Finite Group Databasebeta

← C31×#11466 #21468225

Subgroups — C31×#11466 #21468225

Order 7936.

438 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D4×C31C211yesmaximal, characteristic
2C31×#2112C212yesmaximal, complemented
3C31×#1322C212yesmaximal, complemented
4C31×#1314C212yesmaximal, complemented
5C23×C8×C31C411yescharacteristic
6C23×C8×C31C2211yescharacteristic
7C2×C4×D4×C31C411yescharacteristic
8C2×C31×M32—22no—
9C8×D4×C31—22no—
10C8×D4×C31—22no—
11C2×C31×C4⋊C8C2211yescharacteristic
12C2×C31×C22⋊C8C411yescharacteristic
13C2×C31×C22⋊C8C2211yescharacteristic
14C2×C4×C8×C31C411yescharacteristic
15C31×C22⋊C16—22no—
16C31×C22⋊C16C2214yes—
17C22×D4×C31C811yescharacteristic
18C23×C4×C31C2×C411yescharacteristic
19C23×C4×C31C2×C411yescharacteristic
20C22×C8×C31—21no—
21C22×C8×C31—21no—
22C22×C8×C31—42no—
23C22×C8×C31—42no—
24C22×C8×C31C2×C411yescharacteristic
25C22×C8×C31C2×C411yescharacteristic
26C22×C8×C31C2×C411yescharacteristic
27C22×C8×C31D412yes—
28C22×C8×C31D412yes—
29C22×C8×C31C2311yescharacteristic
30C4×D4×C31—22no—
31C4×D4×C31—22no—
32C2×C4⋊C4×C31C811yescharacteristic
33C2×C22⋊C4×C31C811yescharacteristic
34C2×C22⋊C4×C31C811yescharacteristic
35C2×C42×C31C2×C411yescharacteristic
36C31×M32—44no—
37C2×C16×C31—24no—
38C31×C4⋊C8—22no—
39C31×C22⋊C8—22no—
40C31×C22⋊C8—22no—
41C4×C8×C31—21no—
42C4×C8×C31—21no—
43C24×C31C2×C811yescharacteristic
44C24×C31C2×C811yescharacteristic
45C2×D4×C31—22no—
46C2×D4×C31—22no—
47C2×D4×C31—22no—
48C22×C4×C31—21no—
49C22×C4×C31—21no—
50C22×C4×C31—41no—
51C22×C4×C31—41no—
52C22×C4×C31—41no—
53C22×C4×C31—41no—
54C22×C4×C31C22⋊C412yes—
55C22×C4×C31C2×C811yescharacteristic
56C22×C4×C31C2×C811yescharacteristic
57C22×C4×C31C2×C811yescharacteristic
58C22×C4×C31C2×C811yescharacteristic
59C22×C4×C31M1612yes—
60C22×C4×C31C22×C411yescharacteristic
61C2×C8×C31—24no—
62C2×C8×C31—22no—
63C2×C8×C31—21no—
64C2×C8×C31—21no—
65C2×C8×C31—42no—
66C2×C8×C31—41no—
67C2×C8×C31—42no—
68C2×C8×C31—42no—
69C2×C8×C31—41no—
70C2×C8×C31—41no—
71C2×C8×C31C22⋊C411yescharacteristic
72C2×C8×C31C22⋊C411yescharacteristic
73C2×C8×C31C2×D412yes—
74C4⋊C4×C31—22no—
75C22⋊C4×C31—22no—
76C22⋊C4×C31—22no—
77C42×C31—21no—
78C42×C31—21no—
79C16×C31—44no—
80#11466C3111yesmaximal, characteristic, direct product factor, Sylow
81C23×C31—21no—
82C23×C31—21no—
83C23×C31—21no—
84C23×C31—21no—
85C23×C31—41no—
86C23×C31—41no—
87C23×C31—41no—
88C23×C31—41no—
89C23×C31C22⋊C812yes—
90C23×C31M3212yescomplemented
91C23×C31C22×C811yescharacteristic
92D4×C31—28no—
93C2×C4×C31—21no—
94C2×C4×C31—21no—
95C2×C4×C31—21no—
96C2×C4×C31—22no—
97C2×C4×C31—21no—
98C2×C4×C31—22no—
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—41no—
102C2×C4×C31—42no—
103C2×C4×C31—42no—
104C2×C4×C31—41no—
105C2×C4×C31—41no—
106C2×C4×C31—41no—
107C2×C4×C31—41no—
108C2×C4×C31C22⋊C812yes—
109C2×C4×C31M3212yescomplemented
110C2×C4×C31C2×C22⋊C411yescharacteristic
111C2×C4×C31C2×M1611yescharacteristic
112C8×C31—22no—
113C8×C31—21no—
114C8×C31—41no—
115C8×C31—41no—
116C8×C31#9912yes—
117C2×C8×D4C2×C3111yescharacteristic
118#2112C2×C3112yescomplemented
119#1322C2×C3112yescomplemented
120#1314C2×C3112yescomplemented
121C22×C31—21no—
122C22×C31—21no—
123C22×C31—22no—
124C22×C31—22no—
125C22×C31—22no—
126C22×C31—22no—
127C22×C31—42no—
128C22×C31—42no—
129C22×C31—42no—
130C22×C31—42no—
131C22×C31—41no—
132C22×C31—41no—
133C22×C31C2×C22⋊C811yescharacteristic
134C22×C31C2×M3211yescharacteristic
135C22×C31C2×M3211yescharacteristic
136C4×C31—22no—
137C4×C31—21no—
138C4×C31—22no—
139C4×C31—41no—
140C4×C31—41no—
141C4×C31C2×#9911yescharacteristic
142C4×C31#41311yescharacteristic
143C23×C8C4×C3111yescharacteristic
144C23×C8C22×C3111yescharacteristic
145C2×C4×D4C4×C3111yescharacteristic
146C2×M32—22no—
147C8×D4—22no—
148C8×D4—22no—
149C2×C4⋊C8C22×C3111yescharacteristic
150C2×C22⋊C8C4×C3111yescharacteristic
151C2×C22⋊C8C22×C3111yescharacteristic
152C2×C4×C8C4×C3111yescharacteristic
153C22⋊C16—22no—
154C22⋊C16C22×C3114yes—
155C2×C31—21no—
156C2×C31—21no—
157C2×C31—42no—
158C2×C31—42no—
159C2×C31#145911yescharacteristic
160C2×C31#211211yescharacteristic
161C2×C31#211511yescharacteristic
162C22×D4C8×C3111yescharacteristic
163C23×C4C2×C4×C3111yescharacteristic
164C23×C4C2×C4×C3111yescharacteristic
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—42no—
168C22×C8—42no—
169C22×C8C2×C4×C3111yescharacteristic
170C22×C8C2×C4×C3111yescharacteristic
171C22×C8C2×C4×C3111yescharacteristic
172C22×C8D4×C3112yes—
173C22×C8D4×C3112yes—
174C22×C8C23×C3111yescharacteristic
175C4×D4—22no—
176C4×D4—22no—
177C2×C4⋊C4C8×C3111yescharacteristic
178C2×C22⋊C4C8×C3111yescharacteristic
179C2×C22⋊C4C8×C3111yescharacteristic
180C2×C42C2×C4×C3111yescharacteristic
181M32—44no—
182C2×C16—24no—
183C4⋊C8—22no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C4×C8—21no—
187C4×C8—21no—
188C31#1146611yescharacteristic, direct product factor, Sylow
189C24C2×C8×C3111yescharacteristic
190C24C2×C8×C3111yescharacteristic
191C2×D4—22no—
192C2×D4—22no—
193C2×D4—22no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4C22⋊C4×C3112yes—
201C22×C4C2×C8×C3111yescharacteristic
202C22×C4C2×C8×C3111yescharacteristic
203C22×C4C2×C8×C3111yescharacteristic
204C22×C4C2×C8×C3111yescharacteristic
205C22×C4M16×C3112yes—
206C22×C4C22×C4×C3111yescharacteristic
207C2×C8—24no—
208C2×C8—22no—
209C2×C8—21no—
210C2×C8—21no—
211C2×C8—42no—
212C2×C8—41no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8C22⋊C4×C3111yescharacteristic
218C2×C8C22⋊C4×C3111yescharacteristic
219C2×C8C2×D4×C3112yes—
220C4⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—22no—
223C42—21no—
224C42—21no—
225C16—44no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23—21no—
230C23—41no—
231C23—41no—
232C23—41no—
233C23—41no—
234C23C31×C22⋊C812yes—
235C23C31×M3212yescomplemented
236C23C22×C8×C3111yescharacteristic
237D4—28no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4C31×C22⋊C812yes—
254C2×C4C31×M3212yescomplemented
255C2×C4C2×C22⋊C4×C3111yescharacteristic
256C2×C4C2×M16×C3111yescharacteristic
257C8—22no—
258C8—21no—
259C8—41no—
260C8—41no—
261C8C31×#9912yes—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—22no—
266C22—22no—
267C22—22no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—41no—
273C22—41no—
274C22C2×C31×C22⋊C811yescharacteristic
275C22C2×C31×M3211yescharacteristic
276C22C2×C31×M3211yescharacteristic
277C4—22no—
278C4—21no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4C2×C31×#9911yescharacteristic
283C4C31×#41311yescharacteristic
284C2—21no—
285C2—21no—
286C2—42no—
287C2—42no—
288C2C31×#145911yescharacteristic
289C2C31×#211211yescharacteristic
290C2C31×#211511yescharacteristic
subgroupG/H
centerC2×C4×C31C2×C22⋊C4
commutatorC23C22×C8×C31
Frattini, cosocleC22×C8C23×C31
socleC22×C31C2×C22⋊C8
prime radicalC22×D4×C31C8
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2112C2semidirect
3. C31×#1322C2semidirect
4. C31×#1314C2semidirect
80. #11466C31direct (N × H)
90. C23×C31M32semidirect
109. C2×C4×C31M32semidirect
118. #2112C2×C31semidirect
119. #1322C2×C31semidirect
120. #1314C2×C31semidirect
188. C31#11466direct (N × H)
235. C23C31×M32semidirect
254. C2×C4C31×M32semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D4×C312
C31×#21122
C31×#13222
C31×#13142
#1146631