Finite Group Databasebeta

← C31×#19075 #21475834

Subgroups — C31×#19075 #21475834

Order 7936.

1116 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3548C211yesmaximal, characteristic, complemented
2C31×#3151C212yesmaximal, complemented
3C31×#3138C211yesmaximal, characteristic, complemented
4C31×#1656C218yesmaximal, complemented
5C31×#1526C211yesmaximal, characteristic, complemented
6C31×#1525C212yesmaximal, complemented
7C2×C31×AGL(1,ℤ/8)—24no—
8C31×#562C2214yescomplemented
9C31×#554—22no—
10C31×#550—22no—
11C31×#547—22no—
12C31×#540—22no—
13C31×#537—24no—
14C31×#533C2211yescharacteristic
15C31×#532C2212yes—
16C2×C31×#127C2211yescharacteristic
17C31×#496C2218yes—
18C31×#493—22no—
19C31×#492—22no—
20C31×#490C2214yes—
21C31×#486—22no—
22C31×#418—22no—
23C4×M16×C31C2211yescharacteristic
24C4×M16×C31C2212yes—
25C31×#330C2214yescomplemented
26C31×#329C2218yescomplemented
27C2×#41×C31—24no—
28C2×#41×C31D414yes—
29C22×D4×C31—21no—
30C22×D4×C31—22no—
31C31×AGL(1,ℤ/8)—416no—
32C2×SD16×C31—28no—
33C2×D8×C31—28no—
34C2×M16×C31—22no—
35C2×M16×C31—21no—
36C31×C4⋊Q8D412yes—
37C31×C4⋊Q8D412yes—
38C31×#127—22no—
39C31×#127—21no—
40C31×#127—22no—
41C31×#127D412yes—
42C31×#127C2312yes—
43C31×#125—22no—
44C31×#125C2312yes—
45C31×#124C2314yes—
46C31×#123—28no—
47C31×C22⋊Q8—24no—
48C31×C22⋊Q8—28no—
49C31×C22⋊Q8—22no—
50C31×#121—28no—
51C31×#121—24no—
52C31×#121—28no—
53C31×#121—22no—
54C31×#121—22no—
55C4×Q8×C31—22no—
56C4×D4×C31—24no—
57C4×D4×C31—22no—
58C4×D4×C31—22no—
59C31×#117D412yes—
60C2×C4⋊C4×C31—24no—
61C2×C42×C31C2311yescharacteristic
62C31×#102—28no—
63C31×#97C2312yes—
64C31×#97C2314yes—
65C4×C8×C31—21no—
66C4×C8×C31—22no—
67C24×C31—41no—
68#41×C31—48no—
69#41×C31—88no—
70C2×Q8×C31—22no—
71C2×Q8×C31C2×D414yes—
72C2×D4×C31—28no—
73C2×D4×C31—24no—
74C2×D4×C31—22no—
75C2×D4×C31—22no—
76C2×D4×C31—22no—
77C2×D4×C31—24no—
78C2×D4×C31—48no—
79C2×D4×C31—44no—
80C2×D4×C31—42no—
81C2×D4×C31—41no—
82C2×D4×C31C2×D414yes—
83C22×C4×C31—28no—
84C22×C4×C31—24no—
85C22×C4×C31C2×D411yescharacteristic
86C22×C4×C31C2×D412yes—
87SD16×C31—416no—
88D8×C31—416no—
89M16×C31—28no—
90M16×C31—42no—
91C2×C8×C31—24no—
92C2×C8×C31—22no—
93C4⋊C4×C31—28no—
94C4⋊C4×C31—22no—
95C4⋊C4×C31—22no—
96C4⋊C4×C31—22no—
97C4⋊C4×C31—24no—
98C4⋊C4×C31C2×D414yes—
99C22⋊C4×C31—28no—
100C22⋊C4×C31—22no—
101C22⋊C4×C31—24no—
102C22⋊C4×C31—24no—
103C42×C31—22no—
104C42×C31C2×D411yescharacteristic
105C42×C31C2×D412yes—
106C42×C31C2411yescharacteristic
107#19075C3111yesmaximal, characteristic, direct product factor, Sylow
108C23×C31—24no—
109C23×C31—42no—
110C23×C31—84no—
111C23×C31—82no—
112C23×C31#12011yescharacteristic
113Q8×C31—44no—
114Q8×C31—44no—
115D4×C31—44no—
116D4×C31—48no—
117D4×C31—44no—
118D4×C31—44no—
119D4×C31—44no—
120D4×C31—84no—
121D4×C31—88no—
122D4×C31—84no—
123D4×C31—82no—
124C2×C4×C31—24no—
125C2×C4×C31—22no—
126C2×C4×C31—24no—
127C2×C4×C31—24no—
128C2×C4×C31—48no—
129C2×C4×C31—88no—
130C2×C4×C31#12012yes—
131C2×C4×C31#12011yescharacteristic
132C2×C4×C31C22×D411yescharacteristic
133C2×C4×C31C22×D412yes—
134C8×C31—28no—
135C8×C31—42no—
136#3548C2×C3111yescharacteristic, complemented
137#3151C2×C3112yescomplemented
138#3138C2×C3111yescharacteristic, complemented
139#1656C2×C3118yescomplemented
140#1526C2×C3111yescharacteristic, complemented
141#1525C2×C3112yescomplemented
142C22×C31—22no—
143C22×C31—21no—
144C22×C31—44no—
145C22×C31—44no—
146C22×C31—44no—
147C22×C31—84no—
148C22×C31—82no—
149C22×C31—164no—
150C22×C31C2×#12011yescharacteristic
151C4×C31—22no—
152C4×C31—21no—
153C4×C31—44no—
154C4×C31—44no—
155C4×C31#45314yes—
156C4×C31#45412yes—
157C2×AGL(1,ℤ/8)—24no—
158#562C22×C3114yescomplemented
159#554—22no—
160#550—22no—
161#547—22no—
162#540—22no—
163#537—24no—
164#533C22×C3111yescharacteristic
165#532C22×C3112yes—
166C2×#127C22×C3111yescharacteristic
167#496C22×C3118yes—
168#493—22no—
169#492—22no—
170#490C22×C3114yes—
171#486—22no—
172#418—22no—
173C4×M16C22×C3111yescharacteristic
174C4×M16C22×C3112yes—
175#330C22×C3114yescomplemented
176#329C22×C3118yescomplemented
177C2×C31—41no—
178C2×C31—84no—
179C2×C31—162no—
180C2×C31C2×#45312yes—
181C2×C31C2×#45411yescharacteristic
182C2×#41—24no—
183C2×#41D4×C3114yes—
184C22×D4—22no—
185C22×D4—21no—
186AGL(1,ℤ/8)—416no—
187C2×SD16—28no—
188C2×D8—28no—
189C2×M16—22no—
190C2×M16—21no—
191C4⋊Q8D4×C3112yes—
192C4⋊Q8D4×C3112yes—
193#127—22no—
194#127—21no—
195#127—22no—
196#127D4×C3112yes—
197#127C23×C3112yes—
198#125—22no—
199#125C23×C3112yes—
200#124C23×C3114yes—
201#123—28no—
202C22⋊Q8—24no—
203C22⋊Q8—28no—
204C22⋊Q8—22no—
205#121—28no—
206#121—24no—
207#121—28no—
208#121—22no—
209#121—22no—
210C4×Q8—22no—
211C4×D4—24no—
212C4×D4—22no—
213C4×D4—22no—
214#117D4×C3112yes—
215C2×C4⋊C4—24no—
216C2×C42C23×C3111yescharacteristic
217#102—28no—
218#97C23×C3112yes—
219#97C23×C3114yes—
220C4×C8—21no—
221C4×C8—22no—
222C31#1907511yescharacteristic, direct product factor, Sylow
223C24—41no—
224#41—48no—
225#41—88no—
226C2×Q8—22no—
227C2×Q8C2×D4×C3114yes—
228C2×D4—28no—
229C2×D4—24no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—24no—
234C2×D4—48no—
235C2×D4—44no—
236C2×D4—42no—
237C2×D4—41no—
238C2×D4C2×D4×C3114yes—
239C22×C4—28no—
240C22×C4—24no—
241C22×C4C2×D4×C3111yescharacteristic
242C22×C4C2×D4×C3112yes—
243SD16—416no—
244D8—416no—
245M16—28no—
246M16—42no—
247C2×C8—24no—
248C2×C8—22no—
249C4⋊C4—28no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—24no—
254C4⋊C4C2×D4×C3114yes—
255C22⋊C4—28no—
256C22⋊C4—22no—
257C22⋊C4—24no—
258C22⋊C4—24no—
259C42—22no—
260C42C2×D4×C3111yescharacteristic
261C42C2×D4×C3112yes—
262C42C24×C3111yescharacteristic
263C23—24no—
264C23—42no—
265C23—84no—
266C23—82no—
267C23C31×#12011yescharacteristic
268Q8—44no—
269Q8—44no—
270D4—44no—
271D4—48no—
272D4—44no—
273D4—44no—
274D4—44no—
275D4—84no—
276D4—88no—
277D4—84no—
278D4—82no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4—48no—
284C2×C4—88no—
285C2×C4C31×#12012yes—
286C2×C4C31×#12011yescharacteristic
287C2×C4C22×D4×C3111yescharacteristic
288C2×C4C22×D4×C3112yes—
289C8—28no—
290C8—42no—
291C22—22no—
292C22—21no—
293C22—44no—
294C22—44no—
295C22—44no—
296C22—84no—
297C22—82no—
298C22—164no—
299C22C2×C31×#12011yescharacteristic
300C4—22no—
301C4—21no—
302C4—44no—
303C4—44no—
304C4C31×#45314yes—
305C4C31×#45412yes—
306C2—41no—
307C2—84no—
308C2—162no—
309C2C2×C31×#45312yes—
310C2C2×C31×#45411yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3548C2semidirect
2. C31×#3151C2semidirect
3. C31×#3138C2semidirect
4. C31×#1656C2semidirect
5. C31×#1526C2semidirect
6. C31×#1525C2semidirect
8. C31×#562C22semidirect
25. C31×#330C22semidirect
26. C31×#329C22semidirect
107. #19075C31direct (N × H)
136. #3548C2×C31semidirect
137. #3151C2×C31semidirect
138. #3138C2×C31semidirect
139. #1656C2×C31semidirect
140. #1526C2×C31semidirect
141. #1525C2×C31semidirect
158. #562C22×C31semidirect
175. #330C22×C31semidirect
176. #329C22×C31semidirect
222. C31#19075direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35482
C31×#31512
C31×#31382
C31×#16562
C31×#15262
C31×#15252
#1907531