Finite Group Databasebeta

← #19135727

Subgroups — #19135727

Order 5504.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#14583461C211yesmaximal, characteristic
2C2×#13063309C212yesmaximal, complemented
3C2×#13063239C212yesmaximal, complemented
4#14582760C211yesmaximal, characteristic, complemented
5C43×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D43C2212yes—
7C23×Dic43C2211yescharacteristic
8#13063309—22no—
9#13063309—24no—
10#13063309—24no—
11#13063299—22no—
12#13063295—22no—
13C2×C4⋊Dic43—22no—
14C2×C22⋊Dic43C2211yescharacteristic
15C2×(C2×D43)⋊C4—22no—
16#13063239—24no—
17C43⋊#95—22no—
18C2×C22⋊C4×C43C2211yescharacteristic
19C2×C22⋊C4×C43C2212yes—
20C24×C43C2311yescharacteristic
21C23×D43D412yes—
22C22×C4×C43—22no—
23C22×C4×C43D412yes—
24C2×C22⋊D43—22no—
25C2×C22⋊D43—22no—
26C2×C22⋊D43—22no—
27C2×C22⋊D43—22no—
28C2×C22⋊D43—22no—
29C2×C22⋊D43—22no—
30C22×Dic43—21no—
31C22×Dic43—22no—
32C22×Dic43—22no—
33C22×Dic43—21no—
34C22×Dic43—21no—
35C22×Dic43D412yes—
36C22×Dic43D412yescomplemented
37C2×D172—22no—
38C22⋊C4×C43—22no—
39C22⋊C4×C43—22no—
40C22⋊C4×C43D414yescomplemented
41C22⋊Dic43—22no—
42(C2×D43)⋊C4—28no—
43(C2×D43)⋊C4—24no—
44C4⋊Dic43—28no—
45C4⋊Dic43—22no—
46C23×C43—42no—
47C23×C43C2×D411yescharacteristic
48C23×C43C2×D412yes—
49C23×C43C2×D412yes—
50C23×C43C2×D411yescharacteristic
51C23×C43#4111yescharacteristic
52C22×D43—22no—
53C22×D43—22no—
54C22×D43—22no—
55C22×D43—44no—
56C2×C4×C43—24no—
57C2×C4×C43—22no—
58C2×C4×C43—44no—
59C2×C4×C43—42no—
60C22⋊D43—42no—
61C22⋊D43—42no—
62C22⋊D43—42no—
63C22⋊D43—42no—
64C2×Dic43—22no—
65C2×Dic43—24no—
66C2×Dic43—22no—
67C2×Dic43—22no—
68C2×Dic43—22no—
69C2×Dic43—41no—
70C2×Dic43—42no—
71C2×Dic43—41no—
72C2×Dic43—42no—
73C2×Dic43—41no—
74D172—82no—
75C22×C43—24no—
76C22×C43—22no—
77C22×C43—42no—
78C22×C43—41no—
79C22×C43—41no—
80C22×C43#12012yes—
81C22×C43#12011yescharacteristic
82C22×C43#12112yes—
83C22×C43#12111yescharacteristic
84C22×C43#12711yescharacteristic
85C2×D43—44no—
86C2×D43—42no—
87C2×D43—44no—
88C2×D43—82no—
89C4×C43—44no—
90C4×C43—42no—
91Dic43—42no—
92Dic43—42no—
93Dic43—81no—
94#2022—431nomaximal, Sylow
95C2×C43—21no—
96C2×C43—22no—
97C2×C43—22no—
98C2×C43—21no—
99C2×C43#39211yescharacteristic
100C2×C43#45812yes—
101D43—82no—
102#534—431no—
103C2×#123—432no—
104C2×#99—432no—
105#381—431no—
106#342D4311yescharacteristic, complemented
107C43#202211yescharacteristic, complemented, Sylow
108C22×D4—432no—
109C23×C4—431no—
110#123—864no—
111#123—862no—
112#123—864no—
113#121—862no—
114#120—862no—
115C2×C4⋊C4—862no—
116C2×C22⋊C4—431no—
117C2×C22⋊C4—862no—
118C2×C22⋊C4C2×D4311yescharacteristic
119C2×C22⋊C4C2×D4312yes—
120#99—864no—
121#95—862no—
122C24—432no—
123C24C22×D4311yescharacteristic
124C2×D4—862no—
125C2×D4—862no—
126C2×D4—862no—
127C2×D4—862no—
128C2×D4—862no—
129C2×D4—862no—
130C2×D4—862no—
131C22×C4—22no—
132C22×C4—432no—
133C22×C4—432no—
134C22×C4—861no—
135C22×C4—862no—
136C22×C4—862no—
137C22×C4—861no—
138C22×C4—861no—
139C22×C4D17212yes—
140C4⋊C4—868no—
141C4⋊C4—862no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—868no—
145C22⋊C4—864no—
146C22⋊C4—862no—
147C22⋊C4D17214yescomplemented
148C23—42no—
149C23—862no—
150C23—862no—
151C23—862no—
152C23—1724no—
153C23C2×D17211yescharacteristic
154C23C2×D17212yes—
155C23D4×D4312yes—
156C23D4×D4311yescharacteristic
157C23#1062190211yescharacteristic
158D4—3442no—
159D4—1722no—
160D4—1722no—
161D4—1722no—
162D4—1722no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—864no—
168C2×C4—862no—
169C2×C4—862no—
170C2×C4—862no—
171C2×C4—862no—
172C2×C4—1722no—
173C2×C4—1721no—
174C2×C4—1721no—
175C2×C4—1722no—
176C2×C4—1721no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—3442no—
183C22—1724no—
184C22—1722no—
185C22—1724no—
186C22#1306329512yes—
187C22#1306329511yescharacteristic
188C22#1306330011yescharacteristic
189C22#1306330012yes—
190C22#1306332211yescharacteristic
191C4—44no—
192C4—42no—
193C4—3441no—
194C4—1722no—
195C4—1722no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—3442no—
201C2#1458280911yescharacteristic
202C2#1458309012yes—
subgroupG/H
centerC22#13063295
commutatorC24×C43C23
FrattiniC24C22×D43
FittingC43×#342C2
socleC22×C43#120
hypercenter#342D43
hypocenterC43#2022
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#13063309C2semidirect
3. C2×#13063239C2semidirect
4. #14582760C2semidirect
5. C43×#342C2semidirect
36. C22×Dic43D4semidirect
40. C22⋊C4×C43D4semidirect
106. #342D43semidirect
107. C43#2022semidirect
147. C22⋊C4D172semidirect