Finite Group Databasebeta

← C31×#8299 #21465058

Subgroups — C31×#8299 #21465058

Order 7936.

1502 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C31C211yesmaximal, characteristic
2C31×#1779C212yesmaximal
3C2×C31×#324C214yesmaximal, complemented
4C24×C4×C31C411yescharacteristic
5C24×C4×C31C411yescharacteristic
6C24×C4×C31C2211yescharacteristic
7C22×C4⋊C4×C31—24no—
8C22×C4⋊C4×C31—28no—
9C22×C4⋊C4×C31C412yes—
10C22×C4⋊C4×C31C2212yes—
11C2×C31×C22⋊C8—24no—
12C2×C31×C22⋊C8C2214yes—
13C31×#324—28no—
14C25×C31C2×C411yescharacteristic
15C23×C4×C31—22no—
16C23×C4×C31—22no—
17C23×C4×C31—24no—
18C23×C4×C31—24no—
19C23×C4×C31—22no—
20C23×C4×C31—24no—
21C23×C4×C31—24no—
22C23×C4×C31—44no—
23C23×C4×C31—44no—
24C23×C4×C31C814yescomplemented
25C23×C4×C31C2×C412yes—
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31C2×C412yes—
28C23×C4×C31D414yes—
29C23×C4×C31C2311yescharacteristic
30C22×C8×C31—24no—
31C2×C4⋊C4×C31—232no—
32C2×C4⋊C4×C31—24no—
33C2×C4⋊C4×C31—24no—
34C2×C4⋊C4×C31—24no—
35C2×C4⋊C4×C31—24no—
36C2×C4⋊C4×C31—24no—
37C2×C4⋊C4×C31D418yes—
38C31×C22⋊C8—28no—
39C31×C22⋊C8—48no—
40C24×C31—24no—
41C24×C31—24no—
42C24×C31—22no—
43C24×C31—22no—
44C24×C31C22⋊C412yes—
45C24×C31C2×C812yes—
46C24×C31M1612yes—
47C24×C31C22×C411yescharacteristic
48C22×C4×C31—28no—
49C22×C4×C31—216no—
50C22×C4×C31—28no—
51C22×C4×C31—28no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—216no—
57C22×C4×C31—28no—
58C22×C4×C31—28no—
59C22×C4×C31—22no—
60C22×C4×C31—22no—
61C22×C4×C31—22no—
62C22×C4×C31—28no—
63C22×C4×C31—42no—
64C22×C4×C31—44no—
65C22×C4×C31—42no—
66C22×C4×C31—416no—
67C22×C4×C31—416no—
68C22×C4×C31—44no—
69C22×C4×C31—44no—
70C22×C4×C31—44no—
71C22×C4×C31C22⋊C412yes—
72C22×C4×C31C22⋊C414yes—
73C22×C4×C31C22⋊C414yes—
74C22×C4×C31C2×C814yes—
75C22×C4×C31M1614yes—
76C22×C4×C31C2×D412yes—
77C22×C4×C31C2×D414yes—
78C2×C8×C31—48no—
79C2×C8×C31—44no—
80C4⋊C4×C31—216no—
81C4⋊C4×C31—216no—
82#8299C3111yesmaximal, characteristic, direct product factor, Sylow
83C23×C31—28no—
84C23×C31—216no—
85C23×C31—28no—
86C23×C31—28no—
87C23×C31—28no—
88C23×C31—22no—
89C23×C31—24no—
90C23×C31—22no—
91C23×C31—24no—
92C23×C31—22no—
93C23×C31—22no—
94C23×C31—22no—
95C23×C31—22no—
96C23×C31C22⋊C814yes—
97C23×C31#9914yes—
98C23×C31#10114yes—
99C23×C31C2×C22⋊C412yes—
100C23×C31C2×C22⋊C411yescharacteristic
101C23×C31C22×C811yescharacteristic
102C23×C31C2×M1611yescharacteristic
103C23×C31C2×M1612yes—
104C2×C4×C31—232no—
105C2×C4×C31—24no—
106C2×C4×C31—24no—
107C2×C4×C31—24no—
108C2×C4×C31—24no—
109C2×C4×C31—24no—
110C2×C4×C31—24no—
111C2×C4×C31—24no—
112C2×C4×C31—22no—
113C2×C4×C31—24no—
114C2×C4×C31—24no—
115C2×C4×C31—44no—
116C2×C4×C31—416no—
117C2×C4×C31—44no—
118C2×C4×C31—416no—
119C2×C4×C31—44no—
120C2×C4×C31—44no—
121C2×C4×C31—44no—
122C2×C4×C31C22⋊C818yescomplemented
123C2×C4×C31#12014yes—
124C8×C31—84no—
125C23×C4⋊C4C2×C3111yescharacteristic
126#1779C2×C3112yes—
127C2×#324C2×C3114yescomplemented
128C22×C31—216no—
129C22×C31—216no—
130C22×C31—24no—
131C22×C31—22no—
132C22×C31—22no—
133C22×C31—24no—
134C22×C31—24no—
135C22×C31—24no—
136C22×C31—24no—
137C22×C31—24no—
138C22×C31—22no—
139C22×C31—24no—
140C22×C31—22no—
141C22×C31#32418yescomplemented
142C22×C31#37911yescharacteristic
143C22×C31C2×C22⋊C812yes—
144C22×C31C2×C22⋊C811yescharacteristic
145C22×C31#40712yes—
146C22×C31#40711yescharacteristic
147C22×C31C2×#9912yes—
148C22×C31C2×#10112yes—
149C4×C31—28no—
150C4×C31—24no—
151C4×C31—42no—
152C4×C31—44no—
153C24×C4C4×C3111yescharacteristic
154C24×C4C4×C3111yescharacteristic
155C24×C4C22×C3111yescharacteristic
156C22×C4⋊C4—24no—
157C22×C4⋊C4—28no—
158C22×C4⋊C4C4×C3112yes—
159C22×C4⋊C4C22×C3112yes—
160C2×C22⋊C8—24no—
161C2×C22⋊C8C22×C3114yes—
162#324—28no—
163C2×C31—28no—
164C2×C31—22no—
165C2×C31—22no—
166C2×C31C2×#32412yes—
167C2×C31#146312yes—
168C2×C31#177911yescharacteristic
169C2×C31#178111yescharacteristic
170C2×C31#178411yescharacteristic
171C25C2×C4×C3111yescharacteristic
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—24no—
175C23×C4—24no—
176C23×C4—22no—
177C23×C4—24no—
178C23×C4—24no—
179C23×C4—44no—
180C23×C4—44no—
181C23×C4C8×C3114yescomplemented
182C23×C4C2×C4×C3112yes—
183C23×C4C2×C4×C3111yescharacteristic
184C23×C4C2×C4×C3112yes—
185C23×C4D4×C3114yes—
186C23×C4C23×C3111yescharacteristic
187C22×C8—24no—
188C2×C4⋊C4—232no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4D4×C3118yes—
195C22⋊C8—28no—
196C22⋊C8—48no—
197C31#829911yescharacteristic, direct product factor, Sylow
198C24—24no—
199C24—24no—
200C24—22no—
201C24—22no—
202C24C22⋊C4×C3112yes—
203C24C2×C8×C3112yes—
204C24M16×C3112yes—
205C24C22×C4×C3111yescharacteristic
206C22×C4—28no—
207C22×C4—216no—
208C22×C4—28no—
209C22×C4—28no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—216no—
215C22×C4—28no—
216C22×C4—28no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—28no—
221C22×C4—42no—
222C22×C4—44no—
223C22×C4—42no—
224C22×C4—416no—
225C22×C4—416no—
226C22×C4—44no—
227C22×C4—44no—
228C22×C4—44no—
229C22×C4C22⋊C4×C3112yes—
230C22×C4C22⋊C4×C3114yes—
231C22×C4C22⋊C4×C3114yes—
232C22×C4C2×C8×C3114yes—
233C22×C4M16×C3114yes—
234C22×C4C2×D4×C3112yes—
235C22×C4C2×D4×C3114yes—
236C2×C8—48no—
237C2×C8—44no—
238C4⋊C4—216no—
239C4⋊C4—216no—
240C23—28no—
241C23—216no—
242C23—28no—
243C23—24no—
244C23—22no—
245C23—24no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—28no—
251C23—28no—
252C23—22no—
253C23C31×C22⋊C814yes—
254C23C31×#9914yes—
255C23C31×#10114yes—
256C23C2×C22⋊C4×C3112yes—
257C23C2×C22⋊C4×C3111yescharacteristic
258C23C22×C8×C3111yescharacteristic
259C23C2×M16×C3111yescharacteristic
260C23C2×M16×C3112yes—
261C2×C4—232no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—44no—
273C2×C4—416no—
274C2×C4—44no—
275C2×C4—416no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4C31×C22⋊C818yescomplemented
280C2×C4C31×#12014yes—
281C8—84no—
282C22—216no—
283C22—216no—
284C22—24no—
285C22—22no—
286C22—22no—
287C22—24no—
288C22—24no—
289C22—24no—
290C22—24no—
291C22—24no—
292C22—22no—
293C22—24no—
294C22—22no—
295C22C31×#32418yescomplemented
296C22C31×#37911yescharacteristic
297C22C2×C31×C22⋊C812yes—
298C22C2×C31×C22⋊C811yescharacteristic
299C22C31×#40712yes—
300C22C31×#40711yescharacteristic
301C22C2×C31×#9912yes—
302C22C2×C31×#10112yes—
303C4—28no—
304C4—24no—
305C4—42no—
306C4—44no—
307C2—22no—
308C2—22no—
309C2—28no—
310C2C2×C31×#32412yes—
311C2C31×#146312yes—
312C2C31×#177911yescharacteristic
313C2C31×#178111yescharacteristic
314C2C31×#178411yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C22×C8×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#324C2semidirect
24. C23×C4×C31C8semidirect
82. #8299C31direct (N × H)
122. C2×C4×C31C22⋊C8semidirect
127. C2×#324C2×C31semidirect
141. C22×C31#324semidirect
181. C23×C4C8×C31semidirect
197. C31#8299direct (N × H)
279. C2×C4C31×C22⋊C8semidirect
295. C22C31×#324semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C312
C31×#17792
C2×C31×#3242
#829931