Finite Group Databasebeta

← C31×#25900 #21482659

Subgroups — C31×#25900 #21482659

Order 7936.

1406 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3496C211yesmaximal, characteristic
2C31×#2504C212yesmaximal, complemented
3C31×#2487C211yesmaximal, characteristic, complemented
4C31×#2044C214yesmaximal, complemented
5C31×#1964C212yesmaximal, complemented
6C31×#1790C214yesmaximal, complemented
7C4×C31×#99C211yesmaximal, characteristic, complemented
8C2×C31×H(5,𝔽2)C2212yes—
9C31×#547—22no—
10C31×#546—24no—
11D42×C31—22no—
12C31×#537—21no—
13C31×#534—21no—
14C31×#534C2212yes—
15C31×#532—21no—
16C2×C31×#121—21no—
17C2×C31×#121C2212yes—
18C2×C4×D4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic, complemented
20C2×C31×#99C2212yes—
21C2×C31×#99C2218yescomplemented
22C31×#400—21no—
23C31×#399—21no—
24C31×#397—24no—
25C31×#390—22no—
26C31×#389—21no—
27C31×#386C2212yes—
28C31×#386C2218yescomplemented
29C31×#385C2212yescomplemented
30C31×#382—22no—
31C31×#380—21no—
32C31×#380C2211yescharacteristic, complemented
33C4×C22⋊C4×C31C2212yescomplemented
34C31×#342C2212yescomplemented
35C31×H(5,𝔽2)—28no—
36C31×H(5,𝔽2)—44no—
37C2×#41×C31—22no—
38C2×#41×C31—24no—
39C22×D4×C31—22no—
40C22×D4×C31—24no—
41C22×D4×C31—21no—
42C22×D4×C31D412yes—
43C22×D4×C31C2314yes—
44C22×D4×C31C2311yescharacteristic
45C23×C4×C31D411yescharacteristic
46C23×C4×C31C2312yes—
47C23×C4×C31C2311yescharacteristic
48C31×C4⋊Q8—21no—
49C31×#127—21no—
50C31×#124—22no—
51C31×#123—24no—
52C31×#123—24no—
53C31×C22⋊Q8—24no—
54C31×#121—22no—
55C31×#121—22no—
56C31×#121—24no—
57C31×#121—22no—
58C31×#121—22no—
59C31×#121—22no—
60C31×#121—22no—
61C31×#121—22no—
62C31×#121—22no—
63C31×#120—24no—
64C31×#120—24no—
65C4×D4×C31—22no—
66C4×D4×C31—22no—
67C4×D4×C31—22no—
68C4×D4×C31—22no—
69C2×C4⋊C4×C31—21no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—21no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31D411yescharacteristic
77C2×C4⋊C4×C31D412yes—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—28no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31D414yes—
82C2×C22⋊C4×C31D411yescharacteristic
83C2×C22⋊C4×C31C2314yes—
84C2×C22⋊C4×C31C2312yes—
85C2×C22⋊C4×C31C2311yescharacteristic
86C2×C42×C31—22no—
87C2×C42×C31D411yescharacteristic
88C31×#99—24no—
89C31×#99—48no—
90C31×#95—22no—
91C31×#95—28no—
92C31×#95—21no—
93C31×#95—22no—
94C31×#95—22no—
95C24×C31—22no—
96C24×C31C2×D414yes—
97C24×C31C2×D411yescharacteristic
98C24×C31C2411yescharacteristic
99#41×C31—416no—
100#41×C31—44no—
101#41×C31—44no—
102C2×Q8×C31—22no—
103C2×D4×C31—22no—
104C2×D4×C31—22no—
105C2×D4×C31—24no—
106C2×D4×C31—22no—
107C2×D4×C31—24no—
108C2×D4×C31—24no—
109C2×D4×C31—28no—
110C2×D4×C31—28no—
111C2×D4×C31—22no—
112C2×D4×C31—22no—
113C2×D4×C31—22no—
114C2×D4×C31—22no—
115C2×D4×C31—44no—
116C2×D4×C31—416no—
117C2×D4×C31—44no—
118C2×D4×C31—44no—
119C2×D4×C31—82no—
120C2×D4×C31#4114yes—
121C22×C4×C31—22no—
122C22×C4×C31—24no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—24no—
126C22×C4×C31—22no—
127C22×C4×C31—24no—
128C22×C4×C31—22no—
129C22×C4×C31—42no—
130C22×C4×C31—42no—
131C22×C4×C31—82no—
132C22×C4×C31C2×D414yes—
133C22×C4×C31C2×D412yes—
134C22×C4×C31C2×D411yescharacteristic
135C22×C4×C31C2×D411yescharacteristic
136C22×C4×C31C2×D411yescharacteristic
137C22×C4×C31C2×D411yescharacteristic
138C22×C4×C31C2×D412yes—
139C22×C4×C31C2×D411yescharacteristic
140C4⋊C4×C31—22no—
141C4⋊C4×C31—22no—
142C4⋊C4×C31—22no—
143C4⋊C4×C31—22no—
144C4⋊C4×C31—22no—
145C4⋊C4×C31—42no—
146C4⋊C4×C31—41no—
147C4⋊C4×C31—42no—
148C4⋊C4×C31—41no—
149C4⋊C4×C31—82no—
150C22⋊C4×C31—24no—
151C22⋊C4×C31—24no—
152C22⋊C4×C31—22no—
153C22⋊C4×C31—24no—
154C22⋊C4×C31—22no—
155C22⋊C4×C31—24no—
156C22⋊C4×C31—24no—
157C22⋊C4×C31—24no—
158C22⋊C4×C31—24no—
159C22⋊C4×C31—88no—
160C22⋊C4×C31—82no—
161C42×C31—21no—
162C42×C31—21no—
163C42×C31—44no—
164#25900C3111yesmaximal, characteristic, direct product factor, Sylow
165C23×C31—21no—
166C23×C31—21no—
167C23×C31—24no—
168C23×C31—28no—
169C23×C31—41no—
170C23×C31—41no—
171C23×C31—41no—
172C23×C31—41no—
173C23×C31—44no—
174C23×C31—44no—
175C23×C31—44no—
176C23×C31—82no—
177C23×C31—82no—
178C23×C31#12412yes—
179C23×C31C22×D411yescharacteristic
180C23×C31C22×D412yes—
181C23×C31C2×#4112yes—
182C23×C31H(5,𝔽2)12yes—
183Q8×C31—44no—
184D4×C31—28no—
185D4×C31—44no—
186D4×C31—48no—
187D4×C31—44no—
188D4×C31—44no—
189D4×C31—48no—
190D4×C31—44no—
191D4×C31—82no—
192D4×C31—82no—
193D4×C31—82no—
194C2×C4×C31—21no—
195C2×C4×C31—21no—
196C2×C4×C31—24no—
197C2×C4×C31—22no—
198C2×C4×C31—21no—
199C2×C4×C31—21no—
200C2×C4×C31—24no—
201C2×C4×C31—28no—
202C2×C4×C31—42no—
203C2×C4×C31—41no—
204C2×C4×C31—48no—
205C2×C4×C31—44no—
206C2×C4×C31—42no—
207C2×C4×C31—41no—
208C2×C4×C31—41no—
209C2×C4×C31—44no—
210C2×C4×C31—44no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31—48no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—44no—
219C2×C4×C31—81no—
220C2×C4×C31#12011yescharacteristic
221C2×C4×C31#12012yes—
222C2×C4×C31#12011yescharacteristic
223C2×C4×C31#12412yes—
224#3496C2×C3111yescharacteristic
225#2504C2×C3112yescomplemented
226#2487C2×C3111yescharacteristic, complemented
227#2044C2×C3114yescomplemented
228#1964C2×C3112yescomplemented
229#1790C2×C3114yescomplemented
230C4×#99C2×C3111yescharacteristic, complemented
231C22×C31—21no—
232C22×C31—22no—
233C22×C31—21no—
234C22×C31—22no—
235C22×C31—22no—
236C22×C31—42no—
237C22×C31—42no—
238C22×C31—42no—
239C22×C31—41no—
240C22×C31—41no—
241C22×C31—44no—
242C22×C31—44no—
243C22×C31—44no—
244C22×C31—81no—
245C22×C31—88no—
246C22×C31—164no—
247C22×C31C2×#12011yescharacteristic
248C22×C31C2×#12411yescharacteristic
249C22×C31#53511yescharacteristic
250C22×C31#54614yes—
251C4×C31—22no—
252C4×C31—21no—
253C4×C31—22no—
254C4×C31—44no—
255C4×C31—41no—
256C4×C31—41no—
257C4×C31—82no—
258C4×C31—84no—
259C4×C31—82no—
260C4×C31#45812yes—
261C2×H(5,𝔽2)C22×C3112yes—
262#547—22no—
263#546—24no—
264D42—22no—
265#537—21no—
266#534—21no—
267#534C22×C3112yes—
268#532—21no—
269C2×#121—21no—
270C2×#121C22×C3112yes—
271C2×C4×D4C22×C3111yescharacteristic
272C22×C4⋊C4C22×C3111yescharacteristic, complemented
273C2×#99C22×C3112yes—
274C2×#99C22×C3118yescomplemented
275#400—21no—
276#399—21no—
277#397—24no—
278#390—22no—
279#389—21no—
280#386C22×C3112yes—
281#386C22×C3118yescomplemented
282#385C22×C3112yescomplemented
283#382—22no—
284#380—21no—
285#380C22×C3111yescharacteristic, complemented
286C4×C22⋊C4C22×C3112yescomplemented
287#342C22×C3112yescomplemented
288C2×C31—21no—
289C2×C31—24no—
290C2×C31—21no—
291C2×C31—42no—
292C2×C31—84no—
293C2×C31#243511yescharacteristic
294C2×C31C2×#45811yescharacteristic
295C2×C31#302711yescharacteristic
296H(5,𝔽2)—28no—
297H(5,𝔽2)—44no—
298C2×#41—22no—
299C2×#41—24no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—21no—
303C22×D4D4×C3112yes—
304C22×D4C23×C3114yes—
305C22×D4C23×C3111yescharacteristic
306C23×C4D4×C3111yescharacteristic
307C23×C4C23×C3112yes—
308C23×C4C23×C3111yescharacteristic
309C4⋊Q8—21no—
310#127—21no—
311#124—22no—
312#123—24no—
313#123—24no—
314C22⋊Q8—24no—
315#121—22no—
316#121—22no—
317#121—24no—
318#121—22no—
319#121—22no—
320#121—22no—
321#121—22no—
322#121—22no—
323#121—22no—
324#120—24no—
325#120—24no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4D4×C3111yescharacteristic
338C2×C4⋊C4D4×C3112yes—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4D4×C3111yescharacteristic
343C2×C22⋊C4D4×C3114yes—
344C2×C22⋊C4C23×C3114yes—
345C2×C22⋊C4C23×C3112yes—
346C2×C22⋊C4C23×C3111yescharacteristic
347C2×C42—22no—
348C2×C42D4×C3111yescharacteristic
349#99—24no—
350#99—48no—
351#95—22no—
352#95—22no—
353#95—21no—
354#95—28no—
355#95—22no—
356C31#2590011yescharacteristic, direct product factor, Sylow
357C24—22no—
358C24C2×D4×C3114yes—
359C24C2×D4×C3111yescharacteristic
360C24C24×C3111yescharacteristic
361#41—416no—
362#41—44no—
363#41—44no—
364C2×Q8—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—24no—
368C2×D4—22no—
369C2×D4—24no—
370C2×D4—24no—
371C2×D4—28no—
372C2×D4—28no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—44no—
378C2×D4—416no—
379C2×D4—44no—
380C2×D4—44no—
381C2×D4—82no—
382C2×D4#41×C3114yes—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—82no—
394C22×C4C2×D4×C3114yes—
395C22×C4C2×D4×C3112yes—
396C22×C4C2×D4×C3111yescharacteristic
397C22×C4C2×D4×C3111yescharacteristic
398C22×C4C2×D4×C3111yescharacteristic
399C22×C4C2×D4×C3111yescharacteristic
400C22×C4C2×D4×C3112yes—
401C22×C4C2×D4×C3111yescharacteristic
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—42no—
408C4⋊C4—41no—
409C4⋊C4—42no—
410C4⋊C4—41no—
411C4⋊C4—82no—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—22no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—88no—
422C22⋊C4—82no—
423C42—21no—
424C42—21no—
425C42—44no—
426C23—21no—
427C23—21no—
428C23—24no—
429C23—28no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23—82no—
438C23—82no—
439C23C31×#12412yes—
440C23C22×D4×C3111yescharacteristic
441C23C22×D4×C3112yes—
442C23C2×#41×C3112yes—
443C23C31×H(5,𝔽2)12yes—
444Q8—44no—
445D4—28no—
446D4—44no—
447D4—48no—
448D4—44no—
449D4—44no—
450D4—48no—
451D4—44no—
452D4—82no—
453D4—82no—
454D4—82no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—24no—
462C2×C4—28no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—48no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—44no—
471C2×C4—44no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—48no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—44no—
480C2×C4—81no—
481C2×C4C31×#12011yescharacteristic
482C2×C4C31×#12012yes—
483C2×C4C31×#12011yescharacteristic
484C2×C4C31×#12412yes—
485C22—21no—
486C22—22no—
487C22—21no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—41no—
494C22—41no—
495C22—44no—
496C22—44no—
497C22—44no—
498C22—81no—
499C22—88no—
500C22—164no—
501C22C2×C31×#12011yescharacteristic
502C22C2×C31×#12411yescharacteristic
503C22C31×#53511yescharacteristic
504C22C31×#54614yes—
505C4—22no—
506C4—21no—
507C4—22no—
508C4—44no—
509C4—41no—
510C4—41no—
511C4—82no—
512C4—84no—
513C4—82no—
514C4C31×#45812yes—
515C2—21no—
516C2—24no—
517C2—21no—
518C2—42no—
519C2—84no—
520C2C31×#243511yescharacteristic
521C2C2×C31×#45811yescharacteristic
522C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC31×#3496C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2504C2semidirect
3. C31×#2487C2semidirect
4. C31×#2044C2semidirect
5. C31×#1964C2semidirect
6. C31×#1790C2semidirect
7. C4×C31×#99C2semidirect
19. C22×C4⋊C4×C31C22semidirect
21. C2×C31×#99C22semidirect
28. C31×#386C22semidirect
29. C31×#385C22semidirect
32. C31×#380C22semidirect
33. C4×C22⋊C4×C31C22semidirect
34. C31×#342C22semidirect
164. #25900C31direct (N × H)
225. #2504C2×C31semidirect
226. #2487C2×C31semidirect
227. #2044C2×C31semidirect
228. #1964C2×C31semidirect
229. #1790C2×C31semidirect
230. C4×#99C2×C31semidirect
272. C22×C4⋊C4C22×C31semidirect
274. C2×#99C22×C31semidirect
281. #386C22×C31semidirect
282. #385C22×C31semidirect
285. #380C22×C31semidirect
286. C4×C22⋊C4C22×C31semidirect
287. #342C22×C31semidirect
356. C31#25900direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34962
C31×#25042
C31×#24872
C31×#20442
C31×#19642
C31×#17902
C4×C31×#992
#2590031