Finite Group Databasebeta

← C31×#8532 #21465291

Subgroups — C31×#8532 #21465291

Order 7936.

800 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 150 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
2C31×#1994C211yesmaximal, characteristic, complemented
3C31×#1962C212yesmaximal, complemented
4C31×#1561C211yesmaximal, characteristic, complemented
5C31×#1560C212yesmaximal, complemented
6C31×#562C414yescomplemented
7C31×#554—22no—
8C31×#550—22no—
9C31×#547—22no—
10C31×#540—22no—
11C31×#537—24no—
12C31×#533C2211yescharacteristic
13C31×#532C2212yes—
14C31×#423C2211yescharacteristic
15C31×#423C2212yes—
16C2×C31×#104—24no—
17C43×C31C2211yescharacteristic
18C31×#339—22no—
19C31×#333—22no—
20C31×#332—22no—
21C31×#331—22no—
22C2×#41×C31—24no—
23C2×#41×C31D414yes—
24C2×M16×C31—22no—
25C2×M16×C31—21no—
26C31×C4⋊Q8D412yes—
27C31×C4⋊Q8D412yes—
28C31×#127—22no—
29C31×#127D412yes—
30C31×#125—22no—
31C31×#125C2×C412yes—
32C31×#124C2×C414yes—
33C31×#123—28no—
34C31×C22⋊Q8—24no—
35C31×C22⋊Q8—28no—
36C31×C22⋊Q8—22no—
37C31×#121—28no—
38C31×#121—24no—
39C31×#121—28no—
40C31×#121—22no—
41C31×#121—22no—
42C4×Q8×C31—22no—
43C4×D4×C31—24no—
44C4×D4×C31—22no—
45C4×D4×C31—22no—
46C31×#117D412yes—
47C2×C4⋊C4×C31—24no—
48C2×C42×C31—22no—
49C2×C42×C31—21no—
50C2×C42×C31C2311yescharacteristic
51C31×C4⋊C8—22no—
52C31×C4⋊C8—22no—
53C31×C4⋊C8—22no—
54C31×#104—48no—
55#41×C31—44no—
56#41×C31—44no—
57#41×C31—84no—
58#41×C31—84no—
59C2×Q8×C31—22no—
60C2×Q8×C31C22⋊C414yes—
61C2×D4×C31—28no—
62C2×D4×C31—24no—
63C2×D4×C31—22no—
64C2×D4×C31—22no—
65C2×D4×C31C22⋊C414yes—
66C22×C4×C31—28no—
67C22×C4×C31—24no—
68C22×C4×C31—41no—
69C22×C4×C31C2×D411yescharacteristic
70C22×C4×C31C2×D412yes—
71M16×C31—44no—
72M16×C31—42no—
73C2×C8×C31—42no—
74C2×C8×C31—41no—
75C4⋊C4×C31—28no—
76C4⋊C4×C31—24no—
77C4⋊C4×C31—22no—
78C4⋊C4×C31—22no—
79C4⋊C4×C31—22no—
80C4⋊C4×C31C22⋊C414yes—
81C22⋊C4×C31—28no—
82C22⋊C4×C31—22no—
83C22⋊C4×C31—24no—
84C22⋊C4×C31—24no—
85C42×C31—22no—
86C42×C31—24no—
87C42×C31—22no—
88C42×C31—41no—
89C42×C31—42no—
90C42×C31C22×C411yescharacteristic
91C42×C31C2×D411yescharacteristic
92C42×C31C2×D412yes—
93#8532C3111yesmaximal, characteristic, direct product factor, Sylow
94C23×C31—24no—
95C23×C31#12011yescharacteristic
96Q8×C31—44no—
97Q8×C31—42no—
98Q8×C31—42no—
99D4×C31—44no—
100D4×C31—42no—
101D4×C31—42no—
102D4×C31—42no—
103D4×C31—42no—
104D4×C31—84no—
105D4×C31—88no—
106C2×C4×C31—22no—
107C2×C4×C31—21no—
108C2×C4×C31—22no—
109C2×C4×C31—21no—
110C2×C4×C31—24no—
111C2×C4×C31—24no—
112C2×C4×C31—44no—
113C2×C4×C31—42no—
114C2×C4×C31—44no—
115C2×C4×C31—44no—
116C2×C4×C31—88no—
117C2×C4×C31C2×C22⋊C411yescharacteristic
118C2×C4×C31C2×C22⋊C412yes—
119C2×C4×C31#12012yes—
120C2×C4×C31#12011yescharacteristic
121C8×C31—82no—
122C8×C31—81no—
123#3548C2×C3111yescharacteristic
124#1994C2×C3111yescharacteristic, complemented
125#1962C2×C3112yescomplemented
126#1561C2×C3111yescharacteristic, complemented
127#1560C2×C3112yescomplemented
128C22×C31—22no—
129C22×C31—21no—
130C22×C31—44no—
131C22×C31—44no—
132C22×C31—44no—
133C22×C31#37911yescharacteristic
134C4×C31—22no—
135C4×C31—21no—
136C4×C31—44no—
137C4×C31—44no—
138C4×C31—44no—
139C4×C31#45312yes—
140C4×C31#45411yescharacteristic
141C4×C31#45512yes—
142C4×C31#45611yescharacteristic
143#562C4×C3114yescomplemented
144#554—22no—
145#550—22no—
146#547—22no—
147#540—22no—
148#537—24no—
149#533C22×C3111yescharacteristic
150#532C22×C3112yes—
151#423C22×C3111yescharacteristic
152#423C22×C3112yes—
153C2×#104—24no—
154C43C22×C3111yescharacteristic
155#339—22no—
156#333—22no—
157#332—22no—
158#331—22no—
159C2×C31—41no—
160C2×C31—84no—
161C2×C31#179212yes—
162C2×C31#179311yescharacteristic
163C2×#41—24no—
164C2×#41D4×C3114yes—
165C2×M16—21no—
166C2×M16—22no—
167C4⋊Q8D4×C3112yes—
168C4⋊Q8D4×C3112yes—
169#127—22no—
170#127D4×C3112yes—
171#125—22no—
172#125C2×C4×C3112yes—
173#124C2×C4×C3114yes—
174#123—28no—
175C22⋊Q8—24no—
176C22⋊Q8—28no—
177C22⋊Q8—22no—
178#121—28no—
179#121—24no—
180#121—28no—
181#121—22no—
182#121—22no—
183C4×Q8—22no—
184C4×D4—24no—
185C4×D4—22no—
186C4×D4—22no—
187#117D4×C3112yes—
188C2×C4⋊C4—24no—
189C2×C42—21no—
190C2×C42—22no—
191C2×C42C23×C3111yescharacteristic
192C4⋊C8—22no—
193C4⋊C8—22no—
194C4⋊C8—22no—
195#104—48no—
196C31#853211yescharacteristic, direct product factor, Sylow
197#41—44no—
198#41—44no—
199#41—84no—
200#41—84no—
201C2×Q8—22no—
202C2×Q8C22⋊C4×C3114yes—
203C2×D4—28no—
204C2×D4—24no—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4C22⋊C4×C3114yes—
208C22×C4—28no—
209C22×C4—24no—
210C22×C4—41no—
211C22×C4C2×D4×C3111yescharacteristic
212C22×C4C2×D4×C3112yes—
213M16—44no—
214M16—42no—
215C2×C8—42no—
216C2×C8—41no—
217C4⋊C4—28no—
218C4⋊C4—24no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4C22⋊C4×C3114yes—
223C22⋊C4—28no—
224C22⋊C4—22no—
225C22⋊C4—24no—
226C22⋊C4—24no—
227C42—22no—
228C42—24no—
229C42—22no—
230C42—41no—
231C42—42no—
232C42C22×C4×C3111yescharacteristic
233C42C2×D4×C3111yescharacteristic
234C42C2×D4×C3112yes—
235C23—24no—
236C23C31×#12011yescharacteristic
237Q8—44no—
238Q8—42no—
239Q8—42no—
240D4—44no—
241D4—42no—
242D4—42no—
243D4—42no—
244D4—42no—
245D4—84no—
246D4—88no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—24no—
252C2×C4—24no—
253C2×C4—44no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—88no—
258C2×C4C2×C22⋊C4×C3111yescharacteristic
259C2×C4C2×C22⋊C4×C3112yes—
260C2×C4C31×#12012yes—
261C2×C4C31×#12011yescharacteristic
262C8—82no—
263C8—81no—
264C22—22no—
265C22—21no—
266C22—44no—
267C22—44no—
268C22—44no—
269C22C31×#37911yescharacteristic
270C4—22no—
271C4—21no—
272C4—44no—
273C4—44no—
274C4—44no—
275C4C31×#45312yes—
276C4C31×#45411yescharacteristic
277C4C31×#45512yes—
278C4C31×#45611yescharacteristic
279C2—41no—
280C2—84no—
281C2C31×#179212yes—
282C2C31×#179311yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3548C2
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
2. C31×#1994C2semidirect
3. C31×#1962C2semidirect
4. C31×#1561C2semidirect
5. C31×#1560C2semidirect
6. C31×#562C4semidirect
93. #8532C31direct (N × H)
124. #1994C2×C31semidirect
125. #1962C2×C31semidirect
126. #1561C2×C31semidirect
127. #1560C2×C31semidirect
143. #562C4×C31semidirect
196. C31#8532direct (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×#19942
C31×#19622
C31×#15612
C31×#15602
#853231