Finite Group Databasebeta

← C31×#14341 #21471100

Subgroups — C31×#14341 #21471100

Order 7936.

3246 conjugacy classes of subgroups; only the 542 normal subgroups are shown.

normal subgroups only

This group has 3246 conjugacy classes of subgroups — too many to draw. Only its 542 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
1C23×C22⋊C4×C31C211yesmaximal, characteristic
2C2×C31×#379C212yesmaximal
3C31×#1440C218yesmaximal, complemented
4C31×C22⋊#95C214yesmaximal, complemented
5C26×C31C2211yescharacteristic
6C24×C4×C31C2212yes—
7C22×C22⋊C4×C31—28no—
8C22×C22⋊C4×C31C418yescomplemented
9C22×C22⋊C4×C31C2214yes—
10C22×C22⋊C4×C31C2214yes—
11C22×C22⋊C4×C31C2218yes—
12C31×#379—28no—
13C2×C31×#95C22116yescomplemented
14C25×C31—28no—
15C25×C31—48no—
16C25×C31C2×C414yes—
17C25×C31D418yes—
18C25×C31C2312yes—
19C25×C31C2311yescharacteristic
20C23×C4×C31—28no—
21C23×C4×C31—48no—
22C23×C4×C31C2×C418yes—
23C23×C4×C31C2318yes—
24C23×C4×C31C2314yes—
25C2×C22⋊C4×C31—232no—
26C2×C22⋊C4×C31—216no—
27C2×C22⋊C4×C31—216no—
28C2×C22⋊C4×C31—28no—
29C2×C22⋊C4×C31—216no—
30C2×C22⋊C4×C31—416no—
31C2×C22⋊C4×C31C2×C4116yes—
32C31×#95—416no—
33C24×C31—28no—
34C24×C31—216no—
35C24×C31—232no—
36C24×C31—28no—
37C24×C31—216no—
38C24×C31—416no—
39C24×C31—432no—
40C24×C31—464no—
41C24×C31C22⋊C4116yes—
42C24×C31C22×C414yes—
43C24×C31C22×C412yes—
44C24×C31C2×D418yes—
45C24×C31C2×D414yes—
46C24×C31#4118yes—
47C24×C31C2411yescharacteristic
48C22×C4×C31—216no—
49C22×C4×C31—28no—
50C22×C4×C31—216no—
51C22×C4×C31—28no—
52C22×C4×C31—216no—
53C22×C4×C31—232no—
54C22×C4×C31—416no—
55C22×C4×C31—432no—
56C22×C4×C31C22×C418yes—
57C22⋊C4×C31—232no—
58C22⋊C4×C31—432no—
59C22⋊C4×C31—416no—
60#14341C3111yesmaximal, characteristic, direct product factor, Sylow
61C23×C31—28no—
62C23×C31—216no—
63C23×C31—232no—
64C23×C31—28no—
65C23×C31—216no—
66C23×C31—216no—
67C23×C31—216no—
68C23×C31—216no—
69C23×C31—232no—
70C23×C31—432no—
71C23×C31—464no—
72C23×C31—4128no—
73C23×C31—432no—
74C23×C31C2×C22⋊C418yes—
75C23×C31C2×C22⋊C414yes—
76C23×C31#11718yes—
77C23×C31#123116yes—
78C23×C31C23×C411yescharacteristic
79C23×C31C22×D412yes—
80C23×C31C2×#4114yes—
81C23×C31H(5,𝔽2)18yes—
82C2×C4×C31—28no—
83C2×C4×C31—216no—
84C2×C4×C31—432no—
85C2×C4×C31—416no—
86C2×C4×C31—48no—
87C2×C4×C31—416no—
88C2×C4×C31—432no—
89C23×C22⋊C4C2×C3111yescharacteristic
90C2×#379C2×C3112yes—
91#1440C2×C3118yescomplemented
92C22⋊#95C2×C3114yescomplemented
93C22×C31—28no—
94C22×C31—216no—
95C22×C31—232no—
96C22×C31—216no—
97C22×C31—28no—
98C22×C31—464no—
99C22×C31—416no—
100C22×C31—432no—
101C22×C31#38118yes—
102C22×C31C22×C22⋊C411yescharacteristic
103C22×C31C2×#11712yes—
104C22×C31#51814yes—
105C22×C31C2×#12314yes—
106C22×C31#53418yes—
107C22×C31#538116yes—
108C4×C31—48no—
109C4×C31—88no—
110C26C22×C3111yescharacteristic
111C24×C4C22×C3112yes—
112C22×C22⋊C4—28no—
113C22×C22⋊C4C4×C3118yescomplemented
114C22×C22⋊C4C22×C3114yes—
115C22×C22⋊C4C22×C3114yes—
116C22×C22⋊C4C22×C3118yes—
117#379—28no—
118C2×#95C22×C31116yescomplemented
119C2×C31—28no—
120C2×C31—48no—
121C2×C31C2×#38111yescharacteristic
122C2×C31#230812yes—
123C2×C31#231214yes—
124C2×C31#262218yes—
125C25—28no—
126C25—48no—
127C25C2×C4×C3114yes—
128C25D4×C3118yes—
129C25C23×C3112yes—
130C25C23×C3111yescharacteristic
131C23×C4—28no—
132C23×C4—48no—
133C23×C4C2×C4×C3118yes—
134C23×C4C23×C3118yes—
135C23×C4C23×C3114yes—
136C2×C22⋊C4—232no—
137C2×C22⋊C4—216no—
138C2×C22⋊C4—216no—
139C2×C22⋊C4—28no—
140C2×C22⋊C4—216no—
141C2×C22⋊C4—416no—
142C2×C22⋊C4C2×C4×C31116yes—
143#95—416no—
144C31#1434111yescharacteristic, direct product factor, Sylow
145C24—28no—
146C24—216no—
147C24—232no—
148C24—28no—
149C24—216no—
150C24—416no—
151C24—432no—
152C24—464no—
153C24C22⋊C4×C31116yes—
154C24C22×C4×C3114yes—
155C24C22×C4×C3112yes—
156C24C2×D4×C3118yes—
157C24C2×D4×C3114yes—
158C24#41×C3118yes—
159C24C24×C3111yescharacteristic
160C22×C4—216no—
161C22×C4—28no—
162C22×C4—216no—
163C22×C4—28no—
164C22×C4—216no—
165C22×C4—232no—
166C22×C4—416no—
167C22×C4—432no—
168C22×C4C22×C4×C3118yes—
169C22⋊C4—232no—
170C22⋊C4—432no—
171C22⋊C4—416no—
172C23—28no—
173C23—216no—
174C23—232no—
175C23—28no—
176C23—216no—
177C23—216no—
178C23—216no—
179C23—216no—
180C23—232no—
181C23—432no—
182C23—464no—
183C23—4128no—
184C23—432no—
185C23C2×C22⋊C4×C3118yes—
186C23C2×C22⋊C4×C3114yes—
187C23C31×#11718yes—
188C23C31×#123116yes—
189C23C23×C4×C3111yescharacteristic
190C23C22×D4×C3112yes—
191C23C2×#41×C3114yes—
192C23C31×H(5,𝔽2)18yes—
193C2×C4—28no—
194C2×C4—216no—
195C2×C4—432no—
196C2×C4—416no—
197C2×C4—48no—
198C2×C4—416no—
199C2×C4—432no—
200C22—28no—
201C22—216no—
202C22—232no—
203C22—216no—
204C22—28no—
205C22—464no—
206C22—416no—
207C22—432no—
208C22C31×#38118yes—
209C22C22×C22⋊C4×C3111yescharacteristic
210C22C2×C31×#11712yes—
211C22C31×#51814yes—
212C22C2×C31×#12314yes—
213C22C31×#53418yes—
214C22C31×#538116yes—
215C4—48no—
216C4—88no—
217C2—28no—
218C2—48no—
219C2C2×C31×#38111yescharacteristic
220C2C31×#230812yes—
221C2C31×#231214yes—
222C2C31×#262218yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1440C2semidirect
4. C31×C22⋊#95C2semidirect
8. C22×C22⋊C4×C31C4semidirect
13. C2×C31×#95C22semidirect
60. #14341C31direct (N × H)
91. #1440C2×C31semidirect
92. C22⋊#95C2×C31semidirect
113. C22×C22⋊C4C4×C31semidirect
118. C2×#95C22×C31semidirect
144. C31#14341direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C312
C2×C31×#3792
C31×#14402
C31×C22⋊#952
#1434131