Finite Group Databasebeta

← C31×#7627 #21464386

Subgroups — C31×#7627 #21464386

Order 7936.

594 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic
2C31×#1749C211yesmaximal, characteristic
3C31×#1749C211yesmaximal, characteristic
4C31×#1271C214yesmaximal, complemented
5C22×C4⋊C4×C31—21no—
6C22×C4⋊C4×C31C411yescharacteristic
7C22×C4⋊C4×C31C411yescharacteristic
8C22×C42×C31C2211yescharacteristic
9C2×C31×C22⋊C8—21no—
10C2×C31×C22⋊C8—21no—
11C2×C31×#97—21no—
12C2×C31×#97—21no—
13C31×#389—21no—
14C31×#389—21no—
15C31×#389C412yes—
16C31×#389C2212yes—
17C2×C31×#95—21no—
18C31×#336C2212yes—
19C31×#336C2212yes—
20C23×C4×C31—21no—
21C23×C4×C31—21no—
22C23×C4×C31C2×C411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C23×C4×C31D411yescharacteristic
25C22×C8×C31—22no—
26C22×C8×C31—22no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—24no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—44no—
33C2×C4⋊C4×C31—42no—
34C2×C4⋊C4×C31C2×C412yes—
35C2×C4⋊C4×C31C2×C412yes—
36C2×C42×C31—42no—
37C2×C42×C31C2×C411yescharacteristic
38C2×C42×C31D411yescharacteristic
39C2×C42×C31D411yescharacteristic
40C2×C42×C31C2311yescharacteristic
41C31×C22⋊C8—24no—
42C31×C22⋊C8—24no—
43C31×#97—42no—
44C31×#97—42no—
45C31×#95—22no—
46C31×#95—22no—
47C24×C31C22⋊C411yescharacteristic
48C22×C4×C31—22no—
49C22×C4×C31—22no—
50C22×C4×C31—22no—
51C22×C4×C31—24no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31—41no—
59C22×C4×C31—41no—
60C22×C4×C31—42no—
61C22×C4×C31—42no—
62C22×C4×C31—42no—
63C22×C4×C31—42no—
64C22×C4×C31—42no—
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22×C411yescharacteristic
69C22×C4×C31C2×D411yescharacteristic
70C22×C4×C31C2×D411yescharacteristic
71C2×C8×C31—24no—
72C2×C8×C31—24no—
73C2×C8×C31—42no—
74C2×C8×C31—42no—
75C2×C8×C31—42no—
76C2×C8×C31—42no—
77C4⋊C4×C31—24no—
78C4⋊C4×C31—22no—
79C4⋊C4×C31—44no—
80C4⋊C4×C31—42no—
81C4⋊C4×C31—42no—
82C4⋊C4×C31—44no—
83C4⋊C4×C31M1614yes—
84C42×C31—22no—
85C42×C31—22no—
86C42×C31—41no—
87C42×C31—41no—
88#7627C3111yesmaximal, characteristic, direct product factor, Sylow
89C23×C31—21no—
90C23×C31—21no—
91C23×C31—21no—
92C23×C31—21no—
93C23×C31#10112yes—
94C23×C31#10412yes—
95C23×C31#10412yes—
96C23×C31C2×C22⋊C411yescharacteristic
97C2×C4×C31—28no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
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—24no—
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—44no—
114C2×C4×C31—44no—
115C2×C4×C31—48no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31—84no—
122C2×C4×C31#9912yes—
123C2×C4×C31C2×M1612yes—
124C2×C4×C31AGL(1,ℤ/8)12yes—
125C2×C4×C31#13712yes—
126C8×C31—44no—
127C8×C31—44no—
128C2×#389C2×C3111yescharacteristic
129#1749C2×C3111yescharacteristic
130#1749C2×C3111yescharacteristic
131#1271C2×C3114yescomplemented
132C22×C31—22no—
133C22×C31—22no—
134C22×C31—22no—
135C22×C31—22no—
136C22×C31—22no—
137C22×C31—22no—
138C22×C31#33014yes—
139C22×C31#40711yescharacteristic
140C22×C31C2×#9911yescharacteristic
141C22×C31C2×#10111yescharacteristic
142C22×C31#41811yescharacteristic
143C22×C31#41911yescharacteristic
144C22×C31C2×#10411yescharacteristic
145C22×C31C2×#10411yescharacteristic
146C4×C31—22no—
147C4×C31—22no—
148C4×C31—22no—
149C4×C31—22no—
150C4×C31—44no—
151C4×C31—41no—
152C4×C31—41no—
153C4×C31—82no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4C4×C3111yescharacteristic
156C22×C4⋊C4C4×C3111yescharacteristic
157C22×C42C22×C3111yescharacteristic
158C2×C22⋊C8—21no—
159C2×C22⋊C8—21no—
160C2×#97—21no—
161C2×#97—21no—
162#389—21no—
163#389—21no—
164#389C4×C3112yes—
165#389C22×C3112yes—
166C2×#95—21no—
167#336C22×C3112yes—
168#336C22×C3112yes—
169C2×C31—24no—
170C2×C31#146311yescharacteristic
171C2×C31#149011yescharacteristic
172C2×C31#149111yescharacteristic
173C2×C31#150711yescharacteristic
174C2×C31#150811yescharacteristic
175C2×C31C2×#33011yescharacteristic
176C2×C31#155611yescharacteristic
177C23×C4—21no—
178C23×C4—21no—
179C23×C4C2×C4×C3111yescharacteristic
180C23×C4D4×C3111yescharacteristic
181C23×C4D4×C3111yescharacteristic
182C22×C8—22no—
183C22×C8—22no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—44no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4C2×C4×C3112yes—
192C2×C4⋊C4C2×C4×C3112yes—
193C2×C42—42no—
194C2×C42C2×C4×C3111yescharacteristic
195C2×C42D4×C3111yescharacteristic
196C2×C42D4×C3111yescharacteristic
197C2×C42C23×C3111yescharacteristic
198C22⋊C8—24no—
199C22⋊C8—24no—
200#97—42no—
201#97—42no—
202#95—22no—
203#95—22no—
204C31#762711yescharacteristic, direct product factor, Sylow
205C24C22⋊C4×C3111yescharacteristic
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—24no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
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—24no—
236C4⋊C4—22no—
237C4⋊C4—42no—
238C4⋊C4—44no—
239C4⋊C4—42no—
240C4⋊C4—44no—
241C4⋊C4M16×C3114yes—
242C42—22no—
243C42—22no—
244C42—41no—
245C42—41no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23C31×#10112yes—
251C23C31×#10412yes—
252C23C31×#10412yes—
253C23C2×C22⋊C4×C3111yescharacteristic
254C2×C4—28no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—24no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—44no—
271C2×C4—44no—
272C2×C4—48no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—84no—
279C2×C4C31×#9912yes—
280C2×C4C2×M16×C3112yes—
281C2×C4C31×AGL(1,ℤ/8)12yes—
282C2×C4C31×#13712yes—
283C8—44no—
284C8—44no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22C31×#33014yes—
292C22C31×#40711yescharacteristic
293C22C2×C31×#9911yescharacteristic
294C22C2×C31×#10111yescharacteristic
295C22C31×#41811yescharacteristic
296C22C31×#41911yescharacteristic
297C22C2×C31×#10411yescharacteristic
298C22C2×C31×#10411yescharacteristic
299C4—22no—
300C4—22no—
301C4—22no—
302C4—22no—
303C4—44no—
304C4—41no—
305C4—41no—
306C4—82no—
307C2—24no—
308C2C31×#146311yescharacteristic
309C2C31×#149011yescharacteristic
310C2C31×#149111yescharacteristic
311C2C31×#150711yescharacteristic
312C2C31×#150811yescharacteristic
313C2C2×C31×#33011yescharacteristic
314C2C31×#155611yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC24×C31C22⋊C4
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
4. C31×#1271C2semidirect
88. #7627C31direct (N × H)
131. #1271C2×C31semidirect
204. C31#7627direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C31×#17492
C31×#12712
#762731