Finite Group Databasebeta

← #16847660

Subgroups — #16847660

Order 3968.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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
1#14521846C211yesmaximal, characteristic
2#14521490C211yesmaximal, characteristic, complemented
3#14521304C211yesmaximal, characteristic, complemented
4#14520860C211yesmaximal, characteristic, complemented
5#14520859C211yesmaximal, characteristic, complemented
6#14520830C211yesmaximal, characteristic, complemented
7C31×#510C211yesmaximal, characteristic, complemented
8#41×D31—21no—
9C31×#135C2211yescharacteristic
10C2×Q16×C31C2211yescharacteristic, complemented
11#11758527—21no—
12#11758523—21no—
13#11758495—21no—
14#11758492—21no—
15#11758491—21no—
16#11758488—21no—
17#11758481C2211yescharacteristic
18C2×#92469C2211yescharacteristic
19C31×Q32—21no—
20C31×SD32—21no—
21C31×M32C2211yescharacteristic, complemented
22#11758423—21no—
23#11758417—21no—
24#11758416—21no—
25#11758405C2211yescharacteristic, complemented
26#11758400C2211yescharacteristic, complemented
27#41×C31—21no—
28C2×Q8×C31—21no—
29#92499—21no—
30Q8×D31—21no—
31#92497—21no—
32#92497—41no—
33D4×D31—21no—
34D4×D31—41no—
35#92495—21no—
36#92495—41no—
37C2×C4×D31—41no—
38C2×C4×D31D411yescharacteristic
39Q16×C31—21no—
40Q16×C31—21no—
41Q16×C31D411yescharacteristic
42SD16×C31—21no—
43D8×C31D411yescharacteristic
44C2×C8×C31C2311yescharacteristic
45#92482—21no—
46#92481—21no—
47#92480—21no—
48#92479—21no—
49(C2×D31)⋊C4—41no—
50C4⋊Dic31—21no—
51Dic31⋊C4—41no—
52C2×C31⋊C8D411yescharacteristic
53Dic124D411yescharacteristic
54D248D411yescharacteristic
55#92470—21no—
56#92469—21no—
57#92469—21no—
58C16×C31—21no—
59C31⋊C16—21no—
60C22×D31—41no—
61C22×D31D811yescharacteristic
62Q8×C31—21no—
63Q8×C31—41no—
64Q8×C31—41no—
65D4×C31—21no—
66D4×C31—41no—
67C2×C4×C31—41no—
68C2×C4×C31—41no—
69C2×C4×C31C2×D411yescharacteristic
70C22⋊D31—41no—
71C22⋊D31—41no—
72C22⋊D31—41no—
73C2×Dic31—41no—
74C2×Dic31—41no—
75C2×Dic31D811yescharacteristic
76D124—21no—
77D124—41no—
78C4×D31—21no—
79C4×D31—21no—
80C4×D31—41no—
81C4×D31—41no—
82C4×D31—41no—
83Dic62—21no—
84Dic62—41no—
85C8×C31C2×D411yescharacteristic
86C8×C31C2×D411yescharacteristic
87C31⋊C8—21no—
88#2191—311nomaximal, Sylow
89C22×C31—41no—
90C22×C31C2×D811yescharacteristic
91C2×D31—21no—
92C2×D31—41no—
93C2×D31—41no—
94C2×D31—82no—
95C4×C31—41no—
96C4×C31—81no—
97C4×C31#12011yescharacteristic
98C4×C31AGL(1,ℤ/8)11yescharacteristic
99Dic31—21no—
100Dic31—41no—
101Dic31—81no—
102#575—311no—
103#510—311no—
104#510D3111yescharacteristic, complemented
105#470—311no—
106#360—311no—
107#360—311no—
108#349—311no—
109C2×C31—21no—
110C2×C31—81no—
111C2×C31#44711yescharacteristic
112D31—41no—
113D31—81no—
114C2×#41—621no—
115#137—621no—
116#137—621no—
117AGL(1,ℤ/8)—621no—
118AGL(1,ℤ/8)—621no—
119#135—311no—
120#135—621no—
121#135C2×D3111yescharacteristic
122C2×Q16C2×D3111yescharacteristic, complemented
123C2×M16—311no—
124C22⋊Q8—621no—
125Q32—21no—
126Q32—621no—
127SD32—21no—
128SD32—621no—
129M32—311no—
130M32C2×D3111yescharacteristic, complemented
131#106—311no—
132#103—621no—
133C31#219111yescharacteristic, complemented, Sylow
134#41—21no—
135#41—621no—
136#41—621no—
137#41—621no—
138#41—1241no—
139#41—1241no—
140C2×Q8—21no—
141C2×Q8—621no—
142C2×D4—621no—
143C2×D4—1241no—
144C22×C4—311no—
145C22×C4—1241no—
146Q16—21no—
147Q16—21no—
148Q16—311no—
149Q16—621no—
150Q16C22⋊D3111yescharacteristic
151SD16—21no—
152SD16—621no—
153SD16—621no—
154SD16—621no—
155D8—311no—
156D8—621no—
157D8C22⋊D3111yescharacteristic
158M16—621no—
159M16—621no—
160C2×C8—311no—
161C2×C8C22×D3111yescharacteristic
162C4⋊C4—621no—
163C4⋊C4—1241no—
164C22⋊C4—1241no—
165C16—21no—
166C16—621no—
167C23—311no—
168C23—1241no—
169Q8—21no—
170Q8—41no—
171Q8—41no—
172Q8—621no—
173Q8—1241no—
174D4—21no—
175D4—41no—
176D4—621no—
177D4—1241no—
178D4—1241no—
179D4—1241no—
180D4—1241no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—311no—
184C2×C4—621no—
185C2×C4—621no—
186C2×C4—1241no—
187C2×C4—1241no—
188C2×C4—1241no—
189C2×C4—1241no—
190C2×C4—1241no—
191C2×C4D4×D3111yescharacteristic
192C8—621no—
193C8D4×D3111yescharacteristic
194C8C2×C22⋊D3111yescharacteristic
195C22—41no—
196C22—621no—
197C22—1241no—
198C22—1241no—
199C22—2482no—
200C22D8×D3111yescharacteristic
201C4—41no—
202C4—81no—
203C4—621no—
204C4—1241no—
205C4—2481no—
206C4#1175848811yescharacteristic
207C4#1175851411yescharacteristic
208C2—21no—
209C2—81no—
210C2—1241no—
211C2—2481no—
212C2#1452118111yescharacteristic
subgroupG/H
centerC2#14521181
commutator, cosocleC2×C8×C31C23
FrattiniC2×C8C22×D31
FittingC31×#510C2
socleC2×C31#447
prime radical#14521846C2
hypercenter#510D31
hypocenterC31#2191
LCSG ▷ C2×C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #14521490C2semidirect
3. #14521304C2semidirect
4. #14520860C2semidirect
5. #14520859C2semidirect
6. #14520830C2semidirect
7. C31×#510C2semidirect
10. C2×Q16×C31C22semidirect
21. C31×M32C22semidirect
25. #11758405C22semidirect
26. #11758400C22semidirect
104. #510D31semidirect
122. C2×Q16C2×D31semidirect
130. M32C2×D31semidirect
133. C31#2191semidirect

Maximal subgroups

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

subgroupindex
#145218462
#145214902
#145213042
#145208602
#145208592
#145208302
C31×#5102
#219131