Finite Group Databasebeta

← #14764835

Subgroups — #14764835

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×#10622724C211yesmaximal, characteristic, complemented
2C2×#10622723C211yesmaximal, characteristic, complemented
3#13071832C211yesmaximal, characteristic
4#13069414C212yesmaximal, complemented
5#13069230C212yesmaximal, complemented
6#13069229C212yesmaximal, complemented
7#13068912C212yesmaximal, complemented
8#13068911C211yesmaximal, characteristic, complemented
9#13068801C211yesmaximal, characteristic, complemented
10#13068527C211yesmaximal, characteristic, complemented
11C11×#1752C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×#4313C2211yescharacteristic
17C2×C4×D44C2212yes—
18C2×C11×C22⋊C8C2211yescharacteristic
19C2×C11×#97C2212yes—
20C4×C11×C22⋊C4C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22#10622724—24no—
23#10622723—24no—
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×#66879C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32#10622574C412yes—
33#10622573C412yes—
34C4×(C2×D11)⋊C4C2212yes—
35C2×C4⋊(C11⋊C8)C2212yes—
36#10622286C411yescharacteristic
37#10622285C411yescharacteristic
38#10622284C411yescharacteristic
39#10622269C411yescharacteristic
40C11×#336C2212yes—
41#10622188C2212yes—
42#10622162C2212yes—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11C2×C411yescharacteristic
45C22×C22⋊D11C2×C412yes—
46C2×#4339—22no—
47C2×#4339—22no—
48C2×#4339—42no—
49C2×#4339—42no—
50C22×D44C2×C411yescharacteristic
51C22×D44C2×C412yes—
52C22×C4×D11C2312yes—
53C22×C4×D11C2311yescharacteristic
54C22×Dic22C2×C411yescharacteristic
55C22×C8×C11—42no—
56C22×C8×C11D414yescomplemented
57C22×C8×C11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C2×C11×C22⋊C4C2×C412yes—
61C2×C42×C11C2312yes—
62C2×C22⋊Dic11C2×C411yescharacteristic
63C4×C22⋊D11—22no—
64C4×C22⋊D11—22no—
65C2×(C2×D11)⋊C4C2×C411yescharacteristic
66C2×(C2×D11)⋊C4C2×C412yes—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×C4⋊Dic11C2×C412yes—
71C2×Dic11⋊C4C2×C411yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C2×#4318—22no—
74C2×#4318—42no—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77C22×C11⋊C8C2311yescharacteristic
78C2×#4313—22no—
79C2×#4313—42no—
80C4×D44—42no—
81C4×D44—42no—
82C11×C22⋊C8—22no—
83C11×#97—42no—
84C11×#95C2×C411yescharacteristic
85C11×#95C2×C411yescharacteristic
86C11⋊#95C2×C412yes—
87C11⋊#95C2×C412yes—
88C22⋊(C11⋊C8)—22no—
89(C2×D11)⋊C8—24no—
90(C2×D11)⋊C8—24no—
91(C2×D11)⋊C8—22no—
92(C2×D11)⋊C8—42no—
93(C2×D11)⋊C8—42no—
94(C2×D11)⋊C8—42no—
95#66879—22no—
96Dic11⋊C8—22no—
97C4⋊(C11⋊C8)—42no—
98#22035—111nomaximal, Sylow
99C24×C11C22×C411yescharacteristic
100C23×D11C22×C411yescharacteristic
101C23×D11C22×C412yes—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11#4112yes—
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—22no—
111C2×C22⋊D11—24no—
112C2×C22⋊D11—42no—
113C2×C22⋊D11—42no—
114C2×C22⋊D11—41no—
115C2×C22⋊D11—41no—
116C22×Dic11C22×C411yescharacteristic
117C22×Dic11C22×C411yescharacteristic
118C22×Dic11C22×C412yes—
119C22×Dic11C22×C411yescharacteristic
120#4339—44no—
121#4339—44no—
122#4339—48no—
123C2×D44—22no—
124C2×D44—42no—
125C2×D44—42no—
126C2×D44—42no—
127C2×D44—42no—
128C2×C4×D11—22no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×Dic22—22no—
139C2×Dic22—42no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—44no—
146C2×C8×C11C2×D412yes—
147C2×C8×C11C2×D412yes—
148C11×C22⋊C4—42no—
149C42×C11—22no—
150C42×C11—22no—
151C22⋊Dic11—22no—
152(C2×D11)⋊C4—22no—
153(C2×D11)⋊C4—42no—
154(C2×D11)⋊C4—42no—
155(C2×D11)⋊C4—42no—
156(C2×D11)⋊C4—42no—
157C4⋊Dic11—42no—
158Dic11⋊C4—22no—
159C4×Dic11—21no—
160C4×Dic11—21no—
161#4318—44no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169#4313—44no—
170C2×#435—111no—
171C2×#408—111no—
172#2388—111no—
173#1955—112no—
174#1924—112no—
175#1924—112no—
176#1870—111no—
177#1870—112no—
178#1851—111no—
179#1780—111no—
180#1752D1111yescharacteristic, complemented
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11C4×D412yes—
186C23×C11C23×C411yescharacteristic
187C22×D11—21no—
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—21no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11C4×D412yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11H(5,𝔽2)12yes—
213C2×C4×C11H(5,𝔽2)12yes—
214C22⋊D11—48no—
215C22⋊D11—44no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—21no—
224C2×Dic11—22no—
225C2×Dic11—21no—
226D44—44no—
227D44—48no—
228C4×D11—41no—
229C4×D11—42no—
230C4×D11—41no—
231C4×D11—42no—
232C4×D11—42no—
233C4×D11—42no—
234C4×D11—42no—
235Dic22—44no—
236C8×C11—22no—
237C8×C11—22no—
238C8×C11—42no—
239C11⋊C8—41no—
240C11⋊C8—41no—
241C11⋊C8—42no—
242C22×#41—111no—
243C22×M16—111no—
244C22×M16—111no—
245C23×C8C2×D1111yescharacteristic
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—111no—
253C2×C22⋊C8—112no—
254C2×C22⋊C8—112no—
255C2×C22⋊C8—111no—
256C2×C22⋊C8—112no—
257C2×C22⋊C8—112no—
258C2×C22⋊C8—112no—
259C2×C22⋊C8C2×D1111yescharacteristic
260C2×#97—111no—
261C2×#97C2×D1112yes—
262#395—111no—
263#394—112no—
264#394—111no—
265#393—111no—
266#392—112no—
267#392—111no—
268C4×C22⋊C4—112no—
269C4×C22⋊C4C2×D1111yescharacteristic
270#336—112no—
271#336—112no—
272#336C2×D1112yes—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11C2×C4×D411yescharacteristic
279C22×C11#51812yes—
280C22×C11#56812yes—
281C22×C11#56811yescharacteristic
282C22×C11#56811yescharacteristic
283C2×D11—41no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—41no—
287C2×D11—41no—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—42no—
295C4×C11—22no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11#53411yescharacteristic
299C4×C11#53511yescharacteristic
300C4×C11#53812yes—
301Dic11—42no—
302Dic11—41no—
303Dic11—41no—
304Dic11—41no—
305C2×#41—222no—
306C2×#41—222no—
307C2×#41—442no—
308C2×#41—442no—
309C22×Q8—111no—
310C22×D4—111no—
311C22×D4—112no—
312C22×D4—111no—
313C22×D4—112no—
314C23×C4—111no—
315C23×C4—112no—
316C23×C4C22×D1111yescharacteristic
317C2×M16—222no—
318C2×M16—222no—
319C2×M16—442no—
320C2×M16—442no—
321C22×C8—42no—
322C22×C8—112no—
323C22×C8—111no—
324C22×C8—111no—
325C22×C8D4414yescomplemented
326C22×C8C22×D1112yes—
327C22×C8C22×D1111yescharacteristic
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⋊C4C4×D1112yes—
342C2×C42—111no—
343C2×C42C22×D1112yes—
344C4⋊C8—222no—
345C4⋊C8—442no—
346C22⋊C8—22no—
347C22⋊C8—222no—
348C22⋊C8—224no—
349C22⋊C8—224no—
350C22⋊C8—222no—
351C22⋊C8—442no—
352C22⋊C8—442no—
353C22⋊C8—442no—
354#97—42no—
355#97—222no—
356#95—112no—
357#95—112no—
358#95C4×D1111yescharacteristic
359#95C4×D1111yescharacteristic
360C2×C11—42no—
361C2×C11#232111yescharacteristic
362C2×C11#293011yescharacteristic
363C2×C11#293211yescharacteristic
364C2×C11#297812yes—
365C2×C11#298012yes—
366D11—81no—
367D11—82no—
368C24—111no—
369C24—112no—
370C24C2×C4×D1111yescharacteristic
371#41—444no—
372#41—444no—
373#41—448no—
374C2×Q8—222no—
375C2×Q8—442no—
376C2×D4—222no—
377C2×D4—224no—
378C2×D4—222no—
379C2×D4—442no—
380C2×D4—442no—
381C2×D4—442no—
382C2×D4—442no—
383C2×D4—442no—
384C2×D4—442no—
385C2×D4—441no—
386C2×D4—441no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—111no—
390C22×C4—111no—
391C22×C4—112no—
392C22×C4—111no—
393C22×C4—222no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4C2×C4×D1112yes—
404C22×C4C2×C4×D1112yes—
405C22×C4C2×C4×D1111yescharacteristic
406C22×C4C2×D4412yes—
407C22×C4#433912yes—
408C22×C4C23×D1111yescharacteristic
409M16—444no—
410M16—444no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—44no—
417C2×C8—221no—
418C2×C8—222no—
419C2×C8—221no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8C2×D4412yes—
425C2×C8C2×D4412yes—
426C4⋊C4—222no—
427C4⋊C4—442no—
428C22⋊C4—42no—
429C22⋊C4—222no—
430C22⋊C4—222no—
431C22⋊C4—442no—
432C22⋊C4—442no—
433C22⋊C4—442no—
434C22⋊C4—442no—
435C42—22no—
436C42—22no—
437C42—221no—
438C42—221no—
439C11#2203511yescharacteristic, complemented, Sylow
440C23—22no—
441C23—21no—
442C23—21no—
443C23—22no—
444C23—221no—
445C23—222no—
446C23—222no—
447C23—222no—
448C23—222no—
449C23—222no—
450C23—221no—
451C23—221no—
452C23—222no—
453C23—222no—
454C23—222no—
455C23—222no—
456C23C4×D4412yes—
457C23C22×C4×D1111yescharacteristic
458Q8—444no—
459D4—444no—
460D4—448no—
461D4—448no—
462D4—444no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—221no—
479C2×C4—221no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—441no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—441no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4C4×D4412yes—
491C2×C4C22×D4411yescharacteristic
492C2×C4C2×#433911yescharacteristic
493C2×C4#6703712yes—
494C2×C4#6704212yes—
495C8—22no—
496C8—22no—
497C8—42no—
498C8—441no—
499C8—442no—
500C8—441no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—42no—
505C22—42no—
506C22—441no—
507C22—442no—
508C22—441no—
509C22—442no—
510C22—442no—
511C22—442no—
512C22—442no—
513C22—442no—
514C22—441no—
515C22—442no—
516C22—442no—
517C22—442no—
518C22C2×C4×D4411yescharacteristic
519C22#1062307612yes—
520C22#1062327612yes—
521C22#1062328111yescharacteristic
522C22#1062328111yescharacteristic
523C4—22no—
524C4—42no—
525C4—42no—
526C4—441no—
527C4—441no—
528C4—442no—
529C4—441no—
530C4#1062302411yescharacteristic
531C4#1062305611yescharacteristic
532C4#1062309112yes—
533C2—42no—
534C2—881no—
535C2—882no—
536C2#1307127611yescharacteristic
537C2#1307732111yescharacteristic
538C2#1307733511yescharacteristic
539C2#1307767512yes—
540C2#1307768412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1752C2
prime radical#13071832C2
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22035
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
1. C2×#10622724C2semidirect
2. C2×#10622723C2semidirect
4. #13069414C2semidirect
5. #13069230C2semidirect
6. #13069229C2semidirect
7. #13068912C2semidirect
8. #13068911C2semidirect
9. #13068801C2semidirect
10. #13068527C2semidirect
11. C11×#1752C2semidirect
56. C22×C8×C11D4semidirect
180. #1752D11semidirect
325. C22×C8D44semidirect
439. C11#22035semidirect

Maximal subgroups

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

subgroupindex
C2×#106227242
C2×#106227232
#130718322
#130694142
#130692302
#130692292
#130689122
#130689112
#130688012
#130685272
C11×#17522
#2203511