Finite Group Databasebeta

← C31×#9145 #21465904

Subgroups — C31×#9145 #21465904

Order 7936.

694 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2855C211yesmaximal, characteristic
2C2×C31×#376C211yesmaximal, characteristic
3C31×#1817C211yesmaximal, characteristic
4C2×C31×#328C212yesmaximal
5C31×#1294C212yesmaximal
6C2×C31×C22⋊Q8C2211yescharacteristic
7C22×C42×C31—21no—
8C22×C42×C31C2211yescharacteristic
9C2×C31×C22⋊C8C2212yes—
10C31×#391C412yescomplemented
11C31×#389C412yescomplemented
12C31×#387—22no—
13C31×#385—21no—
14C31×#381—21no—
15C31×#380C2211yescharacteristic
16C31×#376—24no—
17C2×C31×#95—21no—
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—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31C2×C412yes—
33C2×C22⋊C4×C31—21no—
34C2×C22⋊C4×C31—21no—
35C2×C42×C31—28no—
36C2×C42×C31—24no—
37C2×C42×C31—22no—
38C2×C42×C31—22no—
39C2×C42×C31C2×C412yes—
40C2×C42×C31D412yes—
41C31×C22⋊C8—22no—
42C31×C22⋊C8—22no—
43C31×#95—24no—
44C31×#95—22no—
45C31×#95—22no—
46C31×#95—22no—
47C31×#95—22no—
48C31×#95—21no—
49C31×#95D414yes—
50C24×C31C2×D411yescharacteristic
51C2×Q8×C31—22no—
52C2×Q8×C31—42no—
53C22×C4×C31—21no—
54C22×C4×C31—21no—
55C22×C4×C31—24no—
56C22×C4×C31—28no—
57C22×C4×C31—21no—
58C22×C4×C31—24no—
59C22×C4×C31—21no—
60C22×C4×C31—22no—
61C22×C4×C31—22no—
62C22×C4×C31—22no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—42no—
66C22×C4×C31—44no—
67C22×C4×C31—42no—
68C22×C4×C31—42no—
69C22×C4×C31C22⋊C412yes—
70C22×C4×C31C22⋊C412yes—
71C22×C4×C31C22×C411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C22×C4×C31C2×D412yes—
74C22×C4×C31#4112yes—
75C2×C8×C31—44no—
76C2×C8×C31—42no—
77C4⋊C4×C31—22no—
78C4⋊C4×C31—42no—
79C4⋊C4×C31—44no—
80C4⋊C4×C31—42no—
81C22⋊C4×C31—41no—
82C22⋊C4×C31—41no—
83C22⋊C4×C31—42no—
84C42×C31—216no—
85C42×C31—24no—
86C42×C31—24no—
87#9145C3111yesmaximal, characteristic, direct product factor, Sylow
88C23×C31—22no—
89C23×C31—22no—
90C23×C31C2×C22⋊C411yescharacteristic
91C23×C31#12011yescharacteristic
92C23×C31#12311yescharacteristic
93C23×C31#13512yes—
94C23×C31#13712yes—
95Q8×C31—82no—
96C2×C4×C31—24no—
97C2×C4×C31—24no—
98C2×C4×C31—22no—
99C2×C4×C31—22no—
100C2×C4×C31—22no—
101C2×C4×C31—22no—
102C2×C4×C31—28no—
103C2×C4×C31—22no—
104C2×C4×C31—22no—
105C2×C4×C31—22no—
106C2×C4×C31—42no—
107C2×C4×C31—42no—
108C2×C4×C31—44no—
109C2×C4×C31—48no—
110C2×C4×C31—48no—
111C2×C4×C31—42no—
112C2×C4×C31—44no—
113C2×C4×C31—42no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31#10414yes—
122C2×C4×C31C4×D412yes—
123C2×C4×C31#12112yes—
124C8×C31—82no—
125#2855C2×C3111yescharacteristic
126C2×#376C2×C3111yescharacteristic
127#1817C2×C3111yescharacteristic
128C2×#328C2×C3112yes—
129#1294C2×C3112yes—
130C22×C31—21no—
131C22×C31—21no—
132C22×C31—21no—
133C22×C31—21no—
134C22×C31—24no—
135C22×C31—24no—
136C22×C31#38611yescharacteristic
137C22×C31#41012yes—
138C22×C31#41611yescharacteristic
139C22×C31#41911yescharacteristic
140C22×C31C2×#10412yes—
141C22×C31#45212yes—
142C22×C31#48512yes—
143C4×C31—24no—
144C4×C31—22no—
145C4×C31—22no—
146C4×C31—48no—
147C4×C31—42no—
148C4×C31—81no—
149C4×C31—81no—
150C4×C31—82no—
151C2×C22⋊Q8C22×C3111yescharacteristic
152C22×C42—21no—
153C22×C42C22×C3111yescharacteristic
154C2×C22⋊C8C22×C3112yes—
155#391C4×C3112yescomplemented
156#389C4×C3112yescomplemented
157#387—22no—
158#385—21no—
159#381—21no—
160#380C22×C3111yescharacteristic
161#376—24no—
162C2×#95—21no—
163C2×#95C22×C3112yes—
164#336—22no—
165#328—24no—
166C2×C31—22no—
167C2×C31—22no—
168C2×C31#150012yes—
169C2×C31#150612yes—
170C2×C31#187311yescharacteristic
171C2×C31#189611yescharacteristic
172C2×C31#189911yescharacteristic
173C22×Q8C2×C4×C3111yescharacteristic
174C23×C4—22no—
175C23×C4D4×C3111yescharacteristic
176C23×C4D4×C3111yescharacteristic
177C23×C4C23×C3111yescharacteristic
178C22×C8—22no—
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×C4×C3111yescharacteristic
184C2×C4⋊C4C2×C4×C3112yes—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—21no—
187C2×C42—24no—
188C2×C42—28no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42C2×C4×C3112yes—
192C2×C42D4×C3112yes—
193C22⋊C8—22no—
194C22⋊C8—22no—
195#95—24no—
196#95—22no—
197#95—22no—
198#95—22no—
199#95—22no—
200#95—21no—
201#95D4×C3114yes—
202C31#914511yescharacteristic, direct product factor, Sylow
203C24C2×D4×C3111yescharacteristic
204C2×Q8—22no—
205C2×Q8—42no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—24no—
209C22×C4—28no—
210C22×C4—21no—
211C22×C4—24no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—42no—
219C22×C4—44no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4C22⋊C4×C3112yes—
223C22×C4C22⋊C4×C3112yes—
224C22×C4C22×C4×C3111yescharacteristic
225C22×C4C2×D4×C3111yescharacteristic
226C22×C4C2×D4×C3112yes—
227C22×C4#41×C3112yes—
228C2×C8—44no—
229C2×C8—42no—
230C4⋊C4—22no—
231C4⋊C4—42no—
232C4⋊C4—44no—
233C4⋊C4—42no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—42no—
237C42—216no—
238C42—24no—
239C42—24no—
240C23—22no—
241C23—22no—
242C23C2×C22⋊C4×C3111yescharacteristic
243C23C31×#12011yescharacteristic
244C23C31×#12311yescharacteristic
245C23C31×#13512yes—
246C23C31×#13712yes—
247Q8—82no—
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—28no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4—48no—
262C2×C4—48no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4C31×#10414yes—
274C2×C4C4×D4×C3112yes—
275C2×C4C31×#12112yes—
276C8—82no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—24no—
282C22—24no—
283C22C31×#38611yescharacteristic
284C22C31×#41012yes—
285C22C31×#41611yescharacteristic
286C22C31×#41911yescharacteristic
287C22C2×C31×#10412yes—
288C22C31×#45212yes—
289C22C31×#48512yes—
290C4—24no—
291C4—22no—
292C4—22no—
293C4—48no—
294C4—42no—
295C4—81no—
296C4—81no—
297C4—82no—
298C2—22no—
299C2—22no—
300C2C31×#150012yes—
301C2C31×#150612yes—
302C2C31×#187311yescharacteristic
303C2C31×#189611yescharacteristic
304C2C31×#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
10. C31×#391C4semidirect
11. C31×#389C4semidirect
87. #9145C31direct (N × H)
155. #391C4×C31semidirect
156. #389C4×C31semidirect
202. C31#9145direct (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×C31×#3762
C31×#18172
C2×C31×#3282
C31×#12942
#914531