Finite Group Databasebeta

← C131×#10403 #45696287

Subgroups — C131×#10403 #45696287

Order 33536.

716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2656×C131C211yesmaximal, characteristic
2#1874×C131C212yesmaximal, complemented
3C2×#327×C131C212yesmaximal, complemented
4#1442×C131C211yesmaximal, characteristic, complemented
5#1280×C131C211yesmaximal, characteristic, complemented
6C2×#121×C131—21no—
7C2×#121×C131—21no—
8C2×#121×C131C2212yes—
9C22×C4⋊C4×C131C2211yescharacteristic
10C2×#102×C131—22no—
11C2×C22⋊C8×C131C2212yes—
12#399×C131—22no—
13#392×C131—22no—
14C2×#95×C131—21no—
15C2×#95×C131—21no—
16C2×#95×C131C2211yescharacteristic
17C2×#95×C131C2211yescharacteristic
18#340×C131—22no—
19#327×C131—24no—
20C22×D4×C131—22no—
21C22×D4×C131—21no—
22C22×D4×C131—21no—
23C22×D4×C131D412yes—
24C23×C4×C131—21no—
25C23×C4×C131—21no—
26C23×C4×C131D411yescharacteristic
27C23×C4×C131D411yescharacteristic
28C23×C4×C131C2311yescharacteristic
29C22×C8×C131—22no—
30#121×C131—22no—
31#121×C131—22no—
32#121×C131—22no—
33#121×C131—22no—
34#121×C131—42no—
35#121×C131—42no—
36#121×C131—42no—
37#121×C131—42no—
38C2×C4⋊C4×C131—22no—
39C2×C4⋊C4×C131—21no—
40C2×C4⋊C4×C131—21no—
41C2×C4⋊C4×C131—42no—
42C2×C4⋊C4×C131D412yes—
43C2×C22⋊C4×C131—22no—
44C2×C22⋊C4×C131—22no—
45C2×C22⋊C4×C131—22no—
46#102×C131—44no—
47C22⋊C8×C131—22no—
48C22⋊C8×C131—22no—
49#95×C131—22no—
50#95×C131—21no—
51#95×C131—42no—
52#95×C131—42no—
53#95×C131D412yescomplemented
54C24×C131—22no—
55C24×C131C2×D411yescharacteristic
56C2×D4×C131—22no—
57C2×D4×C131—22no—
58C2×D4×C131—42no—
59C2×D4×C131—42no—
60C2×D4×C131—42no—
61C2×D4×C131—42no—
62C2×D4×C131—42no—
63C2×D4×C131—42no—
64C2×D4×C131—42no—
65C2×D4×C131—42no—
66C2×D4×C131—42no—
67C2×D4×C131—42no—
68C2×D4×C131—81no—
69C2×D4×C131—81no—
70C2×D4×C131—81no—
71C2×D4×C131—81no—
72C22×C4×C131—21no—
73C22×C4×C131—21no—
74C22×C4×C131—21no—
75C22×C4×C131—21no—
76C22×C4×C131—22no—
77C22×C4×C131—22no—
78C22×C4×C131—22no—
79C22×C4×C131—41no—
80C22×C4×C131—41no—
81C22×C4×C131—41no—
82C22×C4×C131—41no—
83C22×C4×C131—41no—
84C22×C4×C131—41no—
85C22×C4×C131—41no—
86C22×C4×C131—41no—
87C22×C4×C131—41no—
88C22×C4×C131—41no—
89C22×C4×C131—41no—
90C22×C4×C131—41no—
91C22×C4×C131—41no—
92C22×C4×C131—41no—
93C22×C4×C131—41no—
94C22×C4×C131—41no—
95C22×C4×C131—41no—
96C22×C4×C131—41no—
97C22×C4×C131D812yes—
98C22×C4×C131SD1612yes—
99C22×C4×C131C2×D412yes—
100C22×C4×C131C2×D411yescharacteristic
101C22×C4×C131#4112yes—
102C22×C4×C131#4111yescharacteristic
103C2×C8×C131—42no—
104C2×C8×C131—42no—
105C2×C8×C131—42no—
106C4⋊C4×C131—24no—
107C4⋊C4×C131—22no—
108C4⋊C4×C131—22no—
109C4⋊C4×C131—42no—
110C4⋊C4×C131—42no—
111C4⋊C4×C131—42no—
112C22⋊C4×C131—44no—
113C22⋊C4×C131—44no—
114C22⋊C4×C131—42no—
115C22⋊C4×C131—42no—
116C23×C131—21no—
117C23×C131—21no—
118C23×C131—21no—
119C23×C131—21no—
120C23×C131—42no—
121C23×C131—42no—
122C23×C131—42no—
123C23×C131—42no—
124C23×C131—42no—
125C23×C131—42no—
126C23×C131—42no—
127C23×C131#12011yescharacteristic
128C23×C131#12111yescharacteristic
129C23×C131#12411yescharacteristic
130C23×C131C2×D811yescharacteristic
131C23×C131C2×SD1611yescharacteristic
132C23×C131AGL(1,ℤ/8)11yescharacteristic
133C23×C131AGL(1,ℤ/8)11yescharacteristic
134D4×C131—44no—
135D4×C131—82no—
136D4×C131—84no—
137D4×C131—84no—
138D4×C131—82no—
139D4×C131—82no—
140D4×C131—82no—
141D4×C131—82no—
142C2×C4×C131—22no—
143C2×C4×C131—22no—
144C2×C4×C131—22no—
145C2×C4×C131—22no—
146C2×C4×C131—41no—
147C2×C4×C131—42no—
148C2×C4×C131—41no—
149C2×C4×C131—41no—
150C2×C4×C131—41no—
151C2×C4×C131—41no—
152C2×C4×C131—41no—
153C2×C4×C131—42no—
154C2×C4×C131—42no—
155C2×C4×C131—42no—
156C2×C4×C131—42no—
157C2×C4×C131—42no—
158C2×C4×C131—42no—
159C2×C4×C131—42no—
160C2×C4×C131—42no—
161C2×C4×C131—42no—
162C2×C4×C131—42no—
163C2×C4×C131—42no—
164C2×C4×C131—81no—
165C2×C4×C131—81no—
166C2×C4×C131—81no—
167C2×C4×C131—81no—
168C2×C4×C131—81no—
169C2×C4×C131—81no—
170C2×C4×C131—81no—
171C2×C4×C131—81no—
172C2×C4×C131—81no—
173C2×C4×C131—81no—
174C2×C4×C131#12112yes—
175C2×C4×C131#12312yes—
176C8×C131—82no—
177C22×C131—21no—
178C22×C131—21no—
179C22×C131—21no—
180C22×C131—21no—
181C22×C131—21no—
182C22×C131—21no—
183C22×C131—21no—
184C22×C131—21no—
185C22×C131—21no—
186C22×C131—21no—
187C22×C131—21no—
188C22×C131—21no—
189C22×C131—82no—
190C22×C131—82no—
191C22×C131—82no—
192C22×C131—82no—
193C22×C131—82no—
194C22×C131—82no—
195C22×C131—82no—
196C22×C131#39411yescharacteristic
197C22×C131#44711yescharacteristic
198C22×C131#45011yescharacteristic
199C22×C131#45411yescharacteristic
200C22×C131#45511yescharacteristic
201C22×C131B(4,𝔽2)11yescharacteristic
202C22×C131#45811yescharacteristic
203C22×C131#45911yescharacteristic
204C22×C131#46011yescharacteristic
205C22×C131#48611yescharacteristic
206C22×C131#49011yescharacteristic
207C4×C131—22no—
208C4×C131—22no—
209C4×C131—42no—
210C4×C131—42no—
211C4×C131—82no—
212C4×C131—82no—
213C4×C131—82no—
214C2×C131—21no—
215C2×C131—21no—
216C2×C131—21no—
217C2×C131—21no—
218C2×C131—162no—
219C2×C131#159811yescharacteristic
220C2×C131#160111yescharacteristic
221C2×C131#160711yescharacteristic
222C2×C131#161611yescharacteristic
223C2×C131#204011yescharacteristic
224C2×C131#204111yescharacteristic
225C2×C131#204411yescharacteristic
226#10403C13111yesmaximal, characteristic, direct product factor, Sylow
227C131#1040311yescharacteristic, direct product factor, Sylow
228#2656C2×C13111yescharacteristic
229#1874C2×C13112yescomplemented
230C2×#327C2×C13112yescomplemented
231#1442C2×C13111yescharacteristic, complemented
232#1280C2×C13111yescharacteristic, complemented
233C2×#121—21no—
234C2×#121—21no—
235C2×#121C22×C13112yes—
236C22×C4⋊C4C22×C13111yescharacteristic
237C2×#102—22no—
238C2×C22⋊C8C22×C13112yes—
239#399—22no—
240#392—22no—
241C2×#95—21no—
242C2×#95—21no—
243C2×#95C22×C13111yescharacteristic
244C2×#95C22×C13111yescharacteristic
245#340—22no—
246#327—24no—
247C22×D4—22no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4D4×C13112yes—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4D4×C13111yescharacteristic
254C23×C4D4×C13111yescharacteristic
255C23×C4C23×C13111yescharacteristic
256C22×C8—22no—
257#121—22no—
258#121—22no—
259#121—22no—
260#121—22no—
261#121—42no—
262#121—42no—
263#121—42no—
264#121—42no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4D4×C13112yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273#102—44no—
274C22⋊C8—22no—
275C22⋊C8—22no—
276#95—22no—
277#95—21no—
278#95—42no—
279#95—42no—
280#95D4×C13112yescomplemented
281C24—22no—
282C24C2×D4×C13111yescharacteristic
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—81no—
296C2×D4—81no—
297C2×D4—81no—
298C2×D4—81no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4D8×C13112yes—
325C22×C4SD16×C13112yes—
326C22×C4C2×D4×C13112yes—
327C22×C4C2×D4×C13111yescharacteristic
328C22×C4#41×C13112yes—
329C22×C4#41×C13111yescharacteristic
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—42no—
333C4⋊C4—24no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C22⋊C4—44no—
340C22⋊C4—44no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23#120×C13111yescharacteristic
355C23#121×C13111yescharacteristic
356C23#124×C13111yescharacteristic
357C23C2×D8×C13111yescharacteristic
358C23C2×SD16×C13111yescharacteristic
359C23AGL(1,ℤ/8)×C13111yescharacteristic
360C23AGL(1,ℤ/8)×C13111yescharacteristic
361D4—44no—
362D4—82no—
363D4—84no—
364D4—84no—
365D4—82no—
366D4—82no—
367D4—82no—
368D4—82no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4#121×C13112yes—
402C2×C4#123×C13112yes—
403C8—82no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22#394×C13111yescharacteristic
424C22#447×C13111yescharacteristic
425C22#450×C13111yescharacteristic
426C22#454×C13111yescharacteristic
427C22#455×C13111yescharacteristic
428C22B(4,𝔽2)×C13111yescharacteristic
429C22#458×C13111yescharacteristic
430C22#459×C13111yescharacteristic
431C22#460×C13111yescharacteristic
432C22#486×C13111yescharacteristic
433C22#490×C13111yescharacteristic
434C4—22no—
435C4—22no—
436C4—42no—
437C4—42no—
438C4—82no—
439C4—82no—
440C4—82no—
441C2—21no—
442C2—21no—
443C2—21no—
444C2—21no—
445C2—162no—
446C2#1598×C13111yescharacteristic
447C2#1601×C13111yescharacteristic
448C2#1607×C13111yescharacteristic
449C2#1616×C13111yescharacteristic
450C2#2040×C13111yescharacteristic
451C2#2041×C13111yescharacteristic
452C2#2044×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#120
commutator, Frattini, cosocleC23×C4C23×C131
prime radical#2656×C131C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1874×C131C2semidirect
3. C2×#327×C131C2semidirect
4. #1442×C131C2semidirect
5. #1280×C131C2semidirect
53. #95×C131D4semidirect
226. #10403C131direct (N × H)
227. C131#10403direct (N × H)
229. #1874C2×C131semidirect
230. C2×#327C2×C131semidirect
231. #1442C2×C131semidirect
232. #1280C2×C131semidirect
280. #95D4×C131semidirect

Maximal subgroups

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

subgroupindex
#2656×C1312
#1874×C1312
C2×#327×C1312
#1442×C1312
#1280×C1312
#10403131