Finite Group Databasebeta

← #16858844

Subgroups — #16858844

Order 3968.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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#135×D31C212yesmaximal, complemented
2#14521491C212yesmaximal, complemented
3#14521488C212yesmaximal, complemented
4#14521486C212yesmaximal, complemented
5#14521483C212yesmaximal, complemented
6#14521481C211yesmaximal, characteristic, complemented
7#14521479C212yesmaximal, complemented
8C2×#11758386C211yesmaximal, characteristic, complemented
9C31×#508C211yesmaximal, characteristic, complemented
10#41×D31—22no—
11C31×#135C2212yescomplemented
12#11758527—22no—
13#11758496C2212yes—
14Q16×D31C2212yescomplemented
15#11758493—22no—
16SD16×D31—22no—
17#11758489C2212yes—
18D8×D31C2212yescomplemented
19#11758481C2212yescomplemented
20C2×C8×D31C2211yescharacteristic
21C31×Q32C2211yescharacteristic, complemented
22C31×SD32C2212yescomplemented
23C31×D16C2211yescharacteristic, complemented
24C2×C16×C31C2211yescharacteristic, complemented
25#11758417C2212yescomplemented
26#11758416C2212yescomplemented
27#11758415C2212yescomplemented
28#11758414C2212yescomplemented
29C2×C31⋊C16C2211yescharacteristic, complemented
30Dic248C2211yescharacteristic, complemented
31#11758388C2212yescomplemented
32D496C2211yescharacteristic, complemented
33#11758386C2212yescomplemented
34#11758386C2212yescomplemented
35#41×C31—22no—
36#92499—22no—
37Q8×D31—22no—
38#92497—22no—
39#92497—42no—
40D4×D31—22no—
41D4×D31—42no—
42#92495—22no—
43#92495—42no—
44C2×C4×D31—42no—
45C2×C4×D31D411yescharacteristic
46Q16×C31C2312yes—
47SD16×C31—22no—
48D8×C31C2312yes—
49C2×C8×C31C2311yescharacteristic
50#92482—22no—
51#92481—22no—
52#92480—22no—
53#92479—22no—
54C2×C31⋊C8D411yescharacteristic
55Dic124C2312yes—
56D248C2312yes—
57#92470—22no—
58C8×D31D412yes—
59C8×D31C2312yes—
60C16×C31C2311yescharacteristic
61C16×C31C2311yescharacteristic
62C31⋊C16C2312yes—
63C22×D31—42no—
64C22×D31D811yescharacteristic
65Q8×C31—22no—
66D4×C31—22no—
67D4×C31—42no—
68C2×C4×C31—42no—
69C2×C4×C31C2×D411yescharacteristic
70C22⋊D31—42no—
71C22⋊D31—42no—
72C22⋊D31—42no—
73C2×Dic31—42no—
74C2×Dic31D811yescharacteristic
75D124—22no—
76D124—42no—
77C4×D31—42no—
78C4×D31—42no—
79C4×D31—42no—
80C4×D31D812yes—
81C4×D31C2×D412yes—
82Dic62—22no—
83Dic62—42no—
84C8×C31C2×D411yescharacteristic
85C8×C31C2411yescharacteristic
86C31⋊C8C2×D412yes—
87#3414—311nomaximal, Sylow
88C22×C31—42no—
89C22×C31C2×D811yescharacteristic
90C2×D31—41no—
91C2×D31—42no—
92C2×D31—84no—
93C2×D31C2×D812yes—
94C4×C31—42no—
95C4×C31C2×D811yescharacteristic
96C4×C31C22×D411yescharacteristic
97Dic31—42no—
98Dic31C2×D812yes—
99C2×#135—312no—
100#510—312no—
101#510—312no—
102#509—312no—
103#509—312no—
104#508—312no—
105#508—311no—
106#508D3111yescharacteristic, complemented
107C2×M32—311no—
108C2×C31—21no—
109C2×C31—82no—
110C2×C31C22×D811yescharacteristic
111D31—22no—
112D31—82no—
113C2×#41—622no—
114#135—312no—
115#135—312no—
116#135—312no—
117#135—622no—
118#135—622no—
119#135C2×D3112yescomplemented
120C2×Q16—312no—
121C2×SD16—622no—
122C2×D8—312no—
123C22×C8—311no—
124Q32—312no—
125Q32—311no—
126Q32C2×D3111yescharacteristic, complemented
127SD32—312no—
128SD32—312no—
129SD32—312no—
130SD32C2×D3112yescomplemented
131D16—312no—
132D16—311no—
133D16C2×D3111yescharacteristic, complemented
134M32—312no—
135M32—312no—
136C2×C16—311no—
137C2×C16C2×D3111yescharacteristic, complemented
138C31#341411yescharacteristic, complemented, Sylow
139#41—22no—
140#41—622no—
141#41—622no—
142#41—622no—
143#41—1242no—
144#41—1242no—
145C2×Q8—622no—
146C2×D4—622no—
147C2×D4—1242no—
148C22×C4—311no—
149C22×C4—1242no—
150Q16—312no—
151Q16—622no—
152Q16C22×D3112yes—
153SD16—22no—
154SD16—622no—
155SD16—622no—
156SD16—622no—
157D8—312no—
158D8—622no—
159D8C22×D3112yes—
160C2×C8—311no—
161C2×C8—312no—
162C2×C8—312no—
163C2×C8C22×D3111yescharacteristic
164C16—312no—
165C16C22×D3111yescharacteristic
166C16C22×D3111yescharacteristic
167C23—311no—
168C23—1242no—
169Q8—22no—
170Q8—622no—
171Q8—1242no—
172D4—22no—
173D4—42no—
174D4—622no—
175D4—1242no—
176D4—1242no—
177D4—1242no—
178D4—1242no—
179C2×C4—42no—
180C2×C4—311no—
181C2×C4—312no—
182C2×C4—312no—
183C2×C4—1242no—
184C2×C4—1242no—
185C2×C4—1242no—
186C2×C4—1242no—
187C2×C4D4×D3111yescharacteristic
188C8—312no—
189C8D4×D3111yescharacteristic
190C8C23×D3111yescharacteristic
191C22—42no—
192C22—312no—
193C22—1241no—
194C22—1242no—
195C22—2484no—
196C22D8×D3111yescharacteristic
197C4—42no—
198C4—312no—
199C4—1242no—
200C4D8×D3111yescharacteristic
201C4C2×D4×D3111yescharacteristic
202C2—21no—
203C2—82no—
204C2—622no—
205C2—2482no—
206C2C2×D8×D3111yescharacteristic
subgroupG/H
centerC4D8×D31
commutator, cosocleC8×C31C24
FrattiniC8C23×D31
FittingC31×#508C2
socleC2×C31C22×D8
hypercenter#508D31
hypocenterC31#3414
LCSG ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D31C2semidirect
2. #14521491C2semidirect
3. #14521488C2semidirect
4. #14521486C2semidirect
5. #14521483C2semidirect
6. #14521481C2semidirect
7. #14521479C2semidirect
8. C2×#11758386C2semidirect
9. C31×#508C2semidirect
11. C31×#135C22semidirect
14. Q16×D31C22semidirect
18. D8×D31C22semidirect
19. #11758481C22semidirect
21. C31×Q32C22semidirect
22. C31×SD32C22semidirect
23. C31×D16C22semidirect
24. C2×C16×C31C22semidirect
25. #11758417C22semidirect
26. #11758416C22semidirect
27. #11758415C22semidirect
28. #11758414C22semidirect
29. C2×C31⋊C16C22semidirect
30. Dic248C22semidirect
31. #11758388C22semidirect
32. D496C22semidirect
33. #11758386C22semidirect
34. #11758386C22semidirect
106. #508D31semidirect
119. #135C2×D31semidirect
126. Q32C2×D31semidirect
130. SD32C2×D31semidirect
133. D16C2×D31semidirect
137. C2×C16C2×D31semidirect
138. C31#3414semidirect

Maximal subgroups

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

subgroupindex
#135×D312
#145214912
#145214882
#145214862
#145214832
#145214812
#145214792
C2×#117583862
C31×#5082
#341431