Finite Group Databasebeta

← C131×#12170 #45698054

Subgroups — C131×#12170 #45698054

Order 33536.

356 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 70 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#3259×C131C211yesmaximal, characteristic, complemented
2#2190×C131C212yesmaximal, complemented
3#2053×C131C211yesmaximal, characteristic, complemented
4#1339×C131C212yesmaximal, complemented
5#1328×C131C211yesmaximal, characteristic, complemented
6#575×C131C2211yescharacteristic
7#540×C131—21no—
8#509×C131—22no—
9#478×C131—22no—
10#469×C131C2212yes—
11#466×C131—21no—
12#459×C131—22no—
13#424×C131C2211yescharacteristic
14#416×C131—21no—
15#410×C131—21no—
16#360×C131—22no—
17#349×C131C2212yes—
18H(3,ℤ/4)×C131C2211yescharacteristic
19C2×#41×C131—21no—
20#137×C131—41no—
21AGL(1,ℤ/8)×C131—41no—
22#135×C131—22no—
23C2×D8×C131—21no—
24C2×D8×C131D412yes—
25C2×M16×C131C2311yescharacteristic
26C22×C8×C131D411yescharacteristic
27#127×C131—21no—
28#125×C131—21no—
29#123×C131—42no—
30#121×C131—22no—
31#121×C131—42no—
32C4×D4×C131—22no—
33#117×C131—21no—
34#117×C131D411yescharacteristic
35SD32×C131—42no—
36D16×C131—42no—
37M32×C131—22no—
38#107×C131—21no—
39#106×C131D412yes—
40C4⋊C8×C131—22no—
41#103×C131—41no—
42#102×C131—22no—
43#102×C131—22no—
44#102×C131—41no—
45#99×C131—42no—
46#41×C131—41no—
47#41×C131—41no—
48#41×C131—41no—
49#41×C131—41no—
50C2×Q8×C131—21no—
51C2×D4×C131—21no—
52C2×D4×C131—22no—
53C2×D4×C131—42no—
54C2×D4×C131—41no—
55C2×D4×C131—42no—
56C22×C4×C131—41no—
57C22×C4×C131—42no—
58C22×C4×C131C2×D411yescharacteristic
59Q16×C131—22no—
60SD16×C131—42no—
61D8×C131—22no—
62D8×C131—42no—
63D8×C131—81no—
64M16×C131—41no—
65C2×C8×C131—21no—
66C2×C8×C131—41no—
67C2×C8×C131C2×D412yes—
68C4⋊C4×C131—21no—
69C4⋊C4×C131—22no—
70C4⋊C4×C131—42no—
71C4⋊C4×C131—41no—
72C22⋊C4×C131—42no—
73C22⋊C4×C131—42no—
74C22⋊C4×C131—41no—
75C22⋊C4×C131D812yes—
76C42×C131—21no—
77C42×C131—41no—
78C16×C131—42no—
79C23×C131—41no—
80C23×C131—42no—
81C23×C131C2×D811yescharacteristic
82Q8×C131—41no—
83Q8×C131—41no—
84D4×C131—41no—
85D4×C131—42no—
86D4×C131—41no—
87D4×C131—42no—
88D4×C131—81no—
89D4×C131—81no—
90D4×C131—162no—
91D4×C131—162no—
92C2×C4×C131—21no—
93C2×C4×C131—21no—
94C2×C4×C131—22no—
95C2×C4×C131—41no—
96C2×C4×C131—42no—
97C2×C4×C131—81no—
98C2×C4×C131—81no—
99C2×C4×C131—81no—
100C2×C4×C131—162no—
101C2×C4×C131#12011yescharacteristic
102C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
103C8×C131—22no—
104C8×C131—41no—
105C22×C131—21no—
106C22×C131—41no—
107C22×C131—82no—
108C22×C131—82no—
109C22×C131—81no—
110C22×C131—82no—
111C22×C131—161no—
112C22×C131#44711yescharacteristic
113C4×C131—21no—
114C4×C131—42no—
115C4×C131—82no—
116C4×C131—81no—
117C4×C131—161no—
118C4×C131#45411yescharacteristic
119C4×C131B(4,𝔽2)11yescharacteristic
120C2×C131—21no—
121C2×C131—41no—
122C2×C131—162no—
123C2×C131—161no—
124C2×C131#159811yescharacteristic
125#12170C13111yesmaximal, characteristic, direct product factor, Sylow
126C131#1217011yescharacteristic, direct product factor, Sylow
127#3259C2×C13111yescharacteristic, complemented
128#2190C2×C13112yescomplemented
129#2053C2×C13111yescharacteristic, complemented
130#1339C2×C13112yescomplemented
131#1328C2×C13111yescharacteristic, complemented
132#575C22×C13111yescharacteristic
133#540—21no—
134#509—22no—
135#478—22no—
136#469C22×C13112yes—
137#466—21no—
138#459—22no—
139#424C22×C13111yescharacteristic
140#416—21no—
141#410—21no—
142#360—22no—
143#349C22×C13112yes—
144H(3,ℤ/4)C22×C13111yescharacteristic
145C2×#41—21no—
146#137—41no—
147AGL(1,ℤ/8)—41no—
148#135—22no—
149C2×D8—21no—
150C2×D8D4×C13112yes—
151C2×M16C23×C13111yescharacteristic
152C22×C8D4×C13111yescharacteristic
153#127—21no—
154#125—21no—
155#123—42no—
156#121—22no—
157#121—42no—
158C4×D4—22no—
159#117—21no—
160#117D4×C13111yescharacteristic
161SD32—42no—
162D16—42no—
163M32—22no—
164#107—21no—
165#106D4×C13112yes—
166C4⋊C8—22no—
167#103—41no—
168#102—22no—
169#102—22no—
170#102—41no—
171#99—42no—
172#41—41no—
173#41—41no—
174#41—41no—
175#41—41no—
176C2×Q8—21no—
177C2×D4—21no—
178C2×D4—22no—
179C2×D4—42no—
180C2×D4—41no—
181C2×D4—42no—
182C22×C4—41no—
183C22×C4—42no—
184C22×C4C2×D4×C13111yescharacteristic
185Q16—22no—
186SD16—42no—
187D8—22no—
188D8—42no—
189D8—81no—
190M16—41no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8C2×D4×C13112yes—
194C4⋊C4—21no—
195C4⋊C4—22no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—41no—
201C22⋊C4D8×C13112yes—
202C42—21no—
203C42—41no—
204C16—42no—
205C23—41no—
206C23—42no—
207C23C2×D8×C13111yescharacteristic
208Q8—41no—
209Q8—41no—
210D4—41no—
211D4—42no—
212D4—41no—
213D4—42no—
214D4—81no—
215D4—81no—
216D4—162no—
217D4—162no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—162no—
227C2×C4#120×C13111yescharacteristic
228C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
229C8—22no—
230C8—41no—
231C22—21no—
232C22—41no—
233C22—82no—
234C22—82no—
235C22—81no—
236C22—82no—
237C22—161no—
238C22#447×C13111yescharacteristic
239C4—21no—
240C4—42no—
241C4—82no—
242C4—81no—
243C4—161no—
244C4#454×C13111yescharacteristic
245C4B(4,𝔽2)×C13111yescharacteristic
246C2—21no—
247C2—41no—
248C2—162no—
249C2—161no—
250C2#1598×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1598
commutator, Frattini, cosocleC2×M16C23×C131
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C2×M16×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3259×C131C2semidirect
2. #2190×C131C2semidirect
3. #2053×C131C2semidirect
4. #1339×C131C2semidirect
5. #1328×C131C2semidirect
125. #12170C131direct (N × H)
126. C131#12170direct (N × H)
127. #3259C2×C131semidirect
128. #2190C2×C131semidirect
129. #2053C2×C131semidirect
130. #1339C2×C131semidirect
131. #1328C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3259×C1312
#2190×C1312
#2053×C1312
#1339×C1312
#1328×C1312
#12170131