Finite Group Databasebeta

← C31×#8377 #21465136

Subgroups — C31×#8377 #21465136

Order 7936.

1060 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#548C211yesmaximal, characteristic
2C31×#1799C211yesmaximal, characteristic, complemented
3C31×#1787C212yesmaximal, complemented
4C31×#1519C212yesmaximal, complemented
5C31×#1459C211yesmaximal, characteristic, complemented
6C22×#41×C31C411yescharacteristic, complemented
7C23×Q8×C31C2211yescharacteristic
8C31×#548—24no—
9C31×#548—24no—
10C2×C31×#124—21no—
11C2×C31×#124C411yescharacteristic, complemented
12C2×C31×C22⋊Q8—21no—
13C2×C31×C22⋊Q8C411yescharacteristic, complemented
14C2×C31×#121—21no—
15C2×C31×#121C2211yescharacteristic
16C2×C4×Q8×C31C411yescharacteristic, complemented
17C2×C4×D4×C31—21no—
18C2×C4×D4×C31C2211yescharacteristic
19C2×C31×#103—24no—
20C2×C31×#99—21no—
21C2×C31×C22⋊C8C2212yes—
22C31×#380C2212yes—
23C31×#342—21no—
24C31×#327—24no—
25C31×#324—21no—
26C31×#323—21no—
27C2×#41×C31—22no—
28C2×#41×C31—22no—
29C2×#41×C31—44no—
30C22×Q8×C31—21no—
31C22×Q8×C31—22no—
32C22×Q8×C31—44no—
33C22×Q8×C31C2×C411yescharacteristic
34C22×Q8×C31C2×C411yescharacteristic
35C22×Q8×C31D414yes—
36C22×D4×C31—21no—
37C22×D4×C31—21no—
38C22×D4×C31C2×C411yescharacteristic
39C22×D4×C31D411yescharacteristic
40C23×C4×C31—21no—
41C23×C4×C31—21no—
42C23×C4×C31C2×C411yescharacteristic
43C23×C4×C31C2311yescharacteristic
44C22×C8×C31—22no—
45C31×#124—28no—
46C31×#124—22no—
47C31×#124—22no—
48C31×C22⋊Q8—28no—
49C31×C22⋊Q8—22no—
50C31×C22⋊Q8—22no—
51C31×#121—28no—
52C31×#121—22no—
53C31×#121D414yes—
54C4×Q8×C31—22no—
55C4×Q8×C31—22no—
56C4×D4×C31—28no—
57C4×D4×C31—22no—
58C4×D4×C31—22no—
59C2×C4⋊C4×C31—21no—
60C2×C4⋊C4×C31—21no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31C2×C411yescharacteristic
63C2×C4⋊C4×C31D411yescharacteristic
64C2×C22⋊C4×C31—21no—
65C2×C22⋊C4×C31—21no—
66C2×C22⋊C4×C31—21no—
67C2×C22⋊C4×C31—21no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31D411yescharacteristic
70C2×C22⋊C4×C31D411yescharacteristic
71C2×C42×C31—21no—
72C2×C42×C31C2×C411yescharacteristic
73C31×#103—48no—
74C31×#99—42no—
75C31×C22⋊C8—22no—
76C31×C22⋊C8—22no—
77C31×#95—22no—
78C24×C31—21no—
79C24×C31C22⋊C411yescharacteristic
80C24×C31C2×D411yescharacteristic
81#41×C31—48no—
82#41×C31—44no—
83#41×C31—44no—
84C2×Q8×C31—24no—
85C2×Q8×C31—21no—
86C2×Q8×C31—21no—
87C2×Q8×C31—24no—
88C2×Q8×C31—28no—
89C2×Q8×C31—42no—
90C2×Q8×C31—44no—
91C2×Q8×C31—44no—
92C2×Q8×C31—48no—
93C2×Q8×C31C22⋊C412yes—
94C2×Q8×C31C22⋊C412yes—
95C2×D4×C31—24no—
96C2×D4×C31—22no—
97C2×D4×C31—24no—
98C2×D4×C31—22no—
99C2×D4×C31—21no—
100C2×D4×C31—21no—
101C2×D4×C31—21no—
102C2×D4×C31—44no—
103C2×D4×C31—42no—
104C2×D4×C31—42no—
105C2×D4×C31—41no—
106C2×D4×C31—41no—
107C2×D4×C31C22⋊C412yes—
108C22×C4×C31—21no—
109C22×C4×C31—24no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—24no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—42no—
116C22×C4×C31—44no—
117C22×C4×C31—44no—
118C22×C4×C31—42no—
119C22×C4×C31—42no—
120C22×C4×C31C22⋊C411yescharacteristic
121C22×C4×C31C22⋊C411yescharacteristic
122C22×C4×C31C22⋊C411yescharacteristic
123C22×C4×C31C22×C411yescharacteristic
124C22×C4×C31C2×D412yes—
125C22×C4×C31C2×D412yes—
126C22×C4×C31C2×D411yescharacteristic
127C2×C8×C31—44no—
128C2×C8×C31—42no—
129C4⋊C4×C31—24no—
130C4⋊C4×C31—24no—
131C4⋊C4×C31—21no—
132C4⋊C4×C31—22no—
133C4⋊C4×C31—44no—
134C4⋊C4×C31C22⋊C412yes—
135C22⋊C4×C31—24no—
136C22⋊C4×C31—24no—
137C22⋊C4×C31—24no—
138C22⋊C4×C31—22no—
139C22⋊C4×C31—24no—
140C22⋊C4×C31—22no—
141C22⋊C4×C31—42no—
142C22⋊C4×C31—42no—
143C42×C31—24no—
144C42×C31—21no—
145C42×C31—21no—
146#8377C3111yesmaximal, characteristic, direct product factor, Sylow
147C23×C31—21no—
148C23×C31—22no—
149C23×C31—21no—
150C23×C31—21no—
151C23×C31—41no—
152C23×C31—41no—
153C23×C31—42no—
154C23×C31—42no—
155C23×C31—41no—
156C23×C31—41no—
157C23×C31—41no—
158C23×C31—41no—
159C23×C31C2×C22⋊C411yescharacteristic
160C23×C31#12012yes—
161C23×C31#13512yes—
162C23×C31AGL(1,ℤ/8)11yescharacteristic
163C23×C31#13711yescharacteristic
164Q8×C31—24no—
165Q8×C31—22no—
166Q8×C31—24no—
167Q8×C31—48no—
168Q8×C31—42no—
169Q8×C31#9914yescomplemented
170D4×C31—42no—
171D4×C31—48no—
172D4×C31—42no—
173D4×C31—44no—
174D4×C31—42no—
175D4×C31—44no—
176D4×C31—42no—
177C2×C4×C31—24no—
178C2×C4×C31—22no—
179C2×C4×C31—24no—
180C2×C4×C31—22no—
181C2×C4×C31—21no—
182C2×C4×C31—21no—
183C2×C4×C31—22no—
184C2×C4×C31—22no—
185C2×C4×C31—21no—
186C2×C4×C31—21no—
187C2×C4×C31—21no—
188C2×C4×C31—41no—
189C2×C4×C31—42no—
190C2×C4×C31—48no—
191C2×C4×C31—48no—
192C2×C4×C31—42no—
193C2×C4×C31—42no—
194C2×C4×C31—41no—
195C2×C4×C31—41no—
196C2×C4×C31—42no—
197C2×C4×C31—41no—
198C2×C4×C31—41no—
199C2×C4×C31—82no—
200C2×C4×C31—82no—
201C2×C4×C31—82no—
202C2×C4×C31C2×C22⋊C411yescharacteristic
203C2×C4×C31C2×C22⋊C411yescharacteristic
204C2×C4×C31#12012yes—
205C8×C31—82no—
206C2×#548C2×C3111yescharacteristic
207#1799C2×C3111yescharacteristic, complemented
208#1787C2×C3112yescomplemented
209#1519C2×C3112yescomplemented
210#1459C2×C3111yescharacteristic, complemented
211C22×C31—21no—
212C22×C31—22no—
213C22×C31—21no—
214C22×C31—22no—
215C22×C31—42no—
216C22×C31—41no—
217C22×C31—41no—
218C22×C31—41no—
219C22×C31—42no—
220C22×C31—41no—
221C22×C31—42no—
222C22×C31—41no—
223C22×C31—42no—
224C22×C31—81no—
225C22×C31—81no—
226C22×C31—82no—
227C22×C31—82no—
228C22×C31#37911yescharacteristic
229C22×C31#41611yescharacteristic
230C22×C31#41711yescharacteristic
231C22×C31#44912yes—
232C22×C31#45212yes—
233C4×C31—22no—
234C4×C31—24no—
235C4×C31—21no—
236C4×C31—41no—
237C4×C31—41no—
238C4×C31—42no—
239C4×C31—41no—
240C4×C31—42no—
241C4×C31—162no—
242C4×C31C2×#9912yes—
243C22×#41C4×C3111yescharacteristic, complemented
244C23×Q8C22×C3111yescharacteristic
245#548—24no—
246#548—24no—
247C2×#124—21no—
248C2×#124C4×C3111yescharacteristic, complemented
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8C4×C3111yescharacteristic, complemented
251C2×#121—21no—
252C2×#121C22×C3111yescharacteristic
253C2×C4×Q8C4×C3111yescharacteristic, complemented
254C2×C4×D4—21no—
255C2×C4×D4C22×C3111yescharacteristic
256C2×#103—24no—
257C2×#99—21no—
258C2×C22⋊C8C22×C3112yes—
259#380C22×C3112yes—
260#342—21no—
261#327—24no—
262#324—21no—
263#323—21no—
264C2×C31—22no—
265C2×C31—21no—
266C2×C31—21no—
267C2×C31—22no—
268C2×C31—81no—
269C2×C31—82no—
270C2×C31#178111yescharacteristic
271C2×C31#178811yescharacteristic
272C2×C31#179611yescharacteristic
273C2×#41—22no—
274C2×#41—22no—
275C2×#41—44no—
276C22×Q8—21no—
277C22×Q8—22no—
278C22×Q8—44no—
279C22×Q8C2×C4×C3111yescharacteristic
280C22×Q8C2×C4×C3111yescharacteristic
281C22×Q8D4×C3114yes—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4C2×C4×C3111yescharacteristic
285C22×D4D4×C3111yescharacteristic
286C23×C4—21no—
287C23×C4—21no—
288C23×C4C2×C4×C3111yescharacteristic
289C23×C4C23×C3111yescharacteristic
290C22×C8—22no—
291#124—28no—
292#124—22no—
293#124—22no—
294C22⋊Q8—28no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297#121—28no—
298#121—22no—
299#121D4×C3114yes—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×D4—28no—
303C4×D4—22no—
304C4×D4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4C2×C4×C3111yescharacteristic
309C2×C4⋊C4D4×C3111yescharacteristic
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4D4×C3111yescharacteristic
316C2×C22⋊C4D4×C3111yescharacteristic
317C2×C42—21no—
318C2×C42C2×C4×C3111yescharacteristic
319#103—48no—
320#99—42no—
321C22⋊C8—22no—
322C22⋊C8—22no—
323#95—22no—
324C31#837711yescharacteristic, direct product factor, Sylow
325C24—21no—
326C24C22⋊C4×C3111yescharacteristic
327C24C2×D4×C3111yescharacteristic
328#41—48no—
329#41—44no—
330#41—44no—
331C2×Q8—24no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—24no—
335C2×Q8—28no—
336C2×Q8—42no—
337C2×Q8—44no—
338C2×Q8—44no—
339C2×Q8—48no—
340C2×Q8C22⋊C4×C3112yes—
341C2×Q8C22⋊C4×C3112yes—
342C2×D4—24no—
343C2×D4—22no—
344C2×D4—24no—
345C2×D4—22no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—44no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4C22⋊C4×C3112yes—
355C22×C4—21no—
356C22×C4—24no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—24no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—42no—
363C22×C4—44no—
364C22×C4—44no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4C22⋊C4×C3111yescharacteristic
368C22×C4C22⋊C4×C3111yescharacteristic
369C22×C4C22⋊C4×C3111yescharacteristic
370C22×C4C22×C4×C3111yescharacteristic
371C22×C4C2×D4×C3112yes—
372C22×C4C2×D4×C3112yes—
373C22×C4C2×D4×C3111yescharacteristic
374C2×C8—44no—
375C2×C8—42no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—44no—
381C4⋊C4C22⋊C4×C3112yes—
382C22⋊C4—24no—
383C22⋊C4—24no—
384C22⋊C4—24no—
385C22⋊C4—22no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C22⋊C4—42no—
389C22⋊C4—42no—
390C42—24no—
391C42—21no—
392C42—21no—
393C23—21no—
394C23—22no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23C2×C22⋊C4×C3111yescharacteristic
406C23C31×#12012yes—
407C23C31×#13512yes—
408C23C31×AGL(1,ℤ/8)11yescharacteristic
409C23C31×#13711yescharacteristic
410Q8—24no—
411Q8—22no—
412Q8—24no—
413Q8—48no—
414Q8—42no—
415Q8C31×#9914yescomplemented
416D4—42no—
417D4—48no—
418D4—42no—
419D4—44no—
420D4—42no—
421D4—44no—
422D4—42no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—48no—
437C2×C4—48no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4C2×C22⋊C4×C3111yescharacteristic
449C2×C4C2×C22⋊C4×C3111yescharacteristic
450C2×C4C31×#12012yes—
451C8—82no—
452C22—21no—
453C22—22no—
454C22—21no—
455C22—22no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—42no—
460C22—41no—
461C22—41no—
462C22—42no—
463C22—41no—
464C22—42no—
465C22—81no—
466C22—81no—
467C22—82no—
468C22—82no—
469C22C31×#37911yescharacteristic
470C22C31×#41611yescharacteristic
471C22C31×#41711yescharacteristic
472C22C31×#44912yes—
473C22C31×#45212yes—
474C4—22no—
475C4—24no—
476C4—21no—
477C4—41no—
478C4—41no—
479C4—42no—
480C4—41no—
481C4—42no—
482C4—162no—
483C4C2×C31×#9912yes—
484C2—22no—
485C2—21no—
486C2—21no—
487C2—22no—
488C2—82no—
489C2—81no—
490C2C31×#178111yescharacteristic
491C2C31×#178811yescharacteristic
492C2C31×#179611yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#548C2
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×#1799C2semidirect
3. C31×#1787C2semidirect
4. C31×#1519C2semidirect
5. C31×#1459C2semidirect
6. C22×#41×C31C4semidirect
11. C2×C31×#124C4semidirect
13. C2×C31×C22⋊Q8C4semidirect
16. C2×C4×Q8×C31C4semidirect
146. #8377C31direct (N × H)
169. Q8×C31#99semidirect
207. #1799C2×C31semidirect
208. #1787C2×C31semidirect
209. #1519C2×C31semidirect
210. #1459C2×C31semidirect
243. C22×#41C4×C31semidirect
248. C2×#124C4×C31semidirect
250. C2×C22⋊Q8C4×C31semidirect
253. C2×C4×Q8C4×C31semidirect
324. C31#8377direct (N × H)
415. Q8C31×#99semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5482
C31×#17992
C31×#17872
C31×#15192
C31×#14592
#837731