Finite Group Databasebeta

← C31×#20926 #21477685

Subgroups — C31×#20926 #21477685

Order 7936.

1802 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#137C211yesmaximal, characteristic
2C22×C4×Q8×C31C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic
4C2×C31×#419C211yesmaximal, characteristic, complemented
5C31×#2297C211yesmaximal, characteristic
6C31×#1880C214yesmaximal, complemented
7C31×#1878C214yesmaximal, complemented
8C31×#1736C211yesmaximal, characteristic, complemented
9C31×#1728C211yesmaximal, characteristic, complemented
10C22×#41×C31C2211yescharacteristic
11C23×Q8×C31C2211yescharacteristic
12C2×C31×#137—24no—
13C2×C31×#137—24no—
14C2×C31×#137C418yescomplemented
15C22×Q16×C31C2212yes—
16C22×SD16×C31C2212yes—
17C22×M16×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C2×C4×Q8×C31—24no—
20C2×C4×Q8×C31—24no—
21C2×C4×Q8×C31—22no—
22C2×C4×Q8×C31C2214yes—
23C2×C31×#117C2211yescharacteristic
24C22×C4⋊C4×C31—21no—
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C42×C31—21no—
27C22×C42×C31C2211yescharacteristic
28C31×#419—24no—
29C31×#417—24no—
30C2×C31×#103C2214yes—
31C2×C31×#103C2212yes—
32C2×C31×#102C2212yes—
33C31×#391C2212yes—
34C31×#390C2212yes—
35C31×#386—21no—
36C31×#386—21no—
37C4×C22⋊C4×C31—22no—
38C31×#340C2214yes—
39C31×#336C2214yes—
40C2×#41×C31—22no—
41C2×#41×C31—22no—
42C2×#41×C31—22no—
43C2×#41×C31—22no—
44C2×#41×C31—22no—
45C2×#41×C31C2×C414yes—
46C22×Q8×C31—22no—
47C22×Q8×C31—21no—
48C22×Q8×C31—22no—
49C22×Q8×C31—22no—
50C22×Q8×C31C2×C414yes—
51C22×Q8×C31D414yes—
52C22×Q8×C31D414yes—
53C22×Q8×C31C2311yescharacteristic
54C22×Q8×C31C2312yes—
55C22×D4×C31—21no—
56C22×D4×C31C2311yescharacteristic
57C23×C4×C31—21no—
58C23×C4×C31—21no—
59C23×C4×C31—21no—
60C23×C4×C31D411yescharacteristic
61C23×C4×C31D411yescharacteristic
62C23×C4×C31C2311yescharacteristic
63C31×#137—232no—
64C2×Q16×C31—24no—
65C2×Q16×C31—24no—
66C2×Q16×C31C2×C418yescomplemented
67C2×SD16×C31—24no—
68C2×SD16×C31—24no—
69C2×SD16×C31C2×C418yescomplemented
70C2×M16×C31—22no—
71C2×M16×C31—22no—
72C2×M16×C31—22no—
73C2×M16×C31—22no—
74C2×M16×C31—22no—
75C2×M16×C31C2×C414yes—
76C22×C8×C31C2312yes—
77C22×C8×C31C2312yes—
78C4×Q8×C31—216no—
79C4×Q8×C31—28no—
80C4×Q8×C31—28no—
81C31×#117—22no—
82C31×#117—22no—
83C2×C4⋊C4×C31—28no—
84C2×C4⋊C4×C31—24no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31D414yes—
88C2×C4⋊C4×C31C2312yes—
89C2×C4⋊C4×C31C2312yes—
90C2×C22⋊C4×C31—21no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C42×C31—28no—
94C2×C42×C31—24no—
95C2×C42×C31—22no—
96C2×C42×C31—22no—
97C2×C42×C31—21no—
98C2×C42×C31D412yes—
99C2×C42×C31C2312yes—
100C31×#103—28no—
101C31×#103—24no—
102C31×#102—24no—
103C31×#95—22no—
104C31×#95—22no—
105C24×C31—21no—
106C24×C31C2×D411yescharacteristic
107#41×C31—28no—
108#41×C31—28no—
109#41×C31—44no—
110#41×C31—44no—
111C2×Q8×C31—24no—
112C2×Q8×C31—28no—
113C2×Q8×C31—24no—
114C2×Q8×C31—24no—
115C2×Q8×C31—28no—
116C2×Q8×C31—28no—
117C2×Q8×C31—22no—
118C2×Q8×C31—22no—
119C2×Q8×C31—22no—
120C2×Q8×C31—21no—
121C2×Q8×C31—21no—
122C2×Q8×C31—21no—
123C2×Q8×C31—21no—
124C2×Q8×C31—21no—
125C2×Q8×C31C22⋊C4116yescomplemented
126C2×Q8×C31C22×C412yes—
127C2×Q8×C31C22×C414yes—
128C2×Q8×C31C2×D414yes—
129C2×Q8×C31C2×D414yes—
130C2×D4×C31—24no—
131C2×D4×C31—21no—
132C2×D4×C31—21no—
133C2×D4×C31—21no—
134C2×D4×C31—21no—
135C2×D4×C31—21no—
136C2×D4×C31—42no—
137C2×D4×C31—42no—
138C2×D4×C31C22×C412yes—
139C22×C4×C31—24no—
140C22×C4×C31—22no—
141C22×C4×C31—24no—
142C22×C4×C31—24no—
143C22×C4×C31—22no—
144C22×C4×C31—24no—
145C22×C4×C31—22no—
146C22×C4×C31—24no—
147C22×C4×C31—21no—
148C22×C4×C31—22no—
149C22×C4×C31—24no—
150C22×C4×C31—22no—
151C22×C4×C31—42no—
152C22×C4×C31—44no—
153C22×C4×C31—42no—
154C22×C4×C31—42no—
155C22×C4×C31C22×C412yes—
156C22×C4×C31C2×D412yes—
157C22×C4×C31C2×D412yes—
158C22×C4×C31C2×D412yes—
159C22×C4×C31C2×D412yes—
160C22×C4×C31C2×D411yescharacteristic
161C22×C4×C31C2×D412yes—
162C22×C4×C31#4112yes—
163C22×C4×C31#4112yes—
164C22×C4×C31C2411yescharacteristic
165Q16×C31—216no—
166SD16×C31—216no—
167M16×C31—28no—
168M16×C31—44no—
169C2×C8×C31—22no—
170C2×C8×C31—22no—
171C2×C8×C31—22no—
172C2×C8×C31—22no—
173C2×C8×C31—22no—
174C2×C8×C31C22×C414yes—
175C4⋊C4×C31—216no—
176C4⋊C4×C31—24no—
177C4⋊C4×C31—22no—
178C4⋊C4×C31—22no—
179C4⋊C4×C31—22no—
180C4⋊C4×C31C2×D414yes—
181C22⋊C4×C31—44no—
182C22⋊C4×C31—42no—
183C22⋊C4×C31—44no—
184C42×C31—216no—
185C42×C31—24no—
186C42×C31—22no—
187C42×C31—22no—
188C42×C31—42no—
189#20926C3111yesmaximal, characteristic, direct product factor, Sylow
190C23×C31—22no—
191C23×C31—22no—
192C23×C31—22no—
193C23×C31—41no—
194C23×C31—41no—
195C23×C31—42no—
196C23×C31—42no—
197C23×C31C4×D412yes—
198C23×C31#12012yes—
199C23×C31#12112yes—
200C23×C31C22×D411yescharacteristic
201Q8×C31—24no—
202Q8×C31—24no—
203Q8×C31—24no—
204Q8×C31—216no—
205Q8×C31—22no—
206Q8×C31—22no—
207Q8×C31—41no—
208Q8×C31—41no—
209Q8×C31C2×C22⋊C418yes—
210D4×C31—22no—
211D4×C31—22no—
212D4×C31—48no—
213D4×C31—41no—
214D4×C31—41no—
215C2×C4×C31—28no—
216C2×C4×C31—24no—
217C2×C4×C31—22no—
218C2×C4×C31—24no—
219C2×C4×C31—24no—
220C2×C4×C31—22no—
221C2×C4×C31—216no—
222C2×C4×C31—22no—
223C2×C4×C31—22no—
224C2×C4×C31—24no—
225C2×C4×C31—22no—
226C2×C4×C31—22no—
227C2×C4×C31—44no—
228C2×C4×C31—48no—
229C2×C4×C31—41no—
230C2×C4×C31—41no—
231C2×C4×C31—44no—
232C2×C4×C31—48no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31C2×C22⋊C414yes—
237C2×C4×C31C4×D414yes—
238C2×C4×C31C4×D412yes—
239C2×C4×C31#12012yes—
240C2×C4×C31#12114yes—
241C2×C4×C31#12112yes—
242C2×C4×C31#12314yes—
243C2×C4×C31#13714yescomplemented
244C2×C4×C31C23×C411yescharacteristic
245C2×C4×C31C22×D411yescharacteristic
246C2×C4×C31C22×D411yescharacteristic
247C2×C4×C31C22×D411yescharacteristic
248C2×C4×C31C2×#4111yescharacteristic
249C2×C4×C31C2×#4111yescharacteristic
250C8×C31—24no—
251C8×C31—42no—
252C22×#137C2×C3111yescharacteristic
253C22×C4×Q8C2×C3111yescharacteristic, complemented
254C2×#417C2×C3111yescharacteristic
255C2×#419C2×C3111yescharacteristic, complemented
256#2297C2×C3111yescharacteristic
257#1880C2×C3114yescomplemented
258#1878C2×C3114yescomplemented
259#1736C2×C3111yescharacteristic, complemented
260#1728C2×C3111yescharacteristic, complemented
261C22×C31—24no—
262C22×C31—22no—
263C22×C31—22no—
264C22×C31—24no—
265C22×C31—44no—
266C22×C31—42no—
267C22×C31—81no—
268C22×C31—81no—
269C22×C31—82no—
270C22×C31#38614yes—
271C22×C31C2×C4×D411yescharacteristic
272C22×C31C2×#12011yescharacteristic
273C22×C31C2×#12111yescharacteristic
274C22×C31C2×#13712yes—
275C22×C31#57512yes—
276C4×C31—24no—
277C4×C31—28no—
278C4×C31—42no—
279C4×C31—44no—
280C4×C31—42no—
281C4×C31—82no—
282C4×C31#38614yes—
283C4×C31C22×C22⋊C411yescharacteristic
284C4×C31C2×C4×D411yescharacteristic
285C4×C31C2×#12111yescharacteristic
286C4×C31C2×#12311yescharacteristic
287C22×#41C22×C3111yescharacteristic
288C23×Q8C22×C3111yescharacteristic
289C2×#137—24no—
290C2×#137—24no—
291C2×#137C4×C3118yescomplemented
292C22×Q16C22×C3112yes—
293C22×SD16C22×C3112yes—
294C22×M16C22×C3111yescharacteristic
295C22×M16C22×C3111yescharacteristic
296C2×C4×Q8—24no—
297C2×C4×Q8—24no—
298C2×C4×Q8—22no—
299C2×C4×Q8C22×C3114yes—
300C2×#117C22×C3111yescharacteristic
301C22×C4⋊C4—21no—
302C22×C4⋊C4C22×C3111yescharacteristic
303C22×C42—21no—
304C22×C42C22×C3111yescharacteristic
305#419—24no—
306#417—24no—
307C2×#103C22×C3114yes—
308C2×#103C22×C3112yes—
309C2×#102C22×C3112yes—
310#391C22×C3112yes—
311#390C22×C3112yes—
312#386—21no—
313#386—21no—
314C4×C22⋊C4—22no—
315#340C22×C3114yes—
316#336C22×C3114yes—
317C2×C31—24no—
318C2×C31—82no—
319C2×C31C2×#38611yescharacteristic
320C2×C31C4×#13712yes—
321C2×C31#300411yescharacteristic
322C2×C31#300511yescharacteristic
323C2×C31#303712yes—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41C2×C4×C3114yes—
330C22×Q8—22no—
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8C2×C4×C3114yes—
335C22×Q8D4×C3114yes—
336C22×Q8D4×C3114yes—
337C22×Q8C23×C3111yescharacteristic
338C22×Q8C23×C3112yes—
339C22×D4—21no—
340C22×D4C23×C3111yescharacteristic
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4D4×C3111yescharacteristic
345C23×C4D4×C3111yescharacteristic
346C23×C4C23×C3111yescharacteristic
347#137—232no—
348C2×Q16—24no—
349C2×Q16—24no—
350C2×Q16C2×C4×C3118yescomplemented
351C2×SD16—24no—
352C2×SD16—24no—
353C2×SD16C2×C4×C3118yescomplemented
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16C2×C4×C3114yes—
360C22×C8C23×C3112yes—
361C22×C8C23×C3112yes—
362C4×Q8—216no—
363C4×Q8—28no—
364C4×Q8—28no—
365#117—22no—
366#117—22no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4D4×C3114yes—
372C2×C4⋊C4C23×C3112yes—
373C2×C4⋊C4C23×C3112yes—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C42—28no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—21no—
382C2×C42D4×C3112yes—
383C2×C42C23×C3112yes—
384#103—28no—
385#103—24no—
386#102—24no—
387#95—22no—
388#95—22no—
389C31#2092611yescharacteristic, direct product factor, Sylow
390C24—21no—
391C24C2×D4×C3111yescharacteristic
392#41—28no—
393#41—28no—
394#41—44no—
395#41—44no—
396C2×Q8—24no—
397C2×Q8—28no—
398C2×Q8—24no—
399C2×Q8—24no—
400C2×Q8—28no—
401C2×Q8—28no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8C22⋊C4×C31116yescomplemented
411C2×Q8C22×C4×C3112yes—
412C2×Q8C22×C4×C3114yes—
413C2×Q8C2×D4×C3114yes—
414C2×Q8C2×D4×C3114yes—
415C2×D4—24no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4C22×C4×C3112yes—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—44no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4C22×C4×C3112yes—
441C22×C4C2×D4×C3112yes—
442C22×C4C2×D4×C3112yes—
443C22×C4C2×D4×C3112yes—
444C22×C4C2×D4×C3112yes—
445C22×C4C2×D4×C3111yescharacteristic
446C22×C4C2×D4×C3112yes—
447C22×C4#41×C3112yes—
448C22×C4#41×C3112yes—
449C22×C4C24×C3111yescharacteristic
450Q16—216no—
451SD16—216no—
452M16—28no—
453M16—44no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8C22×C4×C3114yes—
460C4⋊C4—216no—
461C4⋊C4—24no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4C2×D4×C3114yes—
466C22⋊C4—44no—
467C22⋊C4—42no—
468C22⋊C4—44no—
469C42—216no—
470C42—24no—
471C42—22no—
472C42—22no—
473C42—42no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—42no—
481C23C4×D4×C3112yes—
482C23C31×#12012yes—
483C23C31×#12112yes—
484C23C22×D4×C3111yescharacteristic
485Q8—24no—
486Q8—24no—
487Q8—24no—
488Q8—216no—
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8C2×C22⋊C4×C3118yes—
494D4—22no—
495D4—22no—
496D4—48no—
497D4—41no—
498D4—41no—
499C2×C4—28no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—216no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—44no—
512C2×C4—48no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—44no—
516C2×C4—48no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4C2×C22⋊C4×C3114yes—
521C2×C4C4×D4×C3114yes—
522C2×C4C4×D4×C3112yes—
523C2×C4C31×#12012yes—
524C2×C4C31×#12114yes—
525C2×C4C31×#12112yes—
526C2×C4C31×#12314yes—
527C2×C4C31×#13714yescomplemented
528C2×C4C23×C4×C3111yescharacteristic
529C2×C4C22×D4×C3111yescharacteristic
530C2×C4C22×D4×C3111yescharacteristic
531C2×C4C22×D4×C3111yescharacteristic
532C2×C4C2×#41×C3111yescharacteristic
533C2×C4C2×#41×C3111yescharacteristic
534C8—24no—
535C8—42no—
536C22—24no—
537C22—22no—
538C22—22no—
539C22—24no—
540C22—44no—
541C22—42no—
542C22—81no—
543C22—81no—
544C22—82no—
545C22C31×#38614yes—
546C22C2×C4×D4×C3111yescharacteristic
547C22C2×C31×#12011yescharacteristic
548C22C2×C31×#12111yescharacteristic
549C22C2×C31×#13712yes—
550C22C31×#57512yes—
551C4—24no—
552C4—28no—
553C4—42no—
554C4—44no—
555C4—42no—
556C4—82no—
557C4C31×#38614yes—
558C4C22×C22⋊C4×C3111yescharacteristic
559C4C2×C4×D4×C3111yescharacteristic
560C4C2×C31×#12111yescharacteristic
561C4C2×C31×#12311yescharacteristic
562C2—24no—
563C2—82no—
564C2C2×C31×#38611yescharacteristic
565C2C4×C31×#13712yes—
566C2C31×#300411yescharacteristic
567C2C31×#300511yescharacteristic
568C2C31×#303712yes—
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×Q8×C31C2semidirect
4. C2×C31×#419C2semidirect
6. C31×#1880C2semidirect
7. C31×#1878C2semidirect
8. C31×#1736C2semidirect
9. C31×#1728C2semidirect
14. C2×C31×#137C4semidirect
66. C2×Q16×C31C2×C4semidirect
69. C2×SD16×C31C2×C4semidirect
125. C2×Q8×C31C22⋊C4semidirect
189. #20926C31direct (N × H)
243. C2×C4×C31#137semidirect
253. C22×C4×Q8C2×C31semidirect
255. C2×#419C2×C31semidirect
257. #1880C2×C31semidirect
258. #1878C2×C31semidirect
259. #1736C2×C31semidirect
260. #1728C2×C31semidirect
291. C2×#137C4×C31semidirect
350. C2×Q16C2×C4×C31semidirect
353. C2×SD16C2×C4×C31semidirect
389. C31#20926direct (N × H)
410. C2×Q8C22⋊C4×C31semidirect
527. C2×C4C31×#137semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1372
C22×C4×Q8×C312
C2×C31×#4172
C2×C31×#4192
C31×#22972
C31×#18802
C31×#18782
C31×#17362
C31×#17282
#2092631