Finite Group Databasebeta

← #19143911

Subgroups — #19143911

Order 5504.

712 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063373C211yesmaximal, characteristic, complemented
2C2×#13063357C211yesmaximal, characteristic, complemented
3C2×#13063348C211yesmaximal, characteristic, complemented
4#14583479C211yesmaximal, characteristic, complemented
5#14583060C211yesmaximal, characteristic, complemented
6#14583059C211yesmaximal, characteristic, complemented
7#14583053C211yesmaximal, characteristic, complemented
8#14583047C211yesmaximal, characteristic, complemented
9#14583046C211yesmaximal, characteristic, complemented
10#14583039C211yesmaximal, characteristic, complemented
11#14583038C211yesmaximal, characteristic, complemented
12#14582899C211yesmaximal, characteristic, complemented
13#103×D43C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#451C211yesmaximal, characteristic, complemented
16#13063373—24no—
17#13063373—24no—
18C2×#10621902—21no—
19C2×#10621902C2211yescharacteristic
20C2×#10621902C2211yescharacteristic
21C2×#10621902C2211yescharacteristic
22C2×#10621898—21no—
23C2×#10621898—21no—
24C2×#10621898C2211yescharacteristic
25C2×#10621898C2211yescharacteristic
26C2×Q8×D43—21no—
27C2×Q8×D43C2211yescharacteristic
28C2×Q8×D43C2211yescharacteristic
29#13063357—24no—
30#13063348—24no—
31C2×#10621885C2211yescharacteristic
32C2×#10621873C2211yescharacteristic
33C2×#10621884C2211yescharacteristic
34C2×#10621884C2211yescharacteristic
35C2×#10621884C2211yescharacteristic
36C2×D344C2211yescharacteristic
37C2×#10621872C2211yescharacteristic
38C2×C8×D43C2211yescharacteristic
39#13063303—21no—
40#13063301C2211yescharacteristic
41#13063300—21no—
42#13063300C2211yescharacteristic
43#13063299C2211yescharacteristic
44#13063298—21no—
45#13063298—21no—
46C4⋊C4×D43C2211yescharacteristic
47#13063250C2211yescharacteristic
48#13063249C2211yescharacteristic
49#13063249C2211yescharacteristic
50#13063248C2211yescharacteristic
51#13063247C2211yescharacteristic
52#13063245C2211yescharacteristic
53C22⋊(C43⋊C8)C2211yescharacteristic
54(C2×D43)⋊C8C2211yescharacteristic
55(C2×D43)⋊C8C2211yescharacteristic
56C22×Q8×C43C2211yescharacteristic
57C2×Q16×C43C2211yescharacteristic
58C2×Q16×C43C2211yescharacteristic
59C22⋊Q8×C43C2211yescharacteristic
60#103×C43C2211yescharacteristic
61#103×C43C2211yescharacteristic
62C22⋊C8×C43C2211yescharacteristic
63C2×Q8×C43—22no—
64C2×Q8×C43—22no—
65C2×Q8×C43—21no—
66C2×Q8×C43C2311yescharacteristic
67C2×Q8×C43C2311yescharacteristic
68C2×Q8×C43C2311yescharacteristic
69C22×C4×C43—21no—
70C22×C4×C43C2311yescharacteristic
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43D411yescharacteristic
74C2×C22⋊D43D411yescharacteristic
75#10621902—28no—
76#10621902—22no—
77#10621902—22no—
78#10621902—22no—
79#10621902—22no—
80#10621902—22no—
81#10621902D414yescomplemented
82Q8×D43—28no—
83Q8×D43—22no—
84Q8×D43—22no—
85Q8×D43—22no—
86Q8×D43D414yescomplemented
87#10621898—28no—
88#10621898—28no—
89#10621898—22no—
90#10621898—22no—
91#10621898—22no—
92#10621898—22no—
93C2×D172—21no—
94C2×D172—21no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172D411yescharacteristic
98C2×D172C2311yescharacteristic
99C2×D172C2311yescharacteristic
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43—21no—
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—21no—
107C2×C4×D43C2311yescharacteristic
108C2×C4×D43C2311yescharacteristic
109C2×Dic86—21no—
110C2×Dic86—21no—
111C2×Dic86D411yescharacteristic
112C2×Dic86C2311yescharacteristic
113Q16×C43—22no—
114Q16×C43—22no—
115C2×C8×C43C2311yescharacteristic
116C2×C8×C43C2311yescharacteristic
117C4⋊C4×C43—21no—
118C4⋊C4×C43C2311yescharacteristic
119C22⋊C4×C43—21no—
120#10621885—22no—
121#10621884—22no—
122#10621884—22no—
123#10621884—22no—
124(C2×D43)⋊C4—21no—
125(C2×D43)⋊C4—21no—
126(C2×D43)⋊C4—21no—
127C4⋊Dic43C2311yescharacteristic
128Dic43⋊C4—21no—
129Dic43⋊C4—21no—
130C2×C43⋊C8C2311yescharacteristic
131C2×C43⋊C8C2311yescharacteristic
132D344—22no—
133#10621873—22no—
134#10621872—22no—
135C8×D43—22no—
136C23×C43C2×D411yescharacteristic
137C22×D43—21no—
138C22×D43—21no—
139C22×D43C2×D411yescharacteristic
140C22×D43C2×D411yescharacteristic
141Q8×C43—24no—
142Q8×C43—21no—
143Q8×C43—21no—
144Q8×C43—21no—
145Q8×C43—21no—
146Q8×C43C2×D412yes—
147Q8×C43C2×D412yes—
148C2×C4×C43—24no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43C2×D411yescharacteristic
156C2×C4×C43C2411yescharacteristic
157C22⋊D43—24no—
158C22⋊D43—22no—
159C22⋊D43—22no—
160C22⋊D43—81no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43C2×D411yescharacteristic
164C2×Dic43C2×D411yescharacteristic
165D172—24no—
166D172—24no—
167D172—22no—
168D172—21no—
169D172—21no—
170D172—21no—
171D172—42no—
172D172—81no—
173D172C2×D412yes—
174C4×D43—24no—
175C4×D43—24no—
176C4×D43—24no—
177C4×D43—24no—
178C4×D43—21no—
179C4×D43—21no—
180C4×D43—24no—
181C4×D43—42no—
182C4×D43—81no—
183C4×D43C2×D412yes—
184C4×D43C2×D412yes—
185Dic86—24no—
186Dic86—21no—
187Dic86—24no—
188Dic86—22no—
189Dic86C2×D412yes—
190C8×C43—21no—
191C8×C43—21no—
192C43⋊C8—21no—
193C43⋊C8—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43C22×D411yescharacteristic
198C2×D43—21no—
199C2×D43—21no—
200C2×D43—22no—
201C2×D43—21no—
202C2×D43—21no—
203C2×D43—21no—
204C2×D43—41no—
205C2×D43—41no—
206C2×D43—41no—
207C2×D43—41no—
208C2×D43—41no—
209C2×D43#12012yes—
210C4×C43—22no—
211C4×C43—22no—
212C4×C43—21no—
213C4×C43—41no—
214C4×C43—41no—
215C4×C43C22×D411yescharacteristic
216C4×C43C22×D411yescharacteristic
217Dic43—21no—
218Dic43—22no—
219Dic43—41no—
220Dic43#12012yes—
221#3013—431nomaximal, Sylow
222C2×C43—41no—
223C2×C43C2×#12011yescharacteristic
224C2×C43#57711yescharacteristic
225C2×C43#57811yescharacteristic
226D43—22no—
227D43—41no—
228D43—42no—
229D43—81no—
230C2×2−1+4—431no—
231C2×#137—431no—
232C2×#135—431no—
233#537—431no—
234#452—431no—
235#452—431no—
236#451—431no—
237#451D4311yescharacteristic, complemented
238#449—431no—
239#449—431no—
240#448—431no—
241#448—431no—
242#417—431no—
243C2×#103—431no—
244#408—431no—
245C43#301311yescharacteristic, complemented, Sylow
2462−1+4—864no—
2472−1+4—864no—
248C2×#41—431no—
249C2×#41—431no—
250C2×#41—431no—
251C2×#41—431no—
252C2×#41—431no—
253C2×#41—861no—
254C2×#41—861no—
255C2×#41—861no—
256C22×Q8—431no—
257C22×Q8—431no—
258C22×Q8—861no—
259C22×Q8C2×D4311yescharacteristic
260#137—864no—
261#135—864no—
262C2×Q16—431no—
263C2×Q16C2×D4311yescharacteristic
264C2×Q16C2×D4311yescharacteristic
265C2×SD16—431no—
266C2×SD16—431no—
267C2×SD16—431no—
268C2×SD16—431no—
269C2×D8—431no—
270C2×M16—431no—
271C22×C8—431no—
272C22⋊Q8—431no—
273C22⋊Q8—861no—
274C22⋊Q8C2×D4311yescharacteristic
275#121—431no—
276#121—431no—
277#121—861no—
278#121—861no—
279#121—861no—
280C2×C4⋊C4—431no—
281#103—431no—
282#103—431no—
283#103—431no—
284#103—431no—
285#103C2×D4311yescharacteristic
286#103C2×D4311yescharacteristic
287#102—431no—
288#102—431no—
289C22⋊C8—431no—
290C22⋊C8—431no—
291C22⋊C8—431no—
292C22⋊C8C2×D4311yescharacteristic
293#41—434no—
294#41—862no—
295#41—862no—
296#41—862no—
297#41—862no—
298#41—868no—
299#41—868no—
300#41—862no—
301#41—862no—
302#41—862no—
303#41—862no—
304#41—868no—
305#41—862no—
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—21no—
309C2×Q8—431no—
310C2×Q8—434no—
311C2×Q8—431no—
312C2×Q8—861no—
313C2×Q8—861no—
314C2×Q8—862no—
315C2×Q8—862no—
316C2×Q8—868no—
317C2×Q8—862no—
318C2×Q8C22×D4311yescharacteristic
319C2×Q8C22×D4311yescharacteristic
320C2×Q8C22×D4311yescharacteristic
321C2×D4—431no—
322C2×D4—431no—
323C2×D4—431no—
324C2×D4—431no—
325C2×D4—431no—
326C2×D4—861no—
327C2×D4—861no—
328C2×D4—861no—
329C2×D4—861no—
330C2×D4—861no—
331C2×D4—861no—
332C22×C4—21no—
333C22×C4—431no—
334C22×C4—431no—
335C22×C4—861no—
336C22×C4—861no—
337C22×C4—861no—
338C22×C4—861no—
339C22×C4—861no—
340C22×C4—861no—
341C22×C4—861no—
342C22×C4C22×D4311yescharacteristic
343Q16—22no—
344Q16—22no—
345Q16—862no—
346SD16—862no—
347SD16—862no—
348SD16—862no—
349SD16—862no—
350D8—862no—
351M16—862no—
352C2×C8—431no—
353C2×C8—431no—
354C2×C8—862no—
355C2×C8C22×D4311yescharacteristic
356C2×C8C22×D4311yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—431no—
359C4⋊C4—861no—
360C4⋊C4—861no—
361C4⋊C4C22×D4311yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—861no—
364C22⋊C4—861no—
365C22⋊C4—861no—
366C23—431no—
367C23—431no—
368C23—861no—
369C23—861no—
370C23D4×D4311yescharacteristic
371Q8—24no—
372Q8—21no—
373Q8—21no—
374Q8—21no—
375Q8—21no—
376Q8—432no—
377Q8—864no—
378Q8—862no—
379Q8—864no—
380Q8—861no—
381Q8D4×D4312yes—
382Q8D4×D4312yes—
383D4—432no—
384D4—862no—
385D4—864no—
386D4—864no—
387D4—862no—
388D4—862no—
389D4—864no—
390D4—861no—
391D4—861no—
392D4—861no—
393D4—3441no—
394D4—3441no—
395D4—1722no—
396C2×C4—24no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—431no—
404C2×C4—432no—
405C2×C4—432no—
406C2×C4—431no—
407C2×C4—864no—
408C2×C4—864no—
409C2×C4—864no—
410C2×C4—864no—
411C2×C4—864no—
412C2×C4—861no—
413C2×C4—861no—
414C2×C4—861no—
415C2×C4—861no—
416C2×C4—3441no—
417C2×C4—1722no—
418C2×C4D4×D4311yescharacteristic
419C2×C4C23×D4311yescharacteristic
420C8—21no—
421C8—21no—
422C8—861no—
423C8—861no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—432no—
428C22—861no—
429C22—861no—
430C22—862no—
431C22—861no—
432C22—861no—
433C22—861no—
434C22—1721no—
435C22—1721no—
436C22—1721no—
437C22—1721no—
438C22—1721no—
439C22C2×D4×D4311yescharacteristic
440C4—22no—
441C4—22no—
442C4—21no—
443C4—41no—
444C4—41no—
445C4—432no—
446C4—861no—
447C4—862no—
448C4—1721no—
449C4C2×D4×D4311yescharacteristic
450C4C2×D4×D4311yescharacteristic
451C2—41no—
452C2—862no—
453C2—3441no—
454C2—1721no—
455C2—1722no—
456C2#120×D4311yescharacteristic
457C2#1458370811yescharacteristic
458C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#451C2
socleC22×C43C22×D4
hypercenter#451D43
hypocenterC43#3013
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#13063373C2semidirect
2. C2×#13063357C2semidirect
3. C2×#13063348C2semidirect
4. #14583479C2semidirect
5. #14583060C2semidirect
6. #14583059C2semidirect
7. #14583053C2semidirect
8. #14583047C2semidirect
9. #14583046C2semidirect
10. #14583039C2semidirect
11. #14583038C2semidirect
12. #14582899C2semidirect
13. #103×D43C2semidirect
14. #14582864C2semidirect
15. C43×#451C2semidirect
81. #10621902D4semidirect
86. Q8×D43D4semidirect
237. #451D43semidirect
245. C43#3013semidirect