Finite Group Databasebeta

← C2×C31×#2042 #21480261

Subgroups — C2×C31×#2042 #21480261

Order 7936.

1670 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#124C211yesmaximal, characteristic
2C22×C31×#103C211yesmaximal, characteristic, complemented
3C22×C31×#103C211yesmaximal, characteristic, complemented
4C22×C31×#102C211yesmaximal, characteristic
5C22×C31×#102C211yesmaximal, characteristic
6C2×C31×#389C211yesmaximal, characteristic, complemented
7C31×#2042C218yesmaximal, direct product factor
8C2×C31×#336C211yesmaximal, characteristic, complemented
9C23×Q8×C31C2211yescharacteristic
10C23×D4×C31C2211yescharacteristic
11C23×C8×C31C2211yescharacteristic
12C23×C8×C31C2211yescharacteristic
13C2×C31×#124—24no—
14C2×C31×#124—24no—
15C2×C31×#124—22no—
16C2×C31×#124C2214yes—
17C22×C4⋊C4×C31—21no—
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31—21no—
21C22×C22⋊C4×C31—21no—
22C22×C42×C31C2211yescharacteristic
23C2×C31×#103—24no—
24C2×C31×#103—24no—
25C2×C31×#103C2214yescomplemented
26C2×C31×#103C2214yescomplemented
27C2×C31×#102—24no—
28C2×C31×#102—24no—
29C2×C31×#102C2214yes—
30C2×C31×#102C2214yes—
31C31×#389—22no—
32C31×#389C2214yescomplemented
33C2×C31×#95—21no—
34C31×#336C2214yescomplemented
35C25×C31—21no—
36C22×Q8×C31—22no—
37C22×Q8×C31—21no—
38C22×Q8×C31—22no—
39C22×Q8×C31—22no—
40C22×Q8×C31—22no—
41C22×Q8×C31—22no—
42C22×Q8×C31D414yes—
43C22×Q8×C31C2312yes—
44C22×D4×C31—22no—
45C22×D4×C31—21no—
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31D414yes—
51C22×D4×C31C2312yes—
52C23×C4×C31—21no—
53C23×C4×C31—21no—
54C23×C4×C31—21no—
55C23×C4×C31D411yescharacteristic
56C23×C4×C31D411yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C22×C8×C31—22no—
59C22×C8×C31—22no—
60C22×C8×C31—22no—
61C22×C8×C31—22no—
62C22×C8×C31—22no—
63C22×C8×C31—22no—
64C22×C8×C31C2312yes—
65C22×C8×C31C2312yes—
66C31×#124—216no—
67C31×#124—28no—
68C31×#124—28no—
69C2×C4⋊C4×C31—21no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—24no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—44no—
76C2×C4⋊C4×C31D414yes—
77C2×C4⋊C4×C31C2312yes—
78C2×C4⋊C4×C31C2312yes—
79C2×C22⋊C4×C31—28no—
80C2×C22⋊C4×C31—28no—
81C2×C22⋊C4×C31—24no—
82C2×C22⋊C4×C31—24no—
83C2×C42×C31—22no—
84C2×C42×C31—22no—
85C2×C42×C31D412yes—
86C2×C42×C31C2312yes—
87C31×#103—28no—
88C31×#103—28no—
89C31×#102—28no—
90C31×#102—28no—
91C31×#95—24no—
92C24×C31—24no—
93C24×C31—22no—
94C24×C31—42no—
95C24×C31—42no—
96C24×C31—42no—
97C24×C31—42no—
98C24×C31—42no—
99C24×C31—42no—
100C24×C31C2×D411yescharacteristic
101C2×Q8×C31—24no—
102C2×Q8×C31—22no—
103C2×Q8×C31—28no—
104C2×Q8×C31—28no—
105C2×Q8×C31—22no—
106C2×Q8×C31—22no—
107C2×Q8×C31—22no—
108C2×Q8×C31—22no—
109C2×Q8×C31—42no—
110C2×Q8×C31—44no—
111C2×Q8×C31—44no—
112C2×Q8×C31—42no—
113C2×Q8×C31C2×D414yes—
114C2×D4×C31—24no—
115C2×D4×C31—28no—
116C2×D4×C31—28no—
117C2×D4×C31—22no—
118C2×D4×C31—22no—
119C2×D4×C31—22no—
120C2×D4×C31—22no—
121C2×D4×C31—22no—
122C2×D4×C31—44no—
123C2×D4×C31—42no—
124C2×D4×C31—44no—
125C2×D4×C31—42no—
126C2×D4×C31C2×D414yes—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—24no—
130C22×C4×C31—24no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—42no—
139C22×C4×C31—42no—
140C22×C4×C31—42no—
141C22×C4×C31—42no—
142C22×C4×C31—42no—
143C22×C4×C31—42no—
144C22×C4×C31—42no—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D412yes—
150C22×C4×C31C2×D412yes—
151C22×C4×C31#4112yes—
152C22×C4×C31#4112yes—
153C22×C4×C31#4112yes—
154C22×C4×C31C2411yescharacteristic
155C2×C8×C31—22no—
156C2×C8×C31—22no—
157C2×C8×C31—22no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—44no—
162C2×C8×C31—44no—
163C4⋊C4×C31—24no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31—48no—
168C4⋊C4×C31—42no—
169C4⋊C4×C31C2×D414yes—
170C22⋊C4×C31—216no—
171C22⋊C4×C31—216no—
172C42×C31—24no—
173C42×C31—22no—
174C42×C31—22no—
175C2×#2042C3111yesmaximal, characteristic, direct product factor, Sylow
176C23×C31—24no—
177C23×C31—42no—
178C23×C31—42no—
179C23×C31—42no—
180C23×C31—42no—
181C23×C31—42no—
182C23×C31—42no—
183C23×C31—48no—
184C23×C31—48no—
185C23×C31—48no—
186C23×C31—84no—
187C23×C31—84no—
188C23×C31—84no—
189C23×C31—84no—
190C23×C31#12012yes—
191C23×C31#12112yes—
192C23×C31#12412yes—
193C23×C31#13512yes—
194C23×C31#13512yes—
195C23×C31AGL(1,ℤ/8)12yes—
196C23×C31#13712yes—
197C23×C31C22×D411yescharacteristic
198Q8×C31—24no—
199Q8×C31—24no—
200Q8×C31—42no—
201Q8×C31—42no—
202Q8×C31—48no—
203D4×C31—24no—
204D4×C31—24no—
205D4×C31—42no—
206D4×C31—42no—
207D4×C31—48no—
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—48no—
221C2×C4×C31—44no—
222C2×C4×C31—44no—
223C2×C4×C31—48no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—84no—
228C2×C4×C31#12012yes—
229C2×C4×C31#12114yes—
230C2×C4×C31#12114yes—
231C2×C4×C31#12112yes—
232C2×C4×C31#12314yes—
233C2×C4×C31#12314yes—
234C2×C4×C31#12412yes—
235C2×C4×C31C22×D411yescharacteristic
236C2×C4×C31C22×D411yescharacteristic
237C2×C4×C31C22×D411yescharacteristic
238C2×C4×C31C2×#4111yescharacteristic
239C2×C4×C31C2×#4111yescharacteristic
240C2×C4×C31C2×#4111yescharacteristic
241C8×C31—42no—
242C8×C31—42no—
243C22×#124C2×C3111yescharacteristic
244C22×#103C2×C3111yescharacteristic, complemented
245C22×#103C2×C3111yescharacteristic, complemented
246C22×#102C2×C3111yescharacteristic
247C22×#102C2×C3111yescharacteristic
248C2×#389C2×C3111yescharacteristic, complemented
249#2042C2×C3118yesdirect product factor
250C2×#336C2×C3111yescharacteristic, complemented
251C22×C31—44no—
252C22×C31—44no—
253C22×C31—44no—
254C22×C31—82no—
255C22×C31—82no—
256C22×C31—82no—
257C22×C31—82no—
258C22×C31—816no—
259C22×C31#39414yes—
260C22×C31#44914yes—
261C22×C31#45214yes—
262C22×C31#46314yes—
263C22×C31#46414yes—
264C22×C31#48814yes—
265C22×C31#48914yes—
266C22×C31C2×#12011yescharacteristic
267C22×C31C2×#12111yescharacteristic
268C22×C31C2×#12411yescharacteristic
269C22×C31C2×#13511yescharacteristic
270C22×C31C2×#13511yescharacteristic
271C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C31C2×#13711yescharacteristic
273C4×C31—44no—
274C4×C31—42no—
275C4×C31—42no—
276C4×C31—44no—
277C4×C31—82no—
278C4×C31#39414yes—
279C4×C31C2×#12111yescharacteristic
280C4×C31C2×#12111yescharacteristic
281C4×C31C2×#12311yescharacteristic
282C4×C31C2×#12311yescharacteristic
283C23×Q8C22×C3111yescharacteristic
284C23×D4C22×C3111yescharacteristic
285C23×C8C22×C3111yescharacteristic
286C23×C8C22×C3111yescharacteristic
287C2×#124—24no—
288C2×#124—24no—
289C2×#124—22no—
290C2×#124C22×C3114yes—
291C22×C4⋊C4—21no—
292C22×C4⋊C4C22×C3111yescharacteristic
293C22×C4⋊C4C22×C3111yescharacteristic
294C22×C22⋊C4—21no—
295C22×C22⋊C4—21no—
296C22×C42C22×C3111yescharacteristic
297C2×#103—24no—
298C2×#103—24no—
299C2×#103C22×C3114yescomplemented
300C2×#103C22×C3114yescomplemented
301C2×#102—24no—
302C2×#102—24no—
303C2×#102C22×C3114yes—
304C2×#102C22×C3114yes—
305#389—22no—
306#389C22×C3114yescomplemented
307C2×#95—21no—
308#336C22×C3114yescomplemented
309C2×C31—84no—
310C2×C31#204218yesdirect product factor
311C2×C31C2×#39411yescharacteristic
312C2×C31C2×#44911yescharacteristic
313C2×C31C2×#45211yescharacteristic
314C2×C31C2×#46311yescharacteristic
315C2×C31C2×#46411yescharacteristic
316C2×C31C2×#48811yescharacteristic
317C2×C31C2×#48911yescharacteristic
318C25—21no—
319C22×Q8—22no—
320C22×Q8—21no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8D4×C3114yes—
326C22×Q8C23×C3112yes—
327C22×D4—22no—
328C22×D4—21no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4D4×C3114yes—
334C22×D4C23×C3112yes—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4D4×C3111yescharacteristic
339C23×C4D4×C3111yescharacteristic
340C23×C4C23×C3111yescharacteristic
341C22×C8—22no—
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8C23×C3112yes—
348C22×C8C23×C3112yes—
349#124—216no—
350#124—28no—
351#124—28no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4D4×C3114yes—
360C2×C4⋊C4C23×C3112yes—
361C2×C4⋊C4C23×C3112yes—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42D4×C3112yes—
369C2×C42C23×C3112yes—
370#103—28no—
371#103—28no—
372#102—28no—
373#102—28no—
374#95—24no—
375C31C2×#204211yescharacteristic, direct product factor, Sylow
376C24—24no—
377C24—22no—
378C24—42no—
379C24—42no—
380C24—42no—
381C24—42no—
382C24—42no—
383C24—42no—
384C24C2×D4×C3111yescharacteristic
385C2×Q8—24no—
386C2×Q8—22no—
387C2×Q8—28no—
388C2×Q8—28no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—42no—
394C2×Q8—44no—
395C2×Q8—44no—
396C2×Q8—42no—
397C2×Q8C2×D4×C3114yes—
398C2×D4—24no—
399C2×D4—28no—
400C2×D4—28no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—44no—
407C2×D4—42no—
408C2×D4—44no—
409C2×D4—42no—
410C2×D4C2×D4×C3114yes—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4C2×D4×C3112yes—
430C22×C4C2×D4×C3112yes—
431C22×C4C2×D4×C3111yescharacteristic
432C22×C4C2×D4×C3112yes—
433C22×C4C2×D4×C3112yes—
434C22×C4C2×D4×C3112yes—
435C22×C4#41×C3112yes—
436C22×C4#41×C3112yes—
437C22×C4#41×C3112yes—
438C22×C4C24×C3111yescharacteristic
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—44no—
446C2×C8—44no—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—48no—
452C4⋊C4—42no—
453C4⋊C4C2×D4×C3114yes—
454C22⋊C4—216no—
455C22⋊C4—216no—
456C42—24no—
457C42—22no—
458C42—22no—
459C23—24no—
460C23—48no—
461C23—48no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—48no—
469C23—84no—
470C23—84no—
471C23—84no—
472C23—84no—
473C23C31×#12012yes—
474C23C31×#12112yes—
475C23C31×#12412yes—
476C23C31×#13512yes—
477C23C31×#13512yes—
478C23C31×AGL(1,ℤ/8)12yes—
479C23C31×#13712yes—
480C23C22×D4×C3111yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—42no—
484Q8—42no—
485Q8—48no—
486D4—24no—
487D4—24no—
488D4—42no—
489D4—42no—
490D4—48no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—48no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—48no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—84no—
511C2×C4C31×#12012yes—
512C2×C4C31×#12114yes—
513C2×C4C31×#12114yes—
514C2×C4C31×#12112yes—
515C2×C4C31×#12314yes—
516C2×C4C31×#12314yes—
517C2×C4C31×#12412yes—
518C2×C4C22×D4×C3111yescharacteristic
519C2×C4C22×D4×C3111yescharacteristic
520C2×C4C22×D4×C3111yescharacteristic
521C2×C4C2×#41×C3111yescharacteristic
522C2×C4C2×#41×C3111yescharacteristic
523C2×C4C2×#41×C3111yescharacteristic
524C8—42no—
525C8—42no—
526C22—44no—
527C22—44no—
528C22—44no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—816no—
534C22C31×#39414yes—
535C22C31×#44914yes—
536C22C31×#45214yes—
537C22C31×#46314yes—
538C22C31×#46414yes—
539C22C31×#48814yes—
540C22C31×#48914yes—
541C22C2×C31×#12011yescharacteristic
542C22C2×C31×#12111yescharacteristic
543C22C2×C31×#12411yescharacteristic
544C22C2×C31×#13511yescharacteristic
545C22C2×C31×#13511yescharacteristic
546C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
547C22C2×C31×#13711yescharacteristic
548C4—44no—
549C4—42no—
550C4—42no—
551C4—44no—
552C4—82no—
553C4C31×#39414yes—
554C4C2×C31×#12111yescharacteristic
555C4C2×C31×#12111yescharacteristic
556C4C2×C31×#12311yescharacteristic
557C4C2×C31×#12311yescharacteristic
558C2—84no—
559C2C31×#204218yesdirect product factor
560C2C2×C31×#39411yescharacteristic
561C2C2×C31×#44911yescharacteristic
562C2C2×C31×#45211yescharacteristic
563C2C2×C31×#46311yescharacteristic
564C2C2×C31×#46411yescharacteristic
565C2C2×C31×#48811yescharacteristic
566C2C2×C31×#48911yescharacteristic
subgroupG/H
center, socleC24×C31C2×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C31×#103C2semidirect
3. C22×C31×#103C2semidirect
6. C2×C31×#389C2semidirect
7. C31×#2042C2direct (N × H)
8. C2×C31×#336C2semidirect
25. C2×C31×#103C22semidirect
26. C2×C31×#103C22semidirect
32. C31×#389C22semidirect
34. C31×#336C22semidirect
175. C2×#2042C31direct (N × H)
244. C22×#103C2×C31semidirect
245. C22×#103C2×C31semidirect
248. C2×#389C2×C31semidirect
249. #2042C2×C31direct (N × H)
250. C2×#336C2×C31semidirect
299. C2×#103C22×C31semidirect
300. C2×#103C22×C31semidirect
306. #389C22×C31semidirect
308. #336C22×C31semidirect
310. C2×C31#2042direct (N × H)
375. C31C2×#2042direct (N × H)
559. C2C31×#2042direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C22×C31×#1032
C22×C31×#1022
C2×C31×#3892
C31×#20422
C2×C31×#3362
C2×#204231