Finite Group Databasebeta

← #14798877

Subgroups — #14798877

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622790C211yesmaximal, characteristic
2#13070084C211yesmaximal, characteristic, complemented
3#13070077C211yesmaximal, characteristic, complemented
4#13069894C211yesmaximal, characteristic, complemented
5#13069887C211yesmaximal, characteristic
6#13069521C211yesmaximal, characteristic, complemented
7#13069406C211yesmaximal, characteristic, complemented
8#13069110C211yesmaximal, characteristic, complemented
9#13069103C211yesmaximal, characteristic
10#13068739C211yesmaximal, characteristic, complemented
11#13068730C211yesmaximal, characteristic, complemented
12#13068727C211yesmaximal, characteristic, complemented
13#13068667C211yesmaximal, characteristic, complemented
14#13068417C211yesmaximal, characteristic, complemented
15C11×#2949C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C11×#519C2211yescharacteristic
18C11×#518C2211yescharacteristic
19C2×#66995C2211yescharacteristic
20C2×#66985C2211yescharacteristic
21C2×#66954C2211yescharacteristic
22C11×#440—22no—
23C4×C11×SD16—22no—
24C11×#427C2211yescharacteristic
25C11×#419C2211yescharacteristic
26C11×#418C2211yescharacteristic
27C11×#405C2211yescharacteristic
28C2×#66900C2211yescharacteristic
29C2×#66900C2211yescharacteristic
30#10622838C2211yescharacteristic
31C2×#66897C2211yescharacteristic
32C2×#66897C2211yescharacteristic
33#10622828C2211yescharacteristic
34#10622790—22no—
35#10622790—22no—
36#10622745C2211yescharacteristic
37#10622737C2211yescharacteristic
38#10622737C2211yescharacteristic
39C2×#66883C2211yescharacteristic
40C2×#66883C2211yescharacteristic
41#10622714C2211yescharacteristic
42#10622619C2211yescharacteristic
43#10622618C2211yescharacteristic
44#10622618C2211yescharacteristic
45#10622197C2211yescharacteristic
46#10622171C2211yescharacteristic
47#10622171C2211yescharacteristic
48#10622171C2211yescharacteristic
49#10622171C2211yescharacteristic
50#10622171C2211yescharacteristic
51#10622171C2211yescharacteristic
52#10622171C2211yescharacteristic
53#10622169C2211yescharacteristic
54#10622169C2211yescharacteristic
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C2×#4339C2311yescharacteristic
58C2×C11×SD16—21no—
59C2×C11×SD16—21no—
60C2×C11×SD16—21no—
61C2×C11×SD16—21no—
62C2×C11×SD16D412yes—
63C2×C11×SD16D412yes—
64C2×C11×M16C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C11×#117—22no—
71C11×#117C2311yescharacteristic
72C11×#117C2311yescharacteristic
73C11×#117C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×#4326—21no—
76#66995—22no—
77#66995—41no—
78C2×#4325—21no—
79C2×#4324—21no—
80#66985—22no—
81#66985—41no—
82C2×#4323—21no—
83#66979C2311yescharacteristic
84C2×#4318C2311yescharacteristic
85C2×#4318C2311yescharacteristic
86C2×#4318C2311yescharacteristic
87C2×#4318C2311yescharacteristic
88C2×#4318C2311yescharacteristic
89C2×#4318C2311yescharacteristic
90#66954—21no—
91#66954—21no—
92#66954—21no—
93#66954—21no—
94C2×#4313—21no—
95C2×C8×D11—21no—
96C11×#107—21no—
97C11×#106—21no—
98C11×#103—22no—
99C11×#102—22no—
100C11×#97—21no—
101C4×C8×C11—21no—
102#66900—22no—
103#66900—41no—
104#66899—41no—
105#66897—22no—
106#66897—41no—
107#66896—41no—
108#66888—21no—
109#66887—21no—
110#66886—41no—
111#66886—41no—
112#66883—21no—
113#66883—21no—
114#66883—21no—
115#66883—21no—
116#66879—21no—
117C8×Dic11—21no—
118#66870—22no—
119#66869—41no—
120#66869—41no—
121#24987—111nomaximal, Sylow
122C24×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11C2×D412yes—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—21no—
136C22×C4×C11—42no—
137C22×C4×C11C2411yescharacteristic
138C2×C22⋊D11—21no—
139#4339—21no—
140#4339—21no—
141#4339—21no—
142#4339—21no—
143C2×D44#4111yescharacteristic
144C2×C4×D11—21no—
145C2×Dic22#4111yescharacteristic
146C11×SD16—22no—
147C11×SD16—22no—
148C11×SD16—22no—
149C11×SD16—22no—
150C11×M16—21no—
151C11×M16—21no—
152C2×C8×C11—21no—
153C2×C8×C11C2×D411yescharacteristic
154C2×C8×C11C2×D411yescharacteristic
155C2×C8×C11#4111yescharacteristic
156C2×C8×C11#4111yescharacteristic
157C2×C8×C11#4111yescharacteristic
158C2×C8×C11#4111yescharacteristic
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—42no—
163C11×C22⋊C4—21no—
164C11×C22⋊C4—21no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4#4112yes—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—42no—
171C22⋊Dic11—21no—
172#4326—42no—
173#4325—42no—
174#4324—42no—
175#4323—42no—
176C4⋊Dic11—21no—
177C4×Dic11—21no—
178#4318—21no—
179#4318—21no—
180#4318—21no—
181#4318—21no—
182#4318—21no—
183#4318—21no—
184#4318—21no—
185#4318—21no—
186#4318—21no—
187#4318—21no—
188#4318—21no—
189#4318—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196#4313—41no—
197#4313—41no—
198C8×D11—41no—
199C8×D11—41no—
200C2×#471—111no—
201#2949D1111yescharacteristic, complemented
202#2082—111no—
203#2081—111no—
204#2049—111no—
205#2048—111no—
206#1977—111no—
207#1953—111no—
208#1905—111no—
209#1904—111no—
210#1833—111no—
211#1830—111no—
212#1829—111no—
213#1814—111no—
214#1757—111no—
215C23×C11—22no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—161no—
219C23×C11C2×#4111yescharacteristic
220C22×D11—21no—
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—41no—
224Q8×C11—41no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—41no—
228D4×C11—41no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—162no—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C22⋊D11—41no—
243C22⋊D11—41no—
244C2×Dic11—21no—
245C2×Dic11—41no—
246D44—21no—
247D44—21no—
248C4×D11—41no—
249C4×D11—41no—
250Dic22—21no—
251Dic22—21no—
252C8×C11—41no—
253C8×C11#12311yescharacteristic
254C8×C11#12311yescharacteristic
255C8×C11#12311yescharacteristic
256C8×C11#12311yescharacteristic
257C11⋊C8—41no—
258C11⋊C8—41no—
259C11⋊C8—41no—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C2×#137—111no—
264C2×AGL(1,ℤ/8)—111no—
265C22×SD16C2×D1111yescharacteristic
266C2×#131—111no—
267#519C2×D1111yescharacteristic
268#518C2×D1111yescharacteristic
269#471—222no—
270#471—222no—
271#440—22no—
272C4×SD16—22no—
273#430—111no—
274#430—111no—
275C2×#108—111no—
276C2×#108—111no—
277#427C2×D1111yescharacteristic
278#421—111no—
279#421—111no—
280#419—111no—
281#419C2×D1111yescharacteristic
282#418—111no—
283#418C2×D1111yescharacteristic
284#413—111no—
285C2×#101—111no—
286C2×#101—111no—
287C2×#100—111no—
288C2×#100—111no—
289#410—111no—
290#405—111no—
291#405C2×D1111yescharacteristic
292#344—111no—
293#344—111no—
294#344—111no—
295#344—111no—
296#344—111no—
297#344—111no—
298#344—111no—
299#344—111no—
300H(3,ℤ/4)—111no—
301H(3,ℤ/4)—111no—
302C22×C11—41no—
303C22×C11—42no—
304C22×C11—82no—
305C22×C11—161no—
306C22×C11—161no—
307C22×C11#52911yescharacteristic
308C22×C11#54611yescharacteristic
309C22×C11#55511yescharacteristic
310C2×D11—41no—
311C2×D11—81no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—81no—
315C4×C11—81no—
316C4×C11C2×#12311yescharacteristic
317C4×C11#54011yescharacteristic
318C4×C11#54611yescharacteristic
319C4×C11#55311yescharacteristic
320Dic11—41no—
321Dic11—81no—
322C2×#41—111no—
323C22×Q8C22×D1111yescharacteristic
324C22×D4C22×D1111yescharacteristic
325#137—222no—
326#137—441no—
327AGL(1,ℤ/8)—222no—
328AGL(1,ℤ/8)—441no—
329C2×Q16—221no—
330C2×SD16—21no—
331C2×SD16—21no—
332C2×SD16—21no—
333C2×SD16—21no—
334C2×SD16—221no—
335C2×SD16—221no—
336C2×SD16C22⋊D1112yes—
337C2×SD16C22⋊D1112yes—
338C2×D8—221no—
339#131—221no—
340#131—221no—
341#131—221no—
342#131—221no—
343C2×M16—111no—
344C2×M16—111no—
345C2×M16—111no—
346C2×M16—111no—
347C2×M16—111no—
348C2×M16—111no—
349C2×M16—221no—
350C2×M16C22×D1111yescharacteristic
351C22×C8—221no—
352C22×C8C22×D1111yescharacteristic
353C4×Q8—22no—
354C4×Q8—41no—
355C4×D4—22no—
356C4×D4—41no—
357#117—22no—
358#117—111no—
359#117C22×D1111yescharacteristic
360#117C22×D1111yescharacteristic
361#117C22×D1111yescharacteristic
362C2×C22⋊C4—22no—
363#108—221no—
364#108—221no—
365#108—221no—
366#108—221no—
367#108—441no—
368#108—441no—
369#107—21no—
370#106—21no—
371#104—441no—
372#104—441no—
373#103—22no—
374#103—441no—
375#102—22no—
376#102—441no—
377#101—221no—
378#101—222no—
379#101—441no—
380#100—221no—
381#100—222no—
382#100—441no—
383#99—222no—
384#97—21no—
385#97—221no—
386C4×C8—21no—
387C4×C8—221no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—82no—
392C2×C11#242011yescharacteristic
393D11—81no—
394C24—21no—
395#41—221no—
396#41—221no—
397#41—221no—
398#41—221no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—111no—
405C2×Q8C2×C22⋊D1112yes—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—111no—
412C2×D4—221no—
413C2×D4C2×C22⋊D1112yes—
414C22×C4—21no—
415C22×C4—42no—
416C22×C4—221no—
417C22×C4C23×D1111yescharacteristic
418Q16—442no—
419SD16—22no—
420SD16—22no—
421SD16—22no—
422SD16—22no—
423SD16—442no—
424SD16—442no—
425D8—442no—
426M16—21no—
427M16—21no—
428M16—221no—
429M16—221no—
430M16—221no—
431M16—221no—
432M16—221no—
433M16—221no—
434M16—221no—
435M16—221no—
436M16—221no—
437M16—221no—
438M16—221no—
439M16—221no—
440M16—441no—
441M16—441no—
442C2×C8—21no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—441no—
450C2×C8—441no—
451C2×C8#433911yescharacteristic
452C2×C8#433911yescharacteristic
453C2×C8#433911yescharacteristic
454C2×C8#433911yescharacteristic
455C2×C8C2×C22⋊D1111yescharacteristic
456C2×C8C2×C22⋊D1111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—221no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—42no—
465C22⋊C4—221no—
466C22⋊C4#434112yes—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—42no—
471C42—221no—
472C11#2498711yescharacteristic, complemented, Sylow
473C23—22no—
474C23—41no—
475C23—41no—
476C23—161no—
477C23—221no—
478C23C2×#434111yescharacteristic
479Q8—22no—
480Q8—22no—
481Q8—41no—
482Q8—41no—
483Q8—221no—
484Q8—221no—
485D4—22no—
486D4—22no—
487D4—41no—
488D4—41no—
489D4—221no—
490D4—221no—
491D4—441no—
492D4—441no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—162no—
500C2×C4—221no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4C2×#433911yescharacteristic
505C2×C4C2×#433911yescharacteristic
506C2×C4#6703711yescharacteristic
507C2×C4#41×D1111yescharacteristic
508C2×C4#6704211yescharacteristic
509C2×C4C22×C22⋊D1111yescharacteristic
510C8—41no—
511C8—441no—
512C8—441no—
513C8—441no—
514C8—441no—
515C8—441no—
516C8—441no—
517C8#6698211yescharacteristic
518C8#6698211yescharacteristic
519C8#6698211yescharacteristic
520C8#6698211yescharacteristic
521C22—41no—
522C22—42no—
523C22—82no—
524C22—161no—
525C22—161no—
526C22—441no—
527C22—881no—
528C22#1062308811yescharacteristic
529C22#1062309411yescharacteristic
530C22#1062333711yescharacteristic
531C4—42no—
532C4—42no—
533C4—81no—
534C4—81no—
535C4—441no—
536C4—881no—
537C4#1062308911yescharacteristic
538C4#1062309311yescharacteristic
539C4C2×#6698211yescharacteristic
540C4#1062336011yescharacteristic
541C2—21no—
542C2—21no—
543C2—21no—
544C2—82no—
545C2—881no—
546C2#1307210211yescharacteristic
subgroupG/H
centerC2#13072102
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2949C2
socleC2×C11#2420
prime radicalC2×#66985C22
hypercenter#2949D11
hypocenterC11#24987
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2949

Complements

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

NH ≅ G/Ntype
2. #13070084C2semidirect
3. #13070077C2semidirect
4. #13069894C2semidirect
6. #13069521C2semidirect
7. #13069406C2semidirect
8. #13069110C2semidirect
10. #13068739C2semidirect
11. #13068730C2semidirect
12. #13068727C2semidirect
13. #13068667C2semidirect
14. #13068417C2semidirect
15. C11×#2949C2semidirect
201. #2949D11semidirect
472. C11#24987semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106227902
#130700842
#130700772
#130698942
#130698872
#130695212
#130694062
#130691102
#130691032
#130687392
#130687302
#130687272
#130686672
#130684172
C11×#29492
#2498711