Finite Group Databasebeta

← C31×#9508 #21466267

Subgroups — C31×#9508 #21466267

Order 7936.

542 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2975C211yesmaximal, characteristic
2C31×#2486C211yesmaximal, characteristic
3C31×#1821C212yesmaximal, complemented
4C31×#1465C211yesmaximal, characteristic
5C31×#1305C212yesmaximal, complemented
6C2×C31×#123C412yes—
7C2×C4×D4×C31C2211yescharacteristic
8C22×C4⋊C4×C31C2211yescharacteristic
9C31×#436—24no—
10C31×#431—21no—
11C31×#407—21no—
12C31×#407C2212yes—
13C31×#407C2212yes—
14C31×#398—21no—
15C31×#397—21no—
16C31×#389—21no—
17C31×#381C412yes—
18C31×#380—21no—
19C31×#380C2211yescharacteristic
20C31×#343—24no—
21C31×#324—21no—
22C31×#323—21no—
23C22×D4×C31C2×C411yescharacteristic
24C23×C4×C31C2×C412yes—
25C23×C4×C31D411yescharacteristic
26C23×C4×C31C2311yescharacteristic
27C2×M16×C31—22no—
28C2×M16×C31—22no—
29C2×M16×C31D414yes—
30C31×#123—44no—
31C4×D4×C31—22no—
32C4×D4×C31—22no—
33C2×C4⋊C4×C31—22no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—22no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—22no—
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31C2×C411yescharacteristic
42C2×C22⋊C4×C31C2×C412yes—
43C2×C22⋊C4×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C31×C4⋊C8—22no—
46C31×C22⋊C8—22no—
47C31×C22⋊C8—22no—
48C31×C22⋊C8—22no—
49C31×C22⋊C8—22no—
50C31×C22⋊C8—22no—
51C4×C8×C31—22no—
52C31×#95—22no—
53C31×#95—22no—
54C31×#95—21no—
55C24×C31C22⋊C411yescharacteristic
56C24×C31C22×C411yescharacteristic
57C2×D4×C31—22no—
58C2×D4×C31—22no—
59C2×D4×C31—41no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—22no—
63C22×C4×C31—22no—
64C22×C4×C31—24no—
65C22×C4×C31—42no—
66C22×C4×C31—42no—
67C22×C4×C31—42no—
68C22×C4×C31—42no—
69C22×C4×C31C22⋊C411yescharacteristic
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22⋊C411yescharacteristic
72C22×C4×C31C2×D412yes—
73C22×C4×C31C2×D411yescharacteristic
74C22×C4×C31C2×D411yescharacteristic
75C22×C4×C31#4112yes—
76M16×C31—44no—
77M16×C31—44no—
78M16×C31—82no—
79C2×C8×C31—24no—
80C2×C8×C31—42no—
81C4⋊C4×C31—22no—
82C4⋊C4×C31—42no—
83C4⋊C4×C31—44no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—42no—
86C4⋊C4×C31—41no—
87C22⋊C4×C31—22no—
88C22⋊C4×C31—22no—
89C22⋊C4×C31—44no—
90C22⋊C4×C31—42no—
91C42×C31—21no—
92C42×C31—21no—
93#9508C3111yesmaximal, characteristic, direct product factor, Sylow
94C23×C31—21no—
95C23×C31—21no—
96C23×C31—21no—
97C23×C31—21no—
98C23×C31—21no—
99C23×C31—41no—
100C23×C31—41no—
101C23×C31—41no—
102C23×C31—41no—
103C23×C31C2×C22⋊C411yescharacteristic
104C23×C31C4×D412yes—
105D4×C31—44no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—22no—
109C2×C4×C31—24no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—41no—
113C2×C4×C31—42no—
114C2×C4×C31—42no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31—81no—
124C2×C4×C31—84no—
125C2×C4×C31#10012yes—
126C2×C4×C31#12011yescharacteristic
127C2×C4×C31#12112yes—
128C2×C4×C31#12311yescharacteristic
129C8×C31—44no—
130C8×C31—82no—
131#2975C2×C3111yescharacteristic
132#2486C2×C3111yescharacteristic
133#1821C2×C3112yescomplemented
134#1465C2×C3111yescharacteristic
135#1305C2×C3112yescomplemented
136C22×C31—21no—
137C22×C31—21no—
138C22×C31—22no—
139C22×C31—22no—
140C22×C31—22no—
141C22×C31—42no—
142C22×C31—42no—
143C22×C31—42no—
144C22×C31—41no—
145C22×C31—41no—
146C22×C31—41no—
147C22×C31—81no—
148C22×C31#38611yescharacteristic
149C22×C31C2×#10011yescharacteristic
150C22×C31#41311yescharacteristic
151C4×C31—22no—
152C4×C31—21no—
153C4×C31—22no—
154C4×C31—41no—
155C4×C31—41no—
156C4×C31—82no—
157C4×C31—82no—
158C4×C31#45812yes—
159C2×#123C4×C3112yes—
160C2×C4×D4C22×C3111yescharacteristic
161C22×C4⋊C4C22×C3111yescharacteristic
162#436—24no—
163#431—21no—
164#407—21no—
165#407C22×C3112yes—
166#407C22×C3112yes—
167#398—21no—
168#397—21no—
169#389—21no—
170#381C4×C3112yes—
171#380—21no—
172#380C22×C3111yescharacteristic
173#343—24no—
174#324—21no—
175#323—21no—
176C2×C31—21no—
177C2×C31—21no—
178C2×C31—42no—
179C2×C31—81no—
180C2×C31#189011yescharacteristic
181C2×C31#190011yescharacteristic
182C2×C31#191511yescharacteristic
183C22×D4C2×C4×C3111yescharacteristic
184C23×C4C2×C4×C3112yes—
185C23×C4D4×C3111yescharacteristic
186C23×C4C23×C3111yescharacteristic
187C2×M16—22no—
188C2×M16—22no—
189C2×M16D4×C3114yes—
190#123—44no—
191C4×D4—22no—
192C4×D4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4D4×C3111yescharacteristic
200C2×C22⋊C4—22no—
201C2×C22⋊C4C2×C4×C3111yescharacteristic
202C2×C22⋊C4C2×C4×C3112yes—
203C2×C22⋊C4D4×C3111yescharacteristic
204C2×C42D4×C3111yescharacteristic
205C4⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—22no—
210C22⋊C8—22no—
211C4×C8—22no—
212#95—22no—
213#95—22no—
214#95—21no—
215C31#950811yescharacteristic, direct product factor, Sylow
216C24C22⋊C4×C3111yescharacteristic
217C24C22×C4×C3111yescharacteristic
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—41no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4C22⋊C4×C3111yescharacteristic
231C22×C4C22⋊C4×C3111yescharacteristic
232C22×C4C22⋊C4×C3111yescharacteristic
233C22×C4C2×D4×C3112yes—
234C22×C4C2×D4×C3111yescharacteristic
235C22×C4C2×D4×C3111yescharacteristic
236C22×C4#41×C3112yes—
237M16—44no—
238M16—44no—
239M16—82no—
240C2×C8—24no—
241C2×C8—42no—
242C4⋊C4—22no—
243C4⋊C4—42no—
244C4⋊C4—44no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—41no—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C22⋊C4—44no—
251C22⋊C4—42no—
252C42—21no—
253C42—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23C2×C22⋊C4×C3111yescharacteristic
264C23C4×D4×C3112yes—
265D4—44no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—84no—
285C2×C4C31×#10012yes—
286C2×C4C31×#12011yescharacteristic
287C2×C4C31×#12112yes—
288C2×C4C31×#12311yescharacteristic
289C8—44no—
290C8—82no—
291C22—21no—
292C22—21no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C31×#38611yescharacteristic
304C22C2×C31×#10011yescharacteristic
305C22C31×#41311yescharacteristic
306C4—22no—
307C4—21no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4C31×#45812yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—81no—
318C2C31×#189011yescharacteristic
319C2C31×#190011yescharacteristic
320C2C31×#191511yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C24 ▷ 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×#1821C2semidirect
5. C31×#1305C2semidirect
93. #9508C31direct (N × H)
133. #1821C2×C31semidirect
135. #1305C2×C31semidirect
215. C31#9508direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29752
C31×#24862
C31×#18212
C31×#14652
C31×#13052
#950831