Finite Group Databasebeta

← C137×#10297 #46859683

Subgroups — C137×#10297 #46859683

Order 35072.

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

normal subgroups only

This group has 528 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#3209×C137C212yesmaximal
2#2862×C137C211yesmaximal, characteristic
3#1994×C137C211yesmaximal, characteristic
4#1548×C137C212yesmaximal
5#1276×C137C211yesmaximal, characteristic
6#533×C137C2211yescharacteristic
7C2×C4⋊Q8×C137C2212yes—
8#494×C137—22no—
9#487×C137—22no—
10#462×C137—24no—
11#451×C137—24no—
12#431×C137C2212yes—
13#423×C137C2211yescharacteristic
14#391×C137—24no—
15#382×C137—22no—
16C43×C137C2211yescharacteristic
17#339×C137—22no—
18#333×C137—24no—
19C22×Q8×C137D414yes—
20C2×Q16×C137—28no—
21C2×M16×C137—21no—
22C4⋊Q8×C137—22no—
23C4⋊Q8×C137—22no—
24C4⋊Q8×C137—22no—
25C4⋊Q8×C137—22no—
26C4⋊Q8×C137D412yes—
27#125×C137—21no—
28C22⋊Q8×C137—22no—
29C4×Q8×C137—22no—
30#117×C137—21no—
31C2×C4⋊C4×C137—22no—
32C2×C4⋊C4×C137—22no—
33C2×C42×C137—22no—
34C2×C42×C137D412yes—
35C2×C42×C137C2311yescharacteristic
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—24no—
43C2×Q8×C137—22no—
44C2×Q8×C137—24no—
45C2×Q8×C137—48no—
46C22×C4×C137—22no—
47C22×C4×C137—24no—
48C22×C4×C137C2×D412yes—
49C22×C4×C137C2×D411yescharacteristic
50Q16×C137—88no—
51M16×C137—42no—
52C2×C8×C137—24no—
53C2×C8×C137—41no—
54C4⋊C4×C137—22no—
55C4⋊C4×C137—22no—
56C4⋊C4×C137—42no—
57C4⋊C4×C137—42no—
58C4⋊C4×C137—42no—
59C4⋊C4×C137—42no—
60C4⋊C4×C137—42no—
61C22⋊C4×C137—41no—
62C42×C137—22no—
63C42×C137—44no—
64C42×C137—41no—
65C42×C137Q1614yescomplemented
66C42×C137C2×D411yescharacteristic
67C42×C137C2×D412yes—
68C42×C137#4111yescharacteristic
69C23×C137#12011yescharacteristic
70Q8×C137—44no—
71Q8×C137—48no—
72Q8×C137—84no—
73C2×C4×C137—24no—
74C2×C4×C137—24no—
75C2×C4×C137—44no—
76C2×C4×C137—48no—
77C2×C4×C137—42no—
78C2×C4×C137—44no—
79C2×C4×C137#12012yes—
80C2×C4×C137#12112yes—
81C2×C4×C137#12111yescharacteristic
82C2×C4×C137#12711yescharacteristic
83C2×C4×C137C2×Q1612yes—
84C2×C4×C137#13712yes—
85C8×C137—44no—
86C8×C137—81no—
87C22×C137—22no—
88C22×C137#39211yescharacteristic
89C22×C137#45112yes—
90C4×C137—22no—
91C4×C137—44no—
92C4×C137—84no—
93C4×C137—82no—
94C4×C137#45514yes—
95C4×C137#46212yes—
96C4×C137#49411yescharacteristic
97C4×C137#49711yescharacteristic
98C2×C137—22no—
99C2×C137#200412yes—
100C2×C137#201611yescharacteristic
101#10297C13711yesmaximal, characteristic, direct product factor, Sylow
102C137#1029711yescharacteristic, direct product factor, Sylow
103#3209C2×C13712yes—
104#2862C2×C13711yescharacteristic
105#1994C2×C13711yescharacteristic
106#1548C2×C13712yes—
107#1276C2×C13711yescharacteristic
108#533C22×C13711yescharacteristic
109C2×C4⋊Q8C22×C13712yes—
110#494—22no—
111#487—22no—
112#462—24no—
113#451—24no—
114#431C22×C13712yes—
115#423C22×C13711yescharacteristic
116#391—24no—
117#382—22no—
118C43C22×C13711yescharacteristic
119#339—22no—
120#333—24no—
121C22×Q8D4×C13714yes—
122C2×Q16—28no—
123C2×M16—21no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—22no—
128C4⋊Q8D4×C13712yes—
129#125—21no—
130C22⋊Q8—22no—
131C4×Q8—22no—
132#117—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C42—22no—
136C2×C42D4×C13712yes—
137C2×C42C23×C13711yescharacteristic
138C4⋊C8—22no—
139C4⋊C8D4×C13714yes—
140#103—28no—
141C22⋊C8—22no—
142C4×C8—22no—
143#95—28no—
144C2×Q8—24no—
145C2×Q8—22no—
146C2×Q8—24no—
147C2×Q8—48no—
148C22×C4—22no—
149C22×C4—24no—
150C22×C4C2×D4×C13712yes—
151C22×C4C2×D4×C13711yescharacteristic
152Q16—88no—
153M16—42no—
154C2×C8—24no—
155C2×C8—41no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C22⋊C4—41no—
164C42—22no—
165C42—44no—
166C42—41no—
167C42Q16×C13714yescomplemented
168C42C2×D4×C13711yescharacteristic
169C42C2×D4×C13712yes—
170C42#41×C13711yescharacteristic
171C23#120×C13711yescharacteristic
172Q8—44no—
173Q8—48no—
174Q8—84no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—48no—
179C2×C4—42no—
180C2×C4—44no—
181C2×C4#120×C13712yes—
182C2×C4#121×C13712yes—
183C2×C4#121×C13711yescharacteristic
184C2×C4#127×C13711yescharacteristic
185C2×C4C2×Q16×C13712yes—
186C2×C4#137×C13712yes—
187C8—44no—
188C8—81no—
189C22—22no—
190C22#392×C13711yescharacteristic
191C22#451×C13712yes—
192C4—22no—
193C4—44no—
194C4—84no—
195C4—82no—
196C4#455×C13714yes—
197C4#462×C13712yes—
198C4#494×C13711yescharacteristic
199C4#497×C13711yescharacteristic
200C2—22no—
201C2#2004×C13712yes—
202C2#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
65. C42×C137Q16semidirect
101. #10297C137direct (N × H)
102. C137#10297direct (N × H)
167. C42Q16×C137semidirect

Maximal subgroups

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

subgroupindex
#3209×C1372
#2862×C1372
#1994×C1372
#1548×C1372
#1276×C1372
#10297137