Finite Group Databasebeta

← C31×#10733 #21467492

Subgroups — C31×#10733 #21467492

Order 7936.

1550 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#117C211yesmaximal, characteristic
2C2×C31×#407C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
4C2×C31×#339C214yesmaximal, complemented
5C24×C4×C31C2211yescharacteristic
6C22×M16×C31C2212yes—
7C2×C31×#117—21no—
8C2×C31×#117—21no—
9C2×C31×#117—28no—
10C2×C31×#117C412yescomplemented
11C2×C31×#117C2212yes—
12C22×C4⋊C4×C31C412yescomplemented
13C22×C22⋊C4×C31—21no—
14C22×C22⋊C4×C31—21no—
15C22×C42×C31—21no—
16C22×C42×C31C2212yes—
17C31×#407—22no—
18C31×#407C414yescomplemented
19C2×C31×C22⋊C8—21no—
20C2×C31×C22⋊C8—21no—
21C4×C22⋊C4×C31—22no—
22C4×C22⋊C4×C31C414yescomplemented
23C2×C31×#95—21no—
24C31×#339—28no—
25C25×C31D411yescharacteristic
26C23×C4×C31—24no—
27C23×C4×C31—24no—
28C23×C4×C31—22no—
29C23×C4×C31—22no—
30C23×C4×C31C2×C412yes—
31C23×C4×C31C2×C411yescharacteristic
32C23×C4×C31C2×C411yescharacteristic
33C23×C4×C31C2×C412yes—
34C23×C4×C31D411yescharacteristic
35C23×C4×C31D412yes—
36C23×C4×C31D411yescharacteristic
37C23×C4×C31D411yescharacteristic
38C23×C4×C31Q812yes—
39C23×C4×C31C2311yescharacteristic
40C2×M16×C31—22no—
41C2×M16×C31—24no—
42C2×M16×C31—24no—
43C2×M16×C31C2×C414yescomplemented
44C22×C8×C31—22no—
45C31×#117—28no—
46C31×#117—28no—
47C31×#117—24no—
48C31×#117—28no—
49C31×#117D418yes—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—28no—
52C2×C4⋊C4×C31C2×C414yes—
53C2×C22⋊C4×C31—28no—
54C2×C22⋊C4×C31—28no—
55C2×C22⋊C4×C31—22no—
56C2×C22⋊C4×C31—24no—
57C2×C22⋊C4×C31—22no—
58C2×C42×C31—28no—
59C2×C42×C31—22no—
60C2×C42×C31—22no—
61C2×C42×C31—24no—
62C2×C42×C31—24no—
63C2×C42×C31—22no—
64C2×C42×C31C2×C414yescomplemented
65C31×C22⋊C8—24no—
66C31×C22⋊C8—24no—
67C31×#95—24no—
68C24×C31—24no—
69C24×C31—22no—
70C24×C31—22no—
71C24×C31—42no—
72C24×C31C22⋊C411yescharacteristic
73C24×C31C22⋊C412yes—
74C24×C31C22⋊C411yescharacteristic
75C24×C31C4⋊C412yes—
76C24×C31C2×D411yescharacteristic
77C22×C4×C31—22no—
78C22×C4×C31—22no—
79C22×C4×C31—22no—
80C22×C4×C31—22no—
81C22×C4×C31—22no—
82C22×C4×C31—22no—
83C22×C4×C31—28no—
84C22×C4×C31—28no—
85C22×C4×C31—22no—
86C22×C4×C31—22no—
87C22×C4×C31—28no—
88C22×C4×C31—28no—
89C22×C4×C31—22no—
90C22×C4×C31—22no—
91C22×C4×C31—28no—
92C22×C4×C31—28no—
93C22×C4×C31—24no—
94C22×C4×C31—24no—
95C22×C4×C31—44no—
96C22×C4×C31—44no—
97C22×C4×C31—44no—
98C22×C4×C31—42no—
99C22×C4×C31—42no—
100C22×C4×C31C4212yes—
101C22×C4×C31C4212yes—
102C22×C4×C31C22⋊C412yes—
103C22×C4×C31C22⋊C411yescharacteristic
104C22×C4×C31C22⋊C411yescharacteristic
105C22×C4×C31C22⋊C412yes—
106C22×C4×C31C22⋊C412yes—
107C22×C4×C31C4⋊C412yes—
108C22×C4×C31C4⋊C412yes—
109C22×C4×C31C4⋊C412yes—
110C22×C4×C31C4⋊C412yes—
111C22×C4×C31C4⋊C412yes—
112C22×C4×C31C22×C411yescharacteristic
113C22×C4×C31C22×C411yescharacteristic
114C22×C4×C31C22×C411yescharacteristic
115C22×C4×C31C2×D411yescharacteristic
116C22×C4×C31C2×D414yes—
117C22×C4×C31C2×D411yescharacteristic
118C22×C4×C31C2×Q811yescharacteristic
119C22×C4×C31#4114yes—
120M16×C31—28no—
121M16×C31—44no—
122C2×C8×C31—24no—
123C2×C8×C31—42no—
124C2×C8×C31—42no—
125C4⋊C4×C31—28no—
126C4⋊C4×C31—24no—
127C4⋊C4×C31C22⋊C418yescomplemented
128C22⋊C4×C31—216no—
129C22⋊C4×C31—28no—
130C22⋊C4×C31—28no—
131C42×C31—28no—
132C42×C31—28no—
133C42×C31—28no—
134C42×C31—44no—
135#10733C3111yesmaximal, characteristic, direct product factor, Sylow
136C23×C31—21no—
137C23×C31—21no—
138C23×C31—22no—
139C23×C31—22no—
140C23×C31—22no—
141C23×C31—24no—
142C23×C31—24no—
143C23×C31—21no—
144C23×C31—21no—
145C23×C31—24no—
146C23×C31—24no—
147C23×C31—22no—
148C23×C31—22no—
149C23×C31—42no—
150C23×C31—42no—
151C23×C31—48no—
152C23×C31—48no—
153C23×C31#9512yes—
154C23×C31#9512yes—
155C23×C31#10414yes—
156C23×C31C2×C22⋊C411yescharacteristic
157C23×C31C2×C22⋊C411yescharacteristic
158C23×C31C2×C4⋊C411yescharacteristic
159C23×C31#12012yes—
160C23×C31#12312yes—
161C2×C4×C31—21no—
162C2×C4×C31—21no—
163C2×C4×C31—21no—
164C2×C4×C31—21no—
165C2×C4×C31—24no—
166C2×C4×C31—24no—
167C2×C4×C31—24no—
168C2×C4×C31—24no—
169C2×C4×C31—24no—
170C2×C4×C31—24no—
171C2×C4×C31—24no—
172C2×C4×C31—24no—
173C2×C4×C31—24no—
174C2×C4×C31—24no—
175C2×C4×C31—28no—
176C2×C4×C31—28no—
177C2×C4×C31—48no—
178C2×C4×C31—44no—
179C2×C4×C31—48no—
180C2×C4×C31—416no—
181C2×C4×C31—44no—
182C2×C4×C31—44no—
183C2×C4×C31—44no—
184C2×C4×C31#9512yes—
185C2×C4×C31#9512yes—
186C2×C4×C31C2×C4211yescharacteristic
187C2×C4×C31C2×C22⋊C412yes—
188C2×C4×C31C2×C22⋊C411yescharacteristic
189C2×C4×C31C2×C4⋊C411yescharacteristic
190C2×C4×C31C2×C4⋊C411yescharacteristic
191C2×C4×C31#11712yes—
192C2×C4×C31C4×D414yes—
193C2×C4×C31C4×D414yes—
194C2×C4×C31#12012yes—
195C2×C4×C31#12114yes—
196C2×C4×C31C22⋊Q814yes—
197C2×C4×C31#12312yes—
198C8×C31—44no—
199C22×#117C2×C3111yescharacteristic
200C2×#407C2×C3111yescharacteristic
201C2×C4×C22⋊C4C2×C3111yescharacteristic
202C2×#339C2×C3114yescomplemented
203C22×C31—24no—
204C22×C31—24no—
205C22×C31—22no—
206C22×C31—21no—
207C22×C31—21no—
208C22×C31—21no—
209C22×C31—22no—
210C22×C31—21no—
211C22×C31—24no—
212C22×C31—24no—
213C22×C31—22no—
214C22×C31—22no—
215C22×C31—22no—
216C22×C31—48no—
217C22×C31—48no—
218C22×C31—42no—
219C22×C31—42no—
220C22×C31#33914yescomplemented
221C22×C31C2×#9511yescharacteristic
222C22×C31#37911yescharacteristic
223C22×C31#38111yescharacteristic
224C22×C31#38512yes—
225C22×C31#38612yes—
226C22×C31C2×#10412yes—
227C22×C31#42112yes—
228C4×C31—22no—
229C4×C31—22no—
230C4×C31—48no—
231C4×C31—48no—
232C4×C31C4×C22⋊C412yes—
233C4×C31#38012yes—
234C4×C31#38512yes—
235C4×C31#38612yes—
236C24×C4C22×C3111yescharacteristic
237C22×M16C22×C3112yes—
238C2×#117—21no—
239C2×#117—21no—
240C2×#117—28no—
241C2×#117C4×C3112yescomplemented
242C2×#117C22×C3112yes—
243C22×C4⋊C4C4×C3112yescomplemented
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246C22×C42—21no—
247C22×C42C22×C3112yes—
248#407—22no—
249#407C4×C3114yescomplemented
250C2×C22⋊C8—21no—
251C2×C22⋊C8—21no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4C4×C3114yescomplemented
254C2×#95—21no—
255#339—28no—
256C2×C31—22no—
257C2×C31—24no—
258C2×C31—22no—
259C2×C31—42no—
260C2×C31C22⋊#9511yescharacteristic
261C2×C31C2×#33911yescharacteristic
262C2×C31#173311yescharacteristic
263C2×C31#178912yes—
264C2×C31#182612yes—
265C25D4×C3111yescharacteristic
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4C2×C4×C3112yes—
271C23×C4C2×C4×C3111yescharacteristic
272C23×C4C2×C4×C3111yescharacteristic
273C23×C4C2×C4×C3112yes—
274C23×C4D4×C3111yescharacteristic
275C23×C4D4×C3111yescharacteristic
276C23×C4D4×C3112yes—
277C23×C4D4×C3111yescharacteristic
278C23×C4Q8×C3112yes—
279C23×C4C23×C3111yescharacteristic
280C2×M16—22no—
281C2×M16—24no—
282C2×M16—24no—
283C2×M16C2×C4×C3114yescomplemented
284C22×C8—22no—
285#117—28no—
286#117—28no—
287#117—24no—
288#117—28no—
289#117D4×C3118yes—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4C2×C4×C3114yes—
293C2×C22⋊C4—28no—
294C2×C22⋊C4—28no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—22no—
298C2×C42—28no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—24no—
302C2×C42—24no—
303C2×C42—22no—
304C2×C42C2×C4×C3114yescomplemented
305C22⋊C8—24no—
306C22⋊C8—24no—
307#95—24no—
308C31#1073311yescharacteristic, direct product factor, Sylow
309C24—24no—
310C24—22no—
311C24—22no—
312C24—42no—
313C24C22⋊C4×C3111yescharacteristic
314C24C22⋊C4×C3112yes—
315C24C22⋊C4×C3111yescharacteristic
316C24C4⋊C4×C3112yes—
317C24C2×D4×C3111yescharacteristic
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—28no—
325C22×C4—28no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—28no—
329C22×C4—28no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—28no—
333C22×C4—28no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—44no—
337C22×C4—44no—
338C22×C4—44no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4C42×C3112yes—
342C22×C4C42×C3112yes—
343C22×C4C22⋊C4×C3112yes—
344C22×C4C22⋊C4×C3111yescharacteristic
345C22×C4C22⋊C4×C3111yescharacteristic
346C22×C4C22⋊C4×C3112yes—
347C22×C4C22⋊C4×C3112yes—
348C22×C4C4⋊C4×C3112yes—
349C22×C4C4⋊C4×C3112yes—
350C22×C4C4⋊C4×C3112yes—
351C22×C4C4⋊C4×C3112yes—
352C22×C4C4⋊C4×C3112yes—
353C22×C4C22×C4×C3111yescharacteristic
354C22×C4C22×C4×C3111yescharacteristic
355C22×C4C22×C4×C3111yescharacteristic
356C22×C4C2×D4×C3111yescharacteristic
357C22×C4C2×D4×C3111yescharacteristic
358C22×C4C2×D4×C3114yes—
359C22×C4C2×Q8×C3111yescharacteristic
360C22×C4#41×C3114yes—
361M16—28no—
362M16—44no—
363C2×C8—24no—
364C2×C8—42no—
365C2×C8—42no—
366C4⋊C4—28no—
367C4⋊C4—24no—
368C4⋊C4C22⋊C4×C3118yescomplemented
369C22⋊C4—216no—
370C22⋊C4—28no—
371C22⋊C4—28no—
372C42—28no—
373C42—28no—
374C42—28no—
375C42—44no—
376C23—22no—
377C23—22no—
378C23—22no—
379C23—21no—
380C23—21no—
381C23—22no—
382C23—22no—
383C23—24no—
384C23—24no—
385C23—21no—
386C23—21no—
387C23—24no—
388C23—24no—
389C23—42no—
390C23—42no—
391C23—48no—
392C23—48no—
393C23C31×#9512yes—
394C23C31×#9512yes—
395C23C31×#10414yes—
396C23C2×C22⋊C4×C3111yescharacteristic
397C23C2×C22⋊C4×C3111yescharacteristic
398C23C2×C4⋊C4×C3111yescharacteristic
399C23C31×#12012yes—
400C23C31×#12312yes—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—28no—
416C2×C4—28no—
417C2×C4—48no—
418C2×C4—44no—
419C2×C4—48no—
420C2×C4—416no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4C31×#9512yes—
425C2×C4C31×#9512yes—
426C2×C4C2×C42×C3111yescharacteristic
427C2×C4C2×C22⋊C4×C3112yes—
428C2×C4C2×C22⋊C4×C3111yescharacteristic
429C2×C4C2×C4⋊C4×C3111yescharacteristic
430C2×C4C2×C4⋊C4×C3111yescharacteristic
431C2×C4C31×#11712yes—
432C2×C4C4×D4×C3114yes—
433C2×C4C4×D4×C3114yes—
434C2×C4C31×#12012yes—
435C2×C4C31×#12114yes—
436C2×C4C31×C22⋊Q814yes—
437C2×C4C31×#12312yes—
438C8—44no—
439C22—24no—
440C22—24no—
441C22—22no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—22no—
446C22—21no—
447C22—24no—
448C22—24no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—48no—
453C22—48no—
454C22—42no—
455C22—42no—
456C22C31×#33914yescomplemented
457C22C2×C31×#9511yescharacteristic
458C22C31×#37911yescharacteristic
459C22C31×#38111yescharacteristic
460C22C31×#38512yes—
461C22C31×#38612yes—
462C22C2×C31×#10412yes—
463C22C31×#42112yes—
464C4—22no—
465C4—22no—
466C4—48no—
467C4—48no—
468C4C4×C22⋊C4×C3112yes—
469C4C31×#38012yes—
470C4C31×#38512yes—
471C4C31×#38612yes—
472C2—22no—
473C2—24no—
474C2—22no—
475C2—42no—
476C2C31×C22⋊#9511yescharacteristic
477C2C2×C31×#33911yescharacteristic
478C2C31×#173311yescharacteristic
479C2C31×#178912yes—
480C2C31×#182612yes—
subgroupG/H
centerC22×C4×C31C2×D4
commutatorC2×C4C2×C42×C31
Frattini, cosocleC23×C4C23×C31
socleC23×C31C2×C22⋊C4
prime radicalC25×C31D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#339C2semidirect
10. C2×C31×#117C4semidirect
12. C22×C4⋊C4×C31C4semidirect
18. C31×#407C4semidirect
22. C4×C22⋊C4×C31C4semidirect
43. C2×M16×C31C2×C4semidirect
64. C2×C42×C31C2×C4semidirect
127. C4⋊C4×C31C22⋊C4semidirect
135. #10733C31direct (N × H)
202. C2×#339C2×C31semidirect
220. C22×C31#339semidirect
241. C2×#117C4×C31semidirect
243. C22×C4⋊C4C4×C31semidirect
249. #407C4×C31semidirect
253. C4×C22⋊C4C4×C31semidirect
283. C2×M16C2×C4×C31semidirect
304. C2×C42C2×C4×C31semidirect
308. C31#10733direct (N × H)
368. C4⋊C4C22⋊C4×C31semidirect
456. C22C31×#339semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1172
C2×C31×#4072
C2×C4×C22⋊C4×C312
C2×C31×#3392
#1073331