Finite Group Databasebeta

← C31×#17368 #21474127

Subgroups — C31×#17368 #21474127

Order 7936.

1210 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#520C211yesmaximal, characteristic
2C31×#2973C212yesmaximal, complemented
3C31×#1467C212yesmaximal, complemented
4C31×#1465C212yesmaximal, complemented
5C31×#1464C212yesmaximal, complemented
6C31×#1463C212yesmaximal, complemented
7C31×#1459C212yesmaximal, complemented
8C2×C31×#324C212yesmaximal, complemented
9C22×#41×C31C411yescharacteristic
10C31×#520—28no—
11C2×C4×Q8×C31C411yescharacteristic
12C2×C4×Q8×C31C2211yescharacteristic
13C2×C4×D4×C31C411yescharacteristic
14C2×C4×D4×C31C411yescharacteristic
15C2×C4×D4×C31C411yescharacteristic
16C2×C4×D4×C31C2211yescharacteristic
17C2×C4×D4×C31C2211yescharacteristic
18C2×C4×D4×C31C2211yescharacteristic
19C2×C31×#117C411yescharacteristic
20C2×C31×#117C411yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C22×C4⋊C4×C31C411yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C31×#435—28no—
26C31×#432C2214yes—
27C31×#407C2214yes—
28C2×C31×C22⋊C8C2214yes—
29C31×#324C2214yes—
30C31×#324C2214yes—
31C31×#324C2214yes—
32C31×#323C2214yes—
33C2×#41×C31—24no—
34C2×#41×C31—24no—
35C2×#41×C31—24no—
36C22×Q8×C31C2×C411yescharacteristic
37C22×D4×C31C2×C411yescharacteristic
38C22×D4×C31C2×C411yescharacteristic
39C22×D4×C31C2×C411yescharacteristic
40C23×C4×C31C2×C411yescharacteristic
41C23×C4×C31C2×C411yescharacteristic
42C23×C4×C31C2×C411yescharacteristic
43C23×C4×C31C2×C411yescharacteristic
44C23×C4×C31C2×C411yescharacteristic
45C23×C4×C31C2×C411yescharacteristic
46C23×C4×C31C2×C411yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C2×M16×C31—24no—
50C22×C8×C31—24no—
51C4×Q8×C31—24no—
52C4×Q8×C31—24no—
53C4×D4×C31—24no—
54C4×D4×C31—24no—
55C4×D4×C31—24no—
56C4×D4×C31—24no—
57C4×D4×C31—24no—
58C4×D4×C31D418yes—
59C31×#117—24no—
60C31×#117—24no—
61C31×#117—24no—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31—24no—
64C2×C4⋊C4×C31—24no—
65C2×C4⋊C4×C31C2×C411yescharacteristic
66C2×C4⋊C4×C31C2×C411yescharacteristic
67C2×C4⋊C4×C31C2×C411yescharacteristic
68C2×C4⋊C4×C31C2×C411yescharacteristic
69C2×C4⋊C4×C31C2×C411yescharacteristic
70C2×C4⋊C4×C31C2×C411yescharacteristic
71C2×C4⋊C4×C31C2×C411yescharacteristic
72C2×C4⋊C4×C31C2311yescharacteristic
73C2×C4⋊C4×C31C2311yescharacteristic
74C2×C4⋊C4×C31C2311yescharacteristic
75C2×C22⋊C4×C31C2×C411yescharacteristic
76C2×C22⋊C4×C31C2×C411yescharacteristic
77C2×C22⋊C4×C31C2×C411yescharacteristic
78C2×C22⋊C4×C31C2×C411yescharacteristic
79C2×C22⋊C4×C31C2×C411yescharacteristic
80C2×C22⋊C4×C31C2311yescharacteristic
81C2×C42×C31C2×C411yescharacteristic
82C2×C42×C31C2×C411yescharacteristic
83C2×C42×C31C2×C411yescharacteristic
84C2×C42×C31C2×C411yescharacteristic
85C2×C42×C31C2×C411yescharacteristic
86C2×C42×C31C2311yescharacteristic
87C31×C4⋊C8—24no—
88C31×C22⋊C8—24no—
89C31×C22⋊C8—24no—
90C31×C22⋊C8C2318yes—
91C31×#97—24no—
92C24×C31C22×C411yescharacteristic
93C24×C31C22×C411yescharacteristic
94C24×C31C22×C411yescharacteristic
95#41×C31—232no—
96C2×Q8×C31—22no—
97C2×Q8×C31—22no—
98C2×Q8×C31—22no—
99C2×D4×C31—22no—
100C2×D4×C31—22no—
101C2×D4×C31—22no—
102C2×D4×C31—22no—
103C2×D4×C31—22no—
104C2×D4×C31—22no—
105C2×D4×C31—22no—
106C2×D4×C31C22⋊C414yes—
107C2×D4×C31M1614yescomplemented
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—81no—
121C22×C4×C31—81no—
122C22×C4×C31—81no—
123C22×C4×C31—81no—
124C22×C4×C31—81no—
125C22×C4×C31—81no—
126C22×C4×C31M1614yescomplemented
127C22×C4×C31C22×C411yescharacteristic
128C22×C4×C31C22×C411yescharacteristic
129C22×C4×C31C22×C411yescharacteristic
130C22×C4×C31C22×C411yescharacteristic
131C22×C4×C31C22×C411yescharacteristic
132C22×C4×C31C22×C411yescharacteristic
133C22×C4×C31C22×C411yescharacteristic
134C22×C4×C31C22×C411yescharacteristic
135C22×C4×C31C22×C411yescharacteristic
136C22×C4×C31C22×C411yescharacteristic
137C22×C4×C31C22×C411yescharacteristic
138C22×C4×C31C2×D414yes—
139C22×C4×C31C2×D414yes—
140C22×C4×C31C2411yescharacteristic
141M16×C31—84no—
142C2×C8×C31—28no—
143C2×C8×C31—84no—
144C4⋊C4×C31—22no—
145C4⋊C4×C31—22no—
146C4⋊C4×C31—22no—
147C4⋊C4×C31—22no—
148C4⋊C4×C31—22no—
149C4⋊C4×C31—22no—
150C4⋊C4×C31—22no—
151C4⋊C4×C31—22no—
152C4⋊C4×C31—22no—
153C4⋊C4×C31C22⋊C414yes—
154C22⋊C4×C31—22no—
155C22⋊C4×C31—22no—
156C22⋊C4×C31—22no—
157C22⋊C4×C31—22no—
158C22⋊C4×C31C22⋊C414yes—
159C22⋊C4×C31C22⋊C414yes—
160C42×C31—22no—
161C42×C31—22no—
162C42×C31—22no—
163C42×C31—22no—
164C42×C31—22no—
165C42×C31C2×D414yes—
166#17368C3111yesmaximal, characteristic, direct product factor, Sylow
167C23×C31—21no—
168C23×C31—21no—
169C23×C31—21no—
170C23×C31—21no—
171C23×C31—41no—
172C23×C31—41no—
173C23×C31—41no—
174C23×C31—41no—
175C23×C31—41no—
176C23×C31—41no—
177C23×C31C2×C22⋊C412yes—
178C23×C31C2×C22⋊C412yes—
179C23×C31C2×M1612yes—
180C23×C31C2×M1612yes—
181C23×C31C2×M1612yes—
182C23×C31C23×C411yescharacteristic
183Q8×C31—28no—
184D4×C31—28no—
185D4×C31—28no—
186D4×C31—28no—
187C2×C4×C31—28no—
188C2×C4×C31—28no—
189C2×C4×C31—21no—
190C2×C4×C31—21no—
191C2×C4×C31—21no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—21no—
195C2×C4×C31—21no—
196C2×C4×C31—21no—
197C2×C4×C31—28no—
198C2×C4×C31—21no—
199C2×C4×C31—21no—
200C2×C4×C31—21no—
201C2×C4×C31—21no—
202C2×C4×C31—44no—
203C2×C4×C31—44no—
204C2×C4×C31—41no—
205C2×C4×C31—41no—
206C2×C4×C31—41no—
207C2×C4×C31—41no—
208C2×C4×C31—41no—
209C2×C4×C31—41no—
210C2×C4×C31—41no—
211C2×C4×C31—41no—
212C2×C4×C31—82no—
213C2×C4×C31—82no—
214C2×C4×C31—82no—
215C2×C4×C31—82no—
216C2×C4×C31C2×C22⋊C412yes—
217C2×C4×C31C2×C22⋊C412yes—
218C2×C4×C31C2×C22⋊C412yes—
219C2×C4×C31C2×C22⋊C412yes—
220C2×C4×C31C2×M1612yes—
221C2×C4×C31C2×M1612yes—
222C2×C4×C31C2×M1612yes—
223C2×C4×C31C22×D412yes—
224C8×C31—48no—
225C2×#520C2×C3111yescharacteristic
226#2973C2×C3112yescomplemented
227#1467C2×C3112yescomplemented
228#1465C2×C3112yescomplemented
229#1464C2×C3112yescomplemented
230#1463C2×C3112yescomplemented
231#1459C2×C3112yescomplemented
232C2×#324C2×C3112yescomplemented
233C22×C31—21no—
234C22×C31—22no—
235C22×C31—21no—
236C22×C31—22no—
237C22×C31—22no—
238C22×C31—22no—
239C22×C31—22no—
240C22×C31—22no—
241C22×C31—42no—
242C22×C31—42no—
243C22×C31—42no—
244C22×C31—42no—
245C22×C31—42no—
246C22×C31—42no—
247C22×C31—41no—
248C22×C31—41no—
249C22×C31#40714yes—
250C22×C31C22×C22⋊C411yescharacteristic
251C22×C31C22×M1611yescharacteristic
252C22×C31C22×M1611yescharacteristic
253C4×C31—22no—
254C4×C31—22no—
255C4×C31—22no—
256C4×C31—22no—
257C4×C31—22no—
258C4×C31—22no—
259C4×C31—22no—
260C4×C31—22no—
261C4×C31—41no—
262C4×C31—41no—
263C4×C31—41no—
264C4×C31—41no—
265C22×#41C4×C3111yescharacteristic
266#520—28no—
267C2×C4×Q8C4×C3111yescharacteristic
268C2×C4×Q8C22×C3111yescharacteristic
269C2×C4×D4C4×C3111yescharacteristic
270C2×C4×D4C4×C3111yescharacteristic
271C2×C4×D4C4×C3111yescharacteristic
272C2×C4×D4C22×C3111yescharacteristic
273C2×C4×D4C22×C3111yescharacteristic
274C2×C4×D4C22×C3111yescharacteristic
275C2×#117C4×C3111yescharacteristic
276C2×#117C4×C3111yescharacteristic
277C2×#117C22×C3111yescharacteristic
278C22×C4⋊C4C4×C3111yescharacteristic
279C22×C4⋊C4C22×C3111yescharacteristic
280C22×C4⋊C4C22×C3111yescharacteristic
281#435—28no—
282#432C22×C3114yes—
283#407C22×C3114yes—
284C2×C22⋊C8C22×C3114yes—
285#324C22×C3114yes—
286#324C22×C3114yes—
287#324C22×C3114yes—
288#323C22×C3114yes—
289C2×C31—21no—
290C2×C31—21no—
291C2×C31—24no—
292C2×C31—42no—
293C2×C31—42no—
294C2×C31C2×#40711yescharacteristic
295C2×C31#288311yescharacteristic
296C2×C31#288911yescharacteristic
297C2×#41—24no—
298C2×#41—24no—
299C2×#41—24no—
300C22×Q8C2×C4×C3111yescharacteristic
301C22×D4C2×C4×C3111yescharacteristic
302C22×D4C2×C4×C3111yescharacteristic
303C22×D4C2×C4×C3111yescharacteristic
304C23×C4C2×C4×C3111yescharacteristic
305C23×C4C2×C4×C3111yescharacteristic
306C23×C4C2×C4×C3111yescharacteristic
307C23×C4C2×C4×C3111yescharacteristic
308C23×C4C2×C4×C3111yescharacteristic
309C23×C4C2×C4×C3111yescharacteristic
310C23×C4C2×C4×C3111yescharacteristic
311C23×C4C23×C3111yescharacteristic
312C23×C4C23×C3111yescharacteristic
313C2×M16—24no—
314C22×C8—24no—
315C4×Q8—24no—
316C4×Q8—24no—
317C4×D4—24no—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—24no—
321C4×D4—24no—
322C4×D4D4×C3118yes—
323#117—24no—
324#117—24no—
325#117—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4C2×C4×C3111yescharacteristic
330C2×C4⋊C4C2×C4×C3111yescharacteristic
331C2×C4⋊C4C2×C4×C3111yescharacteristic
332C2×C4⋊C4C2×C4×C3111yescharacteristic
333C2×C4⋊C4C2×C4×C3111yescharacteristic
334C2×C4⋊C4C2×C4×C3111yescharacteristic
335C2×C4⋊C4C2×C4×C3111yescharacteristic
336C2×C4⋊C4C23×C3111yescharacteristic
337C2×C4⋊C4C23×C3111yescharacteristic
338C2×C4⋊C4C23×C3111yescharacteristic
339C2×C22⋊C4C2×C4×C3111yescharacteristic
340C2×C22⋊C4C2×C4×C3111yescharacteristic
341C2×C22⋊C4C2×C4×C3111yescharacteristic
342C2×C22⋊C4C2×C4×C3111yescharacteristic
343C2×C22⋊C4C2×C4×C3111yescharacteristic
344C2×C22⋊C4C23×C3111yescharacteristic
345C2×C42C2×C4×C3111yescharacteristic
346C2×C42C2×C4×C3111yescharacteristic
347C2×C42C2×C4×C3111yescharacteristic
348C2×C42C2×C4×C3111yescharacteristic
349C2×C42C2×C4×C3111yescharacteristic
350C2×C42C23×C3111yescharacteristic
351C4⋊C8—24no—
352C22⋊C8—24no—
353C22⋊C8—24no—
354C22⋊C8C23×C3118yes—
355#97—24no—
356C31#1736811yescharacteristic, direct product factor, Sylow
357C24C22×C4×C3111yescharacteristic
358C24C22×C4×C3111yescharacteristic
359C24C22×C4×C3111yescharacteristic
360#41—232no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4C22⋊C4×C3114yes—
372C2×D4M16×C3114yescomplemented
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—81no—
386C22×C4—81no—
387C22×C4—81no—
388C22×C4—81no—
389C22×C4—81no—
390C22×C4—81no—
391C22×C4M16×C3114yescomplemented
392C22×C4C22×C4×C3111yescharacteristic
393C22×C4C22×C4×C3111yescharacteristic
394C22×C4C22×C4×C3111yescharacteristic
395C22×C4C22×C4×C3111yescharacteristic
396C22×C4C22×C4×C3111yescharacteristic
397C22×C4C22×C4×C3111yescharacteristic
398C22×C4C22×C4×C3111yescharacteristic
399C22×C4C22×C4×C3111yescharacteristic
400C22×C4C22×C4×C3111yescharacteristic
401C22×C4C22×C4×C3111yescharacteristic
402C22×C4C22×C4×C3111yescharacteristic
403C22×C4C2×D4×C3114yes—
404C22×C4C2×D4×C3114yes—
405C22×C4C24×C3111yescharacteristic
406M16—84no—
407C2×C8—28no—
408C2×C8—84no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4C22⋊C4×C3114yes—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4C22⋊C4×C3114yes—
424C22⋊C4C22⋊C4×C3114yes—
425C42—22no—
426C42—22no—
427C42—22no—
428C42—22no—
429C42—22no—
430C42C2×D4×C3114yes—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23C2×C22⋊C4×C3112yes—
442C23C2×C22⋊C4×C3112yes—
443C23C2×M16×C3112yes—
444C23C2×M16×C3112yes—
445C23C2×M16×C3112yes—
446C23C23×C4×C3111yescharacteristic
447Q8—28no—
448D4—28no—
449D4—28no—
450D4—28no—
451C2×C4—28no—
452C2×C4—28no—
453C2×C4—28no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4C2×C22⋊C4×C3112yes—
481C2×C4C2×C22⋊C4×C3112yes—
482C2×C4C2×C22⋊C4×C3112yes—
483C2×C4C2×C22⋊C4×C3112yes—
484C2×C4C2×M16×C3112yes—
485C2×C4C2×M16×C3112yes—
486C2×C4C2×M16×C3112yes—
487C2×C4C22×D4×C3112yes—
488C8—48no—
489C22—21no—
490C22—22no—
491C22—21no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—41no—
504C22—41no—
505C22C31×#40714yes—
506C22C22×C22⋊C4×C3111yescharacteristic
507C22C22×M16×C3111yescharacteristic
508C22C22×M16×C3111yescharacteristic
509C4—22no—
510C4—22no—
511C4—22no—
512C4—22no—
513C4—22no—
514C4—22no—
515C4—22no—
516C4—22no—
517C4—41no—
518C4—41no—
519C4—41no—
520C4—41no—
521C2—21no—
522C2—21no—
523C2—24no—
524C2—42no—
525C2—42no—
526C2C2×C31×#40711yescharacteristic
527C2C31×#288311yescharacteristic
528C2C31×#288911yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2973C2semidirect
3. C31×#1467C2semidirect
4. C31×#1465C2semidirect
5. C31×#1464C2semidirect
6. C31×#1463C2semidirect
7. C31×#1459C2semidirect
8. C2×C31×#324C2semidirect
107. C2×D4×C31M16semidirect
126. C22×C4×C31M16semidirect
166. #17368C31direct (N × H)
226. #2973C2×C31semidirect
227. #1467C2×C31semidirect
228. #1465C2×C31semidirect
229. #1464C2×C31semidirect
230. #1463C2×C31semidirect
231. #1459C2×C31semidirect
232. C2×#324C2×C31semidirect
356. C31#17368direct (N × H)
372. C2×D4M16×C31semidirect
391. C22×C4M16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5202
C31×#29732
C31×#14672
C31×#14652
C31×#14642
C31×#14632
C31×#14592
C2×C31×#3242
#1736831