Finite Group Databasebeta

← #19136266

Subgroups — #19136266

Order 5504.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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#14583463C211yesmaximal, characteristic
2#14582873C211yesmaximal, characteristic, complemented
3#14582691C214yesmaximal, complemented
4C43×#410C211yesmaximal, characteristic, complemented
5C22×D172C411yescharacteristic, complemented
6#13063321C2212yes—
7#13063314C412yescomplemented
8#13063299—21no—
9#13063299—21no—
10#13063293—21no—
11#13063293—21no—
12#13063284—21no—
13#13063284C411yescharacteristic, complemented
14#13063240—21no—
15#13063240C2212yescomplemented
16C2×#41×C43C2211yescharacteristic
17#117×C43—21no—
18#99×C43—21no—
19#99×C43C2212yescomplemented
20C23×D43—21no—
21#41×C43—41no—
22#41×C43—41no—
23C2×Q8×C43C2×C411yescharacteristic
24C2×D4×C43D411yescharacteristic
25C2×D4×C43D411yescharacteristic
26C2×D4×C43C2311yescharacteristic
27C22×C4×C43C2×C411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×C4×C43D411yescharacteristic
30C2×C22⋊D43—22no—
31C2×C22⋊D43—22no—
32C2×D172—21no—
33C2×D172—41no—
34C2×D172—41no—
35C2×D172C2×C412yes—
36C4⋊C4×C43—41no—
37C22⋊C4×C43—22no—
38C42×C43—41no—
39C22⋊Dic43—21no—
40C22⋊Dic43—22no—
41(C2×D43)⋊C4—22no—
42(C2×D43)⋊C4—22no—
43C4⋊Dic43—21no—
44C4⋊Dic43—41no—
45C4×Dic43—41no—
46C4×Dic43C2×C412yes—
47C23×C43C22⋊C411yescharacteristic
48C23×C43C2×D411yescharacteristic
49C23×C43C2×D411yescharacteristic
50C22×D43—22no—
51C22×D43—42no—
52C22×D43—82no—
53Q8×C43—41no—
54D4×C43—41no—
55D4×C43—41no—
56D4×C43—41no—
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43—21no—
60C2×C4×C43—21no—
61C2×C4×C43—21no—
62C2×C4×C43—21no—
63C2×C4×C43—42no—
64C2×C4×C43C22⋊C411yescharacteristic
65C2×C4×C43C22⋊C411yescharacteristic
66C2×C4×C43C22⋊C411yescharacteristic
67C2×C4×C43C22×C411yescharacteristic
68C22⋊D43—82no—
69C22⋊D43—82no—
70C2×Dic43—22no—
71C2×Dic43—42no—
72D172—42no—
73D172—41no—
74D172—41no—
75C22×C43—21no—
76C22×C43—21no—
77C22×C43—21no—
78C22×C43—41no—
79C22×C43—41no—
80C22×C43—41no—
81C22×C43C2×C22⋊C411yescharacteristic
82C2×D43—42no—
83C2×D43—42no—
84C2×D43—42no—
85C2×D43—84no—
86C4×C43—21no—
87C4×C43—21no—
88C4×C43—21no—
89C4×C43—82no—
90C4×C43#9911yescharacteristic
91C4×C43#9911yescharacteristic
92Dic43—42no—
93Dic43—82no—
94#2128—431nomaximal, Sylow
95C2×C43—21no—
96C2×C43—41no—
97C2×C43—41no—
98C2×C43—41no—
99C2×C43C2×#9911yescharacteristic
100D43—82no—
101#535—431no—
102#410—431no—
103#410D4311yescharacteristic, complemented
104#353—434no—
105C43#212811yescharacteristic, complemented, Sylow
106C2×#41C2×D4311yescharacteristic
107C22×D4—431no—
108#127—432no—
109#124—432no—
110#121—861no—
111#121—861no—
112#120—861no—
113#120—861no—
114#117—21no—
115#117—431no—
116#117—861no—
117#99—21no—
118#99—432no—
119#99—861no—
120#99C2×D4312yescomplemented
121C24—861no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D4311yescharacteristic
125C2×D4—432no—
126C2×D4—862no—
127C2×D4—862no—
128C2×D4—861no—
129C2×D4—1721no—
130C2×D4—1721no—
131C2×D4D17211yescharacteristic
132C2×D4C22⋊D4311yescharacteristic
133C2×D4C22×D4311yescharacteristic
134C22×C4C4×D4311yescharacteristic
135C22×C4D17211yescharacteristic
136C22×C4C22⋊D4311yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—861no—
139C4⋊C4—1721no—
140C22⋊C4—22no—
141C22⋊C4—861no—
142C22⋊C4—862no—
143C22⋊C4—862no—
144C22⋊C4—862no—
145C42—41no—
146C42—432no—
147C42—1721no—
148C23—862no—
149C23—3442no—
150C23—1722no—
151C23(C2×D43)⋊C411yescharacteristic
152C23C2×D17211yescharacteristic
153C23C2×C22⋊D4311yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—3442no—
159D4—3442no—
160D4—1722no—
161D4—1721no—
162D4—1721no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—862no—
171C2×C4—1722no—
172C2×C4(C2×D43)⋊C411yescharacteristic
173C2×C4(C2×D43)⋊C411yescharacteristic
174C2×C4(C2×D43)⋊C411yescharacteristic
175C2×C4C2×C4×D4311yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—3444no—
183C22—1722no—
184C22—1722no—
185C22—1722no—
186C22C2×(C2×D43)⋊C411yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—3442no—
192C4—1722no—
193C4#1306323911yescharacteristic
194C4#1306323911yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—3442no—
200C2C2×#1306323911yescharacteristic
subgroupG/H
centerC2C2×#13063239
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#410C2
socleC2×C43C2×#99
hypercenter#410D43
hypocenterC43#2128
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #14582873C2semidirect
3. #14582691C2semidirect
4. C43×#410C2semidirect
5. C22×D172C4semidirect
7. #13063314C4semidirect
13. #13063284C4semidirect
15. #13063240C22semidirect
19. #99×C43C22semidirect
103. #410D43semidirect
105. C43#2128semidirect
120. #99C2×D43semidirect