Finite Group Databasebeta

← #16847685

Subgroups — #16847685

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#14521850C211yesmaximal, characteristic
2#14521492C211yesmaximal, characteristic, complemented
3C2×#11758415C211yesmaximal, characteristic, complemented
4#14521325C211yesmaximal, characteristic, complemented
5#14520855C211yesmaximal, characteristic, complemented
6#14520834C211yesmaximal, characteristic, complemented
7C31×#361C211yesmaximal, characteristic, complemented
8#11758561—21no—
9C2×D8×C31C2211yescharacteristic
10#11758509—21no—
11#11758489—21no—
12#11758488—22no—
13D8×D31—21no—
14#11758486—21no—
15C2×Dic124C2211yescharacteristic, complemented
16#11758481C2211yescharacteristic
17#11758478C2211yescharacteristic
18C31×M32C2211yescharacteristic, complemented
19C31×#108C2211yescharacteristic, complemented
20#11758415—22no—
21#11758412—21no—
22C2×C31⋊C16C2211yescharacteristic, complemented
23Dic248—21no—
24#11758388—21no—
25C2×D4×C31—21no—
26C2×C22⋊D31—42no—
27#92497—22no—
28#92497—41no—
29D4×D31—22no—
30D4×D31—41no—
31#92495—21no—
32#92495D411yescharacteristic
33C2×Dic62—21no—
34D8×C31—21no—
35D8×C31D412yes—
36M16×C31—21no—
37C2×C8×C31C2311yescharacteristic
38#92480—22no—
39#92479—22no—
40#92474D411yescharacteristic
41Dic124—21no—
42Dic124—21no—
43Dic124—41no—
44Dic124D411yescharacteristic
45D248D411yescharacteristic
46#92470—21no—
47#92470—41no—
48#92469—21no—
49C8×D31—21no—
50C16×C31—21no—
51C31⋊C16—21no—
52C23×C31—41no—
53C22×D31—42no—
54D4×C31—22no—
55D4×C31—41no—
56C2×C4×C31C2×D411yescharacteristic
57C22⋊D31—21no—
58C22⋊D31—42no—
59C22⋊D31—42no—
60C22⋊D31—41no—
61C2×Dic31—42no—
62C2×Dic31—41no—
63D124—21no—
64D124D811yescharacteristic
65C4×D31—21no—
66C4×D31—41no—
67Dic62—21no—
68Dic62—41no—
69Dic62—41no—
70Dic62D811yescharacteristic
71C8×C31—41no—
72C8×C31C2×D411yescharacteristic
73C8×C31C2×D411yescharacteristic
74C31⋊C8—21no—
75#2194—311nomaximal, Sylow
76C22×C31—42no—
77C22×C31—161no—
78C22×C31AGL(1,ℤ/8)11yescharacteristic
79C2×D31—21no—
80C2×D31—41no—
81C2×D31—162no—
82C4×C31#12011yescharacteristic
83C4×C31C2×D811yescharacteristic
84Dic31—21no—
85Dic31—41no—
86Dic31—81no—
87#576—311no—
88#510—311no—
89C2×SD32—311no—
90#473—311no—
91#361D3111yescharacteristic, complemented
92#359—311no—
93#350—311no—
94C2×C31—21no—
95C2×C31—82no—
96C2×C31#44711yescharacteristic
97D31—41no—
98D31—81no—
99H(5,𝔽2)—621no—
100#137—621no—
101AGL(1,ℤ/8)—621no—
102AGL(1,ℤ/8)—622no—
103#135—311no—
104#135—621no—
105C2×Q16—311no—
106C2×D8—621no—
107C2×D8C2×D3111yescharacteristic
108#131—311no—
109Q32—621no—
110SD32—621no—
111SD32—622no—
112M32C2×D3111yescharacteristic, complemented
113C2×C16—311no—
114#108C2×D3111yescharacteristic, complemented
115#101—621no—
116C31#219411yescharacteristic, complemented, Sylow
117#41—311no—
118#41—622no—
119#41—621no—
120#41—1241no—
121C2×Q8—621no—
122C2×D4—21no—
123C2×D4—622no—
124C2×D4—1241no—
125C2×D4—1242no—
126Q16—311no—
127Q16—621no—
128Q16—621no—
129Q16—1241no—
130SD16—622no—
131SD16—621no—
132SD16—1241no—
133D8—21no—
134D8—311no—
135D8—622no—
136D8D12412yes—
137M16—21no—
138M16—311no—
139M16—621no—
140C2×C8—621no—
141C2×C8C22×D3111yescharacteristic
142C16—21no—
143C16—621no—
144C23—41no—
145C23—1242no—
146Q8—311no—
147Q8—621no—
148Q8—1241no—
149Q8—1241no—
150D4—22no—
151D4—41no—
152D4—311no—
153D4—621no—
154D4—621no—
155D4—1242no—
156D4—1242no—
157D4—1241no—
158C2×C4—621no—
159C2×C4—1242no—
160C2×C4—1241no—
161C2×C4—1241no—
162C2×C4D4×D3111yescharacteristic
163C8—41no—
164C8—621no—
165C8C2×D12411yescharacteristic
166C8D4×D3111yescharacteristic
167C22—42no—
168C22—161no—
169C22—621no—
170C22—1241no—
171C22—4962no—
172C22#1175849111yescharacteristic
173C4—621no—
174C4—1241no—
175C4—2481no—
176C4#1175845911yescharacteristic
177C4D8×D3111yescharacteristic
178C2—21no—
179C2—82no—
180C2—1241no—
181C2—2481no—
182C2#1452118411yescharacteristic
subgroupG/H
centerC2#14521184
commutator, cosocleC2×C8×C31C23
FrattiniC2×C8C22×D31
FittingC31×#361C2
socleC2×C31#447
prime radical#14521850C2
hypercenter#361D31
hypocenterC31#2194
LCSG ▷ C2×C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
2. #14521492C2semidirect
3. C2×#11758415C2semidirect
4. #14521325C2semidirect
5. #14520855C2semidirect
6. #14520834C2semidirect
7. C31×#361C2semidirect
15. C2×Dic124C22semidirect
18. C31×M32C22semidirect
19. C31×#108C22semidirect
22. C2×C31⋊C16C22semidirect
91. #361D31semidirect
112. M32C2×D31semidirect
114. #108C2×D31semidirect
116. C31#2194semidirect

Maximal subgroups

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

subgroupindex
#145218502
#145214922
C2×#117584152
#145213252
#145208552
#145208342
C31×#3612
#219431