Finite Group Databasebeta

← #19134565

Subgroups — #19134565

Order 5504.

588 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 121 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#14582916C212yesmaximal, complemented
2#14582904C212yesmaximal, complemented
3#14582883C211yesmaximal, characteristic, complemented
4#14582873C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C43C211yesmaximal, characteristic
6C2×#10621877C2212yescomplemented
7#13063284C2212yescomplemented
8#13063252—24no—
9#13063246—24no—
10#13063244—21no—
11#13063242—21no—
12#13063240—22no—
13H(5,𝔽2)×C43—24no—
14H(5,𝔽2)×C43—24no—
15C2×#41×C43—21no—
16C2×#41×C43C412yescomplemented
17C2×#41×C43C2211yescharacteristic
18C2×#41×C43C2211yescharacteristic
19C22×D4×C43—22no—
20C22×D4×C43—21no—
21C22×D4×C43C412yescomplemented
22C22×D4×C43C2211yescharacteristic
23C24×C43—22no—
24C24×C43—21no—
25#41×C43—28no—
26#41×C43—24no—
27#41×C43—24no—
28#41×C43—22no—
29#41×C43—22no—
30#41×C43—22no—
31#41×C43D414yes—
32C2×Q8×C43C2×C411yescharacteristic
33C2×Q8×C43D411yescharacteristic
34C2×D4×C43—28no—
35C2×D4×C43—216no—
36C2×D4×C43—24no—
37C2×D4×C43—24no—
38C2×D4×C43—22no—
39C2×D4×C43—21no—
40C2×D4×C43—22no—
41C2×D4×C43—22no—
42C2×D4×C43—21no—
43C2×D4×C43C2×C411yescharacteristic
44C2×D4×C43C2×C412yes—
45C2×D4×C43D414yes—
46C2×D4×C43D411yescharacteristic
47C2×D4×C43D412yes—
48C22×C4×C43—22no—
49C22×C4×C43—21no—
50C22×C4×C43C2×C412yes—
51C22×C4×C43C2311yescharacteristic
52C22⋊Dic43—22no—
53C4⋊Dic43—22no—
54C4×Dic43—22no—
55#10621877—22no—
56#10621877—22no—
57C2×C43⋊C8—22no—
58C23×C43—28no—
59C23×C43—22no—
60C23×C43—21no—
61C23×C43—24no—
62C23×C43—82no—
63C23×C43—84no—
64C23×C43C22⋊C412yes—
65C23×C43C2×D411yescharacteristic
66Q8×C43—21no—
67Q8×C43—22no—
68Q8×C43C22⋊C412yes—
69D4×C43—28no—
70D4×C43—28no—
71D4×C43—24no—
72D4×C43—24no—
73D4×C43—22no—
74D4×C43—21no—
75D4×C43—24no—
76D4×C43—22no—
77D4×C43C22⋊C412yes—
78D4×C43C22⋊C414yes—
79C2×C4×C43—28no—
80C2×C4×C43—21no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—24no—
84C2×C4×C43C22⋊C412yes—
85C2×C4×C43C22×C411yescharacteristic
86C2×C4×C43C2×D412yes—
87C2×C4×C43C2×D412yes—
88C2×C4×C43C2×D411yescharacteristic
89C2×Dic43—42no—
90C43⋊C8—42no—
91C22×C43—22no—
92C22×C43—24no—
93C22×C43—22no—
94C22×C43—41no—
95C22×C43—42no—
96C22×C43—44no—
97C22×C43—42no—
98C22×C43—84no—
99C22×C43—88no—
100C22×C43C2×C22⋊C411yescharacteristic
101C22×C43#12012yes—
102C4×C43—22no—
103C4×C43—22no—
104C4×C43C2×C22⋊C411yescharacteristic
105C4×C43C2×C22⋊C411yescharacteristic
106C4×C43#12012yes—
107Dic43—82no—
108#1795—431nomaximal, Sylow
109C2×C43—22no—
110C2×C43—21no—
111C2×C43—44no—
112C2×C43—42no—
113C2×C43—42no—
114C2×C43#37911yescharacteristic
115C2×H(5,𝔽2)D4311yescharacteristic
116#421—432no—
117#418—432no—
118#413—431no—
119#410—431no—
120C43#179511yescharacteristic, complemented, Sylow
121H(5,𝔽2)—24no—
122H(5,𝔽2)—24no—
123C2×#41—21no—
124C2×#41Dic4312yescomplemented
125C2×#41C2×D4311yescharacteristic
126C2×#41C2×D4311yescharacteristic
127C22×D4—22no—
128C22×D4—21no—
129C22×D4Dic4312yescomplemented
130C22×D4C2×D4311yescharacteristic
131C2×M16—432no—
132#117—432no—
133#104—864no—
134#102—864no—
135#101—861no—
136#100—861no—
137#99—862no—
138C24—22no—
139C24—21no—
140#41—28no—
141#41—24no—
142#41—24no—
143#41—22no—
144#41—22no—
145#41—22no—
146#41C22⋊D4314yes—
147C2×Q8C2×Dic4311yescharacteristic
148C2×Q8C22⋊D4311yescharacteristic
149C2×D4—216no—
150C2×D4—28no—
151C2×D4—22no—
152C2×D4—21no—
153C2×D4—24no—
154C2×D4—24no—
155C2×D4—22no—
156C2×D4—21no—
157C2×D4—22no—
158C2×D4C2×Dic4311yescharacteristic
159C2×D4C2×Dic4312yes—
160C2×D4C22⋊D4312yes—
161C2×D4C22⋊D4311yescharacteristic
162C2×D4C22⋊D4314yes—
163C22×C4—22no—
164C22×C4—21no—
165C22×C4C2×Dic4312yes—
166C22×C4C22×D4311yescharacteristic
167M16—862no—
168M16—862no—
169C2×C8—862no—
170C4⋊C4—862no—
171C22⋊C4—862no—
172C42—862no—
173C23—28no—
174C23—22no—
175C23—21no—
176C23—24no—
177C23—82no—
178C23—84no—
179C23C22⋊Dic4312yes—
180C23C2×C22⋊D4311yescharacteristic
181Q8—21no—
182Q8—22no—
183Q8C22⋊Dic4312yes—
184D4—28no—
185D4—28no—
186D4—24no—
187D4—24no—
188D4—22no—
189D4—21no—
190D4—22no—
191D4—24no—
192D4C22⋊Dic4312yes—
193D4C22⋊Dic4314yes—
194C2×C4—28no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—1722no—
200C2×C4C22⋊Dic4312yes—
201C2×C4C22×Dic4311yescharacteristic
202C2×C4C2×C22⋊D4312yes—
203C2×C4C2×C22⋊D4312yes—
204C2×C4C2×C22⋊D4311yescharacteristic
205C8—1722no—
206C22—22no—
207C22—24no—
208C22—22no—
209C22—41no—
210C22—42no—
211C22—44no—
212C22—42no—
213C22—84no—
214C22—88no—
215C22C2×C22⋊Dic4311yescharacteristic
216C22#1306329412yes—
217C4—22no—
218C4—22no—
219C4—3442no—
220C4C2×C22⋊Dic4311yescharacteristic
221C4C2×C22⋊Dic4311yescharacteristic
222C4#1306329412yes—
223C2—22no—
224C2—21no—
225C2—44no—
226C2—42no—
227C2—42no—
228C2#1458275511yescharacteristic
subgroupG/H
centerC2#14582755
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC2×H(5,𝔽2)×C43C2
socleC2×C43#379
hypercenterC2×H(5,𝔽2)D43
hypocenterC43#1795
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #14582916C2semidirect
2. #14582904C2semidirect
3. #14582883C2semidirect
4. #14582873C2semidirect
6. C2×#10621877C22semidirect
7. #13063284C22semidirect
16. C2×#41×C43C4semidirect
21. C22×D4×C43C4semidirect
120. C43#1795semidirect
124. C2×#41Dic43semidirect
129. C22×D4Dic43semidirect