Finite Group Databasebeta

← C131×#8768 #45694652

Subgroups — C131×#8768 #45694652

Order 33536.

378 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 126 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#2356×C131C211yesmaximal, characteristic
2#1801×C131C211yesmaximal, characteristic
3#1461×C131C211yesmaximal, characteristic
4#1303×C131C212yesmaximal
5#1286×C131C212yesmaximal
6C2×C4×Q8×C131C2211yescharacteristic
7#431×C131C2212yes—
8#423×C131C2212yes—
9C2×#101×C131—21no—
10#391×C131—21no—
11#387×C131—22no—
12#383×C131C412yes—
13#382×C131C2211yescharacteristic
14C4×C4⋊C4×C131—21no—
15C4×C4⋊C4×C131C2211yescharacteristic
16#376×C131C412yes—
17#343×C131—21no—
18#324×C131—22no—
19C22×Q8×C131D411yescharacteristic
20C2×M16×C131—22no—
21C4×Q8×C131—22no—
22C4×Q8×C131—22no—
23C2×C4⋊C4×C131—21no—
24C2×C4⋊C4×C131—21no—
25C2×C4⋊C4×C131D412yes—
26C2×C4⋊C4×C131D411yescharacteristic
27C2×C42×C131—22no—
28C2×C42×C131—21no—
29C2×C42×C131C2×C412yes—
30C2×C42×C131C2311yescharacteristic
31C4⋊C8×C131—22no—
32C4⋊C8×C131—22no—
33C4⋊C8×C131—22no—
34#101×C131—42no—
35C22⋊C8×C131—22no—
36C4×C8×C131—22no—
37#95×C131—22no—
38#95×C131—22no—
39#95×C131—22no—
40#95×C131—21no—
41#95×C131C2×C411yescharacteristic
42#95×C131C2×C412yes—
43#95×C131C2×C411yescharacteristic
44C2×Q8×C131—22no—
45C2×Q8×C131—22no—
46C2×Q8×C131—21no—
47C2×Q8×C131—21no—
48C22×C4×C131—21no—
49C22×C4×C131—22no—
50C22×C4×C131—21no—
51C22×C4×C131C22⋊C412yes—
52C22×C4×C131C22⋊C412yes—
53C22×C4×C131C22×C411yescharacteristic
54C22×C4×C131C2×D411yescharacteristic
55C22×C4×C131C2×D411yescharacteristic
56M16×C131—42no—
57M16×C131—42no—
58C2×C8×C131—42no—
59C2×C8×C131—42no—
60C4⋊C4×C131—22no—
61C4⋊C4×C131—24no—
62C4⋊C4×C131—42no—
63C4⋊C4×C131—42no—
64C42×C131—22no—
65C42×C131—22no—
66C42×C131—44no—
67C42×C131—41no—
68C42×C131—41no—
69C42×C131#4112yes—
70C42×C131#4112yes—
71C23×C131C2×C22⋊C411yescharacteristic
72Q8×C131—42no—
73Q8×C131—42no—
74C2×C4×C131—22no—
75C2×C4×C131—22no—
76C2×C4×C131—22no—
77C2×C4×C131—22no—
78C2×C4×C131—22no—
79C2×C4×C131—41no—
80C2×C4×C131—41no—
81C2×C4×C131—41no—
82C2×C4×C131—41no—
83C2×C4×C131—42no—
84C2×C4×C131—42no—
85C2×C4×C131—41no—
86C2×C4×C131—41no—
87C2×C4×C131—42no—
88C2×C4×C131—42no—
89C2×C4×C131—41no—
90C2×C4×C131#11711yescharacteristic
91C2×C4×C131#11711yescharacteristic
92C2×C4×C131#12312yes—
93C2×C4×C131#12312yes—
94C2×C4×C131#13512yes—
95C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C131#13711yescharacteristic
97C8×C131—82no—
98C8×C131—82no—
99C22×C131—21no—
100C22×C131—21no—
101C22×C131#38111yescharacteristic
102C22×C131#41611yescharacteristic
103C22×C131#41711yescharacteristic
104C4×C131—22no—
105C4×C131—21no—
106C4×C131—21no—
107C4×C131—42no—
108C4×C131—42no—
109C4×C131—42no—
110C4×C131—81no—
111C4×C131—82no—
112C4×C131#48212yes—
113C4×C131#48512yes—
114C2×C131—21no—
115C2×C131—21no—
116C2×C131#182511yescharacteristic
117C2×C131#182711yescharacteristic
118C2×C131#183011yescharacteristic
119#8768C13111yesmaximal, characteristic, direct product factor, Sylow
120C131#876811yescharacteristic, direct product factor, Sylow
121#2356C2×C13111yescharacteristic
122#1801C2×C13111yescharacteristic
123#1461C2×C13111yescharacteristic
124#1303C2×C13112yes—
125#1286C2×C13112yes—
126C2×C4×Q8C22×C13111yescharacteristic
127#431C22×C13112yes—
128#423C22×C13112yes—
129C2×#101—21no—
130#391—21no—
131#387—22no—
132#383C4×C13112yes—
133#382C22×C13111yescharacteristic
134C4×C4⋊C4—21no—
135C4×C4⋊C4C22×C13111yescharacteristic
136#376C4×C13112yes—
137#343—21no—
138#324—22no—
139C22×Q8D4×C13111yescharacteristic
140C2×M16—22no—
141C4×Q8—22no—
142C4×Q8—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4D4×C13112yes—
146C2×C4⋊C4D4×C13111yescharacteristic
147C2×C42—22no—
148C2×C42—21no—
149C2×C42C2×C4×C13112yes—
150C2×C42C23×C13111yescharacteristic
151C4⋊C8—22no—
152C4⋊C8—22no—
153C4⋊C8—22no—
154#101—42no—
155C22⋊C8—22no—
156C4×C8—22no—
157#95—22no—
158#95—22no—
159#95—22no—
160#95—21no—
161#95C2×C4×C13111yescharacteristic
162#95C2×C4×C13112yes—
163#95C2×C4×C13111yescharacteristic
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—21no—
167C2×Q8—21no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4C22⋊C4×C13112yes—
172C22×C4C22⋊C4×C13112yes—
173C22×C4C22×C4×C13111yescharacteristic
174C22×C4C2×D4×C13111yescharacteristic
175C22×C4C2×D4×C13111yescharacteristic
176M16—42no—
177M16—42no—
178C2×C8—42no—
179C2×C8—42no—
180C4⋊C4—22no—
181C4⋊C4—24no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C42—22no—
185C42—22no—
186C42—44no—
187C42—41no—
188C42—41no—
189C42#41×C13112yes—
190C42#41×C13112yes—
191C23C2×C22⋊C4×C13111yescharacteristic
192Q8—42no—
193Q8—42no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4#117×C13111yescharacteristic
211C2×C4#117×C13111yescharacteristic
212C2×C4#123×C13112yes—
213C2×C4#123×C13112yes—
214C2×C4#135×C13112yes—
215C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
216C2×C4#137×C13111yescharacteristic
217C8—82no—
218C8—82no—
219C22—21no—
220C22—21no—
221C22#381×C13111yescharacteristic
222C22#416×C13111yescharacteristic
223C22#417×C13111yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—42no—
228C4—42no—
229C4—42no—
230C4—81no—
231C4—82no—
232C4#482×C13112yes—
233C4#485×C13112yes—
234C2—21no—
235C2—21no—
236C2#1825×C13111yescharacteristic
237C2#1827×C13111yescharacteristic
238C2#1830×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#381
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC23×C131C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
119. #8768C131direct (N × H)
120. C131#8768direct (N × H)

Maximal subgroups

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

subgroupindex
#2356×C1312
#1801×C1312
#1461×C1312
#1303×C1312
#1286×C1312
#8768131