Finite Group Databasebeta

← C31×#7812 #21464571

Subgroups — C31×#7812 #21464571

Order 7936.

398 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2811C211yesmaximal, characteristic
2C31×#2096C211yesmaximal, characteristic
3C31×#2072C212yesmaximal
4C31×#1272C211yesmaximal, characteristic
5C31×#1272C212yesmaximal
6C2×C31×#106—21no—
7C2×C31×#103—22no—
8C2×C31×#103—21no—
9C31×#395—21no—
10C31×#395—22no—
11C31×#391—22no—
12C31×#391—21no—
13C31×#391C2212yes—
14C31×#391C2211yescharacteristic
15C31×#384C2211yescharacteristic
16C31×#340—22no—
17C31×#336C2212yes—
18C31×#336C2211yescharacteristic
19C22×Q8×C31—21no—
20C22×Q8×C31D412yes—
21C22×Q8×C31D411yescharacteristic
22C22×C8×C31—21no—
23C22×C8×C31—22no—
24C2×C4⋊C4×C31—21no—
25C2×C4⋊C4×C31—22no—
26C2×C4⋊C4×C31—21no—
27C2×C4⋊C4×C31—22no—
28C2×C4⋊C4×C31D411yescharacteristic
29C2×C4⋊C4×C31D412yes—
30C2×C42×C31—21no—
31C2×C42×C31C2311yescharacteristic
32C31×#106—42no—
33C31×#103—42no—
34C31×#103—44no—
35C31×#95—21no—
36C31×#95—22no—
37C31×#95—22no—
38C31×#95—22no—
39C31×#95—22no—
40C2×Q8×C31—22no—
41C2×Q8×C31—21no—
42C2×Q8×C31—41no—
43C2×Q8×C31—42no—
44C2×Q8×C31—42no—
45C2×Q8×C31—41no—
46C2×Q8×C31—81no—
47C2×Q8×C31—82no—
48C2×Q8×C31SD1614yes—
49C2×Q8×C31Q1612yes—
50C22×C4×C31—22no—
51C22×C4×C31—21no—
52C22×C4×C31—21no—
53C22×C4×C31—22no—
54C22×C4×C31—41no—
55C22×C4×C31C2×D412yes—
56C22×C4×C31C2×D411yescharacteristic
57C2×C8×C31—22no—
58C2×C8×C31—41no—
59C2×C8×C31—41no—
60C2×C8×C31—42no—
61C2×C8×C31—42no—
62C2×C8×C31—42no—
63C4⋊C4×C31—41no—
64C4⋊C4×C31—42no—
65C4⋊C4×C31—41no—
66C4⋊C4×C31—41no—
67C4⋊C4×C31—42no—
68C4⋊C4×C31—42no—
69C4⋊C4×C31—81no—
70C4⋊C4×C31—82no—
71C42×C31—41no—
72C42×C31—81no—
73#7812C3111yesmaximal, characteristic, direct product factor, Sylow
74C23×C31#12011yescharacteristic
75Q8×C31—44no—
76Q8×C31—42no—
77Q8×C31—82no—
78Q8×C31—81no—
79Q8×C31—84no—
80C2×C4×C31—21no—
81C2×C4×C31—22no—
82C2×C4×C31—22no—
83C2×C4×C31—21no—
84C2×C4×C31—24no—
85C2×C4×C31—22no—
86C2×C4×C31—41no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31—41no—
90C2×C4×C31—41no—
91C2×C4×C31—42no—
92C2×C4×C31—42no—
93C2×C4×C31—42no—
94C2×C4×C31—42no—
95C2×C4×C31—82no—
96C2×C4×C31—81no—
97C2×C4×C31C2×SD1612yes—
98C2×C4×C31C2×Q1611yescharacteristic
99C2×C4×C31#13712yes—
100C2×C4×C31#13711yescharacteristic
101C8×C31—42no—
102C8×C31—82no—
103#2811C2×C3111yescharacteristic
104#2096C2×C3111yescharacteristic
105#2072C2×C3112yes—
106#1272C2×C3111yescharacteristic
107#1272C2×C3112yes—
108C22×C31#44812yes—
109C22×C31#45111yescharacteristic
110C22×C31#45311yescharacteristic
111C22×C31#45512yes—
112C22×C31#45811yescharacteristic
113C4×C31—22no—
114C4×C31—22no—
115C4×C31—21no—
116C4×C31—21no—
117C4×C31—44no—
118C4×C31—42no—
119C4×C31—81no—
120C4×C31—82no—
121C4×C31—161no—
122C2×#106—21no—
123C2×#103—22no—
124C2×#103—21no—
125#395—22no—
126#395—21no—
127#391—22no—
128#391—21no—
129#391C22×C3112yes—
130#391C22×C3111yescharacteristic
131#384C22×C3111yescharacteristic
132#340—22no—
133#336C22×C3112yes—
134#336C22×C3111yescharacteristic
135C2×C31#160812yes—
136C2×C31#161411yescharacteristic
137C2×C31#162311yescharacteristic
138C2×C31#164512yes—
139C2×C31#165911yescharacteristic
140C22×Q8—21no—
141C22×Q8D4×C3112yes—
142C22×Q8D4×C3111yescharacteristic
143C22×C8—21no—
144C22×C8—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4D4×C3112yes—
150C2×C4⋊C4D4×C3111yescharacteristic
151C2×C42—21no—
152C2×C42C23×C3111yescharacteristic
153#106—42no—
154#103—42no—
155#103—44no—
156#95—21no—
157#95—22no—
158#95—22no—
159#95—22no—
160#95—22no—
161C31#781211yescharacteristic, direct product factor, Sylow
162C2×Q8—22no—
163C2×Q8—21no—
164C2×Q8—41no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8—41no—
168C2×Q8—81no—
169C2×Q8—82no—
170C2×Q8SD16×C3114yes—
171C2×Q8Q16×C3112yes—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—41no—
177C22×C4C2×D4×C3112yes—
178C22×C4C2×D4×C3111yescharacteristic
179C2×C8—22no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—42no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—81no—
192C4⋊C4—82no—
193C42—41no—
194C42—81no—
195C23C31×#12011yescharacteristic
196Q8—44no—
197Q8—42no—
198Q8—82no—
199Q8—81no—
200Q8—84no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—24no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—82no—
217C2×C4—81no—
218C2×C4C2×SD16×C3112yes—
219C2×C4C2×Q16×C3111yescharacteristic
220C2×C4C31×#13712yes—
221C2×C4C31×#13711yescharacteristic
222C8—42no—
223C8—82no—
224C22C31×#44812yes—
225C22C31×#45111yescharacteristic
226C22C31×#45311yescharacteristic
227C22C31×#45512yes—
228C22C31×#45811yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—44no—
234C4—42no—
235C4—81no—
236C4—82no—
237C4—161no—
238C2C31×#160812yes—
239C2C31×#161411yescharacteristic
240C2C31×#162311yescharacteristic
241C2C31×#164512yes—
242C2C31×#165911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
73. #7812C31direct (N × H)
161. C31#7812direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28112
C31×#20962
C31×#20722
C31×#12722
#781231