Finite Group Databasebeta

← C31×#7643 #21464402

Subgroups — C31×#7643 #21464402

Order 7936.

646 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 646 conjugacy classes of subgroups — too many to draw. Only its 174 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
1C2×C31×#391C211yesmaximal, characteristic
2C31×#1797C212yesmaximal
3C31×#1272C214yesmaximal, complemented
4C23×Q8×C31C411yescharacteristic
5C22×C4⋊C4×C31C411yescharacteristic
6C22×C42×C31C2211yescharacteristic
7C2×C31×C4⋊C8—22no—
8C2×C31×C22⋊C8—22no—
9C31×#391—22no—
10C31×#391C412yes—
11C31×#391C2212yes—
12C2×C31×#95—22no—
13C31×#336C2214yes—
14C22×Q8×C31—24no—
15C22×Q8×C31—21no—
16C22×Q8×C31—42no—
17C22×Q8×C31—42no—
18C22×Q8×C31C2×C412yes—
19C23×C4×C31—21no—
20C23×C4×C31—21no—
21C23×C4×C31C2×C411yescharacteristic
22C23×C4×C31D412yes—
23C22×C8×C31—24no—
24C2×C4⋊C4×C31—21no—
25C2×C4⋊C4×C31—42no—
26C2×C4⋊C4×C31C2×C412yes—
27C2×C42×C31—42no—
28C2×C42×C31C2×C411yescharacteristic
29C2×C42×C31D412yes—
30C2×C42×C31C2311yescharacteristic
31C31×C4⋊C8—44no—
32C31×C22⋊C8—44no—
33C31×#95—24no—
34C31×#95—24no—
35C24×C31C22⋊C411yescharacteristic
36C2×Q8×C31—24no—
37C2×Q8×C31—22no—
38C2×Q8×C31—416no—
39C2×Q8×C31—42no—
40C2×Q8×C31—42no—
41C2×Q8×C31—42no—
42C2×Q8×C31—42no—
43C2×Q8×C31M1614yes—
44C22×C4×C31—22no—
45C22×C4×C31—22no—
46C22×C4×C31—22no—
47C22×C4×C31—24no—
48C22×C4×C31—22no—
49C22×C4×C31—22no—
50C22×C4×C31—42no—
51C22×C4×C31—42no—
52C22×C4×C31—42no—
53C22×C4×C31—42no—
54C22×C4×C31—44no—
55C22×C4×C31—42no—
56C22×C4×C31C22⋊C411yescharacteristic
57C22×C4×C31C22⋊C412yes—
58C22×C4×C31SD1614yes—
59C22×C4×C31Q1614yes—
60C22×C4×C31C22×C411yescharacteristic
61C22×C4×C31C2×D412yes—
62C2×C8×C31—44no—
63C2×C8×C31—44no—
64C2×C8×C31—44no—
65C4⋊C4×C31—42no—
66C4⋊C4×C31—42no—
67C42×C31—24no—
68C42×C31—41no—
69C42×C31—41no—
70#7643C3111yesmaximal, characteristic, direct product factor, Sylow
71C23×C31—21no—
72C23×C31—21no—
73C23×C31—22no—
74C23×C31#10012yes—
75C23×C31#10314yes—
76C23×C31C2×C22⋊C411yescharacteristic
77Q8×C31—44no—
78Q8×C31—48no—
79Q8×C31—44no—
80C2×C4×C31—28no—
81C2×C4×C31—21no—
82C2×C4×C31—22no—
83C2×C4×C31—22no—
84C2×C4×C31—21no—
85C2×C4×C31—21no—
86C2×C4×C31—21no—
87C2×C4×C31—22no—
88C2×C4×C31—22no—
89C2×C4×C31—24no—
90C2×C4×C31—44no—
91C2×C4×C31—44no—
92C2×C4×C31—48no—
93C2×C4×C31—42no—
94C2×C4×C31—42no—
95C2×C4×C31—42no—
96C2×C4×C31—44no—
97C2×C4×C31—84no—
98C2×C4×C31#9912yes—
99C2×C4×C31#10314yes—
100C2×C4×C31C2×M1612yes—
101C2×C4×C31C2×SD1612yes—
102C2×C4×C31C2×Q1612yes—
103C8×C31—84no—
104C2×#391C2×C3111yescharacteristic
105#1797C2×C3112yes—
106#1272C2×C3114yescomplemented
107C22×C31—22no—
108C22×C31—24no—
109C22×C31—24no—
110C22×C31—22no—
111C22×C31#33314yes—
112C22×C31#40711yescharacteristic
113C22×C31C2×#9911yescharacteristic
114C22×C31C2×#10011yescharacteristic
115C22×C31C2×#10312yes—
116C22×C31#42112yes—
117C4×C31—22no—
118C4×C31—22no—
119C4×C31—22no—
120C4×C31—24no—
121C4×C31—22no—
122C4×C31—44no—
123C4×C31—82no—
124C23×Q8C4×C3111yescharacteristic
125C22×C4⋊C4C4×C3111yescharacteristic
126C22×C42C22×C3111yescharacteristic
127C2×C4⋊C8—22no—
128C2×C22⋊C8—22no—
129#391—22no—
130#391C4×C3112yes—
131#391C22×C3112yes—
132C2×#95—22no—
133#336C22×C3114yes—
134C2×C31—24no—
135C2×C31#146211yescharacteristic
136C2×C31#148712yes—
137C2×C31#152012yes—
138C2×C31#153311yescharacteristic
139C2×C31C2×#33311yescharacteristic
140C22×Q8—24no—
141C22×Q8—21no—
142C22×Q8—42no—
143C22×Q8—42no—
144C22×Q8C2×C4×C3112yes—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4C2×C4×C3111yescharacteristic
148C23×C4D4×C3112yes—
149C22×C8—24no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—42no—
152C2×C4⋊C4C2×C4×C3112yes—
153C2×C42—42no—
154C2×C42C2×C4×C3111yescharacteristic
155C2×C42D4×C3112yes—
156C2×C42C23×C3111yescharacteristic
157C4⋊C8—44no—
158C22⋊C8—44no—
159#95—24no—
160#95—24no—
161C31#764311yescharacteristic, direct product factor, Sylow
162C24C22⋊C4×C3111yescharacteristic
163C2×Q8—24no—
164C2×Q8—22no—
165C2×Q8—416no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—42no—
169C2×Q8—42no—
170C2×Q8M16×C3114yes—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—24no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—44no—
182C22×C4—42no—
183C22×C4C22⋊C4×C3111yescharacteristic
184C22×C4C22⋊C4×C3112yes—
185C22×C4SD16×C3114yes—
186C22×C4Q16×C3114yes—
187C22×C4C22×C4×C3111yescharacteristic
188C22×C4C2×D4×C3112yes—
189C2×C8—44no—
190C2×C8—44no—
191C2×C8—44no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C42—24no—
195C42—41no—
196C42—41no—
197C23—21no—
198C23—21no—
199C23—22no—
200C23C31×#10012yes—
201C23C31×#10314yes—
202C23C2×C22⋊C4×C3111yescharacteristic
203Q8—44no—
204Q8—48no—
205Q8—44no—
206C2×C4—28no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—44no—
217C2×C4—44no—
218C2×C4—48no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—44no—
223C2×C4—84no—
224C2×C4C31×#9912yes—
225C2×C4C31×#10314yes—
226C2×C4C2×M16×C3112yes—
227C2×C4C2×SD16×C3112yes—
228C2×C4C2×Q16×C3112yes—
229C8—84no—
230C22—22no—
231C22—24no—
232C22—24no—
233C22—22no—
234C22C31×#33314yes—
235C22C31×#40711yescharacteristic
236C22C2×C31×#9911yescharacteristic
237C22C2×C31×#10011yescharacteristic
238C22C2×C31×#10312yes—
239C22C31×#42112yes—
240C4—22no—
241C4—22no—
242C4—22no—
243C4—24no—
244C4—22no—
245C4—44no—
246C4—82no—
247C2—24no—
248C2C31×#146211yescharacteristic
249C2C31×#148712yes—
250C2C31×#152012yes—
251C2C31×#153311yescharacteristic
252C2C2×C31×#33311yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1272C2semidirect
70. #7643C31direct (N × H)
106. #1272C2×C31semidirect
161. C31#7643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3912
C31×#17972
C31×#12722
#764331