Finite Group Databasebeta

← C131×#18301 #45704185

Subgroups — C131×#18301 #45704185

Order 33536.

1192 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3449×C131C211yesmaximal, characteristic
2#3206×C131C212yesmaximal, complemented
3#2628×C131C211yesmaximal, characteristic, complemented
4#1604×C131C214yesmaximal, complemented
5#1601×C131C214yesmaximal, complemented
6#1517×C131C212yesmaximal, complemented
7#1458×C131C211yesmaximal, characteristic, complemented
8C22×#41×C131—21no—
9#537×C131—21no—
10#537×C131C2212yes—
11#536×C131—22no—
12#535×C131—22no—
13#534×C131—21no—
14#534×C131C2212yes—
15#532×C131—21no—
16#532×C131C2212yes—
17C2×C4⋊Q8×C131C2211yescharacteristic, complemented
18#525×C131—24no—
19C2×#117×C131C2211yescharacteristic
20#492×C131—22no—
21#487×C131—22no—
22#461×C131—24no—
23#448×C131C2218yescomplemented
24#431×C131C2212yescomplemented
25#400×C131—21no—
26#399×C131—21no—
27#395×C131C2212yescomplemented
28#393×C131C2212yes—
29#389×C131—21no—
30#382×C131C2211yescharacteristic, complemented
31#380×C131—21no—
32#327×C131C2218yescomplemented
33#324×C131C2212yescomplemented
34#323×C131C2212yes—
35C2×#41×C131—22no—
36C2×#41×C131—22no—
37C2×#41×C131—22no—
38C2×#41×C131—22no—
39C2×#41×C131—44no—
40C2×#41×C131—44no—
41C22×Q8×C131—21no—
42C22×Q8×C131C2312yes—
43C22×D4×C131—21no—
44C22×D4×C131—22no—
45C23×C4×C131—22no—
46C23×C4×C131D411yescharacteristic
47C2×SD16×C131—28no—
48C4⋊Q8×C131—21no—
49C4⋊Q8×C131—22no—
50C4⋊Q8×C131—22no—
51C4⋊Q8×C131D412yes—
52#127×C131—21no—
53#127×C131D412yes—
54#124×C131—22no—
55#124×C131—22no—
56#123×C131—24no—
57#123×C131—24no—
58C22⋊Q8×C131—24no—
59C22⋊Q8×C131—24no—
60#121×C131—24no—
61#121×C131—24no—
62#121×C131—22no—
63#121×C131—22no—
64#121×C131—22no—
65#121×C131C2314yes—
66#120×C131—24no—
67#120×C131—24no—
68C4×D4×C131—22no—
69C4×D4×C131—22no—
70C4×D4×C131—22no—
71C4×D4×C131D414yes—
72#117×C131—22no—
73#117×C131—22no—
74C2×C4⋊C4×C131—21no—
75C2×C4⋊C4×C131—21no—
76C2×C4⋊C4×C131—21no—
77C2×C4⋊C4×C131—22no—
78C2×C4⋊C4×C131D411yescharacteristic
79C2×C4⋊C4×C131C2311yescharacteristic
80C2×C22⋊C4×C131—22no—
81C2×C22⋊C4×C131D411yescharacteristic
82C2×C22⋊C4×C131C2311yescharacteristic
83C2×C42×C131D411yescharacteristic
84C2×C42×C131C2311yescharacteristic
85C4⋊C8×C131—22no—
86#103×C131—28no—
87C22⋊C8×C131C2314yes—
88C4×C8×C131—22no—
89#95×C131—22no—
90#95×C131—22no—
91#95×C131—21no—
92#95×C131C2312yes—
93C24×C131—22no—
94C24×C131C2×D411yescharacteristic
95#41×C131—44no—
96#41×C131—48no—
97#41×C131—48no—
98#41×C131—44no—
99#41×C131—44no—
100#41×C131—44no—
101C2×Q8×C131—22no—
102C2×Q8×C131—22no—
103C2×Q8×C131—24no—
104C2×Q8×C131—44no—
105C2×Q8×C131—82no—
106C2×D4×C131—24no—
107C2×D4×C131—22no—
108C2×D4×C131—24no—
109C2×D4×C131—22no—
110C2×D4×C131—22no—
111C2×D4×C131—22no—
112C2×D4×C131—22no—
113C2×D4×C131—44no—
114C2×D4×C131—44no—
115C2×D4×C131—44no—
116C2×D4×C131C2×D414yes—
117C22×C4×C131—21no—
118C22×C4×C131—21no—
119C22×C4×C131—22no—
120C22×C4×C131—24no—
121C22×C4×C131—22no—
122C22×C4×C131—24no—
123C22×C4×C131—22no—
124C22×C4×C131—22no—
125C22×C4×C131—48no—
126C22×C4×C131SD1614yescomplemented
127C22×C4×C131C2×D411yescharacteristic
128C22×C4×C131C2×D411yescharacteristic
129C22×C4×C131C2×D411yescharacteristic
130C22×C4×C131C2×D411yescharacteristic
131C22×C4×C131C2×D411yescharacteristic
132C22×C4×C131C2411yescharacteristic
133SD16×C131—88no—
134C2×C8×C131—24no—
135C4⋊C4×C131—22no—
136C4⋊C4×C131—22no—
137C4⋊C4×C131—22no—
138C4⋊C4×C131—22no—
139C4⋊C4×C131—22no—
140C4⋊C4×C131—42no—
141C4⋊C4×C131—41no—
142C4⋊C4×C131—41no—
143C4⋊C4×C131—42no—
144C4⋊C4×C131—82no—
145C4⋊C4×C131C2×D414yes—
146C22⋊C4×C131—24no—
147C22⋊C4×C131—24no—
148C22⋊C4×C131—22no—
149C22⋊C4×C131—24no—
150C22⋊C4×C131—22no—
151C22⋊C4×C131—24no—
152C22⋊C4×C131—82no—
153C42×C131—21no—
154C42×C131—21no—
155C42×C131C2×D412yes—
156C42×C131C2×D412yes—
157C23×C131—21no—
158C23×C131—21no—
159C23×C131—24no—
160C23×C131—41no—
161C23×C131—41no—
162C23×C131—44no—
163C23×C131—82no—
164C23×C131—82no—
165C23×C131C2×SD1612yes—
166C23×C131C22×D411yescharacteristic
167Q8×C131—44no—
168Q8×C131—48no—
169Q8×C131—44no—
170D4×C131—44no—
171D4×C131—44no—
172D4×C131—48no—
173D4×C131—44no—
174D4×C131—44no—
175D4×C131—44no—
176D4×C131—82no—
177D4×C131—82no—
178D4×C131—82no—
179C2×C4×C131—21no—
180C2×C4×C131—21no—
181C2×C4×C131—24no—
182C2×C4×C131—24no—
183C2×C4×C131—21no—
184C2×C4×C131—21no—
185C2×C4×C131—24no—
186C2×C4×C131—41no—
187C2×C4×C131—41no—
188C2×C4×C131—48no—
189C2×C4×C131—44no—
190C2×C4×C131—48no—
191C2×C4×C131—41no—
192C2×C4×C131—41no—
193C2×C4×C131—42no—
194C2×C4×C131—42no—
195C2×C4×C131—42no—
196C2×C4×C131—42no—
197C2×C4×C131—42no—
198C2×C4×C131—42no—
199C2×C4×C131#12012yes—
200C2×C4×C131#12011yescharacteristic
201C2×C4×C131#12011yescharacteristic
202C2×C4×C131C2×SD1612yes—
203C2×C4×C131C2×SD1612yes—
204C2×C4×C131AGL(1,ℤ/8)12yes—
205C2×C4×C131C22×D412yes—
206C8×C131—44no—
207C22×C131—21no—
208C22×C131—21no—
209C22×C131—22no—
210C22×C131—42no—
211C22×C131—41no—
212C22×C131—41no—
213C22×C131—44no—
214C22×C131—44no—
215C22×C131—44no—
216C22×C131—81no—
217C22×C131—88no—
218C22×C131C2×#12011yescharacteristic
219C22×C131C22×SD1611yescharacteristic
220C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
221C4×C131—22no—
222C4×C131—22no—
223C4×C131—22no—
224C4×C131—44no—
225C4×C131—41no—
226C4×C131—41no—
227C4×C131—82no—
228C4×C131—82no—
229C4×C131#45012yes—
230C4×C131#45012yes—
231C2×C131—21no—
232C2×C131—21no—
233C2×C131—42no—
234C2×C131—84no—
235C2×C131C2×#45011yescharacteristic
236C2×C131#302211yescharacteristic
237C2×C131#302711yescharacteristic
238#18301C13111yesmaximal, characteristic, direct product factor, Sylow
239C131#1830111yescharacteristic, direct product factor, Sylow
240#3449C2×C13111yescharacteristic
241#3206C2×C13112yescomplemented
242#2628C2×C13111yescharacteristic, complemented
243#1604C2×C13114yescomplemented
244#1601C2×C13114yescomplemented
245#1517C2×C13112yescomplemented
246#1458C2×C13111yescharacteristic, complemented
247C22×#41—21no—
248#537—21no—
249#537C22×C13112yes—
250#536—22no—
251#535—22no—
252#534—21no—
253#534C22×C13112yes—
254#532—21no—
255#532C22×C13112yes—
256C2×C4⋊Q8C22×C13111yescharacteristic, complemented
257#525—24no—
258C2×#117C22×C13111yescharacteristic
259#492—22no—
260#487—22no—
261#461—24no—
262#448C22×C13118yescomplemented
263#431C22×C13112yescomplemented
264#400—21no—
265#399—21no—
266#395C22×C13112yescomplemented
267#393C22×C13112yes—
268#389—21no—
269#382C22×C13111yescharacteristic, complemented
270#380—21no—
271#327C22×C13118yescomplemented
272#324C22×C13112yescomplemented
273#323C22×C13112yes—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—22no—
277C2×#41—22no—
278C2×#41—44no—
279C2×#41—44no—
280C22×Q8—21no—
281C22×Q8C23×C13112yes—
282C22×D4—21no—
283C22×D4—22no—
284C23×C4—22no—
285C23×C4D4×C13111yescharacteristic
286C2×SD16—28no—
287C4⋊Q8—21no—
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C4⋊Q8D4×C13112yes—
291#127—21no—
292#127D4×C13112yes—
293#124—22no—
294#124—22no—
295#123—24no—
296#123—24no—
297C22⋊Q8—24no—
298C22⋊Q8—24no—
299#121—24no—
300#121—24no—
301#121—22no—
302#121—22no—
303#121—22no—
304#121C23×C13114yes—
305#120—24no—
306#120—24no—
307C4×D4—22no—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4D4×C13114yes—
311#117—22no—
312#117—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4D4×C13111yescharacteristic
318C2×C4⋊C4C23×C13111yescharacteristic
319C2×C22⋊C4—22no—
320C2×C22⋊C4D4×C13111yescharacteristic
321C2×C22⋊C4C23×C13111yescharacteristic
322C2×C42D4×C13111yescharacteristic
323C2×C42C23×C13111yescharacteristic
324C4⋊C8—22no—
325#103—28no—
326C22⋊C8C23×C13114yes—
327C4×C8—22no—
328#95—22no—
329#95—21no—
330#95—22no—
331#95C23×C13112yes—
332C24—22no—
333C24C2×D4×C13111yescharacteristic
334#41—44no—
335#41—48no—
336#41—48no—
337#41—44no—
338#41—44no—
339#41—44no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—24no—
343C2×Q8—44no—
344C2×Q8—82no—
345C2×D4—24no—
346C2×D4—22no—
347C2×D4—24no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—44no—
353C2×D4—44no—
354C2×D4—44no—
355C2×D4C2×D4×C13114yes—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—24no—
360C22×C4—22no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—48no—
365C22×C4SD16×C13114yescomplemented
366C22×C4C2×D4×C13111yescharacteristic
367C22×C4C2×D4×C13111yescharacteristic
368C22×C4C2×D4×C13111yescharacteristic
369C22×C4C2×D4×C13111yescharacteristic
370C22×C4C2×D4×C13111yescharacteristic
371C22×C4C24×C13111yescharacteristic
372SD16—88no—
373C2×C8—24no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—42no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—42no—
383C4⋊C4—82no—
384C4⋊C4C2×D4×C13114yes—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C22⋊C4—24no—
389C22⋊C4—22no—
390C22⋊C4—24no—
391C22⋊C4—82no—
392C42—21no—
393C42—21no—
394C42C2×D4×C13112yes—
395C42C2×D4×C13112yes—
396C23—21no—
397C23—21no—
398C23—24no—
399C23—41no—
400C23—41no—
401C23—44no—
402C23—82no—
403C23—82no—
404C23C2×SD16×C13112yes—
405C23C22×D4×C13111yescharacteristic
406Q8—44no—
407Q8—48no—
408Q8—44no—
409D4—44no—
410D4—44no—
411D4—48no—
412D4—44no—
413D4—44no—
414D4—44no—
415D4—82no—
416D4—82no—
417D4—82no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—24no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—48no—
428C2×C4—44no—
429C2×C4—48no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4#120×C13112yes—
439C2×C4#120×C13111yescharacteristic
440C2×C4#120×C13111yescharacteristic
441C2×C4C2×SD16×C13112yes—
442C2×C4C2×SD16×C13112yes—
443C2×C4AGL(1,ℤ/8)×C13112yes—
444C2×C4C22×D4×C13112yes—
445C8—44no—
446C22—21no—
447C22—21no—
448C22—22no—
449C22—42no—
450C22—41no—
451C22—41no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—81no—
456C22—88no—
457C22C2×#120×C13111yescharacteristic
458C22C22×SD16×C13111yescharacteristic
459C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
460C4—22no—
461C4—22no—
462C4—22no—
463C4—44no—
464C4—41no—
465C4—41no—
466C4—82no—
467C4—82no—
468C4#450×C13112yes—
469C4#450×C13112yes—
470C2—21no—
471C2—21no—
472C2—42no—
473C2—84no—
474C2C2×#450×C13111yescharacteristic
475C2#3022×C13111yescharacteristic
476C2#3027×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#3449×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
2. #3206×C131C2semidirect
3. #2628×C131C2semidirect
4. #1604×C131C2semidirect
5. #1601×C131C2semidirect
6. #1517×C131C2semidirect
7. #1458×C131C2semidirect
17. C2×C4⋊Q8×C131C22semidirect
23. #448×C131C22semidirect
24. #431×C131C22semidirect
27. #395×C131C22semidirect
30. #382×C131C22semidirect
32. #327×C131C22semidirect
33. #324×C131C22semidirect
126. C22×C4×C131SD16semidirect
238. #18301C131direct (N × H)
239. C131#18301direct (N × H)
241. #3206C2×C131semidirect
242. #2628C2×C131semidirect
243. #1604C2×C131semidirect
244. #1601C2×C131semidirect
245. #1517C2×C131semidirect
246. #1458C2×C131semidirect
256. C2×C4⋊Q8C22×C131semidirect
262. #448C22×C131semidirect
263. #431C22×C131semidirect
266. #395C22×C131semidirect
269. #382C22×C131semidirect
271. #327C22×C131semidirect
272. #324C22×C131semidirect
365. C22×C4SD16×C131semidirect

Maximal subgroups

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

subgroupindex
#3449×C1312
#3206×C1312
#2628×C1312
#1604×C1312
#1601×C1312
#1517×C1312
#1458×C1312
#18301131