Finite Group Databasebeta

← #19134947

Subgroups — #19134947

Order 5504.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#10621883C211yesmaximal, characteristic
2C2×#13063290C211yesmaximal, characteristic, complemented
3C2×#13063250C211yesmaximal, characteristic, complemented
4#14582802C211yesmaximal, characteristic
5#14582661C211yesmaximal, characteristic, complemented
6#14582653C211yesmaximal, characteristic, complemented
7C2×#102×C43C211yesmaximal, characteristic
8C22×Dic86C2211yescharacteristic
9C2×#10621883—22no—
10C2×#10621883—22no—
11C2×#10621883C414yescomplemented
12C22×C43⋊C8C2211yescharacteristic
13#13063290—22no—
14#13063290—22no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×Dic43⋊C4—21no—
17C2×C22⋊Dic43—21no—
18C2×C22⋊Dic43—21no—
19C2×C4×Dic43—21no—
20C2×C4×Dic43C2211yescharacteristic
21#13063250—22no—
22C22×D4×C43C2211yescharacteristic
23C22×C8×C43C2211yescharacteristic
24C2×C4⋊C4×C43C2211yescharacteristic
25#102×C43—22no—
26C24×C43—21no—
27C2×D4×C43—21no—
28C2×D4×C43—21no—
29C2×D4×C43—21no—
30C2×D4×C43—21no—
31C2×D4×C43—21no—
32C2×D4×C43C2×C412yes—
33C22×C4×C43—21no—
34C22×C4×C43C2311yescharacteristic
35C22×Dic43—21no—
36C22×Dic43—21no—
37C22×Dic43D411yescharacteristic
38C22×Dic43D411yescharacteristic
39C2×Dic86—21no—
40C2×Dic86—21no—
41C2×Dic86—21no—
42C2×Dic86C2×C412yes—
43C2×Dic86D412yes—
44C2×Dic86D412yes—
45C2×C8×C43—21no—
46C2×C8×C43—21no—
47C2×C8×C43—21no—
48C4⋊C4×C43—21no—
49C4⋊C4×C43D412yes—
50C22⋊Dic43—42no—
51C22⋊Dic43—42no—
52#10621883—28no—
53C4⋊Dic43—21no—
54C4⋊Dic43—21no—
55Dic43⋊C4—24no—
56C4×Dic43—24no—
57C4×Dic43—21no—
58C4×Dic43—21no—
59C2×C43⋊C8—21no—
60C2×C43⋊C8—21no—
61C2×C43⋊C8C2×C412yes—
62C23×C43—22no—
63C23×C43—41no—
64C23×C43—41no—
65C23×C43—41no—
66C23×C43—41no—
67C23×C43—41no—
68C23×C43—41no—
69C23×C43C2×D411yescharacteristic
70D4×C43—22no—
71D4×C43—22no—
72D4×C43—41no—
73D4×C43—41no—
74C2×C4×C43—22no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43C22×C411yescharacteristic
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43#4111yescharacteristic
82C2×C4×C43#4111yescharacteristic
83C2×Dic43—22no—
84C2×Dic43—21no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43—21no—
90C2×Dic43—21no—
91C2×Dic43—41no—
92C2×Dic43—41no—
93C2×Dic43—41no—
94C2×Dic43SD1612yescomplemented
95Dic86—22no—
96Dic86—22no—
97Dic86—22no—
98Dic86C22⋊C414yescomplemented
99C8×C43—41no—
100C43⋊C8—22no—
101C22×C43—42no—
102C22×C43—42no—
103C22×C43—42no—
104C22×C43—81no—
105C22×C43—81no—
106C22×C43—81no—
107C22×C43—81no—
108C22×C43C4×D411yescharacteristic
109C22×C43#12011yescharacteristic
110C22×C43#12111yescharacteristic
111C22×C43C2×SD1611yescharacteristic
112C22×C43#13511yescharacteristic
113C22×C43AGL(1,ℤ/8)11yescharacteristic
114C22×C43#13711yescharacteristic
115C4×C43—42no—
116C4×C43C2×C22⋊C411yescharacteristic
117C4×C43C4×D411yescharacteristic
118C4×C43#12111yescharacteristic
119C4×C43#12311yescharacteristic
120Dic43—24no—
121Dic43—22no—
122Dic43—41no—
123Dic43—81no—
124#1880—431nomaximal, Sylow
125C2×C43—82no—
126C2×C43#38611yescharacteristic
127C2×C43C4×SD1611yescharacteristic
128C2×C43#44011yescharacteristic
129C2×C43#44811yescharacteristic
130C2×C43#44911yescharacteristic
131C2×C43#46011yescharacteristic
132C2×C43#46411yescharacteristic
133C22×SD16—431no—
134C2×C4×Q8—431no—
135C2×#103—431no—
136C2×#102D4311yescharacteristic
137#390—431no—
138#340—431no—
139#336—431no—
140C43#188011yescharacteristic, complemented, Sylow
141C22×Q8—431no—
142C22×D4C2×D4311yescharacteristic
143C2×SD16—434no—
144C2×SD16—862no—
145C2×SD16—862no—
146C22×C8—431no—
147C22×C8C2×D4311yescharacteristic
148C4×Q8—862no—
149C4×Q8—862no—
150C2×C4⋊C4—431no—
151C2×C4⋊C4—861no—
152C2×C4⋊C4C2×D4311yescharacteristic
153C2×C22⋊C4—861no—
154C2×C22⋊C4—861no—
155C2×C42—431no—
156C2×C42—861no—
157#103—862no—
158#102—22no—
159C24—21no—
160C2×Q8—432no—
161C2×Q8—432no—
162C2×Q8—432no—
163C2×Q8—861no—
164C2×Q8—861no—
165C2×Q8—861no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4C4×D4312yes—
172C22×C4—21no—
173C22×C4—431no—
174C22×C4—431no—
175C22×C4—861no—
176C22×C4—861no—
177C22×C4C22×D4311yescharacteristic
178SD16—868no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—432no—
183C2×C8—861no—
184C2×C8—861no—
185C4⋊C4—21no—
186C4⋊C4—864no—
187C4⋊C4—861no—
188C4⋊C4—861no—
189C4⋊C4C22⋊D4312yes—
190C22⋊C4—1722no—
191C22⋊C4—1722no—
192C42—864no—
193C42—861no—
194C42—861no—
195C23—22no—
196C23—41no—
197C23—41no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23D4×D4311yescharacteristic
203Q8—434no—
204Q8—862no—
205Q8—862no—
206Q8—862no—
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—432no—
215C2×C4—862no—
216C2×C4—861no—
217C2×C4—862no—
218C2×C4—862no—
219C2×C4—861no—
220C2×C4—861no—
221C2×C4—861no—
222C2×C4—861no—
223C2×C4—1721no—
224C2×C4—1721no—
225C2×C4—1721no—
226C2×C4C2×C4×D4311yescharacteristic
227C2×C4#1062189811yescharacteristic
228C2×C4D4×D4311yescharacteristic
229C2×C4D4×D4311yescharacteristic
230C2×C4#1062190011yescharacteristic
231C2×C4C2×C22⋊D4311yescharacteristic
232C8—41no—
233C8—862no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22(C22⋊D43)⋊C411yescharacteristic
242C22#1306329311yescharacteristic
243C22#1306329811yescharacteristic
244C22SD16×D4311yescharacteristic
245C22#1306334411yescharacteristic
246C22#1306334911yescharacteristic
247C22#1306335411yescharacteristic
248C4—42no—
249C4—864no—
250C4—862no—
251C4—3441no—
252C4—1721no—
253C4C22⋊C4×D4311yescharacteristic
254C4C4×C22⋊D4311yescharacteristic
255C4#1306329611yescharacteristic
256C4#1306330711yescharacteristic
257C2—82no—
258C2#1458277511yescharacteristic
259C2#1458299011yescharacteristic
260C2#1458299611yescharacteristic
261C2#1458303611yescharacteristic
262C2#1458304111yescharacteristic
263C2#1458309811yescharacteristic
264C2#1458312011yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC2×#102×C43C2
socleC23×C43C2×D4
hypercenterC2×#102D43
hypocenterC43#1880
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#13063290C2semidirect
3. C2×#13063250C2semidirect
5. #14582661C2semidirect
6. #14582653C2semidirect
11. C2×#10621883C4semidirect
94. C2×Dic43SD16semidirect
98. Dic86C22⋊C4semidirect
140. C43#1880semidirect