Finite Group Databasebeta

← C31×#12793 #21469552

Subgroups — C31×#12793 #21469552

Order 7936.

808 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×#120C211yesmaximal, characteristic
2C2×C31×AΣL(1,𝔽16)C212yesmaximal
3C31×#1800C211yesmaximal, characteristic, complemented
4C31×#1799C211yesmaximal, characteristic, complemented
5C31×#1390C212yesmaximal, complemented
6C24×C4×C31C411yescharacteristic, complemented
7C2×C31×#120C2211yescharacteristic
8C2×C4×D4×C31—21no—
9C2×C4×D4×C31C2211yescharacteristic
10C31×#423—21no—
11C2×C31×#100C2212yes—
12C2×C31×#99C2212yes—
13C31×#386—21no—
14C31×#386C2211yescharacteristic
15C31×#385—21no—
16C31×#385C411yescharacteristic, complemented
17C31×#380—21no—
18C31×#379C411yescharacteristic, complemented
19C4×C22⋊C4×C31—21no—
20C4×C22⋊C4×C31C411yescharacteristic, complemented
21C31×AΣL(1,𝔽16)—24no—
22C31×#343—21no—
23C31×#342—21no—
24C25×C31C2×C411yescharacteristic
25C22×D4×C31—21no—
26C22×D4×C31C2311yescharacteristic
27C23×C4×C31—21no—
28C23×C4×C31—21no—
29C23×C4×C31—44no—
30C23×C4×C31—41no—
31C23×C4×C31—41no—
32C23×C4×C31C2×C411yescharacteristic
33C23×C4×C31C2×C411yescharacteristic
34C23×C4×C31D411yescharacteristic
35C2×M16×C31—22no—
36C31×#120—21no—
37C31×#120—21no—
38C31×#120D412yes—
39C31×#120Q812yes—
40C4×D4×C31—41no—
41C4×D4×C31—41no—
42C4×D4×C31—44no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—41no—
45C2×C4⋊C4×C31D411yescharacteristic
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31—21no—
49C2×C22⋊C4×C31—21no—
50C2×C22⋊C4×C31—22no—
51C2×C22⋊C4×C31C2×C411yescharacteristic
52C2×C22⋊C4×C31C2×C411yescharacteristic
53C2×C22⋊C4×C31C2×C411yescharacteristic
54C2×C22⋊C4×C31D411yescharacteristic
55C2×C42×C31—21no—
56C2×C42×C31D411yescharacteristic
57C31×C4⋊C8—41no—
58C31×C4⋊C8—41no—
59C31×#100—22no—
60C31×#100—22no—
61C31×#99—22no—
62C31×#99—22no—
63C31×#95—21no—
64C31×#95—21no—
65C31×#95—21no—
66C31×#95—41no—
67C24×C31—21no—
68C24×C31—21no—
69C24×C31—42no—
70C24×C31—41no—
71C24×C31—42no—
72C24×C31—41no—
73C24×C31C4⋊C412yescomplemented
74C24×C31C22×C411yescharacteristic
75C24×C31C2×D411yescharacteristic
76C2×D4×C31—22no—
77C2×D4×C31—22no—
78C2×D4×C31—41no—
79C2×D4×C31—41no—
80C2×D4×C31—42no—
81C2×D4×C31—42no—
82C2×D4×C31C2×D411yescharacteristic
83C2×D4×C31C2×Q811yescharacteristic
84C2×D4×C31#4111yescharacteristic
85C2×D4×C31#4111yescharacteristic
86C22×C4×C31—24no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—42no—
95C22×C4×C31—42no—
96C22×C4×C31—42no—
97C22×C4×C31—42no—
98C22×C4×C31—42no—
99C22×C4×C31—42no—
100C22×C4×C31—42no—
101C22×C4×C31—44no—
102C22×C4×C31—44no—
103C22×C4×C31—44no—
104C22×C4×C31—41no—
105C22×C4×C31—41no—
106C22×C4×C31—41no—
107C22×C4×C31—44no—
108C22×C4×C31—42no—
109C22×C4×C31C22⋊C411yescharacteristic
110C22×C4×C31C22⋊C411yescharacteristic
111C22×C4×C31C22⋊C411yescharacteristic
112C22×C4×C31C22⋊C411yescharacteristic
113C22×C4×C31C2×D411yescharacteristic
114M16×C31—42no—
115M16×C31—42no—
116C2×C8×C31—42no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31—42no—
119C4⋊C4×C31—82no—
120C22⋊C4×C31—21no—
121C22⋊C4×C31—22no—
122C22⋊C4×C31—22no—
123C22⋊C4×C31—41no—
124C22⋊C4×C31—41no—
125C22⋊C4×C31—42no—
126C22⋊C4×C31—42no—
127C22⋊C4×C31—42no—
128C22⋊C4×C31—41no—
129C22⋊C4×C31—42no—
130C22⋊C4×C31—42no—
131C22⋊C4×C31C4⋊C412yescomplemented
132C42×C31—21no—
133C42×C31—21no—
134C42×C31—42no—
135#12793C3111yesmaximal, characteristic, direct product factor, Sylow
136C23×C31—22no—
137C23×C31—22no—
138C23×C31—22no—
139C23×C31—21no—
140C23×C31—21no—
141C23×C31—21no—
142C23×C31—21no—
143C23×C31—41no—
144C23×C31—44no—
145C23×C31—42no—
146C23×C31—41no—
147C23×C31—41no—
148C23×C31—41no—
149C23×C31—44no—
150C23×C31—42no—
151C23×C31—41no—
152C23×C31—41no—
153C23×C31—42no—
154C23×C31—42no—
155C23×C31—42no—
156C23×C31—48no—
157C23×C31—42no—
158C23×C31—41no—
159C23×C31—41no—
160C23×C31C2×C22⋊C411yescharacteristic
161C23×C31C2×C4⋊C411yescharacteristic
162C23×C31#11711yescharacteristic
163C23×C31#12111yescharacteristic
164C23×C31C22⋊Q811yescharacteristic
165D4×C31—41no—
166D4×C31—41no—
167D4×C31—41no—
168D4×C31—41no—
169D4×C31—44no—
170D4×C31—44no—
171C2×C4×C31—21no—
172C2×C4×C31—21no—
173C2×C4×C31—22no—
174C2×C4×C31—22no—
175C2×C4×C31—22no—
176C2×C4×C31—21no—
177C2×C4×C31—21no—
178C2×C4×C31—21no—
179C2×C4×C31—44no—
180C2×C4×C31—42no—
181C2×C4×C31—41no—
182C2×C4×C31—41no—
183C2×C4×C31—41no—
184C2×C4×C31—48no—
185C2×C4×C31—42no—
186C2×C4×C31—41no—
187C2×C4×C31—42no—
188C2×C4×C31—44no—
189C2×C4×C31—42no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—41no—
193C2×C4×C31—42no—
194C2×C4×C31—41no—
195C2×C4×C31—41no—
196C2×C4×C31—41no—
197C2×C4×C31—81no—
198C2×C4×C31—82no—
199C2×C4×C31—82no—
200C2×C4×C31—82no—
201C2×C4×C31#9911yescharacteristic
202C2×C4×C31#9911yescharacteristic
203C2×C4×C31#12111yescharacteristic
204C2×C4×C31C22⋊Q811yescharacteristic
205C8×C31—82no—
206C4×#120C2×C3111yescharacteristic
207C2×AΣL(1,𝔽16)C2×C3112yes—
208#1800C2×C3111yescharacteristic, complemented
209#1799C2×C3111yescharacteristic, complemented
210#1390C2×C3112yescomplemented
211C22×C31—21no—
212C22×C31—21no—
213C22×C31—24no—
214C22×C31—21no—
215C22×C31—21no—
216C22×C31—21no—
217C22×C31—21no—
218C22×C31—41no—
219C22×C31—41no—
220C22×C31—41no—
221C22×C31—41no—
222C22×C31—42no—
223C22×C31—42no—
224C22×C31—42no—
225C22×C31—42no—
226C22×C31—44no—
227C22×C31—44no—
228C22×C31—44no—
229C22×C31—44no—
230C22×C31—42no—
231C22×C31—42no—
232C22×C31—41no—
233C22×C31—41no—
234C22×C31—41no—
235C22×C31—42no—
236C22×C31—41no—
237C22×C31—81no—
238C22×C31#38011yescharacteristic
239C22×C31C2×#9911yescharacteristic
240C22×C31#41011yescharacteristic
241C4×C31—21no—
242C4×C31—21no—
243C4×C31—21no—
244C4×C31—42no—
245C4×C31—42no—
246C4×C31—41no—
247C4×C31—41no—
248C4×C31—41no—
249C4×C31—81no—
250C4×C31—162no—
251C4×C31AΣL(1,𝔽16)12yescomplemented
252C24×C4C4×C3111yescharacteristic, complemented
253C2×#120C22×C3111yescharacteristic
254C2×C4×D4—21no—
255C2×C4×D4C22×C3111yescharacteristic
256#423—21no—
257C2×#100C22×C3112yes—
258C2×#99C22×C3112yes—
259#386—21no—
260#386C22×C3111yescharacteristic
261#385—21no—
262#385C4×C3111yescharacteristic, complemented
263#380—21no—
264#379C4×C3111yescharacteristic, complemented
265C4×C22⋊C4—21no—
266C4×C22⋊C4C4×C3111yescharacteristic, complemented
267AΣL(1,𝔽16)—24no—
268#343—21no—
269#342—21no—
270C2×C31—21no—
271C2×C31—21no—
272C2×C31—41no—
273C2×C31—44no—
274C2×C31—41no—
275C2×C31—41no—
276C2×C31—41no—
277C2×C31#179911yescharacteristic
278C2×C31C2×AΣL(1,𝔽16)11yescharacteristic
279C2×C31#212011yescharacteristic
280C25C2×C4×C3111yescharacteristic
281C22×D4—21no—
282C22×D4C23×C3111yescharacteristic
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—44no—
286C23×C4—41no—
287C23×C4—41no—
288C23×C4C2×C4×C3111yescharacteristic
289C23×C4C2×C4×C3111yescharacteristic
290C23×C4D4×C3111yescharacteristic
291C2×M16—22no—
292#120—21no—
293#120—21no—
294#120D4×C3112yes—
295#120Q8×C3112yes—
296C4×D4—41no—
297C4×D4—41no—
298C4×D4—44no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4D4×C3111yescharacteristic
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4C2×C4×C3111yescharacteristic
308C2×C22⋊C4C2×C4×C3111yescharacteristic
309C2×C22⋊C4C2×C4×C3111yescharacteristic
310C2×C22⋊C4D4×C3111yescharacteristic
311C2×C42—21no—
312C2×C42D4×C3111yescharacteristic
313C4⋊C8—41no—
314C4⋊C8—41no—
315#100—22no—
316#100—22no—
317#99—22no—
318#99—22no—
319#95—21no—
320#95—21no—
321#95—21no—
322#95—41no—
323C31#1279311yescharacteristic, direct product factor, Sylow
324C24—21no—
325C24—21no—
326C24—42no—
327C24—41no—
328C24—42no—
329C24—41no—
330C24C4⋊C4×C3112yescomplemented
331C24C22×C4×C3111yescharacteristic
332C24C2×D4×C3111yescharacteristic
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4C2×D4×C3111yescharacteristic
340C2×D4C2×Q8×C3111yescharacteristic
341C2×D4#41×C3111yescharacteristic
342C2×D4#41×C3111yescharacteristic
343C22×C4—24no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4—44no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—44no—
365C22×C4—42no—
366C22×C4C22⋊C4×C3111yescharacteristic
367C22×C4C22⋊C4×C3111yescharacteristic
368C22×C4C22⋊C4×C3111yescharacteristic
369C22×C4C22⋊C4×C3111yescharacteristic
370C22×C4C2×D4×C3111yescharacteristic
371M16—42no—
372M16—42no—
373C2×C8—42no—
374C4⋊C4—41no—
375C4⋊C4—42no—
376C4⋊C4—82no—
377C22⋊C4—21no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4—42no—
385C22⋊C4—41no—
386C22⋊C4—42no—
387C22⋊C4—42no—
388C22⋊C4C4⋊C4×C3112yescomplemented
389C42—21no—
390C42—21no—
391C42—42no—
392C23—22no—
393C23—22no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—22no—
398C23—21no—
399C23—41no—
400C23—44no—
401C23—42no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—44no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—48no—
413C23—42no—
414C23—41no—
415C23—41no—
416C23C2×C22⋊C4×C3111yescharacteristic
417C23C2×C4⋊C4×C3111yescharacteristic
418C23C31×#11711yescharacteristic
419C23C31×#12111yescharacteristic
420C23C31×C22⋊Q811yescharacteristic
421D4—41no—
422D4—41no—
423D4—41no—
424D4—41no—
425D4—44no—
426D4—44no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—48no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—81no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4C31×#9911yescharacteristic
458C2×C4C31×#9911yescharacteristic
459C2×C4C31×#12111yescharacteristic
460C2×C4C31×C22⋊Q811yescharacteristic
461C8—82no—
462C22—21no—
463C22—21no—
464C22—24no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—44no—
478C22—44no—
479C22—44no—
480C22—44no—
481C22—42no—
482C22—42no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—42no—
487C22—41no—
488C22—81no—
489C22C31×#38011yescharacteristic
490C22C2×C31×#9911yescharacteristic
491C22C31×#41011yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—42no—
496C4—42no—
497C4—41no—
498C4—41no—
499C4—41no—
500C4—81no—
501C4—162no—
502C4C31×AΣL(1,𝔽16)12yescomplemented
503C2—21no—
504C2—21no—
505C2—41no—
506C2—44no—
507C2—41no—
508C2—41no—
509C2—41no—
510C2C31×#179911yescharacteristic
511C2C2×C31×AΣL(1,𝔽16)11yescharacteristic
512C2C31×#212011yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC24C22×C4×C31
Frattini, cosocleC22×D4C23×C31
prime radicalC2×C31×#120C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1800C2semidirect
4. C31×#1799C2semidirect
5. C31×#1390C2semidirect
6. C24×C4×C31C4semidirect
16. C31×#385C4semidirect
18. C31×#379C4semidirect
20. C4×C22⋊C4×C31C4semidirect
73. C24×C31C4⋊C4semidirect
131. C22⋊C4×C31C4⋊C4semidirect
135. #12793C31direct (N × H)
208. #1800C2×C31semidirect
209. #1799C2×C31semidirect
210. #1390C2×C31semidirect
251. C4×C31AΣL(1,𝔽16)semidirect
252. C24×C4C4×C31semidirect
262. #385C4×C31semidirect
264. #379C4×C31semidirect
266. C4×C22⋊C4C4×C31semidirect
323. C31#12793direct (N × H)
330. C24C4⋊C4×C31semidirect
388. C22⋊C4C4⋊C4×C31semidirect
502. C4C31×AΣL(1,𝔽16)semidirect

Maximal subgroups

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

subgroupindex
C4×C31×#1202
C2×C31×AΣL(1,𝔽16)2
C31×#18002
C31×#17992
C31×#13902
#1279331