Finite Group Databasebeta

← C31×#18333 #21475092

Subgroups — C31×#18333 #21475092

Order 7936.

950 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3458C211yesmaximal, characteristic, complemented
2C31×#3215C212yesmaximal, complemented
3C31×#2610C211yesmaximal, characteristic
4C31×#1605C212yesmaximal, complemented
5C31×#1602C212yesmaximal, complemented
6C31×#1599C212yesmaximal, complemented
7C31×#1596C212yesmaximal
8C31×#1506C212yesmaximal, complemented
9C31×#1464C211yesmaximal, characteristic, complemented
10C31×#544—22no—
11C31×#544—22no—
12C31×#544—21no—
13C31×#544C2212yes—
14C31×#543—21no—
15C31×#543C2212yes—
16C31×#533—24no—
17C31×#533—21no—
18C31×#533C2212yes—
19C2×C31×#124C2211yescharacteristic
20C2×C31×#117—21no—
21C2×C31×#117C2211yescharacteristic
22C31×#497—22no—
23C31×#489—22no—
24C31×#464—24no—
25C31×#451C2214yes—
26C31×#450C2214yes—
27C31×#432C2212yes—
28C31×#395C2211yescharacteristic
29C31×#394C2211yescharacteristic
30C31×#393C2211yescharacteristic
31C31×#392C2211yescharacteristic
32C31×#390—21no—
33C31×#388—21no—
34C31×#388—21no—
35C31×#386—21no—
36C31×#376C2211yescharacteristic
37C31×#328C2214yes—
38C31×#328C2214yes—
39C31×#324C2212yes—
40C31×#323C2212yes—
41C22×Q8×C31C2311yescharacteristic
42C22×D4×C31—21no—
43C22×D4×C31C2311yescharacteristic
44C23×C4×C31D411yescharacteristic
45C2×Q16×C31—24no—
46C2×SD16×C31—24no—
47C31×C4⋊Q8—24no—
48C31×C4⋊Q8—21no—
49C31×C4⋊Q8—21no—
50C31×C4⋊Q8—24no—
51C31×C4⋊Q8D412yescomplemented
52C31×C4⋊Q8D412yescomplemented
53C31×#125—24no—
54C31×#125—22no—
55C31×#125—24no—
56C31×#125—22no—
57C31×#124—22no—
58C31×#124—22no—
59C31×C22⋊Q8—24no—
60C31×C22⋊Q8—24no—
61C31×C22⋊Q8—24no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8—22no—
64C31×C22⋊Q8—22no—
65C31×C22⋊Q8—24no—
66C31×C22⋊Q8C2314yes—
67C4×Q8×C31—22no—
68C4×Q8×C31—22no—
69C4×Q8×C31—22no—
70C4×Q8×C31D414yescomplemented
71C31×#117—22no—
72C31×#117—22no—
73C31×#117—22no—
74C31×#117—22no—
75C31×#117—22no—
76C31×#117—22no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—21no—
80C2×C4⋊C4×C31D411yescharacteristic
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×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31D411yescharacteristic
90C2×C22⋊C4×C31C2311yescharacteristic
91C2×C42×C31—22no—
92C2×C42×C31—21no—
93C2×C42×C31D411yescharacteristic
94C2×C42×C31C2311yescharacteristic
95C31×C4⋊C8—22no—
96C31×#103—24no—
97C31×#102—24no—
98C31×C22⋊C8C2314yes—
99C31×#97—22no—
100C31×#95—21no—
101C31×#95—21no—
102C31×#95—21no—
103C31×#95C2311yescharacteristic
104C31×#95C2311yescharacteristic
105C24×C31—21no—
106C24×C31C2×D411yescharacteristic
107C2×Q8×C31—22no—
108C2×Q8×C31—22no—
109C2×Q8×C31—22no—
110C2×Q8×C31—22no—
111C2×Q8×C31—81no—
112C2×Q8×C31C2×D414yes—
113C2×D4×C31—22no—
114C2×D4×C31—42no—
115C2×D4×C31—42no—
116C2×D4×C31—81no—
117C2×D4×C31—81no—
118C22×C4×C31—22no—
119C22×C4×C31—21no—
120C22×C4×C31—21no—
121C22×C4×C31—22no—
122C22×C4×C31—21no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31C2×D411yescharacteristic
128C22×C4×C31C2×D411yescharacteristic
129C22×C4×C31C2×D411yescharacteristic
130C22×C4×C31C2×D411yescharacteristic
131C22×C4×C31C2×D411yescharacteristic
132C22×C4×C31C2411yescharacteristic
133Q16×C31—84no—
134SD16×C31—84no—
135C2×C8×C31—24no—
136C4⋊C4×C31—22no—
137C4⋊C4×C31—22no—
138C4⋊C4×C31—22no—
139C4⋊C4×C31—24no—
140C4⋊C4×C31—24no—
141C4⋊C4×C31—22no—
142C4⋊C4×C31—22no—
143C4⋊C4×C31—22no—
144C4⋊C4×C31—22no—
145C4⋊C4×C31—22no—
146C4⋊C4×C31—24no—
147C4⋊C4×C31—22no—
148C4⋊C4×C31—24no—
149C4⋊C4×C31—81no—
150C4⋊C4×C31C2×D414yes—
151C22⋊C4×C31—24no—
152C22⋊C4×C31—24no—
153C22⋊C4×C31—22no—
154C22⋊C4×C31—22no—
155C22⋊C4×C31—42no—
156C22⋊C4×C31—41no—
157C22⋊C4×C31—41no—
158C22⋊C4×C31—42no—
159C22⋊C4×C31—42no—
160C22⋊C4×C31—81no—
161C22⋊C4×C31—81no—
162C42×C31—24no—
163C42×C31—24no—
164C42×C31—21no—
165C42×C31—21no—
166C42×C31—42no—
167C42×C31C2×D412yes—
168C42×C31C2×D412yes—
169#18333C3111yesmaximal, characteristic, direct product factor, Sylow
170C23×C31—21no—
171C23×C31—21no—
172C23×C31—41no—
173C23×C31—41no—
174C23×C31—41no—
175C23×C31—41no—
176C23×C31—41no—
177C23×C31—41no—
178C23×C31—41no—
179C23×C31—41no—
180C23×C31—41no—
181C23×C31#13712yes—
182C23×C31C22×D411yescharacteristic
183Q8×C31—44no—
184Q8×C31—44no—
185Q8×C31—82no—
186Q8×C31—82no—
187Q8×C31—82no—
188D4×C31—44no—
189D4×C31—84no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—21no—
195C2×C4×C31—21no—
196C2×C4×C31—22no—
197C2×C4×C31—24no—
198C2×C4×C31—21no—
199C2×C4×C31—21no—
200C2×C4×C31—24no—
201C2×C4×C31—41no—
202C2×C4×C31—41no—
203C2×C4×C31—41no—
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—41no—
213C2×C4×C31—82no—
214C2×C4×C31—82no—
215C2×C4×C31#12011yescharacteristic
216C2×C4×C31#12011yescharacteristic
217C2×C4×C31#12012yes—
218C2×C4×C31#13712yes—
219C2×C4×C31C22×D412yes—
220C8×C31—44no—
221#3458C2×C3111yescharacteristic, complemented
222#3215C2×C3112yescomplemented
223#2610C2×C3111yescharacteristic
224#1605C2×C3112yescomplemented
225#1602C2×C3112yescomplemented
226#1599C2×C3112yescomplemented
227#1596C2×C3112yes—
228#1506C2×C3112yescomplemented
229#1464C2×C3111yescharacteristic, complemented
230C22×C31—21no—
231C22×C31—21no—
232C22×C31—22no—
233C22×C31—42no—
234C22×C31—41no—
235C22×C31—41no—
236C22×C31—81no—
237C22×C31—81no—
238C22×C31—81no—
239C22×C31—81no—
240C22×C31—81no—
241C22×C31—81no—
242C22×C31—81no—
243C22×C31—81no—
244C22×C31C2×#12011yescharacteristic
245C22×C31C2×#13711yescharacteristic
246C22×C31C2×#13711yescharacteristic
247C4×C31—21no—
248C4×C31—21no—
249C4×C31—22no—
250C4×C31—22no—
251C4×C31—22no—
252C4×C31—42no—
253C4×C31—41no—
254C4×C31—44no—
255C4×C31—41no—
256C4×C31—44no—
257C4×C31—81no—
258C4×C31—81no—
259#544—22no—
260#544—22no—
261#544—21no—
262#544C22×C3112yes—
263#543—21no—
264#543C22×C3112yes—
265#533—24no—
266#533—21no—
267#533C22×C3112yes—
268C2×#124C22×C3111yescharacteristic
269C2×#117—21no—
270C2×#117C22×C3111yescharacteristic
271#497—22no—
272#489—22no—
273#464—24no—
274#451C22×C3114yes—
275#450C22×C3114yes—
276#432C22×C3112yes—
277#395C22×C3111yescharacteristic
278#394C22×C3111yescharacteristic
279#393C22×C3111yescharacteristic
280#392C22×C3111yescharacteristic
281#390—21no—
282#388—21no—
283#388—21no—
284#386—21no—
285#376C22×C3111yescharacteristic
286#328C22×C3114yes—
287#328C22×C3114yes—
288#324C22×C3112yes—
289#323C22×C3112yes—
290C2×C31—21no—
291C2×C31—21no—
292C2×C31—42no—
293C2×C31—161no—
294C2×C31#300411yescharacteristic
295C2×C31#301811yescharacteristic
296C2×C31#302711yescharacteristic
297C22×Q8C23×C3111yescharacteristic
298C22×D4—21no—
299C22×D4C23×C3111yescharacteristic
300C23×C4D4×C3111yescharacteristic
301C2×Q16—24no—
302C2×SD16—24no—
303C4⋊Q8—24no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—24no—
307C4⋊Q8D4×C3112yescomplemented
308C4⋊Q8D4×C3112yescomplemented
309#125—24no—
310#125—22no—
311#125—24no—
312#125—22no—
313#124—22no—
314#124—22no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—24no—
322C22⋊Q8C23×C3114yes—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×Q8D4×C3114yescomplemented
327#117—22no—
328#117—22no—
329#117—22no—
330#117—22no—
331#117—22no—
332#117—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4D4×C3111yescharacteristic
337C2×C4⋊C4C23×C3111yescharacteristic
338C2×C22⋊C4—22no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4D4×C3111yescharacteristic
346C2×C22⋊C4C23×C3111yescharacteristic
347C2×C42—22no—
348C2×C42—21no—
349C2×C42D4×C3111yescharacteristic
350C2×C42C23×C3111yescharacteristic
351C4⋊C8—22no—
352#103—24no—
353#102—24no—
354C22⋊C8C23×C3114yes—
355#97—22no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95C23×C3111yescharacteristic
360#95C23×C3111yescharacteristic
361C31#1833311yescharacteristic, direct product factor, Sylow
362C24—21no—
363C24C2×D4×C3111yescharacteristic
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—81no—
369C2×Q8C2×D4×C3114yes—
370C2×D4—22no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—81no—
374C2×D4—81no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4C2×D4×C3111yescharacteristic
385C22×C4C2×D4×C3111yescharacteristic
386C22×C4C2×D4×C3111yescharacteristic
387C22×C4C2×D4×C3111yescharacteristic
388C22×C4C2×D4×C3111yescharacteristic
389C22×C4C24×C3111yescharacteristic
390Q16—84no—
391SD16—84no—
392C2×C8—24no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—24no—
406C4⋊C4—81no—
407C4⋊C4C2×D4×C3114yes—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—42no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—81no—
418C22⋊C4—81no—
419C42—24no—
420C42—24no—
421C42—21no—
422C42—21no—
423C42—42no—
424C42C2×D4×C3112yes—
425C42C2×D4×C3112yes—
426C23—21no—
427C23—21no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23C31×#13712yes—
438C23C22×D4×C3111yescharacteristic
439Q8—44no—
440Q8—44no—
441Q8—82no—
442Q8—82no—
443Q8—82no—
444D4—44no—
445D4—84no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—24no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4C31×#12011yescharacteristic
472C2×C4C31×#12011yescharacteristic
473C2×C4C31×#12012yes—
474C2×C4C31×#13712yes—
475C2×C4C22×D4×C3112yes—
476C8—44no—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—42no—
481C22—41no—
482C22—41no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C2×C31×#12011yescharacteristic
492C22C2×C31×#13711yescharacteristic
493C22C2×C31×#13711yescharacteristic
494C4—21no—
495C4—21no—
496C4—22no—
497C4—22no—
498C4—22no—
499C4—42no—
500C4—41no—
501C4—44no—
502C4—41no—
503C4—44no—
504C4—81no—
505C4—81no—
506C2—21no—
507C2—21no—
508C2—42no—
509C2—161no—
510C2C31×#300411yescharacteristic
511C2C31×#301811yescharacteristic
512C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#392C22
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
1. C31×#3458C2semidirect
2. C31×#3215C2semidirect
4. C31×#1605C2semidirect
5. C31×#1602C2semidirect
6. C31×#1599C2semidirect
8. C31×#1506C2semidirect
9. C31×#1464C2semidirect
51. C31×C4⋊Q8D4semidirect
52. C31×C4⋊Q8D4semidirect
70. C4×Q8×C31D4semidirect
169. #18333C31direct (N × H)
221. #3458C2×C31semidirect
222. #3215C2×C31semidirect
224. #1605C2×C31semidirect
225. #1602C2×C31semidirect
226. #1599C2×C31semidirect
228. #1506C2×C31semidirect
229. #1464C2×C31semidirect
307. C4⋊Q8D4×C31semidirect
308. C4⋊Q8D4×C31semidirect
326. C4×Q8D4×C31semidirect
361. C31#18333direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34582
C31×#32152
C31×#26102
C31×#16052
C31×#16022
C31×#15992
C31×#15962
C31×#15062
C31×#14642
#1833331