Finite Group Databasebeta

← C31×#9918 #21466677

Subgroups — C31×#9918 #21466677

Order 7936.

812 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#480C211yesmaximal, characteristic, complemented
2C31×#2617C211yesmaximal, characteristic
3C2×C31×#397C211yesmaximal, characteristic, complemented
4C31×#1823C211yesmaximal, characteristic, complemented
5C2×C31×#327C211yesmaximal, characteristic, complemented
6C2×C31×#323C211yesmaximal, characteristic, complemented
7C31×#1294C211yesmaximal, characteristic, complemented
8C2×C31×#121C2211yescharacteristic
9C2×C31×#120—21no—
10C22×C4⋊C4×C31C2211yescharacteristic
11C22×C22⋊C4×C31—21no—
12C22×C22⋊C4×C31C2211yescharacteristic
13C31×#480—22no—
14C31×#480—22no—
15C2×C31×#107—21no—
16C2×C31×#102—21no—
17C2×C31×C22⋊C8C2211yescharacteristic
18C2×C31×C22⋊C8C2211yescharacteristic
19C31×#397—21no—
20C31×#397—22no—
21C31×#397—22no—
22C31×#394—22no—
23C31×#392—21no—
24C31×#386—21no—
25C31×#380C2211yescharacteristic
26C2×C31×#95—21no—
27C2×C31×#95C2211yescharacteristic
28C31×#340—22no—
29C31×#327—22no—
30C31×#323—22no—
31C25×C31D411yescharacteristic
32C22×D4×C31—21no—
33C22×D4×C31—22no—
34C22×D4×C31D411yescharacteristic
35C23×C4×C31—21no—
36C23×C4×C31—21no—
37C23×C4×C31D411yescharacteristic
38C23×C4×C31C2311yescharacteristic
39C22×C8×C31—21no—
40C22×C8×C31—21no—
41C31×#121—21no—
42C31×#121—21no—
43C31×#121—21no—
44C31×#121—21no—
45C31×#120—42no—
46C31×#120—42no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31D411yescharacteristic
53C2×C4⋊C4×C31D412yes—
54C2×C4⋊C4×C31D412yescomplemented
55C2×C22⋊C4×C31—24no—
56C2×C22⋊C4×C31—22no—
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31—21no—
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31—21no—
64C2×C22⋊C4×C31—21no—
65C2×C22⋊C4×C31—22no—
66C2×C22⋊C4×C31—42no—
67C2×C22⋊C4×C31—42no—
68C31×#107—24no—
69C31×#102—24no—
70C31×C22⋊C8—21no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8—21no—
73C31×C22⋊C8D412yescomplemented
74C31×#95—24no—
75C31×#95—22no—
76C31×#95—21no—
77C31×#95—21no—
78C31×#95D412yescomplemented
79C24×C31—21no—
80C24×C31—21no—
81C24×C31—21no—
82C24×C31—21no—
83C24×C31—21no—
84C24×C31—21no—
85C24×C31—21no—
86C24×C31—42no—
87C24×C31—42no—
88C24×C31D812yes—
89C24×C31C2×D411yescharacteristic
90C2×D4×C31—21no—
91C2×D4×C31—21no—
92C2×D4×C31—42no—
93C2×D4×C31—44no—
94C2×D4×C31—41no—
95C2×D4×C31—41no—
96C2×D4×C31—41no—
97C2×D4×C31—41no—
98C2×D4×C31—41no—
99C2×D4×C31—41no—
100C2×D4×C31—82no—
101C2×D4×C31—82no—
102C22×C4×C31—21no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—21no—
106C22×C4×C31—21no—
107C22×C4×C31—22no—
108C22×C4×C31—21no—
109C22×C4×C31—42no—
110C22×C4×C31—42no—
111C22×C4×C31—42no—
112C22×C4×C31—42no—
113C22×C4×C31—41no—
114C22×C4×C31—41no—
115C22×C4×C31—41no—
116C22×C4×C31—41no—
117C22×C4×C31—41no—
118C22×C4×C31—41no—
119C22×C4×C31—41no—
120C22×C4×C31—41no—
121C22×C4×C31C2×D411yescharacteristic
122C22×C4×C31C2×D411yescharacteristic
123C22×C4×C31C2×D411yescharacteristic
124C22×C4×C31C2×D411yescharacteristic
125C22×C4×C31C2×D411yescharacteristic
126C22×C4×C31#4111yescharacteristic
127C2×C8×C31—22no—
128C2×C8×C31—42no—
129C2×C8×C31—42no—
130C2×C8×C31—41no—
131C4⋊C4×C31—22no—
132C4⋊C4×C31—21no—
133C4⋊C4×C31—22no—
134C4⋊C4×C31—21no—
135C4⋊C4×C31—42no—
136C4⋊C4×C31—41no—
137C4⋊C4×C31—41no—
138C22⋊C4×C31—48no—
139C22⋊C4×C31—44no—
140C22⋊C4×C31—41no—
141C22⋊C4×C31—41no—
142C22⋊C4×C31—41no—
143C22⋊C4×C31—41no—
144C22⋊C4×C31—41no—
145C22⋊C4×C31—41no—
146C22⋊C4×C31—41no—
147C22⋊C4×C31—41no—
148C22⋊C4×C31—82no—
149#9918C3111yesmaximal, characteristic, direct product factor, Sylow
150C23×C31—22no—
151C23×C31—22no—
152C23×C31—22no—
153C23×C31—22no—
154C23×C31—22no—
155C23×C31—44no—
156C23×C31—44no—
157C23×C31—42no—
158C23×C31—42no—
159C23×C31—41no—
160C23×C31—41no—
161C23×C31—41no—
162C23×C31—42no—
163C23×C31—42no—
164C23×C31—41no—
165C23×C31—41no—
166C23×C31—41no—
167C23×C31—41no—
168C23×C31—42no—
169C23×C31—42no—
170C23×C31—82no—
171C23×C31—82no—
172C23×C31—81no—
173C23×C31—81no—
174C23×C31#12011yescharacteristic
175C23×C31#12011yescharacteristic
176C23×C31#12111yescharacteristic
177C23×C31C2×D811yescharacteristic
178C23×C31#13511yescharacteristic
179C23×C31AGL(1,ℤ/8)11yescharacteristic
180C23×C31AGL(1,ℤ/8)11yescharacteristic
181D4×C31—42no—
182D4×C31—81no—
183D4×C31—88no—
184D4×C31—81no—
185D4×C31—81no—
186D4×C31—81no—
187D4×C31—81no—
188C2×C4×C31—22no—
189C2×C4×C31—22no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—41no—
193C2×C4×C31—41no—
194C2×C4×C31—42no—
195C2×C4×C31—42no—
196C2×C4×C31—42no—
197C2×C4×C31—41no—
198C2×C4×C31—41no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—42no—
203C2×C4×C31—41no—
204C2×C4×C31—42no—
205C2×C4×C31—41no—
206C2×C4×C31—42no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—82no—
210C2×C4×C31—82no—
211C2×C4×C31—81no—
212C2×C4×C31—81no—
213C2×C4×C31—81no—
214C2×C4×C31—81no—
215C2×C4×C31—81no—
216C2×C4×C31#12011yescharacteristic
217C2×C4×C31#12111yescharacteristic
218C2×C4×C31#12111yescharacteristic
219C2×C4×C31#12711yescharacteristic
220C8×C31—42no—
221C8×C31—81no—
222C2×#480C2×C3111yescharacteristic, complemented
223#2617C2×C3111yescharacteristic
224C2×#397C2×C3111yescharacteristic, complemented
225#1823C2×C3111yescharacteristic, complemented
226C2×#327C2×C3111yescharacteristic, complemented
227C2×#323C2×C3111yescharacteristic, complemented
228#1294C2×C3111yescharacteristic, complemented
229C22×C31—22no—
230C22×C31—22no—
231C22×C31—22no—
232C22×C31—22no—
233C22×C31—21no—
234C22×C31—21no—
235C22×C31—21no—
236C22×C31—21no—
237C22×C31—44no—
238C22×C31—44no—
239C22×C31—42no—
240C22×C31—82no—
241C22×C31—82no—
242C22×C31—82no—
243C22×C31—82no—
244C22×C31—81no—
245C22×C31—81no—
246C22×C31—82no—
247C22×C31—82no—
248C22×C31—81no—
249C22×C31—81no—
250C22×C31—81no—
251C22×C31#39211yescharacteristic
252C22×C31#44711yescharacteristic
253C22×C31#44711yescharacteristic
254C22×C31#44911yescharacteristic
255C22×C31#44911yescharacteristic
256C22×C31#45512yes—
257C22×C31#45812yes—
258C22×C31#46611yescharacteristic
259C22×C31#46911yescharacteristic
260C4×C31—21no—
261C4×C31—21no—
262C4×C31—21no—
263C4×C31—21no—
264C4×C31—82no—
265C4×C31—82no—
266C4×C31—82no—
267C4×C31—81no—
268C4×C31—81no—
269C2×#121C22×C3111yescharacteristic
270C2×#120—21no—
271C22×C4⋊C4C22×C3111yescharacteristic
272C22×C22⋊C4—21no—
273C22×C22⋊C4C22×C3111yescharacteristic
274#480—22no—
275#480—22no—
276C2×#107—21no—
277C2×#102—21no—
278C2×C22⋊C8C22×C3111yescharacteristic
279C2×C22⋊C8C22×C3111yescharacteristic
280#397—21no—
281#397—22no—
282#397—22no—
283#394—22no—
284#392—21no—
285#386—21no—
286#380C22×C3111yescharacteristic
287C2×#95—21no—
288C2×#95C22×C3111yescharacteristic
289#340—22no—
290#327—22no—
291#323—22no—
292C2×C31—21no—
293C2×C31—21no—
294C2×C31—21no—
295C2×C31—21no—
296C2×C31—82no—
297C2×C31—161no—
298C2×C31#160712yes—
299C2×C31#161212yes—
300C2×C31#199911yescharacteristic
301C2×C31#200411yescharacteristic
302C2×C31#202211yescharacteristic
303C25D4×C3111yescharacteristic
304C22×D4—21no—
305C22×D4—22no—
306C22×D4D4×C3111yescharacteristic
307C23×C4—21no—
308C23×C4—21no—
309C23×C4D4×C3111yescharacteristic
310C23×C4C23×C3111yescharacteristic
311C22×C8—21no—
312C22×C8—21no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121—21no—
317#120—42no—
318#120—42no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4D4×C3111yescharacteristic
325C2×C4⋊C4D4×C3112yes—
326C2×C4⋊C4D4×C3112yescomplemented
327C2×C22⋊C4—24no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340#107—24no—
341#102—24no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8D4×C3112yescomplemented
346#95—24no—
347#95—22no—
348#95—21no—
349#95—21no—
350#95D4×C3112yescomplemented
351C31#991811yescharacteristic, direct product factor, Sylow
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—21no—
359C24—42no—
360C24—42no—
361C24D8×C3112yes—
362C24C2×D4×C3111yescharacteristic
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—42no—
366C2×D4—44no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—82no—
374C2×D4—82no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4C2×D4×C3111yescharacteristic
395C22×C4C2×D4×C3111yescharacteristic
396C22×C4C2×D4×C3111yescharacteristic
397C22×C4C2×D4×C3111yescharacteristic
398C22×C4C2×D4×C3111yescharacteristic
399C22×C4#41×C3111yescharacteristic
400C2×C8—22no—
401C2×C8—42no—
402C2×C8—42no—
403C2×C8—41no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—42no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C22⋊C4—48no—
412C22⋊C4—44no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—82no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—44no—
428C23—44no—
429C23—42no—
430C23—42no—
431C23—41no—
432C23—41no—
433C23—42no—
434C23—42no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—42no—
440C23—42no—
441C23—41no—
442C23—82no—
443C23—82no—
444C23—81no—
445C23—81no—
446C23C31×#12011yescharacteristic
447C23C31×#12011yescharacteristic
448C23C31×#12111yescharacteristic
449C23C2×D8×C3111yescharacteristic
450C23C31×#13511yescharacteristic
451C23C31×AGL(1,ℤ/8)11yescharacteristic
452C23C31×AGL(1,ℤ/8)11yescharacteristic
453D4—42no—
454D4—81no—
455D4—88no—
456D4—81no—
457D4—81no—
458D4—81no—
459D4—81no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4C31×#12011yescharacteristic
489C2×C4C31×#12111yescharacteristic
490C2×C4C31×#12111yescharacteristic
491C2×C4C31×#12711yescharacteristic
492C8—42no—
493C8—81no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—44no—
503C22—44no—
504C22—42no—
505C22—82no—
506C22—82no—
507C22—82no—
508C22—82no—
509C22—81no—
510C22—81no—
511C22—82no—
512C22—82no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22C31×#39211yescharacteristic
517C22C31×#44711yescharacteristic
518C22C31×#44711yescharacteristic
519C22C31×#44911yescharacteristic
520C22C31×#44911yescharacteristic
521C22C31×#45512yes—
522C22C31×#45812yes—
523C22C31×#46611yescharacteristic
524C22C31×#46911yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—82no—
530C4—82no—
531C4—82no—
532C4—81no—
533C4—81no—
534C2—21no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—82no—
539C2—161no—
540C2C31×#160712yes—
541C2C31×#161212yes—
542C2C31×#199911yescharacteristic
543C2C31×#200411yescharacteristic
544C2C31×#202211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC31×#2617C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#480C2semidirect
3. C2×C31×#397C2semidirect
4. C31×#1823C2semidirect
5. C2×C31×#327C2semidirect
6. C2×C31×#323C2semidirect
7. C31×#1294C2semidirect
54. C2×C4⋊C4×C31D4semidirect
73. C31×C22⋊C8D4semidirect
78. C31×#95D4semidirect
149. #9918C31direct (N × H)
222. C2×#480C2×C31semidirect
224. C2×#397C2×C31semidirect
225. #1823C2×C31semidirect
226. C2×#327C2×C31semidirect
227. C2×#323C2×C31semidirect
228. #1294C2×C31semidirect
326. C2×C4⋊C4D4×C31semidirect
345. C22⋊C8D4×C31semidirect
350. #95D4×C31semidirect
351. C31#9918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4802
C31×#26172
C2×C31×#3972
C31×#18232
C2×C31×#3272
C2×C31×#3232
C31×#12942
#991831