Finite Group Databasebeta

← C31×#9143 #21465902

Subgroups — C31×#9143 #21465902

Order 7936.

1270 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2848C211yesmaximal, characteristic
2C22×C31×#95C211yesmaximal, characteristic
3C31×#1779C211yesmaximal, characteristic
4C2×C31×#328C212yesmaximal, complemented
5C31×#1294C212yesmaximal, complemented
6C24×C4×C31—21no—
7C24×C4×C31C2211yescharacteristic
8C2×C31×C22⋊Q8C412yescomplemented
9C2×C31×C22⋊Q8C2211yescharacteristic
10C2×C31×C22⋊C8—22no—
11C2×C31×C22⋊C8C2212yes—
12C31×#385—21no—
13C31×#385—22no—
14C31×#380C412yescomplemented
15C31×#380C2211yescharacteristic
16C31×#379—21no—
17C2×C31×#95—21no—
18C2×C31×#95—24no—
19C2×C31×#95C2212yes—
20C31×#328—24no—
21C25×C31D411yescharacteristic
22C22×Q8×C31C2×C411yescharacteristic, complemented
23C23×C4×C31—28no—
24C23×C4×C31—24no—
25C23×C4×C31—22no—
26C23×C4×C31—22no—
27C23×C4×C31—22no—
28C23×C4×C31—44no—
29C23×C4×C31—44no—
30C23×C4×C31—42no—
31C23×C4×C31—42no—
32C23×C4×C31C2×C412yes—
33C23×C4×C31D412yes—
34C23×C4×C31D411yescharacteristic
35C23×C4×C31C2311yescharacteristic
36C22×C8×C31—22no—
37C31×C22⋊Q8—22no—
38C31×C22⋊Q8—22no—
39C31×C22⋊Q8—44no—
40C2×C4⋊C4×C31—22no—
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
43C2×C4⋊C4×C31C2×C412yescomplemented
44C2×C22⋊C4×C31—22no—
45C2×C22⋊C4×C31—22no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C31×C22⋊C8—22no—
49C31×C22⋊C8—22no—
50C31×C22⋊C8—44no—
51C31×#95—24no—
52C31×#95—22no—
53C31×#95—22no—
54C31×#95—21no—
55C31×#95D414yes—
56C24×C31—24no—
57C24×C31—24no—
58C24×C31—21no—
59C24×C31—21no—
60C24×C31—21no—
61C24×C31—21no—
62C24×C31C22⋊C412yes—
63C24×C31SD1612yes—
64C24×C31Q1612yes—
65C24×C31C2×D411yescharacteristic
66C2×Q8×C31—22no—
67C2×Q8×C31—42no—
68C22×C4×C31—216no—
69C22×C4×C31—28no—
70C22×C4×C31—24no—
71C22×C4×C31—24no—
72C22×C4×C31—21no—
73C22×C4×C31—24no—
74C22×C4×C31—21no—
75C22×C4×C31—24no—
76C22×C4×C31—24no—
77C22×C4×C31—21no—
78C22×C4×C31—22no—
79C22×C4×C31—21no—
80C22×C4×C31—42no—
81C22×C4×C31—42no—
82C22×C4×C31—42no—
83C22×C4×C31—42no—
84C22×C4×C31—48no—
85C22×C4×C31—48no—
86C22×C4×C31—48no—
87C22×C4×C31—416no—
88C22×C4×C31—416no—
89C22×C4×C31—44no—
90C22×C4×C31—48no—
91C22×C4×C31—42no—
92C22×C4×C31—42no—
93C22×C4×C31C22⋊C412yes—
94C22×C4×C31C22×C411yescharacteristic
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31C2×D412yes—
97C22×C4×C31#4112yes—
98C2×C8×C31—44no—
99C2×C8×C31—42no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—44no—
102C4⋊C4×C31—42no—
103C4⋊C4×C31—42no—
104C22⋊C4×C31—44no—
105C22⋊C4×C31—44no—
106C22⋊C4×C31—41no—
107C22⋊C4×C31—41no—
108C22⋊C4×C31—41no—
109C22⋊C4×C31—41no—
110#9143C3111yesmaximal, characteristic, direct product factor, Sylow
111C23×C31—24no—
112C23×C31—24no—
113C23×C31—28no—
114C23×C31—24no—
115C23×C31—24no—
116C23×C31—28no—
117C23×C31—28no—
118C23×C31—28no—
119C23×C31—22no—
120C23×C31—22no—
121C23×C31—22no—
122C23×C31—22no—
123C23×C31—22no—
124C23×C31—22no—
125C23×C31—22no—
126C23×C31—22no—
127C23×C31—22no—
128C23×C31—22no—
129C23×C31#9914yes—
130C23×C31#10314yes—
131C23×C31#10414yes—
132C23×C31C2×C22⋊C411yescharacteristic
133C23×C31#12011yescharacteristic
134C23×C31#12311yescharacteristic
135C23×C31C2×SD1611yescharacteristic
136C23×C31C2×Q1611yescharacteristic
137C23×C31AGL(1,ℤ/8)11yescharacteristic
138C23×C31#13711yescharacteristic
139Q8×C31—82no—
140C2×C4×C31—22no—
141C2×C4×C31—22no—
142C2×C4×C31—28no—
143C2×C4×C31—22no—
144C2×C4×C31—22no—
145C2×C4×C31—22no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
148C2×C4×C31—48no—
149C2×C4×C31—48no—
150C2×C4×C31—432no—
151C2×C4×C31—44no—
152C2×C4×C31—48no—
153C2×C4×C31—48no—
154C2×C4×C31—42no—
155C2×C4×C31—42no—
156C2×C4×C31—44no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—42no—
160C2×C4×C31—42no—
161C2×C4×C31—42no—
162C2×C4×C31—42no—
163C2×C4×C31—42no—
164C2×C4×C31C4×D412yes—
165C2×C4×C31#12112yes—
166C8×C31—82no—
167#2848C2×C3111yescharacteristic
168C22×#95C2×C3111yescharacteristic
169#1779C2×C3111yescharacteristic
170C2×#328C2×C3112yescomplemented
171#1294C2×C3112yescomplemented
172C22×C31—28no—
173C22×C31—28no—
174C22×C31—28no—
175C22×C31—28no—
176C22×C31—24no—
177C22×C31—21no—
178C22×C31—24no—
179C22×C31—21no—
180C22×C31—21no—
181C22×C31—24no—
182C22×C31—21no—
183C22×C31—22no—
184C22×C31—24no—
185C22×C31—22no—
186C22×C31—22no—
187C22×C31—24no—
188C22×C31—24no—
189C22×C31—22no—
190C22×C31#32818yescomplemented
191C22×C31#38611yescharacteristic
192C22×C31C2×#9912yes—
193C22×C31C2×#10311yescharacteristic
194C22×C31#41711yescharacteristic
195C22×C31C2×#10412yes—
196C22×C31#45011yescharacteristic
197C22×C31#45111yescharacteristic
198C22×C31#48311yescharacteristic
199C22×C31#48411yescharacteristic
200C4×C31—22no—
201C4×C31—22no—
202C4×C31—48no—
203C4×C31—42no—
204C4×C31—81no—
205C4×C31—81no—
206C4×C31—82no—
207C24×C4—21no—
208C24×C4C22×C3111yescharacteristic
209C2×C22⋊Q8C4×C3112yescomplemented
210C2×C22⋊Q8C22×C3111yescharacteristic
211C2×C22⋊C8—22no—
212C2×C22⋊C8C22×C3112yes—
213#385—21no—
214#385—22no—
215#380C4×C3112yescomplemented
216#380C22×C3111yescharacteristic
217#379—21no—
218C2×#95—21no—
219C2×#95—24no—
220C2×#95C22×C3112yes—
221#328—24no—
222C2×C31—21no—
223C2×C31—28no—
224C2×C31—21no—
225C2×C31—21no—
226C2×C31—21no—
227C2×C31C2×#32812yes—
228C2×C31#150412yes—
229C2×C31#187211yescharacteristic
230C2×C31#189611yescharacteristic
231C2×C31#189811yescharacteristic
232C25D4×C3111yescharacteristic
233C22×Q8C2×C4×C3111yescharacteristic, complemented
234C23×C4—24no—
235C23×C4—28no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—44no—
240C23×C4—44no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4C2×C4×C3112yes—
244C23×C4D4×C3112yes—
245C23×C4D4×C3111yescharacteristic
246C23×C4C23×C3111yescharacteristic
247C22×C8—22no—
248C22⋊Q8—22no—
249C22⋊Q8—22no—
250C22⋊Q8—44no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
254C2×C4⋊C4C2×C4×C3112yescomplemented
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C22⋊C8—22no—
260C22⋊C8—22no—
261C22⋊C8—44no—
262#95—24no—
263#95—22no—
264#95—22no—
265#95—21no—
266#95D4×C3114yes—
267C31#914311yescharacteristic, direct product factor, Sylow
268C24—24no—
269C24—24no—
270C24—21no—
271C24—21no—
272C24—21no—
273C24—21no—
274C24C22⋊C4×C3112yes—
275C24SD16×C3112yes—
276C24Q16×C3112yes—
277C24C2×D4×C3111yescharacteristic
278C2×Q8—22no—
279C2×Q8—42no—
280C22×C4—216no—
281C22×C4—28no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—21no—
285C22×C4—24no—
286C22×C4—21no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—22no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—48no—
297C22×C4—48no—
298C22×C4—48no—
299C22×C4—416no—
300C22×C4—44no—
301C22×C4—416no—
302C22×C4—48no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4C22⋊C4×C3112yes—
306C22×C4C22×C4×C3111yescharacteristic
307C22×C4C2×D4×C3111yescharacteristic
308C22×C4C2×D4×C3112yes—
309C22×C4#41×C3112yes—
310C2×C8—44no—
311C2×C8—42no—
312C4⋊C4—22no—
313C4⋊C4—42no—
314C4⋊C4—44no—
315C4⋊C4—42no—
316C22⋊C4—44no—
317C22⋊C4—44no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C23—24no—
323C23—24no—
324C23—28no—
325C23—24no—
326C23—24no—
327C23—28no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—22no—
333C23—22no—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—28no—
338C23—28no—
339C23—22no—
340C23C31×#9914yes—
341C23C31×#10314yes—
342C23C31×#10414yes—
343C23C2×C22⋊C4×C3111yescharacteristic
344C23C31×#12011yescharacteristic
345C23C31×#12311yescharacteristic
346C23C2×SD16×C3111yescharacteristic
347C23C2×Q16×C3111yescharacteristic
348C23C31×AGL(1,ℤ/8)11yescharacteristic
349C23C31×#13711yescharacteristic
350Q8—82no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—28no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—48no—
360C2×C4—48no—
361C2×C4—432no—
362C2×C4—44no—
363C2×C4—48no—
364C2×C4—48no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—44no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4C4×D4×C3112yes—
376C2×C4C31×#12112yes—
377C8—82no—
378C22—28no—
379C22—28no—
380C22—28no—
381C22—28no—
382C22—24no—
383C22—21no—
384C22—24no—
385C22—21no—
386C22—21no—
387C22—24no—
388C22—21no—
389C22—22no—
390C22—24no—
391C22—22no—
392C22—22no—
393C22—24no—
394C22—24no—
395C22—22no—
396C22C31×#32818yescomplemented
397C22C31×#38611yescharacteristic
398C22C2×C31×#9912yes—
399C22C2×C31×#10311yescharacteristic
400C22C31×#41711yescharacteristic
401C22C2×C31×#10412yes—
402C22C31×#45011yescharacteristic
403C22C31×#45111yescharacteristic
404C22C31×#48311yescharacteristic
405C22C31×#48411yescharacteristic
406C4—22no—
407C4—22no—
408C4—48no—
409C4—42no—
410C4—81no—
411C4—81no—
412C4—82no—
413C2—21no—
414C2—21no—
415C2—21no—
416C2—21no—
417C2—28no—
418C2C2×C31×#32812yes—
419C2C31×#150412yes—
420C2C31×#187211yescharacteristic
421C2C31×#189611yescharacteristic
422C2C31×#189811yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×C31×#328C2semidirect
5. C31×#1294C2semidirect
8. C2×C31×C22⋊Q8C4semidirect
14. C31×#380C4semidirect
22. C22×Q8×C31C2×C4semidirect
42. C2×C4⋊C4×C31C2×C4semidirect
43. C2×C4⋊C4×C31C2×C4semidirect
110. #9143C31direct (N × H)
170. C2×#328C2×C31semidirect
171. #1294C2×C31semidirect
190. C22×C31#328semidirect
209. C2×C22⋊Q8C4×C31semidirect
215. #380C4×C31semidirect
233. C22×Q8C2×C4×C31semidirect
253. C2×C4⋊C4C2×C4×C31semidirect
254. C2×C4⋊C4C2×C4×C31semidirect
267. C31#9143direct (N × H)
396. C22C31×#328semidirect

Maximal subgroups

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

subgroupindex
C31×#28482
C22×C31×#952
C31×#17792
C2×C31×#3282
C31×#12942
#914331