Finite Group Databasebeta

← #14764830

Subgroups — #14764830

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622343C211yesmaximal, characteristic, complemented
2C2×#10622847C211yesmaximal, characteristic, complemented
3#13071829C211yesmaximal, characteristic
4#13069412C212yesmaximal, complemented
5#13069232C212yesmaximal, complemented
6#13069226C212yesmaximal, complemented
7#13068911C211yesmaximal, characteristic, complemented
8#13068910C212yesmaximal, complemented
9#13068798C211yesmaximal, characteristic, complemented
10#13068395C211yesmaximal, characteristic, complemented
11C11×#1780C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C2×C4×C22⋊D11C2211yescharacteristic
14C2×C4×C22⋊D11C2212yes—
15C22×#4318C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×C11×C22⋊C8C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2212yes—
21C2×C11×C22⋊C8C2212yes—
22#10622847—24no—
23#10622844C411yescharacteristic
24#10622842C411yescharacteristic
25#10622836C411yescharacteristic
26#10622836C412yes—
27#10622835C411yescharacteristic
28#10622835C412yes—
29C4×C22⋊Dic11C2211yescharacteristic
30C4×C22⋊Dic11C2212yes—
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2212yes—
35C2×#66879C2211yescharacteristic
36C2×#66879C2212yes—
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2212yes—
39#10622343—24no—
40#10622188C2212yes—
41#10622188C2212yes—
42#10622188C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—42no—
46C2×C11×#41—42no—
47C22×Q8×C11C2×C411yescharacteristic
48C22×D4×C11C2×C412yes—
49C22×D4×C11C2×C411yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11C2×C411yescharacteristic
53C22×C22⋊D11C2×C412yes—
54C22×C4×D11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C2×C22⋊Dic11C2×C411yescharacteristic
59C2×C22⋊Dic11C2×C412yes—
60C2×C22⋊Dic11C2×C412yes—
61C2×C22⋊Dic11C2×C412yes—
62C2×C22⋊Dic11C2×C412yes—
63C4×C22⋊D11—22no—
64C4×C22⋊D11—22no—
65C4×C22⋊D11—42no—
66C4×C22⋊D11—42no—
67C2×(C2×D11)⋊C4C2×C411yescharacteristic
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×Dic11⋊C4C2×C411yescharacteristic
70C2×Dic11⋊C4C2×C412yes—
71C2×C4×Dic11C2311yescharacteristic
72C2×C4×Dic11C2312yes—
73C2×#4318—22no—
74C2×#4318—42no—
75C22×C11⋊C8—42no—
76C22×C11⋊C8D414yescomplemented
77C22×C11⋊C8C2312yes—
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80C2×#4313—22no—
81C2×#4313—42no—
82C11×C22⋊C8—22no—
83C11×C22⋊C8—22no—
84C11×C22⋊C8—42no—
85C11×C22⋊C8—42no—
86C11⋊#95C2×C412yes—
87C11⋊#95C2×C411yescharacteristic
88C11⋊#95C2×C412yes—
89C11⋊#95C2×C411yescharacteristic
90C22⋊(C11⋊C8)—24no—
91C22⋊(C11⋊C8)—24no—
92(C2×D11)⋊C8—22no—
93(C2×D11)⋊C8—42no—
94#66879—22no—
95#66879—42no—
96Dic11⋊C8—22no—
97Dic11⋊C8—42no—
98#22035—111nomaximal, Sylow
99C24×C11C22×C412yes—
100C24×C11C22×C411yescharacteristic
101C23×D11C22×C411yescharacteristic
102C11×#41—44no—
103C11×#41—44no—
104C11×#41—48no—
105C2×Q8×C11—22no—
106C2×Q8×C11—42no—
107C2×D4×C11—24no—
108C2×D4×C11—22no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11#4112yes—
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—22no—
126C2×C22⋊D11—42no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—42no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—42no—
131C22×Dic11C22×C411yescharacteristic
132C22×Dic11C22×C412yes—
133C22×Dic11C22×C411yescharacteristic
134C22×Dic11C22×C412yes—
135C22×Dic11C22×C411yescharacteristic
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C22⋊Dic11—22no—
148C22⋊Dic11—42no—
149C22⋊Dic11—42no—
150C22⋊Dic11—42no—
151C22⋊Dic11—42no—
152(C2×D11)⋊C4—22no—
153(C2×D11)⋊C4—42no—
154Dic11⋊C4—22no—
155Dic11⋊C4—42no—
156C4×Dic11—21no—
157C4×Dic11—21no—
158C4×Dic11—22no—
159C4×Dic11—22no—
160#4318—44no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—44no—
167C2×C11⋊C8C2×D412yes—
168C2×C11⋊C8C2×D412yes—
169#4313—44no—
170C2×#435—111no—
171C2×#408—111no—
172#2388—111no—
173#1955—112no—
174#1924—112no—
175#1924—112no—
176#1870—112no—
177#1870—111no—
178#1851—111no—
179#1780D1111yescharacteristic, complemented
180#1752—111no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11C4×D412yes—
193C23×C11C23×C411yescharacteristic
194C22×D11—21no—
195C22×D11—22no—
196C22×D11—21no—
197C22×D11—21no—
198C22×D11—22no—
199Q8×C11—44no—
200D4×C11—44no—
201D4×C11—48no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11C4×D412yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)12yes—
217C2×C4×C11H(5,𝔽2)12yes—
218C22⋊D11—44no—
219C22⋊D11—48no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—21no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—21no—
232C2×Dic11—22no—
233C4×D11—41no—
234C4×D11—41no—
235C4×D11—42no—
236C8×C11—41no—
237C8×C11—41no—
238C8×C11—42no—
239C11⋊C8—22no—
240C11⋊C8—22no—
241C11⋊C8—42no—
242C22×#41C2×D1111yescharacteristic
243C22×M16—111no—
244C22×M16—111no—
245C23×C8—111no—
246C2×C4×D4—111no—
247C2×C4×D4—112no—
248#435—224no—
249C2×C4⋊C8—111no—
250C2×C4⋊C8—112no—
251#408—224no—
252C2×C22⋊C8—112no—
253C2×C22⋊C8—112no—
254C2×C22⋊C8—111no—
255C2×C22⋊C8—112no—
256C2×C22⋊C8C2×D1111yescharacteristic
257C2×C22⋊C8C2×D1111yescharacteristic
258C2×C22⋊C8C2×D1112yes—
259C2×C22⋊C8C2×D1112yes—
260C2×#97—111no—
261C2×#97—112no—
262#395—111no—
263#394—112no—
264#394—111no—
265#393—111no—
266#392—111no—
267#392—112no—
268C4×C22⋊C4—111no—
269C4×C22⋊C4—112no—
270#336—112no—
271#336—112no—
272#336—112no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11C2×C4×D411yescharacteristic
286C22×C11#51812yes—
287C22×C11#56811yescharacteristic
288C22×C11#56811yescharacteristic
289C22×C11#56812yes—
290C2×D11—41no—
291C2×D11—41no—
292C2×D11—41no—
293C2×D11—42no—
294C2×D11—42no—
295C4×C11—22no—
296C4×C11—42no—
297C4×C11#53411yescharacteristic
298C4×C11#53511yescharacteristic
299C4×C11#53812yes—
300Dic11—41no—
301Dic11—41no—
302Dic11—41no—
303Dic11—42no—
304Dic11—42no—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—42no—
308C2×#41—42no—
309C22×Q8C4×D1111yescharacteristic
310C22×D4—111no—
311C22×D4—112no—
312C22×D4C4×D1112yes—
313C22×D4C4×D1111yescharacteristic
314C23×C4—111no—
315C23×C4C22×D1112yes—
316C23×C4C22×D1111yescharacteristic
317C2×M16—222no—
318C2×M16—222no—
319C2×M16—442no—
320C2×M16—442no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8—114no—
324C22×C8—112no—
325C22×C8—442no—
326C22×C8C22×D1111yescharacteristic
327C22×C8C22×D1112yes—
328C22×C8C22×D1111yescharacteristic
329C4×D4—222no—
330C4×D4—222no—
331C4×D4—442no—
332C4×D4—442no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—112no—
335C2×C22⋊C4—111no—
336C2×C22⋊C4—111no—
337C2×C22⋊C4—112no—
338C2×C22⋊C4—112no—
339C2×C22⋊C4—112no—
340C2×C22⋊C4—112no—
341C2×C22⋊C4—112no—
342C2×C42—111no—
343C2×C42—112no—
344C4⋊C8—222no—
345C4⋊C8—442no—
346C22⋊C8—22no—
347C22⋊C8—22no—
348C22⋊C8—42no—
349C22⋊C8—42no—
350C22⋊C8—222no—
351C22⋊C8—224no—
352C22⋊C8—224no—
353C22⋊C8—442no—
354#97—222no—
355#97—442no—
356#95—112no—
357#95—111no—
358#95—112no—
359#95—111no—
360C2×C11—42no—
361C2×C11—82no—
362C2×C11#232111yescharacteristic
363C2×C11#293011yescharacteristic
364C2×C11#293211yescharacteristic
365C2×C11#297812yes—
366C2×C11#298012yes—
367D11—81no—
368C24—111no—
369C24C2×C4×D1112yes—
370C24C2×C4×D1111yescharacteristic
371#41—44no—
372#41—44no—
373#41—48no—
374C2×Q8—22no—
375C2×Q8—42no—
376C2×D4—24no—
377C2×D4—22no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—42no—
381C2×D4—222no—
382C2×D4—442no—
383C2×D4—441no—
384C2×D4—442no—
385C2×D4—441no—
386C2×D4—442no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—111no—
396C22×C4—112no—
397C22×C4—111no—
398C22×C4—112no—
399C22×C4—111no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4C2×C4×D1112yes—
405C22×C4C2×C4×D1111yescharacteristic
406C22×C4D4×D1112yes—
407C22×C4#434112yes—
408C22×C4C23×D1111yescharacteristic
409M16—444no—
410M16—444no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—112no—
419C2×C8—112no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8—222no—
425C2×C8—444no—
426C4⋊C4—222no—
427C4⋊C4—442no—
428C22⋊C4—222no—
429C22⋊C4—222no—
430C22⋊C4—442no—
431C22⋊C4—442no—
432C22⋊C4—442no—
433C22⋊C4—442no—
434C22⋊C4—442no—
435C42—221no—
436C42—221no—
437C42—222no—
438C42—222no—
439C11#2203511yescharacteristic, complemented, Sylow
440C23—22no—
441C23—22no—
442C23—21no—
443C23—21no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—221no—
452C23—222no—
453C23—221no—
454C23—221no—
455C23—222no—
456C23(C22⋊D11)⋊C412yes—
457C23C22×C4×D1111yescharacteristic
458Q8—44no—
459D4—44no—
460D4—48no—
461D4—444no—
462D4—448no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—221no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—221no—
486C2×C4—222no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4—442no—
490C2×C4(C22⋊D11)⋊C412yes—
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4C2×#434111yescharacteristic
493C2×C4#6703712yes—
494C2×C4#6703712yes—
495C8—41no—
496C8—41no—
497C8—42no—
498C8—222no—
499C8—222no—
500C8—442no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—441no—
514C22—441no—
515C22—441no—
516C22—442no—
517C22—442no—
518C22C2×(C22⋊D11)⋊C411yescharacteristic
519C22#1062301712yes—
520C22#1062328111yescharacteristic
521C22#1062328111yescharacteristic
522C22#1062328112yes—
523C4—22no—
524C4—42no—
525C4—441no—
526C4—441no—
527C4—441no—
528C4—442no—
529C4—442no—
530C4#1062312011yescharacteristic
531C4#1062312311yescharacteristic
532C4#1062312412yes—
533C2—42no—
534C2—82no—
535C2—881no—
536C2#1307127111yescharacteristic
537C2#1307732211yescharacteristic
538C2#1307733111yescharacteristic
539C2#1307767412yes—
540C2#1307768512yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1780C2
prime radical#13071829C2
cosocleC22×C4×C11C24
hypercenter#1780D11
hypocenterC11#22035
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
1. C2×#10622343C2semidirect
2. C2×#10622847C2semidirect
4. #13069412C2semidirect
5. #13069232C2semidirect
6. #13069226C2semidirect
7. #13068911C2semidirect
8. #13068910C2semidirect
9. #13068798C2semidirect
10. #13068395C2semidirect
11. C11×#1780C2semidirect
76. C22×C11⋊C8D4semidirect
179. #1780D11semidirect
439. C11#22035semidirect

Maximal subgroups

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

subgroupindex
C2×#106223432
C2×#106228472
#130718292
#130694122
#130692322
#130692262
#130689112
#130689102
#130687982
#130683952
C11×#17802
#2203511