Finite Group Databasebeta

← C31×#7626 #21464385

Subgroups — C31×#7626 #21464385

Order 7936.

874 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 150 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×#390C211yesmaximal, characteristic
2C31×#1749C212yesmaximal, complemented
3C31×#1270C214yesmaximal, complemented
4C23×D4×C31C411yescharacteristic
5C22×C4⋊C4×C31C411yescharacteristic
6C22×C22⋊C4×C31—22no—
7C22×C42×C31C2211yescharacteristic
8C2×C31×C22⋊C8—22no—
9C2×C31×#97—22no—
10C31×#390—22no—
11C31×#390C412yes—
12C31×#390C2212yes—
13C31×#336C2214yescomplemented
14C25×C31—21no—
15C22×D4×C31—24no—
16C22×D4×C31—21no—
17C22×D4×C31—42no—
18C22×D4×C31—42no—
19C22×D4×C31C2×C412yes—
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×C22⋊C4×C31—24no—
28C2×C22⋊C4×C31—24no—
29C2×C22⋊C4×C31—48no—
30C2×C42×C31—42no—
31C2×C42×C31C2×C411yescharacteristic
32C2×C42×C31D412yes—
33C2×C42×C31C2311yescharacteristic
34C31×C22⋊C8—28no—
35C31×#97—44no—
36C24×C31—24no—
37C24×C31—22no—
38C24×C31—44no—
39C24×C31—42no—
40C24×C31—42no—
41C24×C31—44no—
42C24×C31C22⋊C411yescharacteristic
43C2×D4×C31—24no—
44C2×D4×C31—22no—
45C2×D4×C31—416no—
46C2×D4×C31—42no—
47C2×D4×C31—42no—
48C2×D4×C31—42no—
49C2×D4×C31—42no—
50C2×D4×C31M1614yes—
51C22×C4×C31—22no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—24no—
55C22×C4×C31—24no—
56C22×C4×C31—22no—
57C22×C4×C31—42no—
58C22×C4×C31—44no—
59C22×C4×C31—42no—
60C22×C4×C31C22⋊C412yes—
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22×C411yescharacteristic
63C22×C4×C31C2×D412yes—
64C2×C8×C31—28no—
65C2×C8×C31—44no—
66C2×C8×C31—44no—
67C4⋊C4×C31—42no—
68C4⋊C4×C31—42no—
69C22⋊C4×C31—48no—
70C22⋊C4×C31—48no—
71C42×C31—24no—
72C42×C31—41no—
73C42×C31—41no—
74#7626C3111yesmaximal, characteristic, direct product factor, Sylow
75C23×C31—21no—
76C23×C31—21no—
77C23×C31—22no—
78C23×C31—24no—
79C23×C31—48no—
80C23×C31—416no—
81C23×C31—42no—
82C23×C31—42no—
83C23×C31—44no—
84C23×C31—44no—
85C23×C31—84no—
86C23×C31—88no—
87C23×C31—84no—
88C23×C31#10012yes—
89C23×C31#10414yes—
90C23×C31C2×C22⋊C411yescharacteristic
91D4×C31—44no—
92D4×C31—48no—
93D4×C31—44no—
94C2×C4×C31—28no—
95C2×C4×C31—21no—
96C2×C4×C31—22no—
97C2×C4×C31—21no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—22no—
101C2×C4×C31—22no—
102C2×C4×C31—22no—
103C2×C4×C31—22no—
104C2×C4×C31—48no—
105C2×C4×C31—42no—
106C2×C4×C31—44no—
107C2×C4×C31—84no—
108C2×C4×C31#9912yes—
109C2×C4×C31C2×M1612yes—
110C2×C4×C31AGL(1,ℤ/8)14yes—
111C8×C31—48no—
112C2×#390C2×C3111yescharacteristic
113#1749C2×C3112yescomplemented
114#1270C2×C3114yescomplemented
115C22×C31—22no—
116C22×C31—22no—
117C22×C31—24no—
118C22×C31—24no—
119C22×C31—44no—
120C22×C31—48no—
121C22×C31—816no—
122C22×C31—82no—
123C22×C31—84no—
124C22×C31—82no—
125C22×C31#32914yes—
126C22×C31#40711yescharacteristic
127C22×C31C2×#9911yescharacteristic
128C22×C31C2×#10011yescharacteristic
129C22×C31#41812yes—
130C22×C31C2×#10412yes—
131C4×C31—22no—
132C4×C31—22no—
133C4×C31—24no—
134C4×C31—42no—
135C4×C31—82no—
136C23×D4C4×C3111yescharacteristic
137C22×C4⋊C4C4×C3111yescharacteristic
138C22×C22⋊C4—22no—
139C22×C42C22×C3111yescharacteristic
140C2×C22⋊C8—22no—
141C2×#97—22no—
142#390—22no—
143#390C4×C3112yes—
144#390C22×C3112yes—
145#336C22×C3114yescomplemented
146C2×C31—24no—
147C2×C31—84no—
148C2×C31#146211yescharacteristic
149C2×C31#149012yes—
150C2×C31#150712yes—
151C2×C31C2×#32911yescharacteristic
152C2×C31#155511yescharacteristic
153C25—21no—
154C22×D4—24no—
155C22×D4—21no—
156C22×D4—42no—
157C22×D4—42no—
158C22×D4C2×C4×C3112yes—
159C23×C4—21no—
160C23×C4C2×C4×C3111yescharacteristic
161C23×C4D4×C3112yes—
162C22×C8—24no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—42no—
165C2×C4⋊C4C2×C4×C3112yes—
166C2×C22⋊C4—24no—
167C2×C22⋊C4—24no—
168C2×C22⋊C4—48no—
169C2×C42—42no—
170C2×C42C2×C4×C3111yescharacteristic
171C2×C42D4×C3112yes—
172C2×C42C23×C3111yescharacteristic
173C22⋊C8—28no—
174#97—44no—
175C31#762611yescharacteristic, direct product factor, Sylow
176C24—24no—
177C24—22no—
178C24—44no—
179C24—42no—
180C24—42no—
181C24—44no—
182C24C22⋊C4×C3111yescharacteristic
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—42no—
186C2×D4—42no—
187C2×D4—416no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4M16×C3114yes—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—24no—
195C22×C4—24no—
196C22×C4—22no—
197C22×C4—42no—
198C22×C4—44no—
199C22×C4—42no—
200C22×C4C22⋊C4×C3112yes—
201C22×C4C22⋊C4×C3111yescharacteristic
202C22×C4C22×C4×C3111yescharacteristic
203C22×C4C2×D4×C3112yes—
204C2×C8—28no—
205C2×C8—44no—
206C2×C8—44no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C22⋊C4—48no—
210C22⋊C4—48no—
211C42—24no—
212C42—41no—
213C42—41no—
214C23—21no—
215C23—21no—
216C23—22no—
217C23—24no—
218C23—48no—
219C23—416no—
220C23—42no—
221C23—42no—
222C23—44no—
223C23—44no—
224C23—84no—
225C23—88no—
226C23—84no—
227C23C31×#10012yes—
228C23C31×#10414yes—
229C23C2×C22⋊C4×C3111yescharacteristic
230D4—44no—
231D4—48no—
232D4—44no—
233C2×C4—28no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—48no—
244C2×C4—42no—
245C2×C4—44no—
246C2×C4—84no—
247C2×C4C31×#9912yes—
248C2×C4C2×M16×C3112yes—
249C2×C4C31×AGL(1,ℤ/8)14yes—
250C8—48no—
251C22—22no—
252C22—22no—
253C22—24no—
254C22—24no—
255C22—44no—
256C22—48no—
257C22—816no—
258C22—82no—
259C22—84no—
260C22—82no—
261C22C31×#32914yes—
262C22C31×#40711yescharacteristic
263C22C2×C31×#9911yescharacteristic
264C22C2×C31×#10011yescharacteristic
265C22C31×#41812yes—
266C22C2×C31×#10412yes—
267C4—22no—
268C4—22no—
269C4—24no—
270C4—42no—
271C4—82no—
272C2—24no—
273C2—84no—
274C2C31×#146211yescharacteristic
275C2C31×#149012yes—
276C2C31×#150712yes—
277C2C2×C31×#32911yescharacteristic
278C2C31×#155511yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×D4×C31C4
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
2. C31×#1749C2semidirect
3. C31×#1270C2semidirect
13. C31×#336C22semidirect
74. #7626C31direct (N × H)
113. #1749C2×C31semidirect
114. #1270C2×C31semidirect
145. #336C22×C31semidirect
175. C31#7626direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3902
C31×#17492
C31×#12702
#762631