Finite Group Databasebeta

← #19147474

Subgroups — #19147474

Order 5504.

338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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#14583624C211yesmaximal, characteristic, complemented
2#14583606C211yesmaximal, characteristic
3#14583300C212yesmaximal, complemented
4#14583295C211yesmaximal, characteristic, complemented
5#14583205C212yesmaximal, complemented
6#14583197C212yesmaximal
7#14583195C211yesmaximal, characteristic, complemented
8#14583023C211yesmaximal, characteristic, complemented
9#14582990C212yesmaximal
10C4×#10621883C211yesmaximal, characteristic
11C43×#474C211yesmaximal, characteristic
12C2×#10621883C2211yescharacteristic
13#13063325C2211yescharacteristic
14#13063323—21no—
15#13063316C2212yes—
16#13063316C2212yes—
17#13063315—22no—
18#13063304—21no—
19#13063302—22no—
20Q8×Dic43—21no—
21C4×Dic86C2211yescharacteristic
22C4×Dic86C2211yescharacteristic
23#13063290C2212yes—
24D4×Dic43C2212yes—
25C2×C4⋊Dic43—21no—
26#13063259C2212yes—
27#13063256C2211yescharacteristic
28#13063256C2212yes—
29#13063256C2212yes—
30Dic43⋊C8C2212yes—
31#13063250C2212yes—
32#13063248C2211yescharacteristic
33#13063246C2211yescharacteristic
34C4×C43⋊C8C2211yescharacteristic
35C8×Dic43C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37C4×D4×C43C2211yescharacteristic
38#107×C43C2212yes—
39C4⋊C8×C43C2211yescharacteristic
40#102×C43C2212yes—
41C2×Q8×C43—21no—
42C2×D4×C43C2311yescharacteristic
43C22×C4×C43—21no—
44C22×Dic43—22no—
45C2×Dic86—21no—
46C2×Dic86D411yescharacteristic
47C2×Dic86C2311yescharacteristic
48C2×C8×C43C2312yes—
49C4⋊C4×C43—21no—
50C4⋊C4×C43C2312yes—
51C4⋊C4×C43C2311yescharacteristic
52C22⋊C4×C43—21no—
53C42×C43C2311yescharacteristic
54C22⋊Dic43—22no—
55#10621883Q814yescomplemented
56C4⋊Dic43—21no—
57C4⋊Dic43—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43D411yescharacteristic
60C4⋊Dic43C2311yescharacteristic
61C4⋊Dic43C2312yes—
62Dic43⋊C4—21no—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4D412yes—
67C4×Dic43—21no—
68C4×Dic43—22no—
69C4×Dic43C2312yes—
70C2×C43⋊C8C2311yescharacteristic
71C2×C43⋊C8C2311yescharacteristic
72C23×C43—21no—
73Q8×C43—42no—
74D4×C43—21no—
75D4×C43C2×Q812yes—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43—42no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2411yescharacteristic
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—22no—
85C2×Dic43—82no—
86C2×Dic43C2×D412yes—
87C2×Dic43C2×D412yes—
88Dic86—22no—
89Dic86—21no—
90Dic86—81no—
91Dic86C2×Q812yes—
92C8×C43—22no—
93C43⋊C8—21no—
94C43⋊C8C2×Q812yes—
95C22×C43—22no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43C22×D411yescharacteristic
99C4×C43—21no—
100C4×C43—41no—
101C4×C43—42no—
102C4×C43#13512yes—
103C4×C43C22×Q811yescharacteristic
104C4×C432−1+411yescharacteristic
105Dic43—22no—
106Dic43—22no—
107Dic43—22no—
108Dic43—42no—
109Dic43—41no—
110#3381—431nomaximal, Sylow
111C2×C43—42no—
112C2×C43D4×Q811yescharacteristic
113C2×C43C2×#13511yescharacteristic
114C2×C43#57711yescharacteristic
115#557—431no—
116#554—431no—
117#499—432no—
118#498—431no—
119#479—432no—
120#478—432no—
121#477—431no—
122#474D4311yescharacteristic
123C8×Q8—431no—
124C4×SD16—431no—
125C4×SD16—432no—
126C43#338111yescharacteristic, complemented, Sylow
127C2×SD16—431no—
128C4⋊Q8—431no—
129C4⋊Q8—861no—
130C4⋊Q8C2×D4311yescharacteristic
131#125—432no—
132#125—432no—
133#125—862no—
134C22⋊Q8—862no—
135C22⋊Q8—861no—
136C4×Q8—431no—
137C4×Q8—432no—
138C4×Q8—431no—
139C4×Q8—861no—
140C4×D4—432no—
141C4×D4C2×D4311yescharacteristic
142C2×C4⋊C4—861no—
143#107—432no—
144#107C2×D4312yes—
145#106—432no—
146#106—431no—
147#106—432no—
148C4⋊C8—432no—
149C4⋊C8C2×D4311yescharacteristic
150#103—432no—
151#103—431no—
152#102—431no—
153#102C2×D4312yes—
154C4×C8—432no—
155C4×C8—431no—
156C2×Q8—21no—
157C2×Q8—431no—
158C2×Q8—431no—
159C2×Q8—861no—
160C2×D4C22×D4311yescharacteristic
161C22×C4—21no—
162C22×C4—862no—
163SD16—434no—
164C2×C8—431no—
165C2×C8—431no—
166C2×C8C22×D4312yes—
167C4⋊C4—21no—
168C4⋊C4—431no—
169C4⋊C4—432no—
170C4⋊C4—431no—
171C4⋊C4—432no—
172C4⋊C4—862no—
173C4⋊C4—862no—
174C4⋊C4—862no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—861no—
178C4⋊C4—861no—
179C4⋊C4C22×D4312yes—
180C4⋊C4C22×D4311yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—862no—
183C42—432no—
184C42—862no—
185C42—861no—
186C42C22×D4311yescharacteristic
187C23—21no—
188Q8—42no—
189Q8—432no—
190Q8—862no—
191Q8—861no—
192Q8—3441no—
193D4—21no—
194D4Q8×D4312yes—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—432no—
199C2×C4—432no—
200C2×C4—861no—
201C2×C4—861no—
202C2×C4—862no—
203C2×C4—3442no—
204C2×C4D4×D4311yescharacteristic
205C2×C4D4×D4311yescharacteristic
206C2×C4C23×D4311yescharacteristic
207C8—22no—
208C8—432no—
209C8—861no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22C2×D4×D4311yescharacteristic
214C4—21no—
215C4—41no—
216C4—42no—
217C4—862no—
218C4—862no—
219C4—862no—
220C4—1722no—
221C4—1721no—
222C4#1306334412yes—
223C4C2×Q8×D4311yescharacteristic
224C4#1306337211yescharacteristic
225C2—42no—
226C2#1458356211yescharacteristic
227C2C2×#1306334411yescharacteristic
228C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#474C2
socleC22×C43C22×D4
hypercenter#474D43
hypocenterC43#3381
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #14583624C2semidirect
3. #14583300C2semidirect
4. #14583295C2semidirect
5. #14583205C2semidirect
7. #14583195C2semidirect
8. #14583023C2semidirect
55. #10621883Q8semidirect
126. C43#3381semidirect