Finite Group Databasebeta

← C31×#9151 #21465910

Subgroups — C31×#9151 #21465910

Order 7936.

946 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2848C211yesmaximal, characteristic
2C2×C31×#380C211yesmaximal, characteristic
3C31×#1779C211yesmaximal, characteristic
4C2×C31×#328C212yesmaximal, complemented
5C31×#1294C212yesmaximal, complemented
6C24×C4×C31C2211yescharacteristic
7C2×C31×C22⋊Q8C412yescomplemented
8C2×C31×C22⋊Q8C2211yescharacteristic
9C22×C4⋊C4×C31—21no—
10C22×C22⋊C4×C31—21no—
11C2×C31×C22⋊C8—22no—
12C2×C31×C22⋊C8C2212yes—
13C31×#385—21no—
14C31×#385—22no—
15C31×#380—24no—
16C31×#380C412yescomplemented
17C31×#380C2211yescharacteristic
18C31×#379—21no—
19C2×C31×#95C2212yes—
20C31×#328—24no—
21C25×C31D411yescharacteristic
22C22×Q8×C31C2×C411yescharacteristic
23C23×C4×C31—22no—
24C23×C4×C31—22no—
25C23×C4×C31—22no—
26C23×C4×C31—44no—
27C23×C4×C31C2×C412yes—
28C23×C4×C31D411yescharacteristic
29C23×C4×C31D412yes—
30C23×C4×C31C2311yescharacteristic
31C22×C8×C31—22no—
32C31×C22⋊Q8—22no—
33C31×C22⋊Q8—22no—
34C31×C22⋊Q8—44no—
35C2×C4⋊C4×C31—24no—
36C2×C4⋊C4×C31—22no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—44no—
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C4⋊C4×C31C2×C412yes—
41C2×C22⋊C4×C31—24no—
42C2×C22⋊C4×C31—22no—
43C2×C22⋊C4×C31—22no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—42no—
47C2×C22⋊C4×C31—42no—
48C31×C22⋊C8—22no—
49C31×C22⋊C8—22no—
50C31×C22⋊C8—44no—
51C31×#95—22no—
52C31×#95—22no—
53C31×#95—21no—
54C31×#95D414yes—
55C24×C31—21no—
56C24×C31—21no—
57C24×C31—21no—
58C24×C31—21no—
59C24×C31—42no—
60C24×C31—42no—
61C24×C31C22⋊C412yes—
62C24×C31SD1612yes—
63C24×C31Q1612yes—
64C24×C31C2×D411yescharacteristic
65C2×Q8×C31—22no—
66C2×Q8×C31—42no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—24no—
70C22×C4×C31—24no—
71C22×C4×C31—24no—
72C22×C4×C31—24no—
73C22×C4×C31—24no—
74C22×C4×C31—21no—
75C22×C4×C31—22no—
76C22×C4×C31—21no—
77C22×C4×C31—24no—
78C22×C4×C31—42no—
79C22×C4×C31—42no—
80C22×C4×C31—42no—
81C22×C4×C31—48no—
82C22×C4×C31—48no—
83C22×C4×C31—44no—
84C22×C4×C31—44no—
85C22×C4×C31—42no—
86C22×C4×C31—42no—
87C22×C4×C31C22⋊C412yes—
88C22×C4×C31C22×C411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90C22×C4×C31C2×D412yes—
91C22×C4×C31#4112yes—
92C2×C8×C31—44no—
93C2×C8×C31—42no—
94C4⋊C4×C31—22no—
95C4⋊C4×C31—48no—
96C4⋊C4×C31—42no—
97C4⋊C4×C31—44no—
98C4⋊C4×C31—42no—
99C22⋊C4×C31—44no—
100C22⋊C4×C31—48no—
101C22⋊C4×C31—44no—
102C22⋊C4×C31—41no—
103C22⋊C4×C31—41no—
104C22⋊C4×C31—41no—
105C22⋊C4×C31—41no—
106#9151C3111yesmaximal, characteristic, direct product factor, Sylow
107C23×C31—22no—
108C23×C31—22no—
109C23×C31—22no—
110C23×C31—22no—
111C23×C31—22no—
112C23×C31—22no—
113C23×C31—22no—
114C23×C31—22no—
115C23×C31—22no—
116C23×C31—22no—
117C23×C31—22no—
118C23×C31—22no—
119C23×C31—44no—
120C23×C31—44no—
121C23×C31—42no—
122C23×C31—42no—
123C23×C31—42no—
124C23×C31—42no—
125C23×C31—44no—
126C23×C31—44no—
127C23×C31#10314yes—
128C23×C31C2×C22⋊C411yescharacteristic
129C23×C31#12011yescharacteristic
130C23×C31#12311yescharacteristic
131C23×C31C2×SD1611yescharacteristic
132C23×C31C2×Q1611yescharacteristic
133C23×C31AGL(1,ℤ/8)11yescharacteristic
134C23×C31#13711yescharacteristic
135Q8×C31—82no—
136C2×C4×C31—24no—
137C2×C4×C31—24no—
138C2×C4×C31—22no—
139C2×C4×C31—22no—
140C2×C4×C31—22no—
141C2×C4×C31—22no—
142C2×C4×C31—42no—
143C2×C4×C31—42no—
144C2×C4×C31—48no—
145C2×C4×C31—48no—
146C2×C4×C31—44no—
147C2×C4×C31—44no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—42no—
151C2×C4×C31—42no—
152C2×C4×C31—42no—
153C2×C4×C31—42no—
154C2×C4×C31—42no—
155C2×C4×C31—44no—
156C2×C4×C31—84no—
157C2×C4×C31—84no—
158C2×C4×C31#9914yes—
159C2×C4×C31C4×D412yes—
160C2×C4×C31#12112yes—
161C8×C31—82no—
162#2848C2×C3111yescharacteristic
163C2×#380C2×C3111yescharacteristic
164#1779C2×C3111yescharacteristic
165C2×#328C2×C3112yescomplemented
166#1294C2×C3112yescomplemented
167C22×C31—21no—
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—22no—
172C22×C31—22no—
173C22×C31—22no—
174C22×C31—22no—
175C22×C31—24no—
176C22×C31—24no—
177C22×C31—24no—
178C22×C31—44no—
179C22×C31—44no—
180C22×C31—44no—
181C22×C31—44no—
182C22×C31—42no—
183C22×C31—42no—
184C22×C31—42no—
185C22×C31—42no—
186C22×C31#38611yescharacteristic
187C22×C31C2×#9912yes—
188C22×C31C2×#10311yescharacteristic
189C22×C31#41711yescharacteristic
190C22×C31#42112yes—
191C22×C31#45011yescharacteristic
192C22×C31#45111yescharacteristic
193C22×C31#48311yescharacteristic
194C22×C31#48411yescharacteristic
195C4×C31—22no—
196C4×C31—24no—
197C4×C31—22no—
198C4×C31—84no—
199C4×C31—81no—
200C4×C31—81no—
201C4×C31—82no—
202C24×C4C22×C3111yescharacteristic
203C2×C22⋊Q8C4×C3112yescomplemented
204C2×C22⋊Q8C22×C3111yescharacteristic
205C22×C4⋊C4—21no—
206C22×C22⋊C4—21no—
207C2×C22⋊C8—22no—
208C2×C22⋊C8C22×C3112yes—
209#385—21no—
210#385—22no—
211#380—24no—
212#380C4×C3112yescomplemented
213#380C22×C3111yescharacteristic
214#379—21no—
215C2×#95C22×C3112yes—
216#328—24no—
217C2×C31—21no—
218C2×C31—21no—
219C2×C31—21no—
220C2×C31—21no—
221C2×C31—44no—
222C2×C31#151312yes—
223C2×C31#152012yes—
224C2×C31#187211yescharacteristic
225C2×C31#189711yescharacteristic
226C2×C31#189811yescharacteristic
227C25D4×C3111yescharacteristic
228C22×Q8C2×C4×C3111yescharacteristic
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—44no—
233C23×C4C2×C4×C3112yes—
234C23×C4D4×C3111yescharacteristic
235C23×C4D4×C3112yes—
236C23×C4C23×C3111yescharacteristic
237C22×C8—22no—
238C22⋊Q8—22no—
239C22⋊Q8—22no—
240C22⋊Q8—44no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—44no—
245C2×C4⋊C4C2×C4×C3111yescharacteristic
246C2×C4⋊C4C2×C4×C3112yes—
247C2×C22⋊C4—24no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—42no—
253C2×C22⋊C4—42no—
254C22⋊C8—22no—
255C22⋊C8—22no—
256C22⋊C8—44no—
257#95—22no—
258#95—22no—
259#95—21no—
260#95D4×C3114yes—
261C31#915111yescharacteristic, direct product factor, Sylow
262C24—21no—
263C24—21no—
264C24—21no—
265C24—21no—
266C24—42no—
267C24—42no—
268C24C22⋊C4×C3112yes—
269C24SD16×C3112yes—
270C24Q16×C3112yes—
271C24C2×D4×C3111yescharacteristic
272C2×Q8—22no—
273C2×Q8—42no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—24no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—48no—
289C22×C4—48no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4C22⋊C4×C3112yes—
295C22×C4C22×C4×C3111yescharacteristic
296C22×C4C2×D4×C3111yescharacteristic
297C22×C4C2×D4×C3112yes—
298C22×C4#41×C3112yes—
299C2×C8—44no—
300C2×C8—42no—
301C4⋊C4—22no—
302C4⋊C4—42no—
303C4⋊C4—48no—
304C4⋊C4—44no—
305C4⋊C4—42no—
306C22⋊C4—44no—
307C22⋊C4—48no—
308C22⋊C4—44no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—22no—
325C23—44no—
326C23—44no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23—42no—
331C23—44no—
332C23—44no—
333C23C31×#10314yes—
334C23C2×C22⋊C4×C3111yescharacteristic
335C23C31×#12011yescharacteristic
336C23C31×#12311yescharacteristic
337C23C2×SD16×C3111yescharacteristic
338C23C2×Q16×C3111yescharacteristic
339C23C31×AGL(1,ℤ/8)11yescharacteristic
340C23C31×#13711yescharacteristic
341Q8—82no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—48no—
351C2×C4—48no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—44no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—84no—
363C2×C4—84no—
364C2×C4C31×#9914yes—
365C2×C4C4×D4×C3112yes—
366C2×C4C31×#12112yes—
367C8—82no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—24no—
377C22—24no—
378C22—24no—
379C22—44no—
380C22—44no—
381C22—44no—
382C22—44no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22C31×#38611yescharacteristic
388C22C2×C31×#9912yes—
389C22C2×C31×#10311yescharacteristic
390C22C31×#41711yescharacteristic
391C22C31×#42112yes—
392C22C31×#45011yescharacteristic
393C22C31×#45111yescharacteristic
394C22C31×#48311yescharacteristic
395C22C31×#48411yescharacteristic
396C4—22no—
397C4—24no—
398C4—22no—
399C4—84no—
400C4—81no—
401C4—81no—
402C4—82no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2—44no—
408C2C31×#151312yes—
409C2C31×#152012yes—
410C2C31×#187211yescharacteristic
411C2C31×#189711yescharacteristic
412C2C31×#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
7. C2×C31×C22⋊Q8C4semidirect
16. C31×#380C4semidirect
106. #9151C31direct (N × H)
165. C2×#328C2×C31semidirect
166. #1294C2×C31semidirect
203. C2×C22⋊Q8C4×C31semidirect
212. #380C4×C31semidirect
261. C31#9151direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28482
C2×C31×#3802
C31×#17792
C2×C31×#3282
C31×#12942
#915131