Finite Group Databasebeta

← #19147475

Subgroups — #19147475

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#14583610C211yesmaximal, characteristic
3#14583299C212yesmaximal, complemented
4#14583209C212yesmaximal, complemented
5#14583198C212yesmaximal
6#14583191C211yesmaximal, characteristic, complemented
7#14583176C211yesmaximal, characteristic
8C8×Dic86C211yesmaximal, characteristic, complemented
9C4×#10621873C211yesmaximal, characteristic
10#14582986C212yesmaximal
11C43×#498C211yesmaximal, characteristic, complemented
12C2×#10621873C2211yescharacteristic
13#13063323—21no—
14#13063316C2212yes—
15#13063316C2212yes—
16#13063315—22no—
17#13063305—21no—
18#13063301—22no—
19Q8×Dic43—21no—
20C4×Dic86C2211yescharacteristic
21C4×Dic86C2211yescharacteristic
22#13063290C2212yes—
23C4×D172C2211yescharacteristic
24#13063287C2212yes—
25C4⋊C4×D43—21no—
26#13063258C2212yes—
27#13063258C2212yes—
28#13063257C2211yescharacteristic
29C4⋊(C43⋊C8)C2211yescharacteristic
30Dic43⋊C8C2212yes—
31#13063250C2211yescharacteristic
32#13063248C2212yes—
33#13063247C2211yescharacteristic
34#13063245C2212yes—
35C8×Dic43C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37C4⋊Q8×C43C2211yescharacteristic
38#106×C43C2212yes—
39#106×C43C2212yes—
40C4×C8×C43C2211yescharacteristic
41C2×Q8×C43—21no—
42C2×Q8×C43—21no—
43C2×D172C2311yescharacteristic
44C2×C4×D43—21no—
45C2×C4×D43—22no—
46C2×Dic86D411yescharacteristic
47C2×Dic86C2311yescharacteristic
48C2×C8×C43C2311yescharacteristic
49C2×C8×C43C2311yescharacteristic
50C4⋊C4×C43—21no—
51C4⋊C4×C43—21no—
52C4⋊C4×C43C2312yes—
53C4⋊C4×C43C2312yes—
54C42×C43C2311yescharacteristic
55(C2×D43)⋊C4—21no—
56(C2×D43)⋊C4—22no—
57C4⋊Dic43—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43D411yescharacteristic
60C4⋊Dic43C2311yescharacteristic
61C4⋊Dic43C2311yescharacteristic
62Dic43⋊C4—21no—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4D412yes—
67C4×Dic43—21no—
68C4×Dic43—22no—
69C4×Dic43C2312yes—
70C2×C43⋊C8C2312yes—
71#10621873Q814yescomplemented
72C22×D43—21no—
73Q8×C43—42no—
74Q8×C43—81no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2411yescharacteristic
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43C2×D412yes—
84C2×Dic43C2×D412yes—
85D172—21no—
86D172C2×Q812yes—
87C4×D43—42no—
88C4×D43—82no—
89Dic86—22no—
90Dic86—21no—
91Dic86C2×Q812yes—
92C8×C43—21no—
93C8×C43C2×Q812yes—
94C43⋊C8—22no—
95C22×C43C22×D411yescharacteristic
96C2×D43—22no—
97C2×D43—41no—
98C2×D43—41no—
99C4×C43—21no—
100C4×C43—42no—
101C4×C43—42no—
102C4×C43#13512yes—
103C4×C43C22×Q811yescharacteristic
104C4×C432−1+411yescharacteristic
105Dic43—22no—
106Dic43—22no—
107Dic43—22no—
108Dic43—41no—
109Dic43—41no—
110#3381—431nomaximal, Sylow
111C2×C43D4×Q811yescharacteristic
112C2×C43C2×#13511yescharacteristic
113C2×C43#57711yescharacteristic
114D43—42no—
115#557—431no—
116#554—431no—
117#499—432no—
118#498D4311yescharacteristic, complemented
119#479—432no—
120#478—432no—
121#477—431no—
122#474—431no—
123C8×Q8—431no—
124C4×SD16—432no—
125C4×SD16—431no—
126C43#338111yescharacteristic, complemented, Sylow
127C2×SD16—431no—
128C4⋊Q8—861no—
129C4⋊Q8C2×D4311yescharacteristic
130C4⋊Q8C2×D4311yescharacteristic
131#125—432no—
132#125—432no—
133#125—862no—
134C22⋊Q8—861no—
135C22⋊Q8—862no—
136C4×Q8—431no—
137C4×Q8—432no—
138C4×Q8—431no—
139C4×Q8—861no—
140C4×D4—432no—
141C4×D4—431no—
142C2×C4⋊C4—861no—
143#107—432no—
144#107—432no—
145#106—431no—
146#106C2×D4312yes—
147#106C2×D4312yes—
148C4⋊C8—432no—
149C4⋊C8—431no—
150#103—431no—
151#103—432no—
152#102—431no—
153#102—432no—
154C4×C8—432no—
155C4×C8C2×D4311yescharacteristic
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—431no—
159C2×Q8—431no—
160C2×D4—431no—
161C22×C4—862no—
162C22×C4—861no—
163SD16—434no—
164C2×C8—432no—
165C2×C8C22×D4311yescharacteristic
166C2×C8C22×D4311yescharacteristic
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—431no—
170C4⋊C4—432no—
171C4⋊C4—431no—
172C4⋊C4—431no—
173C4⋊C4—862no—
174C4⋊C4—862no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4—861no—
179C4⋊C4C22×D4312yes—
180C4⋊C4C22×D4312yes—
181C22⋊C4—862no—
182C22⋊C4—861no—
183C42—432no—
184C42—862no—
185C42—861no—
186C42C22×D4311yescharacteristic
187C23—861no—
188Q8—42no—
189Q8—81no—
190Q8—432no—
191Q8—862no—
192Q8—861no—
193D4—432no—
194D4—861no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—432no—
198C2×C4—432no—
199C2×C4—861no—
200C2×C4—861no—
201C2×C4—861no—
202C2×C4—3442no—
203C2×C4—1722no—
204C2×C4D4×D4311yescharacteristic
205C2×C4D4×D4311yescharacteristic
206C2×C4C23×D4311yescharacteristic
207C8—21no—
208C8—862no—
209C8Q8×D4312yes—
210C22—862no—
211C22—1721no—
212C22—1721no—
213C22C2×D4×D4311yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—862no—
218C4—862no—
219C4—862no—
220C4—1721no—
221C4—1721no—
222C4#1306334612yes—
223C4C2×Q8×D4311yescharacteristic
224C4#1306337311yescharacteristic
225C2—1722no—
226C2#1458356411yescharacteristic
227C2C2×#1306334611yescharacteristic
228C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#498C2
socleC22×C43C22×D4
hypercenter#498D43
hypocenterC43#3381
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #14583624C2semidirect
3. #14583299C2semidirect
4. #14583209C2semidirect
6. #14583191C2semidirect
8. C8×Dic86C2semidirect
11. C43×#498C2semidirect
71. #10621873Q8semidirect
118. #498D43semidirect
126. C43#3381semidirect