Finite Group Databasebeta

← C31×#11562 #21468321

Subgroups — C31×#11562 #21468321

Order 7936.

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

normal subgroups only

This group has 444 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×#2486C211yesmaximal, characteristic
2C31×#1465C211yesmaximal, characteristic
3C31×#1460C211yesmaximal, characteristic
4C31×#1317C214yesmaximal, complemented
5C2×C31×#123C412yes—
6C2×C4×D4×C31C2211yescharacteristic
7C22×C4⋊C4×C31C411yescharacteristic
8C31×#431—21no—
9C31×#407—21no—
10C31×#398—21no—
11C31×#397—21no—
12C31×#389—21no—
13C31×#381C2212yes—
14C31×#380—21no—
15C31×#380C411yescharacteristic
16C31×#324—21no—
17C31×#323—21no—
18C31×#323C2212yes—
19C31×#323C2212yes—
20C22×D4×C31C2×C411yescharacteristic
21C23×C4×C31C2×C412yes—
22C23×C4×C31C2×C411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C2×M16×C31—41no—
25C31×#123—44no—
26C4×D4×C31—41no—
27C4×D4×C31—41no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—41no—
33C2×C4⋊C4×C31—41no—
34C2×C4⋊C4×C31D411yescharacteristic
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31C2×C412yes—
37C2×C22⋊C4×C31D411yescharacteristic
38C2×C22⋊C4×C31C2311yescharacteristic
39C2×C42×C31D411yescharacteristic
40C31×C4⋊C8—41no—
41C31×C22⋊C8—22no—
42C31×C22⋊C8—22no—
43C31×C22⋊C8—41no—
44C4×C8×C31—41no—
45C31×#95—21no—
46C31×#95—22no—
47C31×#95—22no—
48C24×C31C22⋊C411yescharacteristic
49C24×C31C22×C411yescharacteristic
50C2×D4×C31—22no—
51C2×D4×C31—22no—
52C2×D4×C31—41no—
53C22×C4×C31—21no—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31—22no—
58C22×C4×C31—22no—
59C22×C4×C31—24no—
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×C31C2×D411yescharacteristic
68C22×C4×C31C2×D411yescharacteristic
69M16×C31—82no—
70C2×C8×C31—42no—
71C2×C8×C31—42no—
72C4⋊C4×C31—41no—
73C4⋊C4×C31—42no—
74C4⋊C4×C31—42no—
75C4⋊C4×C31—41no—
76C4⋊C4×C31—41no—
77C4⋊C4×C31—44no—
78C22⋊C4×C31—41no—
79C22⋊C4×C31—41no—
80C22⋊C4×C31—44no—
81C22⋊C4×C31—42no—
82C42×C31—21no—
83C42×C31—21no—
84#11562C3111yesmaximal, characteristic, direct product factor, Sylow
85C23×C31—21no—
86C23×C31—21no—
87C23×C31—21no—
88C23×C31—21no—
89C23×C31—21no—
90C23×C31—41no—
91C23×C31—41no—
92C23×C31—41no—
93C23×C31—41no—
94C23×C31C2×C22⋊C411yescharacteristic
95C23×C31#13112yes—
96D4×C31—44no—
97C2×C4×C31—21no—
98C2×C4×C31—21no—
99C2×C4×C31—22no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—42no—
104C2×C4×C31—42no—
105C2×C4×C31—42no—
106C2×C4×C31—41no—
107C2×C4×C31—41no—
108C2×C4×C31—41no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
111C2×C4×C31—42no—
112C2×C4×C31—42no—
113C2×C4×C31—42no—
114C2×C4×C31—42no—
115C2×C4×C31—81no—
116C2×C4×C31—84no—
117C2×C4×C31#9911yescharacteristic
118C2×C4×C31#9911yescharacteristic
119C2×C4×C31#10012yes—
120C8×C31—82no—
121C8×C31—82no—
122#2486C2×C3111yescharacteristic
123#1465C2×C3111yescharacteristic
124#1460C2×C3111yescharacteristic
125#1317C2×C3114yescomplemented
126C22×C31—21no—
127C22×C31—21no—
128C22×C31—22no—
129C22×C31—42no—
130C22×C31—42no—
131C22×C31—42no—
132C22×C31—41no—
133C22×C31—41no—
134C22×C31—41no—
135C22×C31—41no—
136C22×C31—41no—
137C22×C31—81no—
138C22×C31#40811yescharacteristic
139C22×C31C2×#9911yescharacteristic
140C22×C31C2×#10011yescharacteristic
141C4×C31—21no—
142C4×C31—22no—
143C4×C31—41no—
144C4×C31—41no—
145C4×C31—41no—
146C4×C31—82no—
147C4×C31—82no—
148C4×C31#35212yes—
149C2×#123C4×C3112yes—
150C2×C4×D4C22×C3111yescharacteristic
151C22×C4⋊C4C4×C3111yescharacteristic
152#431—21no—
153#407—21no—
154#398—21no—
155#397—21no—
156#389—21no—
157#381C22×C3112yes—
158#380—21no—
159#380C4×C3111yescharacteristic
160#324—21no—
161#323—21no—
162#323C22×C3112yes—
163#323C22×C3112yes—
164C2×C31—21no—
165C2×C31—21no—
166C2×C31—42no—
167C2×C31—81no—
168C2×C31#147111yescharacteristic
169C2×C31C2×#35211yescharacteristic
170C2×C31#212311yescharacteristic
171C22×D4C2×C4×C3111yescharacteristic
172C23×C4C2×C4×C3112yes—
173C23×C4C2×C4×C3111yescharacteristic
174C23×C4D4×C3111yescharacteristic
175C2×M16—41no—
176#123—44no—
177C4×D4—41no—
178C4×D4—41no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4D4×C3111yescharacteristic
186C2×C22⋊C4—22no—
187C2×C22⋊C4C2×C4×C3112yes—
188C2×C22⋊C4D4×C3111yescharacteristic
189C2×C22⋊C4C23×C3111yescharacteristic
190C2×C42D4×C3111yescharacteristic
191C4⋊C8—41no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—41no—
195C4×C8—41no—
196#95—21no—
197#95—22no—
198#95—22no—
199C31#1156211yescharacteristic, direct product factor, Sylow
200C24C22⋊C4×C3111yescharacteristic
201C24C22×C4×C3111yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—24no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4C22⋊C4×C3111yescharacteristic
217C22×C4C22⋊C4×C3111yescharacteristic
218C22×C4C22⋊C4×C3111yescharacteristic
219C22×C4C2×D4×C3111yescharacteristic
220C22×C4C2×D4×C3111yescharacteristic
221M16—82no—
222C2×C8—42no—
223C2×C8—42no—
224C4⋊C4—41no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—44no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—44no—
233C22⋊C4—42no—
234C42—21no—
235C42—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23C2×C22⋊C4×C3111yescharacteristic
246C23C31×#13112yes—
247D4—44no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—81no—
267C2×C4—84no—
268C2×C4C31×#9911yescharacteristic
269C2×C4C31×#9911yescharacteristic
270C2×C4C31×#10012yes—
271C8—82no—
272C8—82no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—81no—
285C22C31×#40811yescharacteristic
286C22C2×C31×#9911yescharacteristic
287C22C2×C31×#10011yescharacteristic
288C4—21no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—82no—
294C4—82no—
295C4C31×#35212yes—
296C2—21no—
297C2—21no—
298C2—42no—
299C2—81no—
300C2C31×#147111yescharacteristic
301C2C2×C31×#35211yescharacteristic
302C2C31×#212311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC24C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C24 ▷ C22 ▷ 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×#1317C2semidirect
84. #11562C31direct (N × H)
125. #1317C2×C31semidirect
199. C31#11562direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24862
C31×#14652
C31×#14602
C31×#13172
#1156231