Finite Group Databasebeta

← C31×#11568 #21468327

Subgroups — C31×#11568 #21468327

Order 7936.

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

normal subgroups only

This group has 394 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×#2546C211yesmaximal, characteristic
2C31×#1467C211yesmaximal, characteristic
3C31×#1461C211yesmaximal, characteristic
4C31×#1319C214yesmaximal
5C2×C31×C4⋊Q8C411yescharacteristic
6C2×C31×C4⋊Q8C412yes—
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#432—21no—
9C31×#431—21no—
10C31×#398—21no—
11C31×#398—21no—
12C31×#391C2212yes—
13C31×#389—21no—
14C31×#389—21no—
15C4×C4⋊C4×C31C411yescharacteristic
16C31×#324—21no—
17C31×#324—21no—
18C31×#324C2212yes—
19C31×#324C2212yes—
20C22×Q8×C31C2×C412yes—
21C22×Q8×C31C2×C411yescharacteristic
22C31×C4⋊Q8—41no—
23C31×C4⋊Q8—41no—
24C31×C4⋊Q8—44no—
25C4×Q8×C31—41no—
26C4×Q8×C31—41no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C4⋊C4×C31D411yescharacteristic
34C2×C4⋊C4×C31C2311yescharacteristic
35C2×C42×C31C2×C411yescharacteristic
36C2×C42×C31C2×C412yes—
37C2×C42×C31D411yescharacteristic
38C2×C42×C31D411yescharacteristic
39C31×C4⋊C8—41no—
40C31×C4⋊C8—41no—
41C31×C22⋊C8—22no—
42C31×C22⋊C8—22no—
43C31×#97—41no—
44C4×C8×C31—41no—
45C31×#95—21no—
46C31×#95—22no—
47C31×#95—22no—
48C2×Q8×C31—22no—
49C2×Q8×C31—22no—
50C2×Q8×C31—24no—
51C2×Q8×C31—41no—
52C2×Q8×C31—42no—
53C2×Q8×C31—42no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31C22⋊C411yescharacteristic
57C22×C4×C31C22⋊C411yescharacteristic
58C22×C4×C31C22⋊C411yescharacteristic
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22×C411yescharacteristic
61C22×C4×C31C2×D411yescharacteristic
62C22×C4×C31C2×D411yescharacteristic
63C2×C8×C31—42no—
64C2×C8×C31—42no—
65C4⋊C4×C31—24no—
66C4⋊C4×C31—41no—
67C4⋊C4×C31—41no—
68C4⋊C4×C31—41no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—44no—
71C4⋊C4×C31—41no—
72C4⋊C4×C31—41no—
73C4⋊C4×C31—44no—
74C42×C31—21no—
75C42×C31—21no—
76C42×C31—21no—
77C42×C31—21no—
78C42×C31—21no—
79C42×C31—21no—
80C42×C31—42no—
81#11568C3111yesmaximal, characteristic, direct product factor, Sylow
82C23×C31C2×C22⋊C411yescharacteristic
83Q8×C31—44no—
84Q8×C31—84no—
85C2×C4×C31—21no—
86C2×C4×C31—21no—
87C2×C4×C31—21no—
88C2×C4×C31—21no—
89C2×C4×C31—22no—
90C2×C4×C31—24no—
91C2×C4×C31—21no—
92C2×C4×C31—21no—
93C2×C4×C31—21no—
94C2×C4×C31—21no—
95C2×C4×C31—21no—
96C2×C4×C31—21no—
97C2×C4×C31—42no—
98C2×C4×C31—42no—
99C2×C4×C31—41no—
100C2×C4×C31—41no—
101C2×C4×C31—41no—
102C2×C4×C31—42no—
103C2×C4×C31—42no—
104C2×C4×C31—42no—
105C2×C4×C31#9911yescharacteristic
106C2×C4×C31#9911yescharacteristic
107C2×C4×C31#10012yes—
108C2×C4×C31#13112yes—
109C8×C31—82no—
110C8×C31—82no—
111#2546C2×C3111yescharacteristic
112#1467C2×C3111yescharacteristic
113#1461C2×C3111yescharacteristic
114#1319C2×C3114yes—
115C22×C31—21no—
116C22×C31—21no—
117C22×C31#40811yescharacteristic
118C22×C31C2×#9911yescharacteristic
119C22×C31C2×#10011yescharacteristic
120C4×C31—21no—
121C4×C31—22no—
122C4×C31—22no—
123C4×C31—44no—
124C4×C31—41no—
125C4×C31—41no—
126C4×C31—41no—
127C4×C31—41no—
128C4×C31—82no—
129C4×C31#35612yes—
130C2×C4⋊Q8C4×C3111yescharacteristic
131C2×C4⋊Q8C4×C3112yes—
132C2×C4×Q8C22×C3111yescharacteristic
133#432—21no—
134#431—21no—
135#398—21no—
136#398—21no—
137#391C22×C3112yes—
138#389—21no—
139#389—21no—
140C4×C4⋊C4C4×C3111yescharacteristic
141#324—21no—
142#324—21no—
143#324C22×C3112yes—
144#324C22×C3112yes—
145C2×C31—21no—
146C2×C31—21no—
147C2×C31#147111yescharacteristic
148C2×C31#212911yescharacteristic
149C2×C31C2×#35611yescharacteristic
150C22×Q8C2×C4×C3112yes—
151C22×Q8C2×C4×C3111yescharacteristic
152C4⋊Q8—41no—
153C4⋊Q8—41no—
154C4⋊Q8—44no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4D4×C3111yescharacteristic
163C2×C4⋊C4D4×C3111yescharacteristic
164C2×C4⋊C4C23×C3111yescharacteristic
165C2×C42C2×C4×C3111yescharacteristic
166C2×C42C2×C4×C3112yes—
167C2×C42D4×C3111yescharacteristic
168C2×C42D4×C3111yescharacteristic
169C4⋊C8—41no—
170C4⋊C8—41no—
171C22⋊C8—22no—
172C22⋊C8—22no—
173#97—41no—
174C4×C8—41no—
175#95—21no—
176#95—22no—
177#95—22no—
178C31#1156811yescharacteristic, direct product factor, Sylow
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—24no—
182C2×Q8—41no—
183C2×Q8—42no—
184C2×Q8—42no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4C22⋊C4×C3111yescharacteristic
188C22×C4C22⋊C4×C3111yescharacteristic
189C22×C4C22⋊C4×C3111yescharacteristic
190C22×C4C22⋊C4×C3111yescharacteristic
191C22×C4C22×C4×C3111yescharacteristic
192C22×C4C2×D4×C3111yescharacteristic
193C22×C4C2×D4×C3111yescharacteristic
194C2×C8—42no—
195C2×C8—42no—
196C4⋊C4—24no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—44no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—44no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—42no—
212C23C2×C22⋊C4×C3111yescharacteristic
213Q8—44no—
214Q8—84no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—24no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4C31×#9911yescharacteristic
236C2×C4C31×#9911yescharacteristic
237C2×C4C31×#10012yes—
238C2×C4C31×#13112yes—
239C8—82no—
240C8—82no—
241C22—21no—
242C22—21no—
243C22C31×#40811yescharacteristic
244C22C2×C31×#9911yescharacteristic
245C22C2×C31×#10011yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—44no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—82no—
255C4C31×#35612yes—
256C2—21no—
257C2—21no—
258C2C31×#147111yescharacteristic
259C2C31×#212911yescharacteristic
260C2C2×C31×#35611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ 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
81. #11568C31direct (N × H)
178. C31#11568direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25462
C31×#14672
C31×#14612
C31×#13192
#1156831