Finite Group Databasebeta

← C31×#10437 #21467196

Subgroups — C31×#10437 #21467196

Order 7936.

478 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 146 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×#2582C211yesmaximal, characteristic
2C31×#1844C211yesmaximal, characteristic
3C31×#1803C212yesmaximal
4C2×C31×Q8⋊C8C212yesmaximal
5C31×#1296C211yesmaximal, characteristic
6C2×C4×Q8×C31C2212yes—
7C2×C31×#106—22no—
8C2×C31×C4⋊C8C2212yes—
9C2×C31×#103—22no—
10C2×C4×C8×C31C2211yescharacteristic
11C31×#398—22no—
12C31×#391—22no—
13C31×#389—22no—
14C31×#384C2211yescharacteristic
15C31×#384C2211yescharacteristic
16C31×#340—22no—
17C31×Q8⋊C8—24no—
18C22×Q8×C31D412yes—
19C22×C8×C31—21no—
20C22×C8×C31—22no—
21C4×Q8×C31—22no—
22C4×Q8×C31—22no—
23C4×Q8×C31—22no—
24C4×Q8×C31—22no—
25C2×C4⋊C4×C31—22no—
26C2×C4⋊C4×C31—22no—
27C2×C4⋊C4×C31—22no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31D412yes—
31C2×C4⋊C4×C31D412yes—
32C2×C42×C31—22no—
33C2×C42×C31C2311yescharacteristic
34C31×#106—44no—
35C31×C4⋊C8—22no—
36C31×C4⋊C8—22no—
37C31×#103—44no—
38C4×C8×C31—21no—
39C4×C8×C31D412yes—
40C31×#95—24no—
41C31×#95—22no—
42C2×Q8×C31—22no—
43C2×Q8×C31—22no—
44C2×Q8×C31—22no—
45C2×Q8×C31—22no—
46C2×Q8×C31—22no—
47C2×Q8×C31SD1614yes—
48C22×C4×C31—22no—
49C22×C4×C31—22no—
50C22×C4×C31—22no—
51C22×C4×C31—41no—
52C22×C4×C31C2×D411yescharacteristic
53C22×C4×C31C2×D412yes—
54C2×C8×C31—22no—
55C2×C8×C31—22no—
56C2×C8×C31—22no—
57C2×C8×C31—42no—
58C2×C8×C31—42no—
59C2×C8×C31—42no—
60C4⋊C4×C31—22no—
61C4⋊C4×C31—22no—
62C4⋊C4×C31—42no—
63C4⋊C4×C31—42no—
64C4⋊C4×C31—42no—
65C4⋊C4×C31—42no—
66C4⋊C4×C31—42no—
67C4⋊C4×C31—42no—
68C4⋊C4×C31—42no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—82no—
71C42×C31—42no—
72C42×C31—42no—
73C42×C31C2×D411yescharacteristic
74C42×C31#4111yescharacteristic
75C42×C31#4112yes—
76#10437C3111yesmaximal, characteristic, direct product factor, Sylow
77C23×C31#12011yescharacteristic
78Q8×C31—24no—
79Q8×C31—24no—
80Q8×C31—42no—
81Q8×C31—42no—
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31—24no—
85C2×C4×C31—42no—
86C2×C4×C31—42no—
87C2×C4×C31—42no—
88C2×C4×C31—44no—
89C2×C4×C31—42no—
90C2×C4×C31—42no—
91C2×C4×C31—42no—
92C2×C4×C31—82no—
93C2×C4×C31—81no—
94C2×C4×C31#12111yescharacteristic
95C2×C4×C31#12112yes—
96C2×C4×C31#12312yes—
97C2×C4×C31#12411yescharacteristic
98C2×C4×C31C2×SD1612yes—
99C2×C4×C31#13512yes—
100C2×C4×C31#13712yes—
101C2×C4×C31#13712yes—
102C8×C31—24no—
103C8×C31—82no—
104#2582C2×C3111yescharacteristic
105#1844C2×C3111yescharacteristic
106#1803C2×C3112yes—
107C2×Q8⋊C8C2×C3112yes—
108#1296C2×C3111yescharacteristic
109C22×C31#39411yescharacteristic
110C22×C31#44812yes—
111C22×C31#45212yes—
112C22×C31#45311yescharacteristic
113C22×C31#45611yescharacteristic
114C4×C31—21no—
115C4×C31—21no—
116C4×C31—44no—
117C4×C31—82no—
118C4×C31—82no—
119C4×C31—161no—
120C4×C31#46512yes—
121C4×C31#47012yes—
122C4×C31#48312yes—
123C4×C31#48512yes—
124C2×C4×Q8C22×C3112yes—
125C2×#106—22no—
126C2×C4⋊C8C22×C3112yes—
127C2×#103—22no—
128C2×C4×C8C22×C3111yescharacteristic
129#398—22no—
130#391—22no—
131#389—22no—
132#384C22×C3111yescharacteristic
133#384C22×C3111yescharacteristic
134#340—22no—
135Q8⋊C8—24no—
136C2×C31#162311yescharacteristic
137C2×C31#163011yescharacteristic
138C2×C31#165312yes—
139C2×C31#203512yes—
140C2×C31#203911yescharacteristic
141C22×Q8D4×C3112yes—
142C22×C8—21no—
143C22×C8—22no—
144C4×Q8—22no—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4D4×C3112yes—
154C2×C4⋊C4D4×C3112yes—
155C2×C42—22no—
156C2×C42C23×C3111yescharacteristic
157#106—44no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160#103—44no—
161C4×C8—21no—
162C4×C8D4×C3112yes—
163#95—24no—
164#95—22no—
165C31#1043711yescharacteristic, direct product factor, Sylow
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8—22no—
171C2×Q8SD16×C3114yes—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—41no—
176C22×C4C2×D4×C3111yescharacteristic
177C22×C4C2×D4×C3112yes—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—22no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—42no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—82no—
195C42—42no—
196C42—42no—
197C42C2×D4×C3111yescharacteristic
198C42#41×C3111yescharacteristic
199C42#41×C3112yes—
200C23C31×#12011yescharacteristic
201Q8—24no—
202Q8—24no—
203Q8—42no—
204Q8—42no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—24no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—82no—
216C2×C4—81no—
217C2×C4C31×#12111yescharacteristic
218C2×C4C31×#12112yes—
219C2×C4C31×#12312yes—
220C2×C4C31×#12411yescharacteristic
221C2×C4C2×SD16×C3112yes—
222C2×C4C31×#13512yes—
223C2×C4C31×#13712yes—
224C2×C4C31×#13712yes—
225C8—24no—
226C8—82no—
227C22C31×#39411yescharacteristic
228C22C31×#44812yes—
229C22C31×#45212yes—
230C22C31×#45311yescharacteristic
231C22C31×#45611yescharacteristic
232C4—21no—
233C4—21no—
234C4—44no—
235C4—82no—
236C4—82no—
237C4—161no—
238C4C31×#46512yes—
239C4C31×#47012yes—
240C4C31×#48312yes—
241C4C31×#48512yes—
242C2C31×#162311yescharacteristic
243C2C31×#163011yescharacteristic
244C2C31×#165312yes—
245C2C31×#203512yes—
246C2C31×#203911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
76. #10437C31direct (N × H)
165. C31#10437direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25822
C31×#18442
C31×#18032
C2×C31×Q8⋊C82
C31×#12962
#1043731