Finite Group Databasebeta

← C31×#11787 #21468546

Subgroups — C31×#11787 #21468546

Order 7936.

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

normal subgroups only

This group has 460 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×#2563C211yesmaximal, characteristic
2C4×C31×#99C211yesmaximal, characteristic
3C31×#1465C211yesmaximal, characteristic
4C31×#1351C214yesmaximal, complemented
5C2×C31×C4⋊Q8C411yescharacteristic, complemented
6C2×C4×D4×C31C2211yescharacteristic
7C2×C31×#99—21no—
8C31×#407—21no—
9C31×#393C412yescomplemented
10C31×#393C2212yes—
11C31×#390—21no—
12C31×#382—21no—
13C31×#380—21no—
14C31×#380—21no—
15C4×C4⋊C4×C31C411yescharacteristic, complemented
16C4×C22⋊C4×C31—21no—
17C31×#342C2212yes—
18C31×#324—21no—
19C31×#323C2212yes—
20C22×Q8×C31C2×C412yes—
21C22×D4×C31D411yescharacteristic
22C23×C4×C31D411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C2×M16×C31—41no—
25C31×C4⋊Q8—41no—
26C31×C4⋊Q8—41no—
27C4×D4×C31—41no—
28C4×D4×C31—41no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31C2×C411yescharacteristic
37C2×C22⋊C4×C31C2311yescharacteristic
38C2×C42×C31—21no—
39C2×C42×C31—41no—
40C2×C42×C31C2×C411yescharacteristic
41C31×#99—24no—
42C31×C22⋊C8—22no—
43C31×C22⋊C8—41no—
44C31×#95—22no—
45C31×#95—22no—
46C31×#95—41no—
47C31×#95C2×C412yes—
48C24×C31C22⋊C411yescharacteristic
49C24×C31C2×D411yescharacteristic
50C2×Q8×C31—42no—
51C2×Q8×C31—82no—
52C2×D4×C31—22no—
53C2×D4×C31—22no—
54C2×D4×C31—41no—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—22no—
60C22×C4×C31—22no—
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×C31C22×C411yescharacteristic
68C22×C4×C31C2×D411yescharacteristic
69M16×C31—82no—
70C2×C8×C31—42no—
71C4⋊C4×C31—41no—
72C4⋊C4×C31—42no—
73C4⋊C4×C31—42no—
74C4⋊C4×C31—41no—
75C4⋊C4×C31—41no—
76C22⋊C4×C31—24no—
77C22⋊C4×C31—41no—
78C22⋊C4×C31—41no—
79C22⋊C4×C31—42no—
80C22⋊C4×C31—82no—
81C22⋊C4×C31—82no—
82C42×C31—21no—
83C42×C31—21no—
84C42×C31—42no—
85C42×C31—82no—
86#11787C3111yesmaximal, characteristic, direct product factor, Sylow
87C23×C31—21no—
88C23×C31—21no—
89C23×C31—21no—
90C23×C31—21no—
91C23×C31—21no—
92C23×C31—41no—
93C23×C31—41no—
94C23×C31—41no—
95C23×C31—41no—
96C23×C31C2×C22⋊C411yescharacteristic
97C23×C31#13712yes—
98Q8×C31—84no—
99D4×C31—44no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—22no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—42no—
107C2×C4×C31—42no—
108C2×C4×C31—41no—
109C2×C4×C31—41no—
110C2×C4×C31—41no—
111C2×C4×C31—44no—
112C2×C4×C31—42no—
113C2×C4×C31—42no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—81no—
119C2×C4×C31—81no—
120C2×C4×C31—82no—
121C2×C4×C31—82no—
122C2×C4×C31#9911yescharacteristic
123C2×C4×C31#9911yescharacteristic
124C2×C4×C31#10412yes—
125C8×C31—82no—
126#2563C2×C3111yescharacteristic
127C4×#99C2×C3111yescharacteristic
128#1465C2×C3111yescharacteristic
129#1351C2×C3114yescomplemented
130C22×C31—21no—
131C22×C31—21no—
132C22×C31—22no—
133C22×C31—42no—
134C22×C31—42no—
135C22×C31—41no—
136C22×C31—41no—
137C22×C31—41no—
138C22×C31—41no—
139C22×C31—41no—
140C22×C31—81no—
141C22×C31—81no—
142C22×C31C2×#9911yescharacteristic
143C22×C31#41911yescharacteristic
144C22×C31C2×#10411yescharacteristic
145C4×C31—21no—
146C4×C31—22no—
147C4×C31—41no—
148C4×C31—41no—
149C4×C31—41no—
150C4×C31—82no—
151C4×C31—84no—
152C4×C31—82no—
153C4×C31#35412yes—
154C2×C4⋊Q8C4×C3111yescharacteristic, complemented
155C2×C4×D4C22×C3111yescharacteristic
156C2×#99—21no—
157#407—21no—
158#393C4×C3112yescomplemented
159#393C22×C3112yes—
160#390—21no—
161#382—21no—
162#380—21no—
163#380—21no—
164C4×C4⋊C4C4×C3111yescharacteristic, complemented
165C4×C22⋊C4—21no—
166#342C22×C3112yes—
167#324—21no—
168#323C22×C3112yes—
169C2×C31—21no—
170C2×C31—21no—
171C2×C31—42no—
172C2×C31—81no—
173C2×C31#150811yescharacteristic
174C2×C31#212211yescharacteristic
175C2×C31C2×#35411yescharacteristic
176C22×Q8C2×C4×C3112yes—
177C22×D4D4×C3111yescharacteristic
178C23×C4D4×C3111yescharacteristic
179C23×C4D4×C3111yescharacteristic
180C2×M16—41no—
181C4⋊Q8—41no—
182C4⋊Q8—41no—
183C4×D4—41no—
184C4×D4—41no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4D4×C3111yescharacteristic
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4C2×C4×C3111yescharacteristic
193C2×C22⋊C4C23×C3111yescharacteristic
194C2×C42—21no—
195C2×C42—41no—
196C2×C42C2×C4×C3111yescharacteristic
197#99—24no—
198C22⋊C8—22no—
199C22⋊C8—41no—
200#95—22no—
201#95—22no—
202#95—41no—
203#95C2×C4×C3112yes—
204C31#1178711yescharacteristic, direct product factor, Sylow
205C24C22⋊C4×C3111yescharacteristic
206C24C2×D4×C3111yescharacteristic
207C2×Q8—42no—
208C2×Q8—82no—
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—41no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4C22⋊C4×C3111yescharacteristic
222C22×C4C22⋊C4×C3111yescharacteristic
223C22×C4C22⋊C4×C3111yescharacteristic
224C22×C4C22×C4×C3111yescharacteristic
225C22×C4C2×D4×C3111yescharacteristic
226M16—82no—
227C2×C8—42no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C22⋊C4—24no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—42no—
237C22⋊C4—82no—
238C22⋊C4—82no—
239C42—21no—
240C42—21no—
241C42—42no—
242C42—82no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23C2×C22⋊C4×C3111yescharacteristic
253C23C31×#13712yes—
254Q8—84no—
255D4—44no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—44no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4C31×#9911yescharacteristic
279C2×C4C31×#9911yescharacteristic
280C2×C4C31×#10412yes—
281C8—82no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22—81no—
294C22C2×C31×#9911yescharacteristic
295C22C31×#41911yescharacteristic
296C22C2×C31×#10411yescharacteristic
297C4—21no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—82no—
303C4—84no—
304C4—82no—
305C4C31×#35412yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2C31×#150811yescharacteristic
311C2C31×#212211yescharacteristic
312C2C2×C31×#35411yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1351C2semidirect
5. C2×C31×C4⋊Q8C4semidirect
9. C31×#393C4semidirect
15. C4×C4⋊C4×C31C4semidirect
86. #11787C31direct (N × H)
129. #1351C2×C31semidirect
154. C2×C4⋊Q8C4×C31semidirect
158. #393C4×C31semidirect
164. C4×C4⋊C4C4×C31semidirect
204. C31#11787direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25632
C4×C31×#992
C31×#14652
C31×#13512
#1178731