Finite Group Databasebeta

← C31×#9456 #21466215

Subgroups — C31×#9456 #21466215

Order 7936.

432 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2983C211yesmaximal, characteristic
2C31×#2568C211yesmaximal, characteristic
3C31×#1556C212yesmaximal
4C31×#1467C211yesmaximal, characteristic
5C31×#1285C212yesmaximal
6C2×C31×C4⋊Q8C2211yescharacteristic
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#446—24no—
9C31×#432—21no—
10C31×#432C2212yes—
11C31×#432C2212yes—
12C31×#431—21no—
13C31×#400—21no—
14C31×#400—21no—
15C31×#391—21no—
16C31×#391—21no—
17C31×#391C412yes—
18C31×#382C412yes—
19C4×C4⋊C4×C31C2211yescharacteristic
20C31×#332—24no—
21C31×#324—21no—
22C31×#324—21no—
23C22×Q8×C31—21no—
24C22×Q8×C31C2×C411yescharacteristic
25C31×C4⋊Q8—22no—
26C31×C4⋊Q8—22no—
27C4×Q8×C31—22no—
28C4×Q8×C31—22no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31C2×C412yes—
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C4⋊C4×C31D411yescharacteristic
34C2×C4⋊C4×C31D411yescharacteristic
35C2×C42×C31C2×C412yes—
36C2×C42×C31D411yescharacteristic
37C2×C42×C31D411yescharacteristic
38C2×C42×C31C2311yescharacteristic
39C31×C4⋊C8—22no—
40C31×C4⋊C8—22no—
41C31×C4⋊C8—22no—
42C31×C4⋊C8D414yes—
43C31×C22⋊C8—22no—
44C31×C22⋊C8—22no—
45C31×#97—22no—
46C31×#97—22no—
47C31×#97—22no—
48C4×C8×C31—22no—
49C31×#95—22no—
50C31×#95—22no—
51C31×#95—22no—
52C31×#95—22no—
53C31×#95—21no—
54C2×Q8×C31—22no—
55C2×Q8×C31—22no—
56C2×Q8×C31—41no—
57C2×Q8×C31—44no—
58C2×Q8×C31—41no—
59C2×Q8×C31—41no—
60C22×C4×C31—22no—
61C22×C4×C31—22no—
62C22×C4×C31C22⋊C411yescharacteristic
63C22×C4×C31C22⋊C411yescharacteristic
64C22×C4×C31C22⋊C411yescharacteristic
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22×C411yescharacteristic
67C22×C4×C31C2×D411yescharacteristic
68C22×C4×C31C2×D411yescharacteristic
69C2×C8×C31—24no—
70C2×C8×C31—42no—
71C4⋊C4×C31—22no—
72C4⋊C4×C31—22no—
73C4⋊C4×C31—22no—
74C4⋊C4×C31—24no—
75C4⋊C4×C31—42no—
76C4⋊C4×C31—42no—
77C42×C31—21no—
78C42×C31—21no—
79C42×C31—21no—
80C42×C31—21no—
81C42×C31—42no—
82C42×C31C2×D412yes—
83C42×C31#4112yes—
84#9456C3111yesmaximal, characteristic, direct product factor, Sylow
85C23×C31C2×C22⋊C411yescharacteristic
86Q8×C31—44no—
87Q8×C31—82no—
88Q8×C31—82no—
89C2×C4×C31—21no—
90C2×C4×C31—21no—
91C2×C4×C31—21no—
92C2×C4×C31—21no—
93C2×C4×C31—22no—
94C2×C4×C31—21no—
95C2×C4×C31—21no—
96C2×C4×C31—21no—
97C2×C4×C31—21no—
98C2×C4×C31—21no—
99C2×C4×C31—41no—
100C2×C4×C31—41no—
101C2×C4×C31—41no—
102C2×C4×C31—42no—
103C2×C4×C31—42no—
104C2×C4×C31—44no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31#10112yes—
108C2×C4×C31C4×D412yes—
109C2×C4×C31#12011yescharacteristic
110C2×C4×C31#12112yes—
111C2×C4×C31#12311yescharacteristic
112C8×C31—44no—
113C8×C31—82no—
114#2983C2×C3111yescharacteristic
115#2568C2×C3111yescharacteristic
116#1556C2×C3112yes—
117#1467C2×C3111yescharacteristic
118#1285C2×C3112yes—
119C22×C31—21no—
120C22×C31—21no—
121C22×C31#38611yescharacteristic
122C22×C31C2×#10111yescharacteristic
123C22×C31#41311yescharacteristic
124C4×C31—21no—
125C4×C31—22no—
126C4×C31—22no—
127C4×C31—22no—
128C4×C31—41no—
129C4×C31—41no—
130C4×C31—41no—
131C4×C31—82no—
132C4×C31—82no—
133C4×C31#45412yes—
134C2×C4⋊Q8C22×C3111yescharacteristic
135C2×C4×Q8C22×C3111yescharacteristic
136#446—24no—
137#432—21no—
138#432C22×C3112yes—
139#432C22×C3112yes—
140#431—21no—
141#400—21no—
142#400—21no—
143#391—21no—
144#391—21no—
145#391C4×C3112yes—
146#382C4×C3112yes—
147C4×C4⋊C4C22×C3111yescharacteristic
148#332—24no—
149#324—21no—
150#324—21no—
151C2×C31—21no—
152C2×C31—21no—
153C2×C31#188811yescharacteristic
154C2×C31#190111yescharacteristic
155C2×C31#190911yescharacteristic
156C22×Q8—21no—
157C22×Q8C2×C4×C3111yescharacteristic
158C4⋊Q8—22no—
159C4⋊Q8—22no—
160C4×Q8—22no—
161C4×Q8—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4C2×C4×C3112yes—
165C2×C4⋊C4C2×C4×C3111yescharacteristic
166C2×C4⋊C4D4×C3111yescharacteristic
167C2×C4⋊C4D4×C3111yescharacteristic
168C2×C42C2×C4×C3112yes—
169C2×C42D4×C3111yescharacteristic
170C2×C42D4×C3111yescharacteristic
171C2×C42C23×C3111yescharacteristic
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8D4×C3114yes—
176C22⋊C8—22no—
177C22⋊C8—22no—
178#97—22no—
179#97—22no—
180#97—22no—
181C4×C8—22no—
182#95—22no—
183#95—22no—
184#95—22no—
185#95—22no—
186#95—21no—
187C31#945611yescharacteristic, direct product factor, Sylow
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—41no—
191C2×Q8—44no—
192C2×Q8—41no—
193C2×Q8—41no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4C22⋊C4×C3111yescharacteristic
197C22×C4C22⋊C4×C3111yescharacteristic
198C22×C4C22⋊C4×C3111yescharacteristic
199C22×C4C22⋊C4×C3111yescharacteristic
200C22×C4C22×C4×C3111yescharacteristic
201C22×C4C2×D4×C3111yescharacteristic
202C22×C4C2×D4×C3111yescharacteristic
203C2×C8—24no—
204C2×C8—42no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—24no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—42no—
216C42C2×D4×C3112yes—
217C42#41×C3112yes—
218C23C2×C22⋊C4×C3111yescharacteristic
219Q8—44no—
220Q8—82no—
221Q8—82no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—44no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4C31×#10112yes—
241C2×C4C4×D4×C3112yes—
242C2×C4C31×#12011yescharacteristic
243C2×C4C31×#12112yes—
244C2×C4C31×#12311yescharacteristic
245C8—44no—
246C8—82no—
247C22—21no—
248C22—21no—
249C22C31×#38611yescharacteristic
250C22C2×C31×#10111yescharacteristic
251C22C31×#41311yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—82no—
260C4—82no—
261C4C31×#45412yes—
262C2—21no—
263C2—21no—
264C2C31×#188811yescharacteristic
265C2C31×#190111yescharacteristic
266C2C31×#190911yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
84. #9456C31direct (N × H)
187. C31#9456direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29832
C31×#25682
C31×#15562
C31×#14672
C31×#12852
#945631