Finite Group Databasebeta

← #14756208

Subgroups — #14756208

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622746C211yesmaximal, characteristic
2C2×#10622615C211yesmaximal, characteristic
3#13071209C211yesmaximal, characteristic
4#13070972C211yesmaximal, characteristic, complemented
5#13069256C212yesmaximal, complemented
6#13069249C212yesmaximal, complemented
7#13069242C212yesmaximal, complemented
8#13069235C212yesmaximal, complemented
9C2×#10622167C211yesmaximal, characteristic, complemented
10#13068314C211yesmaximal, characteristic, complemented
11C2×C11×#428C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C11×#428—24no—
20C2×C11×#107C2212yes—
21C2×C11×#106C2212yes—
22#10622826—22no—
23#10622746C418yescomplemented
24C2×#66885C2212yes—
25C2×#66880C2212yes—
26#10622615—24no—
27#10622601C2212yes—
28#10622600—21no—
29#10622600—21no—
30C4⋊C4×Dic11C2212yes—
31C4⋊C4×Dic11C2212yes—
32#10622587C2212yes—
33C2×#66874C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C22⋊C4×Dic11—22no—
38C4×C4⋊Dic11—21no—
39C4×C4⋊Dic11—21no—
40#10622188C2212yes—
41#10622188C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—21no—
47C23×Dic11—21no—
48C2×#4339—22no—
49C2×#4339—22no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339C2×C414yes—
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C22×Dic22C2311yescharacteristic
57C2×C11×M16—22no—
58C2×C11×M16—22no—
59C2×C11×M16C2×C414yes—
60C22×C8×C11C2312yes—
61C11×#117—22no—
62C11×#117D414yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—21no—
71C2×C22⋊Dic11D412yes—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74#66979—22no—
75#66979—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11C2×C414yes—
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11C2312yes—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11C2312yes—
85C22×C11⋊C8—22no—
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C11×#107—24no—
91C11×#106—24no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96#66885C2×C418yescomplemented
97#66880C2×C418yescomplemented
98#66874—22no—
99#66874—22no—
100#66873—22no—
101#66873—22no—
102#21062—111nomaximal, Sylow
103C24×C11C2×D411yescharacteristic
104C23×D11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—81no—
110C22×C4×C11—81no—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11#4112yes—
115C22×C4×C11#4112yes—
116C22×C4×C11#4112yes—
117C22×C4×C11#4112yes—
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—24no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—42no—
122C22×Dic11—24no—
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11—81no—
126C22×Dic11—81no—
127C22×Dic11C2×D412yes—
128C22×Dic11C2×D412yes—
129#4339—28no—
130#4339—28no—
131#4339—44no—
132#4339—44no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44C22×C412yes—
139C2×C4×D11—24no—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22C22×C412yes—
148C11×M16—28no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11C22×C414yes—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4C2×D412yes—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C42×C11—24no—
161C22⋊Dic11—24no—
162(C2×D11)⋊C4—82no—
163(C2×D11)⋊C4—82no—
164C4⋊Dic11—24no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11C22×C414yes—
169C4×Dic11—22no—
170C4×Dic11—22no—
171C4×Dic11—82no—
172C4×Dic11—82no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—44no—
180C2×#428D1111yescharacteristic, complemented
181C2×#417—111no—
182C2×#416—111no—
183#2311—111no—
184#2274—111no—
185#1928—112no—
186#1927—112no—
187#1926—112no—
188#1925—112no—
189C2×#340—111no—
190#1729—111no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11C4×D412yes—
196C23×C11#12112yes—
197C23×C11#12312yes—
198C23×C11C22×D411yescharacteristic
199C22×D11—22no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—84no—
216C2×C4×C11#11714yes—
217C2×C4×C11C4×D412yes—
218C2×C4×C11C4×D414yes—
219C2×C4×C11#12112yes—
220C2×C4×C11#12312yes—
221C2×C4×C11#12414yes—
222C2×C4×C11#12614yes—
223C2×C4×C11C23×C411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C22⋊D11—48no—
230C2×Dic11—24no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—84no—
243D44—22no—
244D44—22no—
245D44—41no—
246D44—41no—
247C4×D11—48no—
248Dic22—22no—
249Dic22—22no—
250Dic22—41no—
251Dic22—41no—
252C8×C11—24no—
253C11⋊C8—41no—
254C11⋊C8—41no—
255C22×#41—111no—
256C22×M16C2×D1111yescharacteristic
257C23×C8—111no—
258C2×#117—111no—
259C2×#117C2×D1111yescharacteristic
260C22×C4⋊C4—111no—
261C22×C4⋊C4C2×D1111yescharacteristic
262#428—24no—
263C2×#107C2×D1112yes—
264C2×#106C2×D1112yes—
265#417—118no—
266#416—224no—
267C2×#103—112no—
268C2×#103—111no—
269C2×#103—111no—
270C2×#102—112no—
271C2×#102—111no—
272C2×#102—111no—
273#391—112no—
274#390—112no—
275#386—222no—
276#380—221no—
277#380—221no—
278C4×C4⋊C4—112no—
279C4×C4⋊C4—112no—
280C4×C4⋊C4—221no—
281C4×C4⋊C4—221no—
282C4×C22⋊C4—222no—
283#340—112no—
284#340—112no—
285#336—112no—
286#336—112no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11#38814yes—
294C22×C11C2×C4×D411yescharacteristic
295C22×C11C2×#12111yescharacteristic
296C22×C11C2×#12311yescharacteristic
297C22×C11#57611yescharacteristic
298C22×C11#57711yescharacteristic
299C22×C11#57711yescharacteristic
300C22×C11#57811yescharacteristic
301C2×D11—42no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—82no—
311C4×C11#38814yes—
312C4×C11C2×#11711yescharacteristic
313C4×C11C2×C4×D411yescharacteristic
314C4×C11C2×#12411yescharacteristic
315C4×C11C2×#12611yescharacteristic
316Dic11—42no—
317Dic11—42no—
318Dic11—44no—
319Dic11—42no—
320C2×#41—114no—
321C2×#41—222no—
322C2×#41—222no—
323C2×#41—222no—
324C2×#41—222no—
325C2×#41—222no—
326C22×Q8—111no—
327C22×D4—111no—
328C22×D4—221no—
329C23×C4—21no—
330C23×C4—221no—
331C23×C4—221no—
332C23×C4C22×D1111yescharacteristic
333C2×M16—22no—
334C2×M16—22no—
335C2×M16C4×D1114yes—
336C22×C8—111no—
337C22×C8—111no—
338C22×C8—222no—
339C22×C8—222no—
340C22×C8—222no—
341C22×C8C22×D1112yes—
342#117—22no—
343#117—222no—
344#117—222no—
345#117C22⋊D1114yes—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—114no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4C22×D1112yes—
356C2×C4⋊C4C22×D1111yescharacteristic
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—112no—
360C2×C22⋊C4—222no—
361C2×C22⋊C4—222no—
362C2×C42—21no—
363C2×C42—112no—
364C2×C42—222no—
365C2×C42—222no—
366#107—24no—
367#106—24no—
368#103—118no—
369#103—222no—
370#103—222no—
371#102—118no—
372#102—222no—
373#102—222no—
374#95—222no—
375#95—222no—
376#95—222no—
377#95—222no—
378C2×C11—24no—
379C2×C11C2×#38811yescharacteristic
380C2×C11#294611yescharacteristic
381C2×C11#294711yescharacteristic
382C2×C11#304511yescharacteristic
383C2×C11#304611yescharacteristic
384C2×C11#309811yescharacteristic
385C2×C11#309911yescharacteristic
386D11—82no—
387C24—221no—
388C24D4×D1111yescharacteristic
389#41—228no—
390#41—228no—
391#41—444no—
392#41—444no—
393C2×Q8—112no—
394C2×Q8—221no—
395C2×Q8—221no—
396C2×Q8—221no—
397C2×Q8—221no—
398C2×Q8—221no—
399C2×D4—112no—
400C2×D4—224no—
401C2×D4—221no—
402C2×D4—221no—
403C2×D4—221no—
404C2×D4—221no—
405C2×D4—221no—
406C2×D4—442no—
407C2×D4—442no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—42no—
412C22×C4—81no—
413C22×C4—81no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—221no—
417C22×C4—222no—
418C22×C4—224no—
419C22×C4—224no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4—881no—
423C22×C4—881no—
424C22×C4C2×C4×D1112yes—
425C22×C4#433912yes—
426C22×C4D4×D1111yescharacteristic
427C22×C4#434112yes—
428C22×C4#434312yes—
429C22×C4#434312yes—
430C22×C4C2×C22⋊D1112yes—
431C22×C4C23×D1111yescharacteristic
432M16—28no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—444no—
442C2×C8C2×C4×D1114yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4—114no—
449C4⋊C4—224no—
450C4⋊C4—222no—
451C4⋊C4—222no—
452C4⋊C4—222no—
453C4⋊C4C2×C22⋊D1112yes—
454C4⋊C4C2×C22⋊D1112yes—
455C22⋊C4—24no—
456C22⋊C4—224no—
457C22⋊C4—882no—
458C22⋊C4—882no—
459C42—24no—
460C42—222no—
461C42—222no—
462C42—882no—
463C42—882no—
464C11#2106211yescharacteristic, complemented, Sylow
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—222no—
470C23—441no—
471C23—441no—
472C23—441no—
473C23—441no—
474C23—441no—
475C23—441no—
476C23#6694612yes—
477C23#6694712yes—
478C23#6699212yes—
479C23C2×D4×D1111yescharacteristic
480Q8—222no—
481Q8—222no—
482Q8—441no—
483Q8—441no—
484D4—222no—
485D4—222no—
486D4—448no—
487D4—441no—
488D4—441no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—84no—
499C2×C4—224no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—441no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—441no—
511C2×C4—448no—
512C2×C4—884no—
513C2×C4#6694514yes—
514C2×C4#6694612yes—
515C2×C4#6694712yes—
516C2×C4#6695114yes—
517C2×C4C4×C22⋊D1114yes—
518C2×C4#6699212yes—
519C2×C4#6700014yes—
520C2×C4C22×C4×D1111yescharacteristic
521C2×C4C2×#433911yescharacteristic
522C2×C4C2×#434111yescharacteristic
523C2×C4C2×#434311yescharacteristic
524C2×C4C2×#434311yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—24no—
527C8—441no—
528C8—441no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—442no—
536C22—442no—
537C22—442no—
538C22—881no—
539C22—881no—
540C22—881no—
541C22—881no—
542C22#1062260314yes—
543C22C2×#6694611yescharacteristic
544C22C2×#6694711yescharacteristic
545C22#1062330511yescharacteristic
546C22#1062330611yescharacteristic
547C22#1062330911yescharacteristic
548C22#1062331011yescharacteristic
549C22C2×#6699211yescharacteristic
550C4—42no—
551C4—42no—
552C4—82no—
553C4—442no—
554C4—442no—
555C4—444no—
556C4—442no—
557C4#1062260314yes—
558C4C2×#6694511yescharacteristic
559C4C2×#6695111yescharacteristic
560C4C2×C4×C22⋊D1111yescharacteristic
561C4C2×#6700011yescharacteristic
562C2—24no—
563C2—882no—
564C2C2×#1062260311yescharacteristic
565C2#1307744611yescharacteristic
566C2#1307745711yescharacteristic
567C2#1307815911yescharacteristic
568C2#1307817011yescharacteristic
569C2#1307859811yescharacteristic
570C2#1307860911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC2×#428D11
hypocenterC11#21062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. #13070972C2semidirect
5. #13069256C2semidirect
6. #13069249C2semidirect
7. #13069242C2semidirect
8. #13069235C2semidirect
9. C2×#10622167C2semidirect
10. #13068314C2semidirect
11. C2×C11×#428C2semidirect
23. #10622746C4semidirect
96. #66885C2×C4semidirect
97. #66880C2×C4semidirect
180. C2×#428D11semidirect
464. C11#21062semidirect

Maximal subgroups

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

subgroupindex
C2×#106227462
C2×#106226152
#130712092
#130709722
#130692562
#130692492
#130692422
#130692352
C2×#106221672
#130683142
C2×C11×#4282
#2106211