Finite Group Databasebeta

← C131×#7237 #45693121

Subgroups — C131×#7237 #45693121

Order 33536.

376 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 94 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#1954×C131C211yesmaximal, characteristic
2#1799×C131C212yesmaximal
3C2×C4×D4×C131C2211yescharacteristic
4C2×C4⋊C8×C131C411yescharacteristic, complemented
5C2×#99×C131—22no—
6C2×C22⋊C8×C131—22no—
7C2×C4×C8×C131C411yescharacteristic, complemented
8#380×C131—22no—
9#342×C131C414yescomplemented
10C22×D4×C131D411yescharacteristic
11C23×C4×C131D412yes—
12C22×C8×C131—21no—
13C22×C8×C131—21no—
14C4×D4×C131—41no—
15C4×D4×C131—41no—
16C2×C4⋊C4×C131—42no—
17C2×C4⋊C4×C131Q811yescharacteristic
18C2×C22⋊C4×C131—24no—
19C2×C22⋊C4×C131C2×C412yes—
20C2×C42×C131C2×C411yescharacteristic
21C4⋊C8×C131—41no—
22#99×C131—42no—
23#99×C131—42no—
24C22⋊C8×C131—44no—
25C4×C8×C131—41no—
26#95×C131—42no—
27C24×C131C22⋊C412yes—
28C2×D4×C131—41no—
29C2×D4×C131—41no—
30C2×D4×C131D811yescharacteristic
31C2×D4×C131SD1612yes—
32C2×D4×C131Q1611yescharacteristic
33C22×C4×C131—22no—
34C22×C4×C131—22no—
35C22×C4×C131—42no—
36C22×C4×C131—42no—
37C22×C4×C131—44no—
38C22×C4×C131C4211yescharacteristic
39C22×C4×C131C22⋊C411yescharacteristic
40C22×C4×C131C4⋊C411yescharacteristic
41C22×C4×C131C4⋊C412yes—
42C2×C8×C131—22no—
43C2×C8×C131—41no—
44C2×C8×C131—41no—
45C2×C8×C131—42no—
46C2×C8×C131—41no—
47C4⋊C4×C131—41no—
48C4⋊C4×C131—82no—
49C4⋊C4×C131—82no—
50C22⋊C4×C131—42no—
51C22⋊C4×C131—44no—
52C22⋊C4×C131—44no—
53C42×C131—21no—
54C42×C131—21no—
55C23×C131—22no—
56C23×C131—22no—
57C23×C131—42no—
58C23×C131—42no—
59C23×C131#9511yescharacteristic
60C23×C131#10212yes—
61C23×C131#10312yes—
62D4×C131—41no—
63D4×C131—42no—
64D4×C131—41no—
65C2×C4×C131—21no—
66C2×C4×C131—21no—
67C2×C4×C131—21no—
68C2×C4×C131—21no—
69C2×C4×C131—21no—
70C2×C4×C131—22no—
71C2×C4×C131—42no—
72C2×C4×C131—42no—
73C2×C4×C131—42no—
74C2×C4×C131—41no—
75C2×C4×C131—82no—
76C2×C4×C131—84no—
77C2×C4×C131—84no—
78C2×C4×C131—84no—
79C2×C4×C131#9911yescharacteristic
80C2×C4×C131#9911yescharacteristic
81C2×C4×C131#10611yescharacteristic
82C2×C4×C131#10711yescharacteristic
83C8×C131—42no—
84C8×C131—81no—
85C22×C131—21no—
86C22×C131—21no—
87C22×C131—22no—
88C22×C131—22no—
89C22×C131—42no—
90C22×C131—42no—
91C22×C131—42no—
92C22×C131—42no—
93C22×C131—82no—
94C22×C131H(3,ℤ/4)11yescharacteristic
95C22×C131#34011yescharacteristic
96C22×C131#34211yescharacteristic
97C4×C131—21no—
98C4×C131—21no—
99C4×C131—21no—
100C4×C131—41no—
101C4×C131—42no—
102C4×C131—164no—
103C4×C131#35311yescharacteristic
104C4×C131#35411yescharacteristic
105C2×C131—21no—
106C2×C131—21no—
107C2×C131—42no—
108C2×C131—42no—
109C2×C131#128911yescharacteristic
110C2×C131#139111yescharacteristic
111C2×C131#139311yescharacteristic
112#7237C13111yesmaximal, characteristic, direct product factor, Sylow
113C131#723711yescharacteristic, direct product factor, Sylow
114#1954C2×C13111yescharacteristic
115#1799C2×C13112yes—
116C2×C4×D4C22×C13111yescharacteristic
117C2×C4⋊C8C4×C13111yescharacteristic, complemented
118C2×#99—22no—
119C2×C22⋊C8—22no—
120C2×C4×C8C4×C13111yescharacteristic, complemented
121#380—22no—
122#342C4×C13114yescomplemented
123C22×D4D4×C13111yescharacteristic
124C23×C4D4×C13112yes—
125C22×C8—21no—
126C22×C8—21no—
127C4×D4—41no—
128C4×D4—41no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4Q8×C13111yescharacteristic
131C2×C22⋊C4—24no—
132C2×C22⋊C4C2×C4×C13112yes—
133C2×C42C2×C4×C13111yescharacteristic
134C4⋊C8—41no—
135#99—42no—
136#99—42no—
137C22⋊C8—44no—
138C4×C8—41no—
139#95—42no—
140C24C22⋊C4×C13112yes—
141C2×D4—41no—
142C2×D4—41no—
143C2×D4D8×C13111yescharacteristic
144C2×D4SD16×C13112yes—
145C2×D4Q16×C13111yescharacteristic
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—44no—
151C22×C4C42×C13111yescharacteristic
152C22×C4C22⋊C4×C13111yescharacteristic
153C22×C4C4⋊C4×C13111yescharacteristic
154C22×C4C4⋊C4×C13112yes—
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8—42no—
159C2×C8—41no—
160C4⋊C4—41no—
161C4⋊C4—82no—
162C4⋊C4—82no—
163C22⋊C4—42no—
164C22⋊C4—44no—
165C22⋊C4—44no—
166C42—21no—
167C42—21no—
168C23—22no—
169C23—22no—
170C23—42no—
171C23—42no—
172C23#95×C13111yescharacteristic
173C23#102×C13112yes—
174C23#103×C13112yes—
175D4—41no—
176D4—42no—
177D4—41no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—41no—
188C2×C4—82no—
189C2×C4—84no—
190C2×C4—84no—
191C2×C4—84no—
192C2×C4#99×C13111yescharacteristic
193C2×C4#99×C13111yescharacteristic
194C2×C4#106×C13111yescharacteristic
195C2×C4#107×C13111yescharacteristic
196C8—42no—
197C8—81no—
198C22—21no—
199C22—21no—
200C22—22no—
201C22—22no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—82no—
207C22H(3,ℤ/4)×C13111yescharacteristic
208C22#340×C13111yescharacteristic
209C22#342×C13111yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—41no—
214C4—42no—
215C4—164no—
216C4#353×C13111yescharacteristic
217C4#354×C13111yescharacteristic
218C2—21no—
219C2—21no—
220C2—42no—
221C2—42no—
222C2#1289×C13111yescharacteristic
223C2#1391×C13111yescharacteristic
224C2#1393×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#342
commutatorC22×C4C42×C131
Frattini, cosocleC2×C4×D4C22×C131
prime radicalC22×D4×C131D4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C22×C4×C131 ◁ C2×C4×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C8×C131C4semidirect
7. C2×C4×C8×C131C4semidirect
9. #342×C131C4semidirect
112. #7237C131direct (N × H)
113. C131#7237direct (N × H)
117. C2×C4⋊C8C4×C131semidirect
120. C2×C4×C8C4×C131semidirect
122. #342C4×C131semidirect

Maximal subgroups

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

subgroupindex
#1954×C1312
#1799×C1312
#7237131