Finite Group Databasebeta

← #19135658

Subgroups — #19135658

Order 5504.

348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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#14583699C211yesmaximal, characteristic
2C2×#13063358C211yesmaximal, characteristic, complemented
3#14583475C211yesmaximal, characteristic, complemented
4#14582915C211yesmaximal, characteristic, complemented
5#14582909C211yesmaximal, characteristic, complemented
6#14582872C211yesmaximal, characteristic, complemented
7C43×#344C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C2×#10621898C2211yescharacteristic
10C22×Dic86C2211yescharacteristic
11#13063358—22no—
12#13063358—21no—
13#13063358—21no—
14#13063358—22no—
15#13063353—21no—
16#13063353—21no—
17#13063347—22no—
18C2×Dic172—21no—
19C2×#10621873—21no—
20#13063325—21no—
21#13063313—21no—
22#13063309—22no—
23#13063305—22no—
24#13063284C2211yescharacteristic
25#13063251—22no—
26#13063250—22no—
27#13063239—22no—
28C2×M16×C43C2211yescharacteristic
29C2×M16×C43C2211yescharacteristic
30#117×C43C2211yescharacteristic
31C22×C4×C43C2311yescharacteristic
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C22×Dic43—21no—
35#10621898—21no—
36#10621898—21no—
37#10621898—21no—
38#10621898—21no—
39#10621898—21no—
40#10621898—21no—
41#10621898—21no—
42#10621898—21no—
43C2×D172D411yescharacteristic
44C2×D172D411yescharacteristic
45C2×C4×D43—21no—
46C2×C4×D43—21no—
47C2×Dic86—21no—
48C2×Dic86—21no—
49C2×Dic86—21no—
50C2×Dic86—21no—
51C2×Dic86—21no—
52C2×Dic86D412yes—
53C2×Dic86D411yescharacteristic
54C2×Dic86D411yescharacteristic
55M16×C43—21no—
56M16×C43—21no—
57M16×C43—21no—
58M16×C43D412yes—
59C2×C8×C43—21no—
60C2×C8×C43D412yes—
61C4⋊C4×C43—21no—
62C22⋊C4×C43D412yes—
63C42×C43—21no—
64C22⋊Dic43—21no—
65(C2×D43)⋊C4—24no—
66C4⋊Dic43—24no—
67C4⋊Dic43—21no—
68C4×Dic43—21no—
69Dic172—24no—
70Dic172—22no—
71D344—22no—
72#10621873—24no—
73#10621873—22no—
74#10621873—22no—
75C23×C43C2×D411yescharacteristic
76C22×D43—21no—
77C22×D43—21no—
78C2×C4×C43—22no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43#4111yescharacteristic
85C22⋊D43—41no—
86C22⋊D43—41no—
87C22⋊D43—41no—
88C22⋊D43—41no—
89C2×Dic43—21no—
90C2×Dic43—22no—
91C2×Dic43—21no—
92C2×Dic43—41no—
93C2×Dic43—41no—
94C2×Dic43—41no—
95D172—21no—
96D172—21no—
97D172—21no—
98D172—21no—
99C4×D43—41no—
100C4×D43—41no—
101C4×D43—41no—
102C4×D43—41no—
103Dic86—22no—
104Dic86—21no—
105Dic86—21no—
106Dic86—21no—
107Dic86—22no—
108Dic86—21no—
109Dic86—41no—
110Dic86—41no—
111C8×C43—22no—
112C8×C43—22no—
113C22×C43—41no—
114C22×C43#12011yescharacteristic
115C22×C43#12111yescharacteristic
116C22×C43#12711yescharacteristic
117C2×D43—42no—
118C2×D43—41no—
119C2×D43—41no—
120C2×D43—81no—
121C4×C43—42no—
122C4×C43#12011yescharacteristic
123C4×C43#12011yescharacteristic
124C4×C43#12111yescharacteristic
125C4×C43#12111yescharacteristic
126Dic43—42no—
127Dic43—41no—
128Dic43—41no—
129Dic43—81no—
130#2009—431nomaximal, Sylow
131C2×C43—21no—
132C2×C43—21no—
133C2×C43—21no—
134C2×C43#39211yescharacteristic
135D43—81no—
136D43—81no—
137#575—431no—
138C2×#137—431no—
139#536—431no—
140#421—431no—
141#419—431no—
142#410—431no—
143#344D4311yescharacteristic, complemented
144C43#200911yescharacteristic, complemented, Sylow
145C2×#41—431no—
146C2×#41—431no—
147C22×Q8—431no—
148#137—862no—
149#137—861no—
150#137—861no—
151#137—862no—
152AGL(1,ℤ/8)—861no—
153AGL(1,ℤ/8)—861no—
154#135—862no—
155C2×Q16—861no—
156C2×SD16—861no—
157C2×M16C2×D4311yescharacteristic
158C2×M16C2×D4311yescharacteristic
159C4⋊Q8—861no—
160#124—861no—
161#123—862no—
162C22⋊Q8—862no—
163#117—431no—
164#117C2×D4311yescharacteristic
165#104—862no—
166#103—862no—
167#99—862no—
168#41—861no—
169#41—861no—
170#41—861no—
171#41—861no—
172#41—861no—
173#41—861no—
174#41—861no—
175#41—861no—
176C2×Q8—432no—
177C2×Q8—431no—
178C2×Q8—431no—
179C2×Q8—861no—
180C2×Q8—861no—
181C2×Q8—861no—
182C2×Q8—861no—
183C2×Q8—861no—
184C2×D4—431no—
185C2×D4—431no—
186C2×D4—861no—
187C2×D4—861no—
188C22×C4—861no—
189C22×C4—861no—
190C22×C4—861no—
191C22×C4C22×D4311yescharacteristic
192Q16—864no—
193Q16—862no—
194SD16—864no—
195SD16—862no—
196SD16—862no—
197D8—862no—
198M16—21no—
199M16—21no—
200M16—21no—
201M16D17212yes—
202C2×C8—21no—
203C2×C8D17212yes—
204C4⋊C4—21no—
205C4⋊C4—864no—
206C4⋊C4—861no—
207C22⋊C4—864no—
208C22⋊C4—861no—
209C22⋊C4D17212yes—
210C42—21no—
211C42—861no—
212C23—861no—
213C23—861no—
214C23C2×D17211yescharacteristic
215Q8—862no—
216Q8—861no—
217Q8—861no—
218Q8—861no—
219Q8—862no—
220Q8—861no—
221Q8—1721no—
222Q8—1721no—
223D4—861no—
224D4—861no—
225D4—861no—
226D4—861no—
227D4—1721no—
228D4—1721no—
229D4—1721no—
230D4—1721no—
231C2×C4—22no—
232C2×C4—862no—
233C2×C4—861no—
234C2×C4—861no—
235C2×C4—1721no—
236C2×C4—1721no—
237C2×C4—1721no—
238C2×C4—1721no—
239C2×C4—1721no—
240C2×C4—1721no—
241C2×C4—1721no—
242C2×C4C2×D17211yescharacteristic
243C2×C4C2×D17211yescharacteristic
244C2×C4D4×D4311yescharacteristic
245C2×C4D4×D4311yescharacteristic
246C2×C4D4×D4311yescharacteristic
247C2×C4#1062190211yescharacteristic
248C8—22no—
249C8—22no—
250C22—41no—
251C22—3441no—
252C22—1722no—
253C22—1721no—
254C22—1721no—
255C22#1306329511yescharacteristic
256C22#1306330011yescharacteristic
257C22#1306332211yescharacteristic
258C4—42no—
259C4—3441no—
260C4—1721no—
261C4—1721no—
262C4—1722no—
263C4#1306329511yescharacteristic
264C4#1306329511yescharacteristic
265C4#1306330011yescharacteristic
266C4#1306330011yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—3441no—
271C2—3441no—
272C2#1458280911yescharacteristic
subgroupG/H
centerC2#14582809
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#344C2
socleC2×C43#392
hypercenter#344D43
hypocenterC43#2009
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. C2×#13063358C2semidirect
3. #14583475C2semidirect
4. #14582915C2semidirect
5. #14582909C2semidirect
6. #14582872C2semidirect
7. C43×#344C2semidirect
143. #344D43semidirect
144. C43#2009semidirect