Finite Group Databasebeta

← C4×C31×#329 #21464981

Subgroups — C4×C31×#329 #21464981

Order 7936.

616 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×#124C211yesmaximal, characteristic
2C4×C31×#97C212yesmaximal, complemented
3C2×C31×#329C212yesmaximal
4C31×#1295C212yesmaximal, complemented
5C2×C31×#124C2211yescharacteristic
6C2×C4×Q8×C31C411yescharacteristic
7C2×C4×D4×C31C411yescharacteristic
8C2×C31×#97—22no—
9C2×C31×#97C2214yes—
10C2×C4×C8×C31—22no—
11C31×#391C411yescharacteristic
12C31×#390C411yescharacteristic
13C31×#388—22no—
14C31×#382C2211yescharacteristic
15C4×C22⋊C4×C31—22no—
16C43×C31C2211yescharacteristic
17C31×#329C418yesdirect product factor
18C22×Q8×C31C2×C411yescharacteristic
19C22×D4×C31C2×C411yescharacteristic
20C23×C4×C31—21no—
21C22×C8×C31—24no—
22C31×#124—22no—
23C31×#124C2×C414yes—
24C4×Q8×C31—42no—
25C4×D4×C31—42no—
26C2×C4⋊C4×C31—21no—
27C2×C4⋊C4×C31C2×C411yescharacteristic
28C2×C4⋊C4×C31C2×C411yescharacteristic
29C2×C22⋊C4×C31—22no—
30C2×C22⋊C4×C31—21no—
31C2×C22⋊C4×C31—22no—
32C2×C42×C31—21no—
33C2×C42×C31C2×C411yescharacteristic
34C2×C42×C31C2×C411yescharacteristic
35C2×C42×C31D412yes—
36C2×C42×C31D412yes—
37C2×C42×C31C2311yescharacteristic
38C31×#97—28no—
39C31×#97—24no—
40C31×#97C2×C418yescomplemented
41C4×C8×C31—28no—
42C31×#95—22no—
43C31×#95—22no—
44C24×C31—21no—
45C2×Q8×C31—21no—
46C2×Q8×C31—41no—
47C2×Q8×C31—41no—
48C2×Q8×C31C4212yes—
49C2×D4×C31—21no—
50C2×D4×C31—41no—
51C2×D4×C31—41no—
52C2×D4×C31C4212yes—
53C22×C4×C31—21no—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31—42no—
57C22×C4×C31—44no—
58C22×C4×C31C22⋊C411yescharacteristic
59C22×C4×C31C22⋊C412yes—
60C22×C4×C31C22⋊C411yescharacteristic
61C22×C4×C31C22×C411yescharacteristic
62C22×C4×C31C2×D412yes—
63C2×C8×C31—28no—
64C2×C8×C31—28no—
65C2×C8×C31—28no—
66C4⋊C4×C31—42no—
67C4⋊C4×C31—41no—
68C4⋊C4×C31—41no—
69C22⋊C4×C31—28no—
70C22⋊C4×C31—42no—
71C22⋊C4×C31—44no—
72C42×C31—22no—
73C42×C31—24no—
74C42×C31—24no—
75C42×C31—41no—
76C42×C31—42no—
77C42×C31C22×C412yes—
78C42×C31#4112yes—
79C4×#329C3111yesmaximal, characteristic, direct product factor, Sylow
80C23×C31—22no—
81C23×C31—41no—
82C23×C31—41no—
83C23×C31—42no—
84C23×C31—42no—
85C23×C31C2×C22⋊C411yescharacteristic
86Q8×C31—42no—
87Q8×C31—42no—
88D4×C31—42no—
89D4×C31—42no—
90C2×C4×C31—21no—
91C2×C4×C31—22no—
92C2×C4×C31—21no—
93C2×C4×C31—22no—
94C2×C4×C31—22no—
95C2×C4×C31—22no—
96C2×C4×C31—22no—
97C2×C4×C31—21no—
98C2×C4×C31—22no—
99C2×C4×C31—41no—
100C2×C4×C31—41no—
101C2×C4×C31—41no—
102C2×C4×C31—41no—
103C2×C4×C31—42no—
104C2×C4×C31—42no—
105C2×C4×C31—84no—
106C2×C4×C31#10012yes—
107C2×C4×C31#10414yes—
108C2×C4×C31#10414yes—
109C2×C4×C31C2×C4211yescharacteristic
110C2×C4×C31#11711yescharacteristic
111C2×C4×C31C4×D414yes—
112C8×C31—216no—
113C4×#124C2×C3111yescharacteristic
114C4×#97C2×C3112yescomplemented
115C2×#329C2×C3112yes—
116#1295C2×C3112yescomplemented
117C22×C31—42no—
118C22×C31—44no—
119C22×C31—81no—
120C22×C31—82no—
121C22×C31—81no—
122C22×C31C4×C22⋊C411yescharacteristic
123C22×C31C2×#10011yescharacteristic
124C22×C31#41311yescharacteristic
125C22×C31C2×#10412yes—
126C22×C31C2×#10412yes—
127C4×C31—21no—
128C4×C31—21no—
129C4×C31—24no—
130C4×C31—24no—
131C4×C31—42no—
132C4×C31—41no—
133C4×C31—81no—
134C4×C31—81no—
135C4×C31#32914yesdirect product factor
136C2×#124C22×C3111yescharacteristic
137C2×C4×Q8C4×C3111yescharacteristic
138C2×C4×D4C4×C3111yescharacteristic
139C2×#97—22no—
140C2×#97C22×C3114yes—
141C2×C4×C8—22no—
142#391C4×C3111yescharacteristic
143#390C4×C3111yescharacteristic
144#388—22no—
145#382C22×C3111yescharacteristic
146C4×C22⋊C4—22no—
147C43C22×C3111yescharacteristic
148#329C4×C3118yesdirect product factor
149C2×C31—82no—
150C2×C31C2×#32911yescharacteristic
151C2×C31#152412yes—
152C2×C31#152511yescharacteristic
153C2×C31C4×#10011yescharacteristic
154C2×C31C4×#10412yes—
155C22×Q8C2×C4×C3111yescharacteristic
156C22×D4C2×C4×C3111yescharacteristic
157C23×C4—21no—
158C22×C8—24no—
159#124—22no—
160#124C2×C4×C3114yes—
161C4×Q8—42no—
162C4×D4—42no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4C2×C4×C3111yescharacteristic
165C2×C4⋊C4C2×C4×C3111yescharacteristic
166C2×C22⋊C4—22no—
167C2×C22⋊C4—21no—
168C2×C22⋊C4—22no—
169C2×C42—21no—
170C2×C42C2×C4×C3111yescharacteristic
171C2×C42C2×C4×C3111yescharacteristic
172C2×C42D4×C3112yes—
173C2×C42D4×C3112yes—
174C2×C42C23×C3111yescharacteristic
175#97—28no—
176#97—24no—
177#97C2×C4×C3118yescomplemented
178C4×C8—28no—
179#95—22no—
180#95—22no—
181C31C4×#32911yescharacteristic, direct product factor, Sylow
182C24—21no—
183C2×Q8—21no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8C42×C3112yes—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4C42×C3112yes—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—42no—
195C22×C4—44no—
196C22×C4C22⋊C4×C3111yescharacteristic
197C22×C4C22⋊C4×C3112yes—
198C22×C4C22⋊C4×C3111yescharacteristic
199C22×C4C22×C4×C3111yescharacteristic
200C22×C4C2×D4×C3112yes—
201C2×C8—28no—
202C2×C8—28no—
203C2×C8—28no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C22⋊C4—28no—
208C22⋊C4—42no—
209C22⋊C4—44no—
210C42—22no—
211C42—24no—
212C42—24no—
213C42—41no—
214C42—42no—
215C42C22×C4×C3112yes—
216C42#41×C3112yes—
217C23—22no—
218C23—41no—
219C23—41no—
220C23—42no—
221C23—42no—
222C23C2×C22⋊C4×C3111yescharacteristic
223Q8—42no—
224Q8—42no—
225D4—42no—
226D4—42no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—84no—
243C2×C4C31×#10012yes—
244C2×C4C31×#10414yes—
245C2×C4C31×#10414yes—
246C2×C4C2×C42×C3111yescharacteristic
247C2×C4C31×#11711yescharacteristic
248C2×C4C4×D4×C3114yes—
249C8—216no—
250C22—42no—
251C22—44no—
252C22—81no—
253C22—82no—
254C22—81no—
255C22C4×C22⋊C4×C3111yescharacteristic
256C22C2×C31×#10011yescharacteristic
257C22C31×#41311yescharacteristic
258C22C2×C31×#10412yes—
259C22C2×C31×#10412yes—
260C4—21no—
261C4—21no—
262C4—24no—
263C4—24no—
264C4—42no—
265C4—41no—
266C4—81no—
267C4—81no—
268C4C31×#32914yesdirect product factor
269C2—82no—
270C2C2×C31×#32911yescharacteristic
271C2C31×#152412yes—
272C2C31×#152511yescharacteristic
273C2C4×C31×#10011yescharacteristic
274C2C4×C31×#10412yes—
subgroupG/H
centerC22×C4×C31C22⋊C4
commutatorC2×C4C2×C42×C31
Frattini, cosocleC2×C42C23×C31
socleC23×C31C2×C22⋊C4
prime radicalC22×D4×C31C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C31×#97C2semidirect
4. C31×#1295C2semidirect
17. C31×#329C4direct (N × H)
40. C31×#97C2×C4semidirect
79. C4×#329C31direct (N × H)
114. C4×#97C2×C31semidirect
116. #1295C2×C31semidirect
135. C4×C31#329direct (N × H)
148. #329C4×C31direct (N × H)
177. #97C2×C4×C31semidirect
181. C31C4×#329direct (N × H)
268. C4C31×#329direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1242
C4×C31×#972
C2×C31×#3292
C31×#12952
C4×#32931