Finite Group Databasebeta

← #14795079

Subgroups — #14795079

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622620C211yesmaximal, characteristic, complemented
2C2×#10622448C211yesmaximal, characteristic, complemented
3#13076969C211yesmaximal, characteristic, complemented
4C4×#66991C211yesmaximal, characteristic
5#13070048C212yesmaximal, complemented
6#13069803C212yesmaximal
7#13069567C211yesmaximal, characteristic, complemented
8#13069377C211yesmaximal, characteristic, complemented
9#13069358C212yesmaximal, complemented
10#13069315C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66991C2211yescharacteristic
14C2×C4×C22⋊D11—21no—
15C2×#66950—21no—
16C2×C42×D11C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102C2212yes—
20C11×#384C2211yescharacteristic
21#10622834C2211yescharacteristic
22C2×#66896C2212yes—
23C4×C22⋊Dic11—21no—
24C2×(C2×D11)⋊C8C2212yes—
25C2×#66879C2212yes—
26#10622620—24no—
27#10622600—21no—
28#10622600C2211yescharacteristic
29#10622600C2212yes—
30#10622598—21no—
31#10622598C2212yes—
32#10622587—21no—
33#10622586C2211yescharacteristic
34C2×#66872C2212yes—
35C2×#66871C2212yes—
36#10622569—21no—
37#10622557—21no—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622448—24no—
41C11×#340C2212yes—
42#10622189C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C22×C22⋊D11—21no—
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×Dic22—21no—
52C22×C8×C11C2312yes—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64#66991—22no—
65#66991—22no—
66C4×C22⋊D11—44no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—21no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80#66950—44no—
81C42×D11—22no—
82C42×D11—22no—
83#66922—22no—
84#66922—22no—
85C11×C4⋊C8—22no—
86C11×#102—24no—
87#66896—24no—
88C11⋊#95—21no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93(C2×D11)⋊C8—24no—
94#66879—24no—
95#66872—24no—
96#66871—24no—
97C4⋊(C11⋊C8)D414yescomplemented
98#24709—111nomaximal, Sylow
99C24×C11—21no—
100C23×D11C2×D411yescharacteristic
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11#4112yes—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C2×C22⋊D11—24no—
116C2×C22⋊D11—42no—
117C2×C22⋊D11—42no—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—22no—
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123C22×Dic11C2×D411yescharacteristic
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—41no—
136C2×Dic22—42no—
137C2×Dic22—42no—
138C2×Dic22—42no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—42no—
148C11×C22⋊C4—42no—
149C42×C11C2×D412yes—
150C42×C11#4112yes—
151C22⋊Dic11—24no—
152C22⋊Dic11—42no—
153C22⋊Dic11—42no—
154(C2×D11)⋊C4—44no—
155(C2×D11)⋊C4—42no—
156C4⋊Dic11—22no—
157C4⋊Dic11—21no—
158C4⋊Dic11—22no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—44no—
162C4⋊Dic11—42no—
163C4⋊Dic11#4112yes—
164Dic11⋊C4—42no—
165C4×Dic11—22no—
166C4×Dic11—22no—
167C4×Dic11—21no—
168C4×Dic11—21no—
169C4×Dic11—42no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8C2×D414yes—
173C2×#474—111no—
174C2×#432—111no—
175#2857—111no—
176C4×#121—111no—
177#2076—112no—
178#2034—112no—
179#1988—111no—
180#1948—111no—
181#1944—112no—
182#1936—112no—
183#1802D1111yescharacteristic, complemented
184C23×C11—22no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11C22×D411yescharacteristic
192C22×D11—21no—
193C22×D11—21no—
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—21no—
197C22×D11—21no—
198C22×D11#13712yes—
199D4×C11—22no—
200D4×C11—22no—
201D4×C11—41no—
202D4×C11—41no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—84no—
212C2×C4×C11#12112yes—
213C2×C4×C11#12112yes—
214C2×C4×C11AGL(1,ℤ/8)12yes—
215C2×C4×C11AGL(1,ℤ/8)12yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C2×C4×C112−1+411yescharacteristic
222C22⋊D11—48no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—22no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—42no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—41no—
241C4×D11—44no—
242C4×D11—41no—
243C4×D11—41no—
244C4×D11—41no—
245C4×D11—41no—
246C4×D11—44no—
247Dic22—84no—
248C8×C11—42no—
249C11⋊C8—24no—
250C2×C4⋊Q8—111no—
251C2×C22⋊Q8—221no—
252C2×#121—111no—
253C2×C4×D4—221no—
254C2×C4×D4C2×D1111yescharacteristic
255C22×C42—111no—
256#474—224no—
257#432—224no—
258C2×#107—112no—
259C2×#106—112no—
260C2×C4⋊C8—111no—
261C2×C4⋊C8C2×D1111yescharacteristic
262C2×#102—112no—
263C2×#102C2×D1112yes—
264C2×C22⋊C8—112no—
265C2×#97—112no—
266#391—221no—
267#390—111no—
268#389—112no—
269#389—111no—
270#389—221no—
271#388—221no—
272#386—221no—
273#384C2×D1111yescharacteristic
274#380—111no—
275#380—112no—
276#380—221no—
277C4×C4⋊C4—111no—
278C4×C22⋊C4—221no—
279#340—112no—
280#340—112no—
281#340—112no—
282#340C2×D1112yes—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11C2×#12111yescharacteristic
291C22×C11#52511yescharacteristic
292C22×C11#53611yescharacteristic
293C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C11C2×#13711yescharacteristic
296C22×C11#57511yescharacteristic
297C2×D11—22no—
298C2×D11—22no—
299C2×D11—22no—
300C2×D11—41no—
301C2×D11—41no—
302C2×D11—41no—
303C2×D11—41no—
304C4×C11—22no—
305C4×C11—82no—
306C4×C11—81no—
307C4×C11#46914yes—
308C4×C11#54711yescharacteristic
309C4×C11#54811yescharacteristic
310C4×C11#55211yescharacteristic
311C4×C11#55611yescharacteristic
312Dic11—42no—
313Dic11—41no—
314Dic11—41no—
315Dic11—41no—
316Dic11—81no—
317Dic11—82no—
318C22×Q8—221no—
319C22×D4—221no—
320C22×D4C22×D1111yescharacteristic
321C23×C4—21no—
322C23×C4—111no—
323C23×C4—111no—
324C23×C4—111no—
325C22×C8—112no—
326C22×C8C22×D1112yes—
327C4⋊Q8—222no—
328C4⋊Q8—222no—
329C22⋊Q8—444no—
330#121—222no—
331#121—222no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—444no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4C22×D1111yescharacteristic
344C2×C4⋊C4C22×D1112yes—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—221no—
347C2×C22⋊C4—221no—
348C2×C22⋊C4—222no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C42—111no—
352C2×C42—111no—
353C2×C42—111no—
354C2×C42—222no—
355C2×C42—222no—
356C2×C42—221no—
357C2×C42C22×D1111yescharacteristic
358#107—224no—
359#106—224no—
360C4⋊C8—22no—
361C4⋊C8—114no—
362#102—24no—
363#102—224no—
364C22⋊C8—224no—
365#97—224no—
366#95—221no—
367#95—221no—
368#95—222no—
369#95—222no—
370#95—221no—
371C2×C11—82no—
372C2×C11#241511yescharacteristic
373C2×C11C2×#46911yescharacteristic
374C2×C11#305611yescharacteristic
375C2×C11#311011yescharacteristic
376C2×C11#311511yescharacteristic
377C2×C11#323511yescharacteristic
378C2×C11#323911yescharacteristic
379D11—42no—
380C24—21no—
381C24—111no—
382C2×Q8—442no—
383C2×Q8—442no—
384C2×Q8—442no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—224no—
391C2×D4—442no—
392C2×D4—442no—
393C2×D4#434112yes—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—111no—
400C22×C4—111no—
401C22×C4—111no—
402C22×C4—222no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4—221no—
412C22×C4—221no—
413C22×C4—221no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4—441no—
417C22×C4D4×D1111yescharacteristic
418C22×C4D4×D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—114no—
424C2×C8—222no—
425C2×C8—222no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—42no—
431C4⋊C4—42no—
432C4⋊C4—112no—
433C4⋊C4—221no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—221no—
437C4⋊C4—221no—
438C4⋊C4—442no—
439C4⋊C4—444no—
440C4⋊C4—442no—
441C22⋊C4—42no—
442C22⋊C4—224no—
443C22⋊C4—442no—
444C22⋊C4—444no—
445C22⋊C4—442no—
446C22⋊C4—442no—
447C42—222no—
448C42—222no—
449C42—221no—
450C42—221no—
451C42—442no—
452C42#433912yes—
453C42D4×D1112yes—
454C11#2470911yescharacteristic, complemented, Sylow
455C23—22no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—112no—
463C23—221no—
464C23—221no—
465C23—221no—
466C23—221no—
467C23—221no—
468C23—221no—
469C23C2×D4×D1111yescharacteristic
470Q8—884no—
471D4—22no—
472D4—22no—
473D4—41no—
474D4—41no—
475D4—448no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—84no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—221no—
488C2×C4—221no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—222no—
494C2×C4—221no—
495C2×C4—444no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—444no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—441no—
506C2×C4—442no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4#6693712yes—
510C2×C4#6693712yes—
511C2×C4#6696412yes—
512C2×C4#6696712yes—
513C2×C4C2×#433911yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×#434111yescharacteristic
516C2×C4#6704011yescharacteristic
517C2×C4#41×D1111yescharacteristic
518C2×C4#6704311yescharacteristic
519C8—42no—
520C8—224no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—222no—
529C22—222no—
530C22—222no—
531C22—441no—
532C22—441no—
533C22—441no—
534C22—441no—
535C22C2×#6693711yescharacteristic
536C22#1062313711yescharacteristic
537C22#1062315911yescharacteristic
538C22C2×#6696411yescharacteristic
539C22C2×#6696711yescharacteristic
540C22#1062330411yescharacteristic
541C22D11×#13711yescharacteristic
542C4—22no—
543C4—81no—
544C4—82no—
545C4—441no—
546C4—442no—
547C4—441no—
548C4—441no—
549C4—881no—
550C4—882no—
551C4#1062239514yes—
552C4#1062304411yescharacteristic
553C4#1062306411yescharacteristic
554C4#1062312911yescharacteristic
555C4#1062316211yescharacteristic
556C2—82no—
557C2—442no—
558C2#1307204711yescharacteristic
559C2C2×#1062239511yescharacteristic
560C2#1307824911yescharacteristic
561C2#1307871411yescharacteristic
562C2#1307876411yescharacteristic
563C2#1307981211yescharacteristic
564C2#1307984511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#1802D11
hypocenterC11#24709
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. C2×#10622620C2semidirect
2. C2×#10622448C2semidirect
3. #13076969C2semidirect
5. #13070048C2semidirect
7. #13069567C2semidirect
8. #13069377C2semidirect
9. #13069358C2semidirect
10. #13069315C2semidirect
11. C11×#1802C2semidirect
97. C4⋊(C11⋊C8)D4semidirect
183. #1802D11semidirect
454. C11#24709semidirect

Maximal subgroups

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

subgroupindex
C2×#106226202
C2×#106224482
#130769692
C4×#669912
#130700482
#130698032
#130695672
#130693772
#130693582
#130693152
C11×#18022
#2470911