Finite Group Databasebeta

← C31×#18443 #21475202

Subgroups — C31×#18443 #21475202

Order 7936.

832 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3563C211yesmaximal, characteristic
2C31×#3239C211yesmaximal, characteristic
3C31×#3230C211yesmaximal, characteristic, complemented
4C31×#2642C211yesmaximal, characteristic, complemented
5C31×#1617C214yesmaximal, complemented
6C31×#1615C214yesmaximal
7C31×#1506C211yesmaximal, characteristic, complemented
8C31×#1500C211yesmaximal, characteristic
9C31×#1470C211yesmaximal, characteristic, complemented
10C31×#564—21no—
11C31×#563—21no—
12C31×#557—21no—
13C31×#554—21no—
14C31×#552—21no—
15C31×#552—22no—
16C31×#552—21no—
17C31×#544—21no—
18C31×#544C2212yes—
19C31×#541—21no—
20C31×#541—22no—
21C31×#539C2212yes—
22C31×#533C2211yescharacteristic
23C2×C31×C4⋊Q8C2211yescharacteristic
24C31×#529C2211yescharacteristic
25C2×C31×#125C2211yescharacteristic
26C31×#501—21no—
27C31×#500—21no—
28C31×#489—21no—
29C31×#487—21no—
30C31×#484C2214yes—
31C31×#484C2212yes—
32C31×#481C2212yes—
33C31×#477—22no—
34C31×#475—21no—
35C31×#474—21no—
36C31×#432C2211yescharacteristic
37C31×#431C2211yescharacteristic
38C31×#400—22no—
39C31×#400C2214yes—
40C31×#391—21no—
41C31×#391—21no—
42C31×#376C2211yescharacteristic
43C31×#328C2214yes—
44C31×#328C2212yes—
45C31×#327C2212yes—
46C31×#324C2214yes—
47C22×Q8×C31—21no—
48C31×C4⋊Q8—21no—
49C31×C4⋊Q8—22no—
50C31×C4⋊Q8—22no—
51C31×C4⋊Q8—21no—
52C31×C4⋊Q8—21no—
53C31×C4⋊Q8—21no—
54C31×C4⋊Q8—21no—
55C31×C4⋊Q8D411yescharacteristic
56C31×C4⋊Q8D411yescharacteristic
57C31×#126—22no—
58C31×#126—22no—
59C31×#126—22no—
60C31×#126—22no—
61C31×#126—21no—
62C31×#125—22no—
63C31×#125—22no—
64C31×#125—22no—
65C31×#125—22no—
66C31×#125—21no—
67C31×#125—22no—
68C31×#125—22no—
69C31×#125—22no—
70C31×#125—22no—
71C31×#125—21no—
72C31×#125—21no—
73C31×#125—21no—
74C31×#125—21no—
75C31×#125—21no—
76C31×#125D411yescharacteristic
77C31×#124D411yescharacteristic
78C31×#123—22no—
79C31×#123—21no—
80C31×#123—22no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8—21no—
83C31×C22⋊Q8—22no—
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8—22no—
86C31×C22⋊Q8—21no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8C2311yescharacteristic
89C31×C22⋊Q8C2312yes—
90C31×#121C2311yescharacteristic
91C4×Q8×C31—21no—
92C4×Q8×C31—22no—
93C4×Q8×C31—21no—
94C4×Q8×C31—21no—
95C4×Q8×C31D411yescharacteristic
96C4×Q8×C31D412yes—
97C4×D4×C31—21no—
98C4×D4×C31—22no—
99C4×D4×C31D411yescharacteristic
100C31×#117—22no—
101C31×#117—21no—
102C31×#117—21no—
103C31×#117—22no—
104C31×#117—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31D412yes—
108C2×C4⋊C4×C31D411yescharacteristic
109C2×C4⋊C4×C31D411yescharacteristic
110C2×C4⋊C4×C31C2312yes—
111C2×C4⋊C4×C31C2312yes—
112C2×C42×C31—21no—
113C2×C42×C31C2311yescharacteristic
114C31×#107—22no—
115C31×#107—24no—
116C31×#106—22no—
117C31×C4⋊C8—21no—
118C31×C4⋊C8—21no—
119C31×#103—22no—
120C31×#103—24no—
121C31×#102—22no—
122C31×C22⋊C8C2312yes—
123C31×C22⋊C8C2312yes—
124C31×#97—21no—
125C4×C8×C31—21no—
126C31×#95—21no—
127C31×#95—24no—
128C31×#95—24no—
129C31×#95C2312yes—
130C2×Q8×C31—22no—
131C2×Q8×C31—21no—
132C2×Q8×C31—44no—
133C2×Q8×C31—41no—
134C2×Q8×C31—41no—
135C2×Q8×C31C2×D412yes—
136C2×Q8×C31C2×D411yescharacteristic
137C2×D4×C31—21no—
138C2×D4×C31C2×D411yescharacteristic
139C22×C4×C31—22no—
140C22×C4×C31—21no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D411yescharacteristic
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2411yescharacteristic
148C2×C8×C31—22no—
149C2×C8×C31—22no—
150C4⋊C4×C31—22no—
151C4⋊C4×C31—22no—
152C4⋊C4×C31—22no—
153C4⋊C4×C31—22no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—21no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31—21no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—21no—
168C4⋊C4×C31—21no—
169C4⋊C4×C31—21no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31—22no—
172C4⋊C4×C31—22no—
173C4⋊C4×C31—21no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—22no—
176C4⋊C4×C31—22no—
177C4⋊C4×C31—41no—
178C4⋊C4×C31—41no—
179C4⋊C4×C31C2×D411yescharacteristic
180C4⋊C4×C31C2×D411yescharacteristic
181C4⋊C4×C31C2×D412yes—
182C22⋊C4×C31—22no—
183C22⋊C4×C31—22no—
184C22⋊C4×C31—22no—
185C22⋊C4×C31—22no—
186C22⋊C4×C31—21no—
187C22⋊C4×C31—21no—
188C22⋊C4×C31—21no—
189C22⋊C4×C31—21no—
190C22⋊C4×C31—21no—
191C42×C31—22no—
192C42×C31—22no—
193C42×C31—22no—
194C42×C31—22no—
195C42×C31—21no—
196C42×C31—42no—
197C42×C31C2×D411yescharacteristic
198C42×C31C2×D411yescharacteristic
199C42×C31C2×D411yescharacteristic
200C42×C31C2×D411yescharacteristic
201#18443C3111yesmaximal, characteristic, direct product factor, Sylow
202C23×C31—21no—
203C23×C31C22×D411yescharacteristic
204Q8×C31—41no—
205Q8×C31—42no—
206Q8×C31—42no—
207Q8×C31—82no—
208Q8×C31—82no—
209Q8×C31—82no—
210D4×C31—41no—
211D4×C31—42no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—21no—
216C2×C4×C31—21no—
217C2×C4×C31—22no—
218C2×C4×C31—21no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—24no—
222C2×C4×C31—41no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—44no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—82no—
231C2×C4×C31#12011yescharacteristic
232C2×C4×C31#12011yescharacteristic
233C2×C4×C31#12011yescharacteristic
234C2×C4×C31#12011yescharacteristic
235C2×C4×C31C22×D411yescharacteristic
236C2×C4×C31C22×D411yescharacteristic
237C8×C31—42no—
238C8×C31—42no—
239#3563C2×C3111yescharacteristic
240#3239C2×C3111yescharacteristic
241#3230C2×C3111yescharacteristic, complemented
242#2642C2×C3111yescharacteristic, complemented
243#1617C2×C3114yescomplemented
244#1615C2×C3114yes—
245#1506C2×C3111yescharacteristic, complemented
246#1500C2×C3111yescharacteristic
247#1470C2×C3111yescharacteristic, complemented
248C22×C31—21no—
249C22×C31—21no—
250C22×C31—41no—
251C22×C31—41no—
252C22×C31—41no—
253C22×C31C2×#12011yescharacteristic
254C22×C31#57812yes—
255C4×C31—21no—
256C4×C31—21no—
257C4×C31—21no—
258C4×C31—21no—
259C4×C31—21no—
260C4×C31—42no—
261C4×C31—41no—
262C4×C31—41no—
263C4×C31—42no—
264C4×C31—42no—
265C4×C31—42no—
266C4×C31—41no—
267C4×C31—82no—
268C4×C31—82no—
269C4×C31#45412yes—
270#564—21no—
271#563—21no—
272#557—21no—
273#554—21no—
274#552—21no—
275#552—21no—
276#552—22no—
277#544—21no—
278#544C22×C3112yes—
279#541—21no—
280#541—22no—
281#539C22×C3112yes—
282#533C22×C3111yescharacteristic
283C2×C4⋊Q8C22×C3111yescharacteristic
284#529C22×C3111yescharacteristic
285C2×#125C22×C3111yescharacteristic
286#501—21no—
287#500—21no—
288#489—21no—
289#487—21no—
290#484C22×C3114yes—
291#484C22×C3112yes—
292#481C22×C3112yes—
293#477—22no—
294#475—21no—
295#474—21no—
296#432C22×C3111yescharacteristic
297#431C22×C3111yescharacteristic
298#400—22no—
299#400C22×C3114yes—
300#391—21no—
301#391—21no—
302#376C22×C3111yescharacteristic
303#328C22×C3114yes—
304#328C22×C3112yes—
305#327C22×C3112yes—
306#324C22×C3114yes—
307C2×C31—22no—
308C2×C31—81no—
309C2×C31#301111yescharacteristic
310C2×C31C2×#45411yescharacteristic
311C2×C31#302811yescharacteristic
312C22×Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8D4×C3111yescharacteristic
321C4⋊Q8D4×C3111yescharacteristic
322#126—22no—
323#126—22no—
324#126—22no—
325#126—22no—
326#126—21no—
327#125—22no—
328#125—22no—
329#125—22no—
330#125—22no—
331#125—21no—
332#125—22no—
333#125—22no—
334#125—22no—
335#125—22no—
336#125—21no—
337#125—21no—
338#125—21no—
339#125—21no—
340#125—21no—
341#125D4×C3111yescharacteristic
342#124D4×C3111yescharacteristic
343#123—22no—
344#123—21no—
345#123—22no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—21no—
352C22⋊Q8—22no—
353C22⋊Q8C23×C3111yescharacteristic
354C22⋊Q8C23×C3112yes—
355#121C23×C3111yescharacteristic
356C4×Q8—21no—
357C4×Q8—22no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8D4×C3111yescharacteristic
361C4×Q8D4×C3112yes—
362C4×D4—21no—
363C4×D4—22no—
364C4×D4D4×C3111yescharacteristic
365#117—22no—
366#117—21no—
367#117—21no—
368#117—22no—
369#117—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4D4×C3111yescharacteristic
373C2×C4⋊C4D4×C3112yes—
374C2×C4⋊C4D4×C3111yescharacteristic
375C2×C4⋊C4C23×C3112yes—
376C2×C4⋊C4C23×C3112yes—
377C2×C42—21no—
378C2×C42C23×C3111yescharacteristic
379#107—22no—
380#107—24no—
381#106—22no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384#103—22no—
385#103—24no—
386#102—22no—
387C22⋊C8C23×C3112yes—
388C22⋊C8C23×C3112yes—
389#97—21no—
390C4×C8—21no—
391#95—21no—
392#95—24no—
393#95—24no—
394#95C23×C3112yes—
395C31#1844311yescharacteristic, direct product factor, Sylow
396C2×Q8—22no—
397C2×Q8—21no—
398C2×Q8—44no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8C2×D4×C3112yes—
402C2×Q8C2×D4×C3111yescharacteristic
403C2×D4—21no—
404C2×D4C2×D4×C3111yescharacteristic
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4C2×D4×C3112yes—
410C22×C4C2×D4×C3111yescharacteristic
411C22×C4C2×D4×C3111yescharacteristic
412C22×C4C2×D4×C3112yes—
413C22×C4C24×C3111yescharacteristic
414C2×C8—22no—
415C2×C8—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4C2×D4×C3111yescharacteristic
446C4⋊C4C2×D4×C3111yescharacteristic
447C4⋊C4C2×D4×C3112yes—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—21no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C42—22no—
458C42—22no—
459C42—22no—
460C42—22no—
461C42—21no—
462C42—42no—
463C42C2×D4×C3111yescharacteristic
464C42C2×D4×C3111yescharacteristic
465C42C2×D4×C3111yescharacteristic
466C42C2×D4×C3111yescharacteristic
467C23—21no—
468C23C22×D4×C3111yescharacteristic
469Q8—41no—
470Q8—42no—
471Q8—42no—
472Q8—82no—
473Q8—82no—
474Q8—82no—
475D4—41no—
476D4—42no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—82no—
496C2×C4C31×#12011yescharacteristic
497C2×C4C31×#12011yescharacteristic
498C2×C4C31×#12011yescharacteristic
499C2×C4C31×#12011yescharacteristic
500C2×C4C22×D4×C3111yescharacteristic
501C2×C4C22×D4×C3111yescharacteristic
502C8—42no—
503C8—42no—
504C22—21no—
505C22—21no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22C2×C31×#12011yescharacteristic
510C22C31×#57812yes—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—41no—
518C4—41no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—41no—
523C4—82no—
524C4—82no—
525C4C31×#45412yes—
526C2—22no—
527C2—81no—
528C2C31×#301111yescharacteristic
529C2C2×C31×#45411yescharacteristic
530C2C31×#302811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#121C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#3230C2semidirect
4. C31×#2642C2semidirect
5. C31×#1617C2semidirect
7. C31×#1506C2semidirect
9. C31×#1470C2semidirect
201. #18443C31direct (N × H)
241. #3230C2×C31semidirect
242. #2642C2×C31semidirect
243. #1617C2×C31semidirect
245. #1506C2×C31semidirect
247. #1470C2×C31semidirect
395. C31#18443direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35632
C31×#32392
C31×#32302
C31×#26422
C31×#16172
C31×#16152
C31×#15062
C31×#15002
C31×#14702
#1844331