Finite Group Databasebeta

← C131×#8766 #45694650

Subgroups — C131×#8766 #45694650

Order 33536.

422 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 142 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#2351×C131C211yesmaximal, characteristic
2#1801×C131C211yesmaximal, characteristic
3#1461×C131C211yesmaximal, characteristic
4#1303×C131C212yesmaximal
5#1286×C131C212yesmaximal
6C2×C4×Q8×C131—21no—
7C2×C4×Q8×C131C2211yescharacteristic
8#431×C131C2212yes—
9#423×C131C2212yes—
10C2×#101×C131—21no—
11#389×C131—21no—
12#389×C131—22no—
13#382×C131C412yes—
14#382×C131C2211yescharacteristic
15C4×C4⋊C4×C131C412yes—
16C4×C4⋊C4×C131C2211yescharacteristic
17#343×C131—21no—
18#324×C131—22no—
19C22×Q8×C131D411yescharacteristic
20C2×M16×C131—22no—
21C4×Q8×C131—22no—
22C4×Q8×C131—22no—
23C4×Q8×C131—42no—
24C4×Q8×C131—42no—
25C2×C4⋊C4×C131—22no—
26C2×C4⋊C4×C131—22no—
27C2×C4⋊C4×C131—21no—
28C2×C4⋊C4×C131—21no—
29C2×C4⋊C4×C131D412yes—
30C2×C4⋊C4×C131D411yescharacteristic
31C2×C42×C131—22no—
32C2×C42×C131—21no—
33C2×C42×C131C2×C412yes—
34C2×C42×C131C2311yescharacteristic
35C4⋊C8×C131—22no—
36C4⋊C8×C131—22no—
37C4⋊C8×C131—22no—
38#101×C131—42no—
39C22⋊C8×C131—22no—
40C4×C8×C131—22no—
41#95×C131—22no—
42#95×C131—21no—
43#95×C131C2×C411yescharacteristic
44#95×C131C2×C412yes—
45#95×C131C2×C411yescharacteristic
46C2×Q8×C131—22no—
47C2×Q8×C131—22no—
48C2×Q8×C131D812yes—
49C2×Q8×C131SD1612yes—
50C22×C4×C131—21no—
51C22×C4×C131—21no—
52C22×C4×C131—22no—
53C22×C4×C131C22⋊C412yes—
54C22×C4×C131C22⋊C412yes—
55C22×C4×C131C22×C411yescharacteristic
56C22×C4×C131C2×D411yescharacteristic
57C22×C4×C131C2×D411yescharacteristic
58M16×C131—42no—
59M16×C131—42no—
60C2×C8×C131—42no—
61C2×C8×C131—42no—
62C4⋊C4×C131—24no—
63C4⋊C4×C131—22no—
64C4⋊C4×C131—42no—
65C4⋊C4×C131—44no—
66C4⋊C4×C131—44no—
67C4⋊C4×C131—41no—
68C4⋊C4×C131—41no—
69C42×C131—22no—
70C42×C131—22no—
71C42×C131—44no—
72C42×C131—41no—
73C42×C131—41no—
74C42×C131#4112yes—
75C42×C131#4112yes—
76C23×C131C2×C22⋊C411yescharacteristic
77Q8×C131—24no—
78Q8×C131—24no—
79C2×C4×C131—22no—
80C2×C4×C131—22no—
81C2×C4×C131—22no—
82C2×C4×C131—22no—
83C2×C4×C131—41no—
84C2×C4×C131—41no—
85C2×C4×C131—41no—
86C2×C4×C131—41no—
87C2×C4×C131—42no—
88C2×C4×C131—41no—
89C2×C4×C131—42no—
90C2×C4×C131—41no—
91C2×C4×C131—42no—
92C2×C4×C131—42no—
93C2×C4×C131—41no—
94C2×C4×C131#10214yes—
95C2×C4×C131#11711yescharacteristic
96C2×C4×C131#11711yescharacteristic
97C2×C4×C131#12312yes—
98C2×C4×C131#12312yes—
99C2×C4×C131C2×D811yescharacteristic
100C2×C4×C131C2×SD1611yescharacteristic
101C2×C4×C131#13712yes—
102C8×C131—82no—
103C8×C131—82no—
104C22×C131—21no—
105C22×C131—21no—
106C22×C131#38111yescharacteristic
107C22×C131C2×#10211yescharacteristic
108C22×C131#41911yescharacteristic
109C4×C131—24no—
110C4×C131—22no—
111C4×C131—21no—
112C4×C131—21no—
113C4×C131—42no—
114C4×C131—42no—
115C4×C131—82no—
116C4×C131—81no—
117C4×C131#48012yes—
118C4×C131#48312yes—
119C2×C131—21no—
120C2×C131—21no—
121C2×C131#182311yescharacteristic
122C2×C131#182711yescharacteristic
123C2×C131#183011yescharacteristic
124#8766C13111yesmaximal, characteristic, direct product factor, Sylow
125C131#876611yescharacteristic, direct product factor, Sylow
126#2351C2×C13111yescharacteristic
127#1801C2×C13111yescharacteristic
128#1461C2×C13111yescharacteristic
129#1303C2×C13112yes—
130#1286C2×C13112yes—
131C2×C4×Q8—21no—
132C2×C4×Q8C22×C13111yescharacteristic
133#431C22×C13112yes—
134#423C22×C13112yes—
135C2×#101—21no—
136#389—21no—
137#389—22no—
138#382C4×C13112yes—
139#382C22×C13111yescharacteristic
140C4×C4⋊C4C4×C13112yes—
141C4×C4⋊C4C22×C13111yescharacteristic
142#343—21no—
143#324—22no—
144C22×Q8D4×C13111yescharacteristic
145C2×M16—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—42no—
149C4×Q8—42no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4D4×C13112yes—
155C2×C4⋊C4D4×C13111yescharacteristic
156C2×C42—22no—
157C2×C42—21no—
158C2×C42C2×C4×C13112yes—
159C2×C42C23×C13111yescharacteristic
160C4⋊C8—22no—
161C4⋊C8—22no—
162C4⋊C8—22no—
163#101—42no—
164C22⋊C8—22no—
165C4×C8—22no—
166#95—22no—
167#95—21no—
168#95C2×C4×C13111yescharacteristic
169#95C2×C4×C13112yes—
170#95C2×C4×C13111yescharacteristic
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8D8×C13112yes—
174C2×Q8SD16×C13112yes—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4C22⋊C4×C13112yes—
179C22×C4C22⋊C4×C13112yes—
180C22×C4C22×C4×C13111yescharacteristic
181C22×C4C2×D4×C13111yescharacteristic
182C22×C4C2×D4×C13111yescharacteristic
183M16—42no—
184M16—42no—
185C2×C8—42no—
186C2×C8—42no—
187C4⋊C4—24no—
188C4⋊C4—22no—
189C4⋊C4—42no—
190C4⋊C4—44no—
191C4⋊C4—44no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C42—22no—
195C42—22no—
196C42—44no—
197C42—41no—
198C42—41no—
199C42#41×C13112yes—
200C42#41×C13112yes—
201C23C2×C22⋊C4×C13111yescharacteristic
202Q8—24no—
203Q8—24no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4#102×C13114yes—
220C2×C4#117×C13111yescharacteristic
221C2×C4#117×C13111yescharacteristic
222C2×C4#123×C13112yes—
223C2×C4#123×C13112yes—
224C2×C4C2×D8×C13111yescharacteristic
225C2×C4C2×SD16×C13111yescharacteristic
226C2×C4#137×C13112yes—
227C8—82no—
228C8—82no—
229C22—21no—
230C22—21no—
231C22#381×C13111yescharacteristic
232C22C2×#102×C13111yescharacteristic
233C22#419×C13111yescharacteristic
234C4—24no—
235C4—22no—
236C4—21no—
237C4—21no—
238C4—42no—
239C4—42no—
240C4—82no—
241C4—81no—
242C4#480×C13112yes—
243C4#483×C13112yes—
244C2—21no—
245C2—21no—
246C2#1823×C13111yescharacteristic
247C2#1827×C13111yescharacteristic
248C2#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
124. #8766C131direct (N × H)
125. C131#8766direct (N × H)

Maximal subgroups

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

subgroupindex
#2351×C1312
#1801×C1312
#1461×C1312
#1303×C1312
#1286×C1312
#8766131