Finite Group Databasebeta

← C31×#24019 #21480778

Subgroups — C31×#24019 #21480778

Order 7936.

1286 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3486C211yesmaximal, characteristic
2C31×#3092C212yesmaximal, complemented
3C2×C31×#391C211yesmaximal, characteristic, complemented
4C31×#2038C214yesmaximal, complemented
5C31×#1896C212yesmaximal, complemented
6C31×#1857C212yesmaximal, complemented
7C31×#1793C212yesmaximal, complemented
8C31×#1784C211yesmaximal, characteristic, complemented
9C2×C31×2−1+4C2211yescharacteristic
10C23×Q8×C31C2211yescharacteristic
11D4×Q8×C31—22no—
12D4×Q8×C31—22no—
13C31×#548—22no—
14C31×#548—22no—
15C31×#536—22no—
16C31×#536C2212yes—
17C31×#525—22no—
18C31×#525C2212yes—
19C31×#519C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C42×C31C2211yescharacteristic
22C31×#484—22no—
23C31×#483—22no—
24C31×#481—22no—
25C31×#480—22no—
26C31×#428C2214yes—
27C2×C31×#104C2214yes—
28C31×#417C2214yes—
29C2×C31×#101C2212yes—
30C2×C31×#101C2212yes—
31C31×#407C2212yes—
32C31×#391—22no—
33C31×#391C2212yes—
34C31×#391C2212yes—
35C2×C31×#95—22no—
36C31×#339C2214yes—
37C31×2−1+4—24no—
38C31×2−1+4—42no—
39C2×#41×C31—22no—
40C2×#41×C31—22no—
41C2×#41×C31C2312yes—
42C22×Q8×C31—22no—
43C22×Q8×C31—24no—
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31—42no—
47C22×Q8×C31D412yes—
48C22×Q8×C31C2311yescharacteristic
49C22×Q8×C31C2311yescharacteristic
50C23×C4×C31—21no—
51C23×C4×C31—21no—
52C23×C4×C31D412yes—
53C23×C4×C31C2311yescharacteristic
54C2×M16×C31C2314yes—
55C31×C4⋊Q8—24no—
56C31×C4⋊Q8—22no—
57C31×#124—24no—
58C31×#124—22no—
59C31×#123—24no—
60C31×#123—22no—
61C31×C22⋊Q8—22no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8—24no—
64C31×C22⋊Q8—24no—
65C31×C22⋊Q8—22no—
66C31×C22⋊Q8—22no—
67C31×C22⋊Q8D412yes—
68C31×C22⋊Q8D412yes—
69C31×#121—22no—
70C31×#121—22no—
71C31×#121D412yes—
72C31×#121D412yes—
73C31×#120—22no—
74C4×Q8×C31—22no—
75C4×Q8×C31—22no—
76C4×D4×C31—24no—
77C4×D4×C31—24no—
78C4×D4×C31—22no—
79C4×D4×C31—22no—
80C31×#117—22no—
81C31×#117C2312yes—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31C2312yes—
86C2×C42×C31—21no—
87C2×C42×C31—42no—
88C2×C42×C31C2312yes—
89C31×#107—24no—
90C31×#106—24no—
91C31×#104—44no—
92C31×#103—24no—
93C31×#102—24no—
94C31×#101—24no—
95C31×#101—42no—
96C31×C22⋊C8—22no—
97C31×C22⋊C8—22no—
98C31×#95—24no—
99C31×#95—24no—
100C24×C31C2×D411yescharacteristic
101#41×C31—24no—
102#41×C31—24no—
103#41×C31—44no—
104#41×C31—48no—
105#41×C31—44no—
106C2×Q8×C31—22no—
107C2×Q8×C31—24no—
108C2×Q8×C31—24no—
109C2×Q8×C31—22no—
110C2×Q8×C31—22no—
111C2×Q8×C31—22no—
112C2×Q8×C31—22no—
113C2×Q8×C31—22no—
114C2×Q8×C31—42no—
115C2×Q8×C31—48no—
116C2×Q8×C31—48no—
117C2×Q8×C31—48no—
118C2×Q8×C31C2×D412yes—
119C2×Q8×C31#4114yes—
120C2×D4×C31—22no—
121C2×D4×C31—22no—
122C2×D4×C31—22no—
123C2×D4×C31—22no—
124C2×D4×C31C2×D412yes—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—24no—
128C22×C4×C31—24no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—24no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—42no—
136C22×C4×C31—42no—
137C22×C4×C31—42no—
138C22×C4×C31—44no—
139C22×C4×C31—41no—
140C22×C4×C31—41no—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2411yescharacteristic
147M16×C31—24no—
148M16×C31—24no—
149C2×C8×C31—24no—
150C4⋊C4×C31—22no—
151C4⋊C4×C31—22no—
152C4⋊C4×C31—24no—
153C4⋊C4×C31—24no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—24no—
157C4⋊C4×C31—42no—
158C4⋊C4×C31C2×D412yes—
159C4⋊C4×C31C2×D412yes—
160C22⋊C4×C31—24no—
161C22⋊C4×C31—24no—
162C22⋊C4×C31—22no—
163C22⋊C4×C31—22no—
164C22⋊C4×C31—22no—
165C22⋊C4×C31—22no—
166C22⋊C4×C31—22no—
167C42×C31—24no—
168C42×C31—22no—
169C42×C31—24no—
170C42×C31—42no—
171#24019C3111yesmaximal, characteristic, direct product factor, Sylow
172C23×C31—21no—
173C23×C31—21no—
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—22no—
177C23×C31#12011yescharacteristic
178C23×C31#12011yescharacteristic
179C23×C31C22×D411yescharacteristic
180Q8×C31—28no—
181Q8×C31—24no—
182Q8×C31—48no—
183Q8×C31—44no—
184Q8×C31—44no—
185D4×C31—24no—
186D4×C31—44no—
187D4×C31—42no—
188D4×C31—42no—
189D4×C31—44no—
190D4×C31—44no—
191C2×C4×C31—22no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—22no—
195C2×C4×C31—24no—
196C2×C4×C31—24no—
197C2×C4×C31—24no—
198C2×C4×C31—22no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—22no—
202C2×C4×C31—22no—
203C2×C4×C31—22no—
204C2×C4×C31—44no—
205C2×C4×C31—44no—
206C2×C4×C31—48no—
207C2×C4×C31—48no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—44no—
211C2×C4×C31—44no—
212C2×C4×C31—42no—
213C2×C4×C31—82no—
214C2×C4×C31—82no—
215C2×C4×C31#12012yes—
216C2×C4×C31#12314yes—
217C2×C4×C31C22×D412yes—
218C2×C4×C31C2×#4112yes—
219C2×C4×C31H(5,𝔽2)12yes—
220C8×C31—44no—
221#3486C2×C3111yescharacteristic
222#3092C2×C3112yescomplemented
223C2×#391C2×C3111yescharacteristic, complemented
224#2038C2×C3114yescomplemented
225#1896C2×C3112yescomplemented
226#1857C2×C3112yescomplemented
227#1793C2×C3112yescomplemented
228#1784C2×C3111yescharacteristic, complemented
229C22×C31—24no—
230C22×C31—24no—
231C22×C31—21no—
232C22×C31—21no—
233C22×C31—21no—
234C22×C31—21no—
235C22×C31—21no—
236C22×C31—21no—
237C22×C31—42no—
238C22×C31—42no—
239C22×C31—42no—
240C22×C31#45412yes—
241C22×C31#45612yes—
242C22×C31C2×#12011yescharacteristic
243C22×C31C2×#12311yescharacteristic
244C22×C31#53411yescharacteristic
245C4×C31—22no—
246C4×C31—24no—
247C4×C31—44no—
248C4×C31—42no—
249C4×C31—42no—
250C4×C31—42no—
251C4×C31—42no—
252C4×C31—82no—
253C4×C31#54614yes—
254C2×2−1+4C22×C3111yescharacteristic
255C23×Q8C22×C3111yescharacteristic
256D4×Q8—22no—
257D4×Q8—22no—
258#548—22no—
259#548—22no—
260#536—22no—
261#536C22×C3112yes—
262#525—22no—
263#525C22×C3112yes—
264#519C22×C3111yescharacteristic
265C22×C4⋊C4C22×C3111yescharacteristic
266C22×C42C22×C3111yescharacteristic
267#484—22no—
268#483—22no—
269#481—22no—
270#480—22no—
271#428C22×C3114yes—
272C2×#104C22×C3114yes—
273#417C22×C3114yes—
274C2×#101C22×C3112yes—
275C2×#101C22×C3112yes—
276#407C22×C3112yes—
277#391—22no—
278#391C22×C3112yes—
279#391C22×C3112yes—
280C2×#95—22no—
281#339C22×C3114yes—
282C2×C31—21no—
283C2×C31—21no—
284C2×C31—22no—
285C2×C31—22no—
286C2×C31—82no—
287C2×C31#240511yescharacteristic
288C2×C31C2×#45411yescharacteristic
289C2×C31C2×#45611yescharacteristic
2902−1+4—24no—
2912−1+4—42no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41C23×C3112yes—
295C22×Q8—22no—
296C22×Q8—24no—
297C22×Q8—22no—
298C22×Q8—22no—
299C22×Q8—42no—
300C22×Q8D4×C3112yes—
301C22×Q8C23×C3111yescharacteristic
302C22×Q8C23×C3111yescharacteristic
303C23×C4—21no—
304C23×C4—21no—
305C23×C4D4×C3112yes—
306C23×C4C23×C3111yescharacteristic
307C2×M16C23×C3114yes—
308C4⋊Q8—24no—
309C4⋊Q8—22no—
310#124—24no—
311#124—22no—
312#123—24no—
313#123—22no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8D4×C3112yes—
321C22⋊Q8D4×C3112yes—
322#121—22no—
323#121—22no—
324#121D4×C3112yes—
325#121D4×C3112yes—
326#120—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—22no—
332C4×D4—22no—
333#117—22no—
334#117C23×C3112yes—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4C23×C3112yes—
339C2×C42—21no—
340C2×C42—42no—
341C2×C42C23×C3112yes—
342#107—24no—
343#106—24no—
344#104—44no—
345#103—24no—
346#102—24no—
347#101—24no—
348#101—42no—
349C22⋊C8—22no—
350C22⋊C8—22no—
351#95—24no—
352#95—24no—
353C31#2401911yescharacteristic, direct product factor, Sylow
354C24C2×D4×C3111yescharacteristic
355#41—24no—
356#41—24no—
357#41—44no—
358#41—48no—
359#41—44no—
360C2×Q8—22no—
361C2×Q8—24no—
362C2×Q8—24no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—42no—
369C2×Q8—48no—
370C2×Q8—48no—
371C2×Q8—48no—
372C2×Q8C2×D4×C3112yes—
373C2×Q8#41×C3114yes—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4C2×D4×C3112yes—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—44no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4C2×D4×C3112yes—
396C22×C4C2×D4×C3111yescharacteristic
397C22×C4C2×D4×C3112yes—
398C22×C4C2×D4×C3112yes—
399C22×C4C2×D4×C3112yes—
400C22×C4C24×C3111yescharacteristic
401M16—24no—
402M16—24no—
403C2×C8—24no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—24no—
411C4⋊C4—42no—
412C4⋊C4C2×D4×C3112yes—
413C4⋊C4C2×D4×C3112yes—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C42—24no—
422C42—22no—
423C42—24no—
424C42—42no—
425C23—22no—
426C23—22no—
427C23—21no—
428C23—21no—
429C23—22no—
430C23C31×#12011yescharacteristic
431C23C31×#12011yescharacteristic
432C23C22×D4×C3111yescharacteristic
433Q8—28no—
434Q8—24no—
435Q8—48no—
436Q8—44no—
437Q8—44no—
438D4—24no—
439D4—44no—
440D4—44no—
441D4—44no—
442D4—42no—
443D4—42no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—44no—
458C2×C4—44no—
459C2×C4—48no—
460C2×C4—48no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4C31×#12012yes—
469C2×C4C31×#12314yes—
470C2×C4C22×D4×C3112yes—
471C2×C4C2×#41×C3112yes—
472C2×C4C31×H(5,𝔽2)12yes—
473C8—44no—
474C22—24no—
475C22—24no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22C31×#45412yes—
486C22C31×#45612yes—
487C22C2×C31×#12011yescharacteristic
488C22C2×C31×#12311yescharacteristic
489C22C31×#53411yescharacteristic
490C4—22no—
491C4—24no—
492C4—44no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—82no—
498C4C31×#54614yes—
499C2—21no—
500C2—22no—
501C2—22no—
502C2—21no—
503C2—82no—
504C2C31×#240511yescharacteristic
505C2C2×C31×#45411yescharacteristic
506C2C2×C31×#45611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3486C2
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
2. C31×#3092C2semidirect
3. C2×C31×#391C2semidirect
4. C31×#2038C2semidirect
5. C31×#1896C2semidirect
6. C31×#1857C2semidirect
7. C31×#1793C2semidirect
8. C31×#1784C2semidirect
171. #24019C31direct (N × H)
222. #3092C2×C31semidirect
223. C2×#391C2×C31semidirect
224. #2038C2×C31semidirect
225. #1896C2×C31semidirect
226. #1857C2×C31semidirect
227. #1793C2×C31semidirect
228. #1784C2×C31semidirect
353. C31#24019direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34862
C31×#30922
C2×C31×#3912
C31×#20382
C31×#18962
C31×#18572
C31×#17932
C31×#17842
#2401931