Finite Group Databasebeta

← #14804503

Subgroups — #14804503

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622477C212yesmaximal, complemented
2C2×#10622454C211yesmaximal, characteristic, complemented
3C2×#10622447C211yesmaximal, characteristic, complemented
4#13073565C211yesmaximal, characteristic, complemented
5#13073532C211yesmaximal, characteristic
6#13069814C212yesmaximal, complemented
7#13069622C212yesmaximal, complemented
8#13069417C211yesmaximal, characteristic, complemented
9#13069038C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#1948C211yesmaximal, characteristic, complemented
12C22×#4314C2212yes—
13C22×C8×D11C2212yes—
14C2×#66950C2212yes—
15C2×#66950C2212yes—
16C2×#66948—21no—
17C2×#66948C2212yes—
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C11×#106C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C11×#384C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C8C2212yes—
26C2×#66880C2212yes—
27#10622604—22no—
28#10622600—21no—
29#10622600C2212yes—
30C2×#66874C2212yes—
31C2×#66874C2212yes—
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34#10622552—21no—
35#10622548—21no—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622477—28no—
38#10622454—24no—
39#10622447—24no—
40#10622290—22no—
41C11×#340C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×D44—22no—
45C22×D44D411yescharacteristic
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C22×C4×D11C2312yes—
49C22×Dic22C2312yes—
50C22×C8×C11C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4D412yes—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72C2×#4314—24no—
73C2×#4314—24no—
74C2×#4314—42no—
75C2×C8×D11—24no—
76C2×C8×D11—24no—
77C2×C8×D11—42no—
78#66950—24no—
79#66950—24no—
80#66950—42no—
81#66950—42no—
82#66948—24no—
83#66948—42no—
84#66948—44no—
85C4×D44—22no—
86C4×D44—22no—
87C4×D44—22no—
88C4×D44—22no—
89#66922—22no—
90#66922—22no—
91C11×#106—24no—
92C11×C4⋊C8D414yescomplemented
93C11×#95—21no—
94C11⋊#95—22no—
95(C2×D11)⋊C8—24no—
96#66880—24no—
97#66874—24no—
98#66874—42no—
99#66873—22no—
100#66873D414yescomplemented
101C4×C11⋊C8—22no—
102#25385—111nomaximal, Sylow
103C23×D11—21no—
104C23×D11C2×D412yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11C2×D412yes—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—44no—
122C2×D44—44no—
123C2×D44—82no—
124C2×D44SD1614yescomplemented
125C2×D44C2×D412yes—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—42no—
133C2×C4×D11—42no—
134C2×C4×D11—42no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11C2×D414yes—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—81no—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4#4112yes—
152C42×C11—42no—
153C42×C11C2×D412yes—
154C42×C11#4112yes—
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4—44no—
157(C2×D11)⋊C4—44no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—44no—
160(C2×D11)⋊C4—42no—
161C4⋊Dic11—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—44no—
165C4⋊Dic11—44no—
166C4⋊Dic11—42no—
167C4⋊Dic11—42no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8C2×D412yes—
174#4314—48no—
175C8×D11—48no—
176C2×#465—112no—
177C2×#461—111no—
178C2×C8×D4—111no—
179#2542—111no—
180#2537—111no—
181#2035—112no—
182#2000—112no—
183#1956—111no—
184#1948D1111yescharacteristic, complemented
185#1892—112no—
186C4×#102—111no—
187C23×C11C22×D411yescharacteristic
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11C2×SD1614yes—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11#12112yes—
214C2×C4×C11#12112yes—
215C2×C4×C11C2×SD1612yes—
216C2×C4×C11#13512yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11H(5,𝔽2)11yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232D44—22no—
233D44—22no—
234D44—28no—
235D44—41no—
236D44—41no—
237D44—88no—
238C4×D11—42no—
239C4×D11—42no—
240C4×D11—42no—
241C4×D11—42no—
242C4×D11—84no—
243Dic22—42no—
244Dic22—42no—
245Dic22—42no—
246Dic22—42no—
247C8×C11—24no—
248C11⋊C8—22no—
249C11⋊C8—41no—
250C22×SD16—112no—
251C23×C8—112no—
252C2×C4⋊Q8—111no—
253C2×C22⋊Q8—112no—
254C2×C22⋊Q8—112no—
255C2×#121—112no—
256C2×#121—221no—
257C2×C4×D4—111no—
258C2×C4×D4—111no—
259#465—228no—
260#461—224no—
261C8×D4—224no—
262C2×#106C2×D1112yes—
263C2×C4⋊C8C2×D1111yescharacteristic
264C2×#103—112no—
265C2×#103—112no—
266C2×#103—112no—
267C2×#102—111no—
268C2×#102—111no—
269C2×C22⋊C8—112no—
270C2×C4×C8—111no—
271#399—222no—
272#394—222no—
273#390—221no—
274#384—221no—
275#384C2×D1111yescharacteristic
276#380—112no—
277#380—221no—
278C4×C4⋊C4C2×D1111yescharacteristic
279#340—111no—
280#340—111no—
281#340C2×D1112yes—
282C22×C11C2×#12111yescharacteristic
283C22×C11D4211yescharacteristic
284C22×C11#54611yescharacteristic
285C22×C11C22×SD1611yescharacteristic
286C22×C11C2×#13511yescharacteristic
287C22×C11#57711yescharacteristic
288C22×C11#57811yescharacteristic
289C2×D11—24no—
290C2×D11—24no—
291C2×D11—24no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—42no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C4×C11—22no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—82no—
307C4×C11#46514yescomplemented
308C4×C11#53211yescharacteristic
309C4×C11#54011yescharacteristic
310C4×C11D4211yescharacteristic
311C4×C11#55011yescharacteristic
312Dic11—42no—
313Dic11—82no—
314Dic11—81no—
315C22×Q8—112no—
316C22×D4—111no—
317C22×D4—111no—
318C22×D4—222no—
319C23×C4—112no—
320C23×C4—221no—
321C2×SD16—224no—
322C2×SD16—224no—
323C2×SD16—442no—
324C22×C8—111no—
325C22×C8—111no—
326C22×C8—224no—
327C22×C8—224no—
328C22×C8—442no—
329C22×C8C22×D1112yes—
330C4⋊Q8—222no—
331C4⋊Q8—222no—
332C22⋊Q8—224no—
333C22⋊Q8—224no—
334C22⋊Q8—442no—
335C22⋊Q8—442no—
336#121—224no—
337#121—442no—
338#121—444no—
339C4×D4—222no—
340C4×D4—222no—
341C4×D4—222no—
342C4×D4—222no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4C22×D1112yes—
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C22⋊C4—112no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—221no—
360C2×C42—21no—
361C2×C42C22×D1111yescharacteristic
362#106—24no—
363C4⋊C8D4414yescomplemented
364#103—224no—
365#103—224no—
366#103—442no—
367#102—114no—
368#102—222no—
369C22⋊C8—224no—
370C4×C8—222no—
371#95—21no—
372#95—222no—
373C2×C11#242811yescharacteristic
374C2×C11C2×#46511yescharacteristic
375C2×C11#306311yescharacteristic
376C2×C11D4×SD1611yescharacteristic
377C2×C11#328311yescharacteristic
378C2×C11#329811yescharacteristic
379C2×C11#330311yescharacteristic
380D11—44no—
381D11—82no—
382C24—112no—
383C24—221no—
384C2×Q8—222no—
385C2×Q8—222no—
386C2×Q8—222no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×D4—114no—
391C2×D4—112no—
392C2×D4—222no—
393C2×D4—222no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—221no—
399C2×D4—444no—
400C2×D4—444no—
401C2×D4—882no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—112no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—221no—
413C22×C4—222no—
414C22×C4—442no—
415C22×C4—442no—
416C22×C4—442no—
417C22×C4D4×D1111yescharacteristic
418C22×C4D4×D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420SD16—448no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—112no—
424C2×C8—221no—
425C2×C8—221no—
426C2×C8—221no—
427C2×C8—221no—
428C2×C8—221no—
429C2×C8—448no—
430C2×C8C2×D4414yes—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—42no—
436C4⋊C4—81no—
437C4⋊C4—222no—
438C4⋊C4—221no—
439C4⋊C4—221no—
440C4⋊C4—444no—
441C4⋊C4—444no—
442C4⋊C4—442no—
443C4⋊C4—442no—
444C4⋊C4D4×D1112yes—
445C4⋊C4#434312yes—
446C22⋊C4—224no—
447C22⋊C4—444no—
448C22⋊C4—444no—
449C22⋊C4—444no—
450C22⋊C4—444no—
451C22⋊C4—442no—
452C42—42no—
453C42C2×D4412yes—
454C42#434312yes—
455C11#2538511yescharacteristic, complemented, Sylow
456C23—114no—
457C23—222no—
458C23—222no—
459C23—222no—
460C23—222no—
461C23—222no—
462C23—222no—
463C23—222no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23—441no—
469C23—441no—
470C23C2×D4×D1111yescharacteristic
471Q8—442no—
472Q8—442no—
473Q8—442no—
474Q8—442no—
475D4—228no—
476D4—222no—
477D4—222no—
478D4—441no—
479D4—441no—
480D4—888no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—884no—
506C2×C4#6694812yes—
507C2×C4#6694812yes—
508C2×C4SD16×D1112yes—
509C2×C4#6696912yes—
510C2×C4C22×D4411yescharacteristic
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4C2×#434311yescharacteristic
513C2×C4C2×#434311yescharacteristic
514C2×C4#6704211yescharacteristic
515C2×C4#6704211yescharacteristic
516C8—24no—
517C8—222no—
518C8—441no—
519C22—224no—
520C22—224no—
521C22—224no—
522C22—442no—
523C22—442no—
524C22—442no—
525C22—442no—
526C22—442no—
527C22—442no—
528C22—442no—
529C22—881no—
530C22—881no—
531C22—881no—
532C22—881no—
533C22C2×#6694811yescharacteristic
534C22#1062314011yescharacteristic
535C22#1062316111yescharacteristic
536C22C2×SD16×D1111yescharacteristic
537C22C2×#6696911yescharacteristic
538C22#1062330611yescharacteristic
539C22#1062331011yescharacteristic
540C4—22no—
541C4—42no—
542C4—42no—
543C4—82no—
544C4—442no—
545C4—882no—
546C4—881no—
547C4#1062247714yescomplemented
548C4D4×D4411yescharacteristic
549C4#1062310811yescharacteristic
550C4#1062322911yescharacteristic
551C4#1062325611yescharacteristic
552C2—444no—
553C2—882no—
554C2#1307220211yescharacteristic
555C2C2×#1062247711yescharacteristic
556C2#1307830811yescharacteristic
557C2#1308030711yescharacteristic
558C2#1308033311yescharacteristic
559C2#1308047811yescharacteristic
560C2#1308054111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1948C2
socleC23×C11C22×D4
prime radical#13073532C2
hypercenter#1948D11
hypocenterC11#25385
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
1. C2×#10622477C2semidirect
2. C2×#10622454C2semidirect
3. C2×#10622447C2semidirect
4. #13073565C2semidirect
6. #13069814C2semidirect
7. #13069622C2semidirect
8. #13069417C2semidirect
9. #13069038C2semidirect
10. C4×#66873C2semidirect
11. C11×#1948C2semidirect
92. C11×C4⋊C8D4semidirect
100. #66873D4semidirect
124. C2×D44SD16semidirect
184. #1948D11semidirect
307. C4×C11#465semidirect
363. C4⋊C8D44semidirect
455. C11#25385semidirect
547. C4#10622477semidirect

Maximal subgroups

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

subgroupindex
C2×#106224772
C2×#106224542
C2×#106224472
#130735652
#130735322
#130698142
#130696222
#130694172
#130690382
C4×#668732
C11×#19482
#2538511