Finite Group Databasebeta

← #14770614

Subgroups — #14770614

Order 2816.

1366 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623249C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic, complemented
3#13071575C211yesmaximal, characteristic, complemented
4#13069544C211yesmaximal, characteristic, complemented
5#13069541C212yesmaximal, complemented
6#13069438C212yesmaximal, complemented
7#13068624C212yesmaximal, complemented
8#13068613C211yesmaximal, characteristic, complemented
9#13068443C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C11×#1957C211yesmaximal, characteristic, complemented
12C22×#4341—21no—
13C2×C11×#127C2211yescharacteristic
14C2×#66993C2212yes—
15C2×#66992—22no—
16C2×#66991—21no—
17C2×D4×Dic11C2212yes—
18#10623249—24no—
19#10623249C418yescomplemented
20C2×C4×D44C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#102C2212yes—
23C2×C11×#102C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C11×#384C2211yescharacteristic
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66879C2212yes—
31C2×Dic11⋊C8C2212yes—
32#10622591—22no—
33#10622590C2212yes—
34C4⋊C4×Dic11—21no—
35C4⋊C4×Dic11C2212yes—
36#10622587—21no—
37C2×#66873C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622292—24no—
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43#10622167C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—22no—
49C23×Dic11—22no—
50C2×#4341—28no—
51C2×#4341—44no—
52C2×#4341—44no—
53C22×D44C2311yescharacteristic
54C22×C4×D11—21no—
55C22×Dic22D411yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C11×#127—22no—
59C11×#127C2×C414yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—22no—
65#66993—24no—
66#66993C2×C418yes—
67#66992—216no—
68#66991—28no—
69D4×Dic11—24no—
70D4×Dic11C2×C418yes—
71C2×(C2×D11)⋊C4—21no—
72C2×C4⋊Dic11D411yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×Dic11⋊C4D412yes—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11C2312yes—
80C22×C11⋊C8C2312yes—
81C4×D44—22no—
82C4×D44C2×C414yes—
83C4×Dic22C2×C414yes—
84C4×Dic22D414yes—
85C11×#102—24no—
86C11×#102—42no—
87C4×C8×C11—22no—
88#66896—24no—
89#66896—42no—
90C11⋊#95—21no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94#66885—22no—
95#66885—22no—
96#66879—24no—
97Dic11⋊C8—24no—
98#66873—42no—
99C4⋊(C11⋊C8)—22no—
100#22545—111nomaximal, Sylow
101C24×C11—22no—
102C23×D11—21no—
103C2×D4×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11—81no—
113C2×D4×C11—81no—
114C2×D4×C11C22×C414yes—
115C22×C4×C11—22no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—28no—
120C2×C22⋊D11—28no—
121C2×C22⋊D11—44no—
122C2×C22⋊D11—44no—
123C2×C22⋊D11—82no—
124C2×C22⋊D11—82no—
125C22×Dic11—28no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—44no—
130C22×Dic11—44no—
131C22×Dic11C2×D412yes—
132C22×Dic11C2×D412yes—
133#4341—432no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44C22×C412yes—
140C2×C4×D11—24no—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22C22⋊C414yes—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11#4112yescomplemented
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—81no—
156C42×C11C22×C412yes—
157C42×C11C2×D412yes—
158C22⋊Dic11—28no—
159(C2×D11)⋊C4—24no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11C22⋊C414yes—
165C4⋊Dic11C22×C412yes—
166C4⋊Dic11#4112yescomplemented
167Dic11⋊C4C22⋊C418yes—
168C4×Dic11—42no—
169C4×Dic11—82no—
170C4×Dic11C22×C414yes—
171C4×Dic11C2×D414yes—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×#550—111no—
176C2×#446—111no—
177#2355—111no—
178#1982—112no—
179#1982—111no—
180#1961—112no—
181#1957D1111yescharacteristic, complemented
182#1804—112no—
183#1802—111no—
184#1762—112no—
185C4×#102—111no—
186C23×C11—24no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11C22×D411yescharacteristic
194C22×D11—22no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201D4×C11—24no—
202D4×C11—24no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—48no—
206D4×C11—84no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11C2×C22⋊C412yes—
213C2×C4×C11C2×C22⋊C412yes—
214C2×C4×C11AGL(1,ℤ/8)12yes—
215C2×C4×C11AGL(1,ℤ/8)12yes—
216C2×C4×C11C23×C411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11H(5,𝔽2)11yescharacteristic
221C2×C4×C112−1+411yescharacteristic
222C22⋊D11—416no—
223C22⋊D11—88no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—416no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11C2×C22⋊C414yes—
239C2×Dic11C2×C22⋊C414yes—
240D44—22no—
241D44—22no—
242D44—41no—
243D44—41no—
244C4×D11—48no—
245Dic22—28no—
246C8×C11—22no—
247C8×C11—41no—
248C11⋊C8—42no—
249C22×#41—221no—
250#550—118no—
251#550—224no—
252C2×#127—112no—
253C2×#127C2×D1111yescharacteristic
254C2×#121—221no—
255C2×#121—222no—
256C2×C4×Q8—111no—
257C2×C4×D4—112no—
258C2×C4×D4—111no—
259#446—224no—
260C2×C4⋊C8—112no—
261C2×C4⋊C8—111no—
262C2×#102—112no—
263C2×#102—111no—
264C2×#102—111no—
265C2×#102—112no—
266C2×#102—112no—
267C2×#102C2×D1112yes—
268C2×#102C2×D1112yes—
269C2×#97—112no—
270C2×C4×C8C2×D1111yescharacteristic
271#391—221no—
272#387—222no—
273#384C2×D1111yescharacteristic
274#382—112no—
275C4×C4⋊C4—112no—
276C4×C4⋊C4—111no—
277C4×C4⋊C4—221no—
278#340—111no—
279#340—111no—
280#340—112no—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11—44no—
284C22×C11—82no—
285C22×C11—82no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11C22×C22⋊C411yescharacteristic
289C22×C11#54811yescharacteristic
290C22×C11#55011yescharacteristic
291C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C11#57611yescharacteristic
294C22×C11#57711yescharacteristic
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C4×C11—22no—
303C4×C11—82no—
304C4×C11#41814yes—
305C4×C11C4×#4111yescharacteristic
306C4×C11#52011yescharacteristic
307C4×C11#54811yescharacteristic
308C4×C11#55011yescharacteristic
309Dic11—24no—
310Dic11—24no—
311Dic11—42no—
312Dic11—42no—
313Dic11—81no—
314C2×#41—228no—
315C2×#41—444no—
316C2×#41—444no—
317C22×Q8—111no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4—111no—
321C22×D4—222no—
322C22×D4—222no—
323C22×D4C22×D1112yes—
324C23×C4—222no—
325C23×C4—221no—
326C22×C8—112no—
327C22×C8C22×D1111yescharacteristic
328C22×C8C22×D1111yescharacteristic
329#127—22no—
330#127—118no—
331#127—224no—
332#127C4×D1114yes—
333#121—228no—
334#121—2216no—
335C4×Q8—114no—
336C4×Q8—114no—
337C4×D4—118no—
338C4×D4—114no—
339C4×D4—224no—
340C4×D4—222no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4C22×D1112yes—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—221no—
351C2×C42—112no—
352C2×C42—221no—
353C2×C42—222no—
354C2×C42C22×D1111yescharacteristic
355C4⋊C8—224no—
356C4⋊C8—222no—
357#102—24no—
358#102—42no—
359#102—222no—
360#102—224no—
361#102—222no—
362#102—442no—
363#102—442no—
364#97—224no—
365C4×C8—22no—
366#95—222no—
367#95—222no—
368#95—222no—
369#95—221no—
370C2×C11—84no—
371C2×C11#234111yescharacteristic
372C2×C11C2×#41811yescharacteristic
373C2×C11#289711yescharacteristic
374C2×C11#336611yescharacteristic
375C2×C11#336811yescharacteristic
376C2×C11#339711yescharacteristic
377C2×C11#339911yescharacteristic
378D11—82no—
379C24—22no—
380C24—221no—
381#41—4432no—
382C2×Q8—114no—
383C2×Q8—222no—
384C2×Q8—222no—
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—81no—
395C2×D4—81no—
396C2×D4—112no—
397C2×D4—228no—
398C2×D4—228no—
399C2×D4—221no—
400C2×D4—221no—
401C2×D4—221no—
402C2×D4—221no—
403C2×D4—221no—
404C2×D4—444no—
405C2×D4—444no—
406C2×D4—882no—
407C2×D4—882no—
408C2×D4C2×C4×D1114yes—
409C22×C4—22no—
410C22×C4—112no—
411C22×C4—112no—
412C22×C4—228no—
413C22×C4—221no—
414C22×C4—221no—
415C22×C4—224no—
416C22×C4—221no—
417C22×C4—444no—
418C22×C4—444no—
419C22×C4—442no—
420C22×C4—442no—
421C22×C4D4×D1111yescharacteristic
422C22×C4D4×D1111yescharacteristic
423C22×C4C23×D1111yescharacteristic
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—222no—
430C2×C8—222no—
431C2×C8—222no—
432C2×C8#434112yescomplemented
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—42no—
436C4⋊C4—81no—
437C4⋊C4—118no—
438C4⋊C4—114no—
439C4⋊C4—112no—
440C4⋊C4—112no—
441C4⋊C4—221no—
442C4⋊C4—221no—
443C4⋊C4—221no—
444C4⋊C4—221no—
445C22⋊C4—228no—
446C22⋊C4—224no—
447C42—114no—
448C42—114no—
449C42—442no—
450C42—882no—
451C42C2×C4×D1112yes—
452C42D4×D1112yes—
453C11#2254511yescharacteristic, complemented, Sylow
454C23—24no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—222no—
462C23—441no—
463C23—441no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23C2×D4×D1111yescharacteristic
469Q8—228no—
470D4—24no—
471D4—24no—
472D4—42no—
473D4—42no—
474D4—48no—
475D4—84no—
476D4—222no—
477D4—222no—
478D4—4416no—
479D4—441no—
480D4—441no—
481D4—888no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—114no—
488C2×C4—114no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—4416no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—448no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4C22⋊C4×D1112yes—
505C2×C4C22⋊C4×D1112yes—
506C2×C4#6696412yes—
507C2×C4#6696712yes—
508C2×C4C22×C4×D1111yescharacteristic
509C2×C4C2×D4×D1111yescharacteristic
510C2×C4C2×#434111yescharacteristic
511C2×C4#6703711yescharacteristic
512C2×C4#41×D1111yescharacteristic
513C2×C4#6704311yescharacteristic
514C8—22no—
515C8—41no—
516C8—442no—
517C22—44no—
518C22—44no—
519C22—44no—
520C22—82no—
521C22—82no—
522C22—82no—
523C22—82no—
524C22—442no—
525C22—442no—
526C22—442no—
527C22—881no—
528C22—881no—
529C22—881no—
530C22—881no—
531C22C2×C22⋊C4×D1111yescharacteristic
532C22#1062320811yescharacteristic
533C22#1062324911yescharacteristic
534C22C2×#6696411yescharacteristic
535C22#1062328811yescharacteristic
536C22C2×#6696711yescharacteristic
537C22#1062329311yescharacteristic
538C4—22no—
539C4—82no—
540C4—224no—
541C4—224no—
542C4—442no—
543C4—442no—
544C4—881no—
545C4#1062238314yes—
546C4C4×#434111yescharacteristic
547C4#1062307711yescharacteristic
548C4#1062312911yescharacteristic
549C4#1062313011yescharacteristic
550C2—84no—
551C2—882no—
552C2#1307145511yescharacteristic
553C2C2×#1062238311yescharacteristic
554C2#1307713711yescharacteristic
555C2#1308132811yescharacteristic
556C2#1308135011yescharacteristic
557C2#1308164111yescharacteristic
558C2#1308166311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1957C2
socleC23×C11C22×D4
prime radicalC2×#10623249C2
cosocleC22×C4×C11C24
hypercenter#1957D11
hypocenterC11#22545
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. C2×#10622292C2semidirect
3. #13071575C2semidirect
4. #13069544C2semidirect
5. #13069541C2semidirect
6. #13069438C2semidirect
7. #13068624C2semidirect
8. #13068613C2semidirect
9. #13068443C2semidirect
10. C4×#66885C2semidirect
11. C11×#1957C2semidirect
19. #10623249C4semidirect
151. C2×C8×C11#41semidirect
166. C4⋊Dic11#41semidirect
181. #1957D11semidirect
432. C2×C8#4341semidirect
453. C11#22545semidirect

Maximal subgroups

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

subgroupindex
C2×#106232492
C2×#106222922
#130715752
#130695442
#130695412
#130694382
#130686242
#130686132
#130684432
C4×#668852
C11×#19572
#2254511