Finite Group Databasebeta

← #19144075

Subgroups — #19144075

Order 5504.

584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#13063350C212yesmaximal, complemented
2C2×#13063322C211yesmaximal, characteristic, complemented
3#14583099C214yesmaximal, complemented
4#14583094C214yesmaximal, complemented
5#14582923C211yesmaximal, characteristic, complemented
6#14582903C212yesmaximal, complemented
7C4×#41×C43C211yesmaximal, characteristic, complemented
8C22×D172—22no—
9C22×D172C2212yes—
10#13063350—28no—
11C2×#10621884C2214yescomplemented
12C2×#10621882C2214yescomplemented
13C2×#10621877C2212yes—
14#13063322—21no—
15#13063322—21no—
16#13063322C2214yes—
17C4⋊(C43⋊C8)C2214yescomplemented
18#13063245C2218yescomplemented
19C2×#41×C43C2211yescharacteristic
20C4×Q8×C43C2212yescomplemented
21C4×D4×C43—22no—
22C4×D4×C43C2212yescomplemented
23#117×C43—21no—
24#117×C43C2211yescharacteristic
25C2×C42×C43—21no—
26C2×C42×C43C2211yescharacteristic
27C23×D43—22no—
28#41×C43—22no—
29#41×C43D414yescomplemented
30C2×Q8×C43C2311yescharacteristic
31C2×D4×C43—21no—
32C2×D4×C43C2311yescharacteristic
33C22×C4×C43—21no—
34C22×C4×C43—22no—
35C22×C4×C43D412yes—
36C22×C4×C43C2311yescharacteristic
37C2×D172—22no—
38C2×D172—24no—
39C2×D172—24no—
40C2×D172—24no—
41C2×D172—24no—
42C2×D172—48no—
43C2×D172C2314yes—
44C4⋊C4×C43—22no—
45C4⋊C4×C43C2312yes—
46C22⋊C4×C43—22no—
47C22⋊C4×C43—21no—
48C42×C43—21no—
49C42×C43—22no—
50C42×C43D411yescharacteristic
51C42×C43D411yescharacteristic
52C42×C43C2312yes—
53#10621884—28no—
54#10621882—28no—
55#10621877—24no—
56C2×C43⋊C8C2314yes—
57C23×C43—21no—
58C23×C43C2×D411yescharacteristic
59C22×D43—24no—
60C22×D43—48no—
61C22×D43—44no—
62Q8×C43—21no—
63Q8×C43C2×D412yescomplemented
64D4×C43—24no—
65D4×C43—21no—
66D4×C43C2×D412yescomplemented
67C2×C4×C43—21no—
68C2×C4×C43—24no—
69C2×C4×C43—24no—
70C2×C4×C43—22no—
71C2×C4×C43—44no—
72C2×C4×C43C2×D412yes—
73C2×C4×C43C2×D412yes—
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2×D412yes—
76C2×C4×C43#4112yes—
77C2×C4×C43C2411yescharacteristic
78D172—24no—
79D172—24no—
80D172—48no—
81D172—44no—
82D172—48no—
83C43⋊C8—24no—
84C22×C43—22no—
85C22×C43—22no—
86C22×C43—42no—
87C22×C43#12112yes—
88C22×C43C22×D411yescharacteristic
89C2×D43—44no—
90C2×D43—48no—
91C2×D43—88no—
92C4×C43—22no—
93C4×C43—22no—
94C4×C43—42no—
95C4×C43#12112yes—
96C4×C43AGL(1,ℤ/8)14yescomplemented
97C4×C43C22×D411yescharacteristic
98C4×C43C2×#4111yescharacteristic
99#3038—431nomaximal, Sylow
100C2×C43—22no—
101C2×C43—42no—
102C2×C43C2×#12111yescharacteristic
103C2×C43C2×AGL(1,ℤ/8)12yes—
104D43—84no—
105C2×AGL(1,ℤ/8)—432no—
106C2×#127—431no—
107C4×#41D4311yescharacteristic, complemented
108#460—434no—
109#459—434no—
110#423—431no—
111#418—432no—
112C43#303811yescharacteristic, complemented, Sylow
113C2×#41C2×D4311yescharacteristic
114C22×D4—432no—
115C22×D4—862no—
116AGL(1,ℤ/8)—868no—
117C2×SD16—434no—
118C2×D8—434no—
119C2×M16—432no—
120#127—434no—
121#127—861no—
122#127—861no—
123C4×Q8C2×D4312yescomplemented
124C4×D4—22no—
125C4×D4C2×D4312yescomplemented
126#117—21no—
127#117C2×D4311yescharacteristic
128C2×C42—21no—
129C2×C42C2×D4311yescharacteristic
130C4⋊C8—434no—
131#102—438no—
132C24—862no—
133#41—22no—
134#41D17214yescomplemented
135C2×Q8C22×D4311yescharacteristic
136C2×D4—21no—
137C2×D4—434no—
138C2×D4—864no—
139C2×D4—864no—
140C2×D4—864no—
141C2×D4—864no—
142C2×D4—862no—
143C2×D4—1728no—
144C2×D4C22×D4311yescharacteristic
145C22×C4—21no—
146C22×C4—22no—
147C22×C4C22⋊D4312yes—
148C22×C4C22×D4311yescharacteristic
149SD16—868no—
150D8—868no—
151M16—864no—
152C2×C8—434no—
153C4⋊C4—22no—
154C4⋊C4C22×D4312yes—
155C22⋊C4—21no—
156C22⋊C4—22no—
157C42—21no—
158C42—22no—
159C42C22⋊D4311yescharacteristic
160C42C22⋊D4311yescharacteristic
161C42C22×D4312yes—
162C23—21no—
163C23—864no—
164C23—1728no—
165C23—1724no—
166C23C2×C22⋊D4311yescharacteristic
167Q8—21no—
168Q8C2×D17212yescomplemented
169D4—24no—
170D4—21no—
171D4—864no—
172D4—864no—
173D4—1728no—
174D4—1724no—
175D4—1728no—
176D4C2×D17212yescomplemented
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—44no—
182C2×C4C2×D17212yes—
183C2×C4#1062189812yes—
184C2×C4C2×C22⋊D4312yes—
185C2×C4C2×C22⋊D4311yescharacteristic
186C2×C4C2×C22⋊D4312yes—
187C2×C4C23×D4311yescharacteristic
188C8—864no—
189C22—22no—
190C22—22no—
191C22—42no—
192C22—3448no—
193C22—1724no—
194C22—1728no—
195C22#1306329912yes—
196C22C22×C22⋊D4311yescharacteristic
197C4—22no—
198C4—22no—
199C4—42no—
200C4#1306329912yes—
201C4#1306335014yescomplemented
202C4C22×D17211yescharacteristic
203C4C2×#1062189811yescharacteristic
204C2—22no—
205C2—42no—
206C2—3444no—
207C2C2×#1306329911yescharacteristic
208C2C2×#1306335012yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC4×#41×C43C2
socleC22×C43C22×D4
hypercenterC4×#41D43
hypocenterC43#3038
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13063350C2semidirect
2. C2×#13063322C2semidirect
3. #14583099C2semidirect
4. #14583094C2semidirect
5. #14582923C2semidirect
6. #14582903C2semidirect
7. C4×#41×C43C2semidirect
11. C2×#10621884C22semidirect
12. C2×#10621882C22semidirect
17. C4⋊(C43⋊C8)C22semidirect
18. #13063245C22semidirect
20. C4×Q8×C43C22semidirect
22. C4×D4×C43C22semidirect
29. #41×C43D4semidirect
63. Q8×C43C2×D4semidirect
66. D4×C43C2×D4semidirect
96. C4×C43AGL(1,ℤ/8)semidirect
107. C4×#41D43semidirect
112. C43#3038semidirect
123. C4×Q8C2×D43semidirect
125. C4×D4C2×D43semidirect
134. #41D172semidirect
168. Q8C2×D172semidirect
176. D4C2×D172semidirect
201. C4#13063350semidirect