Finite Group Databasebeta

← #19146928

Subgroups — #19146928

Order 5504.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583607C211yesmaximal, characteristic, complemented
2#14583567C211yesmaximal, characteristic
3#14583244C211yesmaximal, characteristic, complemented
4#14583214C211yesmaximal, characteristic, complemented
5#14583210C211yesmaximal, characteristic, complemented
6#14583193C211yesmaximal, characteristic, complemented
7#14583148C211yesmaximal, characteristic, complemented
8#14583097C211yesmaximal, characteristic, complemented
9#14583059C211yesmaximal, characteristic, complemented
10#14583058C211yesmaximal, characteristic, complemented
11#14582991C211yesmaximal, characteristic, complemented
12#14582975C211yesmaximal, characteristic, complemented
13#14582901C211yesmaximal, characteristic, complemented
14#14582897C211yesmaximal, characteristic, complemented
15C43×#468C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063321—21no—
23#13063321C2211yescharacteristic
24#13063315—21no—
25#13063305—21no—
26#13063302—21no—
27#13063301C2211yescharacteristic
28#13063300C2211yescharacteristic
29#13063298—21no—
30#13063297—21no—
31Q8×Dic43C2211yescharacteristic
32#13063290C2211yescharacteristic
33C4×C22⋊D43C2211yescharacteristic
34(C22⋊D43)⋊C4—21no—
35(C22⋊D43)⋊C4—21no—
36C2×C4⋊Dic43C2211yescharacteristic
37C4⋊C4×D43C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063258C2211yescharacteristic
40Dic43⋊C8C2211yescharacteristic
41#13063250C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C2×M16×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#107×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70#10621900—22no—
71#10621900—41no—
72#10621898—22no—
73#10621898—41no—
74C2×D172—21no—
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79C2×Dic86—21no—
80C2×Dic86C2311yescharacteristic
81SD16×C43—41no—
82M16×C43—41no—
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C4⋊C4×C43—21no—
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C22⋊C4×C43—21no—
89C22⋊C4×C43—21no—
90C22⋊Dic43D411yescharacteristic
91#10621885—22no—
92#10621884—41no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4D411yescharacteristic
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4D411yescharacteristic
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110#10621872—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43C2×D411yescharacteristic
115Q8×C43—21no—
116Q8×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—81no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—22no—
128C22⋊D43—42no—
129C22⋊D43—42no—
130C22⋊D43—42no—
131C22⋊D43—81no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—42no—
136C2×Dic43—81no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140D172—21no—
141D172—21no—
142D172—81no—
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—42no—
146C4×D43—81no—
147Dic86—21no—
148Dic86—81no—
149Dic86#4112yes—
150C8×C43—21no—
151C8×C43—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43C22×D411yescharacteristic
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C4×C43—21no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43H(5,𝔽2)11yescharacteristic
173Dic43—22no—
174Dic43—21no—
175Dic43—21no—
176Dic43—41no—
177Dic43—41no—
178Dic43#13712yes—
179#3333—431nomaximal, Sylow
180C2×C43—41no—
181C2×C43—81no—
182C2×C43#54611yescharacteristic
183C2×C43C2×#13711yescharacteristic
184C2×C43#57611yescharacteristic
185D43—41no—
186D43—81no—
187#554—431no—
188#550—431no—
189#486—431no—
190#480—431no—
191#480—431no—
192#477—431no—
193#468—431no—
194#468D4311yescharacteristic, complemented
195#460—431no—
196#452—431no—
197#452—431no—
198C4×Q16—431no—
199#436—431no—
200#417—431no—
201#417—431no—
202C43#333311yescharacteristic, complemented, Sylow
203C2×#41—431no—
204C2×#41—431no—
205C2×Q16—431no—
206C2×SD16—431no—
207C2×SD16C2×D4311yescharacteristic
208C2×M16—431no—
209C2×M16C2×D4311yescharacteristic
210C4⋊Q8—431no—
211#127—431no—
212#127—861no—
213#125—861no—
214C22⋊Q8—431no—
215C22⋊Q8—861no—
216C22⋊Q8—861no—
217C22⋊Q8C2×D4311yescharacteristic
218#121—431no—
219#121—861no—
220#121—861no—
221#121C2×D4311yescharacteristic
222C4×Q8—431no—
223C4×Q8—431no—
224C4×D4—431no—
225C4×D4—861no—
226C4×D4—861no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229#107—431no—
230#107—431no—
231#107C2×D4311yescharacteristic
232C4⋊C8—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#103C2×D4311yescharacteristic
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242#102C2×D4311yescharacteristic
243C22⋊C8—431no—
244C22⋊C8—431no—
245C4×C8—431no—
246#41—862no—
247#41—862no—
248#41—1721no—
249#41—1721no—
250C2×Q8—431no—
251C2×Q8—861no—
252C2×Q8C22×D4311yescharacteristic
253C2×D4—21no—
254C2×D4—431no—
255C2×D4—431no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4C22×D4311yescharacteristic
262C22×C4—431no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4C22×D4311yescharacteristic
268Q16—862no—
269SD16—41no—
270SD16—1721no—
271M16—41no—
272M16—1721no—
273C2×C8—431no—
274C2×C8—431no—
275C2×C8C22×D4311yescharacteristic
276C2×C8C22×D4311yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—431no—
279C4⋊C4—431no—
280C4⋊C4—431no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4C22×D4311yescharacteristic
288C4⋊C4C22×D4311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—431no—
292C22⋊C4—431no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C42—431no—
296C42—861no—
297C42—861no—
298C23—21no—
299C23—431no—
300C23—861no—
301C23D4×D4311yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—432no—
305Q8—861no—
306Q8—3441no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—862no—
311D4—861no—
312D4—861no—
313D4—3441no—
314D4—3441no—
315D4—1722no—
316D4—1722no—
317D4—1722no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—431no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—3441no—
332C2×C4—3441no—
333C2×C4—1722no—
334C2×C4—1722no—
335C2×C4D4×D4311yescharacteristic
336C2×C4C23×D4311yescharacteristic
337C8—21no—
338C8—21no—
339C8—861no—
340C8—861no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—861no—
348C22—861no—
349C22—861no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22C2×D4×D4311yescharacteristic
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—432no—
359C4—861no—
360C4—861no—
361C4—862no—
362C4—1721no—
363C4—1721no—
364C4#41×D4311yescharacteristic
365C4#1306337011yescharacteristic
366C2—41no—
367C2—81no—
368C2—3441no—
369C2—1721no—
370C2#1458353811yescharacteristic
371C2#137×D4311yescharacteristic
372C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#468C2
socleC22×C43C22×D4
hypercenter#468D43
hypocenterC43#3333
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #14583607C2semidirect
3. #14583244C2semidirect
4. #14583214C2semidirect
5. #14583210C2semidirect
6. #14583193C2semidirect
7. #14583148C2semidirect
8. #14583097C2semidirect
9. #14583059C2semidirect
10. #14583058C2semidirect
11. #14582991C2semidirect
12. #14582975C2semidirect
13. #14582901C2semidirect
14. #14582897C2semidirect
15. C43×#468C2semidirect
194. #468D43semidirect
202. C43#3333semidirect