Finite Group Databasebeta

← C131×#9955 #45695839

Subgroups — C131×#9955 #45695839

Order 33536.

888 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3189×C131C211yesmaximal, characteristic, complemented
2C2×#450×C131C211yesmaximal, characteristic
3#2435×C131C211yesmaximal, characteristic
4#1996×C131C211yesmaximal, characteristic, complemented
5#1786×C131C211yesmaximal, characteristic
6#1520×C131C211yesmaximal, characteristic, complemented
7#1282×C131C211yesmaximal, characteristic, complemented
8C23×D4×C131C2211yescharacteristic
9C22×SD16×C131—21no—
10C2×#124×C131—21no—
11C2×C22⋊Q8×C131C2211yescharacteristic
12C2×C22⋊Q8×C131C2211yescharacteristic
13#484×C131—21no—
14#484×C131—21no—
15#467×C131—22no—
16#451×C131—21no—
17#451×C131—21no—
18#450×C131—22no—
19#450×C131—22no—
20C2×#102×C131—21no—
21C2×#102×C131—22no—
22C2×C22⋊C8×C131C2211yescharacteristic
23C2×C22⋊C8×C131C2211yescharacteristic
24#394×C131—22no—
25#390×C131—21no—
26#380×C131C2211yescharacteristic
27#379×C131—22no—
28C4×C22⋊C4×C131C2211yescharacteristic
29#342×C131—22no—
30#328×C131—22no—
31C25×C131—21no—
32C22×Q8×C131D411yescharacteristic
33C22×Q8×C131D411yescharacteristic
34C22×D4×C131—21no—
35C22×D4×C131—21no—
36C22×D4×C131—21no—
37C22×D4×C131—21no—
38C22×D4×C131—21no—
39C22×D4×C131—44no—
40C22×D4×C131D412yes—
41C23×C4×C131C2311yescharacteristic
42C2×Q16×C131—22no—
43C2×SD16×C131—24no—
44C2×SD16×C131—44no—
45C22×C8×C131—21no—
46C22×C8×C131D412yes—
47#124×C131—44no—
48C22⋊Q8×C131—21no—
49C22⋊Q8×C131—21no—
50C22⋊Q8×C131—21no—
51C22⋊Q8×C131—21no—
52C22⋊Q8×C131—21no—
53C22⋊Q8×C131—21no—
54C22⋊Q8×C131—21no—
55C22⋊Q8×C131—21no—
56C2×C4⋊C4×C131—21no—
57C2×C4⋊C4×C131—21no—
58C2×C4⋊C4×C131—21no—
59C2×C4⋊C4×C131D411yescharacteristic
60C2×C4⋊C4×C131D411yescharacteristic
61C2×C22⋊C4×C131—24no—
62C2×C22⋊C4×C131—21no—
63C2×C22⋊C4×C131—21no—
64C2×C22⋊C4×C131—21no—
65C2×C22⋊C4×C131—24no—
66C2×C22⋊C4×C131D412yes—
67C2×C42×C131—21no—
68#107×C131—22no—
69#103×C131—22no—
70#103×C131—22no—
71#102×C131—24no—
72#102×C131—44no—
73C22⋊C8×C131—21no—
74C22⋊C8×C131—21no—
75C22⋊C8×C131—21no—
76C22⋊C8×C131D412yes—
77#95×C131—21no—
78#95×C131—21no—
79C24×C131—22no—
80C24×C131—44no—
81C24×C131—41no—
82C24×C131—41no—
83C24×C131—42no—
84C24×C131—42no—
85C24×C131—82no—
86C24×C131C2×D411yescharacteristic
87C2×Q8×C131—21no—
88C2×Q8×C131—21no—
89C2×Q8×C131—21no—
90C2×Q8×C131—21no—
91C2×Q8×C131—42no—
92C2×Q8×C131—42no—
93C2×D4×C131—24no—
94C2×D4×C131—24no—
95C2×D4×C131—24no—
96C2×D4×C131—22no—
97C2×D4×C131—22no—
98C2×D4×C131—42no—
99C2×D4×C131—42no—
100C2×D4×C131—42no—
101C2×D4×C131—44no—
102C2×D4×C131—44no—
103C2×D4×C131—44no—
104C2×D4×C131—41no—
105C2×D4×C131—41no—
106C22×C4×C131—22no—
107C22×C4×C131—21no—
108C22×C4×C131—21no—
109C22×C4×C131—21no—
110C22×C4×C131—21no—
111C22×C4×C131—42no—
112C22×C4×C131—41no—
113C22×C4×C131C2×D411yescharacteristic
114C22×C4×C131C2×D411yescharacteristic
115C22×C4×C131C2×D411yescharacteristic
116C22×C4×C131C2×D411yescharacteristic
117C22×C4×C131C2×D411yescharacteristic
118C22×C4×C131#4111yescharacteristic
119Q16×C131—82no—
120SD16×C131—48no—
121C2×C8×C131—22no—
122C2×C8×C131—22no—
123C2×C8×C131—42no—
124C2×C8×C131—42no—
125C4⋊C4×C131—21no—
126C4⋊C4×C131—21no—
127C4⋊C4×C131—21no—
128C4⋊C4×C131—21no—
129C4⋊C4×C131—42no—
130C4⋊C4×C131—41no—
131C4⋊C4×C131—41no—
132C4⋊C4×C131—41no—
133C4⋊C4×C131—41no—
134C22⋊C4×C131—22no—
135C22⋊C4×C131—22no—
136C22⋊C4×C131—48no—
137C22⋊C4×C131—41no—
138C22⋊C4×C131—41no—
139C22⋊C4×C131—41no—
140C22⋊C4×C131—41no—
141C22⋊C4×C131—42no—
142C22⋊C4×C131—84no—
143C42×C131—42no—
144C23×C131—24no—
145C23×C131—41no—
146C23×C131—41no—
147C23×C131—44no—
148C23×C131—44no—
149C23×C131—44no—
150C23×C131—42no—
151C23×C131—42no—
152C23×C131—44no—
153C23×C131—82no—
154C23×C131—82no—
155C23×C131—88no—
156C23×C131—88no—
157C23×C131—82no—
158C23×C131—81no—
159C23×C131—81no—
160C23×C131#12011yescharacteristic
161C23×C131#12111yescharacteristic
162C23×C131#12711yescharacteristic
163C23×C131#13512yes—
164C23×C131#13712yes—
165Q8×C131—42no—
166Q8×C131—42no—
167Q8×C131—42no—
168Q8×C131—81no—
169D4×C131—24no—
170D4×C131—24no—
171D4×C131—42no—
172D4×C131—42no—
173D4×C131—44no—
174D4×C131—44no—
175C2×C4×C131—22no—
176C2×C4×C131—22no—
177C2×C4×C131—22no—
178C2×C4×C131—41no—
179C2×C4×C131—41no—
180C2×C4×C131—41no—
181C2×C4×C131—42no—
182C2×C4×C131—42no—
183C2×C4×C131—42no—
184C2×C4×C131—42no—
185C2×C4×C131—41no—
186C2×C4×C131—41no—
187C2×C4×C131—41no—
188C2×C4×C131—41no—
189C2×C4×C131—42no—
190C2×C4×C131—81no—
191C2×C4×C131—81no—
192C2×C4×C131—81no—
193C2×C4×C131—81no—
194C2×C4×C131—81no—
195C2×C4×C131#12011yescharacteristic
196C2×C4×C131#12011yescharacteristic
197C2×C4×C131#12111yescharacteristic
198C2×C4×C131#12111yescharacteristic
199C8×C131—42no—
200C8×C131—42no—
201C22×C131—21no—
202C22×C131—21no—
203C22×C131—21no—
204C22×C131—21no—
205C22×C131—21no—
206C22×C131—21no—
207C22×C131—42no—
208C22×C131—42no—
209C22×C131—48no—
210C22×C131—44no—
211C22×C131—84no—
212C22×C131—84no—
213C22×C131—88no—
214C22×C131—84no—
215C22×C131—82no—
216C22×C131—82no—
217C22×C131#39211yescharacteristic
218C22×C131#45212yes—
219C22×C131#46412yes—
220C22×C131#49511yescharacteristic
221C22×C131#49711yescharacteristic
222C4×C131—21no—
223C4×C131—21no—
224C4×C131—21no—
225C4×C131—82no—
226C4×C131—81no—
227C4×C131—81no—
228C4×C131—81no—
229C4×C131—81no—
230C4×C131—161no—
231C4×C131B(4,𝔽2)12yes—
232C2×C131—22no—
233C2×C131—21no—
234C2×C131—22no—
235C2×C131—21no—
236C2×C131—84no—
237C2×C131#200811yescharacteristic
238C2×C131#201511yescharacteristic
239C2×C131#202111yescharacteristic
240#9955C13111yesmaximal, characteristic, direct product factor, Sylow
241C131#995511yescharacteristic, direct product factor, Sylow
242#3189C2×C13111yescharacteristic, complemented
243C2×#450C2×C13111yescharacteristic
244#2435C2×C13111yescharacteristic
245#1996C2×C13111yescharacteristic, complemented
246#1786C2×C13111yescharacteristic
247#1520C2×C13111yescharacteristic, complemented
248#1282C2×C13111yescharacteristic, complemented
249C23×D4C22×C13111yescharacteristic
250C22×SD16—21no—
251C2×#124—21no—
252C2×C22⋊Q8C22×C13111yescharacteristic
253C2×C22⋊Q8C22×C13111yescharacteristic
254#484—21no—
255#484—21no—
256#467—22no—
257#451—21no—
258#451—21no—
259#450—22no—
260#450—22no—
261C2×#102—21no—
262C2×#102—22no—
263C2×C22⋊C8C22×C13111yescharacteristic
264C2×C22⋊C8C22×C13111yescharacteristic
265#394—22no—
266#390—21no—
267#380C22×C13111yescharacteristic
268#379—22no—
269C4×C22⋊C4C22×C13111yescharacteristic
270#342—22no—
271#328—22no—
272C25—21no—
273C22×Q8D4×C13111yescharacteristic
274C22×Q8D4×C13111yescharacteristic
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—44no—
281C22×D4D4×C13112yes—
282C23×C4C23×C13111yescharacteristic
283C2×Q16—22no—
284C2×SD16—24no—
285C2×SD16—44no—
286C22×C8—21no—
287C22×C8D4×C13112yes—
288#124—44no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4D4×C13111yescharacteristic
301C2×C4⋊C4D4×C13111yescharacteristic
302C2×C22⋊C4—24no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4D4×C13112yes—
308C2×C42—21no—
309#107—22no—
310#103—22no—
311#103—22no—
312#102—24no—
313#102—44no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C22⋊C8D4×C13112yes—
318#95—21no—
319#95—21no—
320C24—22no—
321C24—44no—
322C24—41no—
323C24—41no—
324C24—42no—
325C24—42no—
326C24—82no—
327C24C2×D4×C13111yescharacteristic
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—44no—
345C2×D4—41no—
346C2×D4—41no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4C2×D4×C13111yescharacteristic
355C22×C4C2×D4×C13111yescharacteristic
356C22×C4C2×D4×C13111yescharacteristic
357C22×C4C2×D4×C13111yescharacteristic
358C22×C4C2×D4×C13111yescharacteristic
359C22×C4#41×C13111yescharacteristic
360Q16—82no—
361SD16—48no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—42no—
365C2×C8—42no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—42no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—48no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—42no—
383C22⋊C4—84no—
384C42—42no—
385C23—24no—
386C23—41no—
387C23—41no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—42no—
392C23—42no—
393C23—44no—
394C23—82no—
395C23—82no—
396C23—88no—
397C23—88no—
398C23—82no—
399C23—81no—
400C23—81no—
401C23#120×C13111yescharacteristic
402C23#121×C13111yescharacteristic
403C23#127×C13111yescharacteristic
404C23#135×C13112yes—
405C23#137×C13112yes—
406Q8—42no—
407Q8—42no—
408Q8—42no—
409Q8—81no—
410D4—24no—
411D4—24no—
412D4—42no—
413D4—42no—
414D4—44no—
415D4—44no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4#120×C13111yescharacteristic
437C2×C4#120×C13111yescharacteristic
438C2×C4#121×C13111yescharacteristic
439C2×C4#121×C13111yescharacteristic
440C8—42no—
441C8—42no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—42no—
449C22—42no—
450C22—48no—
451C22—44no—
452C22—84no—
453C22—84no—
454C22—88no—
455C22—84no—
456C22—82no—
457C22—82no—
458C22#392×C13111yescharacteristic
459C22#452×C13112yes—
460C22#464×C13112yes—
461C22#495×C13111yescharacteristic
462C22#497×C13111yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—82no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—161no—
472C4B(4,𝔽2)×C13112yes—
473C2—22no—
474C2—21no—
475C2—22no—
476C2—21no—
477C2—84no—
478C2#2008×C13111yescharacteristic
479C2#2015×C13111yescharacteristic
480C2#2021×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC23×C4C23×C131
prime radicalC23×D4×C131C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3189×C131C2semidirect
4. #1996×C131C2semidirect
6. #1520×C131C2semidirect
7. #1282×C131C2semidirect
240. #9955C131direct (N × H)
241. C131#9955direct (N × H)
242. #3189C2×C131semidirect
245. #1996C2×C131semidirect
247. #1520C2×C131semidirect
248. #1282C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3189×C1312
C2×#450×C1312
#2435×C1312
#1996×C1312
#1786×C1312
#1520×C1312
#1282×C1312
#9955131