64C42×C137Q1614yes—
65C42×C137C2×D411yescharacteristic
66C42×C137C2×D412yes—
67C42×C137#4111yescharacteristic
68C23×C137#12011yescharacteristic
69Q8×C137—44no—
70Q8×C137—84no—
71Q8×C137—84no—
72C2×C4×C137—24no—
73C2×C4×C137—24no—
74C2×C4×C137—44no—
75C2×C4×C137—48no—
76C2×C4×C137—42no—
77C2×C4×C137—44no—
78C2×C4×C137#12012yes—
79C2×C4×C137#12112yes—
80C2×C4×C137#12111yescharacteristic
81C2×C4×C137#12711yescharacteristic
82C2×C4×C137C2×Q1612yes—
83C2×C4×C137#13712yes—
84C8×C137—44no—
85C8×C137—81no—
86C22×C137—22no—
87C22×C137#39211yescharacteristic
88C22×C137#45112yes—
89C4×C137—22no—
90C4×C137—44no—
91C4×C137—84no—
92C4×C137—82no—
93C4×C137#45414yes—
94C4×C137#46212yes—
95C4×C137#49411yescharacteristic
96C4×C137#49711yescharacteristic
97C2×C137—22no—
98C2×C137#200312yes—
99C2×C137#201611yescharacteristic
100#10295C13711yesmaximal, characteristic, direct product factor, Sylow
101C137#1029511yescharacteristic, direct product factor, Sylow
102#3230C2×C13712yes—
103#2862C2×C13711yescharacteristic
104#1994C2×C13711yescharacteristic
105#1549C2×C13712yes—
106#1276C2×C13711yescharacteristic
107#533C22×C13711yescharacteristic
108C2×C4⋊Q8C22×C13712yes—
109#500—22no—
110#487—22no—
111#484—24no—
112#477—24no—
113#431C22×C13712yes—
114#423C22×C13711yescharacteristic
115#391—24no—
116#382—22no—
117C43C22×C13711yescharacteristic
118#339—22no—
119#332—24no—
120C22×Q8—22no—
121C2×M16—21no—
122C4⋊Q8—22no—
123C4⋊Q8—22no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8D4×C13712yes—
127#125—21no—
128C22⋊Q8—22no—
129C4×Q8—22no—
130#117—21no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4D4×C13714yes—
133C2×C42—22no—
134C2×C42D4×C13712yes—
135C2×C42C23×C13711yescharacteristic
136#107—28no—
137C4⋊C8—22no—
138C4⋊C8D4×C13714yes—
139#103—28no—
140C22⋊C8—22no—
141C4×C8—22no—
142#95—28no—
143C2×Q8—22no—
144C2×Q8—48no—
145C2×Q8—42no—
146C2×Q8—42no—
147C22×C4—22no—
148C22×C4—24no—
149C22×C4C2×D4×C13712yes—
150C22×C4C2×D4×C13711yescharacteristic
151M16—42no—
152C2×C8—24no—
153C2×C8—41no—
154C4⋊C4—24no—
155C4⋊C4—22no—
156C4⋊C4—24no—
157C4⋊C4—22no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—41no—
162C42—22no—
163C42—44no—
164C42—41no—
165C42Q16×C13714yes—
166C42C2×D4×C13711yescharacteristic
167C42C2×D4×C13712yes—
168C42#41×C13711yescharacteristic
169C23#120×C13711yescharacteristic
170Q8—44no—
171Q8—84no—
172Q8—84no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4#120×C13712yes—
180C2×C4#121×C13712yes—
181C2×C4#121×C13711yescharacteristic
182C2×C4#127×C13711yescharacteristic
183C2×C4C2×Q16×C13712yes—
184C2×C4#137×C13712yes—
185C8—44no—
186C8—81no—
187C22—22no—
188C22#392×C13711yescharacteristic
189C22#451×C13712yes—
190C4—22no—
191C4—44no—
192C4—84no—
193C4—82no—
194C4#454×C13714yes—
195C4#462×C13712yes—
196C4#494×C13711yescharacteristic
197C4#497×C13711yescharacteristic
198C2—22no—
199C2#2003×C13712yes—
200C2#2016×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
100. #10295C137direct (N × H)
101. C137#10295direct (N × H)

Maximal subgroups

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

subgroupindex
#3230×C1372
#2862×C1372
#1994×C1372
#1549×C1372
#1276×C1372
#10295137