Finite Group Databasebeta

← C31×#7692 #21464451

Subgroups — C31×#7692 #21464451

Order 7936.

444 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2860C211yesmaximal, characteristic
2C31×#1745C211yesmaximal, characteristic, complemented
3C31×#1744C211yesmaximal, characteristic, complemented
4C31×#1271C212yesmaximal, complemented
5C31×#1270C212yesmaximal
6C2×C31×#126—21no—
7C2×C31×#97—21no—
8C2×C4×C8×C31—21no—
9C31×#390C411yescharacteristic
10C31×#390C411yescharacteristic
11C31×#390C2211yescharacteristic
12C31×#389C411yescharacteristic
13C31×#389C411yescharacteristic
14C31×#389C2211yescharacteristic
15C31×#388—21no—
16C31×#388—21no—
17C31×#388—21no—
18C43×C31C2211yescharacteristic
19C31×#336—21no—
20C31×#336—21no—
21C31×#336C2212yes—
22C31×#336C2212yes—
23C22×D4×C31C2×C411yescharacteristic
24C22×C8×C31—22no—
25C22×C8×C31—22no—
26C31×#126—44no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31C2×C411yescharacteristic
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C22⋊C4×C31—21no—
34C2×C22⋊C4×C31—21no—
35C2×C22⋊C4×C31—21no—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31C2×C411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C2×C42×C31D411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C2×C42×C31C2311yescharacteristic
46C31×#97—24no—
47C4×C8×C31—24no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C24×C31—21no—
52C2×D4×C31—22no—
53C2×D4×C31—41no—
54C2×D4×C31—41no—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31—21no—
58C22×C4×C31C22⋊C411yescharacteristic
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22⋊C411yescharacteristic
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22×C411yescharacteristic
63C22×C4×C31C2×D411yescharacteristic
64C22×C4×C31C2×D411yescharacteristic
65C2×C8×C31—24no—
66C2×C8×C31—24no—
67C2×C8×C31—42no—
68C2×C8×C31—42no—
69C2×C8×C31—42no—
70C2×C8×C31—42no—
71C4⋊C4×C31—22no—
72C4⋊C4×C31—42no—
73C4⋊C4×C31—42no—
74C4⋊C4×C31—41no—
75C4⋊C4×C31—41no—
76C4⋊C4×C31—42no—
77C22⋊C4×C31—42no—
78C22⋊C4×C31—42no—
79C22⋊C4×C31—42no—
80C22⋊C4×C31—42no—
81C22⋊C4×C31—42no—
82C22⋊C4×C31—42no—
83C42×C31—22no—
84C42×C31—22no—
85C42×C31—22no—
86C42×C31—22no—
87C42×C31—22no—
88C42×C31—41no—
89C42×C31—41no—
90#7692C3111yesmaximal, characteristic, direct product factor, Sylow
91C23×C31—41no—
92C23×C31—41no—
93C23×C31—41no—
94C23×C31—41no—
95C23×C31—41no—
96C23×C31—41no—
97C23×C31—41no—
98C23×C31C2×C22⋊C411yescharacteristic
99D4×C31—82no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31#10412yes—
126C2×C4×C31#10412yes—
127C2×C4×C31#13112yes—
128C2×C4×C31#13512yes—
129C2×C4×C31AGL(1,ℤ/8)12yes—
130C8×C31—44no—
131C8×C31—44no—
132#2860C2×C3111yescharacteristic
133#1745C2×C3111yescharacteristic, complemented
134#1744C2×C3111yescharacteristic, complemented
135#1271C2×C3112yescomplemented
136#1270C2×C3112yes—
137C22×C31—81no—
138C22×C31—81no—
139C22×C31—81no—
140C22×C31—81no—
141C22×C31—81no—
142C22×C31—81no—
143C22×C31—81no—
144C22×C31#40811yescharacteristic
145C22×C31#41011yescharacteristic
146C22×C31#41311yescharacteristic
147C22×C31#41611yescharacteristic
148C22×C31#41811yescharacteristic
149C22×C31C2×#10411yescharacteristic
150C22×C31C2×#10411yescharacteristic
151C4×C31—22no—
152C4×C31—22no—
153C4×C31—22no—
154C4×C31—22no—
155C4×C31—22no—
156C4×C31—41no—
157C4×C31—41no—
158C4×C31—81no—
159C4×C31—81no—
160C4×C31—81no—
161C2×#126—21no—
162C2×#97—21no—
163C2×C4×C8—21no—
164#390C4×C3111yescharacteristic
165#390C4×C3111yescharacteristic
166#390C22×C3111yescharacteristic
167#389C4×C3111yescharacteristic
168#389C4×C3111yescharacteristic
169#389C22×C3111yescharacteristic
170#388—21no—
171#388—21no—
172#388—21no—
173C43C22×C3111yescharacteristic
174#336—21no—
175#336—21no—
176#336C22×C3112yes—
177#336C22×C3112yes—
178C2×C31—161no—
179C2×C31#147311yescharacteristic
180C2×C31#148411yescharacteristic
181C2×C31#149411yescharacteristic
182C2×C31#150011yescharacteristic
183C2×C31#150511yescharacteristic
184C2×C31#152411yescharacteristic
185C2×C31#155311yescharacteristic
186C22×D4C2×C4×C3111yescharacteristic
187C22×C8—22no—
188C22×C8—22no—
189#126—44no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C2×C4×C3111yescharacteristic
194C2×C4⋊C4C2×C4×C3111yescharacteristic
195C2×C4⋊C4C2×C4×C3111yescharacteristic
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C42C2×C4×C3111yescharacteristic
203C2×C42C2×C4×C3111yescharacteristic
204C2×C42D4×C3111yescharacteristic
205C2×C42D4×C3111yescharacteristic
206C2×C42D4×C3111yescharacteristic
207C2×C42D4×C3111yescharacteristic
208C2×C42C23×C3111yescharacteristic
209#97—24no—
210C4×C8—24no—
211#95—21no—
212#95—21no—
213#95—21no—
214C31#769211yescharacteristic, direct product factor, Sylow
215C24—21no—
216C2×D4—22no—
217C2×D4—41no—
218C2×D4—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊C4×C3111yescharacteristic
223C22×C4C22⋊C4×C3111yescharacteristic
224C22×C4C22⋊C4×C3111yescharacteristic
225C22×C4C22⋊C4×C3111yescharacteristic
226C22×C4C22×C4×C3111yescharacteristic
227C22×C4C2×D4×C3111yescharacteristic
228C22×C4C2×D4×C3111yescharacteristic
229C2×C8—24no—
230C2×C8—24no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C4⋊C4—22no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C42—22no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—22no—
252C42—41no—
253C42—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23C2×C22⋊C4×C3111yescharacteristic
262D4—82no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4C31×#10412yes—
289C2×C4C31×#10412yes—
290C2×C4C31×#13112yes—
291C2×C4C31×#13512yes—
292C2×C4C31×AGL(1,ℤ/8)12yes—
293C8—44no—
294C8—44no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22—81no—
299C22—81no—
300C22—81no—
301C22—81no—
302C22C31×#40811yescharacteristic
303C22C31×#41011yescharacteristic
304C22C31×#41311yescharacteristic
305C22C31×#41611yescharacteristic
306C22C31×#41811yescharacteristic
307C22C2×C31×#10411yescharacteristic
308C22C2×C31×#10411yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—81no—
317C4—81no—
318C4—81no—
319C2—161no—
320C2C31×#147311yescharacteristic
321C2C31×#148411yescharacteristic
322C2C31×#149411yescharacteristic
323C2C31×#150011yescharacteristic
324C2C31×#150511yescharacteristic
325C2C31×#152411yescharacteristic
326C2C31×#155311yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1745C2semidirect
3. C31×#1744C2semidirect
4. C31×#1271C2semidirect
90. #7692C31direct (N × H)
133. #1745C2×C31semidirect
134. #1744C2×C31semidirect
135. #1271C2×C31semidirect
214. C31#7692direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28602
C31×#17452
C31×#17442
C31×#12712
C31×#12702
#769231