Finite Group Databasebeta

← C31×#8611 #21465370

Subgroups — C31×#8611 #21465370

Order 7936.

486 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
1C2×C8×D4×C31C211yesmaximal, characteristic
2C31×#1810C212yesmaximal, complemented
3C31×#1465C212yesmaximal
4C31×#1293C212yesmaximal, complemented
5C23×C8×C31C411yescharacteristic
6C23×C8×C31C2211yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C8×D4×C31—22no—
9C8×D4×C31—22no—
10C2×C31×#108—22no—
11C2×C31×C4⋊C8C411yescharacteristic
12C31×#407C2214yes—
13C2×C31×C22⋊C8C411yescharacteristic
14C2×C31×C22⋊C8C2211yescharacteristic
15C2×C4×C8×C31C411yescharacteristic
16C31×#341—22no—
17C31×#324—22no—
18C31×#323—22no—
19C22×D4×C31Q811yescharacteristic
20C23×C4×C31C2×C411yescharacteristic
21C23×C4×C31C2311yescharacteristic
22C2×M16×C31—24no—
23C22×C8×C31—21no—
24C22×C8×C31—21no—
25C22×C8×C31—42no—
26C22×C8×C31—42no—
27C22×C8×C31C2×C411yescharacteristic
28C22×C8×C31C2×C411yescharacteristic
29C22×C8×C31C2×C411yescharacteristic
30C22×C8×C31C2×C411yescharacteristic
31C22×C8×C31D412yes—
32C22×C8×C31D412yes—
33C4×D4×C31—22no—
34C4×D4×C31—22no—
35C2×C4⋊C4×C31D411yescharacteristic
36C2×C22⋊C4×C31D411yescharacteristic
37C2×C22⋊C4×C31Q811yescharacteristic
38C2×C42×C31C2×C411yescharacteristic
39C31×#108—44no—
40C31×C4⋊C8—22no—
41C31×C22⋊C8—22no—
42C31×C22⋊C8—22no—
43C31×C22⋊C8—24no—
44C31×C22⋊C8—24no—
45C4×C8×C31—21no—
46C4×C8×C31—21no—
47C24×C31C4⋊C411yescharacteristic
48C24×C31C2×Q811yescharacteristic
49C2×D4×C31—22no—
50C2×D4×C31—22no—
51C2×D4×C31—22no—
52C22×C4×C31—21no—
53C22×C4×C31—21no—
54C22×C4×C31—41no—
55C22×C4×C31—41no—
56C22×C4×C31—41no—
57C22×C4×C31—41no—
58C22×C4×C31C4⋊C411yescharacteristic
59C22×C4×C31C4⋊C411yescharacteristic
60C22×C4×C31C4⋊C411yescharacteristic
61C22×C4×C31C22×C411yescharacteristic
62C22×C4×C31C2×D412yes—
63C22×C4×C31C2×D411yescharacteristic
64C22×C4×C31#4112yes—
65M16×C31—44no—
66M16×C31—44no—
67C2×C8×C31—24no—
68C2×C8×C31—22no—
69C2×C8×C31—21no—
70C2×C8×C31—21no—
71C2×C8×C31—41no—
72C2×C8×C31—42no—
73C2×C8×C31—42no—
74C2×C8×C31—42no—
75C2×C8×C31—41no—
76C2×C8×C31—41no—
77C2×C8×C31—44no—
78C2×C8×C31C22⋊C411yescharacteristic
79C2×C8×C31C22⋊C412yes—
80C2×C8×C31C22⋊C411yescharacteristic
81C4⋊C4×C31—22no—
82C22⋊C4×C31—22no—
83C22⋊C4×C31—22no—
84C42×C31—21no—
85C42×C31—21no—
86#8611C3111yesmaximal, characteristic, direct product factor, Sylow
87C23×C31—21no—
88C23×C31—21no—
89C23×C31—21no—
90C23×C31—21no—
91C23×C31—41no—
92C23×C31—41no—
93C23×C31—41no—
94C23×C31—41no—
95C23×C31#10812yescomplemented
96C23×C31C2×C4⋊C411yescharacteristic
97C23×C31C22⋊Q812yes—
98D4×C31—28no—
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—22no—
103C2×C4×C31—21no—
104C2×C4×C31—22no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—41no—
108C2×C4×C31—42no—
109C2×C4×C31—42no—
110C2×C4×C31—41no—
111C2×C4×C31—41no—
112C2×C4×C31—41no—
113C2×C4×C31—41no—
114C2×C4×C31#10812yescomplemented
115C2×C4×C31C2×C22⋊C411yescharacteristic
116C2×C4×C31#11711yescharacteristic
117C2×C4×C31#12112yes—
118C8×C31—21no—
119C8×C31—22no—
120C8×C31—41no—
121C8×C31—41no—
122C8×C31—84no—
123C8×C31#9912yes—
124C2×C8×D4C2×C3111yescharacteristic
125#1810C2×C3112yescomplemented
126#1465C2×C3112yes—
127#1293C2×C3112yescomplemented
128C22×C31—21no—
129C22×C31—21no—
130C22×C31—22no—
131C22×C31—22no—
132C22×C31—22no—
133C22×C31—22no—
134C22×C31—42no—
135C22×C31—42no—
136C22×C31—42no—
137C22×C31—42no—
138C22×C31—41no—
139C22×C31—41no—
140C22×C31#38011yescharacteristic
141C22×C31C2×#10811yescharacteristic
142C22×C31C2×#10811yescharacteristic
143C4×C31—22no—
144C4×C31—21no—
145C4×C31—22no—
146C4×C31—41no—
147C4×C31—41no—
148C4×C31C2×#9911yescharacteristic
149C4×C31#41011yescharacteristic
150C23×C8C4×C3111yescharacteristic
151C23×C8C22×C3111yescharacteristic
152C2×C4×D4C22×C3111yescharacteristic
153C8×D4—22no—
154C8×D4—22no—
155C2×#108—22no—
156C2×C4⋊C8C4×C3111yescharacteristic
157#407C22×C3114yes—
158C2×C22⋊C8C4×C3111yescharacteristic
159C2×C22⋊C8C22×C3111yescharacteristic
160C2×C4×C8C4×C3111yescharacteristic
161#341—22no—
162#324—22no—
163#323—22no—
164C2×C31—21no—
165C2×C31—21no—
166C2×C31—42no—
167C2×C31—42no—
168C2×C31#179911yescharacteristic
169C2×C31#181011yescharacteristic
170C2×C31#181311yescharacteristic
171C22×D4Q8×C3111yescharacteristic
172C23×C4C2×C4×C3111yescharacteristic
173C23×C4C23×C3111yescharacteristic
174C2×M16—24no—
175C22×C8—21no—
176C22×C8—21no—
177C22×C8—42no—
178C22×C8—42no—
179C22×C8C2×C4×C3111yescharacteristic
180C22×C8C2×C4×C3111yescharacteristic
181C22×C8C2×C4×C3111yescharacteristic
182C22×C8C2×C4×C3111yescharacteristic
183C22×C8D4×C3112yes—
184C22×C8D4×C3112yes—
185C4×D4—22no—
186C4×D4—22no—
187C2×C4⋊C4D4×C3111yescharacteristic
188C2×C22⋊C4D4×C3111yescharacteristic
189C2×C22⋊C4Q8×C3111yescharacteristic
190C2×C42C2×C4×C3111yescharacteristic
191#108—44no—
192C4⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—22no—
195C22⋊C8—24no—
196C22⋊C8—24no—
197C4×C8—21no—
198C4×C8—21no—
199C31#861111yescharacteristic, direct product factor, Sylow
200C24C4⋊C4×C3111yescharacteristic
201C24C2×Q8×C3111yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—22no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4C4⋊C4×C3111yescharacteristic
212C22×C4C4⋊C4×C3111yescharacteristic
213C22×C4C4⋊C4×C3111yescharacteristic
214C22×C4C22×C4×C3111yescharacteristic
215C22×C4C2×D4×C3112yes—
216C22×C4C2×D4×C3111yescharacteristic
217C22×C4#41×C3112yes—
218M16—44no—
219M16—44no—
220C2×C8—24no—
221C2×C8—22no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—44no—
231C2×C8C22⋊C4×C3111yescharacteristic
232C2×C8C22⋊C4×C3112yes—
233C2×C8C22⋊C4×C3111yescharacteristic
234C4⋊C4—22no—
235C22⋊C4—22no—
236C22⋊C4—22no—
237C42—21no—
238C42—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23C31×#10812yescomplemented
248C23C2×C4⋊C4×C3111yescharacteristic
249C23C31×C22⋊Q812yes—
250D4—28no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4C31×#10812yescomplemented
267C2×C4C2×C22⋊C4×C3111yescharacteristic
268C2×C4C31×#11711yescharacteristic
269C2×C4C31×#12112yes—
270C8—21no—
271C8—22no—
272C8—41no—
273C8—41no—
274C8—84no—
275C8C31×#9912yes—
276C22—21no—
277C22—21no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—22no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—42no—
286C22—41no—
287C22—41no—
288C22C31×#38011yescharacteristic
289C22C2×C31×#10811yescharacteristic
290C22C2×C31×#10811yescharacteristic
291C4—22no—
292C4—21no—
293C4—22no—
294C4—41no—
295C4—41no—
296C4C2×C31×#9911yescharacteristic
297C4C31×#41011yescharacteristic
298C2—21no—
299C2—21no—
300C2—42no—
301C2—42no—
302C2C31×#179911yescharacteristic
303C2C31×#181011yescharacteristic
304C2C31×#181311yescharacteristic
subgroupG/H
center, socleC22×C31#380
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×D4×C31Q8
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
2. C31×#1810C2semidirect
4. C31×#1293C2semidirect
86. #8611C31direct (N × H)
95. C23×C31#108semidirect
114. C2×C4×C31#108semidirect
125. #1810C2×C31semidirect
127. #1293C2×C31semidirect
199. C31#8611direct (N × H)
247. C23C31×#108semidirect
266. C2×C4C31×#108semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D4×C312
C31×#18102
C31×#14652
C31×#12932
#861131