Finite Group Databasebeta

← C31×#7667 #21464426

Subgroups — C31×#7667 #21464426

Order 7936.

568 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
1C31×#2857C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic
3C2×C31×#336C211yesmaximal, characteristic
4C31×#1272C214yesmaximal, complemented
5C23×C8×C31—21no—
6C2×C31×C4⋊Q8C411yescharacteristic
7C2×C31×C22⋊Q8C412yes—
8C22×C42×C31C2211yescharacteristic
9C2×C31×C4⋊C8—21no—
10C2×C31×C22⋊C8—21no—
11C31×#391C2212yes—
12C31×#389—21no—
13C31×#389—21no—
14C31×#384C411yescharacteristic
15C31×#380—21no—
16C31×#380—21no—
17C31×#336—21no—
18C31×#336C2212yes—
19C31×#336C2212yes—
20C22×Q8×C31C2×C412yes—
21C23×C4×C31C2×C411yescharacteristic
22C23×C4×C31D411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C22×C8×C31—24no—
25C22×C8×C31—22no—
26C22×C8×C31—22no—
27C22×C8×C31—42no—
28C22×C8×C31—42no—
29C31×C4⋊Q8—42no—
30C31×C22⋊Q8—44no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31C2×C412yes—
37C2×C22⋊C4×C31—22no—
38C2×C42×C31—42no—
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C2×C42×C31C2311yescharacteristic
43C31×C4⋊C8—42no—
44C31×C22⋊C8—42no—
45C31×#95—22no—
46C31×#95—22no—
47C24×C31C22⋊C411yescharacteristic
48C2×Q8×C31—24no—
49C2×Q8×C31—42no—
50C2×Q8×C31—42no—
51C22×C4×C31—22no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—41no—
58C22×C4×C31—41no—
59C22×C4×C31—41no—
60C22×C4×C31C22⋊C411yescharacteristic
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22⋊C411yescharacteristic
63C22×C4×C31SD1612yes—
64C22×C4×C31SD1612yes—
65C22×C4×C31Q1612yes—
66C22×C4×C31Q1612yes—
67C22×C4×C31C22×C411yescharacteristic
68C22×C4×C31C2×D411yescharacteristic
69C22×C4×C31C2×D411yescharacteristic
70C2×C8×C31—24no—
71C2×C8×C31—42no—
72C2×C8×C31—48no—
73C2×C8×C31—42no—
74C2×C8×C31—42no—
75C2×C8×C31—42no—
76C2×C8×C31—42no—
77C4⋊C4×C31—42no—
78C4⋊C4×C31—44no—
79C4⋊C4×C31—42no—
80C4⋊C4×C31—42no—
81C4⋊C4×C31—42no—
82C4⋊C4×C31—42no—
83C22⋊C4×C31—44no—
84C42×C31—22no—
85C42×C31—22no—
86C42×C31—41no—
87C42×C31—41no—
88#7667C3111yesmaximal, characteristic, direct product factor, Sylow
89C23×C31—21no—
90C23×C31—21no—
91C23×C31—21no—
92C23×C31—21no—
93C23×C31#10012yes—
94C23×C31#10312yes—
95C23×C31#10312yes—
96C23×C31C2×C22⋊C411yescharacteristic
97Q8×C31—84no—
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—24no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—42no—
112C2×C4×C31—42no—
113C2×C4×C31—44no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31#9912yes—
121C2×C4×C31#10312yes—
122C2×C4×C31#10312yes—
123C2×C4×C31#10412yes—
124C2×C4×C31#13112yes—
125C2×C4×C31C2×SD1611yescharacteristic
126C2×C4×C31C2×SD1611yescharacteristic
127C2×C4×C31C2×Q1611yescharacteristic
128C2×C4×C31C2×Q1611yescharacteristic
129C8×C31—44no—
130C8×C31—82no—
131#2857C2×C3111yescharacteristic
132#1797C2×C3111yescharacteristic
133C2×#336C2×C3111yescharacteristic
134#1272C2×C3114yescomplemented
135C22×C31—22no—
136C22×C31—22no—
137C22×C31—22no—
138C22×C31—22no—
139C22×C31—22no—
140C22×C31—22no—
141C22×C31#33314yes—
142C22×C31#40811yescharacteristic
143C22×C31C2×#9911yescharacteristic
144C22×C31C2×#10011yescharacteristic
145C22×C31C2×#10311yescharacteristic
146C22×C31C2×#10311yescharacteristic
147C22×C31C2×#10411yescharacteristic
148C22×C31#42111yescharacteristic
149C4×C31—22no—
150C4×C31—21no—
151C4×C31—21no—
152C4×C31—21no—
153C4×C31—22no—
154C4×C31—21no—
155C4×C31—41no—
156C4×C31—82no—
157C4×C31—82no—
158C4×C31#32814yes—
159C23×C8—21no—
160C2×C4⋊Q8C4×C3111yescharacteristic
161C2×C22⋊Q8C4×C3112yes—
162C22×C42C22×C3111yescharacteristic
163C2×C4⋊C8—21no—
164C2×C22⋊C8—21no—
165#391C22×C3112yes—
166#389—21no—
167#389—21no—
168#384C4×C3111yescharacteristic
169#380—21no—
170#380—21no—
171#336—21no—
172#336C22×C3112yes—
173#336C22×C3112yes—
174C2×C31—24no—
175C2×C31#147111yescharacteristic
176C2×C31#148111yescharacteristic
177C2×C31#149311yescharacteristic
178C2×C31C2×#32811yescharacteristic
179C2×C31#152011yescharacteristic
180C2×C31#153011yescharacteristic
181C2×C31C2×#33311yescharacteristic
182C22×Q8C2×C4×C3112yes—
183C23×C4C2×C4×C3111yescharacteristic
184C23×C4D4×C3111yescharacteristic
185C23×C4D4×C3111yescharacteristic
186C22×C8—24no—
187C22×C8—22no—
188C22×C8—22no—
189C22×C8—42no—
190C22×C8—42no—
191C4⋊Q8—42no—
192C22⋊Q8—44no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×C4×C3112yes—
199C2×C22⋊C4—22no—
200C2×C42—42no—
201C2×C42C2×C4×C3111yescharacteristic
202C2×C42D4×C3111yescharacteristic
203C2×C42D4×C3111yescharacteristic
204C2×C42C23×C3111yescharacteristic
205C4⋊C8—42no—
206C22⋊C8—42no—
207#95—22no—
208#95—22no—
209C31#766711yescharacteristic, direct product factor, Sylow
210C24C22⋊C4×C3111yescharacteristic
211C2×Q8—24no—
212C2×Q8—42no—
213C2×Q8—42no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4C22⋊C4×C3111yescharacteristic
224C22×C4C22⋊C4×C3111yescharacteristic
225C22×C4C22⋊C4×C3111yescharacteristic
226C22×C4SD16×C3112yes—
227C22×C4SD16×C3112yes—
228C22×C4Q16×C3112yes—
229C22×C4Q16×C3112yes—
230C22×C4C22×C4×C3111yescharacteristic
231C22×C4C2×D4×C3111yescharacteristic
232C22×C4C2×D4×C3111yescharacteristic
233C2×C8—24no—
234C2×C8—42no—
235C2×C8—48no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—44no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C22⋊C4—44no—
247C42—22no—
248C42—22no—
249C42—41no—
250C42—41no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23C31×#10012yes—
256C23C31×#10312yes—
257C23C31×#10312yes—
258C23C2×C22⋊C4×C3111yescharacteristic
259Q8—84no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4C31×#9912yes—
283C2×C4C31×#10312yes—
284C2×C4C31×#10312yes—
285C2×C4C31×#10412yes—
286C2×C4C31×#13112yes—
287C2×C4C2×SD16×C3111yescharacteristic
288C2×C4C2×SD16×C3111yescharacteristic
289C2×C4C2×Q16×C3111yescharacteristic
290C2×C4C2×Q16×C3111yescharacteristic
291C8—44no—
292C8—82no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22C31×#33314yes—
300C22C31×#40811yescharacteristic
301C22C2×C31×#9911yescharacteristic
302C22C2×C31×#10011yescharacteristic
303C22C2×C31×#10311yescharacteristic
304C22C2×C31×#10311yescharacteristic
305C22C2×C31×#10411yescharacteristic
306C22C31×#42111yescharacteristic
307C4—22no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—22no—
312C4—21no—
313C4—41no—
314C4—82no—
315C4—82no—
316C4C31×#32814yes—
317C2—24no—
318C2C31×#147111yescharacteristic
319C2C31×#148111yescharacteristic
320C2C31×#149311yescharacteristic
321C2C2×C31×#32811yescharacteristic
322C2C31×#152011yescharacteristic
323C2C31×#153011yescharacteristic
324C2C2×C31×#33311yescharacteristic
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×#1272C2semidirect
88. #7667C31direct (N × H)
134. #1272C2×C31semidirect
209. C31#7667direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28572
C31×#17972
C2×C31×#3362
C31×#12722
#766731