Finite Group Databasebeta

← #19133662

Subgroups — #19133662

Order 5504.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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#14583571C211yesmaximal, characteristic, complemented
2#14583276C211yesmaximal, characteristic, complemented
3#14583099C211yesmaximal, characteristic, complemented
4#14583095C211yesmaximal, characteristic, complemented
5#14582642C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic, complemented
7C43×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10621902—21no—
9C2×#10621884—21no—
10C2×D344—21no—
11C2×D344—22no—
12#13063322—21no—
13#13063322C2211yescharacteristic
14#13063322C2211yescharacteristic
15#13063300—22no—
16#13063300—21no—
17C4×D172—21no—
18C4×D172C2211yescharacteristic
19C4⋊(C43⋊C8)C2211yescharacteristic
20#13063247—21no—
21#13063245—21no—
22C4×Q8×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4×C8×C43C2211yescharacteristic
25C2×Q8×C43D411yescharacteristic
26#10621902—42no—
27#10621902—42no—
28C2×D172—22no—
29C2×D172—21no—
30C2×D172—21no—
31C2×D172—22no—
32C2×D172—21no—
33C2×D172—21no—
34C2×D172—21no—
35C2×D172D411yescharacteristic
36C2×D172D412yes—
37C2×C4×D43—22no—
38C2×C4×D43—21no—
39C2×C8×C43—21no—
40C2×C8×C43—21no—
41C4⋊C4×C43—21no—
42C4⋊C4×C43D411yescharacteristic
43C42×C43—21no—
44C42×C43C2311yescharacteristic
45#10621884—42no—
46(C2×D43)⋊C4—22no—
47(C2×D43)⋊C4—21no—
48C4⋊Dic43D411yescharacteristic
49C2×C43⋊C8—21no—
50D344—44no—
51D344—42no—
52C22×D43—21no—
53C22×D43—22no—
54C22×D43—41no—
55Q8×C43—21no—
56Q8×C43D812yescomplemented
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43C2×D411yescharacteristic
60C2×C4×C43C2×D411yescharacteristic
61C2×C4×C43C2×D411yescharacteristic
62C2×Dic43—21no—
63D172—21no—
64D172—21no—
65D172—42no—
66D172—44no—
67D172—42no—
68D172—41no—
69D172—41no—
70D172—41no—
71D172—41no—
72D172—41no—
73D172—41no—
74D172—41no—
75D172—41no—
76D172—82no—
77C4×D43—44no—
78C4×D43—41no—
79C4×D43—41no—
80C8×C43—22no—
81C8×C43—41no—
82C43⋊C8—41no—
83C22×C43#12011yescharacteristic
84C2×D43—42no—
85C2×D43—41no—
86C2×D43—41no—
87C2×D43—42no—
88C2×D43—42no—
89C2×D43—41no—
90C2×D43—81no—
91C2×D43—81no—
92C2×D43—81no—
93C4×C43—22no—
94C4×C43—21no—
95C4×C43—41no—
96C4×C43C2×D811yescharacteristic
97C4×C43#13511yescharacteristic
98C4×C43AGL(1,ℤ/8)11yescharacteristic
99C4×C43AGL(1,ℤ/8)11yescharacteristic
100Dic43—41no—
101#1621—431nomaximal, Sylow
102C2×C43#44711yescharacteristic
103C2×C43#44911yescharacteristic
104C2×C43#45311yescharacteristic
105D43—81no—
106D43—82no—
107D43—161no—
108#550—431no—
109#493—431no—
110#460—431no—
111#459—431no—
112#331—431no—
113Q8⋊C8D4311yescharacteristic, complemented
114D4⋊C8—431no—
115C43#162111yescharacteristic, complemented, Sylow
116C2×#41—861no—
117C2×SD16—861no—
118C2×D8—861no—
119C2×D8—862no—
120#127—431no—
121#127—431no—
122#127—861no—
123#121—862no—
124#121—861no—
125C4×Q8C2×D4311yescharacteristic
126C4×D4—431no—
127C4×D4—861no—
128C4⋊C8—431no—
129C4⋊C8C2×D4311yescharacteristic
130#102—861no—
131#102—861no—
132C4×C8C2×D4311yescharacteristic
133#41—1722no—
134#41—1722no—
135C2×Q8D17211yescharacteristic
136C2×D4—431no—
137C2×D4—432no—
138C2×D4—862no—
139C2×D4—862no—
140C2×D4—861no—
141C2×D4—861no—
142C2×D4—861no—
143C2×D4—861no—
144C2×D4—861no—
145C22×C4—862no—
146C22×C4—861no—
147SD16—1722no—
148D8—1724no—
149D8—1722no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—861no—
153C4⋊C4—21no—
154C4⋊C4—431no—
155C4⋊C4D17211yescharacteristic
156C22⋊C4—862no—
157C22⋊C4—861no—
158C42—21no—
159C42C22×D4311yescharacteristic
160C23—861no—
161C23—862no—
162C23—1721no—
163Q8—21no—
164Q8D34412yescomplemented
165D4—861no—
166D4—861no—
167D4—3442no—
168D4—1722no—
169D4—1722no—
170D4—1724no—
171D4—1721no—
172D4—1721no—
173D4—1721no—
174D4—1721no—
175D4—1721no—
176D4—1721no—
177D4—1721no—
178D4—1721no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—861no—
182C2×C4—1724no—
183C2×C4—1721no—
184C2×C4—1721no—
185C2×C4C2×D17211yescharacteristic
186C2×C4D4×D4311yescharacteristic
187C2×C4D4×D4311yescharacteristic
188C8—22no—
189C8—41no—
190C8—1721no—
191C22—3441no—
192C22—3441no—
193C22—3441no—
194C22—1721no—
195C22—1722no—
196C22—1721no—
197C22—1722no—
198C22—1722no—
199C22—1721no—
200C22#1306329511yescharacteristic
201C4—21no—
202C4—22no—
203C4—41no—
204C4—1721no—
205C4C2×D34411yescharacteristic
206C4#1306334811yescharacteristic
207C4#1306335211yescharacteristic
208C4#1306335311yescharacteristic
209C2—3441no—
210C2—3442no—
211C2—6881no—
212C2#1458303511yescharacteristic
213C2#1458304711yescharacteristic
214C2#1458306811yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×Q8⋊C8C2
socleC22×C43#120
hypercenterQ8⋊C8D43
hypocenterC43#1621
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #14583571C2semidirect
2. #14583276C2semidirect
3. #14583099C2semidirect
4. #14583095C2semidirect
5. #14582642C2semidirect
6. #14582628C2semidirect
7. C43×Q8⋊C8C2semidirect
56. Q8×C43D8semidirect
113. Q8⋊C8D43semidirect
115. C43#1621semidirect
164. Q8D344semidirect