Finite Group Databasebeta

← C131×#13602 #45699486

Subgroups — C131×#13602 #45699486

Order 33536.

326 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 90 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#3131×C131C211yesmaximal, characteristic
2#2132×C131C211yesmaximal, characteristic
3#2126×C131C211yesmaximal, characteristic
4#1414×C131C214yesmaximal, complemented
5#533×C131C411yescharacteristic, complemented
6#532×C131C2211yescharacteristic
7#488×C131C412yescomplemented
8#488×C131C2212yes—
9#487×C131—21no—
10#486×C131—21no—
11#416×C131—21no—
12#416×C131—21no—
13#413×C131—21no—
14#410×C131—21no—
15C2×C4×C8×C131C411yescharacteristic, complemented
16#356×C131—21no—
17#355×C131C2212yes—
18#354×C131C2212yes—
19#353×C131—21no—
20C2×#41×C131D411yescharacteristic
21C2×#41×C131D411yescharacteristic
22C2×M16×C131—41no—
23C22×C8×C131—21no—
24C4⋊Q8×C131—21no—
25C4⋊Q8×C131D411yescharacteristic
26#127×C131D411yescharacteristic
27#125×C131C2×C412yes—
28#124×C131C2×C411yescharacteristic
29#124×C131C2311yescharacteristic
30C22⋊Q8×C131—41no—
31#121×C131—41no—
32C4×Q8×C131—41no—
33C4×D4×C131—41no—
34#117×C131—21no—
35#117×C131—41no—
36C2×C42×C131C2×C411yescharacteristic
37#103×C131—22no—
38#103×C131—22no—
39#102×C131—22no—
40#102×C131—22no—
41#101×C131—22no—
42#100×C131—41no—
43#99×C131—22no—
44#99×C131—41no—
45C4×C8×C131—21no—
46C4×C8×C131C2×C412yes—
47#41×C131—41no—
48#41×C131—41no—
49#41×C131—41no—
50#41×C131—41no—
51C2×Q8×C131—41no—
52C2×Q8×C131C22⋊C411yescharacteristic
53C2×Q8×C131C2×D411yescharacteristic
54C2×D4×C131—21no—
55C2×D4×C131—21no—
56C2×D4×C131—41no—
57C2×D4×C131C22⋊C411yescharacteristic
58C2×D4×C131C2×D411yescharacteristic
59C22×C4×C131—21no—
60C22×C4×C131—21no—
61C22×C4×C131—21no—
62C22×C4×C131C22⋊C411yescharacteristic
63M16×C131—42no—
64M16×C131—81no—
65C2×C8×C131—22no—
66C2×C8×C131—41no—
67C2×C8×C131—41no—
68C2×C8×C131—81no—
69C4⋊C4×C131—22no—
70C4⋊C4×C131—41no—
71C4⋊C4×C131—42no—
72C4⋊C4×C131—41no—
73C4⋊C4×C131—81no—
74C22⋊C4×C131—41no—
75C22⋊C4×C131—41no—
76C22⋊C4×C131—41no—
77C22⋊C4×C131—42no—
78C42×C131—21no—
79C42×C131—41no—
80C42×C131—81no—
81C42×C131C22⋊C411yescharacteristic
82C42×C131C22×C411yescharacteristic
83C23×C131—21no—
84C23×C131—21no—
85C23×C131#9911yescharacteristic
86Q8×C131—41no—
87Q8×C131—41no—
88Q8×C131—82no—
89D4×C131—41no—
90D4×C131—41no—
91D4×C131—82no—
92D4×C131—81no—
93D4×C131—81no—
94C2×C4×C131—21no—
95C2×C4×C131—21no—
96C2×C4×C131—21no—
97C2×C4×C131—21no—
98C2×C4×C131—21no—
99C2×C4×C131—21no—
100C2×C4×C131—42no—
101C2×C4×C131—41no—
102C2×C4×C131—41no—
103C2×C4×C131—41no—
104C2×C4×C131—41no—
105C2×C4×C131—42no—
106C2×C4×C131—82no—
107C2×C4×C131#9911yescharacteristic
108C2×C4×C131C2×C22⋊C411yescharacteristic
109C8×C131—42no—
110C8×C131—82no—
111C22×C131—21no—
112C22×C131—41no—
113C22×C131—41no—
114C22×C131—41no—
115C22×C131—81no—
116C22×C131—81no—
117C22×C131C2×#9911yescharacteristic
118C4×C131—22no—
119C4×C131—21no—
120C4×C131—41no—
121C4×C131—41no—
122C4×C131—41no—
123C4×C131—82no—
124C4×C131—162no—
125C4×C131#35411yescharacteristic
126C4×C131#35411yescharacteristic
127C2×C131—21no—
128C2×C131—41no—
129C2×C131—81no—
130C2×C131—81no—
131C2×C131C2×#35411yescharacteristic
132#13602C13111yesmaximal, characteristic, direct product factor, Sylow
133C131#1360211yescharacteristic, direct product factor, Sylow
134#3131C2×C13111yescharacteristic
135#2132C2×C13111yescharacteristic
136#2126C2×C13111yescharacteristic
137#1414C2×C13114yescomplemented
138#533C4×C13111yescharacteristic, complemented
139#532C22×C13111yescharacteristic
140#488C4×C13112yescomplemented
141#488C22×C13112yes—
142#487—21no—
143#486—21no—
144#416—21no—
145#416—21no—
146#413—21no—
147#410—21no—
148C2×C4×C8C4×C13111yescharacteristic, complemented
149#356—21no—
150#355C22×C13112yes—
151#354C22×C13112yes—
152#353—21no—
153C2×#41D4×C13111yescharacteristic
154C2×#41D4×C13111yescharacteristic
155C2×M16—41no—
156C22×C8—21no—
157C4⋊Q8—21no—
158C4⋊Q8D4×C13111yescharacteristic
159#127D4×C13111yescharacteristic
160#125C2×C4×C13112yes—
161#124C2×C4×C13111yescharacteristic
162#124C23×C13111yescharacteristic
163C22⋊Q8—41no—
164#121—41no—
165C4×Q8—41no—
166C4×D4—41no—
167#117—21no—
168#117—41no—
169C2×C42C2×C4×C13111yescharacteristic
170#103—22no—
171#103—22no—
172#102—22no—
173#102—22no—
174#101—22no—
175#100—41no—
176#99—22no—
177#99—41no—
178C4×C8—21no—
179C4×C8C2×C4×C13112yes—
180#41—41no—
181#41—41no—
182#41—41no—
183#41—41no—
184C2×Q8—41no—
185C2×Q8C22⋊C4×C13111yescharacteristic
186C2×Q8C2×D4×C13111yescharacteristic
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—41no—
190C2×D4C22⋊C4×C13111yescharacteristic
191C2×D4C2×D4×C13111yescharacteristic
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4C22⋊C4×C13111yescharacteristic
196M16—42no—
197M16—81no—
198C2×C8—22no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—81no—
202C4⋊C4—22no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—81no—
207C22⋊C4—41no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C22⋊C4—42no—
211C42—21no—
212C42—41no—
213C42—81no—
214C42C22⋊C4×C13111yescharacteristic
215C42C22×C4×C13111yescharacteristic
216C23—21no—
217C23—21no—
218C23#99×C13111yescharacteristic
219Q8—41no—
220Q8—41no—
221Q8—82no—
222D4—41no—
223D4—41no—
224D4—82no—
225D4—81no—
226D4—81no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—82no—
240C2×C4#99×C13111yescharacteristic
241C2×C4C2×C22⋊C4×C13111yescharacteristic
242C8—42no—
243C8—82no—
244C22—21no—
245C22—41no—
246C22—41no—
247C22—41no—
248C22—81no—
249C22—81no—
250C22C2×#99×C13111yescharacteristic
251C4—22no—
252C4—21no—
253C4—41no—
254C4—41no—
255C4—41no—
256C4—82no—
257C4—162no—
258C4#354×C13111yescharacteristic
259C4#354×C13111yescharacteristic
260C2—21no—
261C2—41no—
262C2—81no—
263C2—81no—
264C2C2×#354×C13111yescharacteristic
subgroupG/H
centerC4×C131#354
commutatorC42C22×C4×C131
Frattini, cosocle#124C23×C131
socleC2×C131C2×#354
prime radical#532×C131C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C131 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ #532×C131 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1414×C131C2semidirect
5. #533×C131C4semidirect
7. #488×C131C4semidirect
15. C2×C4×C8×C131C4semidirect
132. #13602C131direct (N × H)
133. C131#13602direct (N × H)
137. #1414C2×C131semidirect
138. #533C4×C131semidirect
140. #488C4×C131semidirect
148. C2×C4×C8C4×C131semidirect

Maximal subgroups

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

subgroupindex
#3131×C1312
#2132×C1312
#2126×C1312
#1414×C1312
#13602131