Finite Group Databasebeta

← C31×#9394 #21466153

Subgroups — C31×#9394 #21466153

Order 7936.

506 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 154 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×#2982C211yesmaximal, characteristic
2C31×#2546C211yesmaximal, characteristic
3C31×#1801C211yesmaximal, characteristic
4C31×#1546C212yesmaximal
5C31×#1303C212yesmaximal
6C2×C31×C4⋊Q8—21no—
7C2×C31×C4⋊Q8C2211yescharacteristic
8C2×C4×Q8×C31C2211yescharacteristic
9C8×Q8×C31—24no—
10C31×#431—22no—
11C31×#431C2212yes—
12C31×#423C2212yes—
13C2×C31×#101—21no—
14C31×#398C414yes—
15C31×#391—21no—
16C31×#389—22no—
17C4×C4⋊C4×C31C2211yescharacteristic
18C31×#343—21no—
19C31×#332—24no—
20C22×Q8×C31—21no—
21C22×Q8×C31D411yescharacteristic
22C2×M16×C31—22no—
23C31×C4⋊Q8—22no—
24C31×C4⋊Q8—22no—
25C31×C4⋊Q8—42no—
26C31×C4⋊Q8—42no—
27C4×Q8×C31—22no—
28C4×Q8×C31—22no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—24no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31C2×C412yes—
33C2×C4⋊C4×C31C2×C412yes—
34C2×C4⋊C4×C31D411yescharacteristic
35C2×C42×C31—21no—
36C2×C42×C31D412yes—
37C2×C42×C31C2311yescharacteristic
38C31×C4⋊C8—24no—
39C31×C4⋊C8—22no—
40C31×C4⋊C8—22no—
41C31×C4⋊C8D414yes—
42C31×#101—42no—
43C31×C22⋊C8—22no—
44C4×C8×C31—24no—
45C4×C8×C31—22no—
46C31×#95—24no—
47C31×#95C2×C412yes—
48C2×Q8×C31—22no—
49C2×Q8×C31—22no—
50C2×Q8×C31—42no—
51C2×Q8×C31—41no—
52C2×Q8×C31—41no—
53C2×Q8×C31—42no—
54C2×Q8×C31D812yes—
55C2×Q8×C31SD1612yes—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31C22⋊C412yes—
59C22×C4×C31C22⋊C412yes—
60C22×C4×C31C22×C411yescharacteristic
61C22×C4×C31C2×D411yescharacteristic
62C22×C4×C31C2×D411yescharacteristic
63M16×C31—42no—
64M16×C31—42no—
65C2×C8×C31—24no—
66C2×C8×C31—42no—
67C4⋊C4×C31—24no—
68C4⋊C4×C31—24no—
69C4⋊C4×C31—22no—
70C4⋊C4×C31—24no—
71C4⋊C4×C31—48no—
72C4⋊C4×C31—41no—
73C4⋊C4×C31—41no—
74C42×C31—22no—
75C42×C31—22no—
76C42×C31—41no—
77C42×C31—41no—
78C42×C31C2×D412yes—
79C42×C31#4112yes—
80#9394C3111yesmaximal, characteristic, direct product factor, Sylow
81C23×C31C2×C22⋊C411yescharacteristic
82Q8×C31—24no—
83Q8×C31—24no—
84Q8×C31—82no—
85Q8×C31—82no—
86C2×C4×C31—22no—
87C2×C4×C31—22no—
88C2×C4×C31—22no—
89C2×C4×C31—24no—
90C2×C4×C31—22no—
91C2×C4×C31—41no—
92C2×C4×C31—42no—
93C2×C4×C31—42no—
94C2×C4×C31—42no—
95C2×C4×C31—42no—
96C2×C4×C31—42no—
97C2×C4×C31—42no—
98C2×C4×C31#10214yes—
99C2×C4×C31C4×D412yes—
100C2×C4×C31#12011yescharacteristic
101C2×C4×C31#12112yes—
102C2×C4×C31#12311yescharacteristic
103C2×C4×C31C2×D811yescharacteristic
104C2×C4×C31C2×SD1611yescharacteristic
105C2×C4×C31#13512yes—
106C8×C31—44no—
107C8×C31—82no—
108#2982C2×C3111yescharacteristic
109#2546C2×C3111yescharacteristic
110#1801C2×C3111yescharacteristic
111#1546C2×C3112yes—
112#1303C2×C3112yes—
113C22×C31—21no—
114C22×C31—21no—
115C22×C31#38611yescharacteristic
116C22×C31C2×#10211yescharacteristic
117C22×C31#41611yescharacteristic
118C4×C31—21no—
119C4×C31—24no—
120C4×C31—22no—
121C4×C31—44no—
122C4×C31—42no—
123C4×C31—82no—
124C4×C31#45612yes—
125C4×C31#46512yes—
126C4×C31#46612yes—
127C2×C4⋊Q8—21no—
128C2×C4⋊Q8C22×C3111yescharacteristic
129C2×C4×Q8C22×C3111yescharacteristic
130C8×Q8—24no—
131#431—22no—
132#431C22×C3112yes—
133#423C22×C3112yes—
134C2×#101—21no—
135#398C4×C3114yes—
136#391—21no—
137#389—22no—
138C4×C4⋊C4C22×C3111yescharacteristic
139#343—21no—
140#332—24no—
141C2×C31—21no—
142C2×C31—21no—
143C2×C31#188611yescharacteristic
144C2×C31#189311yescharacteristic
145C2×C31#191511yescharacteristic
146C22×Q8—21no—
147C22×Q8D4×C3111yescharacteristic
148C2×M16—22no—
149C4⋊Q8—22no—
150C4⋊Q8—22no—
151C4⋊Q8—42no—
152C4⋊Q8—42no—
153C4×Q8—22no—
154C4×Q8—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4C2×C4×C3112yes—
159C2×C4⋊C4C2×C4×C3112yes—
160C2×C4⋊C4D4×C3111yescharacteristic
161C2×C42—21no—
162C2×C42D4×C3112yes—
163C2×C42C23×C3111yescharacteristic
164C4⋊C8—24no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167C4⋊C8D4×C3114yes—
168#101—42no—
169C22⋊C8—22no—
170C4×C8—24no—
171C4×C8—22no—
172#95—24no—
173#95C2×C4×C3112yes—
174C31#939411yescharacteristic, direct product factor, Sylow
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—42no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—42no—
181C2×Q8D8×C3112yes—
182C2×Q8SD16×C3112yes—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4C22⋊C4×C3112yes—
186C22×C4C22⋊C4×C3112yes—
187C22×C4C22×C4×C3111yescharacteristic
188C22×C4C2×D4×C3111yescharacteristic
189C22×C4C2×D4×C3111yescharacteristic
190M16—42no—
191M16—42no—
192C2×C8—24no—
193C2×C8—42no—
194C4⋊C4—24no—
195C4⋊C4—24no—
196C4⋊C4—22no—
197C4⋊C4—24no—
198C4⋊C4—48no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C42—22no—
202C42—22no—
203C42—41no—
204C42—41no—
205C42C2×D4×C3112yes—
206C42#41×C3112yes—
207C23C2×C22⋊C4×C3111yescharacteristic
208Q8—24no—
209Q8—24no—
210Q8—82no—
211Q8—82no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4C31×#10214yes—
225C2×C4C4×D4×C3112yes—
226C2×C4C31×#12011yescharacteristic
227C2×C4C31×#12112yes—
228C2×C4C31×#12311yescharacteristic
229C2×C4C2×D8×C3111yescharacteristic
230C2×C4C2×SD16×C3111yescharacteristic
231C2×C4C31×#13512yes—
232C8—44no—
233C8—82no—
234C22—21no—
235C22—21no—
236C22C31×#38611yescharacteristic
237C22C2×C31×#10211yescharacteristic
238C22C31×#41611yescharacteristic
239C4—21no—
240C4—24no—
241C4—22no—
242C4—44no—
243C4—42no—
244C4—82no—
245C4C31×#45612yes—
246C4C31×#46512yes—
247C4C31×#46612yes—
248C2—21no—
249C2—21no—
250C2C31×#188611yescharacteristic
251C2C31×#189311yescharacteristic
252C2C31×#191511yescharacteristic
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
80. #9394C31direct (N × H)
174. C31#9394direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29822
C31×#25462
C31×#18012
C31×#15462
C31×#13032
#939431