Finite Group Databasebeta

← C31×#1894 #16841827

Subgroups — C31×#1894 #16841827

Order 3968.

360 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 128 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×M16×C31C211yesmaximal, characteristic
2C2×C31×C22⋊Q8C211yesmaximal, characteristic
3C2×C31×#103C212yesmaximal, complemented
4C31×#380C211yesmaximal, characteristic
5C31×#340C212yesmaximal, complemented
6C22×Q8×C31C2211yescharacteristic
7C23×C4×C31C2211yescharacteristic
8C2×M16×C31—22no—
9C2×M16×C31—24no—
10C22×C8×C31C2212yes—
11C31×C22⋊Q8—22no—
12C31×C22⋊Q8C414yescomplemented
13C2×C4⋊C4×C31—21no—
14C2×C4⋊C4×C31C2212yes—
15C2×C4⋊C4×C31C2211yescharacteristic
16C2×C22⋊C4×C31—21no—
17C2×C22⋊C4×C31—21no—
18C31×#103—24no—
19C31×#95—21no—
20C24×C31D411yescharacteristic
21C2×Q8×C31—21no—
22C2×Q8×C31—22no—
23C2×Q8×C31—22no—
24C2×Q8×C31C2×C412yes—
25C22×C4×C31—22no—
26C22×C4×C31—22no—
27C22×C4×C31—21no—
28C22×C4×C31—21no—
29C22×C4×C31—22no—
30C22×C4×C31C2×C412yes—
31C22×C4×C31D411yescharacteristic
32C22×C4×C31D412yes—
33C22×C4×C31C2311yescharacteristic
34M16×C31—28no—
35C2×C8×C31—22no—
36C2×C8×C31—22no—
37C2×C8×C31D414yes—
38C4⋊C4×C31—24no—
39C4⋊C4×C31—21no—
40C4⋊C4×C31—22no—
41C4⋊C4×C31—22no—
42C4⋊C4×C31C2×C412yes—
43C22⋊C4×C31—24no—
44C22⋊C4×C31—42no—
45C23×C31—22no—
46C23×C31—21no—
47C23×C31—21no—
48C23×C31—22no—
49C23×C31C22⋊C412yes—
50C23×C31C2×D411yescharacteristic
51Q8×C31—24no—
52Q8×C31—41no—
53Q8×C31—41no—
54C2×C4×C31—22no—
55C2×C4×C31—24no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—42no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31—42no—
64C2×C4×C31—42no—
65C2×C4×C31—42no—
66C2×C4×C31C22⋊C412yes—
67C2×C4×C31C22×C411yescharacteristic
68C2×C4×C31C2×D412yes—
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31#4112yes—
71C8×C31—24no—
72#1894C3111yesmaximal, characteristic, direct product factor, Sylow
73C22×C31—22no—
74C22×C31—22no—
75C22×C31—22no—
76C22×C31—42no—
77C22×C31—42no—
78C22×C31C2×C22⋊C411yescharacteristic
79C22×C31#12112yes—
80C22×C31AGL(1,ℤ/8)11yescharacteristic
81C22×C31#13711yescharacteristic
82C22×C31#13712yes—
83C4×C31—22no—
84C4×C31—42no—
85C4×C31—42no—
86C4×C31—82no—
87C4×C31C4×D412yes—
88C4×C31#12011yescharacteristic
89C4×C31#12311yescharacteristic
90C22×M16C2×C3111yescharacteristic
91C2×C22⋊Q8C2×C3111yescharacteristic
92C2×#103C2×C3112yescomplemented
93#380C2×C3111yescharacteristic
94#340C2×C3112yescomplemented
95C2×C31—42no—
96C2×C31#38611yescharacteristic
97C2×C31#41711yescharacteristic
98C2×C31#41911yescharacteristic
99C2×C31#46812yes—
100C2×C31#47012yes—
101C22×Q8C22×C3111yescharacteristic
102C23×C4C22×C3111yescharacteristic
103C2×M16—22no—
104C2×M16—24no—
105C22×C8C22×C3112yes—
106C22⋊Q8—22no—
107C22⋊Q8C4×C3114yescomplemented
108C2×C4⋊C4—21no—
109C2×C4⋊C4C22×C3112yes—
110C2×C4⋊C4C22×C3111yescharacteristic
111C2×C22⋊C4—21no—
112C2×C22⋊C4—21no—
113#103—24no—
114#95—21no—
115C31#189411yescharacteristic, direct product factor, Sylow
116C24D4×C3111yescharacteristic
117C2×Q8—21no—
118C2×Q8—22no—
119C2×Q8—22no—
120C2×Q8C2×C4×C3112yes—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—22no—
126C22×C4C2×C4×C3112yes—
127C22×C4D4×C3111yescharacteristic
128C22×C4D4×C3112yes—
129C22×C4C23×C3111yescharacteristic
130M16—28no—
131C2×C8—22no—
132C2×C8—22no—
133C2×C8D4×C3114yes—
134C4⋊C4—24no—
135C4⋊C4—21no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C4⋊C4C2×C4×C3112yes—
139C22⋊C4—24no—
140C22⋊C4—42no—
141C23—22no—
142C23—21no—
143C23—21no—
144C23—22no—
145C23C22⋊C4×C3112yes—
146C23C2×D4×C3111yescharacteristic
147Q8—24no—
148Q8—41no—
149Q8—41no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4C22⋊C4×C3112yes—
163C2×C4C22×C4×C3111yescharacteristic
164C2×C4C2×D4×C3112yes—
165C2×C4C2×D4×C3111yescharacteristic
166C2×C4#41×C3112yes—
167C8—24no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22C2×C22⋊C4×C3111yescharacteristic
174C22C31×#12112yes—
175C22C31×AGL(1,ℤ/8)11yescharacteristic
176C22C31×#13711yescharacteristic
177C22C31×#13712yes—
178C4—22no—
179C4—42no—
180C4—42no—
181C4—82no—
182C4C4×D4×C3112yes—
183C4C31×#12011yescharacteristic
184C4C31×#12311yescharacteristic
185C2—42no—
186C2C31×#38611yescharacteristic
187C2C31×#41711yescharacteristic
188C2C31×#41911yescharacteristic
189C2C31×#46812yes—
190C2C31×#47012yes—
subgroupG/H
center, socleC23×C31C2×D4
commutatorC2×C4C22×C4×C31
Frattini, cosocleC22×C4C23×C31
prime radicalC24×C31D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#103C2semidirect
5. C31×#340C2semidirect
12. C31×C22⋊Q8C4semidirect
72. #1894C31direct (N × H)
92. C2×#103C2×C31semidirect
94. #340C2×C31semidirect
107. C22⋊Q8C4×C31semidirect
115. C31#1894direct (N × H)

Maximal subgroups

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

subgroupindex
C22×M16×C312
C2×C31×C22⋊Q82
C2×C31×#1032
C31×#3802
C31×#3402
#189431