Finite Group Databasebeta

← C131×#9219 #45695103

Subgroups — C131×#9219 #45695103

Order 33536.

594 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C131C211yesmaximal, characteristic
2C2×C8×D4×C131C211yesmaximal, characteristic
3#1956×C131C211yesmaximal, characteristic, complemented
4#1802×C131C211yesmaximal, characteristic
5C2×#332×C131C211yesmaximal, characteristic, complemented
6#1296×C131C211yesmaximal, characteristic, complemented
7#1277×C131C211yesmaximal, characteristic, complemented
8C23×C8×C131—21no—
9C2×C4⋊Q8×C131C2211yescharacteristic
10C2×C4×D4×C131C2211yescharacteristic
11#474×C131—22no—
12#474×C131C414yescomplemented
13C8×D4×C131—22no—
14C8×D4×C131—22no—
15C2×#107×C131—21no—
16C2×C4⋊C8×C131C2211yescharacteristic
17C2×C4⋊C8×C131C2211yescharacteristic
18C2×C4⋊C8×C131C2211yescharacteristic
19C2×#103×C131—21no—
20C2×#103×C131—21no—
21C2×#102×C131—21no—
22C2×#102×C131—21no—
23C2×C22⋊C8×C131—21no—
24C2×C4×C8×C131C2211yescharacteristic
25#384×C131C2211yescharacteristic
26#340×C131—21no—
27#332×C131—22no—
28C22×Q8×C131—21no—
29C22×D4×C131D411yescharacteristic
30C23×C4×C131—21no—
31C22×C8×C131—24no—
32C22×C8×C131—21no—
33C22×C8×C131—21no—
34C22×C8×C131—21no—
35C22×C8×C131—42no—
36C22×C8×C131—42no—
37C22×C8×C131D411yescharacteristic
38C22×C8×C131D411yescharacteristic
39C4⋊Q8×C131—21no—
40C4⋊Q8×C131—21no—
41C4⋊Q8×C131—21no—
42C4⋊Q8×C131C2×C412yes—
43C4×D4×C131—21no—
44C4×D4×C131—21no—
45C4×D4×C131C2×C412yes—
46C4×D4×C131D412yes—
47C2×C4⋊C4×C131—21no—
48C2×C4⋊C4×C131—21no—
49C2×C4⋊C4×C131—21no—
50C2×C4⋊C4×C131—21no—
51C2×C4⋊C4×C131—21no—
52C2×C4⋊C4×C131D411yescharacteristic
53C2×C22⋊C4×C131—21no—
54C2×C42×C131C2311yescharacteristic
55#107×C131—24no—
56C4⋊C8×C131—21no—
57C4⋊C8×C131—21no—
58C4⋊C8×C131—21no—
59C4⋊C8×C131—21no—
60C4⋊C8×C131C2×C412yes—
61C4⋊C8×C131D412yes—
62#103×C131—42no—
63#103×C131—42no—
64#102×C131—24no—
65#102×C131—42no—
66C22⋊C8×C131—24no—
67C4×C8×C131—21no—
68C4×C8×C131—21no—
69C24×C131—21no—
70C2×Q8×C131—22no—
71C2×Q8×C131—41no—
72C2×Q8×C131—41no—
73C2×Q8×C131—41no—
74C2×Q8×C131—41no—
75C2×Q8×C131—41no—
76C2×D4×C131—21no—
77C2×D4×C131—21no—
78C2×D4×C131—21no—
79C2×D4×C131C22⋊C412yes—
80C2×D4×C131SD1612yes—
81C2×D4×C131Q1612yes—
82C22×C4×C131—21no—
83C22×C4×C131—22no—
84C22×C4×C131—22no—
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×C131C2×D411yescharacteristic
92C22×C4×C131C2×D411yescharacteristic
93C22×C4×C131#4111yescharacteristic
94C2×C8×C131—21no—
95C2×C8×C131—21no—
96C2×C8×C131—22no—
97C2×C8×C131—21no—
98C2×C8×C131—22no—
99C2×C8×C131—21no—
100C2×C8×C131—21no—
101C2×C8×C131—48no—
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×C131D812yes—
110C4⋊C4×C131—21no—
111C4⋊C4×C131—22no—
112C4⋊C4×C131—22no—
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—
120C4⋊C4×C131C22⋊C412yes—
121C22⋊C4×C131—22no—
122C22⋊C4×C131—22no—
123C42×C131C22×C411yescharacteristic
124C42×C131C2×D411yescharacteristic
125C42×C131C2×D411yescharacteristic
126C42×C131#4111yescharacteristic
127C23×C131—22no—
128C23×C131—22no—
129C23×C131—22no—
130C23×C131—41no—
131C23×C131—41no—
132C23×C131—41no—
133C23×C131—41no—
134C23×C131#12111yescharacteristic
135Q8×C131—42no—
136Q8×C131—42no—
137Q8×C131—81no—
138Q8×C131—81no—
139D4×C131—22no—
140D4×C131—22no—
141D4×C131—22no—
142D4×C131#10314yescomplemented
143C2×C4×C131—21no—
144C2×C4×C131—21no—
145C2×C4×C131—22no—
146C2×C4×C131—41no—
147C2×C4×C131—41no—
148C2×C4×C131—42no—
149C2×C4×C131—42no—
150C2×C4×C131—42no—
151C2×C4×C131—42no—
152C2×C4×C131—42no—
153C2×C4×C131—81no—
154C2×C4×C131—81no—
155C2×C4×C131—81no—
156C2×C4×C131—81no—
157C2×C4×C131—81no—
158C2×C4×C131C2×C22⋊C411yescharacteristic
159C2×C4×C131C4×D411yescharacteristic
160C2×C4×C131C4×D411yescharacteristic
161C2×C4×C131#12011yescharacteristic
162C2×C4×C131#12111yescharacteristic
163C2×C4×C131#12311yescharacteristic
164C2×C4×C131C2×D811yescharacteristic
165C2×C4×C131C2×SD1611yescharacteristic
166C2×C4×C131C2×Q1611yescharacteristic
167C2×C4×C131#13511yescharacteristic
168C2×C4×C131#13511yescharacteristic
169C2×C4×C131#13511yescharacteristic
170C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
172C8×C131—22no—
173C8×C131—42no—
174C8×C131—42no—
175C8×C131—41no—
176C8×C131—81no—
177C22×C131—24no—
178C22×C131—42no—
179C22×C131—42no—
180C22×C131—42no—
181C22×C131—42no—
182C22×C131—42no—
183C22×C131—42no—
184C22×C131#38611yescharacteristic
185C22×C131#45911yescharacteristic
186C22×C131#46311yescharacteristic
187C22×C131#46511yescharacteristic
188C22×C131#46711yescharacteristic
189C22×C131#47111yescharacteristic
190C22×C131#47311yescharacteristic
191C4×C131—21no—
192C4×C131—21no—
193C4×C131—42no—
194C4×C131—82no—
195C4×C131—161no—
196C4×C131C2×#10311yescharacteristic
197C4×C131#41611yescharacteristic
198C4×C131C4×D811yescharacteristic
199C4×C131#44211yescharacteristic
200C4×C131#44711yescharacteristic
201C4×C131#44911yescharacteristic
202C4×C131#46511yescharacteristic
203C4×C131#46711yescharacteristic
204C2×C131—44no—
205C2×C131#166511yescharacteristic
206C2×C131#166911yescharacteristic
207C2×C131#167911yescharacteristic
208C2×C131#168311yescharacteristic
209C2×C131#187911yescharacteristic
210C2×C131#189211yescharacteristic
211C2×C131#190811yescharacteristic
212#9219C13111yesmaximal, characteristic, direct product factor, Sylow
213C131#921911yescharacteristic, direct product factor, Sylow
214C2×#474C2×C13111yescharacteristic
215C2×C8×D4C2×C13111yescharacteristic
216#1956C2×C13111yescharacteristic, complemented
217#1802C2×C13111yescharacteristic
218C2×#332C2×C13111yescharacteristic, complemented
219#1296C2×C13111yescharacteristic, complemented
220#1277C2×C13111yescharacteristic, complemented
221C23×C8—21no—
222C2×C4⋊Q8C22×C13111yescharacteristic
223C2×C4×D4C22×C13111yescharacteristic
224#474—22no—
225#474C4×C13114yescomplemented
226C8×D4—22no—
227C8×D4—22no—
228C2×#107—21no—
229C2×C4⋊C8C22×C13111yescharacteristic
230C2×C4⋊C8C22×C13111yescharacteristic
231C2×C4⋊C8C22×C13111yescharacteristic
232C2×#103—21no—
233C2×#103—21no—
234C2×#102—21no—
235C2×#102—21no—
236C2×C22⋊C8—21no—
237C2×C4×C8C22×C13111yescharacteristic
238#384C22×C13111yescharacteristic
239#340—21no—
240#332—22no—
241C22×Q8—21no—
242C22×D4D4×C13111yescharacteristic
243C23×C4—21no—
244C22×C8—24no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—42no—
249C22×C8—42no—
250C22×C8D4×C13111yescharacteristic
251C22×C8D4×C13111yescharacteristic
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8C2×C4×C13112yes—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C2×C4×C13112yes—
259C4×D4D4×C13112yes—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C13111yescharacteristic
266C2×C22⋊C4—21no—
267C2×C42C23×C13111yescharacteristic
268#107—24no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8C2×C4×C13112yes—
274C4⋊C8D4×C13112yes—
275#103—42no—
276#103—42no—
277#102—24no—
278#102—42no—
279C22⋊C8—24no—
280C4×C8—21no—
281C4×C8—21no—
282C24—21no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4C22⋊C4×C13112yes—
293C2×D4SD16×C13112yes—
294C2×D4Q16×C13112yes—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4C2×D4×C13111yescharacteristic
305C22×C4C2×D4×C13111yescharacteristic
306C22×C4#41×C13111yescharacteristic
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—48no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8D8×C13112yes—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—81no—
333C4⋊C4C22⋊C4×C13112yes—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C42C22×C4×C13111yescharacteristic
337C42C2×D4×C13111yescharacteristic
338C42C2×D4×C13111yescharacteristic
339C42#41×C13111yescharacteristic
340C23—22no—
341C23—22no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#121×C13111yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352D4—22no—
353D4—22no—
354D4—22no—
355D4#103×C13114yescomplemented
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4C2×C22⋊C4×C13111yescharacteristic
372C2×C4C4×D4×C13111yescharacteristic
373C2×C4C4×D4×C13111yescharacteristic
374C2×C4#120×C13111yescharacteristic
375C2×C4#121×C13111yescharacteristic
376C2×C4#123×C13111yescharacteristic
377C2×C4C2×D8×C13111yescharacteristic
378C2×C4C2×SD16×C13111yescharacteristic
379C2×C4C2×Q16×C13111yescharacteristic
380C2×C4#135×C13111yescharacteristic
381C2×C4#135×C13111yescharacteristic
382C2×C4#135×C13111yescharacteristic
383C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
384C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
385C8—22no—
386C8—42no—
387C8—42no—
388C8—41no—
389C8—81no—
390C22—24no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22#386×C13111yescharacteristic
398C22#459×C13111yescharacteristic
399C22#463×C13111yescharacteristic
400C22#465×C13111yescharacteristic
401C22#467×C13111yescharacteristic
402C22#471×C13111yescharacteristic
403C22#473×C13111yescharacteristic
404C4—21no—
405C4—21no—
406C4—42no—
407C4—82no—
408C4—161no—
409C4C2×#103×C13111yescharacteristic
410C4#416×C13111yescharacteristic
411C4C4×D8×C13111yescharacteristic
412C4#442×C13111yescharacteristic
413C4#447×C13111yescharacteristic
414C4#449×C13111yescharacteristic
415C4#465×C13111yescharacteristic
416C4#467×C13111yescharacteristic
417C2—44no—
418C2#1665×C13111yescharacteristic
419C2#1669×C13111yescharacteristic
420C2#1679×C13111yescharacteristic
421C2#1683×C13111yescharacteristic
422C2#1879×C13111yescharacteristic
423C2#1892×C13111yescharacteristic
424C2#1908×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#121
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. #1956×C131C2semidirect
5. C2×#332×C131C2semidirect
6. #1296×C131C2semidirect
7. #1277×C131C2semidirect
12. #474×C131C4semidirect
142. D4×C131#103semidirect
212. #9219C131direct (N × H)
213. C131#9219direct (N × H)
216. #1956C2×C131semidirect
218. C2×#332C2×C131semidirect
219. #1296C2×C131semidirect
220. #1277C2×C131semidirect
225. #474C4×C131semidirect
355. D4#103×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C1312
C2×C8×D4×C1312
#1956×C1312
#1802×C1312
C2×#332×C1312
#1296×C1312
#1277×C1312
#9219131