Finite Group Databasebeta

← C131×#29915 #45715799

Subgroups — C131×#29915 #45715799

Order 33536.

706 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2855×C131C211yesmaximal, characteristic
2#2285×C131C211yesmaximal, characteristic
3#2100×C131C211yesmaximal, characteristic, complemented
4#2099×C131C211yesmaximal, characteristic, complemented
5#2096×C131C211yesmaximal, characteristic, complemented
6#2095×C131C211yesmaximal, characteristic, complemented
7#2085×C131C212yesmaximal, complemented
8#2074×C131C212yesmaximal, complemented
9#1873×C131C212yesmaximal
10#1854×C131C212yesmaximal
11#1817×C131C211yesmaximal, characteristic
12C2×C22⋊Q8×C131C2211yescharacteristic
13C2×#117×C131C2212yes—
14C22×C42×C131C2211yescharacteristic
15C2×#107×C131C2212yes—
16C2×#106×C131C2212yes—
17C2×#103×C131C2212yes—
18C2×#103×C131C2212yes—
19C2×C22⋊C8×C131C2212yes—
20#391×C131C2211yescharacteristic
21#391×C131C2211yescharacteristic
22#389×C131C2211yescharacteristic
23#389×C131C2211yescharacteristic
24#387×C131—21no—
25#387×C131—21no—
26#385×C131—21no—
27#384×C131C2211yescharacteristic
28#384×C131C2211yescharacteristic
29#382×C131C2212yes—
30#381×C131—21no—
31#380×C131—21no—
32#380×C131—21no—
33#380×C131C2211yescharacteristic
34C4×C4⋊C4×C131—21no—
35C4×C4⋊C4×C131—21no—
36#340×C131C2212yes—
37#340×C131C2212yes—
38#340×C131C2212yes—
39#340×C131C2212yes—
40#336×C131C2212yes—
41#336×C131C2211yescharacteristic
42#336×C131C2211yescharacteristic
43C22×Q8×C131C2311yescharacteristic
44C23×C4×C131D411yescharacteristic
45C23×C4×C131D411yescharacteristic
46C23×C4×C131C2311yescharacteristic
47C22×C8×C131C2312yes—
48C22×C8×C131C2312yes—
49C22⋊Q8×C131—24no—
50#117×C131—42no—
51#117×C131—42no—
52C2×C4⋊C4×C131—21no—
53C2×C4⋊C4×C131—21no—
54C2×C4⋊C4×C131—21no—
55C2×C4⋊C4×C131—21no—
56C2×C4⋊C4×C131—21no—
57C2×C4⋊C4×C131—21no—
58C2×C4⋊C4×C131—21no—
59C2×C4⋊C4×C131C2311yescharacteristic
60C2×C4⋊C4×C131C2311yescharacteristic
61C2×C4⋊C4×C131C2311yescharacteristic
62C2×C4⋊C4×C131C2312yes—
63C2×C4⋊C4×C131C2312yes—
64C2×C22⋊C4×C131—22no—
65C2×C22⋊C4×C131—21no—
66C2×C22⋊C4×C131—21no—
67C2×C42×C131—24no—
68C2×C42×C131—22no—
69C2×C42×C131D411yescharacteristic
70C2×C42×C131D411yescharacteristic
71C2×C42×C131C2311yescharacteristic
72C2×C42×C131C2311yescharacteristic
73#107×C131—42no—
74#106×C131—42no—
75#103×C131—42no—
76#103×C131—42no—
77C22⋊C8×C131—24no—
78#95×C131—21no—
79#95×C131—21no—
80#95×C131—21no—
81#95×C131—21no—
82#95×C131—21no—
83#95×C131—21no—
84#95×C131—22no—
85#95×C131—22no—
86#95×C131—21no—
87C24×C131C2×D411yescharacteristic
88C2×Q8×C131—22no—
89C2×Q8×C131—22no—
90C2×Q8×C131—21no—
91C2×Q8×C131—21no—
92C22×C4×C131—22no—
93C22×C4×C131—21no—
94C22×C4×C131—21no—
95C22×C4×C131—22no—
96C22×C4×C131—22no—
97C22×C4×C131—22no—
98C22×C4×C131—22no—
99C22×C4×C131—21no—
100C22×C4×C131—21no—
101C22×C4×C131—21no—
102C22×C4×C131—22no—
103C22×C4×C131—22no—
104C22×C4×C131—21no—
105C22×C4×C131—41no—
106C22×C4×C131—41no—
107C22×C4×C131C2×D411yescharacteristic
108C22×C4×C131C2×D411yescharacteristic
109C22×C4×C131C2×D411yescharacteristic
110C22×C4×C131C2×D411yescharacteristic
111C22×C4×C131C2×D411yescharacteristic
112C22×C4×C131#4114yes—
113C22×C4×C131C2411yescharacteristic
114C2×C8×C131—22no—
115C2×C8×C131—22no—
116C2×C8×C131—22no—
117C2×C8×C131—22no—
118C2×C8×C131—22no—
119C2×C8×C131—22no—
120C4⋊C4×C131—22no—
121C4⋊C4×C131—22no—
122C4⋊C4×C131—22no—
123C4⋊C4×C131—22no—
124C4⋊C4×C131—22no—
125C4⋊C4×C131—22no—
126C4⋊C4×C131—21no—
127C4⋊C4×C131—21no—
128C4⋊C4×C131—42no—
129C4⋊C4×C131—42no—
130C4⋊C4×C131—42no—
131C4⋊C4×C131—42no—
132C4⋊C4×C131—42no—
133C4⋊C4×C131—42no—
134C4⋊C4×C131—42no—
135C22⋊C4×C131—42no—
136C22⋊C4×C131—44no—
137C22⋊C4×C131—42no—
138C42×C131—22no—
139C42×C131—22no—
140C42×C131—22no—
141C42×C131—22no—
142C42×C131—44no—
143C23×C131—21no—
144C23×C131—21no—
145C23×C131—21no—
146C23×C131—21no—
147C23×C131—21no—
148C23×C131—21no—
149C23×C131#12312yes—
150C23×C131C22×D411yescharacteristic
151Q8×C131—42no—
152Q8×C131—42no—
153C2×C4×C131—21no—
154C2×C4×C131—21no—
155C2×C4×C131—21no—
156C2×C4×C131—21no—
157C2×C4×C131—21no—
158C2×C4×C131—21no—
159C2×C4×C131—24no—
160C2×C4×C131—24no—
161C2×C4×C131—21no—
162C2×C4×C131—21no—
163C2×C4×C131—21no—
164C2×C4×C131—21no—
165C2×C4×C131—21no—
166C2×C4×C131—21no—
167C2×C4×C131—44no—
168C2×C4×C131—44no—
169C2×C4×C131—41no—
170C2×C4×C131—41no—
171C2×C4×C131—42no—
172C2×C4×C131—42no—
173C2×C4×C131—41no—
174C2×C4×C131—41no—
175C2×C4×C131—41no—
176C2×C4×C131—41no—
177C2×C4×C131—41no—
178C2×C4×C131—42no—
179C2×C4×C131—41no—
180C2×C4×C131—42no—
181C2×C4×C131—41no—
182C2×C4×C131—41no—
183C2×C4×C131—41no—
184C2×C4×C131—41no—
185C2×C4×C131—42no—
186C2×C4×C131—42no—
187C2×C4×C131#12312yes—
188C2×C4×C131#13512yes—
189C2×C4×C131#13712yes—
190C2×C4×C131C2×#4112yes—
191C2×C4×C131H(5,𝔽2)12yes—
192C2×C4×C1312−1+411yescharacteristic
193C2×C4×C1312−1+411yescharacteristic
194C8×C131—42no—
195C8×C131—42no—
196C22×C131—22no—
197C22×C131—22no—
198C22×C131—22no—
199C22×C131—41no—
200C22×C131—41no—
201C22×C131—41no—
202C22×C131—41no—
203C22×C131C2×#12311yescharacteristic
204C22×C131#53511yescharacteristic
205C22×C131#53611yescharacteristic
206C22×C131C2×#13511yescharacteristic
207C22×C131C2×#13711yescharacteristic
208C22×C131#57511yescharacteristic
209C22×C131#57511yescharacteristic
210C4×C131—22no—
211C4×C131—22no—
212C4×C131—22no—
213C4×C131—41no—
214C4×C131—41no—
215C4×C131—81no—
216C4×C131—81no—
217C4×C131—82no—
218C4×C131—82no—
219C4×C131—81no—
220C4×C131—81no—
221C4×C131#53912yes—
222C4×C131#53912yes—
223C2×C131—42no—
224C2×C131#262311yescharacteristic
225C2×C131#309111yescharacteristic
226C2×C131#309511yescharacteristic
227C2×C131#321011yescharacteristic
228C2×C131#321911yescharacteristic
229C2×C131#323311yescharacteristic
230C2×C131#323711yescharacteristic
231#29915C13111yesmaximal, characteristic, direct product factor, Sylow
232C131#2991511yescharacteristic, direct product factor, Sylow
233#2855C2×C13111yescharacteristic
234#2285C2×C13111yescharacteristic
235#2100C2×C13111yescharacteristic, complemented
236#2099C2×C13111yescharacteristic, complemented
237#2096C2×C13111yescharacteristic, complemented
238#2095C2×C13111yescharacteristic, complemented
239#2085C2×C13112yescomplemented
240#2074C2×C13112yescomplemented
241#1873C2×C13112yes—
242#1854C2×C13112yes—
243#1817C2×C13111yescharacteristic
244C2×C22⋊Q8C22×C13111yescharacteristic
245C2×#117C22×C13112yes—
246C22×C42C22×C13111yescharacteristic
247C2×#107C22×C13112yes—
248C2×#106C22×C13112yes—
249C2×#103C22×C13112yes—
250C2×#103C22×C13112yes—
251C2×C22⋊C8C22×C13112yes—
252#391C22×C13111yescharacteristic
253#391C22×C13111yescharacteristic
254#389C22×C13111yescharacteristic
255#389C22×C13111yescharacteristic
256#387—21no—
257#387—21no—
258#385—21no—
259#384C22×C13111yescharacteristic
260#384C22×C13111yescharacteristic
261#382C22×C13112yes—
262#381—21no—
263#380—21no—
264#380—21no—
265#380C22×C13111yescharacteristic
266C4×C4⋊C4—21no—
267C4×C4⋊C4—21no—
268#340C22×C13112yes—
269#340C22×C13112yes—
270#340C22×C13112yes—
271#340C22×C13112yes—
272#336C22×C13112yes—
273#336C22×C13111yescharacteristic
274#336C22×C13111yescharacteristic
275C22×Q8C23×C13111yescharacteristic
276C23×C4D4×C13111yescharacteristic
277C23×C4D4×C13111yescharacteristic
278C23×C4C23×C13111yescharacteristic
279C22×C8C23×C13112yes—
280C22×C8C23×C13112yes—
281C22⋊Q8—24no—
282#117—42no—
283#117—42no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4C23×C13112yes—
292C2×C4⋊C4C23×C13112yes—
293C2×C4⋊C4C23×C13111yescharacteristic
294C2×C4⋊C4C23×C13111yescharacteristic
295C2×C4⋊C4C23×C13111yescharacteristic
296C2×C22⋊C4—22no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C42—24no—
300C2×C42—22no—
301C2×C42D4×C13111yescharacteristic
302C2×C42D4×C13111yescharacteristic
303C2×C42C23×C13111yescharacteristic
304C2×C42C23×C13111yescharacteristic
305#107—42no—
306#106—42no—
307#103—42no—
308#103—42no—
309C22⋊C8—24no—
310#95—22no—
311#95—22no—
312#95—21no—
313#95—21no—
314#95—21no—
315#95—21no—
316#95—21no—
317#95—21no—
318#95—21no—
319C24C2×D4×C13111yescharacteristic
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—21no—
323C2×Q8—21no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4C2×D4×C13111yescharacteristic
340C22×C4C2×D4×C13111yescharacteristic
341C22×C4C2×D4×C13111yescharacteristic
342C22×C4C2×D4×C13111yescharacteristic
343C22×C4C2×D4×C13111yescharacteristic
344C22×C4#41×C13114yes—
345C22×C4C24×C13111yescharacteristic
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C22⋊C4—42no—
368C22⋊C4—44no—
369C22⋊C4—42no—
370C42—22no—
371C42—22no—
372C42—22no—
373C42—22no—
374C42—44no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23#123×C13112yes—
382C23C22×D4×C13111yescharacteristic
383Q8—42no—
384Q8—42no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4#123×C13112yes—
420C2×C4#135×C13112yes—
421C2×C4#137×C13112yes—
422C2×C4C2×#41×C13112yes—
423C2×C4H(5,𝔽2)×C13112yes—
424C2×C42−1+4×C13111yescharacteristic
425C2×C42−1+4×C13111yescharacteristic
426C8—42no—
427C8—42no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22C2×#123×C13111yescharacteristic
436C22#535×C13111yescharacteristic
437C22#536×C13111yescharacteristic
438C22C2×#135×C13111yescharacteristic
439C22C2×#137×C13111yescharacteristic
440C22#575×C13111yescharacteristic
441C22#575×C13111yescharacteristic
442C4—22no—
443C4—22no—
444C4—22no—
445C4—41no—
446C4—41no—
447C4—81no—
448C4—81no—
449C4—82no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4#539×C13112yes—
454C4#539×C13112yes—
455C2—42no—
456C2#2623×C13111yescharacteristic
457C2#3091×C13111yescharacteristic
458C2#3095×C13111yescharacteristic
459C2#3210×C13111yescharacteristic
460C2#3219×C13111yescharacteristic
461C2#3233×C13111yescharacteristic
462C2#3237×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC24×C131C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2100×C131C2semidirect
4. #2099×C131C2semidirect
5. #2096×C131C2semidirect
6. #2095×C131C2semidirect
7. #2085×C131C2semidirect
8. #2074×C131C2semidirect
231. #29915C131direct (N × H)
232. C131#29915direct (N × H)
235. #2100C2×C131semidirect
236. #2099C2×C131semidirect
237. #2096C2×C131semidirect
238. #2095C2×C131semidirect
239. #2085C2×C131semidirect
240. #2074C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2855×C1312
#2285×C1312
#2100×C1312
#2099×C1312
#2096×C1312
#2095×C1312
#2085×C1312
#2074×C1312
#1873×C1312
#1854×C1312
#1817×C1312
#29915131