Finite Group Databasebeta

← #19133532

Subgroups — #19133532

Order 5504.

310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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#14583480C211yesmaximal, characteristic, complemented
2#14583035C212yesmaximal, complemented
3#14582816C211yesmaximal, characteristic, complemented
4#14582634C212yesmaximal, complemented
5C43×#324C211yesmaximal, characteristic, complemented
6C2×#10621898—21no—
7C22×D172C2211yescharacteristic
8C2×D344—22no—
9#13063305—22no—
10#13063300—22no—
11#13063299—21no—
12#13063299C2212yes—
13C2×(C2×D43)⋊C4—21no—
14C2×(C2×D43)⋊C4—21no—
15#13063247—22no—
16C43⋊#95C2211yescharacteristic
17C2×C4⋊C4×C43C2211yescharacteristic
18C22⋊C8×C43C2212yes—
19C23×D43—21no—
20C22×C4×C43D411yescharacteristic
21C22×C4×C43D411yescharacteristic
22C22×C4×C43C2311yescharacteristic
23C2×C22⋊D43—22no—
24C22×Dic43—21no—
25#10621898—42no—
26#10621898—42no—
27C2×D172—21no—
28C2×D172—21no—
29C2×D172—22no—
30C2×D172—42no—
31C2×D172D412yes—
32C2×C4×D43—22no—
33C2×Dic86—21no—
34C2×C8×C43—22no—
35C4⋊C4×C43—22no—
36(C2×D43)⋊C4—22no—
37(C2×D43)⋊C4—22no—
38(C2×D43)⋊C4—42no—
39(C2×D43)⋊C4—42no—
40C4⋊Dic43—21no—
41C4⋊Dic43D412yes—
42D344—44no—
43C23×C43C2×D411yescharacteristic
44C22×D43—22no—
45C22×D43—22no—
46C22×D43—41no—
47C22×D43—41no—
48C22×D43—41no—
49C22×D43—41no—
50C22×D43—41no—
51C22×D43—41no—
52C2×C4×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—21no—
55C2×C4×C43—41no—
56C2×C4×C43—41no—
57C2×C4×C43D812yescomplemented
58C2×C4×C43C2×D412yes—
59C22⋊D43—42no—
60C22⋊D43—42no—
61C2×Dic43—22no—
62C2×Dic43—41no—
63C2×Dic43—41no—
64C2×Dic43—41no—
65D172—24no—
66D172—42no—
67D172—42no—
68D172—42no—
69D172—81no—
70C4×D43—44no—
71Dic86—42no—
72C8×C43—42no—
73C22×C43—21no—
74C22×C43—21no—
75C22×C43#12011yescharacteristic
76C22×C43C2×D811yescharacteristic
77C22×C43AGL(1,ℤ/8)11yescharacteristic
78C2×D43—42no—
79C2×D43—42no—
80C2×D43—42no—
81C2×D43—42no—
82C2×D43—42no—
83C2×D43—42no—
84C2×D43—81no—
85C2×D43—81no—
86C2×D43—81no—
87C2×D43—81no—
88C4×C43—22no—
89C4×C43—22no—
90C4×C43—41no—
91Dic43—42no—
92Dic43—81no—
93#1598—431nomaximal, Sylow
94C2×C43—21no—
95C2×C43—21no—
96C2×C43#44711yescharacteristic
97C2×C43#45411yescharacteristic
98C2×C43B(4,𝔽2)11yescharacteristic
99D43—82no—
100D43—82no—
101#537—431no—
102#447—432no—
103#394—431no—
104#327—432no—
105#324D4311yescharacteristic, complemented
106C43#159811yescharacteristic, complemented, Sylow
107C2×#41—861no—
108C22×D4—431no—
109C2×D8—862no—
110C22⋊Q8—862no—
111#121—432no—
112#121—862no—
113#121—861no—
114C2×C4⋊C4C2×D4311yescharacteristic
115C2×C22⋊C4—861no—
116C2×C22⋊C4—861no—
117#102—862no—
118C22⋊C8C2×D4312yes—
119#95—431no—
120C24—861no—
121#41—1722no—
122#41—1722no—
123C2×Q8—861no—
124C2×D4—432no—
125C2×D4—861no—
126C2×D4—861no—
127C2×D4—862no—
128C2×D4—862no—
129C2×D4—1722no—
130C22×C4—862no—
131C22×C4—861no—
132C22×C4D17211yescharacteristic
133C22×C4D17211yescharacteristic
134C22×C4C22×D4311yescharacteristic
135D8—1724no—
136C2×C8—22no—
137C4⋊C4—22no—
138C4⋊C4—432no—
139C4⋊C4—861no—
140C22⋊C4—862no—
141C22⋊C4—862no—
142C22⋊C4—1722no—
143C22⋊C4—1722no—
144C23—862no—
145C23—862no—
146C23—1721no—
147C23—1721no—
148C23—1721no—
149C23—1721no—
150C23—1721no—
151C23—1721no—
152C23C2×D17211yescharacteristic
153Q8—1722no—
154D4—864no—
155D4—3441no—
156D4—1722no—
157D4—1722no—
158D4—1722no—
159D4—1722no—
160D4—1722no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—862no—
167C2×C4—1724no—
168C2×C4—1721no—
169C2×C4—1721no—
170C2×C4—1721no—
171C2×C4D34412yescomplemented
172C2×C4D4×D4312yes—
173C8—42no—
174C22—21no—
175C22—21no—
176C22—3441no—
177C22—3441no—
178C22—3441no—
179C22—3441no—
180C22—1722no—
181C22—1722no—
182C22—1722no—
183C22—1722no—
184C22—1722no—
185C22—1722no—
186C22#1306329511yescharacteristic
187C22C2×D34411yescharacteristic
188C22#1306335311yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—3441no—
193C4—1722no—
194C2—21no—
195C2—21no—
196C2—3442no—
197C2—3442no—
198C2#1458303511yescharacteristic
199C2#1458307411yescharacteristic
200C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#324C2
socleC22×C43#120
hypercenter#324D43
hypocenterC43#1598
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
1. #14583480C2semidirect
2. #14583035C2semidirect
3. #14582816C2semidirect
4. #14582634C2semidirect
5. C43×#324C2semidirect
57. C2×C4×C43D8semidirect
105. #324D43semidirect
106. C43#1598semidirect
171. C2×C4D344semidirect