Finite Group Databasebeta

← C31×#11781 #21468540

Subgroups — C31×#11781 #21468540

Order 7936.

482 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2548C211yesmaximal, characteristic
2C4×C31×#101C211yesmaximal, characteristic, complemented
3C31×#1467C211yesmaximal, characteristic, complemented
4C31×#1345C214yesmaximal, complemented
5C2×C31×#127C411yescharacteristic
6C2×C31×#124—21no—
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#432—21no—
9C2×C31×#101—21no—
10C4×M16×C31—21no—
11C31×#394C412yes—
12C31×#394C2212yes—
13C31×#390—21no—
14C31×#390—21no—
15C31×#390—21no—
16C4×C4⋊C4×C31C411yescharacteristic
17C31×#343C2212yes—
18C31×#324—21no—
19C31×#324C2212yes—
20C22×Q8×C31D411yescharacteristic
21C22×D4×C31—21no—
22C22×D4×C31—21no—
23C22×D4×C31C2×C412yes—
24C2×M16×C31—22no—
25C31×#127—41no—
26C31×#127—41no—
27C31×#124—44no—
28C4×Q8×C31—41no—
29C4×Q8×C31—41no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C4⋊C4×C31C2311yescharacteristic
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—22no—
38C2×C42×C31—21no—
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C31×C4⋊C8—41no—
43C31×#101—24no—
44C31×C22⋊C8—22no—
45C31×#97—41no—
46C31×#97—41no—
47C4×C8×C31—41no—
48C31×#95C2×C412yes—
49C24×C31—22no—
50C2×Q8×C31—22no—
51C2×Q8×C31—22no—
52C2×Q8×C31—41no—
53C2×D4×C31—42no—
54C2×D4×C31—42no—
55C2×D4×C31—42no—
56C2×D4×C31—42no—
57C2×D4×C31—42no—
58C2×D4×C31—41no—
59C2×D4×C31—41no—
60C2×D4×C31—42no—
61C2×D4×C31—82no—
62C22×C4×C31—22no—
63C22×C4×C31C22⋊C411yescharacteristic
64C22×C4×C31C22⋊C411yescharacteristic
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22×C411yescharacteristic
68C22×C4×C31C2×D411yescharacteristic
69C22×C4×C31C2×D411yescharacteristic
70M16×C31—24no—
71M16×C31—42no—
72C2×C8×C31—42no—
73C2×C8×C31—42no—
74C4⋊C4×C31—41no—
75C4⋊C4×C31—41no—
76C4⋊C4×C31—41no—
77C4⋊C4×C31—42no—
78C22⋊C4×C31—44no—
79C22⋊C4×C31—44no—
80C22⋊C4×C31—82no—
81C22⋊C4×C31—82no—
82C42×C31—21no—
83C42×C31—21no—
84C42×C31—21no—
85C42×C31—21no—
86C42×C31—21no—
87C42×C31—21no—
88C42×C31—42no—
89#11781C3111yesmaximal, characteristic, direct product factor, Sylow
90C23×C31—42no—
91C23×C31—42no—
92C23×C31—42no—
93C23×C31—42no—
94C23×C31—42no—
95C23×C31—42no—
96C23×C31—42no—
97C23×C31C2×C22⋊C411yescharacteristic
98Q8×C31—44no—
99D4×C31—82no—
100D4×C31—84no—
101D4×C31—84no—
102D4×C31—82no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—22no—
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—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31#9911yescharacteristic
121C2×C4×C31#9911yescharacteristic
122C2×C4×C31#10412yes—
123C2×C4×C31AGL(1,ℤ/8)12yes—
124C8×C31—44no—
125C8×C31—82no—
126#2548C2×C3111yescharacteristic
127C4×#101C2×C3111yescharacteristic, complemented
128#1467C2×C3111yescharacteristic, complemented
129#1345C2×C3114yescomplemented
130C22×C31—21no—
131C22×C31—21no—
132C22×C31—82no—
133C22×C31—82no—
134C22×C31—82no—
135C22×C31—82no—
136C22×C31—82no—
137C22×C31—82no—
138C22×C31—82no—
139C22×C31C2×#9911yescharacteristic
140C22×C31#41811yescharacteristic
141C22×C31C2×#10411yescharacteristic
142C4×C31—21no—
143C4×C31—22no—
144C4×C31—22no—
145C4×C31—41no—
146C4×C31—41no—
147C4×C31—41no—
148C4×C31—41no—
149C4×C31—82no—
150C4×C31#35512yes—
151C2×#127C4×C3111yescharacteristic
152C2×#124—21no—
153C2×C4×Q8C22×C3111yescharacteristic
154#432—21no—
155C2×#101—21no—
156C4×M16—21no—
157#394C4×C3112yes—
158#394C22×C3112yes—
159#390—21no—
160#390—21no—
161#390—21no—
162C4×C4⋊C4C4×C3111yescharacteristic
163#343C22×C3112yes—
164#324—21no—
165#324C22×C3112yes—
166C2×C31—21no—
167C2×C31—21no—
168C2×C31—162no—
169C2×C31#150711yescharacteristic
170C2×C31#212211yescharacteristic
171C2×C31C2×#35511yescharacteristic
172C22×Q8D4×C3111yescharacteristic
173C22×D4—21no—
174C22×D4—21no—
175C22×D4C2×C4×C3112yes—
176C2×M16—22no—
177#127—41no—
178#127—41no—
179#124—44no—
180C4×Q8—41no—
181C4×Q8—41no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×C4×C3111yescharacteristic
184C2×C4⋊C4D4×C3111yescharacteristic
185C2×C4⋊C4C23×C3111yescharacteristic
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C42—21no—
191C2×C42C2×C4×C3111yescharacteristic
192C2×C42D4×C3111yescharacteristic
193C2×C42D4×C3111yescharacteristic
194C4⋊C8—41no—
195#101—24no—
196C22⋊C8—22no—
197#97—41no—
198#97—41no—
199C4×C8—41no—
200#95C2×C4×C3112yes—
201C31#1178111yescharacteristic, direct product factor, Sylow
202C24—22no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—42no—
210C2×D4—42no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—42no—
214C2×D4—82no—
215C22×C4—22no—
216C22×C4C22⋊C4×C3111yescharacteristic
217C22×C4C22⋊C4×C3111yescharacteristic
218C22×C4C22⋊C4×C3111yescharacteristic
219C22×C4C22⋊C4×C3111yescharacteristic
220C22×C4C22×C4×C3111yescharacteristic
221C22×C4C2×D4×C3111yescharacteristic
222C22×C4C2×D4×C3111yescharacteristic
223M16—24no—
224M16—42no—
225C2×C8—42no—
226C2×C8—42no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C22⋊C4—44no—
232C22⋊C4—44no—
233C22⋊C4—82no—
234C22⋊C4—82no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—42no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23C2×C22⋊C4×C3111yescharacteristic
250Q8—44no—
251D4—82no—
252D4—84no—
253D4—84no—
254D4—82no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4C31×#9911yescharacteristic
273C2×C4C31×#9911yescharacteristic
274C2×C4C31×#10412yes—
275C2×C4C31×AGL(1,ℤ/8)12yes—
276C8—44no—
277C8—82no—
278C22—21no—
279C22—21no—
280C22—82no—
281C22—82no—
282C22—82no—
283C22—82no—
284C22—82no—
285C22—82no—
286C22—82no—
287C22C2×C31×#9911yescharacteristic
288C22C31×#41811yescharacteristic
289C22C2×C31×#10411yescharacteristic
290C4—21no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—82no—
298C4C31×#35512yes—
299C2—21no—
300C2—21no—
301C2—162no—
302C2C31×#150711yescharacteristic
303C2C31×#212211yescharacteristic
304C2C2×C31×#35511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC2×C31×#127C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C31×#101C2semidirect
3. C31×#1467C2semidirect
4. C31×#1345C2semidirect
89. #11781C31direct (N × H)
127. C4×#101C2×C31semidirect
128. #1467C2×C31semidirect
129. #1345C2×C31semidirect
201. C31#11781direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25482
C4×C31×#1012
C31×#14672
C31×#13452
#1178131