Finite Group Databasebeta

← C31×#9023 #21465782

Subgroups — C31×#9023 #21465782

Order 7936.

616 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#400C211yesmaximal, characteristic
2C31×#2316C211yesmaximal, characteristic
3C31×#1824C212yesmaximal
4C2×C31×#324C211yesmaximal, characteristic
5C31×#1294C212yesmaximal
6C2×C31×#117—21no—
7C22×C4⋊C4×C31C2211yescharacteristic
8C22×C4⋊C4×C31C2211yescharacteristic
9C2×C31×C22⋊C8C2212yes—
10C31×#400—22no—
11C31×#400C414yescomplemented
12C31×#389—24no—
13C31×#380—21no—
14C31×#380C2212yes—
15C2×C31×#95—21no—
16C2×C31×#95—21no—
17C2×C31×#95C2211yescharacteristic
18C31×#340—24no—
19C31×#324—22no—
20C23×C4×C31—21no—
21C23×C4×C31—21no—
22C23×C4×C31D411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C23×C4×C31C2311yescharacteristic
25C22×C8×C31—22no—
26C31×#117—42no—
27C31×#117—42no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—22no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—22no—
35C2×C4⋊C4×C31C2×C412yes—
36C2×C4⋊C4×C31C2×C412yes—
37C2×C4⋊C4×C31D412yes—
38C2×C4⋊C4×C31D414yes—
39C2×C22⋊C4×C31—22no—
40C2×C42×C31—22no—
41C31×C22⋊C8—22no—
42C31×C22⋊C8—22no—
43C31×#95—22no—
44C31×#95—24no—
45C31×#95—24no—
46C31×#95—21no—
47C31×#95—22no—
48C31×#95C2×C412yes—
49C24×C31C2×D411yescharacteristic
50C22×C4×C31—21no—
51C22×C4×C31—21no—
52C22×C4×C31—21no—
53C22×C4×C31—21no—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31—24no—
59C22×C4×C31—42no—
60C22×C4×C31—42no—
61C22×C4×C31—42no—
62C22×C4×C31—42no—
63C22×C4×C31—44no—
64C22×C4×C31—41no—
65C22×C4×C31—41no—
66C22×C4×C31—41no—
67C22×C4×C31—41no—
68C22×C4×C31C22⋊C412yes—
69C22×C4×C31C22⋊C412yes—
70C22×C4×C31SD1612yes—
71C22×C4×C31Q1612yes—
72C22×C4×C31C22×C411yescharacteristic
73C22×C4×C31C2×D412yes—
74C22×C4×C31C2×D411yescharacteristic
75C22×C4×C31#4112yes—
76C2×C8×C31—44no—
77C2×C8×C31—42no—
78C4⋊C4×C31—24no—
79C4⋊C4×C31—24no—
80C4⋊C4×C31—24no—
81C4⋊C4×C31—44no—
82C4⋊C4×C31—44no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—82no—
85C22⋊C4×C31—42no—
86C22⋊C4×C31—42no—
87C42×C31—44no—
88#9023C3111yesmaximal, characteristic, direct product factor, Sylow
89C23×C31—22no—
90C23×C31—22no—
91C23×C31C2×C22⋊C411yescharacteristic
92C23×C31#12011yescharacteristic
93C23×C31#12311yescharacteristic
94C23×C31C2×SD1611yescharacteristic
95C23×C31C2×Q1611yescharacteristic
96C23×C31AGL(1,ℤ/8)11yescharacteristic
97C23×C31#13711yescharacteristic
98C2×C4×C31—22no—
99C2×C4×C31—22no—
100C2×C4×C31—22no—
101C2×C4×C31—22no—
102C2×C4×C31—24no—
103C2×C4×C31—22no—
104C2×C4×C31—22no—
105C2×C4×C31—22no—
106C2×C4×C31—41no—
107C2×C4×C31—41no—
108C2×C4×C31—42no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
111C2×C4×C31—42no—
112C2×C4×C31—42no—
113C2×C4×C31—44no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—44no—
117C2×C4×C31—44no—
118C2×C4×C31—44no—
119C2×C4×C31—81no—
120C2×C4×C31—82no—
121C2×C4×C31—82no—
122C2×C4×C31—82no—
123C2×C4×C31—82no—
124C2×C4×C31#10314yes—
125C2×C4×C31C4×D412yes—
126C2×C4×C31#12112yes—
127C8×C31—82no—
128C2×#400C2×C3111yescharacteristic
129#2316C2×C3111yescharacteristic
130#1824C2×C3112yes—
131C2×#324C2×C3111yescharacteristic
132#1294C2×C3112yes—
133C22×C31—22no—
134C22×C31—22no—
135C22×C31—22no—
136C22×C31—22no—
137C22×C31—21no—
138C22×C31—21no—
139C22×C31—21no—
140C22×C31—21no—
141C22×C31#38611yescharacteristic
142C22×C31C2×#10311yescharacteristic
143C22×C31#41711yescharacteristic
144C22×C31#45011yescharacteristic
145C22×C31#45111yescharacteristic
146C22×C31#45412yes—
147C22×C31#45812yes—
148C22×C31#48311yescharacteristic
149C22×C31#48411yescharacteristic
150C4×C31—24no—
151C4×C31—22no—
152C4×C31—22no—
153C4×C31—42no—
154C4×C31—82no—
155C4×C31—84no—
156C4×C31—82no—
157C2×#117—21no—
158C22×C4⋊C4C22×C3111yescharacteristic
159C22×C4⋊C4C22×C3111yescharacteristic
160C2×C22⋊C8C22×C3112yes—
161#400—22no—
162#400C4×C3114yescomplemented
163#389—24no—
164#380—21no—
165#380C22×C3112yes—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95C22×C3111yescharacteristic
169#340—24no—
170#324—22no—
171C2×C31—21no—
172C2×C31—21no—
173C2×C31—21no—
174C2×C31—21no—
175C2×C31#161612yes—
176C2×C31#161712yes—
177C2×C31#187211yescharacteristic
178C2×C31#188811yescharacteristic
179C2×C31#189011yescharacteristic
180C23×C4—21no—
181C23×C4—21no—
182C23×C4D4×C3111yescharacteristic
183C23×C4D4×C3111yescharacteristic
184C23×C4C23×C3111yescharacteristic
185C22×C8—22no—
186#117—42no—
187#117—42no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4C2×C4×C3112yes—
196C2×C4⋊C4C2×C4×C3112yes—
197C2×C4⋊C4D4×C3112yes—
198C2×C4⋊C4D4×C3114yes—
199C2×C22⋊C4—22no—
200C2×C42—22no—
201C22⋊C8—22no—
202C22⋊C8—22no—
203#95—22no—
204#95—24no—
205#95—24no—
206#95—21no—
207#95—22no—
208#95C2×C4×C3112yes—
209C31#902311yescharacteristic, direct product factor, Sylow
210C24C2×D4×C3111yescharacteristic
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—44no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4C22⋊C4×C3112yes—
230C22×C4C22⋊C4×C3112yes—
231C22×C4SD16×C3112yes—
232C22×C4Q16×C3112yes—
233C22×C4C22×C4×C3111yescharacteristic
234C22×C4C2×D4×C3112yes—
235C22×C4C2×D4×C3111yescharacteristic
236C22×C4#41×C3112yes—
237C2×C8—44no—
238C2×C8—42no—
239C4⋊C4—24no—
240C4⋊C4—24no—
241C4⋊C4—24no—
242C4⋊C4—44no—
243C4⋊C4—44no—
244C4⋊C4—42no—
245C4⋊C4—82no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C42—44no—
249C23—22no—
250C23—22no—
251C23C2×C22⋊C4×C3111yescharacteristic
252C23C31×#12011yescharacteristic
253C23C31×#12311yescharacteristic
254C23C2×SD16×C3111yescharacteristic
255C23C2×Q16×C3111yescharacteristic
256C23C31×AGL(1,ℤ/8)11yescharacteristic
257C23C31×#13711yescharacteristic
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—44no—
274C2×C4—42no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—42no—
279C2×C4—81no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4C31×#10314yes—
285C2×C4C4×D4×C3112yes—
286C2×C4C31×#12112yes—
287C8—82no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22C31×#38611yescharacteristic
297C22C2×C31×#10311yescharacteristic
298C22C31×#41711yescharacteristic
299C22C31×#45011yescharacteristic
300C22C31×#45111yescharacteristic
301C22C31×#45412yes—
302C22C31×#45812yes—
303C22C31×#48311yescharacteristic
304C22C31×#48411yescharacteristic
305C4—24no—
306C4—22no—
307C4—22no—
308C4—42no—
309C4—82no—
310C4—84no—
311C4—82no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2C31×#161612yes—
317C2C31×#161712yes—
318C2C31×#187211yescharacteristic
319C2C31×#188811yescharacteristic
320C2C31×#189011yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
11. C31×#400C4semidirect
88. #9023C31direct (N × H)
162. #400C4×C31semidirect
209. C31#9023direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4002
C31×#23162
C31×#18242
C2×C31×#3242
C31×#12942
#902331