Finite Group Databasebeta

← C131×#7409 #45693293

Subgroups — C131×#7409 #45693293

Order 33536.

268 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 46 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#2007×C131C211yesmaximal, characteristic
2#1394×C131C211yesmaximal, characteristic, complemented
3#1272×C131C211yesmaximal, characteristic, complemented
4C2×#137×C131—21no—
5#537×C131C411yescharacteristic
6C2×#104×C131—21no—
7C2×#101×C131—21no—
8#391×C131C2211yescharacteristic
9#343×C131C411yescharacteristic
10#336×C131—21no—
11C2×#41×C131—21no—
12C22×Q8×C131D411yescharacteristic
13#137×C131—42no—
14#137×C131—41no—
15#137×C131—41no—
16C2×Q16×C131—41no—
17C2×SD16×C131—41no—
18C2×M16×C131—21no—
19C2×M16×C131—41no—
20C22×C8×C131—41no—
21C22⋊Q8×C131—41no—
22#121×C131—41no—
23#121×C131—41no—
24C2×C4⋊C4×C131C2×C411yescharacteristic
25C2×C42×C131D411yescharacteristic
26#104×C131—42no—
27#101×C131—22no—
28#101×C131—41no—
29#95×C131—41no—
30#41×C131—41no—
31#41×C131—41no—
32#41×C131—41no—
33#41×C131—41no—
34C2×Q8×C131—21no—
35C2×Q8×C131—21no—
36C2×Q8×C131—41no—
37C2×Q8×C131—41no—
38C2×Q8×C131D811yescharacteristic
39C2×Q8×C131SD1611yescharacteristic
40C2×D4×C131—21no—
41C2×D4×C131—41no—
42C2×D4×C131—41no—
43C22×C4×C131—21no—
44C22×C4×C131—21no—
45C22×C4×C131—21no—
46C22×C4×C131—41no—
47C22×C4×C131C22⋊C411yescharacteristic
48Q16×C131—42no—
49Q16×C131—42no—
50SD16×C131—42no—
51SD16×C131—42no—
52M16×C131—22no—
53M16×C131—41no—
54M16×C131—42no—
55M16×C131—81no—
56C2×C8×C131—41no—
57C2×C8×C131—42no—
58C2×C8×C131—81no—
59C2×C8×C131—81no—
60C2×C8×C131—81no—
61C4⋊C4×C131—41no—
62C4⋊C4×C131—41no—
63C22⋊C4×C131—42no—
64C42×C131—41no—
65C23×C131—41no—
66C23×C131#9911yescharacteristic
67Q8×C131—41no—
68Q8×C131—41no—
69Q8×C131—41no—
70Q8×C131—41no—
71Q8×C131—81no—
72D4×C131—41no—
73D4×C131—41no—
74D4×C131—81no—
75D4×C131—81no—
76D4×C131—161no—
77C2×C4×C131—21no—
78C2×C4×C131—21no—
79C2×C4×C131—21no—
80C2×C4×C131—21no—
81C2×C4×C131—21no—
82C2×C4×C131—21no—
83C2×C4×C131—41no—
84C2×C4×C131—41no—
85C2×C4×C131—41no—
86C2×C4×C131—41no—
87C2×C4×C131—41no—
88C2×C4×C131—41no—
89C2×C4×C131—81no—
90C2×C4×C131—81no—
91C2×C4×C131—81no—
92C2×C4×C131#10211yescharacteristic
93C2×C4×C131#10411yescharacteristic
94C8×C131—42no—
95C8×C131—82no—
96C8×C131—82no—
97C22×C131—21no—
98C22×C131—21no—
99C22×C131—81no—
100C22×C131—81no—
101C22×C131—81no—
102C22×C131#32711yescharacteristic
103C22×C131AΣL(1,𝔽16)11yescharacteristic
104C22×C131#35311yescharacteristic
105C4×C131—21no—
106C4×C131—21no—
107C4×C131—41no—
108C4×C131—41no—
109C4×C131—41no—
110C4×C131—41no—
111C4×C131—81no—
112C4×C131—81no—
113C2×C131—21no—
114C2×C131—21no—
115C2×C131—161no—
116C2×C131#134311yescharacteristic
117C2×C131#140311yescharacteristic
118C2×C131#140511yescharacteristic
119#7409C13111yesmaximal, characteristic, direct product factor, Sylow
120C131#740911yescharacteristic, direct product factor, Sylow
121#2007C2×C13111yescharacteristic
122#1394C2×C13111yescharacteristic, complemented
123#1272C2×C13111yescharacteristic, complemented
124C2×#137—21no—
125#537C4×C13111yescharacteristic
126C2×#104—21no—
127C2×#101—21no—
128#391C22×C13111yescharacteristic
129#343C4×C13111yescharacteristic
130#336—21no—
131C2×#41—21no—
132C22×Q8D4×C13111yescharacteristic
133#137—42no—
134#137—41no—
135#137—41no—
136C2×Q16—41no—
137C2×SD16—41no—
138C2×M16—21no—
139C2×M16—41no—
140C22×C8—41no—
141C22⋊Q8—41no—
142#121—41no—
143#121—41no—
144C2×C4⋊C4C2×C4×C13111yescharacteristic
145C2×C42D4×C13111yescharacteristic
146#104—42no—
147#101—22no—
148#101—41no—
149#95—41no—
150#41—41no—
151#41—41no—
152#41—41no—
153#41—41no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8D8×C13111yescharacteristic
159C2×Q8SD16×C13111yescharacteristic
160C2×D4—21no—
161C2×D4—41no—
162C2×D4—41no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—41no—
167C22×C4C22⋊C4×C13111yescharacteristic
168Q16—42no—
169Q16—42no—
170SD16—42no—
171SD16—42no—
172M16—22no—
173M16—41no—
174M16—42no—
175M16—81no—
176C2×C8—41no—
177C2×C8—42no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C22⋊C4—42no—
184C42—41no—
185C23—41no—
186C23#99×C13111yescharacteristic
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—81no—
192D4—41no—
193D4—41no—
194D4—81no—
195D4—81no—
196D4—161no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—81no—
212C2×C4#102×C13111yescharacteristic
213C2×C4#104×C13111yescharacteristic
214C8—42no—
215C8—82no—
216C8—82no—
217C22—21no—
218C22—21no—
219C22—81no—
220C22—81no—
221C22—81no—
222C22#327×C13111yescharacteristic
223C22AΣL(1,𝔽16)×C13111yescharacteristic
224C22#353×C13111yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—41no—
230C4—41no—
231C4—81no—
232C4—81no—
233C2—21no—
234C2—21no—
235C2—161no—
236C2#1343×C13111yescharacteristic
237C2#1403×C13111yescharacteristic
238C2#1405×C13111yescharacteristic
subgroupG/H
center, socleC22×C131AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C131
Frattini, cosocle#391C22×C131
prime radical#537×C131C4
LCSG ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C131 ◁ C22×C4×C131 ◁ #391×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1394×C131C2semidirect
3. #1272×C131C2semidirect
119. #7409C131direct (N × H)
120. C131#7409direct (N × H)
122. #1394C2×C131semidirect
123. #1272C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2007×C1312
#1394×C1312
#1272×C1312
#7409131