Finite Group Databasebeta

← C31×#8766 #21465525

Subgroups — C31×#8766 #21465525

Order 7936.

422 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 142 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×#2351C211yesmaximal, characteristic
2C31×#1801C211yesmaximal, characteristic
3C31×#1461C211yesmaximal, characteristic
4C31×#1303C212yesmaximal
5C31×#1286C212yesmaximal
6C2×C4×Q8×C31—21no—
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#431C2212yes—
9C31×#423C2212yes—
10C2×C31×#101—21no—
11C31×#389—21no—
12C31×#389—22no—
13C31×#382C412yes—
14C31×#382C2211yescharacteristic
15C4×C4⋊C4×C31C412yes—
16C4×C4⋊C4×C31C2211yescharacteristic
17C31×#343—21no—
18C31×#324—22no—
19C22×Q8×C31D411yescharacteristic
20C2×M16×C31—22no—
21C4×Q8×C31—22no—
22C4×Q8×C31—22no—
23C4×Q8×C31—42no—
24C4×Q8×C31—42no—
25C2×C4⋊C4×C31—22no—
26C2×C4⋊C4×C31—22no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31D412yes—
30C2×C4⋊C4×C31D411yescharacteristic
31C2×C42×C31—22no—
32C2×C42×C31—21no—
33C2×C42×C31C2×C412yes—
34C2×C42×C31C2311yescharacteristic
35C31×C4⋊C8—22no—
36C31×C4⋊C8—22no—
37C31×C4⋊C8—22no—
38C31×#101—42no—
39C31×C22⋊C8—22no—
40C4×C8×C31—22no—
41C31×#95—22no—
42C31×#95—21no—
43C31×#95C2×C411yescharacteristic
44C31×#95C2×C412yes—
45C31×#95C2×C411yescharacteristic
46C2×Q8×C31—22no—
47C2×Q8×C31—22no—
48C2×Q8×C31D812yes—
49C2×Q8×C31SD1612yes—
50C22×C4×C31—21no—
51C22×C4×C31—21no—
52C22×C4×C31—22no—
53C22×C4×C31C22⋊C412yes—
54C22×C4×C31C22⋊C412yes—
55C22×C4×C31C22×C411yescharacteristic
56C22×C4×C31C2×D411yescharacteristic
57C22×C4×C31C2×D411yescharacteristic
58M16×C31—42no—
59M16×C31—42no—
60C2×C8×C31—42no—
61C2×C8×C31—42no—
62C4⋊C4×C31—24no—
63C4⋊C4×C31—22no—
64C4⋊C4×C31—42no—
65C4⋊C4×C31—44no—
66C4⋊C4×C31—44no—
67C4⋊C4×C31—41no—
68C4⋊C4×C31—41no—
69C42×C31—22no—
70C42×C31—22no—
71C42×C31—44no—
72C42×C31—41no—
73C42×C31—41no—
74C42×C31#4112yes—
75C42×C31#4112yes—
76#8766C3111yesmaximal, characteristic, direct product factor, Sylow
77C23×C31C2×C22⋊C411yescharacteristic
78Q8×C31—24no—
79Q8×C31—24no—
80C2×C4×C31—22no—
81C2×C4×C31—22no—
82C2×C4×C31—22no—
83C2×C4×C31—22no—
84C2×C4×C31—41no—
85C2×C4×C31—41no—
86C2×C4×C31—41no—
87C2×C4×C31—41no—
88C2×C4×C31—42no—
89C2×C4×C31—41no—
90C2×C4×C31—42no—
91C2×C4×C31—41no—
92C2×C4×C31—42no—
93C2×C4×C31—42no—
94C2×C4×C31—41no—
95C2×C4×C31#10214yes—
96C2×C4×C31#11711yescharacteristic
97C2×C4×C31#11711yescharacteristic
98C2×C4×C31#12312yes—
99C2×C4×C31#12312yes—
100C2×C4×C31C2×D811yescharacteristic
101C2×C4×C31C2×SD1611yescharacteristic
102C2×C4×C31#13712yes—
103C8×C31—82no—
104C8×C31—82no—
105#2351C2×C3111yescharacteristic
106#1801C2×C3111yescharacteristic
107#1461C2×C3111yescharacteristic
108#1303C2×C3112yes—
109#1286C2×C3112yes—
110C22×C31—21no—
111C22×C31—21no—
112C22×C31#38111yescharacteristic
113C22×C31C2×#10211yescharacteristic
114C22×C31#41911yescharacteristic
115C4×C31—24no—
116C4×C31—22no—
117C4×C31—21no—
118C4×C31—21no—
119C4×C31—42no—
120C4×C31—42no—
121C4×C31—82no—
122C4×C31—81no—
123C4×C31#48012yes—
124C4×C31#48312yes—
125C2×C4×Q8—21no—
126C2×C4×Q8C22×C3111yescharacteristic
127#431C22×C3112yes—
128#423C22×C3112yes—
129C2×#101—21no—
130#389—21no—
131#389—22no—
132#382C4×C3112yes—
133#382C22×C3111yescharacteristic
134C4×C4⋊C4C4×C3112yes—
135C4×C4⋊C4C22×C3111yescharacteristic
136#343—21no—
137#324—22no—
138C2×C31—21no—
139C2×C31—21no—
140C2×C31#182311yescharacteristic
141C2×C31#182711yescharacteristic
142C2×C31#183011yescharacteristic
143C22×Q8D4×C3111yescharacteristic
144C2×M16—22no—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—42no—
148C4×Q8—42no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4D4×C3112yes—
154C2×C4⋊C4D4×C3111yescharacteristic
155C2×C42—22no—
156C2×C42—21no—
157C2×C42C2×C4×C3112yes—
158C2×C42C23×C3111yescharacteristic
159C4⋊C8—22no—
160C4⋊C8—22no—
161C4⋊C8—22no—
162#101—42no—
163C22⋊C8—22no—
164C4×C8—22no—
165#95—22no—
166#95—21no—
167#95C2×C4×C3111yescharacteristic
168#95C2×C4×C3112yes—
169#95C2×C4×C3111yescharacteristic
170C31#876611yescharacteristic, direct product factor, Sylow
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8D8×C3112yes—
174C2×Q8SD16×C3112yes—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4C22⋊C4×C3112yes—
179C22×C4C22⋊C4×C3112yes—
180C22×C4C22×C4×C3111yescharacteristic
181C22×C4C2×D4×C3111yescharacteristic
182C22×C4C2×D4×C3111yescharacteristic
183M16—42no—
184M16—42no—
185C2×C8—42no—
186C2×C8—42no—
187C4⋊C4—24no—
188C4⋊C4—22no—
189C4⋊C4—42no—
190C4⋊C4—44no—
191C4⋊C4—44no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C42—22no—
195C42—22no—
196C42—44no—
197C42—41no—
198C42—41no—
199C42#41×C3112yes—
200C42#41×C3112yes—
201C23C2×C22⋊C4×C3111yescharacteristic
202Q8—24no—
203Q8—24no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4C31×#10214yes—
220C2×C4C31×#11711yescharacteristic
221C2×C4C31×#11711yescharacteristic
222C2×C4C31×#12312yes—
223C2×C4C31×#12312yes—
224C2×C4C2×D8×C3111yescharacteristic
225C2×C4C2×SD16×C3111yescharacteristic
226C2×C4C31×#13712yes—
227C8—82no—
228C8—82no—
229C22—21no—
230C22—21no—
231C22C31×#38111yescharacteristic
232C22C2×C31×#10211yescharacteristic
233C22C31×#41911yescharacteristic
234C4—24no—
235C4—22no—
236C4—21no—
237C4—21no—
238C4—42no—
239C4—42no—
240C4—82no—
241C4—81no—
242C4C31×#48012yes—
243C4C31×#48312yes—
244C2—21no—
245C2—21no—
246C2C31×#182311yescharacteristic
247C2C31×#182711yescharacteristic
248C2C31×#183011yescharacteristic
subgroupG/H
center, socleC22×C31#381
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
76. #8766C31direct (N × H)
170. C31#8766direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23512
C31×#18012
C31×#14612
C31×#13032
C31×#12862
#876631