Finite Group Databasebeta

← C31×#9411 #21466170

Subgroups — C31×#9411 #21466170

Order 7936.

606 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C31×#2561C211yesmaximal, characteristic
2C31×#2312C211yesmaximal, characteristic
3C31×#1508C212yesmaximal, complemented
4C31×#1462C211yesmaximal, characteristic
5C31×#1297C212yesmaximal, complemented
6C2×C31×C22⋊Q8C2211yescharacteristic
7C22×C22⋊C4×C31C2211yescharacteristic
8C31×#407C2212yes—
9C31×#397C412yescomplemented
10C31×#393C412yescomplemented
11C31×#388—22no—
12C31×#388—24no—
13C31×#381—21no—
14C31×#380—21no—
15C31×#379—21no—
16C31×#379—21no—
17C4×C22⋊C4×C31C2211yescharacteristic
18C4×C22⋊C4×C31C2212yes—
19C31×#328—24no—
20C31×#323—22no—
21C25×C31D411yescharacteristic
22C22×Q8×C31C2×C411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C23×C4×C31C2311yescharacteristic
25C2×M16×C31—22no—
26C31×C22⋊Q8—22no—
27C31×C22⋊Q8—22no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31C2×C411yescharacteristic
31C2×C22⋊C4×C31—22no—
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—21no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31C2×C412yes—
41C2×C22⋊C4×C31D412yes—
42C2×C42×C31—21no—
43C2×C42×C31—22no—
44C31×C22⋊C8—22no—
45C31×C22⋊C8—22no—
46C31×#95—22no—
47C31×#95—22no—
48C31×#95—22no—
49C31×#95C2×C412yes—
50C31×#95D414yes—
51C24×C31—21no—
52C24×C31—21no—
53C24×C31—42no—
54C24×C31—42no—
55C24×C31—81no—
56C24×C31C22⋊C412yes—
57C24×C31C2×D411yescharacteristic
58C2×Q8×C31—22no—
59C2×Q8×C31—81no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—22no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—24no—
66C22×C4×C31—42no—
67C22×C4×C31—81no—
68C22×C4×C31C22⋊C412yes—
69C22×C4×C31C22×C411yescharacteristic
70C22×C4×C31C2×D412yes—
71C22×C4×C31C2×D411yescharacteristic
72C22×C4×C31#4112yes—
73M16×C31—82no—
74C2×C8×C31—42no—
75C4⋊C4×C31—22no—
76C4⋊C4×C31—42no—
77C4⋊C4×C31—82no—
78C22⋊C4×C31—24no—
79C22⋊C4×C31—24no—
80C22⋊C4×C31—44no—
81C22⋊C4×C31—42no—
82C22⋊C4×C31—44no—
83C22⋊C4×C31—41no—
84C22⋊C4×C31—41no—
85C22⋊C4×C31—82no—
86C22⋊C4×C31—82no—
87C22⋊C4×C31—82no—
88C42×C31—81no—
89C42×C31—82no—
90#9411C3111yesmaximal, characteristic, direct product factor, Sylow
91C23×C31—22no—
92C23×C31—22no—
93C23×C31—22no—
94C23×C31—22no—
95C23×C31—22no—
96C23×C31—41no—
97C23×C31—42no—
98C23×C31—42no—
99C23×C31—42no—
100C23×C31—42no—
101C23×C31—42no—
102C23×C31—42no—
103C23×C31—81no—
104C23×C31—81no—
105C23×C31—88no—
106C23×C31C2×C22⋊C411yescharacteristic
107C23×C31#12011yescharacteristic
108C23×C31#12311yescharacteristic
109Q8×C31—82no—
110C2×C4×C31—22no—
111C2×C4×C31—41no—
112C2×C4×C31—42no—
113C2×C4×C31—42no—
114C2×C4×C31—41no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—44no—
119C2×C4×C31—42no—
120C2×C4×C31—44no—
121C2×C4×C31—42no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—42no—
125C2×C4×C31—42no—
126C2×C4×C31—44no—
127C2×C4×C31—81no—
128C2×C4×C31C4×D412yes—
129C2×C4×C31#12112yes—
130C8×C31—82no—
131#2561C2×C3111yescharacteristic
132#2312C2×C3111yescharacteristic
133#1508C2×C3112yescomplemented
134#1462C2×C3111yescharacteristic
135#1297C2×C3112yescomplemented
136C22×C31—21no—
137C22×C31—21no—
138C22×C31—21no—
139C22×C31—21no—
140C22×C31—21no—
141C22×C31—21no—
142C22×C31—21no—
143C22×C31—44no—
144C22×C31—44no—
145C22×C31—42no—
146C22×C31—42no—
147C22×C31—42no—
148C22×C31—82no—
149C22×C31—84no—
150C22×C31—84no—
151C22×C31#38611yescharacteristic
152C22×C31#42112yes—
153C22×C31#45512yes—
154C4×C31—22no—
155C4×C31—22no—
156C4×C31—42no—
157C4×C31—84no—
158C4×C31—82no—
159C4×C31—81no—
160C4×C31—81no—
161C2×C22⋊Q8C22×C3111yescharacteristic
162C22×C22⋊C4C22×C3111yescharacteristic
163#407C22×C3112yes—
164#397C4×C3112yescomplemented
165#393C4×C3112yescomplemented
166#388—22no—
167#388—24no—
168#381—21no—
169#380—21no—
170#379—21no—
171#379—21no—
172C4×C22⋊C4C22×C3111yescharacteristic
173C4×C22⋊C4C22×C3112yes—
174#328—24no—
175#323—22no—
176C2×C31—22no—
177C2×C31—22no—
178C2×C31—41no—
179C2×C31—82no—
180C2×C31#188511yescharacteristic
181C2×C31#189711yescharacteristic
182C2×C31#191311yescharacteristic
183C25D4×C3111yescharacteristic
184C22×Q8C2×C4×C3111yescharacteristic
185C23×C4D4×C3111yescharacteristic
186C23×C4C23×C3111yescharacteristic
187C2×M16—22no—
188C22⋊Q8—22no—
189C22⋊Q8—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4C2×C4×C3111yescharacteristic
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4C2×C4×C3112yes—
203C2×C22⋊C4D4×C3112yes—
204C2×C42—21no—
205C2×C42—22no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208#95—22no—
209#95—22no—
210#95—22no—
211#95C2×C4×C3112yes—
212#95D4×C3114yes—
213C31#941111yescharacteristic, direct product factor, Sylow
214C24—21no—
215C24—21no—
216C24—42no—
217C24—42no—
218C24—81no—
219C24C22⋊C4×C3112yes—
220C24C2×D4×C3111yescharacteristic
221C2×Q8—22no—
222C2×Q8—81no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—24no—
229C22×C4—42no—
230C22×C4—81no—
231C22×C4C22⋊C4×C3112yes—
232C22×C4C22×C4×C3111yescharacteristic
233C22×C4C2×D4×C3112yes—
234C22×C4C2×D4×C3111yescharacteristic
235C22×C4#41×C3112yes—
236M16—82no—
237C2×C8—42no—
238C4⋊C4—22no—
239C4⋊C4—42no—
240C4⋊C4—82no—
241C22⋊C4—24no—
242C22⋊C4—24no—
243C22⋊C4—44no—
244C22⋊C4—42no—
245C22⋊C4—44no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—82no—
249C22⋊C4—82no—
250C22⋊C4—82no—
251C42—81no—
252C42—82no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—41no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—81no—
266C23—81no—
267C23—88no—
268C23C2×C22⋊C4×C3111yescharacteristic
269C23C31×#12011yescharacteristic
270C23C31×#12311yescharacteristic
271Q8—82no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—44no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4C4×D4×C3112yes—
291C2×C4C31×#12112yes—
292C8—82no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—44no—
301C22—44no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—82no—
306C22—84no—
307C22—84no—
308C22C31×#38611yescharacteristic
309C22C31×#42112yes—
310C22C31×#45512yes—
311C4—22no—
312C4—22no—
313C4—42no—
314C4—84no—
315C4—82no—
316C4—81no—
317C4—81no—
318C2—22no—
319C2—22no—
320C2—41no—
321C2—82no—
322C2C31×#188511yescharacteristic
323C2C31×#189711yescharacteristic
324C2C31×#191311yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1508C2semidirect
5. C31×#1297C2semidirect
9. C31×#397C4semidirect
10. C31×#393C4semidirect
90. #9411C31direct (N × H)
133. #1508C2×C31semidirect
135. #1297C2×C31semidirect
164. #397C4×C31semidirect
165. #393C4×C31semidirect
213. C31#9411direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25612
C31×#23122
C31×#15082
C31×#14622
C31×#12972
#941131