Finite Group Databasebeta

← #14784656

Subgroups — #14784656

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077550C211yesmaximal, characteristic, complemented
2#13077517C211yesmaximal, characteristic
3#13070198C211yesmaximal, characteristic, complemented
4#13070194C211yesmaximal, characteristic, complemented
5#13070072C211yesmaximal, characteristic, complemented
6#13070070C211yesmaximal, characteristic, complemented
7#13069920C211yesmaximal, characteristic
8#13069902C211yesmaximal, characteristic
9#13069789C211yesmaximal, characteristic, complemented
10#13069788C211yesmaximal, characteristic, complemented
11#13068453C211yesmaximal, characteristic, complemented
12#13068417C211yesmaximal, characteristic, complemented
13#13068416C211yesmaximal, characteristic, complemented
14#13068371C211yesmaximal, characteristic, complemented
15C11×#1764C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17#10623353C2211yescharacteristic
18C2×#66954C2211yescharacteristic
19#10623001C2211yescharacteristic
20C2×C11×#104C2211yescharacteristic
21C11×#416C2211yescharacteristic
22C11×#405C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24#10622853C2211yescharacteristic
25#10622850C2211yescharacteristic
26#10622849C2211yescharacteristic
27#10622758—22no—
28#10622757—22no—
29#10622752C2211yescharacteristic
30#10622745C2211yescharacteristic
31#10622737C2211yescharacteristic
32#10622726C2211yescharacteristic
33#10622715C2211yescharacteristic
34#10622715C2211yescharacteristic
35#10622714C2211yescharacteristic
36#10622714C2211yescharacteristic
37#10622714C2211yescharacteristic
38#10622619C2211yescharacteristic
39C2×#66869C2211yescharacteristic
40#10622537C2211yescharacteristic
41#10622292—22no—
42C8×Dic22—22no—
43C11×#341C2211yescharacteristic
44C11×#339C2211yescharacteristic
45C11⋊#338C2211yescharacteristic
46#10622197C2211yescharacteristic
47#10622195C2211yescharacteristic
48#10622194C2211yescharacteristic
49#10622194C2211yescharacteristic
50#10622190C2211yescharacteristic
51#10622171C2211yescharacteristic
52#10622169C2211yescharacteristic
53#10622169C2211yescharacteristic
54#10622161C2211yescharacteristic
55C2×C11×#41C2311yescharacteristic
56C2×#4339C2311yescharacteristic
57C11×#131—21no—
58C11×#131—21no—
59C11×#131—21no—
60C11×#131—21no—
61C2×C11×M16—21no—
62C2×C11×M16C2311yescharacteristic
63C2×C11×M16C2311yescharacteristic
64C22×C8×C11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#117C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69#67004—21no—
70#67003—22no—
71#67002—21no—
72#66995—21no—
73#66985—21no—
74#66979C2311yescharacteristic
75#66979C2311yescharacteristic
76#66979C2311yescharacteristic
77#66977—22no—
78C2×#4318C2311yescharacteristic
79C2×#4318C2311yescharacteristic
80C2×#4318C2311yescharacteristic
81C2×#4318C2311yescharacteristic
82#66954—21no—
83#66954—21no—
84#66954—21no—
85#66954—21no—
86C2×#4313—21no—
87C2×C8×D11—21no—
88#66923—21no—
89#66922—21no—
90C4×Dic22—22no—
91C11×#104—21no—
92C11×#104—21no—
93C11×#103—21no—
94C11×#102—21no—
95C11×#97—21no—
96C4×C8×C11—21no—
97C4×C8×C11—21no—
98C4×C8×C11—21no—
99#66901—22no—
100#66900—21no—
101#66898—22no—
102#66897—21no—
103#66889—22no—
104#66888—21no—
105#66887—21no—
106#66886—22no—
107#66885—21no—
108#66880—21no—
109#66879—21no—
110#66879—21no—
111#66879D412yes—
112Dic11⋊C8—22no—
113Dic11⋊C8—22no—
114C8×Dic11—21no—
115C8×Dic11—21no—
116C8×Dic11D412yes—
117#66870—22no—
118#66869—21no—
119#66869—21no—
120C4⋊(C11⋊C8)—22no—
121#23833—111nomaximal, Sylow
122C11×#41—21no—
123C11×#41—21no—
124C11×#41—21no—
125C11×#41—21no—
126C2×Q8×C11#4111yescharacteristic
127C2×D4×C11—21no—
128C2×D4×C11#4111yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—21no—
133#4339—21no—
134#4339—21no—
135#4339—21no—
136#4339—21no—
137C2×D44#4111yescharacteristic
138C2×C4×D11—21no—
139C2×Dic22—22no—
140C2×Dic22#4111yescharacteristic
141C11×M16—21no—
142C11×M16—21no—
143C11×M16—21no—
144C11×M16—21no—
145C11×M16—41no—
146C11×M16—41no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—41no—
153C2×C8×C11—41no—
154C2×C8×C11C2×D411yescharacteristic
155C2×C8×C11C2×D411yescharacteristic
156C2×C8×C11#4111yescharacteristic
157C2×C8×C11#4111yescharacteristic
158C2×C8×C11#4111yescharacteristic
159C2×C8×C11#4111yescharacteristic
160C11×C4⋊C4—21no—
161C11×C22⋊C4—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11#4111yescharacteristic
165C42×C11#4111yescharacteristic
166C22⋊Dic11—21no—
167C22⋊Dic11—21no—
168C22⋊Dic11#4112yes—
169#4326—22no—
170#4325—22no—
171#4324—22no—
172#4323—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177Dic11⋊C4—24no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11C2×D412yes—
181#4318—21no—
182#4318—21no—
183#4318—21no—
184#4318—21no—
185#4318—21no—
186#4318—21no—
187#4318—21no—
188#4318—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8C2×D412yes—
193#4313—41no—
194#4313—41no—
195C8×D11—41no—
196C8×D11—41no—
197#2960—111no—
198#2955—111no—
199#2103—111no—
200#2102—111no—
201#2080—111no—
202#2080—111no—
203#2053—111no—
204#2050—111no—
205#2031—111no—
206#2031—111no—
207#1764—111no—
208#1764D1111yescharacteristic, complemented
209#1757—111no—
210#1757—111no—
211#1747—111no—
212C23×C11—21no—
213C23×C11C2×#4111yescharacteristic
214C22×D11—21no—
215Q8×C11—21no—
216Q8×C11—21no—
217D4×C11—21no—
218D4×C11—21no—
219D4×C11—41no—
220D4×C11—41no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C22⋊D11—41no—
235C22⋊D11—41no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—21no—
239C2×Dic11—41no—
240D44—21no—
241D44—21no—
242C4×D11—41no—
243C4×D11—41no—
244Dic22—21no—
245Dic22—21no—
246Dic22—44no—
247C8×C11—41no—
248C8×C11—41no—
249C8×C11—41no—
250C8×C11#12411yescharacteristic
251C8×C11#12411yescharacteristic
252C8×C11#12411yescharacteristic
253C8×C11#12411yescharacteristic
254C11⋊C8—22no—
255C11⋊C8—41no—
256C11⋊C8—41no—
257C11⋊C8—41no—
258#575—111no—
259C2×#131—111no—
260C2×#131C2×D1111yescharacteristic
261#533—111no—
262#446—222no—
263C8×Q8—222no—
264#444—222no—
265#443—222no—
266#430—111no—
267#424—111no—
268#424—111no—
269#423—111no—
270#421—111no—
271#421—111no—
272C2×#104—111no—
273C2×#104C2×D1111yescharacteristic
274#416—111no—
275#416C2×D1111yescharacteristic
276#413—111no—
277#413—111no—
278#410—111no—
279#410—111no—
280#405—111no—
281#405—111no—
282#405—111no—
283#405C2×D1111yescharacteristic
284C2×C4×C8C2×D1111yescharacteristic
285#344—111no—
286#344—111no—
287#344—111no—
288#344—111no—
289#341—111no—
290#341C2×D1111yescharacteristic
291#339—111no—
292#339C2×D1111yescharacteristic
293#338—111no—
294H(3,ℤ/4)—111no—
295H(3,ℤ/4)—111no—
296H(3,ℤ/4)—111no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—81no—
300C22×C11#52511yescharacteristic
301C22×C11#52911yescharacteristic
302C22×C11#52911yescharacteristic
303C2×D11—41no—
304C2×D11—81no—
305C4×C11—22no—
306C4×C11—41no—
307C4×C11—41no—
308C4×C11—81no—
309C4×C11#52511yescharacteristic
310C4×C11C2×#12411yescharacteristic
311C4×C11#52911yescharacteristic
312C4×C11#52911yescharacteristic
313Dic11—42no—
314Dic11—42no—
315Dic11—41no—
316Dic11—81no—
317C2×#41—111no—
318C2×#41C22×D1111yescharacteristic
319#137—221no—
320#137—221no—
321AGL(1,ℤ/8)—221no—
322AGL(1,ℤ/8)—221no—
323#135—222no—
324#131—21no—
325#131—21no—
326#131—21no—
327#131—21no—
328#131—221no—
329#131—221no—
330#131—221no—
331#131—221no—
332C2×M16—21no—
333C2×M16—111no—
334C2×M16—111no—
335C2×M16—111no—
336C2×M16—111no—
337C2×M16—221no—
338C2×M16C22×D1111yescharacteristic
339C2×M16C22×D1111yescharacteristic
340C22×C8—21no—
341C22×C8—221no—
342C22×C8C22×D1111yescharacteristic
343C22×C8C22×D1111yescharacteristic
344C4⋊Q8—221no—
345#125—221no—
346C22⋊Q8—222no—
347C4×Q8—222no—
348#117—111no—
349#117—111no—
350#117—111no—
351#117C22×D1111yescharacteristic
352C2×C42C22×D1111yescharacteristic
353#108—222no—
354C4⋊C8—222no—
355C4⋊C8—222no—
356C4⋊C8—222no—
357#104—21no—
358#104—21no—
359#104—222no—
360#104—222no—
361#104—221no—
362#104—221no—
363#103—21no—
364#103—221no—
365#102—21no—
366#102—221no—
367#101—221no—
368#101—221no—
369#100—221no—
370#100—221no—
371#99—222no—
372#99—222no—
373#97—21no—
374#97—112no—
375#97—221no—
376#97—221no—
377C4×C8—21no—
378C4×C8—21no—
379C4×C8—21no—
380C4×C8—112no—
381C4×C8—221no—
382C4×C8—221no—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11—21no—
386C2×C11—81no—
387C2×C11#239811yescharacteristic
388D11—81no—
389#41—21no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—221no—
394#41—221no—
395#41—221no—
396#41—221no—
397C2×Q8—111no—
398C2×Q8—222no—
399C2×Q8#433911yescharacteristic
400C2×D4—21no—
401C2×D4—111no—
402C2×D4—221no—
403C2×D4#433911yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—221no—
407C22×C4C23×D1111yescharacteristic
408Q16—222no—
409SD16—222no—
410SD16—222no—
411D8—222no—
412M16—21no—
413M16—21no—
414M16—21no—
415M16—21no—
416M16—41no—
417M16—41no—
418M16—221no—
419M16—221no—
420M16—221no—
421M16—221no—
422M16—221no—
423M16—221no—
424M16—221no—
425M16—221no—
426M16—441no—
427M16—441no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—41no—
434C2×C8—41no—
435C2×C8—112no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—441no—
440C2×C8—441no—
441C2×C8#433911yescharacteristic
442C2×C8#433911yescharacteristic
443C2×C8D4×D1111yescharacteristic
444C2×C8D4×D1111yescharacteristic
445C2×C8#434111yescharacteristic
446C2×C8#434111yescharacteristic
447C4⋊C4—21no—
448C4⋊C4—224no—
449C4⋊C4—222no—
450C4⋊C4—221no—
451C4⋊C4—221no—
452C4⋊C4—221no—
453C22⋊C4—21no—
454C22⋊C4—112no—
455C22⋊C4—221no—
456C22⋊C4—221no—
457C42—21no—
458C42—21no—
459C42—112no—
460C42—221no—
461C42—221no—
462C42#433911yescharacteristic
463C42#433911yescharacteristic
464C11#2383311yescharacteristic, complemented, Sylow
465C23—21no—
466C23—221no—
467C23#41×D1111yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—221no—
471Q8—221no—
472Q8—444no—
473D4—21no—
474D4—21no—
475D4—41no—
476D4—41no—
477D4—221no—
478D4—221no—
479D4—441no—
480D4—441no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—221no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4C2×#433911yescharacteristic
495C2×C4C2×#433911yescharacteristic
496C2×C4C2×#433911yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4C2×#434111yescharacteristic
499C2×C4#41×D1111yescharacteristic
500C8—41no—
501C8—41no—
502C8—41no—
503C8—222no—
504C8—441no—
505C8—441no—
506C8—441no—
507C8#6693811yescharacteristic
508C8#6693811yescharacteristic
509C8#6693811yescharacteristic
510C8#6693811yescharacteristic
511C22—41no—
512C22—41no—
513C22—81no—
514C22—441no—
515C22—881no—
516C22#1062305911yescharacteristic
517C22#1062306911yescharacteristic
518C22#1062307811yescharacteristic
519C4—22no—
520C4—41no—
521C4—41no—
522C4—81no—
523C4—442no—
524C4—442no—
525C4—441no—
526C4—881no—
527C4#1062301011yescharacteristic
528C4C2×#6693811yescharacteristic
529C4#1062307811yescharacteristic
530C4#1062308811yescharacteristic
531C2—21no—
532C2—21no—
533C2—21no—
534C2—81no—
535C2—881no—
536C2#1307190311yescharacteristic
subgroupG/H
centerC8#66938
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1764C2
socleC2×C11#2398
prime radical#10623353C22
hypercenter#1764D11
hypocenterC11#23833
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #1764

Complements

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

NH ≅ G/Ntype
1. #13077550C2semidirect
3. #13070198C2semidirect
4. #13070194C2semidirect
5. #13070072C2semidirect
6. #13070070C2semidirect
9. #13069789C2semidirect
10. #13069788C2semidirect
11. #13068453C2semidirect
12. #13068417C2semidirect
13. #13068416C2semidirect
14. #13068371C2semidirect
15. C11×#1764C2semidirect
208. #1764D11semidirect
464. C11#23833semidirect

Maximal subgroups

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

subgroupindex
#130775502
#130775172
#130701982
#130701942
#130700722
#130700702
#130699202
#130699022
#130697892
#130697882
#130684532
#130684172
#130684162
#130683712
C11×#17642
#2383311