Finite Group Databasebeta

← C131×#29636 #45715520

Subgroups — C131×#29636 #45715520

Order 33536.

1502 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3449×C131C211yesmaximal, characteristic, complemented
2#2482×C131C211yesmaximal, characteristic, complemented
3#2404×C131C212yesmaximal, complemented
4#2044×C131C214yesmaximal, complemented
5#2021×C131C214yesmaximal, complemented
6#1820×C131C211yesmaximal, characteristic, complemented
7#1782×C131C212yesmaximal, complemented
8C22×#41×C131C2212yes—
9#537×C131—21no—
10#537×C131—21no—
11#536×C131—22no—
12#535×C131—22no—
13#534×C131C2214yes—
14#532×C131—22no—
15#525×C131—24no—
16C2×#120×C131C2214yes—
17C2×#117×C131C2211yescharacteristic
18C22×C22⋊C4×C131C2211yescharacteristic
19C2×#99×C131C2218yes—
20#399×C131—21no—
21#397×C131—21no—
22#393×C131—22no—
23#392×C131—22no—
24#388×C131—22no—
25#386×C131—24no—
26#386×C131C2214yes—
27#385×C131C2212yes—
28#381×C131C2211yescharacteristic
29#381×C131C2212yes—
30#379×C131C2212yes—
31#342×C131C2214yes—
32C25×C131C2311yescharacteristic
33C2×#41×C131—22no—
34C2×#41×C131—22no—
35C2×#41×C131—22no—
36C2×#41×C131—22no—
37C2×#41×C131—48no—
38C22×Q8×C131D412yescomplemented
39C22×D4×C131—24no—
40C22×D4×C131D412yescomplemented
41C22×D4×C131C2314yes—
42C23×C4×C131D414yescomplemented
43C23×C4×C131C2311yescharacteristic
44C23×C4×C131C2311yescharacteristic
45C4⋊Q8×C131—22no—
46#127×C131—22no—
47#124×C131—24no—
48#123×C131—28no—
49C22⋊Q8×C131—24no—
50C22⋊Q8×C131—24no—
51#121×C131—24no—
52#121×C131—24no—
53#121×C131—24no—
54#121×C131—24no—
55#120×C131—28no—
56#120×C131—48no—
57C4×D4×C131—24no—
58C4×D4×C131—24no—
59#117×C131—22no—
60#117×C131—22no—
61C2×C4⋊C4×C131—22no—
62C2×C4⋊C4×C131D411yescharacteristic, complemented
63C2×C4⋊C4×C131D411yescharacteristic, complemented
64C2×C22⋊C4×C131—21no—
65C2×C22⋊C4×C131—22no—
66C2×C22⋊C4×C131—22no—
67C2×C22⋊C4×C131—24no—
68C2×C22⋊C4×C131—21no—
69C2×C22⋊C4×C131—22no—
70C2×C22⋊C4×C131—24no—
71C2×C22⋊C4×C131—22no—
72C2×C22⋊C4×C131C2312yes—
73C2×C22⋊C4×C131C2314yes—
74C2×C22⋊C4×C131C2312yes—
75C2×C42×C131D412yescomplemented
76#99×C131—48no—
77#95×C131—21no—
78#95×C131—22no—
79#95×C131—22no—
80#95×C131—24no—
81#95×C131—21no—
82#95×C131—22no—
83C24×C131—21no—
84C24×C131—22no—
85C24×C131—24no—
86C24×C131—42no—
87C24×C131—81no—
88C24×C131C2×D414yes—
89C24×C131C2411yescharacteristic
90#41×C131—48no—
91#41×C131—48no—
92#41×C131—48no—
93#41×C131—48no—
94C2×Q8×C131—22no—
95C2×Q8×C131—22no—
96C2×Q8×C131—44no—
97C2×D4×C131—24no—
98C2×D4×C131—24no—
99C2×D4×C131—28no—
100C2×D4×C131—28no—
101C2×D4×C131—24no—
102C2×D4×C131—24no—
103C2×D4×C131—22no—
104C2×D4×C131—22no—
105C2×D4×C131—44no—
106C2×D4×C131—48no—
107C2×D4×C131—48no—
108C2×D4×C131—84no—
109C22×C4×C131—24no—
110C22×C4×C131—24no—
111C22×C4×C131—24no—
112C22×C4×C131—22no—
113C22×C4×C131—24no—
114C22×C4×C131—22no—
115C22×C4×C131—21no—
116C22×C4×C131—44no—
117C22×C4×C131—44no—
118C22×C4×C131—81no—
119C22×C4×C131C2×D414yes—
120C22×C4×C131C2×D411yescharacteristic
121C22×C4×C131C2×D411yescharacteristic
122C22×C4×C131C2×D412yes—
123C22×C4×C131C2×D412yes—
124C22×C4×C131C2×D412yes—
125C22×C4×C131C2×D412yes—
126C4⋊C4×C131—24no—
127C4⋊C4×C131—24no—
128C4⋊C4×C131—22no—
129C4⋊C4×C131—22no—
130C4⋊C4×C131—82no—
131C22⋊C4×C131—28no—
132C22⋊C4×C131—28no—
133C22⋊C4×C131—24no—
134C22⋊C4×C131—24no—
135C22⋊C4×C131—28no—
136C22⋊C4×C131—48no—
137C22⋊C4×C131—44no—
138C22⋊C4×C131—41no—
139C22⋊C4×C131—41no—
140C22⋊C4×C131—42no—
141C22⋊C4×C131—82no—
142C22⋊C4×C131—84no—
143C42×C131—22no—
144C42×C131—22no—
145C23×C131—22no—
146C23×C131—24no—
147C23×C131—24no—
148C23×C131—24no—
149C23×C131—24no—
150C23×C131—41no—
151C23×C131—41no—
152C23×C131—44no—
153C23×C131—44no—
154C23×C131—42no—
155C23×C131—44no—
156C23×C131—41no—
157C23×C131—42no—
158C23×C131—41no—
159C23×C131—44no—
160C23×C131—42no—
161C23×C131—88no—
162C23×C131C22×D412yes—
163C23×C131C22×D411yescharacteristic
164C23×C131H(5,𝔽2)14yes—
165Q8×C131—44no—
166Q8×C131—44no—
167D4×C131—44no—
168D4×C131—44no—
169D4×C131—48no—
170D4×C131—48no—
171D4×C131—84no—
172D4×C131—84no—
173D4×C131—816no—
174C2×C4×C131—24no—
175C2×C4×C131—24no—
176C2×C4×C131—22no—
177C2×C4×C131—22no—
178C2×C4×C131—22no—
179C2×C4×C131—22no—
180C2×C4×C131—24no—
181C2×C4×C131—24no—
182C2×C4×C131—24no—
183C2×C4×C131—48no—
184C2×C4×C131—48no—
185C2×C4×C131—42no—
186C2×C4×C131—42no—
187C2×C4×C131—42no—
188C2×C4×C131—42no—
189C2×C4×C131—44no—
190C2×C4×C131—44no—
191C2×C4×C131—42no—
192C2×C4×C131—44no—
193C2×C4×C131—41no—
194C2×C4×C131—44no—
195C2×C4×C131—42no—
196C2×C4×C131#12011yescharacteristic
197C2×C4×C131#12011yescharacteristic
198C2×C4×C131#12012yes—
199C22×C131—21no—
200C22×C131—22no—
201C22×C131—21no—
202C22×C131—22no—
203C22×C131—44no—
204C22×C131—48no—
205C22×C131—48no—
206C22×C131—44no—
207C22×C131—44no—
208C22×C131—44no—
209C22×C131—42no—
210C22×C131—44no—
211C22×C131—84no—
212C22×C131—84no—
213C22×C131—82no—
214C22×C131—81no—
215C22×C131—81no—
216C22×C131C2×#12011yescharacteristic
217C22×C131#53414yes—
218C22×C131#53512yes—
219C4×C131—21no—
220C4×C131—22no—
221C4×C131—21no—
222C4×C131—44no—
223C4×C131—42no—
224C4×C131—42no—
225C4×C131—82no—
226C4×C131—84no—
227C4×C131—81no—
228C2×C131—24no—
229C2×C131—22no—
230C2×C131—82no—
231C2×C131—84no—
232C2×C131#261311yescharacteristic
233C2×C131#302511yescharacteristic
234C2×C131#302711yescharacteristic
235#29636C13111yesmaximal, characteristic, direct product factor, Sylow
236C131#2963611yescharacteristic, direct product factor, Sylow
237#3449C2×C13111yescharacteristic, complemented
238#2482C2×C13111yescharacteristic, complemented
239#2404C2×C13112yescomplemented
240#2044C2×C13114yescomplemented
241#2021C2×C13114yescomplemented
242#1820C2×C13111yescharacteristic, complemented
243#1782C2×C13112yescomplemented
244C22×#41C22×C13112yes—
245#537—21no—
246#537—21no—
247#536—22no—
248#535—22no—
249#534C22×C13114yes—
250#532—22no—
251#525—24no—
252C2×#120C22×C13114yes—
253C2×#117C22×C13111yescharacteristic
254C22×C22⋊C4C22×C13111yescharacteristic
255C2×#99C22×C13118yes—
256#399—21no—
257#397—21no—
258#393—22no—
259#392—22no—
260#388—22no—
261#386—24no—
262#386C22×C13114yes—
263#385C22×C13112yes—
264#381C22×C13112yes—
265#381C22×C13111yescharacteristic
266#379C22×C13112yes—
267#342C22×C13114yes—
268C25C23×C13111yescharacteristic
269C2×#41—22no—
270C2×#41—22no—
271C2×#41—22no—
272C2×#41—22no—
273C2×#41—48no—
274C22×Q8D4×C13112yescomplemented
275C22×D4—24no—
276C22×D4D4×C13112yescomplemented
277C22×D4C23×C13114yes—
278C23×C4D4×C13114yescomplemented
279C23×C4C23×C13111yescharacteristic
280C23×C4C23×C13111yescharacteristic
281C4⋊Q8—22no—
282#127—22no—
283#124—24no—
284#123—28no—
285C22⋊Q8—24no—
286C22⋊Q8—24no—
287#121—24no—
288#121—24no—
289#121—24no—
290#121—24no—
291#120—28no—
292#120—48no—
293C4×D4—24no—
294C4×D4—24no—
295#117—22no—
296#117—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4D4×C13111yescharacteristic, complemented
299C2×C4⋊C4D4×C13111yescharacteristic, complemented
300C2×C22⋊C4—22no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4C23×C13114yes—
309C2×C22⋊C4C23×C13112yes—
310C2×C22⋊C4C23×C13112yes—
311C2×C42D4×C13112yescomplemented
312#99—48no—
313#95—22no—
314#95—21no—
315#95—22no—
316#95—21no—
317#95—22no—
318#95—24no—
319C24—21no—
320C24—22no—
321C24—24no—
322C24—42no—
323C24—81no—
324C24C2×D4×C13114yes—
325C24C24×C13111yescharacteristic
326#41—48no—
327#41—48no—
328#41—48no—
329#41—48no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—44no—
333C2×D4—24no—
334C2×D4—24no—
335C2×D4—28no—
336C2×D4—28no—
337C2×D4—24no—
338C2×D4—24no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—44no—
342C2×D4—48no—
343C2×D4—48no—
344C2×D4—84no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—44no—
353C22×C4—44no—
354C22×C4—81no—
355C22×C4C2×D4×C13114yes—
356C22×C4C2×D4×C13111yescharacteristic
357C22×C4C2×D4×C13111yescharacteristic
358C22×C4C2×D4×C13112yes—
359C22×C4C2×D4×C13112yes—
360C22×C4C2×D4×C13112yes—
361C22×C4C2×D4×C13112yes—
362C4⋊C4—24no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—82no—
367C22⋊C4—28no—
368C22⋊C4—28no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—28no—
372C22⋊C4—48no—
373C22⋊C4—44no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—42no—
377C22⋊C4—82no—
378C22⋊C4—84no—
379C42—22no—
380C42—22no—
381C23—22no—
382C23—24no—
383C23—24no—
384C23—24no—
385C23—24no—
386C23—41no—
387C23—41no—
388C23—44no—
389C23—44no—
390C23—42no—
391C23—44no—
392C23—41no—
393C23—42no—
394C23—41no—
395C23—44no—
396C23—42no—
397C23—88no—
398C23C22×D4×C13112yes—
399C23C22×D4×C13111yescharacteristic
400C23H(5,𝔽2)×C13114yes—
401Q8—44no—
402Q8—44no—
403D4—44no—
404D4—44no—
405D4—48no—
406D4—48no—
407D4—84no—
408D4—84no—
409D4—816no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—48no—
420C2×C4—48no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—41no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4#120×C13111yescharacteristic
433C2×C4#120×C13111yescharacteristic
434C2×C4#120×C13112yes—
435C22—21no—
436C22—22no—
437C22—21no—
438C22—22no—
439C22—44no—
440C22—48no—
441C22—48no—
442C22—44no—
443C22—44no—
444C22—42no—
445C22—44no—
446C22—44no—
447C22—84no—
448C22—84no—
449C22—82no—
450C22—81no—
451C22—81no—
452C22C2×#120×C13111yescharacteristic
453C22#534×C13114yes—
454C22#535×C13112yes—
455C4—21no—
456C4—22no—
457C4—21no—
458C4—42no—
459C4—42no—
460C4—44no—
461C4—84no—
462C4—82no—
463C4—81no—
464C2—24no—
465C2—22no—
466C2—82no—
467C2—84no—
468C2#2613×C13111yescharacteristic
469C2#3025×C13111yescharacteristic
470C2#3027×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC24C24×C131
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3449×C131C2semidirect
2. #2482×C131C2semidirect
3. #2404×C131C2semidirect
4. #2044×C131C2semidirect
5. #2021×C131C2semidirect
6. #1820×C131C2semidirect
7. #1782×C131C2semidirect
38. C22×Q8×C131D4semidirect
40. C22×D4×C131D4semidirect
42. C23×C4×C131D4semidirect
62. C2×C4⋊C4×C131D4semidirect
63. C2×C4⋊C4×C131D4semidirect
75. C2×C42×C131D4semidirect
235. #29636C131direct (N × H)
236. C131#29636direct (N × H)
237. #3449C2×C131semidirect
238. #2482C2×C131semidirect
239. #2404C2×C131semidirect
240. #2044C2×C131semidirect
241. #2021C2×C131semidirect
242. #1820C2×C131semidirect
243. #1782C2×C131semidirect
274. C22×Q8D4×C131semidirect
276. C22×D4D4×C131semidirect
278. C23×C4D4×C131semidirect
298. C2×C4⋊C4D4×C131semidirect
299. C2×C4⋊C4D4×C131semidirect
311. C2×C42D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3449×C1312
#2482×C1312
#2404×C1312
#2044×C1312
#2021×C1312
#1820×C1312
#1782×C1312
#29636131