Finite Group Databasebeta

← C31×#23568 #21480327

Subgroups — C31×#23568 #21480327

Order 7936.

1240 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
1C2×C31×#533C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C31C212yesmaximal, complemented
3C4×C31×#121C211yesmaximal, characteristic
4C31×#2058C211yesmaximal, characteristic, complemented
5C31×#2043C211yesmaximal, characteristic, complemented
6C31×#2035C212yesmaximal, complemented
7C31×#2023C211yesmaximal, characteristic, complemented
8C31×#2013C211yesmaximal, characteristic, complemented
9C31×#2000C212yesmaximal
10C4×C31×#103C212yesmaximal, complemented
11C4×C31×C22⋊C8C211yesmaximal, characteristic, complemented
12C22×SD16×C31C2212yes—
13C31×#533—28no—
14C2×C31×C4⋊Q8C2211yescharacteristic
15C2×C31×C4⋊Q8C2211yescharacteristic
16C2×C31×#125—21no—
17C2×C31×C22⋊Q8—21no—
18C2×C31×C22⋊Q8C2212yes—
19C2×C31×#121C2211yescharacteristic
20C2×C4×Q8×C31—21no—
21C2×C4×Q8×C31C2212yes—
22C2×C4×D4×C31—21no—
23C2×C4×D4×C31C2211yescharacteristic
24C2×C31×#117—21no—
25C22×C42×C31C2211yescharacteristic
26C4×SD16×C31—28no—
27C2×C31×#106C2212yes—
28C2×C31×#103C2212yes—
29C2×C31×#103C2212yes—
30C2×C31×#103C2212yes—
31C2×C31×#102C2212yes—
32C2×C31×C22⋊C8C2212yes—
33C2×C4×C8×C31C2212yes—
34C31×#390C2211yescharacteristic
35C31×#389C2211yescharacteristic
36C31×#388—21no—
37C31×#386—21no—
38C31×#380C2211yescharacteristic
39C4×C4⋊C4×C31C2211yescharacteristic
40C4×C22⋊C4×C31—21no—
41C31×#340C2212yes—
42C31×#340C2212yes—
43C31×#336C2211yescharacteristic
44C31×#336C2211yescharacteristic
45C22×Q8×C31—21no—
46C22×Q8×C31C2312yes—
47C22×D4×C31—21no—
48C22×D4×C31C2311yescharacteristic
49C23×C4×C31—21no—
50C23×C4×C31D411yescharacteristic
51C23×C4×C31D411yescharacteristic
52C23×C4×C31C2311yescharacteristic
53C2×SD16×C31—24no—
54C2×SD16×C31—24no—
55C2×SD16×C31—24no—
56C22×C8×C31C2312yes—
57C22×C8×C31C2312yes—
58C31×C4⋊Q8—24no—
59C31×C4⋊Q8—24no—
60C31×#125—28no—
61C31×C22⋊Q8—28no—
62C31×C22⋊Q8—24no—
63C31×C22⋊Q8—24no—
64C31×#121—22no—
65C31×#121—22no—
66C4×Q8×C31—28no—
67C4×Q8×C31—24no—
68C4×Q8×C31D418yescomplemented
69C4×D4×C31—24no—
70C4×D4×C31—44no—
71C31×#117—28no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31C2311yescharacteristic
79C2×C4⋊C4×C31C2311yescharacteristic
80C2×C4⋊C4×C31C2312yes—
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—21no—
84C2×C22⋊C4×C31—21no—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C42×C31—22no—
89C2×C42×C31—24no—
90C2×C42×C31—21no—
91C2×C42×C31D411yescharacteristic
92C2×C42×C31D411yescharacteristic
93C2×C42×C31C2311yescharacteristic
94C2×C42×C31C2311yescharacteristic
95C31×#106—24no—
96C31×#103—24no—
97C31×#103—24no—
98C31×#103—24no—
99C31×#102—24no—
100C31×C22⋊C8—24no—
101C4×C8×C31—24no—
102C31×#95—21no—
103C31×#95—21no—
104C31×#95—21no—
105C24×C31—21no—
106C24×C31C2×D411yescharacteristic
107C2×Q8×C31—24no—
108C2×Q8×C31—22no—
109C2×Q8×C31—22no—
110C2×Q8×C31—22no—
111C2×Q8×C31—22no—
112C2×Q8×C31—22no—
113C2×Q8×C31—42no—
114C2×Q8×C31—42no—
115C2×Q8×C31C2×D414yes—
116C2×D4×C31—24no—
117C2×D4×C31—22no—
118C2×D4×C31—22no—
119C2×D4×C31—21no—
120C2×D4×C31—42no—
121C2×D4×C31—42no—
122C2×D4×C31#4112yes—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—21no—
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—21no—
133C22×C4×C31—21no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—41no—
137C22×C4×C31—42no—
138C22×C4×C31—42no—
139C22×C4×C31—42no—
140C22×C4×C31SD1614yescomplemented
141C22×C4×C31C2×D411yescharacteristic
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D411yescharacteristic
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2411yescharacteristic
147SD16×C31—216no—
148C2×C8×C31—22no—
149C2×C8×C31—22no—
150C2×C8×C31—22no—
151C2×C8×C31—22no—
152C2×C8×C31—22no—
153C2×C8×C31#4114yes—
154C4⋊C4×C31—24no—
155C4⋊C4×C31—24no—
156C4⋊C4×C31—28no—
157C4⋊C4×C31—24no—
158C4⋊C4×C31—28no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—42no—
164C4⋊C4×C31C2×D414yes—
165C4⋊C4×C31#4112yes—
166C22⋊C4×C31—28no—
167C22⋊C4×C31—24no—
168C22⋊C4×C31—42no—
169C22⋊C4×C31—42no—
170C22⋊C4×C31—42no—
171C22⋊C4×C31—42no—
172C42×C31—22no—
173C42×C31—22no—
174C42×C31—28no—
175C42×C31—22no—
176C42×C31—42no—
177C42×C31C2×D414yes—
178#23568C3111yesmaximal, characteristic, direct product factor, Sylow
179C23×C31—21no—
180C23×C31—21no—
181C23×C31—21no—
182C23×C31—21no—
183C23×C31—21no—
184C23×C31—21no—
185C23×C31—22no—
186C23×C31—41no—
187C23×C31—41no—
188C23×C31—41no—
189C23×C31—41no—
190C23×C31—41no—
191C23×C31—41no—
192C23×C31C2×SD1612yes—
193C23×C31C22×D411yescharacteristic
194Q8×C31—24no—
195Q8×C31—24no—
196Q8×C31—48no—
197Q8×C31—42no—
198Q8×C31—42no—
199D4×C31—24no—
200D4×C31—48no—
201D4×C31—42no—
202C2×C4×C31—21no—
203C2×C4×C31—21no—
204C2×C4×C31—21no—
205C2×C4×C31—21no—
206C2×C4×C31—21no—
207C2×C4×C31—21no—
208C2×C4×C31—28no—
209C2×C4×C31—21no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—21no—
213C2×C4×C31—22no—
214C2×C4×C31—21no—
215C2×C4×C31—44no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—41no—
219C2×C4×C31—42no—
220C2×C4×C31—41no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—41no—
225C2×C4×C31—41no—
226C2×C4×C31—41no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—41no—
230C2×C4×C31—84no—
231C2×C4×C31#12012yes—
232C2×C4×C31#12012yes—
233C2×C4×C31C2×SD1612yes—
234C2×C4×C31C2×SD1612yes—
235C2×C4×C31#13512yes—
236C2×C4×C31#13712yes—
237C2×C4×C31C22×D412yes—
238C2×C4×C31C2×#4111yescharacteristic
239C2×C4×C31C2×#4112yes—
240C2×C4×C31C2×#4111yescharacteristic
241C8×C31—24no—
242C8×C31—42no—
243C2×#533C2×C3111yescharacteristic, complemented
244C2×C4×SD16C2×C3112yescomplemented
245C4×#121C2×C3111yescharacteristic
246#2058C2×C3111yescharacteristic, complemented
247#2043C2×C3111yescharacteristic, complemented
248#2035C2×C3112yescomplemented
249#2023C2×C3111yescharacteristic, complemented
250#2013C2×C3111yescharacteristic, complemented
251#2000C2×C3112yes—
252C4×#103C2×C3112yescomplemented
253C4×C22⋊C8C2×C3111yescharacteristic, complemented
254C22×C31—22no—
255C22×C31—22no—
256C22×C31—22no—
257C22×C31—41no—
258C22×C31—41no—
259C22×C31—41no—
260C22×C31—41no—
261C22×C31—42no—
262C22×C31—42no—
263C22×C31—42no—
264C22×C31—81no—
265C22×C31—81no—
266C22×C31—81no—
267C22×C31—81no—
268C22×C31C2×#12011yescharacteristic
269C22×C31#52511yescharacteristic
270C22×C31#53211yescharacteristic
271C22×C31C22×SD1611yescharacteristic
272C22×C31C2×#13511yescharacteristic
273C22×C31C2×#13711yescharacteristic
274C22×C31#57511yescharacteristic
275C4×C31—22no—
276C4×C31—22no—
277C4×C31—22no—
278C4×C31—42no—
279C4×C31—41no—
280C4×C31—44no—
281C4×C31—44no—
282C4×C31—81no—
283C4×C31—81no—
284C4×C31#44814yes—
285C4×C31#52512yes—
286C4×C31#53212yes—
287C22×SD16C22×C3112yes—
288#533—28no—
289C2×C4⋊Q8C22×C3111yescharacteristic
290C2×C4⋊Q8C22×C3111yescharacteristic
291C2×#125—21no—
292C2×C22⋊Q8—21no—
293C2×C22⋊Q8C22×C3112yes—
294C2×#121C22×C3111yescharacteristic
295C2×C4×Q8—21no—
296C2×C4×Q8C22×C3112yes—
297C2×C4×D4—21no—
298C2×C4×D4C22×C3111yescharacteristic
299C2×#117—21no—
300C22×C42C22×C3111yescharacteristic
301C4×SD16—28no—
302C2×#106C22×C3112yes—
303C2×#103C22×C3112yes—
304C2×#103C22×C3112yes—
305C2×#103C22×C3112yes—
306C2×#102C22×C3112yes—
307C2×C22⋊C8C22×C3112yes—
308C2×C4×C8C22×C3112yes—
309#390C22×C3111yescharacteristic
310#389C22×C3111yescharacteristic
311#388—21no—
312#386—21no—
313#380C22×C3111yescharacteristic
314C4×C4⋊C4C22×C3111yescharacteristic
315C4×C22⋊C4—21no—
316#340C22×C3112yes—
317#340C22×C3112yes—
318#336C22×C3111yescharacteristic
319#336C22×C3111yescharacteristic
320C2×C31—42no—
321C2×C31—82no—
322C2×C31#238811yescharacteristic
323C2×C31C2×#44811yescharacteristic
324C2×C31#300211yescharacteristic
325C2×C31#310111yescharacteristic
326C2×C31#310711yescharacteristic
327C2×C31#316711yescharacteristic
328C2×C31#317211yescharacteristic
329C22×Q8—21no—
330C22×Q8C23×C3112yes—
331C22×D4—21no—
332C22×D4C23×C3111yescharacteristic
333C23×C4—21no—
334C23×C4D4×C3111yescharacteristic
335C23×C4D4×C3111yescharacteristic
336C23×C4C23×C3111yescharacteristic
337C2×SD16—24no—
338C2×SD16—24no—
339C2×SD16—24no—
340C22×C8C23×C3112yes—
341C22×C8C23×C3112yes—
342C4⋊Q8—24no—
343C4⋊Q8—24no—
344#125—28no—
345C22⋊Q8—28no—
346C22⋊Q8—24no—
347C22⋊Q8—24no—
348#121—22no—
349#121—22no—
350C4×Q8—28no—
351C4×Q8—24no—
352C4×Q8D4×C3118yescomplemented
353C4×D4—24no—
354C4×D4—44no—
355#117—28no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4C23×C3111yescharacteristic
363C2×C4⋊C4C23×C3111yescharacteristic
364C2×C4⋊C4C23×C3112yes—
365C2×C4⋊C4C23×C3111yescharacteristic
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—21no—
375C2×C42D4×C3111yescharacteristic
376C2×C42D4×C3111yescharacteristic
377C2×C42C23×C3111yescharacteristic
378C2×C42C23×C3111yescharacteristic
379#106—24no—
380#103—24no—
381#103—24no—
382#103—24no—
383#102—24no—
384C22⋊C8—24no—
385C4×C8—24no—
386#95—21no—
387#95—21no—
388#95—21no—
389C31#2356811yescharacteristic, direct product factor, Sylow
390C24—21no—
391C24C2×D4×C3111yescharacteristic
392C2×Q8—24no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—42no—
399C2×Q8—42no—
400C2×Q8C2×D4×C3114yes—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4#41×C3112yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—41no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4SD16×C3114yescomplemented
426C22×C4C2×D4×C3111yescharacteristic
427C22×C4C2×D4×C3111yescharacteristic
428C22×C4C2×D4×C3111yescharacteristic
429C22×C4C2×D4×C3111yescharacteristic
430C22×C4C2×D4×C3111yescharacteristic
431C22×C4C24×C3111yescharacteristic
432SD16—216no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8#41×C3114yes—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—28no—
442C4⋊C4—24no—
443C4⋊C4—28no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—42no—
449C4⋊C4C2×D4×C3114yes—
450C4⋊C4#41×C3112yes—
451C22⋊C4—28no—
452C22⋊C4—24no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C42—22no—
458C42—22no—
459C42—28no—
460C42—22no—
461C42—42no—
462C42C2×D4×C3114yes—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—22no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23C2×SD16×C3112yes—
477C23C22×D4×C3111yescharacteristic
478Q8—24no—
479Q8—24no—
480Q8—48no—
481Q8—42no—
482Q8—42no—
483D4—24no—
484D4—48no—
485D4—42no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—28no—
493C2×C4—21no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—84no—
515C2×C4C31×#12012yes—
516C2×C4C31×#12012yes—
517C2×C4C2×SD16×C3112yes—
518C2×C4C2×SD16×C3112yes—
519C2×C4C31×#13512yes—
520C2×C4C31×#13712yes—
521C2×C4C22×D4×C3112yes—
522C2×C4C2×#41×C3111yescharacteristic
523C2×C4C2×#41×C3112yes—
524C2×C4C2×#41×C3111yescharacteristic
525C8—24no—
526C8—42no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22C2×C31×#12011yescharacteristic
542C22C31×#52511yescharacteristic
543C22C31×#53211yescharacteristic
544C22C22×SD16×C3111yescharacteristic
545C22C2×C31×#13511yescharacteristic
546C22C2×C31×#13711yescharacteristic
547C22C31×#57511yescharacteristic
548C4—22no—
549C4—22no—
550C4—22no—
551C4—42no—
552C4—41no—
553C4—44no—
554C4—44no—
555C4—81no—
556C4—81no—
557C4C31×#44814yes—
558C4C31×#52512yes—
559C4C31×#53212yes—
560C2—42no—
561C2—82no—
562C2C31×#238811yescharacteristic
563C2C2×C31×#44811yescharacteristic
564C2C31×#300211yescharacteristic
565C2C31×#310111yescharacteristic
566C2C31×#310711yescharacteristic
567C2C31×#316711yescharacteristic
568C2C31×#317211yescharacteristic
subgroupG/H
centerC22×C4×C31C2×D4
commutator, Frattini, cosocleC22×C4C24×C31
socleC23×C31C22×D4
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#533C2semidirect
2. C2×C4×SD16×C31C2semidirect
4. C31×#2058C2semidirect
5. C31×#2043C2semidirect
6. C31×#2035C2semidirect
7. C31×#2023C2semidirect
8. C31×#2013C2semidirect
10. C4×C31×#103C2semidirect
11. C4×C31×C22⋊C8C2semidirect
68. C4×Q8×C31D4semidirect
140. C22×C4×C31SD16semidirect
178. #23568C31direct (N × H)
243. C2×#533C2×C31semidirect
244. C2×C4×SD16C2×C31semidirect
246. #2058C2×C31semidirect
247. #2043C2×C31semidirect
248. #2035C2×C31semidirect
249. #2023C2×C31semidirect
250. #2013C2×C31semidirect
252. C4×#103C2×C31semidirect
253. C4×C22⋊C8C2×C31semidirect
352. C4×Q8D4×C31semidirect
389. C31#23568direct (N × H)
425. C22×C4SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5332
C2×C4×SD16×C312
C4×C31×#1212
C31×#20582
C31×#20432
C31×#20352
C31×#20232
C31×#20132
C31×#20002
C4×C31×#1032
C4×C31×C22⋊C82
#2356831