Finite Group Databasebeta

← C131×#12968 #45698852

Subgroups — C131×#12968 #45698852

Order 33536.

424 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 114 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#2979×C131C211yesmaximal, characteristic
2#2126×C131C211yesmaximal, characteristic
3#1884×C131C211yesmaximal, characteristic
4#1868×C131C212yesmaximal, complemented
5#1391×C131C212yesmaximal, complemented
6#568×C131C2211yescharacteristic
7#532×C131C2211yescharacteristic
8#436×C131—22no—
9C8×D4×C131—22no—
10#431×C131—21no—
11#424×C131—22no—
12#421×C131—21no—
13#410×C131C2211yescharacteristic
14#410×C131C2212yes—
15#408×C131—21no—
16#408×C131C2212yes—
17#354×C131C412yescomplemented
18#353×C131C412yescomplemented
19#344×C131—22no—
20#339×C131—21no—
21C2×#41×C131D411yescharacteristic
22C2×#41×C131C2311yescharacteristic
23#131×C131—42no—
24C2×M16×C131—22no—
25C2×M16×C131—21no—
26C2×M16×C131—21no—
27C2×M16×C131D412yes—
28C22×C8×C131—21no—
29C22×C8×C131D412yes—
30C4⋊Q8×C131Q811yescharacteristic
31#127×C131C2×C411yescharacteristic
32#124×C131C2×C411yescharacteristic
33#124×C131Q811yescharacteristic
34#121×C131—22no—
35C4×D4×C131—22no—
36#117×C131—22no—
37#117×C131—21no—
38C2×C42×C131D411yescharacteristic
39C4⋊C8×C131—21no—
40C4⋊C8×C131—21no—
41C4⋊C8×C131—44no—
42#104×C131—42no—
43#99×C131—22no—
44#99×C131—22no—
45#99×C131C2×C414yes—
46C22⋊C8×C131—22no—
47C22⋊C8×C131—22no—
48C22⋊C8×C131—22no—
49C4×C8×C131—22no—
50#41×C131—41no—
51#41×C131—41no—
52#41×C131—41no—
53#41×C131—41no—
54C2×Q8×C131C4⋊C411yescharacteristic
55C2×Q8×C131C2×Q811yescharacteristic
56C2×D4×C131—22no—
57C2×D4×C131—21no—
58C2×D4×C131C4⋊C411yescharacteristic
59C2×D4×C131C22×C411yescharacteristic
60C2×D4×C131#4112yes—
61C22×C4×C131—21no—
62C22×C4×C131—21no—
63C22×C4×C131C2×D411yescharacteristic
64C22×C4×C131C2×D412yes—
65M16×C131—22no—
66M16×C131—42no—
67M16×C131—41no—
68M16×C131—42no—
69M16×C131—81no—
70C2×C8×C131—24no—
71C2×C8×C131—22no—
72C2×C8×C131—22no—
73C2×C8×C131—41no—
74C2×C8×C131—42no—
75C2×C8×C131—81no—
76C4⋊C4×C131—22no—
77C4⋊C4×C131—42no—
78C4⋊C4×C131—41no—
79C22⋊C4×C131—22no—
80C22⋊C4×C131—22no—
81C22⋊C4×C131—24no—
82C22⋊C4×C131—41no—
83C42×C131—21no—
84C42×C131—42no—
85C42×C131—41no—
86C42×C131C4⋊C411yescharacteristic
87C42×C131C4⋊C411yescharacteristic
88C23×C131—21no—
89C23×C131C4×D412yes—
90C23×C131#12311yescharacteristic
91Q8×C131—41no—
92Q8×C131—41no—
93D4×C131—41no—
94D4×C131—42no—
95D4×C131—41no—
96D4×C131—44no—
97D4×C131—81no—
98C2×C4×C131—21no—
99C2×C4×C131—22no—
100C2×C4×C131—21no—
101C2×C4×C131—22no—
102C2×C4×C131—21no—
103C2×C4×C131—21no—
104C2×C4×C131—21no—
105C2×C4×C131—42no—
106C2×C4×C131—41no—
107C2×C4×C131—41no—
108C2×C4×C131—44no—
109C2×C4×C131—81no—
110C2×C4×C131C2×C4⋊C411yescharacteristic
111C2×C4×C131#12011yescharacteristic
112C2×C4×C131C22⋊Q812yes—
113C8×C131—42no—
114C8×C131—42no—
115C8×C131—42no—
116C22×C131—22no—
117C22×C131—21no—
118C22×C131—41no—
119C22×C131—42no—
120C22×C131—42no—
121C22×C131—41no—
122C22×C131#38511yescharacteristic
123C4×C131—22no—
124C4×C131—21no—
125C4×C131—22no—
126C4×C131—41no—
127C4×C131—41no—
128C4×C131—84no—
129C4×C131—161no—
130C4×C131B(4,𝔽2)11yescharacteristic
131C4×C131#45811yescharacteristic
132C2×C131—21no—
133C2×C131—42no—
134C2×C131—41no—
135C2×C131—81no—
136C2×C131#186711yescharacteristic
137#12968C13111yesmaximal, characteristic, direct product factor, Sylow
138C131#1296811yescharacteristic, direct product factor, Sylow
139#2979C2×C13111yescharacteristic
140#2126C2×C13111yescharacteristic
141#1884C2×C13111yescharacteristic
142#1868C2×C13112yescomplemented
143#1391C2×C13112yescomplemented
144#568C22×C13111yescharacteristic
145#532C22×C13111yescharacteristic
146#436—22no—
147C8×D4—22no—
148#431—21no—
149#424—22no—
150#421—21no—
151#410C22×C13111yescharacteristic
152#410C22×C13112yes—
153#408—21no—
154#408C22×C13112yes—
155#354C4×C13112yescomplemented
156#353C4×C13112yescomplemented
157#344—22no—
158#339—21no—
159C2×#41D4×C13111yescharacteristic
160C2×#41C23×C13111yescharacteristic
161#131—42no—
162C2×M16—22no—
163C2×M16—21no—
164C2×M16—21no—
165C2×M16D4×C13112yes—
166C22×C8—21no—
167C22×C8D4×C13112yes—
168C4⋊Q8Q8×C13111yescharacteristic
169#127C2×C4×C13111yescharacteristic
170#124C2×C4×C13111yescharacteristic
171#124Q8×C13111yescharacteristic
172#121—22no—
173C4×D4—22no—
174#117—22no—
175#117—21no—
176C2×C42D4×C13111yescharacteristic
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—44no—
180#104—42no—
181#99—22no—
182#99—22no—
183#99C2×C4×C13114yes—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187C4×C8—22no—
188#41—41no—
189#41—41no—
190#41—41no—
191#41—41no—
192C2×Q8C4⋊C4×C13111yescharacteristic
193C2×Q8C2×Q8×C13111yescharacteristic
194C2×D4—22no—
195C2×D4—21no—
196C2×D4C4⋊C4×C13111yescharacteristic
197C2×D4C22×C4×C13111yescharacteristic
198C2×D4#41×C13112yes—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4C2×D4×C13111yescharacteristic
202C22×C4C2×D4×C13112yes—
203M16—22no—
204M16—42no—
205M16—41no—
206M16—42no—
207M16—81no—
208C2×C8—24no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—41no—
212C2×C8—42no—
213C2×C8—81no—
214C4⋊C4—22no—
215C4⋊C4—42no—
216C4⋊C4—41no—
217C22⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—24no—
220C22⋊C4—41no—
221C42—21no—
222C42—42no—
223C42—41no—
224C42C4⋊C4×C13111yescharacteristic
225C42C4⋊C4×C13111yescharacteristic
226C23—21no—
227C23C4×D4×C13112yes—
228C23#123×C13111yescharacteristic
229Q8—41no—
230Q8—41no—
231D4—41no—
232D4—42no—
233D4—41no—
234D4—44no—
235D4—81no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—44no—
247C2×C4—81no—
248C2×C4C2×C4⋊C4×C13111yescharacteristic
249C2×C4#120×C13111yescharacteristic
250C2×C4C22⋊Q8×C13112yes—
251C8—42no—
252C8—42no—
253C8—42no—
254C22—22no—
255C22—21no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22#385×C13111yescharacteristic
261C4—22no—
262C4—21no—
263C4—22no—
264C4—41no—
265C4—41no—
266C4—84no—
267C4—161no—
268C4B(4,𝔽2)×C13111yescharacteristic
269C4#458×C13111yescharacteristic
270C2—21no—
271C2—42no—
272C2—41no—
273C2—81no—
274C2#1867×C13111yescharacteristic
subgroupG/H
centerC4×C131B(4,𝔽2)
commutatorC2×D4C22×C4×C131
Frattini, cosocleC2×#41C23×C131
socleC2×C131#1867
prime radical#532×C131C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C131 ◁ C2×C4×C131 ◁ C2×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1868×C131C2semidirect
5. #1391×C131C2semidirect
17. #354×C131C4semidirect
18. #353×C131C4semidirect
137. #12968C131direct (N × H)
138. C131#12968direct (N × H)
142. #1868C2×C131semidirect
143. #1391C2×C131semidirect
155. #354C4×C131semidirect
156. #353C4×C131semidirect

Maximal subgroups

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

subgroupindex
#2979×C1312
#2126×C1312
#1884×C1312
#1868×C1312
#1391×C1312
#12968131