Finite Group Databasebeta

← #19135636

Subgroups — #19135636

Order 5504.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13063351C212yesmaximal, complemented
2#14583480C211yesmaximal, characteristic, complemented
3C2×#13063253C212yesmaximal, complemented
4#14582668C211yesmaximal, characteristic, complemented
5C43×#390C211yesmaximal, characteristic, complemented
6C2×#10621898C2212yes—
7#13063351—24no—
8#13063351—24no—
9C2×#10621883—22no—
10C2×#10621882—22no—
11C2×#10621877C2212yes—
12#13063305—22no—
13#13063300—22no—
14#13063299—22no—
15#13063253—24no—
16C22×D4×C43C2211yescharacteristic
17C2×C4⋊C4×C43C2211yescharacteristic
18C2×C22⋊C4×C43—22no—
19C2×C42×C43C2211yescharacteristic
20C24×C43—21no—
21C2×D4×C43—21no—
22C2×D4×C43—22no—
23C2×D4×C43—22no—
24C2×D4×C43D412yescomplemented
25C22×C4×C43—21no—
26C22×C4×C43D412yes—
27C22×C4×C43C2311yescharacteristic
28C2×C22⋊D43—22no—
29#10621898—22no—
30#10621898—22no—
31#10621898—22no—
32#10621898—22no—
33C2×D172—22no—
34C2×D172D412yes—
35C2×C4×D43—22no—
36C2×Dic86D412yes—
37C4⋊C4×C43—22no—
38C22⋊C4×C43—44no—
39C42×C43—22no—
40#10621883—28no—
41#10621882—28no—
42(C2×D43)⋊C4—24no—
43C4⋊Dic43—22no—
44#10621877—22no—
45#10621877D414yescomplemented
46C2×C43⋊C8—22no—
47C23×C43—22no—
48C23×C43—42no—
49C23×C43—42no—
50C23×C43—41no—
51C23×C43—41no—
52C23×C43C2×D411yescharacteristic
53C22×D43—22no—
54D4×C43—24no—
55D4×C43—42no—
56C2×C4×C43—22no—
57C2×C4×C43—22no—
58C2×C4×C43—41no—
59C2×C4×C43—41no—
60C2×C4×C43—42no—
61C2×C4×C43C2×D411yescharacteristic
62C2×C4×C43C2×D412yes—
63C2×C4×C43C2×D412yes—
64C2×C4×C43#4111yescharacteristic
65C22⋊D43—42no—
66C22⋊D43—42no—
67C2×Dic43—22no—
68D172—22no—
69D172—22no—
70D172—82no—
71C4×D43—42no—
72C4×D43—42no—
73Dic86—22no—
74Dic86—22no—
75C43⋊C8—24no—
76C22×C43—21no—
77C22×C43—21no—
78C22×C43—44no—
79C22×C43—42no—
80C22×C43—82no—
81C22×C43—81no—
82C22×C43—81no—
83C22×C43#12011yescharacteristic
84C22×C43#12111yescharacteristic
85C22×C43#12711yescharacteristic
86C2×D43—42no—
87C2×D43—42no—
88C2×D43—42no—
89C4×C43—42no—
90C4×C43—42no—
91C4×C43#12012yes—
92C4×C43#12112yes—
93Dic43—42no—
94#2006—431nomaximal, Sylow
95C2×C43—21no—
96C2×C43—21no—
97C2×C43—82no—
98C2×C43#39211yescharacteristic
99C2×C43#45311yescharacteristic
100C2×C43#45411yescharacteristic
101D43—82no—
102C2×AGL(1,ℤ/8)—432no—
103#537—431no—
104C2×#104—432no—
105#390D4311yescharacteristic, complemented
106#343—431no—
107C43#200611yescharacteristic, complemented, Sylow
108C2×#41—432no—
109C22×D4C2×D4311yescharacteristic
110AGL(1,ℤ/8)—864no—
111AGL(1,ℤ/8)—864no—
112C2×SD16—862no—
113C2×D8—862no—
114C2×M16—432no—
115C22⋊Q8—862no—
116#121—862no—
117#121—862no—
118C2×C4⋊C4C2×D4311yescharacteristic
119C2×C22⋊C4—22no—
120C2×C42C2×D4311yescharacteristic
121#104—864no—
122C24—21no—
123#41—862no—
124#41—862no—
125#41—862no—
126#41—862no—
127C2×Q8—432no—
128C2×D4—21no—
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—432no—
132C2×D4—862no—
133C2×D4—862no—
134C2×D4D17212yescomplemented
135C22×C4—21no—
136C22×C4—862no—
137C22×C4C22⋊D4312yes—
138C22×C4C22×D4311yescharacteristic
139SD16—868no—
140D8—868no—
141M16—434no—
142M16—862no—
143C2×C8—862no—
144C4⋊C4—22no—
145C4⋊C4—862no—
146C22⋊C4—44no—
147C22⋊C4—864no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—862no—
155C23C2×C22⋊D4311yescharacteristic
156Q8—862no—
157Q8—862no—
158D4—24no—
159D4—42no—
160D4—862no—
161D4—862no—
162D4—3442no—
163D4—1722no—
164D4—1722no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—862no—
171C2×C4—1722no—
172C2×C4—1722no—
173C2×C4C2×D17211yescharacteristic
174C2×C4#1062189811yescharacteristic
175C2×C4D4×D4312yes—
176C2×C4D4×D4312yes—
177C8—864no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—1722no—
186C22—1722no—
187C22—1722no—
188C22#1306329311yescharacteristic
189C22#1306329911yescharacteristic
190C22#1306332111yescharacteristic
191C4—42no—
192C4—42no—
193C4—1722no—
194C4#1306329512yes—
195C4#1306329812yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—3442no—
200C2#1458280811yescharacteristic
201C2#1458306611yescharacteristic
202C2#1458307111yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#390C2
socleC22×C43#120
hypercenter#390D43
hypocenterC43#2006
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13063351C2semidirect
2. #14583480C2semidirect
3. C2×#13063253C2semidirect
4. #14582668C2semidirect
5. C43×#390C2semidirect
24. C2×D4×C43D4semidirect
45. #10621877D4semidirect
105. #390D43semidirect
107. C43#2006semidirect
134. C2×D4D172semidirect