Finite Group Databasebeta

← C131×#9179 #45695063

Subgroups — C131×#9179 #45695063

Order 33536.

620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3036×C131C211yesmaximal, characteristic
2#2349×C131C211yesmaximal, characteristic, complemented
3#1517×C131C211yesmaximal, characteristic, complemented
4#1502×C131C211yesmaximal, characteristic, complemented
5#1478×C131C211yesmaximal, characteristic, complemented
6#1303×C131C211yesmaximal, characteristic, complemented
7#1286×C131C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C131—21no—
9#532×C131C2211yescharacteristic
10C2×C4×D4×C131—21no—
11C2×C4×D4×C131C2211yescharacteristic
12#463×C131—22no—
13#461×C131C412yescomplemented
14#459×C131C412yescomplemented
15#431×C131C2211yescharacteristic
16#431×C131C2211yescharacteristic
17#423×C131C2211yescharacteristic
18#417×C131—21no—
19#389×C131—21no—
20#385×C131—22no—
21#382×C131C2211yescharacteristic
22#380×C131—21no—
23C4×C4⋊C4×C131C2211yescharacteristic
24C2×#95×C131—21no—
25#327×C131—21no—
26#327×C131—21no—
27#327×C131—22no—
28D4⋊C8×C131—22no—
29C2×#41×C131—21no—
30C22×D4×C131D411yescharacteristic
31C23×C4×C131—21no—
32C23×C4×C131—22no—
33AGL(1,ℤ/8)×C131—42no—
34AGL(1,ℤ/8)×C131—42no—
35C2×SD16×C131—22no—
36C2×D8×C131—22no—
37C2×M16×C131—21no—
38C4⋊Q8×C131C2×C411yescharacteristic, complemented
39#127×C131C2×C411yescharacteristic, complemented
40#124×C131—21no—
41#121×C131—21no—
42#121×C131—21no—
43C4×D4×C131—21no—
44C4×D4×C131—21no—
45C4×D4×C131—21no—
46C4×D4×C131—21no—
47C4×D4×C131—42no—
48C4×D4×C131—42no—
49C4×D4×C131C2×C412yes—
50C4×D4×C131D412yes—
51C2×C4⋊C4×C131—21no—
52C2×C4⋊C4×C131—21no—
53C2×C4⋊C4×C131—22no—
54C2×C4⋊C4×C131D411yescharacteristic
55C2×C22⋊C4×C131—21no—
56C2×C22⋊C4×C131—22no—
57C2×C42×C131—21no—
58C2×C42×C131C2311yescharacteristic
59C4⋊C8×C131—21no—
60C4⋊C8×C131—21no—
61C4⋊C8×C131—21no—
62C4⋊C8×C131C2×C412yescomplemented
63#103×C131—22no—
64#102×C131—22no—
65C22⋊C8×C131—21no—
66C22⋊C8×C131—21no—
67C4×C8×C131—21no—
68C4×C8×C131—21no—
69#95×C131—22no—
70#95×C131—21no—
71#95×C131D411yescharacteristic
72#95×C131D411yescharacteristic
73#95×C131D412yes—
74C24×C131—21no—
75#41×C131—41no—
76#41×C131—41no—
77#41×C131—41no—
78#41×C131—41no—
79C2×Q8×C131—21no—
80C2×D4×C131—21no—
81C2×D4×C131—21no—
82C2×D4×C131—21no—
83C2×D4×C131—21no—
84C2×D4×C131—21no—
85C2×D4×C131—21no—
86C2×D4×C131—41no—
87C2×D4×C131C22⋊C412yes—
88C2×D4×C131D812yes—
89C2×D4×C131SD1612yes—
90C22×C4×C131—21no—
91C22×C4×C131—21no—
92C22×C4×C131—22no—
93C22×C4×C131—22no—
94C22×C4×C131—22no—
95C22×C4×C131—21no—
96C22×C4×C131—44no—
97C22×C4×C131—44no—
98C22×C4×C131—41no—
99C22×C4×C131—82no—
100C22×C4×C131—82no—
101C22×C4×C131C2×D411yescharacteristic
102C22×C4×C131C2×D411yescharacteristic
103C22×C4×C131C2×D411yescharacteristic
104SD16×C131—44no—
105D8×C131—44no—
106M16×C131—41no—
107M16×C131—41no—
108C2×C8×C131—22no—
109C2×C8×C131—41no—
110C2×C8×C131—41no—
111C4⋊C4×C131—21no—
112C4⋊C4×C131—21no—
113C4⋊C4×C131—21no—
114C4⋊C4×C131—42no—
115C4⋊C4×C131—41no—
116C4⋊C4×C131—41no—
117C4⋊C4×C131—82no—
118C4⋊C4×C131C22⋊C412yes—
119C22⋊C4×C131—22no—
120C22⋊C4×C131—22no—
121C22⋊C4×C131—44no—
122C22⋊C4×C131—41no—
123C22⋊C4×C131—41no—
124C42×C131—41no—
125C42×C131—41no—
126C42×C131C22×C411yescharacteristic
127C42×C131C2×D411yescharacteristic
128C42×C131#4111yescharacteristic
129C42×C131#4111yescharacteristic
130C23×C131—22no—
131C23×C131—22no—
132C23×C131—22no—
133C23×C131—42no—
134C23×C131—42no—
135C23×C131—41no—
136C23×C131#12011yescharacteristic
137Q8×C131—41no—
138Q8×C131—41no—
139D4×C131—22no—
140D4×C131—22no—
141D4×C131—22no—
142D4×C131—41no—
143D4×C131—41no—
144D4×C131—81no—
145D4×C131—81no—
146D4×C131—81no—
147D4×C131—81no—
148D4×C131#10214yes—
149C2×C4×C131—22no—
150C2×C4×C131—22no—
151C2×C4×C131—41no—
152C2×C4×C131—41no—
153C2×C4×C131—42no—
154C2×C4×C131—41no—
155C2×C4×C131—41no—
156C2×C4×C131—41no—
157C2×C4×C131—41no—
158C2×C4×C131—42no—
159C2×C4×C131—42no—
160C2×C4×C131—41no—
161C2×C4×C131—41no—
162C2×C4×C131—42no—
163C2×C4×C131—82no—
164C2×C4×C131—82no—
165C2×C4×C131—88no—
166C2×C4×C131—81no—
167C2×C4×C131—81no—
168C2×C4×C131C2×C22⋊C411yescharacteristic
169C2×C4×C131C4×D411yescharacteristic
170C2×C4×C131C4×D411yescharacteristic
171C2×C4×C131#12111yescharacteristic
172C2×C4×C131#12111yescharacteristic
173C2×C4×C131#12311yescharacteristic
174C2×C4×C131C2×D811yescharacteristic
175C2×C4×C131C2×SD1611yescharacteristic
176C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C131#13711yescharacteristic
178C8×C131—42no—
179C8×C131—81no—
180C8×C131—81no—
181C22×C131—21no—
182C22×C131—21no—
183C22×C131—24no—
184C22×C131—44no—
185C22×C131—44no—
186C22×C131—42no—
187C22×C131—42no—
188C22×C131—81no—
189C22×C131—81no—
190C22×C131—81no—
191C22×C131#38611yescharacteristic
192C22×C131#44711yescharacteristic
193C22×C131#44811yescharacteristic
194C4×C131—21no—
195C4×C131—21no—
196C4×C131—21no—
197C4×C131—21no—
198C4×C131—42no—
199C4×C131—42no—
200C4×C131—81no—
201C4×C131—82no—
202C4×C131—81no—
203C4×C131C2×#10211yescharacteristic
204C4×C131#41711yescharacteristic
205C4×C131#48011yescharacteristic
206C4×C131#48111yescharacteristic
207C2×C131—21no—
208C2×C131—21no—
209C2×C131—44no—
210C2×C131—161no—
211C2×C131#187411yescharacteristic
212C2×C131#190411yescharacteristic
213C2×C131#190611yescharacteristic
214#9179C13111yesmaximal, characteristic, direct product factor, Sylow
215C131#917911yescharacteristic, direct product factor, Sylow
216#3036C2×C13111yescharacteristic
217#2349C2×C13111yescharacteristic, complemented
218#1517C2×C13111yescharacteristic, complemented
219#1502C2×C13111yescharacteristic, complemented
220#1478C2×C13111yescharacteristic, complemented
221#1303C2×C13111yescharacteristic, complemented
222#1286C2×C13111yescharacteristic, complemented
223C2×AGL(1,ℤ/8)—21no—
224#532C22×C13111yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4C22×C13111yescharacteristic
227#463—22no—
228#461C4×C13112yescomplemented
229#459C4×C13112yescomplemented
230#431C22×C13111yescharacteristic
231#431C22×C13111yescharacteristic
232#423C22×C13111yescharacteristic
233#417—21no—
234#389—21no—
235#385—22no—
236#382C22×C13111yescharacteristic
237#380—21no—
238C4×C4⋊C4C22×C13111yescharacteristic
239C2×#95—21no—
240#327—21no—
241#327—21no—
242#327—22no—
243D4⋊C8—22no—
244C2×#41—21no—
245C22×D4D4×C13111yescharacteristic
246C23×C4—21no—
247C23×C4—22no—
248AGL(1,ℤ/8)—42no—
249AGL(1,ℤ/8)—42no—
250C2×SD16—22no—
251C2×D8—22no—
252C2×M16—21no—
253C4⋊Q8C2×C4×C13111yescharacteristic, complemented
254#127C2×C4×C13111yescharacteristic, complemented
255#124—21no—
256#121—21no—
257#121—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—42no—
263C4×D4—42no—
264C4×D4C2×C4×C13112yes—
265C4×D4D4×C13112yes—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4D4×C13111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C42—21no—
273C2×C42C23×C13111yescharacteristic
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8C2×C4×C13112yescomplemented
278#103—22no—
279#102—22no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C4×C8—21no—
283C4×C8—21no—
284#95—22no—
285#95—21no—
286#95D4×C13111yescharacteristic
287#95D4×C13111yescharacteristic
288#95D4×C13112yes—
289C24—21no—
290#41—41no—
291#41—41no—
292#41—41no—
293#41—41no—
294C2×Q8—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4C22⋊C4×C13112yes—
303C2×D4D8×C13112yes—
304C2×D4SD16×C13112yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—44no—
312C22×C4—44no—
313C22×C4—41no—
314C22×C4—82no—
315C22×C4—82no—
316C22×C4C2×D4×C13111yescharacteristic
317C22×C4C2×D4×C13111yescharacteristic
318C22×C4C2×D4×C13111yescharacteristic
319SD16—44no—
320D8—44no—
321M16—41no—
322M16—41no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—42no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—82no—
333C4⋊C4C22⋊C4×C13112yes—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—44no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C42—41no—
340C42—41no—
341C42C22×C4×C13111yescharacteristic
342C42C2×D4×C13111yescharacteristic
343C42#41×C13111yescharacteristic
344C42#41×C13111yescharacteristic
345C23—22no—
346C23—22no—
347C23—22no—
348C23—42no—
349C23—42no—
350C23—41no—
351C23#120×C13111yescharacteristic
352Q8—41no—
353Q8—41no—
354D4—22no—
355D4—22no—
356D4—22no—
357D4—41no—
358D4—41no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4#102×C13114yes—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—88no—
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×D8×C13111yescharacteristic
390C2×C4C2×SD16×C13111yescharacteristic
391C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
392C2×C4#137×C13111yescharacteristic
393C8—42no—
394C8—81no—
395C8—81no—
396C22—21no—
397C22—21no—
398C22—24no—
399C22—44no—
400C22—44no—
401C22—42no—
402C22—42no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22#386×C13111yescharacteristic
407C22#447×C13111yescharacteristic
408C22#448×C13111yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—42no—
414C4—42no—
415C4—82no—
416C4—81no—
417C4—81no—
418C4C2×#102×C13111yescharacteristic
419C4#417×C13111yescharacteristic
420C4#480×C13111yescharacteristic
421C4#481×C13111yescharacteristic
422C2—21no—
423C2—21no—
424C2—44no—
425C2—161no—
426C2#1874×C13111yescharacteristic
427C2#1904×C13111yescharacteristic
428C2#1906×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC42C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radical#3036×C131C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2349×C131C2semidirect
3. #1517×C131C2semidirect
4. #1502×C131C2semidirect
5. #1478×C131C2semidirect
6. #1303×C131C2semidirect
7. #1286×C131C2semidirect
13. #461×C131C4semidirect
14. #459×C131C4semidirect
38. C4⋊Q8×C131C2×C4semidirect
39. #127×C131C2×C4semidirect
62. C4⋊C8×C131C2×C4semidirect
214. #9179C131direct (N × H)
215. C131#9179direct (N × H)
217. #2349C2×C131semidirect
218. #1517C2×C131semidirect
219. #1502C2×C131semidirect
220. #1478C2×C131semidirect
221. #1303C2×C131semidirect
222. #1286C2×C131semidirect
228. #461C4×C131semidirect
229. #459C4×C131semidirect
253. C4⋊Q8C2×C4×C131semidirect
254. #127C2×C4×C131semidirect
277. C4⋊C8C2×C4×C131semidirect

Maximal subgroups

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

subgroupindex
#3036×C1312
#2349×C1312
#1517×C1312
#1502×C1312
#1478×C1312
#1303×C1312
#1286×C1312
#9179131