Finite Group Databasebeta

← #19134562

Subgroups — #19134562

Order 5504.

588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#13063370C211yesmaximal, characteristic
2#14582917C211yesmaximal, characteristic, complemented
3#14582915C211yesmaximal, characteristic, complemented
4#14582904C211yesmaximal, characteristic, complemented
5#14582881C211yesmaximal, characteristic, complemented
6#14582872C211yesmaximal, characteristic, complemented
7C43×#418C211yesmaximal, characteristic, complemented
8#13063370—22no—
9#13063370—22no—
10#13063370—22no—
11#13063370—22no—
12C2×#10621898C2211yescharacteristic
13C2×#10621898C2211yescharacteristic
14C2×#10621900—21no—
15C2×#10621900C412yescomplemented
16C22×C22⋊D43—22no—
17C2×D4×D43—21no—
18C2×D4×D43C412yescomplemented
19C2×#10621877C2211yescharacteristic, complemented
20#13063284C2211yescharacteristic, complemented
21#13063253—22no—
22#13063251—22no—
23#13063246—22no—
24#13063243—21no—
25#13063241—21no—
26#13063239—22no—
27C22×D4×C43C2211yescharacteristic
28C2×M16×C43C2211yescharacteristic, complemented
29#117×C43C2211yescharacteristic, complemented
30#102×C43—22no—
31C24×C43—21no—
32C23×D43—22no—
33C2×D4×C43—21no—
34C2×D4×C43—21no—
35C2×D4×C43—21no—
36C2×D4×C43C2×C412yes—
37C2×D4×C43D412yes—
38C2×D4×C43D412yes—
39C22×C4×C43C2311yescharacteristic
40C2×C22⋊D43—28no—
41C2×C22⋊D43—28no—
42C2×C22⋊D43—22no—
43C2×C22⋊D43—21no—
44C2×C22⋊D43—22no—
45C2×C22⋊D43D412yes—
46C22×Dic43—22no—
47#10621900—24no—
48#10621900—24no—
49#10621900—24no—
50#10621900—24no—
51D4×D43—24no—
52D4×D43—24no—
53D4×D43—24no—
54D4×D43—24no—
55#10621898—21no—
56#10621898—21no—
57#10621898—21no—
58#10621898—21no—
59#10621898—21no—
60#10621898—21no—
61#10621898D412yes—
62#10621898D412yes—
63C2×D172C2×C411yescharacteristic
64C2×D172D411yescharacteristic
65C2×C4×D43—21no—
66C2×C4×D43C2×C412yes—
67C2×Dic86C2×C411yescharacteristic
68C2×Dic86D411yescharacteristic
69M16×C43—21no—
70M16×C43—21no—
71C2×C8×C43—21no—
72C4⋊C4×C43—21no—
73C22⋊C4×C43—21no—
74C42×C43—21no—
75C22⋊Dic43—21no—
76C4⋊Dic43—21no—
77C4×Dic43—21no—
78#10621877—21no—
79#10621877—21no—
80C2×C43⋊C8—21no—
81C23×C43—22no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43—82no—
85C23×C43C2×D411yescharacteristic
86C22×D43—21no—
87C22×D43—28no—
88C22×D43—84no—
89C22×D43C22⋊C412yes—
90D4×C43—22no—
91D4×C43—22no—
92D4×C43—22no—
93D4×C43C22⋊C414yes—
94C2×C4×C43—41no—
95C2×C4×C43C22×C411yescharacteristic
96C2×C4×C43C2×D411yescharacteristic
97C2×C4×C43C2×D411yescharacteristic
98C2×C4×C43C2×D411yescharacteristic
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43C2×D411yescharacteristic
101C22⋊D43—28no—
102C22⋊D43—28no—
103C22⋊D43—22no—
104C22⋊D43—22no—
105C22⋊D43—22no—
106C22⋊D43—22no—
107C2×Dic43—28no—
108C2×Dic43—21no—
109C2×Dic43—41no—
110C2×Dic43C22⋊C412yes—
111D172—21no—
112D172—21no—
113D172—21no—
114D172C22⋊C412yes—
115C4×D43—22no—
116C4×D43—22no—
117C4×D43—22no—
118C4×D43—22no—
119Dic86—21no—
120Dic86—21no—
121Dic86—21no—
122Dic86C22⋊C412yes—
123C8×C43—41no—
124C43⋊C8—41no—
125C22×C43—24no—
126C22×C43—41no—
127C22×C43—44no—
128C22×C43—82no—
129C22×C43—82no—
130C22×C43C2×C22⋊C411yescharacteristic
131C22×C43#12011yescharacteristic
132C22×C43#12011yescharacteristic
133C2×D43—22no—
134C2×D43—22no—
135C2×D43—42no—
136C2×D43—42no—
137C2×D43—88no—
138C4×C43—81no—
139C4×C43C2×C22⋊C411yescharacteristic
140C4×C43C2×C22⋊C411yescharacteristic
141C4×C43#12011yescharacteristic
142C4×C43#12011yescharacteristic
143Dic43—22no—
144Dic43—22no—
145Dic43—81no—
146#1795—431nomaximal, Sylow
147C2×C43—21no—
148C2×C43—21no—
149C2×C43—21no—
150C2×C43—44no—
151C2×C43#37911yescharacteristic
152D43—42no—
153D43—42no—
154C2×H(5,𝔽2)—431no—
155#421—431no—
156#421—431no—
157#418—431no—
158#418D4311yescharacteristic, complemented
159#413—431no—
160#410—431no—
161C43#179511yescharacteristic, complemented, Sylow
162H(5,𝔽2)—862no—
163H(5,𝔽2)—862no—
164H(5,𝔽2)—862no—
165H(5,𝔽2)—862no—
166C2×#41—431no—
167C2×#41—432no—
168C2×#41—431no—
169C2×#41—861no—
170C22×D4—432no—
171C22×D4—861no—
172C22×D4—862no—
173C22×D4C2×D4311yescharacteristic
174C2×M16—431no—
175C2×M16C2×D4311yescharacteristic, complemented
176#117—431no—
177#117C2×D4311yescharacteristic, complemented
178#104—862no—
179#104—862no—
180#102—22no—
181#102—862no—
182#101—861no—
183#100—861no—
184#99—862no—
185C24—21no—
186C24—862no—
187#41—432no—
188#41—432no—
189#41—864no—
190#41—864no—
191#41—864no—
192#41—864no—
193#41—861no—
194#41—861no—
195#41—861no—
196#41—861no—
197#41—861no—
198#41—861no—
199C2×Q8—431no—
200C2×Q8—431no—
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—432no—
205C2×D4—431no—
206C2×D4—431no—
207C2×D4—862no—
208C2×D4—864no—
209C2×D4—864no—
210C2×D4—864no—
211C2×D4—862no—
212C2×D4—868no—
213C2×D4—868no—
214C2×D4—861no—
215C2×D4—864no—
216C2×D4C4×D4312yes—
217C2×D4D17212yes—
218C2×D4C22⋊D4312yes—
219C22×C4—432no—
220C22×C4—862no—
221C22×C4—861no—
222C22×C4C22×D4311yescharacteristic
223M16—21no—
224M16—21no—
225M16—861no—
226M16—861no—
227C2×C8—21no—
228C2×C8—861no—
229C4⋊C4—21no—
230C4⋊C4—861no—
231C22⋊C4—21no—
232C22⋊C4—861no—
233C42—21no—
234C42—861no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—82no—
239C23—432no—
240C23—868no—
241C23—861no—
242C23—3444no—
243C23D4×D4311yescharacteristic
244Q8—432no—
245Q8—861no—
246Q8—861no—
247Q8—861no—
248D4—22no—
249D4—22no—
250D4—22no—
251D4—432no—
252D4—868no—
253D4—868no—
254D4—862no—
255D4—862no—
256D4—862no—
257D4—862no—
258D4—861no—
259D4—861no—
260D4—861no—
261D4(C2×D43)⋊C414yes—
262C2×C4—41no—
263C2×C4—432no—
264C2×C4—868no—
265C2×C4—861no—
266C2×C4—862no—
267C2×C4—862no—
268C2×C4—862no—
269C2×C4—862no—
270C2×C4—1721no—
271C2×C4C2×C4×D4311yescharacteristic
272C2×C4C2×D17211yescharacteristic
273C2×C4D4×D4311yescharacteristic
274C2×C4D4×D4311yescharacteristic
275C2×C4D4×D4311yescharacteristic
276C2×C4C2×C22⋊D4311yescharacteristic
277C8—41no—
278C8—1721no—
279C22—24no—
280C22—41no—
281C22—44no—
282C22—82no—
283C22—82no—
284C22—862no—
285C22—862no—
286C22—3448no—
287C22—1722no—
288C22—1722no—
289C22C22⋊C4×D4311yescharacteristic
290C22#1306329311yescharacteristic
291C22#1306329511yescharacteristic
292C4—81no—
293C4—862no—
294C4—862no—
295C4—3441no—
296C4C22⋊C4×D4311yescharacteristic
297C4C2×(C2×D43)⋊C411yescharacteristic
298C4#1306329311yescharacteristic
299C4#1306329511yescharacteristic
300C2—21no—
301C2—21no—
302C2—21no—
303C2—44no—
304C2—1722no—
305C2—1722no—
306C2#1458275411yescharacteristic
subgroupG/H
centerC2#14582754
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#418C2
socleC2×C43#379
hypercenter#418D43
hypocenterC43#1795
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #14582917C2semidirect
3. #14582915C2semidirect
4. #14582904C2semidirect
5. #14582881C2semidirect
6. #14582872C2semidirect
7. C43×#418C2semidirect
15. C2×#10621900C4semidirect
18. C2×D4×D43C4semidirect
19. C2×#10621877C22semidirect
20. #13063284C22semidirect
28. C2×M16×C43C22semidirect
29. #117×C43C22semidirect
158. #418D43semidirect
161. C43#1795semidirect
175. C2×M16C2×D43semidirect
177. #117C2×D43semidirect