Finite Group Databasebeta

← C131×#13401 #45699285

Subgroups — C131×#13401 #45699285

Order 33536.

390 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3067×C131C211yesmaximal, characteristic
2#2155×C131C211yesmaximal, characteristic, complemented
3#2145×C131C211yesmaximal, characteristic, complemented
4#2138×C131C211yesmaximal, characteristic, complemented
5C2×#350×C131C211yesmaximal, characteristic, complemented
6#1812×C131C211yesmaximal, characteristic, complemented
7#1382×C131C211yesmaximal, characteristic, complemented
8#575×C131—21no—
9C2×#135×C131C2211yescharacteristic
10C2×#131×C131C2211yescharacteristic
11C2×M32×C131C2211yescharacteristic
12C22×C16×C131C2211yescharacteristic
13#473×C131—21no—
14#472×C131—21no—
15#471×C131—22no—
16C2×#108×C131C2211yescharacteristic
17#427×C131C2211yescharacteristic
18#427×C131C2211yescharacteristic
19#413×C131—21no—
20#410×C131—21no—
21#365×C131—22no—
22#360×C131—22no—
23#358×C131—21no—
24#357×C131—21no—
25#350×C131—22no—
26H(3,ℤ/4)×C131—21no—
27C2×#41×C131—21no—
28C2×#41×C131D411yescharacteristic
29#137×C131—22no—
30#137×C131—41no—
31AGL(1,ℤ/8)×C131—22no—
32AGL(1,ℤ/8)×C131—41no—
33#135×C131—21no—
34#135×C131—21no—
35#135×C131—21no—
36#135×C131—21no—
37#135×C131—42no—
38C2×Q16×C131D411yescharacteristic
39C2×SD16×C131—21no—
40C2×D8×C131D411yescharacteristic
41#131×C131—21no—
42#131×C131—21no—
43#131×C131—21no—
44#131×C131—21no—
45C2×M16×C131—21no—
46C2×M16×C131—21no—
47C2×M16×C131D411yescharacteristic
48C22×C8×C131—21no—
49C22×C8×C131C2311yescharacteristic
50#117×C131—21no—
51#117×C131—21no—
52M32×C131—21no—
53M32×C131D412yes—
54C2×C16×C131—21no—
55C2×C16×C131—21no—
56C2×C16×C131—21no—
57C2×C16×C131—21no—
58#108×C131—21no—
59#108×C131D412yes—
60#107×C131—21no—
61#107×C131—21no—
62#106×C131—21no—
63#106×C131—21no—
64#101×C131—22no—
65#100×C131—22no—
66#99×C131—42no—
67#41×C131—21no—
68#41×C131—21no—
69#41×C131—21no—
70#41×C131—21no—
71#41×C131—41no—
72#41×C131—41no—
73#41×C131—41no—
74#41×C131—41no—
75C2×Q8×C131—21no—
76C2×Q8×C131SD1611yescharacteristic
77C2×D4×C131—21no—
78C2×D4×C131—21no—
79C2×D4×C131—41no—
80C2×D4×C131SD1611yescharacteristic
81C22×C4×C131—21no—
82C22×C4×C131—41no—
83C22×C4×C131C2×D411yescharacteristic
84Q16×C131—21no—
85Q16×C131—21no—
86Q16×C131—42no—
87SD16×C131—42no—
88SD16×C131—42no—
89SD16×C131—41no—
90SD16×C131—41no—
91D8×C131—21no—
92D8×C131—21no—
93D8×C131—42no—
94M16×C131—21no—
95M16×C131—22no—
96M16×C131—21no—
97M16×C131—41no—
98M16×C131—41no—
99M16×C131—41no—
100C2×C8×C131—21no—
101C2×C8×C131—41no—
102C2×C8×C131—41no—
103C2×C8×C131—41no—
104C2×C8×C131C2×D411yescharacteristic
105C2×C8×C131C2×D411yescharacteristic
106C2×C8×C131C2×D411yescharacteristic
107C2×C8×C131#4111yescharacteristic
108C2×C8×C131#4111yescharacteristic
109C2×C8×C131#4111yescharacteristic
110C4⋊C4×C131—41no—
111C4⋊C4×C131—41no—
112C22⋊C4×C131—41no—
113C22⋊C4×C131—41no—
114C42×C131—41no—
115C42×C131—41no—
116C16×C131—22no—
117C16×C131—41no—
118C23×C131—21no—
119C23×C131—41no—
120C23×C131AGL(1,ℤ/8)11yescharacteristic
121Q8×C131—21no—
122Q8×C131—21no—
123Q8×C131—41no—
124Q8×C131—41no—
125D4×C131—21no—
126D4×C131—21no—
127D4×C131—41no—
128D4×C131—41no—
129D4×C131—41no—
130D4×C131—41no—
131D4×C131—81no—
132D4×C131—81no—
133C2×C4×C131—21no—
134C2×C4×C131—41no—
135C2×C4×C131—41no—
136C2×C4×C131—41no—
137C2×C4×C131—81no—
138C2×C4×C131—81no—
139C2×C4×C131—81no—
140C2×C4×C131—81no—
141C2×C4×C131#12011yescharacteristic
142C2×C4×C131#12111yescharacteristic
143C2×C4×C131#12311yescharacteristic
144C2×C4×C131C2×SD1611yescharacteristic
145C2×C4×C131#13511yescharacteristic
146C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
147C8×C131—41no—
148C8×C131—42no—
149C8×C131#12111yescharacteristic
150C8×C131#12111yescharacteristic
151C8×C131#12311yescharacteristic
152C8×C131#12411yescharacteristic
153C22×C131—41no—
154C22×C131—41no—
155C22×C131—81no—
156C22×C131—81no—
157C22×C131—161no—
158C22×C131#44911yescharacteristic
159C22×C131#46911yescharacteristic
160C22×C131#48111yescharacteristic
161C4×C131—41no—
162C4×C131—81no—
163C4×C131—161no—
164C4×C131—161no—
165C4×C131#39411yescharacteristic
166C4×C131#45011yescharacteristic
167C4×C131#46511yescharacteristic
168C4×C131#48211yescharacteristic
169C2×C131—21no—
170C2×C131—21no—
171C2×C131—21no—
172C2×C131—81no—
173C2×C131—161no—
174C2×C131#203411yescharacteristic
175#13401C13111yesmaximal, characteristic, direct product factor, Sylow
176C131#1340111yescharacteristic, direct product factor, Sylow
177#3067C2×C13111yescharacteristic
178#2155C2×C13111yescharacteristic, complemented
179#2145C2×C13111yescharacteristic, complemented
180#2138C2×C13111yescharacteristic, complemented
181C2×#350C2×C13111yescharacteristic, complemented
182#1812C2×C13111yescharacteristic, complemented
183#1382C2×C13111yescharacteristic, complemented
184#575—21no—
185C2×#135C22×C13111yescharacteristic
186C2×#131C22×C13111yescharacteristic
187C2×M32C22×C13111yescharacteristic
188C22×C16C22×C13111yescharacteristic
189#473—21no—
190#472—21no—
191#471—22no—
192C2×#108C22×C13111yescharacteristic
193#427C22×C13111yescharacteristic
194#427C22×C13111yescharacteristic
195#413—21no—
196#410—21no—
197#365—22no—
198#360—22no—
199#358—21no—
200#357—21no—
201#350—22no—
202H(3,ℤ/4)—21no—
203C2×#41—21no—
204C2×#41D4×C13111yescharacteristic
205#137—22no—
206#137—41no—
207AGL(1,ℤ/8)—22no—
208AGL(1,ℤ/8)—41no—
209#135—21no—
210#135—21no—
211#135—21no—
212#135—21no—
213#135—42no—
214C2×Q16D4×C13111yescharacteristic
215C2×SD16—21no—
216C2×D8D4×C13111yescharacteristic
217#131—21no—
218#131—21no—
219#131—21no—
220#131—21no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16D4×C13111yescharacteristic
224C22×C8—21no—
225C22×C8C23×C13111yescharacteristic
226#117—21no—
227#117—21no—
228M32—21no—
229M32D4×C13112yes—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234#108—21no—
235#108D4×C13112yes—
236#107—21no—
237#107—21no—
238#106—21no—
239#106—21no—
240#101—22no—
241#100—22no—
242#99—42no—
243#41—21no—
244#41—21no—
245#41—21no—
246#41—21no—
247#41—41no—
248#41—41no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×Q8SD16×C13111yescharacteristic
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4SD16×C13111yescharacteristic
257C22×C4—21no—
258C22×C4—41no—
259C22×C4C2×D4×C13111yescharacteristic
260Q16—21no—
261Q16—21no—
262Q16—42no—
263SD16—42no—
264SD16—42no—
265SD16—41no—
266SD16—41no—
267D8—21no—
268D8—21no—
269D8—42no—
270M16—21no—
271M16—22no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—41no—
276C2×C8—21no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8C2×D4×C13111yescharacteristic
281C2×C8C2×D4×C13111yescharacteristic
282C2×C8C2×D4×C13111yescharacteristic
283C2×C8#41×C13111yescharacteristic
284C2×C8#41×C13111yescharacteristic
285C2×C8#41×C13111yescharacteristic
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42—41no—
291C42—41no—
292C16—22no—
293C16—41no—
294C23—21no—
295C23—41no—
296C23AGL(1,ℤ/8)×C13111yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—41no—
300Q8—41no—
301D4—21no—
302D4—21no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—41no—
307D4—81no—
308D4—81no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4#120×C13111yescharacteristic
318C2×C4#121×C13111yescharacteristic
319C2×C4#123×C13111yescharacteristic
320C2×C4C2×SD16×C13111yescharacteristic
321C2×C4#135×C13111yescharacteristic
322C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
323C8—41no—
324C8—42no—
325C8#121×C13111yescharacteristic
326C8#121×C13111yescharacteristic
327C8#123×C13111yescharacteristic
328C8#124×C13111yescharacteristic
329C22—41no—
330C22—41no—
331C22—81no—
332C22—81no—
333C22—161no—
334C22#449×C13111yescharacteristic
335C22#469×C13111yescharacteristic
336C22#481×C13111yescharacteristic
337C4—41no—
338C4—81no—
339C4—161no—
340C4—161no—
341C4#394×C13111yescharacteristic
342C4#450×C13111yescharacteristic
343C4#465×C13111yescharacteristic
344C4#482×C13111yescharacteristic
345C2—21no—
346C2—21no—
347C2—21no—
348C2—81no—
349C2—161no—
350C2#2034×C13111yescharacteristic
subgroupG/H
centerC4×C131#482
commutator, Frattini, cosocleC22×C8C23×C131
socleC2×C131#2034
prime radical#3067×C131C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C131 ◁ C22×C4×C131 ◁ C2×#131×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2155×C131C2semidirect
3. #2145×C131C2semidirect
4. #2138×C131C2semidirect
5. C2×#350×C131C2semidirect
6. #1812×C131C2semidirect
7. #1382×C131C2semidirect
175. #13401C131direct (N × H)
176. C131#13401direct (N × H)
178. #2155C2×C131semidirect
179. #2145C2×C131semidirect
180. #2138C2×C131semidirect
181. C2×#350C2×C131semidirect
182. #1812C2×C131semidirect
183. #1382C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3067×C1312
#2155×C1312
#2145×C1312
#2138×C1312
C2×#350×C1312
#1812×C1312
#1382×C1312
#13401131