Finite Group Databasebeta

← C31×#10014 #21466773

Subgroups — C31×#10014 #21466773

Order 7936.

566 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3103C212yesmaximal
2C31×#2399C211yesmaximal, characteristic, complemented
3C31×#1963C211yesmaximal, characteristic
4C31×#1487C212yesmaximal, complemented
5C31×#1274C211yesmaximal, characteristic, complemented
6C31×#532C2211yescharacteristic
7C2×C4×Q8×C31C2212yes—
8C31×#481—22no—
9C31×#475—22no—
10C31×#460—22no—
11C31×#448—22no—
12C4×SD16×C31—24no—
13C31×#431C2212yes—
14C31×#423C2211yescharacteristic
15C2×C31×#104—22no—
16C31×#398—22no—
17C31×#395—22no—
18C4×C4⋊C4×C31—22no—
19C31×#376C2211yescharacteristic
20C31×Q8⋊C8—24no—
21C2×#41×C31—21no—
22C22×Q8×C31D412yes—
23C2×SD16×C31—24no—
24C2×M16×C31—21no—
25C31×C4⋊Q8D411yescharacteristic
26C31×#127D411yescharacteristic
27C31×#124—21no—
28C31×#121—22no—
29C4×Q8×C31—22no—
30C4×Q8×C31—22no—
31C4×Q8×C31—22no—
32C4×Q8×C31—22no—
33C4×D4×C31—22no—
34C2×C4⋊C4×C31—24no—
35C2×C4⋊C4×C31—22no—
36C2×C4⋊C4×C31D412yes—
37C2×C42×C31—22no—
38C2×C42×C31D412yes—
39C2×C42×C31C2311yescharacteristic
40C31×#106—24no—
41C31×C4⋊C8—22no—
42C31×C4⋊C8—22no—
43C31×#104—44no—
44C31×#103—24no—
45C31×#102—24no—
46C31×C22⋊C8—22no—
47C4×C8×C31D414yes—
48C31×#95—22no—
49C31×#95—22no—
50C31×#95—22no—
51#41×C31—42no—
52#41×C31—42no—
53C2×Q8×C31—22no—
54C2×Q8×C31—22no—
55C2×Q8×C31—21no—
56C2×Q8×C31—44no—
57C2×D4×C31—22no—
58C2×D4×C31—21no—
59C2×D4×C31—41no—
60C22×C4×C31—22no—
61C22×C4×C31—22no—
62C22×C4×C31—22no—
63C22×C4×C31—41no—
64C22×C4×C31C2×D412yes—
65C22×C4×C31C2×D411yescharacteristic
66SD16×C31—48no—
67M16×C31—42no—
68C2×C8×C31—24no—
69C2×C8×C31—41no—
70C4⋊C4×C31—22no—
71C4⋊C4×C31—22no—
72C4⋊C4×C31—22no—
73C4⋊C4×C31—48no—
74C4⋊C4×C31—42no—
75C4⋊C4×C31—42no—
76C22⋊C4×C31—42no—
77C42×C31—22no—
78C42×C31—42no—
79C42×C31—42no—
80C42×C31SD1614yescomplemented
81C42×C31C2×D411yescharacteristic
82C42×C31C2×D412yes—
83C42×C31#4111yescharacteristic
84#10014C3111yesmaximal, characteristic, direct product factor, Sylow
85C23×C31—41no—
86C23×C31#12011yescharacteristic
87Q8×C31—24no—
88Q8×C31—24no—
89Q8×C31—42no—
90Q8×C31—42no—
91Q8×C31—42no—
92D4×C31—44no—
93D4×C31—42no—
94D4×C31—82no—
95C2×C4×C31—24no—
96C2×C4×C31—24no—
97C2×C4×C31—42no—
98C2×C4×C31—44no—
99C2×C4×C31—42no—
100C2×C4×C31—42no—
101C2×C4×C31—44no—
102C2×C4×C31—42no—
103C2×C4×C31—41no—
104C2×C4×C31—81no—
105C2×C4×C31—81no—
106C2×C4×C31#12012yes—
107C2×C4×C31#12112yes—
108C2×C4×C31#12111yescharacteristic
109C2×C4×C31#12711yescharacteristic
110C2×C4×C31C2×SD1612yes—
111C2×C4×C31#13712yes—
112C8×C31—44no—
113C8×C31—81no—
114#3103C2×C3112yes—
115#2399C2×C3111yescharacteristic, complemented
116#1963C2×C3111yescharacteristic
117#1487C2×C3112yescomplemented
118#1274C2×C3111yescharacteristic, complemented
119C22×C31—22no—
120C22×C31—82no—
121C22×C31—81no—
122C22×C31#39211yescharacteristic
123C22×C31#44812yes—
124C4×C31—22no—
125C4×C31—22no—
126C4×C31—44no—
127C4×C31—44no—
128C4×C31—82no—
129C4×C31—81no—
130C4×C31#46112yes—
131C4×C31#49211yescharacteristic
132C4×C31#49711yescharacteristic
133#532C22×C3111yescharacteristic
134C2×C4×Q8C22×C3112yes—
135#481—22no—
136#475—22no—
137#460—22no—
138#448—22no—
139C4×SD16—24no—
140#431C22×C3112yes—
141#423C22×C3111yescharacteristic
142C2×#104—22no—
143#398—22no—
144#395—22no—
145C4×C4⋊C4—22no—
146#376C22×C3111yescharacteristic
147Q8⋊C8—24no—
148C2×C31—22no—
149C2×C31—161no—
150C2×C31#201012yes—
151C2×C31#201311yescharacteristic
152C2×#41—21no—
153C22×Q8D4×C3112yes—
154C2×SD16—24no—
155C2×M16—21no—
156C4⋊Q8D4×C3111yescharacteristic
157#127D4×C3111yescharacteristic
158#124—21no—
159#121—22no—
160C4×Q8—22no—
161C4×Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×D4—22no—
165C2×C4⋊C4—24no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4D4×C3112yes—
168C2×C42—22no—
169C2×C42D4×C3112yes—
170C2×C42C23×C3111yescharacteristic
171#106—24no—
172C4⋊C8—22no—
173C4⋊C8—22no—
174#104—44no—
175#103—24no—
176#102—24no—
177C22⋊C8—22no—
178C4×C8D4×C3114yes—
179#95—22no—
180#95—22no—
181#95—22no—
182C31#1001411yescharacteristic, direct product factor, Sylow
183#41—42no—
184#41—42no—
185C2×Q8—22no—
186C2×Q8—22no—
187C2×Q8—21no—
188C2×Q8—44no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—41no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—41no—
196C22×C4C2×D4×C3112yes—
197C22×C4C2×D4×C3111yescharacteristic
198SD16—48no—
199M16—42no—
200C2×C8—24no—
201C2×C8—41no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—48no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C22⋊C4—42no—
209C42—22no—
210C42—42no—
211C42—42no—
212C42SD16×C3114yescomplemented
213C42C2×D4×C3111yescharacteristic
214C42C2×D4×C3112yes—
215C42#41×C3111yescharacteristic
216C23—41no—
217C23C31×#12011yescharacteristic
218Q8—24no—
219Q8—24no—
220Q8—42no—
221Q8—42no—
222Q8—42no—
223D4—44no—
224D4—42no—
225D4—82no—
226C2×C4—24no—
227C2×C4—24no—
228C2×C4—42no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4C31×#12012yes—
238C2×C4C31×#12112yes—
239C2×C4C31×#12111yescharacteristic
240C2×C4C31×#12711yescharacteristic
241C2×C4C2×SD16×C3112yes—
242C2×C4C31×#13712yes—
243C8—44no—
244C8—81no—
245C22—22no—
246C22—82no—
247C22—81no—
248C22C31×#39211yescharacteristic
249C22C31×#44812yes—
250C4—22no—
251C4—22no—
252C4—44no—
253C4—44no—
254C4—82no—
255C4—81no—
256C4C31×#46112yes—
257C4C31×#49211yescharacteristic
258C4C31×#49711yescharacteristic
259C2—22no—
260C2—161no—
261C2C31×#201012yes—
262C2C31×#201311yescharacteristic
subgroupG/H
centerC2×C4×C31#127
commutator, Frattini, cosocleC2×C42C23×C31
socleC22×C31#392
prime radicalC31×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2399C2semidirect
4. C31×#1487C2semidirect
5. C31×#1274C2semidirect
80. C42×C31SD16semidirect
84. #10014C31direct (N × H)
115. #2399C2×C31semidirect
117. #1487C2×C31semidirect
118. #1274C2×C31semidirect
182. C31#10014direct (N × H)
212. C42SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#31032
C31×#23992
C31×#19632
C31×#14872
C31×#12742
#1001431