Finite Group Databasebeta

← C131×#18302 #45704186

Subgroups — C131×#18302 #45704186

Order 33536.

1032 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3458×C131C211yesmaximal, characteristic, complemented
2#3208×C131C212yesmaximal, complemented
3#2619×C131C211yesmaximal, characteristic
4#1599×C131C214yesmaximal, complemented
5#1596×C131C214yesmaximal, complemented
6#1518×C131C212yesmaximal, complemented
7#1458×C131C211yesmaximal, characteristic, complemented
8#544×C131—22no—
9#544×C131—22no—
10#544×C131—21no—
11#544×C131C2212yes—
12#543×C131—21no—
13#543×C131C2212yes—
14#533×C131—24no—
15#533×C131—21no—
16#533×C131C2212yes—
17C2×#127×C131C2211yescharacteristic
18C2×#121×C131—21no—
19C2×#117×C131—21no—
20C2×#117×C131C2211yescharacteristic
21#492×C131—22no—
22#486×C131—22no—
23#460×C131—24no—
24#450×C131C2218yes—
25#431×C131C2212yes—
26#394×C131—21no—
27#394×C131C2212yes—
28#392×C131—21no—
29#392×C131C2212yes—
30#390×C131—21no—
31#382×C131C2211yescharacteristic
32#328×C131C2218yes—
33#324×C131C2212yes—
34#323×C131C2212yes—
35C22×D4×C131—22no—
36C22×D4×C131—21no—
37C22×D4×C131—21no—
38C22×D4×C131C2312yes—
39C23×C4×C131D411yescharacteristic
40C2×SD16×C131—28no—
41C4⋊Q8×C131—24no—
42C4⋊Q8×C131—21no—
43C4⋊Q8×C131—21no—
44C4⋊Q8×C131—24no—
45C4⋊Q8×C131D412yescomplemented
46C4⋊Q8×C131D412yescomplemented
47#127×C131—22no—
48#127×C131—22no—
49#125×C131—24no—
50#125×C131—22no—
51#125×C131—24no—
52#125×C131—22no—
53C22⋊Q8×C131—24no—
54C22⋊Q8×C131—24no—
55C22⋊Q8×C131—24no—
56C22⋊Q8×C131—22no—
57C22⋊Q8×C131—22no—
58C22⋊Q8×C131—22no—
59C22⋊Q8×C131—24no—
60C22⋊Q8×C131C2314yes—
61#121×C131—44no—
62C4×Q8×C131—22no—
63C4×Q8×C131—22no—
64C4×Q8×C131—22no—
65C4×Q8×C131D414yescomplemented
66#117×C131—22no—
67#117×C131—22no—
68#117×C131—22no—
69#117×C131—22no—
70#117×C131—22no—
71#117×C131—22no—
72C2×C4⋊C4×C131—21no—
73C2×C4⋊C4×C131—21no—
74C2×C4⋊C4×C131—21no—
75C2×C4⋊C4×C131D411yescharacteristic
76C2×C4⋊C4×C131C2311yescharacteristic
77C2×C22⋊C4×C131—22no—
78C2×C22⋊C4×C131—22no—
79C2×C22⋊C4×C131—22no—
80C2×C22⋊C4×C131—22no—
81C2×C22⋊C4×C131D411yescharacteristic
82C2×C22⋊C4×C131C2311yescharacteristic
83C2×C42×C131—22no—
84C2×C42×C131D411yescharacteristic
85C2×C42×C131C2311yescharacteristic
86C4⋊C8×C131—22no—
87#102×C131—28no—
88C22⋊C8×C131C2314yes—
89C4×C8×C131—22no—
90#95×C131—21no—
91#95×C131C2312yes—
92C24×C131—22no—
93C24×C131C2×D411yescharacteristic
94C2×Q8×C131—22no—
95C2×Q8×C131—22no—
96C2×Q8×C131—22no—
97C2×Q8×C131C2×D414yes—
98C2×D4×C131—24no—
99C2×D4×C131—44no—
100C2×D4×C131—42no—
101C2×D4×C131—41no—
102C2×D4×C131—41no—
103C2×D4×C131—42no—
104C2×D4×C131—42no—
105C2×D4×C131—82no—
106C2×D4×C131—82no—
107C2×D4×C131—82no—
108C2×D4×C131—82no—
109C22×C4×C131—21no—
110C22×C4×C131—21no—
111C22×C4×C131—22no—
112C22×C4×C131—22no—
113C22×C4×C131—22no—
114C22×C4×C131—22no—
115C22×C4×C131SD1614yescomplemented
116C22×C4×C131C2×D411yescharacteristic
117C22×C4×C131C2×D411yescharacteristic
118C22×C4×C131C2×D411yescharacteristic
119C22×C4×C131C2×D411yescharacteristic
120C22×C4×C131C2×D411yescharacteristic
121C22×C4×C131C2411yescharacteristic
122SD16×C131—88no—
123C2×C8×C131—24no—
124C4⋊C4×C131—22no—
125C4⋊C4×C131—22no—
126C4⋊C4×C131—22no—
127C4⋊C4×C131—24no—
128C4⋊C4×C131—24no—
129C4⋊C4×C131—22no—
130C4⋊C4×C131—22no—
131C4⋊C4×C131—22no—
132C4⋊C4×C131—22no—
133C4⋊C4×C131—22no—
134C4⋊C4×C131—24no—
135C4⋊C4×C131—22no—
136C4⋊C4×C131—24no—
137C4⋊C4×C131—42no—
138C4⋊C4×C131C2×D414yes—
139C22⋊C4×C131—24no—
140C22⋊C4×C131—24no—
141C22⋊C4×C131—22no—
142C22⋊C4×C131—22no—
143C22⋊C4×C131—44no—
144C22⋊C4×C131—82no—
145C22⋊C4×C131—82no—
146C42×C131—24no—
147C42×C131—24no—
148C42×C131—21no—
149C42×C131—21no—
150C42×C131C2×D412yes—
151C42×C131C2×D412yes—
152C23×C131—21no—
153C23×C131—21no—
154C23×C131—41no—
155C23×C131—41no—
156C23×C131—42no—
157C23×C131—42no—
158C23×C131—42no—
159C23×C131—42no—
160C23×C131—42no—
161C23×C131—42no—
162C23×C131—42no—
163C23×C131C2×SD1612yes—
164C23×C131C22×D411yescharacteristic
165Q8×C131—44no—
166Q8×C131—82no—
167Q8×C131—82no—
168Q8×C131—82no—
169D4×C131—48no—
170D4×C131—84no—
171D4×C131—88no—
172D4×C131—82no—
173D4×C131—82no—
174C2×C4×C131—21no—
175C2×C4×C131—21no—
176C2×C4×C131—24no—
177C2×C4×C131—24no—
178C2×C4×C131—24no—
179C2×C4×C131—21no—
180C2×C4×C131—21no—
181C2×C4×C131—24no—
182C2×C4×C131—41no—
183C2×C4×C131—41no—
184C2×C4×C131—41no—
185C2×C4×C131—41no—
186C2×C4×C131—42no—
187C2×C4×C131—42no—
188C2×C4×C131—42no—
189C2×C4×C131—82no—
190C2×C4×C131—82no—
191C2×C4×C131#12012yes—
192C2×C4×C131#12011yescharacteristic
193C2×C4×C131#12011yescharacteristic
194C2×C4×C131C2×SD1612yes—
195C2×C4×C131C2×SD1612yes—
196C2×C4×C131#13712yes—
197C2×C4×C131C22×D412yes—
198C8×C131—44no—
199C22×C131—21no—
200C22×C131—21no—
201C22×C131—22no—
202C22×C131—42no—
203C22×C131—41no—
204C22×C131—41no—
205C22×C131—81no—
206C22×C131—82no—
207C22×C131—82no—
208C22×C131—82no—
209C22×C131—82no—
210C22×C131—82no—
211C22×C131—82no—
212C22×C131—82no—
213C22×C131C2×#12011yescharacteristic
214C22×C131C22×SD1611yescharacteristic
215C22×C131C2×#13711yescharacteristic
216C4×C131—22no—
217C4×C131—22no—
218C4×C131—22no—
219C4×C131—41no—
220C4×C131—44no—
221C4×C131—41no—
222C4×C131—44no—
223C4×C131—82no—
224C4×C131#44812yes—
225C4×C131#44812yes—
226C2×C131—21no—
227C2×C131—21no—
228C2×C131—42no—
229C2×C131—162no—
230C2×C131C2×#44811yescharacteristic
231C2×C131#302111yescharacteristic
232C2×C131#302711yescharacteristic
233#18302C13111yesmaximal, characteristic, direct product factor, Sylow
234C131#1830211yescharacteristic, direct product factor, Sylow
235#3458C2×C13111yescharacteristic, complemented
236#3208C2×C13112yescomplemented
237#2619C2×C13111yescharacteristic
238#1599C2×C13114yescomplemented
239#1596C2×C13114yescomplemented
240#1518C2×C13112yescomplemented
241#1458C2×C13111yescharacteristic, complemented
242#544—22no—
243#544—22no—
244#544—21no—
245#544C22×C13112yes—
246#543—21no—
247#543C22×C13112yes—
248#533—24no—
249#533—21no—
250#533C22×C13112yes—
251C2×#127C22×C13111yescharacteristic
252C2×#121—21no—
253C2×#117—21no—
254C2×#117C22×C13111yescharacteristic
255#492—22no—
256#486—22no—
257#460—24no—
258#450C22×C13118yes—
259#431C22×C13112yes—
260#394—21no—
261#394C22×C13112yes—
262#392—21no—
263#392C22×C13112yes—
264#390—21no—
265#382C22×C13111yescharacteristic
266#328C22×C13118yes—
267#324C22×C13112yes—
268#323C22×C13112yes—
269C22×D4—22no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4C23×C13112yes—
273C23×C4D4×C13111yescharacteristic
274C2×SD16—28no—
275C4⋊Q8—24no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—24no—
279C4⋊Q8D4×C13112yescomplemented
280C4⋊Q8D4×C13112yescomplemented
281#127—22no—
282#127—22no—
283#125—24no—
284#125—22no—
285#125—24no—
286#125—22no—
287C22⋊Q8—24no—
288C22⋊Q8—24no—
289C22⋊Q8—24no—
290C22⋊Q8—22no—
291C22⋊Q8—22no—
292C22⋊Q8—22no—
293C22⋊Q8—24no—
294C22⋊Q8C23×C13114yes—
295#121—44no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×Q8—22no—
299C4×Q8D4×C13114yescomplemented
300#117—22no—
301#117—22no—
302#117—22no—
303#117—22no—
304#117—22no—
305#117—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4D4×C13111yescharacteristic
310C2×C4⋊C4C23×C13111yescharacteristic
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4D4×C13111yescharacteristic
316C2×C22⋊C4C23×C13111yescharacteristic
317C2×C42—22no—
318C2×C42D4×C13111yescharacteristic
319C2×C42C23×C13111yescharacteristic
320C4⋊C8—22no—
321#102—28no—
322C22⋊C8C23×C13114yes—
323C4×C8—22no—
324#95—21no—
325#95C23×C13112yes—
326C24—22no—
327C24C2×D4×C13111yescharacteristic
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8C2×D4×C13114yes—
332C2×D4—24no—
333C2×D4—44no—
334C2×D4—42no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4—82no—
340C2×D4—82no—
341C2×D4—82no—
342C2×D4—82no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4SD16×C13114yescomplemented
350C22×C4C2×D4×C13111yescharacteristic
351C22×C4C2×D4×C13111yescharacteristic
352C22×C4C2×D4×C13111yescharacteristic
353C22×C4C2×D4×C13111yescharacteristic
354C22×C4C2×D4×C13111yescharacteristic
355C22×C4C24×C13111yescharacteristic
356SD16—88no—
357C2×C8—24no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—42no—
372C4⋊C4C2×D4×C13114yes—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—44no—
378C22⋊C4—82no—
379C22⋊C4—82no—
380C42—24no—
381C42—24no—
382C42—21no—
383C42—21no—
384C42C2×D4×C13112yes—
385C42C2×D4×C13112yes—
386C23—21no—
387C23—21no—
388C23—41no—
389C23—41no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23C2×SD16×C13112yes—
398C23C22×D4×C13111yescharacteristic
399Q8—44no—
400Q8—82no—
401Q8—82no—
402Q8—82no—
403D4—48no—
404D4—84no—
405D4—88no—
406D4—82no—
407D4—82no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—24no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4#120×C13112yes—
426C2×C4#120×C13111yescharacteristic
427C2×C4#120×C13111yescharacteristic
428C2×C4C2×SD16×C13112yes—
429C2×C4C2×SD16×C13112yes—
430C2×C4#137×C13112yes—
431C2×C4C22×D4×C13112yes—
432C8—44no—
433C22—21no—
434C22—21no—
435C22—22no—
436C22—42no—
437C22—41no—
438C22—41no—
439C22—81no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22—82no—
444C22—82no—
445C22—82no—
446C22—82no—
447C22C2×#120×C13111yescharacteristic
448C22C22×SD16×C13111yescharacteristic
449C22C2×#137×C13111yescharacteristic
450C4—22no—
451C4—22no—
452C4—22no—
453C4—41no—
454C4—44no—
455C4—41no—
456C4—44no—
457C4—82no—
458C4#448×C13112yes—
459C4#448×C13112yes—
460C2—21no—
461C2—21no—
462C2—42no—
463C2—162no—
464C2C2×#448×C13111yescharacteristic
465C2#3021×C13111yescharacteristic
466C2#3027×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#2619×C131C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3458×C131C2semidirect
2. #3208×C131C2semidirect
4. #1599×C131C2semidirect
5. #1596×C131C2semidirect
6. #1518×C131C2semidirect
7. #1458×C131C2semidirect
45. C4⋊Q8×C131D4semidirect
46. C4⋊Q8×C131D4semidirect
65. C4×Q8×C131D4semidirect
115. C22×C4×C131SD16semidirect
233. #18302C131direct (N × H)
234. C131#18302direct (N × H)
235. #3458C2×C131semidirect
236. #3208C2×C131semidirect
238. #1599C2×C131semidirect
239. #1596C2×C131semidirect
240. #1518C2×C131semidirect
241. #1458C2×C131semidirect
279. C4⋊Q8D4×C131semidirect
280. C4⋊Q8D4×C131semidirect
299. C4×Q8D4×C131semidirect
349. C22×C4SD16×C131semidirect

Maximal subgroups

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

subgroupindex
#3458×C1312
#3208×C1312
#2619×C1312
#1599×C1312
#1596×C1312
#1518×C1312
#1458×C1312
#18302131