Finite Group Databasebeta

← C131×#7403 #45693287

Subgroups — C131×#7403 #45693287

Order 33536.

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

normal subgroups only

This group has 282 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#2013×C131C211yesmaximal, characteristic
2#1393×C131C211yesmaximal, characteristic
3#1318×C131C211yesmaximal, characteristic
4C22×SD16×C131—21no—
5C2×C4⋊Q8×C131C411yescharacteristic, complemented
6C2×#103×C131—21no—
7C2×#99×C131—21no—
8#390×C131C2211yescharacteristic
9#336×C131C411yescharacteristic, complemented
10#324×C131—21no—
11C22×Q8×C131—21no—
12C22×D4×C131D411yescharacteristic
13C2×SD16×C131—42no—
14C2×SD16×C131—42no—
15C2×SD16×C131—41no—
16C2×SD16×C131—41no—
17C22×C8×C131—21no—
18C4⋊Q8×C131—42no—
19C2×C4⋊C4×C131—41no—
20C2×C4⋊C4×C131D411yescharacteristic
21C2×C22⋊C4×C131—41no—
22C2×C22⋊C4×C131—41no—
23C2×C42×C131C2×C411yescharacteristic
24#103×C131—42no—
25#99×C131—22no—
26#99×C131—41no—
27C22⋊C8×C131—41no—
28C24×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×D4×C131—21no—
36C2×D4×C131—41no—
37C2×D4×C131—41no—
38C2×D4×C131D811yescharacteristic
39C2×D4×C131SD1611yescharacteristic
40C22×C4×C131—21no—
41C22×C4×C131—21no—
42C22×C4×C131—41no—
43C22×C4×C131—81no—
44C22×C4×C131C22⋊C411yescharacteristic
45SD16×C131—44no—
46SD16×C131—44no—
47C2×C8×C131—22no—
48C2×C8×C131—41no—
49C2×C8×C131—41no—
50C2×C8×C131—81no—
51C4⋊C4×C131—41no—
52C4⋊C4×C131—42no—
53C4⋊C4×C131—42no—
54C22⋊C4×C131—42no—
55C22⋊C4×C131—82no—
56C22⋊C4×C131—81no—
57C42×C131—41no—
58C23×C131—21no—
59C23×C131—21no—
60C23×C131—41no—
61C23×C131—41no—
62C23×C131—81no—
63C23×C131—81no—
64C23×C131#9911yescharacteristic
65Q8×C131—42no—
66Q8×C131—42no—
67Q8×C131—81no—
68Q8×C131—81no—
69D4×C131—41no—
70D4×C131—41no—
71D4×C131—81no—
72C2×C4×C131—21no—
73C2×C4×C131—21no—
74C2×C4×C131—22no—
75C2×C4×C131—41no—
76C2×C4×C131—41no—
77C2×C4×C131—42no—
78C2×C4×C131—41no—
79C2×C4×C131—81no—
80C2×C4×C131—81no—
81C2×C4×C131—81no—
82C2×C4×C131—82no—
83C2×C4×C131—161no—
84C2×C4×C131—161no—
85C2×C4×C131#10211yescharacteristic
86C2×C4×C131#10411yescharacteristic
87C8×C131—42no—
88C8×C131—161no—
89C22×C131—21no—
90C22×C131—21no—
91C22×C131—41no—
92C22×C131—41no—
93C22×C131—81no—
94C22×C131—81no—
95C22×C131—81no—
96C22×C131—81no—
97C22×C131—161no—
98C22×C131#32711yescharacteristic
99C22×C131AΣL(1,𝔽16)11yescharacteristic
100C22×C131#35311yescharacteristic
101C4×C131—21no—
102C4×C131—21no—
103C4×C131—42no—
104C4×C131—82no—
105C4×C131—81no—
106C4×C131—162no—
107C2×C131—21no—
108C2×C131—21no—
109C2×C131—81no—
110C2×C131—81no—
111C2×C131#134311yescharacteristic
112C2×C131#140711yescharacteristic
113C2×C131#140911yescharacteristic
114#7403C13111yesmaximal, characteristic, direct product factor, Sylow
115C131#740311yescharacteristic, direct product factor, Sylow
116#2013C2×C13111yescharacteristic
117#1393C2×C13111yescharacteristic
118#1318C2×C13111yescharacteristic
119C22×SD16—21no—
120C2×C4⋊Q8C4×C13111yescharacteristic, complemented
121C2×#103—21no—
122C2×#99—21no—
123#390C22×C13111yescharacteristic
124#336C4×C13111yescharacteristic, complemented
125#324—21no—
126C22×Q8—21no—
127C22×D4D4×C13111yescharacteristic
128C2×SD16—42no—
129C2×SD16—42no—
130C2×SD16—41no—
131C2×SD16—41no—
132C22×C8—21no—
133C4⋊Q8—42no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4D4×C13111yescharacteristic
136C2×C22⋊C4—41no—
137C2×C22⋊C4—41no—
138C2×C42C2×C4×C13111yescharacteristic
139#103—42no—
140#99—22no—
141#99—41no—
142C22⋊C8—41no—
143C24—21no—
144C2×Q8—22no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×D4—21no—
151C2×D4—41no—
152C2×D4—41no—
153C2×D4D8×C13111yescharacteristic
154C2×D4SD16×C13111yescharacteristic
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—41no—
158C22×C4—81no—
159C22×C4C22⋊C4×C13111yescharacteristic
160SD16—44no—
161SD16—44no—
162C2×C8—22no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—81no—
166C4⋊C4—41no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C22⋊C4—42no—
170C22⋊C4—82no—
171C22⋊C4—81no—
172C42—41no—
173C23—21no—
174C23—21no—
175C23—41no—
176C23—41no—
177C23—81no—
178C23—81no—
179C23#99×C13111yescharacteristic
180Q8—42no—
181Q8—42no—
182Q8—81no—
183Q8—81no—
184D4—41no—
185D4—41no—
186D4—81no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4—161no—
199C2×C4—161no—
200C2×C4#102×C13111yescharacteristic
201C2×C4#104×C13111yescharacteristic
202C8—42no—
203C8—161no—
204C22—21no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—81no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—161no—
213C22#327×C13111yescharacteristic
214C22AΣL(1,𝔽16)×C13111yescharacteristic
215C22#353×C13111yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—82no—
220C4—81no—
221C4—162no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—81no—
226C2#1343×C13111yescharacteristic
227C2#1407×C13111yescharacteristic
228C2#1409×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#353
commutatorC2×C42C2×C4×C131
Frattini, cosocle#390C22×C131
prime radicalC22×D4×C131D4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C131 ◁ C22×C4×C131 ◁ #390×C131 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊Q8×C131C4semidirect
9. #336×C131C4semidirect
114. #7403C131direct (N × H)
115. C131#7403direct (N × H)
120. C2×C4⋊Q8C4×C131semidirect
124. #336C4×C131semidirect

Maximal subgroups

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

subgroupindex
#2013×C1312
#1393×C1312
#1318×C1312
#7403131