Finite Group Databasebeta

← C31×#11169 #21467928

Subgroups — C31×#11169 #21467928

Order 7936.

1110 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 222 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
1C22×C31×#99C212yesmaximal
2C31×#2308C211yesmaximal, characteristic
3C2×C31×#342C214yesmaximal, complemented
4C23×D4×C31C2211yescharacteristic
5C22×C22⋊C4×C31C2212yes—
6C22×C22⋊C4×C31C2214yes—
7C2×C31×#99—24no—
8C2×C31×#99—28no—
9C31×#386—24no—
10C31×#381C412yescomplemented
11C31×#379C412yescomplemented
12C31×#342—28no—
13C25×C31C2×C411yescharacteristic
14C25×C31C2311yescharacteristic
15C22×D4×C31—24no—
16C22×D4×C31—24no—
17C22×D4×C31—24no—
18C22×D4×C31D414yes—
19C23×C4×C31—22no—
20C23×C4×C31—24no—
21C23×C4×C31C2×C411yescharacteristic
22C2×C22⋊C4×C31—24no—
23C2×C22⋊C4×C31—24no—
24C2×C22⋊C4×C31—24no—
25C2×C22⋊C4×C31—24no—
26C2×C22⋊C4×C31—24no—
27C2×C22⋊C4×C31—24no—
28C2×C22⋊C4×C31—24no—
29C2×C22⋊C4×C31—22no—
30C2×C22⋊C4×C31—24no—
31C2×C22⋊C4×C31C2×C414yes—
32C2×C22⋊C4×C31D418yes—
33C31×#99—216no—
34C31×#95—24no—
35C24×C31—22no—
36C24×C31—24no—
37C24×C31—82no—
38C24×C31—82no—
39C24×C31C22⋊C412yes—
40C24×C31C22×C411yescharacteristic
41C24×C31C2×D412yes—
42C24×C31C2×D414yes—
43C24×C31#4114yes—
44C24×C31#4114yes—
45C2×D4×C31—24no—
46C2×D4×C31—28no—
47C2×D4×C31—28no—
48C2×D4×C31—24no—
49C2×D4×C31—44no—
50C2×D4×C31—44no—
51C2×D4×C31—44no—
52C2×D4×C31—44no—
53C22×C4×C31—22no—
54C22×C4×C31—24no—
55C22×C4×C31—24no—
56C22×C4×C31—28no—
57C22×C4×C31—44no—
58C22×C4×C31—44no—
59C22×C4×C31—44no—
60C22×C4×C31—84no—
61C22×C4×C31—88no—
62C22×C4×C31C22⋊C412yes—
63C22⋊C4×C31—28no—
64C22⋊C4×C31—28no—
65C22⋊C4×C31—28no—
66C22⋊C4×C31—42no—
67C22⋊C4×C31—44no—
68C22⋊C4×C31—44no—
69C22⋊C4×C31—42no—
70C22⋊C4×C31—84no—
71#11169C3111yesmaximal, characteristic, direct product factor, Sylow
72C23×C31—22no—
73C23×C31—24no—
74C23×C31—44no—
75C23×C31—48no—
76C23×C31—42no—
77C23×C31—44no—
78C23×C31—44no—
79C23×C31—84no—
80C23×C31—84no—
81C23×C31—84no—
82C23×C31—88no—
83C23×C31C2×C22⋊C411yescharacteristic
84C23×C31#11712yes—
85C23×C31C4×D414yes—
86C23×C31#12012yes—
87C23×C31#12114yes—
88C23×C31#12114yes—
89C23×C31#12314yes—
90C23×C31#12312yes—
91C23×C31#12314yes—
92C23×C31#12414yes—
93C23×C31#12614yes—
94D4×C31—48no—
95D4×C31—48no—
96C2×C4×C31—22no—
97C2×C4×C31—24no—
98C2×C4×C31—44no—
99C2×C4×C31—48no—
100C2×C4×C31—44no—
101C2×C4×C31—48no—
102C2×C4×C31—88no—
103C2×C4×C31—88no—
104C2×C4×C31—88no—
105C2×C4×C31—88no—
106C22×#99C2×C3112yes—
107#2308C2×C3111yescharacteristic
108C2×#342C2×C3114yescomplemented
109C22×C31—22no—
110C22×C31—28no—
111C22×C31—24no—
112C22×C31—44no—
113C22×C31—44no—
114C22×C31—44no—
115C22×C31—44no—
116C22×C31—42no—
117C22×C31—42no—
118C22×C31—44no—
119C22×C31—44no—
120C22×C31—44no—
121C22×C31—42no—
122C22×C31—84no—
123C22×C31—88no—
124C22×C31#38111yescharacteristic
125C22×C31#38612yes—
126C22×C31#38814yes—
127C22×C31#39414yes—
128C22×C31#39714yes—
129C4×C31—42no—
130C4×C31—84no—
131C4×C31—88no—
132C23×D4C22×C3111yescharacteristic
133C22×C22⋊C4C22×C3112yes—
134C22×C22⋊C4C22×C3114yes—
135C2×#99—24no—
136C2×#99—28no—
137#386—24no—
138#381C4×C3112yescomplemented
139#379C4×C3112yescomplemented
140#342—28no—
141C2×C31—22no—
142C2×C31—24no—
143C2×C31—24no—
144C2×C31—24no—
145C2×C31—82no—
146C2×C31#144011yescharacteristic
147C2×C31#182812yes—
148C25C2×C4×C3111yescharacteristic
149C25C23×C3111yescharacteristic
150C22×D4—24no—
151C22×D4—24no—
152C22×D4—24no—
153C22×D4D4×C3114yes—
154C23×C4—22no—
155C23×C4—24no—
156C23×C4C2×C4×C3111yescharacteristic
157C2×C22⋊C4—24no—
158C2×C22⋊C4—24no—
159C2×C22⋊C4—24no—
160C2×C22⋊C4—24no—
161C2×C22⋊C4—24no—
162C2×C22⋊C4—24no—
163C2×C22⋊C4—24no—
164C2×C22⋊C4—22no—
165C2×C22⋊C4—24no—
166C2×C22⋊C4C2×C4×C3114yes—
167C2×C22⋊C4D4×C3118yes—
168#99—216no—
169#95—24no—
170C31#1116911yescharacteristic, direct product factor, Sylow
171C24—22no—
172C24—24no—
173C24—82no—
174C24—82no—
175C24C22⋊C4×C3112yes—
176C24C22×C4×C3111yescharacteristic
177C24C2×D4×C3112yes—
178C24C2×D4×C3114yes—
179C24#41×C3114yes—
180C24#41×C3114yes—
181C2×D4—24no—
182C2×D4—28no—
183C2×D4—28no—
184C2×D4—24no—
185C2×D4—44no—
186C2×D4—44no—
187C2×D4—44no—
188C2×D4—44no—
189C22×C4—22no—
190C22×C4—24no—
191C22×C4—24no—
192C22×C4—28no—
193C22×C4—44no—
194C22×C4—44no—
195C22×C4—44no—
196C22×C4—84no—
197C22×C4—88no—
198C22×C4C22⋊C4×C3112yes—
199C22⋊C4—28no—
200C22⋊C4—28no—
201C22⋊C4—28no—
202C22⋊C4—42no—
203C22⋊C4—44no—
204C22⋊C4—44no—
205C22⋊C4—42no—
206C22⋊C4—84no—
207C23—22no—
208C23—24no—
209C23—44no—
210C23—48no—
211C23—42no—
212C23—44no—
213C23—44no—
214C23—84no—
215C23—84no—
216C23—84no—
217C23—88no—
218C23C2×C22⋊C4×C3111yescharacteristic
219C23C31×#11712yes—
220C23C4×D4×C3114yes—
221C23C31×#12012yes—
222C23C31×#12114yes—
223C23C31×#12114yes—
224C23C31×#12314yes—
225C23C31×#12312yes—
226C23C31×#12314yes—
227C23C31×#12414yes—
228C23C31×#12614yes—
229D4—48no—
230D4—48no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—44no—
234C2×C4—48no—
235C2×C4—44no—
236C2×C4—48no—
237C2×C4—88no—
238C2×C4—88no—
239C2×C4—88no—
240C2×C4—88no—
241C22—22no—
242C22—28no—
243C22—24no—
244C22—44no—
245C22—44no—
246C22—44no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—44no—
251C22—44no—
252C22—44no—
253C22—42no—
254C22—84no—
255C22—88no—
256C22C31×#38111yescharacteristic
257C22C31×#38612yes—
258C22C31×#38814yes—
259C22C31×#39414yes—
260C22C31×#39714yes—
261C4—42no—
262C4—84no—
263C4—88no—
264C2—22no—
265C2—24no—
266C2—24no—
267C2—24no—
268C2—82no—
269C2C31×#144011yescharacteristic
270C2C31×#182812yes—
subgroupG/H
center, socleC22×C31#381
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#342C2semidirect
10. C31×#381C4semidirect
11. C31×#379C4semidirect
71. #11169C31direct (N × H)
108. C2×#342C2×C31semidirect
138. #381C4×C31semidirect
139. #379C4×C31semidirect
170. C31#11169direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#992
C31×#23082
C2×C31×#3422
#1116931