Finite Group Databasebeta

← C131×#32995 #45718879

Subgroups — C131×#32995 #45718879

Order 33536.

1246 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#3428×C131C211yesmaximal, characteristic
2#3095×C131C212yesmaximal, complemented
3#2432×C131C211yesmaximal, characteristic
4#1886×C131C212yesmaximal, complemented
5#1885×C131C212yesmaximal, complemented
6#1857×C131C212yesmaximal, complemented
7#1856×C131C212yesmaximal, complemented
8#1826×C131C212yesmaximal, complemented
9#1785×C131C211yesmaximal, characteristic
10C22×#41×C131C2211yescharacteristic
11C2×C4⋊Q8×C131C2211yescharacteristic
12C2×#124×C131C2211yescharacteristic
13C2×C22⋊Q8×C131C2211yescharacteristic
14#520×C131—22no—
15#520×C131—22no—
16#519×C131C2212yes—
17#518×C131—22no—
18#518×C131C2212yes—
19C4×#41×C131—24no—
20C2×#117×C131—22no—
21C2×#117×C131C2212yes—
22#485×C131—24no—
23#484×C131—22no—
24#483×C131—22no—
25#428×C131C2214yes—
26#419×C131C2214yes—
27C2×#101×C131C2212yes—
28C2×#100×C131C2212yes—
29#407×C131C2212yes—
30#394×C131—22no—
31#391×C131C2211yescharacteristic
32#390×C131C2211yescharacteristic
33#385×C131—22no—
34C4×C22⋊C4×C131C2211yescharacteristic
35#339×C131C2214yes—
36#339×C131C2214yes—
37C2×#41×C131—24no—
38C2×#41×C131—24no—
39C2×#41×C131—22no—
40C2×#41×C131—22no—
41C22×Q8×C131C2311yescharacteristic
42C22×Q8×C131C2311yescharacteristic
43C22×D4×C131D412yes—
44C22×D4×C131C2311yescharacteristic
45C23×C4×C131D412yes—
46C23×C4×C131C2311yescharacteristic
47C2×M16×C131C2314yes—
48C4⋊Q8×C131—24no—
49#124×C131—24no—
50C22⋊Q8×C131—22no—
51C22⋊Q8×C131—22no—
52C4×Q8×C131—24no—
53C4×Q8×C131—24no—
54C4×D4×C131—28no—
55C4×D4×C131—28no—
56C4×D4×C131—24no—
57C4×D4×C131—24no—
58#117×C131—24no—
59#117×C131—24no—
60#117×C131—22no—
61#117×C131—24no—
62#117×C131—22no—
63#117×C131D414yes—
64#117×C131C2314yes—
65C2×C4⋊C4×C131—22no—
66C2×C4⋊C4×C131—22no—
67C2×C4⋊C4×C131—22no—
68C2×C4⋊C4×C131—21no—
69C2×C4⋊C4×C131D412yes—
70C2×C4⋊C4×C131D412yes—
71C2×C4⋊C4×C131C2311yescharacteristic
72C2×C22⋊C4×C131—24no—
73C2×C22⋊C4×C131—22no—
74C2×C22⋊C4×C131—22no—
75C2×C22⋊C4×C131—21no—
76C2×C22⋊C4×C131—21no—
77C2×C22⋊C4×C131—22no—
78C2×C42×C131—24no—
79C2×C42×C131—22no—
80C2×C42×C131C2311yescharacteristic
81C2×C42×C131C2311yescharacteristic
82#107×C131—24no—
83#106×C131—24no—
84#103×C131—24no—
85#103×C131—24no—
86#101×C131—24no—
87#100×C131—24no—
88C22⋊C8×C131—22no—
89C22⋊C8×C131—22no—
90#95×C131—22no—
91#95×C131—21no—
92C24×C131C2×D411yescharacteristic
93C24×C131C2×D412yes—
94#41×C131—216no—
95#41×C131—216no—
96C2×Q8×C131—22no—
97C2×Q8×C131—22no—
98C2×Q8×C131—22no—
99C2×Q8×C131—22no—
100C2×Q8×C131—22no—
101C2×Q8×C131#4114yes—
102C2×D4×C131—24no—
103C2×D4×C131—24no—
104C2×D4×C131—24no—
105C2×D4×C131—22no—
106C2×D4×C131—22no—
107C2×D4×C131#4114yes—
108C22×C4×C131—24no—
109C22×C4×C131—22no—
110C22×C4×C131—22no—
111C22×C4×C131—24no—
112C22×C4×C131—22no—
113C22×C4×C131—22no—
114C22×C4×C131—21no—
115C22×C4×C131—24no—
116C22×C4×C131—24no—
117C22×C4×C131—22no—
118C22×C4×C131—22no—
119C22×C4×C131—21no—
120C22×C4×C131—21no—
121C22×C4×C131—21no—
122C22×C4×C131C2×D411yescharacteristic
123C22×C4×C131C2×D412yes—
124C22×C4×C131C2×D412yes—
125C22×C4×C131C2×D412yes—
126C22×C4×C131C2411yescharacteristic
127M16×C131—24no—
128M16×C131—24no—
129C2×C8×C131—24no—
130C4⋊C4×C131—24no—
131C4⋊C4×C131—24no—
132C4⋊C4×C131—22no—
133C4⋊C4×C131—22no—
134C4⋊C4×C131—22no—
135C4⋊C4×C131—41no—
136C4⋊C4×C131—41no—
137C4⋊C4×C131—44no—
138C4⋊C4×C131C2×D414yes—
139C4⋊C4×C131C2×D414yes—
140C22⋊C4×C131—28no—
141C22⋊C4×C131—24no—
142C22⋊C4×C131—24no—
143C22⋊C4×C131—42no—
144C22⋊C4×C131—44no—
145C22⋊C4×C131—42no—
146C22⋊C4×C131—44no—
147C42×C131—28no—
148C42×C131—24no—
149C42×C131—24no—
150C42×C131—22no—
151C42×C131—22no—
152C23×C131—22no—
153C23×C131—21no—
154C23×C131—21no—
155C23×C131—22no—
156C23×C131—41no—
157C23×C131—41no—
158C23×C131—42no—
159C23×C131—42no—
160C23×C131#12012yes—
161C23×C131#12314yes—
162C23×C131C22×D411yescharacteristic
163Q8×C131—28no—
164Q8×C131—44no—
165D4×C131—216no—
166D4×C131—28no—
167C2×C4×C131—28no—
168C2×C4×C131—28no—
169C2×C4×C131—22no—
170C2×C4×C131—21no—
171C2×C4×C131—21no—
172C2×C4×C131—22no—
173C2×C4×C131—24no—
174C2×C4×C131—24no—
175C2×C4×C131—22no—
176C2×C4×C131—24no—
177C2×C4×C131—24no—
178C2×C4×C131—41no—
179C2×C4×C131—41no—
180C2×C4×C131—41no—
181C2×C4×C131—42no—
182C2×C4×C131—41no—
183C2×C4×C131—41no—
184C2×C4×C131—41no—
185C2×C4×C131—41no—
186C2×C4×C131—41no—
187C2×C4×C131—41no—
188C2×C4×C131—82no—
189C2×C4×C131—82no—
190C2×C4×C131—84no—
191C2×C4×C131—84no—
192C2×C4×C131#12011yescharacteristic
193C2×C4×C131#12011yescharacteristic
194C2×C4×C131#12314yes—
195C2×C4×C131C22×D412yes—
196C2×C4×C131C2×#4112yes—
197C2×C4×C131C2×#4112yes—
198C8×C131—44no—
199C22×C131—21no—
200C22×C131—21no—
201C22×C131—22no—
202C22×C131—24no—
203C22×C131—22no—
204C22×C131—22no—
205C22×C131—44no—
206C22×C131—42no—
207C22×C131—42no—
208C22×C131—81no—
209C22×C131—82no—
210C22×C131—81no—
211C22×C131C2×#12011yescharacteristic
212C22×C131C2×#12311yescharacteristic
213C22×C131C2×#12311yescharacteristic
214C4×C131—21no—
215C4×C131—21no—
216C4×C131—24no—
217C4×C131—42no—
218C4×C131—44no—
219C4×C131—44no—
220C4×C131—81no—
221C4×C131—81no—
222C4×C131—81no—
223C4×C131#52514yes—
224C2×C131—21no—
225C2×C131—21no—
226C2×C131—42no—
227C2×C131—44no—
228C2×C131#284911yescharacteristic
229C2×C131#301811yescharacteristic
230C2×C131#302211yescharacteristic
231#32995C13111yesmaximal, characteristic, direct product factor, Sylow
232C131#3299511yescharacteristic, direct product factor, Sylow
233#3428C2×C13111yescharacteristic
234#3095C2×C13112yescomplemented
235#2432C2×C13111yescharacteristic
236#1886C2×C13112yescomplemented
237#1885C2×C13112yescomplemented
238#1857C2×C13112yescomplemented
239#1856C2×C13112yescomplemented
240#1826C2×C13112yescomplemented
241#1785C2×C13111yescharacteristic
242C22×#41C22×C13111yescharacteristic
243C2×C4⋊Q8C22×C13111yescharacteristic
244C2×#124C22×C13111yescharacteristic
245C2×C22⋊Q8C22×C13111yescharacteristic
246#520—22no—
247#520—22no—
248#519C22×C13112yes—
249#518—22no—
250#518C22×C13112yes—
251C4×#41—24no—
252C2×#117—22no—
253C2×#117C22×C13112yes—
254#485—24no—
255#484—22no—
256#483—22no—
257#428C22×C13114yes—
258#419C22×C13114yes—
259C2×#101C22×C13112yes—
260C2×#100C22×C13112yes—
261#407C22×C13112yes—
262#394—22no—
263#391C22×C13111yescharacteristic
264#390C22×C13111yescharacteristic
265#385—22no—
266C4×C22⋊C4C22×C13111yescharacteristic
267#339C22×C13114yes—
268#339C22×C13114yes—
269C2×#41—24no—
270C2×#41—24no—
271C2×#41—22no—
272C2×#41—22no—
273C22×Q8C23×C13111yescharacteristic
274C22×Q8C23×C13111yescharacteristic
275C22×D4D4×C13112yes—
276C22×D4C23×C13111yescharacteristic
277C23×C4D4×C13112yes—
278C23×C4C23×C13111yescharacteristic
279C2×M16C23×C13114yes—
280C4⋊Q8—24no—
281#124—24no—
282C22⋊Q8—22no—
283C22⋊Q8—22no—
284C4×Q8—24no—
285C4×Q8—24no—
286C4×D4—28no—
287C4×D4—28no—
288C4×D4—24no—
289C4×D4—24no—
290#117—24no—
291#117—24no—
292#117—22no—
293#117—24no—
294#117—22no—
295#117D4×C13114yes—
296#117C23×C13114yes—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4D4×C13112yes—
302C2×C4⋊C4D4×C13112yes—
303C2×C4⋊C4C23×C13111yescharacteristic
304C2×C22⋊C4—24no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—22no—
310C2×C42—24no—
311C2×C42—22no—
312C2×C42C23×C13111yescharacteristic
313C2×C42C23×C13111yescharacteristic
314#107—24no—
315#106—24no—
316#103—24no—
317#103—24no—
318#101—24no—
319#100—24no—
320C22⋊C8—22no—
321C22⋊C8—22no—
322#95—21no—
323#95—22no—
324C24C2×D4×C13111yescharacteristic
325C24C2×D4×C13112yes—
326#41—216no—
327#41—216no—
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8#41×C13114yes—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4#41×C13114yes—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4C2×D4×C13111yescharacteristic
355C22×C4C2×D4×C13112yes—
356C22×C4C2×D4×C13112yes—
357C22×C4C2×D4×C13112yes—
358C22×C4C24×C13111yescharacteristic
359M16—24no—
360M16—24no—
361C2×C8—24no—
362C4⋊C4—24no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—44no—
370C4⋊C4C2×D4×C13114yes—
371C4⋊C4C2×D4×C13114yes—
372C22⋊C4—28no—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—42no—
376C22⋊C4—44no—
377C22⋊C4—42no—
378C22⋊C4—44no—
379C42—28no—
380C42—24no—
381C42—24no—
382C42—22no—
383C42—22no—
384C23—22no—
385C23—21no—
386C23—21no—
387C23—22no—
388C23—41no—
389C23—41no—
390C23—42no—
391C23—42no—
392C23#120×C13112yes—
393C23#123×C13114yes—
394C23C22×D4×C13111yescharacteristic
395Q8—28no—
396Q8—44no—
397D4—216no—
398D4—28no—
399C2×C4—28no—
400C2×C4—28no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—84no—
423C2×C4—84no—
424C2×C4#120×C13111yescharacteristic
425C2×C4#120×C13111yescharacteristic
426C2×C4#123×C13114yes—
427C2×C4C22×D4×C13112yes—
428C2×C4C2×#41×C13112yes—
429C2×C4C2×#41×C13112yes—
430C8—44no—
431C22—21no—
432C22—21no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—24no—
437C22—44no—
438C22—42no—
439C22—42no—
440C22—81no—
441C22—82no—
442C22—81no—
443C22C2×#120×C13111yescharacteristic
444C22C2×#123×C13111yescharacteristic
445C22C2×#123×C13111yescharacteristic
446C4—21no—
447C4—21no—
448C4—24no—
449C4—42no—
450C4—44no—
451C4—44no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4#525×C13114yes—
456C2—21no—
457C2—21no—
458C2—42no—
459C2—44no—
460C2#2849×C13111yescharacteristic
461C2#3018×C13111yescharacteristic
462C2#3022×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC22×#41×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3095×C131C2semidirect
4. #1886×C131C2semidirect
5. #1885×C131C2semidirect
6. #1857×C131C2semidirect
7. #1856×C131C2semidirect
8. #1826×C131C2semidirect
231. #32995C131direct (N × H)
232. C131#32995direct (N × H)
234. #3095C2×C131semidirect
236. #1886C2×C131semidirect
237. #1885C2×C131semidirect
238. #1857C2×C131semidirect
239. #1856C2×C131semidirect
240. #1826C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3428×C1312
#3095×C1312
#2432×C1312
#1886×C1312
#1885×C1312
#1857×C1312
#1856×C1312
#1826×C1312
#1785×C1312
#32995131