Finite Group Databasebeta

← #14804248

Subgroups — #14804248

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622306C211yesmaximal, characteristic, complemented
2C2×#10622375C212yesmaximal, complemented
3C2×#10622632C211yesmaximal, characteristic, complemented
4#13073562C211yesmaximal, characteristic
5#13071674C211yesmaximal, characteristic, complemented
6#13069935C212yesmaximal, complemented
7#13069705C212yesmaximal, complemented
8#13069543C211yesmaximal, characteristic, complemented
9#13069334C211yesmaximal, characteristic, complemented
10#13068972C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66993C2212yes—
14C22×#4324C2212yes—
15C2×#66983—21no—
16C2×#66983—21no—
17C22×#4314C2212yes—
18C22×#4314C2212yes—
19C2×#66940C2212yes—
20C2×#66927C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×Dic11⋊C8C2212yes—
27#10622632—24no—
28#10622601C2212yes—
29#10622587C2212yes—
30C2×#66874C2212yes—
31C2×#66873C2212yes—
32C2×#66873C2212yes—
33#10622573—22no—
34C4×C4⋊Dic11—21no—
35C4×C4⋊Dic11C2211yescharacteristic
36#10622541—21no—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622375—28no—
39#10622306—24no—
40#10622266—22no—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43#10622188C2212yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×C22⋊D11—22no—
47C22×C22⋊D11—22no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44C2312yes—
51C22×Dic22C2312yes—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62#66993—24no—
63#66993—42no—
64C2×#4324—24no—
65C2×#4324—24no—
66C2×#4324—42no—
67#66983—44no—
68#66983—44no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11D411yescharacteristic
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11C2312yes—
78C22×C11⋊C8C2312yes—
79C2×#4314—24no—
80C2×#4314—24no—
81C2×#4314—24no—
82C2×#4314—24no—
83C2×#4314—42no—
84C2×#4314—42no—
85#66940—24no—
86#66940—42no—
87#66927—22no—
88#66927—22no—
89#66922—22no—
90#66922D414yescomplemented
91C11×#102—22no—
92C11×#102D414yescomplemented
93C4×C8×C11—22no—
94C11×#95—21no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97C11⋊#95D412yes—
98Dic11⋊C8—24no—
99#66874—24no—
100#66873—24no—
101#66873—42no—
102C4⋊(C11⋊C8)—22no—
103#25366—111nomaximal, Sylow
104C24×C11—21no—
105C23×D11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11C2×D412yes—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—44no—
122C2×C22⋊D11—44no—
123C2×C22⋊D11—44no—
124C2×C22⋊D11—44no—
125C2×C22⋊D11—82no—
126C2×C22⋊D11—82no—
127C22×Dic11—22no—
128C22×Dic11C2×D412yes—
129C22×Dic11C2×D412yes—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—42no—
137C2×D44—42no—
138C2×D44—42no—
139C2×D44—42no—
140C2×D44—81no—
141C2×D44—81no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22C2×D414yes—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11C2×D412yes—
153C2×C8×C11#4112yes—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4C2×D412yes—
160C11×C22⋊C4—42no—
161C42×C11—42no—
162C42×C11C2×D412yes—
163C42×C11#4112yes—
164#4324—48no—
165(C2×D11)⋊C4—44no—
166(C2×D11)⋊C4—44no—
167C4⋊Dic11—24no—
168C4⋊Dic11—24no—
169C4⋊Dic11—22no—
170C4⋊Dic11SD1614yescomplemented
171Dic11⋊C4—44no—
172C4×Dic11—22no—
173C4×Dic11—22no—
174C4×Dic11—44no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178#4314—48no—
179#4314—48no—
180C2×#492—111no—
181C2×#460—112no—
182C2×#461—111no—
183#2541—111no—
184#2365—111no—
185#2055—112no—
186#2014—112no—
187#1982—111no—
188#1939—111no—
189#1880—112no—
190C4×#102D1111yescharacteristic, complemented
191C23×C11—22no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11C22×D411yescharacteristic
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206D4×C11—22no—
207D4×C11—22no—
208D4×C11—41no—
209D4×C11—41no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—84no—
222C2×C4×C11#12112yes—
223C2×C4×C11#12112yes—
224C2×C4×C11C2×SD1612yes—
225C2×C4×C11AGL(1,ℤ/8)12yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11H(5,𝔽2)11yescharacteristic
231C2×C4×C11H(5,𝔽2)11yescharacteristic
232C22⋊D11—88no—
233C22⋊D11—88no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11C2×SD1614yes—
243D44—42no—
244D44—42no—
245D44—42no—
246D44—42no—
247D44—84no—
248D44—84no—
249Dic22—24no—
250Dic22—24no—
251Dic22—42no—
252Dic22—42no—
253C8×C11—22no—
254C8×C11—22no—
255C11⋊C8—42no—
256C22×SD16—112no—
257C22×SD16—112no—
258C22×SD16—112no—
259C2×C4⋊Q8—111no—
260C2×#127—112no—
261C2×#127—111no—
262C2×#121—221no—
263C2×#121—221no—
264C2×C4×Q8—112no—
265C2×C4×D4C2×D1111yescharacteristic
266#492—224no—
267#461—224no—
268#460—228no—
269C2×C4⋊C8—112no—
270C2×C4⋊C8—111no—
271C2×#103—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102C2×D1111yescharacteristic
275C2×#102C2×D1111yescharacteristic
276C2×C4×C8C2×D1111yescharacteristic
277#392—222no—
278#391—112no—
279#390—112no—
280#389—221no—
281#387—222no—
282C4×C4⋊C4—111no—
283C4×C4⋊C4—221no—
284C4×C4⋊C4C2×D1111yescharacteristic
285#340C2×D1111yescharacteristic
286#340C2×D1111yescharacteristic
287#336—112no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11C2×#12111yescharacteristic
296C22×C11D4211yescharacteristic
297C22×C11#55011yescharacteristic
298C22×C11C22×SD1611yescharacteristic
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C11#57711yescharacteristic
301C22×C11#57711yescharacteristic
302C2×D11—82no—
303C2×D11—82no—
304C2×D11—82no—
305C2×D11—82no—
306C2×D11—82no—
307C2×D11—82no—
308C2×D11—82no—
309C4×C11—22no—
310C4×C11—42no—
311C4×C11—81no—
312C4×C11—81no—
313C4×C11#46014yescomplemented
314C4×C11#53211yescharacteristic
315C4×C11#54011yescharacteristic
316C4×C11D4211yescharacteristic
317C4×C11#54611yescharacteristic
318Dic11—24no—
319Dic11—44no—
320Dic11—42no—
321C22×Q8—112no—
322C22×D4—112no—
323C22×D4—222no—
324C22×D4—222no—
325C22×D4—221no—
326C22×D4—221no—
327C22×D4C22×D1111yescharacteristic
328C23×C4—21no—
329C2×SD16—224no—
330C2×SD16—224no—
331C2×SD16—224no—
332C2×SD16—224no—
333C2×SD16—224no—
334C2×SD16—224no—
335C2×SD16—442no—
336C2×SD16—442no—
337C2×SD16—442no—
338C22×C8—112no—
339C22×C8C22×D1111yescharacteristic
340C22×C8C22×D1111yescharacteristic
341C4⋊Q8—114no—
342C4⋊Q8—222no—
343#127—224no—
344#127—222no—
345#127—222no—
346#127—442no—
347#121—444no—
348#121—444no—
349C4×Q8—224no—
350C4×Q8—442no—
351C4×D4—22no—
352C4×D4—22no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C42—21no—
365C2×C42—112no—
366C2×C42—222no—
367C2×C42C22×D1111yescharacteristic
368C4⋊C8—224no—
369C4⋊C8—222no—
370#103—224no—
371#102—22no—
372#102—224no—
373#102—442no—
374#102D4414yescomplemented
375C4×C8—22no—
376#95—21no—
377#95—112no—
378#95—222no—
379#95—222no—
380C2×C11—82no—
381C2×C11#242811yescharacteristic
382C2×C11C2×#46011yescharacteristic
383C2×C11#304311yescharacteristic
384C2×C11#327211yescharacteristic
385C2×C11D4×SD1611yescharacteristic
386C2×C11#339211yescharacteristic
387C2×C11#339711yescharacteristic
388D11—162no—
389C24—21no—
390C24—222no—
391C2×Q8—114no—
392C2×Q8—222no—
393C2×Q8—222no—
394C2×Q8—222no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—444no—
409C2×D4—444no—
410C2×D4—444no—
411C2×D4—444no—
412C2×D4—442no—
413C2×D4—442no—
414C2×D4—442no—
415C2×D4—442no—
416C2×D4—881no—
417C2×D4—881no—
418C2×D4—882no—
419C2×D4—882no—
420C2×D4C2×D4412yes—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—222no—
430C22×C4D4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4C23×D1111yescharacteristic
433SD16—448no—
434SD16—448no—
435SD16—448no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8C2×D4412yes—
444C2×C8#433912yes—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—114no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—222no—
454C4⋊C4—444no—
455C4⋊C4C2×D4412yes—
456C22⋊C4—42no—
457C22⋊C4—444no—
458C22⋊C4—444no—
459C42—42no—
460C42—222no—
461C42—222no—
462C42—444no—
463C42#433912yes—
464C42D4×D1112yes—
465C11#2536611yescharacteristic, complemented, Sylow
466C23—22no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—442no—
474C23—442no—
475C23—442no—
476C23—442no—
477C23—442no—
478C23—442no—
479C23—442no—
480C23C2×D4×D1111yescharacteristic
481Q8—224no—
482Q8—224no—
483Q8—442no—
484Q8—442no—
485D4—22no—
486D4—22no—
487D4—41no—
488D4—41no—
489D4—442no—
490D4—442no—
491D4—442no—
492D4—442no—
493D4—884no—
494D4—888no—
495D4—888no—
496D4—884no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—84no—
509C2×C4—114no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4#6693712yes—
519C2×C4#6693712yes—
520C2×C4#6696412yes—
521C2×C4SD16×D1112yes—
522C2×C4C22×D4411yescharacteristic
523C2×C4C2×#433911yescharacteristic
524C2×C4C2×#433911yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4#6704211yescharacteristic
527C2×C4#6704211yescharacteristic
528C8—22no—
529C8—22no—
530C8—442no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—882no—
539C22—882no—
540C22—882no—
541C22—882no—
542C22—882no—
543C22—882no—
544C22—882no—
545C22C2×#6693711yescharacteristic
546C22D4×D4411yescharacteristic
547C22#1062308411yescharacteristic
548C22C2×#6696411yescharacteristic
549C22C2×SD16×D1111yescharacteristic
550C22#1062330111yescharacteristic
551C22#1062330111yescharacteristic
552C4—22no—
553C4—42no—
554C4—81no—
555C4—81no—
556C4—224no—
557C4—444no—
558C4—442no—
559C4#1062237514yescomplemented
560C4#1062300811yescharacteristic
561C4#1062306611yescharacteristic
562C4D4×D4411yescharacteristic
563C4#1062308111yescharacteristic
564C2—82no—
565C2—1762no—
566C2#1307220411yescharacteristic
567C2C2×#1062237511yescharacteristic
568C2#1307814011yescharacteristic
569C2#1308021711yescharacteristic
570C2SD16×D4411yescharacteristic
571C2#1308159511yescharacteristic
572C2#1308163411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radical#13073562C2
hypercenterC4×#102D11
hypocenterC11#25366
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. C2×#10622306C2semidirect
2. C2×#10622375C2semidirect
3. C2×#10622632C2semidirect
5. #13071674C2semidirect
6. #13069935C2semidirect
7. #13069705C2semidirect
8. #13069543C2semidirect
9. #13069334C2semidirect
10. #13068972C2semidirect
11. C4×C11×#102C2semidirect
90. #66922D4semidirect
92. C11×#102D4semidirect
170. C4⋊Dic11SD16semidirect
190. C4×#102D11semidirect
313. C4×C11#460semidirect
374. #102D44semidirect
465. C11#25366semidirect
559. C4#10622375semidirect

Maximal subgroups

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

subgroupindex
C2×#106223062
C2×#106223752
C2×#106226322
#130735622
#130716742
#130699352
#130697052
#130695432
#130693342
#130689722
C4×C11×#1022
#2536611