Finite Group Databasebeta

← C31×#10289 #21467048

Subgroups — C31×#10289 #21467048

Order 7936.

614 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 130 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×#3226C212yesmaximal
2C31×#2868C211yesmaximal, characteristic, complemented
3C31×#1962C211yesmaximal, characteristic
4C31×#1546C212yesmaximal, complemented
5C31×#1276C211yesmaximal, characteristic, complemented
6C31×#532C2211yescharacteristic
7C2×C31×C4⋊Q8—22no—
8C2×C31×C4⋊Q8C2212yes—
9C31×#500—22no—
10C31×#486—22no—
11C31×#480—24no—
12C31×#474—24no—
13C31×#431C2212yes—
14C31×#423C2211yescharacteristic
15C2×C31×#104—22no—
16C31×#384—24no—
17C43×C31C2211yescharacteristic
18C31×#332—24no—
19C2×#41×C31—21no—
20C22×Q8×C31—22no—
21C2×M16×C31—21no—
22C31×C4⋊Q8—22no—
23C31×C4⋊Q8—22no—
24C31×C4⋊Q8—22no—
25C31×C4⋊Q8—22no—
26C31×C4⋊Q8—44no—
27C31×C4⋊Q8—44no—
28C31×C4⋊Q8D411yescharacteristic
29C31×#127D411yescharacteristic
30C31×#124—21no—
31C31×#121—22no—
32C4×D4×C31—22no—
33C2×C4⋊C4×C31—28no—
34C2×C4⋊C4×C31—22no—
35C2×C4⋊C4×C31D414yes—
36C2×C42×C31—22no—
37C2×C42×C31D412yes—
38C2×C42×C31C2311yescharacteristic
39C31×#107—28no—
40C31×C4⋊C8—22no—
41C31×C4⋊C8D414yes—
42C31×#104—44no—
43C31×#102—28no—
44C31×C22⋊C8—22no—
45C4×C8×C31—22no—
46#41×C31—42no—
47#41×C31—42no—
48C2×Q8×C31—21no—
49C2×Q8×C31—42no—
50C2×Q8×C31—42no—
51C2×Q8×C31—44no—
52C2×Q8×C31—44no—
53C2×D4×C31—22no—
54C2×D4×C31—21no—
55C2×D4×C31—41no—
56C22×C4×C31—22no—
57C22×C4×C31—24no—
58C22×C4×C31—41no—
59C22×C4×C31C2×D412yes—
60C22×C4×C31C2×D411yescharacteristic
61M16×C31—42no—
62C2×C8×C31—24no—
63C2×C8×C31—41no—
64C4⋊C4×C31—24no—
65C4⋊C4×C31—22no—
66C4⋊C4×C31—24no—
67C4⋊C4×C31—416no—
68C4⋊C4×C31—42no—
69C4⋊C4×C31—42no—
70C22⋊C4×C31—42no—
71C42×C31—28no—
72C42×C31—22no—
73C42×C31D814yes—
74C42×C31C2×D411yescharacteristic
75C42×C31C2×D412yes—
76C42×C31#4111yescharacteristic
77#10289C3111yesmaximal, characteristic, direct product factor, Sylow
78C23×C31—41no—
79C23×C31#12011yescharacteristic
80Q8×C31—42no—
81Q8×C31—84no—
82Q8×C31—82no—
83Q8×C31—82no—
84D4×C31—44no—
85D4×C31—42no—
86D4×C31—82no—
87C2×C4×C31—28no—
88C2×C4×C31—24no—
89C2×C4×C31—24no—
90C2×C4×C31—41no—
91C2×C4×C31—44no—
92C2×C4×C31—48no—
93C2×C4×C31—81no—
94C2×C4×C31—81no—
95C2×C4×C31#12012yes—
96C2×C4×C31#12112yes—
97C2×C4×C31#12111yescharacteristic
98C2×C4×C31#12711yescharacteristic
99C2×C4×C31C2×D812yes—
100C2×C4×C31AGL(1,ℤ/8)12yes—
101C8×C31—44no—
102C8×C31—81no—
103#3226C2×C3112yes—
104#2868C2×C3111yescharacteristic, complemented
105#1962C2×C3111yescharacteristic
106#1546C2×C3112yescomplemented
107#1276C2×C3111yescharacteristic, complemented
108C22×C31—22no—
109C22×C31—82no—
110C22×C31—81no—
111C22×C31#39211yescharacteristic
112C22×C31#44712yes—
113C4×C31—28no—
114C4×C31—22no—
115C4×C31—84no—
116C4×C31—81no—
117C4×C31#45614yes—
118C4×C31#45912yes—
119C4×C31#49311yescharacteristic
120C4×C31#49611yescharacteristic
121#532C22×C3111yescharacteristic
122C2×C4⋊Q8—22no—
123C2×C4⋊Q8C22×C3112yes—
124#500—22no—
125#486—22no—
126#480—24no—
127#474—24no—
128#431C22×C3112yes—
129#423C22×C3111yescharacteristic
130C2×#104—22no—
131#384—24no—
132C43C22×C3111yescharacteristic
133#332—24no—
134C2×C31—22no—
135C2×C31—161no—
136C2×C31#200512yes—
137C2×C31#201111yescharacteristic
138C2×#41—21no—
139C22×Q8—22no—
140C2×M16—21no—
141C4⋊Q8—22no—
142C4⋊Q8—22no—
143C4⋊Q8—22no—
144C4⋊Q8—22no—
145C4⋊Q8—44no—
146C4⋊Q8—44no—
147C4⋊Q8D4×C3111yescharacteristic
148#127D4×C3111yescharacteristic
149#124—21no—
150#121—22no—
151C4×D4—22no—
152C2×C4⋊C4—28no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4D4×C3114yes—
155C2×C42—22no—
156C2×C42D4×C3112yes—
157C2×C42C23×C3111yescharacteristic
158#107—28no—
159C4⋊C8—22no—
160C4⋊C8D4×C3114yes—
161#104—44no—
162#102—28no—
163C22⋊C8—22no—
164C4×C8—22no—
165C31#1028911yescharacteristic, direct product factor, Sylow
166#41—42no—
167#41—42no—
168C2×Q8—21no—
169C2×Q8—42no—
170C2×Q8—42no—
171C2×Q8—44no—
172C2×Q8—44no—
173C2×D4—22no—
174C2×D4—21no—
175C2×D4—41no—
176C22×C4—22no—
177C22×C4—24no—
178C22×C4—41no—
179C22×C4C2×D4×C3112yes—
180C22×C4C2×D4×C3111yescharacteristic
181M16—42no—
182C2×C8—24no—
183C2×C8—41no—
184C4⋊C4—24no—
185C4⋊C4—22no—
186C4⋊C4—24no—
187C4⋊C4—416no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C22⋊C4—42no—
191C42—28no—
192C42—22no—
193C42D8×C3114yes—
194C42C2×D4×C3111yescharacteristic
195C42C2×D4×C3112yes—
196C42#41×C3111yescharacteristic
197C23—41no—
198C23C31×#12011yescharacteristic
199Q8—42no—
200Q8—84no—
201Q8—82no—
202Q8—82no—
203D4—44no—
204D4—42no—
205D4—82no—
206C2×C4—28no—
207C2×C4—24no—
208C2×C4—24no—
209C2×C4—48no—
210C2×C4—41no—
211C2×C4—44no—
212C2×C4—81no—
213C2×C4—81no—
214C2×C4C31×#12012yes—
215C2×C4C31×#12112yes—
216C2×C4C31×#12111yescharacteristic
217C2×C4C31×#12711yescharacteristic
218C2×C4C2×D8×C3112yes—
219C2×C4C31×AGL(1,ℤ/8)12yes—
220C8—44no—
221C8—81no—
222C22—22no—
223C22—82no—
224C22—81no—
225C22C31×#39211yescharacteristic
226C22C31×#44712yes—
227C4—28no—
228C4—22no—
229C4—84no—
230C4—81no—
231C4C31×#45614yes—
232C4C31×#45912yes—
233C4C31×#49311yescharacteristic
234C4C31×#49611yescharacteristic
235C2—22no—
236C2—161no—
237C2C31×#200512yes—
238C2C31×#201111yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2868C2semidirect
4. C31×#1546C2semidirect
5. C31×#1276C2semidirect
77. #10289C31direct (N × H)
104. #2868C2×C31semidirect
106. #1546C2×C31semidirect
107. #1276C2×C31semidirect
165. C31#10289direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32262
C31×#28682
C31×#19622
C31×#15462
C31×#12762
#1028931