Finite Group Databasebeta

← C31×#33127 #21489886

Subgroups — C31×#33127 #21489886

Order 7936.

768 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3095C211yesmaximal, characteristic, complemented
2C31×#3094C211yesmaximal, characteristic
3C2×C31×#468C211yesmaximal, characteristic
4C31×#2873C211yesmaximal, characteristic, complemented
5C31×#1977C212yesmaximal, complemented
6C31×#1952C212yesmaximal, complemented
7C31×#1931C212yesmaximal, complemented
8C31×#1930C212yesmaximal, complemented
9C31×#1901C211yesmaximal, characteristic, complemented
10C31×#1900C211yesmaximal, characteristic
11C31×#1811C211yesmaximal, characteristic, complemented
12C22×SD16×C31C2211yescharacteristic
13C22×M16×C31C2211yescharacteristic
14C22×M16×C31C2211yescharacteristic
15C2×C31×C22⋊Q8C2211yescharacteristic
16C2×C31×#121C2211yescharacteristic
17C2×C31×#117C2211yescharacteristic
18C31×#485—22no—
19C31×#484—21no—
20C31×#483—21no—
21C31×#482—22no—
22C31×#481—21no—
23C31×#480—21no—
24C31×#468—22no—
25C31×#468—22no—
26C2×C31×#108C2212yes—
27C31×#428C2212yes—
28C31×#428C2212yes—
29C2×C31×#107C2211yescharacteristic
30C31×#419C2212yes—
31C31×#418C2212yes—
32C2×C31×#103C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#101C2212yes—
35C2×C31×#100C2212yes—
36C31×#407C2211yescharacteristic
37C31×#407C2211yescharacteristic
38C31×#405—22no—
39C31×#405C2212yes—
40C31×#405C2212yes—
41C4×M16×C31—22no—
42C31×#343C2212yes—
43C31×#343C2212yes—
44C31×#341C2212yes—
45C22×Q8×C31C2311yescharacteristic
46C22×D4×C31—21no—
47C22×D4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C2×SD16×C31—22no—
50C2×SD16×C31—24no—
51C2×M16×C31—21no—
52C2×M16×C31—24no—
53C2×M16×C31—24no—
54C2×M16×C31D412yes—
55C2×M16×C31D412yes—
56C2×M16×C31C2312yes—
57C2×M16×C31C2312yes—
58C2×M16×C31C2312yes—
59C22×C8×C31—21no—
60C22×C8×C31C2311yescharacteristic
61C22×C8×C31C2311yescharacteristic
62C31×C22⋊Q8—21no—
63C31×C22⋊Q8—21no—
64C31×C22⋊Q8—21no—
65C31×C22⋊Q8—21no—
66C31×#121—21no—
67C31×#121—21no—
68C31×#121—21no—
69C31×#121—21no—
70C31×#117—21no—
71C31×#117—21no—
72C31×#117D412yes—
73C31×#117C2312yes—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31D411yescharacteristic
76C2×C4⋊C4×C31D411yescharacteristic
77C2×C4⋊C4×C31C2311yescharacteristic
78C2×C4⋊C4×C31C2311yescharacteristic
79C2×C22⋊C4×C31—21no—
80C2×C22⋊C4×C31—21no—
81C2×C22⋊C4×C31—21no—
82C2×C42×C31—21no—
83C31×#108—24no—
84C31×#107—22no—
85C31×#107—22no—
86C31×#107—22no—
87C31×#106—22no—
88C31×#106—22no—
89C31×#103—22no—
90C31×#103—22no—
91C31×#103—22no—
92C31×#102—22no—
93C31×#102—22no—
94C31×#102—22no—
95C31×#101—24no—
96C31×#100—24no—
97C31×C22⋊C8—21no—
98C31×C22⋊C8—21no—
99C31×C22⋊C8—21no—
100C31×C22⋊C8—21no—
101C31×#97—22no—
102C31×#97—22no—
103C4×C8×C31—22no—
104C4×C8×C31—22no—
105C24×C31—21no—
106C24×C31#4111yescharacteristic
107C2×Q8×C31—21no—
108C2×Q8×C31—21no—
109C2×Q8×C31—22no—
110C2×Q8×C31—22no—
111C2×D4×C31—21no—
112C2×D4×C31—21no—
113C2×D4×C31—22no—
114C2×D4×C31—22no—
115C2×D4×C31—41no—
116C2×D4×C31—41no—
117C2×D4×C31—82no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—21no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31C2×D411yescharacteristic
126C22×C4×C31C2×D411yescharacteristic
127C22×C4×C31C2×D411yescharacteristic
128C22×C4×C31C2×D411yescharacteristic
129C22×C4×C31#4111yescharacteristic
130C22×C4×C31C2411yescharacteristic
131SD16×C31—44no—
132M16×C31—24no—
133M16×C31—22no—
134M16×C31—24no—
135M16×C31—24no—
136M16×C31—22no—
137M16×C31—22no—
138M16×C31—22no—
139M16×C31—22no—
140M16×C31#4114yes—
141C2×C8×C31—24no—
142C2×C8×C31—22no—
143C2×C8×C31—22no—
144C2×C8×C31—22no—
145C2×C8×C31—22no—
146C2×C8×C31C2×D412yes—
147C2×C8×C31C2×D412yes—
148C2×C8×C31#4114yes—
149C4⋊C4×C31—21no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—21no—
153C4⋊C4×C31—21no—
154C4⋊C4×C31—21no—
155C4⋊C4×C31—41no—
156C4⋊C4×C31—41no—
157C4⋊C4×C31C2×D412yes—
158C4⋊C4×C31C2×D412yes—
159C22⋊C4×C31—22no—
160C22⋊C4×C31—22no—
161C22⋊C4×C31—41no—
162C22⋊C4×C31—41no—
163C22⋊C4×C31—41no—
164C22⋊C4×C31—41no—
165C42×C31—22no—
166C42×C31—22no—
167#33127C3111yesmaximal, characteristic, direct product factor, Sylow
168C23×C31—22no—
169C23×C31—41no—
170C23×C31—41no—
171C23×C31—41no—
172C23×C31—42no—
173C23×C31—81no—
174C23×C31—81no—
175C23×C31#12111yescharacteristic
176C23×C31#12111yescharacteristic
177C23×C31C2×#4111yescharacteristic
178Q8×C31—41no—
179Q8×C31—41no—
180Q8×C31—42no—
181D4×C31—41no—
182D4×C31—41no—
183D4×C31—42no—
184D4×C31—82no—
185D4×C31—82no—
186C2×C4×C31—22no—
187C2×C4×C31—21no—
188C2×C4×C31—21no—
189C2×C4×C31—21no—
190C2×C4×C31—21no—
191C2×C4×C31—22no—
192C2×C4×C31—22no—
193C2×C4×C31—22no—
194C2×C4×C31—22no—
195C2×C4×C31—41no—
196C2×C4×C31—41no—
197C2×C4×C31—41no—
198C2×C4×C31—42no—
199C2×C4×C31—81no—
200C2×C4×C31—81no—
201C2×C4×C31—81no—
202C2×C4×C31—81no—
203C2×C4×C31#12111yescharacteristic
204C2×C4×C31#12111yescharacteristic
205C2×C4×C31C22×D411yescharacteristic
206C2×C4×C31C22×D411yescharacteristic
207C2×C4×C31C2×#4112yes—
208C2×C4×C31C2×#4112yes—
209C8×C31—22no—
210C8×C31—24no—
211C8×C31—42no—
212C8×C31—42no—
213C8×C31#12314yes—
214#3095C2×C3111yescharacteristic, complemented
215#3094C2×C3111yescharacteristic
216C2×#468C2×C3111yescharacteristic
217#2873C2×C3111yescharacteristic, complemented
218#1977C2×C3112yescomplemented
219#1952C2×C3112yescomplemented
220#1931C2×C3112yescomplemented
221#1930C2×C3112yescomplemented
222#1901C2×C3111yescharacteristic, complemented
223#1900C2×C3111yescharacteristic
224#1811C2×C3111yescharacteristic, complemented
225C22×C31—21no—
226C22×C31—21no—
227C22×C31—21no—
228C22×C31—21no—
229C22×C31—21no—
230C22×C31—21no—
231C22×C31—21no—
232C22×C31—21no—
233C22×C31—82no—
234C22×C31—81no—
235C22×C31—81no—
236C22×C31—81no—
237C22×C31—162no—
238C22×C31C2×#12111yescharacteristic
239C22×C31#52912yes—
240C4×C31—21no—
241C4×C31—21no—
242C4×C31—42no—
243C4×C31—42no—
244C4×C31—81no—
245C4×C31—81no—
246C4×C31—81no—
247C4×C31C2×#12311yescharacteristic
248C4×C31#52511yescharacteristic
249C4×C31#53212yes—
250C22×SD16C22×C3111yescharacteristic
251C22×M16C22×C3111yescharacteristic
252C22×M16C22×C3111yescharacteristic
253C2×C22⋊Q8C22×C3111yescharacteristic
254C2×#121C22×C3111yescharacteristic
255C2×#117C22×C3111yescharacteristic
256#485—22no—
257#484—21no—
258#483—21no—
259#482—22no—
260#481—21no—
261#480—21no—
262#468—22no—
263#468—22no—
264C2×#108C22×C3112yes—
265#428C22×C3112yes—
266#428C22×C3112yes—
267C2×#107C22×C3111yescharacteristic
268#419C22×C3112yes—
269#418C22×C3112yes—
270C2×#103C22×C3111yescharacteristic
271C2×#102C22×C3111yescharacteristic
272C2×#101C22×C3112yes—
273C2×#100C22×C3112yes—
274#407C22×C3111yescharacteristic
275#407C22×C3111yescharacteristic
276#405—22no—
277#405C22×C3112yes—
278#405C22×C3112yes—
279C4×M16—22no—
280#343C22×C3112yes—
281#343C22×C3112yes—
282#341C22×C3112yes—
283C2×C31—22no—
284C2×C31—41no—
285C2×C31—41no—
286C2×C31—161no—
287C2×C31#285411yescharacteristic
288C2×C31#306811yescharacteristic
289C2×C31#306911yescharacteristic
290C22×Q8C23×C3111yescharacteristic
291C22×D4—21no—
292C22×D4C23×C3111yescharacteristic
293C23×C4C23×C3111yescharacteristic
294C2×SD16—22no—
295C2×SD16—24no—
296C2×M16—21no—
297C2×M16—24no—
298C2×M16—24no—
299C2×M16D4×C3112yes—
300C2×M16D4×C3112yes—
301C2×M16C23×C3112yes—
302C2×M16C23×C3112yes—
303C2×M16C23×C3112yes—
304C22×C8—21no—
305C22×C8C23×C3111yescharacteristic
306C22×C8C23×C3111yescharacteristic
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#117—21no—
316#117—21no—
317#117D4×C3112yes—
318#117C23×C3112yes—
319C2×C4⋊C4—21no—
320C2×C4⋊C4D4×C3111yescharacteristic
321C2×C4⋊C4D4×C3111yescharacteristic
322C2×C4⋊C4C23×C3111yescharacteristic
323C2×C4⋊C4C23×C3111yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C42—21no—
328#108—24no—
329#107—22no—
330#107—22no—
331#107—22no—
332#106—22no—
333#106—22no—
334#103—22no—
335#103—22no—
336#103—22no—
337#102—22no—
338#102—22no—
339#102—22no—
340#101—24no—
341#100—24no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346#97—22no—
347#97—22no—
348C4×C8—22no—
349C4×C8—22no—
350C31#3312711yescharacteristic, direct product factor, Sylow
351C24—21no—
352C24#41×C3111yescharacteristic
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—82no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4C2×D4×C3111yescharacteristic
372C22×C4C2×D4×C3111yescharacteristic
373C22×C4C2×D4×C3111yescharacteristic
374C22×C4C2×D4×C3111yescharacteristic
375C22×C4#41×C3111yescharacteristic
376C22×C4C24×C3111yescharacteristic
377SD16—44no—
378M16—24no—
379M16—22no—
380M16—24no—
381M16—24no—
382M16—22no—
383M16—22no—
384M16—22no—
385M16—22no—
386M16#41×C3114yes—
387C2×C8—24no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8C2×D4×C3112yes—
393C2×C8C2×D4×C3112yes—
394C2×C8#41×C3114yes—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4C2×D4×C3112yes—
404C4⋊C4C2×D4×C3112yes—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C42—22no—
412C42—22no—
413C23—22no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—42no—
418C23—81no—
419C23—81no—
420C23C31×#12111yescharacteristic
421C23C31×#12111yescharacteristic
422C23C2×#41×C3111yescharacteristic
423Q8—41no—
424Q8—41no—
425Q8—42no—
426D4—41no—
427D4—41no—
428D4—42no—
429D4—82no—
430D4—82no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4C31×#12111yescharacteristic
449C2×C4C31×#12111yescharacteristic
450C2×C4C22×D4×C3111yescharacteristic
451C2×C4C22×D4×C3111yescharacteristic
452C2×C4C2×#41×C3112yes—
453C2×C4C2×#41×C3112yes—
454C8—22no—
455C8—24no—
456C8—42no—
457C8—42no—
458C8C31×#12314yes—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—82no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—162no—
472C22C2×C31×#12111yescharacteristic
473C22C31×#52912yes—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—42no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4C2×C31×#12311yescharacteristic
482C4C31×#52511yescharacteristic
483C4C31×#53212yes—
484C2—22no—
485C2—41no—
486C2—41no—
487C2—161no—
488C2C31×#285411yescharacteristic
489C2C31×#306811yescharacteristic
490C2C31×#306911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#121
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3095C2semidirect
4. C31×#2873C2semidirect
5. C31×#1977C2semidirect
6. C31×#1952C2semidirect
7. C31×#1931C2semidirect
8. C31×#1930C2semidirect
9. C31×#1901C2semidirect
11. C31×#1811C2semidirect
167. #33127C31direct (N × H)
214. #3095C2×C31semidirect
217. #2873C2×C31semidirect
218. #1977C2×C31semidirect
219. #1952C2×C31semidirect
220. #1931C2×C31semidirect
221. #1930C2×C31semidirect
222. #1901C2×C31semidirect
224. #1811C2×C31semidirect
350. C31#33127direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30952
C31×#30942
C2×C31×#4682
C31×#28732
C31×#19772
C31×#19522
C31×#19312
C31×#19302
C31×#19012
C31×#19002
C31×#18112
#3312731