Finite Group Databasebeta

← C31×#23616 #21480375

Subgroups — C31×#23616 #21480375

Order 7936.

1102 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#428C211yesmaximal, characteristic, complemented
2C2×C31×#424C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic
4C2×C31×#416C211yesmaximal, characteristic
5C31×#2317C211yesmaximal, characteristic, complemented
6C31×#2311C211yesmaximal, characteristic
7C31×#2068C212yesmaximal, complemented
8C31×#2067C212yesmaximal, complemented
9C31×#2066C212yesmaximal, complemented
10C31×#2065C212yesmaximal, complemented
11C2×C31×#340C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C22×M16×C31C2211yescharacteristic
14C23×C8×C31C2211yescharacteristic
15C2×C31×#117C2211yescharacteristic
16C2×C31×#117C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C31×#428—24no—
20C2×C31×#107C2212yes—
21C2×C31×#106C2212yes—
22C31×#424—24no—
23C2×C31×C4⋊C8C2212yes—
24C2×C31×C4⋊C8C2212yes—
25C31×#417—24no—
26C31×#416—24no—
27C2×C31×#103C2211yescharacteristic
28C2×C31×#103C2212yes—
29C2×C31×#103C2211yescharacteristic
30C2×C31×#102C2211yescharacteristic
31C2×C31×#102C2212yes—
32C2×C31×#102C2211yescharacteristic
33C31×#391C2212yes—
34C31×#390C2212yes—
35C31×#389C2212yes—
36C31×#389C2212yes—
37C31×#386—22no—
38C31×#385—22no—
39C31×#384—21no—
40C31×#382—21no—
41C31×#380—21no—
42C31×#380—21no—
43C31×#340C2212yes—
44C31×#340C2212yes—
45C2×#41×C31—22no—
46C2×#41×C31—22no—
47C2×#41×C31—22no—
48C2×#41×C31—22no—
49C2×#41×C31—22no—
50C2×#41×C31Q814yes—
51C22×Q8×C31C2311yescharacteristic
52C22×D4×C31—21no—
53C22×D4×C31C2311yescharacteristic
54C23×C4×C31—21no—
55C23×C4×C31—21no—
56C23×C4×C31—21no—
57C23×C4×C31C2311yescharacteristic
58C2×M16×C31—22no—
59C2×M16×C31—22no—
60C2×M16×C31D414yes—
61C22×C8×C31—22no—
62C22×C8×C31—22no—
63C22×C8×C31—22no—
64C22×C8×C31C2311yescharacteristic
65C22×C8×C31C2311yescharacteristic
66C22×C8×C31C2312yes—
67C31×#117—22no—
68C31×#117—22no—
69C31×#117—22no—
70C31×#117D414yes—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31D411yescharacteristic
80C2×C4⋊C4×C31D411yescharacteristic
81C2×C4⋊C4×C31C2312yes—
82C2×C4⋊C4×C31C2312yes—
83C2×C4⋊C4×C31C2311yescharacteristic
84C2×C4⋊C4×C31C2311yescharacteristic
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31D412yes—
89C2×C42×C31—21no—
90C2×C42×C31C2312yes—
91C31×#107—24no—
92C31×#106—24no—
93C31×C4⋊C8—24no—
94C31×C4⋊C8—24no—
95C31×#103—24no—
96C31×#103—22no—
97C31×#103—22no—
98C31×#102—24no—
99C31×#102—22no—
100C31×#102—22no—
101C31×#95—22no—
102C31×#95—22no—
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—21no—
112C2×Q8×C31—21no—
113C2×Q8×C31—21no—
114C2×Q8×C31—21no—
115C2×Q8×C31—21no—
116C2×Q8×C31C2×Q812yes—
117C2×D4×C31—24no—
118C2×D4×C31—21no—
119C2×D4×C31—21no—
120C2×D4×C31—21no—
121C2×D4×C31—21no—
122C2×D4×C31—21no—
123C2×D4×C31—42no—
124C2×D4×C31—42no—
125C2×D4×C31C2×Q812yes—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—24no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—42no—
133C22×C4×C31—42no—
134C22×C4×C31—42no—
135C22×C4×C31—42no—
136C22×C4×C31—81no—
137C22×C4×C31—81no—
138C22×C4×C31—81no—
139C22×C4×C31—81no—
140C22×C4×C31C2×D412yes—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×Q812yes—
146C22×C4×C31#4112yes—
147C22×C4×C31#4112yes—
148C22×C4×C31#4112yes—
149C22×C4×C31C2411yescharacteristic
150M16×C31—28no—
151C2×C8×C31—22no—
152C2×C8×C31—22no—
153C2×C8×C31—21no—
154C2×C8×C31—21no—
155C2×C8×C31—21no—
156C2×C8×C31—21no—
157C2×C8×C31—21no—
158C2×C8×C31—21no—
159C2×C8×C31—44no—
160C2×C8×C31C2×D414yes—
161C4⋊C4×C31—22no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—21no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—42no—
170C4⋊C4×C31—42no—
171C4⋊C4×C31—82no—
172C4⋊C4×C31—82no—
173C4⋊C4×C31C2×D412yes—
174C4⋊C4×C31C2×D412yes—
175C22⋊C4×C31—24no—
176C22⋊C4×C31—24no—
177C22⋊C4×C31—82no—
178C22⋊C4×C31—82no—
179C42×C31—24no—
180C42×C31—22no—
181C42×C31—22no—
182#23616C3111yesmaximal, characteristic, direct product factor, Sylow
183C23×C31—21no—
184C23×C31—21no—
185C23×C31—21no—
186C23×C31—21no—
187C23×C31—22no—
188C23×C31—41no—
189C23×C31—41no—
190C23×C31—41no—
191C23×C31—41no—
192C23×C31—41no—
193C23×C31—41no—
194C23×C31#12112yes—
195C23×C31#12112yes—
196C23×C31C22⋊Q812yes—
197C23×C31C22×D411yescharacteristic
198Q8×C31—22no—
199Q8×C31—22no—
200Q8×C31—41no—
201Q8×C31—41no—
202D4×C31—22no—
203D4×C31—22no—
204D4×C31—48no—
205D4×C31—41no—
206D4×C31—41no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—22no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—41no—
217C2×C4×C31—41no—
218C2×C4×C31—41no—
219C2×C4×C31—41no—
220C2×C4×C31—41no—
221C2×C4×C31—41no—
222C2×C4×C31—48no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—84no—
230C2×C4×C31—84no—
231C2×C4×C31#12114yes—
232C2×C4×C31#12112yes—
233C2×C4×C31#12112yes—
234C2×C4×C31C22⋊Q814yes—
235C2×C4×C31C22⋊Q814yes—
236C2×C4×C31C22⋊Q812yes—
237C2×C4×C31#12614yes—
238C2×C4×C31C22×D411yescharacteristic
239C2×C4×C31C22×D411yescharacteristic
240C2×C4×C31C22×Q811yescharacteristic
241C2×C4×C31C2×#4111yescharacteristic
242C2×C4×C31C2×#4111yescharacteristic
243C2×C4×C31C2×#4111yescharacteristic
244C8×C31—24no—
245C8×C31—41no—
246C8×C31—41no—
247C2×#428C2×C3111yescharacteristic, complemented
248C2×#424C2×C3111yescharacteristic, complemented
249C2×#417C2×C3111yescharacteristic
250C2×#416C2×C3111yescharacteristic
251#2317C2×C3111yescharacteristic, complemented
252#2311C2×C3111yescharacteristic
253#2068C2×C3112yescomplemented
254#2067C2×C3112yescomplemented
255#2066C2×C3112yescomplemented
256#2065C2×C3112yescomplemented
257C2×#340C2×C3111yescharacteristic, complemented
258C22×C31—22no—
259C22×C31—22no—
260C22×C31—22no—
261C22×C31—22no—
262C22×C31—22no—
263C22×C31—22no—
264C22×C31—42no—
265C22×C31—42no—
266C22×C31—42no—
267C22×C31—81no—
268C22×C31—81no—
269C22×C31—81no—
270C22×C31—81no—
271C22×C31#39614yes—
272C22×C31C2×#12111yescharacteristic
273C22×C31C2×#12111yescharacteristic
274C22×C31C2×C22⋊Q811yescharacteristic
275C22×C31#57611yescharacteristic
276C22×C31#57711yescharacteristic
277C22×C31#57711yescharacteristic
278C22×C31#57811yescharacteristic
279C4×C31—42no—
280C4×C31—42no—
281C4×C31—42no—
282C4×C31—42no—
283C4×C31—42no—
284C4×C31—82no—
285C4×C31—82no—
286C4×C31#39614yes—
287C4×C31C2×#12111yescharacteristic
288C4×C31C2×C22⋊Q811yescharacteristic
289C4×C31C2×C22⋊Q811yescharacteristic
290C4×C31C2×#12611yescharacteristic
291C22×#41C22×C3111yescharacteristic
292C22×M16C22×C3111yescharacteristic
293C23×C8C22×C3111yescharacteristic
294C2×#117C22×C3111yescharacteristic
295C2×#117C22×C3111yescharacteristic
296C22×C4⋊C4C22×C3111yescharacteristic
297C22×C4⋊C4C22×C3111yescharacteristic
298#428—24no—
299C2×#107C22×C3112yes—
300C2×#106C22×C3112yes—
301#424—24no—
302C2×C4⋊C8C22×C3112yes—
303C2×C4⋊C8C22×C3112yes—
304#417—24no—
305#416—24no—
306C2×#103C22×C3111yescharacteristic
307C2×#103C22×C3112yes—
308C2×#103C22×C3111yescharacteristic
309C2×#102C22×C3111yescharacteristic
310C2×#102C22×C3112yes—
311C2×#102C22×C3111yescharacteristic
312#391C22×C3112yes—
313#390C22×C3112yes—
314#389C22×C3112yes—
315#389C22×C3112yes—
316#386—22no—
317#385—22no—
318#384—21no—
319#382—21no—
320#380—21no—
321#380—21no—
322#340C22×C3112yes—
323#340C22×C3112yes—
324C2×C31—24no—
325C2×C31—82no—
326C2×C31C2×#39611yescharacteristic
327C2×C31#304511yescharacteristic
328C2×C31#304611yescharacteristic
329C2×C31#306211yescharacteristic
330C2×C31#306311yescharacteristic
331C2×C31#308311yescharacteristic
332C2×C31#308411yescharacteristic
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41Q8×C3114yes—
339C22×Q8C23×C3111yescharacteristic
340C22×D4—21no—
341C22×D4C23×C3111yescharacteristic
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4C23×C3111yescharacteristic
346C2×M16—22no—
347C2×M16—22no—
348C2×M16D4×C3114yes—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8C23×C3111yescharacteristic
353C22×C8C23×C3111yescharacteristic
354C22×C8C23×C3112yes—
355#117—22no—
356#117—22no—
357#117—22no—
358#117D4×C3114yes—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4D4×C3111yescharacteristic
368C2×C4⋊C4D4×C3111yescharacteristic
369C2×C4⋊C4C23×C3112yes—
370C2×C4⋊C4C23×C3112yes—
371C2×C4⋊C4C23×C3111yescharacteristic
372C2×C4⋊C4C23×C3111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4D4×C3112yes—
377C2×C42—21no—
378C2×C42C23×C3112yes—
379#107—24no—
380#106—24no—
381C4⋊C8—24no—
382C4⋊C8—24no—
383#103—24no—
384#103—22no—
385#103—22no—
386#102—24no—
387#102—22no—
388#102—22no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95—22no—
393C31#2361611yescharacteristic, direct product factor, Sylow
394C24—21no—
395C24C2×D4×C3111yescharacteristic
396#41—28no—
397#41—28no—
398#41—44no—
399#41—44no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8C2×Q8×C3112yes—
406C2×D4—24no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4C2×Q8×C3112yes—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—81no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4C2×D4×C3112yes—
430C22×C4C2×D4×C3112yes—
431C22×C4C2×D4×C3111yescharacteristic
432C22×C4C2×D4×C3112yes—
433C22×C4C2×D4×C3112yes—
434C22×C4C2×Q8×C3112yes—
435C22×C4#41×C3112yes—
436C22×C4#41×C3112yes—
437C22×C4#41×C3112yes—
438C22×C4C24×C3111yescharacteristic
439M16—28no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—44no—
449C2×C8C2×D4×C3114yes—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—82no—
461C4⋊C4—82no—
462C4⋊C4C2×D4×C3112yes—
463C4⋊C4C2×D4×C3112yes—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—82no—
467C22⋊C4—82no—
468C42—24no—
469C42—22no—
470C42—22no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—22no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23C31×#12112yes—
483C23C31×#12112yes—
484C23C31×C22⋊Q812yes—
485C23C22×D4×C3111yescharacteristic
486Q8—22no—
487Q8—22no—
488Q8—41no—
489Q8—41no—
490D4—22no—
491D4—22no—
492D4—48no—
493D4—41no—
494D4—41no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—48no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—84no—
518C2×C4—84no—
519C2×C4C31×#12112yes—
520C2×C4C31×#12112yes—
521C2×C4C31×#12114yes—
522C2×C4C31×C22⋊Q812yes—
523C2×C4C31×C22⋊Q814yes—
524C2×C4C31×C22⋊Q814yes—
525C2×C4C31×#12614yes—
526C2×C4C22×D4×C3111yescharacteristic
527C2×C4C22×D4×C3111yescharacteristic
528C2×C4C22×Q8×C3111yescharacteristic
529C2×C4C2×#41×C3111yescharacteristic
530C2×C4C2×#41×C3111yescharacteristic
531C2×C4C2×#41×C3111yescharacteristic
532C8—24no—
533C8—41no—
534C8—41no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22C31×#39614yes—
549C22C2×C31×#12111yescharacteristic
550C22C2×C31×#12111yescharacteristic
551C22C2×C31×C22⋊Q811yescharacteristic
552C22C31×#57611yescharacteristic
553C22C31×#57711yescharacteristic
554C22C31×#57711yescharacteristic
555C22C31×#57811yescharacteristic
556C4—42no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—82no—
562C4—82no—
563C4C31×#39614yes—
564C4C2×C31×#12111yescharacteristic
565C4C2×C31×C22⋊Q811yescharacteristic
566C4C2×C31×C22⋊Q811yescharacteristic
567C4C2×C31×#12611yescharacteristic
568C2—24no—
569C2—82no—
570C2C2×C31×#39611yescharacteristic
571C2C31×#304511yescharacteristic
572C2C31×#304611yescharacteristic
573C2C31×#306211yescharacteristic
574C2C31×#306311yescharacteristic
575C2C31×#308311yescharacteristic
576C2C31×#308411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#428C2semidirect
2. C2×C31×#424C2semidirect
5. C31×#2317C2semidirect
7. C31×#2068C2semidirect
8. C31×#2067C2semidirect
9. C31×#2066C2semidirect
10. C31×#2065C2semidirect
11. C2×C31×#340C2semidirect
182. #23616C31direct (N × H)
247. C2×#428C2×C31semidirect
248. C2×#424C2×C31semidirect
251. #2317C2×C31semidirect
253. #2068C2×C31semidirect
254. #2067C2×C31semidirect
255. #2066C2×C31semidirect
256. #2065C2×C31semidirect
257. C2×#340C2×C31semidirect
393. C31#23616direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4282
C2×C31×#4242
C2×C31×#4172
C2×C31×#4162
C31×#23172
C31×#23112
C31×#20682
C31×#20672
C31×#20662
C31×#20652
C2×C31×#3402
#2361631