Finite Group Databasebeta

← C31×#18143 #21474902

Subgroups — C31×#18143 #21474902

Order 7936.

1170 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#544C211yesmaximal, characteristic, complemented
2C31×#3007C212yesmaximal
3C31×#2406C211yesmaximal, characteristic
4C31×#1605C214yesmaximal, complemented
5C31×#1599C214yesmaximal, complemented
6C31×#1511C212yesmaximal, complemented
7C31×#1463C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C2×C31×#137—22no—
10C31×#544—24no—
11C31×#544—22no—
12C31×#544C2214yes—
13C2×C31×C4⋊Q8—22no—
14C2×C31×#125—22no—
15C2×C31×#123—21no—
16C2×C31×C22⋊Q8—21no—
17C2×C31×C22⋊Q8C2212yes—
18C2×C31×#117—21no—
19C22×C4⋊C4×C31C2211yescharacteristic
20C31×#452—24no—
21C31×#451C2214yes—
22C31×#450C2214yes—
23C31×#417—22no—
24C31×#407C2212yes—
25C31×#395C2212yes—
26C31×#394C2212yes—
27C31×#386—21no—
28C31×#385—22no—
29C31×#381C2211yescharacteristic
30C31×#328C2218yes—
31C31×#324C2214yes—
32C2×#41×C31—22no—
33C2×#41×C31—22no—
34C2×#41×C31—44no—
35C22×Q8×C31—21no—
36C22×Q8×C31D412yes—
37C22×Q8×C31C2311yescharacteristic
38C22×D4×C31—21no—
39C22×D4×C31C2311yescharacteristic
40C23×C4×C31—21no—
41C23×C4×C31D411yescharacteristic
42C23×C4×C31D411yescharacteristic
43C23×C4×C31C2311yescharacteristic
44C31×#137—48no—
45C2×Q16×C31—24no—
46C2×SD16×C31—24no—
47C2×M16×C31—22no—
48C31×C4⋊Q8—28no—
49C31×C4⋊Q8—28no—
50C31×#125—28no—
51C31×#125—28no—
52C31×#123—44no—
53C31×C22⋊Q8—24no—
54C31×C22⋊Q8—24no—
55C31×C22⋊Q8—22no—
56C31×C22⋊Q8—22no—
57C31×C22⋊Q8D414yes—
58C31×C22⋊Q8C2314yes—
59C31×#117—24no—
60C31×#117—24no—
61C2×C4⋊C4×C31—21no—
62C2×C4⋊C4×C31—21no—
63C2×C4⋊C4×C31—21no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31D412yes—
70C2×C4⋊C4×C31D412yes—
71C2×C4⋊C4×C31C2312yes—
72C2×C22⋊C4×C31—22no—
73C2×C22⋊C4×C31—21no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—22no—
76C2×C42×C31—22no—
77C31×#103—24no—
78C31×#102—24no—
79C31×C22⋊C8—22no—
80C31×C22⋊C8C2314yes—
81C31×#95—22no—
82C31×#95—21no—
83C31×#95C2312yes—
84C24×C31—21no—
85C24×C31C2×D411yescharacteristic
86#41×C31—28no—
87#41×C31—44no—
88#41×C31—44no—
89#41×C31—44no—
90C2×Q8×C31—24no—
91C2×Q8×C31—22no—
92C2×Q8×C31—22no—
93C2×Q8×C31—42no—
94C2×Q8×C31—44no—
95C2×Q8×C31—82no—
96C2×Q8×C31C2×D414yes—
97C2×D4×C31—24no—
98C2×D4×C31—22no—
99C2×D4×C31—42no—
100C2×D4×C31—42no—
101C2×D4×C31—41no—
102C2×D4×C31—41no—
103C22×C4×C31—21no—
104C22×C4×C31—21no—
105C22×C4×C31—24no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—21no—
109C22×C4×C31—21no—
110C22×C4×C31—21no—
111C22×C4×C31—22no—
112C22×C4×C31—42no—
113C22×C4×C31—42no—
114C22×C4×C31—42no—
115C22×C4×C31—42no—
116C22×C4×C31—42no—
117C22×C4×C31C2×D412yes—
118C22×C4×C31C2×D412yes—
119C22×C4×C31C2×D412yes—
120C22×C4×C31C2×D411yescharacteristic
121C22×C4×C31C2×D412yes—
122C22×C4×C31C2411yescharacteristic
123Q16×C31—48no—
124SD16×C31—48no—
125M16×C31—44no—
126C2×C8×C31—24no—
127C4⋊C4×C31—24no—
128C4⋊C4×C31—24no—
129C4⋊C4×C31—24no—
130C4⋊C4×C31—28no—
131C4⋊C4×C31—24no—
132C4⋊C4×C31—24no—
133C4⋊C4×C31—22no—
134C4⋊C4×C31—24no—
135C4⋊C4×C31—24no—
136C4⋊C4×C31—44no—
137C4⋊C4×C31C2×D414yes—
138C22⋊C4×C31—24no—
139C22⋊C4×C31—24no—
140C22⋊C4×C31—44no—
141C22⋊C4×C31—42no—
142C22⋊C4×C31—44no—
143C42×C31—28no—
144#18143C3111yesmaximal, characteristic, direct product factor, Sylow
145C23×C31—22no—
146C23×C31—22no—
147C23×C31—22no—
148C23×C31—41no—
149C23×C31—41no—
150C23×C31—42no—
151C23×C31—41no—
152C23×C31—42no—
153C23×C31#12011yescharacteristic
154C23×C31#12011yescharacteristic
155C23×C31C22×D411yescharacteristic
156Q8×C31—24no—
157Q8×C31—44no—
158Q8×C31—42no—
159Q8×C31—82no—
160Q8×C31—84no—
161D4×C31—24no—
162D4×C31—42no—
163D4×C31—44no—
164D4×C31—44no—
165C2×C4×C31—24no—
166C2×C4×C31—24no—
167C2×C4×C31—22no—
168C2×C4×C31—22no—
169C2×C4×C31—24no—
170C2×C4×C31—22no—
171C2×C4×C31—24no—
172C2×C4×C31—24no—
173C2×C4×C31—22no—
174C2×C4×C31—41no—
175C2×C4×C31—42no—
176C2×C4×C31—41no—
177C2×C4×C31—48no—
178C2×C4×C31—44no—
179C2×C4×C31—41no—
180C2×C4×C31—41no—
181C2×C4×C31—42no—
182C2×C4×C31—44no—
183C2×C4×C31—42no—
184C2×C4×C31—42no—
185C2×C4×C31—42no—
186C2×C4×C31—42no—
187C2×C4×C31—81no—
188C2×C4×C31#12012yes—
189C2×C4×C31#13714yescomplemented
190C2×C4×C31C22×D412yes—
191C8×C31—44no—
192C2×#544C2×C3111yescharacteristic, complemented
193#3007C2×C3112yes—
194#2406C2×C3111yescharacteristic
195#1605C2×C3114yescomplemented
196#1599C2×C3114yescomplemented
197#1511C2×C3112yescomplemented
198#1463C2×C3111yescharacteristic, complemented
199C22×C31—21no—
200C22×C31—21no—
201C22×C31—21no—
202C22×C31—21no—
203C22×C31—21no—
204C22×C31—21no—
205C22×C31—21no—
206C22×C31—44no—
207C22×C31—44no—
208C22×C31—42no—
209C22×C31—82no—
210C22×C31—81no—
211C22×C31—81no—
212C22×C31B(4,𝔽2)12yes—
213C22×C31C2×#12011yescharacteristic
214C22×C31C2×#13712yes—
215C4×C31—24no—
216C4×C31—22no—
217C4×C31—22no—
218C4×C31—44no—
219C4×C31—42no—
220C4×C31—42no—
221C4×C31—44no—
222C4×C31—82no—
223C22×#41C22×C3111yescharacteristic
224C2×#137—22no—
225#544—24no—
226#544—22no—
227#544C22×C3114yes—
228C2×C4⋊Q8—22no—
229C2×#125—22no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8C22×C3112yes—
233C2×#117—21no—
234C22×C4⋊C4C22×C3111yescharacteristic
235#452—24no—
236#451C22×C3114yes—
237#450C22×C3114yes—
238#417—22no—
239#407C22×C3112yes—
240#395C22×C3112yes—
241#394C22×C3112yes—
242#386—21no—
243#385—22no—
244#381C22×C3111yescharacteristic
245#328C22×C3118yes—
246#324C22×C3114yes—
247C2×C31—22no—
248C2×C31—22no—
249C2×C31—41no—
250C2×C31—82no—
251C2×C31#300411yescharacteristic
252C2×C31#302011yescharacteristic
253C2×C31C2×B(4,𝔽2)11yescharacteristic
254C2×#41—22no—
255C2×#41—22no—
256C2×#41—44no—
257C22×Q8—21no—
258C22×Q8D4×C3112yes—
259C22×Q8C23×C3111yescharacteristic
260C22×D4—21no—
261C22×D4C23×C3111yescharacteristic
262C23×C4—21no—
263C23×C4D4×C3111yescharacteristic
264C23×C4D4×C3111yescharacteristic
265C23×C4C23×C3111yescharacteristic
266#137—48no—
267C2×Q16—24no—
268C2×SD16—24no—
269C2×M16—22no—
270C4⋊Q8—28no—
271C4⋊Q8—28no—
272#125—28no—
273#125—28no—
274#123—44no—
275C22⋊Q8—24no—
276C22⋊Q8—24no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C22⋊Q8D4×C3114yes—
280C22⋊Q8C23×C3114yes—
281#117—24no—
282#117—24no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4D4×C3112yes—
292C2×C4⋊C4D4×C3112yes—
293C2×C4⋊C4C23×C3112yes—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C42—22no—
299#103—24no—
300#102—24no—
301C22⋊C8—22no—
302C22⋊C8C23×C3114yes—
303#95—21no—
304#95—22no—
305#95C23×C3112yes—
306C31#1814311yescharacteristic, direct product factor, Sylow
307C24—21no—
308C24C2×D4×C3111yescharacteristic
309#41—28no—
310#41—44no—
311#41—44no—
312#41—44no—
313C2×Q8—24no—
314C2×Q8—22no—
315C2×Q8—22no—
316C2×Q8—42no—
317C2×Q8—44no—
318C2×Q8—82no—
319C2×Q8C2×D4×C3114yes—
320C2×D4—24no—
321C2×D4—22no—
322C2×D4—42no—
323C2×D4—42no—
324C2×D4—41no—
325C2×D4—41no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4C2×D4×C3112yes—
341C22×C4C2×D4×C3112yes—
342C22×C4C2×D4×C3112yes—
343C22×C4C2×D4×C3111yescharacteristic
344C22×C4C2×D4×C3112yes—
345C22×C4C24×C3111yescharacteristic
346Q16—48no—
347SD16—48no—
348M16—44no—
349C2×C8—24no—
350C4⋊C4—24no—
351C4⋊C4—24no—
352C4⋊C4—24no—
353C4⋊C4—28no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—22no—
357C4⋊C4—24no—
358C4⋊C4—24no—
359C4⋊C4—44no—
360C4⋊C4C2×D4×C3114yes—
361C22⋊C4—24no—
362C22⋊C4—24no—
363C22⋊C4—44no—
364C22⋊C4—42no—
365C22⋊C4—44no—
366C42—28no—
367C23—22no—
368C23—22no—
369C23—22no—
370C23—41no—
371C23—41no—
372C23—42no—
373C23—41no—
374C23—42no—
375C23C31×#12011yescharacteristic
376C23C31×#12011yescharacteristic
377C23C22×D4×C3111yescharacteristic
378Q8—24no—
379Q8—44no—
380Q8—42no—
381Q8—82no—
382Q8—84no—
383D4—24no—
384D4—42no—
385D4—44no—
386D4—44no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—48no—
400C2×C4—44no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—44no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4C31×#12012yes—
411C2×C4C31×#13714yescomplemented
412C2×C4C22×D4×C3112yes—
413C8—44no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—44no—
422C22—44no—
423C22—42no—
424C22—82no—
425C22—81no—
426C22—81no—
427C22C31×B(4,𝔽2)12yes—
428C22C2×C31×#12011yescharacteristic
429C22C2×C31×#13712yes—
430C4—24no—
431C4—22no—
432C4—22no—
433C4—44no—
434C4—42no—
435C4—42no—
436C4—44no—
437C4—82no—
438C2—22no—
439C2—22no—
440C2—41no—
441C2—82no—
442C2C31×#300411yescharacteristic
443C2C31×#302011yescharacteristic
444C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
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
1. C2×C31×#544C2semidirect
4. C31×#1605C2semidirect
5. C31×#1599C2semidirect
6. C31×#1511C2semidirect
7. C31×#1463C2semidirect
144. #18143C31direct (N × H)
189. C2×C4×C31#137semidirect
192. C2×#544C2×C31semidirect
195. #1605C2×C31semidirect
196. #1599C2×C31semidirect
197. #1511C2×C31semidirect
198. #1463C2×C31semidirect
306. C31#18143direct (N × H)
411. C2×C4C31×#137semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5442
C31×#30072
C31×#24062
C31×#16052
C31×#15992
C31×#15112
C31×#14632
#1814331