Finite Group Databasebeta

← C31×#9144 #21465903

Subgroups — C31×#9144 #21465903

Order 7936.

738 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2855C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
3C31×#1817C211yesmaximal, characteristic
4C2×C31×#328C212yesmaximal
5C31×#1294C212yesmaximal
6C2×C31×C22⋊Q8C2211yescharacteristic
7C22×C4⋊C4×C31—21no—
8C22×C42×C31—21no—
9C22×C42×C31C2211yescharacteristic
10C2×C31×C22⋊C8C2212yes—
11C31×#391C412yescomplemented
12C31×#389C412yescomplemented
13C31×#387—22no—
14C31×#385—21no—
15C31×#381—21no—
16C31×#380C2211yescharacteristic
17C4×C4⋊C4×C31—24no—
18C2×C31×#95C2212yes—
19C31×#336—22no—
20C31×#328—24no—
21C22×Q8×C31C2×C411yescharacteristic
22C23×C4×C31—22no—
23C23×C4×C31D411yescharacteristic
24C23×C4×C31D411yescharacteristic
25C23×C4×C31C2311yescharacteristic
26C22×C8×C31—22no—
27C31×C22⋊Q8—22no—
28C31×C22⋊Q8—22no—
29C2×C4⋊C4×C31—28no—
30C2×C4⋊C4×C31—24no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C4⋊C4×C31C2×C412yes—
35C2×C22⋊C4×C31—21no—
36C2×C22⋊C4×C31—21no—
37C2×C42×C31—22no—
38C2×C42×C31—22no—
39C2×C42×C31—24no—
40C2×C42×C31—42no—
41C2×C42×C31—42no—
42C2×C42×C31C2×C412yes—
43C2×C42×C31D412yes—
44C31×C22⋊C8—22no—
45C31×C22⋊C8—22no—
46C31×#95—22no—
47C31×#95—22no—
48C31×#95—22no—
49C31×#95—22no—
50C31×#95—21no—
51C31×#95D414yes—
52C24×C31C2×D411yescharacteristic
53C2×Q8×C31—22no—
54C2×Q8×C31—42no—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—24no—
62C22×C4×C31—28no—
63C22×C4×C31—24no—
64C22×C4×C31—22no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—42no—
68C22×C4×C31—44no—
69C22×C4×C31—42no—
70C22×C4×C31—42no—
71C22×C4×C31C22⋊C412yes—
72C22×C4×C31C22⋊C412yes—
73C22×C4×C31SD1612yes—
74C22×C4×C31Q1612yes—
75C22×C4×C31C22×C411yescharacteristic
76C22×C4×C31C2×D411yescharacteristic
77C22×C4×C31C2×D412yes—
78C22×C4×C31#4112yes—
79C2×C8×C31—44no—
80C2×C8×C31—42no—
81C4⋊C4×C31—216no—
82C4⋊C4×C31—22no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—44no—
85C4⋊C4×C31—42no—
86C22⋊C4×C31—41no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—41no—
89C22⋊C4×C31—41no—
90C42×C31—24no—
91C42×C31—24no—
92C42×C31—48no—
93#9144C3111yesmaximal, characteristic, direct product factor, Sylow
94C23×C31—22no—
95C23×C31—22no—
96C23×C31C2×C22⋊C411yescharacteristic
97C23×C31#12011yescharacteristic
98C23×C31#12311yescharacteristic
99C23×C31C2×SD1611yescharacteristic
100C23×C31C2×Q1611yescharacteristic
101C23×C31AGL(1,ℤ/8)11yescharacteristic
102C23×C31#13711yescharacteristic
103Q8×C31—82no—
104C2×C4×C31—24no—
105C2×C4×C31—24no—
106C2×C4×C31—22no—
107C2×C4×C31—22no—
108C2×C4×C31—22no—
109C2×C4×C31—22no—
110C2×C4×C31—22no—
111C2×C4×C31—22no—
112C2×C4×C31—22no—
113C2×C4×C31—22no—
114C2×C4×C31—22no—
115C2×C4×C31—22no—
116C2×C4×C31—28no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—44no—
120C2×C4×C31—48no—
121C2×C4×C31—48no—
122C2×C4×C31—44no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—42no—
126C2×C4×C31—42no—
127C2×C4×C31—42no—
128C2×C4×C31—42no—
129C2×C4×C31—42no—
130C2×C4×C31#10314yes—
131C2×C4×C31#10414yes—
132C2×C4×C31C4×D412yes—
133C2×C4×C31#12112yes—
134C8×C31—82no—
135#2855C2×C3111yescharacteristic
136C2×C4×C4⋊C4C2×C3111yescharacteristic
137#1817C2×C3111yescharacteristic
138C2×#328C2×C3112yes—
139#1294C2×C3112yes—
140C22×C31—21no—
141C22×C31—21no—
142C22×C31—21no—
143C22×C31—21no—
144C22×C31—22no—
145C22×C31—22no—
146C22×C31—22no—
147C22×C31—22no—
148C22×C31#38611yescharacteristic
149C22×C31#41012yes—
150C22×C31C2×#10311yescharacteristic
151C22×C31#41711yescharacteristic
152C22×C31C2×#10412yes—
153C22×C31#45011yescharacteristic
154C22×C31#45111yescharacteristic
155C22×C31#48311yescharacteristic
156C22×C31#48411yescharacteristic
157C4×C31—24no—
158C4×C31—24no—
159C4×C31—22no—
160C4×C31—22no—
161C4×C31—48no—
162C4×C31—81no—
163C4×C31—81no—
164C4×C31—82no—
165C2×C22⋊Q8C22×C3111yescharacteristic
166C22×C4⋊C4—21no—
167C22×C42—21no—
168C22×C42C22×C3111yescharacteristic
169C2×C22⋊C8C22×C3112yes—
170#391C4×C3112yescomplemented
171#389C4×C3112yescomplemented
172#387—22no—
173#385—21no—
174#381—21no—
175#380C22×C3111yescharacteristic
176C4×C4⋊C4—24no—
177C2×#95C22×C3112yes—
178#336—22no—
179#328—24no—
180C2×C31—21no—
181C2×C31—21no—
182C2×C31—21no—
183C2×C31—21no—
184C2×C31#150312yes—
185C2×C31#150912yes—
186C2×C31#187211yescharacteristic
187C2×C31#189611yescharacteristic
188C2×C31#189911yescharacteristic
189C22×Q8C2×C4×C3111yescharacteristic
190C23×C4—22no—
191C23×C4D4×C3111yescharacteristic
192C23×C4D4×C3111yescharacteristic
193C23×C4C23×C3111yescharacteristic
194C22×C8—22no—
195C22⋊Q8—22no—
196C22⋊Q8—22no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—28no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×C4×C3111yescharacteristic
202C2×C4⋊C4C2×C4×C3112yes—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C42—22no—
206C2×C42—22no—
207C2×C42—24no—
208C2×C42—42no—
209C2×C42—42no—
210C2×C42C2×C4×C3112yes—
211C2×C42D4×C3112yes—
212C22⋊C8—22no—
213C22⋊C8—22no—
214#95—22no—
215#95—22no—
216#95—22no—
217#95—22no—
218#95—21no—
219#95D4×C3114yes—
220C31#914411yescharacteristic, direct product factor, Sylow
221C24C2×D4×C3111yescharacteristic
222C2×Q8—22no—
223C2×Q8—42no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—24no—
231C22×C4—28no—
232C22×C4—24no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4—44no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4C22⋊C4×C3112yes—
241C22×C4C22⋊C4×C3112yes—
242C22×C4SD16×C3112yes—
243C22×C4Q16×C3112yes—
244C22×C4C22×C4×C3111yescharacteristic
245C22×C4C2×D4×C3111yescharacteristic
246C22×C4C2×D4×C3112yes—
247C22×C4#41×C3112yes—
248C2×C8—44no—
249C2×C8—42no—
250C4⋊C4—216no—
251C4⋊C4—22no—
252C4⋊C4—42no—
253C4⋊C4—44no—
254C4⋊C4—42no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C42—24no—
260C42—24no—
261C42—48no—
262C23—22no—
263C23—22no—
264C23C2×C22⋊C4×C3111yescharacteristic
265C23C31×#12011yescharacteristic
266C23C31×#12311yescharacteristic
267C23C2×SD16×C3111yescharacteristic
268C23C2×Q16×C3111yescharacteristic
269C23C31×AGL(1,ℤ/8)11yescharacteristic
270C23C31×#13711yescharacteristic
271Q8—82no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—28no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—44no—
288C2×C4—48no—
289C2×C4—48no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4C31×#10314yes—
299C2×C4C31×#10414yes—
300C2×C4C4×D4×C3112yes—
301C2×C4C31×#12112yes—
302C8—82no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22C31×#38611yescharacteristic
312C22C31×#41012yes—
313C22C2×C31×#10311yescharacteristic
314C22C31×#41711yescharacteristic
315C22C2×C31×#10412yes—
316C22C31×#45011yescharacteristic
317C22C31×#45111yescharacteristic
318C22C31×#48311yescharacteristic
319C22C31×#48411yescharacteristic
320C4—24no—
321C4—24no—
322C4—22no—
323C4—22no—
324C4—48no—
325C4—81no—
326C4—81no—
327C4—82no—
328C2—21no—
329C2—21no—
330C2—21no—
331C2—21no—
332C2C31×#150312yes—
333C2C31×#150912yes—
334C2C31×#187211yescharacteristic
335C2C31×#189611yescharacteristic
336C2C31×#189911yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
11. C31×#391C4semidirect
12. C31×#389C4semidirect
93. #9144C31direct (N × H)
170. #391C4×C31semidirect
171. #389C4×C31semidirect
220. C31#9144direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28552
C2×C4×C4⋊C4×C312
C31×#18172
C2×C31×#3282
C31×#12942
#914431