Finite Group Databasebeta

← C131×#8976 #45694860

Subgroups — C131×#8976 #45694860

Order 33536.

592 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C131C211yesmaximal, characteristic
2#2354×C131C211yesmaximal, characteristic
3#1987×C131C211yesmaximal, characteristic, complemented
4#1956×C131C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C131C211yesmaximal, characteristic
6#1296×C131C211yesmaximal, characteristic, complemented
7#1279×C131C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C131C2211yescharacteristic
9C2×C4×D4×C131C2211yescharacteristic
10C2×#117×C131—21no—
11#476×C131—22no—
12#476×C131C414yescomplemented
13C2×#106×C131—21no—
14C2×C4⋊C8×C131C2211yescharacteristic
15C2×C4⋊C8×C131C2211yescharacteristic
16C2×#103×C131—22no—
17C2×#102×C131—21no—
18C2×C4×C8×C131C2211yescharacteristic
19#390×C131—21no—
20#388×C131—22no—
21#384×C131C2211yescharacteristic
22#380×C131—21no—
23C4×C4⋊C4×C131—21no—
24C4×C4⋊C4×C131C2211yescharacteristic
25#340×C131—21no—
26#340×C131—21no—
27D4⋊C8×C131—22no—
28C22×Q8×C131—21no—
29C22×D4×C131D411yescharacteristic
30C23×C4×C131—21no—
31C22×C8×C131—21no—
32C22×C8×C131—21no—
33C22×C8×C131—21no—
34C4⋊Q8×C131—21no—
35C4⋊Q8×C131—21no—
36C4⋊Q8×C131—21no—
37C4⋊Q8×C131C2×C412yes—
38C4×D4×C131—21no—
39C4×D4×C131—21no—
40C4×D4×C131C2×C412yes—
41C4×D4×C131D412yes—
42#117×C131—42no—
43#117×C131—42no—
44C2×C4⋊C4×C131—21no—
45C2×C4⋊C4×C131—21no—
46C2×C4⋊C4×C131—21no—
47C2×C4⋊C4×C131—21no—
48C2×C4⋊C4×C131D411yescharacteristic
49C2×C4⋊C4×C131D411yescharacteristic
50C2×C4⋊C4×C131D411yescharacteristic
51C2×C4⋊C4×C131D412yes—
52C2×C22⋊C4×C131—21no—
53C2×C22⋊C4×C131—22no—
54C2×C22⋊C4×C131—22no—
55C2×C42×C131—22no—
56C2×C42×C131—21no—
57C2×C42×C131C2311yescharacteristic
58#106×C131—24no—
59C4⋊C8×C131—21no—
60C4⋊C8×C131—21no—
61C4⋊C8×C131—21no—
62C4⋊C8×C131C2×C412yes—
63#103×C131—44no—
64#102×C131—24no—
65C4×C8×C131—21no—
66C4×C8×C131—21no—
67#95×C131—22no—
68#95×C131—21no—
69C24×C131—21no—
70C2×Q8×C131—22no—
71C2×Q8×C131—42no—
72C2×Q8×C131—42no—
73C2×Q8×C131—41no—
74C2×D4×C131—21no—
75C2×D4×C131—21no—
76C2×D4×C131—21no—
77C2×D4×C131—21no—
78C2×D4×C131—21no—
79C2×D4×C131C22⋊C412yes—
80C22×C4×C131—21no—
81C22×C4×C131—21no—
82C22×C4×C131—22no—
83C22×C4×C131—22no—
84C22×C4×C131—21no—
85C22×C4×C131—22no—
86C22×C4×C131—41no—
87C22×C4×C131—41no—
88C22×C4×C131—41no—
89C22×C4×C131—41no—
90C22×C4×C131—41no—
91C22×C4×C131C2×D411yescharacteristic
92C22×C4×C131C2×D411yescharacteristic
93C22×C4×C131C2×D411yescharacteristic
94C2×C8×C131—22no—
95C2×C8×C131—22no—
96C2×C8×C131—41no—
97C2×C8×C131—41no—
98C2×C8×C131—41no—
99C2×C8×C131—41no—
100C2×C8×C131—41no—
101C2×C8×C131—41no—
102C2×C8×C131—41no—
103C4⋊C4×C131—21no—
104C4⋊C4×C131—21no—
105C4⋊C4×C131—22no—
106C4⋊C4×C131—22no—
107C4⋊C4×C131—21no—
108C4⋊C4×C131—21no—
109C4⋊C4×C131—42no—
110C4⋊C4×C131—41no—
111C4⋊C4×C131—41no—
112C4⋊C4×C131—41no—
113C4⋊C4×C131—41no—
114C4⋊C4×C131—41no—
115C4⋊C4×C131—41no—
116C4⋊C4×C131C22⋊C412yes—
117C4⋊C4×C131SD1612yes—
118C22⋊C4×C131—22no—
119C22⋊C4×C131—22no—
120C22⋊C4×C131—44no—
121C22⋊C4×C131—82no—
122C42×C131—44no—
123C42×C131—41no—
124C42×C131—41no—
125C42×C131C22×C411yescharacteristic
126C42×C131C2×D411yescharacteristic
127C42×C131#4111yescharacteristic
128C42×C131#4111yescharacteristic
129C23×C131—22no—
130C23×C131—41no—
131C23×C131—41no—
132C23×C131—41no—
133C23×C131—41no—
134C23×C131—41no—
135C23×C131—41no—
136C23×C131#12011yescharacteristic
137Q8×C131—44no—
138Q8×C131—82no—
139D4×C131—22no—
140D4×C131—22no—
141D4×C131—41no—
142D4×C131—41no—
143C2×C4×C131—21no—
144C2×C4×C131—21no—
145C2×C4×C131—22no—
146C2×C4×C131—22no—
147C2×C4×C131—41no—
148C2×C4×C131—41no—
149C2×C4×C131—41no—
150C2×C4×C131—41no—
151C2×C4×C131—42no—
152C2×C4×C131—42no—
153C2×C4×C131—42no—
154C2×C4×C131—42no—
155C2×C4×C131—42no—
156C2×C4×C131—42no—
157C2×C4×C131—41no—
158C2×C4×C131—41no—
159C2×C4×C131—42no—
160C2×C4×C131—41no—
161C2×C4×C131—42no—
162C2×C4×C131—81no—
163C2×C4×C131—81no—
164C2×C4×C131C2×C22⋊C411yescharacteristic
165C2×C4×C131C4×D411yescharacteristic
166C2×C4×C131C4×D411yescharacteristic
167C2×C4×C131#12111yescharacteristic
168C2×C4×C131#12111yescharacteristic
169C2×C4×C131#12311yescharacteristic
170C2×C4×C131C2×SD1611yescharacteristic
171C2×C4×C131#13511yescharacteristic
172C2×C4×C131#13511yescharacteristic
173C2×C4×C131#13511yescharacteristic
174C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C131#13711yescharacteristic
176C2×C4×C131#13711yescharacteristic
177C2×C4×C131#13711yescharacteristic
178C8×C131—42no—
179C8×C131—42no—
180C8×C131—81no—
181C22×C131—42no—
182C22×C131—42no—
183C22×C131—42no—
184C22×C131—81no—
185C22×C131—81no—
186C22×C131—81no—
187C22×C131—81no—
188C22×C131#38611yescharacteristic
189C22×C131#45011yescharacteristic
190C22×C131#45211yescharacteristic
191C22×C131#45211yescharacteristic
192C22×C131#45211yescharacteristic
193C22×C131#45311yescharacteristic
194C22×C131#45411yescharacteristic
195C4×C131—21no—
196C4×C131—21no—
197C4×C131—42no—
198C4×C131—42no—
199C4×C131—82no—
200C4×C131—82no—
201C4×C131—81no—
202C4×C131#41611yescharacteristic
203C4×C131#41911yescharacteristic
204C4×C131C4×SD1611yescharacteristic
205C4×C131#44011yescharacteristic
206C4×C131#46111yescharacteristic
207C4×C131#46311yescharacteristic
208C4×C131#48511yescharacteristic
209C4×C131#48511yescharacteristic
210C2×C131—82no—
211C2×C131#163111yescharacteristic
212C2×C131#163411yescharacteristic
213C2×C131#163511yescharacteristic
214C2×C131#163811yescharacteristic
215C2×C131#187311yescharacteristic
216C2×C131#187711yescharacteristic
217C2×C131#188311yescharacteristic
218#8976C13111yesmaximal, characteristic, direct product factor, Sylow
219C131#897611yescharacteristic, direct product factor, Sylow
220C2×#476C2×C13111yescharacteristic
221#2354C2×C13111yescharacteristic
222#1987C2×C13111yescharacteristic, complemented
223#1956C2×C13111yescharacteristic, complemented
224C2×D4⋊C8C2×C13111yescharacteristic
225#1296C2×C13111yescharacteristic, complemented
226#1279C2×C13111yescharacteristic, complemented
227C2×C4⋊Q8C22×C13111yescharacteristic
228C2×C4×D4C22×C13111yescharacteristic
229C2×#117—21no—
230#476—22no—
231#476C4×C13114yescomplemented
232C2×#106—21no—
233C2×C4⋊C8C22×C13111yescharacteristic
234C2×C4⋊C8C22×C13111yescharacteristic
235C2×#103—22no—
236C2×#102—21no—
237C2×C4×C8C22×C13111yescharacteristic
238#390—21no—
239#388—22no—
240#384C22×C13111yescharacteristic
241#380—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4C22×C13111yescharacteristic
244#340—21no—
245#340—21no—
246D4⋊C8—22no—
247C22×Q8—21no—
248C22×D4D4×C13111yescharacteristic
249C23×C4—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8C2×C4×C13112yes—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4C2×C4×C13112yes—
260C4×D4D4×C13112yes—
261#117—42no—
262#117—42no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4D4×C13111yescharacteristic
268C2×C4⋊C4D4×C13111yescharacteristic
269C2×C4⋊C4D4×C13111yescharacteristic
270C2×C4⋊C4D4×C13112yes—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C42—22no—
275C2×C42—21no—
276C2×C42C23×C13111yescharacteristic
277#106—24no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8C2×C4×C13112yes—
282#103—44no—
283#102—24no—
284C4×C8—21no—
285C4×C8—21no—
286#95—22no—
287#95—21no—
288C24—21no—
289C2×Q8—22no—
290C2×Q8—42no—
291C2×Q8—42no—
292C2×Q8—41no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4C22⋊C4×C13112yes—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4C2×D4×C13111yescharacteristic
311C22×C4C2×D4×C13111yescharacteristic
312C22×C4C2×D4×C13111yescharacteristic
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4C22⋊C4×C13112yes—
336C4⋊C4SD16×C13112yes—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—44no—
340C22⋊C4—82no—
341C42—44no—
342C42—41no—
343C42—41no—
344C42C22×C4×C13111yescharacteristic
345C42C2×D4×C13111yescharacteristic
346C42#41×C13111yescharacteristic
347C42#41×C13111yescharacteristic
348C23—22no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23#120×C13111yescharacteristic
356Q8—44no—
357Q8—82no—
358D4—22no—
359D4—22no—
360D4—41no—
361D4—41no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4C2×C22⋊C4×C13111yescharacteristic
384C2×C4C4×D4×C13111yescharacteristic
385C2×C4C4×D4×C13111yescharacteristic
386C2×C4#121×C13111yescharacteristic
387C2×C4#121×C13111yescharacteristic
388C2×C4#123×C13111yescharacteristic
389C2×C4C2×SD16×C13111yescharacteristic
390C2×C4#135×C13111yescharacteristic
391C2×C4#135×C13111yescharacteristic
392C2×C4#135×C13111yescharacteristic
393C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
394C2×C4#137×C13111yescharacteristic
395C2×C4#137×C13111yescharacteristic
396C2×C4#137×C13111yescharacteristic
397C8—42no—
398C8—42no—
399C8—81no—
400C22—42no—
401C22—42no—
402C22—42no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22#386×C13111yescharacteristic
408C22#450×C13111yescharacteristic
409C22#452×C13111yescharacteristic
410C22#452×C13111yescharacteristic
411C22#452×C13111yescharacteristic
412C22#453×C13111yescharacteristic
413C22#454×C13111yescharacteristic
414C4—21no—
415C4—21no—
416C4—42no—
417C4—42no—
418C4—82no—
419C4—82no—
420C4—81no—
421C4#416×C13111yescharacteristic
422C4#419×C13111yescharacteristic
423C4C4×SD16×C13111yescharacteristic
424C4#440×C13111yescharacteristic
425C4#461×C13111yescharacteristic
426C4#463×C13111yescharacteristic
427C4#485×C13111yescharacteristic
428C4#485×C13111yescharacteristic
429C2—82no—
430C2#1631×C13111yescharacteristic
431C2#1634×C13111yescharacteristic
432C2#1635×C13111yescharacteristic
433C2#1638×C13111yescharacteristic
434C2#1873×C13111yescharacteristic
435C2#1877×C13111yescharacteristic
436C2#1883×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#120
commutatorC42C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1987×C131C2semidirect
4. #1956×C131C2semidirect
6. #1296×C131C2semidirect
7. #1279×C131C2semidirect
12. #476×C131C4semidirect
218. #8976C131direct (N × H)
219. C131#8976direct (N × H)
222. #1987C2×C131semidirect
223. #1956C2×C131semidirect
225. #1296C2×C131semidirect
226. #1279C2×C131semidirect
231. #476C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1312
#2354×C1312
#1987×C1312
#1956×C1312
C2×D4⋊C8×C1312
#1296×C1312
#1279×C1312
#8976131