Finite Group Databasebeta

← C31×#7607 #21464366

Subgroups — C31×#7607 #21464366

Order 7936.

612 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic
2C31×#1817C211yesmaximal, characteristic
3C31×#1728C211yesmaximal, characteristic
4C31×#1271C214yesmaximal, complemented
5C22×M16×C31—21no—
6C22×C4⋊C4×C31—21no—
7C22×C4⋊C4×C31C411yescharacteristic
8C22×C4⋊C4×C31C411yescharacteristic
9C22×C42×C31C2211yescharacteristic
10C2×C31×C22⋊C8—21no—
11C31×#389—21no—
12C31×#389—21no—
13C31×#389C412yes—
14C31×#389C2212yes—
15C2×C31×#95—21no—
16C31×#336—21no—
17C31×#336—21no—
18C31×#336C2212yes—
19C31×#336C2212yes—
20C23×C4×C31—21no—
21C23×C4×C31—21no—
22C23×C4×C31C2×C411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C23×C4×C31D411yescharacteristic
25C2×M16×C31—24no—
26C2×M16×C31—42no—
27C2×M16×C31—42no—
28C22×C8×C31—22no—
29C22×C8×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—24no—
32C2×C4⋊C4×C31—22no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—22no—
35C2×C4⋊C4×C31—44no—
36C2×C4⋊C4×C31—42no—
37C2×C4⋊C4×C31C2×C412yes—
38C2×C4⋊C4×C31C2×C412yes—
39C2×C42×C31—42no—
40C2×C42×C31C2×C411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C2×C42×C31D411yescharacteristic
43C2×C42×C31C2311yescharacteristic
44C31×C22⋊C8—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—22no—
52C22×C4×C31—22no—
53C22×C4×C31—24no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31—41no—
59C22×C4×C31—42no—
60C22×C4×C31—42no—
61C22×C4×C31—42no—
62C22×C4×C31—42no—
63C22×C4×C31—42no—
64C22×C4×C31C22⋊C411yescharacteristic
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31SD1612yes—
68C22×C4×C31Q1612yes—
69C22×C4×C31C22×C411yescharacteristic
70C22×C4×C31C2×D411yescharacteristic
71C22×C4×C31C2×D411yescharacteristic
72M16×C31—48no—
73C2×C8×C31—24no—
74C2×C8×C31—42no—
75C2×C8×C31—42no—
76C2×C8×C31—42no—
77C2×C8×C31—42no—
78C2×C8×C31—42no—
79C4⋊C4×C31—24no—
80C4⋊C4×C31—22no—
81C4⋊C4×C31—42no—
82C4⋊C4×C31—44no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—44no—
85C4⋊C4×C31M1614yescomplemented
86C42×C31—41no—
87C42×C31—41no—
88C42×C31—41no—
89C42×C31—41no—
90#7607C3111yesmaximal, characteristic, direct product factor, Sylow
91C23×C31—21no—
92C23×C31—21no—
93C23×C31—21no—
94C23×C31—21no—
95C23×C31#9912yes—
96C23×C31#10312yes—
97C23×C31#10412yes—
98C23×C31C2×C22⋊C411yescharacteristic
99C2×C4×C31—28no—
100C2×C4×C31—24no—
101C2×C4×C31—24no—
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—24no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—44no—
117C2×C4×C31—48no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31—84no—
124C2×C4×C31#10112yes—
125C2×C4×C31#10312yes—
126C2×C4×C31C2×M1612yes—
127C2×C4×C31C2×SD1611yescharacteristic
128C2×C4×C31C2×Q1611yescharacteristic
129C2×C4×C31AGL(1,ℤ/8)12yes—
130C8×C31—44no—
131C8×C31—82no—
132C2×#389C2×C3111yescharacteristic
133#1817C2×C3111yescharacteristic
134#1728C2×C3111yescharacteristic
135#1271C2×C3114yescomplemented
136C22×C31—22no—
137C22×C31—22no—
138C22×C31—22no—
139C22×C31—22no—
140C22×C31—22no—
141C22×C31—22no—
142C22×C31#32814yes—
143C22×C31#40711yescharacteristic
144C22×C31C2×#9911yescharacteristic
145C22×C31C2×#10111yescharacteristic
146C22×C31C2×#10311yescharacteristic
147C22×C31#41811yescharacteristic
148C22×C31C2×#10411yescharacteristic
149C22×C31#42111yescharacteristic
150C4×C31—22no—
151C4×C31—22no—
152C4×C31—21no—
153C4×C31—22no—
154C4×C31—21no—
155C4×C31—22no—
156C4×C31—44no—
157C4×C31—41no—
158C4×C31—82no—
159C22×M16—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4C4×C3111yescharacteristic
162C22×C4⋊C4C4×C3111yescharacteristic
163C22×C42C22×C3111yescharacteristic
164C2×C22⋊C8—21no—
165#389—21no—
166#389—21no—
167#389C4×C3112yes—
168#389C22×C3112yes—
169C2×#95—21no—
170#336—21no—
171#336—21no—
172#336C22×C3112yes—
173#336C22×C3112yes—
174C2×C31—24no—
175C2×C31#146311yescharacteristic
176C2×C31#148711yescharacteristic
177C2×C31#149011yescharacteristic
178C2×C31C2×#32811yescharacteristic
179C2×C31#151011yescharacteristic
180C2×C31#152811yescharacteristic
181C2×C31#154911yescharacteristic
182C23×C4—21no—
183C23×C4—21no—
184C23×C4C2×C4×C3111yescharacteristic
185C23×C4D4×C3111yescharacteristic
186C23×C4D4×C3111yescharacteristic
187C2×M16—24no—
188C2×M16—42no—
189C2×M16—42no—
190C22×C8—22no—
191C22×C8—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—44no—
199C2×C4⋊C4C2×C4×C3112yes—
200C2×C4⋊C4C2×C4×C3112yes—
201C2×C42—42no—
202C2×C42C2×C4×C3111yescharacteristic
203C2×C42D4×C3111yescharacteristic
204C2×C42D4×C3111yescharacteristic
205C2×C42C23×C3111yescharacteristic
206C22⋊C8—42no—
207#95—22no—
208#95—22no—
209C31#760711yescharacteristic, direct product factor, Sylow
210C24C22⋊C4×C3111yescharacteristic
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—41no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4C22⋊C4×C3111yescharacteristic
228C22×C4C22⋊C4×C3111yescharacteristic
229C22×C4C22⋊C4×C3111yescharacteristic
230C22×C4SD16×C3112yes—
231C22×C4Q16×C3112yes—
232C22×C4C22×C4×C3111yescharacteristic
233C22×C4C2×D4×C3111yescharacteristic
234C22×C4C2×D4×C3111yescharacteristic
235M16—48no—
236C2×C8—24no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C4⋊C4—24no—
243C4⋊C4—22no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—44no—
247C4⋊C4—44no—
248C4⋊C4M16×C3114yescomplemented
249C42—41no—
250C42—41no—
251C42—41no—
252C42—41no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23C31×#9912yes—
258C23C31×#10312yes—
259C23C31×#10412yes—
260C23C2×C22⋊C4×C3111yescharacteristic
261C2×C4—28no—
262C2×C4—21no—
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—24no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—44no—
279C2×C4—48no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—84no—
286C2×C4C31×#10112yes—
287C2×C4C31×#10312yes—
288C2×C4C2×M16×C3112yes—
289C2×C4C2×SD16×C3111yescharacteristic
290C2×C4C2×Q16×C3111yescharacteristic
291C2×C4C31×AGL(1,ℤ/8)12yes—
292C8—44no—
293C8—82no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22C31×#32814yes—
301C22C31×#40711yescharacteristic
302C22C2×C31×#9911yescharacteristic
303C22C2×C31×#10111yescharacteristic
304C22C2×C31×#10311yescharacteristic
305C22C31×#41811yescharacteristic
306C22C2×C31×#10411yescharacteristic
307C22C31×#42111yescharacteristic
308C4—22no—
309C4—22no—
310C4—21no—
311C4—22no—
312C4—21no—
313C4—22no—
314C4—44no—
315C4—41no—
316C4—82no—
317C2—24no—
318C2C31×#146311yescharacteristic
319C2C31×#148711yescharacteristic
320C2C31×#149011yescharacteristic
321C2C2×C31×#32811yescharacteristic
322C2C31×#151011yescharacteristic
323C2C31×#152811yescharacteristic
324C2C31×#154911yescharacteristic
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
85. C4⋊C4×C31M16semidirect
90. #7607C31direct (N × H)
135. #1271C2×C31semidirect
209. C31#7607direct (N × H)
248. C4⋊C4M16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C31×#18172
C31×#17282
C31×#12712
#760731