Finite Group Databasebeta

← C131×#10428 #45696312

Subgroups — C131×#10428 #45696312

Order 33536.

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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#2822×C131C211yesmaximal, characteristic
2#1992×C131C212yesmaximal
3#1836×C131C211yesmaximal, characteristic
4C2×#330×C131C212yesmaximal
5#1295×C131C211yesmaximal, characteristic
6C2×#125×C131C2212yes—
7C2×#97×C131C2212yes—
8C2×#97×C131C2211yescharacteristic
9#400×C131—22no—
10#398×C131—22no—
11#398×C131—22no—
12#384×C131C2211yescharacteristic
13#382×C131C2211yescharacteristic
14#340×C131—22no—
15#340×C131—22no—
16#340×C131—22no—
17#330×C131—24no—
18C22×C8×C131—22no—
19C22×C8×C131—21no—
20#125×C131—22no—
21#125×C131—22no—
22#125×C131—22no—
23#125×C131—22no—
24C2×C4⋊C4×C131—22no—
25C2×C4⋊C4×C131—22no—
26C2×C4⋊C4×C131—22no—
27C2×C4⋊C4×C131—21no—
28C2×C4⋊C4×C131—22no—
29C2×C4⋊C4×C131D412yes—
30C2×C4⋊C4×C131D412yes—
31C2×C4⋊C4×C131D412yes—
32C2×C42×C131C2311yescharacteristic
33#97×C131—22no—
34#97×C131—21no—
35#97×C131—22no—
36#97×C131D412yes—
37#95×C131—24no—
38#95×C131—22no—
39#95×C131—22no—
40C22×C4×C131—22no—
41C22×C4×C131—22no—
42C22×C4×C131—22no—
43C22×C4×C131—41no—
44C22×C4×C131C2×D412yes—
45C22×C4×C131C2×D411yescharacteristic
46C2×C8×C131—24no—
47C2×C8×C131—22no—
48C2×C8×C131—42no—
49C2×C8×C131—41no—
50C2×C8×C131—41no—
51C2×C8×C131—42no—
52C4⋊C4×C131—22no—
53C4⋊C4×C131—22no—
54C4⋊C4×C131—22no—
55C4⋊C4×C131—22no—
56C4⋊C4×C131—42no—
57C4⋊C4×C131—44no—
58C4⋊C4×C131—42no—
59C4⋊C4×C131—42no—
60C4⋊C4×C131—42no—
61C4⋊C4×C131—42no—
62C4⋊C4×C131—42no—
63C4⋊C4×C131—82no—
64C42×C131C2×D411yescharacteristic
65C42×C131#4111yescharacteristic
66C42×C131#4112yes—
67C23×C131#12011yescharacteristic
68C2×C4×C131—22no—
69C2×C4×C131—21no—
70C2×C4×C131—21no—
71C2×C4×C131—22no—
72C2×C4×C131—42no—
73C2×C4×C131—42no—
74C2×C4×C131—42no—
75C2×C4×C131—42no—
76C2×C4×C131—42no—
77C2×C4×C131—42no—
78C2×C4×C131—42no—
79C2×C4×C131—42no—
80C2×C4×C131—42no—
81C2×C4×C131—81no—
82C2×C4×C131—82no—
83C2×C4×C131#12112yes—
84C2×C4×C131#12111yescharacteristic
85C2×C4×C131#12312yes—
86C2×C4×C131#12411yescharacteristic
87C8×C131—44no—
88C8×C131—42no—
89C22×C131#39411yescharacteristic
90C22×C131#45411yescharacteristic
91C22×C131#45412yes—
92C22×C131#45511yescharacteristic
93C22×C131#45612yes—
94C4×C131—22no—
95C4×C131—22no—
96C4×C131—21no—
97C4×C131—21no—
98C4×C131—82no—
99C4×C131—82no—
100C4×C131—82no—
101C4×C131—161no—
102C2×C131#165811yescharacteristic
103C2×C131#166311yescharacteristic
104C2×C131#166412yes—
105C2×C131#203812yes—
106C2×C131#204011yescharacteristic
107#10428C13111yesmaximal, characteristic, direct product factor, Sylow
108C131#1042811yescharacteristic, direct product factor, Sylow
109#2822C2×C13111yescharacteristic
110#1992C2×C13112yes—
111#1836C2×C13111yescharacteristic
112C2×#330C2×C13112yes—
113#1295C2×C13111yescharacteristic
114C2×#125C22×C13112yes—
115C2×#97C22×C13112yes—
116C2×#97C22×C13111yescharacteristic
117#400—22no—
118#398—22no—
119#398—22no—
120#384C22×C13111yescharacteristic
121#382C22×C13111yescharacteristic
122#340—22no—
123#340—22no—
124#340—22no—
125#330—24no—
126C22×C8—22no—
127C22×C8—21no—
128#125—22no—
129#125—22no—
130#125—22no—
131#125—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4D4×C13112yes—
138C2×C4⋊C4D4×C13112yes—
139C2×C4⋊C4D4×C13112yes—
140C2×C42C23×C13111yescharacteristic
141#97—22no—
142#97—21no—
143#97—22no—
144#97D4×C13112yes—
145#95—24no—
146#95—22no—
147#95—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—41no—
152C22×C4C2×D4×C13112yes—
153C22×C4C2×D4×C13111yescharacteristic
154C2×C8—24no—
155C2×C8—22no—
156C2×C8—42no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—42no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—44no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—82no—
172C42C2×D4×C13111yescharacteristic
173C42#41×C13111yescharacteristic
174C42#41×C13112yes—
175C23#120×C13111yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4#121×C13112yes—
192C2×C4#121×C13111yescharacteristic
193C2×C4#123×C13112yes—
194C2×C4#124×C13111yescharacteristic
195C8—44no—
196C8—42no—
197C22#394×C13111yescharacteristic
198C22#454×C13112yes—
199C22#454×C13111yescharacteristic
200C22#455×C13111yescharacteristic
201C22#456×C13112yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—82no—
208C4—82no—
209C4—161no—
210C2#1658×C13111yescharacteristic
211C2#1663×C13111yescharacteristic
212C2#1664×C13112yes—
213C2#2038×C13112yes—
214C2#2040×C13111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C131#120
commutator, Frattini, cosocleC2×C42C23×C131
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
107. #10428C131direct (N × H)
108. C131#10428direct (N × H)

Maximal subgroups

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

subgroupindex
#2822×C1312
#1992×C1312
#1836×C1312
C2×#330×C1312
#1295×C1312
#10428131