Finite Group Databasebeta

← #14764020

Subgroups — #14764020

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622847C211yesmaximal, characteristic
2#13071107C211yesmaximal, characteristic
3#13068799C212yesmaximal, complemented
4#13068798C212yesmaximal, complemented
5#13068794C212yesmaximal, complemented
6#13068793C212yesmaximal, complemented
7#13068598C212yesmaximal, complemented
8#13068594C212yesmaximal, complemented
9C2×C11×#408C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C11×#408—24no—
18C2×C11×C22⋊C8C2212yes—
19C2×C11×C22⋊C8C2212yes—
20#10622847—24no—
21#10622843C411yescharacteristic
22#10622843C411yescharacteristic
23#10622834C411yescharacteristic
24#10622834C411yescharacteristic
25#10622833C412yes—
26#10622833C412yes—
27C4×C22⋊Dic11C2212yes—
28C4×C22⋊Dic11C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31C2×Dic11⋊C8C2212yes—
32C2×Dic11⋊C8C2212yes—
33C2×Dic11⋊C8C2212yes—
34C2×Dic11⋊C8C2212yes—
35#10622188C2212yes—
36#10622188C2212yes—
37#10622188C2212yes—
38#10622188C2212yes—
39C2×C11×#41—41no—
40C2×C11×#41—41no—
41C2×C11×#41—41no—
42C2×C11×#41—41no—
43C2×C11×#41D414yes—
44C2×C11×#41Q814yes—
45C22×Q8×C11C2×C411yescharacteristic
46C22×D4×C11C2×C411yescharacteristic
47C22×D4×C11C2×C411yescharacteristic
48C22×D4×C11C2×C411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2×C412yes—
53C2×C11×M16—22no—
54C2×C11×M16—41no—
55C2×C11×M16—41no—
56C22×C8×C11—22no—
57C22×C8×C11—41no—
58C22×C8×C11—41no—
59C22×C8×C11C2312yes—
60C22×C8×C11C2312yes—
61C2×C22⋊Dic11C2×C412yes—
62C2×C22⋊Dic11C2×C412yes—
63C2×C22⋊Dic11C2×C412yes—
64C2×C22⋊Dic11C2×C412yes—
65C2×C22⋊Dic11C2×C412yes—
66#66979—41no—
67#66979—41no—
68C2×C4⋊Dic11C2×C411yescharacteristic
69C2×C4⋊Dic11C2×C411yescharacteristic
70C2×C4×Dic11—41no—
71C2×C4×Dic11—41no—
72C2×C4×Dic11C2×C411yescharacteristic
73C2×C4×Dic11C2×C411yescharacteristic
74C2×C4×Dic11C2312yes—
75C2×C4×Dic11C2312yes—
76C2×#4318—22no—
77C2×#4318—41no—
78C2×#4318—41no—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—41no—
81C22×C11⋊C8—41no—
82C22×C11⋊C8C2312yes—
83C22×C11⋊C8C2312yes—
84C11×C22⋊C8—24no—
85C11×C22⋊C8—24no—
86C11⋊#95C2×C412yes—
87C11⋊#95C2×C412yes—
88C11⋊#95C2×C412yes—
89C11⋊#95C2×C412yes—
90C22⋊(C11⋊C8)—24no—
91C22⋊(C11⋊C8)—24no—
92Dic11⋊C8—42no—
93Dic11⋊C8—42no—
94Dic11⋊C8—42no—
95Dic11⋊C8—42no—
96#21936—111nomaximal, Sylow
97C24×C11C22×C411yescharacteristic
98C24×C11C22×C411yescharacteristic
99C24×C11C22×C411yescharacteristic
100C11×#41—44no—
101C11×#41—44no—
102C11×#41—44no—
103C11×#41—44no—
104C2×Q8×C11—41no—
105C2×Q8×C11—41no—
106C2×Q8×C11C4⋊C414yes—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C2×D4×C11—41no—
113C2×D4×C11C4⋊C414yes—
114C2×D4×C11C4⋊C414yes—
115C2×D4×C11C4⋊C414yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×Q812yes—
135C22×C4×C11C2×Q812yes—
136C22×C4×C11C2×Q812yes—
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—24no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11C22×C412yes—
142C22×Dic11C22×C412yes—
143C22×Dic11C22×C412yes—
144C22×Dic11C22×C412yes—
145C11×M16—44no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—44no—
153C22⋊Dic11—24no—
154C22⋊Dic11—24no—
155C22⋊Dic11—42no—
156C22⋊Dic11—42no—
157C22⋊Dic11—42no—
158C4⋊Dic11—41no—
159C4⋊Dic11—41no—
160C4×Dic11—22no—
161C4×Dic11—22no—
162C4×Dic11—22no—
163C4×Dic11—22no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166#4318—44no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—44no—
174C2×#408—111no—
175C2×#408D1111yescharacteristic
176#2297—111no—
177#1851—112no—
178#1851—112no—
179#1850—112no—
180#1850—112no—
181#1798—112no—
182#1797—112no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11C2×C4⋊C412yes—
196C23×C11C2×C4⋊C412yes—
197C23×C11C2×C4⋊C412yes—
198C23×C11C23×C411yescharacteristic
199Q8×C11—44no—
200D4×C11—44no—
201D4×C11—44no—
202D4×C11—44no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11C2×C4⋊C412yes—
222C2×C4×C11C2×C4⋊C412yes—
223C2×C4×C11C2×C4⋊C412yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×Q811yescharacteristic
226C2×C4×C11H(5,𝔽2)11yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—48no—
242C2×Dic11#13114yes—
243C8×C11—42no—
244C8×C11—42no—
245C11⋊C8—42no—
246C11⋊C8—42no—
247C22×#41C2×D1111yescharacteristic
248C22×M16—111no—
249C22×M16C2×D1111yescharacteristic
250C23×C8—111no—
251C23×C8C2×D1111yescharacteristic
252C2×#117—111no—
253C22×C42—111no—
254C2×C4⋊C8—112no—
255C2×C4⋊C8—112no—
256C2×C4⋊C8—112no—
257C2×C4⋊C8—112no—
258#408—24no—
259#408—224no—
260C2×C22⋊C8—112no—
261C2×C22⋊C8—112no—
262C2×C22⋊C8C2×D1112yes—
263C2×C22⋊C8C2×D1112yes—
264#391—111no—
265#391—111no—
266#390—111no—
267#390—111no—
268#386—112no—
269#386—112no—
270C4×C22⋊C4—112no—
271C4×C22⋊C4—112no—
272#336—112no—
273#336—112no—
274#336—112no—
275#336—112no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—24no—
280C22×C11—24no—
281C22×C11—24no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—41no—
291C22×C11C22×C4⋊C411yescharacteristic
292C22×C11#51811yescharacteristic
293C22×C11#51811yescharacteristic
294C22×C11C2×#13112yes—
295C22×C11#56812yes—
296C4×C11—22no—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11#53411yescharacteristic
300C4×C11#53411yescharacteristic
301C4×C11#54311yescharacteristic
302C4×C11#54311yescharacteristic
303Dic11—24no—
304Dic11—42no—
305Dic11—42no—
306Dic11—42no—
307C2×#41—41no—
308C2×#41—41no—
309C2×#41—41no—
310C2×#41—41no—
311C2×#41Dic2214yes—
312C2×#41C22⋊D1114yes—
313C22×Q8C4×D1111yescharacteristic
314C22×D4C4×D1111yescharacteristic
315C22×D4C4×D1111yescharacteristic
316C22×D4C4×D1111yescharacteristic
317C23×C4—112no—
318C23×C4C22×D1111yescharacteristic
319C23×C4C22×D1111yescharacteristic
320C23×C4C22×D1111yescharacteristic
321C2×M16—22no—
322C2×M16—41no—
323C2×M16—41no—
324C2×M16—222no—
325C2×M16—441no—
326C2×M16—441no—
327C22×C8—22no—
328C22×C8—41no—
329C22×C8—41no—
330C22×C8—112no—
331C22×C8—112no—
332C22×C8—222no—
333C22×C8—441no—
334C22×C8—441no—
335C22×C8C22×D1112yes—
336C22×C8C22×D1112yes—
337#117—441no—
338#117—441no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—111no—
341C2×C22⋊C4—112no—
342C2×C22⋊C4—112no—
343C2×C22⋊C4—112no—
344C2×C22⋊C4—112no—
345C2×C22⋊C4—112no—
346C2×C42—112no—
347C2×C42—112no—
348C2×C42—111no—
349C2×C42—111no—
350C2×C42—441no—
351C2×C42—441no—
352C4⋊C8—442no—
353C4⋊C8—442no—
354C4⋊C8—442no—
355C4⋊C8—442no—
356C22⋊C8—24no—
357C22⋊C8—24no—
358C22⋊C8—224no—
359C22⋊C8—224no—
360#95—112no—
361#95—112no—
362#95—112no—
363#95—112no—
364C2×C11—42no—
365C2×C11—42no—
366C2×C11—42no—
367C2×C11#231511yescharacteristic
368C2×C11#290612yes—
369C2×C11#297612yes—
370C2×C11#297911yescharacteristic
371C2×C11#298011yescharacteristic
372C24C2×C4×D1111yescharacteristic
373C24C2×C4×D1111yescharacteristic
374C24C2×C4×D1111yescharacteristic
375#41—44no—
376#41—44no—
377#41—44no—
378#41—44no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×Q8Dic11⋊C414yes—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4Dic11⋊C414yes—
389C2×D4Dic11⋊C414yes—
390C2×D4Dic11⋊C414yes—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—112no—
404C22×C4—112no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—224no—
408C22×C4—442no—
409C22×C4—442no—
410C22×C4C2×Dic2212yes—
411C22×C4C2×Dic2212yes—
412C22×C4C2×Dic2212yes—
413C22×C4C2×C4×D1111yescharacteristic
414C22×C4C2×C4×D1111yescharacteristic
415C22×C4C2×C4×D1111yescharacteristic
416C22×C4C2×C22⋊D1112yes—
417C22×C4C2×C22⋊D1112yes—
418C22×C4C2×C22⋊D1112yes—
419C22×C4C23×D1111yescharacteristic
420M16—44no—
421M16—444no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—44no—
429C2×C8—222no—
430C2×C8—222no—
431C2×C8—222no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—444no—
436C4⋊C4—441no—
437C4⋊C4—441no—
438C22⋊C4—224no—
439C22⋊C4—224no—
440C22⋊C4—442no—
441C22⋊C4—442no—
442C22⋊C4—442no—
443C42—222no—
444C42—222no—
445C42—222no—
446C42—222no—
447C42—441no—
448C42—441no—
449C11#2193611yescharacteristic, complemented, Sylow
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23C2×Dic11⋊C412yes—
463C23C2×Dic11⋊C412yes—
464C23C2×Dic11⋊C412yes—
465C23C22×C4×D1111yescharacteristic
466Q8—44no—
467D4—44no—
468D4—44no—
469D4—44no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—114no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—448no—
501C2×C4C2×Dic11⋊C412yes—
502C2×C4C2×Dic11⋊C412yes—
503C2×C4C2×Dic11⋊C412yes—
504C2×C4C22×Dic2211yescharacteristic
505C2×C4#6703711yescharacteristic
506C2×C4#6703711yescharacteristic
507C2×C4#6703711yescharacteristic
508C2×C4#6703711yescharacteristic
509C2×C4C22×C22⋊D1111yescharacteristic
510C8—42no—
511C8—42no—
512C8—442no—
513C8—442no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—24no—
518C22—24no—
519C22—24no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22#1062301711yescharacteristic
530C22#1062301711yescharacteristic
531C22D11×#13112yes—
532C22#1062328112yes—
533C22C22×Dic11⋊C411yescharacteristic
534C4—22no—
535C4—22no—
536C4—22no—
537C4—224no—
538C4—442no—
539C4—442no—
540C4—442no—
541C4#1062301411yescharacteristic
542C4#1062301411yescharacteristic
543C4#1062333511yescharacteristic
544C4#1062333511yescharacteristic
545C2—42no—
546C2—42no—
547C2—42no—
548C2#1307122811yescharacteristic
549C2#1307718212yes—
550C2#1307765912yes—
551C2#1307768011yescharacteristic
552C2#1307768511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#408C2
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#408D11
hypocenterC11#21936
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
3. #13068799C2semidirect
4. #13068798C2semidirect
5. #13068794C2semidirect
6. #13068793C2semidirect
7. #13068598C2semidirect
8. #13068594C2semidirect
449. C11#21936semidirect

Maximal subgroups

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

subgroupindex
C2×#106228472
#130711072
#130687992
#130687982
#130687942
#130687932
#130685982
#130685942
C2×C11×#4082
#2193611