Finite Group Databasebeta

← #16855955

Subgroups — #16855955

Order 3968.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#14521654C211yesmaximal, characteristic, complemented
2#14521523C211yesmaximal, characteristic, complemented
3#14521374C212yesmaximal, complemented
4#14521350C212yesmaximal, complemented
5#14521245C212yesmaximal, complemented
6#14521185C212yesmaximal, complemented
7#14521162C212yesmaximal, complemented
8C4×D248C212yesmaximal, complemented
9C31×#433C211yesmaximal, characteristic, complemented
10C22×D124C2211yescharacteristic
11C31×#117C2211yescharacteristic
12#11758507C2212yes—
13#11758503C2211yescharacteristic
14C2×D248C2212yes—
15C2×D248C2212yes—
16#11758471—22no—
17#11758470—22no—
18#11758461—22no—
19C22⋊C4×D31—22no—
20#11758451C2211yescharacteristic, complemented
21C4×D124C2212yes—
22C4×D124C2212yes—
23C4×D124C2212yescomplemented
24#11758447C2211yescharacteristic, complemented
25C31×C4⋊C8C2212yescomplemented
26C31×C22⋊C8C2212yes—
27C31×#97C2211yescharacteristic, complemented
28C4×C8×C31C2211yescharacteristic, complemented
29#11758409C2212yes—
30#11758409C2212yes—
31#11758409C2212yescomplemented
32#11758409C2212yescomplemented
33#11758406C2212yescomplemented
34#11758405C2212yescomplemented
35C23×D31—21no—
36C22×C4×C31C2311yescharacteristic
37C2×C22⋊D31—22no—
38C2×D124—21no—
39C2×D124—24no—
40C2×D124—22no—
41C2×D124C2312yes—
42C2×D124C2312yes—
43C2×C4×D31—22no—
44C2×C4×D31—22no—
45C2×C4×D31—22no—
46C2×C8×C31C2312yes—
47C2×C8×C31C2312yes—
48C4⋊C4×C31D412yes—
49C22⋊C4×C31D412yes—
50C42×C31C2311yescharacteristic
51C42×C31C2311yescharacteristic
52C22⋊Dic31—21no—
53(C2×D31)⋊C4—22no—
54(C2×D31)⋊C4—22no—
55(C2×D31)⋊C4—22no—
56(C2×D31)⋊C4—22no—
57C4⋊Dic31C2312yes—
58C4⋊Dic31C2312yes—
59Dic31⋊C4—22no—
60C4×Dic31—21no—
61D248—24no—
62D248—24no—
63C23×C31C2×D411yescharacteristic
64C22×D31—22no—
65C22×D31—24no—
66C22×D31—22no—
67C22×D31—82no—
68C2×C4×C31—22no—
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31C2×D412yes—
71C2×C4×C31C2×D412yes—
72C2×C4×C31C2411yescharacteristic
73C22⋊D31—82no—
74C2×Dic31—22no—
75C2×Dic31—22no—
76D124—24no—
77D124—22no—
78D124—22no—
79D124—22no—
80D124—82no—
81D124#4114yes—
82C4×D31—82no—
83C4×D31—82no—
84C4×D31—82no—
85C8×C31—22no—
86C8×C31—22no—
87#3122—311nomaximal, Sylow
88C22×C31—21no—
89C22×C31—22no—
90C22×C31C22×D411yescharacteristic
91C2×D31—24no—
92C2×D31—42no—
93C2×D31—42no—
94C2×D31—42no—
95C2×D31—42no—
96C2×D31—42no—
97C2×D31—84no—
98C4×C31—21no—
99C4×C31—22no—
100C4×C31—22no—
101C4×C31C2×#4112yes—
102Dic31—42no—
103Dic31—42no—
104#540—311no—
105#518—311no—
106#482—312no—
107#478—312no—
108#459—312no—
109#447—312no—
110#442—312no—
111C4×D8—312no—
112#433D3111yescharacteristic, complemented
113C2×C31—41no—
114C2×C31#52511yescharacteristic
115C2×C31#57612yes—
116D31—44no—
117D31—82no—
118C22×D4—311no—
119C2×D8—312no—
120C2×D8—312no—
121#127—311no—
122#125—311no—
123#123—622no—
124#121—312no—
125#121—622no—
126C4×D4—312no—
127C4×D4—312no—
128C4×D4—312no—
129C4×D4—622no—
130#117—311no—
131#117C2×D3111yescharacteristic
132C2×C22⋊C4—622no—
133#107—312no—
134#106—312no—
135C4⋊C8C2×D3112yescomplemented
136#102—312no—
137#102—312no—
138#102—312no—
139#102—312no—
140C22⋊C8C2×D3112yes—
141#97C2×D3111yescharacteristic, complemented
142C4×C8C2×D3111yescharacteristic, complemented
143C31#312211yescharacteristic, complemented, Sylow
144C24—621no—
145C2×D4—312no—
146C2×D4—312no—
147C2×D4—624no—
148C2×D4—622no—
149C2×D4—621no—
150C2×D4—622no—
151C22×C4—622no—
152C22×C4—622no—
153C22×C4—622no—
154C22×C4C22×D3111yescharacteristic
155D8—624no—
156D8—624no—
157C2×C8C22×D3112yes—
158C2×C8C22×D3112yes—
159C4⋊C4—312no—
160C4⋊C4—312no—
161C4⋊C4—622no—
162C4⋊C4D12412yes—
163C22⋊C4—621no—
164C22⋊C4—622no—
165C22⋊C4—622no—
166C22⋊C4—622no—
167C22⋊C4—622no—
168C22⋊C4D12412yes—
169C42—621no—
170C42C22×D3111yescharacteristic
171C42C22×D3111yescharacteristic
172C23—624no—
173C23—622no—
174C23—622no—
175C23—2482no—
176C23C2×D12411yescharacteristic
177D4—314no—
178D4—624no—
179D4—622no—
180D4—622no—
181D4—622no—
182D4—2482no—
183D4—2482no—
184C2×C4—22no—
185C2×C4—622no—
186C2×C4—622no—
187C2×C4—2482no—
188C2×C4—2482no—
189C2×C4—2482no—
190C2×C4C2×D12411yescharacteristic
191C2×C4C2×D12412yes—
192C2×C4C2×D12412yes—
193C2×C4C23×D3111yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—624no—
199C22—1242no—
200C22—1242no—
201C22—1242no—
202C22—1242no—
203C22—1242no—
204C22—2484no—
205C22C22×D12411yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—1242no—
210C4—1242no—
211C4#41×D3112yes—
212C2—41no—
213C2—1244no—
214C2—2482no—
215C2#1452156111yescharacteristic
216C2#1452185412yes—
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#433C2
socleC22×C31C22×D4
hypercenter#433D31
hypocenterC31#3122
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14521654C2semidirect
2. #14521523C2semidirect
3. #14521374C2semidirect
4. #14521350C2semidirect
5. #14521245C2semidirect
6. #14521185C2semidirect
7. #14521162C2semidirect
8. C4×D248C2semidirect
9. C31×#433C2semidirect
20. #11758451C22semidirect
23. C4×D124C22semidirect
24. #11758447C22semidirect
25. C31×C4⋊C8C22semidirect
27. C31×#97C22semidirect
28. C4×C8×C31C22semidirect
31. #11758409C22semidirect
32. #11758409C22semidirect
33. #11758406C22semidirect
34. #11758405C22semidirect
112. #433D31semidirect
135. C4⋊C8C2×D31semidirect
141. #97C2×D31semidirect
142. C4×C8C2×D31semidirect
143. C31#3122semidirect

Maximal subgroups

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

subgroupindex
#145216542
#145215232
#145213742
#145213502
#145212452
#145211852
#145211622
C4×D2482
C31×#4332
#312231