Finite Group Databasebeta

← C131×#19469 #45705353

Subgroups — C131×#19469 #45705353

Order 33536.

610 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#3206×C131C211yesmaximal, characteristic
2#3112×C131C211yesmaximal, characteristic
3C2×#475×C131C211yesmaximal, characteristic, complemented
4#2984×C131C211yesmaximal, characteristic, complemented
5#1704×C131C212yesmaximal, complemented
6#1686×C131C212yesmaximal, complemented
7#1684×C131C212yesmaximal, complemented
8#1666×C131C212yesmaximal, complemented
9#1573×C131C211yesmaximal, characteristic, complemented
10#1556×C131C211yesmaximal, characteristic, complemented
11#1551×C131C211yesmaximal, characteristic
12#532×C131C2211yescharacteristic
13C2×C4⋊Q8×C131C2211yescharacteristic
14C2×C4×Q8×C131C2211yescharacteristic
15#492×C131C2212yes—
16#487×C131C2212yes—
17#480×C131—21no—
18#477×C131C2211yescharacteristic
19#477×C131C2211yescharacteristic
20#475×C131—21no—
21#475×C131—21no—
22#475×C131C2212yes—
23#475×C131C2212yes—
24#461×C131—22no—
25#460×C131C2211yescharacteristic
26#460×C131C2211yescharacteristic
27#448×C131—21no—
28#448×C131—21no—
29#448×C131—21no—
30#446×C131—22no—
31#446×C131C2212yes—
32C8×Q8×C131C2212yes—
33#440×C131—21no—
34#440×C131—21no—
35#432×C131—21no—
36#432×C131C2211yescharacteristic
37#432×C131C2211yescharacteristic
38#431×C131—21no—
39#431×C131C2211yescharacteristic
40C2×#106×C131—21no—
41C2×C4⋊C8×C131C2211yescharacteristic
42C2×#103×C131—21no—
43#335×C131C2212yes—
44#334×C131C2212yes—
45#333×C131C2212yes—
46#332×C131C2212yes—
47#332×C131C2212yes—
48#331×C131C2212yes—
49C2×#41×C131—21no—
50C22×Q8×C131—21no—
51C22×Q8×C131D411yescharacteristic
52C2×SD16×C131—21no—
53C2×SD16×C131—21no—
54C2×SD16×C131—22no—
55C2×SD16×C131—22no—
56C22×C8×C131—21no—
57C4⋊Q8×C131—21no—
58C4⋊Q8×C131—21no—
59C4⋊Q8×C131—21no—
60C4⋊Q8×C131C2312yes—
61C4⋊Q8×C131C2311yescharacteristic
62#127×C131C2311yescharacteristic
63#124×C131—21no—
64#121×C131—21no—
65#121×C131—21no—
66C4×Q8×C131—21no—
67C4×Q8×C131—21no—
68C4×Q8×C131D411yescharacteristic
69C4×Q8×C131D411yescharacteristic
70C4×Q8×C131C2311yescharacteristic
71C4×Q8×C131C2311yescharacteristic
72C4×D4×C131—21no—
73C4×D4×C131—21no—
74C2×C4⋊C4×C131—21no—
75C2×C4⋊C4×C131—21no—
76C2×C4⋊C4×C131—21no—
77C2×C4⋊C4×C131D411yescharacteristic
78C2×C42×C131—21no—
79C2×C42×C131C2311yescharacteristic
80#107×C131—21no—
81#107×C131—21no—
82#106×C131—22no—
83#106×C131—22no—
84C4⋊C8×C131—22no—
85C4⋊C8×C131—22no—
86C4⋊C8×C131—21no—
87C4⋊C8×C131D412yes—
88C4⋊C8×C131C2312yes—
89C4⋊C8×C131C2312yes—
90C4⋊C8×C131C2311yescharacteristic
91C4⋊C8×C131C2311yescharacteristic
92#103×C131—22no—
93#103×C131—22no—
94#103×C131—21no—
95#103×C131—21no—
96#103×C131—22no—
97#103×C131—22no—
98#102×C131—21no—
99#102×C131—21no—
100C22⋊C8×C131—21no—
101C22⋊C8×C131—21no—
102C22⋊C8×C131D411yescharacteristic
103C22⋊C8×C131D411yescharacteristic
104#97×C131—22no—
105#97×C131—21no—
106#97×C131—21no—
107C4×C8×C131—22no—
108C4×C8×C131C2312yes—
109#41×C131—82no—
110C2×Q8×C131—21no—
111C2×Q8×C131—22no—
112C2×Q8×C131—22no—
113C2×Q8×C131—21no—
114C2×Q8×C131—41no—
115C2×Q8×C131—41no—
116C2×Q8×C131—82no—
117C2×Q8×C131C2×D411yescharacteristic
118C2×Q8×C131C2×D411yescharacteristic
119C2×D4×C131—21no—
120C2×D4×C131—21no—
121C2×D4×C131—21no—
122C2×D4×C131—41no—
123C22×C4×C131—21no—
124C22×C4×C131—21no—
125C22×C4×C131—41no—
126C22×C4×C131—41no—
127C22×C4×C131C2×D411yescharacteristic
128C22×C4×C131C2×D411yescharacteristic
129C22×C4×C131#4111yescharacteristic
130SD16×C131—42no—
131SD16×C131—42no—
132SD16×C131—82no—
133SD16×C131—82no—
134C2×C8×C131—22no—
135C2×C8×C131—21no—
136C2×C8×C131—21no—
137C2×C8×C131—22no—
138C2×C8×C131—42no—
139C2×C8×C131C2×D412yes—
140C2×C8×C131C2×D412yes—
141C4⋊C4×C131—21no—
142C4⋊C4×C131—21no—
143C4⋊C4×C131—21no—
144C4⋊C4×C131—21no—
145C4⋊C4×C131—21no—
146C4⋊C4×C131—21no—
147C4⋊C4×C131—22no—
148C4⋊C4×C131—21no—
149C4⋊C4×C131—22no—
150C4⋊C4×C131—41no—
151C4⋊C4×C131—41no—
152C4⋊C4×C131C2×D411yescharacteristic
153C4⋊C4×C131C2×D411yescharacteristic
154C22⋊C4×C131—41no—
155C22⋊C4×C131—41no—
156C42×C131—21no—
157C42×C131—21no—
158C42×C131—21no—
159C42×C131—21no—
160C42×C131C2×D411yescharacteristic
161C42×C131C2×D411yescharacteristic
162C42×C131#4111yescharacteristic
163C42×C131C2411yescharacteristic
164C23×C131—41no—
165C23×C131#12111yescharacteristic
166Q8×C131—21no—
167Q8×C131—21no—
168Q8×C131—21no—
169Q8×C131—42no—
170Q8×C131—42no—
171Q8×C131—42no—
172Q8×C131—81no—
173Q8×C131—82no—
174Q8×C131#13712yes—
175D4×C131—41no—
176D4×C131—41no—
177D4×C131—42no—
178D4×C131—81no—
179D4×C131—82no—
180C2×C4×C131—21no—
181C2×C4×C131—22no—
182C2×C4×C131—21no—
183C2×C4×C131—21no—
184C2×C4×C131—22no—
185C2×C4×C131—21no—
186C2×C4×C131—21no—
187C2×C4×C131—21no—
188C2×C4×C131—42no—
189C2×C4×C131—42no—
190C2×C4×C131—41no—
191C2×C4×C131—42no—
192C2×C4×C131—82no—
193C2×C4×C131—82no—
194C2×C4×C131#12111yescharacteristic
195C2×C4×C131#12111yescharacteristic
196C2×C4×C131#12111yescharacteristic
197C2×C4×C131C22×D411yescharacteristic
198C2×C4×C131C22×D411yescharacteristic
199C2×C4×C131C2×#4111yescharacteristic
200C8×C131—22no—
201C8×C131—22no—
202C8×C131—41no—
203C8×C131—42no—
204C8×C131—41no—
205C8×C131—42no—
206C22×C131—21no—
207C22×C131—21no—
208C22×C131—81no—
209C22×C131—81no—
210C22×C131—81no—
211C22×C131#47112yes—
212C22×C131C2×#12111yescharacteristic
213C4×C131—21no—
214C4×C131—21no—
215C4×C131—22no—
216C4×C131—21no—
217C4×C131—21no—
218C4×C131—41no—
219C4×C131—41no—
220C4×C131—41no—
221C4×C131—82no—
222C4×C131—81no—
223C4×C131C2×#13711yescharacteristic
224C4×C131#57511yescharacteristic
225C4×C131#57712yes—
226C2×C131—22no—
227C2×C131—161no—
228C2×C131#304311yescharacteristic
229C2×C131#305611yescharacteristic
230C2×C131C2×#47111yescharacteristic
231#19469C13111yesmaximal, characteristic, direct product factor, Sylow
232C131#1946911yescharacteristic, direct product factor, Sylow
233#3206C2×C13111yescharacteristic
234#3112C2×C13111yescharacteristic
235C2×#475C2×C13111yescharacteristic, complemented
236#2984C2×C13111yescharacteristic, complemented
237#1704C2×C13112yescomplemented
238#1686C2×C13112yescomplemented
239#1684C2×C13112yescomplemented
240#1666C2×C13112yescomplemented
241#1573C2×C13111yescharacteristic, complemented
242#1556C2×C13111yescharacteristic, complemented
243#1551C2×C13111yescharacteristic
244#532C22×C13111yescharacteristic
245C2×C4⋊Q8C22×C13111yescharacteristic
246C2×C4×Q8C22×C13111yescharacteristic
247#492C22×C13112yes—
248#487C22×C13112yes—
249#480—21no—
250#477C22×C13111yescharacteristic
251#477C22×C13111yescharacteristic
252#475—21no—
253#475—21no—
254#475C22×C13112yes—
255#475C22×C13112yes—
256#461—22no—
257#460C22×C13111yescharacteristic
258#460C22×C13111yescharacteristic
259#448—21no—
260#448—21no—
261#448—21no—
262#446—22no—
263#446C22×C13112yes—
264C8×Q8C22×C13112yes—
265#440—21no—
266#440—21no—
267#432—21no—
268#432C22×C13111yescharacteristic
269#432C22×C13111yescharacteristic
270#431—21no—
271#431C22×C13111yescharacteristic
272C2×#106—21no—
273C2×C4⋊C8C22×C13111yescharacteristic
274C2×#103—21no—
275#335C22×C13112yes—
276#334C22×C13112yes—
277#333C22×C13112yes—
278#332C22×C13112yes—
279#332C22×C13112yes—
280#331C22×C13112yes—
281C2×#41—21no—
282C22×Q8—21no—
283C22×Q8D4×C13111yescharacteristic
284C2×SD16—21no—
285C2×SD16—21no—
286C2×SD16—22no—
287C2×SD16—22no—
288C22×C8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8C23×C13112yes—
293C4⋊Q8C23×C13111yescharacteristic
294#127C23×C13111yescharacteristic
295#124—21no—
296#121—21no—
297#121—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8D4×C13111yescharacteristic
301C4×Q8D4×C13111yescharacteristic
302C4×Q8C23×C13111yescharacteristic
303C4×Q8C23×C13111yescharacteristic
304C4×D4—21no—
305C4×D4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4D4×C13111yescharacteristic
310C2×C42—21no—
311C2×C42C23×C13111yescharacteristic
312#107—21no—
313#107—21no—
314#106—22no—
315#106—22no—
316C4⋊C8—22no—
317C4⋊C8—22no—
318C4⋊C8—21no—
319C4⋊C8D4×C13112yes—
320C4⋊C8C23×C13112yes—
321C4⋊C8C23×C13112yes—
322C4⋊C8C23×C13111yescharacteristic
323C4⋊C8C23×C13111yescharacteristic
324#103—22no—
325#103—22no—
326#103—21no—
327#103—21no—
328#103—22no—
329#103—22no—
330#102—21no—
331#102—21no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8D4×C13111yescharacteristic
335C22⋊C8D4×C13111yescharacteristic
336#97—22no—
337#97—21no—
338#97—21no—
339C4×C8—22no—
340C4×C8C23×C13112yes—
341#41—82no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—82no—
349C2×Q8C2×D4×C13111yescharacteristic
350C2×Q8C2×D4×C13111yescharacteristic
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—41no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4C2×D4×C13111yescharacteristic
360C22×C4C2×D4×C13111yescharacteristic
361C22×C4#41×C13111yescharacteristic
362SD16—42no—
363SD16—42no—
364SD16—82no—
365SD16—82no—
366C2×C8—22no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—22no—
370C2×C8—42no—
371C2×C8C2×D4×C13112yes—
372C2×C8C2×D4×C13112yes—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4C2×D4×C13111yescharacteristic
385C4⋊C4C2×D4×C13111yescharacteristic
386C22⋊C4—41no—
387C22⋊C4—41no—
388C42—21no—
389C42—21no—
390C42—21no—
391C42—21no—
392C42C2×D4×C13111yescharacteristic
393C42C2×D4×C13111yescharacteristic
394C42#41×C13111yescharacteristic
395C42C24×C13111yescharacteristic
396C23—41no—
397C23#121×C13111yescharacteristic
398Q8—21no—
399Q8—21no—
400Q8—21no—
401Q8—42no—
402Q8—42no—
403Q8—42no—
404Q8—81no—
405Q8—82no—
406Q8#137×C13112yes—
407D4—41no—
408D4—41no—
409D4—42no—
410D4—81no—
411D4—82no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4#121×C13111yescharacteristic
427C2×C4#121×C13111yescharacteristic
428C2×C4#121×C13111yescharacteristic
429C2×C4C22×D4×C13111yescharacteristic
430C2×C4C22×D4×C13111yescharacteristic
431C2×C4C2×#41×C13111yescharacteristic
432C8—22no—
433C8—22no—
434C8—41no—
435C8—42no—
436C8—41no—
437C8—42no—
438C22—21no—
439C22—21no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22#471×C13112yes—
444C22C2×#121×C13111yescharacteristic
445C4—21no—
446C4—21no—
447C4—22no—
448C4—21no—
449C4—21no—
450C4—41no—
451C4—41no—
452C4—41no—
453C4—82no—
454C4—81no—
455C4C2×#137×C13111yescharacteristic
456C4#575×C13111yescharacteristic
457C4#577×C13112yes—
458C2—22no—
459C2—161no—
460C2#3043×C13111yescharacteristic
461C2#3056×C13111yescharacteristic
462C2C2×#471×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#121
commutator, Frattini, cosocleC42C24×C131
prime radical#532×C131C22
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
3. C2×#475×C131C2semidirect
4. #2984×C131C2semidirect
5. #1704×C131C2semidirect
6. #1686×C131C2semidirect
7. #1684×C131C2semidirect
8. #1666×C131C2semidirect
9. #1573×C131C2semidirect
10. #1556×C131C2semidirect
231. #19469C131direct (N × H)
232. C131#19469direct (N × H)
235. C2×#475C2×C131semidirect
236. #2984C2×C131semidirect
237. #1704C2×C131semidirect
238. #1686C2×C131semidirect
239. #1684C2×C131semidirect
240. #1666C2×C131semidirect
241. #1573C2×C131semidirect
242. #1556C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3206×C1312
#3112×C1312
C2×#475×C1312
#2984×C1312
#1704×C1312
#1686×C1312
#1684×C1312
#1666×C1312
#1573×C1312
#1556×C1312
#1551×C1312
#19469131