Finite Group Databasebeta

← C31×#11382 #21468141

Subgroups — C31×#11382 #21468141

Order 7936.

1142 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 1142 conjugacy classes of subgroups — too many to draw. Only its 286 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×C4⋊Q8C211yesmaximal, characteristic
2C2×C31×#343C214yesmaximal
3C31×#1728C212yesmaximal
4C23×Q8×C31C412yes—
5C22×M16×C31C2214yes—
6C2×C31×C4⋊Q8—28no—
7C2×C31×C4⋊Q8—24no—
8C22×C4⋊C4×C31C412yes—
9C22×C4⋊C4×C31C2212yes—
10C22×C42×C31C2211yescharacteristic
11C31×#343—28no—
12C31×#336—24no—
13C22×Q8×C31—28no—
14C22×Q8×C31—24no—
15C22×Q8×C31—48no—
16C23×C4×C31C2×C411yescharacteristic
17C23×C4×C31C2×C411yescharacteristic
18C23×C4×C31C2×C414yes—
19C23×C4×C31C2311yescharacteristic
20C2×M16×C31—24no—
21C2×M16×C31—28no—
22C2×M16×C31—28no—
23C2×M16×C31Q818yescomplemented
24C22×C8×C31—24no—
25C31×C4⋊Q8—232no—
26C2×C4⋊C4×C31—28no—
27C2×C4⋊C4×C31—24no—
28C2×C4⋊C4×C31—24no—
29C2×C4⋊C4×C31—24no—
30C2×C4⋊C4×C31D418yes—
31C2×C42×C31—24no—
32C2×C42×C31D414yes—
33C24×C31C22×C411yescharacteristic
34C2×Q8×C31—216no—
35C2×Q8×C31—432no—
36C2×Q8×C31—48no—
37C2×Q8×C31—48no—
38C22×C4×C31—22no—
39C22×C4×C31—22no—
40C22×C4×C31—24no—
41C22×C4×C31—24no—
42C22×C4×C31—24no—
43C22×C4×C31—24no—
44C22×C4×C31—48no—
45C22×C4×C31C22⋊C412yes—
46C22×C4×C31C22⋊C412yes—
47C22×C4×C31C22⋊C418yes—
48C22×C4×C31C2×D414yes—
49C22×C4×C31C2×D412yes—
50C22×C4×C31C2×Q814yes—
51C22×C4×C31#4114yes—
52M16×C31—216no—
53M16×C31—48no—
54C2×C8×C31—28no—
55C2×C8×C31—44no—
56C2×C8×C31—44no—
57C4⋊C4×C31—216no—
58C4⋊C4×C31—216no—
59C42×C31—28no—
60#11382C3111yesmaximal, characteristic, direct product factor, Sylow
61C23×C31—22no—
62C23×C31—22no—
63C23×C31C2×C22⋊C412yes—
64C23×C31C2×C22⋊C411yescharacteristic
65C23×C31C4×Q814yes—
66Q8×C31—432no—
67C2×C4×C31—28no—
68C2×C4×C31—28no—
69C2×C4×C31—22no—
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31—28no—
74C2×C4×C31—48no—
75C2×C4×C31—48no—
76C2×C4×C31—48no—
77C2×C4×C31#10014yes—
78C2×C4×C31#10114yes—
79C2×C4×C31#12014yes—
80C2×C4×C31C22⋊Q814yes—
81C2×C4×C31C22⋊Q818yes—
82C2×C4×C31#12412yes—
83C2×C4×C31#12414yes—
84C2×C4×C31C4⋊Q814yes—
85C2×C4×C31C4⋊Q812yes—
86C8×C31—48no—
87C22×C4⋊Q8C2×C3111yescharacteristic
88C2×#343C2×C3114yes—
89#1728C2×C3112yes—
90C22×C31—28no—
91C22×C31—22no—
92C22×C31—22no—
93C22×C31#37911yescharacteristic
94C22×C31#39114yes—
95C22×C31#39112yes—
96C22×C31C2×#10012yes—
97C22×C31C2×#10112yes—
98C4×C31—24no—
99C4×C31—24no—
100C4×C31—48no—
101C4×C31#39314yes—
102C4×C31#39514yes—
103C23×Q8C4×C3112yes—
104C22×M16C22×C3114yes—
105C2×C4⋊Q8—28no—
106C2×C4⋊Q8—24no—
107C22×C4⋊C4C4×C3112yes—
108C22×C4⋊C4C22×C3112yes—
109C22×C42C22×C3111yescharacteristic
110#343—28no—
111#336—24no—
112C2×C31—24no—
113C2×C31#144611yescharacteristic
114C2×C31#178311yescharacteristic
115C2×C31#178411yescharacteristic
116C2×C31#199714yes—
117C22×Q8—28no—
118C22×Q8—24no—
119C22×Q8—48no—
120C23×C4C2×C4×C3111yescharacteristic
121C23×C4C2×C4×C3111yescharacteristic
122C23×C4C2×C4×C3114yes—
123C23×C4C23×C3111yescharacteristic
124C2×M16—24no—
125C2×M16—28no—
126C2×M16—28no—
127C2×M16Q8×C3118yescomplemented
128C22×C8—24no—
129C4⋊Q8—232no—
130C2×C4⋊C4—28no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4—24no—
133C2×C4⋊C4—24no—
134C2×C4⋊C4D4×C3118yes—
135C2×C42—24no—
136C2×C42D4×C3114yes—
137C31#1138211yescharacteristic, direct product factor, Sylow
138C24C22×C4×C3111yescharacteristic
139C2×Q8—216no—
140C2×Q8—432no—
141C2×Q8—48no—
142C2×Q8—48no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—24no—
146C22×C4—24no—
147C22×C4—24no—
148C22×C4—24no—
149C22×C4—48no—
150C22×C4C22⋊C4×C3112yes—
151C22×C4C22⋊C4×C3112yes—
152C22×C4C22⋊C4×C3118yes—
153C22×C4C2×D4×C3114yes—
154C22×C4C2×D4×C3112yes—
155C22×C4C2×Q8×C3114yes—
156C22×C4#41×C3114yes—
157M16—216no—
158M16—48no—
159C2×C8—28no—
160C2×C8—44no—
161C2×C8—44no—
162C4⋊C4—216no—
163C4⋊C4—216no—
164C42—28no—
165C23—22no—
166C23—22no—
167C23C2×C22⋊C4×C3112yes—
168C23C2×C22⋊C4×C3111yescharacteristic
169C23C4×Q8×C3114yes—
170Q8—432no—
171C2×C4—28no—
172C2×C4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—28no—
178C2×C4—48no—
179C2×C4—48no—
180C2×C4—48no—
181C2×C4C31×#10014yes—
182C2×C4C31×#10114yes—
183C2×C4C31×#12014yes—
184C2×C4C31×C22⋊Q814yes—
185C2×C4C31×C22⋊Q818yes—
186C2×C4C31×#12412yes—
187C2×C4C31×#12414yes—
188C2×C4C31×C4⋊Q814yes—
189C2×C4C31×C4⋊Q812yes—
190C8—48no—
191C22—28no—
192C22—22no—
193C22—22no—
194C22C31×#37911yescharacteristic
195C22C31×#39114yes—
196C22C31×#39112yes—
197C22C2×C31×#10012yes—
198C22C2×C31×#10112yes—
199C4—24no—
200C4—24no—
201C4—48no—
202C4C31×#39314yes—
203C4C31×#39514yes—
204C2—24no—
205C2C31×#144611yescharacteristic
206C2C31×#178311yescharacteristic
207C2C31×#178411yescharacteristic
208C2C31×#199714yes—
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C22×C4
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
23. C2×M16×C31Q8semidirect
60. #11382C31direct (N × H)
127. C2×M16Q8×C31semidirect
137. C31#11382direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×C4⋊Q82
C2×C31×#3432
C31×#17282
#1138231