Finite Group Databasebeta

← C31×#19171 #21475930

Subgroups — C31×#19171 #21475930

Order 7936.

682 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3152C211yesmaximal, characteristic
2C31×#3103C211yesmaximal, characteristic
3C2×C31×#475C211yesmaximal, characteristic, complemented
4Q8×M16×C31C211yesmaximal, characteristic, complemented
5C31×#1690C212yesmaximal, complemented
6C31×#1686C212yesmaximal, complemented
7C31×#1670C212yesmaximal, complemented
8C31×#1666C212yesmaximal, complemented
9C31×#1565C211yesmaximal, characteristic, complemented
10C31×#1547C211yesmaximal, characteristic
11C31×#1546C211yesmaximal, characteristic, complemented
12C2×C31×#137—21no—
13C2×C31×#137—21no—
14C31×#532C2211yescharacteristic
15C2×C31×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C31C2211yescharacteristic
17C31×#497—22no—
18C31×#494C2212yes—
19C31×#492C2212yes—
20C31×#481—21no—
21C31×#475—21no—
22C31×#475—21no—
23C31×#475C2211yescharacteristic
24C31×#475C2211yescharacteristic
25C31×#475C2212yes—
26C31×#475C2212yes—
27C31×#460C2211yescharacteristic
28C31×#460C2211yescharacteristic
29C31×#448—21no—
30C31×#446—22no—
31C31×#446C2212yes—
32C8×Q8×C31C2212yes—
33C4×SD16×C31—21no—
34C4×SD16×C31—21no—
35C31×#431C2211yescharacteristic
36C2×C31×#106—21no—
37C31×#423—21no—
38C31×#423C2211yescharacteristic
39C2×C31×C4⋊C8C2211yescharacteristic
40C2×C31×#103—21no—
41C4×M16×C31—21no—
42C4×M16×C31C2211yescharacteristic
43C31×#335C2212yes—
44C31×#334C2212yes—
45C31×#332C2212yes—
46C31×#332C2212yes—
47C31×#332C2212yes—
48C31×#331C2212yes—
49C2×#41×C31—21no—
50C22×Q8×C31—21no—
51C22×Q8×C31D411yescharacteristic
52C31×#137—44no—
53C31×#137—44no—
54C2×Q16×C31—22no—
55C2×Q16×C31—22no—
56C2×SD16×C31—21no—
57C2×SD16×C31—21no—
58C2×SD16×C31—22no—
59C2×SD16×C31—22no—
60C2×M16×C31—21no—
61C2×M16×C31D411yescharacteristic
62C2×M16×C31D411yescharacteristic
63C22×C8×C31—21no—
64C31×C4⋊Q8—21no—
65C31×C4⋊Q8—21no—
66C31×C4⋊Q8—21no—
67C31×C4⋊Q8C2312yes—
68C31×C4⋊Q8C2311yescharacteristic
69C31×#127C2311yescharacteristic
70C31×#124—21no—
71C31×#121—21no—
72C31×#121—21no—
73C4×Q8×C31—21no—
74C4×Q8×C31—21no—
75C4×Q8×C31D411yescharacteristic
76C4×Q8×C31D411yescharacteristic
77C4×Q8×C31C2311yescharacteristic
78C4×Q8×C31C2311yescharacteristic
79C4×D4×C31—21no—
80C4×D4×C31—21no—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31D411yescharacteristic
85C2×C42×C31—21no—
86C2×C42×C31C2311yescharacteristic
87C31×#106—22no—
88C31×#106—22no—
89C31×#106—21no—
90C31×#106—21no—
91C31×C4⋊C8—22no—
92C31×C4⋊C8—22no—
93C31×C4⋊C8—21no—
94C31×C4⋊C8—21no—
95C31×C4⋊C8C2312yes—
96C31×C4⋊C8C2312yes—
97C31×C4⋊C8C2311yescharacteristic
98C31×C4⋊C8C2311yescharacteristic
99C31×#103—22no—
100C31×#103—22no—
101C31×#103—21no—
102C31×#103—21no—
103C31×#102—21no—
104C31×#102—21no—
105C31×C22⋊C8—21no—
106C31×#97—22no—
107C31×#97D412yes—
108C4×C8×C31—22no—
109C4×C8×C31—21no—
110C4×C8×C31C2312yes—
111#41×C31—42no—
112#41×C31—42no—
113C2×Q8×C31—21no—
114C2×Q8×C31—22no—
115C2×Q8×C31—21no—
116C2×Q8×C31—22no—
117C2×Q8×C31—41no—
118C2×Q8×C31—41no—
119C2×Q8×C31—42no—
120C2×Q8×C31—42no—
121C2×Q8×C31C2×D411yescharacteristic
122C2×Q8×C31C2×D411yescharacteristic
123C2×D4×C31—21no—
124C2×D4×C31—21no—
125C2×D4×C31—21no—
126C2×D4×C31—41no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—41no—
130C22×C4×C31—41no—
131C22×C4×C31C2×D411yescharacteristic
132C22×C4×C31C2×D411yescharacteristic
133C22×C4×C31#4111yescharacteristic
134Q16×C31—44no—
135Q16×C31—44no—
136SD16×C31—44no—
137SD16×C31—42no—
138SD16×C31—42no—
139SD16×C31—44no—
140M16×C31—22no—
141M16×C31—42no—
142M16×C31SD1614yescomplemented
143C2×C8×C31—22no—
144C2×C8×C31—21no—
145C2×C8×C31—21no—
146C2×C8×C31—22no—
147C2×C8×C31—42no—
148C2×C8×C31C2×D412yes—
149C2×C8×C31C2×D412yes—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—21no—
153C4⋊C4×C31—21no—
154C4⋊C4×C31—21no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—21no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—41no—
160C4⋊C4×C31—41no—
161C4⋊C4×C31C2×D411yescharacteristic
162C4⋊C4×C31C2×D411yescharacteristic
163C22⋊C4×C31—41no—
164C22⋊C4×C31—41no—
165C42×C31—21no—
166C42×C31—21no—
167C42×C31—21no—
168C42×C31—21no—
169C42×C31C2×D411yescharacteristic
170C42×C31C2×D411yescharacteristic
171C42×C31#4111yescharacteristic
172C42×C31C2411yescharacteristic
173#19171C3111yesmaximal, characteristic, direct product factor, Sylow
174C23×C31—41no—
175C23×C31#12111yescharacteristic
176Q8×C31—21no—
177Q8×C31—21no—
178Q8×C31—21no—
179Q8×C31—42no—
180Q8×C31—42no—
181Q8×C31—41no—
182Q8×C31—42no—
183Q8×C31—41no—
184Q8×C31—82no—
185Q8×C31#13712yescomplemented
186D4×C31—41no—
187D4×C31—41no—
188D4×C31—41no—
189D4×C31—41no—
190D4×C31—81no—
191D4×C31—82no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—21no—
195C2×C4×C31—21no—
196C2×C4×C31—21no—
197C2×C4×C31—21no—
198C2×C4×C31—41no—
199C2×C4×C31—42no—
200C2×C4×C31—41no—
201C2×C4×C31—42no—
202C2×C4×C31—81no—
203C2×C4×C31—82no—
204C2×C4×C31—82no—
205C2×C4×C31#12111yescharacteristic
206C2×C4×C31#12111yescharacteristic
207C2×C4×C31#12111yescharacteristic
208C2×C4×C31C2×SD1612yes—
209C2×C4×C31AGL(1,ℤ/8)12yes—
210C2×C4×C31C22×D411yescharacteristic
211C2×C4×C31C22×D411yescharacteristic
212C2×C4×C31C2×#4111yescharacteristic
213C8×C31—22no—
214C8×C31—42no—
215C8×C31—41no—
216C8×C31—42no—
217C8×C31—41no—
218C8×C31C2×SD1614yes—
219#3152C2×C3111yescharacteristic
220#3103C2×C3111yescharacteristic
221C2×#475C2×C3111yescharacteristic, complemented
222Q8×M16C2×C3111yescharacteristic, complemented
223#1690C2×C3112yescomplemented
224#1686C2×C3112yescomplemented
225#1670C2×C3112yescomplemented
226#1666C2×C3112yescomplemented
227#1565C2×C3111yescharacteristic, complemented
228#1547C2×C3111yescharacteristic
229#1546C2×C3111yescharacteristic, complemented
230C22×C31—21no—
231C22×C31—21no—
232C22×C31—81no—
233C22×C31—81no—
234C22×C31—81no—
235C22×C31#46012yes—
236C22×C31C2×#12111yescharacteristic
237C4×C31—21no—
238C4×C31—22no—
239C4×C31—21no—
240C4×C31—21no—
241C4×C31—41no—
242C4×C31—41no—
243C4×C31—41no—
244C4×C31—81no—
245C4×C31—82no—
246C4×C31#46012yes—
247C4×C31C22×SD1611yescharacteristic
248C4×C31C2×AGL(1,ℤ/8)11yescharacteristic
249C4×C31C2×#13711yescharacteristic
250C4×C31#57511yescharacteristic
251C2×#137—21no—
252C2×#137—21no—
253#532C22×C3111yescharacteristic
254C2×C4⋊Q8C22×C3111yescharacteristic
255C2×C4×Q8C22×C3111yescharacteristic
256#497—22no—
257#494C22×C3112yes—
258#492C22×C3112yes—
259#481—21no—
260#475—21no—
261#475—21no—
262#475C22×C3112yes—
263#475C22×C3112yes—
264#475C22×C3111yescharacteristic
265#475C22×C3111yescharacteristic
266#460C22×C3111yescharacteristic
267#460C22×C3111yescharacteristic
268#448—21no—
269#446—22no—
270#446C22×C3112yes—
271C8×Q8C22×C3112yes—
272C4×SD16—21no—
273C4×SD16—21no—
274#431C22×C3111yescharacteristic
275C2×#106—21no—
276#423—21no—
277#423C22×C3111yescharacteristic
278C2×C4⋊C8C22×C3111yescharacteristic
279C2×#103—21no—
280C4×M16—21no—
281C4×M16C22×C3111yescharacteristic
282#335C22×C3112yes—
283#334C22×C3112yes—
284#332C22×C3112yes—
285#332C22×C3112yes—
286#332C22×C3112yes—
287#331C22×C3112yes—
288C2×C31—22no—
289C2×C31—161no—
290C2×C31C2×#46011yescharacteristic
291C2×C31#305611yescharacteristic
292C2×C31#306911yescharacteristic
293C2×#41—21no—
294C22×Q8—21no—
295C22×Q8D4×C3111yescharacteristic
296#137—44no—
297#137—44no—
298C2×Q16—22no—
299C2×Q16—22no—
300C2×SD16—21no—
301C2×SD16—21no—
302C2×SD16—22no—
303C2×SD16—22no—
304C2×M16—21no—
305C2×M16D4×C3111yescharacteristic
306C2×M16D4×C3111yescharacteristic
307C22×C8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8C23×C3112yes—
312C4⋊Q8C23×C3111yescharacteristic
313#127C23×C3111yescharacteristic
314#124—21no—
315#121—21no—
316#121—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8D4×C3111yescharacteristic
320C4×Q8D4×C3111yescharacteristic
321C4×Q8C23×C3111yescharacteristic
322C4×Q8C23×C3111yescharacteristic
323C4×D4—21no—
324C4×D4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4D4×C3111yescharacteristic
329C2×C42—21no—
330C2×C42C23×C3111yescharacteristic
331#106—22no—
332#106—22no—
333#106—21no—
334#106—21no—
335C4⋊C8—22no—
336C4⋊C8—22no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339C4⋊C8C23×C3112yes—
340C4⋊C8C23×C3112yes—
341C4⋊C8C23×C3111yescharacteristic
342C4⋊C8C23×C3111yescharacteristic
343#103—22no—
344#103—22no—
345#103—21no—
346#103—21no—
347#102—21no—
348#102—21no—
349C22⋊C8—21no—
350#97—22no—
351#97D4×C3112yes—
352C4×C8—22no—
353C4×C8—21no—
354C4×C8C23×C3112yes—
355C31#1917111yescharacteristic, direct product factor, Sylow
356#41—42no—
357#41—42no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8—22no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—42no—
365C2×Q8—42no—
366C2×Q8C2×D4×C3111yescharacteristic
367C2×Q8C2×D4×C3111yescharacteristic
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—41no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4C2×D4×C3111yescharacteristic
377C22×C4C2×D4×C3111yescharacteristic
378C22×C4#41×C3111yescharacteristic
379Q16—44no—
380Q16—44no—
381SD16—44no—
382SD16—42no—
383SD16—42no—
384SD16—44no—
385M16—22no—
386M16—42no—
387M16SD16×C3114yescomplemented
388C2×C8—22no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—22no—
392C2×C8—42no—
393C2×C8C2×D4×C3112yes—
394C2×C8C2×D4×C3112yes—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4C2×D4×C3111yescharacteristic
407C4⋊C4C2×D4×C3111yescharacteristic
408C22⋊C4—41no—
409C22⋊C4—41no—
410C42—21no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42C2×D4×C3111yescharacteristic
415C42C2×D4×C3111yescharacteristic
416C42#41×C3111yescharacteristic
417C42C24×C3111yescharacteristic
418C23—41no—
419C23C31×#12111yescharacteristic
420Q8—21no—
421Q8—21no—
422Q8—21no—
423Q8—42no—
424Q8—42no—
425Q8—41no—
426Q8—42no—
427Q8—41no—
428Q8—82no—
429Q8C31×#13712yescomplemented
430D4—41no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—81no—
435D4—82no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4C31×#12111yescharacteristic
450C2×C4C31×#12111yescharacteristic
451C2×C4C31×#12111yescharacteristic
452C2×C4C2×SD16×C3112yes—
453C2×C4C31×AGL(1,ℤ/8)12yes—
454C2×C4C22×D4×C3111yescharacteristic
455C2×C4C22×D4×C3111yescharacteristic
456C2×C4C2×#41×C3111yescharacteristic
457C8—22no—
458C8—42no—
459C8—41no—
460C8—42no—
461C8—41no—
462C8C2×SD16×C3114yes—
463C22—21no—
464C22—21no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22C31×#46012yes—
469C22C2×C31×#12111yescharacteristic
470C4—21no—
471C4—22no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—82no—
479C4C31×#46012yes—
480C4C22×SD16×C3111yescharacteristic
481C4C2×C31×AGL(1,ℤ/8)11yescharacteristic
482C4C2×C31×#13711yescharacteristic
483C4C31×#57511yescharacteristic
484C2—22no—
485C2—161no—
486C2C2×C31×#46011yescharacteristic
487C2C31×#305611yescharacteristic
488C2C31×#306911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#121
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#532C22
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
3. C2×C31×#475C2semidirect
4. Q8×M16×C31C2semidirect
5. C31×#1690C2semidirect
6. C31×#1686C2semidirect
7. C31×#1670C2semidirect
8. C31×#1666C2semidirect
9. C31×#1565C2semidirect
11. C31×#1546C2semidirect
142. M16×C31SD16semidirect
173. #19171C31direct (N × H)
185. Q8×C31#137semidirect
221. C2×#475C2×C31semidirect
222. Q8×M16C2×C31semidirect
223. #1690C2×C31semidirect
224. #1686C2×C31semidirect
225. #1670C2×C31semidirect
226. #1666C2×C31semidirect
227. #1565C2×C31semidirect
229. #1546C2×C31semidirect
355. C31#19171direct (N × H)
387. M16SD16×C31semidirect
429. Q8C31×#137semidirect

Maximal subgroups

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

subgroupindex
C31×#31522
C31×#31032
C2×C31×#4752
Q8×M16×C312
C31×#16902
C31×#16862
C31×#16702
C31×#16662
C31×#15652
C31×#15472
C31×#15462
#1917131