Finite Group Databasebeta

← C131×#13408 #45699292

Subgroups — C131×#13408 #45699292

Order 33536.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#495×C131C211yesmaximal, characteristic
2C2×#358×C131C211yesmaximal, characteristic, complemented
3C2×#358×C131C211yesmaximal, characteristic, complemented
4C2×#357×C131C211yesmaximal, characteristic
5C2×#357×C131C211yesmaximal, characteristic
6#1942×C131C211yesmaximal, characteristic, complemented
7#1374×C131C211yesmaximal, characteristic, complemented
8C22×Q16×C131C2211yescharacteristic
9C22×SD16×C131—21no—
10C22×D8×C131C2211yescharacteristic
11C2×#124×C131—21no—
12C22×C16×C131C2211yescharacteristic
13C22×C16×C131C2211yescharacteristic
14#495×C131—22no—
15#495×C131—22no—
16C2×#107×C131C2211yescharacteristic
17C2×#107×C131C2211yescharacteristic
18C2×C4×C8×C131C2211yescharacteristic
19#389×C131—21no—
20#358×C131—22no—
21#358×C131—22no—
22#357×C131—22no—
23#357×C131—22no—
24#340×C131—21no—
25C22×Q8×C131—21no—
26C22×D4×C131—21no—
27C2×Q16×C131—21no—
28C2×Q16×C131—21no—
29C2×Q16×C131—21no—
30C2×Q16×C131—21no—
31C2×Q16×C131—21no—
32C2×Q16×C131D412yes—
33C2×SD16×C131—24no—
34C2×SD16×C131—42no—
35C2×SD16×C131—42no—
36C2×D8×C131—21no—
37C2×D8×C131—21no—
38C2×D8×C131—21no—
39C2×D8×C131—21no—
40C2×D8×C131—21no—
41C2×D8×C131D412yes—
42C22×C8×C131D411yescharacteristic
43C22×C8×C131C2311yescharacteristic
44#124×C131—24no—
45#124×C131—42no—
46C2×C4⋊C4×C131—21no—
47C2×C4⋊C4×C131—21no—
48C2×C4⋊C4×C131—41no—
49C2×C22⋊C4×C131—41no—
50C2×C22⋊C4×C131—41no—
51C2×C42×C131D411yescharacteristic
52C2×C16×C131—21no—
53C2×C16×C131—21no—
54C2×C16×C131—21no—
55C2×C16×C131—21no—
56C2×C16×C131—21no—
57C2×C16×C131—21no—
58#107×C131—21no—
59#107×C131—21no—
60#107×C131—21no—
61#107×C131D412yes—
62C4×C8×C131—21no—
63C4×C8×C131—21no—
64#95×C131—41no—
65C24×C131—41no—
66C2×Q8×C131—22no—
67C2×Q8×C131—41no—
68C2×Q8×C131—41no—
69C2×Q8×C131—41no—
70C2×Q8×C131—41no—
71C2×Q8×C131—41no—
72C2×D4×C131—22no—
73C2×D4×C131—41no—
74C2×D4×C131—41no—
75C2×D4×C131—41no—
76C2×D4×C131—41no—
77C2×D4×C131—41no—
78C22×C4×C131—41no—
79C22×C4×C131—41no—
80C22×C4×C131—41no—
81C22×C4×C131D811yescharacteristic
82C22×C4×C131D811yescharacteristic
83C22×C4×C131C2×D411yescharacteristic
84Q16×C131—22no—
85Q16×C131—22no—
86Q16×C131—41no—
87Q16×C131—41no—
88SD16×C131—48no—
89D8×C131—22no—
90D8×C131—22no—
91D8×C131—41no—
92D8×C131—41no—
93C2×C8×C131—21no—
94C2×C8×C131—21no—
95C2×C8×C131SD1612yes—
96C2×C8×C131C2×D411yescharacteristic
97C2×C8×C131C2×D411yescharacteristic
98C2×C8×C131C2×D411yescharacteristic
99C2×C8×C131#4111yescharacteristic
100C2×C8×C131#4111yescharacteristic
101C2×C8×C131#4111yescharacteristic
102C4⋊C4×C131—22no—
103C4⋊C4×C131—41no—
104C4⋊C4×C131—41no—
105C4⋊C4×C131—41no—
106C4⋊C4×C131—82no—
107C22⋊C4×C131—44no—
108C22⋊C4×C131—44no—
109C42×C131—21no—
110C42×C131—21no—
111C16×C131—41no—
112C16×C131—41no—
113C23×C131—42no—
114C23×C131—81no—
115C23×C131—81no—
116C23×C131—81no—
117C23×C131—81no—
118C23×C131—81no—
119C23×C131—81no—
120C23×C131C2×D811yescharacteristic
121Q8×C131—42no—
122Q8×C131—42no—
123Q8×C131—81no—
124Q8×C131—81no—
125D4×C131—42no—
126D4×C131—42no—
127D4×C131—81no—
128D4×C131—81no—
129C2×C4×C131—21no—
130C2×C4×C131—21no—
131C2×C4×C131—21no—
132C2×C4×C131—21no—
133C2×C4×C131—21no—
134C2×C4×C131—21no—
135C2×C4×C131—42no—
136C2×C4×C131—42no—
137C2×C4×C131—81no—
138C2×C4×C131—81no—
139C2×C4×C131—81no—
140C2×C4×C131—81no—
141C2×C4×C131—81no—
142C2×C4×C131—81no—
143C2×C4×C131—81no—
144C2×C4×C131#12011yescharacteristic
145C2×C4×C131#12111yescharacteristic
146C2×C4×C131#12411yescharacteristic
147C2×C4×C131C2×SD1611yescharacteristic
148C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
150C8×C131—22no—
151C8×C131#12111yescharacteristic
152C8×C131#12111yescharacteristic
153C8×C131#12311yescharacteristic
154C8×C131#12311yescharacteristic
155C22×C131—82no—
156C22×C131—82no—
157C22×C131—82no—
158C22×C131—161no—
159C22×C131—161no—
160C22×C131—161no—
161C22×C131—161no—
162C22×C131#44711yescharacteristic
163C22×C131#45911yescharacteristic
164C22×C131#48611yescharacteristic
165C22×C131#50811yescharacteristic
166C22×C131#50811yescharacteristic
167C22×C131#50911yescharacteristic
168C22×C131#51011yescharacteristic
169C4×C131—41no—
170C4×C131—41no—
171C4×C131—82no—
172C4×C131—82no—
173C4×C131—161no—
174C4×C131#39411yescharacteristic
175C4×C131#45011yescharacteristic
176C4×C131#46011yescharacteristic
177C4×C131#49011yescharacteristic
178C2×C131—162no—
179C2×C131#204111yescharacteristic
180C2×C131#218611yescharacteristic
181C2×C131#218911yescharacteristic
182C2×C131#221011yescharacteristic
183C2×C131#221111yescharacteristic
184C2×C131#224211yescharacteristic
185C2×C131#224311yescharacteristic
186#13408C13111yesmaximal, characteristic, direct product factor, Sylow
187C131#1340811yescharacteristic, direct product factor, Sylow
188C2×#495C2×C13111yescharacteristic
189C2×#358C2×C13111yescharacteristic, complemented
190C2×#358C2×C13111yescharacteristic, complemented
191C2×#357C2×C13111yescharacteristic
192C2×#357C2×C13111yescharacteristic
193#1942C2×C13111yescharacteristic, complemented
194#1374C2×C13111yescharacteristic, complemented
195C22×Q16C22×C13111yescharacteristic
196C22×SD16—21no—
197C22×D8C22×C13111yescharacteristic
198C2×#124—21no—
199C22×C16C22×C13111yescharacteristic
200C22×C16C22×C13111yescharacteristic
201#495—22no—
202#495—22no—
203C2×#107C22×C13111yescharacteristic
204C2×#107C22×C13111yescharacteristic
205C2×C4×C8C22×C13111yescharacteristic
206#389—21no—
207#358—22no—
208#358—22no—
209#357—22no—
210#357—22no—
211#340—21no—
212C22×Q8—21no—
213C22×D4—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16D4×C13112yes—
220C2×SD16—24no—
221C2×SD16—42no—
222C2×SD16—42no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8D4×C13112yes—
229C22×C8D4×C13111yescharacteristic
230C22×C8C23×C13111yescharacteristic
231#124—24no—
232#124—42no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—41no—
236C2×C22⋊C4—41no—
237C2×C22⋊C4—41no—
238C2×C42D4×C13111yescharacteristic
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245#107—21no—
246#107—21no—
247#107—21no—
248#107D4×C13112yes—
249C4×C8—21no—
250C4×C8—21no—
251#95—41no—
252C24—41no—
253C2×Q8—22no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×D4—22no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4D8×C13111yescharacteristic
269C22×C4D8×C13111yescharacteristic
270C22×C4C2×D4×C13111yescharacteristic
271Q16—22no—
272Q16—22no—
273Q16—41no—
274Q16—41no—
275SD16—48no—
276D8—22no—
277D8—22no—
278D8—41no—
279D8—41no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8SD16×C13112yes—
283C2×C8C2×D4×C13111yescharacteristic
284C2×C8C2×D4×C13111yescharacteristic
285C2×C8C2×D4×C13111yescharacteristic
286C2×C8#41×C13111yescharacteristic
287C2×C8#41×C13111yescharacteristic
288C2×C8#41×C13111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—82no—
294C22⋊C4—44no—
295C22⋊C4—44no—
296C42—21no—
297C42—21no—
298C16—41no—
299C16—41no—
300C23—42no—
301C23—81no—
302C23—81no—
303C23—81no—
304C23—81no—
305C23—81no—
306C23—81no—
307C23C2×D8×C13111yescharacteristic
308Q8—42no—
309Q8—42no—
310Q8—81no—
311Q8—81no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4—81no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4#120×C13111yescharacteristic
332C2×C4#121×C13111yescharacteristic
333C2×C4#124×C13111yescharacteristic
334C2×C4C2×SD16×C13111yescharacteristic
335C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
336C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
337C8—22no—
338C8#121×C13111yescharacteristic
339C8#121×C13111yescharacteristic
340C8#123×C13111yescharacteristic
341C8#123×C13111yescharacteristic
342C22—82no—
343C22—82no—
344C22—82no—
345C22—161no—
346C22—161no—
347C22—161no—
348C22—161no—
349C22#447×C13111yescharacteristic
350C22#459×C13111yescharacteristic
351C22#486×C13111yescharacteristic
352C22#508×C13111yescharacteristic
353C22#508×C13111yescharacteristic
354C22#509×C13111yescharacteristic
355C22#510×C13111yescharacteristic
356C4—41no—
357C4—41no—
358C4—82no—
359C4—82no—
360C4—161no—
361C4#394×C13111yescharacteristic
362C4#450×C13111yescharacteristic
363C4#460×C13111yescharacteristic
364C4#490×C13111yescharacteristic
365C2—162no—
366C2#2041×C13111yescharacteristic
367C2#2186×C13111yescharacteristic
368C2#2189×C13111yescharacteristic
369C2#2210×C13111yescharacteristic
370C2#2211×C13111yescharacteristic
371C2#2242×C13111yescharacteristic
372C2#2243×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×D8
commutator, Frattini, cosocleC22×C8C23×C131
prime radicalC22×D8×C131C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ C2×C4×C8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#358×C131C2semidirect
3. C2×#358×C131C2semidirect
6. #1942×C131C2semidirect
7. #1374×C131C2semidirect
186. #13408C131direct (N × H)
187. C131#13408direct (N × H)
189. C2×#358C2×C131semidirect
190. C2×#358C2×C131semidirect
193. #1942C2×C131semidirect
194. #1374C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#495×C1312
C2×#358×C1312
C2×#357×C1312
#1942×C1312
#1374×C1312
#13408131