Finite Group Databasebeta

← #19135699

Subgroups — #19135699

Order 5504.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#14583699C211yesmaximal, characteristic, complemented
2#14583697C212yesmaximal, complemented
3#14582865C212yesmaximal, complemented
4C43⋊#338C211yesmaximal, characteristic, complemented
5C43×#408C211yesmaximal, characteristic, complemented
6C2×#10621898C2212yes—
7#13063358—22no—
8#13063356—22no—
9#13063355—22no—
10#13063353—22no—
11#13063351—22no—
12#13063350—22no—
13#13063347—22no—
14#13063345—24no—
15C2×#10621877C2212yes—
16(C2×D43)⋊C8—24no—
17C2×#41×C43C2211yescharacteristic
18C2×M16×C43C2211yescharacteristic
19C22×C8×C43C2211yescharacteristic
20C22⋊C8×C43—22no—
21#41×C43—22no—
22#41×C43—22no—
23C2×Q8×C43D411yescharacteristic
24C2×D4×C43—21no—
25C2×D4×C43D411yescharacteristic
26C22×C4×C43—21no—
27C22×C4×C43C2311yescharacteristic
28C2×C22⋊D43—22no—
29#10621898—22no—
30#10621898—22no—
31#10621898—22no—
32#10621898—22no—
33C2×D172D412yes—
34C2×C4×D43—22no—
35C2×Dic86D412yes—
36M16×C43—22no—
37C2×C8×C43—21no—
38C2×C8×C43—22no—
39C2×C8×C43D412yes—
40#10621885—24no—
41#10621884—24no—
42#10621883—24no—
43#10621882—24no—
44#10621877—22no—
45#10621877—22no—
46C2×C43⋊C8D414yes—
47Dic172—22no—
48D344—22no—
49#10621873—24no—
50C23×C43—21no—
51C23×C43#4111yescharacteristic
52C22×D43—22no—
53Q8×C43—22no—
54D4×C43—22no—
55D4×C43—42no—
56C2×C4×C43—21no—
57C2×C4×C43—41no—
58C2×C4×C43—41no—
59C2×C4×C43C2×D411yescharacteristic
60C2×C4×C43C2×D412yes—
61C2×C4×C43C2×D412yes—
62C2×C4×C43C2×D411yescharacteristic
63C22⋊D43—42no—
64C22⋊D43—42no—
65C2×Dic43—22no—
66D172—22no—
67D172—22no—
68C4×D43—42no—
69C4×D43—42no—
70Dic86—22no—
71Dic86—22no—
72C8×C43—22no—
73C8×C43—41no—
74C43⋊C8—24no—
75C22×C43—41no—
76C22×C43—42no—
77C22×C43—41no—
78C22×C43#12112yes—
79C22×C43#12111yescharacteristic
80C2×D43—44no—
81C2×D43—42no—
82C4×C43—41no—
83C4×C43#12011yescharacteristic
84C4×C43#12012yes—
85C4×C43#12711yescharacteristic
86Dic43—42no—
87#2017—431nomaximal, Sylow
88C2×C43—22no—
89C2×C43—21no—
90C2×C43—81no—
91C2×C43#39211yescharacteristic
92D43—82no—
93#575—432no—
94#575—431no—
95#408—432no—
96#408D4311yescharacteristic, complemented
97#338—431no—
98C43#201711yescharacteristic, complemented, Sylow
99C2×#41—432no—
100C2×#41C2×D4311yescharacteristic
101#137—862no—
102#137—862no—
103#137—862no—
104AGL(1,ℤ/8)—862no—
105AGL(1,ℤ/8)—862no—
106AGL(1,ℤ/8)—862no—
107#135—864no—
108#135—862no—
109C2×M16—432no—
110C2×M16C2×D4311yescharacteristic
111C22×C8C2×D4311yescharacteristic
112C22⋊C8—22no—
113C22⋊C8—864no—
114#41—22no—
115#41—22no—
116#41—862no—
117#41—862no—
118#41—862no—
119#41—862no—
120C2×Q8—432no—
121C2×Q8D17211yescharacteristic
122C2×D4—21no—
123C2×D4—432no—
124C2×D4—862no—
125C2×D4D17211yescharacteristic
126C22×C4—21no—
127C22×C4—862no—
128C22×C4C22×D4311yescharacteristic
129Q16—862no—
130Q16—864no—
131SD16—864no—
132SD16—864no—
133SD16—864no—
134D8—862no—
135D8—864no—
136M16—22no—
137M16—862no—
138M16—862no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—434no—
142C2×C8C22⋊D4312yes—
143C23—21no—
144C23—862no—
145C23#1062189811yescharacteristic
146Q8—22no—
147Q8—862no—
148Q8—862no—
149D4—22no—
150D4—42no—
151D4—862no—
152D4—862no—
153D4—1722no—
154D4—1722no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—862no—
159C2×C4—1722no—
160C2×C4—1722no—
161C2×C4C2×D17211yescharacteristic
162C2×C4D4×D4312yes—
163C2×C4D4×D4312yes—
164C2×C4C2×C22⋊D4311yescharacteristic
165C8—22no—
166C8—41no—
167C8—864no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—1724no—
172C22—1722no—
173C22#1306329812yes—
174C22#1306329911yescharacteristic
175C4—41no—
176C4—1722no—
177C4#1306329311yescharacteristic
178C4#1306329512yes—
179C4#1306332111yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—3442no—
184C2#1458280811yescharacteristic
subgroupG/H
centerC4#13063321
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#408C2
socleC2×C43#392
hypercenter#408D43
hypocenterC43#2017
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #14583699C2semidirect
2. #14583697C2semidirect
3. #14582865C2semidirect
4. C43⋊#338C2semidirect
5. C43×#408C2semidirect
96. #408D43semidirect
98. C43#2017semidirect