Finite Group Databasebeta

← C131×#7405 #45693289

Subgroups — C131×#7405 #45693289

Order 33536.

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

normal subgroups only

This group has 252 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#2016×C131C211yesmaximal, characteristic
2#1394×C131C211yesmaximal, characteristic
3#1319×C131C211yesmaximal, characteristic
4C22×Q16×C131—21no—
5C2×C4⋊Q8×C131C411yescharacteristic
6C2×#103×C131—21no—
7C2×#101×C131—21no—
8#391×C131C2211yescharacteristic
9#336×C131C411yescharacteristic
10#324×C131—21no—
11C22×Q8×C131—21no—
12C22×Q8×C131D411yescharacteristic
13C2×Q16×C131—42no—
14C2×Q16×C131—42no—
15C2×Q16×C131—41no—
16C2×Q16×C131—41no—
17C2×M16×C131—41no—
18C22×C8×C131—21no—
19C4⋊Q8×C131—42no—
20C2×C4⋊C4×C131—41no—
21C2×C4⋊C4×C131D411yescharacteristic
22C2×C42×C131C2×C411yescharacteristic
23#103×C131—42no—
24#101×C131—22no—
25#101×C131—41no—
26C22⋊C8×C131—41no—
27#95×C131—41no—
28C2×Q8×C131—21no—
29C2×Q8×C131—22no—
30C2×Q8×C131—41no—
31C2×Q8×C131—41no—
32C2×Q8×C131—41no—
33C2×Q8×C131—41no—
34C2×Q8×C131—41no—
35C2×Q8×C131—41no—
36C2×Q8×C131—41no—
37C2×Q8×C131D811yescharacteristic
38C2×Q8×C131SD1611yescharacteristic
39C22×C4×C131—21no—
40C22×C4×C131—21no—
41C22×C4×C131—21no—
42C22×C4×C131—41no—
43C22×C4×C131C22⋊C411yescharacteristic
44Q16×C131—44no—
45Q16×C131—44no—
46M16×C131—42no—
47M16×C131—81no—
48C2×C8×C131—22no—
49C2×C8×C131—41no—
50C2×C8×C131—41no—
51C2×C8×C131—81no—
52C2×C8×C131—81no—
53C4⋊C4×C131—41no—
54C4⋊C4×C131—42no—
55C4⋊C4×C131—42no—
56C42×C131—41no—
57C23×C131#9911yescharacteristic
58Q8×C131—41no—
59Q8×C131—41no—
60Q8×C131—42no—
61Q8×C131—42no—
62Q8×C131—81no—
63Q8×C131—81no—
64Q8×C131—81no—
65C2×C4×C131—21no—
66C2×C4×C131—21no—
67C2×C4×C131—22no—
68C2×C4×C131—21no—
69C2×C4×C131—21no—
70C2×C4×C131—41no—
71C2×C4×C131—41no—
72C2×C4×C131—41no—
73C2×C4×C131—41no—
74C2×C4×C131—42no—
75C2×C4×C131—41no—
76C2×C4×C131—81no—
77C2×C4×C131—81no—
78C2×C4×C131—81no—
79C2×C4×C131#10211yescharacteristic
80C2×C4×C131#10411yescharacteristic
81C8×C131—42no—
82C8×C131—82no—
83C8×C131—161no—
84C22×C131—21no—
85C22×C131—21no—
86C22×C131#32711yescharacteristic
87C22×C131AΣL(1,𝔽16)11yescharacteristic
88C22×C131#35311yescharacteristic
89C4×C131—21no—
90C4×C131—21no—
91C4×C131—42no—
92C4×C131—41no—
93C4×C131—41no—
94C4×C131—82no—
95C4×C131—81no—
96C2×C131—21no—
97C2×C131—21no—
98C2×C131#134311yescharacteristic
99C2×C131#140711yescharacteristic
100C2×C131#141111yescharacteristic
101#7405C13111yesmaximal, characteristic, direct product factor, Sylow
102C131#740511yescharacteristic, direct product factor, Sylow
103#2016C2×C13111yescharacteristic
104#1394C2×C13111yescharacteristic
105#1319C2×C13111yescharacteristic
106C22×Q16—21no—
107C2×C4⋊Q8C4×C13111yescharacteristic
108C2×#103—21no—
109C2×#101—21no—
110#391C22×C13111yescharacteristic
111#336C4×C13111yescharacteristic
112#324—21no—
113C22×Q8—21no—
114C22×Q8D4×C13111yescharacteristic
115C2×Q16—42no—
116C2×Q16—42no—
117C2×Q16—41no—
118C2×Q16—41no—
119C2×M16—41no—
120C22×C8—21no—
121C4⋊Q8—42no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4D4×C13111yescharacteristic
124C2×C42C2×C4×C13111yescharacteristic
125#103—42no—
126#101—22no—
127#101—41no—
128C22⋊C8—41no—
129#95—41no—
130C2×Q8—21no—
131C2×Q8—22no—
132C2×Q8—41no—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8—41no—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—41no—
139C2×Q8D8×C13111yescharacteristic
140C2×Q8SD16×C13111yescharacteristic
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—41no—
145C22×C4C22⋊C4×C13111yescharacteristic
146Q16—44no—
147Q16—44no—
148M16—42no—
149M16—81no—
150C2×C8—22no—
151C2×C8—41no—
152C2×C8—41no—
153C2×C8—81no—
154C2×C8—81no—
155C4⋊C4—41no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C42—41no—
159C23#99×C13111yescharacteristic
160Q8—41no—
161Q8—41no—
162Q8—42no—
163Q8—42no—
164Q8—81no—
165Q8—81no—
166Q8—81no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—81no—
181C2×C4#102×C13111yescharacteristic
182C2×C4#104×C13111yescharacteristic
183C8—42no—
184C8—82no—
185C8—161no—
186C22—21no—
187C22—21no—
188C22#327×C13111yescharacteristic
189C22AΣL(1,𝔽16)×C13111yescharacteristic
190C22#353×C13111yescharacteristic
191C4—21no—
192C4—21no—
193C4—42no—
194C4—41no—
195C4—41no—
196C4—82no—
197C4—81no—
198C2—21no—
199C2—21no—
200C2#1343×C13111yescharacteristic
201C2#1407×C13111yescharacteristic
202C2#1411×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#353
commutatorC2×C42C2×C4×C131
Frattini, cosocle#391C22×C131
prime radicalC23×C131#99
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C131 ◁ C22×C4×C131 ◁ #391×C131 ◁ G

Complements

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

NH ≅ G/Ntype
101. #7405C131direct (N × H)
102. C131#7405direct (N × H)

Maximal subgroups

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

subgroupindex
#2016×C1312
#1394×C1312
#1319×C1312
#7405131