Finite Group Databasebeta

← C31×#10735 #21467494

Subgroups — C31×#10735 #21467494

Order 7936.

3062 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C31C211yesmaximal, characteristic
2C2×C31×#379C211yesmaximal, characteristic
3C2×C31×#379C211yesmaximal, characteristic
4C2×C31×#342C214yesmaximal, complemented
5C26×C31C2211yescharacteristic
6C24×C4×C31—21no—
7C22×C22⋊C4×C31—21no—
8C22×C22⋊C4×C31—22no—
9C22×C22⋊C4×C31—28no—
10C22×C22⋊C4×C31—22no—
11C22×C22⋊C4×C31C414yescomplemented
12C22×C22⋊C4×C31C414yescomplemented
13C22×C22⋊C4×C31C2212yes—
14C22×C22⋊C4×C31C2212yes—
15C22×C22⋊C4×C31C2212yes—
16C31×#379—22no—
17C31×#379—21no—
18C31×#379—22no—
19C31×#379—21no—
20C31×#379C414yescomplemented
21C31×#342—28no—
22C25×C31—24no—
23C25×C31—24no—
24C25×C31—48no—
25C25×C31C2×C412yes—
26C25×C31C2×C412yes—
27C25×C31C2×C412yes—
28C25×C31D411yescharacteristic
29C25×C31D412yes—
30C25×C31D412yes—
31C25×C31D411yescharacteristic
32C25×C31Q812yes—
33C25×C31C2311yescharacteristic
34C23×C4×C31—28no—
35C23×C4×C31—24no—
36C23×C4×C31—22no—
37C23×C4×C31—22no—
38C23×C4×C31—48no—
39C23×C4×C31C2×C414yescomplemented
40C2×C22⋊C4×C31—28no—
41C2×C22⋊C4×C31—216no—
42C2×C22⋊C4×C31—24no—
43C2×C22⋊C4×C31—24no—
44C2×C22⋊C4×C31—22no—
45C2×C22⋊C4×C31—216no—
46C2×C22⋊C4×C31—24no—
47C2×C22⋊C4×C31—24no—
48C2×C22⋊C4×C31—28no—
49C2×C22⋊C4×C31—24no—
50C2×C22⋊C4×C31—24no—
51C2×C22⋊C4×C31—24no—
52C2×C22⋊C4×C31—22no—
53C2×C22⋊C4×C31—22no—
54C2×C22⋊C4×C31—22no—
55C2×C22⋊C4×C31—24no—
56C2×C22⋊C4×C31—48no—
57C2×C22⋊C4×C31—48no—
58C2×C22⋊C4×C31C2×C414yes—
59C2×C22⋊C4×C31C2×C414yescomplemented
60C2×C22⋊C4×C31D418yes—
61C24×C31—28no—
62C24×C31—22no—
63C24×C31—22no—
64C24×C31—28no—
65C24×C31—28no—
66C24×C31—24no—
67C24×C31—24no—
68C24×C31—28no—
69C24×C31—28no—
70C24×C31—24no—
71C24×C31—22no—
72C24×C31—28no—
73C24×C31—28no—
74C24×C31—24no—
75C24×C31—22no—
76C24×C31—48no—
77C24×C31—48no—
78C24×C31—44no—
79C24×C31—48no—
80C24×C31—44no—
81C24×C31—44no—
82C24×C31—48no—
83C24×C31—44no—
84C24×C31—432no—
85C24×C31—432no—
86C24×C31C4214yes—
87C24×C31C22⋊C412yes—
88C24×C31C22⋊C412yes—
89C24×C31C22⋊C414yes—
90C24×C31C22⋊C412yes—
91C24×C31C22⋊C412yes—
92C24×C31C4⋊C412yes—
93C24×C31C4⋊C414yes—
94C24×C31C4⋊C414yes—
95C24×C31C4⋊C412yes—
96C24×C31C22×C411yescharacteristic
97C24×C31C22×C411yescharacteristic
98C24×C31C22×C411yescharacteristic
99C24×C31C2×D411yescharacteristic
100C24×C31C2×D411yescharacteristic
101C24×C31C2×D411yescharacteristic
102C24×C31C2×D414yes—
103C24×C31C2×Q811yescharacteristic
104C24×C31#4114yes—
105C22×C4×C31—216no—
106C22×C4×C31—24no—
107C22×C4×C31—28no—
108C22×C4×C31—24no—
109C22×C4×C31—24no—
110C22×C4×C31—28no—
111C22×C4×C31—432no—
112C22×C4×C31—416no—
113C22×C4×C31—48no—
114C22×C4×C31—48no—
115C22×C4×C31—44no—
116C22×C4×C31—48no—
117C22⋊C4×C31—216no—
118C22⋊C4×C31—24no—
119C22⋊C4×C31—28no—
120C22⋊C4×C31—28no—
121C22⋊C4×C31—416no—
122C22⋊C4×C31—48no—
123C22⋊C4×C31—48no—
124C22⋊C4×C31—42no—
125C22⋊C4×C31—42no—
126C22⋊C4×C31—44no—
127C22⋊C4×C31—42no—
128C22⋊C4×C31—42no—
129C22⋊C4×C31C22⋊C418yescomplemented
130#10735C3111yesmaximal, characteristic, direct product factor, Sylow
131C23×C31—216no—
132C23×C31—216no—
133C23×C31—28no—
134C23×C31—28no—
135C23×C31—22no—
136C23×C31—22no—
137C23×C31—24no—
138C23×C31—24no—
139C23×C31—24no—
140C23×C31—24no—
141C23×C31—24no—
142C23×C31—24no—
143C23×C31—28no—
144C23×C31—28no—
145C23×C31—28no—
146C23×C31—28no—
147C23×C31—28no—
148C23×C31—22no—
149C23×C31—28no—
150C23×C31—22no—
151C23×C31—28no—
152C23×C31—24no—
153C23×C31—28no—
154C23×C31—24no—
155C23×C31—24no—
156C23×C31—24no—
157C23×C31—44no—
158C23×C31—44no—
159C23×C31—44no—
160C23×C31—44no—
161C23×C31—44no—
162C23×C31—44no—
163C23×C31—42no—
164C23×C31—42no—
165C23×C31—48no—
166C23×C31—42no—
167C23×C31—42no—
168C23×C31—48no—
169C23×C31—432no—
170C23×C31—432no—
171C23×C31—416no—
172C23×C31—416no—
173C23×C31—416no—
174C23×C31—432no—
175C23×C31—432no—
176C23×C31—416no—
177C23×C31—48no—
178C23×C31—48no—
179C23×C31#9514yes—
180C23×C31#9514yes—
181C23×C31#9918yes—
182C23×C31C2×C4211yescharacteristic
183C23×C31C2×C22⋊C411yescharacteristic
184C23×C31C2×C22⋊C411yescharacteristic
185C23×C31C2×C22⋊C412yes—
186C23×C31C2×C22⋊C411yescharacteristic
187C23×C31C2×C4⋊C411yescharacteristic
188C23×C31C2×C4⋊C411yescharacteristic
189C23×C31C2×C4⋊C411yescharacteristic
190C23×C31#11712yes—
191C23×C31C4×D414yes—
192C23×C31C4×D414yes—
193C23×C31#12012yes—
194C23×C31#12012yes—
195C23×C31#12114yes—
196C23×C31C22⋊Q814yes—
197C23×C31#12312yes—
198C23×C31#12312yes—
199C2×C4×C31—28no—
200C2×C4×C31—432no—
201C2×C4×C31—416no—
202C2×C4×C31—48no—
203C2×C4×C31—48no—
204C2×C4×C31—44no—
205C2×C4×C31—44no—
206C2×C4×C31—48no—
207C2×C4×C31—88no—
208C2×C4×C31—88no—
209C23×C22⋊C4C2×C3111yescharacteristic
210C2×#379C2×C3111yescharacteristic
211C2×#379C2×C3111yescharacteristic
212C2×#342C2×C3114yescomplemented
213C22×C31—28no—
214C22×C31—28no—
215C22×C31—216no—
216C22×C31—24no—
217C22×C31—28no—
218C22×C31—28no—
219C22×C31—216no—
220C22×C31—24no—
221C22×C31—24no—
222C22×C31—22no—
223C22×C31—22no—
224C22×C31—24no—
225C22×C31—22no—
226C22×C31—22no—
227C22×C31—22no—
228C22×C31—22no—
229C22×C31—24no—
230C22×C31—24no—
231C22×C31—24no—
232C22×C31—42no—
233C22×C31—42no—
234C22×C31—44no—
235C22×C31—42no—
236C22×C31—44no—
237C22×C31—42no—
238C22×C31—416no—
239C22×C31—416no—
240C22×C31—416no—
241C22×C31—416no—
242C22×C31—44no—
243C22×C31—44no—
244C22×C31—48no—
245C22×C31—48no—
246C22×C31#34218yescomplemented
247C22×C31C2×#9511yescharacteristic
248C22×C31C4×C22⋊C412yes—
249C22×C31#37911yescharacteristic
250C22×C31#38012yes—
251C22×C31#38111yescharacteristic
252C22×C31#38512yes—
253C22×C31#38512yes—
254C22×C31#38612yes—
255C22×C31#38612yes—
256C22×C31C2×#9914yes—
257C4×C31—48no—
258C4×C31—84no—
259C4×C31—84no—
260C26C22×C3111yescharacteristic
261C24×C4—21no—
262C22×C22⋊C4—21no—
263C22×C22⋊C4—22no—
264C22×C22⋊C4—28no—
265C22×C22⋊C4—22no—
266C22×C22⋊C4C4×C3114yescomplemented
267C22×C22⋊C4C4×C3114yescomplemented
268C22×C22⋊C4C22×C3112yes—
269C22×C22⋊C4C22×C3112yes—
270C22×C22⋊C4C22×C3112yes—
271#379—22no—
272#379—21no—
273#379—22no—
274#379—21no—
275#379C4×C3114yescomplemented
276#342—28no—
277C2×C31—21no—
278C2×C31—22no—
279C2×C31—28no—
280C2×C31—21no—
281C2×C31—22no—
282C2×C31—22no—
283C2×C31—22no—
284C2×C31—22no—
285C2×C31—44no—
286C2×C31C22⋊#9511yescharacteristic
287C2×C31C2×#34212yes—
288C2×C31#189814yes—
289C25—24no—
290C25—24no—
291C25—48no—
292C25C2×C4×C3112yes—
293C25C2×C4×C3112yes—
294C25C2×C4×C3112yes—
295C25D4×C3111yescharacteristic
296C25D4×C3112yes—
297C25D4×C3111yescharacteristic
298C25D4×C3112yes—
299C25Q8×C3112yes—
300C25C23×C3111yescharacteristic
301C23×C4—28no—
302C23×C4—24no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—48no—
306C23×C4C2×C4×C3114yescomplemented
307C2×C22⋊C4—28no—
308C2×C22⋊C4—216no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—216no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—48no—
324C2×C22⋊C4—48no—
325C2×C22⋊C4C2×C4×C3114yes—
326C2×C22⋊C4C2×C4×C3114yescomplemented
327C2×C22⋊C4D4×C3118yes—
328C31#1073511yescharacteristic, direct product factor, Sylow
329C24—28no—
330C24—22no—
331C24—22no—
332C24—28no—
333C24—28no—
334C24—24no—
335C24—24no—
336C24—28no—
337C24—28no—
338C24—24no—
339C24—22no—
340C24—28no—
341C24—28no—
342C24—24no—
343C24—22no—
344C24—44no—
345C24—48no—
346C24—48no—
347C24—44no—
348C24—44no—
349C24—48no—
350C24—48no—
351C24—44no—
352C24—432no—
353C24—432no—
354C24C42×C3114yes—
355C24C22⋊C4×C3112yes—
356C24C22⋊C4×C3112yes—
357C24C22⋊C4×C3114yes—
358C24C22⋊C4×C3112yes—
359C24C22⋊C4×C3112yes—
360C24C4⋊C4×C3112yes—
361C24C4⋊C4×C3114yes—
362C24C4⋊C4×C3114yes—
363C24C4⋊C4×C3112yes—
364C24C22×C4×C3111yescharacteristic
365C24C22×C4×C3111yescharacteristic
366C24C22×C4×C3111yescharacteristic
367C24C2×D4×C3111yescharacteristic
368C24C2×D4×C3111yescharacteristic
369C24C2×D4×C3111yescharacteristic
370C24C2×D4×C3114yes—
371C24C2×Q8×C3111yescharacteristic
372C24#41×C3114yes—
373C22×C4—216no—
374C22×C4—24no—
375C22×C4—28no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—28no—
379C22×C4—432no—
380C22×C4—48no—
381C22×C4—416no—
382C22×C4—48no—
383C22×C4—44no—
384C22×C4—48no—
385C22⋊C4—216no—
386C22⋊C4—24no—
387C22⋊C4—28no—
388C22⋊C4—28no—
389C22⋊C4—416no—
390C22⋊C4—48no—
391C22⋊C4—48no—
392C22⋊C4—42no—
393C22⋊C4—42no—
394C22⋊C4—44no—
395C22⋊C4—42no—
396C22⋊C4—42no—
397C22⋊C4C22⋊C4×C3118yescomplemented
398C23—216no—
399C23—216no—
400C23—24no—
401C23—24no—
402C23—24no—
403C23—24no—
404C23—28no—
405C23—28no—
406C23—22no—
407C23—22no—
408C23—24no—
409C23—24no—
410C23—24no—
411C23—24no—
412C23—28no—
413C23—28no—
414C23—28no—
415C23—28no—
416C23—28no—
417C23—22no—
418C23—28no—
419C23—22no—
420C23—28no—
421C23—24no—
422C23—28no—
423C23—24no—
424C23—44no—
425C23—44no—
426C23—44no—
427C23—44no—
428C23—44no—
429C23—44no—
430C23—42no—
431C23—42no—
432C23—48no—
433C23—42no—
434C23—42no—
435C23—48no—
436C23—432no—
437C23—432no—
438C23—416no—
439C23—416no—
440C23—416no—
441C23—432no—
442C23—432no—
443C23—416no—
444C23—48no—
445C23—48no—
446C23C31×#9514yes—
447C23C31×#9514yes—
448C23C31×#9918yes—
449C23C2×C42×C3111yescharacteristic
450C23C2×C22⋊C4×C3111yescharacteristic
451C23C2×C22⋊C4×C3111yescharacteristic
452C23C2×C22⋊C4×C3112yes—
453C23C2×C22⋊C4×C3111yescharacteristic
454C23C2×C4⋊C4×C3111yescharacteristic
455C23C2×C4⋊C4×C3111yescharacteristic
456C23C2×C4⋊C4×C3111yescharacteristic
457C23C31×#11712yes—
458C23C4×D4×C3114yes—
459C23C4×D4×C3114yes—
460C23C31×#12012yes—
461C23C31×#12012yes—
462C23C31×#12114yes—
463C23C31×C22⋊Q814yes—
464C23C31×#12312yes—
465C23C31×#12312yes—
466C2×C4—28no—
467C2×C4—432no—
468C2×C4—416no—
469C2×C4—48no—
470C2×C4—48no—
471C2×C4—48no—
472C2×C4—44no—
473C2×C4—44no—
474C2×C4—88no—
475C2×C4—88no—
476C22—28no—
477C22—28no—
478C22—216no—
479C22—24no—
480C22—28no—
481C22—28no—
482C22—216no—
483C22—24no—
484C22—24no—
485C22—22no—
486C22—22no—
487C22—24no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—24no—
493C22—24no—
494C22—24no—
495C22—42no—
496C22—42no—
497C22—44no—
498C22—42no—
499C22—44no—
500C22—42no—
501C22—416no—
502C22—416no—
503C22—416no—
504C22—416no—
505C22—44no—
506C22—44no—
507C22—48no—
508C22—48no—
509C22C31×#34218yescomplemented
510C22C2×C31×#9511yescharacteristic
511C22C4×C22⋊C4×C3112yes—
512C22C31×#37911yescharacteristic
513C22C31×#38012yes—
514C22C31×#38111yescharacteristic
515C22C31×#38512yes—
516C22C31×#38512yes—
517C22C31×#38612yes—
518C22C31×#38612yes—
519C22C2×C31×#9914yes—
520C4—48no—
521C4—84no—
522C4—84no—
523C2—21no—
524C2—22no—
525C2—28no—
526C2—21no—
527C2—22no—
528C2—22no—
529C2—22no—
530C2—22no—
531C2—44no—
532C2C31×C22⋊#9511yescharacteristic
533C2C2×C31×#34212yes—
534C2C31×#189814yes—
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C2×C42×C31
Frattini, cosocleC25C23×C31
prime radicalC26×C31C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C26×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#342C2semidirect
11. C22×C22⋊C4×C31C4semidirect
12. C22×C22⋊C4×C31C4semidirect
20. C31×#379C4semidirect
39. C23×C4×C31C2×C4semidirect
59. C2×C22⋊C4×C31C2×C4semidirect
129. C22⋊C4×C31C22⋊C4semidirect
130. #10735C31direct (N × H)
212. C2×#342C2×C31semidirect
246. C22×C31#342semidirect
266. C22×C22⋊C4C4×C31semidirect
267. C22×C22⋊C4C4×C31semidirect
275. #379C4×C31semidirect
306. C23×C4C2×C4×C31semidirect
326. C2×C22⋊C4C2×C4×C31semidirect
328. C31#10735direct (N × H)
397. C22⋊C4C22⋊C4×C31semidirect
509. C22C31×#342semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C312
C2×C31×#3792
C2×C31×#3422
#1073531