Finite Group Databasebeta

← #14790140

Subgroups — #14790140

Order 2816.

1330 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623258C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic
3#13073538C211yesmaximal, characteristic, complemented
4#13069942C212yesmaximal, complemented
5#13069750C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069551C211yesmaximal, characteristic, complemented
8#13068961C212yesmaximal
9#13068860C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic, complemented
11C2×C11×#474C211yesmaximal, characteristic, complemented
12C22×Q8×D11—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66999—21no—
16C22×#4323C2211yescharacteristic
17C2×#66977—21no—
18#10623258—24no—
19#10623258—24no—
20C2×#66949—22no—
21C2×#66946C2212yes—
22C2×#66941C2212yes—
23C2×C4×D44C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#474—24no—
26C2×C11×#107C2212yes—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#102C2212yes—
29#10622834C2212yes—
30C2×#66896C2211yescharacteristic
31#10622825—21no—
32C2×#66885C2212yes—
33C4×#4323—24no—
34#10622586C2212yes—
35C2×#66873C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622561—22no—
38#10622548C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622189C2212yes—
41#10622188C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C2×Q8×D11—28no—
49C2×Q8×D11—44no—
50C2×Q8×D11—44no—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C22×C4×D11—22no—
54C22×Dic22—22no—
55C22×Dic22D411yescharacteristic
56C22×C8×C11C2312yes—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D414yes—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68#66999—28no—
69C2×#4323—22no—
70C2×#4323—22no—
71C2×#4323Q814yescomplemented
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11D411yescharacteristic
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2311yescharacteristic
79#66977—44no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4D412yes—
83C2×C4×Dic11C2312yes—
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86#66949—216no—
87#66946—24no—
88#66946—24no—
89#66941—24no—
90#66941—24no—
91C4×D44—22no—
92C4×D44D414yes—
93C4×Dic22—22no—
94C4×Dic22—22no—
95C11×#107—24no—
96C11×C4⋊C8—22no—
97C11×#102—24no—
98#66896—22no—
99C11⋊#95—22no—
100#66885—24no—
101#66873—22no—
102#66871—22no—
103C4×C11⋊C8—22no—
104#24326—111nomaximal, Sylow
105C24×C11—21no—
106C23×D11—21no—
107C2×Q8×C11—24no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11C2×Q812yescomplemented
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11C2×D412yes—
127C22×Dic11C2×D412yes—
128Q8×D11—432no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44C2×D412yes—
133C2×D44C2×Q812yes—
134C2×D44#4112yes—
135C2×C4×D11—28no—
136C2×C4×D11—24no—
137C2×C4×D11—44no—
138C2×C4×D11—44no—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C2×Dic22—28no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—44no—
145C2×Dic22—44no—
146C2×Dic22D814yescomplemented
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4C2×D414yes—
155C11×C22⋊C4—42no—
156C42×C11C2×D412yes—
157C42×C11C2×D412yes—
158C22⋊Dic11—44no—
159C22⋊Dic11—82no—
160#4323—28no—
161(C2×D11)⋊C4—28no—
162(C2×D11)⋊C4—24no—
163C4⋊Dic11—22no—
164C4⋊Dic11—21no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—42no—
168C4⋊Dic11—81no—
169C4⋊Dic11C2×D412yes—
170Dic11⋊C4—28no—
171Dic11⋊C4—24no—
172Dic11⋊C4—44no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8C2×Q812yescomplemented
181C2×D4×Q8—111no—
182C2×#474D1111yescharacteristic, complemented
183C2×C4×D8—111no—
184#2538—111no—
185#2057—112no—
186#2023—112no—
187#1990—111no—
188#1984—111no—
189#1879—112no—
190#1862—112no—
191#1802—111no—
192C23×C11—22no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11C22×D411yescharacteristic
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207Q8×C11—48no—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—41no—
211D4×C11—41no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—24no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—84no—
221C2×C4×C11#12012yes—
222C2×C4×C11#12012yes—
223C2×C4×C11C2×D812yes—
224C2×C4×C11AGL(1,ℤ/8)12yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×Q811yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C112−1+411yescharacteristic
230C2×C4×C112−1+411yescharacteristic
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11C2×D814yes—
243D44—22no—
244D44—22no—
245D44—22no—
246D44C22⋊Q814yescomplemented
247C4×D11—416no—
248C4×D11—48no—
249Dic22—28no—
250Dic22—416no—
251C8×C11—42no—
252C11⋊C8—22no—
253C11⋊C8—41no—
254C23×Q8—221no—
255C22×D8—111no—
256D4×Q8—224no—
257D4×Q8—224no—
258C2×C4⋊Q8—112no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×C22⋊Q8—222no—
261C2×C22⋊Q8—221no—
262C2×C22⋊Q8—221no—
263C2×C4×Q8—111no—
264C2×C4×D4—112no—
265C2×C4×D4—111no—
266C2×C4×D4C2×D1111yescharacteristic
267#474—24no—
268C4×D8—224no—
269C2×#107—111no—
270C2×#107C2×D1112yes—
271C2×C4⋊C8C2×D1111yescharacteristic
272C2×#102—111no—
273C2×#102—112no—
274C2×#102—111no—
275C2×#102C2×D1112yes—
276C2×C4×C8—111no—
277#396—222no—
278#390—112no—
279#389—112no—
280#384—111no—
281#380—221no—
282#340—112no—
283#340—112no—
284#340—112no—
285#336—112no—
286#336—112no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11C2×#12011yescharacteristic
295C22×C11#54811yescharacteristic
296C22×C11D4×Q811yescharacteristic
297C22×C11C22×D811yescharacteristic
298C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C11#57711yescharacteristic
300C22×C11#57811yescharacteristic
301C2×D11—24no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C4×C11—22no—
309C4×C11—44no—
310C4×C11—81no—
311C4×C11#44714yes—
312C4×C11C2×C22⋊Q811yescharacteristic
313C4×C11#53611yescharacteristic
314C4×C11#54811yescharacteristic
315C4×C11D4×Q811yescharacteristic
316Dic11—24no—
317Dic11—42no—
318Dic11—42no—
319Dic11—82no—
320C22×Q8—21no—
321C22×Q8—111no—
322C22×Q8—222no—
323C22×Q8—228no—
324C22×Q8—444no—
325C22×Q8—444no—
326C22×D4—111no—
327C22×D4C22×D1111yescharacteristic
328C23×C4—21no—
329C23×C4—222no—
330C23×C4—221no—
331C2×D8—114no—
332C2×D8—222no—
333C2×D8—222no—
334C22×C8—111no—
335C22×C8—111no—
336C22×C8C22×D1112yes—
337C4⋊Q8—22no—
338C4⋊Q8—224no—
339C4⋊Q8—224no—
340C4⋊Q8C22⋊D1114yes—
341C22⋊Q8—2216no—
342C22⋊Q8—228no—
343C22⋊Q8—444no—
344C4×Q8—222no—
345C4×Q8—222no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—114no—
349C4×D4—224no—
350C4×D4—224no—
351C4×D4—222no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—112no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4C22×D1111yescharacteristic
362C2×C4⋊C4C22×D1112yes—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—221no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C42—112no—
369C2×C42C22×D1111yescharacteristic
370#107—24no—
371#107—222no—
372C4⋊C8—22no—
373#102—24no—
374#102—222no—
375#102—222no—
376#102—224no—
377C4×C8—222no—
378#95—222no—
379C2×C11—82no—
380C2×C11#240911yescharacteristic
381C2×C11C2×#44711yescharacteristic
382C2×C11#301311yescharacteristic
383C2×C11#335811yescharacteristic
384C2×C11#336711yescharacteristic
385C2×C11Q8×D811yescharacteristic
386C2×C11#338411yescharacteristic
387D11—44no—
388C24—21no—
389C24—221no—
390C2×Q8—24no—
391C2×Q8—42no—
392C2×Q8—42no—
393C2×Q8—114no—
394C2×Q8—228no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×Q8—444no—
398C2×Q8—444no—
399C2×Q8—4432no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—112no—
406C2×D4—112no—
407C2×D4—112no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4Q8×D1112yescomplemented
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—112no—
418C22×C4—112no—
419C22×C4—228no—
420C22×C4—221no—
421C22×C4—224no—
422C22×C4—222no—
423C22×C4—444no—
424C22×C4—444no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4D4×D1111yescharacteristic
428C22×C4D4×D1111yescharacteristic
429C22×C4C23×D1111yescharacteristic
430D8—228no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—112no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—112no—
445C4⋊C4—228no—
446C4⋊C4—224no—
447C4⋊C4—222no—
448C4⋊C4—221no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—444no—
452C4⋊C4—442no—
453C4⋊C4—881no—
454C4⋊C4C2×C22⋊D1114yes—
455C22⋊C4—42no—
456C22⋊C4—228no—
457C22⋊C4—224no—
458C22⋊C4—444no—
459C22⋊C4—882no—
460C42—222no—
461C42—222no—
462C42D4×D1112yes—
463C42C2×C22⋊D1112yes—
464C11#2432611yescharacteristic, complemented, Sylow
465C23—22no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—222no—
473C23—222no—
474C23—222no—
475C23—441no—
476C23—441no—
477C23—441no—
478C23—441no—
479C23C2×D4×D1111yescharacteristic
480Q8—48no—
481Q8—228no—
482Q8—4416no—
483D4—22no—
484D4—22no—
485D4—41no—
486D4—41no—
487D4—114no—
488D4—222no—
489D4—222no—
490D4—222no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—84no—
500C2×C4—114no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—4416no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—448no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4D8×D1112yes—
515C2×C4#6696412yes—
516C2×C4#6699012yes—
517C2×C4#6699012yes—
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4C2×Q8×D1111yescharacteristic
520C2×C4#6704011yescharacteristic
521C2×C4#41×D1111yescharacteristic
522C2×C4#6704311yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C8—42no—
525C8—222no—
526C8—441no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—224no—
535C22—442no—
536C22—442no—
537C22—442no—
538C22—442no—
539C22—442no—
540C22—442no—
541C22#1062316311yescharacteristic
542C22#1062316411yescharacteristic
543C22C2×D8×D1111yescharacteristic
544C22C2×#6696411yescharacteristic
545C22#1062330911yescharacteristic
546C22#1062331011yescharacteristic
547C22C2×#6699011yescharacteristic
548C4—22no—
549C4—44no—
550C4—81no—
551C4—224no—
552C4—442no—
553C4—442no—
554C4—882no—
555C4#1062276914yes—
556C4D11×C22⋊Q811yescharacteristic
557C4#1062315911yescharacteristic
558C4Q8×C22⋊D1111yescharacteristic
559C4#1062336211yescharacteristic
560C2—82no—
561C2—444no—
562C2#1307197711yescharacteristic
563C2C2×#1062276911yescharacteristic
564C2#1307793011yescharacteristic
565C2#1308125011yescharacteristic
566C2#1308133311yescharacteristic
567C2#1308146611yescharacteristic
568C2#1308151911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#474D11
hypocenterC11#24326
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623258C2semidirect
3. #13073538C2semidirect
4. #13069942C2semidirect
5. #13069750C2semidirect
6. #13069578C2semidirect
7. #13069551C2semidirect
9. #13068860C2semidirect
10. #13068617C2semidirect
11. C2×C11×#474C2semidirect
71. C2×#4323Q8semidirect
115. C2×D4×C11C2×Q8semidirect
146. C2×Dic22D8semidirect
180. C2×C11⋊C8C2×Q8semidirect
182. C2×#474D11semidirect
246. D44C22⋊Q8semidirect
411. C2×D4Q8×D11semidirect
464. C11#24326semidirect

Maximal subgroups

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

subgroupindex
C2×#106232582
C2×C4×#43232
#130735382
#130699422
#130697502
#130695782
#130695512
#130689612
#130688602
#130686172
C2×C11×#4742
#2432611