Finite Group Databasebeta

← #19135649

Subgroups — #19135649

Order 5504.

380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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#14583697C211yesmaximal, characteristic, complemented
2C2×#13063353C211yesmaximal, characteristic, complemented
3#14583463C211yesmaximal, characteristic, complemented
4#14582903C211yesmaximal, characteristic, complemented
5#14582872C211yesmaximal, characteristic, complemented
6#14582671C211yesmaximal, characteristic, complemented
7C43×#421C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C22×D172C2211yescharacteristic
10#13063356—21no—
11#13063355—21no—
12#13063353—22no—
13#13063353—22no—
14#13063351—21no—
15#13063350—21no—
16#13063345—22no—
17C2×#10621873—21no—
18C2×D344—21no—
19C2×#10621877C2211yescharacteristic
20#13063321—21no—
21#13063314—21no—
22#13063299—22no—
23#13063293—22no—
24#13063284C2211yescharacteristic
25#13063245—22no—
26#13063239—22no—
27C2×#41×C43C2211yescharacteristic
28C2×M16×C43C2211yescharacteristic
29#117×C43C2211yescharacteristic
30#104×C43—22no—
31C23×D43—21no—
32#41×C43—21no—
33#41×C43—21no—
34#41×C43—21no—
35#41×C43—21no—
36C2×Q8×C43D411yescharacteristic
37C2×D4×C43—21no—
38C2×D4×C43D411yescharacteristic
39C22×C4×C43—21no—
40C22×C4×C43C2311yescharacteristic
41C2×C22⋊D43—24no—
42C2×C22⋊D43—21no—
43#10621898—21no—
44#10621898—21no—
45#10621898—21no—
46#10621898—21no—
47C2×D172—21no—
48C2×D172—21no—
49C2×D172—21no—
50C2×D172—21no—
51C2×D172—21no—
52C2×D172D412yes—
53C2×D172D411yescharacteristic, complemented
54C2×C4×D43—21no—
55C2×Dic86D411yescharacteristic, complemented
56M16×C43—21no—
57M16×C43D412yescomplemented
58C2×C8×C43—21no—
59C4⋊C4×C43—21no—
60C22⋊C4×C43—21no—
61C42×C43—21no—
62C22⋊Dic43D412yes—
63#10621885—22no—
64#10621884—22no—
65#10621883—22no—
66#10621882—22no—
67(C2×D43)⋊C4—24no—
68C4⋊Dic43—21no—
69C4×Dic43—21no—
70#10621877—21no—
71#10621877—21no—
72C2×C43⋊C8D412yescomplemented
73D344—24no—
74#10621873—24no—
75C23×C43—21no—
76C23×C43C2×D411yescharacteristic
77C22×D43—22no—
78C22×D43—21no—
79C22×D43—41no—
80C22×D43—41no—
81C22×D43—82no—
82Q8×C43—21no—
83Q8×C43—21no—
84D4×C43—21no—
85D4×C43—21no—
86D4×C43—41no—
87D4×C43—41no—
88C2×C4×C43—21no—
89C2×C4×C43—41no—
90C2×C4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43C2×D411yescharacteristic
93C2×C4×C43C2×D411yescharacteristic
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2×D411yescharacteristic
97C2×C4×C43#4111yescharacteristic
98C22⋊D43—41no—
99C22⋊D43—41no—
100C22⋊D43—84no—
101C2×Dic43—22no—
102C2×Dic43—21no—
103D172—22no—
104D172—21no—
105D172—21no—
106D172—22no—
107D172—41no—
108D172—41no—
109C4×D43—41no—
110C4×D43—41no—
111Dic86—21no—
112Dic86—21no—
113C8×C43—22no—
114C43⋊C8—22no—
115C22×C43—41no—
116C22×C43—42no—
117C22×C43—41no—
118C22×C43#12011yescharacteristic
119C22×C43#12111yescharacteristic
120C22×C43#12711yescharacteristic
121C2×D43—44no—
122C2×D43—42no—
123C2×D43—41no—
124C2×D43—82no—
125C2×D43—82no—
126C2×D43—81no—
127C4×C43—41no—
128C4×C43—81no—
129C4×C43#12011yescharacteristic
130C4×C43#12011yescharacteristic
131C4×C43#12111yescharacteristic
132C4×C43#12111yescharacteristic
133Dic43—42no—
134Dic43—41no—
135#2008—431nomaximal, Sylow
136C2×C43—21no—
137C2×C43—21no—
138C2×C43—21no—
139C2×C43—81no—
140C2×C43#39211yescharacteristic
141D43—82no—
142D43—81no—
143#575—431no—
144C2×AGL(1,ℤ/8)—431no—
145#535—431no—
146#421D4311yescharacteristic, complemented
147#418—431no—
148#410—431no—
149#344—431no—
150C43#200811yescharacteristic, complemented, Sylow
151C2×#41—431no—
152C2×#41C2×D4311yescharacteristic
153C22×D4—431no—
154#137—861no—
155#137—861no—
156AGL(1,ℤ/8)—862no—
157AGL(1,ℤ/8)—861no—
158AGL(1,ℤ/8)—861no—
159AGL(1,ℤ/8)—862no—
160#135—862no—
161C2×SD16—861no—
162C2×D8—861no—
163C2×M16—431no—
164C2×M16C2×D4311yescharacteristic
165#127—861no—
166#124—861no—
167#121—862no—
168#120—862no—
169#117—431no—
170#117C2×D4311yescharacteristic
171#104—22no—
172#102—862no—
173#99—862no—
174C24—861no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—861no—
180#41—861no—
181#41—861no—
182#41—861no—
183C2×Q8—431no—
184C2×Q8D17211yescharacteristic
185C2×D4—21no—
186C2×D4—432no—
187C2×D4—431no—
188C2×D4—864no—
189C2×D4—861no—
190C2×D4—861no—
191C2×D4—861no—
192C2×D4—861no—
193C2×D4—861no—
194C2×D4—861no—
195C2×D4D17211yescharacteristic
196C22×C4—21no—
197C22×C4—861no—
198C22×C4C22×D4311yescharacteristic
199Q16—862no—
200SD16—864no—
201SD16—862no—
202SD16—862no—
203D8—864no—
204D8—862no—
205M16—21no—
206M16—861no—
207M16—861no—
208M16C22⋊D4312yescomplemented
209C2×C8—21no—
210C2×C8—432no—
211C4⋊C4—21no—
212C4⋊C4—861no—
213C22⋊C4—21no—
214C22⋊C4—432no—
215C22⋊C4—864no—
216C42—21no—
217C42—861no—
218C23—21no—
219C23—861no—
220C23—862no—
221C23—3442no—
222C23—1721no—
223C23—1721no—
224C23D4×D4311yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—861no—
228Q8—861no—
229D4—21no—
230D4—21no—
231D4—41no—
232D4—41no—
233D4—861no—
234D4—862no—
235D4—861no—
236D4—862no—
237D4—3444no—
238D4—1721no—
239D4—1721no—
240D4—1721no—
241D4—1721no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—862no—
247C2×C4—861no—
248C2×C4—1721no—
249C2×C4—1721no—
250C2×C4C2×D17211yescharacteristic
251C2×C4#1062189811yescharacteristic
252C2×C4D4×D4311yescharacteristic
253C2×C4D4×D4311yescharacteristic
254C2×C4D4×D4311yescharacteristic
255C2×C4C2×C22⋊D4311yescharacteristic
256C8—22no—
257C8—862no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22—3441no—
262C22—3442no—
263C22—3442no—
264C22—1724no—
265C22—1721no—
266C22—1722no—
267C22#1306329511yescharacteristic
268C22#1306329811yescharacteristic
269C22#1306332111yescharacteristic
270C4—41no—
271C4—81no—
272C4—1722no—
273C4—1721no—
274C4#1306329311yescharacteristic
275C4#1306329511yescharacteristic
276C4#1306329811yescharacteristic
277C4#1306329911yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—81no—
282C2—3442no—
283C2—3441no—
284C2#1458280811yescharacteristic
subgroupG/H
centerC2#14582808
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#421C2
socleC2×C43#392
hypercenter#421D43
hypocenterC43#2008
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #14583697C2semidirect
2. C2×#13063353C2semidirect
3. #14583463C2semidirect
4. #14582903C2semidirect
5. #14582872C2semidirect
6. #14582671C2semidirect
7. C43×#421C2semidirect
53. C2×D172D4semidirect
55. C2×Dic86D4semidirect
57. M16×C43D4semidirect
72. C2×C43⋊C8D4semidirect
146. #421D43semidirect
150. C43#2008semidirect
208. M16C22⋊D43semidirect