Finite Group Databasebeta

← C31×#19076 #21475835

Subgroups — C31×#19076 #21475835

Order 7936.

1000 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3548C211yesmaximal, characteristic
2C31×#3165C211yesmaximal, characteristic, complemented
3C31×#3152C211yesmaximal, characteristic, complemented
4C31×#3141C211yesmaximal, characteristic, complemented
5C31×#1661C218yesmaximal, complemented
6C31×#1526C211yesmaximal, characteristic, complemented
7C31×#1525C211yesmaximal, characteristic, complemented
8C31×#1525C211yesmaximal, characteristic, complemented
9C2×C31×#137—22no—
10C31×#562C2214yes—
11C31×#554—21no—
12C31×#554—21no—
13C31×#550—21no—
14C31×#550—21no—
15C31×#547—21no—
16C31×#547—21no—
17C31×#540—22no—
18C31×#537—22no—
19C31×#537—22no—
20C31×#533C2211yescharacteristic
21C31×#532C2211yescharacteristic
22C31×#532C2211yescharacteristic
23C2×C31×C4⋊Q8C2211yescharacteristic
24C31×#501C2214yes—
25C31×#500—21no—
26C31×#498—21no—
27C31×#497C2214yes—
28C31×#494—21no—
29C31×#492—21no—
30C31×#489C2214yes—
31C31×#487—21no—
32C31×#486—21no—
33C31×#428—22no—
34C31×#417—22no—
35C4×M16×C31C2211yescharacteristic
36C4×M16×C31C2211yescharacteristic
37C4×M16×C31C2211yescharacteristic
38C31×#330C2214yes—
39C31×#329C2214yes—
40C31×#329C2214yes—
41C2×#41×C31—22no—
42C2×#41×C31—22no—
43C2×#41×C31D412yes—
44C2×#41×C31D412yes—
45C22×Q8×C31—21no—
46C31×#137—48no—
47C2×Q16×C31—24no—
48C2×SD16×C31—24no—
49C2×M16×C31—21no—
50C2×M16×C31—21no—
51C2×M16×C31—21no—
52C31×C4⋊Q8—21no—
53C31×C4⋊Q8—21no—
54C31×C4⋊Q8—21no—
55C31×C4⋊Q8D411yescharacteristic
56C31×C4⋊Q8D411yescharacteristic
57C31×C4⋊Q8D411yescharacteristic
58C31×C4⋊Q8D411yescharacteristic
59C31×C4⋊Q8C2312yes—
60C31×#127—22no—
61C31×#127D411yescharacteristic
62C31×#127D411yescharacteristic
63C31×#125—22no—
64C31×#125C2312yes—
65C31×#124C2312yes—
66C31×#124C2312yes—
67C31×#123—24no—
68C31×#123—24no—
69C31×C22⋊Q8—22no—
70C31×C22⋊Q8—22no—
71C31×C22⋊Q8—24no—
72C31×C22⋊Q8—24no—
73C31×C22⋊Q8—21no—
74C31×C22⋊Q8—21no—
75C31×#121—24no—
76C31×#121—24no—
77C31×#121—22no—
78C31×#121—22no—
79C31×#121—24no—
80C31×#121—24no—
81C31×#121—21no—
82C31×#121—21no—
83C31×#121—21no—
84C31×#121—21no—
85C4×Q8×C31—21no—
86C4×Q8×C31—21no—
87C4×D4×C31—22no—
88C4×D4×C31—22no—
89C4×D4×C31—21no—
90C4×D4×C31—21no—
91C4×D4×C31—21no—
92C4×D4×C31—21no—
93C31×#117D412yes—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—22no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C42×C31C2311yescharacteristic
99C31×#107—24no—
100C31×#106—24no—
101C31×#103—24no—
102C31×#102—24no—
103C31×#97C2312yes—
104C31×#97C2312yes—
105C31×#97C2312yes—
106C4×C8×C31—21no—
107C4×C8×C31—21no—
108C4×C8×C31—21no—
109#41×C31—44no—
110#41×C31—44no—
111#41×C31—84no—
112#41×C31—84no—
113C2×Q8×C31—21no—
114C2×Q8×C31—21no—
115C2×Q8×C31—22no—
116C2×Q8×C31—44no—
117C2×Q8×C31—41no—
118C2×Q8×C31C2×D412yes—
119C2×Q8×C31C2×D412yes—
120C2×D4×C31—24no—
121C2×D4×C31—24no—
122C2×D4×C31—22no—
123C2×D4×C31—22no—
124C2×D4×C31—21no—
125C2×D4×C31—21no—
126C2×D4×C31—21no—
127C2×D4×C31—21no—
128C2×D4×C31C2×D412yes—
129C2×D4×C31C2×D412yes—
130C22×C4×C31—24no—
131C22×C4×C31—24no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—41no—
135C22×C4×C31C2×D411yescharacteristic
136C22×C4×C31C2×D411yescharacteristic
137C22×C4×C31C2×D411yescharacteristic
138Q16×C31—48no—
139SD16×C31—48no—
140M16×C31—24no—
141M16×C31—24no—
142M16×C31—42no—
143C2×C8×C31—22no—
144C2×C8×C31—22no—
145C2×C8×C31—22no—
146C4⋊C4×C31—24no—
147C4⋊C4×C31—24no—
148C4⋊C4×C31—21no—
149C4⋊C4×C31—21no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—21no—
153C4⋊C4×C31—21no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—41no—
159C4⋊C4×C31—41no—
160C4⋊C4×C31C2×D412yes—
161C4⋊C4×C31C2×D412yes—
162C22⋊C4×C31—24no—
163C22⋊C4×C31—24no—
164C22⋊C4×C31—22no—
165C22⋊C4×C31—22no—
166C22⋊C4×C31—22no—
167C22⋊C4×C31—22no—
168C22⋊C4×C31—22no—
169C42×C31—22no—
170C42×C31C2×D411yescharacteristic
171C42×C31C2×D411yescharacteristic
172C42×C31C2×D411yescharacteristic
173C42×C31C2411yescharacteristic
174#19076C3111yesmaximal, characteristic, direct product factor, Sylow
175C23×C31—22no—
176C23×C31—22no—
177C23×C31#12011yescharacteristic
178Q8×C31—42no—
179Q8×C31—42no—
180Q8×C31—44no—
181Q8×C31—42no—
182Q8×C31—42no—
183Q8×C31—82no—
184D4×C31—42no—
185D4×C31—42no—
186D4×C31—42no—
187D4×C31—42no—
188D4×C31—42no—
189D4×C31—42no—
190D4×C31—82no—
191D4×C31—82no—
192D4×C31—84no—
193D4×C31—84no—
194C2×C4×C31—22no—
195C2×C4×C31—22no—
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—44no—
202C2×C4×C31—44no—
203C2×C4×C31—42no—
204C2×C4×C31—84no—
205C2×C4×C31—84no—
206C2×C4×C31—82no—
207C2×C4×C31#12011yescharacteristic
208C2×C4×C31#12011yescharacteristic
209C2×C4×C31#12011yescharacteristic
210C2×C4×C31C22×D411yescharacteristic
211C2×C4×C31C22×D411yescharacteristic
212C2×C4×C31C22×D411yescharacteristic
213C8×C31—24no—
214C8×C31—24no—
215C8×C31—42no—
216#3548C2×C3111yescharacteristic
217#3165C2×C3111yescharacteristic, complemented
218#3152C2×C3111yescharacteristic, complemented
219#3141C2×C3111yescharacteristic, complemented
220#1661C2×C3118yescomplemented
221#1526C2×C3111yescharacteristic, complemented
222#1525C2×C3111yescharacteristic, complemented
223#1525C2×C3111yescharacteristic, complemented
224C22×C31—21no—
225C22×C31—21no—
226C22×C31—21no—
227C22×C31—42no—
228C22×C31—42no—
229C22×C31—42no—
230C22×C31—42no—
231C22×C31—42no—
232C22×C31—42no—
233C22×C31C2×#12011yescharacteristic
234C4×C31—21no—
235C4×C31—21no—
236C4×C31—21no—
237C4×C31—42no—
238C4×C31—42no—
239C4×C31—42no—
240C4×C31—42no—
241C4×C31—82no—
242C4×C31#45312yes—
243C4×C31#45512yes—
244C4×C31#45612yes—
245C2×#137—22no—
246#562C22×C3114yes—
247#554—21no—
248#554—21no—
249#550—21no—
250#550—21no—
251#547—21no—
252#547—21no—
253#540—22no—
254#537—22no—
255#537—22no—
256#533C22×C3111yescharacteristic
257#532C22×C3111yescharacteristic
258#532C22×C3111yescharacteristic
259C2×C4⋊Q8C22×C3111yescharacteristic
260#501C22×C3114yes—
261#500—21no—
262#498—21no—
263#497C22×C3114yes—
264#494—21no—
265#492—21no—
266#489C22×C3114yes—
267#487—21no—
268#486—21no—
269#428—22no—
270#417—22no—
271C4×M16C22×C3111yescharacteristic
272C4×M16C22×C3111yescharacteristic
273C4×M16C22×C3111yescharacteristic
274#330C22×C3114yes—
275#329C22×C3114yes—
276#329C22×C3114yes—
277C2×C31—41no—
278C2×C31—82no—
279C2×C31—82no—
280C2×C31C2×#45311yescharacteristic
281C2×C31C2×#45511yescharacteristic
282C2×C31C2×#45611yescharacteristic
283C2×#41—22no—
284C2×#41—22no—
285C2×#41D4×C3112yes—
286C2×#41D4×C3112yes—
287C22×Q8—21no—
288#137—48no—
289C2×Q16—24no—
290C2×SD16—24no—
291C2×M16—21no—
292C2×M16—21no—
293C2×M16—21no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8D4×C3111yescharacteristic
298C4⋊Q8D4×C3111yescharacteristic
299C4⋊Q8D4×C3111yescharacteristic
300C4⋊Q8D4×C3111yescharacteristic
301C4⋊Q8C23×C3112yes—
302#127—22no—
303#127D4×C3111yescharacteristic
304#127D4×C3111yescharacteristic
305#125—22no—
306#125C23×C3112yes—
307#124C23×C3112yes—
308#124C23×C3112yes—
309#123—24no—
310#123—24no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317#121—24no—
318#121—24no—
319#121—22no—
320#121—22no—
321#121—24no—
322#121—24no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335#117D4×C3112yes—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C42C23×C3111yescharacteristic
341#107—24no—
342#106—24no—
343#103—24no—
344#102—24no—
345#97C23×C3112yes—
346#97C23×C3112yes—
347#97C23×C3112yes—
348C4×C8—21no—
349C4×C8—21no—
350C4×C8—21no—
351C31#1907611yescharacteristic, direct product factor, Sylow
352#41—44no—
353#41—44no—
354#41—84no—
355#41—84no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—44no—
360C2×Q8—41no—
361C2×Q8C2×D4×C3112yes—
362C2×Q8C2×D4×C3112yes—
363C2×D4—24no—
364C2×D4—24no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4C2×D4×C3112yes—
372C2×D4C2×D4×C3112yes—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—41no—
378C22×C4C2×D4×C3111yescharacteristic
379C22×C4C2×D4×C3111yescharacteristic
380C22×C4C2×D4×C3111yescharacteristic
381Q16—48no—
382SD16—48no—
383M16—24no—
384M16—24no—
385M16—42no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4C2×D4×C3112yes—
404C4⋊C4C2×D4×C3112yes—
405C22⋊C4—24no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C42—22no—
413C42C2×D4×C3111yescharacteristic
414C42C2×D4×C3111yescharacteristic
415C42C2×D4×C3111yescharacteristic
416C42C24×C3111yescharacteristic
417C23—22no—
418C23—22no—
419C23C31×#12011yescharacteristic
420Q8—42no—
421Q8—42no—
422Q8—44no—
423Q8—42no—
424Q8—42no—
425Q8—82no—
426D4—42no—
427D4—42no—
428D4—42no—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—82no—
433D4—82no—
434D4—84no—
435D4—84no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—84no—
447C2×C4—84no—
448C2×C4—82no—
449C2×C4C31×#12011yescharacteristic
450C2×C4C31×#12011yescharacteristic
451C2×C4C31×#12011yescharacteristic
452C2×C4C22×D4×C3111yescharacteristic
453C2×C4C22×D4×C3111yescharacteristic
454C2×C4C22×D4×C3111yescharacteristic
455C8—24no—
456C8—24no—
457C8—42no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22C2×C31×#12011yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—82no—
476C4C31×#45312yes—
477C4C31×#45512yes—
478C4C31×#45612yes—
479C2—41no—
480C2—82no—
481C2—82no—
482C2C2×C31×#45311yescharacteristic
483C2C2×C31×#45511yescharacteristic
484C2C2×C31×#45611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3548C2
LCSG ▷ C42 ▷ 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×#3165C2semidirect
3. C31×#3152C2semidirect
4. C31×#3141C2semidirect
5. C31×#1661C2semidirect
6. C31×#1526C2semidirect
7. C31×#1525C2semidirect
8. C31×#1525C2semidirect
174. #19076C31direct (N × H)
217. #3165C2×C31semidirect
218. #3152C2×C31semidirect
219. #3141C2×C31semidirect
220. #1661C2×C31semidirect
221. #1526C2×C31semidirect
222. #1525C2×C31semidirect
223. #1525C2×C31semidirect
351. C31#19076direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35482
C31×#31652
C31×#31522
C31×#31412
C31×#16612
C31×#15262
C31×#15252
#1907631