Finite Group Databasebeta

← C31×#8350 #21465109

Subgroups — C31×#8350 #21465109

Order 7936.

1114 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3496C211yesmaximal, characteristic
2C31×#1893C212yesmaximal, complemented
3C31×#1869C211yesmaximal, characteristic, complemented
4C31×#1799C211yesmaximal, characteristic, complemented
5C31×#1519C212yesmaximal, complemented
6C2×C31×H(5,𝔽2)—21no—
7C23×C8×C31C2211yescharacteristic, complemented
8C31×#547—22no—
9C31×#546—24no—
10D42×C31—22no—
11C31×#537C412yescomplemented
12C31×#534—21no—
13C31×#534C412yescomplemented
14C31×#532—21no—
15C2×C31×#121—21no—
16C2×C31×#121C2212yes—
17C2×C4×D4×C31C2211yescharacteristic
18C2×C31×#102—22no—
19C2×C31×#99—21no—
20C2×C31×C22⋊C8—21no—
21C2×C31×C22⋊C8C2211yescharacteristic, complemented
22C31×#380C2212yescomplemented
23C31×#342—21no—
24C31×#340—22no—
25C31×#336—21no—
26C31×#327—24no—
27C31×H(5,𝔽2)—44no—
28C31×H(5,𝔽2)—42no—
29C31×H(5,𝔽2)—42no—
30C2×#41×C31—24no—
31C2×#41×C31—22no—
32C22×D4×C31—24no—
33C22×D4×C31—22no—
34C22×D4×C31—22no—
35C22×D4×C31—21no—
36C22×D4×C31D411yescharacteristic
37C22×D4×C31D412yes—
38C23×C4×C31D411yescharacteristic
39C23×C4×C31C2311yescharacteristic
40C22×C8×C31—21no—
41C22×C8×C31—22no—
42C22×C8×C31—21no—
43C22×C8×C31—42no—
44C31×C4⋊Q8—21no—
45C31×#127—21no—
46C31×#124—22no—
47C31×#123—24no—
48C31×#123—24no—
49C31×C22⋊Q8—24no—
50C31×#121—22no—
51C31×#121—22no—
52C31×#121—24no—
53C31×#121—22no—
54C31×#121—22no—
55C31×#121—22no—
56C31×#121—22no—
57C31×#121C2×C414yes—
58C31×#121D414yes—
59C31×#120—24no—
60C31×#120—24no—
61C4×D4×C31—22no—
62C4×D4×C31—22no—
63C4×D4×C31—22no—
64C4×D4×C31—22no—
65C2×C4⋊C4×C31—21no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31C2×C411yescharacteristic
68C2×C4⋊C4×C31D412yes—
69C2×C22⋊C4×C31—22no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—22no—
72C2×C22⋊C4×C31C2×C411yescharacteristic
73C2×C22⋊C4×C31D411yescharacteristic
74C2×C42×C31D411yescharacteristic
75C31×#102—44no—
76C31×#99—42no—
77C31×C22⋊C8—22no—
78C31×C22⋊C8—42no—
79C31×#95—22no—
80C24×C31—22no—
81C24×C31—22no—
82C24×C31C22⋊C411yescharacteristic
83C24×C31C2×D411yescharacteristic
84#41×C31—44no—
85#41×C31—48no—
86#41×C31—48no—
87#41×C31—44no—
88C2×Q8×C31—22no—
89C2×D4×C31—22no—
90C2×D4×C31—22no—
91C2×D4×C31—24no—
92C2×D4×C31—22no—
93C2×D4×C31—24no—
94C2×D4×C31—24no—
95C2×D4×C31—22no—
96C2×D4×C31—22no—
97C2×D4×C31—22no—
98C2×D4×C31—42no—
99C2×D4×C31—42no—
100C2×D4×C31—48no—
101C2×D4×C31—48no—
102C2×D4×C31—44no—
103C2×D4×C31—44no—
104C2×D4×C31—42no—
105C2×D4×C31—42no—
106C2×D4×C31—42no—
107C2×D4×C31—42no—
108C2×D4×C31—81no—
109C2×D4×C31—81no—
110C2×D4×C31C22⋊C414yes—
111C2×D4×C31D812yes—
112C2×D4×C31SD1612yes—
113C22×C4×C31—22no—
114C22×C4×C31—24no—
115C22×C4×C31—22no—
116C22×C4×C31—21no—
117C22×C4×C31—21no—
118C22×C4×C31—41no—
119C22×C4×C31—41no—
120C22×C4×C31—41no—
121C22×C4×C31—41no—
122C22×C4×C31—42no—
123C22×C4×C31C22⋊C411yescharacteristic
124C22×C4×C31C22⋊C411yescharacteristic
125C22×C4×C31C22⋊C411yescharacteristic
126C22×C4×C31C22×C411yescharacteristic
127C22×C4×C31C2×D412yes—
128C22×C4×C31C2×D411yescharacteristic
129C22×C4×C31C2×D412yes—
130C2×C8×C31—22no—
131C2×C8×C31—24no—
132C2×C8×C31—42no—
133C2×C8×C31—41no—
134C2×C8×C31—41no—
135C2×C8×C31—41no—
136C2×C8×C31—41no—
137C2×C8×C31—41no—
138C4⋊C4×C31—22no—
139C4⋊C4×C31—22no—
140C4⋊C4×C31—22no—
141C4⋊C4×C31—22no—
142C4⋊C4×C31—42no—
143C4⋊C4×C31—42no—
144C4⋊C4×C31C22⋊C414yes—
145C22⋊C4×C31—24no—
146C22⋊C4×C31—24no—
147C22⋊C4×C31—22no—
148C22⋊C4×C31—24no—
149C22⋊C4×C31—22no—
150C22⋊C4×C31—24no—
151C22⋊C4×C31—42no—
152C22⋊C4×C31—42no—
153C42×C31—21no—
154C42×C31—21no—
155#8350C3111yesmaximal, characteristic, direct product factor, Sylow
156C23×C31—21no—
157C23×C31—21no—
158C23×C31—24no—
159C23×C31—41no—
160C23×C31—41no—
161C23×C31—41no—
162C23×C31—41no—
163C23×C31—44no—
164C23×C31—42no—
165C23×C31—42no—
166C23×C31—82no—
167C23×C31—82no—
168C23×C31—82no—
169C23×C31—82no—
170C23×C31#10212yescomplemented
171C23×C31C2×C22⋊C411yescharacteristic
172C23×C31#12012yes—
173C23×C31C2×D811yescharacteristic
174C23×C31C2×SD1611yescharacteristic
175C23×C31AGL(1,ℤ/8)12yes—
176Q8×C31—44no—
177D4×C31—24no—
178D4×C31—24no—
179D4×C31—44no—
180D4×C31—44no—
181D4×C31—48no—
182D4×C31—44no—
183D4×C31—44no—
184D4×C31—44no—
185D4×C31—44no—
186D4×C31—42no—
187D4×C31—42no—
188D4×C31—82no—
189D4×C31—82no—
190C2×C4×C31—21no—
191C2×C4×C31—21no—
192C2×C4×C31—22no—
193C2×C4×C31—21no—
194C2×C4×C31—22no—
195C2×C4×C31—21no—
196C2×C4×C31—21no—
197C2×C4×C31—21no—
198C2×C4×C31—24no—
199C2×C4×C31—41no—
200C2×C4×C31—42no—
201C2×C4×C31—48no—
202C2×C4×C31—44no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—41no—
206C2×C4×C31—41no—
207C2×C4×C31—41no—
208C2×C4×C31—41no—
209C2×C4×C31—81no—
210C2×C4×C31—82no—
211C2×C4×C31—82no—
212C2×C4×C31—82no—
213C2×C4×C31#10212yescomplemented
214C2×C4×C31C2×C22⋊C412yes—
215C2×C4×C31#12011yescharacteristic
216C2×C4×C31#12011yescharacteristic
217C8×C31—42no—
218C8×C31—81no—
219#3496C2×C3111yescharacteristic
220#1893C2×C3112yescomplemented
221#1869C2×C3111yescharacteristic, complemented
222#1799C2×C3111yescharacteristic, complemented
223#1519C2×C3112yescomplemented
224C22×C31—21no—
225C22×C31—22no—
226C22×C31—21no—
227C22×C31—22no—
228C22×C31—22no—
229C22×C31—41no—
230C22×C31—41no—
231C22×C31—42no—
232C22×C31—42no—
233C22×C31—41no—
234C22×C31—41no—
235C22×C31—44no—
236C22×C31—44no—
237C22×C31—44no—
238C22×C31—81no—
239C22×C31—162no—
240C22×C31—162no—
241C22×C31—164no—
242C22×C31#37911yescharacteristic
243C22×C31C2×#10211yescharacteristic
244C22×C31#41811yescharacteristic
245C22×C31#44712yes—
246C22×C31#45012yes—
247C4×C31—22no—
248C4×C31—21no—
249C4×C31—22no—
250C4×C31—41no—
251C4×C31—44no—
252C4×C31—41no—
253C4×C31—162no—
254C4×C31B(4,𝔽2)11yescharacteristic
255C4×C31#45811yescharacteristic
256C2×H(5,𝔽2)—21no—
257C23×C8C22×C3111yescharacteristic, complemented
258#547—22no—
259#546—24no—
260D42—22no—
261#537C4×C3112yescomplemented
262#534—21no—
263#534C4×C3112yescomplemented
264#532—21no—
265C2×#121—21no—
266C2×#121C22×C3112yes—
267C2×C4×D4C22×C3111yescharacteristic
268C2×#102—22no—
269C2×#99—21no—
270C2×C22⋊C8—21no—
271C2×C22⋊C8C22×C3111yescharacteristic, complemented
272#380C22×C3112yescomplemented
273#342—21no—
274#340—22no—
275#336—21no—
276#327—24no—
277C2×C31—22no—
278C2×C31—21no—
279C2×C31—21no—
280C2×C31—22no—
281C2×C31—42no—
282C2×C31—84no—
283C2×C31#178611yescharacteristic
284C2×C31#179011yescharacteristic
285C2×C31#179411yescharacteristic
286H(5,𝔽2)—44no—
287H(5,𝔽2)—42no—
288H(5,𝔽2)—42no—
289C2×#41—24no—
290C2×#41—22no—
291C22×D4—24no—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—21no—
295C22×D4D4×C3111yescharacteristic
296C22×D4D4×C3112yes—
297C23×C4D4×C3111yescharacteristic
298C23×C4C23×C3111yescharacteristic
299C22×C8—21no—
300C22×C8—22no—
301C22×C8—21no—
302C22×C8—42no—
303C4⋊Q8—21no—
304#127—21no—
305#124—22no—
306#123—24no—
307#123—24no—
308C22⋊Q8—24no—
309#121—22no—
310#121—22no—
311#121—24no—
312#121—22no—
313#121—22no—
314#121—22no—
315#121—22no—
316#121C2×C4×C3114yes—
317#121D4×C3114yes—
318#120—24no—
319#120—24no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4C2×C4×C3111yescharacteristic
327C2×C4⋊C4D4×C3112yes—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4C2×C4×C3111yescharacteristic
332C2×C22⋊C4D4×C3111yescharacteristic
333C2×C42D4×C3111yescharacteristic
334#102—44no—
335#99—42no—
336C22⋊C8—22no—
337C22⋊C8—42no—
338#95—22no—
339C31#835011yescharacteristic, direct product factor, Sylow
340C24—22no—
341C24—22no—
342C24C22⋊C4×C3111yescharacteristic
343C24C2×D4×C3111yescharacteristic
344#41—44no—
345#41—48no—
346#41—48no—
347#41—44no—
348C2×Q8—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—24no—
352C2×D4—22no—
353C2×D4—24no—
354C2×D4—24no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—48no—
361C2×D4—48no—
362C2×D4—44no—
363C2×D4—44no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—81no—
369C2×D4—81no—
370C2×D4C22⋊C4×C3114yes—
371C2×D4D8×C3112yes—
372C2×D4SD16×C3112yes—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—42no—
383C22×C4C22⋊C4×C3111yescharacteristic
384C22×C4C22⋊C4×C3111yescharacteristic
385C22×C4C22⋊C4×C3111yescharacteristic
386C22×C4C22×C4×C3111yescharacteristic
387C22×C4C2×D4×C3112yes—
388C22×C4C2×D4×C3111yescharacteristic
389C22×C4C2×D4×C3112yes—
390C2×C8—22no—
391C2×C8—24no—
392C2×C8—42no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—41no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4C22⋊C4×C3114yes—
405C22⋊C4—24no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—24no—
409C22⋊C4—22no—
410C22⋊C4—24no—
411C22⋊C4—42no—
412C22⋊C4—42no—
413C42—21no—
414C42—21no—
415C23—21no—
416C23—21no—
417C23—24no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—44no—
423C23—42no—
424C23—42no—
425C23—82no—
426C23—82no—
427C23—82no—
428C23—82no—
429C23C31×#10212yescomplemented
430C23C2×C22⋊C4×C3111yescharacteristic
431C23C31×#12012yes—
432C23C2×D8×C3111yescharacteristic
433C23C2×SD16×C3111yescharacteristic
434C23C31×AGL(1,ℤ/8)12yes—
435Q8—44no—
436D4—24no—
437D4—24no—
438D4—44no—
439D4—44no—
440D4—48no—
441D4—44no—
442D4—44no—
443D4—44no—
444D4—44no—
445D4—42no—
446D4—42no—
447D4—82no—
448D4—82no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—48no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—81no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4C31×#10212yescomplemented
473C2×C4C2×C22⋊C4×C3112yes—
474C2×C4C31×#12011yescharacteristic
475C2×C4C31×#12011yescharacteristic
476C8—42no—
477C8—81no—
478C22—21no—
479C22—22no—
480C22—21no—
481C22—22no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—42no—
486C22—42no—
487C22—41no—
488C22—41no—
489C22—44no—
490C22—44no—
491C22—44no—
492C22—81no—
493C22—162no—
494C22—162no—
495C22—164no—
496C22C31×#37911yescharacteristic
497C22C2×C31×#10211yescharacteristic
498C22C31×#41811yescharacteristic
499C22C31×#44712yes—
500C22C31×#45012yes—
501C4—22no—
502C4—21no—
503C4—22no—
504C4—44no—
505C4—41no—
506C4—41no—
507C4—162no—
508C4C31×B(4,𝔽2)11yescharacteristic
509C4C31×#45811yescharacteristic
510C2—22no—
511C2—21no—
512C2—21no—
513C2—22no—
514C2—42no—
515C2—84no—
516C2C31×#178611yescharacteristic
517C2C31×#179011yescharacteristic
518C2C31×#179411yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#3496C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1893C2semidirect
3. C31×#1869C2semidirect
4. C31×#1799C2semidirect
5. C31×#1519C2semidirect
7. C23×C8×C31C22semidirect
11. C31×#537C4semidirect
13. C31×#534C4semidirect
21. C2×C31×C22⋊C8C22semidirect
22. C31×#380C22semidirect
155. #8350C31direct (N × H)
170. C23×C31#102semidirect
213. C2×C4×C31#102semidirect
220. #1893C2×C31semidirect
221. #1869C2×C31semidirect
222. #1799C2×C31semidirect
223. #1519C2×C31semidirect
257. C23×C8C22×C31semidirect
261. #537C4×C31semidirect
263. #534C4×C31semidirect
271. C2×C22⋊C8C22×C31semidirect
272. #380C22×C31semidirect
339. C31#8350direct (N × H)
429. C23C31×#102semidirect
472. C2×C4C31×#102semidirect

Maximal subgroups

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

subgroupindex
C31×#34962
C31×#18932
C31×#18692
C31×#17992
C31×#15192
#835031