Finite Group Databasebeta

← C131×#7407 #45693291

Subgroups — C131×#7407 #45693291

Order 33536.

240 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 42 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#2017×C131C211yesmaximal, characteristic
2#1392×C131C211yesmaximal, characteristic, complemented
3#1315×C131C211yesmaximal, characteristic, complemented
4#575×C131—21no—
5#575×C131C411yescharacteristic
6#413×C131—21no—
7#408×C131—21no—
8#408×C131C2211yescharacteristic
9C22⋊C16×C131—21no—
10#338×C131C411yescharacteristic
11C2×#41×C131—21no—
12C2×#41×C131D411yescharacteristic
13#137×C131—41no—
14#137×C131—41no—
15#137×C131—41no—
16AGL(1,ℤ/8)×C131—41no—
17AGL(1,ℤ/8)×C131—41no—
18AGL(1,ℤ/8)×C131—41no—
19#135×C131—42no—
20#135×C131—41no—
21C2×M16×C131—21no—
22C2×M16×C131—41no—
23C2×M16×C131C2×C411yescharacteristic
24C22×C8×C131D411yescharacteristic
25C2×C16×C131—41no—
26#101×C131—41no—
27#100×C131—22no—
28C22⋊C8×C131—41no—
29C22⋊C8×C131—42no—
30#41×C131—41no—
31#41×C131—41no—
32#41×C131—41no—
33#41×C131—41no—
34#41×C131—41no—
35#41×C131—41no—
36C2×Q8×C131—21no—
37C2×Q8×C131D811yescharacteristic
38C2×D4×C131—21no—
39C2×D4×C131—21no—
40C2×D4×C131—41no—
41C2×D4×C131SD1611yescharacteristic
42C22×C4×C131—21no—
43C22×C4×C131—41no—
44C22×C4×C131C22⋊C411yescharacteristic
45Q16×C131—41no—
46Q16×C131—42no—
47SD16×C131—42no—
48SD16×C131—42no—
49SD16×C131—42no—
50D8×C131—41no—
51D8×C131—42no—
52M16×C131—41no—
53M16×C131—41no—
54M16×C131—41no—
55M16×C131—42no—
56M16×C131—81no—
57C2×C8×C131—22no—
58C2×C8×C131—21no—
59C2×C8×C131—21no—
60C2×C8×C131—41no—
61C2×C8×C131—81no—
62C16×C131—81no—
63C23×C131—21no—
64C23×C131—41no—
65C23×C131#10411yescharacteristic
66Q8×C131—41no—
67Q8×C131—41no—
68Q8×C131—41no—
69D4×C131—41no—
70D4×C131—41no—
71D4×C131—41no—
72D4×C131—81no—
73D4×C131—81no—
74D4×C131—81no—
75C2×C4×C131—21no—
76C2×C4×C131—21no—
77C2×C4×C131—21no—
78C2×C4×C131—41no—
79C2×C4×C131—41no—
80C2×C4×C131—41no—
81C2×C4×C131—81no—
82C2×C4×C131—81no—
83C2×C4×C131#9911yescharacteristic
84C2×C4×C131#10211yescharacteristic
85C8×C131—42no—
86C8×C131—41no—
87C8×C131—41no—
88C8×C131—82no—
89C22×C131—21no—
90C22×C131—41no—
91C22×C131—41no—
92C22×C131—81no—
93C22×C131—82no—
94C22×C131—81no—
95C22×C131#32711yescharacteristic
96C4×C131—21no—
97C4×C131—41no—
98C4×C131—81no—
99C4×C131AΣL(1,𝔽16)11yescharacteristic
100C4×C131#35311yescharacteristic
101C2×C131—21no—
102C2×C131—41no—
103C2×C131—81no—
104C2×C131—161no—
105C2×C131#134311yescharacteristic
106#7407C13111yesmaximal, characteristic, direct product factor, Sylow
107C131#740711yescharacteristic, direct product factor, Sylow
108#2017C2×C13111yescharacteristic
109#1392C2×C13111yescharacteristic, complemented
110#1315C2×C13111yescharacteristic, complemented
111#575—21no—
112#575C4×C13111yescharacteristic
113#413—21no—
114#408—21no—
115#408C22×C13111yescharacteristic
116C22⋊C16—21no—
117#338C4×C13111yescharacteristic
118C2×#41—21no—
119C2×#41D4×C13111yescharacteristic
120#137—41no—
121#137—41no—
122#137—41no—
123AGL(1,ℤ/8)—41no—
124AGL(1,ℤ/8)—41no—
125AGL(1,ℤ/8)—41no—
126#135—41no—
127#135—42no—
128C2×M16—21no—
129C2×M16—41no—
130C2×M16C2×C4×C13111yescharacteristic
131C22×C8D4×C13111yescharacteristic
132C2×C16—41no—
133#101—41no—
134#100—22no—
135C22⋊C8—41no—
136C22⋊C8—42no—
137#41—41no—
138#41—41no—
139#41—41no—
140#41—41no—
141#41—41no—
142#41—41no—
143C2×Q8—21no—
144C2×Q8D8×C13111yescharacteristic
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—41no—
148C2×D4SD16×C13111yescharacteristic
149C22×C4—21no—
150C22×C4—41no—
151C22×C4C22⋊C4×C13111yescharacteristic
152Q16—41no—
153Q16—42no—
154SD16—42no—
155SD16—42no—
156SD16—42no—
157D8—41no—
158D8—42no—
159M16—41no—
160M16—41no—
161M16—41no—
162M16—42no—
163M16—81no—
164C2×C8—22no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—41no—
168C2×C8—81no—
169C16—81no—
170C23—21no—
171C23—41no—
172C23#104×C13111yescharacteristic
173Q8—41no—
174Q8—41no—
175Q8—41no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4—81no—
180D4—81no—
181D4—81no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4#99×C13111yescharacteristic
191C2×C4#102×C13111yescharacteristic
192C8—42no—
193C8—41no—
194C8—41no—
195C8—82no—
196C22—21no—
197C22—41no—
198C22—41no—
199C22—81no—
200C22—82no—
201C22—81no—
202C22#327×C13111yescharacteristic
203C4—21no—
204C4—41no—
205C4—81no—
206C4AΣL(1,𝔽16)×C13111yescharacteristic
207C4#353×C13111yescharacteristic
208C2—21no—
209C2—41no—
210C2—81no—
211C2—161no—
212C2#1343×C13111yescharacteristic
subgroupG/H
centerC4×C131#353
commutatorC2×M16C2×C4×C131
Frattini, cosocle#408C22×C131
socleC2×C131#1343
prime radical#2017×C131C2
LCSG ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C131 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ #408×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1392×C131C2semidirect
3. #1315×C131C2semidirect
106. #7407C131direct (N × H)
107. C131#7407direct (N × H)
109. #1392C2×C131semidirect
110. #1315C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2017×C1312
#1392×C1312
#1315×C1312
#7407131