Finite Group Databasebeta

← C31×#20912 #21477671

Subgroups — C31×#20912 #21477671

Order 7936.

2278 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C22×C31×#117C211yesmaximal, characteristic, complemented
3C2×C31×#418C212yesmaximal, complemented
4C2×C31×#407C211yesmaximal, characteristic, complemented
5C31×#1875C214yesmaximal, complemented
6C31×#1874C214yesmaximal, complemented
7C31×#1736C212yesmaximal, complemented
8C23×D4×C31—21no—
9C23×D4×C31C2211yescharacteristic
10C24×C4×C31C2211yescharacteristic
11C22×M16×C31C2212yes—
12C2×C31×#121—24no—
13C2×C31×#121—21no—
14C2×C31×#121—21no—
15C2×C31×#121C418yescomplemented
16C2×C31×#121C2212yes—
17C2×C31×#121C2212yes—
18C2×C31×#117—21no—
19C2×C31×#117—21no—
20C2×C31×#117—28no—
21C2×C31×#117C2212yes—
22C2×C31×#117C2212yescomplemented
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2212yescomplemented
25C22×C22⋊C4×C31—21no—
26C22×C22⋊C4×C31—21no—
27C22×C42×C31—21no—
28C31×#418—28no—
29C2×C31×#102C2218yescomplemented
30C31×#407—24no—
31C2×C31×C22⋊C8C2212yescomplemented
32C2×C31×C22⋊C8C2212yescomplemented
33C31×#340C2218yescomplemented
34C25×C31—21no—
35C25×C31D411yescharacteristic
36C22×D4×C31—28no—
37C22×D4×C31—22no—
38C22×D4×C31—22no—
39C22×D4×C31—24no—
40C22×D4×C31—21no—
41C22×D4×C31—22no—
42C22×D4×C31—24no—
43C22×D4×C31—48no—
44C22×D4×C31C2×C414yescomplemented
45C22×D4×C31C2312yes—
46C23×C4×C31—24no—
47C23×C4×C31—24no—
48C23×C4×C31—22no—
49C23×C4×C31—21no—
50C23×C4×C31C2×C414yes—
51C23×C4×C31D411yescharacteristic
52C23×C4×C31D411yescharacteristic
53C23×C4×C31D411yescharacteristic
54C23×C4×C31D414yes—
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C2×M16×C31—24no—
59C2×M16×C31—24no—
60C2×M16×C31—24no—
61C22×C8×C31C2314yes—
62C31×#121—28no—
63C31×#121—28no—
64C31×#121—24no—
65C31×#121—24no—
66C31×#121C2×C418yes—
67C31×#121C2×C418yescomplemented
68C31×#117—28no—
69C31×#117—28no—
70C31×#117—24no—
71C31×#117—28no—
72C31×#117D418yescomplemented
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—28no—
77C2×C4⋊C4×C31C2×C414yescomplemented
78C2×C4⋊C4×C31C2312yes—
79C2×C4⋊C4×C31C2314yes—
80C2×C22⋊C4×C31—28no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—28no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—22no—
86C2×C42×C31—28no—
87C2×C42×C31—22no—
88C2×C42×C31—22no—
89C31×#102—216no—
90C31×C22⋊C8—24no—
91C31×C22⋊C8—24no—
92C24×C31—22no—
93C24×C31—22no—
94C24×C31—24no—
95C24×C31—24no—
96C24×C31—22no—
97C24×C31—42no—
98C24×C31—44no—
99C24×C31—44no—
100C24×C31—42no—
101C24×C31—42no—
102C24×C31C22⋊C414yes—
103C24×C31C2×D411yescharacteristic
104C24×C31C2×D411yescharacteristic
105C24×C31C2×D411yescharacteristic
106C2×D4×C31—28no—
107C2×D4×C31—28no—
108C2×D4×C31—24no—
109C2×D4×C31—216no—
110C2×D4×C31—24no—
111C2×D4×C31—22no—
112C2×D4×C31—24no—
113C2×D4×C31—432no—
114C2×D4×C31—48no—
115C2×D4×C31—48no—
116C2×D4×C31—42no—
117C2×D4×C31—48no—
118C2×D4×C31—42no—
119C2×D4×C31C22×C414yes—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—216no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—216no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—28no—
133C22×C4×C31—24no—
134C22×C4×C31—24no—
135C22×C4×C31—22no—
136C22×C4×C31—44no—
137C22×C4×C31—44no—
138C22×C4×C31—44no—
139C22×C4×C31C22⋊C414yes—
140C22×C4×C31C22⋊C414yes—
141C22×C4×C31C22⋊C414yes—
142C22×C4×C31C22×C412yes—
143C22×C4×C31C22×C412yes—
144C22×C4×C31C22×C412yes—
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D412yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D412yes—
151C22×C4×C31C2×D414yes—
152C22×C4×C31#4114yes—
153C22×C4×C31C2411yescharacteristic
154M16×C31—48no—
155C2×C8×C31—24no—
156C2×C8×C31—24no—
157C2×C8×C31—24no—
158C4⋊C4×C31—28no—
159C4⋊C4×C31—24no—
160C4⋊C4×C31—24no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31C22×C414yes—
163C4⋊C4×C31C2×D418yescomplemented
164C22⋊C4×C31—28no—
165C22⋊C4×C31—28no—
166C22⋊C4×C31—28no—
167C22⋊C4×C31—28no—
168C42×C31—28no—
169C42×C31—28no—
170#20912C3111yesmaximal, characteristic, direct product factor, Sylow
171C23×C31—21no—
172C23×C31—21no—
173C23×C31—22no—
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—21no—
177C23×C31—21no—
178C23×C31—22no—
179C23×C31—22no—
180C23×C31—28no—
181C23×C31—28no—
182C23×C31—24no—
183C23×C31—44no—
184C23×C31—48no—
185C23×C31—48no—
186C23×C31—48no—
187C23×C31—48no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—44no—
191C23×C31—44no—
192C23×C31—48no—
193C23×C31—88no—
194C23×C31—88no—
195C23×C31C2×C22⋊C412yes—
196C23×C31C2×C22⋊C412yes—
197C23×C31C2×C22⋊C412yes—
198C23×C31#12012yes—
199C23×C31#12312yes—
200C23×C31AGL(1,ℤ/8)14yes—
201C23×C31C22×D411yescharacteristic
202D4×C31—28no—
203D4×C31—416no—
204D4×C31—416no—
205D4×C31—44no—
206D4×C31—48no—
207C2×C4×C31—21no—
208C2×C4×C31—21no—
209C2×C4×C31—21no—
210C2×C4×C31—21no—
211C2×C4×C31—28no—
212C2×C4×C31—24no—
213C2×C4×C31—24no—
214C2×C4×C31—24no—
215C2×C4×C31—24no—
216C2×C4×C31—28no—
217C2×C4×C31—28no—
218C2×C4×C31—24no—
219C2×C4×C31—28no—
220C2×C4×C31—416no—
221C2×C4×C31—48no—
222C2×C4×C31—44no—
223C2×C4×C31—44no—
224C2×C4×C31—44no—
225C2×C4×C31C2×C22⋊C412yes—
226C2×C4×C31C2×C22⋊C412yes—
227C2×C4×C31C2×C22⋊C412yes—
228C2×C4×C31C4×D418yes—
229C2×C4×C31#12012yes—
230C2×C4×C31#12118yes—
231C2×C4×C31#12312yes—
232C2×C4×C31C23×C411yescharacteristic
233C2×C4×C31C22×D412yes—
234C2×C4×C31C22×D411yescharacteristic
235C2×C4×C31C2×#4112yes—
236C8×C31—44no—
237C22×#121C2×C3111yescharacteristic
238C22×#117C2×C3111yescharacteristic, complemented
239C2×#418C2×C3112yescomplemented
240C2×#407C2×C3111yescharacteristic, complemented
241#1875C2×C3114yescomplemented
242#1874C2×C3114yescomplemented
243#1736C2×C3112yescomplemented
244C22×C31—24no—
245C22×C31—24no—
246C22×C31—22no—
247C22×C31—22no—
248C22×C31—22no—
249C22×C31—24no—
250C22×C31—24no—
251C22×C31—22no—
252C22×C31—22no—
253C22×C31—22no—
254C22×C31—22no—
255C22×C31—416no—
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—44no—
259C22×C31—44no—
260C22×C31—44no—
261C22×C31—816no—
262C22×C31—84no—
263C22×C31—84no—
264C22×C31#38614yes—
265C22×C31#41814yescomplemented
266C22×C31C22×C22⋊C411yescharacteristic
267C22×C31C2×#12011yescharacteristic
268C22×C31C2×#12311yescharacteristic
269C22×C31C2×AGL(1,ℤ/8)12yes—
270C22×C31#57512yes—
271C4×C31—22no—
272C4×C31—22no—
273C4×C31—44no—
274C4×C31—48no—
275C4×C31#38614yes—
276C4×C31C2×C4×D412yes—
277C4×C31C2×#12112yes—
278C23×D4—21no—
279C23×D4C22×C3111yescharacteristic
280C24×C4C22×C3111yescharacteristic
281C22×M16C22×C3112yes—
282C2×#121—24no—
283C2×#121—21no—
284C2×#121—21no—
285C2×#121C4×C3118yescomplemented
286C2×#121C22×C3112yes—
287C2×#121C22×C3112yes—
288C2×#117—21no—
289C2×#117—21no—
290C2×#117—28no—
291C2×#117C22×C3112yes—
292C2×#117C22×C3112yescomplemented
293C22×C4⋊C4C22×C3111yescharacteristic
294C22×C4⋊C4C22×C3112yescomplemented
295C22×C22⋊C4—21no—
296C22×C22⋊C4—21no—
297C22×C42—21no—
298#418—28no—
299C2×#102C22×C3118yescomplemented
300#407—24no—
301C2×C22⋊C8C22×C3112yescomplemented
302C2×C22⋊C8C22×C3112yescomplemented
303#340C22×C3118yescomplemented
304C2×C31—24no—
305C2×C31—24no—
306C2×C31—42no—
307C2×C31—84no—
308C2×C31C2×#38611yescharacteristic
309C2×C31C2×#41811yescharacteristic
310C2×C31#289611yescharacteristic
311C2×C31#300612yes—
312C2×C31#309412yes—
313C25—21no—
314C25D4×C3111yescharacteristic
315C22×D4—28no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—24no—
319C22×D4—21no—
320C22×D4—22no—
321C22×D4—24no—
322C22×D4—48no—
323C22×D4C2×C4×C3114yescomplemented
324C22×D4C23×C3112yes—
325C23×C4—24no—
326C23×C4—24no—
327C23×C4—21no—
328C23×C4—22no—
329C23×C4C2×C4×C3114yes—
330C23×C4D4×C3111yescharacteristic
331C23×C4D4×C3111yescharacteristic
332C23×C4D4×C3111yescharacteristic
333C23×C4D4×C3114yes—
334C23×C4C23×C3111yescharacteristic
335C23×C4C23×C3111yescharacteristic
336C23×C4C23×C3111yescharacteristic
337C2×M16—24no—
338C2×M16—24no—
339C2×M16—24no—
340C22×C8C23×C3114yes—
341#121—28no—
342#121—28no—
343#121—24no—
344#121—24no—
345#121C2×C4×C3118yes—
346#121C2×C4×C3118yescomplemented
347#117—28no—
348#117—28no—
349#117—24no—
350#117—28no—
351#117D4×C3118yescomplemented
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4C2×C4×C3114yescomplemented
357C2×C4⋊C4C23×C3112yes—
358C2×C4⋊C4C23×C3114yes—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C42—28no—
366C2×C42—22no—
367C2×C42—22no—
368#102—216no—
369C22⋊C8—24no—
370C22⋊C8—24no—
371C31#2091211yescharacteristic, direct product factor, Sylow
372C24—22no—
373C24—22no—
374C24—24no—
375C24—24no—
376C24—22no—
377C24—42no—
378C24—44no—
379C24—44no—
380C24—42no—
381C24—42no—
382C24C22⋊C4×C3114yes—
383C24C2×D4×C3111yescharacteristic
384C24C2×D4×C3111yescharacteristic
385C24C2×D4×C3111yescharacteristic
386C2×D4—28no—
387C2×D4—28no—
388C2×D4—24no—
389C2×D4—216no—
390C2×D4—24no—
391C2×D4—22no—
392C2×D4—24no—
393C2×D4—432no—
394C2×D4—48no—
395C2×D4—48no—
396C2×D4—42no—
397C2×D4—48no—
398C2×D4—42no—
399C2×D4C22×C4×C3114yes—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—216no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—216no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—28no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—44no—
419C22×C4C22⋊C4×C3114yes—
420C22×C4C22⋊C4×C3114yes—
421C22×C4C22⋊C4×C3114yes—
422C22×C4C22×C4×C3112yes—
423C22×C4C22×C4×C3112yes—
424C22×C4C22×C4×C3112yes—
425C22×C4C2×D4×C3111yescharacteristic
426C22×C4C2×D4×C3111yescharacteristic
427C22×C4C2×D4×C3112yes—
428C22×C4C2×D4×C3112yes—
429C22×C4C2×D4×C3111yescharacteristic
430C22×C4C2×D4×C3112yes—
431C22×C4C2×D4×C3114yes—
432C22×C4#41×C3114yes—
433C22×C4C24×C3111yescharacteristic
434M16—48no—
435C2×C8—24no—
436C2×C8—24no—
437C2×C8—24no—
438C4⋊C4—28no—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4C22×C4×C3114yes—
443C4⋊C4C2×D4×C3118yescomplemented
444C22⋊C4—28no—
445C22⋊C4—28no—
446C22⋊C4—28no—
447C22⋊C4—28no—
448C42—28no—
449C42—28no—
450C23—21no—
451C23—21no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—28no—
456C23—21no—
457C23—21no—
458C23—22no—
459C23—22no—
460C23—28no—
461C23—24no—
462C23—44no—
463C23—48no—
464C23—48no—
465C23—48no—
466C23—48no—
467C23—42no—
468C23—42no—
469C23—44no—
470C23—44no—
471C23—48no—
472C23—88no—
473C23—88no—
474C23C2×C22⋊C4×C3112yes—
475C23C2×C22⋊C4×C3112yes—
476C23C2×C22⋊C4×C3112yes—
477C23C31×#12012yes—
478C23C31×#12312yes—
479C23C31×AGL(1,ℤ/8)14yes—
480C23C22×D4×C3111yescharacteristic
481D4—28no—
482D4—416no—
483D4—416no—
484D4—44no—
485D4—48no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—28no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—28no—
496C2×C4—28no—
497C2×C4—24no—
498C2×C4—28no—
499C2×C4—416no—
500C2×C4—48no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4C2×C22⋊C4×C3112yes—
505C2×C4C2×C22⋊C4×C3112yes—
506C2×C4C2×C22⋊C4×C3112yes—
507C2×C4C4×D4×C3118yes—
508C2×C4C31×#12012yes—
509C2×C4C31×#12118yes—
510C2×C4C31×#12312yes—
511C2×C4C23×C4×C3111yescharacteristic
512C2×C4C22×D4×C3112yes—
513C2×C4C22×D4×C3111yescharacteristic
514C2×C4C2×#41×C3112yes—
515C8—44no—
516C22—24no—
517C22—24no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—24no—
522C22—24no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—416no—
528C22—42no—
529C22—42no—
530C22—44no—
531C22—44no—
532C22—44no—
533C22—816no—
534C22—84no—
535C22—84no—
536C22C31×#38614yes—
537C22C31×#41814yescomplemented
538C22C22×C22⋊C4×C3111yescharacteristic
539C22C2×C31×#12011yescharacteristic
540C22C2×C31×#12311yescharacteristic
541C22C2×C31×AGL(1,ℤ/8)12yes—
542C22C31×#57512yes—
543C4—22no—
544C4—22no—
545C4—44no—
546C4—48no—
547C4C31×#38614yes—
548C4C2×C4×D4×C3112yes—
549C4C2×C31×#12112yes—
550C2—24no—
551C2—24no—
552C2—42no—
553C2—84no—
554C2C2×C31×#38611yescharacteristic
555C2C2×C31×#41811yescharacteristic
556C2C31×#289611yescharacteristic
557C2C31×#300612yes—
558C2C31×#309412yes—
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C31×#117C2semidirect
3. C2×C31×#418C2semidirect
4. C2×C31×#407C2semidirect
5. C31×#1875C2semidirect
6. C31×#1874C2semidirect
7. C31×#1736C2semidirect
15. C2×C31×#121C4semidirect
22. C2×C31×#117C22semidirect
24. C22×C4⋊C4×C31C22semidirect
29. C2×C31×#102C22semidirect
31. C2×C31×C22⋊C8C22semidirect
32. C2×C31×C22⋊C8C22semidirect
33. C31×#340C22semidirect
44. C22×D4×C31C2×C4semidirect
67. C31×#121C2×C4semidirect
72. C31×#117D4semidirect
77. C2×C4⋊C4×C31C2×C4semidirect
163. C4⋊C4×C31C2×D4semidirect
170. #20912C31direct (N × H)
238. C22×#117C2×C31semidirect
239. C2×#418C2×C31semidirect
240. C2×#407C2×C31semidirect
241. #1875C2×C31semidirect
242. #1874C2×C31semidirect
243. #1736C2×C31semidirect
265. C22×C31#418semidirect
285. C2×#121C4×C31semidirect
292. C2×#117C22×C31semidirect
294. C22×C4⋊C4C22×C31semidirect
299. C2×#102C22×C31semidirect
301. C2×C22⋊C8C22×C31semidirect
302. C2×C22⋊C8C22×C31semidirect
303. #340C22×C31semidirect
323. C22×D4C2×C4×C31semidirect
346. #121C2×C4×C31semidirect
351. #117D4×C31semidirect
356. C2×C4⋊C4C2×C4×C31semidirect
371. C31#20912direct (N × H)
443. C4⋊C4C2×D4×C31semidirect
537. C22C31×#418semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C22×C31×#1172
C2×C31×#4182
C2×C31×#4072
C31×#18752
C31×#18742
C31×#17362
#2091231