Finite Group Databasebeta

← C31×#19029 #21475788

Subgroups — C31×#19029 #21475788

Order 7936.

824 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3563C211yesmaximal, characteristic
2C31×#3238C211yesmaximal, characteristic
3C2×C31×#501C211yesmaximal, characteristic, complemented
4C31×#3139C211yesmaximal, characteristic, complemented
5C31×#1664C214yesmaximal, complemented
6C31×#1663C214yesmaximal, complemented
7C31×#1531C211yesmaximal, characteristic, complemented
8C31×#1528C211yesmaximal, characteristic, complemented
9C31×#1524C211yesmaximal, characteristic
10C31×#564C2212yes—
11C31×#563C2212yes—
12C31×#557—21no—
13C31×#554—21no—
14C31×#552—21no—
15C31×#552—22no—
16C31×#552—21no—
17C31×#544—21no—
18C31×#544—21no—
19C31×#541—21no—
20C31×#541—22no—
21C31×#539—21no—
22C31×#533C2211yescharacteristic
23C2×C31×C4⋊Q8C2211yescharacteristic
24C31×#529C2211yescharacteristic
25C2×C31×#125C2211yescharacteristic
26C31×#501—22no—
27C31×#501C2214yes—
28C31×#501C2212yes—
29C31×#491C2214yes—
30C31×#489C2212yes—
31C31×#487—21no—
32C31×#487—21no—
33C31×#483—21no—
34C31×#480—21no—
35C31×#477—21no—
36C31×#476—21no—
37C31×#432C2211yescharacteristic
38C2×C31×#107—21no—
39C2×C31×#106—21no—
40C31×#419—22no—
41C4×M16×C31C2211yescharacteristic
42C2×C31×#97C2211yescharacteristic
43C31×#330C2212yes—
44C31×#330C2214yes—
45C31×#330C2214yes—
46C31×#329C2212yes—
47C22×Q8×C31—21no—
48C2×M16×C31—21no—
49C22×C8×C31—21no—
50C31×C4⋊Q8—22no—
51C31×C4⋊Q8—21no—
52C31×C4⋊Q8—22no—
53C31×C4⋊Q8—21no—
54C31×C4⋊Q8—21no—
55C31×C4⋊Q8—21no—
56C31×C4⋊Q8D411yescharacteristic
57C31×C4⋊Q8D411yescharacteristic
58C31×C4⋊Q8C2312yes—
59C31×#126—22no—
60C31×#126—22no—
61C31×#126—22no—
62C31×#126—22no—
63C31×#126—21no—
64C31×#125—22no—
65C31×#125—22no—
66C31×#125—21no—
67C31×#125—22no—
68C31×#125—22no—
69C31×#125—22no—
70C31×#125—22no—
71C31×#125—22no—
72C31×#125—22no—
73C31×#125—21no—
74C31×#125—21no—
75C31×#125D412yes—
76C31×#125C2312yes—
77C31×#125C2312yes—
78C31×#125C2311yescharacteristic
79C31×#124C2311yescharacteristic
80C31×#123—22no—
81C31×#123—22no—
82C31×#123—21no—
83C31×C22⋊Q8—22no—
84C31×C22⋊Q8—21no—
85C31×C22⋊Q8—21no—
86C31×C22⋊Q8—22no—
87C31×C22⋊Q8—21no—
88C31×C22⋊Q8—21no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8D411yescharacteristic
92C31×#121D411yescharacteristic
93C4×Q8×C31—21no—
94C4×Q8×C31—22no—
95C4×Q8×C31—21no—
96C4×Q8×C31—21no—
97C4×Q8×C31—21no—
98C4×Q8×C31D411yescharacteristic
99C4×D4×C31—22no—
100C4×D4×C31—21no—
101C4×D4×C31D411yescharacteristic
102C31×#117—22no—
103C31×#117—21no—
104C31×#117—22no—
105C31×#117—21no—
106C31×#117D412yes—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31D411yescharacteristic
113C2×C4⋊C4×C31D411yescharacteristic
114C2×C42×C31C2311yescharacteristic
115C31×#107—24no—
116C31×#107—22no—
117C31×#106—24no—
118C31×#106—22no—
119C31×C4⋊C8—21no—
120C31×#103—22no—
121C31×#103—24no—
122C31×#103—24no—
123C31×#102—22no—
124C31×C22⋊C8—21no—
125C31×#97—21no—
126C31×#97C2312yes—
127C31×#97C2312yes—
128C31×#97C2312yes—
129C4×C8×C31—21no—
130C2×Q8×C31—22no—
131C2×Q8×C31—21no—
132C2×Q8×C31—21no—
133C2×Q8×C31—22no—
134C2×Q8×C31—44no—
135C2×Q8×C31—41no—
136C2×Q8×C31C2×D411yescharacteristic
137C2×D4×C31—21no—
138C2×D4×C31C2×D411yescharacteristic
139C22×C4×C31—21no—
140C22×C4×C31—22no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—41no—
144C22×C4×C31C2×D411yescharacteristic
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×D411yescharacteristic
147M16×C31—42no—
148C2×C8×C31—24no—
149C2×C8×C31—22no—
150C2×C8×C31—22no—
151C2×C8×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—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—21no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—21no—
171C4⋊C4×C31—21no—
172C4⋊C4×C31—22no—
173C4⋊C4×C31—22no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—22no—
176C4⋊C4×C31—41no—
177C4⋊C4×C31—41no—
178C4⋊C4×C31C2×D412yes—
179C4⋊C4×C31C2×D412yes—
180C4⋊C4×C31C2×D412yes—
181C4⋊C4×C31C2×D411yescharacteristic
182C4⋊C4×C31C2×D412yes—
183C4⋊C4×C31C2×D411yescharacteristic
184C22⋊C4×C31—22no—
185C22⋊C4×C31—22no—
186C22⋊C4×C31—22no—
187C22⋊C4×C31—21no—
188C22⋊C4×C31—22no—
189C22⋊C4×C31—21no—
190C22⋊C4×C31—21no—
191C22⋊C4×C31—21no—
192C22⋊C4×C31—21no—
193C42×C31—22no—
194C42×C31—22no—
195C42×C31—22no—
196C42×C31—22no—
197C42×C31—21no—
198C42×C31C2×D411yescharacteristic
199C42×C31C2×D411yescharacteristic
200C42×C31C2×D411yescharacteristic
201C42×C31C2411yescharacteristic
202#19029C3111yesmaximal, characteristic, direct product factor, Sylow
203C23×C31—21no—
204C23×C31#12011yescharacteristic
205Q8×C31—41no—
206Q8×C31—44no—
207Q8×C31—42no—
208Q8×C31—81no—
209Q8×C31—82no—
210Q8×C31—82no—
211D4×C31—41no—
212D4×C31—42no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—21no—
217C2×C4×C31—21no—
218C2×C4×C31—22no—
219C2×C4×C31—21no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—41no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—81no—
227C2×C4×C31—82no—
228C2×C4×C31—82no—
229C2×C4×C31#12011yescharacteristic
230C2×C4×C31#12011yescharacteristic
231C2×C4×C31#12011yescharacteristic
232C2×C4×C31C22×D411yescharacteristic
233C2×C4×C31C22×D411yescharacteristic
234C2×C4×C31C22×D411yescharacteristic
235C8×C31—24no—
236C8×C31—42no—
237C8×C31—42no—
238#3563C2×C3111yescharacteristic
239#3238C2×C3111yescharacteristic
240C2×#501C2×C3111yescharacteristic, complemented
241#3139C2×C3111yescharacteristic, complemented
242#1664C2×C3114yescomplemented
243#1663C2×C3114yescomplemented
244#1531C2×C3111yescharacteristic, complemented
245#1528C2×C3111yescharacteristic, complemented
246#1524C2×C3111yescharacteristic
247C22×C31—21no—
248C22×C31—21no—
249C22×C31—41no—
250C22×C31—41no—
251C22×C31—41no—
252C22×C31#45412yes—
253C22×C31C2×#12011yescharacteristic
254C4×C31—21no—
255C4×C31—21no—
256C4×C31—21no—
257C4×C31—21no—
258C4×C31—21no—
259C4×C31—42no—
260C4×C31—41no—
261C4×C31—41no—
262C4×C31—42no—
263C4×C31—42no—
264C4×C31—42no—
265C4×C31—41no—
266C4×C31—82no—
267C4×C31#45612yes—
268#564C22×C3112yes—
269#563C22×C3112yes—
270#557—21no—
271#554—21no—
272#552—21no—
273#552—22no—
274#552—21no—
275#544—21no—
276#544—21no—
277#541—21no—
278#541—22no—
279#539—21no—
280#533C22×C3111yescharacteristic
281C2×C4⋊Q8C22×C3111yescharacteristic
282#529C22×C3111yescharacteristic
283C2×#125C22×C3111yescharacteristic
284#501—22no—
285#501C22×C3114yes—
286#501C22×C3112yes—
287#491C22×C3114yes—
288#489C22×C3112yes—
289#487—21no—
290#487—21no—
291#483—21no—
292#480—21no—
293#477—21no—
294#476—21no—
295#432C22×C3111yescharacteristic
296C2×#107—21no—
297C2×#106—21no—
298#419—22no—
299C4×M16C22×C3111yescharacteristic
300C2×#97C22×C3111yescharacteristic
301#330C22×C3112yes—
302#330C22×C3114yes—
303#330C22×C3114yes—
304#329C22×C3112yes—
305C2×C31—22no—
306C2×C31—81no—
307C2×C31C2×#45411yescharacteristic
308C2×C31C2×#45611yescharacteristic
309C2×C31#302211yescharacteristic
310C22×Q8—21no—
311C2×M16—21no—
312C22×C8—21no—
313C4⋊Q8—22no—
314C4⋊Q8—21no—
315C4⋊Q8—22no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8D4×C3111yescharacteristic
320C4⋊Q8D4×C3111yescharacteristic
321C4⋊Q8C23×C3112yes—
322#126—22no—
323#126—22no—
324#126—22no—
325#126—22no—
326#126—21no—
327#125—22no—
328#125—22no—
329#125—21no—
330#125—22no—
331#125—22no—
332#125—22no—
333#125—22no—
334#125—22no—
335#125—22no—
336#125—21no—
337#125—21no—
338#125D4×C3112yes—
339#125C23×C3112yes—
340#125C23×C3111yescharacteristic
341#125C23×C3112yes—
342#124C23×C3111yescharacteristic
343#123—22no—
344#123—22no—
345#123—21no—
346C22⋊Q8—22no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—22no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8D4×C3111yescharacteristic
355#121D4×C3111yescharacteristic
356C4×Q8—21no—
357C4×Q8—22no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8D4×C3111yescharacteristic
362C4×D4—22no—
363C4×D4—21no—
364C4×D4D4×C3111yescharacteristic
365#117—22no—
366#117—21no—
367#117—22no—
368#117—21no—
369#117D4×C3112yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4D4×C3111yescharacteristic
376C2×C4⋊C4D4×C3111yescharacteristic
377C2×C42C23×C3111yescharacteristic
378#107—24no—
379#107—22no—
380#106—24no—
381#106—22no—
382C4⋊C8—21no—
383#103—22no—
384#103—24no—
385#103—24no—
386#102—22no—
387C22⋊C8—21no—
388#97—21no—
389#97C23×C3112yes—
390#97C23×C3112yes—
391#97C23×C3112yes—
392C4×C8—21no—
393C31#1902911yescharacteristic, direct product factor, Sylow
394C2×Q8—22no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—22no—
398C2×Q8—44no—
399C2×Q8—41no—
400C2×Q8C2×D4×C3111yescharacteristic
401C2×D4—21no—
402C2×D4C2×D4×C3111yescharacteristic
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—41no—
408C22×C4C2×D4×C3111yescharacteristic
409C22×C4C2×D4×C3111yescharacteristic
410C22×C4C2×D4×C3111yescharacteristic
411M16—42no—
412C2×C8—24no—
413C2×C8—22no—
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—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4C2×D4×C3112yes—
443C4⋊C4C2×D4×C3112yes—
444C4⋊C4C2×D4×C3112yes—
445C4⋊C4C2×D4×C3111yescharacteristic
446C4⋊C4C2×D4×C3112yes—
447C4⋊C4C2×D4×C3111yescharacteristic
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—21no—
452C22⋊C4—22no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C42—22no—
458C42—22no—
459C42—22no—
460C42—22no—
461C42—21no—
462C42C2×D4×C3111yescharacteristic
463C42C2×D4×C3111yescharacteristic
464C42C2×D4×C3111yescharacteristic
465C42C24×C3111yescharacteristic
466C23—21no—
467C23C31×#12011yescharacteristic
468Q8—41no—
469Q8—44no—
470Q8—42no—
471Q8—81no—
472Q8—82no—
473Q8—82no—
474D4—41no—
475D4—42no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—81no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4C31×#12011yescharacteristic
493C2×C4C31×#12011yescharacteristic
494C2×C4C31×#12011yescharacteristic
495C2×C4C22×D4×C3111yescharacteristic
496C2×C4C22×D4×C3111yescharacteristic
497C2×C4C22×D4×C3111yescharacteristic
498C8—24no—
499C8—42no—
500C8—42no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22C31×#45412yes—
507C22C2×C31×#12011yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—42no—
514C4—41no—
515C4—41no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—41no—
520C4—82no—
521C4C31×#45612yes—
522C2—22no—
523C2—81no—
524C2C2×C31×#45411yescharacteristic
525C2C2×C31×#45611yescharacteristic
526C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#501C2semidirect
4. C31×#3139C2semidirect
5. C31×#1664C2semidirect
6. C31×#1663C2semidirect
7. C31×#1531C2semidirect
8. C31×#1528C2semidirect
202. #19029C31direct (N × H)
240. C2×#501C2×C31semidirect
241. #3139C2×C31semidirect
242. #1664C2×C31semidirect
243. #1663C2×C31semidirect
244. #1531C2×C31semidirect
245. #1528C2×C31semidirect
393. C31#19029direct (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×#32382
C2×C31×#5012
C31×#31392
C31×#16642
C31×#16632
C31×#15312
C31×#15282
C31×#15242
#1902931