Finite Group Databasebeta

← C131×#10474 #45696358

Subgroups — C131×#10474 #45696358

Order 33536.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C131C211yesmaximal, characteristic
2#1984×C131C211yesmaximal, characteristic, complemented
3#1957×C131C211yesmaximal, characteristic
4#1803×C131C211yesmaximal, characteristic, complemented
5C2×#335×C131C211yesmaximal, characteristic, complemented
6C2×#331×C131C211yesmaximal, characteristic
7#1296×C131C211yesmaximal, characteristic, complemented
8C22×SD16×C131—21no—
9C2×#127×C131C2211yescharacteristic
10C2×C4×Q8×C131C2211yescharacteristic
11#460×C131—22no—
12#460×C131—22no—
13C2×C4⋊C8×C131C2211yescharacteristic
14C2×C4⋊C8×C131C2211yescharacteristic
15C2×C4⋊C8×C131C2211yescharacteristic
16C2×#103×C131—21no—
17C2×#102×C131—21no—
18C2×#102×C131—21no—
19C2×#102×C131—21no—
20C2×C4×C8×C131C2211yescharacteristic
21#384×C131C2211yescharacteristic
22#340×C131—21no—
23#336×C131—21no—
24#336×C131—21no—
25#335×C131—22no—
26#331×C131—22no—
27C22×Q8×C131D411yescharacteristic
28C22×D4×C131—21no—
29C22×D4×C131—21no—
30C22×D4×C131—21no—
31C2×SD16×C131—24no—
32C2×SD16×C131—42no—
33C2×SD16×C131—42no—
34C22×C8×C131—21no—
35C22×C8×C131—21no—
36C22×C8×C131—21no—
37C22×C8×C131D411yescharacteristic
38C22×C8×C131D411yescharacteristic
39#127×C131—21no—
40#127×C131—21no—
41#127×C131—21no—
42#127×C131D412yes—
43C4×Q8×C131—21no—
44C4×Q8×C131—21no—
45C4×Q8×C131—21no—
46C4×Q8×C131—21no—
47C2×C4⋊C4×C131—21no—
48C2×C4⋊C4×C131—21no—
49C2×C4⋊C4×C131—21no—
50C2×C4⋊C4×C131—21no—
51C2×C4⋊C4×C131D411yescharacteristic
52C2×C42×C131—21no—
53C2×C42×C131C2311yescharacteristic
54C4⋊C8×C131—21no—
55C4⋊C8×C131—21no—
56C4⋊C8×C131—21no—
57C4⋊C8×C131—21no—
58C4⋊C8×C131—21no—
59C4⋊C8×C131D412yes—
60#103×C131—42no—
61#102×C131—24no—
62#102×C131—42no—
63#102×C131—42no—
64C4×C8×C131—21no—
65C4×C8×C131—21no—
66C24×C131—41no—
67C2×Q8×C131—21no—
68C2×Q8×C131—21no—
69C2×Q8×C131—21no—
70C2×Q8×C131—21no—
71C2×Q8×C131—21no—
72C2×Q8×C131D812yes—
73C2×D4×C131—22no—
74C2×D4×C131—22no—
75C2×D4×C131—22no—
76C2×D4×C131—41no—
77C2×D4×C131—41no—
78C2×D4×C131—41no—
79C2×D4×C131—41no—
80C2×D4×C131—41no—
81C2×D4×C131—41no—
82C2×D4×C131—41no—
83C2×D4×C131—41no—
84C2×D4×C131—41no—
85C2×D4×C131—41no—
86C2×D4×C131—41no—
87C2×D4×C131—81no—
88C2×D4×C131—81no—
89C22×C4×C131—21no—
90C22×C4×C131—21no—
91C22×C4×C131—41no—
92C22×C4×C131C2×D411yescharacteristic
93C22×C4×C131C2×D411yescharacteristic
94C22×C4×C131#4111yescharacteristic
95SD16×C131—48no—
96C2×C8×C131—21no—
97C2×C8×C131—21no—
98C2×C8×C131—22no—
99C2×C8×C131—21no—
100C2×C8×C131—21no—
101C2×C8×C131—21no—
102C2×C8×C131—41no—
103C2×C8×C131—41no—
104C2×C8×C131—41no—
105C2×C8×C131—41no—
106C2×C8×C131—41no—
107C2×C8×C131—41no—
108C2×C8×C131—41no—
109C2×C8×C131—41no—
110C2×C8×C131SD1612yescomplemented
111C4⋊C4×C131—21no—
112C4⋊C4×C131—21no—
113C4⋊C4×C131—41no—
114C4⋊C4×C131—41no—
115C4⋊C4×C131—41no—
116C4⋊C4×C131—41no—
117C4⋊C4×C131—41no—
118C4⋊C4×C131—41no—
119C4⋊C4×C131—81no—
120C42×C131—41no—
121C42×C131—41no—
122C42×C131C2×D411yescharacteristic
123C42×C131C2×D411yescharacteristic
124C42×C131#4111yescharacteristic
125C42×C131#4111yescharacteristic
126C23×C131—42no—
127C23×C131—81no—
128C23×C131—81no—
129C23×C131—81no—
130C23×C131—81no—
131C23×C131—81no—
132C23×C131—81no—
133C23×C131#12111yescharacteristic
134Q8×C131—22no—
135Q8×C131—22no—
136Q8×C131—41no—
137Q8×C131—41no—
138D4×C131—42no—
139D4×C131—42no—
140D4×C131—42no—
141D4×C131—42no—
142D4×C131—82no—
143D4×C131—82no—
144D4×C131—81no—
145D4×C131—81no—
146D4×C131—81no—
147D4×C131—81no—
148C2×C4×C131—21no—
149C2×C4×C131—21no—
150C2×C4×C131—22no—
151C2×C4×C131—41no—
152C2×C4×C131—41no—
153C2×C4×C131—41no—
154C2×C4×C131—41no—
155C2×C4×C131—41no—
156C2×C4×C131—81no—
157C2×C4×C131—81no—
158C2×C4×C131—81no—
159C2×C4×C131#12011yescharacteristic
160C2×C4×C131#12111yescharacteristic
161C2×C4×C131#12111yescharacteristic
162C2×C4×C131#12311yescharacteristic
163C2×C4×C131#12311yescharacteristic
164C2×C4×C131#12411yescharacteristic
165C2×C4×C131C2×D811yescharacteristic
166C2×C4×C131C2×SD1611yescharacteristic
167C2×C4×C131#13511yescharacteristic
168C2×C4×C131#13511yescharacteristic
169C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C131#13711yescharacteristic
172C2×C4×C131#13711yescharacteristic
173C8×C131—22no—
174C8×C131—42no—
175C8×C131—41no—
176C8×C131—81no—
177C8×C131—81no—
178C22×C131—82no—
179C22×C131—82no—
180C22×C131—82no—
181C22×C131—161no—
182C22×C131—161no—
183C22×C131—161no—
184C22×C131—161no—
185C22×C131#39411yescharacteristic
186C22×C131#46011yescharacteristic
187C22×C131#46411yescharacteristic
188C22×C131#46611yescharacteristic
189C22×C131#46811yescharacteristic
190C22×C131#47111yescharacteristic
191C22×C131#47211yescharacteristic
192C4×C131—21no—
193C4×C131—21no—
194C4×C131—42no—
195C4×C131—81no—
196C4×C131—161no—
197C4×C131#44711yescharacteristic
198C4×C131#45211yescharacteristic
199C4×C131#46111yescharacteristic
200C4×C131#46311yescharacteristic
201C4×C131#46511yescharacteristic
202C4×C131#46811yescharacteristic
203C4×C131#48011yescharacteristic
204C4×C131#48211yescharacteristic
205C2×C131—162no—
206C2×C131#166811yescharacteristic
207C2×C131#168211yescharacteristic
208C2×C131#168611yescharacteristic
209C2×C131#169811yescharacteristic
210C2×C131#203311yescharacteristic
211C2×C131#205111yescharacteristic
212C2×C131#205511yescharacteristic
213#10474C13111yesmaximal, characteristic, direct product factor, Sylow
214C131#1047411yescharacteristic, direct product factor, Sylow
215C2×#460C2×C13111yescharacteristic
216#1984C2×C13111yescharacteristic, complemented
217#1957C2×C13111yescharacteristic
218#1803C2×C13111yescharacteristic, complemented
219C2×#335C2×C13111yescharacteristic, complemented
220C2×#331C2×C13111yescharacteristic
221#1296C2×C13111yescharacteristic, complemented
222C22×SD16—21no—
223C2×#127C22×C13111yescharacteristic
224C2×C4×Q8C22×C13111yescharacteristic
225#460—22no—
226#460—22no—
227C2×C4⋊C8C22×C13111yescharacteristic
228C2×C4⋊C8C22×C13111yescharacteristic
229C2×C4⋊C8C22×C13111yescharacteristic
230C2×#103—21no—
231C2×#102—21no—
232C2×#102—21no—
233C2×#102—21no—
234C2×C4×C8C22×C13111yescharacteristic
235#384C22×C13111yescharacteristic
236#340—21no—
237#336—21no—
238#336—21no—
239#335—22no—
240#331—22no—
241C22×Q8D4×C13111yescharacteristic
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—21no—
245C2×SD16—24no—
246C2×SD16—42no—
247C2×SD16—42no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8D4×C13111yescharacteristic
252C22×C8D4×C13111yescharacteristic
253#127—21no—
254#127—21no—
255#127—21no—
256#127D4×C13112yes—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C13111yescharacteristic
266C2×C42—21no—
267C2×C42C23×C13111yescharacteristic
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8D4×C13112yes—
274#103—42no—
275#102—24no—
276#102—42no—
277#102—42no—
278C4×C8—21no—
279C4×C8—21no—
280C24—41no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8D8×C13112yes—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—81no—
302C2×D4—81no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4C2×D4×C13111yescharacteristic
307C22×C4C2×D4×C13111yescharacteristic
308C22×C4#41×C13111yescharacteristic
309SD16—48no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8SD16×C13112yescomplemented
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—81no—
334C42—41no—
335C42—41no—
336C42C2×D4×C13111yescharacteristic
337C42C2×D4×C13111yescharacteristic
338C42#41×C13111yescharacteristic
339C42#41×C13111yescharacteristic
340C23—42no—
341C23—81no—
342C23—81no—
343C23—81no—
344C23—81no—
345C23—81no—
346C23—81no—
347C23#121×C13111yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—41no—
351Q8—41no—
352D4—42no—
353D4—42no—
354D4—42no—
355D4—42no—
356D4—82no—
357D4—82no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4#120×C13111yescharacteristic
374C2×C4#121×C13111yescharacteristic
375C2×C4#121×C13111yescharacteristic
376C2×C4#123×C13111yescharacteristic
377C2×C4#123×C13111yescharacteristic
378C2×C4#124×C13111yescharacteristic
379C2×C4C2×D8×C13111yescharacteristic
380C2×C4C2×SD16×C13111yescharacteristic
381C2×C4#135×C13111yescharacteristic
382C2×C4#135×C13111yescharacteristic
383C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
384C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
385C2×C4#137×C13111yescharacteristic
386C2×C4#137×C13111yescharacteristic
387C8—22no—
388C8—42no—
389C8—41no—
390C8—81no—
391C8—81no—
392C22—82no—
393C22—82no—
394C22—82no—
395C22—161no—
396C22—161no—
397C22—161no—
398C22—161no—
399C22#394×C13111yescharacteristic
400C22#460×C13111yescharacteristic
401C22#464×C13111yescharacteristic
402C22#466×C13111yescharacteristic
403C22#468×C13111yescharacteristic
404C22#471×C13111yescharacteristic
405C22#472×C13111yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—161no—
411C4#447×C13111yescharacteristic
412C4#452×C13111yescharacteristic
413C4#461×C13111yescharacteristic
414C4#463×C13111yescharacteristic
415C4#465×C13111yescharacteristic
416C4#468×C13111yescharacteristic
417C4#480×C13111yescharacteristic
418C4#482×C13111yescharacteristic
419C2—162no—
420C2#1668×C13111yescharacteristic
421C2#1682×C13111yescharacteristic
422C2#1686×C13111yescharacteristic
423C2#1698×C13111yescharacteristic
424C2#2033×C13111yescharacteristic
425C2#2051×C13111yescharacteristic
426C2#2055×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#121
commutator, Frattini, cosocleC2×C42C23×C131
prime radicalC2×#127×C131C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1984×C131C2semidirect
4. #1803×C131C2semidirect
5. C2×#335×C131C2semidirect
7. #1296×C131C2semidirect
110. C2×C8×C131SD16semidirect
213. #10474C131direct (N × H)
214. C131#10474direct (N × H)
216. #1984C2×C131semidirect
218. #1803C2×C131semidirect
219. C2×#335C2×C131semidirect
221. #1296C2×C131semidirect
324. C2×C8SD16×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C1312
#1984×C1312
#1957×C1312
#1803×C1312
C2×#335×C1312
C2×#331×C1312
#1296×C1312
#10474131