Finite Group Databasebeta

← C31×#8305 #21465064

Subgroups — C31×#8305 #21465064

Order 7936.

1154 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 182 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×#124C211yesmaximal, characteristic
2C31×#1817C212yesmaximal, complemented
3C2×C31×#323C214yesmaximal, complemented
4C23×Q8×C31C411yescharacteristic
5C23×D4×C31C411yescharacteristic
6C2×C31×#124—28no—
7C2×C31×#124—24no—
8C22×C22⋊C4×C31C412yes—
9C22×C22⋊C4×C31C2212yes—
10C22×C42×C31C2211yescharacteristic
11C2×C31×C22⋊C8C2214yes—
12C31×#336—24no—
13C31×#323—28no—
14C25×C31C2×C412yes—
15C22×Q8×C31—24no—
16C22×Q8×C31—22no—
17C22×Q8×C31—44no—
18C22×D4×C31—24no—
19C22×D4×C31—22no—
20C22×D4×C31—44no—
21C23×C4×C31C2×C411yescharacteristic
22C23×C4×C31C2×C411yescharacteristic
23C23×C4×C31C2×C412yes—
24C23×C4×C31C2311yescharacteristic
25C22×C8×C31—24no—
26C31×#124—232no—
27C2×C22⋊C4×C31—24no—
28C2×C22⋊C4×C31—24no—
29C2×C22⋊C4×C31—24no—
30C2×C22⋊C4×C31—24no—
31C2×C22⋊C4×C31—24no—
32C2×C22⋊C4×C31D418yes—
33C2×C42×C31—24no—
34C2×C42×C31D414yes—
35C31×C22⋊C8—28no—
36C24×C31—22no—
37C24×C31—22no—
38C24×C31—28no—
39C24×C31—44no—
40C24×C31—44no—
41C24×C31C22⋊C414yes—
42C24×C31C22×C411yescharacteristic
43C2×Q8×C31—28no—
44C2×Q8×C31—416no—
45C2×Q8×C31—44no—
46C2×Q8×C31—44no—
47C2×D4×C31—28no—
48C2×D4×C31—416no—
49C2×D4×C31—44no—
50C2×D4×C31—44no—
51C22×C4×C31—22no—
52C22×C4×C31—24no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—24no—
57C22×C4×C31—42no—
58C22×C4×C31—44no—
59C22×C4×C31C22⋊C412yes—
60C22×C4×C31C22⋊C412yes—
61C22×C4×C31C22⋊C414yes—
62C22×C4×C31C2×D412yes—
63C22×C4×C31C2×D414yes—
64C2×C8×C31—48no—
65C2×C8×C31—44no—
66C22⋊C4×C31—216no—
67C22⋊C4×C31—216no—
68C42×C31—28no—
69#8305C3111yesmaximal, characteristic, direct product factor, Sylow
70C23×C31—22no—
71C23×C31—22no—
72C23×C31—24no—
73C23×C31—28no—
74C23×C31—44no—
75C23×C31—44no—
76C23×C31—44no—
77C23×C31—44no—
78C23×C31—44no—
79C23×C31—44no—
80C23×C31—44no—
81C23×C31—44no—
82C23×C31—816no—
83C23×C31C2×C22⋊C412yes—
84C23×C31C2×C22⋊C411yescharacteristic
85C23×C31#13114yes—
86Q8×C31—416no—
87D4×C31—416no—
88C2×C4×C31—28no—
89C2×C4×C31—22no—
90C2×C4×C31—24no—
91C2×C4×C31—22no—
92C2×C4×C31—22no—
93C2×C4×C31—24no—
94C2×C4×C31—24no—
95C2×C4×C31—44no—
96C2×C4×C31—44no—
97C2×C4×C31—44no—
98C2×C4×C31—44no—
99C2×C4×C31—44no—
100C2×C4×C31#10014yes—
101C2×C4×C31#12014yes—
102C8×C31—84no—
103C22×#124C2×C3111yescharacteristic
104#1817C2×C3112yescomplemented
105C2×#323C2×C3114yescomplemented
106C22×C31—28no—
107C22×C31—22no—
108C22×C31—22no—
109C22×C31—44no—
110C22×C31—44no—
111C22×C31—44no—
112C22×C31—88no—
113C22×C31—88no—
114C22×C31—88no—
115C22×C31#37911yescharacteristic
116C22×C31#40814yes—
117C22×C31#40812yes—
118C22×C31#41012yes—
119C22×C31C2×#10012yes—
120C4×C31—24no—
121C4×C31—24no—
122C4×C31—42no—
123C4×C31—44no—
124C23×Q8C4×C3111yescharacteristic
125C23×D4C4×C3111yescharacteristic
126C2×#124—28no—
127C2×#124—24no—
128C22×C22⋊C4C4×C3112yes—
129C22×C22⋊C4C22×C3112yes—
130C22×C42C22×C3111yescharacteristic
131C2×C22⋊C8C22×C3114yes—
132#336—24no—
133#323—28no—
134C2×C31—24no—
135C2×C31—84no—
136C2×C31#146914yes—
137C2×C31#178011yescharacteristic
138C2×C31#178211yescharacteristic
139C2×C31#178311yescharacteristic
140C25C2×C4×C3112yes—
141C22×Q8—24no—
142C22×Q8—22no—
143C22×Q8—44no—
144C22×D4—24no—
145C22×D4—22no—
146C22×D4—44no—
147C23×C4C2×C4×C3111yescharacteristic
148C23×C4C2×C4×C3111yescharacteristic
149C23×C4C2×C4×C3112yes—
150C23×C4C23×C3111yescharacteristic
151C22×C8—24no—
152#124—232no—
153C2×C22⋊C4—24no—
154C2×C22⋊C4—24no—
155C2×C22⋊C4—24no—
156C2×C22⋊C4—24no—
157C2×C22⋊C4—24no—
158C2×C22⋊C4D4×C3118yes—
159C2×C42—24no—
160C2×C42D4×C3114yes—
161C22⋊C8—28no—
162C31#830511yescharacteristic, direct product factor, Sylow
163C24—22no—
164C24—22no—
165C24—28no—
166C24—44no—
167C24—44no—
168C24C22⋊C4×C3114yes—
169C24C22×C4×C3111yescharacteristic
170C2×Q8—28no—
171C2×Q8—416no—
172C2×Q8—44no—
173C2×Q8—44no—
174C2×D4—28no—
175C2×D4—416no—
176C2×D4—44no—
177C2×D4—44no—
178C22×C4—22no—
179C22×C4—24no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—24no—
184C22×C4—42no—
185C22×C4—44no—
186C22×C4C22⋊C4×C3112yes—
187C22×C4C22⋊C4×C3112yes—
188C22×C4C22⋊C4×C3114yes—
189C22×C4C2×D4×C3112yes—
190C22×C4C2×D4×C3114yes—
191C2×C8—48no—
192C2×C8—44no—
193C22⋊C4—216no—
194C22⋊C4—216no—
195C42—28no—
196C23—22no—
197C23—22no—
198C23—24no—
199C23—28no—
200C23—44no—
201C23—44no—
202C23—44no—
203C23—44no—
204C23—44no—
205C23—44no—
206C23—44no—
207C23—44no—
208C23—816no—
209C23C2×C22⋊C4×C3112yes—
210C23C2×C22⋊C4×C3111yescharacteristic
211C23C31×#13114yes—
212Q8—416no—
213D4—416no—
214C2×C4—28no—
215C2×C4—24no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—22no—
220C2×C4—24no—
221C2×C4—44no—
222C2×C4—44no—
223C2×C4—44no—
224C2×C4—44no—
225C2×C4—44no—
226C2×C4C31×#10014yes—
227C2×C4C31×#12014yes—
228C8—84no—
229C22—28no—
230C22—22no—
231C22—22no—
232C22—44no—
233C22—44no—
234C22—44no—
235C22—88no—
236C22—88no—
237C22—88no—
238C22C31×#37911yescharacteristic
239C22C31×#40814yes—
240C22C31×#40812yes—
241C22C31×#41012yes—
242C22C2×C31×#10012yes—
243C4—24no—
244C4—24no—
245C4—42no—
246C4—44no—
247C2—24no—
248C2—84no—
249C2C31×#146914yes—
250C2C31×#178011yescharacteristic
251C2C31×#178211yescharacteristic
252C2C31×#178311yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC23×D4×C31C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1817C2semidirect
3. C2×C31×#323C2semidirect
69. #8305C31direct (N × H)
104. #1817C2×C31semidirect
105. C2×#323C2×C31semidirect
162. C31#8305direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C31×#18172
C2×C31×#3232
#830531