Finite Group Databasebeta

← C31×#18353 #21475112

Subgroups — C31×#18353 #21475112

Order 7936.

946 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3501C211yesmaximal, characteristic
2C31×#3195C212yesmaximal, complemented
3C31×#2638C211yesmaximal, characteristic
4C31×#1611C212yesmaximal, complemented
5C31×#1608C212yesmaximal, complemented
6C31×#1605C212yesmaximal, complemented
7C31×#1602C212yesmaximal, complemented
8C31×#1511C212yesmaximal, complemented
9C31×#1465C211yesmaximal, characteristic
10C31×#554—24no—
11C31×#554—22no—
12D4×Q8×C31—22no—
13C31×#544C2212yes—
14C31×#543—21no—
15C31×#543C2212yes—
16C31×#533—21no—
17C2×C31×C22⋊Q8—21no—
18C2×C31×C22⋊Q8C2212yes—
19C2×C31×C22⋊Q8C2211yescharacteristic
20C31×#518—21no—
21C2×C4×D4×C31C2211yescharacteristic
22C31×#483—22no—
23C31×#483C2214yes—
24C31×#470—24no—
25C31×#451—22no—
26C31×#451C2214yes—
27C31×#407C2212yes—
28C31×#398C2211yescharacteristic
29C31×#397—21no—
30C31×#397C2211yescharacteristic
31C31×#395C2211yescharacteristic
32C31×#394—21no—
33C31×#393C2211yescharacteristic
34C31×#387—21no—
35C31×#385—21no—
36C31×#381C2211yescharacteristic
37C31×#328C2214yes—
38C31×#328C2214yes—
39C31×#324C2212yes—
40C31×#323C2212yes—
41C22×Q8×C31—21no—
42C22×Q8×C31D412yes—
43C22×Q8×C31C2311yescharacteristic
44C22×D4×C31D411yescharacteristic
45C23×C4×C31D411yescharacteristic
46C23×C4×C31C2311yescharacteristic
47C2×Q16×C31—24no—
48C2×M16×C31—22no—
49C31×C4⋊Q8—21no—
50C31×C4⋊Q8—21no—
51C31×C4⋊Q8—24no—
52C31×#125—22no—
53C31×#125—24no—
54C31×C22⋊Q8—22no—
55C31×C22⋊Q8—22no—
56C31×C22⋊Q8—24no—
57C31×C22⋊Q8—24no—
58C31×C22⋊Q8—24no—
59C31×C22⋊Q8—22no—
60C31×C22⋊Q8—22no—
61C31×C22⋊Q8—22no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8—24no—
64C31×C22⋊Q8—22no—
65C31×C22⋊Q8—22no—
66C31×C22⋊Q8D414yes—
67C31×C22⋊Q8C2314yes—
68C4×Q8×C31—22no—
69C4×Q8×C31—22no—
70C4×D4×C31—24no—
71C4×D4×C31—24no—
72C4×D4×C31—22no—
73C4×D4×C31—22no—
74C31×#117—22no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—21no—
80C2×C4⋊C4×C31—21no—
81C2×C4⋊C4×C31D412yes—
82C2×C4⋊C4×C31C2311yescharacteristic
83C2×C4⋊C4×C31C2311yescharacteristic
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31D411yescharacteristic
91C2×C22⋊C4×C31C2311yescharacteristic
92C2×C42×C31D411yescharacteristic
93C31×#106—24no—
94C31×#103—24no—
95C31×#103—24no—
96C31×C22⋊C8—22no—
97C31×C22⋊C8C2314yes—
98C31×#95—21no—
99C31×#95—21no—
100C31×#95—21no—
101C31×#95—21no—
102C31×#95—21no—
103C31×#95C2311yescharacteristic
104C31×#95C2311yescharacteristic
105C24×C31C2×D411yescharacteristic
106C24×C31C2×D411yescharacteristic
107C2×Q8×C31—22no—
108C2×Q8×C31—22no—
109C2×Q8×C31—22no—
110C2×Q8×C31—22no—
111C2×Q8×C31—81no—
112C2×Q8×C31—82no—
113C2×Q8×C31—82no—
114C2×Q8×C31C2×D414yes—
115C2×D4×C31—22no—
116C2×D4×C31—22no—
117C2×D4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—81no—
129C22×C4×C31—81no—
130C22×C4×C31C2×D411yescharacteristic
131C22×C4×C31C2×D411yescharacteristic
132C22×C4×C31C2×D411yescharacteristic
133C22×C4×C31C2×D411yescharacteristic
134C22×C4×C31C2×D412yes—
135C22×C4×C31C2×D412yes—
136C22×C4×C31C2411yescharacteristic
137Q16×C31—84no—
138M16×C31—82no—
139C2×C8×C31—24no—
140C4⋊C4×C31—22no—
141C4⋊C4×C31—24no—
142C4⋊C4×C31—22no—
143C4⋊C4×C31—22no—
144C4⋊C4×C31—24no—
145C4⋊C4×C31—22no—
146C4⋊C4×C31—24no—
147C4⋊C4×C31—22no—
148C4⋊C4×C31—24no—
149C4⋊C4×C31—22no—
150C4⋊C4×C31—22no—
151C4⋊C4×C31—41no—
152C4⋊C4×C31—41no—
153C4⋊C4×C31—42no—
154C4⋊C4×C31—81no—
155C4⋊C4×C31C2×D414yes—
156C22⋊C4×C31—24no—
157C22⋊C4×C31—24no—
158C22⋊C4×C31—22no—
159C22⋊C4×C31—24no—
160C22⋊C4×C31—22no—
161C22⋊C4×C31—42no—
162C22⋊C4×C31—42no—
163C22⋊C4×C31—81no—
164C22⋊C4×C31—81no—
165C42×C31—24no—
166C42×C31—21no—
167C42×C31—21no—
168#18353C3111yesmaximal, characteristic, direct product factor, Sylow
169C23×C31—21no—
170C23×C31—21no—
171C23×C31—21no—
172C23×C31—21no—
173C23×C31—41no—
174C23×C31—41no—
175C23×C31—41no—
176C23×C31—41no—
177C23×C31#12012yes—
178C23×C31#13712yes—
179C23×C31C22×D411yescharacteristic
180Q8×C31—44no—
181Q8×C31—44no—
182Q8×C31—44no—
183Q8×C31—82no—
184Q8×C31—82no—
185D4×C31—28no—
186C2×C4×C31—21no—
187C2×C4×C31—21no—
188C2×C4×C31—21no—
189C2×C4×C31—24no—
190C2×C4×C31—24no—
191C2×C4×C31—21no—
192C2×C4×C31—42no—
193C2×C4×C31—41no—
194C2×C4×C31—42no—
195C2×C4×C31—41no—
196C2×C4×C31—42no—
197C2×C4×C31—41no—
198C2×C4×C31—41no—
199C2×C4×C31—41no—
200C2×C4×C31—41no—
201C2×C4×C31—41no—
202C2×C4×C31—41no—
203C2×C4×C31—41no—
204C2×C4×C31—41no—
205C2×C4×C31—41no—
206C2×C4×C31—41no—
207C2×C4×C31—41no—
208C2×C4×C31—41no—
209C2×C4×C31—41no—
210C2×C4×C31—41no—
211C2×C4×C31—81no—
212C2×C4×C31—82no—
213C2×C4×C31—82no—
214C2×C4×C31—82no—
215C2×C4×C31—82no—
216C2×C4×C31#12011yescharacteristic
217C2×C4×C31#12011yescharacteristic
218C2×C4×C31#13712yes—
219C2×C4×C31C22×D412yes—
220C8×C31—44no—
221#3501C2×C3111yescharacteristic
222#3195C2×C3112yescomplemented
223#2638C2×C3111yescharacteristic
224#1611C2×C3112yescomplemented
225#1608C2×C3112yescomplemented
226#1605C2×C3112yescomplemented
227#1602C2×C3112yescomplemented
228#1511C2×C3112yescomplemented
229#1465C2×C3111yescharacteristic
230C22×C31—21no—
231C22×C31—21no—
232C22×C31—22no—
233C22×C31—22no—
234C22×C31—22no—
235C22×C31—22no—
236C22×C31—42no—
237C22×C31—41no—
238C22×C31—41no—
239C22×C31—81no—
240C22×C31—81no—
241C22×C31—81no—
242C22×C31C2×#12011yescharacteristic
243C22×C31C2×#13711yescharacteristic
244C22×C31C2×#13711yescharacteristic
245C4×C31—22no—
246C4×C31—22no—
247C4×C31—21no—
248C4×C31—21no—
249C4×C31—41no—
250C4×C31—44no—
251C4×C31—41no—
252C4×C31—44no—
253C4×C31—81no—
254C4×C31—81no—
255C4×C31—81no—
256C4×C31—81no—
257#554—24no—
258#554—22no—
259D4×Q8—22no—
260#544C22×C3112yes—
261#543—21no—
262#543C22×C3112yes—
263#533—21no—
264C2×C22⋊Q8—21no—
265C2×C22⋊Q8C22×C3112yes—
266C2×C22⋊Q8C22×C3111yescharacteristic
267#518—21no—
268C2×C4×D4C22×C3111yescharacteristic
269#483—22no—
270#483C22×C3114yes—
271#470—24no—
272#451—22no—
273#451C22×C3114yes—
274#407C22×C3112yes—
275#398C22×C3111yescharacteristic
276#397—21no—
277#397C22×C3111yescharacteristic
278#395C22×C3111yescharacteristic
279#394—21no—
280#393C22×C3111yescharacteristic
281#387—21no—
282#385—21no—
283#381C22×C3111yescharacteristic
284#328C22×C3114yes—
285#328C22×C3114yes—
286#324C22×C3112yes—
287#323C22×C3112yes—
288C2×C31—21no—
289C2×C31—21no—
290C2×C31—42no—
291C2×C31—42no—
292C2×C31#300411yescharacteristic
293C2×C31#302211yescharacteristic
294C2×C31#302611yescharacteristic
295C22×Q8—21no—
296C22×Q8D4×C3112yes—
297C22×Q8C23×C3111yescharacteristic
298C22×D4D4×C3111yescharacteristic
299C23×C4D4×C3111yescharacteristic
300C23×C4C23×C3111yescharacteristic
301C2×Q16—24no—
302C2×M16—22no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—24no—
306#125—22no—
307#125—24no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8—24no—
311C22⋊Q8—24no—
312C22⋊Q8—24no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—24no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8D4×C3114yes—
321C22⋊Q8C23×C3114yes—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×D4—24no—
325C4×D4—24no—
326C4×D4—22no—
327C4×D4—22no—
328#117—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4D4×C3112yes—
336C2×C4⋊C4C23×C3111yescharacteristic
337C2×C4⋊C4C23×C3111yescharacteristic
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4D4×C3111yescharacteristic
345C2×C22⋊C4C23×C3111yescharacteristic
346C2×C42D4×C3111yescharacteristic
347#106—24no—
348#103—24no—
349#103—24no—
350C22⋊C8—22no—
351C22⋊C8C23×C3114yes—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95C23×C3111yescharacteristic
358#95C23×C3111yescharacteristic
359C31#1835311yescharacteristic, direct product factor, Sylow
360C24C2×D4×C3111yescharacteristic
361C24C2×D4×C3111yescharacteristic
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—81no—
367C2×Q8—82no—
368C2×Q8—82no—
369C2×Q8C2×D4×C3114yes—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—81no—
384C22×C4—81no—
385C22×C4C2×D4×C3111yescharacteristic
386C22×C4C2×D4×C3111yescharacteristic
387C22×C4C2×D4×C3111yescharacteristic
388C22×C4C2×D4×C3111yescharacteristic
389C22×C4C2×D4×C3112yes—
390C22×C4C2×D4×C3112yes—
391C22×C4C24×C3111yescharacteristic
392Q16—84no—
393M16—82no—
394C2×C8—24no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—24no—
400C4⋊C4—22no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—42no—
409C4⋊C4—81no—
410C4⋊C4C2×D4×C3114yes—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—22no—
414C22⋊C4—24no—
415C22⋊C4—22no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—81no—
419C22⋊C4—81no—
420C42—24no—
421C42—21no—
422C42—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23C31×#12012yes—
432C23C31×#13712yes—
433C23C22×D4×C3111yescharacteristic
434Q8—44no—
435Q8—44no—
436Q8—44no—
437Q8—82no—
438Q8—82no—
439D4—28no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—21no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—81no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4C31×#12011yescharacteristic
471C2×C4C31×#12011yescharacteristic
472C2×C4C31×#13712yes—
473C2×C4C22×D4×C3112yes—
474C8—44no—
475C22—21no—
476C22—21no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—42no—
482C22—41no—
483C22—41no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22C2×C31×#12011yescharacteristic
488C22C2×C31×#13711yescharacteristic
489C22C2×C31×#13711yescharacteristic
490C4—22no—
491C4—22no—
492C4—21no—
493C4—21no—
494C4—41no—
495C4—44no—
496C4—41no—
497C4—44no—
498C4—81no—
499C4—81no—
500C4—81no—
501C4—81no—
502C2—21no—
503C2—21no—
504C2—42no—
505C2—42no—
506C2C31×#300411yescharacteristic
507C2C31×#302211yescharacteristic
508C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
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×#3195C2semidirect
4. C31×#1611C2semidirect
5. C31×#1608C2semidirect
6. C31×#1605C2semidirect
7. C31×#1602C2semidirect
8. C31×#1511C2semidirect
168. #18353C31direct (N × H)
222. #3195C2×C31semidirect
224. #1611C2×C31semidirect
225. #1608C2×C31semidirect
226. #1605C2×C31semidirect
227. #1602C2×C31semidirect
228. #1511C2×C31semidirect
359. C31#18353direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35012
C31×#31952
C31×#26382
C31×#16112
C31×#16082
C31×#16052
C31×#16022
C31×#15112
C31×#14652
#1835331