Finite Group Databasebeta

← C31×#8486 #21465245

Subgroups — C31×#8486 #21465245

Order 7936.

686 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3559C211yesmaximal, characteristic
2C31×#1998C211yesmaximal, characteristic, complemented
3C31×#1557C211yesmaximal, characteristic, complemented
4C31×#1529C211yesmaximal, characteristic, complemented
5C31×#1495C211yesmaximal, characteristic, complemented
6C31×#1484C211yesmaximal, characteristic, complemented
7C31×#1470C211yesmaximal, characteristic, complemented
8C31×#563—21no—
9C31×#562—21no—
10C31×#554—21no—
11C31×#553—21no—
12C31×#553—21no—
13C31×#547—22no—
14C31×#547—21no—
15C31×#544—21no—
16C31×#540—21no—
17C31×#539—22no—
18C31×#539C412yes—
19C31×#537C412yes—
20C31×#532C2211yescharacteristic
21C31×#529C2211yescharacteristic
22C2×C31×#125C2211yescharacteristic
23C31×#432C2211yescharacteristic
24C31×#431C2211yescharacteristic
25C31×#423C2211yescharacteristic
26C4×M16×C31C2211yescharacteristic
27C31×#343—21no—
28C31×#343—21no—
29C31×#332—21no—
30C31×#331—21no—
31C31×#330—21no—
32C31×#329—21no—
33C31×Q8⋊C8—21no—
34C31×D4⋊C8—22no—
35C31×D4⋊C8—21no—
36C31×#324—22no—
37C2×#41×C31—22no—
38C2×#41×C31—21no—
39C2×M16×C31—21no—
40C2×M16×C31—21no—
41C31×C4⋊Q8—21no—
42C31×C4⋊Q8—22no—
43C31×C4⋊Q8D411yescharacteristic
44C31×#127D411yescharacteristic
45C31×#126—22no—
46C31×#126—22no—
47C31×#126—21no—
48C31×#125—21no—
49C31×#125—22no—
50C31×#125—21no—
51C31×#125—21no—
52C31×#125—21no—
53C31×#125—21no—
54C31×#125D411yescharacteristic
55C31×#124—21no—
56C31×#124D411yescharacteristic
57C31×#123—22no—
58C31×#123—22no—
59C31×#123—22no—
60C31×#123—22no—
61C31×#123—22no—
62C31×#123—22no—
63C31×#123—21no—
64C31×C22⋊Q8—22no—
65C31×C22⋊Q8—22no—
66C31×C22⋊Q8—22no—
67C31×C22⋊Q8—22no—
68C31×C22⋊Q8—22no—
69C31×C22⋊Q8—22no—
70C31×C22⋊Q8C2×C411yescharacteristic
71C31×#121—21no—
72C31×#121—22no—
73C31×#121—21no—
74C31×#121—22no—
75C31×#121—22no—
76C31×#121—22no—
77C31×#121—21no—
78C31×#121C2×C411yescharacteristic
79C31×#121C2×C412yes—
80C4×Q8×C31D411yescharacteristic
81C4×D4×C31—22no—
82C4×D4×C31—21no—
83C4×D4×C31—21no—
84C4×D4×C31—22no—
85C4×D4×C31—21no—
86C4×D4×C31—21no—
87C4×D4×C31D411yescharacteristic
88C4×D4×C31D412yes—
89C31×#117—21no—
90C31×#117—21no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31C2×C412yes—
94C2×C4⋊C4×C31D412yes—
95C2×C4⋊C4×C31D411yescharacteristic
96C2×C4⋊C4×C31D411yescharacteristic
97C2×C42×C31C2311yescharacteristic
98C31×C4⋊C8—21no—
99C31×C4⋊C8—21no—
100C31×C4⋊C8—21no—
101C31×C4⋊C8—21no—
102C31×C22⋊C8—21no—
103C31×C22⋊C8—21no—
104C31×#97—21no—
105C31×#97—21no—
106C4×C8×C31—21no—
107C4×C8×C31—21no—
108#41×C31—82no—
109#41×C31—84no—
110C2×Q8×C31—22no—
111C2×Q8×C31—21no—
112C2×Q8×C31C22⋊C411yescharacteristic
113C2×D4×C31—22no—
114C2×D4×C31—21no—
115C2×D4×C31—22no—
116C2×D4×C31—22no—
117C2×D4×C31—21no—
118C2×D4×C31—21no—
119C2×D4×C31C22⋊C411yescharacteristic
120C2×D4×C31C22⋊C412yes—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—21no—
125C22×C4×C31—22no—
126C22×C4×C31C22⋊C412yes—
127C22×C4×C31C22⋊C412yes—
128C22×C4×C31C22×C411yescharacteristic
129C22×C4×C31C2×D411yescharacteristic
130C22×C4×C31C2×D411yescharacteristic
131M16×C31—22no—
132M16×C31—41no—
133M16×C31—42no—
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—22no—
143C4⋊C4×C31—22no—
144C4⋊C4×C31—21no—
145C4⋊C4×C31—21no—
146C4⋊C4×C31—21no—
147C4⋊C4×C31—22no—
148C4⋊C4×C31—21no—
149C4⋊C4×C31—21no—
150C4⋊C4×C31—22no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—21no—
153C4⋊C4×C31—21no—
154C4⋊C4×C31—21no—
155C4⋊C4×C31C22⋊C412yes—
156C4⋊C4×C31C22⋊C411yescharacteristic
157C4⋊C4×C31C22⋊C411yescharacteristic
158C22⋊C4×C31—22no—
159C22⋊C4×C31—22no—
160C22⋊C4×C31—22no—
161C22⋊C4×C31—22no—
162C22⋊C4×C31—22no—
163C22⋊C4×C31—21no—
164C22⋊C4×C31—21no—
165C22⋊C4×C31—22no—
166C22⋊C4×C31—21no—
167C22⋊C4×C31—21no—
168C22⋊C4×C31—21no—
169C22⋊C4×C31—22no—
170C42×C31—22no—
171C42×C31—21no—
172C42×C31C2×D411yescharacteristic
173C42×C31C2×D411yescharacteristic
174C42×C31C2×D411yescharacteristic
175C42×C31C2×D411yescharacteristic
176#8486C3111yesmaximal, characteristic, direct product factor, Sylow
177C23×C31—21no—
178C23×C31—22no—
179C23×C31C2×C22⋊C411yescharacteristic
180Q8×C31—41no—
181Q8×C31—81no—
182Q8×C31—82no—
183D4×C31—42no—
184D4×C31—41no—
185D4×C31—44no—
186D4×C31—42no—
187D4×C31—41no—
188D4×C31—41no—
189D4×C31—81no—
190D4×C31—82no—
191D4×C31—82no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—21no—
195C2×C4×C31—21no—
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—21no—
199C2×C4×C31—22no—
200C2×C4×C31—41no—
201C2×C4×C31—41no—
202C2×C4×C31—41no—
203C2×C4×C31—41no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—82no—
207C2×C4×C31—82no—
208C2×C4×C31—82no—
209C2×C4×C31—82no—
210C2×C4×C31C2×C22⋊C411yescharacteristic
211C2×C4×C31C2×C22⋊C411yescharacteristic
212C2×C4×C31#12011yescharacteristic
213C2×C4×C31#12011yescharacteristic
214C2×C4×C31#12011yescharacteristic
215C2×C4×C31#12011yescharacteristic
216C8×C31—42no—
217C8×C31—81no—
218C8×C31—81no—
219C8×C31—81no—
220#3559C2×C3111yescharacteristic
221#1998C2×C3111yescharacteristic, complemented
222#1557C2×C3111yescharacteristic, complemented
223#1529C2×C3111yescharacteristic, complemented
224#1495C2×C3111yescharacteristic, complemented
225#1484C2×C3111yescharacteristic, complemented
226#1470C2×C3111yescharacteristic, complemented
227C22×C31—21no—
228C22×C31—21no—
229C22×C31—21no—
230C22×C31—41no—
231C22×C31—42no—
232C22×C31—42no—
233C22×C31—41no—
234C22×C31—42no—
235C22×C31—41no—
236C22×C31#37911yescharacteristic
237C4×C31—21no—
238C4×C31—21no—
239C4×C31—21no—
240C4×C31—21no—
241C4×C31—21no—
242C4×C31—41no—
243C4×C31—42no—
244C4×C31—42no—
245C4×C31—41no—
246C4×C31—42no—
247C4×C31—41no—
248C4×C31#45411yescharacteristic
249C4×C31#45611yescharacteristic
250#563—21no—
251#562—21no—
252#554—21no—
253#553—21no—
254#553—21no—
255#547—22no—
256#547—21no—
257#544—21no—
258#540—21no—
259#539—22no—
260#539C4×C3112yes—
261#537C4×C3112yes—
262#532C22×C3111yescharacteristic
263#529C22×C3111yescharacteristic
264C2×#125C22×C3111yescharacteristic
265#432C22×C3111yescharacteristic
266#431C22×C3111yescharacteristic
267#423C22×C3111yescharacteristic
268C4×M16C22×C3111yescharacteristic
269#343—21no—
270#343—21no—
271#332—21no—
272#331—21no—
273#330—21no—
274#329—21no—
275Q8⋊C8—21no—
276D4⋊C8—22no—
277D4⋊C8—21no—
278#324—22no—
279C2×C31—41no—
280C2×C31—81no—
281C2×C31—82no—
282C2×C31#179111yescharacteristic
283C2×C31#179311yescharacteristic
284C2×C31#179511yescharacteristic
285C2×#41—22no—
286C2×#41—21no—
287C2×M16—21no—
288C2×M16—21no—
289C4⋊Q8—21no—
290C4⋊Q8—22no—
291C4⋊Q8D4×C3111yescharacteristic
292#127D4×C3111yescharacteristic
293#126—22no—
294#126—22no—
295#126—21no—
296#125—21no—
297#125—22no—
298#125—21no—
299#125—21no—
300#125—21no—
301#125—21no—
302#125D4×C3111yescharacteristic
303#124—21no—
304#124D4×C3111yescharacteristic
305#123—22no—
306#123—22no—
307#123—22no—
308#123—22no—
309#123—22no—
310#123—22no—
311#123—21no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8C2×C4×C3111yescharacteristic
319#121—21no—
320#121—22no—
321#121—21no—
322#121—22no—
323#121—22no—
324#121—22no—
325#121—21no—
326#121C2×C4×C3111yescharacteristic
327#121C2×C4×C3112yes—
328C4×Q8D4×C3111yescharacteristic
329C4×D4—22no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—22no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4D4×C3111yescharacteristic
336C4×D4D4×C3112yes—
337#117—21no—
338#117—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4C2×C4×C3112yes—
342C2×C4⋊C4D4×C3112yes—
343C2×C4⋊C4D4×C3111yescharacteristic
344C2×C4⋊C4D4×C3111yescharacteristic
345C2×C42C23×C3111yescharacteristic
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352#97—21no—
353#97—21no—
354C4×C8—21no—
355C4×C8—21no—
356C31#848611yescharacteristic, direct product factor, Sylow
357#41—82no—
358#41—84no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8C22⋊C4×C3111yescharacteristic
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4C22⋊C4×C3111yescharacteristic
369C2×D4C22⋊C4×C3112yes—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4C22⋊C4×C3112yes—
376C22×C4C22⋊C4×C3112yes—
377C22×C4C22×C4×C3111yescharacteristic
378C22×C4C2×D4×C3111yescharacteristic
379C22×C4C2×D4×C3111yescharacteristic
380M16—22no—
381M16—41no—
382M16—42no—
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—41no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4C22⋊C4×C3112yes—
405C4⋊C4C22⋊C4×C3111yescharacteristic
406C4⋊C4C22⋊C4×C3111yescharacteristic
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—22no—
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—22no—
419C42—22no—
420C42—21no—
421C42C2×D4×C3111yescharacteristic
422C42C2×D4×C3111yescharacteristic
423C42C2×D4×C3111yescharacteristic
424C42C2×D4×C3111yescharacteristic
425C23—22no—
426C23—21no—
427C23C2×C22⋊C4×C3111yescharacteristic
428Q8—41no—
429Q8—81no—
430Q8—82no—
431D4—42no—
432D4—41no—
433D4—44no—
434D4—42no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4—82no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4C2×C22⋊C4×C3111yescharacteristic
459C2×C4C2×C22⋊C4×C3111yescharacteristic
460C2×C4C31×#12011yescharacteristic
461C2×C4C31×#12011yescharacteristic
462C2×C4C31×#12011yescharacteristic
463C2×C4C31×#12011yescharacteristic
464C8—42no—
465C8—81no—
466C8—81no—
467C8—81no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—42no—
472C22—41no—
473C22—42no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22C31×#37911yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—42no—
485C4—41no—
486C4—42no—
487C4—41no—
488C4—41no—
489C4C31×#45411yescharacteristic
490C4C31×#45611yescharacteristic
491C2—41no—
492C2—82no—
493C2—81no—
494C2C31×#179111yescharacteristic
495C2C31×#179311yescharacteristic
496C2C31×#179511yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3559C2
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
2. C31×#1998C2semidirect
3. C31×#1557C2semidirect
4. C31×#1529C2semidirect
5. C31×#1495C2semidirect
6. C31×#1484C2semidirect
7. C31×#1470C2semidirect
176. #8486C31direct (N × H)
221. #1998C2×C31semidirect
222. #1557C2×C31semidirect
223. #1529C2×C31semidirect
224. #1495C2×C31semidirect
225. #1484C2×C31semidirect
226. #1470C2×C31semidirect
356. C31#8486direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35592
C31×#19982
C31×#15572
C31×#15292
C31×#14952
C31×#14842
C31×#14702
#848631