Finite Group Databasebeta

← C131×#12365 #45698249

Subgroups — C131×#12365 #45698249

Order 33536.

346 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 78 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#3291×C131C211yesmaximal, characteristic
2#2230×C131C212yesmaximal, complemented
3#1708×C131C211yesmaximal, characteristic, complemented
4#1359×C131C211yesmaximal, characteristic, complemented
5#1335×C131C212yesmaximal, complemented
6#577×C131—22no—
7#498×C131C2211yescharacteristic, complemented
8#492×C131C2211yescharacteristic
9#487×C131—21no—
10#486×C131—21no—
11#471×C131—22no—
12#456×C131—21no—
13#453×C131—21no—
14#443×C131C2212yes—
15#365×C131—22no—
16#364×C131C2212yescomplemented
17#360×C131—22no—
18C82×C131C2211yescharacteristic, complemented
192−1+4×C131—21no—
20H(5,𝔽2)×C131—21no—
21#137×C131—22no—
22#137×C131—42no—
23AGL(1,ℤ/8)×C131—22no—
24AGL(1,ℤ/8)×C131—42no—
25#135×C131—42no—
26#135×C131D412yes—
27C2×SD16×C131—22no—
28C2×SD16×C131—42no—
29#131×C131—22no—
30C4⋊Q8×C131—21no—
31C4⋊Q8×C131D411yescharacteristic
32#127×C131D411yescharacteristic
33M32×C131—22no—
34#108×C131D412yes—
35#106×C131—22no—
36#104×C131—22no—
37#103×C131—42no—
38#102×C131—42no—
39#101×C131—21no—
40#100×C131—21no—
41C4×C8×C131—21no—
42C4×C8×C131C2311yescharacteristic
43#41×C131—22no—
44#41×C131—42no—
45#41×C131—42no—
46#41×C131—81no—
47C2×Q8×C131—21no—
48C2×Q8×C131—41no—
49C2×Q8×C131—42no—
50C2×D4×C131—21no—
51C2×D4×C131—41no—
52C2×D4×C131—42no—
53C2×D4×C131—81no—
54Q16×C131—42no—
55Q16×C131SD1612yes—
56SD16×C131—22no—
57SD16×C131—42no—
58SD16×C131—42no—
59SD16×C131—42no—
60SD16×C131—42no—
61D8×C131—42no—
62D8×C131SD1612yes—
63M16×C131—22no—
64M16×C131—42no—
65C2×C8×C131—22no—
66C2×C8×C131—42no—
67C2×C8×C131C2×D412yes—
68C4⋊C4×C131—41no—
69C4⋊C4×C131—41no—
70C4⋊C4×C131—41no—
71C42×C131C2×D411yescharacteristic
72C16×C131—42no—
73C23×C131—41no—
74C23×C131—81no—
75Q8×C131—22no—
76Q8×C131—42no—
77Q8×C131—82no—
78Q8×C131—81no—
79D4×C131—22no—
80D4×C131—42no—
81D4×C131—42no—
82D4×C131—82no—
83D4×C131—82no—
84D4×C131—81no—
85C2×C4×C131—21no—
86C2×C4×C131—42no—
87C2×C4×C131—41no—
88C2×C4×C131—81no—
89C2×C4×C131—82no—
90C2×C4×C131—81no—
91C2×C4×C131#12011yescharacteristic
92C8×C131—42no—
93C8×C131—42no—
94C8×C131C2×SD1612yes—
95C8×C131AGL(1,ℤ/8)12yes—
96C22×C131—42no—
97C22×C131—81no—
98C22×C131—161no—
99C22×C131—321no—
100C22×C131#45311yescharacteristic
101C4×C131—22no—
102C4×C131—42no—
103C4×C131—81no—
104C4×C131—161no—
105C4×C131#45012yes—
106C2×C131—21no—
107C2×C131—82no—
108C2×C131—161no—
109C2×C131#162911yescharacteristic
110#12365C13111yesmaximal, characteristic, direct product factor, Sylow
111C131#1236511yescharacteristic, direct product factor, Sylow
112#3291C2×C13111yescharacteristic
113#2230C2×C13112yescomplemented
114#1708C2×C13111yescharacteristic, complemented
115#1359C2×C13111yescharacteristic, complemented
116#1335C2×C13112yescomplemented
117#577—22no—
118#498C22×C13111yescharacteristic, complemented
119#492C22×C13111yescharacteristic
120#487—21no—
121#486—21no—
122#471—22no—
123#456—21no—
124#453—21no—
125#443C22×C13112yes—
126#365—22no—
127#364C22×C13112yescomplemented
128#360—22no—
129C82C22×C13111yescharacteristic, complemented
1302−1+4—21no—
131H(5,𝔽2)—21no—
132#137—22no—
133#137—42no—
134AGL(1,ℤ/8)—22no—
135AGL(1,ℤ/8)—42no—
136#135—42no—
137#135D4×C13112yes—
138C2×SD16—22no—
139C2×SD16—42no—
140#131—22no—
141C4⋊Q8—21no—
142C4⋊Q8D4×C13111yescharacteristic
143#127D4×C13111yescharacteristic
144M32—22no—
145#108D4×C13112yes—
146#106—22no—
147#104—22no—
148#103—42no—
149#102—42no—
150#101—21no—
151#100—21no—
152C4×C8—21no—
153C4×C8C23×C13111yescharacteristic
154#41—22no—
155#41—42no—
156#41—42no—
157#41—81no—
158C2×Q8—21no—
159C2×Q8—41no—
160C2×Q8—42no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4—42no—
164C2×D4—81no—
165Q16—42no—
166Q16SD16×C13112yes—
167SD16—22no—
168SD16—42no—
169SD16—42no—
170SD16—42no—
171SD16—42no—
172D8—42no—
173D8SD16×C13112yes—
174M16—22no—
175M16—42no—
176C2×C8—22no—
177C2×C8—42no—
178C2×C8C2×D4×C13112yes—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C42C2×D4×C13111yescharacteristic
183C16—42no—
184C23—41no—
185C23—81no—
186Q8—22no—
187Q8—42no—
188Q8—82no—
189Q8—81no—
190D4—22no—
191D4—42no—
192D4—42no—
193D4—82no—
194D4—82no—
195D4—81no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—81no—
200C2×C4—82no—
201C2×C4—81no—
202C2×C4#120×C13111yescharacteristic
203C8—42no—
204C8—42no—
205C8C2×SD16×C13112yes—
206C8AGL(1,ℤ/8)×C13112yes—
207C22—42no—
208C22—81no—
209C22—161no—
210C22—321no—
211C22#453×C13111yescharacteristic
212C4—22no—
213C4—42no—
214C4—81no—
215C4—161no—
216C4#450×C13112yes—
217C2—21no—
218C2—82no—
219C2—161no—
220C2#1629×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1629
commutator, Frattini, cosocleC4×C8C23×C131
prime radical#3291×C131C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C4×C8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2230×C131C2semidirect
3. #1708×C131C2semidirect
4. #1359×C131C2semidirect
5. #1335×C131C2semidirect
7. #498×C131C22semidirect
16. #364×C131C22semidirect
18. C82×C131C22semidirect
110. #12365C131direct (N × H)
111. C131#12365direct (N × H)
113. #2230C2×C131semidirect
114. #1708C2×C131semidirect
115. #1359C2×C131semidirect
116. #1335C2×C131semidirect
118. #498C22×C131semidirect
127. #364C22×C131semidirect
129. C82C22×C131semidirect

Maximal subgroups

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

subgroupindex
#3291×C1312
#2230×C1312
#1708×C1312
#1359×C1312
#1335×C1312
#12365131